PLEASE HELP ME TO ANSWER THIS QUESTION.
A right pyramid PQRST has a rectangular base QRST. Given
that W is the midpoint of QS and RT, the lengths of QT = 8 cm,
TS = 6 cm and point P is vertically above point W, calculate
(a) PT, in cm, if PW = 12 cm
(b) the value of < PTR [angle PTR]
THANK YOU!!!
Answers
Answer:
(a) PT = 13 cm
(b) <PTR = [tex]39.7^{o}[/tex]
Step-by-step explanation:
(a) Applying the Pythagoras theorem to QST, we have;
[tex]QS^{2}[/tex] = [tex]ST^{2}[/tex] + [tex]QT^{2}[/tex]
= [tex]6^{2}[/tex] + [tex]8^{2}[/tex]
[tex]QS^{2}[/tex] = 36 + 64
100
QS = [tex]\sqrt{100}[/tex]
= 10
QS = 10 cm
Since QS = TR, then;
WT = [tex]\frac{1}{2}[/tex] TR
= [tex]\frac{1}{2}[/tex] x 10
WT = 5 cm
Thus, applying Pathagoras theorem to PWT;
[tex]PT^{2}[/tex] = [tex]PW^{2}[/tex] + [tex]WT^{2}[/tex]
= [tex]12^{2}[/tex] + [tex]5^{2}[/tex]
= 144 + 25
[tex]PT^{2}[/tex] = 169
PT = [tex]\sqrt{169}[/tex]
= 13
PT = 13 cm
(b) To determine <PTR, TR = 10 cm. Apply the required trigonometric function;
Cos θ = [tex]\frac{adjacent}{hypotenuse}[/tex]
Cos θ = [tex]\frac{10}{13}[/tex]
= 0.7692
θ = [tex]Cos^{-1}[/tex] 0.7692
= 39.7179
θ = [tex]39.7^{o}[/tex]
Therefore, <PTR = [tex]39.7^{o}[/tex]
Related Questions
what is the VOLUME of this rectangular prism!
Answers
Answer:
There`s no photo but I can still help tell you how to solve the volume of a rectangular prism. Just multiply the length by the width, and then that by the height.
The formula is V = lwh
Hope this helps
Can someone please help me with my homework its due in two hours!!!!!! Please i need it done soon.
Answers
Answer:
see explanation
Step-by-step explanation:
so, when a=-3, c is -20. now, to find b when a is -3, plug a (which is -3) into the equation b=4a-5 to get b=-17. so b=-17, c=-20. b is obviously larger (remember the negative sign)
when c is 21, a is 5. plug numbers in to get b=15.
when a is 6, there is no clear value for c, so i'd guess undefined. b however is 19
we can plot the line and the points, for problem 4 and all points above the line means that c is greater than b, and when below it's less than. doing this we get when a is 12, when a is 0, and when a is 5. hope this was clear
The diameter of a spindle in a small motor is supposed to be 4.1 millimeters (mm) with a standard deviation of 0.1 mm. If the spindle is either too small or too large, the motor will not work properly. The manufacturer measures the diameter in a sample of 41 spindles to determine whether the mean diameter has moved away from the required measurement. Suppose the sample has an average diameter of 4.01 mm.
Required:
What are the null and alternative hypotheses?
Answers
Answer:
The null hypothesis is [tex]H_0: \mu = 4.1[/tex]
The alternate hypothesis is [tex]H_a: \mu \neq 4.1[/tex]
Step-by-step explanation:
The diameter of a spindle in a small motor is supposed to be 4.1 millimeters
This means that the null hypothesis is that the diameter has the supposed value, that is, [tex]H_0: \mu = 4.1[/tex]
If the spindle is either too small or too large, the motor will not work properly. The manufacturer measures the diameter in a sample of 41 spindles to determine whether the mean diameter has moved away from the required measurement.
Tests if it has moved away, that is, if the mean is different from the specified value of 4.1. So the alternate hypothesis is [tex]H_a: \mu \neq 4.1[/tex]
Question 4 of 10
When the input is x = 3 for the parent function f(x) = x, what is the output?
O A. f(x) = 3
O B. f(x) = -3
O C. f(x) = 0
O D. f(x) = 1
Answers
Answer:
A
Step-by-step explanation:
f(x) = x
x = 3
->
f(3) = 3
A
Simplify.
10/-4 - √3
Answers
Answer:
here you go. hope this helps
Answer:
-4.23205080...
Step-by-step explanation:
It takes 2 workers 6 hours to paint a school hall.
How long would it take 4 workers to paint the same hall
Answers
Answer:
it will take 3 hour to paint the wall
Answer:
3 hours
Step-by-step explanation:
because we know that 2 x 3 = 6 and 4 x 3 = 12 basically your finding the median. if the number of values is an even number, the median will be the average of the two middle numbers
Sentence: It will take 3 hours for 4 workers to paint the same wall.
can someone help me answers these questions
Answers
Answer:
3) 156°
4) 24°
5) 24°
6) 24°
Step-by-step explanation:
m∡2: 180 - 156 = 24°
m∡3: 156° (is vertical to angle labeled as 156°)
m∡4: 24° (is vertical to angle 2)
m∡5: 156°
m∡6: 24° (alternate-interior to angle 4)
m∡7: 156° (corresponding angle with ∡3)
m∡8: 24° (vertical with angle 6)
Answer:
Step-by-step explanation:
m∠2 = m∠4 = m∠8 = 180° - 156° = 24°
m∠8 = 156°
What are the coordinates for the vertex of the parabola represented by the quadratic equation
y=1/2(x + 4)^2 – 2?
Answers
Answer:
(-4, -2).
Step-by-step explanation:
Compare y = (1/2)(x + 4)^2 – 2 to the standard equation:
y = a(x - h)^2 + k whose vertex is at (h, k).
We see that h = -4 and k = -2. Thus, the vertex of the vertex of the given parabola are (-4, -2).
What type of units are used to describe volume?
Answers
Answer:
The most basic common unit is Liters (L), but people also commonly use milliliters (mL) and cubic centimeter (cm^3).
Evaluate each expression if x = 3.
a. 2^x
b. x^2
c. 1^x
d. x^1
e. (1/2)^x
Answers
Answer:
a) 2³ = 2×2×2×=8
b) 3²=3×3=9
c) 1³=1×1×1=1
d) 3¹=3
e) 1/2³=1/2×1/2×1/2=1/8
The volumes of two cubes are 32ft^3 and 1372ft^3
1. What is the ratio of their volumes?
2. What is the scale factor?
3. What is the ratio of their surface areas?
4. Find the surface are of the smaller cube if the larger cube has a surface area of 196ft^2
Answers
Answer:
1) 8 : 343
2) 42.875 or 42 ⅞
3) 4 : 49
4) 16ft²
Step-by-step explanation:
Volume of cube: s³
Surface area of cube: 6s²
_____________________
32ft^3 and 1372ft^3 →
32 : 1372 = 8 : 343
343 / 8 = 42 ⅞ = 42.875
s³ → 6s²
s³ = 8, s = 2, s² = 4.
s³ = 343, s = 7, s² = 49.
These are proportional so it is already in the simplest ratio so it is not necessary to multiply by 6.
s³ → 8 : 343
6s² → 4 : 49
(4 / 49) × 196ft² = 16ft²
63 is 9% of what number?
Answers
Answer:
63 is 9% of 700.
Step-by-step explanation:
To solve this problem you multiply 63 by 100 and then divide the total by 9 as follows: (63 x 100) / 9
Thus, the answer is 700.
A cube has an A on 3 sides and a B on 3 sides. Rolling it 50 times results in 17 A's and 33 B's.
Using this observed probability, how many A's would be rolled in 750 tries?
Answers
I posted 2 question of this but nobody answered first answer gets brainliest and a thanks and 5 stars and 20 points and do all of them or half no links ASAP guessers will be reported
Answers
Answer:
14. 13.65
15. 7.53
17. 0.0371
18. 0.81
19. 0.864
Here are some answers! Hope this helps
which equation has (2, -1) as a solution
a. y=2x-1
b. y=x+3
c. y=x-3
d. y=-2x+1
Answers
Answer:
y=x-3
-1＝2-3＝-1
............
answer all of them please
easy math questions for 20 points
Answers
2) 4
3) 60
4) 18
5) 6
6) 4
7) 9
8) 4
9) 4
10) $35
11) 8
12) 9
13) 56
14) 10000
15) 78
16) $50
17) 10
18) 1,2,3,4,6,12
19) 1,2
20) 1000
21) 8
22) 5
23) 12
24) 366
25) 35
Sin 0= 8/17 determine the value of tan?
Answers
Answer:
tan theta = 8/15
Step-by-step explanation:
Sin is equal to opposite over hypotenuse. So it means that the side opposite from theta is 8, and the hypotenuse is 17.
To find the value of the adjacent side from theta, use the Pythagorean Theorem.
a^2 + b^2 = c^2
8^2 + b^2 = 17^2
64 + b^2 = 289
Subtract 64.
b^2 = 225
Take the square root.
b = 15.
So that means:
the side opposite from theta is 8,
the side adjacent from theta is 15,
the hypotenuse is 17.
Now we take tan, opposite over adjacent, and use the values from the triangle.
tan = opposite / adjacent
tan = 8/15.
Help
Find the experimental probability that 4 of 4
children in a family are boys.
The problem has been simulated by tossing 4
coins (one to represent each child). Let "heads"
represent a boy and "tails" represent a girl. A
sample of 20 coin tosses is shown.
HTHн HTTH TTTT THTT НТНТ
HHTT HHHT THHT HTTH ТОНН
HTTT НТНТ ТОНН ТНТН HTHн
TTHT HTTT НТНТ HHHT HHHH
Experimental Probability = [?]%
Enter
Answers
Answer:
5%
Step-by-step explanation:
I didn't see any more than I HHHH
There are 20 total tosses.
1 was successful
P(4 heads)= 1/20
Experimental Probability = 1/20 * 100 = 0.05 * 100 = 5%
If you see more than one HHHH put the number that you count over 20 and multiply by 100.
Answer:
sorry sorry sorry sorry sorry
three consecutive integers have a sum of 255 find the integers
Answers
Answer:
Step-by-step explanation:
Givens
Let the smallest integer = x - 1 (You'll see why in a moment).
Let the middle integer = x
Let the largest ingeger = x + 1
Equation
x - 1 + x + x + 1 = 255
Solution
Combine like terms on the left.
3x - 1 + 1 = 255
3x = 255 Divide by 3
3x/3 = 255/3
x = 85
So the smallest number is 84
The middle number is 85
The largest number is 86
Total 255
Do you see why I made the smallest number x - 1?
It is because the -1 and the plus 1 cancel out.
Please realize the question says consecutive integers. It does not say consecutive odd or consecutive even integers.
Which of the following sentences describes an equilateral triangle?
A:
Two sides are the same length.
B:
Each angle is less than 90 degrees.
C:
One of the angles equals 90 degrees.
D:
The lengths of all three sides are the same.
Answers
Ms. Gonzalez had $70 to purchase school supplies for her class. She bought 29 glue sticks and 29 boxes of crayons. Each glue stick cost $1.29, and each box of crayons cost $0.79. How much money did Ms. Gonzalez have left after these purchases?
Answers
What is -4/7 as an equivalent fraction
Answers
Answer:
There are many answers
Step-by-step explanation:
So, since we are finding the equivalent fraction there can be many answers
Here are 5 answers that can help you
• -8/14
• -12/21
• -16/28
• -40/70
• -24/42
HELP ME WITH THISSS!!!!!!!!!!!!!!!!!!!
Answers
Does anyone know the answer to this?
Answers
Answer:
x=18 and y=106
Step-by-step explanation:
Please help mehhhhhh
Answers
Answer: They should be 1.5 apart from each other
The product of two numbers is 75
one of the two numbers is a perfect squar. The other is a prime number. Find the sum of the two numbers.
Answers
Answer: 8
Step-by-step explanation: numbers are 5 and 3.
5²·3 =75
The ratio of children to adults is 4 to 3. How many children are there if there are 2700 adults?
Answers
Answer:
2025 children
Step-by-step explanation:
4 2700
-- = --------
3 x
cross multiply
4x = 8100
x = 2025
In the
accompanying diagram of circle O, chords AB and CD intersect at E and
AC:CB:BD:DÀ= 4:2:6:8
What is the measure of AC?
Answers
Answer:
72°
Step-by-step explanation:
4+2+6+8=20
360÷20=18
AC=4x18=72
GEOMETRY!! I will give brainliest
Answers
Answer
The triangle is scalene triangle
Answer:
Scalene triangle
Step-by-step explanation:
Find the Total surface area of the triangular prism below.
Answers
Answer:
The surface area of any prism is the total area of all its sides and faces. A triangular prism has three rectangular sides and two triangular faces. To find the area of the rectangular sides, use the formula A = lw, where A = area, l = length, and h = height. To find the area of the triangular faces, use the formula A = 1/2bh, where A = area, b = base, and h = height. Once you have the areas of all sides and faces, you simply add them together to get the surface area.
Step-by-step explanation:
Formula
Area of a triangle
A = 1/2bh
Area of a rectangle
A = lw
Surface area of triangular prism
SA = bh + (s1 + s2 + s3)H
Hope it helps... Please mark as the Brainliest!!!