A 25-foot ladder is leaning against the side of a house so that the bottom of the ladder is 15 feet from the base of the house. Will the ladder reach a window that is 21.5 feet above the ground?

Answer:

( - 36, 24 )

Step-by-step explanation:

(- 9, 6)

( - 9×4, 6×4)

( - 36, 24 )

The acceleration is 4.24 m^2/s

They are accelerations and vector quantities. The direction of an object's acceleration is determined by the direction of the net force acting on it. Acceleration describes the rate at which a speed changes over time.

The velocity is changing over time. The velocity is actually changing at a constant rate of 10 m/s per second. If an object's velocity is changing, it is said to be accelerating; it has acceleration.

According to question,

Acceleration = final velocity- initial velocity/ time

Final velocity = 14.8 and initial velocity = 4.2

Hence, acceleration = 14.8-4.2/2.5

=10.6/2.5

=4.24.

The acceleration is 4.24 m^2/s.

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The answers to all the subparts are:

So, (A) To make the same shade of green:

Then, cups of yellow paint when blue paint is just 1 cup:
10/2 = 5/1 = 5

Therefore, 5 cups of yellow paint will be needed with 1 cup of blue paint to make the same green shade.

(B) New pair of numbers to make the same green shade:

Old pair:

Another pair:

The new pair would be:

Therefore, the new pair to make the same shade of green will be 4 cups of blue paint and 20 cups of yellow paint.

(C) Proportional relationship:

Old pair:

Proportional relationship will be:

Therefore, the proportional relationship of the table will be x : 5y.

(D) Constant of proportionality:

According to part (C), the Constant of proportionality will be x : 5y.

Therefore, the answers to all the subparts are:

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A number, a variable, or a mix of numbers, variables, and operation symbols make up an expression. The translation is as follows:

a) 4 - k

b) 8 - x

c) 6 + d

d) x + 5

e) 8 / x

f) 2 + x = 8

g) 1/2n-12

A number, a variable, or a mix of numbers, variables, and operation symbols make up an expression. Two expressions joined by an equal sign form an equation.

Arithmetic operations like subtraction, addition, division, multiplication, and exponentiation are used to combine variables and integers to produce any algebraic expression. A variable, a number, or a variable and number with an exponent as a product can all be used as the phrase.

The translation is as follows:

a) 4 - k

b) 8 - x

c) 6 + d

d) x + 5

e) 8 / x

f) 2 + x = 8

g) 1/2n-12

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The function has an average rate of change f is 1/2 over the interval

The possible graph that completes the question is added as an attachment

The interval is given as

-3 ≤ x ≤ 9

This can be rewritten as

x = -3 to x = 9

This can also be represented as

(a, b) = [-3, 9]

From the attached graph, we have

f(-3) = -1.5

Also, we have

f(9) = 0.5

The estimate (to one decimal place) of the average rate of change f is calculated as

Rate = [f(b) - f(a)]/[b - a]

This gives

Rate = [f(9) - f(-3)]/[9 + 3]

So, we have

Rate = [0.5 + 1.5]/[9 + 3]

Evaluate

Rate = 2/12

Simplify

Rate  = 1/6

Hence, the average rate of change f is 1/6

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The roots are

The polynomial can be modellled as ;

Let us use f(2) to obtain a value for a

The polynomal f(x) is given as

The value of the given equation is 12.

In order to solve this question, the BODMAS rule would be used. The BODMAS rule gives the order in which mathematical operations can be solved. The order is:

In the numerator:

the addition would be done first: 3² + 1 = 9 + 1 = 10

Then the subtraction would be done next = 14 - 10 = 4

Now determine the square of the term in the bracket : 4²= 16

In the denominator:

The multiplication would be solved first: 3 x 1/4 = 3/4

The next step is  to solve the division : 1 ÷ 3/4 = 1 x 4/3 = 4/3

The fraction becomes : 16 ÷ 4/3

16 x 3/4 = 12

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Answer:

The answer is 432

Step-by-step explanation:

I did the k 12 quiz and I got it right! good luck

The inequality written for the given statement is x≤10. Therefore, option A is the correct answer.

The given statement is "The water level will be 10 feet or lower by tomorrow."

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

The inequality for the given statement is x≤10

The inequality written for the given statement is x≤10. Therefore, option A is the correct answer.

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"Your question is incomplete, probably the complete question/missing part is:"

Choose the inequality that represents the statement.

The water level will be 10 feet or lower by tomorrow.

A. x≤10

B. x<10

C. x>10

D. x=10

we have the equation

3x=0

is the same that

x=0

This is a vertical line (is the equation of the y-axis)

two ordered pairs that lies in this line are

(0,4) and (0,10)

graph the line

plot the points and join them

see the attached figure

The  mean can be written as mean A= x+ y/2

A data set's mean (average) is calculated by summing all of the numbers in the set, then dividing by the total number of values in the set.

Only numerical variables—regardless of whether they are discrete or continuous—can be used to determine the mean. Simply dividing the total number of values in a data set by the sum of all of the values yields it.

The mean formula is

= {Sum of Observation} ÷ {Total numbers of Observations}

Given:

mean A of two numbers, x and y

So, the mean can be written as

mean A= x+ y/2

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The additional information you will need to show that triangles RST and UTS are congruent by SSS congruence is: c. RT ≅ US.

To prove that two triangles are congruent to each other using the SSS congruence as a criteria, we need to know or be able to show that the three sides of one triangle are congruent to the corresponding 3 sides of the other triangle.

If this criterion is met, then we have enough information needed to show the two instruments are congruent by the SSS congruence.

RS ≅ UT as marked in the diagram shown. Also, by the reflexive property, we ST ≅ TS.

We already know two pairs of sides are congruent to each other in both triangles.

In other to prove the triangles are congruent by SSS congruence, the additional information needed is: c. RT ≅ US.

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Answer:

Step-by-step explanation:The additional information you will need to show that triangles RST and UTS are congruent by SSS congruence is: c. RT ≅ US.

How to Prove Two Triangles are Congruent by SSS Congruence Postulate?

To prove that two triangles are congruent to each other using the SSS congruence as a criteria, we need to know or be able to show that the three sides of one triangle are congruent to the corresponding 3 sides of the other triangle.

If this criterion is met, then we have enough information needed to show the two instruments are congruent by the SSS congruence.

RS ≅ UT as marked in the diagram shown. Also, by the reflexive property, we ST ≅ TS.

We already know two pairs of sides are congruent to each other in both triangles.

In other to prove the triangles are congruent by SSS congruence, the additional information needed is: c. RT ≅ US.

The option that would give the estimated volume of the Pyramid of Giza is = [tex]\frac{53,000 . 150 }{3}[/tex]

A pyramid is a 3-dimensional shape that is made up of a polygonal base and 4 triangular faces. The 4 triangular faces are joined at a vertex. Types of pyramids include a square pyramid, rectangle pyramid, triangle pyramid.

The volume of a pyramid is the amount of space that is a three-dimensional shape.

Volume of a pyramid = 1/3 x (base area x height)

1/3 x (53,000. 150)

= [tex]\frac{53,000 . 150 }{3}[/tex]

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Step-by-step explanation:

so, it is

12 / (1 - (2x + 3))

yes, that is

12 / (1 - 2x - 3) = 12 /(-2x -2) | divide both sides by -2

-6/(x + 1)

The values of the angles m∠1 and m∠3 is equal to 73°.

A transversal may be defined as a line which cuts a pair of parallel lines and forms several angles. When transversal cuts parallel lines the alternate interior angles are equal as well as the corresponding angles are equal. Also, the pair of vertically opposite angles are equal. From the figure attached. ∠4 = ∠8 as they are corresponding angles. So, m∠8 = m∠4 = 107°. Now, we know that ∠1 and ∠4 formed a pair of linear angles and the sum of the measures of the linear angles is 180°. So,

m∠1 + m∠4 = 180°

We know, m∠4 = 107°

m∠1 = 180° - 107°

m∠1 = 73°

Now, ∠1 and ∠3 are vertically opposite angles, so they are equal as the parallel lines are cut by transversal. Therefore, m∠1 = m∠3

=> m∠1 = 73°

=> m∠3 = 73°

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Step-by-step explanation:

If the data shows a leaner relationship between two variables, the line that best fits this linear relationship is known as a least-squares regression line, which minimizes the vertical distance from the data points to the regression line.

The side length of a square is 7 inches drawn by the Peter.

According to the question, the ratio of a square's side length to its perimeter is always one to four.

According to the story, Peter drew a square with such a perimeter of 28 inches.

Divide 28 inches by 4 to get the side length of a square Peter drew.

= 28/4

= 7 inches

As a result, the side length of a square is 7 inches.

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Answer:

[tex]x=\frac{\sqrt{2}}{2}[/tex]

Step-by-step explanation:

x^2+x^2=1

x^2=1/2

x=1/sqrt2

x=sqrt2/2

:]

There are 158,184,000 possible license plates consisting of 3 letters followed by 4 digits.

Based on the given information, since the letters and digits may be repeated, there are:

26 ways to fill in the first letter

26 ways to fill in the second letter

26 ways to fill in the third letter

9 ways to fill in the first digit *(first digit cannot be 0)

10 ways to fill in the second digit

10 ways to fill in the third digit and

10 ways to fill in the first digit

Thus, by Fundamental Principle of Counting, there are 158,184,000 possible license plates.

26 x 26 x 26 x 9 x 10 x 10 x 10 = 158,184,000

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Answer:

64

Step-by-step explanation:

4^3 = 4 x 4 x 4 which can be written as 2^6 which is equivalent to 64 too

(If this is what you're asking)

Using addition of polynomials, the function modeling the number of people attending degree-granting institutions is:

P(t) = 48.7t² + 678.5t + 17667.4.

The number of males is given by:

M(t) = 19.7t² + 310.5t + 7539.6.

The number of females is given by:

F(t) = 28t² + 368t + 10127.8.

The total number is given by the addition of the number of males and of females, that is:

P(t) = M(t) + F(t).

Which is an addition of polynomials. To add the polynomials, we combine the like terms, that is, adding the terms that have the same variable and exponent. Hence:

P(t) = M(t) + F(t).

P(t) = 19.7t² + 310.5t + 7539.6 + 28t² + 368t + 10127.8.

P(t) = 48.7t² + 678.5t + 17667.4.

Which is the desired function.

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The width of the living room on the new blueprint is 15 feet.

Based on the information, the scale of the original blueprint will be:

= 2 in / 5 ft

The width of the original blueprint is 6 inches, the actual width of the living room will be:

2/5 = 6/x

where x = width of living room

Cross multiply

x = 5 × 6 / 2

x = 15 feet.

The width is 15 feet.

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The ratios that can be used to compare the soda and punch recipes are as follows;

1. Emily:

Mason's recipe for soda is y = (1/2)•x

Tyler's recipe; y = (3/5)•x

Julio's

Mason's recipe; y = (1/3)•x

Tyler's recipe; y = (3/8)•x

2. Please see the completed values in the table in the elucidation that follows

3. The equivalent ratio relationship in each graph is given by the constant ratio of each coordinate pair.

4. The recipe that has the strongest lemon lime taste is given by the graph that has the steepest slope

The slope of a graph is given by the ratio of the rise to the run of a graph

1. The unit rate for Mason's recipe is (1/2) cup of lemon–lime per cup of club

While the unit rate for Tyler's recipe for club soda is (3/5) cup of lemon and lime per cup of club

Mathematically, we have

Emily;

Mason's recipe; y = (1/2)•x

Tyler's recipe; y = (3/5)•x

Julio;

Mason's recipe; y = (1/3)•x

Tyler's recipe; y = (3/8)•x

Carlos's recipe; y = (2/5)•x

Zeb's recipe; y = (1/5)•x

2. The values in the table becomes;

Lemon–lime; 1/3, 2/3, 1, 4/3, 5/3, 6/3

Total punch; 1, 2, 3, 4, 5, 6

Lemon–lime; 3/8, 3/4, 9/8, 3/2, 15/8, 9/4

Total punch; 1, 2, 3, 4, 5, 6

Lemon–lime; 2/5, 4/5, 6/5, 8/5, 2, 12/5

Total punch; 1, 2, 3, 4, 5, 6

Lemon–lime; 1/5, 2/5, 3/5, 4/5, 1, 6/5

Total punch; 1, 2, 3, 4, 5, 6

3. Each graph represents equivalent ratios given that the value of the ratio of data point is a constant, that is, we have;

For Mason, 1:(1/3) = 2:(2/3) = 3:1...

For Tyler, 1:(3/8) = 2:(3/4) = 3:(9/8)...

For Carlos, 1:(2/5), 2:(4/5), 3:(6/5)...

For Zeb, 1:(1/5), 2:(2/5), 3:(3/5)...

4. The slope of each graph is given by the number of cups of lemon–lime per one cup of total punch,

The recipe that has the strongest lemon–lime taste is given by the recipe that has the most lemon–lime per each cup of total punch

Which gives;

The recipe that has the strongest lemon–lime can be found from the graph that has the largest slope, which is given by Carlos's recipe.

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Answer:

x=7

Step-by-step explanation:

7=2x-7

-2x-7-7

-2x=-14

x=-14÷2

x=-7

Answer:

8

Step-by-step explanation:

8x3 = 24
8+ 16 = 24

Answer:

A. 6°C

B. -4°C

C. -0.7°C

D. -1°C

Answer:

A. 6°C < 7°C.

B. -4°C < -3°C.

C. -0.8°C < -0.7°C < -0.1°C

D. -1°C > -2°C

The statement which completes each of the open sentences are given below:

32 ÷ 8 + 1 is not equal to  3² - 1

15 ÷ ( 1 + 2) is not equal to  15 ÷ 1 +2

4² is not equal to  4 . 2

3 ( x - 4 + x) is not equal to  3x - 4 + x when x = 4

3 ( x - 4 + x) is not equal to  3x - 4 + x when x = 2

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Answer:

Step-by-step explanation:

6 + 12x

6 ( 1 + 2x )