Find the value of f(–3) and g(3) if f(x) = –6x + 3 and g(x) = 3x + 21x–3.

f(–3) = 21
g(3) = 9.78

f(–3) = –18
g(3) = –9.78

f(–3) = –3
g(3) = 30.04

f(–3) = 15
g(3) = 8.22

B is correct. I’ve noticed that you’ve posted a lot of questions like this, so here’s how I remember it. Soh-Cah-Toa

Soh stands for Sin=Opposite (the side opposite to the angle) over hypotenuse (the side opposite to the right angle)

Cah stands for Cos=Adjecent (the side next to the angle that is not the hypotenuse) over the hypotenuse

Toa stands for Tan=opposite over adjacent

Good luck! Hope I helped you understand.

Answer:

sin of 52 is 0.98662759204

cos of 47 is 0.99233546915

Step-by-step explanation:

Answer:

90

Step-by-step explanation:

10x - x = 81

9x = 81

x = 9

larger number = 10 x 9 = 90

For this case we have that "x" is the variable that represents the smallest number to find. Let and the variable that represents the largest number, then:[tex]y = 10x\\y-x = 81[/tex]

Substituting the first equation in the second:

[tex]10x-x = 81\\9x = 81\\x = \frac {81} {9}\\x = 9[/tex]

So, the biggest number is:

[tex]y = 10 * 9 \\y = 90[/tex]

Answer:

10x

90

ANSWER

[tex]16\pi \: sq.in[/tex]

EXPLANATION

The area of a sector is calculated using the formula,

[tex]Area = \frac{arc \: measure}{360 \degree} \times \pi {r}^{2} [/tex]

The arc measure is given as 45°

The radius of the circle is 8 inches.

We substitute to obtain,

[tex]Area = \frac{45 \degree}{360 \degree} \times \pi \times {8}^{2} [/tex]

[tex]Area = \frac{1}{4} \times 64\pi = 16\pi[/tex]

The answer is:

The correct option is the second option:

[tex]SectorArea=8\pi in^{2}[/tex]

To answer the question, we need to calculate the total area of the circle (which corresponds to 360°) and then, calculate the equivalent area to the sector of the arc that measures 45°

Calculating the total area, we have:

[tex]TotalArea=\pi radius^{2} \\\\TotalArea=\pi 8^{2} =64\pi in^{2}[/tex]

Now, we need to consider that the calculated area (total area) correspondes to all 360° that conforms the interior angle of a circle, now, if we want to calculate the area that represents a sector of the arc that measures 45°, we have to use the following formula:

[tex]SectorArea=\frac{360\°}{45\° }*TotalArea\\\\SectorArea=\frac{45\°}{360\° }*64\pi in^{2}=\frac{1}{8} *64\pi in^{2}\\\\SectorArea=8\pi in^{2}[/tex]

Hence, we have that the correct option is the second option:

[tex]SectorArea=8\pi in^{2}[/tex]

Have a nice day!

Step-by-step explanation:

[tex](4x - 2).6(2x + 7) \\ = (4x - 2)(12x + 42) \\ = 48 {x}^{2} + 168x - 24x - 84 \\ = 48 {x}^{2} + 144x - 84[/tex]

then

[tex]a = 48 \\ b = 144 \\ c = - 84[/tex]

Answer:

(1, 3)

Step-by-step explanation:

If the translation is ...

(3, 2) + (a, b) = (4, 5)

Then we can find (a, b) by subtraction:

(4, 5) -(3, 2) = (a, b) = (4-3, 5-2) = (1, 3)

Not the image of point (0, 0) will be ...

(0, 0) + (a, b) = image

(0, 0) + (1, 3) = (0+1, 0+3) = (1, 3)

The image of the point is (1, 3).

Answer:

  a.  {(5, 0.6)}

Step-by-step explanation:

A graph is a useful tool. It can help you find that the set of points that satisfies both functions is ...

  {(5, 0.6)}

_____

Comment on the graph

Strictly speaking, the points connecting the dots of the second function are not part of the function. They are there simply to provide a visual aid in locating the points. As we see, the line goes through point (5, 0.6) exactly.

Answer:

C. 7  1/2 pounds; 120 ounces

Step-by-step explanation:

I'll assume you wanted to write each loaf weighs 1 and 1/4 (1.25) pounds  and not 114 pounds... since that makes sense considering the choices for answer.

So, to get the total weight of the 6 loafs, we multiply by 6 the weight of one...

TP = 6 * 1.25 = 7.5 or 7 1/2 pounds

To get that in ounces, we just have to remember there are 16 ounces per pound... so

TO = 7.5 lbs * 16 ounces/lbs = 120 ounces

Answer:

  b ≈ 3.1

Step-by-step explanation:

The law of sines tells you ...

  b/sin(B) = c/sin(C)

Here, you have to find angle C based on the sum of the angles of a triangle being 180°.

 C = 180° - A - B = 180° - 69° - 32° = 79°

Multiplying the above law of sines equation by sin(B), you have ...

  b = c·sin(B)/sinc(C) = 5.7·sin(32°)/sin(79°) ≈ 3.07707

  b ≈ 3.1 . . . . . rounded to tenths

Answer:

[tex]\displaystyle 3,1 ≈ b[/tex]

Step-by-step explanation:

First, find [tex]\displaystyle m∠C,[/tex]accourding to the Triangle-Sum Theorem:

[tex]\displaystyle 180° = 32° + 69° + m∠C \hookrightarrow 180° = 101° + m∠C; 79 = m∠C[/tex]

Now that we have all three angles, we can solve for edge b

[the second edge], using the Law of Sines:

[tex]\displaystyle \frac{c}{sin∠C} = \frac{b}{sin∠B} = \frac{a}{sin∠A} \\ \\ \frac{5,7}{sin\:79°} = \frac{b}{sin\:32°} \hookrightarrow 3,0770743283... = \frac{5,7sin\:32°}{sin\:79°} \\ \\ 3,1 ≈ b[/tex]

I am joyous to assist you at any time.

Answer:

D)

y > x + 4

y ≥ -3x - 2

Step-by-step explanation:

Blue line's boundary is above the line and dotted (>) so the equation: y > x + 4

Red line's boundary is above the line and solid (≥) so the equation: y ≥ -3x - 2

Answer

D)

y > x + 4

y ≥ -3x - 2

Answer:

D

Step-by-step explanation:

Answer:

in the US, yes

in some other English-speaking countries, no

Step-by-step explanation:

"Standard form" depends on where you live. In the UK, the "standard form" of a quadratic equation is what is called "vertex form" in the US. That form is ...

3(x +1/3)^2 +29/3 = 0

In the US, the equation you show is in standard form.

[tex]\bf \textit{Double Angle Identities} \\\\ cos(2\theta)= \begin{cases} cos^2(\theta)-sin^2(\theta)\\ \boxed{1-2sin^2(\theta)}\\ 2cos^2(\theta)-1 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ cos(2\theta )+sin^2(\theta )=0\implies \boxed{1-2sin^2(\theta)}+sin^2(\theta )=0 \\\\\\ 1-sin^2(\theta )=0\implies 1=sin^2(\theta )\implies \pm\sqrt{1}=sin(\theta ) \\\\\\ \pm 1=sin(\theta )\implies sin^{-1}(\pm 1) = \theta \implies \theta = \begin{cases} \frac{\pi }{2}\\\\ \frac{3\pi }{2} \end{cases}[/tex]

To solve the equation cos(2θ) + sin^2(θ) = 0 using a double- or half-angle formula, rewrite the equation and combine like terms to simplify.

To solve the equation cos(2θ) + sin^2(θ) = 0 using a double- or half-angle formula, we can rewrite the equation as:

2cos^2(θ) - 1 + sin^2(θ) = 0

Using the identity sin^2(θ) = 1 - cos^2(θ), we can substitute and simplify:

2cos^2(θ) - 1 + (1 - cos^2(θ)) = 0

Combining like terms, we have:

-cos^2(θ) + cos^2(θ) = 0

This simplifies to:

0 = 0

Since 0 = 0 is a true statement, the equation is satisfied for all values of θ within the interval [0, 2π).

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Answer:

No real solution

Step-by-step explanation:

There is no perfect squares in 50

ANSWER

[tex]x = \pm5\sqrt{2} [/tex]

EXPLANATION

The given equation is:

[tex]50 - {x}^{2} = 0[/tex]

Group the constant term to get:

[tex]- {x}^{2} = 0 - 50[/tex]

[tex] - {x}^{2}=- 50[/tex]

[tex]{x}^{2}=50[/tex]

Take square root to get:

[tex]x = \pm \sqrt{50} [/tex]

We simplify further to remove the perfect square.

[tex]x = \pm \sqrt{25 \times 2} [/tex]

[tex]x = \pm \sqrt{25} \times \sqrt{2} [/tex]

[tex]x = \pm5\sqrt{2} [/tex]

Answer:

  d. Distributive property

Step-by-step explanation:

The Distributive property of multiplication over addition is what allows you to multiply each of the terms in parentheses by the factor outside parentheses. It tells you ...

  a(b +c) = ab + ac

It works both ways, also allowing you to remove a common factor to outside parentheses.

Answer:

-7x+3y+3

Step-by-step explanation:

(4-5+4)=3

(-2x-5x)=-7x

(-4y+7y)=3y

For this case we must simplify the following expression:

[tex]4-5-2x-4y + 4-5x + 7y[/tex]

We must combine similar terms, taking into account that equal signs are added and the same sign is placed, while different signs are subtracted and the sign of the greater is placed:

[tex]4-5 + 4-2x-5x-4y + 7y =\\3-7x + 3y[/tex]

Answer:

[tex]3-7x + 3y[/tex]

Check the picture below.

make sure your calculator is in Degree mode.

Answer:

Find the attached

Step-by-step explanation:

To graph the given function, we would need to obtain pairs of points (x, f(x)). We can let x be;

-5, -4, -3, 3, 4, 5

we simply substitute each value of x in the given function to obtain the value of the function corresponding to the given x value;

when x = -5, f(-5) =  |-5+2| - 3 = 0

when x = -4, f(-4) =  |-4+2| - 3 = -1

when x = -3, f(-3) =  |-3+2| - 3 = -2

when x = 3, f(3) =  |3+2| - 3 = 2

when x = 4, f(4) =  |4+2| - 3 = 3

when x = 5, f(5) =  |5+2| - 3 = 4

The graph of the function is as shown in the attachment below.

Answer:

Find the attached

Step-by-step explanation:

To graph the given function, we would need to obtain pairs of points (x, f(x)). We can let x be;

-5, -4, -3, 3, 4, 5

we simply substitute each value of x in the given function to obtain the value of the function corresponding to the given x value;

when x = -5, f(-5) =  |-5+2| - 3 = 0

when x = -4, f(-4) =  |-4+2| - 3 = -1

when x = -3, f(-3) =  |-3+2| - 3 = -2

when x = 3, f(3) =  |3+2| - 3 = 2

when x = 4, f(4) =  |4+2| - 3 = 3

when x = 5, f(5) =  |5+2| - 3 = 4

Answer:

$33.00

Step-by-step explanation:

You find out how much the sale price is by subtracting 25% of 40 from 40:

40 - [(.25)(40)] and that equals 30.  So the sale price is $30.  Now if the tax is 10% (.1 in decimal form), we find the total cost by adding .1(30) to 30:

30 + [(.1)(30)] which is $33

Answers:

#1: A

#2:C

#4:D

First put your numbers in order from least to greatest (These are negative numbers so that means that the smallest number is the one farthest away from zero)

-49, -43, -39, -18, -14, -12, -9

Mean is adding all the numbers together and dividing the sum by how many numbers there are in the data set

-49 + (-43) + (-39) + (-18) + (-14) + (-12) + (-9) = -184

There are seven numbers so divide -184 by 7:

-184 ÷ 7 ≈ 26.29

Median is the number in the middle. Take away the smallest number and the biggest number on each layer until you get to the middle

-49, -43, -39, -18, -14, -12, -9

       -43, -39, -18, -14, -12

              -39, -18, -14

                      -18 <-------------------Median

Mode is whatever number appears the most often in the data. In this case all the numbers appear only once so there is no mode

Range is subtracting the largest number by the smallest number

-9 - (-49) = 40

2. Data in order

13, 13, 13, 15, 21, 23, 25, 37

Outlier is the number that is a number that is rather far from the other number in the data

a. In this case the outlier is 37

b. 13 + 13 + 13 + 15 + 21 + 23 + 25 + 37 = 160

160 ÷ 8 = 20

c. 13 + 13 + 13 + 15 + 21 + 23 + 25  = 123

123 ÷ 7 = 17.57

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

Mean = 26.29

Median =  -18

Mode = 40

2 a.  37

2 b.  20

2 c.  17.57

Step-by-step explanation:

Mean = -49 + (-43) + (-39) + (-18) + (-14) + (-12) + (-9) = -184

There are seven numbers so divide -184 by 7:

-184 ÷ 7 ≈ 26.29

Median =

-49, -43, -39, -18, -14, -12, -9

       -43, -39, -18, -14, -12

              -39, -18, -14

                      -18

Mode =

-9 - (-49) = 40

2.

13, 13, 13, 15, 21, 23, 25, 37

Outlier is the number that is an odd number

a. In this case the outlier is 37

b. 13 + 13 + 13 + 15 + 21 + 23 + 25 + 37 = 160

160 ÷ 8 = 20

c. 13 + 13 + 13 + 15 + 21 + 23 + 25  = 123

123 ÷ 7 = 17.57

Answer:

6x is indeed the Greatest Common Factor.

Step-by-step explanation:

6x[3 - y² + 2y⁶]

Answer: 56

Step-by-step explanation:

4=(a+b-24)/2

32=a+b

32+24=56

Answer:

The perimeter of the triangle is 56 cm.

Step-by-step explanation:

Given:

The length of the hypotenuse is 24 cm

Radius of the circle r=4 cm

To Find:

The perimeter of the triangle=?

Solution:

Let us see the below diagram representing situation.  

Here, first we have drawn the radius of circle perpendicular to the sides of triangle,

We have Taken PB = 4 because, it is a side of square formed there, and we take OC as x.

Then, QC also becomes x as they are tangents from single point, so they are equal.

Now, AQ becomes 24 – x as AC is 24 according to given information.

So, perimeter = AB + BC + CA  

Perimeter = (24 – x + 4) + (4 + x) + (24 – x + x)

Perimeter = 28 – x + 4 + x + 24  

Perimeter = 28 + 28 = 56

Hence, the perimeter of the triangle is 56 cm.

Hello There!

Martha’s first step would represent “Associative Property Of Addition”

This basically means that you can add or multiply these numbers regardless of how they are grouped in a sequence.

ANSWER

[tex]y \geqslant \frac{1}{4} x - 1[/tex]

EXPLANATION

The graph has a solid boundary line.

The region above the boundary line is shaded

Therefore the inequality sign involved is '≥'

The boundary line has equation

[tex]y = \frac{1}{4} x - 1[/tex]

We can now conclude that, the inequality graphed above is

[tex]y \geqslant \frac{1}{4} x - 1[/tex]

Answer:

The answer is

Step-by-step explanation:

The inequality in the  graphed above is y≥1/4x-1

Answer: An obtuse angle is any angle greater than 90° and less than 180°

Step-by-step explanation:

Answer:

An obtuse angle is more than 90 degrees so anything above 90 degrees is obtuse while anything below is either an acute, strait, or right angle.

Step-by-step explanation:

Answer:

8 guppies

Step-by-step explanation:

Let:

x = number of goldfishes

y = number of guppies

We can come up with two equations:

x + y = 26

3x +4y = 86

We use the first equation to come up with a solution for one of the unknowns:

x = 26 - y

We can use this to substitute the x on the second equation:

[tex]3x + 4y = 86\\\\3(26-y) + 4y=86\\\\78 - 3y + 4y = 86\\\\78 + y = 86\\\\y = 86 - 78\\\\y = 8[/tex]

So she bought 8 guppies.

The total guppies Samantha buys are 8 and the total goldfish she buys are 18 and this can be determined by forming the linear equation.

Given :

Let the total number of goldfish be 'x' and the total number of guppies be 'y'. Then the linear equation that represents the total number of fish is given by:

x + y = 26  

x = 26 - y   ---- (1)

The linear equation that represents the total spent $86 is given by:

3x + 4y = 86    --- (2)

Now, substitute the value of 'x' in equation (2).

3(26 - y) + 4y = 86

Simplify the above equation.

78 - 3y + 4y = 86

y = 86 - 78

y = 8

Now, substitute the value of 'y' in equation (1).

x = 26 - 8

x = 18

So, Samantha buys 8 guppies.

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Answer:

30,000           5,000        400      10.    7

----------              ----

XXX                   V                CD.     X     VII

The question appears to be a misunderstanding as the number '35,417' is already represented as numerals, which are symbols used to denote numbers. Therefore, '35,417' is already in its correct numeral form.

The student is asking for the number '35,417' to be written in numerals but it is already written in numerals. Numerals are symbols used to represent numbers. For example, the numeral for the number one is 1, and the numeral for the number two is 2. Therefore, the numeral representation for '35,417' is simply 35,417.

The question appears to be a misunderstanding as the number '35,417' is already represented as numerals, which are symbols used to denote numbers. Therefore, '35,417' is already in its correct numeral form.

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Answer:

I think 478.4   ._.

Step-by-step explanation:

First, find out how many gallons of gasoline she can buy with $18.50 by dividing 18.50 by 1.25 to get 14.8 gallons. Then, since he already has 6 gallons in his tank, add 6 to 14.8 = 20.8. Finally multiply this by the ratio of gallons to miles (23) to get 478.4

Answer:

A

Step-by-step explanation:

The average rate of change is the change in attendance over change in time.

Δy / Δx

(333.7 - 298.3) / (5 - 2)

11.8

So the average rate of change is an increase of 11.8 thousand people per year.

The average rate of change from Year 2 to Year 5 is 11.8 if at year 2 the attendance is 298.3 and at year 5 the attendance is 333.7

It is defined as the change in values of a dependent variable with respect to the independent variables.

We have to find the average rate of change from Year 2 to Year 5:

At year 2 the attendance = 298.3

At year 5 the attendance = 333.7

Average rate of change = (333.7-298.3)/(5-2)

= 11.8

Thus, the average rate of change from Year 2 to Year 5 is 11.8 if at year 2 the attendance is 298.3 and at year 5 the attendance is 333.7

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Answer:the answer is C

Step-by-step explanation: