The ornament below is composed of two congruent square pyramids. Each square pyramid has base side lengths of 2 inches and a height of 2.5 inches.



What is the volume, in cubic inches, of the ornament?

Answer: (x-30)^2=4

Step-by-step explanation:

Answer:

Option D is correct.

Step-by-step explanation:

[tex]\frac{10}{\sqrt{x}-\sqrt{x-5}}\\[/tex] We need to rationalize this term and find the answer.

To rationalize the term we multiply and divide the above expression by [tex]\sqrt{x}+\sqrt{x-5}[/tex]

Solving:

[tex]\frac{10}{\sqrt{x}-\sqrt{x-5}}\\=\frac{10}{\sqrt{x}-\sqrt{x-5}} * \frac{\sqrt{x}+\sqrt{x-5}}{\sqrt{x}+\sqrt{x-5}} \\Multiplying\\=\frac{10*(\sqrt{x}+\sqrt{x-5})}{\sqrt{x}-\sqrt{x-5}*\sqrt{x}+\sqrt{x-5}}\\=\frac{10*(\sqrt{x}+\sqrt{x-5})}{(\sqrt{x})^2-(\sqrt{x-5})^2}\\=\frac{10*(\sqrt{x}+\sqrt{x-5})}{x-(x-5)}\\=\frac{10*(\sqrt{x}+\sqrt{x-5})}{x-x+5)}\\=\frac{10*(\sqrt{x}+\sqrt{x-5})}{5}\\=2*(\sqrt{x}+\sqrt{x-5})[/tex]

So, Option D is correct.

Answer:

The correct option is D) [tex]2\left(\sqrt{x}+\sqrt{x-5}\right)[/tex].

Step-by-step explanation:

Consider the provided radical expression.

[tex]\frac{10}{\sqrt{x}-\sqrt{x-5}}[/tex]

Multiply by the conjugate [tex]\frac{\sqrt{x}+\sqrt{x-5}}{\sqrt{x}+\sqrt{x-5}}[/tex]

[tex]\frac{10\left(\sqrt{x}+\sqrt{x-5}\right)}{\left(\sqrt{x}-\sqrt{x-5}\right)\left(\sqrt{x}+\sqrt{x-5}\right)}[/tex]

[tex]\frac{10\left(\sqrt{x}+\sqrt{x-5}\right)}{\left(x-(x-5))}[/tex]

[tex]\frac{10\left(\sqrt{x}+\sqrt{x-5}\right)}{5}[/tex]

[tex]2\left(\sqrt{x}+\sqrt{x-5}\right)[/tex]

Hence, the correct option is D) [tex]2\left(\sqrt{x}+\sqrt{x-5}\right)[/tex].

Answer:

x=35

Step-by-step explanation:

ANSWER

x=35°

EXPLANATION

We want to find the value of x, when

[tex] \cos(x) = \sin(20 + x) \degree[/tex]

and 0°<x<90°

Recall that the sine and cosine are complementary trigonometric ratios.

Hence cos x = sin (90-x)

Our equation now, becomes;

[tex] \sin(90 - x) \degree= \sin(20 + x) \degree[/tex]

We now equate the argument to get,

[tex]90 - x=20 + x[/tex]

Group similar terms to obtain:

[tex]90 - 20 = x + x[/tex]

[tex]70 = 2x[/tex]

This implies that,

[tex]x = 35 \degree[/tex]

Answer:

the polygon is not regular and the 360/n formula is only applies to regular polygons

Step-by-step explanation:

Answer:

54

Step-by-step explanation:

Estimate=Population size × Sample proportion

population size =  120

sample proportion = (9)/(9+6+5) = 9/20 (check on Cymath as a resource)

estimate = 120 x 9/20 = 54

​

The estimation will be 54 for the number of mothers.

The estimation is the approximated results of anything it can be the possibility or probability of any event to happen or any number to come.

Estimate=Population size × Sample proportion

population size =  120

sample proportion = (9)/(9+6+5) = 9/20 (check on Cymath as a resource)

Estimate = 120 x 9/20 = 54

Hence estimation will be 54 for the number of mothers.

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Answer:

384

Step-by-step explanation:

Answer:

They answer 256 because you will multiply the border four times (4x4x4x4) to get the perimeter of border.

Answer:

B

Step-by-step explanation: divide 520 by 8 and you get 65

Answer: is B 65

Step-by-step explanation:

520 divided by 8

=65 per hour

Answer:

B. 65

Step-by-step explanation:

You have to average it out.

520÷8=65

the answer for this question is 20 x cube by 5

For this case, we must simplify the following expression:

[tex]\sqrt [3] {\frac {4x} {5}}[/tex]

For this, we follow the steps below:

We rewrite the expression as:

[tex]\frac {\sqrt [3] {4x}} {\sqrt [3] {5}}[/tex]

We multiply by:

[tex]\frac {(\sqrt [3] {5}) ^ 2} {(\sqrt [3] {5}) ^ 2}\\\frac {\sqrt [3] {4x}} {\sqrt [3] {5}} * \frac {(\sqrt [3] {5}) ^ 2} {(\sqrt [3] {5}) ^ 2} =[/tex]

We have by definition of multiplication of powers of equal base that:

[tex]a ^ m * a ^ n = a ^ {m + n}[/tex]

So:

[tex]\\\frac {\sqrt [3] {4x} * (\sqrt [3] {5}) ^ 2} {\sqrt [3] {5}) ^ 3} =\\\frac {\sqrt [3] {4x} * (\sqrt [3] {5}) ^ 2} {5} =[/tex]

We know that:

[tex](\sqrt [3] {5}) ^ 2 = \sqrt [3] {5 ^ 2}[/tex]

So, we have:

[tex]\frac {\sqrt [3] {4x} * \sqrt [3] {5 ^ 2}} {5} =\\\frac {\sqrt [3] {4x} * \sqrt [3] {25}} {5} =\\\frac {\sqrt [3] {100x}} {5}[/tex]

Answer:

Option c

Answer:

10c=113

113=c10

Step-by-step explanation:

Either is same. For multiplication, even though you flip it, it is same.

Answer:

10c=113

113=c10

c=113/10

Step-by-step explanation:

Answer:

+ 1

Step-by-step explanation:

Given

x² + 2x = 9

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(1)x + 1² = 9 + 1²

(x + 1)² = 10

Answer:x =(-2-√-32)/-2=1+2i√ 2 = 1.0000-2.8284i

x =(-2+√-32)/-2=1-2i√ 2 = 1.0000+2.8284

Step-by-step explanation:

-3x - 12 > 8x + 21

Step 1: Combine like terms

x's go with x's (-3x and 8x). To do this add 3x to both sides

(-3x + 3x)  - 12 > (8x + 3x) + 21

-12 > 11x + 21

Normal numbers go with normal numbers (-12 and 21). To do this subtract 21 to both sides

(-12 - 21) > 11x + (21 - 21)

-33 > 11x

Step 2: Isolate x by dividing 11 to both sides

-33/11 > 11x / 11

-3 > x

Hope this helped!

Answer:

[tex]x\:<\:-3[/tex]

Step-by-step explanation:

The given inequality is:

[tex]-3x-12\:>\:8x+21[/tex]

We group similar terms to obtain:

[tex]-12-21\:>\:8x+3x[/tex]

Combine the similar terms to obtain:

[tex]-33\:>\:11x[/tex]

Divide both sides by 11;

[tex]-3\:>\:x[/tex]

Or

[tex]x\:<\:-3[/tex]

19

418 divided by 22 is equal to 19

And that’s the answer

Answer: 2.29 x 10^4

Step-by-step explanation:

22.9 x 10^4 is the answer oof I’m sorry

Substitute y = x + 1 into 2x - 5y = 4

-3x - 5 = 4

Solve for x in -3x - 5 = 4

x = -3

Substitute x = -3 into y = x + 1

y = -2

Therefore,

x = -3

y = -2

Answer:

x=2.4

Step-by-step explanation:

We can take the ratios and solve for the unknown side

AE       ED

----- = ---------

JN       MN

Substituting in

1         3

----- = ---------

.8       x

Using cross products

1x = 3*.8

1x = 2.4

x = 2.4

Answer:

23

Step-by-step explanation:

The median is the number in the middle of the data once it is organized from least to greatest, so that is what we must do first.

[tex]2,5,7,8,8,11,12,14,20,23,23,25,27,28,29,31,36,36,42[/tex]

There are 19 numbers, that means that the 10th value will be the number in the middle

This means that the median is 23

Answer:

I = 0.5

Answer

B

Step-by-step explanation:

When R = 20, plug in R

I = 10/R

I = 10/20

I = 1/2

I = 0.5

Answer

B

Answer:

[tex]\large\boxed{0.000000057=5.7\cdot10^{-8}}[/tex]

Step-by-step explanation:

[tex]\text{Scientific notation:}\\\\a\cdot10^k\\\\\text{where}\ 1\leq a<10\ \text{and}\ k\in\mathbb{Z}\\-------------------------\\\\0\underbrace{.00000005}_{8\rightarrow}7=5.7\cdot10^{-8}[/tex]

If you move the comma several places to the right, the exponent at 10 is negative.

If you move the comma several places to the left, the exponent at 10 is positive.

Answer:

(x,y) = (-6.12,-11.76)

Step-by-step explanation:

2x+4y=-48 => eq(i)

4x-9y=57  => eq(ii)

We need to solve these equations simultaneously to find the values of x and y.

Multiplying eq(i) with 2 and subtracting both equations

4x + 16y = -96

4x - 9y  = 57

-    +         -

__________

25 y = -153

y = -153/25

y = -6.12

Putting value of y in eq(i)

2x + 4(-6.12) = - 48

2x - 24.48 = -48

2x = -48 + 24.48

2x = -23.52

x= -23.52/2

x= -11.76

So, values of x and y are -6.12 and -11.76

(x,y) = (-6.12,-11.76)

The solution to the system of linear equations is [tex]\(x = -6\) and \(y = -9\).[/tex]

Let's solve the system of linear equations:

[tex]1. \(2x + 4y = -48\)\\2. \(4x - 9y = 57\)[/tex]

We can use the substitution or elimination method. I'll use the elimination method here:

Multiply the first equation by 2 to make the coefficients of [tex]\(x\)[/tex]in both equations the same:

[tex]1. \(4x + 8y = -96\)\\2. \(4x - 9y = 57\)[/tex]

Now, subtract the second equation from the first to eliminate [tex]\(x\):[/tex]

[tex]\((4x + 8y) - (4x - 9y) = -96 - 57\)[/tex]

Simplify:

[tex]\(17y = -153\)[/tex]

Now, solve for \(y\):

[tex]\(y = -\frac{153}{17} = -9\)[/tex]

Now that we have \(y\), substitute it back into one of the original equations. I'll use the first equation:

[tex]\(2x + 4(-9) = -48\)[/tex]

Simplify:

[tex]\(2x - 36 = -48\)[/tex]

Add 36 to both sides:

[tex]\(2x = -12\)[/tex]

Divide by 2:

[tex]\(x = -6\)[/tex]

So, the solution to the system of linear equations is [tex]\(x = -6\) and \(y = -9\).[/tex]

Answer:

8 tons < 20,000

Step-by-step explanation:

1 ton = 2000 pounds

so 8 tons would be 16,000 which makes it less than 20,000

Final answer:

An adult African elephant that weighs approximately 8 tons is not equal to 20,000 pounds; instead, 8 tons equals 16,000 pounds. The provided comparison in the question is incorrect.

Explanation:

To determine if an adult African elephant that weighs approximately 8 tons is equal to 20,000 pounds, we need to convert tons to pounds using the unit equivalence 1 ton = 2,000 pounds. Multiplying 8 tons by the unit equivalence gives us:

8 × 2,000 = 16,000 pounds.

Knowing that the range of weight of a male African elephant is between 12,000 and 16,000 pounds, we can see that 8 tons does not equal 20,000 pounds. Therefore, the comparison 8 tons = 20,000 pounds is incorrect.

A correct comparison would be 8 tons = 16,000 pounds, which is not one of the options provided in the question.

As for the water bottle containing 2,000 milliliters, this is simply stating the volume capacity of the bottle but does not relate to the conversion between tons and pounds.

Answer:

13

Step-by-step explanation:

The average rate of change of f(x) in the closed interval [ a, b ] is

[tex]\frac{f(b)-f(a)}{b-a}[/tex]

Here [ a, b ] = [2, 6 ]

f(b) = f(6) = 6² + 5(6) - 8 = 36 + 30 - 8 = 58

f(a) = f(2) = 2² + 5(2) - 8 = 4 + 10 - 8 = 6

Hence

average rate of change = [tex]\frac{58-6}{6-2}[/tex] = [tex]\frac{52}{4}[/tex] = 13

Final answer:

The average rate of change of the function f(x) = x^2 + 5x - 8 from x = 2 to x = 6 is calculated to be 13.

Explanation:

The average rate of change of a function f(x) from x = a to x = b is found by the formula Δf / Δx = (f(b) - f(a)) / (b - a). In this case, we have f(x) = x^2 + 5x - 8, and we want to find the average rate of change from x = 2 to x = 6.

Therefore, the average rate of change of the function from x = 2 to x = 6 is 13.

Answer:

B. There is sufficient evidence to support the claim that less than 25% of the population believes that there is no solid evidence to support global warming.

Step-by-step explanation:

The following information has been availed;

n = 1501

sample proportion = 20% = 0.2

Level of significance = 0.01 = 1%

We are required to test the claim that less than 25% of the population believes that there is no solid evidence of global warming. In mathematical notation this claim can be written as;

p < 0.25, where p is the population proportion. From this information, we can formulate the following set of hypotheses;

H0: p ≥ 0.25

Ha: p < 0.25 (claim). This will be a left-tailed test.

The test statistic for hypothesis on population proportions is z, defined by the formula;

[tex]z=\frac{sampleproportion-p}{\sqrt{\frac{p(1-p)}{n} } }[/tex]

where p is the population proportion under the null hypothesis, that is p = 0.25.

Using the given information , the test statistic becomes;

[tex]z=\frac{0.2-0.25}{\sqrt{\frac{0.25(1-0.25)}{1501} }}=-4.4736[/tex]

The next step is to compute the p-value in our left-tailed test;

p-value = P(Z < -4.4736) = 0

Our p-value is less than the level of significance and thus we reject the null hypothesis in favor of the alternative hypothesis which is also our claim. The final conclusion is thus;

There is sufficient evidence to support the claim that less than 25% of the population believes that there is no solid evidence to support global warming.

The function m(x) = x + 5/(x-1) has the same domain as the composition of functions (m.n)(x) because they both have the domain of all real numbers except 1.

The domain of a function is the set of all possible input values (often called 'x-values') which will give valid output values. In other words, it's all the values x can take on. The function m(x) = x +5/(x-1) will be undefined when the denominator equals zero, so x cannot equal 1. Therefore, the domain of m(x) is all real numbers except 1.

On the other hand, the function n(x) = x - 3 doesn't have any restrictions and can take on all real numbers. However, (m.n)(x) refers to a composition of functions, specifically m(n(x)). This will inherit the domain restrictions from m(x). Therefore, the function that has the same domain as (m.n)(x) is m(x) because the composition will allow inputs for all real numbers except 1, as dictated by m(x).

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Answer:

(4,2) and (8,2)

Step-by-step explanation:

The mid segment unites the middle of two sides of a triangle.  In this case, the question wants us to have it parallel to BC, so it has to unite the middle of AB to the middle of AC.

The use of the clear grid in this case makes that we don't have to use any angle calculation.

If you start from point B, you'll need to go 6 units to the right and 8 units up to meet with A. That means the center point is located 3 units right and 4 units high from point B... so, we have point (4,2).

Starting from C, we do a similar calculation.  you need to go 2 units to the left and 8 units up... so the mid-point is 1 unit to the left and 4 units up... so (8,2).

For this case we have the following functions:

[tex]f (x) = x-3\\g (x) = x + 11[/tex]

We must find the product of the functions:

[tex]f (x) * g (x) = (x-3) (x + 11)[/tex]

We apply distributive property, which states:

[tex](a + b) (c + d) = ac + ad + bc + bd[/tex]

So:

[tex]f (x) * g (x) = x ^ 2 + 11x-3x-33 = x ^ 2 + 8x-33[/tex]

Answer:

[tex]x ^ 2 + 8x-33[/tex]

Answer:   [tex]f(x).g(x)=x^2+8x-33.[/tex]

Step-by-step explanation:  We are given the following two functions ;

[tex]f(x)=x-3,~~~~~~~~g(x)=x+11.[/tex]

We are to find the value of [tex]f(x).g(x).[/tex]

To find the required expression, we need to multiply the expressions for both the functions f(x) and g(x).

therefore, we get

[tex]f(x).g(x)\\\\=(x-3).(x+11)\\\\=x(x+11)-3(x+11)\\\\=x^2+11x-3x-33\\\\=x^2+8x-33.[/tex]

Thus, [tex]f(x).g(x)=x^2+8x-33.[/tex]

Answer:

C cannot represent a function

Step-by-step explanation:

For every income (the left column) can have only one outcome (the right column).

Each constituent of one set, such as Set (A), is transferred to a particular member of another set (B), such as Set (B). Then the correct option is C.

A function is a statement, rule, or law that establishes the connection between two variables. In mathematics, functions are everywhere and are necessary for constructing physical connections.

Just one function, also known as an input feature function, was among the most prevalent forms of functions. We will also study the opposite of this function here.

Thus, the correct option is C.

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The poster is a parallelogram, and it's area is:

A = bh

A = 20 x 10

A = 200 in.^2

Note: ^2 after in. means squared for area.

The area of the triangle that Janelle cut out of the poster board is:

A = 1/2bh

A = 1/2 x 10 x 9

A = 90/2

A = 45 in.^2

The area of the poster board that she has left is: 200 - 45 = 155 in.^2

Answer: 155 in.

The area of the poster board that she has left is,

⇒ 155 in²

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Now, The area of the parallelogram is,

⇒ Area of Parallelogram:

A= base × height

A= 20 in × 10 in

A= 200 in²

And, Area of Triangle:

A= 1/2 base * height

A= 1/2 (10 in)(9 in)

A= 1/2 (90)

A= 45 in²

Thus, The Area of Poster Left is,

A= Parallelogram Area - Triangle Area

A= 200 in² - 45 in²

A= 155 in²

Thus, 155 in² is the area of the poster board she has left.

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ANSWER

{(0, −4), (2, 6), (4, 16)}

EXPLANATION

The given function is

[tex]y = 5x - 4[/tex]

when x=0,

y=5(0)-4

y=-4

(0,-4)

When x=2,

y=5(2)-4

y=6

(2,6)

When x=4

y=5(4)-4

y=16

(4,16)

The correct choice is

{(0, −4), (2, 6), (4, 16)}

Answer:

{(0, −4), (2, 6), (4, 16)}

Step-by-step explanation:

Since, in an order pair the first value represents the input value and second value represents the output value,

i.e. (a, b) is an order pair ⇒ a = input, b = output,

Here, the given function,

[tex]y = 5x - 4[/tex]

(i) For the relation {(0, −4), (2, 6), (4, 20)},

At ( 4, 20), y = 5(4) - 4 = 20 - 4 = 16 ( false ),

(ii) For the relation {(0, −4), (2, 6), (4, 16)},

At (0, −4), y = 5(0) - 4 = -4 ( true ),

At (2, 6), y = 5(2) - 4 = 10 - 4 = 6 ( true ),

At ( 4, 16), y = 5(4) - 4 = 20 - 4 = 16 ( true ),

(iii) For the relation {(0, 4), (2, 6), (4, 20)},

At (0, 4), y = 5(0) - 4 = -4 ( false ),

(iv) For the relation {(0, 4), (2, −6), (4, 20)}

At (2, -6), y = 5(2) - 4 = 6 ( false ),

Hence, (ii) represents possible inputs and outputs of the function.

Answer:

1) cos (3x)

2) [tex]\frac{-(1-\sqrt{3})^{2}}{2}[/tex]

Step-by-step explanation:

Given expression:

cos(7x)cos(4x)+sin(7x)sin(4x)

By using the trigonometric identity

cos(a)cos(b) + sin(a)sin(b) = cos(a-b)

we have:

cos(7x)cos(4x)+sin(7x)sin(4x) = cos(7x - 4x)

                                               = cos(3x)!

part 2:

tan (-π/12)

by using property tan(-x)= - tan(x)

=-tan(π/12)

= - tan(π/6 / 2)

Using tan(x/2) = [tex]\sqrt{\frac{1 - cos(x)}{1+cos(x)} }[/tex]

= - [tex]\sqrt{\frac{1 - cos(pi/6)}{1+cos(pi/6)} }[/tex]

cos π/6 = [tex]\frac{\sqrt{3} }{2}[/tex]

= -[tex]\sqrt{\frac{1-\frac{\sqrt{3} }{2} }{1+\frac{\sqrt{3} }{2} } }[/tex]

= - [tex]\sqrt{7-4\sqrt{3} }[/tex]

= - 2+[tex]\sqrt{3}[/tex]

= [tex]-\frac{(1-\sqrt{3}) ^{2} }{2}[/tex]

!

Answer:

True statements are,

A, B, D, E , and F

Step-by-step explanation:

Properties of a square

1) All sides are equal

2) All angles are equal to 90°

3) Opposite sides are parallel

A. WXYZ is a parallelogram

True (property 3)

B. <W is right angle

True  (Property 2)

C. WXYZ is a trapezoid

False

D. WX ≅ XY

True  (Property 1)

E. <W congruent to <Y

True (Property 1)

F. <W is supplementary to <Y

True (Property 2)

True statements are,

A, B, D, E , and F

Answer: A. WXYZ is a parallelogram

B. [tex]\angle{W}[/tex] is a right angle.

D. [tex]\overline{WX}\cong\overline{XY}[/tex]

E. [tex]\angle{W}\cong\angle{Y}[/tex]

F. [tex]\angle{W}[/tex] is supplementary to  [tex]\angle{Y}[/tex].

Step-by-step explanation:

Given: WXYZ is a square.

A. A square is a parallelogram because its opposite sides are equal.

B. [tex]\angle{W}[/tex] is a right angle , since all the interior angles in a square area right angle.

C. A trapezoid has two equal parallel sides and two non-parallel sides.

But square has opposite sides parallel , therefore WXYZ is not a trapezoid.

D. Since all the sides of a square are congruent to each other , therefore

[tex]\overline{WX}\cong\overline{XY}[/tex]

E. Since all the angles of a square are congruent to each other , therefore

[tex]\angle{W}\cong\angle{Y}[/tex]

F. Since , all the interior angles in a square area right angle.

Thus, [tex]\angle{W}+\angle{Y}=90^{\circ}+90^{\circ}=180^{\circ}[/tex]

Hence,  [tex]\angle{W}[/tex] is supplementary to  [tex]\angle{Y}[/tex].