If f(x) = -x^2 + 6x - 1 and g(x) = 3x^2 - 4x - 1, find (f + g)(x).
O A. (f+g)(x) = 2x2 + 2x - 2
B. (f+g)(x) = 4154x2 + 10x
O C. (f+g)(x) = 2x2 - 10x
O D. (f+g)(x) = 4x2 + 10x + 2

Answer:

4\pm\sqrt{19}

Step-by-step explanation:

Move everything to left side

[tex]x^{2} -8x -3 =0[/tex]

Now to solve this square equation we need to find Descriminant

[tex]D=b^{2} -4ac=64+12=76[/tex]

As Descriminant D is greater than 0 then we have 2 solutions which we can calculate by this formula

[tex]x_{1,2}=\frac{-b\pm\sqrt{D}}{2a} =\frac{8\pm2\sqrt{19}}{2}=4\pm\sqrt{19}[/tex]

Completing the square in mathematics is a technique used to solve quadratic equations by transforming them into a perfect square trinomial form. It helps in finding the roots of the equation more efficiently.

Completing the square involves transforming a quadratic equation into a perfect square trinomial form to solve it. In the case of x^2 - 8x = 3, the steps would include halving the coefficient of x, squaring that value, and adding/subtracting it to both sides of the equation to complete the square.

The solution set for the equation x^2 - 8x = 3 would be {4 + √19, 4 - √19}, as completing the square helps in finding the roots of the quadratic equation.

Completing the square is a helpful technique in mathematics for solving quadratic equations more easily and efficiently.

Answer:

C

Step-by-step explanation:

You are choosing 3 from a total of 12. Order does not matter. So you are working with combinations. The answer symbolically is

12C3

12C3 = 12!/(9!3!)

12C3 = 12 * 11 * 10 * 9!/(9! 3!)

12C3 = 12 * 11 * 10/6

12C3 = 2 * 11 * 10

12C3 = 220

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

We have 12 choices for the first selection, 11 for the second, and 10 for the third. There are 12*11*10 = 1320 permutations. If your teacher was asking about permutations, then you would be done at this point. However, your teacher is asking about combinations. With combinations, order does not matter.

For any group of 3 items, there are 3! = 3*2*1 = 6 ways to arrange this group. This means that we must divide 1320 over 6 to correct for the fact that we overcounted by a factor of 6

In this case,

number of combinations = (number of permutations)/6

number of combinations = 1320/6

number of combinations = 220

More generally, I'm using the connection that

nCr = (nPr)/(r!)

Answer:

Step-by-step explanation:

Identify the first term of the sequence. First terms are -24, 13, 28. Find the matching f(1). There are two choices for each first term.

Then determine the relation of each term to the previous term. In two of the sequences, a factor of 4 is involved. For the sequence starting with -24, the adjacent terms have the same sign, so the factor is +4. For the sequence starting with 28, adjacent terms have alternating signs, so the factor is -4.

For the sequence starting with 13, the second term is 3 times the first, but it is also 26 added to the first. You have to look at the next term to see if the sequence is geometric with a ratio of 3, or arithmetic with a difference of 26. The latter is the case, so the recursive definition will involve addition, not multiplication.

The recursively defined functions are shown above in the order of the given sequences.

Answer: just took the test

Step-by-step explanation:

#plato

Answer:

A. their volumes are equal

Step-by-step explanation:

we know that

The volume of a prism is equal to

[tex]V=BH[/tex]

where

B is the area of the base and H is the height of the prism

therefore

If two distinct prisms have bases of equal area and altitudes of equal length, then

Their volumes are equal

The other options not necessarily must be true

Answer:

x =35.

Step-by-step explanation:

x / 20 = 14 / 8

Cross multiply:

8x = 20*14

8x = 280

x = 35.

The study of proportions in triangles involves understanding similar triangles' corresponding side ratios and how area scales with linear dimensions. The ratios help determine unknown lengths and compare triangles, and the square of the scale factor relates to how area changes.

Understanding Proportions in Triangles

Proportions play a crucial role in the study of triangles, particularly when dealing with similar triangles. Similar triangles have corresponding sides that are in proportion and this concept can be applied in various problems to find unknown lengths or to compare triangles. For instance, if two triangles are similar, then the ratio of their corresponding sides are equal. This can be denoted as a₁ = A₁/A2 or a3 = A3/A2, where A1, A2, and A3 represent the lengths of the sides in one triangle, and a1 and a3 are the proportional sides in the other.

Area scaling is another important concept derived from proportions. If a triangle's sides are scaled by a factor, its area scales by the square of that factor. For example, if the sides of one triangle are twice as long as the sides of a similar triangle, the area of the larger triangle is four times greater, since 2 squared equals 4. This principle can be easily demonstrated by cutting the larger triangle into four smaller triangles identical to the original smaller one, showing that the larger triangle has four times more area as illustrated in fig. (b).

In summary, proportions are crucial when working with similar triangles and understanding how changes in linear dimensions affect the area of a triangle. When comparing triangles, the ratios of corresponding sides and areas can provide valuable insights and are foundational in various applications within geometry.

Answer:

Step-by-step explanation:

The point-slope form of an equation:

[tex]y-y_1=m(x-x_1)[/tex]

m - slope

The slope-intercept form of an equation of a line:

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

m - slope

b - y-intercept

We have the equation of a line:

[tex]y=5x-3[/tex]

therefore the slope m = 5.

Put the value of the slope and the coordinates of the given point (-2, -13) to the equation of a line:

[tex]y-(-13)=5(x-(-2))\\\\y+13=5(x+2)[/tex]

Step-by-step explanation:

A + B + C

2/3 + 5/3 + 9/3

16/3

Or as a proper fraction, 5⅓.

Answer:

c) 15m + 2n

Step-by-step explanation:

8m+4n+7m−2n

Combine like terms

8m+7m +4n−2n

15m +2n

8m + 4n + 7m - 2n

You wouldn't have any trouble with this at all if it said

8monkeys + 4nuts + 7monkeys - 2nuts

First you would look through it to see how many monkeys there are all together.  You would addum up.

8monkeys + 7monkeys = 15 monkeys

Then you would look through it to see how many nuts there are all together, and you would addum up.

4nuts - 2nuts = 2 nuts

Then you would write these results on one line:

15monkeys + 2nuts .

Why should it be a big tough deal when  there's just a bunch of m's and n's ?

First, just look through it to see how many m's there are all together, and addum up:

8 m's + 7 m's = 15 m's

Then just look through it to see how many n's there are all together, and addum up:

4 n's - 2 n's = 2 n's

Then write these results on one line:

15 m + 2 n .

That's choice-c .

Answer:  A . The point where the three angle bisector intersect.

Step-by-step explanation:

The incenter of a triangle is a point constructing the origin of a circle inscribed inside it. The incenter of a triangle is created by taking the intersection of the angle bisectors of the three vertices of the triangle such that it is equidistant from all the vertices of the triangle.

Therefore, the statement which best describes the incenter of a triangle is " the point where the three angle bisector intersect"

Answer:

The point where the three angle bisector intersect.

Step-by-step explanation:

Answer:

See attachment

Step-by-step explanation:

The first function is [tex]y=2x-5[/tex].

The slope is [tex]m=2[/tex] and the y-intercept is [tex]b=5[/tex].

The second equation is [tex]x+3y=27[/tex].

The slope intercept form is [tex]y=\frac{1}{3}x+9[/tex]

The slope is [tex]m=\frac{1}{3}[/tex] and y-intercept is [tex]b=9[/tex]

The graph of these two functions is shown in the attachment.

Answer:

56.0650

Step-by-step explanation:

here is your answer

i hope this is what u want

In this question the number that is in the 4th decimal place is...

56.0649702307

Nine is the 4th decimal, so this is the number that you will determine if it gets rounded or not.

This question wants you to have four decimal places left after you finish rounding

To determine if you round up or stay the same you must look at the number after the asked decimal place. In this case the number after the 4th decimal is 7. A number will round up if this number (7) is 5 or greater. If it is smaller then 5 then the decimal will not round up.

In this case 7 is bigger then 5. This means that the 4th decimal place (9) will round up

56.0650

^^^Since the fourth decimal is 9 when you round up the next number is ten. This means that the rounding will be bumped to the number in front of the 9 and the 9 will simply become zero.

Let me know if this makes sense!

~Just a girl in love with Shawn Mendes

[tex]\bf \cfrac{x^5y^3}{x^2-x-6}\cdot \cfrac{x^2-9}{x^2y^4}\implies \cfrac{x^5y^3}{x^2-x-6}\cdot \cfrac{\stackrel{\textit{difference of squares}}{x^2-3^2}}{x^2y^4} \\\\\\ \cfrac{x^5y^3}{~~\begin{matrix} (x-3) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~(x+2)}\cdot \cfrac{~~\begin{matrix} (x-3) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~(x+3)}{x^2y^4}\implies \cfrac{x^5y^3}{x+2}\cdot \cfrac{x+3}{x^2y^4}[/tex]

[tex]\bf \cfrac{x^5y^3}{x^2y^4}\implies \cfrac{x^5x^{-2}}{y^4y^{-3}}\cdot \cfrac{x+3}{x+2}\implies \cfrac{x^{5-2}}{y^{4-3}}\cdot \cfrac{x+3}{x+2}\implies \cfrac{x^3(x+3)}{y(x+2)}\implies \cfrac{x^4+3x^3}{yx+2y}[/tex]

Answer:

m=2

Step-by-step explanation:

6x - 3y + 6 = 0

Subtract 6x from both sides.

-3y + 6 = -6x

Subtract 6 from both sides.

-3y = -6x - 6

Find the GCF of both sides by, which, in this case, is -3. Divide both sides by the GCF, -3.

y = 2x + 2

Since the formula for linear equations is:

y = mx + b , 2 in the slope.

Answer:

Because the translation is 4 units towards the right, it will be x + 4

and because it is 3 units down, it will be y - 3

(x,y) → (x + 4, y - 3)

Step-by-step explanation:

Final answer:

The translation of a triangle 4 units right and 3 units down is described by the rule (x, y) → (x+4, y-3).

Explanation:

The rule that describes the translation of a triangle 4 units to the right and 3 units down in the coordinate plane can be represented as (x, y) → (x+4, y-3). This represents a translation where each point (x, y) of the triangle is moved to a new point obtained by adding 4 to the x-coordinate and subtracting 3 from the y-coordinate. In terms of transformation geometry, this rule effectively shifts the entire shape without rotating, resizing, or otherwise distorting it.

Answer:

2

Step-by-step explanation:

did it on edge

Option (B) Column 1 has entries honor roll, foreign language, total. Column 2 is labeled not on honor roll. Column 3 is labeled no foreign language. Column 4 is labeled total is the correct answer.

A table of values is a set of ordered pairs usually resulting from substituting numbers into an equation (relation). By using this variable within the equation or in the other function, the value of the other variable or the missing number in the equation can be found easily.

For the given situation,

The diagram shows the two-way table.

Mrs. Vanwhy made a two-way table to show which students made honor roll and which students study a foreign language.

From the data, the table that shows all the required data for Mrs. Vanwhy  to organize her data should consist of honor roll, foreign language, not on honor roll, no foreign language.

Hence we can conclude that option (B) Column 1 has entries honor roll, foreign language, total. Column 2 is labeled not on honor roll. Column 3 is labeled no foreign language. Column 4 is labeled total is the correct answer.

Learn more about table of values here

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Answer:

1308

Step-by-step explanation:

6⋅2+1296

According to PEMDAS, we multiply first

12 +1296

Then we add

1308

For this case we have that the cost for each gallon of gasoline is given by:

[tex]\frac {10.5} {3} = 3.5[/tex]

We have that the total number of gallons is equal to 20.

As the family is going to make only one trip then, the total cost is given by:

[tex]20 * 3.5 = 70[/tex]

Answer:

the family should budget 70 $ to make the one-way trip

The salesman earned $280 in commission last month, which was calculated by taking 40% of the $700 worth of merchandise he sold.

This question is about calculating commission which falls under the topic of percentage calculations in math. The salesman earns a 40% commission on the merchandise he sells. So, to find out how much he earned in commission last month, we need to calculate 40% of the total value of merchandise he sold, which is $700.

To do this, multiply $700 by 40% (or 0.4 in decimal form). That would give you $280. So, the salesman earned $280 in commission last month.

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To find out how much commission the salesman earned, we need to calculate 40% of the $700 worth of merchandise that he sold. The commission rate is expressed as a percentage, which we can also write as a decimal for the purpose of calculation.
First, let's convert the commission rate from a percentage to a decimal. To do this, we divide the percentage by 100:
40% / 100 = 0.40
Now that we have the commission rate as a decimal, we can calculate the commission by multiplying the sales amount by the commission rate.
The calculation is as follows:
Commission = Sales Amount × Commission Rate
Commission = $700 × 0.40
Calculating this gives us:
Commission = $280
Therefore, the salesman earned $280 in commission last month.

Answer:

10.5

Step-by-step explanation:

tan(55°)=15/b

b=15/tan(55°)

=10.5

Answer:

AC ≈ 10.5

Step-by-step explanation:

tan55° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{15}{b}[/tex]

Multiply both sides by b

b × tan55° = 15 ( divide both sides by tan55° )

b = [tex]\frac{15}{tan55}[/tex] ≈ 10.5

Hence b = AC ≈ 10.5 ( to the nearest tenth )

Answer:

2nd choice

Step-by-step explanation:

How you have to is multiply the coordinates by 2 since the scale factor you want to dilate image at is at 2.

That is the pre-image is (x,y) and the image is (2x,2y) per each point.

A(3,5) becomes A'(3*2,5*2)=A'(6,10)

B(6,1) becomes B'(6*2,1*2)=B'(12,2)

C(5,9) becomes C'(5*2,9*2)=C'(10,18)

So 2nd choice.

The coordinates of the dilated triangle are (6,10) , (12,2) and (10,18)

The scale factor is a measure for similar figures, who look the same but have different scales or measures

A' = (3 x 2, 5 x 2) = (6, 10)

B' = (6 x 2, 1x 2) = (12,2)

Similarly C' will be (10 , 18)

So the coordinates of the dilated triangle are (6,10) , (12,2) and (10,18)

So option B is correct.

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Answer:

See below.

Step-by-step explanation:

Increases by 25% :- it is 80 * 1.25 = 100.

100 decreased by 25% = 100 * 0.75

= 75.

Answer:

75

Step-by-step explanation:

We are given that 80 is increased by 25% and then decreased by 25% so we are to find the final value.

Increase of 25% in 80 = 25% of 80

= 25/100 × 80

= 20

So our new value after 25% increase = 80 + 20 = 100

Now this new value is decreased by 25% = (100 - 25)% of 100

= 75/100 × 100

= 75

Answer:

1

Step-by-step explanation:

Combine like terms first by subtracting 6x from both sides.

[tex]6x+2=9x-1\\2=3x-1[/tex]

Next, add 1 to both sides.

[tex]2=3x-1\\3=3x[/tex]

Finally, divide both sides by 3.

[tex]3=3x\\1=x[/tex]

Answer:

Flip a fair coin. It has a 50% chance of landing heads up and a 50% chance of landing tails up. Therefore, the person who will do the dishes will be chosen at random.

Answer:

B: Put each person's name on a separate piece of paper in a bag.  Randomly draw a name. The person whose name is chosen does the dishes.

D: Roll a number cube. If the number rolled is even, Alexa does the dishes. If the number is odd, Bart does the dishes.

Step-by-step explanation:

I got it right:)

Answer:

She has 250 dollars left

Step-by-step explanation:

The first lawn she gained 25 dollars

+25

Then she gained 75 dollars

+25 +75=100

She mowed lawns for 5 weeks making the same amount 5 weeks at 100 dollars

5*100 = 500

She earned a total of 500 dollars

She spent 250 dollars

500-250 = 250

She has 250 dollars left

Answer:

C.

Step-by-step explanation:

If equal changes in x result in equal changes in y, then the function is linear.

A. Are the changes from (2, 4) to (4, 1) and from (4, 1) to (6, 11) equal?

The change from (2, 4) to (4, 1):

When x changes from 2 to 4, the change is 4 - 2 = 2.

y changes from -9 to 1; the change is 1 - (-9) = 10

The change from (4, 1) to (6, 11):

When x changes from 4 to 6, the change is 6 - 4 = 2.

y changes from 1 to 11; the change is 11 - 1 = 10

For a change in x of 2, the change in y is 10 in both cases. This function is linear.

B. Are the changes from (2, -14) to (4, -16) and from (4, -16) to (6, -18) equal?

The change from (2, -14) to (4, -16):

When x changes from 2 to 4, the change is 4 - 2 = 2.

y changes from -14 to -16; the change is -16 - (-14) = -2

The change from (4, -16) to (6, -18):

When x changes from 4 to 6, the change is 6 - 4 = 2.

y changes from -16 to -18; the change is -18 - (-16) = -2

For a change in x of 2, the change in y is -2 in both cases. This function is linear.

C. Are the changes from (2, 0) to (4, 6) and from (4, 6) to (6, 16) equal?

The change from (2, 0) to (4, 6):

When x changes from 2 to 4, the change is 4 - 2 = 2.

y changes from 0 to 6; the change is 6 - 0 = 6

The change from (4, 6) to (6, 16):

When x changes from 4 to 6, the change is 6 - 4 = 2.

y changes from 6 to 16; the change is 16 - 6 = 10

For a change in x of 2, the change in y is 6 in one case and 10 in the other case. This function is not linear.

D. Are the changes from (2, -9) to (4, -6) and from (4, -6) to (6, -3) equal?

The change from (2, -9) to (4, -6):

When x changes from 2 to 4, the change is 4 - 2 = 2.

y changes from -9 to -6; the change is - 9 - (-6) = -3

The change from (4, -6) to (6, -3):

When x changes from 4 to 6, the change is 6 - 4 = 2.

y changes from -6 to -3; the change is -6 - (-3) = -3

For a change in x of 2, the change in y is -3 in both cases. This function is linear.

Answer:

25 nickels and 23 quarters

Step-by-step explanation:

The smallest possible integer solution is 23 nickels and 25 quarters.

23×0.05 + 25×0.25 = 1.15 + 6.25 = $7.40.

That's already over $7.00.

We can't solve the problem as stated unless we use fractional numbers of coins, and that's impossible.

Assume the correct ratio is 25/23

Let n = number of nickels

and q = number of quarters. Then we have two conditions.

(1)                                n/q = 25/23

(2)             0.05n + 0.25q = 7

(3)                                    n = (25/23)q     Multiplied (1) by q

(4) 0.05(25/23)q + 0.25q = 7                  Substituted (3) into (1)

          0.05435q + 0.25q = 7                  Simplified

                          0.3043q = 7                  Combined like terms

(5)                                   q = 23              Divided each side by 0.3043

                                 n/23 = 25/23         Substituted (5) into (1)

                                       n = 25              Divided each side by 23

There are 25 nickels and 23 quarters.

Check:

(1) 25/23 = 25/23     (2) 0.05×25 + 0.25×23 = 7

                                                     1.25 + 5.75 = 7

                                                                     7 = 7

OK.  

Answer:

1,100

Step-by-step explanation: The hundreds place is the second 1 from the left. That number will stay as it is or go up one number, based on the number to its right, which in this case is a 3. If the 3 is the number 5 or larger, then the 1 would round up to a 2, but since the 3 is less than 5, the 1 stays a 1. All numbers to the right of the place value you are rounding to become zeros.

Rounding 1137 to the nearest hundred:

Answer:

15

Step-by-step explanation:

Population size= 2107+903+1505+1499

                        = 6014

Calculating the sample of ward B by using the stratified random sampling formula:

Stratified Random Sample, np= ( Np / N ) * n

where

np= pth stratum  sample size

Np= pth stratum  population size

N = population  size

n = sample size

Stratified Sample (ward B) = 100 / 6014 * 903 = 15 !

Answer:

34 cans. If you set it up as ratios (5/2.85 = x/19.38), make the number of cans you need to know "x" and solve for x.

Final answer:

To determine how many cans of baked beans can be bought for $19.38, divide $19.38 by the cost of each can, which is found by dividing the total cost of 5 cans by 5. The result is that you can buy 34 cans of baked beans for $19.38.

Explanation:

To find out how many cans of baked beans can be bought for $19.38, we need to determine the cost of each can. Given that 5 cans of baked beans cost $2.85, we can divide the total cost by the number of cans to find the cost of each can: $2.85 ÷ 5 = $0.57 per can.

Next, we divide the amount of money we have, $19.38, by the cost of each can to find the number of cans we can buy: $19.38 ÷ $0.57 = 34 cans.

So, for $19.38, we can buy 34 cans of baked beans.