1.00
Given the following functions f(x) and g(x), solve (f + g)(3) and select the correct answer below:
f(x) = 2x + 21
g(x) = x - 24
0-27
0-21
06
48

Answer:

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

Step-by-step explanation:

The equation of a line in the pending intercept form has the following form:

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

Where m is the slope of the line and b is the intercept with the y axis.

If we know two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] that belong to the line then:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]b=y_1-mx_1[/tex]

In this case:

[tex](x_1, y_1)=(2,11)[/tex]

[tex](x_2, y_2)=(4,17)[/tex]

[tex]m=\frac{17-11}{4-2}[/tex]

[tex]m=\frac{6}{2}[/tex]

[tex]m=3[/tex]

[tex]b=11-3(2)[/tex]

[tex]b=11-6[/tex]

[tex]b=5[/tex]

Finally the equation is:

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

Answer:y=3x-5

Step-by-step explanation:

Answer:

The distance between (3,5) (-2,7) is 29 blocks or squares

Step-by-step explanation:

Please mark brainliest and have a great day!

recall your d = rt, distance = rate * time.

b = rate of the boat in still water

c = rate of the currrent

the distance going upstream is 8 miles, the distance going downstream is also the same 8 miles.

the boat took 1 hour going upstream, now, the boat is not going "b" mph fast, since it's going against the current, the current is eroding speed from, thus the boat going up is really going "b - c" fast.

likewise, when the boat goes downstream, is not going "b" fast either, is going faster because is going with the current and thus is really going "b + c" fast, and we know that trip back took 1/2 hour or 30 minutes.

[tex]\bf \begin{array}{lcccl} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ \cline{2-4}&\\ Upstream&8&b-c&1\\ Downstream&8&b+c&\frac{1}{2} \end{array}\qquad \begin{cases} 8=(b-c)(1)\\ 8+c=\boxed{b}\\ \cline{1-1} 8=(b+c)\left( \frac{1}{2} \right) \end{cases}[/tex]

[tex]\bf \stackrel{\textit{substituting in the 2nd equation}~\hfill }{8=\left(\boxed{8+c}+c \right)\cfrac{1}{2}\implies 8=(8+2c)\cfrac{1}{2}}\implies 16=8+2c \\\\\\ 8=2c\implies \cfrac{8}{2}=c\implies \blacktriangleright 4=c \blacktriangleleft \\\\\\ \stackrel{\textit{we know that }~\hfill }{8+c=b\implies 8+4=b\implies \blacktriangleright 12=b \blacktriangleleft}[/tex]

To find the speed of the boat in still water and the speed of the current, two equations are formed using the distances and times of the upstream and downstream trips. Solving the equations reveals that the speed of the boat is 12 miles/hour and the speed of the current is 4 miles/hour.

The problem describes a boat moving upstream and then downstream in a river with a constant current. To solve for the speed of the boat in still water and the speed of the current, we use some simple algebra based on the relative speeds of the boat and the current.

Let's denote:

When going upstream, the boat's effective speed is (b-c), and when going downstream, it is (b+c). We are told that the boat went 8 miles upstream in 1 hour and the return trip only took 30 minutes (or 0.5 hours).

Therefore, for the upstream trip:

Distance = Speed × Time

8 miles = (b - c) × 1 hour

8 = b - c ...... (equation 1)

For the downstream trip:

8 miles = (b + c) × 0.5 hours

16 = b + c ...... (equation 2)

Solve the two equations simultaneously:

Add equation 1 and equation 2:

8 + 16 = (b - c) + (b + c)

24 = 2b

b = 12 miles/hour

Substitute b into equation 1:

8 = 12 - c

c = 4 miles/hour

Therefore, the speed of the boat in still water is 12 miles/hour and the speed of the current is 4 miles/hour.

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Answer:

We know that in a scalene triangle all sides (and angles) are different.

Let

z = length of longest side

y =  length of second side

x =  length of shortest side

The perimeter of the scalene triangle is 60 cm

x + y + z = 60 cm

The length of the longest side is 4 times that of the shortest side.

z = 4*x

We are left with the following equations

x + y + z = 60

z = 4*x

We will test every affirmation

Number one

The value of x can equal 40.

FALSE. The longest side cannot be greater than the perimeter.

Number two

The longest side can equal 30 cm

z = 30 cm

x = 30/4 cm = 7.5 cm

y = [60 -30 - 7.5] cm  = 22.5 cm

This statement is TRUE

Number three

The shortest side can equal 7 cm

x = 7 cm

z = 4*7 cm = 28 cm

y = [60 -28 - 7] cm  = 25 cm

This statement is TRUE

Number four

The value of x can equal 25

x = 25 cm

z = 4*25 cm = 100 cm

The longest side cannot be greater than the perimeter.

This statement is FALSE

Number five

The shortest side can equal 5

x = 5 cm

z = 4*5 cm = 20 cm

y = [60 -20 - 5] cm  = 35 cm

This statement is FALSE. The second side (y) cannot be greater than the longest side (z).

Answer:

8 inches

Step-by-step explanation:

We are given:  2L+2W=38  or simplified version: L+W=19

                          L=3+W

So plug 2nd equation into first, like so, (3+W)+W=19

                                                                 3+W+W=19

                                                                 3+2W=19

                                                                     2W=16

                                                                       W=8

The width of rectangle is,

⇒ W = 8 inches

We have to given that,

The perimeter of a rectangle is 38 inches.

And, the length is 3 inches more than the width.

Let us assume that,

Width = W

Length = W + 3

Hence, We get;

2 (W + W + 3) = 38

2 (2W + 3) = 38

4W + 6 = 38

4W = 38 - 6

4W = 32

W = 32/4

W = 8

Therefore, The width of rectangle is,

⇒ W = 8 inches

Learn more about the rectangle visit:

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Answer:

In Step 4, Daryl multiplied 12 and 100 incorrectly.

Step-by-step explanation:

12 x 100 = 1200, not 120

Answer:

B. 3b - 2 = 4.

Step-by-step explanation:

Let us check each equation by plugging in the value of b = 2 to see if it is true.

A. 2 × 2 + 24 = 4 + 24 = 28.

28 ≠ 30 . So A is not true.

B. 3 × 2 - 2 = 6 - 2 = 4.

4 = 4. B is true!

C. 2 + 4 = 6.

6 ≠ 8. C is not true.

D. 2 × 2 - 3 = 4 - 3 = 1.

1 ≠ 0. D is not true.

I hope this helps!

Answer:

Option A asymptote.

Step-by-step explanation:

Asymptotes are lines to which the graph approaches very it can come very close to it but will never touch it. Asymptote are the limits of a graph.

IN the given graph of Hyperbola the two blue lines representing the Hyperbola are coming too close to the red lines but not touching it .

The two red lines are called the Asymptotoes of the Hyprbola.It is the limit of the Hyperbola.

Step-by-step explanation:

Answer:

It is an asymptote.

Step-by-step explanation:

I did it on A P E X

Answer: y = 4(x + 1) - 2

Step-by-step explanation:

" increases by 4 for every x + 1" means the slope is 4 and the value inside the parentheses with x is +1

"crosses the y-axis at -2" means the y-intercept is -2

Input those values into the formula: y = m(x) + b    where

Answer:

2401 • x^2

Step-by-step explanation:

7 √x7 √x • 7 √x • 7

=(7)^4  (√x)^4

=2401 • x^2

Answer:

C) (6,2)

Step-by-step explanation:

To solve the system of equations, solve one of the equations for y, then plug the result into the other equation to get the value of x. When you get x, substitute it back into one of the original equations to find the value of y, which is 2.

To find the solution to the system of linear equations, we can use the method of substitution or elimination. Let's use the method of substitution and solve for x and y. The solution is (6, 2).

To find the solution to the system of linear equations, we can use the method of substitution or elimination. Let's use the method of substitution:

From the second equation, we can isolate y by subtracting 5x from both sides: y = 32 - 5x

Substitute this expression for y in the first equation: 3x - 2(32 - 5x) = 14

Simplify and solve for x: 3x - 64 + 10x = 14, 13x - 64 = 14, 13x = 78, x = 6

Now substitute the value of x back into one of the original equations and solve for y: 5(6) + y = 32, 30 + y = 32, y = 2

Therefore, the solution to the system of linear equations is x = 6 and y = 2, which can be written as (6, 2).

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Answer:

x=1.25

Step-by-step explanation:

We want to solve [tex]\log_3(x+1)=\log_6(5-x)[/tex] by graphing.

We let  [tex]y=\log_3(x+1)[/tex] and also

[tex]y=\log_6(5-x)[/tex].

We graph both equations to obtain the graph shown in the attachment.

The two graphs intersect at (1.25,0.74)

Therefore the solution to [tex]\log_3(x+1)=\log_6(5-x)[/tex]  is the x-coordinate of the point of intersection of the two graphs which is x=1.25.

Answer:  a and d

Step-by-step explanation:

I got it right on edge

Answer

Step-by-step explanation:

If you deposit money, your bank account shows it as +3

3 degrees below zero = - 3 o F which is darn cold.

3 floors below ground level = - 3 floors below ground level

3 feet above sea level = +3 feet

3 degrees about 0 = + 3

3 dollars lost = -3 dollars.

In order to solve this equation you must first simplify, then you re-range the terms, then solve.

[tex]12(x + -360) = 120[/tex]

[tex]12(-360 + x) = 120[/tex]

[tex](-360 \times 12 + x \times 12) = 120[/tex]

[tex](-4320 + 12x) = 120[/tex]

[tex]+ 4320+ 4320[/tex]

[tex]12x = 4440[/tex]

[tex]4440 \div 12 = 370[/tex]

[tex]x = 370[/tex]

Which means your answer is "x=370."

Hope this helps.

Answer:

x=2/5 or

x=0.4

Step-by-step explanation:

Answer:

[tex]\frac{2}{5}[/tex] or 0.4.

Step-by-step explanation:

[tex]\frac{2}{3}[/tex]+[tex]\frac{1x}{3}[/tex]=2x

[tex]\frac{2}{3}[/tex]=2x-[tex]\frac{1x}{3}[/tex]

[tex]\frac{2}{3}[/tex]=[tex]\frac{6x-x}{3}[/tex]

[tex]\frac{2}{3}[/tex]=[tex]\frac{5x}{3}[/tex]

x=[tex]\frac{2}{5}[/tex]

or

x=0.4

Answer:

“Look at the graph of the relationship. Find the y-value of the point that corresponds to x = 1. That value is the unit rate.”

“Look at the graph of the relationship. Count the number of units up and the number of units to the right one must move to arrive at the next point on the graph. Write these two numbers as a fraction.”

“Look at the graph of the relationship. Find the x-value of the point that corresponds to y = 2. That value is the unit rate.”

“Look at the graph of the relationship. Find two points which have y-values that are one unit apart. The unit rate is the difference in the corresponding x-values.”

Step-by-step explanation:

Answer: A. “Look at the graph of the relationship. Find the y-value of the point that corresponds to x = 1. That value is the unit rate.”

Answer:

40

Step-by-step explanation:

6x7-8/4 =42 - 2 = 40

To solve the expression 6x7-8/4, follow PEMDAS rule: Multiply 6 by 7, divide 8 by 4, and subtract the result from the multiplication.

To solve the expression 6x7-8/4 using the order of operations, we follow the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication, and Division (from left to right), and Addition and Subtraction (from left to right). Firstly, we perform the multiplication: 6x7 = 42. Then, we divide 8 by 4, which equals 2. Finally, we subtract 2 from 42, which gives us the final answer of 40.

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Answer:

C. 3.2

If GF = 3.2 a possible measure of TS is 3.2

Answer:

C

Step-by-step explanation:

Answer:

-4w^2- 8w

Step-by-step explanation:

-4w(w+2), use distributive property, (-4w x w)+(-4w x 2)= (-4w^2)+-8w

Answer:

a = 6, b = 4, c = 2

Step-by-step explanation

see attached

Answer:

The required values are a=6, b=4 and c=2.

Step-by-step explanation:

The given expression is

[tex]\sqrt{x^{12}y^{9}z^{5}}=(x^{a}y^bz^c)\sqrt{yz}[/tex]          .... (1)

It can be written as

[tex]\sqrt{x^{12}\cdot y^{8}\cdot y\cdot z^{4}\cdot z}[/tex]

[tex]\sqrt{x^{12}\cdot y^{8}\cdot z^{4}\cdot y\cdot z}[/tex]

[tex]\sqrt{(x^{6})^2\cdot (y^{4})^2\cdot (z^{2})^2\cdot y\cdot z}[/tex]     [tex][\because (a^m)^n=a^{mn}][/tex]

[tex]\sqrt{(x^{6}y^4z^2)^2\cdot y\cdot z}[/tex]          [tex][\because a^xb^x=(ab)^x][/tex]

[tex](x^{6}y^4z^2)\sqrt{yz}[/tex]               .... (2)       [tex][\because \sqrt{x^2}=x][/tex]

From (1) and (2), we get

[tex]a=6,b=4,c=2[/tex]

Therefore the required values are a=6, b=4 and c=2.

Answer:

Step-by-step explanation:

"Find the values of x that satisfy 3x - 2x^2 = 7."  Please do not use " × " to represent a variable; " × " is an operator, the "multiply" operator.

Rearrange these three terms in descending order by powers of x:

-2x^2 + 3x - 7 = 0.   Here the coefficients are a = -2, b = 3 and c = -7, and so the discriminant of this quadratic is b^2-4ac, or 9 - 4(-2)(-7), or 9 - 56, or -47.

Because the discriminant is negative, we'll have two different complex roots here.  The quadratic formula becomes

       -3 ± i√47         -3 ± i√47

x = ----------------- = -------------------

        2(-2)                     -4

The question involves solving a quadratic equation using the quadratic formula. Substituting a, b, and c values into the formula will give us the solutions for x, with the discriminant indicating the nature of the roots.

The question asks for the solution to the quadratic equation 3x - 2x² = 7.

To solve this equation, we first move all terms to one side of the equal sign to set the equation to zero:

2x² - 3x + 7 = 0

Since this is a quadratic equation, we can use the quadratic formula:

x = [-b ± √(b² - 4ac)] / (2a)

In this case, a = -2, b = 3, and c = -7. We substitute these values into the quadratic formula to find the values of x:

x = [(-3) ± √((3)² - 4(-2)(-7))] / (2(-2))

The discriminant, √(b² - 4ac), will determine the nature of the roots.

Depending on the value of the discriminant, the solutions may be real and distinct, real and equal, or complex.

There would be 2 intercepts, the X and the Y.

To find the X intercept, set Y to 0 and solve for x.

To find the Y intercept, set X to 0 and solve for y.

x -2y = 2

x-2(0) = 2

x-0 = 2

x = 2

0 -2y = 2

-2y=2

y = 2/-2

y = -1

The x intercept is (2,0)

The y intercept is (0,-1)

Not sure what format you need the answer in, you may only need x = 2 and y = -1.

Answer:

Step-by-step explanation:

Remote interior angles are defined as the two angles that are inside the triangle and opposite from the exterior angle.

In this case, [tex]\angle 3[/tex] and [tex]\angle 2[/tex] are remote interior angles of 1, because they are opposite to it, which is the exterior angle.

Therefore, the right choices are A and B.

The remote interior angles of 1 are -90°, -60°, and -30°.

Remote interior angles are angles formed by two lines and a transversal where the interior angles are not adjacent or consecutive. In the given options, the remote interior angles of 1 are:

These angles are considered remote interior angles because they are not adjacent or consecutive to 1°.

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Answer:

The ten millions place

Step-by-step explanation:

because the three after it is the unit million then the 8 being before the 3 would definitely be it's tens

Answer:

Scales-No equal sides

Isosceles- 2 Equal

Equilateral-

Right-90 degree

Obtuse- Obtuse Angle

Answer:

D. Farming and medicine

Step-by-step explanation:

When they arrived in America, the Europeans found a populated territory. Its inhabitants, however, were ignorant of writing and left no documents about their own past.  The knowledge we have about the native tribes of the 16th century is mainly based on accounts and descriptions of European travelers who were here at the time.

These travelers report that the Indians survived from hunting, fishing, extractivism, and had great advances in agriculture.  They settled in the valleys of navigable rivers, where fertile lands existed. They stayed in place for about four years. After the natural resources of the place had been exhausted, they migrated to another region with better resources for agriculture.  Travelers also report that the Indians were advancing in medicine, which was based on medicinal plants, but effective for many health problems.

Answer:

∴ (g ο f)(2) = 216  

Step-by-step explanation:

* Lets revise at first the meaning of f of g (composite function)

- A composite function is a function that depends on another function

- A composite function is created when one function is substituted into

 another function  

- Example:

# (g ο f)(x) is the composite function that is formed when f(x) is  

 substituted for x in g(x).

* Now lets solve the problem

∵ f(x) = 2x + 2

∵ g(x) = x³

- We need to find (g ο f)(2), so we will substitute x by f(x) in g(x)

∴ (g ο f)(x) = (2x + 2)³

- Now substitute x by 2

∴ (g ο f)(2) = [2(2) + 2]³ = [4 + 2]³ = [6]³ = 216

* * (g ο f)(2) = 216  

# Another way

- We can find f(2) at first and then substitute the x by the answer

 in g(x)

∵ f(x) = 2x + 2

∴ f(2) = 2(2) + 2 = 4 + 2 = 6

∵ g(x) = x³

∴ g(6) = (6)³ = 216

* (g ο f)(2) = 216  

Answer:

x = -10

Step-by-step explanation:

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Subtract 8 from both sides:

x + 8 (-8) = -2 (-8)

x = -2 - 8

Simplify. Combine like terms:

x = -2 - 8

x = -10

x = -10 is your answer

~

Answer:

x = -10

Step-by-step explanation:

x+8 = -2

          +

 -8    -8

__________

x=          -10

Step-by-step answer:

Assuming the equation is y=-x+k,

where k is a constant, such as 5, pi, 10/7, etc.

then the slope is the coefficient of the term containing x, namely

-1  (since -x is a shorthand for (-1)*x ).

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 is the slope of the line

b: It is the cut point with the "y" axis

We have, according to the data provided, that the line is of the form:

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

That means that the slope is -1.

ANswer:

[tex]m = -1[/tex]