Question 4
The roof of a patio is in the shape of a triangle.
What is the value of x, the distance from the base of the roof to the top of the roof?
(A) 2 feet
B 8 feet
C) 13 feet
(D) 22 feet
Answers
The value of x, the distance from the base of the roof to the top of the roof is 8 feet
The length of the base of the triangle = 30 feet
The side of the triangle = 17 feet
The triangle is the combination of two right triangles
Consider one right triangle
The base length = 30 / 2 = 15 feet
The side of the triangle = 17 feet
The length of the third side = x
Here we have to apply Pythagorean theorem
Then
17^2 = 15^2 + x^2
x^2 = 17^2 - 15^2
x^2 = 289 - 225
x^2 = 64
x = 8 feet
Therefore, the height of the roof is 8 feet
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Related Questions
You draw one card from a 52-card deck. Then the card is replaced in the deck and the deck is shuffled, and you draw again. Find the probability of drawing a six the first time and a spade the second time
Answers
Answer:
1/4(1/4)=1/16, or 6.25% chance.
Step-by-step explanation:
There are 13 spades in a deck of 52 cards. This is a 13/52, or 1/4 chance of selecting one. As the cards are replaced we just multiply the probabilities of picking a spade.
I hope this helps!
what is the probability that either event will occur?
Answers
The probability that either event will occur is P ( C ) = 0.89
Given data ,
Let the probability that either event will occur be P ( C )
P ( A ) = 20/36
P ( B ) = 12/36
where P ( A or B ) = P ( C )
P ( C ) = P ( A ) + P ( B )
P ( C ) = 32/36
P ( C ) = 0.88888
Hence , the probability is P ( C ) = 0.89
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Calculate the new price. Original price: $19.99, discount 30%
Answers
19.99 times 30.00 divided by 100 = 19.99 x 30.00/100 = 19.99 x 0.3 = 6.00 (this is the discount)
Subtract the discount from the price before the discount to get the final price:
Final price = 19.99 minus 6.00 = 19.99 - 6.00 = 13.99
So an item that costs 19.99 when discounted 30% will cost 13.99.
Hope this helps : )
Answer: 30 percent of 19.99 is 13.99
Step-by-step explanation: if you add a 30% discount to the 19.99$ the price will be lowered by 6.00$.
Find the most important variable in the problem. How long does it take to drive 341 miles at 63 miles per hour? A. The rate of travel B. The time it takes to complete the trip C. The total distance of the trip
Answers
The time it takes to complete the trip
Today Olivia is carrying her history textbook and her lunch in her backpack. If the history textbook weighs 1/2 of a pound and her lunch weighs 2/3 of a pound, how much weight is in Olivia's backpack?
Answers
Weight is in Olivia's backpack is 5/6 pound.
As in the given problem olivia's history book weights 1/2 of a pound and
her lunch weighs 2/3 of a pound.
As both the units are same,
Thus total weight must be summation of both history book and her lunch box.
total weight is =1/2 +2/3 pound
= (3+2)/6
that is equal to 5/6 pound.
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If a line falls on the points (25, 24) and (15, 17), what is its slope? Enter your answer as a fraction in lowest terms. Use a slash mark (/) as the fraction bar
Answers
Answer:
7/10
Step-by-step explanation:
We can use the slope formula to find the slope
m = ( y2-y1)/(x2-x1) where ( x1,y1) and (x2,y2) are two points on the line
m = ( 24-17)/(25-15)
= 7/10
= 7/10
Givin (2, 4) and 6, 12), what is The slope of the line between these two points?
Answers
Answer:
m=4 or slope =4
Step-by-step explanation:\(m=\frac{y2-y1}{x2-x1\\}\)
so \(m=\frac{12-4}{6-2}\) which is the same as 8/2. So all in all the slope is 4.
please help me. I need help with sentences I don’t know what to puttttttt.
Answers
5/6 having denominator 35
Answers
Answer:( 175/6)
Step-by-step explanation: 5*35/6=175/6 sour our numerator is 175/6. So sour answer is (175/6)/35
If r+s/r =3 and t+r/t =5, what is the value of s/t ?
Answers
Answer:15
Step-by-step explanation:1) 1/2
2) 3/5
3)4
D) 8
5) 16
plz branliest
Maya’s unpaid balance is $205.16. Her APR is 14.4% and she has $82.10 in new transactions. What is her new balance? Responses $289.72 $289.72 $290.71 $290.71 $316.80 $316.80 $533.45
Answers
Based on the information given the new balance is $289.72.
New balanceFirst step is to calculate the finance charge
\(\text{Finance charge}=205.16\times(0.144\div12 \ \text{months})\)
\(\text{Finance charge}=205.16\times0.012\)
\(\text{Finance charge}=2.46\)
Second step is to calculate the New balance
\(\text{New balance}=205.16+2.46+82.10\)
\(\text{New balance}=\bold{\$289.72}\)
In conclusion, the new balance is $289.72.
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If the product of three identical numbers is 1000, find one of the number?
Answers
Answer:
10
Step-by-step explanation:
Three identical numbers whose product is 1000
10 * 10 * 10
karla is offered a job as parking lot attendant. the job will pay 2400 per month, paid biweekly. along with the base salary, the company offers to pay half the cost of medical insurance and will match karlas contribution to a retirment plan up to a total of 1500. if the full cost of the medical insurance is 450 a month and karla plans to contribute the full 1500 every year tpa retirement plan, what is the actual annual value of this job to karla?
Answers
The actual annual value of this job to Karla is 33000.
What are arithmetic operations?
Arithmetic operations is a branch of mathematics that studies numbers and the operations on numbers that are useful in all other branches of mathematics. It consists primarily of operations like addition, subtraction, multiplication, and division.
We have,
the job will pay 2400 per month,
if the full cost of the medical insurance is 450 a month and Karla plans to contribute the full 1500 every year tpa retirement plan,
the actual annual value of this job to Karla is:
2400 per month
annual value = 2400 * 12 = 28,800
the medical insurance is 450 a month
half the cost of medical insurance is 225 a month
annual value = 225 * 12 = 2700
the full 1500 every year tpa retirement plan,
So, the total value is:
= 28,800 + 2700 + 1500
= 33000
Hence, the actual annual value of this job to Karla is 33000.
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(12²-15+17)+16= what is the answer
Answers
162
Step-by-step explanation:
(12 square - 15 + 17) + 16
=(144 - 15 + 17) + 16
=146 + 16
=162
Can someone pls explain
Answers
163. The distance between A(-5, 6) and B(5, -5) is: AB ≈ 14.9 units
164. Applying the Pythagorean theorem, we have: Diagonal ≈ 21.2 ft.
165. Marissa's final answer is wrong. It should be, c = √676 = 26 units.
166. Missing side = 29 ft.
What is the Pythagorean Theorem?The Pythagorean theorem states that c² = a² + b², given that a and b are shorter legs and c is the hypotenuse or longest leg of the right triangle.
163. The distance between A(-5, 6) and B(5, -5):
AB = √[(5−(−5))² + (−5−6)²]
AB = √221
AB ≈ 14.9 units
164. Apply the Pythagorean theorem to find the diagonal:
Diagonal = √(15² + 15²) ≈ 21.2 ft.
165. The answer Marissa got is wrong. The final answer which is the square root of 676 is:
c = √676 = 26 units.
166. Missing side = √(20² + 21²) = 29 ft.
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........................................................................................
Solve
........................................................................................
Answers
Answer:
10 - 15%
Step-by-step explanation:
Just guessing
Write the quadratic equation in standard form and then choose the value of "b."
(2x - 1)(x + 5) = 0
O
10
011
pllllllls help me
Answers
\((2x-1)(x+5)=2x^2+9x-5=0\).
The quadratic equation has a general form of
\(ax^2+bx+c=0\).
So your "b" is 9.
Hope this helps.
Answer: Answer is in the steps
Step-by-step explanation:
(2x-1)(x+5) = 0 First expand the left side by apply the distributive property twice.
(2x -1)(x+5) =0
x(2x -1) = 2x^2 -1x
5(2x -1) = 10x -5
Now rewrite them all together
2x^2 - 1x +10x -5 = 0 combine like terms on the left side.
\(2x^{2}\) + 9x -5 = 0 a is the first leading coefficient,b is the second leading coefficient, and c is the constant.
So in this case, the value of b is 9.
if a small cup is 10 oz and cost 2.69 what is the cost per ounces
Answers
Answer:
The cost per ounce of the small cup is $0.269
Step-by-step explanation:
To find the cost per ounce, we can divide the cost of the cup by the number of ounces it holds.
Cost per ounce = Cost of the cup ÷ Number of ounces in the cup
Cost of the cup = $2.69
Number of ounces in the cup = 10 oz
So,
Cost per ounce = $2.69 ÷ 10 oz
Cost per ounce = $0.269 per oz (rounded to the nearest thousandth)
Therefore, the cost per ounce of the small cup is $0.269.
7/8 ^2
Choose the correct expanded form for the following expression .
Evaluate 7/8^2
Answers
The correct expanded form for the following expression is 7/8 × 7/8.
What is expanded form?The division of numbers into their component ones, tens, hundreds, thousands, ten thousand, and so forth creates the expanded form of the number. The expanded version of the number is the sum of each digit times its place value, which is used to represent the number. A number is broken down to show the value of each of its digits in order to be written in expanded form. 144 would then be converted to 100 + 40 + 4 = 144. It can be used to compute sums as well. When a number is expanded to show the value of each digit, it is written in expanded form. The numerical value of each digit in the number we are writing is represented using extended form.
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Will give brainliest if you answer no 1
Answers
Answer:
74
Step-by-step explanation:
Consider the following statement. (Assume that all sets are subsets of a universal set U.)
For all sets A, B, and C, if A ⊆ B and B ∩ C = ∅ then A ∩ C = ∅.
Construct a proof for the statement by selecting sentences from the following scrambled list and putting them in the correct order. Use the element method for proving that a set equals the empty set.
Then x ∈ B because A ⊆ B. In addition, we know that x ∈ C.
Then (A ∩ C)c = U.
Hence x ∈ B ∩ C by definition of intersection.
Then by definition of intersection and complement A = U.
By definition of intersection x ∈ A and x ∈ C.
Therefore A ⊈ B.
Thus B ∩ C ≠∅ by definition of ∅.
Proof by contradiction:
Suppose that there exists sets A, B, and C such that A ⊆ B, and B ∩ C = ∅ and A ∩ C ≠∅. Then there exists an element x such that x ∈ A ∩ C.
---Select--- Then x ∈ B because A ⊆ B. In addition, we know that x ∈ C. Then (A ∩ C)ᶜ = U. Hence x ∈ B ∩ C by definition of intersection. Then by definition of intersection and complement A = U. By definition of intersection x ∈ A and x ∈ C. Therefore A ⊈ B. Thus B ∩ C ≠∅ by definition of ∅.
---Select--- Then x ∈ B because A ⊆ B. In addition, we know that x ∈ C. Then (A ∩ C)ᶜ = U. Hence x ∈ B ∩ C by definition of intersection. Then by definition of intersection and complement A = U. By definition of intersection x ∈ A and x ∈ C. Therefore A ⊈ B. Thus B ∩ C ≠∅ by definition of ∅.
---Select--- Then x ∈ B because A ⊆ B. In addition, we know that x ∈ C. Then (A ∩ C)ᶜ = U. Hence x ∈ B ∩ C by definition of intersection. Then by definition of intersection and complement A = U. By definition of intersection x ∈ A and x ∈ C. Therefore A ⊈ B. Thus B ∩ C ≠∅ by definition of ∅.
---Select--- Then x ∈ B because A ⊆ B. In addition, we know that x ∈ C. Then (A ∩ C)ᶜ = U. Hence x ∈ B ∩ C by definition of intersection. Then by definition of intersection and complement A = U. By definition of intersection x ∈ A and x ∈ C. Therefore A ⊈ B. Thus B ∩ C ≠∅ by definition of ∅.
But this contradicts the supposition. Hence the supposition is false, and so A ∩ C = ∅.
Answers
The correct order of the given statements is- 1, 2, 3, 4, 5, 6, followed by 7.
Here, we are given the following statement-
For all sets A, B and C if A ≤ B and B∩C = Φ
then A∩C = Ф
We can use the proof-by-contradiction method to prove the given statement as shown below-
Suppose that there exist 3 sets, that are- A, B, and C
Such that A ≤ B, B∩C = Φ
and A∩C ≠ Φ
Then, there must exist an element x such that x ∈ A∩C
Now, by the definition of intersection, we have- x ∈ A and x ∈ C
Then x ∈ B because A ≤ B. Additionally, we know that x ∈ C
Hence, by the definition of intersection, x ∈ B∩C
Thus, B∩C ≠ Φ by definition of null set (Φ)
But this contradicts the supposition. Hence, our assumption is false and so A∩C = Ф.
The correct order of the given statements is- 1, 2, 3, 4, 5, 6, followed by 7.
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A boy walks 5km due north and then 4km due east. Find the bearing of his current position from the starting point, how far is the boy now from the starting point
Answers
a dvd has a diameter of 16 centimeters.what is the the area of the dvd?round the answer to the nearest hundredth.use 3.14 for n
Answers
Answer:
A = 201 cm²
Step-by-step explanation:
We know that the area of a circle can be calculated with the formula:
A = πr² = π(d/2)²
with d being the diameter.
Therefore:
A = 3.14(8cm)² = 201 cm²
Radius = half of 16=8
Formula is pi*r2
3.14*64=200.96
B) What is the cost of making 35 items?
And c. The domain
Answers
The cost of making 35 items is 1100 and the domain is (-∞,∞)
The cost of making 35 items :
x = 35plug the value into the cost equation
C(35) = 10(35) + 800
C(35) = 350 + 800
C(35) = 1100
Hence, cost of making 35 items is 1100
The domain of the functionSince the value of X can be any real number, we can plug in any real number for x and get a real number output.
Hence, the domain = (-∞,∞)
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f(x) = x2 + 10х=What is the average rate of change of fover the interval [-2, -1]?
Answers
Given
\(f(x)=x^2+10\)To find the average rate of change of f over the interval [-2,-1].
Explanation:
It is given that,
\(f(x)=x^2+10\)The average rate of change is given by,
\(Average\text{ }rate\text{ }of\text{ }change=\frac{f(b)-f(a)}{b-a}\)That implies,
\(\begin{gathered} f(-1)=(-1)^2+10 \\ =1+10 \\ =11 \end{gathered}\)Also,
\(\begin{gathered} f(-2)=(-2)^^2+10 \\ =4+10 \\ =14 \end{gathered}\)Therefore,
\(\begin{gathered} Average\text{ }rate\text{ }of\text{ }change=\frac{f(-1)-f(-2)}{-1+2} \\ =\frac{11-14}{1} \\ =-3 \end{gathered}\)Hence, the average rate of change is -3.
Find the height of the right circular cylinder of greatest volume that can be
inscribed in a right circular cone with radius 5 cm and height 12 cm.
Answers
The height of the cylinder with the greatest volume that can be inscribed in the given cone is 4 cm.
What is the volume of the cylinder and cone?The volume of the cylinder is given as V = πr²h and the volume of the cone is V = 1/3πr²h.
Let the radius and height of the cylinder "r" and "h", respectively. Since the cylinder is inscribed in the cone, the height of the cylinder plus the height of the cone must be equal to the total height of the cone:
h + 2r = 12 (1)
The volume of the cylinder, which is given by: V = πr²h
Using equation (1), we can express h in terms of r, h = 12 - 2r
Substituting this into the formula for the volume, we get:
V = πr²(12 - 2r)
Expanding this expression and simplifying it, we obtain:
V = 12πr² - 2πr³
To find the maximum volume, we need to take the derivative of V with respect to r and set it equal to zero:
dV/dr = 24πr - 6πr² = 0
Solving for r, we get:
r = 0 or r = 4
The radius of the cylinder must be r = 4 cm. Using equation (1), we can find the height of the cylinder:
h = 12 - 2r = 4 cm
Thus, the height of the cylinder with the greatest volume that can be inscribed in the given cone is 4 cm.
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Brandon is landscaping his backyard. He bought 2 7\8tons of decorative rock and 1 2\5 tons of boulders. How many total tons of rock did he buy?
Answers
Answer:
4 11/40 hope this helps :)
Step-by-step explanation:
Answer:
4 11/40
Step-by-step explanation:
I had this question
Math help guys please
Answers
Answer:
- 4 / 9
Step-by-step explanation:
..........................
PLZ HELP!!
Which of the following shows how the distributive property can be used to find -22(1.5)?
O-22(-1) + -22(-0.5)
O 22(1) + 22( 0.5)
O-22(1) + -22(0.5)
0 -22(0.75) +-22(-0.75)
Answers
Answer:
the answer is c
Step-by-step explanation:
hope this helped
Answer:
c. -22(1) + -22(0.5)
Step-by-step explanation:
(B^3)^2 without exponents
Answers
Answer:
B⁶
Step-by-step explanation:
The simplified value of (B³)² is B⁶.
The given expression is \((B^3)^2\).
What is an exponent?An exponent is a quantity representing the power to which a given number or expression is to be raised.
We can write the given expression as:
\((B.B.B)^2\)
\(=(B.B.B)*(B.B.B)\)
\(=B.B.B.B.B.B\)
\(=B^6\)
Hence, the simplified value of (B³)² is B⁶.
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