A building 50ft high casts a 75ft shadow. Sarah casts a 6ft shadow. The triangle formed by the building and it’s shadow is similar to the triangle formed by Sarah and her shadow. How tall is Sarah.

Answer:

Option B is correct.

Step-by-step explanation:

A proportional relationship is a relationship between two variables where the ratio between the two variables is always the same.

Divide b/a for each option, the option having same ratio for the complete tables have proportional relationship

a)

9/3 = 3

12/4 = 3

20/5 = 4

b)

25/20 = 5/4

30/24 = 5/4

40/32 = 5/4

c)

12/4 = 3

15/5 = 3

24/6 = 4

d)

4/3 = 4/3

9/6 = 3/2

12/16 = 3/4

So, Option B is correct.

Answer: Second Option

Step-by-step explanation:

It is said that two variables a and b are propocionales if when b increases then a increases in a constant rate.

That is, a and b are proportional if the quotient between b and a is always equal to a constant k.

[tex]\frac{b}{a}=k[/tex]

To know which of the tables shows a proportional relationship identify in which of the tables the division of b between a always is constant

You can verify that the table where the quotient of b enters a is always constant is in the second table

[tex]\frac{b}{a}=\frac{5}{4}[/tex]

Answer:

x = -2 or x = -3/2 thus B. & D. are the answer  

Step-by-step explanation:

Solve for x:

2 x^2 + 7 x + 6 = 0

Hint: | Factor the left hand side.

The left hand side factors into a product with two terms:

(x + 2) (2 x + 3) = 0

Hint: | Find the roots of each term in the product separately.

Split into two equations:

x + 2 = 0 or 2 x + 3 = 0

Hint: | Look at the first equation: Solve for x.

Subtract 2 from both sides:

x = -2 or 2 x + 3 = 0

Hint: | Look at the second equation: Isolate terms with x to the left hand side.

Subtract 3 from both sides:

x = -2 or 2 x = -3

Hint: | Solve for x.

Divide both sides by 2:

Answer:  x = -2 or x = -3/2

Answer:

B and D

Step-by-step explanation:

Given

2x² + 7x + 6 = 0

To factorise the quadratic

Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 2 × 6 = 12 and sum = + 7

The factors are + 4 and + 3

Use these factors to split the x- term

2x² + 4x + 3x + 6 = 0 ( factor the first/second and third/fourth terms )

2x(x + 2) + 3(x + 2) = 0 ← factor out (x + 2) from each term

(x + 2)(2x + 3) = 0

Equate each factor to zero and solve for x

x + 2 = 0 → x = - 2 → D

2x + 3 = 0 ⇒ 2x = - 3 ⇒ x = - [tex]\frac{3}{2}[/tex] → B

Answer:

consistent  

Solution at (3,2)

Step-by-step explanation:

A consistent and independent solution to a system of linear equations is one point

A consistent and dependent solution to a system of linear equations is where they are the same line ( they could also be called equivalent)

An inconsistent solution is where there is no solution, the lines do not cross

Since the lines cross at exactly one point, this is a consistent and dependent solution

The solution is at x = 3  ( 3 units to the right of the origin)

and y = 2 ( 2 units up from the origin)

(3,2)

Answer:

Consistent :)

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Noting the following rule of radicals

[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] = [tex]\sqrt{ab}[/tex]

Given

([tex]\sqrt{2}[/tex] + [tex]\sqrt{3}[/tex])( [tex]\sqrt{5}[/tex] - [tex]\sqrt{7}[/tex] )

Each term in the second factor is multiplied by each term in the first factor

= [tex]\sqrt{2}[/tex]([tex]\sqrt{5}[/tex] - [tex]\sqrt{7}[/tex]) + [tex]\sqrt{3}[/tex]([tex]\sqrt{5}[/tex] - [tex]\sqrt{7}[/tex]) ← distribute parenthesis

= [tex]\sqrt{10}[/tex] - [tex]\sqrt{14}[/tex] + [tex]\sqrt{15}[/tex] - [tex]\sqrt{21}[/tex]

Answer:

[tex]\frac{\sqrt[3]{100x}}{5}[/tex]

Step-by-step explanation:

we have

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

Multiply inside by [tex]\frac{25}{25}[/tex]

so

[tex]\sqrt[3]{\frac{4x*25}{5*25}}[/tex]

[tex]\sqrt[3]{\frac{100x}{125}}[/tex]

Remember that

[tex]\sqrt[3]{125}=5[/tex]

substitute

[tex]\sqrt[3]{\frac{100x}{125}}=\frac{\sqrt[3]{100x}}{\sqrt[3]{125}}=\frac{\sqrt[3]{100x}}{5}[/tex]

Multiply the two brackets together

(x+2)(3x-3)

x(3x)*(-3)(x)+2(3x)(2*-3)

3x^2-3x+6x-6

3x^2+3x-6

Answer is : 3x^2+3x-6

Answer

A. x5y3

Step-by-step explanation:

Answer:

150(.40)^n is your equation

Step-by-step explanation:

Answer:

[tex]=150\cdot{0.4^n}[/tex]

Step-by-step explanation:

Let n be the number of rounds. Lets look at n=1 which is round one. Therefore if 40% of the contestants are eliminated then we can write an expression of the number of contestants eliminated:

[tex]=150\cdot{0.4}[/tex]

For round two, n=2:

[tex]=150\cdot{0.4)\cdot{0.4}=150\cdot{0.4^2}[/tex]

Therefore for the n number of rounds:

[tex]=150\cdot{0.4^n}[/tex]

Answer:

(2.4 , -1)

Step-by-step explanation:

Too many commas in second ordered pair but this is how I will interpret the question:

Find the midpoint of (3.2,2.5) and (1.6,-4.5)

So just average x's  : (3.2+1.6)/2 =4.8/2=2.4

And

    just average y's : (2.5+-4.5)/2=-2/2=-1

The midpoint is (average x's , average y's)

Your midpoint is (2.4             ,     -1             )

answer (2.4 , -1)

Answer: 0.167 is the part of the hall that was not occupied. Or 16.7 %

Step-by-step explanation:

300-250=50 this is the number of seats not occupied since 250 is the amount occupied.

So, 50/300=5/30 which can be converted to a number which is 0.1666666667. It says to round to the thousandths place, which is the 3rd number. That is 0.167

Answer:

0.167 part of the hall was not occupied

Step-by-step explanation:

Given :In a concert hall, 250 seats out of 300 were occupied.

To Find :To the nearest thousand, what part of the hall was not occupied?

Solution:

Total seats = 300

Occupied seats = 250

Unoccupied seats = 300-250 = 50

So, The part of the hall was not occupied = [tex]\frac{\text{unoccupied seats}}{\text{total seats}}[/tex]

                                                                     = [tex]\frac{50}{300}[/tex]

                                                                     = [tex]0.167[/tex]

Hence 0.167 part of the hall was not occupied

Answer:

B. By simplifying 9 to [tex]3^{2}[/tex] to make both powers base three and subtracting the exponents

Step-by-step explanation:

When you have a division the quotient of powers property states that the exponents should be substracted, and by simplifying 9 to [tex]3^{2}[/tex] you end up with an equation like this:

[tex]\frac{3^{4} }{3^{2} }[/tex]=[tex]3^{2}[/tex]

Then you just have to substract the exponent from the denominator from the numerator´s exponent, which would be:

4-2=2

and the resultant equation would be:

[tex]3^{2} =3^{2}[/tex]

The Quotient of Powers Property allows you to subtract exponents when dividing expressions with the same base. The expression 3^4/9 simplifies to 3^2 because 9 can be expressed as 3^2, therefore their exponents are subtracted (4-2=2).

In this question, the Quotient of Powers Property is used. This property states that to divide where the base remains the same, you subtract the exponents. In the expression 3^4/9 = 3^2, we know that 9 can be expressed as 3^2.

Therefore, it becomes 3^4/3^2. According to the Quotient of Powers Property, we subtract the exponent of the denominator from the exponent of the numerator (4-2=2). Hence the expression simplifies to 3^2. The correct choice is B: By simplifying 9 to 3^2 to make both powers base three and subtracting the exponents.

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Hello There!

The answer would be the first one.

This is saying that Tom can not save exactly 50.25 but he must save more than that

Answer:

A

Step-by-step explanation:

(f - g)(x) = f(x) - g(x)

f(x) - g(x)

= 3x² - 2x + 4 - (5x² + 6x - 8) ← distribute parenthesis by - 1

= 3x² - 2x + 4 - 5x² - 6x + 8 ← collect like terms

= - 2x² - 8x + 12 → A

Answer:

The complete factorization is 3x² (x - 5)² ⇒ 2nd answer

Step-by-step explanation:

* Lets revise how to factorize a trinomial

- Find the greatest common factor of the coefficients of the three terms

∵ The trinomial is 3x^4 - 30x³ + 75x²

- The greatest common factor of 3 , 30 , 75 is 3

∵ 3 ÷ 3 = 1

∵ 30 ÷ 3 = 10

∵ 75 ÷ 3 = 25

∴ 3x^4 - 30x³ + 75x² = 3(x^4 - 10x³ + 25x²)

- Now lets find the greatest common factor of the variable x

∵ x² is the greatest common factor of the three terms

∵ x^4 ÷ x² = x²

∵ 10x³ ÷ x² = 10x

∵ 25x² ÷ x² = 25

∴ 3(x^4 - 10x³ + 25x²) = 3x² (x² - 10x + 25)

- Lets factorize (x² - 10x + 25)

∵ √x² = x

∵ √25 = 5

∵ 2 × 5 × x = 10x

∴ x² - 10x + 25 is a completing square

∴ (x² - 10x + 25) = (x - 5)²

∴ 3x² (x² - 10x + 25) = 3x² (x - 5)²

* The complete factorization is 3x² (x - 5)²

Answer:

3x^2 (x-5)^2

Step-by-step explanation:

3x^4 − 30x^3 + 75x^2

We can factor out a 3x^2 from each term

3x^2 (x^2 -10x +25)

The term inside the parentheses can be factored

What 2 numbers multiply to 25 and add to -10

-5*-5 = 25

-5+-5 = -10

3x^2 (x-5) (x-5)

3x^2 (x-5)^2

[tex]\bf slope = m = \cfrac{rise}{run} \implies \cfrac{ f(x_2) - f(x_1)}{ x_2 - x_1}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array}\\\\[-0.35em] \rule{34em}{0.25pt}\\\\ f(x)= x^2+3x-12\qquad \begin{cases} x_1=3\\ x_2=5 \end{cases}\implies \cfrac{f(5)-f(3)}{5-3} \\\\\\ \cfrac{[(5)^2+3(5)-12]~~-~~[(3)^2+3(3)-12]}{2}\implies \cfrac{[25+3]~~-~~[9-3]}{2} \\\\\\ \cfrac{28-6}{2}\implies \cfrac{22}{2}\implies 11[/tex]

Answer:

D. Acute

Step-by-step explanation:

This is an acute angle because the angle is less then 90 degrees.

<FOA is an Acute angle (D).

How I know...

Acute angles are angles are below 90 degrees (aka LESS then a right angle)

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

16

Step-by-step explanation:

4 groups of 4 is 16:

[tex]\left\begin{array}{cccc}*&*&*&*\*&*&*&*&*\*&*&*&*&*\*&*&*&*&*\end{array}\right[/tex]

[tex]125 = \frac{1}{125} {}^{y - 1} \\ 125 = ( {5}^{ - 2} ) {}^{y - 1} \\ \\ {5}^{3} = {5}^{2 - 2y} \\ 3 = 2 - 2y \\ - 0.5 = y[/tex]

Answer:

The answer is [tex]y=-0.5[/tex]

Step-by-step explanation:

In order to determine the "y" value, we have to change the way of we see the equation.

In these cases, when the variable is in the exponent and  it is possible to make two exponents in each side of the equation, we have to equal bases and then we have to make other equation between the exponents of both sides.

So,

[tex]125=(\frac{1}{25})^y^-^1\\(5)^3=(5^-^2)^y^-^1\\(5)^3=(5)^-^2^*^y^+^2\\[/tex]

Then, we have to make an equation between the exponents of both sides:

[tex]3=-2*y+2\\2*y=2-3\\2*y=-1\\y=\frac{-1}{2}=-0.5\\ y=-0.5[/tex]

Finally, the value of "y" is -0.5

Answer:

A. The answer is our unit prices when our profit is 0

Step-by-step explanation:

The zeros are the x-intercepts, when the curve passes through the x-axis.

I'm going to call our function P

P(x)=-0.5x^2+221x-224 is equal to 0 (our profit is equal to 0) when x (the unit price is such and such)

The answer is our unit prices when our profit is 0

The expression represents the monthly profit from sales of a product at a given unit price. The zero(s) of the expression represent the unit price(s) when the profit is equal to 0.

The expression -0.5x^2 + 221x - 224 represents the monthly profit, in thousands of dollars, from sales of a product when it is sold at a unit price of x dollars.

The zero(s) of the expression are the unit price(s) when the profit is equal to 0. To find the zero(s), we need to set the expression equal to 0 and solve for x.

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Answer:

Step-by-step explanation:

−7−4p+5

−4p+(−7+5)

Ans  

−4p−2

your answer is: -4p - 2

Explanation:

first, ignore the -4p for now. do the small equation without the variable. SO, we would do 7 - 5 = 2.

there aren't any addition symbols being used in the equation and there aren't any other numbers with the p variable. this means that the -4p will stay the same. so we would end up with -4p - 2

(this isn't the normal way of solving this, but I did my own way and got the same answer)

Answer:

√113

or

10.6301458127

Step-by-step explanation:

Plug the coordinated into this equation and make sure you match up the corrdinates in the correct order

d = √(x2 - x1)^2 + (y2 - y1)^2

The number next to the number does NOT mean multiply it mean like this

(x2, y2)  and (x1, y1) so you would plug them in like this:

d = √(-6 - 2)^2 + (4 - (-3))^2

d = √(-8)^2 + (7)^2

d = √(64 + 49

d = √113

or 10.6301458127

Answer with Step-by-step explanation:

The distance(d) between the points (a,b) and (c,d) is given by:

[tex]d=\sqrt{(c-a)^2+(d-b)^2}[/tex]

Here, we have to find distance between (2,-3) and (-6,4)

(a,b)=(2,-3) and (c,d)=(-6,4)

[tex]d=\sqrt{(-6-2)^2+(4-(-3))^2}[/tex]

[tex]d=\sqrt{8^2+7^2}[/tex]

[tex]d=\sqrt{64+49}[/tex]

[tex]d=\sqrt{113}[/tex]

Hence, the distance between the points (2 -3) and (-6 4) on the coordinate plane is:

[tex]\sqrt{113}[/tex]

Answer: Option D

D. 41​

Step-by-step explanation:

A value [tex]x_i[/tex] is considered an outlier if

[tex]x_i> Q_3 + 1.5IQR[/tex]

or

[tex]x_i <Q_1 - 1.5IQR[/tex]

Where

[tex]Q_3[/tex] is the third quartile

[tex]Q_1[/tex] is the first quartile

IQR is the interquartile range.

[tex]IQR = Q_3-Q_1[/tex]

In this case:

[tex]Q_3=92\\Q_1=72[/tex]

So

[tex]IQR = 92-72 =20[/tex]

[tex]Q_3 + 1.5IQR = 92 + 1.5*20 = 122[/tex]

[tex]Q_1 - 1.5IQR=72-1.5*20=42[/tex]

Then the outlier values will be all those greater than 122 or less than 42

Therefore the answer is the option D.

Answer:

45

Step-by-step explanation:

The 4 part of the ratio represents 30 red ribbons

Divide 30 by 4 to find the value of one part of the ratio

30 ÷ 4 = 7.5, hence

6 × 7.5 = 45 ← number of green ribbons

Answer:

336

Step-by-step explanation:

Using the definition of n[tex]P_{r}[/tex] = n ! / (n- r) !

where n ! = n(n - 1)(n - 2).... × 3 × 2 × 1

8[tex]P_{3}[/tex]

= 8 ! / (8 - 3) !

= 8 ! / 5 !

= [tex]\frac{8(7)(6)(5)(4)(3)(2)(1)}{5(4)(3)(2)(1)}[/tex]

[ cancel 5(4)(3)(2)(1) on numerator/denominator

= 8 × 7 × 6 = 336

ANSWER

[tex]^8P_3 = 336[/tex]

EXPLANATION

Recall that;

[tex]^nP_r = \frac{n!}{(n - r)!} [/tex]

The given expression is:

[tex]^8P_3[/tex]

We substitute n=8 and r=3

[tex]^8P_3 =\frac{8!}{(8- 3)!} [/tex]

[tex]^8P_3 =\frac{8!}{(5)!} [/tex]

This simplifies to :

[tex]^8P_3 =\frac{8 \times 7 \times 6 \times 5!}{5!} [/tex]

We cancel out the common factors to get:

[tex]^8P_3 = 8 \times 7 \times 6[/tex]

[tex]^8P_3 = 336[/tex]

Answer:

{-5,-4,2}

Step-by-step explanation:

The domain is the inputs and the range is the outputs

The outputs are the y values

{ -5,2,-4,2}

We only list them once and in order from smallest to largest

{-5,-4,2}

Answer:

[tex]4\pi[/tex] or 12.56

Step-by-step explanation:

[tex]\pi r^{2}[/tex] is the formula to find the area of a circle.

if we plug '2' in... [tex]\pi2^{2}[/tex]

which equals to [tex]4\pi[/tex]

if we multiply 4 with pi, it equals to 12.56

Answer:

Area of circle = 12.56 sq. units

Step-by-step explanation:

radius =  2

Area of circle = π r² sq. units

                       = 3.14 * 2 * 2 = 12.56 sq. units

Answer:

Step-by-step explanation:

it's -2

The percentage change of 134 to 106 will be -20.89% .

Given ,

Number changed from 134 to 106 .

Now,

Here initially the number was = 134

After reduction the number was = 106

Percentage change = final - initial / initial * 100

Final number = 106

Initial number = 134

so,

Percentage change = 106 -134/134 * 100

Percentage change = -28/134 *100

Percentage change = -20.89%

Thus the percentage change is -20 .89% and the negative sign shows the declining nature of number .

Know more about percentages,

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Answer:

27

Step-by-step explanation:

Answer:

The length of the shorter piece is  13 inches

Step-by-step explanation:

Let's represent the longer piece of pipe with the variable L and the shorter piece of pipe with variable S.

Since the pipe is going to be the length of  L and S together, we can make this equation:

L+S=52

Also we know that the longer piece is three times the shorter piece or

L=3S

Substitute the second equation into the first equation.

L+S=52

3S+S=52

4S=52

Divide both sides by 4

4S/4=52/4

S=13 inches

The length of the shorter piece is 13 inches....

To find the length of longer piece, put the value S=13 in L=3S

L=3S

L=3(13)

L=39 inches

The length of the longer piece is 39 inches....

Answer:

It is (2, 2).

Step-by-step explanation: