A flagpole is 48 feet tall.
A 50-foot-long support
wire connects the top
of the flagpole to a
stake in the ground.
How far from the base
of the flagpole is the
stake?

Answer:

37

Step-by-step explanation:

Linear pairs are supplementary (adds up to 180)

m∠1 + m∠2 = 180

3x + 4 + 2x - 9 = 180

5x - 5 = 180

5x = 185

x = 37

Hope this helps :)

Have a nice day!

The equation that can be used to find the value of x is (2.5x+1.5)4=36, and the value of x is 3.

The area of a rectangle is the product of its length and breadth. It is given by the formula,

Area of rectangle  =  Length × width

Given the length of the rectangle is 2.5x+1.5, while the width is 4. Also, it is mentioned in the question that the area of the rectangle is 36 square units. Therefore, we can write the area of the rectangle as,

[tex](2.5 x+1.5) \times 4 = 36\\\\(2.5 x \times 4) +(1.5\times 4) = 36\\\\10x + 6=36\\\\x = \dfrac{36-6}{10}\\\\x = 3[/tex]

Hence, the equation that can be used to find the value of x is (2.5x+1.5)4=36, and the value of x is 3.

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Answer:

Option A

Step-by-step explanation:

Given expression:

Option A

⇒ (x - 4)(3x + 2)

⇒ (x × 3x) + (2 × x) + (-4 × 3x) + (-4 × 2)

⇒ (3x²) + (2x) + (-12x) + (-8)

⇒ 3x² + 2x - 12x - 8

⇒ 3x² - 10x - 8

3x² - 10x - 8 = 3x² - 10x - 8 (Yes!)

Option B

⇒ (3x - 4)(x - 2)

⇒ (3x × x) + (3x × -2) + (-4 × x) + (-4 × -2)

⇒ (3x²) + (-6x) + (-4x) + (8)

⇒ 3x² - 6x - 4x + (8)

⇒ 3x² - 10x + 8

3x² - 10x - 8 = 3x² - 10x + 8 (No!)

Option C

⇒ (3x - 4)(x + 2)

⇒ (3x × x) + (3x × 2) + (-4 × x) + (-4 × 2)

⇒ (3x²) + (6x) + (-4x) + (-8)

⇒ 3x² + 6x - 4x - 8

⇒ 3x² + 2x - 8

3x² - 10x - 8 = 3x² + 2x - 8 (No!)

Option D

⇒ (3x - 2)(x - 4)

⇒ (3x × x) + (3x × -4) + (-2 × x) + (-2 × -4)

⇒ (3x²) + (-12x) + (-2x) + (8)

⇒ 3x² - 12x - 2x + 8

⇒ 3x² - 14x + 8

3x² - 10x - 8 = 3x² - 14x + 8 (No!)

Since the expression of option A has the same value as the given expression, option A is correct.

Answer:

Hi! Let's find which expression is equivalent to [tex]3x^{2} - 10x - 8[/tex]. First, remember that expressions are equivalent when they have identical solutions or roots. That means we have to do three things:

- solve [tex]3x^{2} - 10x - 8[/tex]

- review the listed expressions

- determine which solution is equivalent to the solution of [tex]3x^{2} - 10x - 8[/tex]

First, let's solve [tex]3x^{2} - 10x - 8[/tex].

Use the sum-product pattern -

3x^2 - 10x - 8

3x^2 + 2x - 12x - 8

Common factor from the two pairs -

3x^2 + 2x - 12x - 8

x(3x + 2) - 4(3x + 2)

Rewrite in factored form -

x(3x + 2) - 4(3x + 2)

(x - 4)(3x + 2)

Now, let's review the listed expressions. We have:

A. (x - 4)(3x + 2)

B. (3x - 4)(x - 2)

C. (3x - 4)(x + 2)

D. (3x - 2)(x + 4)

We're looking for one of these expressions to be equivalent to the solution of [tex]3x^{2} - 10x - 8[/tex], which we know is (x - 4)(3x + 2). The first choice, A. (x - 4)(3x + 2), would be our answer!

I hope this helps you. Have a wonderful day and let me know if I can help you with anything else! =)

Answer:

[tex]4\sqrt{5}[/tex]

Step-by-step explanation:

[tex]\sqrt{80}=\sqrt{16*5} =\sqrt{16}*\sqrt{5}=4\sqrt{5}[/tex]

series: 125, 25, 5, ...

We can identify geometric series by:

√first term x third term = second term

√125 x 5 = 25

Hence this is a geometric series.

Common difference:

25 ÷ 5      or     125 ÷ 25

5                            5

The common difference is equal to 5.

Answer:

Below in bold.

Step-by-step explanation:

588000 is close to 600000

6% of this = 600000 * 0.06

= 36,000 sq. miles.

Answer:

35,280 square miles

Step-by-step explanation:

Answer:

104

Step-by-step explanation:

Simple addition:

Add the units place first:

2+2 = 4

Now add the tens together:

60+40= 100

Now add the 2 numbers together to give you 104.

The volume of the sphere is the amount of space in it, and the value closest to the radius is 3.5 cm

The volume is given as:

V = 179.6

The volume is calculated using:

V = 4/3πr³

So, we have:

4/3πr³ = 179.6

Multiply both sides by 3/4

πr³ = 134/7

Divide both sides by π

r³ = 42.88

Take the cube root of both sides

r = 3.5

Hence, the value closest to the radius is 3.5 cm

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The equation he should you use to find the final number of moles of gas in the balloon after the deflation is n1/v1 = n2/v2

The molarity of a solution is the ratio of the mole of the substance to its volume

Since the mole "n" is directy proportional to the volume, hence;

n = kv
k = n/v

Hence the equation he should you use to find the final number of moles of gas in the balloon after the deflation is n1/v1 = n2/v2

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Answer:

answer in picture

Step-by-step explanation:

Answer:

(-4 + 2 • h(4))^2

Step-by-step explanation:

h(4)h(4)

↓

h(4) • h(4) = (-4 +2 • h(4)) • (-4 +2 • h(4))

↓

Calculate

(-4+2× h(4)) × (-4+2× h(4))

Simplify using exponent rule with same base

a^n • a^m = a^n+m

(-4+2× h(4))^2

I hope this helps out.

Answer:

120

Step-by-step explanation:

because its parallel to 3 and if its a reflection or rotation of it it would be the same so it would be 120 degrees

It's not entirely clear what the full instructions are, and I wish your teacher posted a diagram of figures A and B. However, I think I know what your teacher is after.

I'm assuming this is pertaining to similar polygons.

The larger figure has a side length of 88 ft and corresponds to the smaller side length of 11 ft. This is a scale factor of 11/88 = 1/8 = 0.125

What it means is that we multiply each larger side length by 1/8 or 0.125 to get the smaller corresponding side length. In other words, 88*(1/8) = 11

Square this linear scale factor to get the area scale factor

(1/8)^2 = (0.125)^2 = 0.015625

This value of 0.015625 is the area scale factor. We multiply this by the area of figure A to get

4928*0.015625 = 77

This is how your teacher got 77 as the final answer for figure B.

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

Admittedly this concept is a bit confusing at first.

Let's do another example.

Consider a 2 by 3 rectangle of area 2*3 = 6 square units.

Now apply a linear scale factor of 4 to quadruple each side. We get a 8 by 12 rectangle of area 8*12 = 96.

Notice the jump from 6 to 96 is "times 16" (since 96/6 = 16) and it's no coincidence that 16 is 4^2, i.e. the result of squaring the linear scale factor.

new area = (area scale factor)*(old area)

new area = 16*(old area)

new area = 16*6

new area = 96

This shows that 16 is the area scale factor.

Answer:

Mean = 75

Median = 73.5

Mode = 95

Range = 36

Step-by-step explanation:

Given:

Sort:

To find:

Mean:

[tex]\displaystyle \large{\dfrac{1}{n}\sum_{i =1}^n x_i = \dfrac{x_1+x_2+x_3+...+x_n}{n}}[/tex]

Sum of all data divides by amount.

[tex]\displaystyle \large{\dfrac{59+60+70+77+89+95}{6}=\dfrac{450}{6}}\\\\\displaystyle \large{\therefore mean=75}[/tex]

Therefore, mean = 75

Median:

If it’s exact middle then that’s the median. However, if two data or values happen to be in middle:

[tex]\displaystyle \large{\dfrac{x_1+x_2}{2}}[/tex]

From 59,60,70,77,89,95, since 70 and 77 are in middle:

[tex]\displaystyle \large{\dfrac{70+77}{2} = \dfrac{147}{2}}\\\displaystyle \large{\therefore median = 73.5}[/tex]

Therefore, median = 73.5

Mode:

The highest value or/and the highest amount of data. Mode can have more than one.

From sorted data, there are no repetitive data nor same data. Consider the highest value:

Therefore, mode = 95

Range:

[tex]\displaystyle \large{x_{max}-x_{min}}[/tex] or highest value - lowest value

Thus:

[tex]\displaystyle \large{95-59 = 36}[/tex]

Therefore, range = 36

Answer:

a = [tex]\sqrt{68}[/tex] = 8.2

Step-by-step explanation:

Look at picture ↓

[tex]Hope[/tex] [tex]this[/tex] [tex]helps![/tex] [tex]:)[/tex]

Answer:

60

Step-by-step explanation:

You have the proper formula. You just need to swap some things around so we aren't solving for C. C is always the hypotenuse, the diagonal line opposite the right triangle. A and B can be either side unless specified.

1. The side we're solving for can either be called a or b. Let's call it A.

2. Now, switch around the theorem to solve for a: [tex]C^2-B^2=A^2\\[/tex]

3. Plug in what we know: [tex]8^2-2^2=a^2[/tex]

4. It simplifies down to [tex]60=a^2[/tex]

5. The  "[tex]a^2[/tex] " means to square the a. We need to undo that to get a by itself. The opposite of squared is the square root

6. This leaves us to take the square root of both sides, which isolates a.

7. [tex]\sqrt{60}[/tex] is the answer. It's asking for it in the square root so we don't need to simplify it.

Answer:

The answer is:

[tex](56 - 28 \sqrt{3} )m[/tex]

Step-by-step explanation:

Let the broken part is (x) m

so other part is (14-x) m

[tex] \sin(60) = \frac{14 - x}{x} [/tex]

[tex] \sin(60) = \frac{ \sqrt{3} }{2} [/tex]

[tex] = x = (56 - 28 \sqrt{3} )m[/tex]

Answer:

Question 3:

f(3) = (3,-8) this is because -2*-2=4*-2=-8.

Questions 4:

D. (1,7)

Answer:

720

Step-by-step explanation:

Answer:

720

Step-by-step explanation:

6! = 6*5*4*3*2*1 = 720

Answer:

The answer is three

Step-by-step explanation:

The formula to find the area is the width times the length. The area of the big rectangle is three times more than the smaller rectangle.

Answer:

45:4 or 4:45

Step-by-step explanation:

Depends on which

The space inside the steps will be 0.04 cubic meter

The space in a three dimensional region occupied by any body is called as volume.

Assume the steps have the dimensions shown in the diagram below.

We can decompose them into two rectangular prisms.

The lower prism has the dimensions 20 in × 16 in × 6 in.

The upper prism has the dimensions 20 in ×   8 in × 6 in.

1. Volume of lower prism

V = lwh = 20 in × 16 in × 6 in = 1920 in³

2. Volume of upper prism

V = lwh = 20 in × 8 in × 6 in = 960 in³

3. Volume of steps

V = 1920 in³ + 960 in³ = 2880 in³

Or the volume in meter will be 2880 cubic inches = 0.04 cubic meters.

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The statement "The slope of the linear regression line can be calculated using any two points in the data." is always true for any two points.

Linear regression shows the relationship between two variables by fitting a linear equation to observed data. One variable is considered to be an explanatory variable, and the other is considered to be a dependent variable.

A linear regression line has an equation of the form Y = a + bX, where X is the explanatory variable and Y is the dependent variable.

Firstly, as per difinition the equation of linear regression line is

y= a + bx, where b is the slope of the line and a is intercept .

The formula to calculate the slope of the line be,

[tex]b=\frac{n(\sum xy)-(\sum x)(\sum y)}{n(\sum x^{2}) - (\sum x)^2 }[/tex]

here n represent the number of data given in a question, x and y are the two points.

If we look at the formula with point x and y the slope can't be calculated.

Also, the equation of linear regression line , y= a+ bx also contain two points (x, y).

As per the discussion it is not possible to calculate the slope of linear regression line without two points.

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Answer:

JK = 18

Step-by-step explanation:

LK = x - 1

KJ = x + 11

LJ = LK + KJ = x - 1 + x + 11

-> LJ = 2x + 10

LM = 12

By tangent secant segment theorem:

[tex]LK \times LJ = JM^2 \\ \\ \implies \: (x - 1)(2x + 10) = {(12)}^{2} \\ \\ \implies \: x (2x + 10) - 1(2x + 10) = 144\\ \\ \implies \: 2x^{2} + 10x - 2x - 10 - 144 = 0\\ \\ \implies \: 2x^{2} + 8x - 154 = 0\\ \\ \implies \: 2(x^{2} + 4x - 77) = 0\\ \\ \implies \: x^{2} + 4x - 77 = 0\\ \\ \implies \: x^{2} + 11x - 7x- 77 = 0\\ \\ \implies \: x(x + 11) - 7(x + 11) = 0\\ \\ \implies \: (x + 11) (x - 7) = 0 \\ \\ \implies \: (x + 11) = 0 \: \: or \: \: (x - 7) = 0 \\ \\ \implies \: x = - 11 \: \: or \: \: x = 7 \\ \\ x \: can \: not \: be \: negative \\ \implies \: x \neq \: - 11 \\ \\ \implies \: x = 7 \\ \\ \implies \: JK = x + 11 = 7 + 11 \\ \\ \implies \: \huge \: { \orange{JK =18}}[/tex]

Hope it helps you in your learning process.

Have a great day ahead.

Answer:

135 choices

Step-by-step explanation:

5 choices for 1st dig

3 choices for 2nd dig

9 choices for third digit

5 x 3 x 9 = 135

Answer:

135

Step-by-step explanation:

But, for the last digit that is go from 0-9 except the 4

So it also depends on the range for the last digit

Hope this helped! :)

Answer:

110 pages

Step-by-step explanation:

Let number of pages read on 1st day = x

-> No. of pages read on 2nd day = 2x

& No. of pages read on 3rd day = x - 6

Total no of pages read = 458

-> x + 2x + x - 6 = 458

-> 4x - 6 = 458

-> 4x = 458 + 6

-> 4x = 464

-> x = 464/4

-> x = 116

No of pages read on third day = x - 6 = 116 - 6 = 110

Answer:

18x⁴ - 30x³ + 66x² - 40x + 56

Step-by-step explanation:

1) Distribute

2) Distribute

3) Distribute

4) Combine like terms

Expression

Example: 2 + 2 = 4

Combination

Answer:

The product would be 18x^4 - 30x^3 + 66x^2 - 40x + 56

Step-by-step explanation:

Answer:

hi I need actually a lot of help with Matt since I'm not the best?

Answer:

A' = (-4, -2.5)

B' = (1.5, 2.5)

C' = (-1, 5)

Step-by-step explanation:

Dilation using the origin as a center means that we multiply each coordinate by 0.5:

[tex]A = (-8, -5)\\ \\B = (3, 5)\\ \\C = (-2, 10)[/tex]

[tex]A' = (-4, -2.5)\\ \\B' = (1.5, 2.5)\\ \\C' = (-1, 5)[/tex]

Answer:

A

Step-by-step explanation:

Y intercept is -3

Rise 2 run 1