Variables y and x have a proportional relationship, and y = 21 when x = 14.

What is the value of x when y = 12?

Enter your answer in the box.

x =
please help

Answer:

The answer:

A. [tex]x= \frac{-5+ \sqrt{-11} }{2}[/tex]

F.[tex]x= \frac{-5- \sqrt{-11} }{2}[/tex]

Step-by-step explanation:

Step 1: Solve with quadratic formula

Step 2: Simplify

Step 3: Separate the solution

Answer:

[tex]\large {\textsf{A and F}}\ \implies \bold{x_1}=\dfrac{-5-\sqrt{-11}}{2},\ \bold{x_2}=\dfrac{-5+\sqrt{-11}}{2}[/tex]

Step-by-step explanation:

Quadratic Formula: [tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

Standard Form of a Quadratic Equation: ax² + bx + c = 0, where a ≠ 0.

Given polynomial: x² + 5x + 9

⇒ a = 1, b = 5, c = 9

Step 1: Rewrite to Standard Form.

⇒ x² + 5x + 9 = 0

Step 2: Substitute the values of a, b, and c into the formula.

⇒ a = 1, b = 5, c = 9

[tex]x=\dfrac{-5\pm\sqrt{\bold{5^2}-4\bold{(1)(9)}}}{\bold{2(1)}}\\\\x=\dfrac{-5\pm\sqrt{25\bold{\ - \ 4(9)}}}{2}\\\\x=\dfrac{-5\pm\sqrt{\bold{25-36}}}{2}\\\\x=\dfrac{-5\pm\sqrt{-11}}{2}[/tex]

Step 3: Separate into two possible cases.

[tex]x_1=\dfrac{-5-\sqrt{-11}}{2}\\\\x_2=\dfrac{-5+\sqrt{-11}}{2}[/tex]

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The range of the function will be all values that are greater than 17 that is y > 17

The range of a function is the dependent variable of the function for which it exists,

Given the linear function

y = 8x + 1

If the value of x is 2, hence;

y = 8(2) + 1

y = 17

Hence the range of the function will be all values that are greater than 17 that is y > 17

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Answer:

3 decimal places; 189/750 = 0.252

Step-by-step explanation:

Answer:

3 decimal places.

189/750 = 0.252

Step-by-step explanation:

If you are allowed to use a calculator, you divide. 189/750 means 189 ÷ 750.

You will get 0.252, which is three decimal places. If you are not allowed to use a calculator, you must do long division. The 750 goes outside the dividing frame and the 189 goes inside. There is an unwritten decimal point after the 9 in 189. Since 750 does not go into 189, put 0. to begin and put zeros after the 189 to do the long division. See image. Hopefully you can just use a calculator.

Using percentages, we have that Puja Limbu did 80% of the problems and Raju Lama did 73.3%, hence Puja Limbu had the better performance.

The percentage of an amount a over a total amount b is given by a multiplied by 100% and divided by b, that is:

[tex]P = \frac{a}{b} \times 100\%[/tex]

The percentage for Puja Limbu is:

[tex]P = \frac{8}{10} \times 100\% = 80\%[/tex]

The percentage for Raju Lama is:

[tex]P = \frac{11}{15} \times 100\% = 73.3\%[/tex]

80% > 73.3%, hence Puja Limbu had the better performance.

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Answer:

-4n+7

Step-by-step explanation:

because you take away 4 each time and the nber that would come before 3 is 7.

The equation that represents Camille's profit p as a function of the number of doughnuts sold, n is P = 1.35n - 60

She bought 120 doughnuts for $60.

Therefore,

cost  = $60

Her profit was $48 once she sold 80 doughnuts.

p = profit

n = number of doughnuts sold.

Therefore,

let

x = amount she is selling each doughnuts

p = nx - 60

Using the information given we have:

48 = (80x) - 60

Therefore,

x = $1.35

Hence, for any number of doughnuts then, we have the profit equation as follows:

P = 1.35n - 60

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A picture of the dilated figure with its points at (-2, 10), (2, 6), and (-8, 4) is provided.

Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered.

The complete question is;

"Graph the image of this figure after a dilation with a scale factor of 2 centered at (2, 2) .

Use the polygon tool to graph the dilated figure."

The center of dilation and figure are first translated, making the origin the center of dilation.

We map every point because the point (2, 2), which is our center of dilatation, must be translated left 2 and down 2 to become the origin.

(x, y)→(x-2, y-2)

Each point will be multiplied by two when the scale factor is two, giving us the rule.

(x, y)→(2x-4, 2y-4)

In order to return the figure to its original location, we must translate it right 2 and up 2; this gives us the rule.

(x,y)→(2x-4+2, 2y-4+2) = (2x-2, 2y-2)

At the top of the original figure, the first point is (0, 6). When we use the transformation, we get

(0, 6)→(2*0-2, 2*6-2) = (0-2, 12-2) = (-2, 10)

The pre-rightmost image's point is (2, 4). The results of using the transformation rule are;

(2, 4)→(2*2-2, 2*4-2) = (4-2, 8-2) = (2, 6)

The pre-leftmost image's point is at (-3, 3). The transformation rule being applied, w

(-3, 3)→(-3*2-2, 3*2-2) = (-6-2, 6-2) = (-8, 4)

Hence,an picture of the dilated figure with its points at (-2, 10), (2, 6), and (-8, 4) is provided.

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An expression is defined as a set of numbers, variables, and mathematical operations. The given statement can be modeled as (3m+7)/27 < n.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The given statement "The quotient of 7 more than three times a number m and the number 27 less than n" can be modeled as an algebraic expression as shown below.

(3m+7)/27 < n

Hence, the given statement can be modeled as (3m+7)/27 < n.

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Answer:

17 in.

Step-by-step explanation:

There are two same angles shown, so two sides are equal. We can form an equation x+4=4x+1. Solution is x=1, then both unknown sides are 5 in. long. Given all side lengths we add them 7+5+5+15 getting the perimeter.

Answer:

15 sqrt a ^4

Step-by-step explanation:

The graph for Mei Mei' trip is attached accordingly. Also attached are the  values derived from the question.

The secret to comprehending the graph is to understand that every time Mei Mei spent while she was on the way to bank and back were are all computed cumulatively.

This means that when she stops at the store which is 8 blocks away from home (that is 2 blocks per min x 4 mins = 8blocks) the time spent is recorded as 4 + 5 at location 8 blocks, which is equals 9 minutes.

Also take note of the fact that the time spent is plotted on the x-axis and the blocks away from home on the y-axis.

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Answer: $0.24

Step-by-step explanation:

9.5 inches --> $2.28
1 inch--->X
now cross multiply it and get,

9.5X = 2.28*1
X = 2.28/9.5

so its $0.24 per inch

Answer:

Use the graphing calculator to graph the system of equations and find the solution where x is the total hats sold and y is the total t-shirts sold.

x + y = 152,

8.5x + 12y = 1,656

How many hats were sold?

hats

Step-by-step explanation:

a) 74.857% of adult men are shorter than Michael

b) 84.134% of adult men are taller than Jack

c) 58.991% of adult men are of height between Jack and Michael

Within one standard deviation of the mean is 68% of the population. Within two standard deviations of the mean, 95% of the population is located. The median is within 3 standard deviations for 99.7% of the population.

Given:

µ = 70in,  σ = 3in.

We know Z = (x-µ)/σ

a) Actor Michael B. Jordan is 6’0” (72”) tall.

Z = (72-70)/3 = 0.67

So, the probability of an adult man having a height of 0-72 inches, and no greater is 74.857%

b. Comedian Jack Black is 5’7’ (67”) tall.

Z = (67-70)/3 = -1

The corresponding value is .15866 which can be the probability of an adult man having a height of 0-67 inches, and no greater.

But  the percentage of those taller than jack is = 1 – .15866 = 0.84134

c) P(X < 72) – P(x < 67)

= 0.74857 – 0.15866

= 0.58991

= 58.991%

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The Question attached here is incomplete, the complete question is

a. Actor Michael B. Jordan is 6’0” (72”) tall.  What percentage of adult men are shorter than Michael?

b. Comedian Jack Black is 5’7’ (67”) tall. What percentage of adult men are taller than Jack?

c. What percentage of adult men are of height between Jack and Michael?

Step-by-step explanation:

-6<2x-4<4

-2<2x<8

-1<x<4

x = (-1,4)

Answer:

Step-by-step explanation:

x² + y² = 81

x + y = √81

x + y = 9

x ≥ 9

y ≤ 9

If ÐABC and ÐCBD are a linear pair, then it means that their sum is 180°.

Linear pair of angles are angles formed when two lines intersect each other at a single point.

Now, the angles are also said to be linear if they are adjacent to each other after the intersection of the two lines and the sum of the linear pair of angles is always equal to 180°.

Looking at the definition above we can say that if ÐABC and ÐCBD are a linear pair, then it means that their sum is 180°.

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Option fourth ''Table B, because the given condition is that the student is taking a foreign language" is correct.

It is defined as the frequency that can be evaluated by the two-way frequency table. Usually, we can obtain this frequency by dividing the frequency that is not in the total frequency cell by the total frequency.

We have two tables given in the question.

The conditional relative frequency tables show the results of a survey asking students whether they are taking a foreign language or not.

The condition is: "Assuming a student is taking a foreign language"

Table B can be used to answer the above statement.

Thus, option fourth ''Table B, because the given condition is that the student is taking a foreign language" is correct.

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Answer:

Option b: Table A, because the given condition is that the student is taking a foreign language.

Step-by-step explanation:

on ed

Answer: 41

Step-by-step explanation:

If each line costs 2, then for the four-line ad, the cost is the initial price plus 4(2), meaning the initial cost is 25-8=17.

Thus, the cost of a 12-line ad is 17+2(12)=41

Answer:

Multiply the denominator and numerator with root 2 to get a fair denominator and simplify if needed. Hope it helps

Answer:

1 + √3 - √5

Step-by-step explanation:

The given √2/√2 equals 1, and so we now have 1 + √3 - √5, whose denominator is the integer 1.  There's nothing left to rationalize.

Standard form of quadratic equation: ax² + bx + c

Here given equation: f(x) = -(x - 4)²  + 2

Simplify the equation:

⇒ f(x) = -(x - 4)² + 2

Use perfect square formula: (a + b)² = a² + 2ab + b²

⇒ f(x) = -(x² + 2(x)(-4) + (-4)²) + 2

⇒ f(x) = -(x² - 8x + 16) + 2

⇒ f(x) = -x² + 8x - 16 + 2

⇒ f(x) = -x² + 8x - 14

[tex]\hrulefill[/tex]

Here given equation: f(x) = (x - 4)²  + 2

Simplify the equation:

⇒ f(x) = (x - 4)² + 2​

⇒ f(x) = x² + 2(x)(-4) + (-4)² + 2

⇒ f(x) = x² - 8x + 16 + 2

⇒ f(x) = x² - 8x + 18

Answer:

f(x)=x²-8x+18

Step-by-step explanation:

f(x) = (x-4)² + 2​

To find the answer for the first part (x-4)², you need to use the formula.

This is the formula: (a-b)²=a²-2ab+b²

Plug in x for a and -4 for b.

(x-4)²=x²-8x+16

Now, put x²-8x+16 for (x-4)².

f(x)=x²-8x+16+2

Add like terms.

f(x)=x²-8x+18

Our answer is already in standard form because it is from greatest to least.

Hope this helps!

If not, I am sorry.

By applying a composition of f(x) = - (1/2) · x² + 5 · x with respect to g(x) = x² + 2 and evaluating the resulting expression at x = - 2, the value of f(g (-2)) is 12. (Correct choice: C)

Let be f and g functions, there is a composition of f with respect to g when the input of the former is substituted by the output of the latter. It is to notice that composition is a binary operation between functions.

If we know that f(x) = - (1/2) · x² + 5 · x, g(x) = x² + 2 and x = -2, then the composed function evaluated is:

f(g (x)) = - (1/2) · (x² + 2)² + 5 · (x² + 2)

f(g (- 2)) = - (1/2) · 6² + 5 · 6

f(g (- 2)) = 12

By applying a composition of f(x) = - (1/2) · x² + 5 · x with respect to g(x) = x² + 2 and evaluating the resulting expression at x = - 2, the value of f(g (-2)) is 12. (Correct choice: C)

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Answer:

most likely b

Step-by-step explanation:

the more than symbol tells me that it is going to move past 10.

Answer:

Reason -

In the question it is given that triangle ABC is congruent to triangle DEF

if a triangle is congruent to other triangle than the corresponding parts of it (.ie sides and angles) are equal to that of other

The graph is shown below:

A statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.

Rearrange unknown terms to the left side of the equation:

|x|  > 7/2-1

Now,

|x|  > (7-2)/ 2

Calculate the sum or difference:

|x|  > 5/ 2

Convert the absolute inequality to standard inequality:

x> 5/2  or  x< -5/2

Solve the inequality:

x> 5/2

Solve the inequality:

x< -5/2

Graph on number line is attached

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[tex]{\huge \underline{{ \fbox \color{red}{A}}{\fbox \color{green}{n}}{\fbox \color{purple}{s}}{\fbox \color{brown}{w}}{\fbox \color{yellow}{e}}{\fbox \color{gray}{r } }}}[/tex]

[tex] \sf \dfrac{2}{15} \div \dfrac{3}{20} = \dfrac{2 \times 20}{15 \times 3} = \dfrac{40}{45} = \dfrac{8}{9} [/tex]

Answer :-

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \Rrightarrow \dfrac{8}{9} [/tex]

I hope I've helped : )

[tex]\dfrac{1}{50}[/tex]

[tex] \cfrac{2}{15} \times \cfrac{3}{20} [/tex]

[tex] \cfrac{2 \times 3}{15 \times 20} [/tex]

[tex] \cfrac{6}{15 \times 20} [/tex]

[tex] \cfrac{6}{300} [/tex]

[tex] \cfrac{1}{50} [/tex]

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Answer:

35 miles/hour

Step-by-step explanation:

See attached image.

Part 1

Using the distance formula,

[tex]AB=\sqrt{(-2-1)^{2}+(2-7)^{2}}=\sqrt{34}\\\\BC=\sqrt{(-2-4)^{2}+(2-2)^{2}}=6\\\\AC=\sqrt{(1-4)^{2}+(7-2)^{2}}=\sqrt{34}[/tex]

So, the measure of the longest side is 6 units.

Part 2

Triangle ABD will have vertices A(1,7), B(-2, 2), and D(1,2).

We already know that [tex]AB=\sqrt{34}[/tex]

Using the distance formula,

[tex]AD=\sqrt{(1-1)^{2}+(7-2)^{2}}=5\\\\BD=\sqrt{(-2-1)^{2}+(2-2)^{2}}=3[/tex]

So, ABD is a scalene triangle.

Part 3

From part 2, we know that the length of side AD is 5 units.

Answer:

Maybe the question could've been 2+2+1. I'd say read the question properly.

Step-by-step explanation:

In which case, 2+2+1= 5