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Applying the Pythagorean Theorem, the ladder's height from the ground is: 24.3 ft.

If we know any two sides of a right triangle, the Pythagorean Theorem can be used to find the length of the third side, c, if c is the longest side, and a and b are the shorter sides of the right triangle, we ill have the equation:

c² = a² + b².

The ladder forms a right triangle with the wall of the building. Therefore:

Substitute

25² = 6² + b²

b = √(25² - 6²)

b = 24.3 ft.

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Given:

To Determine: The identity that is equivalent to the given tangent

Note that, the identity rule below would be applied

Also,

And also,

From the given tangent, we can re-write it as below:

Therefore:

Also:

And also,

It can be observed from the option provided, the correct options is

I and III only

The price the supermarket can charge per egg that is between the prices of per egg for the two different-sized cartons is $0.245 per egg.

According to the question,

We have the following information:

Cost of 12 eggs in a carton = $3.00

Cost of 18 eggs in another carton = $4.32

Now, to find the charge per egg that is between the prices of per egg for these different-sized cartons, we will first find the charge per egg of both of them.

We know that to find the cost of 1 product we divide the given cost by the number of products.

Cost of 12 eggs in a carton = $3.00

Cost of 1 egg = $ (3.00/12)

Cost of 1 egg = $0.25

Cost of 18 eggs in another carton = $4.32

Cost of 1 egg = $(4.32/18)

Cost of 1 egg = $0.24

Now, we have to find the price of egg between 0.24 and 0.25.

Note the difference between these two charges is 0.01.

We will divide it by 2 to find the exact middle charge:

0.01/2 = 0.005

We can add this in $0.24 or subtract it from$ 0.25.

$0.24 + $0.005 = $0.245

Hence, price the supermarket can charge per egg is $0.245.

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The property of a rhombus regarding the two diagonals states that they bisect each other at right angles.

Hence, option D is the correct answer.

1) We need to find out a pattern for the powers that have a base 2:

Note that from 4 to 4 powers the last digit starts to repeat itself.

2) So, let's proceed with this dividing the exponent 2058 by 4:

Now, note that the remainder is 2, therefore we can state that:

Answer:

B

I hope that this helps

Using elimination method, we get the result  630 + 630 + 35 = n

What is elimination method?

The elimination method involves removing one of the variables from a system of linear equations by adding or subtracting from the system and multiplying or dividing the variable coefficients.

You need an equation that can determine n, 630's total, and 35 more than 630.

More

The value "35 more in June than in May" refers to the value "35 more than 630." That value is represented by the sum (630 +35).

Total two months

In total, there will be two months' worth of delivered papers.

May deliveries + June deliveries = n

630 + (630 +35) = n

Eliminating parentheses, this expression is ...

630 + 630 + 35 = n

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The plotted function and the function y = 3x - 6 represent a straight line and have have same slope and hence, both the lines are parallel to each other.

The general equation of a straight line is of the form -

y = mx + c

where -

[m] is slope of line

[c] is y - intercept

Given is a equation of a straight line and a graph of a straight line.

We have the following equation -

y = 3x - 6

For this equation, the slope of the straight line will be [m] = 3 and the y - intercept would be [c] = - 6. Refer to the graph attached with green color for all the possible set of solution.

Now, the equation of the line plotted on graph -

m = (4 - 0)/(0 + 1.3)

m = 3.07

m = 3 (approx.)

Its y - intercept [c] = 4

Therefore, the equation of the plotted line -

y = 3x + 4

Now, both the lines are plotted on the graph. It can be seen from the graph and from the equation that they have same slope and hence, both the lines are parallel to each other.

Therefore, the plotted function and the function y = 3x - 6 represent a straight line and have have same slope and hence, both the lines are parallel to each other.

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[The complete question needs the plotted graph. It is attached at the end  of the answer]

The radius is 1.13 inches and the height of the cylinder is 4.52 inches.

From the information, it's important to use the volume of a cylinder to illustrate the information.

Use the volume of a cylinder.

V = πr²h

V = volume.

r = radius

h = height

where:

V = 18

h = 2(2r) = 4r

Plug in the values into the equation and solve for r.

18 = πr²(4r)

18 = 4πr³

Divide both sides of the equation by 4π.

9 / (2π) = r³

r³ = 1.43

r = 1.13 inches.

Finally, multiply the radius by 4 to get the height. This will be:

= 4 × 1.13

= 4.52 inches.

In conclusion, the height is 4.52 inches.

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Answer:

Step-by-step explanation:

Given that,

To find the standard form of the equation of the parabola with a focus at (0, 9) and a directrix y = -9.

What is a parabola?

A parabola is a cross-section cut out of the cone and represented by an equation

Focus of the prabola = (h , k + F ) =  (0, 9)

Since the directrix, y =  -9

F = -9

k + F = 9

k = 0

Vertex of the parabola = (h,  k  )

                                    =  (0, 0)

Standard equation of the parabola

( y - k ) = 4a (x - h)²

( y - 0 ) = 4a (x - 0)²

y = 4 * 9 x²

y = 36 x²

Thus, the required expression for the parabola with focus at (0, -9) and a directrix y = 9 is y = 36x².

Given:

f(x)=6x+3

Required:

To calculate the average rate

Explanation:

Required answer:

30

Answer:

$435,400

Step-by-step explanation:

Price of one ticket: $311,000/5,000

Price of one ticket: $62.20

Price of 7000 tickets: $62.20 x 7000

Price of 7000 tickets: $435,400

Answer:

6

Step-by-step explanation:

Using the intersecting chords theorem,

[tex]x^2=36 \\ \\ x=6 (x>0)[/tex]

The distance between home plate and first base is -1 feet

what is distance ?

Distance is a numerical or occasionally qualitative measurment of how far apart objects or point are . in physics or everyday usage , distance may refer to a physical length.

How to determine the number

From the information given, we have that;

The expression for the number of feet between home plate and first base is given as;

√81-√100

Where;

√81 is the number of feet at home plate

√100 is the number of feet at the first base

To determine the distance, we take find the square root of the numbers and substitute, we have;

9 - 10 Find the difference

-1 feet

Thus, the distance between home plate and first base is -1 feet

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ANSWER

YES, the base is 4 ......option B

The quadratic function in vertex form is y = -1/2(x + 1)^2 - 2

The vertex is given as

(h, k) = (-1,-2)

The point is also given as

(x, y) = (3, -10)

Quadratic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k

Substitute (h, k) = (-1,-2)  in y = a(x - h)^2 + k

y = a(x + 1)^2 - 2

Substitute (x, y) = (3, -10)

-10 = a(3 + 1)^2 - 2

So, we have

-10 = a(4)^2 - 2

Add 2 to all sides

-8 = a(16)

Divide by 16

a = -1/2

Substitute a = -1/2 in y = a(x + 1)^2 - 2

y = -1/2(x + 1)^2 - 2

Hence, the equation is y = -1/2(x + 1)^2 - 2

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Answer:

[tex]\textsf{The quotient is $\boxed{10}\;x+\boxed{16}$}[/tex]

[tex]\textsf{The remainder is $\boxed{28}\:x^2+\boxed{10}\:x+\boxed{22}$}[/tex]

Step-by-step explanation:

Definitions

Dividend: The polynomial which has to be divided.

Divisor: The expression by which the dividend is divided.

Quotient: The result of the division.

Remainder: The part left over.

Long Division Method of dividing polynomials

Given:

[tex]\textsf{Dividend}: \quad 10x^4-14x^3-10x^2+6x-10[/tex]

[tex]\textsf{Divisor}: \quad x^3-3x^2+x-2[/tex]

Therefore:

[tex]\large \begin{array}{r}10x+16\phantom{)}\\x^3-3x^2+x-2{\overline{\smash{\big)}\,10x^4-14x^3-10x^2+6x-10\phantom{)}}}\\{-~\phantom{(}\underline{(10x^4-30x^3+10x^2-20x)\phantom{-b)}}\\16x^3-20x^2+26x-10\phantom{)}\\-~\phantom{()}\underline{(16x^3-48x^2+16x-32)\phantom{}}\\28x^2+10x+22\phantom{)}\\\end{array}[/tex]

Solution:

[tex]10x+16+\dfrac{28x^2+10x+22}{x^3-3x^2+x-2}[/tex]

[tex]\textsf{The quotient is $\boxed{10}\;x+\boxed{16}$}[/tex]

[tex]\textsf{The remainder is $\boxed{28}\:x^2+\boxed{10}\:x+\boxed{22}$}[/tex]

ANSWER

EXPLANATION

We want to find the equation of the perpendicular bisector of the line segment with the given endpoints.

To do this, we first have to find the slope of the given line, since the slope of a line perpendicular to a given line is the negative inverse of the slope of the line.

Then, we have to find the midpoint of the given line since the line is a bisector, it passes through the midpoint of the given line segment.

To find the slope of the line, apply the formula for the slope of a line:

where (x1, y1) and (x2, y2) are the two endpoints of the line segment

Hence, the slope of the line is:

The negative inverse of this is:

To find the midpoint of the endpoints, apply the formula for midpoint:

Hence, the midpoint of the given endpoints are:

Now, we have the slope and an endpoint of the perpendicular bisector.

To find the equation of the line, we have to apply the point-slope method:

Therefore, the equation of the perpendicular bisector of the line segment is:

Answer:

a

Step-by-step explanation:

to rotate 180 degrees, simply invert both signs

ANSWER :

f(x) = (3x-2)(x-3)(x-4)(x-2)^3

EXPLANATION :

A polynomial with a degree of 6 has 6 factors.

f(x) = (x - a)(x - b)(x - c)(x - d)(x - e)(x - f) with 6 roots or x-intercepts.

But the problems states that it has 4 x-intercepts, so we will reduced the number of roots but maintaining the number of factors.

f(x) = (x - a)(x - b)(x - c)(x - d)(x - a)(x - a).

From here, we still have 6 factors but only 4 x-intercepts, the last two factors (x - a) is the same as the first factor.

So we can rewrite this as :

Next is to have a y-intercept of 64, y-intercept is the value of f(x) when x = 0

Substitute 0 to the function.

Now we have f(0) = a^3bcd and f(0) = 64 as the definition from above.

We need to find the factors of 64,

64 = 8 x 4 x 3 x 2/3

And we can rewrite the equation as :

From here, we can observe that,

a^3 = 8 ⇒ a = 2

b = 4

c = 3

d = 2/3

So the function will be :

Explanation in 2/3

Since we only need 4 distinct factors of 64.

8 x 4 x 3 x 2/3

8 x 4 = 32

The product of the 3rd and 4th factor should be 2, in order to get 64.

Since from the first

Answer:

Equation of line is given as y = mx + c, where m is the gradient and c is the y-intercept.

First find the gradient. Formula for gradient is given as (y2-y1)÷(x2-x1) or (y1-y2)÷(x1-x2).

Gradient = (2-0)÷(0-4) = -1/2

Equation of line is y = -1/2x + c

Substitute either one of the points into the equation to find c.

0 = -1/2(4) + c

c = 2

Hence, the equation of the line is y = -1/2x + 2.

Recall the following trigonometric identities. If the legs of the right triangle have lengths a and b, the hypotenuse has length c, and the side a is adjacent to an angle θ, then:

Then, for the given right triangle:

Then, x and y are given by the expressions:

Therefore, the answers are:

1. The decrease in dollars, based on a 7.5 percent decrease, is $615.

2. The balance in the account at the end of last year was $7,585.

A percentage is a ratio or proportion of a variable in another.

For instance, the percentage decrease in the investment account was 7.5%, which in dollar terms amounts to $615.

The percentage reference gives an idea of the investment status and the fractional effect that the decrease had on it.

Initial investment = $8,200

Decrease in investment = 7.5%

Decrease in dollars = $615 ($8,200 x 7.5%)

Balance = $7,585 ($8,200 - $615)

Thus, Tammy's investment account decreased to $7,585 by $615, representing a 7.5% decrease.

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Answer is option A

Because the other side (AB) is 15 and the other rectangle (JM) is 10, so the realation between them is 15/10 = 3/2

But, since DC and ML relation is NOT 3/2, then the rectanlges are not similar

Using a linear function, it is found that:

a) The table is completed in the first image at the end of the answer.

b) The function is: s(w) = 125 - 10.50w.

c) The graph of the function is given by the second image at the end of the answer.

The slope-intercept representation of a linear function is shown by the rule presented below:

y = mx + b

The coefficients of the function are presented as follows:

In the context of this problem, the slope and the intercept are given as follows:

Hence the function is given as follows:

s(w) = 125 - 10.50w.

The numeric values to complete the table are given as follows:

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The philosophy of dilation is to resize uniformly the figure in question. Under this intuitive idea, dilation is the answer. Now, what does uniformly mean here?

It means that, as can be seen in the figure, the length of every side of the right triangle can be calculated by multiplying its corresponding side in the left ("small") triangle by a constant. However, this can be done from the right triangle to the left triangle; that's why I put a bidirectional arrow.

Finally, I want to give you some motivation for this concept: Every time you are resizing an image on your phone or in your computer, you're applying this concept.

SOLUTION

Given the question on the question tab;

Explanation:

Final answer:

.

A piece-wise function is a function that changes its value, based on the input

That is a function its range depends on the domain.

The correct answer is the third option

Explanation

The quotient is the number obtained by dividing one number by another

for example:

the quotient of a and b is

so

Step 1

Let

number 1=23x

number 2=15 t

so, the quotient would be

therefore, the answer is C:

I hope this helps you