The square pyramid shown below has a base with sides of 12 units. The vertical height of the pyramid is 15
units.
15
12

The vertices of the reflected square.

Let's calculate them:

A' = (-0.914, 3.914)

B' = (-2.828, 5.828)

C' = (-0.086, 7.086)

D' = (1.828, 5.172)

The vertices of the image of the square ABCD after reflecting it about the line through (0, 0) and (-2, 2), we can use the following steps:

Find the equation of the reflection line:

The reflection line passes through (0, 0) and (-2, 2).

We can calculate the slope (m) of the line using the formula (y2 - y1) / (x2 - x1):

m = (2 - 0) / (-2 - 0) = 2 / -2 = -1.

Using the point-slope form of a line (y - y1) = m(x - x1), we can use either of the given points to write the equation of the line:

y - 0 = -1(x - 0)

y = -x.

Find the midpoint of each side of the square:

The midpoints of the sides of a square are also the midpoints of its diagonals.

The midpoint of AB is ((4+6)/2, (3+4)/2) = (5, 3.5).

The midpoint of BC is ((6+5)/2, (4+6)/2) = (5.5, 5).

The midpoint of CD is ((5+3)/2, (6+5)/2) = (4, 5.5).

The midpoint of DA is ((3+4)/2, (5+3)/2) = (3.5, 4).

Reflect the midpoints about the line:

To reflect a point (x, y) about the line y = -x, we can find the perpendicular distance (d) from the point to the line and use it to determine the reflected point.

The perpendicular distance d from the line y = -x to a point (x, y) is given by the formula:

d = (y + x) / √(2).

The coordinates of the reflected points can be found using the formula for reflection across a line:

x' = x - 2d / √(2)

y' = y - 2d / √(2).

Calculate the reflected vertices:

The coordinates of the reflected vertices are as follows:

A' = (4 - 2(3.5 + 5) / √(2), 3 - 2(3.5 - 5) / √(2))

B' = (6 - 2(5 + 5) / √(2), 4 - 2(5 - 5) / √(2))

C' = (5 - 2(5.5 + 5) / √(2), 6 - 2(5.5 - 5) / √(2))

D' = (3 - 2(4 + 5) / √(2), 5 - 2(4 - 5) / √(2))

Now we can plot the original square ABCD and its image A'B'C'D' on the same graph to visualize the reflection.

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Answer:

These two statements are equivalent because statement A is the contrapositive of statement B.

Step-by-step explanation:

In logic, when we have an "if" statement we can have its contrapositive or its converse.

Given a "if p, then q" (p is the hypothesis and q is the conclusion), the converse is "if q, then p", in other words, we interchange the hypothesis and the conclusion.

Now, given a "if p, then q", the contrapositive is "if not q, then not p". In other words, we take the negation of both the hypothesis and the conclusion and then we interchange them.

Now, let's take a look at our statements:

If a and b are two real numbers, and if ab = 0, then either a = 0 or b = 0.

In this case:

p = a and b are two real numbers and ab=0

q = either a = 0 or b = 0

Now, let's take the negative of p and q:

The negative of p would be: a and b are two real numbers and their product is not zero.

The negative of q would be: neither of the two real numbers is zero

Now, given than the contrapositive is "if not q, then not p" we would have:

If neither of two real numbers is zero, then their product is not zero.

We can see that this last sentence is the contrapositive of the first one and thus:

These two statements are equivalent because statement A is the contrapositive of statement B.

Answer:

1,1/2,1/3,1/4

Step-by-step explanation:

an = 1/n

n is the term number

a1 = 1/1 =1

a2 = 1/2

a3= 1/3

a4 = 1/4

The first 4 terms are 1,1/2,1/3,1/4

Answer:

A football pass of 9 yards

Step-by-step explanation:

-9 AKA negative 9. Negative can also mean down or left or backwards even.

A hold 9 feet deep is dug down

9 dollars withdrawn from the bank means your down 9 dollars

A pass of 9 yards is positive yardage

9 below 0 is a temperature of negative nine

The only one that isn't negative, but is positive is a football pass of 9 yards

Answer:

Answer: (-1,4)

SOLUTION:

xϵR:

x+1

14x

−

x−4

9x−30

<0

x+1



=0 x−4



=0

⇒x



=−1 x



=4

14(x−4)−(x+1)(7x−30)<0

14x

2

−56x−(9x

2

−30x+9x−30)<0

14x

2

−56x−9x

2

+30x−9x+30<0

5x

2

−35x+30<0

x

2

−7x+6<0

x

2

−6x+6<0

x(x−6)−1(x−6)<0

(x−1)(x−6)<0

⇒x>1 & x<6

⇒xϵ;(1,4)∪(4,6)

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Answer:

30 units^2

Step-by-step explanation:

Answer:

30

Step-by-step explanation:

Multiply length times width

Each side is 6 units. That would be your length

And both the top and bottom are 5 units each. This would be your width.

5 times 6= 30

Step-by-step explanation:

x + (4x - 20) = 180

5x - 20 = 180

5x = 180 + 20

5x = 200

x = 200/5

x = 40°

Option → D

Answer:

\(x = 40\)

Answer D is correct

Step-by-step explanation:

Angles in a straight line is added up to 180°

Therefore,

\(x + 4x - 20 = 180 \\ 5x - 20 = 180 \\ 5x = 180 + 20 \\ 5x = 200 \\ \frac{5x}{5} = \frac{200}{5} \\ x = 40 \degree\)

Hope this helps you.

Let me know if you have any other questions:-):-)

The 36th derivative of f(x) = cos(2x) is \(2^{17}\)* cos(2x).

To find the 36th derivative of the function f(x) = cos(2x), we can apply the chain rule repeatedly. The chain rule states that if we have a composite function y = f(g(x)), then its derivative is given by dy/dx = f'(g(x)) * g'(x).

Let's start by finding the first few derivatives of f(x) = cos(2x):

f'(x) = -2sin(2x)

f''(x) = -4cos(2x)

f'''(x) = 8sin(2x)

f''''(x) = 16cos(2x)

We observe a pattern where the derivatives of cos(2x) alternate between sin(2x) and cos(2x), with the signs changing accordingly.

Based on this pattern, we can see that the 36th derivative will be:

f^(36)(x) =\((-1)^{17} * 2^{17} *\) cos(2x)

Simplifying this expression, we have:

f^(36)(x) = \(2^{17} * cos(2x)\)

Therefore, the 36th derivative of f(x) = cos(2x) is\(2^{17\) * cos(2x).

It's important to note that in this case, the number 36 is even, and since the derivatives of cos(2x) follow a repeating pattern every 4 derivatives, the sign (-1) raised to the power of 17 accounts for the change in sign in the 36th derivative.

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Answer: Adams heart Beats 1,440 more times than Blake’s in 120 minutes.

Step-by-step explanation:

Adam: 74 x 120 = 8,880

Blake: 62 x 120 = 7,440

8,880 - 7,440 = 1,440

Answer:

1440

Step-by-step explanation: you multiply

74 x 120 and 62 x 120

8,880             7,440 then subtract the two

8,880 - 7,740 = 1,440

Answer:

169.67in²

Step-by-step explanation:

This problem bothers on the mensuration of solid shapes, a cone

The expression for the total surface area of the cone is

A= πrl + πr²

Given data

Diameter d =9in

Radius r = d/2= 9/2= 4.5in

Slant height l = 7.5in

A= πrl + πr²

Substituting our given data we have

A= 3.142*4.5*7.5+ 3.142*4.5²

A= 106.04+63.63

A= 169.67in²

The total surface area is 169.67in²

Answer:

Step-by-step explanation:

(1)

The angle pair is forming a straight angle, we call them supplementary angles too:

(2)

The two angles forming a right angle, so the angles are complementary:

(3)

The two opposite angles formed by intersecting two lines are called vertical angles and are of equal measure:

\( \tt \: x + 25 + 75 = 180 \degree \\ \sf \:[linear \: pair] \)

\( \tt \: x + 100 = 180 \degree \)

\( \tt \: x = 180 - 100\)

\( \boxed{\tt \: x = 80}\)

\( \tt \: x -50 + 10 = 90 \degree \\ \sf \:[complementary \: angles] \)

\( \tt \: x - 40 = 90\)

\( \tt \: x = 90 + 40\)

\( \boxed{ \tt \: x = 130 }\)

\( \tt \: x + 33=67 \degree \\ \sf \:[Vertically\: Opposite\:angles] \)

\( \tt \: x = 67 - 33\)

\( \boxed{ \tt \: x = 34}\)

Answer:

1, 0.75, 1.25, 3, 0

Step-by-step explanation:

To find the value of the function, we find the y coordinate of the point with the given x value.

The required order from least to greatest is √3 − 1, 2√10 ÷ 5, √14, 3√2, √19 + 1 and 6

An arrangement of numbers in which the numbers are arranged from smallest to greatest numbers is called ascending order.

Given that, some numbers, 3√2, √3 − 1, √19 + 1, 6, 2√10 ÷ 5 and √14.

We need to order them from least to greatest,

3√2 = 4.24

√3 − 1 = 0.73

√19 + 1 = 5.35

6

2√10 ÷ 5 = 1.26

√14 = 3.74

The order from least to greatest is :-

0.73, 1.26, 3.74, 4.24, 5.35 and 6

i.e.

√3 − 1, 2√10 ÷ 5, √14, 3√2, √19 + 1 and 6

Hence, the required order from least to greatest is √3 − 1, 2√10 ÷ 5, √14, 3√2, √19 + 1 and 6

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Answer:

the second one

Step-by-step explanation:

Answer: The quotient is 199.277777778, the answer is the hundreds place

Step-by-step explanation:

199.277777778, the 1 in 199 is in the hundreds place :)

Answer:

The answer is A

Step-by-step explanation:

Edg : )

Answer:

A

Step-by-step explanation:

Answer:

what are you trying to ask? 2x2 is 4+4 is 8 that is 4 more than twice the number 2 if that is what you want to know

Step-by-step explanation:

4 more than twice what number?

Answer:

Therefore, the product of 2x+y and 5x-y+3 is 10x^2 + 13x - y^2 + 4xy + 6.

Step-by-step explanation:

Using FOIL (first, outer, inner, last) method, we can multiply the two expressions:

(2x+y)(5x-y+3) = 10x^2 - 2xy + 15x + 3y + 5xy - y^2 + 6x - 3y

Simplifying the terms by combining like terms and rearranging, we get:

10x^2 + 13x - y^2 + 4xy + 6

The value of a, b, and c are 1, -2, and 6 respectively.

The y-intercept of this quadratic function is 6.

The axis of symmetry of this quadratic function is 1.

The vertex of this quadratic function is (1, 5).

Mathematically, the axis of symmetry of a quadratic function can be calculated by using this mathematical expression:

Axis of symmetry, Xmax = -b/2a

Where:

a and b represents the coefficients of the first and second term in the quadratic function.

For the given quadratic function f(x) = x² - 2x + 6, we have:

Axis of symmetry, Xmax = -b/2a

Axis of symmetry, Xmax = -(-2)/2(1)

Axis of symmetry, Xmax = 2/2 = 1.

Vertex (h, k) = (1, 5).

In Mathematics, the y-intercept of any graph such as a quadratic function, generally occur at the point where the value of "x" is equal to zero (x = 0).

y-intercept = 6.

Lastly, we would create a table and then graph the quadratic function as follows;

x         y

0         6

2         2

5         11

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Step-by-step explanation:

Given

f(x) = 2x + 6

g(x) = 3x²

f(g(-3)) = ?

Now

g(-3) = 3 * (-3)²

= 3* 9

=27

Also,

f(g(-3)) = f(27)

= 2* 27 + 6

= 60

Hope it helps :)

Answer:   \(y=-\dfrac{16}{9}(x+3)^2+4\)

Step-by-step explanation:

Use the vertex formula:  y = a(x - h)² + k    where

We can see that the vertex of the curve is (-3, 4)  -->  h = -3, k = 4

and it is a reflection over the x-axis --> a-value is negative

We need to find the a-value. Choose another point on the curve and plug it into the vertex formula for (x, y) and then solve for a.

I will choose (x, y) = (-3/2, 0)

\(0=a\bigg(\dfrac{-3}{2}+3\bigg)^2+4\\\\\\-4=a\bigg(\dfrac{3}{2}\bigg)^2\\\\\\-4\bigg(\dfrac{2}{3}\bigg)^2=a\\\\\\-\dfrac{16}{9}=a\)

Now that we know the vertex and the a-value, we can input them into the vertex formula:

                         \(\large\boxed{y=-\dfrac{16}{9}(x+3)^2+4}\)

Answer:

Answer:  

Step-by-step explanation:

Use the vertex formula:  y = a(x - h)² + k    where

a is the vertical stretch

-a is a reflection over the x-axis

(h, k) is the vertex

We can see that the vertex of the curve is (-3, 4)  -->  h = -3, k = 4

and it is a reflection over the x-axis --> a-value is negative

We need to find the a-value. Choose another point on the curve and plug it into the vertex formula for (x, y) and then solve for a.

I will choose (x, y) = (-3/2, 0)

Now that we know the vertex and the a-value, we can input them into the vertex formula:

Answer:

it's hardware.

.

hope I helped!

Answer:15x+35=110

Step-by-step explanation:

The missing quantities are

Social Security= $217

Medicare = $‭50.75‬

Net Pay is $‭2,633.67‬

First, Taxable income is therefore;

= 3,500 - (76.90 x 4 )

= $‭3,192.4‬0

Federal Income Tax (FIT).

With taxable income of $‭3,192.4‬0, the tax is $565.15 plus 28% of anything above $‭3,073.

= 565.15 + (28% x (‭3,192.4‬0 - 3,073))

= 565.15 + 33.43

= $‭598.58

and, Social Security

= Gross pay x 6.2%

= 3,500 x 6.2%

= $‭217‬

and, Medicare

= 3,500 x 1.45%

= $‭50.75‬

Then, the Net Pay

= 3,500 - 598.58 - 217 - 50.75

= $‭2,633.67‬

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Answer: 3A “new hydraulic pump

Cost les than a used furnace?”

Step-by-step explanation: New equipment is always going to be higher than anything you buy used you basically get half off for taking the chance.

The statement that cannot be true is

A new hydraulic pump costs less than a used furnace.

Option D is the correct answer.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Cost of a new air compressor = €300.

Cost of a used air compressor = €200.

i.e 300 - 100 = 200

Now,

Cost of a used furnace = < €200.

This means,

Cost of a new furnace = < (€200 + £100).

Cost of a new hydraulic pump > €200.

Amount Nicole paid = €230.

Now,

Nicole bought a new furnace.

This is possible.

A new furnace costs more than a used air compressor.

This is possible.

A new hydraulic pump costs more than a new furnace.

This is possible.

A new hydraulic pump costs less than a used furnace.

This is not possible.

i.e

Cost of a used furnace = < €200.

Cost of a new hydraulic pump > €200.

Nicole bought a used hydraulic pump.

This is possible.

Thus,

A new hydraulic pump costs less than a used furnace is not possible.

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Answer:

Option D

Step-by-step explanation:

→ Add the x-coordinates together divide by 2 and then add the y-coordinated together and then divide by 2

- 1 + -6 = -1 - 5 = -7 ÷ 2 = -3.5

5 + -2 = 3 ÷ 2 = 1.5

Answer:

first subtract the 2 cancelling out on the left side, making the -3 a -5, then add y cancelling out the left side, making the right side -5+y, than your equation is 5x=-5+y, dividing the 5 off makes x=-5+y/5. :)

Answer:

-------------------------

Given two legs of a right triangle and we need to find the hypotenuse.

Use Pythagorean theorem:

The matching choice is C.

Answer:

right; increase