A blueprint for a house shows the height of the house to be inches. The actual house is feet tall. What is the unit rate in feet per inch?
If you place a 45-foot ladder against the top of a 36-foot building, how many feet will the bottom of the ladder be from the bottom of the building?
Using pythagorean theorem
The bottom of the ladder will be 27 feet from the bottom of the building.
To find the distance from the bottom of the ladder to the bottom of the building, 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 lengths of the other two sides.
In this case, the ladder forms the hypotenuse, and the building forms one of the other sides of the right triangle. Let's denote the length from the bottom of the ladder to the bottom of the building as x.
According to the Pythagorean theorem:
[tex]\[ \text{Hypotenuse}^2 = \text{Adjacent side}^2 + \text{Opposite side}^2 \][/tex]
Given:
- Length of the ladder (hypotenuse) = 45 feet
- Height of the building (opposite side) = 36 feet
We need to find the length of the adjacent side (the distance from the bottom of the ladder to the bottom of the building).
[tex]\[ 45^2 = x^2 + 36^2 \][/tex]
2025 = [tex]x^2[/tex] + 1296
[tex]x^2[/tex] = 2025 - 1296
[tex]x^2[/tex] = 729
x = [tex]\sqrt{729}[/tex]
x = 27
The area of a circular place is 45 square inches. Estimate the radius to the nearest integer.
Estimate: 67times85 plzz help me out with my home work!!
When a figure is rotated, its angle measures (remains the same OR may change), and its orientation (remain the same OR may change).
please help me solve if it remains the same or may change
A copy machine makes 36 copies per minute. How long does it take to make 135 copies
Final answer:
It takes 3.75 minutes for a copy machine that makes 36 copies per minute to make 135 copies.
Explanation:
To calculate how long it takes to make 135 copies with a machine that copies at the rate of 36 copies per minute, you can use a simple division. First, divide the total number of copies needed by the number of copies the machine can make per minute.
So, the calculation would be: 135 copies divided by 36 copies per minute = 3.75 minutes.
Therefore, it would take 3.75 minutes for the copy machine to make 135 copies.
The community garden has $125 to purchase new plants that cost $15.99 each and bags of soil that cost $12.54 each, where x is the number of purchased plants and y is the number of purchased bags of soil. Which inequality represents this situation?
Answer:
[tex]15.99x+12.54y\leq 125[/tex]
Step-by-step explanation:
Let
x------> the number of purchased plants
y------> the number of purchased bags of soil
we know that
The inequality that represent the situation is equal to
[tex]15.99x+12.54y\leq 125[/tex]
The solution is the triangular shaded area
see the attached figure
Two similar triangles are shown below: Which two sets of angles are corresponding angles? ∠w and ∠v; ∠x and ∠y ∠w and ∠y; ∠x and ∠v ∠w and ∠z; ∠x and ∠v ∠w and ∠z; ∠x and ∠y
The answer is <w and <v; <x and <y. hope that helps
Answer:
<w, <v; <x, <y
Step-by-step explanation:
I just took the test. May I have Brainiest? I still need four to level up... TwT
which is true about the functional relationship shown in the graph
Answer:
D) it shows the functional relationship , the cost of the apples is a function of weight.
Step-by-step explanation:
Given : Graph between cost of the apples and the weight of apples.
To find : Which is true about the functional relationship shown in the graph.
Solution : We can see from the graph is showing the relation between cost of an apple and weight of apple .
Therefore, D) it shows the functional relationship , the cost of the apples is a function of weight.
PLEASE HELP ME ASAP!!!
Each dimension of a right triangle with legs of length 6 cm and 8 cm and a hypotenuse of length 10 cm is multiplied by 1/2 to form a similar right triangle. How is the ratio of perimeters related to the ratio of corresponding sides? How is the ratio of areas related to the ratio of corresponding sides?
The ratio of perimeters is one-fourth of the ratio of corresponding sides.
The ratio of areas is the cube of the ratio of corresponding sides.
The ratio of perimeters is equal to the ratio of corresponding sides.
The ratio of areas is the cube of the ratio of corresponding sides.
The ratio of perimeters is one-fourth of the ratio of corresponding sides.
The ratio of areas is the square of the ratio of corresponding sides.
The ratio of perimeters is equal to the ratio of corresponding sides.
The ratio of areas is the square of the ratio of corresponding sides.
The ratio of perimeters is equal to the ratio of corresponding sides. The ratio of areas is the square of the ratio of corresponding sides.
Explanation:The ratio of perimeters is equal to the ratio of corresponding sides. The ratio of areas is the square of the ratio of corresponding sides.
For a right triangle with legs of length 6 cm and 8 cm and a hypotenuse of length 10 cm, if each dimension is multiplied by 1/2 to form a similar triangle, the corresponding sides of the new triangle will be 3 cm, 4 cm, and 5 cm. The ratio of perimeters, 4 + 3 + 5 = 12, is equal to the ratio of corresponding sides, 6 + 4 + 5 = 15. So, the statement that the ratio of perimeters is equal to the ratio of corresponding sides is true.
The ratio of areas can be calculated by squaring the ratio of corresponding sides. So, the ratio of areas for the original right triangle will be (6 * 8) = 48 and for the similar triangle it will be (3 * 4) = 12. The ratio of areas, 48:12, simplifies to 4:1, which is indeed the square of the ratio of corresponding sides, 15:3.
If a roadrunner bird can run 14 miles per hour and that's 7 times faster than an ostrich can walk. How fast does an ostrich walk?
The speed of an ostrich is 2 miles/hr.
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
Given, a roadrunner bird can run 14 miles per hour, which is 14 miles/hr and it is faster by 7 times than an ostrich.
∴ The speed of ostrich is (14/7) miles/hr.
= 2 miles/hr.
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Lizzie makes 20 minutes of phone calls each day. Which plan will give Liza enough minutes for June with between 30 and 50 minutes left? Show your work
The 'Share' plan will be enough for Liza with 650 minutes.
What is an expression?Expressions in maths are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.
Given that, Lizzie makes 20 minutes of phone calls each day
There are 30 days in June,
Minutes required in the given month = 20*30 = 600
She should choose the Share plan with 650 minutes so that she will have enough minutes plus 50 minutes left.
Hence, The 'Share' plan will be enough for Liza with 650 minutes.
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9s - 5g = -4y, for s
which expressions are equivalent to 647 x 39
Answer:25233
Step-by-step explanation:
Use the figure to find the measures of the numbered angles
What is the justification for each step in solving the inequality?
−5(4x+6)<−18x+6+4x
Select from the drop-down menus to correctly justify each step. *Answer choices are in parentheses*
−5(4x+6)<−18x+6+4x Given
−20x−30<−18x+6+4x (Combine like terms) (Distributive Property) (Subtraction Property of Order)
−20x−30<−14x+6 Combine like terms
−6x−30<6 (Addition Property of Order) (Division Property of Order) (Multiplication Property of Order)
−6x<36 (Addition Property of Order) (Division Property of Order) (Multiplication Property of Order)
x>−6 Division Property of Order
Answer:
Step-by-step explanation:
−5(4x 6)<−18x 6 4x given
−20x−30<−18x 6 4x distributive property
−20x−30<−14x 6 combine like terms
−6x−30<6 addition property of order
−6x < 36 addition property of order
x>−6 division property of order
The circle in the diagram is moved from Quadrant IV to the shaded region in Quadrant II. How does this affect the probability that a dart that hits the rectangular region lands in the circle?
The probability that a dart hits the circle when moved from Quadrant IV to Quadrant II stays the same if the size of the circle and the rectangular region remain unchanged, as it is dependent on the area ratio of the circle to the rectangle.
Explanation:When the circle is moved from Quadrant IV to the shaded region in Quadrant II, the probability that a dart hitting the rectangular region lands in the circle depends on whether the size of the circle or its position relative to the overall dartboard (the rectangle) changes. The probability is determined by the ratio of the area of the circle to the area of the rectangle. If the circle remains the same size and merely shifts positions, the probability does not change. However, if moving the circle changes its size or if it overlaps differently with the rectangular region, then the probability will be affected. To calculate the probability, you would divide the area of the circle by the area of the rectangle. Provided there are no changes to the size of the circle or rectangular area, the probability remains constant despite the move.
Ken went to the store for his mother. He spent $2.37 on groceries. In addition, his mother said he could spend $0.35 on candy. What was his change from a five dollar bill? Enter one digit in each box below.
$[______] [______] [_____]
2.37 + 0.35 = 2.72 total spent
5.00 - 2.72 = $2.28 change back
Saturn is located at a distance of 9.54 AU from the Sun what is its orbital period
Answer:
C. 29.46 years
Step-by-step explanation:
The other person is correct, thank you.
Saturn's mean distance from the Sun at 9.54 AU gives it an orbital period of about 29.46 Earth years.
The student is asking about the orbital period of Saturn based on its average distance from the Sun, expressed in astronomical units (AU). According to Kepler's third law of planetary motion, there is a relationship between the orbital period of a planet and its average distance from the Sun. For Saturn, its mean distance from the Sun is approximately 9.54 AU, and its orbital period is roughly 29.46 Earth years.
Kepler's third law states that the square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit. This can be expressed mathematically as p² = a³, where p is the orbital period in Earth years and a is the semi-major axis in AU. By checking Saturn's given values for p² (29.46 * 29.46 = 867.9) and a³ (9.54 * 9.54 * 9.54 = 868.3), we can see that Saturn's data approximates the relation of Kepler's third law effectively, confirming that an orbital period of 29.46 years for Saturn's distance from the Sun is consistent.
The speed of light is 3 x 10^8 meters/seconds. If the sun is 1.5 x 10^11 meters from earth, how many seconds does it take light to reach the earth? Express your answer in scientific notation.
The sunlight takes about 8 minutes and 20 seconds to reach earth.
We have given that,
The speed of light is 3 x 10^8 meters/seconds.
D = r x t distance is equal to the rate of speed multiplied by time.
What is the formula for time?Thus t = d ÷ r
This is the relationship we'll use to solve this problem.
Now, let's organize our data
r = 300,000,000 m/s
Let's write this using scientific notation
r = 3 x 108 m/s
d = 1.5 x 1011 m
t = d ÷ r ⇒ t = 1.5 x 1011 ÷ 3 x 108 or
t = 0.5 x 103
That is 500 seconds or about 8.3 minutes so basically the answer is the sunlight takes about 8 minutes and 20 seconds to reach earth.
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What is the value of v? 45(v−7)=2 Enter your answer in the box.
7 2/45 would be the correct answer
Circle the step the error has occurred. Explain why it is an error.
Given: 2(10 – 13x) = -34x + 60
Step 1: Distribute 20 – 26x = -34x + 60
Step 2: Addition property of Equality -26x = -34x + 80
Step 3: Addition property of Equality 8x = 80
Step 4: Division Property of Equality x = 10
Answer:
Step 2 has an error
Step-by-step explanation:
Given equation,
2(10 - 13x) = -34x + 60
By distributive property,
20 - 26x = -34x + 60
Now, we need to isolate x on the left side of the equation,
For this we need to eliminate constant term from the left side,
20 will be eliminated by subtracting 20 from both sides ( subtraction property of equality )
I.e. Step 2 has an error,
We need to use subtraction property of equality instead of using addition property of Equality,
Note : The correct steps would be,
Step 2 : 20 - 26x = -34x + 60 ( Subtraction property of equality )
Step 3 : 8x = 40 ( addition property of Equality )
Step 4 : x = 5 ( Division Property of Equality )
A coat was sold by a shopkeeper at a gain of 5%. If it had been sold for 1650 less, he would have had a 5% loss. Find CP
The cost price is 16500
Further explanationLet's learn about the basic formula about Profit and Loss
[tex]\texttt{Profit = Selling Price - Cost Price}[/tex]
[tex]\texttt{Selling Price = Cost Price ( 100\% + Profit\% )}[/tex]
[tex]\texttt{Loss = Cost Price - Selling Price}[/tex]
[tex]\texttt{Selling Price = Cost Price ( 100\% - Loss\% )}[/tex]
Let us tackle the problem !
Given:
Gain Percentage = 5%
Loss Percentage = 5%
Difference of Sales Price = 1650
Unknown:
Cost Price = ?
Solution:
[tex]\texttt{Initial Sales Price} = \texttt{Cost Price} \times ( 100\% + \texttt{Gain Percentage} )[/tex]
[tex]\texttt{Initial Sales Price} = \texttt{Cost Price} \times ( 100\% + 5\% )[/tex]
[tex]\texttt{Initial Sales Price} = \texttt{Cost Price} \times ( 105\% )[/tex]
[tex]\texttt{ }[/tex]
[tex]\texttt{Final Sales Price} = \texttt{Cost Price} \times ( 100\% - \texttt{Loss Percentage} )[/tex]
[tex]\texttt{Final Sales Price} = \texttt{Cost Price} \times ( 100\% - 5\% )[/tex]
[tex]\texttt{Final Sales Price} = \texttt{Cost Price} \times ( 95\% )[/tex]
[tex]\texttt{ }[/tex]
[tex]\texttt{Difference of Sales Price} = \texttt{Initial Sales Price} - \texttt{Final Sales Price}[/tex]
[tex]1650 = \texttt{Cost Price} \times ( 105\% ) - \texttt{Cost Price} \times ( 95\% )[/tex]
[tex]1650 = \texttt{Cost Price} \times ( 105\% - 95\% )[/tex]
[tex]1650 = \texttt{Cost Price} \times ( 10\% )[/tex]
[tex]\texttt{Cost Price} = 1650 \div ( 10\% )[/tex]
[tex]\texttt{Cost Price} = 16500[/tex]
Learn moreInfinite Number of Solutions : https://brainly.com/question/5450548System of Equations : https://brainly.com/question/1995493System of Linear equations : https://brainly.com/question/3291576Student's Shirt : https://brainly.com/question/909783Answer detailsGrade: Middle School
Subject: Mathematics
Chapter: Percentage
Keywords: Linear , Equations , 1 , Variable , Line , Gradient , Point , Multiplication , Division , Exponent , PEMDAS , percentange , percent , cookies , chocolate , chip , paper , fourth , pieces
I need help with this problem, I don't know how to solve it at all :(
5-6/w=(w-28)/7w
Period 1 has 15 students in it and a test average of 86%. Period 2 has 21 students in it and an average of 88%. Period 3 has 12 students in it and an average of 95%. Use weighted means to find the overall average of the classes
Answer:
The overall average of the classes is 89.125%
Step-by-step explanation:
For calculate the average of the class using weighted means, it is necessary to take into account the number of students of every period. So, the average can be calculated as:
[tex]Average =\frac{(x_1*a_1) +( x_2*a_2) + (x_3*a_3)}{x_1 + x_2 + x_3}[/tex]
Where is[tex]x_1, x_2[/tex] and [tex]x_3[/tex] are the number of students for period 1 , 2 and 3 respectively and [tex]a_1, a_2[/tex] and [tex]a_3[/tex] are the average of period 1, 2 and 3 respectively.
Replacing the values of x1 by 15 students, x2 by 21 students, x3 by 12 students, a1 by 86%, a2 by 88% and a3 by 95%, we get:
[tex]Average = \frac{(15*86)+(21*88)+(12*95)}{15+21+12}[/tex]
Average = 89.125%
So, using weighted means, the overall average of the classes is 89.125%
A rectangular garden is to be fenced so that one of the sides is 5 feet longer than an adjacent side (s). Which of the following quadratic functions can be used to represent the area of the garden?
A) A=s^2
B) A= s^2+5s
C) A=s^2+5
D) A=5s^2
Select the sets that are not functions.
Choose all that apply.
A = {(1, 2), (2, 3), (3, 4), (4, 5)}
B = {(1, 2), (2, 1), (3, 0), (4, -1)}
C = {(-1, 3), (0, 3), (1, 3), (2, 3)}
D = {(1, 1), (1, 2), (1, 3), (1, 4)}
E = {(6, 2), (7, 3), (6, -1), (5, 4)}
Answer with Step-by-step explanation:
A function is a map from a set A to another set B such that
the image of any point in a has a unique image in set B.
A = {(1, 2), (2, 3), (3, 4), (4, 5)}
It is a function since image of 1,2,3 and 4 is unique.
B = {(1, 2), (2, 1), (3, 0), (4, -1)}
It is a function since image of 1,2,3 and 4 is unique.
C = {(-1, 3), (0, 3), (1, 3), (2, 3)}
It is a function since image of -1,0,1 and 2 is unique.
D = {(1, 1), (1, 2), (1, 3), (1, 4)}
It is not a function since image of 1 is not unique.
E = {(6, 2), (7, 3), (6, -1), (5, 4)}
It is not a function since image of 6 is not unique.
Hence, sets that are not functions are:
D = {(1, 1), (1, 2), (1, 3), (1, 4)}
E = {(6, 2), (7, 3), (6, -1), (5, 4)}
This is more math X-20=-35
Would you classify 256 as a perfect square, perfect cube, both, or neither
In a certain card game , For every four blue cards, there are three yellow cards. There are a total of 84 blue and yellow cards in the game how many blue cards are in the game
Answer:
It is 48
Step-by-step explanation: