The diagram shows a 9cm x 7cm rectangle-based pyramid. all the diagonal sides - TA, TB, TC, AND TD- are length 12cm. M is the midpoint of the rectangular base.
Work out angle TAC, to 1 decimal place.
Answers
Answer:
∠TAC is approximately equal to 61.6°
Step-by-step explanation:
The given parameters for the pyramid are;
The dimension for the rectangular base are; Length = 9 cm, width = 7 cm
The length of the diagonal sides, TA, TB, TC, and TD = 12 cm each
The midpoint of the rectangular base = Point M
The diagonal AC = AM + MC
AM = MC as given M is the midpoint of the rectangular base
∴ AC = AM + MC = 2·AM
By Pythagoras' theorem, AC = √(9² + 7²) = √130
AC = √130 cm
∴ AM = AC/2 = (√130)/2 cm
Alternatively, AM = √((9/2 cm)² + (7/2 cm)²) = √(32.5) cm
∠TAC = ∠TAM
By trigonometric ratios, we have;
[tex]cos (\theta) = \dfrac{Length \ of \ adjacent \ side \ to \ angle }{Length \ of \ hypotenuse\ side \ to \ angle}[/tex]
[tex]\therefore cos (\angle TAM) = cos (\angle TAC) = \dfrac{\left (\dfrac{\sqrt{130} }{2} \right )}{12} = \dfrac{\sqrt{130} }{2 \times 12} = \dfrac{\sqrt{130} }{24}[/tex]
[tex]\angle TAC = arccos \left ( \dfrac{\sqrt{130} }{24} \right ) \approx 61.6 ^{\circ} \ to 1 \ decimal \ place[/tex]
The measure of angle TAC is 61.6 degrees
The given parameters are:
[tex]\mathbf{AB = 7}[/tex]
[tex]\mathbf{BC = 9}[/tex]
Start by calculating length AC, using the following Pythagoras theorem.
[tex]\mathbf{AC = \sqrt{AB^2 + BC^2}}[/tex]
So, we have:
[tex]\mathbf{AC = \sqrt{7^2 + 9^2}}[/tex]
[tex]\mathbf{AC = \sqrt{49 + 81}}[/tex]
[tex]\mathbf{AC = \sqrt{130}}[/tex]
[tex]\mathbf{AC = 11.40}[/tex]
Next, we calculate side length AM
[tex]\mathbf{AM = \frac{AC}{2}}[/tex]
So, we have:
[tex]\mathbf{AM = \frac{11.40}{2}}[/tex]
[tex]\mathbf{AM = 5.70}[/tex]
The measure of angle TAC is calculated using the following cosine ratio
[tex]\mathbf{cos(A)= \frac{AM}{TA}}[/tex]
So, we have:
[tex]\mathbf{cos(A)= \frac{5.70}{12}}[/tex]
[tex]\mathbf{cos(A)= 0.475}[/tex]
Take arc cos of both sides
[tex]\mathbf{A= 61.6}[/tex]
Hence, the measure of angle TAC is 61.6 degrees
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Related Questions
is 1/4 closer to 0, 1/2, 1
Answers
Answer:
it is closer to 0 :):):):):)
The given point 1/4 lie closer to 0& 1/2 than 1
What is a decimal number?A decimal number is a number that consists of a whole number and a fractional part separated by a point. For example – 3.5, 6.79, 78.32, etc.
Given here: Given the proper fraction as 1/4
To convert a fraction to a decimal, we'll just divide the numerator...by the denominator.
Thus 1/4=0.25
1/2=0.5
Now the difference between each of the given points is 1/2-1/4=0.25
And 1/4-0=0.25
Also 1-1/4=0.75
Thus the point 1/4 is equidistant from the points 0 and 1/2 but is 0.75 units away from 1
Hence, The given point 1/4 lie closer to 0& 1/2 than 1
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What is the area of the triangle
A- 300mm
B- 60 mm
C- 150 mm
D- 375 mm
Answers
Answer:
150
Step-by-step explanation:
A=B*H/2
A=15*20/2
A=300/2
A=150
Ignore the hypotenuse btw
Answer:
C - 150 mm²
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightGeometry
Area of a Triangle: A = 1/2bhStep-by-step explanation:
Step 1: Define Variables
Base b = 15 mm
Height h = 20 mm
Step 2: Find Area A
Substitute [T Area Formula]: A = 1/2(15 mm)(20 mm)Evaluate Multiplication: A = 1/2(300 mm²)Evaluate Multiplication: A = 150 mm²consider the functions f and g
Answers
Answer:
its B hope this helps :)
Step-by-step explanation:
Answer:
C. 9Step-by-step explanation:
Given
f(x) = -x³g(x) = |1/8x - 1|To find
Value of (g ο f)(4)Solution
(g ο f)(x) = g(f(x)) = |1/8(-x)³ - 1|, replace x with f(x) in the function g(x)(g ο f)(4) = | 1/8(-4)³ - 1 | = | -8 - 1 | = | - 9| = 9Correct option is C
Consider the function f(x) = |x|. Let g(x) = |–4(x – 7)|.
Which shows the graphs of f(x) and g(x)?
A.) On a coordinate plane, y = g (x) opens up and goes through (negative 3, 4), has a vertex at (negative 2, 0) and goes through (0, 7). Y = f (x) opens up and goes through (negative 4, 4), has a vertex at (0, 0), and goes through (4, 4).
B.) On a coordinate plane, y = g (x) opens up and goes through (6, 4), has a vertex at (7, 0) and goes through (8, 4). Y = f (x) opens up and goes through (negative 4, 4), has a vertex at (0, 0), and goes through (4, 4).
C.) On a coordinate plane, y = g (x) opens down and goes through (6, negative 4), has a vertex at (7, 0) and goes through (8, negative 4). Y = f (x) opens up and goes through (negative 4, 4), has a vertex at (0, 0), and goes through (4, 4).
D.) On a coordinate plane, y = g (x) opens up and goes through (negative 8, 4), has a vertex at (negative 7, 0) and goes through (negative 6, 4). Y = f (x) opens up and goes through (negative 4, 4), has a vertex at (0, 0), and goes through (4, 4).
Answers
Answer:
B
Step-by-step explanation:
On edge 2020
The graph of absolute value function f(x) and g(x) are:
On a coordinate plane, y = g (x) opens up and goes through (6, 4), has a vertex at (7, 0) and goes through (8, 4). Y = f (x) opens up and goes through (negative 4, 4), has a vertex at (0, 0), and goes through (4, 4).
The correct answer is an option (B)
What is an absolute value function?"A function of the form f(t) = |t| ."
What is a graph of a function?"It is a set of points on the coordinate plane that follows given function."
For given question,
We have been given an absolute value function f(x) = |x|
and absolute value function g(x) = |-4(x - 7)|
The graph of f(x) = |x| is like a 'V', with its vertex at (0, 0).
Y = f (x) opens up and goes through (-4, 4), has a vertex at (0, 0), and goes through (4, 4)
Consider absolute value function, h(x) = |x - 7|
A function h(x) is the function f(x) is translated horizontally 7 units right.
The graph of h(x) = |x - 7| is like a 'V', with its vertex at (7, 0).
Now consider absolute value function g(x) = |-4(x - 7)|
A function g(x) is the function h(x) is compressed inside by factor 4.
So, the graph of y = g (x) opens up and goes through (6, 4), has a vertex at (7, 0) and goes through (8, 4).
Therefore, the graph of absolute value function f(x) and g(x) are:
On a coordinate plane, y = g (x) opens up and goes through (6, 4), has a vertex at (7, 0) and goes through (8, 4). Y = f (x) opens up and goes through (negative 4, 4), has a vertex at (0, 0), and goes through (4, 4).
The correct answer is an option (B)
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Solve each of the following multiplication problems.
58 × 40 =
412 × 328 =
1,679 × 45 =
4,926 × 184 =
100 × 78 =
99 × 88 =
236,407 × 1,294 =
10,000 × 641 =
46,001 × 9,008 =
Answers
Answer:
414,377,008
:p hope this helped
Answer:
Solve each of the following multiplication problems.
58 × 40 = 2320
412 × 328 = 135,136
1,679 × 45 = 75,555
4,926 × 184 = 906,384
100 × 78 = 7,800
99 × 88 = 8,712
236,407 × 1,294 = 305,910,658
10,000 × 641 = 6,410,000
46,001 × 9,008 =414,377,008
Step-by-step explanation:
whoever answers first get brainliest
Answers
by what percent will a fraction change if its numerator is decreased by 75% and denominator is decreased by 50%
Answers
Answer:
50%
Step-by-step explanation:
first the numerator is decreased by 75% so its 0.25. the denominator is decreased by 50% so its 0.5. Then, we will divide 0.25 and 0.5 which equals 0.5. to find %, do 0.5*100 which equals 50%
The fraction will decrease by 0.5 or 50%
Let the original fraction be a/b. If the numerator is decreased by 75% and the denominator is decreased by 50%, the resulting faction will be:
0.25a/0.50b
Taking the ratio of the quotient of the result will give:
0.25a/0.50b
= 25/100a * 100/50 b
= 25a/50b
= 0.5a/b
Hence the fraction will decrease by 0.5 or 50%
Learn more on percentages here: https://brainly.com/question/19247356
Please help me with this
Answers
My bad, it is a 120 obtuse angle.
Use a protractor
Step-by-step explanation:
I had this question
Insert geometric means in each geometric sequence.
( with solution )
1. ___, 24, ___, ___, 3/64
2. ___, 1/4, 1/2, ___
3. 81, ___, ___, ___, ___, 1/3
With Solution☺️!
Thank You So Much❤️✨
Answers
Answer:
[tex]\underline{192}, 24, \underline{3}, \underline{\dfrac{3}{8}}, \dfrac{3}{64}[/tex]
[tex]\underline{\dfrac{1}8}, \dfrac{1}{4}, \dfrac{1}{2}, \underline{1}[/tex]
[tex]81, \underline{27, 9, 3, 1},\dfrac{1}{3}[/tex]
Step-by-step explanation:
Given the Geometric sequences:
1. ___, 24, ___, ___, 3/64
2. ___, 1/4, 1/2, ___
3. 81, ___, ___, ___, ___, 1/3
To find:
The values in the blanks of the given geometric sequences.
Solution:
First of all, let us learn about the [tex]n^{th}[/tex] term of a geometric sequence.
[tex]a_n=ar^{n-1}[/tex]
Where [tex]a[/tex] is the first term and
[tex]r[/tex] is the common ratio by which each term varies from the previous term.
Considering the first sequence, we are given the second and fifth terms of the sequences.
Applying the above formula:
[tex]ar = 24\\ar^4 = \dfrac{3}{64}[/tex]
Solving the above equation:
[tex]r = \dfrac{1}{8}[/tex]
Therefore, the sequence is:
[tex]\underline{192}, 24, \underline{3}, \underline{\dfrac{3}{8}}, \dfrac{3}{64}[/tex]
Considering the second given sequence:
[tex]ar = \dfrac{1}{4}\\ar^2 = \dfrac{1}{2}\\\text{Solving the above equations}, r = 2[/tex]
Therefore, the sequence is:
[tex]\underline{\dfrac{1}8}, \dfrac{1}{4}, \dfrac{1}{2}, \underline{1}[/tex]
Considering the third sequence:
[tex]a = 81\\ar^5=\dfrac{1}{3}\\\Rightarrow r = 3[/tex]
Therefore, the sequence is:
[tex]81, \underline{27, 9, 3, 1},\dfrac{1}{3}[/tex]
A recipe calls for 4 oz of raisins. If I use 224 oz of raisins, how many batches of this recipe did I make?
Answers
Answer:
56 batches
Step-by-step explanation:
224/4 = 56
Search cos jk and tan jk knowing that sin jk = 8/3
Answers
Answer:
cosjk = √55 i/3
tanjk = 8/√55 i
Step-by-step explanation:
Given
sin jk = 8/3
According to SOH CAH TOA
Sin theta = opposite/hypotenuse = 8/3
Opposite = 8
hypotenuse = 3
Get the adjacent using the pythagoras theorem
hyp² = opp²+adj²
adj² = hyp² - opp²
adj² = 3² - 8²
adj² = 9-64
adj² = -55
adj = √-55
adj = √55 i (i = √-1)
Get cosjk
cosjk = adj/hyp
cosjk = √55 i/3
Get tanjk
tanjk = opp/adj
tanjk = 8/√55 i
Complete the table for the given rule.
Rule: y = 6x-4
Please help
Answers
y = 6x - 4
Substitute the given x values to solve for y.
x = 1:
y = 6(1) - 4
y = 6 - 4
y = 2
1 = 2
x = 3:
y = 6(3) - 4
y = 18 - 4
y = 14
3 = 14
x = 10:
y = 6(10) - 4
y = 60 - 4
y = 56
10 = 56
x y
1 2
3 14
10 56
You have 18 stamps from Mexico in your stamp collection.
These stamps represent of your collection. The rest of the
stamps are from the United States. How many stamps are
from the United States?
12
24
30
48
Answers
Fraction of stamp from Mexico = 3/8 of total stamps. So total number of stamps are 48.
I will mark BRAINILY to first correct answer!! EXTRA POINTSSS!
What is the area?
A) 46
B) 64
C) 108
D) 147
Answers
What does Z equal? A.37 B.51 C.39
Answers
Answer:
B
Step-by-step explanation:
Please see the attached picture for the full solution.
What is the value of x?
Answers
Answer:
x=17
Step-by-step explanation:
we know the sum of angles in atriangle is 180°
x +17 + 4x -34 +6x +10 = 180
x+4x+6x +17 -34 +10 = 180
11x -7 =180
11x = 180 +7
x = 187/11 = 17
PLEEAAASE HELPPPPP
Distance = ________ x time
A. flow
B. rate
C. work
Answers
Answer:
B:rate
Step-by-step explanation:
the formula distance= rate × time
Answer:
B
Step-by-step explanation:
The formula for distance is rate × time.
Flow and work don't make sense. Also, work is force × distance.
However, you were given rate is equal to distance/time (r=d/t) and were asked to find what distance would be:
in that case, we'll isolate d onto one side
here's the equation
r=d/t
multiply by t on both sides
rt=d, or rate × time equals distance
either way it's B
Hope this helps!
Can somebody check my work? For geometry
Answers
Answer:
Yeah I think you're correct I got the same
Step-by-step explanation:
The quarterback threw 30 passes during the game. He completed 12 of them. What is his percent of completion?
Answers
12= percent of completion
Turn this info into a fraction and divide by denominator
12/30=.4
Now times your decimal by 100 to get in percentage form
40%
Ernesto measured the height of a door frame as 6.35 feet, but the actual height was 6.5 feet. What is the percentage of error in Ernesto's measurement? (5 points)
a
2.31%
b
1.98%
c
2.36%
d
2.02%
Answers
Answer:
A or B
Step-by-step explanation:
sry if im wrong-happy new year!
Helpppppp I don’t knowwwewww I’ll mark as brainlist
Answers
Answer:I think D I just got off of this sorry if I’m wrong
Step-by-step explanation:
Answer:
choose c beacuse it is closer to and is not false
Step-by-step explanation:
:D
If x= -6, which inequality is true?
A-5-3x > 10
B-3-5x < -14
C1 - 2x > 13
D2-x<-3
18-34
Answers
Answer:
B
this is because the way the other 3 are set up it just makes it b
multiply each sides by what?
-8x(_)=-3(_)
Answers
Answer:
-8 × 3 = - 3 × ( 8)
or -21 = -21
Answer:
-21
Step-by-step explanation:
Help I'm on standpoint!
Answers
Answer:
the third option
Step-by-step explanation:
The value of a car, C(t), t years after 2011, is modeled by the following function.
C(t) = 50,000(0.9)^t - 2,000
Which graph represents this function?
Answers
9514 1404 393
Answer:
B
Step-by-step explanation:
At t=0, the value is ...
C(0) = 50,000·(0.9^0) -2000 = 48,000
At t=20, the value is ...
C(20) = 50,000(0.9^20) -2000 = 6079 -2000 = 4079
The only graph that matches these end points is B.
Answer:
The correct answer is Graph B depicted in the picture.
Step-by-step explanation:
I have taken the test on Plato and have answered correctly.
-0.6w=2.4
Please answer
Hggjigj
Answers
Answer: 3
Step-by-step explanation:
-0.6/(-0.6)=2.4+(-0.6)
Final Answer: [tex]w = -4[/tex]
Steps/Reasons/Explanation:
Question: Solve [tex]-0.6w = 2.4[/tex].
Step 1: Divide both sides by [tex]-0.6[/tex].
[tex]w = -\frac{2.4}{0.6}[/tex]
Step 2: Simplify [tex]\frac{2.4}{0.6}[/tex] to [tex]4[/tex].
[tex]w = -4[/tex]
~I hope I helped you :)~
Which number line shows the correct placement of -200, 75, and -150?
Answers
Answer:
in the explanation
Step-by-step explanation:
In the number line, the left most number would be -200 as it's the lowest, the middle would be -150, as this number is in between the other two, and the right most would be 75, as it's the greatest.
Hope this helps!
2. Find the greatest common factor of 1700 and 1938. Show your work.
Answers
*Answer**
To get the Greates Common Factor (GCF) of 1700 and 1938 we need to factor each value first and then we choose all the copies of factors and multiply them:
1700: 2 2 5 5 17
1938: 2 3 17 19
GCF: 2 17
The Greates Common Factor (GCF) is: 2 x 17 = 34
which sum or difference is equivalent to the following expression 15x - 20/5
A 15x - 4
B 10x - 15
C 3x - 4
D3x - 20
Answers
Answer: A
Step-by-step explanation:
Answer:
I think A 15x -4
Step-by-step explanation:
a. 15x-4
a. 15x-4
if -x>4 then what would be true about x? why?
Answers
Answer:
x will have to be a negative number to be come positive 2 negatives = positive