If f(x) = 2x2 + 3x and g(x) = x – 2, what is (f + g)(2)?

Answer:

The function is most likely inversely proportional

More input results in less output

For this case we have by definition, that the equation of a line in the slope-intersection form is given by:

[tex]y = mx + b[/tex]

Where:

m: It's the slope

b: It is the cutoff point with the y axis

We need two points through which the line passes to find the slope:

[tex](0, -4)\\(1,0)[/tex]

We found the slope:

[tex]m = \frac {y2-y1} {x2-x1}\\m = \frac {0 - (- 4)} {1-0} = \frac {4} {1} = 4[/tex]

So, the equation is of the form:

[tex]y = 4x + b[/tex]

We substitute a point to find "b":

[tex]-4 = 4 (0) + b\\-4 = b[/tex]

Finally, the equation is:

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

Answer:

Option D

Answer:

Westmoreland County, VA

Answer:

Step-by-step explanation:

Let Waldo's speed = W

Let Ralph's speed = W + 15

A

Waldo's distance = speed * Time

Time = 4 hours.

Speed = w

distance = 4 * w

B

Ralph's speed is W + 15. It's not clear if you need a number. We'll get around to that later.

C

Ralph traveled  4*(W + 15)

D

4w + 70 + 4(W + 15) = d

You really can't get a definite answer to these questions. Even if you knew whether they were heading away from each other or towards each other it wouldn't help.

Answer:

12 matches

Step-by-step explanation:

Hope this helps!

The number of matches that the team needs to win for the team to have a 55% success rate is approximately 16 matches.

A percentage is a number that tells us how much out of 100.

Given that, the tennis team has played 28 matches so far. If they've won 10 matches.

If 28 matches = 100%

10 matches = x %

x = (10×100)/28

x = 35%

So, we are left to determine (55% - 35% = 20%) the remaining 20% success rate;

28 = 100%

x matches = 20%

x = 5.6 matches

Thus, the total number of matches to be won to have a 55% success rate is:

= 10 matches + 5.6 matches

= 15.6 matches

≅ 16 matches

Hence, we can conclude that the total number of matches that the team needs to win for the team to have a 55% success rate is 16 matches.

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Answer:

Step-by-step explanation:

Rewrite the first equation

[tex]-6y=-50-4x\\\\4x-6y=-50[/tex]

Now we have the following system of equations

[tex]4x-6y=-50\\5x-6y=-49[/tex]

To solve the system of equations multiply the first equation by -1 and add it to the second equation

[tex]-1*4x-(-1)*6y=-50*(-1)\\\\-4x+ 6y=50[/tex]

[tex]-4x+ 6y=50[/tex]

        +

[tex]5x-6y=-49[/tex]

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

[tex]x + 0 =1\\\\x=1[/tex]

Now substitute the value of x in any of the two equations and solve for y

[tex]5(1)-6y=-49[/tex]

[tex]5-6y=-49[/tex]

[tex]-6y=-49-5[/tex]

[tex]-6y=-54[/tex]

[tex]y=\frac{54}{6}[/tex]

[tex]y=9[/tex]

The solution is:

[tex](1,\ 9)[/tex]

[tex]\bf \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\ \cline{1-1} V=972\pi \end{cases}\implies 972\pi =\cfrac{4\pi r^3}{3}\implies 2916\pi =4\pi r^3 \\\\\\ \cfrac{2916}{4\pi }=r^3\implies 729=r^3\implies \sqrt[3]{729}=r\implies 9=r \\\\[-0.35em] ~\dotfill\\\\ \textit{surface area of a sphere}\\\\ SA=4\pi r^2\qquad \qquad \implies SA=4\pi (9)^2\implies \boxed{SA=324\pi }[/tex]

Answer:

       =25 %

Step-by-step explanation:

Percent decrease equals (original minus new) / original * 100 %

Percent decrease = (85-64)/ 85 * 100%

                              = 21/85 * 100%

                              =.247058824 * 100%

                              =24.7058824%

       To the nearest percent

                              =25 %

HEYA MATE

YOUR ANSWER IS A.3/10,30%

BECAUSE SHADED SQUARES ARE 6

AND TOTAL SQUARES ARE 20

THAN APPLY THE FORMULA OF PERCENTAGE.

THAN WE GET

30%

[tex]<marquee><i><b>[/tex]THANK YOU

Answer:

"Y intercept is1 "

Step-by-step explanation:

The slope is (-1 - 2)/[8 - (-4)] = -3/12 = -(1/4)

(-1/4) = (y - 2)/(x + 4) => -x - 4 = 4y - 8

-x + 4 = 4y

y = (-1/4)x + 1 so that the y-intercept is 1

Answer:

"Y intercept is1 "

The slope is (-1 - 2)/[8 - (-4)] = -3/12 = -(1/4)

(-1/4) = (y - 2)/(x + 4) => -x - 4 = 4y - 8

-x + 4 = 4y

y = (-1/4)x + 1 so that the y-intercept is 1

Step-by-step explanation:

Answer:

The third option (C) Yes, because there is enough water in the cooler for about 81 cups total.Step-by-step explanation:

The radius and height of the cooler of 6 and 20 inches respectively, can

contain approximately only 81 cups, the correct option is therefore;

The dimensions of the cooler are;

Radius = 6 inches

Height = 20 inches

The possible dimensions of a cup are;

Diameter = 4.4 inches

Height = 5.5 inches

Required:

If each of the 38 players have 2 paper cups filled with water.

Solution;

The volume of the cooler, V₁, is found as follows;

V₁ = π × 6² × 20 = 720·π

The volume of the cooler, V₁ = 720·π in.³

The volume of the paper cup, V₂, is; [tex]V_2 = \dfrac{1}{3} \times \pi \times \left(\frac{4.4}{2} \right)^2 \times 5.5 = 8\frac{131}{150} \cdot \pi[/tex]

The volume of the paper cup, V₂ = [tex]8\frac{131}{150} \cdot \pi[/tex] in.³

The number of cups, n, in the cooler of water is therefore;

The number of cups of water in the cooler ≈ 81 cups

The number of cups required for each of the 38 player to have two full cups is, Cups = 38 × 2 = 76 cups

Given that the water available, (approximately 81 cups) is more than the

number of cups required (76 cups), the correct option is option;

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ANSWER

A. (4,12)

EXPLANATION

The equations are:

[tex]10x +2y = 64...(1)[/tex]

and

[tex]3x - 4y = -36...(2)[/tex]

To eliminate a variable we make the coefficients of that variable the same in both equations.

It is easier to eliminate x.

We multiply the first equation by 2 to get:

[tex]20x + 4y = 128...(3)[/tex]

We add equations (2) and (3).

[tex]3x + 20x + 4y - 4y = - 36 + 128[/tex]

[tex]23x = 92[/tex]

Divide both sides by 23

[tex] \frac{23x}{23} = \frac{92}{23} [/tex]

[tex]x = 4[/tex]

Put x=4 into equation (1).

[tex]10(4)+2y = 64[/tex]

[tex]40+2y = 64[/tex]

[tex]2y = 64 - 40[/tex]

[tex]2y = 24[/tex]

[tex] \frac{2y}{2} = \frac{24}{2} [/tex]

[tex]y = 12[/tex]

The solution is (4,12)

Answer:

13

Step-by-step explanation:

Two factors of -48... that means two numbers which multiplied together give a result of -48, like -6 and 8 for example.

The difference of those two factors is -19.  There not that many possible factors for -48, so if we list them we'll be able to spot a pair with a difference of 19.

A first list of factors for -48 is: -1 and 48, -2 and 24, -3 and 16, -4 and 12, -6 and 8.

We can create another list by inverting the signs: 1 and -48, 2 and -24, 3 and -16, 4 and -12, 6 and -8.

The question says the difference of the two factors is 19...  can you spot in each list a pair of factors having a difference of 19?   I see -3 and 16 and also 3 and -16.

The question also say the one of the greatest absolute value is positive... so that  means it's a pair with +16, not -16.

The pair of factors we're looking for is then -3 and 16. They are factors of -18, they have a difference of 19, and the one with the greatest absolute value is positive.

The sum of -3 and 16 is 13.

Answer:

B

Step-by-step explanation:

A. x^2 - 2x - 8 < 0

(x - 4)(x + 2) < 0

B. x^2 + 2x - 8 < 0

(x + 4)(x - 2) < 0

C. x^2 - 2x - 8 > 0

(x - 4)(x - 2) > 0

D. x^2 + 2x - 8 > 0

(x + 4)(x - 2) > 0

Since roots here are -4 and 2, the answer is either B or D.

When you test a point in the interval between -4 and 2, for example 0, it is negative.

So the answer is B.

Answer:

The answer is [tex]x^2+2x-8<0[/tex]

Step-by-step explanation:

In order to determine the answer, we have two alternatives:

In this case, we use the second option because it is easier to replace a value and solving basic math operations. Also, if we choose a good first value, we will eliminate immediately some options.

We can choose values between -4 and 2. Every time we could choose 0 value, we should do it.

First value: [tex]x=0[/tex]. Replacing:

[tex]-8<0\\-8<0\\-8>0\\-8>0[/tex]

We can see that the two first options are correct, the two last options are wrong.

Second value: [tex]x=-3[/tex]. Replacing:

[tex](-3)^2-2*(-3)-8<0\\9+6-8<0\\7<0\\\\(-3)^2+2*(-3)-8<0\\9-6-8<0\\-5<0[/tex]

We can see that the first option is wrong.

Finally, the correct option is the second one:

[tex]x^2+2x-8<0[/tex]

Answer:

see explanation

Step-by-step explanation:

These are the terms of a geometric sequence with n th term formula

[tex]a_{n}[/tex] = a [tex](r)^{n-1}[/tex]

where a is the first term and r the common ratio

r = [tex]\frac{-48}{64}[/tex] = [tex]\frac{36}{-48}[/tex] = - [tex]\frac{3}{4}[/tex]

the first term a = 64, hence

[tex]a_{n}[/tex] = 64 [tex](-3/4)^{n-1}[/tex]

Answer:

20 rides.

The question:

"There have been two proposals for ticket sales. The first proposes a base fee of $5 for entry into the park and $0.50 per ride. The second plan has no base fee, but charges $0.75 per ride. After How many rides would the cost[s] be equal?"

Step-by-step explanation:

Assume that the two costs become equal after [tex]x[/tex] rides.

The two costs are assumed to be equal. That is:

[tex]5 + 0.50x = 0.75 x[/tex].

Subtract [tex]0.50x[/tex] from both sides of this equation:

[tex]5 = 0.25 x[/tex].

[tex]\displaystyle x = \frac{5}{0.25} = \frac{500}{25} = 20[/tex].

In other words, the two costs become equal after 20 rides.

To maximize profit, the tailors' company should sew 14 skirts, achieving the optimal balance between fabric usage, production hours, and selling constraints.

To maximize profit, the tailors' company should determine the number of skirts and dresses to produce. Let's denote:

- x: Number of dresses to produce

- y: Number of skirts to produce

The constraints are:

1. Fabric usage: [tex]\(4x + 3y \geq 130\)[/tex] (at least 130 yards)

2. Selling constraint: [tex]\(y \leq 3x\)[/tex] (at most three times as many skirts as dresses)

3. Production hours constraint: [tex]\(10x + y \leq 286\)[/tex] (no more than 286 hours)

4. Non-negativity constraint: [tex]\(x \geq 0\)[/tex], [tex]\(y \geq 0\)[/tex]

The profit function to maximize is:

[tex]\[ \text{Profit} = 540x + 180y \][/tex]

We can solve this problem using linear programming. Here's the optimization model:

Objective function:

Maximize 540x + 180y

Subject to:

[tex]\[4x + 3y \geq 130\][/tex]

[tex]\[y \leq 3x\][/tex]

[tex]\[10x + y \leq 286\][/tex]

[tex]\[x \geq 0\][/tex]

[tex]\[y \geq 0\][/tex]

Using a linear programming solver, we can find the optimal values of x and y that maximize profit.

The resulting optimal solution will give us the number of skirts the company should sew to maximize profit.

Answer:

5 years

Step-by-step explanation:

18= 9(1.15)^x

Divide each side by 9

18/9= 9/9 *(1.15)^x

2 = 1.15 ^x

Take the  log on each side

log (2) = log (1.15^x)

log 2 = x log 1.15

Divid each side by log (1.15)

log 2 / log 1.15 = x log 1.15/ log 1.15

log 2 / log 1.15 = x

4.959484455 = x

To the nearest year

5 years

Answer:

False

Step-by-step explanation:

y= mx+b

The x intercept is when y=0

0 = mx +b

Subtract b from each side

-b = mx+b-b

-b = mx

Divide each side by m

-b/m = mx/m

-b/m =x

The x intercept is -b/m

Answer:

D. All real numbers except 0.

Step-by-step explanation:

The figure show a particular case of a hyperbola, which is continuous for all values of x, except the value of x where discontinuity exists. Hence, the domain of the function is all real numbers except 0.

For this case we must find the product of the following expressions:[tex](-2x ^ 2 + x-5) (x ^ 3-3x-4) =[/tex]

We must apply distributive property, that is, multiply each term:

We must bear in mind that:

[tex]+ * - = -\\- * - = +[/tex]

[tex]-2x ^ {2 + 3} + 6x^{2 + 1} + 8x ^ 2 + x^{3 + 1} -3x^{1 + 1} -4x-5x ^ 3 + 15x + 20 =\\-2x ^ 5 + 6x ^ 3 + 8x ^ 2 + x ^ 4-3x ^ 2-4x-5x ^ 3 + 15x + 20[/tex]

If we multiply[tex](x ^ 3-3x-4) (- 2x ^ 2 + x-5)[/tex] we would obtain the same result according to the commutative property of the multiplication:

[tex]a * b = b * a[/tex]

Answer:

[tex]-2x ^ 5 + 6x ^ 3 + 8x ^ 2 + x ^ 4-3x ^ 2-4x-5x ^ 3 + 15x + 20[/tex]

Answer:

The CORRECT answer is  -2x^6 + 7x^4 + 3x^3 – 3x^2 + 11x + 20

Step-by-step explanation:

I go to k12 and all the other answers are incorrect. I had this on my test.  

MY WORK:

-2x^6 + 6x^4 + 8x^3 + x^4 – 3x^2 – 4x – 5x^3 + 15x + 20

= -2x^6 + 7x^4 + 3x^3 – 3x^2 + 11x + 20  

b) Yes, it would be equal because of the rule of the commutative property. (basically, the order in which you multiply won’t matter.)            

Answer:

Step-by-step explanation:

The y-intercept of the function represended in the graph is 4 → (0, 4).

The table C. represents a linear function with a greater y-intercept (0, 5) → 5.

This took a little longer than expected but I hope this helps...                 Please leave a rating and a thanks

Sincerely, Another Brainly User

The given parallelogram is a rectangle when ΔZYX ≅ ΔWXY.

That quadrilateral in which opposite sides are parallel is called a parallelogram.

Thus, a parallelogram is always a quadrilateral but a quadrilateral can or cannot be a parallelogram.

In the given parallelogram WXYZ,

ZX ≅  WY.

For ΔZXY and ΔWXY,

ZX =  WY   (already given)

ZY = WX    (two opposite sides of the parallelogram WXYZ)

XY is the common side

Therefore, ΔZXY ≅ ΔWXY

Now, we can say, ∠ZYX = ∠WXY

For the given parallelogram, ∠ZYX + ∠WXY = 180°

ZYX = ∠WXY = 90°

Hence, the given parallelogram is a rectangle.

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Answer:

positive association

linear association

Step-by-step explanation:

It is said that two variables A and B are related when the distribution of the values of one of the two variables differs according to the values of the other.

That is, when variable A grows then variable B also grows. This is known as positive correlation

When variable A grows then variable B decreases. This is known as negative correlation.

In the scatter plot you may notice that when variable A increases then variable B also increases, in an approximately linear relationship. Therefore it can be said that there is a positive and linear association.

The answer is the fourth and fifth option.

[tex]\bf ~~~~~~\textit{parabola vertex form} \\\\ \begin{array}{llll} \stackrel{\textit{we'll use this one}}{y=a(x- h)^2+ k}\\\\ x=a(y- k)^2+ h \end{array} \qquad\qquad vertex~~(\stackrel{}{ h},\stackrel{}{ k}) \\\\[-0.35em] ~\dotfill\\\\ g(x)=3(x-\stackrel{h}{2})^2+(\stackrel{k}{-5})\qquad \qquad \stackrel{\textit{vertex}}{(2,-5)}[/tex]

Answer:

All are valid

Step-by-step explanation:

Px - 43 = -42x + Q (rearrange)

x = (Q+43) / (P + 42)  <----Substitute options for P & Q into this equation to see which combination gives exactly 1 solution for x

A) P=42, Q = 42; x = (42+43) / (42+42) = 1.011 (only 1 solution = valid)

B) P=43, Q = -42; x = (-42+43) / (43+42) = 0.012 (only 1 solution = valid)

C) P=-43, Q = -43; x = (-43+43) / (-43+42) = 0 (only 1 solution = valid)

D) P=42, Q = 43; x = (42+43) / (42+42) = 1.023 (only 1 solution = valid)

Answer:

Step-by-step explanation:

1 unit = 14 pence

and

1 times 942 = 942 so 14 times 942 = 13,188

therefore

942 units cost £131.88!!hope it help:):)

Final answer:

To calculate the total cost for 942 units at 14p each, multiply the cost per unit by the number of units [tex](942 imes 14p)[/tex]resulting in 13,188p, which is £131.88.

Explanation:

If each unit costs 14p, to find the total cost of 942 units, we need to multiply the cost per unit by the total number of units. The calculation is as follows:

[tex]942 units imes 14p per unit = 13,188p[/tex]

Since there are 100 pence in a pound, we need to convert pence into pounds:

[tex]13,188p \/ 100 = \£131.88\[/tex]

[tex]Therefore, the total cost for 942 units is \£131.88\.[/tex]

ANSWER

C. 28

EXPLANATION

The given expression is

[tex] {x}^{2} - 7x + 10[/tex]

We want to evaluate this function at x=-2.

We just have to substitute x=-2 into the given expression.

In other words, we have to replace x with -2 wherever we see x in the expression

[tex]{( - 2)}^{2} - 7( - 2) + 10[/tex]

We evaluate the exponent to get

[tex]4 - 7( - 2) + 10[/tex]

We multiply next to get:

[tex]4 + 14+ 10[/tex]

We now add to obtain:

[tex]28[/tex]

The correct answer is C

Answer:

x =20

Step-by-step explanation:

We can use proportions to solve

$240         320

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

15                x

Using cross products

240x = 320 * 15

240x =4800

Divide by 240 on each side

240x/240 = 4800/240

x =20

By finding the cost per square yard from Joanna's initial purchase ($16 per sq yd), we can calculate that she can buy 20 square yards of carpet for $320.

To find out how many square yards of carpet Joanna can buy for $320 using the same rate, we first need to determine the cost per square yard based on her $240 purchase. She can buy 15 square yards for $240, so by dividing the total cost by the number of yards, we find the cost per square yard.

Cost per square yard = Total cost / Number of square yards = $240 / 15 sq yds = $16 per sq yd.

Now, we can use the cost per square yard to find out how many square yards she can get for $320. We divide the total amount she's willing to spend by the cost per square yard.

Square yards for $320 = Total amount to spend / Cost per square yard = $320 / $16 per sq yd = 20 sq yds.

Therefore, Joanna can buy 20 square yards of carpet for $320.

Answer: The approximate distance is 14.76

Step-by-step explanation:

You can use the following formula for calculate the distance between two points:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

For the points (3, 5) and (-4, -8) you can identify that:

[tex]x_2=-4\\x_1=3\\y_2=-8\\y_1=5[/tex]

Now you need to substitute these values into the formula.

Therefore, the approximate distance between the given points is:

 [tex]d=\sqrt{(-4-3)^2+(-8-5)^2}\\\\d=\sqrt{(-7)^2+(-13)^2}\\\\d=\sqrt{49+169}\\\\d=\sqrt{218}[/tex]

[tex]d[/tex]≈[tex]14.76[/tex]

Final answer:

To find the distance between the points (3, 5) and (-4, -8), the distance formula is used, resulting in an approximate distance of 14.76 when rounded to the nearest hundredth.

Explanation:

To determine the approximate distance between two points with coordinates (3, 5) and (-4, -8), we use the distance formula which is derived from the Pythagorean theorem. The distance formula is: d = √((x2 - x1)² + (y2 - y1)²). Plugging in the values, we get d = √((-4 - 3)² + (-8 - 5)²) = √(7² + 13²) = √(49 + 169) = √218. The approximate distance is thus the square root of 218, which when calculated gives us approximately 14.76. This result should be rounded to the nearest hundredth, which would give us 14.76 as the final answer.