Which statement best explains the relationship between
lines FG and HJ?
V
2
х
O They are perpendicular because their slopes are
equal
They are perpendicular because their slopes are
negative reciprocals.
O They are not perpendicular because their slopes are
equal.
They are not perpendicular because their slopes are
not negative reciprocals.
Answers
Answer: They are not perpendicular because their slopes are not negative reciprocals.
Step-by-step explanation:
For these two lines to be perpendicular, their slopes have to be negative reciprocals.
Slope of FG.
F = (-4, 1)
G = (0, -2)
= (Y₂ - Y₁) / (X₂ - X₁)
= (-2 - 1) / (0 + 4)
= -3/4
Slope of HJ
J = (0 , 4)
H = (-4, -2)
Slope = (Y₂ - Y₁) / (X₂ - X₁)
= (-2 - 4) / (-4 -0)
= 6/4
= 3/2
The slopes of these lines are not negative reciprocals so these lines are not perpendicular.
Related Questions
F(x)=2x^3-2x+1 relativeminimum
Answers
Step-by-step explanation:
F(x) = 2x³ - 3x + 1.
d/dx [2x³ - 3x + 1] = 6x² - 3.
Firstly, we wish to find the stationary points of F(x).
When 6x² - 3 = 0, x = -0.707 or x = 0.707.
Now we use Second Derivative test:
d/dx [6x² - 3] = 12x.
Since 12(-0.707) < 0, x = -0.707 is a relative maximum point.
Since 12(0.707) > 0, x = 0.707 is a relative minimum point.
Hence x = 0.707. To find the exact point you can substitute the value of x back into the equation 2x³ - 3x +1.
pls help asap no trolls!
Answers
Answer:
b = 6
c = 9
Step-by-step explanation:
if triangles PQR and JHI are congruent, then (b + 48) must equal 9b
9b = b + 48
8b = 48
b = 6
if triangles PQR and JHI are congruent, then (c + 9) must equal 2c:
2c = c + 9
c = 9
what is the greatest common factor of 4x²+2x
Answers
Answer:
2x
Step-by-step explanation:
Because both terms are divisible by 2x. So, that's the greatest common factor. Whichever term is the greatest and can divide both the numbers it the GFC.
Solve for .
2.
(100+30x)
30.rº
Answers
Answer:
x = 1[tex]\frac{1}{3}[/tex]
Step-by-step explanation:
As you can see, the two angles are supplementary as they lie on the same straight line so they should add up to 180°.
100 + 30x + 30x = 180
Evaluate like terms.
60x + 100 = 180
Isolate 60x.
60x = 180 - 100
= 80
Find x.
x = 80 ÷ 60
x = 1[tex]\frac{1}{3}[/tex]
The demand for tickets to an amusement park is given by p = 70 - 0.2q, where p is the price of a ticket in dollars and q is the number of people attending at that price.
a. What price generates an attendance of 3,000 people? What is the total revenue at that price? What is the total revenue if the price is $20?
b. Write the revenue function as a function of attendance, q, at the amusement park.
c. What attendance maximizes revenue?
d. What price should be charged to maximize revenue?
e. What is the maximum revenue? Can we determine the corresponding profit?
Answers
Answer:
Step-by-step explanation:
From the information given:
p = 70 - 0.02q
when:
q = 3000
p = 70 - 0.02 (3000)
p = 70 - 60
p = 10 dollars
The total revenue = price × number of people
= 10 × 3000
= 30000 dollars
If the price is $20
20 = 70 - 0.02q
0.02q = 70 - 20
0.02q = 50
q = 50/0.02
q = 2500
∴
If price is $20, The total revenue = 20 × 2500
= 50000 dollars
b)
The revenue function R = price × attendance
R = p × q
R = (70 - 0.02q)q
R = 70q - 0.02q²
c)
R(q) = 70q - 0.02q²
Taking the differential of the value on the right hand side.
R'(q) = 70 × (1) - 0.02 × (2q)
R'(q) = 70 - 0.04q
If we set R'(q) = 0
70 - 0.04q = 0
70 = 0.04q
q = 70/0.04
q = 1750 (critical point)
R"(q) = 0 - 0.04 × 1
R"(q) = -0.04
R"(1750) = -0.04 < 0
∴
R is maximum when q = 1750
d)
At q = 1750
p = 70 - 0.02(q)
p = 70 - 0.02(1750)
p = 70 - 35
p = 35 dollars
e)
R(q) = 70q - 0.02q² because R is max at q = 1750
R(1750) = 70 × 1750 - 0.02 × (1750)²
R_(max) = 122500 - 61250
R_(max) = 61250 dollars
Given that the actual price is 20 dollars when the price is changed to 35 dollars, we have a maximum revenue of:
Suppose:
p = 20 and q = 2500 (from a)
Then;
R = p × q
R = 20 × 2500
R = 50000 dollars
If R = 35, then q = 1750
R_{max} = 35 × 1750
R_{max} = 61250 dollars
∴
Profit = R_{max} - R
Profit = 61250 - 50000
Profit = 11250 dollars
What is the point-slope form of a line with slope -3 that contains the point
(10, -1)?
Answers
Answer:
y - (-1) = -3(x-10)
y+1= -3x+30
y= -3x+30-1
y= -3x+29
order from least to greatest 1.25, 1.52, 1.02, 1.50
Answers
Answer:
1.02 1.25 1.50 1.52.
Step-by-step explanation:
|•-•|
Answer:
1.02
1.25
1.5
1.52
Step-by-step explanation:
:)
$1.50 is what fraction of $7.00?
Answers
21.4285714286%
or
4.66666667 i think
A bowl weighs 11/40 lb. Express this as a decimal. The denominator is 4. I need help with this pls.
Answers
Answer: 0.275
Step-by-step explanation:
Answer:
7/10
Step-by-step explanation:
You subtract 11 from 4 and get 7 and then you divide 40 by 4 and get 10 hope that helps:)
Helpppppp meeee please and thank you
Answers
Answer:
a
Step-by-step explanation:
Solve for x.
Question 2 options:
A)
5
B)
7
C)
4
D)
6
Answers
I don’t knowwwwwwwwww helppp!!
Answers
Answer:
24 units squared
Step-by-step explanation:
the area of a parallelogram is its length times height
Use the following long division
Answers
What is this? I don't know and I'm struggling bad please help
Answers
Answer:
steeper
Step-by-step explanation:
y = mx + c where m is the slope and c is the y-intercept.
The slope has been changed from 2 to 4. The higher the slope, the steeper it is. Thus, the slope is steeper now.
Answer:
i'm not sure sorry
Step-by-step explanation:
Can someone help me
Answers
Answer:
1) The distance between points is: [tex]\sqrt{290}[/tex]
Option B is correct option.
2) The distance between points is: [tex]\sqrt{10}[/tex]
Option A is correct option.
Step-by-step explanation:
Find the distance between points
Question 1
(8,-5),(-3,8)
The formula used is: [tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
We have [tex]x_1=8, y_1=-5,x_2=-3,y_2=8[/tex]
Putting values and finding distance
[tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\Distance=\sqrt{(-3-8)^2+(8-(-5))^2}\\Distance=\sqrt{(-11)^2+(8+5)^2}\\Distance=\sqrt{(-11)^2+(13)^2}\\Distance=\sqrt{121+169}\\Distance=\sqrt{290}[/tex]
So, the distance between points is: [tex]\sqrt{290}[/tex]
Option B is correct option.
Question 2
(-1,6),(-4,-7)
The formula used is: [tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
We have [tex]x_1=-1, y_1=6,x_2=-4,y_2=-7[/tex]
Putting values and finding distance
[tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\Distance=\sqrt{(-4-(-1))^2+(-7+6)^2}\\Distance=\sqrt{(-4+1)^2+(-1)^2}\\Distance=\sqrt{(-3)^2+(-1)^2}\\Distance=\sqrt{9+1}\\Distance=\sqrt{10}[/tex]
So, the distance between points is: [tex]\sqrt{10}[/tex]
Option A is correct option.
Express the ratio below in its simplest form.
3 and 1 half :4.5
Answers
3 1/2 : 45 = 7 : 90
Solution:
Change values to whole numbers.
Convert any mixed numbers to fractions.
Convert 3 1/2
3 1/2 = 7/2
We now have:
3 1/2 : 45 = 7/2 : 45
Convert the whole number 45 to a fraction with 1 in the denominator.
We then have:
3 1/2 : 45 = 7/2 : 45/1
Convert fractions to integers by eliminating the denominators.
Our two fractions have unlike denominators so we find the Least Common Denominator and rewrite our fractions as necessary with the common denominator
LCD(7/2, 45/1) = 2
We now have:
3 1/2 : 45 = 7/2 : 90/2
Our two fractions now have like denominators so we can multiply both by 2 to eliminate the denominators.
We then have:
3 1/2 : 45 = 7 : 90
Try to reduce the ratio further with the greatest common factor (GCF).
The GCF of 7 and 90 is 1
Divide both terms by the GCF, 1:
7 ÷ 1 = 7
90 ÷ 1 = 90
The ratio 7 : 90 cannot be reduced further by dividing both terms by the GCF = 1 :
Therefore:
3 1/2 : 45 = 7 : 90
Answer:
Convert the decimal number to a fraction by placing the decimal number over a power of ten. Since there is 1 number to the right of the decimal point, place the decimal number over 101 (10)
. Next, add the whole number to the left of the decimal.
4 5/10
Reduce the fractional part of the mixed number.
4 1/2
Reduce the fraction.
9/2
Step-by-step explanation:
Based on your understanding of sound waves,
Explain what happens to sound waves when you turn up the volume on your speakers and
Explain what happens to the sound waves when a singer hits the high pitched notes during the National Anthem. Be sure to use the terms amplitude and frequency in your answer.
Answers
Answer:
The frequency increases as the pitch increases, and the amplitude increases as the volume increases
Step-by-step explanation:
One spring day, Caroline noted the time of day and the temperature, in degrees
Fahrenheit. Her findings are as follows: At 6 a.m., the temperature was 52° F. For the
next 3 hours, the temperature rose 2° per hour. For the next 6 hours, it rose 1° per
hour. The temperature then stayed steady until 6 p.m. For the next 3 hours, the
temperature dropped 1° per hour. The temperature then dropped steadily until the
temperature was 60° at midnight. On the set of axes below, graph Caroline's data.
Answers
Answer:
Please see attached graph
Step-by-step explanation:
In the attached image you will find the red dots hour per hour that reflect the temperature changes described in the text. The finer red line joins the points to give continuity to the graph.
What is this? Please answer with an explanation
Answers
Find the acute angle between the lines. 5x ? y = 2, 6x + y = 6
Answers
Answer:
Acute angle Ф = 20.77° (Approx)
Step-by-step explanation:
Given:
5x - y = 2
6x + y = 6
Find:
Acute angle
Computation:
5x - y = 2
6x + y = 6
So,
y = 5x - 2.....eq1
y = -6x + 6......eq2
Slop line y = mx + c
On comparison
m1 = 5 , m2 = -6
So,
TanФ = I(m1-m2)/(1+m1m2)I
TanФ = I(5+6)/(1-30)I
TanФ = 11/29
Ф = 20.77° (Approx)
Acute angle Ф = 20.77° (Approx)
1. Kilometers and inches are some units used to measure length. What are some other
units used to measure length?
2. Tablespoons and liters are some units used to measure volume. What are some
other units used to measure volume?
100 point please helppp
Answers
Answer:
length- inches, meters, millameters
Volume- gallon, quart, cups, teaspoons
Step-by-step explanation:
Answer:
ength- inches, meters, millameters
Volume- gallon, quart, cups, teaspoons
Step-by-step explanation:
9. Consider the function, f(x) = x4 – 5x2 + 4. Select the statements that are true. In the box provided,
explain the choices you selected.
a. The degree of the polynomial is 5.
b. When graphed, this polynomial will look like a "W"
C. The zeros of this polynomial are (-2, 0), (-1,0), (1, 0) and (2,0).
d. The zeros of this polynomial are (-2, 0), (1, 0) and (3, 0)
Explanation of choices:
Answers
Answer:
the degree of the polynomial is 5
for the figure shown below, find the value of the variable and the measure of the angles.
x is
measure angle P
measure angle Q
measure angle R
Answers
Answer:
All triangles has a total angle of 180. So x+38+2x+18+x=180
Solve for x: 4x+56=180 so 4x=124, x=31
Florida ran 1.2 miles and Walked 4.8 laps
Answers
Step-by-step explanation:
This is because laps would be the dependent variable, so we know the number of them (4.8) would be multiplied by the variable (x). We also know that 1.2 is the constant. Now we can solve to make sure this is the right equation.
4.8x + 1.2 = 3.6
4.8x = 2.4
x = 0.5
What is the measure of z G?
Answers
Zg is a measure of weight
Hey there!
Your lines EF and FG has the measure of 6 ✅
One of the triangle(s) has both sides equivalent lengths which is the isosceles triangle
Since pretty much every is most likely “equivalent” it’ll be an isosceles triangle
∠E ≅ ∠ G
∠E = 28° so that means ∠G = 28°
Answer: ∠G = 28° (Option D.)
Good luck on your assignment and enjoy your day!
~LoveYourselfFirst:)
Need help please !!!!!!
Answers
Answer:
200 patients
Step-by-step explanation:
60% = 120
100% = ?
100×120 = 12000÷60= 200
Which will help your answer, "To what power must a student raise the number 5 to have an answer of 626"?
a. log625(5)=x
b. logx(5)=x
c. log5(x)=625
d. log5(625)=x
Answers
Answer:
D.
5^x=625
I hope it will be useful.
Answer:
The Answer us D
Step-by-step explanation:
log5(625)=x
x=4
20 points!!!
y=5(x - 5)(x+3)
written in vertex form and standard form
Answers
Vertex form:
y = 5 (x - 1)^2 - 80
Standard Form:
y = 5x^2 - 10x - 75
what is the equation of the line in point slope form that has a slope of -7/8, going through point (12,-3)
Answers
Answer:
y= (-7/8)x +7.5
Step-by-step explanation:
We know that the form for the equation of a line is
y= mx+b, with m being the slope, so our equation is
y=(-7/8)x+b. As b should be a constant, we need to find b. Plugging (12,-3) in, we have -3 = (-7/8)(12)+b = -10.5+b. Adding 10.5 to both sides, we get b= 7.5, making our equation
y= (-7/8)x +7.5
Write an equation for the line parallel to the given line that contains C. C(1,4); y = 1/8x-4 (Write in slope intercept form)
Answers
Answer:
he equation of the line is parallel to the given line and passing through the point C( 1,4) is x - 8 y + 31=0
slope intercept form
[tex]y = \frac{x}{8} + \frac{31}{8}[/tex]
Step-by-step explanation:
Explanation:-
Given equation of the line
y = 1/8x-4
8 y = x - 32
x - 8 y -32=0
The equation of the line is parallel to the given line a x + b y + k=0
x - 8 y + k=0
This line is passing through the point ( 1,4)
x - 8 y + k=0
1 - 32 + k =0
k = 31
The equation of the line is parallel to the given line and passing through the point C( 1,4) is x - 8 y + 31=0
slope intercept form
8 y = x + 31
[tex]y = \frac{x}{8} + \frac{31}{8}[/tex]