What is the value of f(3) on the following graph?

Answer:

16

Explanation:

The angles ∠1 and ∠2 are complementary, meaning

Visually,

Now, ∠1 = 74; therefore,

subtracting 74 from both sides gives

which is our answer!

ANSWER

24901.55 miles

EXPLANATION

We have to find the circumference of the earth using the diameter given.

The formula for circumference is:

where D = diameter

Therefore, the circumference is:

Solution

Step 1:

Step 2

Step 3

Domain definition

Final answer

Since we know the future alue of the account, using the formula for the compounded interest with n = 365 (since the account is compounded daily), t=10, r = 4% and A=50000 in the following equation:

using these values and solving for P, we get:

therefore, the original amount deposited 10 years ago is $33,516.74

Taylor's scored 22 points

Erin scored 18 points

Nya scored 54 points

Aaron scored 64 points

Let Taylor's point = x

Erin scored 4 less points than Taylor:

Erin's score = x - 4

Nya scored three times as many points as Erin:

Nya's score = 3(x - 4)

Aaron scored 10 more points than Nya:

Aaron's score = Nya's score + 10

= 3(x - 4) + 10

The total score of the four friend = 158 points

Taylor's score + Erin's score + Nya's score + Aaron's score = 158

x + (x - 4) + 3(x -4) + 3(x-4) + 10 = 158

Expand the parenthesis:

x + x -4 + 3x - 12 + 3x - 12 + 10 = 158

collect like terms:

x + x + 3x + 3x - 4 - 12 - 12 + 10 = 158

8x - 18 = 158

8x = 158 + 18

8x = 176

Divide both sides by 8:

8x/8 = 176/8

x = 22

Taylor's scored 22 points

Erin scored : x-4 = 22- 4 = 18 points

Nya scored : 3(x-4) = 3(22-4) = 3(18) = 54 points

Aaron scored: 3(x-4) + 10 = 54 + 10 = 64 points

ANSWER

The first number is 3 and the second number is 7

EXPLANATION

Let the first number be x.

Let the second number be y.

The first line of the word problem is:

One number added to three times another number is 24.

This means that:

x + 3(y) = 24

=> x + 3y = 24 ______(1)

The second line of the word problem is:

Five times the first number added to three times the other number is 36.

5(x) + 3(y) = 36

5x + 3y = 36 ______(2)

Now, we have a system of equations:

x + 3y = 24 ____(1)

5x + 3y = 36 ___(2)

From the first equation, we have that:

x = 24 - 3y

Substitute that into the second equation:

5(24 - 3y) + 3y = 36

120 - 15y + 3y = 36

Collect like terms:

-15y + 3y = 36 - 120

-12y = -84

Divide through by -12:

y = -84 / -12

y = 7

Recall that:

x = 24 - 3y

=> x = 24 - 3(7) = 24 - 21

x = 3

Therefore, the first number is 3 and the second number is 7.

The first step is to substitute values of x into each equation.

For y = x^2 + 1,

if x = - 2, y = (- 2)^2 + 1 = 4 + 1 = 5

if x = - 1, y = (- 1)^2 + 1 = 1 + 1 = 2

if x = 0, y = (0)^2 + 1 = 0 + 1 = 1

if x = 1, y = (1)^2 + 1 = 1 + 1 = 2

if x = 2, y = (2)^2 + 1 = 4 + 1 = 5

We would plot the corresponding values of x and y on the graph as shown below

For y = 3^(x + 1),

if x = - 2, y = 3^(-2 + 1) = 3^-1 = 0.33

if x = - 1, y = 3^(-1 + 1) = 3^0 = 1

if x = 0, y = 3^(0 + 1) = 3^1 = 3

if x = 1, y = 3^(1 + 1) = 3^2 = 9

if x = 2, y = 3^(2 + 1) = 3^3 = 27

We would plot the corresponding values of x and y on the graph as shown below

Notice that the triangle △GEF is an isosceles triangle, since GE=EF (both sides are radii of the circle).

Since △GEF is an isosceles triangle with GE=EF, then the measure of the angles opposed to those sides is the same:

Since the line FH is tangent to the circle, the angle ∠HFE is a right angle.

Since ∠HFG and ∠GFE are adjacent angles, then:

Substitute m∠HFG=62 and m∠HFE=90 to find m∠GFE:

Since the sum of the internal angles of any triangle is 180 degrees, then:

Substitute the values of m∠GFE and m∠EGF:

Therefore:

14h + 6 = 2(5 + 7h) - 4

First , apply distributive porperty to solve the parentheses:

14h+6 =2(5)+2(7h)-4

14h+6 = 10+14h-4

Move the "h " terms to the left:

14h-14h = 10-4-6

0 = 0

h has infinite solutions.

Given the polynomial:

A stem and leaf plot is a table where each of the data is divided into two parts. The stem, that is the first digit and the leaf is the last digits. Let's say that we have the following set of data.

If we want to make a stem and leaf plot of that data, we first write a column where we place the first digit of each number without repetition, like this:

These are the stems. Now the leaves are the last digit of each number put in order next to the corresponding first digit, like this:

Given:

Therefore the point P be ( 1.6 ,0)

We can calculate a percent change by calculating the difference between the actual state and the previous state and then dividing this difference by the previuos state.

Finally, multypling by 100% gives the percentage change.

Here we have the last state as the future population (4823 thousand people). The actual state (in this case the state to which wew want to compare the variation ir change) is 5700 thousand people.

The difference is 4823 - 5700 = -877.

Then, we can divide it by the actual population and we will have:

This is equivalent to:

If we have to round to nearest tenth, the percent change is 15.4%.

To calculate the speed a vehicle is traveling you have to use the following formula:

Where

S: speed

d: distance

t: time

The car traveled d=156miles in t=3hs

Its speed can be calculated as:

The car's speed was 52 miles per hour

The polynomial function of least degree with only real coefficients will be;  y = x³ - 8 · x² + 22 · x - 20.

Algebraic expressions called polynomials include constants and indeterminates. Polynomials can be thought of as a type of mathematics.

The statement indicates that the polynomial has  real coefficients having zeros 3 and 1 - 32 and a lead coefficient of 1.

By algebra of quadratic equations, equations with real coefficients with complex roots are α + i β and α - i β. Then we get;

y = 1 · (x - 3) · (x - 3 - i) · (x - 3 + i)

y = (x - 3) · [x² - 3 · x - i · x - 3 · x + i · x + (3 + i) · (3 - i)]

y = (x - 3) · (x² - 6 · x + 9 - i²)

y = (x - 3) · (x² - 6 · x + 10)

y = x³ - 6 · x² + 10 · x - 2 · x² + 12 · x - 20

y = x³ - 8 · x² + 22 · x - 20

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Answer:

[tex]p(x)=x^3-5x^2+16x-30[/tex]

Step-by-step explanation:

Given information:

For any complex number  [tex]z = a+bi[/tex] , the complex conjugate of the number is defined as  [tex]z^*=a-bi[/tex].  

If f(z) is a polynomial with real coefficients, and z₁ is a root of f(z)=0, then its complex conjugate z₁* is also a root of f(z)=0.

Therefore, if p(x) is a polynomial with real coefficients, and (1 - 3i) is a root of p(x)=0, then its complex conjugate (1 + 3i) is also a root of p(x)=0.

Therefore, the polynomial in factored form is:

[tex]p(x)=a(x-3)(x-(1-3i))(x-(1+3i))[/tex]

As the leading coefficient is 1, then a = 1:

[tex]p(x)=(x-3)(x-(1-3i))(x-(1+3i))[/tex]

Expand the polynomial:

[tex]\implies p(x)=(x-3)(x-(1-3i))(x-(1+3i))[/tex]

[tex]\implies p(x)=(x-3)(x-1+3i)(x-1-3i)[/tex]

[tex]\implies p(x)=(x-3)(x^2-x-3xi-x+1+3i+3ix-3i-9i^2)[/tex]

[tex]\implies p(x)=(x-3)(x^2-x-x-3xi+3ix+1+3i-3i-9i^2)[/tex]

[tex]\implies p(x)=(x-3)(x^2-2x+1-9(-1))[/tex]

[tex]\implies p(x)=(x-3)(x^2-2x+10)[/tex]

[tex]\implies p(x)=x^3-2x^2+10x-3x^2+6x-30[/tex]

[tex]\implies p(x)=x^3-2x^2-3x^2+10x+6x-30[/tex]

[tex]\implies p(x)=x^3-5x^2+16x-30[/tex]

Given:

Measurements of hole are 48ft 39ft and and 9ft

Required:

Volume in cubic yd

total number of trip

total cost of trip

Explanation:

First we need to convert given measurements from ft to yd

A)

B)

11 cubic yd in 1 trip

then

624 cubic yd in x trip

C)

cost for 1 trip is $1175

then

cost for 57 trip is y

Final answer:

Volume in cubic yd is 624

total number of trips is 57

total cost of trip $66975

Answer:11

Step-by-step explanation:

The volume from tanks A and B are taken as 3 and 5 gallons respectively.

Here,
Let the volume taken from tank A and tank B be x and y.
According to the question,
x + y = 8 - - - - - (1)
And
Composition of the alcohol in Tank A = 1/3
Composition of the alcohol in tank B =  1 /5
x / 3 + y / 5 = 8 / 4
5x + 3y = 30
From equation 1
5(y8 - y) + 3y = 30
-5y + 40  + 3y = 30
-2y = -10
y = 5
Now, put y in equation 1
x = 8 - 5
x = 3

Thus, the Volume from tanks A and B are taken as 3 and 5 gallons respectively.

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Step-by-step explanation:

make the fractions decimals and put them on the plot

Answer:

26

Step-by-step explanation:

Just plug -3 in where ever you see x

[tex]f(x)=5-7x\\f(-3)=5-7(-3)\\f(-3)=5+21\\f(-3)=26[/tex]

y = 2

so,

x + 4 * 2 = 3

x = 3 - 4 * 2 = 3 - 8 = -5

so,

x = -5 and y = 2

Answer:

True.

The graph is linear, but not proportional.​

Explanation:

Given the graph in the attached image;

The graph is linear because it is a straight line graph.

A linear graph is always straight.

A proportional relationship in which the two components have a constant ratio.

The proportional graph is a straight line graph that passes through the origin (0,0).

Since the given graph does not pass through the origin, it is not a proportional graph.

Therefore, The graph is linear, but not proportional.​

The rate at which the length of a side is decreasing when the area of the triangle is 100 cm² is equal to -0.227 centimeters per minute.

Rate of change is a type of function that describes the average rate at which a quantity either decreases or increases with respect to another quantity.

Mathematically, the area of an equilateral triangle can be calculated by using this formula;

A = (√3/4)s²

Where:

Next, we would determine the side length of a square by making s the subject of formula as follows:

s = (√4A)/√3

s = (√4 × 100)/√3

Side length, s = 15.20

Note: The rate of change (dA/dt) is negative because it is decreasing.

By applying chain rule of differentiation, the rate of change (dA/dt) in area of this equilateral triangle with respect to time is given by:

dA/dt = (√3/4)(2s)ds/dt

dA/dt = (√3/4) × (2 × 15.20) × -3

dA/dt = -0.227 centimeters per minute.

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Since we have the value for selling each shirt, the earnings that came from the hats sold and the total earnings we can complete equation using a linear equation in which the cost of each shirt will represent the slope and the y-intercept will be the earnings that came from the hats, like this:

then clear the equation for x in order to find how many shirts were sold

The fractions you have to add are 1/3 and -5/6

The denominators are "3" and "6"

The common denominator between both numbers is 6.

6*1=6

3*2=6

Multiply 1/3 by factor 2 so that both fractions will have the same denominator

Now you can add both fractions

The result is not in its most reduced form, to siplify the fraction divide both the numerator and denominator by 3

The result is -1/2, in the number line:

Step 1

State the null and alternative hypothesis

Step 2

State the p-value of the significance level.

Step 3

Calculate the statistical test

The t-test formula is given as

Where

Step 4

Find the p-value from the t-test.

Step 5

Conclusion

The result is not significant at p<0.01. Therefore, the null hypothesis is rejected. It cannot be concluded that the mean in this area is higher than the national average because the p-value is greater than 0.01t

Given:

Required:

We need to find the points are included in the solution

Explanation:

Recall that the solution of the system of inequalities is the intersection region of all the solutions in the system.

The points G and F lie inside the intersection.

The points in the solution are G and F.

Final answer:

Points F and G.

Answer:

400 miles each day

Step-by-step explanation:

You have 1600 miles divided into four days.

1600 / 4

We can use the basic fact that multiplying a number by ten simply means shifting everything to the left, for example 2 x 10 = 20, we just shifted 2 to the left and inserted a 0.

So for this problem, we can do the same. Divide 1600 by 100, or 10 x 10, then divide by 4.

1600/16 = 100

16/4 = 4.

Now, since we divided by ten twice before, we can get the right answer by multiplying by ten twice.

4 x 10 = 40

40 x 10 = 400

The graph of the proportional relationship would look like A line passes through the point (0, 0) and continues through the point (12, 3).

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

A proportional relationship graph between two variables is a relationship where the ratio between the two variables is always the same.

The given table is

x  12  8  24

y  3   2   6

The graph of the proportional relationship would look like.

A line passes through the point (0, 0) and continues through the point (12, 3).

In the ordered pair the first value represents the x axis  value and second value represents the y value. The ordered pair (12, 3) is coordinated with the values of x and y in the table.

Hence the graph of the proportional relationship would look like A line passes through the point (0, 0) and continues through the point (12, 3).

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Solution

Step 1: Simplify the expression

Step 2: Divide the both side by -2

Therefore the correct value of y = - 30