What is (f + g)(x)?
f(x) = -3x² + 3
g(x) = −3x

In Week 1,

Salesman C got larger paycheck than Salesman A and Salesman B.

Mathematically, an equation can be defined as a statement that supports the equality of two expressions, which are connected by the equals sign “=”. For example, 2x – 5 = 13.

Here,

2x – 5 and 13 are expressions

The sign that connects these two expressions is “=”.

In algebra, an equation is a condition on a variable. It is satisfied only for a definite value of the variable. That means, the equation 2x – 5 = 13 is satisfied only for x = 9.

Given,

Commission of salesman A per sale = $65

Commission of salesman B per sale = $40

Commission of salesman C per sale = $0

Salary of salesman A per week = $0

Salary of salesman B per week = $300

Salary of salesman C per week = $900

No. of sales × commission + salary = total earning

In week 1.

Earning of A

11 × $65 + $0 = $715

Earning of B

14 × $40 + $300 = $860

Earning of C

16 ×$0 + $900 = $900

In week 2.

Earning of A

14 × $65 + $0 = $910

Earning of B

15 × $40 + $300 = $900

Earning of C

12 ×$0 + $900 = $900

In week 3.

Earning of A

16 × $65 + $0 = $1040

Earning of B

13 × $40 + $300 = $820

Earning of C

111 ×$0 + $900 = $900

By the above calculation Salesman C received $900 in week 1 which is greater than Salesman A and Salesman B.

In week 2 and week 3 his paycheck is smaller than both of the other salesman.

Hence, Salesman C  received larger paycheck than both of the other salesmen in Week 1.

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The inequality to find the cost of the pizza they should order is c ≤ 14. The cost is at most $14.

Inequalities are simply created through the connection of two expressions. In this case, it should be noted that the expressions in an inequality are not always equal. Inequalities implies that the expressions are not equal. Here, they are denoted by the symbols ≥ < > ≤.

Since Trey and three of his friends are ordering a pizza and they want to spend at most $3.50 per person. An inequality to find the cost of the pizza they can order is:

c ≤ (3.50 × 4)

c ≤ 14

The cost will be at most $14.

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Answer: B

Step-by-step explanation: To get the boys part of the ratio you will have to subtract 30 students and 14 students that are girls because all together there are 30 students and since we only know that 14 of them are girls that leaves the rest of the students boys. 30 - 14 = 16  so now we know how many boys there are. 16:14 can be reduced by 2 and that equals to 8:7.

Hope this helps!

The ratio of boys to girls is equal to: B. 8 :7

Given the following data:

To calculate the ratio of boys to girls:

First of all, we would determine the number of boys in the art class by subtracting the number of girl students from the total number of students in this class.

[tex]Total \;students = boys + girls\\\\30=boys + 14\\\\Boys =30-14[/tex]

Boys = 16 students.

For the ratio:

[tex]B:G=16:14[/tex]

Dividing by 2, we have:

[tex]B:G=8:7[/tex]

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Answer:

check: 2,3,5,8

Step-by-step explanation:

Answer:

6 chairs

Step-by-step explanation:

The break even Point on gaming chairs can be expressed as :

Revenue = Cost

Revenue, R = 50x

Cost, C = 30x + 120

R = C

50x = 30x + 120

50 - 30x = 120

20x = 120

Divide both sides by 20

20x/ 20 = 120 / 20

x = 6

Hence, 6 chairs must be sold for the company to break even.

Answer:660,000

Step-by-step explanation:

principle= 24,000

rate=5.5%

time = 5years

simple interest= P×R×T

. =24000×5.5×5

. = 660,000

Answer:

b.

Step-by-step explanation:

The age of your uncle is modeled by:

y = 2 + 3*x

Evaluating it, we can see that when you are 12 years old, your uncle will be 38 years old.

Let's define the variables: y as your uncle's age and x as your age.

Here we know that your uncle is 2 years older than 3 times your age, so we can write the linear equation:

y = 2 + 3*x

This is the equation we needed to find.

b) If you are 12 years old, then we can write x = 12 in the equation above, then we will get:

y = 2 + 3*12

y = 2 + 36

y = 38

That's the age of your uncle.

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The expression 14x⁴y³ - 42x³y⁴ is rewritten to 14x³y³(x - y)

An algebraic expression can be described as a mathematical expression that is made up of terms, coefficients, variables, factors and constants.

They are also made up of some arithmetic operations, such as;

From the information given, we have the algebraic expression;

14x⁴y³ - 42x³y⁴

Now, factor the common numbers, we have;

14(x⁴y³ - 3x³y⁴)

Factor the common variables, we get;

14x³y³(x - y)

Hence, the expression is 14x³y³(x - y)

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Answer:

No

Step-by-step explanation:

The slopes of perpendicular lines must always be the negative reciprocal of each other. If one slope is negative, for the other to be perpendicular to it, it must be positive, and vise versa.

Answer:

No

Step-by-step explanation:

Interesting question. Subtle.

The formula for two lines to be perpendicular is m1 * m1 = -1 That means that two lines cannot be minus -- only 1 of them can be. The reason is that if both were minus when multiplied together would give a positive result -- not minus one. For example, suppose you have

y = x + 2  

y = 2x + 3.

These 2 lines will cross and they are not parallel, but neither are they perpendicular. I'm not going to solve this to find out where they cross -- that's not what you are asking.

Now suppose you have two other lines

y = - 2x + 3

y = 1/2 x + 1

These two lines should be perpendicular

-2 * 1/2 =  - 1 which is the condition of perpendicular.

Separate graphs have been uploaded to help you understand.

Answer:

7) perpendicular

8) perpendicular

Step-by-step explanation:

If the equations are in the form:

y = mx + b

(they all are in this form in these questions)

the m, the number in front of the x, is the slope.

If the slopes are the "negative reciprocals" (opposite signs and flipped over from each other) of each other, then the lines are perpendicular.

You can also do a quick check by, if the m values are multiplied together you should get -1.

1/3 • - 3 = -1

1 • -1 = -1

1/3 and -3 have opposite signs and are reciprocals (flipped over)

1 and -1 are opposite signs. It isn't very obvious maybe that they are reciprocals, but they are. Like 1/1 flipped over is 1/1.

The steps to solve the equation  (5y - 1)/2 = 7 are assigned and attached

The expression in the problem is (5y - 1)/2 = 7

Clearing the fraction

The fraction is cleared by applying the Multiplication Property of Equality

(5y - 1)/2 = 7

5y - 1 = 14

Adding 1 to both sides of the equation is done using Addition Property of Equality

5y - 1 + 1 = 14 + 1

5y = 15

Making y the subject of formula Division Property of Equality is applied

5y / 5 = 15 / 5

y = 5

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Answer: 17

Step-by-step explanation:

Answer:

x = 17°

Step-by-step explanation:

The given angles are,

→ 6x + 8

→ 4x + 2

Now we have to,

→ find the required value of x.

Forming the equation,

→ (6x + 8) + (4x + 2) = 180°

{As two angles in a straight line is 180°}

Then the value of x will be,

→ (6x + 8) + (4x + 2) = 180°

→ 6x + 4x + 8 + 2 = 180°

→ 10x + 10 = 180°

→ 10x = 180° - 10

→ x = 170/10

→ [ x = 17° ]

Hence, the value of x is 17°.

The Diwali occurred on 0.408 or 40.8% of the year in 2017.

To find the fraction of the year that Diwali occurred in 2017, we need to divide the number of days between Diwali and the start of the year by the total number of days in the year.

Diwali occurred on Thursday, October 19, 2017. The start of the year 2017 is January 1, 2017 which is a Sunday.

There are 365 days in a non-leap year. Since 2017 is not a leap year, there are 365 days in that year.

So the fraction of the year that Diwali occurred in 2017 can be calculated as: (days between Diwali and the start of the year) / (total days in the year) = ( 19 + 31 + 30 + 31 + 30 + 19 ) / 365 = (148) / 365 = 0.408

So, the Diwali occurred on 0.408 or 40.8% of the year in 2017.

Therefore, Diwali occurred on 0.408 or 40.8%

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Answer:

See below

Step-by-step explanation:

This is a parabola in vertex form where the vertex is (-2,7) and the parabola is vertically compressed by a factor of 3.

A right triangle with congruent legs and acute angles is an Isosceles Right Triangle.

A special right triangle is a right triangle that has a consistent characteristic that facilitates calculations on the triangle or for which straightforward formulas are available.

Angles in a right triangle, for instance, might create straightforward connections like 45°-45°-90°. An "angle-based" right triangle is what this is. When the side lengths of a right triangle form ratios of whole numbers, such as 3:4:5, or other unusual numbers, like the golden ratio, the triangle is said to be "side-based."

Without using more complex techniques, one can rapidly determine different lengths in geometric problems by understanding the relationships between the angles or side ratios of certain particular right triangles.

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The fourth point is (-6.5, -14)

Vertices of a parallelogram?

The three vertices you've provided are (-7,-6), (6,3), and (4,-4). To find the fourth vertex of a parallelogram, we can use the fact that opposite sides of a parallelogram are parallel and congruent, meaning they have the same length and the same slope.

The three vertices you've provided are (-7,-6), (6,3), and (4,-4). To find the fourth vertex of a parallelogram, we can use the fact that opposite sides of a parallelogram are parallel and congruent, meaning they have the same length and the same slope.

One way to find the fourth vertex is to use the vector that connects one vertex to another. The vector from (-7,-6) to (6,3) is (13,9), and from (6,3) to (4,-4) is (-2,-7)

If we use the vector which is opposite of (-2,-7) that is (2,7) and add it to the third point (4,-4) , we will get the fourth point.

(2,7) + (4,-4) = (6,3)

so the fourth point is (6,3)

Another way is to find the midpoint of the diagonal of the parallelogram which are (-7,-6) and (4,-4) and then add the vector which is opposite of (6,3) to (4,-4) that is (-6,-9) which is also the vector from (6,3) to (4,-4)

Midpoint of (-7,-6) and (4,-4) = (-0.5,-5)

(-0.5,-5) + (-6,-9) = (-6.5, -14)

Hence, the fourth point is (-6.5, -14)

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Check the picture below, so the parabola looks more or less like so, with a vertex at (0 , 5) and a "p" distance of negative 2 units, since it's opening to the left, so

[tex]\textit{horizontal parabola vertex form with focus point distance} \\\\ 4p(x- h)=(y- k)^2 \qquad \begin{cases} \stackrel{vertex}{(h,k)}\qquad \stackrel{focus~point}{(h+p,k)}\qquad \stackrel{directrix}{x=h-p}\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ \stackrel{p~is~negative}{op ens~\supset}\qquad \stackrel{p~is~positive}{op ens~\subset} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\begin{cases} h=0\\ k=5\\ p=-2 \end{cases}\implies 4(-2)(~~x-0~~) = (~~y-5~~)^2\implies {\Large \begin{array}{llll} -8x=(y-5)^2 \end{array}}[/tex]

Answer:

m∠ABC = 55°

Step-by-step explanation:

m∠BAC = 50° because ∡BAC ≅ ∡DCA

since there are 180° in ΔABC the m∠ABC = 180-(75+50) which equals 55°

Answer:

11.7

Step-by-step explanation:

use the distance formula known as pythagorem theorem and plug in the x and y values.

Here is your answer :

Answer 1 :

Volume of the Cylinder = πr²h

Therefore, The Volume of the Cylinder is 50.27 Feet

By Rounding, 50 Units/Feet

Answer 2 :

So, volume is always cubed since you have l x w x h.

A cubic ft is 12 in x 12 in x 12 in = 1728 in3.

35328.78/1728 = 20.44  

20.44 x 7.48 = 152.89

About 153 gallons

HOPE IT HELPS

its a virus dont  fall for it

Step-by-step explanation:

Answer:

x=10

Step-by-step explanation:

a^2=b(b+c)

12^2=8(8+x)

144=64+8x

-64 -64

______

80=8x

x=10

Since you're feeding it three times a day, you should feed your goat 0.74 ounces per feeding.

The act of feeding involves giving a baby a mother's breast milk, either directly from the breast or by expressing (pump-out) the milk from the breast and giving it to the baby in a bottle.

In the traditional method of measurement, a pound is used to measure weight. In the conventional system, ounces are smaller weight units that are defined in terms of pounds. 1 pound Equals 16 ounces.

Goats typically need around 2% to 4% of their body weight in feed per day. If your goat weighs 7 pounds, and you want to feed it 2% of its body weight per day, you would need to feed it 0.14 pounds of food per day, or 2.24 ounces per day. Since you're feeding it three times a day, you should feed it 0.74 ounces per feeding.

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Answer:

looool

Step-by-step explanation:

Answer:

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

15 inches of wire costs 90 cents, then 1 inch of wire costs:

The length of wire for 72 cents:

Answer:

sry i thought i knew how to do it but I can't remember

Step-by-step explanation:

Answer:

(x + 5)² + 10

Step-by-step explanation:

Given

x² + 10x + 35

To complete the square

add/ subtract ( half the coefficient of the x- term)² to x² + 10x

x² + 2(5)x + 25 - 25 + 35

= (x + 5)² + 10