Which functions are even? Select all that apply

Answer:

y = x^2 +3x-10

Step-by-step explanation:

If we know the roots of a quadratic function, we know that

y = (x -a) (x-b)  where a and b are the roots

y = (x-2 ) (x--5)

y = (x-2)(x+5)

We need to foil this out to get this in standard form of ax^2 + bx+c

FOIL  (x-2) (x+5)

First x*x:  x^2

outer : 5*x = 5x

inner:  -2x  = -2x

last :  -2*5  = -10

Add them up

x^2 +5x-2x-10

x^2 +3x-10

Final answer:

A quadratic equation in standard form with roots 2 and -5 is obtained by multiplying (x - 2)(x + 5), which simplifies to x² + 3x - 10 = 0.

Explanation:

To write a quadratic equation in standard form with integer coefficients that has roots 2 and -5, we use the fact that if α and β are roots of a quadratic equation, the equation can be written as:

ax² + bx + c = 0

Where:

The quadratic equation in standard form using the roots 2 and -5 is given by:

(x - 2)(x + 5) = 0

Expanding this we get:

x² + 5x - 2x - 10

Which simplifies to:

x² + 3x - 10 = 0

Thus, the quadratic equation with integer coefficients and roots 2 and -5 is x² + 3x - 10 = 0.

Answer:

Correct choice is B

Step-by-step explanation:

The function [tex]f(x)=20x[/tex] represents the situation, where x is the number of sold video games and f(x) is the total cost of sold games.

Jason  must sell a minimum of 5 games, this means that [tex]x\ge 5.[/tex] He has 30 video games he can sell, then [tex]x\le 30.[/tex] Thus, the domain of the function is [tex]5\le x\le 30.[/tex]

The range of the function f(x) is

[tex]20\cdot 5\le f(x)\le 20\cdot 30,\\ \\100\le f(x)\le 600.[/tex]

Answers:

Equation is 2*(2*W+W) = 102

Width is 17

Length is 34

=============================

Explanation:

L = 2*W because the length is twice the width

2*(L+W) = P is the perimeter formula

Replace P with the given perimeter (102). Also replace L with 2*W. Then isolate W

2*(L+W) = P

2*(2*W+W) = 102

2*(3W) = 102

6W = 102

6W/6 = 102/6

W = 17

If the width is W = 17, then the length is

L = 2*W = 2*17 = 34

So the width and length of this rectangle is 17 by 34

---------

Check:

P = 2*(L+W)

P = 2*(34+17)

P = 2*51

P = 102

Answer is confirmed

To find the length and width of a rectangle with given perimeter and lengths as twice of the width, first plug the length into the perimeter formula. Solve the resulting equation for width. Substitute this width into the length formula to get the length.

In this problem, we have a rectangle where the length (L) = 2 * width (W). Also, the perimeter of the rectangle (P) = 2L + 2W. The given perimeter is 102 inches.

Since L = 2W, substituting this equation into the formula for perimeter, we get P = (2*2W) + 2W = 102.

This simplifies to 6W = 102, and therefore W = 102 / 6 = 17 inches. Substituting the width back into the equation L = 2W, we find that the length (L) is 2 * 17 = 34 inches.

So, the width is 17 inches and the length is 34 inches.

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Answer:

The correct option is b. 15

Explanation:

We are given that a freight train travels at an average speed of 60 mph.

Also we are given that the average speed of passenger train is 72 mph.

We are also given that the freight train leaves 3 hours before passenger train. So the number of miles covered by freight train in 3 hours is:

[tex]3 \times 60 = 180[/tex] miles.

Let X be the number of hours it takes the passenger train to catch up the freight train.

Therefore, we have:

[tex]180 + 60 \times X = 72 \times X[/tex]

[tex]72X-60X = 180[/tex]

[tex]12X=180[/tex]

[tex]X=\frac{180}{12}[/tex]

[tex]X=15[/tex]

Therefore, the passenger train will take 15 hours to catch up the freight train.

Answer:

sorry im answering late but the answer is C. 18

Step-by-step explanation:

60 x 18 = 1,080

72 started 3 hours later so that means you subtract 3 from 18 which equals 15 and 72 x 15 = 1,080

ur answer is 18

Answer:

110 Walnuts

Step-by-step explanation:

Firstly, there are 6 bags and 330 walnuts. You divide 330 by 6 and you get 55. 330/6. Now, you multiply 55 by 2 and you get your answer. So basically in each bag there are 55 walnuts and if you multiply that by 6 you get 330 again. Hope this helped!

Answer:

110 walnuts

Step-by-step explanation:

330÷6 is 55

55•2 is 110

Answer:

1. [tex]a_{n}=\frac{1}{3} a_{n-1}[/tex] where [tex]a_{1} =27[/tex]

2. [tex]2^{x+1}[/tex]

3. The domain is {-12,-8,0,1}. The range is {0,12,8}.

Step-by-step explanation:

1. The recursive formula is defined as an implicit way of writing the rule of a function or pattern. It is implicit because it uses previous terms to find the next term in the pattern. We multiply, add, subtract or divide a previous term by a constant value or expression to find the next. In this case, 27 becomes 9 through division by 3 or multiplication by 1/3. The pattern continues 9(1/3)=3 and so forth.

2. The function f(x) is an exponential and has a general form of [tex]y=ab^x[/tex]. We know f(x) is [tex]2^x[/tex]. The points of g(x) all changed from f(x) by shifting over to the left. This transformation occurred by [tex]2^{x+1}[/tex].

3. Domain is defined as the set of all x-values. Range is defined as the set of all y-values. The domain is {-12,-8,0,1}. The range is {0,12,8}.

Final answer:

Ms. Keller will grade 17.5 projects in seven hours at her current rate of 2.5 projects per hour.

Explanation:

The student's question is about determining at what rate Ms. Keller is grading projects and how many projects she will grade in seven hours based on her current pace. Since Ms. Keller has graded five projects in two hours, her grading rate is 5 projects / 2 hours, which simplifies to 2.5 projects per hour. To find out how many projects Ms. Keller will grade in seven hours at this rate, we multiply 2.5 projects/hour by 7 hours, resulting in 17.5 projects.

Therefore, Ms. Keller will grade 17.5 projects in seven hours at a rate of 2.5 projects per hour.

Answer:

(2,1)

Step-by-step explanation:

You are only asking that the graph be drawn and that the minimum be stated. You are not asking how the minimum was obtained (by completing the square).

The graph (using Desmos) shows that the min is at (2,1)

Graphing is a mighty powerful tool, wouldn't you say? It tells you the answer before you have to do one bit of algebra.

Answer:

The Constant of Proportionality is 4.

Step-by-step explanation:

This is because in the table provided,

The correct answer to the question is 4.

I did the quiz and got an A on it.

Hope it helps, I'm on K12 OHVA aswell.

Answer: 8.75

Step-by-step explanation: Divide 166.25 by 19

Mr Rice will purchase 8.75 ft of edging

if we derive equation for this question, then we have:

166.25 = 19Y

Y= [tex]\frac{166.25}{19 }[/tex]

Y= 8.75

To determine the lengths of edging Mr Rice will need to purchase, the total length of edging on the flower beds (166.25) will be divided by the total length of an edging being sold (19) i.e. 166.25 ÷ 19

= 166.25 ÷ 19

= [tex]\frac{166.25}{19 }[/tex]

= 8.75

Therefore, the total length of edging Mr Rice will need to purchase is 9 ft.

The above mathematical expression is a number problem, and was solved with the aid of division.

The term, division, is a basic arithmetic operation which deals with splitting or dividing two or more numerical values into different equal part.

In this case, it could be observed that the significant numbers that were divided are 166.25 and 19, resulting to 8.75. It is also a function of BODMAS (which is an order of operations).

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Answer:

Step-by-step explanation:

Set A: {32, 12, 24, 46, 18, 22, 14}

Mean =24 : Median =22:

Mean>Median hence positive skewed

Set B: {4, 12, 11, 14, 11, 5, 12, 13, 18, 14}

Mean =11.4 and median = 12

Mean <Median, hence negative skewed

Set C: {5, 4, 9, 12, 14, 26, 22, 18}

Mean=13.75 and median = 13

Mean >Median hence positive skewed

Set D: {1, 1, 1, 2, 2, 3, 3, 4, 5, 6}

Mean =2.8 Median = 2.5

Mean>Median Hence positive skewed

Answer:

18

Step-by-step explanation:

8x10= 18

Area of the rectangular cutting board is 80 square inches.

According to the problem,

∴ Area of the rectangle = (8 x 10) square inches

                                 = 80 square inches

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Answer:

The midpoint is (-6,-4)

Step-by-step explanation:

The formula for the midpoint is

midpoint = (x1+x2)/2, (y1+y2)/2

Substituting what we know

               = (-8+-4)/2, (-1+-7)/2

                = -12/2, -8/2

                  = -6, -4

Final answer:

The midpoint M of the line segment joining points S = (-8, -1) and T = (-4, -7) is calculated using the midpoint formula and is found to be M = (-6, -4).

Explanation:

The midpoint M of the line segment joining the points S and T can be found using the midpoint formula. To find the midpoint M between the points S = (-8, -1) and T = (-4, -7), you need to take the average of the x-coordinates and the y-coordinates separately.

The midpoint M's x-coordinate is the average of the x-coordinates of S and T: ((-8 + (-4)) / 2 = -6. Similarly, the midpoint M's y-coordinate is the average of the y-coordinates of S and T: ((-1 + (-7)) / 2 = -4.

Therefore, the midpoint M is located at (-6, -4).

The greatest number he can spend on is $5 since he has $10 he will have $5 reamining.

Answer:

option B

Step-by-step explanation:

[tex]2x^2-4x+16=0[/tex]

We need to solve this equation using quadratic formula

[tex]x= \frac{-b+-\sqrt{b^2-4ac}}{2a}[/tex]

a=2, b= -4, c=16

Plug in the values in the formula

[tex]x= \frac{-(-4)+-\sqrt{(-4)^2-4(2)(16}}{2(2)}[/tex]

[tex]x= \frac{4+-\sqrt{16-128}}{4}[/tex]

[tex]x= \frac{4+-\sqrt{-112}}{4}[/tex]

Simplify the square root. the value of square root (-1) = 'i'

[tex]x= \frac{4+-4i\sqrt{7}}{4}[/tex]

Now we divide by 4

[tex]x= 1+-i\sqrt{7}[/tex]

So there are two complex roots. since the degree of polynomial is 2

Answer:

B

Step-by-step explanation:

I took the test :)

Answer:

x = -9, -3

Step-by-step explanation:

x^2 + 12x + 27 = 0

We need 2 numbers whose product is  + 27 and whose sum is + 12. These are 3 and 9. So the factors are:-

(x + 3)(x + 9)  and this = 0

So (x + 3) = 0  or x + 9 = 0

x = -3 , -9

Answer:

-5 and 7

Step-by-step explanation:

we need to find numbers a and b such that a+b=-2 and ab=-35.

a=5 and b=-7 satisfy both conditions, so our equation can be re-written:

(x + 5)(x-7) = 0

According to the zero-product property, we know that

x+5=0 or x-7=0, which means

x=-5x or x=7

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Answer:

48

Step-by-step explanation:

you need 4 one-fourth cups to make one cup. multiply 12 by 4 and you get 48

By dividing the total amount of soup (12 cups) by the amount of soup per bowl (1/4 cup), we find that Joe can fill 48 bowls.

The student poses a question related to division and unit conversion. To address the student's question, we should calculate how many bowls Joe can fill by dividing the total amount of soup by the amount used for each bowl. Joe has 12 cups of soup and uses 1/4 cup of soup for each bowl. The calculation would be:

Number of bowls = Total cups of soup / Cups of soup per bowl

Number of bowls = 12 cups / 1/4 cup per bowl

Number of bowls = 12 / 0.25

Number of bowls = 48

Therefore, Joe will use 48 bowls to serve the 12 cups of soup, with 1/4 cup of soup in each bowl.

Answer:

(x^2 +6)/2

or  1/2 x^2 +3

Step-by-step explanation:

f(x)= sqrt(2x-6)

y =sqrt(2x-6)

To find the inverse function, we interchange the x and y and solve for y

x = sqrt(2y-6)

Square each side

x^2 = sqrt(2y-6)^2

x^2 = 2y-6

Add 6 to each to each side

x^2 +6 = 2y-6+6

x^2 +6 = 2y

Divide each side by 2

(x^2 +6)/2 = 2y/2

(x^2 +6)/2 = y

The inverse function is

(x^2 +6)/2

or  1/2 x^2 +3

Two functions f(x) and g(x) are inverses if:

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

The solution is:

[tex]g(x) = \frac{1}{2} x^{2} + 3[/tex]

Now we want to find the inverse function to:

[tex]f(x) = \sqrt{2x - 6}[/tex]

Because this is a square root function, we know that the inverse must be a quadratic function, so let's try with something like:

[tex]g(x) = a*x^2 + c[/tex]

Now we can use the first property to get:

[tex]g(f(x)) = a*f(x)^2 + c = x\\\\ = a*\sqrt{2x - 6}^2 + c = x\\\\= a*(2x - 6) + c = x\\\\2*a*x -6*a + c = x[/tex]

Then we must have:

2*a  =1

a = 1/2

And:

-6*a + c = 0

-6*(1/2) + c = 0

-3 + c = 0

c = 4

Then the inverse function is:

[tex]g(x) = \frac{1}{2} x^{2} + 3[/tex]

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ΔABC ≅ ΔDEF

I find it easier to see the congruencies if I write them underneath each other:

∠A ≅ ∠D           [tex]\overline{AB}[/tex] ≅ [tex]\overline{DE}[/tex]

∠B ≅ ∠E            [tex]\overline{BC}[/tex] ≅ [tex]\overline{EF}[/tex]

∠C ≅ ∠F            [tex]\overline{AC}[/tex] ≅ [tex]\overline{DF}[/tex]

[tex]\text{The formula of a midpoint:}\\\\\left(\dfrac{x_1+x_2}{2};\ \dfrac{y_1+y_2}{2}\right)[/tex]

[tex]\text{We have}\\\\\text{endpoint}\ (-2,\ -14)\to x_1=-2,\ y_1=-14\\\\\text{midpoint}\ (-11,\ -20)\\\\\text{Therefore we have the equations:}\\\\\dfrac{-2+x_2}{2}=-11\qquad\text{multiply both sides by 2}\\\\-2+x_2=-22\qquad\text{add 2 to both sides}\\\\\boxed{x_2=-20}\\\\\dfrac{-14+y_2}{2}=-20\qquad\text{multiply both sides by 2}\\\\-14+y_2=-40\qquad\text{add 14 to both sides}\\\\\boxed{y_2=-26}\\\\Answer:\ \boxed{(-20,\ -26)}[/tex]

Final answer:

To find the other endpoint of a line segment when given the midpoint and one endpoint, use the formulas x2 = 2xm - x1 and y2 = 2ym - y1. For the given midpoint (-11, -20) and endpoint (-2, -14), the other endpoint is calculated to be (-20, -26).

Explanation:

To find the coordinates of the other endpoint of a segment when the midpoint and one endpoint are known, the midpoint formula can be used in reverse. For a line segment with endpoints (x1, y1) and (x2, y2) and midpoint (xm, ym), the coordinates of the midpoint are found by the formulas xm = (x1 + x2)/2 and ym = (y1 + y2)/2. If one endpoint is known, say (x1, y1) = (-2, -14) and the midpoint is (xm, ym) = (-11, -20), we can find the other endpoint (x2, y2) by rearranging the formulas: x2 = 2xm - x1 and y2 = 2ym - y1.

Calculating the values we get:

x2 = 2(-11) - (-2) = -22 + 2 = -20

y2 = 2(-20) - (-14) = -40 + 14 = -26

Therefore, the coordinates of the other endpoint are (-20, -26).

Option: C is the correct answer.

                 C.   Vector d

Vector--

We know that the vector is used to represent a quantity which have both magnitude as well as direction.

The vector is represented in a diagram with the help of a line segment with an arrow.

We know that the negative of a vector reverses the direction of the original vector i.e. it directs to the opposite direction of the original vector.

i.e. both have the same starting point but the direction changes.

Here by looking at the figure we observe that the negative of the vector v is the vector d.

Answer:

The more 'chocolatey' chocolate milk is the one prepared by Nell's mom.

Step-by-step explanation:

This problem can be solved by establishing the ratio of chocolate syrup for one ounce of milk in each beverage.

For mom's chocolate milk:

[tex]\frac{30mL}{2ounces} = 15\frac{mL}{ounce}[/tex]

For dad's chocolate milk:

[tex]\frac{65mL}{5ounces} = 13\frac{mL}{ounce}[/tex]

We know that:

15 > 13

So we can conclude that mom's chocolate milk is more 'chocolatey'.

Answer:

[tex]f(x)=33*(1.07)^x[/tex]

Step-by-step explanation:

Let f(x) be our exponential growth function representing growth after x years.

We are asked to find the exponential function that satisfies the given conditions: Initial value = 33, increasing at a rate of 7% per year.

Since an exponential growth function is in form: [tex]y=a*(1+r)^x[/tex], where a= initial value of function and r = growth rate in decimal form.

Given:

a=33  

r=7%.

Let us convert our given rate in decimal form.

[tex]7\text{ percent}=\frac{7}{100}=0.07[/tex]

Now let us substitute our given values in exponential function form:

[tex]f(x)=33*(1+0.07)^x[/tex]

[tex]f(x)=33*(1.07)^x[/tex]

Therefore, the exponential function that satisfies our given conditions will be [tex]f(x)=33*(1.07)^x[/tex].

Answer: ∠R = 137°

Step-by-step explanation:

The opposite angles of a quadrilateral are supplementary (equal to 180°).

Since ∠P and ∠R are opposite angles, their sum is 180°

∠P + ∠R = 180°

y + 3y + 8 = 180

4y + 8 = 180

4y = 172

y = 43

∠R = 3y + 8

     = 3(43) + 8

     = 129 + 8

     = 137

Answer:

12x

Step-by-step explanation:

number 1 is 12x bcuz two x plues ten equals 12x although i did it another way i still got it right just letting you no im working on the second one

The outside angle is equal to the sum of the two opposite inside angles.

So you have:

X + 82 = 2X+10

Subtract 1 X from each side:

82 = X+10

Subtract 10 from each side:

x = 72

Now you can calculate the exterior angle by replacing x with 72:

2x+10 = 2(72) +10 = 144+10 = 154

Answer:

226.50

Step-by-step explanation:

11.50*15=172.5(0)+4.50*12=54.0226.50

Answer:

It’s $226.50

Step-by-step explanation: