Answer:
[tex]\textsf{a)} \quad x = 17[/tex]
[tex]\textsf{b)} \quad T_n=3n^2-3n-1[/tex]
[tex]\textsf{a)} \quad x = 20[/tex]
[tex]\textsf{b)} \quad T_n=3n^2-4n+5[/tex]
Step-by-step explanation:
Given quadratic number pattern:
-1, 5, x, 35, ...To find the equation for the nth term, we can use the general form of a quadratic equation:
[tex]\boxed{T_n=an^2 + bn + c}[/tex]
where n is the position of the term.
Let's substitute the values of T₁, T₂ and T₄ into the quadratic equation: to create three equations:
[tex]\begin{aligned}T_1=a(1)^2+b(1)+c&=-1\\a+b+c&=-1\end{aligned}[/tex]
[tex]\begin{aligned}T_2=a(2)^2+b(2)+c&=5\\4a+2b+c&=5\end{aligned}[/tex]
[tex]\begin{aligned}T_4=a(4)^2+b(4)+c&=35\\16a+4b+c&=35\end{aligned}[/tex]
Rearrange the first equation to isolate c:
[tex]c=-a-b-1[/tex]
Substitute this into the second and third equations:
[tex]\begin{aligned}4a+2b+(-a-b-1)&=5\\3a+b&=6\end{ailgned}[/tex]
[tex]\begin{aligned}16a+4b+(-a-b-1)&=35\\15a+3b&=36\end{ailgned}[/tex]
Solve the equations simultaneously by rearranged the first equation to isolate b and substituting this into the second equation and solving for a:
[tex]b=-3a+6[/tex]
[tex]\begin{aligned}15a+3(-3a+6)&=36 \\15a-9a+18&=36\\6a&=18\\a&=3 \end{aligned}[/tex]
Substitute the found value of a into the equation for b and solve for b:
[tex]\begin{aligned}b&=-3a+6\\&=-3(3)+6\\&=-9+6\\&=-3\end{aligned}[/tex]
Finally, substitute the found values of a and b into the equation for c and solve for c:
[tex]\begin{aligned}c&=-a-b-1\\&=-3-(-3)-1\\&=-3+3-1\\&=-1\end{aligned}[/tex]
Therefore, the equation for the nth term is:
[tex]\boxed{T_n=3n^2-3n-1}[/tex]
The value of x is the 3rd term. Therefore, to find the value of x, substitute n = 3 into the equation for the nth term:
[tex]\begin{aligned}T_3&=3(3)^2-3(3)-1\\&=3(9)-3(3)-1\\&=27-9-1\\&=18-1\\&=17\end{aligned}[/tex]
Therefore, the value of x is 17.
[tex]\hrulefill[/tex]
Given quadratic number pattern:
4, 9, x, 37, ...To find the equation for the nth term, we can use the general form of a quadratic equation:
[tex]\boxed{T_n=an^2 + bn + c}[/tex]
where n is the position of the term.
Let's substitute the values of T₁, T₂ and T₄ into the quadratic equation: to create three equations:
[tex]\begin{aligned}T_1=a(1)^2+b(1)+c&=4\\a+b+c&=4\end{aligned}[/tex]
[tex]\begin{aligned}T_2=a(2)^2+b(2)+c&=9\\4a+2b+c&=9\end{aligned}[/tex]
[tex]\begin{aligned}T_4=a(4)^2+b(4)+c&=37\\16a+4b+c&=37\end{aligned}[/tex]
Rearrange the first equation to isolate c:
[tex]c=-a-b+4[/tex]
Substitute this into the second and third equations:
[tex]\begin{aligned}4a+2b+(-a-b+4)&=9\\3a+b&=5\end{ailgned}[/tex]
[tex]\begin{aligned}16a+4b+(-a-b+4)&=37\\15a+3b&=33\end{ailgned}[/tex]
Solve the equations simultaneously by rearranged the first equation to isolate b and substituting this into the second equation and solving for a:
[tex]b=-3a+5[/tex]
[tex]\begin{aligned}15a+3(-3a+5)&=33 \\15a-9a+15&=33\\6a&=18\\a&=3 \end{aligned}[/tex]
Substitute the found value of a into the equation for b and solve for b:
[tex]\begin{aligned}b&=-3a+5\\&=-3(3)+5\\&=-9+5\\&=-4\end{aligned}[/tex]
Finally, substitute the found values of a and b into the equation for c and solve for c:
[tex]\begin{aligned}c&=-a-b+4\\&=-3-(-4)+4\\&=-3+4+4\\&=5\end{aligned}[/tex]
Therefore, the equation for the nth term is:
[tex]\boxed{T_n=3n^2-4n+5}[/tex]
The value of x is the 3rd term. Therefore, to find the value of x, substitute n = 3 into the equation for the nth term:
[tex]\begin{aligned}T_3&=3(3)^2-4(3)+5\\&=3(9)-4(3)+5\\&=27-12+5\\&=15+5\\&=20\end{aligned}[/tex]
Therefore, the value of x is 20.
Which three lengths CAN be the lengths of the sides of a triangle? A. 12cm, 5cm, 17cm, B. 10cm, 15cm, 24cm C. 9cm, 22cm, 11cm D. 21cm, 7cm, 6cmWhich three lengths CAN be the lengths of the sides of a triangle? A. 12cm, 5cm, 17cm, B. 10cm, 15cm, 24cm C. 9cm, 22cm, 11cm D. 21cm, 7cm, 6cmWhich three lengths CAN be the lengths of the sides of a triangle? A. 12cm, 5cm, 17cm, B. 10cm, 15cm, 24cm C. 9cm, 22cm, 11cm D. 21cm, 7cm, 6cmWhich three lengths CAN be the lengths of the sides of a triangle? A. 12cm, 5cm, 17cm, B. 10cm, 15cm, 24cm C. 9cm, 22cm, 11cm D. 21cm, 7cm, 6cmWhich three lengths CAN be the lengths of the sides of a triangle? A. 12cm, 5cm, 17cm, B. 10cm, 15cm, 24cm C. 9cm, 22cm, 11cm D. 21cm, 7cm, 6cmWhich three lengths CAN be the lengths of the sides of a triangle? A. 12cm, 5cm, 17cm, B. 10cm, 15cm, 24cm C. 9cm, 22cm, 11cm D. 21cm, 7cm, 6cm
Based on the Triangle Inequality Theorem the possible lengths of the sides of a triangle are:
B. 10cm, 15cm, 24cmD. 21cm, 7cm, 6cmWhat are the possible lengths of the sides of a triangle?The Triangle Inequality Theorem which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side, is used to determine if three lengths can be the lengths of the sides of a triangle.
Considering each option:
A. 12cm, 5cm, 17cm:
12 + 5 > 17 (not satisfied)
5 + 17 > 12 (satisfied)
12 + 17 > 5 (satisfied)
B. 10cm, 15cm, 24cm:
10 + 15 > 24 (satisfied)
15 + 24 > 10 (satisfied)
10 + 24 > 15 (satisfied)
C. 9cm, 22cm, 11cm:
9 + 22 > 11 (satisfied)
22 + 11 > 9 (satisfied)
9 + 11 > 22 (not satisfied)
D. 21cm, 7cm, 6cm:
21 + 7 > 6 (satisfied)
7 + 6 > 21 (not satisfied)
21 + 6 > 7 (satisfied)
Hence, option B and D are correct.
Learn more about sides of a triangle at: https://brainly.com/question/30241889
#SPJ1
The average national utility price is $270.48. Over a 6-month period, what is the average utility price in Orlando? How
does this compare with the national average?
The average utility price in Orlando for the 6 month period, and the way it compares to the national average is d. $ 308. 83 ; higher than the national average .
How to find the average ?The information for Orlando is April, the cost was 288 dollars; May, 310 dollars; June, 325 dollars; July, 294 dollars; August, 293 dollars; September, 343 dollars.
The average is:
= ( 288 + 310 + 325 + 294 + 293 + 343 ) / 6
= 1, 853 / 6
= $ 308. 83
This average is higher than the national average of $ 308. 83.
Find out more on average at https://brainly.com/question/26303626
#SPJ1
Full question is:
The average national utility price is $270.48. Over a 6-month period, what is the average utility price in Orlando? How does this compare with the national average?
A graph titled Orlando, Florida, has month on the x-axis and utility price on the y-axis. In April, the cost was 288 dollars; May, 310 dollars; June, 325 dollars; July, 294 dollars; August, 293 dollars; September, 343 dollars.
a. $370.60; higher than the national average
b. $292.17; higher than the national average
c. $38.35; lower than the national average
d. $308.83; higher than the national average
A javelin throwing arena is illustrated
alongside. It has the shape of a sector of
a circle of radius 100 m. The throwing
line is 5 m from the centre. A white line
is painted on the two 95 m straights and
on the two circular arcs.
a Find the total length of the painted
white line.
b If the shaded landing area is grassed,
what is the total area of grass?
a. The total length of the painted white line in the javelin throwing arena is approximately 255.984 meters.
b. The total area of grass in the shaded landing area of the javelin throwing arena is approximately 1624.6 square meters.
What is the total length of the painted white line?To find the total length of the painted white line, we need to calculate the length of the two straight segments and the two circular arcs.
a) Total length of the painted white line:
Let's break it down into components:
1. The two straight segments: Each straight segment is 95 meters long, and there are two of them.
Length of straight segments = 2 * 95 = 190 meters
2. The two circular arcs:
The throwing arena is a sector of a circle with a radius of 100 meters. The angle of the sector can be calculated using trigonometry. The angle can be found by taking the inverse cosine of the ratio of the adjacent side (which is the radius minus the throwing line distance) to the hypotenuse (which is the radius).
Angle (in radians) = cos⁻¹((radius - throwing line distance) / radius)
Now, the length of each circular arc can be calculated using the formula for the length of an arc of a circle:
Length of circular arc = radius * angle
Let's calculate the angle first:
Angle (in radians) = cos⁻¹((100 - 5) / 100)
Angle = cos⁻¹(95 / 100)
Angle ≈ 0.32492 radians
Now, we can calculate the length of each circular arc:
Length of each circular arc = 100 * 0.32492 ≈ 32.492 meters
Since there are two circular arcs, the total length of the painted white line is:
Total length = 190 (straight segments) + 2 * 32.492 (circular arcs)
Total length ≈ 255.984 meters
b) Total area of grass in the shaded landing area:
The shaded landing area is the sector of the circle with a radius of 100 meters and the angle we calculated above.
The formula to calculate the area of a sector of a circle is:
Area of sector = (angle / 2π) * π * radius²
Area of the shaded landing area = (0.32492 / (2π)) * π * 100²
Area of the shaded landing area ≈ (0.32492 / 2) * 10000
Area of the shaded landing area ≈ 1624.6 square meters
So, the total area of grass in the shaded landing area is approximately 1624.6 square meters.
Learn more on segments here;
https://brainly.com/question/28322552
#SPJ2
Write a quadratic equation whose roots are 5 + i radical 2 and 5 – i radical 2
____ x^2 + _____ x+ ______=0
The quadratic equation with roots 5 + i√2 and 5 - i√2 is:
x^2 - 10x + 27 = 0
To write a quadratic equation with roots 5 + i√2 and 5 - i√2, we can use the fact that complex roots occur in conjugate pairs. Therefore, the equation will have the form:
(x - root1)(x - root2) = 0
Substituting the given roots:
(x - (5 + i√2))(x - (5 - i√2)) = 0
Now, we expand the equation:
(x - 5 - i√2)(x - 5 + i√2) = 0
Using the difference of squares formula:
((x - 5)^2 - (i√2)^2) = 0
Simplifying the equation:
(x - 5)^2 + 2 = 0
Expanding the square:
x^2 - 10x + 25 + 2 = 0
Combining like terms:
x^2 - 10x + 27 = 0
Therefore, the quadratic equation with roots 5 + i√2 and 5 - i√2 is:
x^2 - 10x + 27 = 0
For more questions on quadratic equation
https://brainly.com/question/30262991
#SPJ8
Shannon's living room is a 12 by 18 foot rectangle. She wants to cover
as much of the floor as possible with 6 foot diameter circular rugs
without overlap. How much of the living room floor space can Shannon
cover with the circular rugs to the nearest square foot?
(Use π = 3.14)
A) 170 ft²
B) 216 ft²
C) 386 ft²
D) 678 ft²
Answer:
First, we need to figure out how many circular rugs can fit in the living room without overlap.
One way to approach this is to find the area of each circular rug (using the formula A = πr^2, where r = 3 feet since the diameter is 6 feet).
A = π(3)^2 = 28.26 square feet
Next, we can find the area of the living room:
A = 12 x 18 = 216 square feet
To figure out how many circular rugs can fit, we can divide the living room area by the rug area:
216/28.26 ≈ 7.64
Since we can't have partial rugs, we need to round down, which means Shannon can fit 7 circular rugs in her living room without overlap.
The total area covered by the circular rugs would be:
7 x 28.26 = 197.82 square feet
Therefore, the closest answer choice to the nearest square foot is A) 170 ft².
Answer:A
Step-by-step explanation:
She can put 2 circles together width wise because 6+6 = 12
She can put 3 circles together length wise because 6+6+6 = 18
So she can put 6 circles in total.
The area of one circle is found with the equation A=πr^2
The diameter is 6ft, so the radius is 3ft, so
A=π*3ft^2
A=28.26ft²
This is the area of one circle. We need to find the area of 6 because 6 can fit in total.
28.26ft² * 6= 169.56 ft²
Why is °=(−°)? PLSS HELP NOW
100 Points! Geometry question. Photo attached. Find x in the right triangle. Please show as much work as possible. Thank you!
Answer:
x = 12
Step-by-step explanation:
sin45 = x/17 (sin = opposite/hypotenuse)
x = (sin45)(17) = 12.02 ≈ 12
there's 240 candy bars 1/4 of candy bars are snickers 1/3 of the candy bars are twix 1/8 of the candy bars are hershey. how many candy bars are Mars? explain not with a lot of words but in numbers please.
Answer:
you have to add all the fractions of the candy1/4+1/3+1/8
=17/24
subtract from 1Step-by-step explanation:
1-17/24
=7/24
multiply with the total number of candy7/24×240
=70
Which graph represents the solution set to the system of inequalities?
Y ≤ 2X+2
1/2X + Y <7
Y- 3 ≥ 0
ANSWER is Down Below
The solution set to the system of inequalities will be the overlapping region or the intersection of the shaded regions from all three inequalities.
The system of inequalities consists of three inequalities:
y ≤ 2x + 2
(1/2)x + y < 7
y - 3 ≥ 0
Let's analyze each inequality:
y ≤ 2x + 2 represents a shaded region below the line with a slope of 2 and a y-intercept of 2.
(1/2)x + y < 7 represents a shaded region below the line with a slope of -1/2 and a y-intercept of 7.
y - 3 ≥ 0 represents a shaded region above the line with a slope of 0 and a y-intercept of 3.
The solution set to the system of inequalities will be the overlapping region or the intersection of the shaded regions from all three inequalities.
For more questions on inequalities
https://brainly.com/question/1870140
#SPJ8
Do the ratios 1/3 and 28/36 form a proportion?
No, the given two fractions/ratios do not form a proportion.
Two ratios are said to be forming proportions if and only if the reduced forms of fractions of the two ratios are the same or are equal to each other. For example - [tex]\frac{3}{6}[/tex] and [tex]\frac{1}{2}[/tex] are in proportion because [tex]\frac{3}{6}[/tex] when reduced to the simplest form gives [tex]\frac{1}{2}[/tex] which is the same as the other given ratio.
In the given question, one ratio given is [tex]\frac{1}{3}[/tex] and the other one is [tex]\frac{28}{36}[/tex]. Reducing the second ratio to the simplest form we get [tex]\frac{7}{9}[/tex]. Clearly, the two fractions are not equal. Hence, the given two ratios are not in proportion.
Learn more about ratios and proportions -
https://brainly.com/question/29774220
Eleanor used a ruler to report the length of a
piece of wood as 9.7 inches.
Part A:
What is the range of values in inches for the
actual measurement of the piece of wood?
Part B :
How many significant digits does the measurement have?
Answer:
Part A: The actual measurement of the piece of wood could be between 9.65 and 9.75 inches.
Part B: The measurement has three significant digits.
Step-by-step explanation:
Significant digits are the digits in a number that carry meaning in terms of the precision or accuracy of the measurement. In this case, the number 9.7 has three significant digits, which means that the measurement is accurate to the tenths place.
Two math students were asked to write an exponential growth equation that had a starting value of 300 and a growth rate of 2%. Pierre thinks the answer is y=300(1.02)^x and Scott thinks that the answer is y=300(1.2)^x. Are either of them right and why?
Incorrect, the correct exponential growth equation as it accurately represents a starting value of 300 and a growth rate of 2%. Scott's equation
Neither Pierre nor Scott has the correct exponential growth equation.
The exponential growth equation represents a relationship where a quantity increases or grows exponentially over time. It is typically represented as y = a(1 + r)^x, where "a" represents the initial or starting value, "r" represents the growth rate (expressed as a decimal), "x" represents the time or number of periods, and "y" represents the resulting value after the growth.
In this case, Pierre's equation is y =[tex]300(1.02)^x.[/tex]This equation suggests a growth rate of 2% (0.02 as a decimal), which means that the quantity would increase by 2% with each period. This aligns with the given growth rate of 2%. Thus, Pierre's equation is correct.
On the other hand, Scott's equation is y = [tex]300(1.2)^x[/tex]. This equation suggests a growth rate of 20% (0.2 as a decimal), which means that the quantity would increase by 20% with each period. However, the given growth rate is 2%, not 20%. Therefore, Scott's equation is incorrect.
To summarize, Pierre's equation, y = 300(1.02)^x, is the correct exponential growth equation as it accurately represents a starting value of 300 and a growth rate of 2%. Scott's equation, y = 300(1.2)^x, does not match the given growth rate and is therefore incorrect.
for more such question on exponential visit
https://brainly.com/question/30127596
#SPJ8
Miguel is going camping with 3 friends. He packed sandwiches for everyone to share equally. How many sandwiches did Miguel pack for each camper?
Miguel has 3 friends and he packed sandwiches for everyone to share equally means that Miguel packed 3 sandwiches for each camper.
How to determine amount?If Miguel packed 4 sandwiches, then he would have packed 1 sandwich for each camper:
Number of sandwiches per camper = Total number of sandwiches / Number of campers
There are 4 campers, so plug that into the equation to get:
Number of sandwiches per camper = Total number of sandwiches / 4
Solve for the total number of sandwiches by multiplying both sides of the equation by 4:
Total number of sandwiches = Number of sandwiches per camper × 4
So, the total number of sandwiches is 4 × Number of sandwiches per camper.
Each camper will get 1 sandwich, so plug that into the equation to get:
Total number of sandwiches = 1 × 4
Which means there are a total of 4 sandwiches.
Therefore, Miguel packed 1 sandwich for each camper.
Find out more on fractions here: https://brainly.com/question/78672
#SPJ1
What is the value of x in the systems:
5x + 2y = 3
2x + 3y = -1
Answer: The value of x = 1 and y = -1
Step-by Step Explanation:
We have 5x + 2y = 3 -----(i)
and 2x + 3y = -1 -----(ii)
By substitution method,
from (i), x = 3-2y/5
Putting the value of x in equation (ii),
we get, 2(3-2y/5) + 3y = -1
6 - 4y/5 + 3y =-1
6 - 4y + 15y = -5
6 - 11y = -5
-11y = -5 - 6
-11y = -11
y = -1
And, x = 3-2(-1)/5
x = 3+2/5
x = 1
Therefore, x=1 and y=−1
Read more about solving these type of equations,
https://brainly.com/question/50000312
Use a table of values to graph the following exponential function. (see attachment)
y= 2^x
Please graph
By using the table of values, a graph of the exponential function is shown in the image below.
What is an exponential function?In Mathematics and Geometry, an exponential function can be modeled by using this mathematical equation:
[tex]f(x) = a(b)^x[/tex]
Where:
a represents the initial value or y-intercept.x represents x-variable.b represents the rate of change, common ratio, decay rate, or growth rate.Based on the information provided above, we can logically deduce the following exponential function;
[tex]y = 2^x[/tex]
Next, we would create a table of values based on the exponential function;
when x = 0, the y-value is given by;
y = 2⁰
y = 1
when x = 1, the y-value is given by;
y = 2¹
y = 2
x y____
-2 0.25
-1 0.5
0 1
1 2
2 4
Read more on exponential functions here: brainly.com/question/28246301
#SPJ1
The average fourth grader is about three times as tall as the average newborn baby. If babies are on average 45cm 7mm when they are born, What is the height of the average fourth grader?
The height of the average fourth grader is 137cm 1mm. This height can be determined by multiplying 3 by the average height of a newborn baby.
Given information,
The average height of babies = 45 cm 7mm
45 cm 7 mm is equivalent to 45.7 cm (since there are 10 millimeters in a centimeter).
Let the height of a fourth grader be x.
According to the question,
The height of a fourth grader (x) = 3 × the average height of a newborn baby
The height of a fourth grader (x) = 3 × 45.7
The height of a fourth grader (x)= 137.1 = 137cm 1mm
Therefore, the height of a fourth grader is 137cm 1mm.
Learn more about average, here:
https://brainly.com/question/31796355
#SPJ1
The top of a kitchen table measures 160cm by 90cm. A beetle walks diagonally across the table from one corner to the other. Calculate how far the beetle walks.
Answer: To calculate the distance the beetle walks diagonally across the table, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the two sides of the right triangle formed by the table are 160 cm and 90 cm. Let's call the hypotenuse (the distance the beetle walks) "d."
So, applying the Pythagorean theorem, we have:
d^2 = 160^2 + 90^2
Simplifying:
d^2 = 25600 + 8100
d^2 = 33700
Taking the square root of both sides:
d ≈ √33700
d ≈ 183.54 cm
Therefore, the beetle walks approximately 183.54 cm diagonally across the kitchen table.
100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Answer: is X = 5 within the diagram.
1.3 A cake recipe calls for 0.8 kg of flower, 650g of sugar and 900 000mg of butter. (2) 1.3.1 Determine the total mass of the ingredients. Give you answer in kilograms. 1.3.2 If sugar comes in 150g bags at cost of R5.95 per 150g, determine the total cost of the (2) sugar needed for this recipe.
1. The total in mass of the ingredients used is 2.35kg
2. The cost of sugar needed is R25.78.
What is word problem?A word problem is a few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.
These statements are interpreted into mathematical equation or expression.
1. The recipes are ;
0.8kg = 800g
sugar = 650g
butter = 900000 mg = 900000/1000 = 900g
Therefore the total mass of ingredients
= 800 + 650 +900
= 2350g
in kilograms, 1000g is 1kg
2350g = 2350/1000
= 2.35kg
2. If 150g = R5.95
1g = 5.95/150
650g = 5.95 × 650/150
= R25.78.
learn more about word problem from
https://brainly.com/question/21405634
#SPJ1
!!!!!PLEASE HELP 100 POINTS AND WILL MARK BRAINLIEST!!!!!
Find the probability that a point chosen randomly inside the rectangle is in each given shape. Round to the nearest tenth of a percent (!!!!!SHOW YOUR WORK!!!!!)
A) Inside the Square
B) Outside the Triangle
A square and a traingle are present in a large rectangle with given dimensions in the figure.
Area of the rectangle is :[tex]\qquad\displaystyle \tt \dashrightarrow \: 12 \times 8[/tex]
[tex]\qquad\displaystyle \tt \dashrightarrow \: 96 \: \: unit {}^{2} [/tex]
Area of square :[tex]\qquad\displaystyle \tt \dashrightarrow \: 4 \times 4[/tex]
[tex]\qquad\displaystyle \tt \dashrightarrow \: 16 \: \: unit {}^{2} [/tex]
Area of triangle :[tex]\qquad\displaystyle \tt \dashrightarrow \: \frac{1}{2} \times 4 \times 5[/tex]
[tex]\qquad\displaystyle \tt \dashrightarrow \: \frac{1}{2} \times 4 \times 5[/tex]
[tex]\qquad\displaystyle \tt \dashrightarrow \: 2 \times 5[/tex]
[tex]\qquad\displaystyle \tt \dashrightarrow \: 10 \: \: unit {}^{2} [/tex]
Problem 1 : Inside the square[ area of square / total area ]
[tex]\qquad\displaystyle \tt \dashrightarrow \: p(inside \: \: the \: \: square) = \frac{16}{96} [/tex]
[tex]\qquad\displaystyle \tt \dashrightarrow \: p(inside \: \: the \: \: square) = \frac{1}{6} [/tex]
Problem 2 : Outside the triangle[ total area except area of triangle / total area ]
[tex]\qquad\displaystyle \tt \dashrightarrow \: p(outside \: the \: triangle) = \frac{96 - 10}{96} [/tex]
[tex]\qquad\displaystyle \tt \dashrightarrow \: p(outside \: the \: triangle) = \frac{86 }{96} [/tex]
[tex]\qquad\displaystyle \tt \dashrightarrow \: p(outside \: the \: triangle) = \frac{43}{48} [/tex]
Select the correct answer.
Which statement is true about this equation?
-9(x + 3) + 12 = -3(2x + 5) - 3x
The equation has one solution, x = 1.
OB.
The equation has one solution, x = 0.
O C.
The equation has no solution.
O D. The equation has infinitely many solutions.
O A.
Reset
Next
Answer:
Infinite solutions (D).
Step-by-step explanation:
Here is how:
To determine the true statement about the given equation, let's simplify it step by step:
-9(x + 3) + 12 = -3(2x + 5) - 3x
Distributing the -9 and -3 on the left and right sides respectively:
-9x - 27 + 12 = -6x - 15 - 3x
Combining like terms:
-9x - 15 = -9x - 15
Now, let's analyze the equation. We have -9x on both sides, and -15 on both sides. By subtracting -9x from both sides and -15 from both sides, we obtain:
0 = 0
This equation is true regardless of the value of x. In other words, it holds for all values of x. Therefore, the equation has infinitely many solutions.
Answer:
The correct answer is: "The equation has one solution, x = 0"
Can somebody please help me thank tou
Answer:
Step-by-step explanation: On the left side find the number that is able to make that sum true for that equation. on the right side you just subtract the answer with the number to get your answer.
Answer:
Step-by-step explanation:
I Think this is the answer
On the left side find the number that is able to make that sum true for that equation. on the right side you just subtract the answer with the number to get your answer
Question 10 (1 point)
A
33
7 in.
B
C
The value of AB is,
⇒ AB = 5.9
(rounded to nearest tenth)
We have to given that,
A right triangle ABC is shown.
Now, By trigonometry formula,
we get;
⇒ cos 33° = Base / Hypotenuse
Substitute all the values, we get;
⇒ cos 33° = AB / 7
⇒ 0.84 = AB / 7
⇒ AB = 0.84 × 7
⇒ AB = 5.88
⇒ AB = 5.9
(rounded to nearest tenth)
Thus, We get;
AB = 5.9
(rounded to nearest tenth)
Learn more about trigonometric ratios at:
brainly.com/question/1836193
#SPJ1
Recta de pendiente 1⁄4 que pasa por (3,0).
The equation of the line with a slope of 1/4 that passes through the point (3,0) is y = 1/4x - 3/4.
To find the equation of a line with a slope of 1/4 that passes through the point (3,0), we can use the point-slope form of the equation of a line.
The point-slope form of a line is:
y - y1 = m(x - x1)
where (x1, y1) is the given point and m is the slope.
Substituting the values into the formula, we have:
y - 0 = 1/4(x - 3)
Simplifying:
y = 1/4(x - 3)
Distributing 1/4 throughout the expression:
y = 1/4x - 3/4
Therefore, the equation of the line with a slope of 1/4 that passes through the point (3,0) is y = 1/4x - 3/4.
For more questions on slope
https://brainly.com/question/18907612
#SPJ8
Use the Law of Sines to find the length of side b in AABC. Round to the nearest tenth. Show your work.
Consider ▲ ABC.
B
28°
112°
37
The length of side b in triangle ABC is 18.7 units.
What is the law of sines?In Mathematics and Geometry, the law of sines is also referred to as sine law or sine rule and it can be defined as an equation that relates the side lengths of a triangle to the sines of its angles.
In Mathematics and Geometry, the law of sine is modeled or represented by this mathematical equation (ratio):
[tex]\frac{sinA}{a} =\frac{sinB}{b} =\frac{sinC}{c}[/tex]
In this context, the value of b can be determined as follows;
sin112/37 = sin28/b
b = 37sin28/sin112
b = 17.3705/0.9272
b = 18.7 units.
Read more on sine rule here: https://brainly.com/question/12854075
#SPJ1
All of the pairs of corresponding angles and sides in ΔCAT and ΔDOG are congruent. Based on this information, which of the following is a true statement?
A true statement based on the given information is that ΔCAT and ΔDOG are similar triangles, meaning their corresponding angles are congruent and their corresponding sides are in proportion.
If all pairs of corresponding angles and sides in triangles ΔCAT and ΔDOG are congruent, it implies that the two triangles are similar. In similar triangles, the corresponding angles are congruent, and the corresponding sides are in proportion.
Based on this information, the following true statement can be made:
The ratio of the lengths of the corresponding sides in ΔCAT and ΔDOG is equal.
For example, if the corresponding sides are CA and DO, the ratio CA/DO will be equal to the ratio of the lengths of the other corresponding sides.
for such more question on congruent
https://brainly.com/question/1675117
#SPJ8
50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answer: its D! not 8!!!
Step-by-step explanation:
A rectangles field is 135 meters long and 100 meters wide give the length and width of another rectangular field that has the same perimeter but a larger area
Answer: if the length of the second rectangular field is 200 meters, the width should be 35 meters to have the same perimeter but a larger area.
Step-by-step explanation:
STEP1:- Let's denote the length of the second rectangular field as L2 and the width as W2.
The perimeter of a rectangle is given by the formula:
Perimeter = 2(length + width).
For the first rectangular field with length L1 = 135 meters and width W1 = 100 meters, the perimeter is:
Perimeter1 = 2(135 + 100) = 470 meters.
STEP 2:- To find the length and width of the second rectangular field with the same perimeter but a larger area, we need to consider that the perimeters of both rectangles are equal.
Perimeter1 = Perimeter2
470 = 2(L2 + W2)
STEP 3 :- To determine the larger area, we need to find the corresponding length and width. However, there are multiple solutions for this problem. We can set an arbitrary value for one of the dimensions and calculate the other.
For example, let's assume the length of the second rectangular field as L2 = 200 meters:
470 = 2(200 + W2)
470 = 400 + 2W2
2W2 = 470 - 400
2W2 = 70
W2 = 35 meters
HENCE L2 = 200 meters and W2 = 35 meters
need help! dont know what to do!
Answer:
y < 2x +6
Step-by-step explanation:
You want an inequality for the given graph.
What to doHere are some steps you can follow, in no particular order.
identify the type of boundary line: solid or dashed (dashed)locate the shading: above the line or below it (below)locate the y-intercept (+6)identify the slope (rise/run = 4/2 = 2)When you have this information, you can write the inequality in slope-intercept form.
Using the informationWhen the boundary line is dashed, the inequality symbol you use will not include the "or equal to" case. It will be one of < or >.
When the shading is below the line, the values of y that satisfy the inequality will be less than (<) those on the boundary line. If shading is above, the y-values will be greater than (>) those on the line.
The slope and intercept go into the inequality like this:
y < mx + b . . . . . . where m is the slope, and b is the y-intercept
For a dashed line, shaded below, with m=2 and b=6, the inequality is ...
y < 2x +6
__
Additional comment
There are two points identified on the boundary line: (-2, 2) and (0, 6). The slope formula can be used to find the slope:
m = (y2 -y1)/(x2 -x1)
m = (6 -2)/(0 -(-2)) = 4/2 = 2
The point (0, 6) on the y-axis is the y-intercept. The y-value there is 6.
<95141404393>
2. Consider this dilation.
Pre-image
9 cm
B
Image
3 cm B
(a) Find the scale factor. Show your work. (5 points)
(2- a.) Scale factor= Image length
Pre-image length