Part I
Find the domain and the range of the following function.
f(x)=
x+3, for x≤ -3
1, for -3 1/2x, for x ≥4
The domain of the function is
(Type your answer in interval notation)

Answer:

Step-by-step explanation:

The domain is the set of x-values and the range is the set of y-values.

To solve this problem we will use the following property of triangles:

So if we are given the angles a and b of a triangle, the third side c, must be:1) The angles are a =

i. 70°

2) a = 48° and b = 62°, so we have:

h. 73°

3) a = 41° and b = 86°, so we have:

j. 53°

4) a = 61° and b = 88°, so we have:

d. 31°

5) a = 55° and b = 92°, so we have:

b. 33°

Answers

0. j. 70°

1. h. 73°

2. j. 53°

3. d. 31°

4. b. 33°

Answer:

x=6

Step-by-step explanation:

[tex]9(x - 1) - 13x = - 3(x + 5)[/tex]

[tex]9x - 9 - 13x = - 3x - 15[/tex]

[tex]9x - 13x + 3x = - 15 + 9[/tex]

[tex] - x = - 6[/tex]

[tex] \frac{ - \times }{ -1 } = \frac{ - 6}{ - 1} [/tex]

[tex]x = 6[/tex]

The change that Grant received to the nearest cent after giving the delivery driver with a $100 bill is $ 32.6.

This is a question of percentages.

Given that:-

Price of bouquet of flowers = $ 55

Sales tax % = 6.5 %

Tip % = 15 %

Delivery fee= $10

We have to find the change that Grant received to the nearest cent after giving the delivery driver with a $100 bill.

Sales tax = (6.5/100)*55 = $3.575

$55 + $3.575 = $58.575

Tip = (15/100)*58.575 = $ 8.78625

Total money paid by Grant = 55 + 3.575 + 8.78625 = $ 67.36125 ≈ $ 67.4

Hence,

Change received by Grant = 100 - 67.4 = $ 32.6

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the loan payment on a fixed term mortgage loan of $100,000 at 8% for 30 years will be $ 340,000.

Principal amount = $ 100,000

Interest rate = 8 %

Time period = 30 years.

Now, the interest is simple interest as it is a fixed rate/ fixed term mortgage.

So, the interest will be:

Simple interest = p r t / 100

SI = 100,000 × 8 × 30 / 100

SI = $ 240,000

Amount will be:

A = $100,000 + $ 240,000

A = $ 340,000

Therefore, we get that, the loan payment on a fixed term mortgage loan of $100,000 at 8% for 30 years will be $ 340,000.

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Answer:

A

Step-by-step explanation:

Answer:

(0, 8) and (-4, 0)

Step-by-step explanation:

Equation is -2x + y = 8

Manipulate this equation so that it becomes a slope-intercept form of equation

To do this:

Add 2x on both sides

-2x + 2x + y = 2x + 8

y = 2x + 8

Once we have this, 2 points which definitely lie on the line are its x and y intercepts

This is the equation of a line with slope = 2 and x-intercept = 8

x-intercept is y-value when x = 0
We can check by plugging in 0 for x in y = 2x + 8

=> y = 2(0) + 8 = 8

=> Point(0, 8) is one of the ordered pairs

Similarly we can find the x-intercept by setting y = 0 and solving for x

Setting y = 0 in y = 2x + 8

=> 0 = 2x + 8

Switch sides

2x + 8 = 0

Subtract 8 from both sides

2x + 8 - 8 = 0 - 8

2x = -8

Divide both sides by 2

=> 2x/2 = -8/2

x = -4

So (-4, 0) is another point on the line

Two ordered pairs are therefore

(0, 8) and (-4, 0)

The attached graph shows you that it is indeed so

Using proportions, it is found that Victor has a higher ratio of of sand dollars to starfish.

A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the context of the problem using multiplications such as division or multiplication.

One example of proportions is for ratio problems, as:

Hence the ratios of sand dollars to starfish for Victor and Cheyenne are given as follows:

0.6 > 0.5, hence Victor has the higher ratio.

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Answer

B n G = {2}

B u G = {-2, -1 , 0 , 2, 3, 4, 5, 7)

Step-by-step explanation:

Given the following two sets

B = { -2, 2, 3, 5}

G = { -1, 0, 2, 4, 7}

Part A

Find the intersection of B and G

The intersection of two sets is defined as the set of all the elements in set A that is also present in set G

Hence, the set of elements that is present in set B and set G is 2

Mathematically, B n G = {2}

Part B

Find the union of set B and set G

The union of two sets is a set containing all elements that are in both sets B and G

B u G = {-2, -1 , 0 , 2, 3, 4, 5, 7)

Total number of jerseys he have now is 32 jerseys.

A coach has 12 jerseys in beginning. Now, he buys 2 sets of jerseys.

Each set of jerseys have 10 jerseys.

2 set of jerseys have 20 jerseys.

Using unitary method this can also be written as,

1 set ---------------->  10 jerseys

2set ---------------->  20 jerseys

So, total of 20 jerseys are present in 2 sets of jerseys.

Total number of jerseys he have now = 12 jerseys + jerseys in two sets

Total number of jerseys he have now = 12 jerseys + 20 jerseys = 32 jerseys

So we can write, he have total of 32 jerseys now.

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Step 1: Write the given expression

Step2: Expand the expression

Hence

hence the righ

The step function and its graph that represents the relationship between the number x of days and the total cost y of renting the chipper are present in the first option.

Given:

Charge for 1 day = $100

Charge for each additional day = $50

Let's assume

The cost of rent is y.

The number of days is x.

The total cost, y according to the data provided can be calculated by the equation,

y = 100 + 50x

Using y = mx+c, when graphing a step function that represents the relationship between the number of days and the total cost,

The gradient or slope will be always 50 for the graph.

So, when x = 0, y = 100 + 0 = 100

When x = 1, y = 100 + 50 = 150

When x = 2, y = 100 + 50 × 2 = 200

When x = 3, y = 100 + 50 × 3 = 250

Thus the step function is,

f(x) = 100 , if 0 < x ≤ 1

f(x) = 150 , if 1 < x ≤ 2

f(x) = 200 , if 2 < x ≤ 3

f(x) = 250 , if 3 < x ≤ 4

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Answer:

2702700

Step-by-step explanation:

Hi there ,

Given:

In a running competition, a bronze, silver and gold medal must be given to the top three girls and three boys. If 15 boys and 11 girls are competing.

To find:

How many different ways could the six medals possible be given out?

Explanation:

As given,

The number of boys competing in a competition = 15

The number of girls competing in a competition = 11

Three medals are given to top three girls and three medals are given to top three boys.

(I have given the rest of the answer in the images below :-)

If this helped you out do mark me as brainliest and stay positive :)

A fellow mate

Cheers !

A two-variable linear equation is one with the formula ax + by + c = 0.

The solution of the system exists  (1, 1) and (2, 4).

Let the system of Equations be

y = 3x - 2 and y = x²

From these Equations:

x² = 3x - 2,

simplifying the above equation, we get

⇒ x² - 3x + 2 = 0

⇒ x = 1, 2.

Therefore, the value of x exists x = 1, 2.

Therefore, the solution of the system exists  (1, 1) and (2, 4).

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Okay so draw a diagram with a ladder leaning against a wall and draw the ground now label the diagram take the hypotenuse is ladder and the base is distance between the ladder and the wall while the perpendicular is the wall

As we know hypo=√perpendicular^2+base^2 if we want to finder the p(perpendicular) the formula changes to p=√hypo^2-base^2 put the no in the places of the equation It should look something like this p=√20^2-10^2 use calculate to solve the answer should be 17. 32

Data

Given;

Hypo(h)= 20

Base(b)= 10

Required;

Perpendicular (p)=

Solution

As we know

hypo=√perpendicular^2+base^2

by changing the formula to find p

p=√hypo^2-b^2 -----eqi

by putting the values in eq i

p=√20^2-10^2

p=17.32

∠4 ≅ ∠5 Alternate internal angles

Applying the description we have the table is completed as follows

Statement                                          Reasons

x is parallel to y                                    Given

w is a transversal                                  Given  

angle 4 is congruent to angle 1           Vertical opposite angle

angle 1 is congruent to angle 5            Corresponding angle

angle 4 is congruent to angle 5           Alternate internal angles

The prove ∠4 ≅ ∠5 is done by the Alternate angle theorem

∠4 ≅ ∠ 1 vertical opposite angles

∠ 1 ≅ ∠5  Corresponding angle

then we can say that

∠ 1 ≅ ∠4 ≅ ∠5

hence: ∠4 ≅ ∠5 Alternate internal angles

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Answer:

A ✔ vertical angles

B ✔ corresponding angles theorem

C ✔ transitive property

Step-by-step explanation: i hope this helps :)

To solve an inequality, we need to isolate the value of x, and to do so we will perform a series of calculations in such a way that it remains the inequality unchanged, or at least still true.

To do so, we will perform first a sum of 2x to both sides of it, as follows:

Now, we subtract 3 from both sides:

To finish it, we divide both sides by 2:

In another way, we can express the following:

It means that the solution is option B.

To solve the second part, we need a filled line that comes from the negative infinity and goes until 2, but it must be including the number 2, and for this reason, the correct answer in the second part is:

D.

INFORMATION:

Using the graph of f(x) = x^2, we must describe transformations for the function g(x)=-8x^2

STEP BY STEP EXPLANATION:

First, we need to use the graph of f(x) = x^2 which is

Then, if analyze difference between f(x) and g(x), we can see that g(x) = -1*8*f(x)

So, to graph g(x) we have two transformations:

- Multiply f(x) by -1: When we multiply by -1 we obtain the parabola opening down

- Multiply f(x) by 8: When we multiply by 8 we obtain a more closed parabola

Finally, the final graph would be

ANSWER:

We have the following:

We can see that time is located on the x axis and the price of gasoline is located on y, we can conclude that in both periods the price increases, but in the first it increases slowly and in the second it increases quickly

Therefore, the answer is:

First, the price of gasoline in New mexico increases slowly, and then it increases quickly

The employer will charge $55 for 5 hours

The first step is to calculate the amount charged for an hour

22= 2

x= 1

cross multiply

2x= 22

x= 22/2

x= 11

The amount charged for 5 hours can be calculated as follows

11= 1

y= 5

cross multiply

y= 55

Hence $55 will be charged for 5 hours

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Answer:

0.1 gallons = 11.8 miles

10 gallons - 1,180 miles

Step-by-step explanation:

We are asked to find the probability that it contains cookies given that it contains coffee.

This is called conditional probability and is given by

This means that the probability of event A given that event B has occurred.

For the given case, it becomes

The probability P(Cookies and Coffee) is the intersection of the column "Cookies" and the row "Coffee" divided by the grand total.

The probability P(Coffee) is the row total of the row "Coffee" divided by the grand total.

Finally, the conditional probability is

Therefore, the probability that it contains cookies given that it contains coffee is 0.25

The length of one side of the base is 7 inches.

The height of the box is 3.5 inches.

The minimum surface area of the box is 147 inch².

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If on January 1, a company purchased new furniture at a cost of $26,000. The furniture is estimated to have a useful life of 5 years and a salvage value of $3200. The  book value of the furniture on December 31 of the first year is: $21,440.

Given data:

Cost = $26,000

Useful life  = 5 years

Salvage value = $3,200

First step is to calculate the  depreciation expenses:

Particular Amount

Cost $26,000

Less: Salvage value ($3,200)

Net cost (a) $22,800

Useful life (b) 5

Depreciation expenses (a/b) $4,560

($22,800 / 5 years)

Second step is to compute the  book value of furniture on 31 Dec of first year:

To determine the book value we would have to deduct the depreciation expenses from the cost.

Particular Amount

Cost of an furniture $26,000

Less: Depreciation ($4,560)

Book value $21,440

Therefore we can conclude that the book value is the amount of $21,440.

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The complete question is:

On January 1, a company purchased new furniture ata cost of $26,000. The furniture is estimated to have a useful life of 5 years and a salvage value of $3200The company uses the straight-line method of depreciation. What is the book value of the furniture on December 31 of the first year?

Answer:

The given function is a power function.

[tex]\textsf{The constant of variation is $\sqrt[3]{\dfrac{7}{5}}$}.[/tex]

[tex]\textsf{The power is $\dfrac{1}{3}$}.[/tex]

Step-by-step explanation:

Power function

Any function that can be written in the form:

[tex]\boxed{f(x)=k \cdot x^a}[/tex]

where:

Given function:

[tex]f(x)=\sqrt[3]{\dfrac{7x}{5}}[/tex]

[tex]\textsf{Apply radical rule} \quad \sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b}:[/tex]

[tex]f(x)=\sqrt[3]{\dfrac{7}{5}\cdot x}[/tex]

[tex]\implies f(x)=\sqrt[3]{\dfrac{7}{5}} \cdot \sqrt[3]{x}[/tex]

[tex]\textsf{Apply exponent rule} \quad \sqrt[n]{a}=a^{\frac{1}{n}}:[/tex]

[tex]\implies f(x)=\sqrt[3]{\dfrac{7}{5}} \cdot x^{\frac{1}{3}}[/tex]

Therefore, the given function is a power function.

[tex]\textsf{The constant of variation is $\sqrt[3]{\dfrac{7}{5}}$}.[/tex]

[tex]\textsf{The power is $\dfrac{1}{3}$}.[/tex]

I hope this is clear enough , although I did not arrive at the same answer using x in both equation .

It is given that the product of 7 and a number, increased by 3, is equal to twice the number, subtracted from 39.

It is required to find the number.

To do this, write the statement as an algebraic statement.

Let the number be x.

The product of 7 and a number is:

The product of 7 and a number increased by 3 is:

Twice the number is:

Twice the number subtracted from 39 is:

Since it is given that these expressions are equal, it follows that:

Solve the resulting equation for x:

The number is 4.

The functions are solved below

What is a function?

A function from either a given Set X to a set Y allocates exactly one item of Y to each member of X. The set X is known as the function's domain, while the set Y is known as the function's codomain.

The functions are solved as follows

(a) f(4) = 6x4 = 24

(b) g(2) = 9x2² + 5 = 36 + 5 = 41

(c) f(1) = 6x1 = 6

(d) g(0) = 9x0² + 5 = 0 + 5 = 5

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The linear combination of the given vector is computed to be:

[tex]-4u+v=\left[\begin{array}{ccc}23\\-28\\\end{array}\right][/tex]

given data

[tex]u=\left[\begin{array}{ccc}-6\\6\\\end{array}\right][/tex]

[tex]v=\left[\begin{array}{ccc}-1\\-4\\\end{array}\right][/tex]

Required to compute the linear combination in the form -4u + v

solving for -4u

[tex]-4u=\left[\begin{array}{ccc}-6*-4\\6*-4\\\end{array}\right][/tex]

[tex]-4u=\left[\begin{array}{ccc}24\\-24\\\end{array}\right][/tex]

solving for -4u + v

[tex]-4u+v=\left[\begin{array}{ccc}24+-1\\-24+-4\\\end{array}\right][/tex]

[tex]-4u+v=\left[\begin{array}{ccc}24-1\\-24-4\\\end{array}\right][/tex]

[tex]-4u+v=\left[\begin{array}{ccc}23\\-28\\\end{array}\right][/tex]

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Answer: what

Step-by-step explanation:bye