The tables represent two linear functions in a system,
What is the solution to this system?
(1,0)
(1,6)
(8, 26)
(8, -22)

[tex]y=3\cdot0 + 2\cdot0 - 13=-13[/tex]

The y-intercept is [tex](0,-13)[/tex]

To do solve this you must isolate x. First subtract 16 to both sides (what you do on one side you must do to the other). Since 16 is being added to x, subtraction (the opposite of addition) will cancel it out (make it zero) from the left side and bring it over to the right side.

x + (16 - 16) = 24 - 16

x = 8

Check:

8 + 16 = 24

24 = 24

Hope this helped!

~Just a girl in love with Shawn Mendes

if you subtract 16 from both sides you would get x=8

Answer:

g(- 8) = - 62

Step-by-step explanation:

Equate 8x + 2 to - 62

8x + 2 = - 62 ( subtract 2 from both sides )

8x = - 64 ( divide both sides by 8 )

x = - 8

Hence g(- 8) = - 62

if the diameter is 14, then its radius must be half that, or 7.

[tex]\bf \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\ \cline{1-1} r=7 \end{cases}\implies V=\cfrac{4\pi (7)^3}{3}\implies \stackrel{\pi =3.14}{V=1436.03} \\\\[-0.35em] ~\dotfill\\\\ \textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\ \cline{1-1} r=7\\ h=14 \end{cases}\implies V=\pi (7)^2(14)\implies \stackrel{\pi =3.14}{V=2154.04}[/tex]

Answer:16.66

Step-by-step explanation:

To convert 1/6 into a percent, multiply by 100 to get approximately 16.67 percent.

To convert a fraction to a percent, you can follow a standard way of expressing the fraction such that the denominator equals 100. For 1/6, you want to find what number over 100 is equivalent to it. To do so, you can set up a proportion where 1/6 equals x/100. Solving for x, you would cross-multiply and divide to get:

1 * 100 = 6 * x
[tex]\( x = \frac{100}{6} \)[/tex]
x ≈ 16.67

Therefore, 1/6 as a percent is approximately 16.67 percent.

Final answer:

To convert 720° to radians, multiply by π/180 to get 4π rad. This shows that 720° is equivalent to 4π radians.

Explanation:

To convert 720° to radians, we use the relationship that 1 revolution equals 360° or 2π radians. Therefore, to convert degrees to radians, you multiply the number of degrees by π/180. In this case:

720° × (π rad / 180°) = 4π rad

Thus, 720° is equal to 4π radians. The concept of angular velocity is related to radians as it is the rate of change of an angle with time, and using radians can be especially useful in calculations involving angular motion.

Answer:

[ -8 , 9 ]

Step-by-step explanation:

You are looking at where f(t), the function, is on its y values.

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Answer:

Step-by-step explanation:

Parallel lines have the same slope.

The formula of a slope:

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

We have the points A(-4, 0) and B(2, -3). Substitute:

[tex]m=\dfrac{-3-0}{2-(-4)}=\dfrac{-3}{6}=-\dfrac{1}{2}[/tex]

C(-2, 2).

The point on the x-axis D(x , 0).

The slope:

[tex]m=\dfrac{0-2}{x-(-2)}=\dfrac{-2}{x+2}[/tex]

Put the value of the slope:

[tex]\dfrac{-2}{x+2}=\dfrac{-1}{2}[/tex]           change the signs

[tex]\dfrac{2}{x+2}=\dfrac{1}{2}[/tex]           cross multiply

[tex]x+2=(2)(2)[/tex]

[tex]x+2=4[/tex]            subtract 2 from both sides

[tex]x=2[/tex]

Answer:

x = 4/9

C

Step-by-step explanation:

log_2(6x/) - log_2(x^(1/2) = 2         Given

log_2(6x/x^1/2) = 2                         Subtracting logs means division

log_2(6 x^(1 - 1/2)) = 2                     Subtract powers on the x s

log_2(6 x^(1/2) ) = 2                         Take the anti log of both sides

6 x^1/2 = 2^2                                    Combine the right

6 x^1/2 = 4                                        Divide by 6  

x^1/2 = 4/6 = 2/3                               which gives 2/3 now square both sides

x = (2/3)^2                                      

x = 4/9

Answer:

Option c

Step-by-step explanation:

The given logarithmic equation is

[tex]log_{2} (6x)-log_{2}(\sqrt{x})=2[/tex]

[tex]log_{2}[\frac{(6x)}{\sqrt{x}}]=2[/tex] [since log[tex](\frac{a}{b})[/tex]= log a - log b]

[tex]log_{2}[\frac{(6\sqrt{x})\times\sqrt{x}}{\sqrt{x}}]=2[/tex] [since x = [tex](\sqrt{x})(\sqrt{x})[/tex]]

[tex]log_{2}(6\sqrt{x} )=2[/tex]

[tex]6\sqrt{x} =2^2[/tex]  [logₐ b = c then [tex]a^{c}=b[/tex]

[tex]6\sqrt{x} =4[/tex]

[tex]\sqrt{x} =\frac{4}{6}[/tex]

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

[tex]x=(\frac{2}{3})^2[/tex]

        = [tex]\frac{4}{9}[/tex]

Option c is the answer.

Answer:

g and h

Step-by-step explanation:

both g and h have constant relationships while f's f(x) values aren't constant so it doesn't have a linear relationship

Answer:

Of the three functions g and h represent linear relationship.

Step-by-step explanation:

If a function has constant rate of change for all points, then the function is called a linear function.

If a lines passes through two points, then the slope of the line is

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

The slope of function f(x) on [1,2] is

[tex]m_1=\frac{11-5}{2-1}=6[/tex]

The slope of function f(x) on [2,3] is

[tex]m_2=\frac{29-11}{3-2}=18\neq m_1[/tex]

Since f(x) has different slopes on different intervals, therefore f(x) does not represents a linear relationship.

From the given table of g(x) it is clear that the value of g(x) is increased by 8 units for every 2 units. So, the function g(x) has constant rate of change, i.e.,

[tex]m=\frac{8}{2}=4[/tex]

From the given table of h(x) it is clear that the value of h(x) is increased by 6.8 units for every 2 units. So, the function h(x) has constant rate of change, i.e.,

[tex]m=\frac{6.8}{2}=3.4[/tex]

Since the function g and h have constant rate of change, therefore g and h represent linear relationship.

[tex]f(g(x))=x[/tex] when [tex]g(x)=f^{-1}(x)[/tex]

So [tex]f(g(2))=2[/tex]

The value of f(g(2)) is 2 since g(x) is the inverse of f(x).

An inverse function that does the opposite operation of the actual function. It is denoted by f⁻¹(x).

The given function is f(x) and g(x) is the inverse of f(x) i..e, g(x) = f⁻¹(x).

Then,

f(g(x)) = f(f⁻¹(x))

         = x

Thus,

f(g(2)) = 2 (since x=2)

Therefore, the value of f(g(2)) = 2.

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Answer:

c

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( where m is the slope and c the y- intercept )

Given y = 2x - 3 ← in slope- intercept form

with m = 2

• Parallel lines have equal slopes, hence

y = 2x + c ← is the partial equation of the parallel line

To find c substitute (- 1, 2) into the partial equation

2 = - 2 + c ⇒ c = 2 + 2 = 4

y = 2x + 4 → c

Answer:

[tex]\large\boxed{(-6b^3-362.6)+(2b^3-362)=-4b^3-724.5}[/tex]

Step-by-step explanation:

[tex](-6b^3-362.6)+(2b^3-362)\\\\=-6b^3-362.6+2b^3-362\qquad\text{combine like terms}\\\\=(-6b^3+2b^3)+(-362.5-362)\\\\=-4b^3-724.5[/tex]

Answer:

(x + 4)(x + 5)

Step-by-step explanation:

Given

x² + 9x + 20

Consider the factors of the constant term (+ 20) which sum to give the coefficient of the x- term (+ 9)

The factors are + 4 and + 5, since

4 × 5 = 20 and 5 + 4 = 9, hence

x² + 9x + 20 = (x + 4)(x + 5)

Answer: 0.67 (to 3 s.f)

Step-by-step explanation:

f(x)=g(x)

-3x + 4 = 2

-3x = -2

x = 2/3

x = 0.67

Hope it helped

Answer:

Choice number one:

[tex]\displaystyle \frac{5}{10}\cdot \frac{4}{9}[/tex].

Step-by-step explanation:

The question is asking for the possibility that event [tex]A[/tex] and [tex]B[/tex] happen at the same time. However, whether [tex]A[/tex] occurs or not will influence the probability of [tex]B[/tex]. In other words, [tex]A[/tex] and [tex]B[/tex] are not independent. The probability that both [tex]A[/tex] and [tex]B[/tex] occur needs to be found as the product of

5 out of the ten numbers are even. The probability that event [tex]A[/tex] occurs is:

[tex]\displaystyle P(A) = \frac{5}{10}[/tex].

In case A occurs, there will only be four cards with even numbers out of the nine cards that are still in the bag. The conditional probability of getting a second card with an even number on it, given that the first card is even, will be:

[tex]\displaystyle P(B|A) = \frac{4}{9}[/tex].

The probability that both [tex]A[/tex] and [tex]B[/tex] occurs will be:

[tex]\displaystyle P(A \cap B) = P(B\cap A) =  P(A) \cdot P(B|A) = \frac{5}{10}\cdot \frac{4}{9}[/tex].

Answer:

3 miles per hour

Step-by-step explanation:

Let x miles per hour be the current of the river.

1. The boat travels 2.4 miles downstream with the speed of (21+x) miles per hour. It takes him

[tex]\dfrac{2.4}{21+x}\ hours.[/tex]

2. The boat travels 1.8 miles upstream with the speed of (21-x) miles per hour. It takes him

[tex]\dfrac{1.8}{21-x}\ hours.[/tex]

3. The time is the same, so

[tex]\dfrac{2.4}{21+x}=\dfrac{1.8}{21-x}[/tex]

Cross multiply:

[tex]2.4(21-x)=1.8(21+x)[/tex]

Multiply it by 10:

[tex]24(21-x)=18(21+x)[/tex]

Divide it by 6:

[tex]4(21-x)=3(21+x)\\ \\84-4x=63+3x\\ \\84-63=3x+4x\\ \\7x=21\\ \\x=3\ mph[/tex]

Answer:

I believe the answer is 12 • (x + 11) .

Answer:

15625

Step-by-step explanation:

Let us consider each dial individually.

We have 25 choices for the first dial.

We then have 25 choices for the second dial.

We then have 25 choices for the third dial.

Let us consider any particular combination, the probability that combination is right is (probability the first number is right) * (probability the second number is right) * (probability the third number is right) = 1/25 * 1/25 * 1/25 = 1/15625

Therefore there are 15625 combinations

Answer:

.05

Step-by-step explanation:

See The attachment for explanation

Hope it helps you...☺

Final answer:

To order the relative frequencies from least to greatest, calculate the relative frequency for each data value by dividing the frequency by the total number of data values. Then, determine the cumulative relative frequency by adding all previous relative frequencies to the relative frequency for the current row. Finally, list the data values in increasing order of their relative frequencies.

Explanation:

The given data is:

114,950; 158,000; 230,500; 387,000; 389,950; 479,000; 488,800; 529,000; 575,000; 639,000; 659,000; 1,095,000; 5,500,000

To order the relative frequencies from least to greatest, we need to determine the relative frequency for each data value. The relative frequency is found by dividing the frequency by the total number of data values. The cumulative relative frequency is the sum of all previous relative frequencies. Here are the calculations:

Relative Frequency:
114,950 : 0.00002
158,000 : 0.00003
230,500 : 0.00005
387,000 : 0.00008
389,950 : 0.00008
479,000 : 0.00010
488,800 : 0.00010
529,000 : 0.00011
575,000 : 0.00012
639,000 : 0.00013
659,000 : 0.00013
1,095,000 : 0.00022
5,500,000 : 0.00100

Now we can order the relative frequencies from least to greatest:

114,950 : 0.00002
158,000 : 0.00003
230,500 : 0.00005
387,000 : 0.00008
389,950 : 0.00008
479,000 : 0.00010
488,800 : 0.00010
529,000 : 0.00011
575,000 : 0.00012
639,000 : 0.00013
659,000 : 0.00013
1,095,000 : 0.00022
5,500,000 : 0.00100

The correct option is B.

The probability [tex]\( P(A \cap B \cap C) \)[/tex] from the Venn diagram is [tex]\( \frac{2}{25} \)[/tex], as 4 out of 50 elements overlap.

To find [tex]\( P(A \cap B \cap C) \)[/tex] from the given Venn diagram, we need to identify the part of the diagram where all three sets A, B, and C overlap, and then calculate the probability of landing in that part of the diagram.

The numbers within each section of the Venn diagram represent the number of elements in that section. The overlapping section of A, B, and C is the center where all three circles intersect, which has the number 4 in it. This means there are 4 elements that are in all three sets A, B, and C.

To calculate the probability [tex]\( P(A \cap B \cap C) \)[/tex], we need to divide the number of elements in [tex]\( A \cap B \cap C \)[/tex] by the total number of elements in the sample space. The sample space in this case is all the numbers within the Venn diagram.

The total number of elements in the Venn diagram is the sum of all the numbers inside the circles.

Let's calculate it step by step.

The probability [tex]\( P(A \cap B \cap C) \)[/tex] is [tex]\( \frac{4}{50} \)[/tex], which simplifies to [tex]\( \frac{2}{25} \)[/tex]. Therefore, the answer is 2/25. Here is the step-by-step calculation:

1. Count the number of elements in the intersection of A, B, and C, which is 4.

2. Count the total number of elements in the sample space, which is 50.

3. Divide the number of elements in [tex]\( A \cap B \cap C \)[/tex] by the total number of elements in the sample space to find the probability:

[tex]\[ P(A \cap B \cap C) = \frac{4}{50} = \frac{2}{25} \][/tex]

This is the required probability.

The complete question is here:

Options

A.2/25

B.3/25

C.4/25

D.1/25

Answer: On APEX it’s 2/25

Step-by-step explanation:

Answer: 4b + 3r

Step-by-step explanation: The student correctly subtracted the 2b, but accidentally added the r instead of subtracting it, she likely misunderstood the parentheses.

The correct answer would be 4b + 3r

Answer:

Third option     ✔ 4b + 3r

Step-by-step explanation:

E D G E N U I T Y

Answer:

length of shortest piece = 13 in

length of middle piece =  19 in

length of longest piece =  22 in

Step-by-step explanation:

Total length of sandwich = 54 inch

Let shortest piece = x

Middle piece = x+6

Longest piece = x+9

Add this pieces will make complete sandwich

x+(x+6)+(x+9) = 54

Solving

x+x+6+x+9 = 54

Combining like terms

x+x+x+6+9 = 54

3x + 15 = 54

3x = 54 -15

3x = 39

x = 13

So, length of shortest piece = x = 13 in

length of middle piece = x+6 = 13+6 = 19 in

length of longest piece = x+9 = 13+9 = 22 in

Answer:

The three pieces should be 13 , 19 , 22 inches

Step-by-step explanation:

* Lets study the information to solve the problem

- The length of the sandwich is 54 in

- The sandwich will cut into three pieces

- The middle piece is 6 inches longer than the shortest piece

- The shortest piece is 9 inches shorter than the longest piece

* Lets change the above statements to equations

∵ The shortest piece is common in the two statements

∴ Let the length of the shortest piece is x ⇒ (1)

∵ The middle piece is 6 inches longer than the shortest piece

∴ The length of the middle piece = x + 6 ⇒ (2)

∵ The shortest piece is 9 inches shorter than the longest piece

∴ The longest piece is 9 inches longer than the shortest piece

∴ The longest piece = x + 9 ⇒ (3)

∵ the length of the three pieces = 54 inches

- Add the length of the three pieces and equate them by 54

∴ Add (1) , (2) , (3)

∴ x + (x + 6) + (x + 9) = 54 ⇒ add the like terms

∴ 3x + 15 = 54 ⇒ subtract 15 from both sides

∴ 3x = 39 ⇒ divide both sides by 3

∴ x = 13

* The length of the shortest piece is 13 inches

∵ The length of the middle piece = x + 6

∴ The length of the middle piece = 13 + 6 = 19 inches

* The length of the middle piece is 19 inches

∵ The length of the longest piece = x + 9

∴ The length of the longest piece = 13 + 9 = 22 inches

* The length of the longest piece is 22 inches

* The lengths of the three pieces are 13 , 19 , 22 inches

Answer:

the awncer would be x=0

Step-by-step explanation:

.

Answer:

F(4) = G(4) and F(12) = G(12) ⇒ answer B

Step-by-step explanation:

* Lets explain the meaning of the common solutions of two equation

- If two equations intersect at one point, (x , y) where x and y have the

 same values for both equations

- The point (x , y) belongs to the two graphs

- Ex: If (2 , 3) is a common solution of f(x) and g(x) , then the graphs of

 f(x) and g(x) meet each other at the point (2 , 3) that means f(2) = 3

 and g(2) = 3

- So f(2) = g(2)

* Lets solve the problem

∵ F(x) = Ix - 6I

∵ G(x) = 0.5 x

∵ The two graphs intersected at points (4 , 2) and (12 , 6)

- That means the two points (4 , 2) and (2 , 6) on the two graphs

∴ F(4) = 2 and G(4) = 2

∴ F(12) = 6 and G(12) = 6

- That means the two points are common solutions for both equations

∴ The solutions of the equation |x - 6|= 0.5 x are x = 4 and x = 12

∴ F(4) = G(4) and F(12) = G(12)

∴ The  best reasons which justifies Kiana's conclusion is;

   F(4) = G(4) and F(12) = G(12)

- Look to the attached graph to more understanding

- The red graph is F(x)

- The blue graph is G(x)

The best justification of Kiana's conclusion is ; F(4) = G(4) and F(12) = G(12) Option B

The justification for Kiana's conclusion is that the values of x and y at the points of intersection are the same for both equations.

This means that the point (x, y) belongs to both graphs.

For example, if (2, 3) is a common solution of f(x) and g(x), then the graphs of f(x) and g(x) intersect at the point (2, 3), which implies that f(2) = 3 and g(2) = 3. Therefore, f(2) = g(2).

To solve the problem at hand, we have

F(x) = |x - 6| and G(x)

= 0.5x.

Given that the two graphs intersect at the points (4, 2) and (12, 6),

Consequently, F(4) = 2 and G(4) = 2, as well as

F(12) = 6 and

G(12) = 6.

These common solutions indicate that the solutions of the equation

|x - 6| = 0.5x are

x = 4 and x = 12.

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Answer:

x =0 and x = 4

Step-by-step explanation:

It is a quadratic function and hence will have two roots. It cuts graph at 2 points( x - axis ). Hence has two roots.

Answer:

42 degrees

Step-by-step explanation:

So we are given that m<BOC+m<AOB=90

So we have (6x-6)+(5x+8)=90

11x+2=90

11x=88

x=8

We are asked to find m<BOC

m<BOC=6x-6=6(8)-6=48-6=42

The answer is:

The ordered pair satisfies the following system of equations since it satisfies both equations.

If we need to know if the ordered pair (-11/3,2/3) satisfies the system of equations we need to evaluate it and check if it satisfies both equations, we must remember that the condition that determines if the system of equations is satisfied is that both equations must be satisfied.

So, evaluating the ordered pair, we have:

First equation:

[tex]-x+5y=7\\\\-(\frac{-11}{3})+5*\frac{2}{3}=7\\\\\frac{11}{3}+\frac{10}{3}=7\\\\\frac{11+10}{3}=7\\\\\frac{21}{3}=7\\\\7=7[/tex]

We have that the equation is satisfied.

Second equation:

[tex]-x-7y=-1\\\\-(\frac{-11}{3})-7*\frac{2}{3}=-1\\\\\frac{11}{3}-\frac{14}{3}=-1\\\\\frac{11-14}{3}=7\\\\\frac{-3}{3}=-1\\\\-1=-1[/tex]

We have that the equation is satisfied.

Hence, we have that the ordered pair satisfies the system of equations since it satisfies both equations

Have a nice day!

Final answer:

The ordered pair (-11/3, 2/3) satisfies both equations in the given system, making it a solution to the system of equations.

Explanation:

To determine if the ordered pair (-11/3, 2/3) satisfies the given system of equations, we substitute x with -11/3 and y with 2/3 into both equations.

For the first equation -x + 5y = 7, we get:
-(-11/3) + 5(2/3) = 7
11/3 + 10/3 = 7
21/3 = 7
7 = 7
This confirms that the ordered pair satisfies the first equation.

For the second equation -x - 7y = -1, we calculate:
-(-11/3) - 7(2/3) = -1
11/3 - 14/3 = -1
-3/3 = -1
-1 = -1
The ordered pair also satisfies the second equation.

Since the ordered pair satisfies both equations, it is a solution to the system.

Answer: Last Option

[tex]H (m) = 25 + 3m\\H (m) = 10 + 8m[/tex]

Step-by-step explanation:

The initial height of the plant of species A is 25 cm and grows 3 centimeters per month.

If m represents the number of months elapsed then the equation for the height of the plant of species A is:

[tex]H (m) = 25 + 3m[/tex]

For species B the initial height is 10 cm and it grows 8 cm each month

If m represents the number of months elapsed then the equation for the height of the plant of species B is:

[tex]H (m) = 10 + 8m[/tex]

Finally, the system of equations is:

[tex]H (m) = 25 + 3m\\H (m) = 10 + 8m[/tex]

The answer is the last option