3 + b/d

HELP !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

The piece-wise linear functions can be written as follows:

A linear function is modeled by:

y = mx + b

In which:

For x equal or less than -2, the line passes through (-3,-3) and (-2,-2), hence the rule is:

[tex]f(x) = x, x \leq -2[/tex].

For x greater than -2 up to 1, the y-intercept is of -7, and the line also passes through (1,-8), hence the rule is:

[tex]f(x) = -x - 7, -2 < x \leq 1[/tex].

For x greater than 1, the function goes through (2,-5) and (3,-3), hence the slope is:

m = (-3 - (-5))(3 - 2) = 2.

The rule is:

y = 2x + b.

When x = 2, y = -5, hence:

-5 = 2(2) + b

b = -9.

Hence:

[tex]f(x) = 2x - 9, x > 1[/tex].

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Using the relation between velocity, distance and time, it is found that it took the knight 20 hours to traveled from one kingdom to another.

Velocity is distance divided by time, hence:

v = d/t

On the first day, he traveled at a speed of 10 mph, a distance of d, hence:

10 = d/t

t = d/10

On the second day, he traveled at a speed of 8 mph, a distance of 180 - d, hence:

8 = (180 - d)/t

t = (180 - d)/8

Equaling both equations for t, we find the distance on the first day, hence:

d/10 = (180 - d)/8

8d = 1800 - 10d

18d = 1800

d = 100 miles.

The time on the first day was:

t = 0.1d = 0.1 x 100 = 10 hours.

On the second day he traveled the same amount of time, hence, in total, he traveled 20 hours.

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The area of QOR from the given diagram is 2π square centimeters

A sector is said to be a part of a circle made of the arc of the circle along with its two radii.

The formula for calculating the area of a sector is expressed as;

A = r²β/2

where

r is the radius of the circle

β is the angle subtended

Given the following parameters

<QOR = 180 - <POQ

<QOR = 180 - 135

<QOR = 45 degrees

Determine the radius

L = rβ

π = r(π/4)

1 = r/4

r =  4

Determine the area of QOR

Area = 4²(π)/8

Area = 2π

Hence the area of QOR from the given diagram is 2π square centimeters

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22

bc I know that is 22 so just put that

Answer: 4/5

Step-by-step explanation: For a line to be parallel to another line there must be two conditions true.

Condition 1: Both lines must have the same slope (i.e the same x in the form y = mx + b)

Condition 2: Both lines must have different y-intercepts (i.e different b in the form y = mx + b)

Thus, if you are looking for the slope of the line parallel to y = 4/5x - 3, we can look at condition 1, and see that the slope should also be 4/5 for the other line.

Remember that an ordered pair is of the form (x, y), then the ordered pairs on the inverse of the relation are (x, -x/5).

Assuming the given relation is:

y + 5x = 0

We can rewrite it to:

y = -5x

Then the inverse will be a function g(x) such that:

y = -5*g(x) = x

Solving for g(x):

g(x) = (-x/5).

Then the inverse of the relation is:

y = -x/5

Remember that an ordered pair is of the form (x, y), then the ordered pairs on the inverse of the relation are (x, -x/5).

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After rounding to the nearest tenth, we get:

[tex]\frac{2.1}{1.488} = 1.5[/tex]

We have the quotient:

[tex]\frac{2.1}{1.488}[/tex]

If you multiply the numerator and denominator by 1000, you will get the simpler quotient:

[tex]\frac{2100}{1488}[/tex]

It gives:

[tex]\frac{2100}{1488} = 1.45[/tex]

Now we want to round it to the nearest tenth, which is the first digit after the decimal point.

To do so, we need to look at the number at the right of it.

In this case, we can see a 5, so we should round up, then we have:

[tex]\frac{2100}{1488} = 1.5[/tex]

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Paul's rent budget is $750, given that his food budget of $225, is 30 percent of his rent budget.

Fractions are representation of quantities as a part of a certain quantity.

Written as a/b, read as a by b, and functions as a divided by b, represents a fraction showing a parts of b equal parts.

a is called the numerator, and b is called the denominator.

Percentages are modified fractions where the whole quantity is represented by 100.

To convert a fraction into percentages we multiply it by 100, while to convert percentages to fraction divided by 100.

In the question, we are given that Paul's budget for food is 30% of the budget he has for rent.

We are asked if his budget for food is $225, what is his budget for rent.

We assume Paul's budget for rent to be $x.

We know that Paul's food's budget is 30 percent of his rent.

Hence, Paul's food budget = 30% of x.

or, Paul's budget for food = 30/100 * x {To convert percentages to fraction divided by 100}

But, we know that Paul's food budget is $225. Thus, we can show that:

225 = 30/100 * x,

or, x = (225*100)/30 = 750.

Thus, Paul's rent budget is $750, given that his food budget of $225, is 30 percent of his rent budget.

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The time taken to the closest minutes for the pie to cool to 80∘F is 123 minutes

T(t) = 68e^−0.0174t + 72

80 = 68e^−0.0174t + 72

80 - 72 = 68e^−0.0174t

8 = 68e^−0.0174t

e^−0.0174t = 8/68

e^−0.0174t = 0.11764705882352

ln e (−0.0174t) = ln (0.11764705882352)

1 × −0.0174t = -2.1400661634962708

-0.0174t = -2.1400661634962708

t = -2.1400661634962708 / -0.0174

t = 122.9923

Approximately,

t = 123 minutes

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Answer:

  -7, 15

Step-by-step explanation:

The positive difference between E and G is 11.

  G - E = 11

  G = 11 + E = 11 + 4

  G = 15 . . . . . . . . . . . . . when G is right of E

__

  E - G = 11

  E - 11 = G = 4 - 11

  G = -7 . . . . . . . . . . . . when G is left of E

Possible coordinates for G are -7 and 15.

Answer:

[tex]15x^3 +10x^2 - 15x[/tex]

Step-by-step explanation:

Hello!

Use the distributive property and multiply like terms.

The simplified form is [tex]15x^3 +10x^2 - 15x[/tex].

Answer: A. x = 4

Step-by-step explanation:

Substituting 4 for x..

(4+7)^2 = 121

(11)^2 = 121

11 * 11 = 121

Answer:

1/4

Step-by-step explanation:

Chances of getting tails out of all the numbers (including heads)

Totals numbers (including heads & tails): 12

Tails & Even Number: 3

3/12 simplified to 1/4

When the coordinate satisfies the original inequality, if a stays the same, b must be greater than its previous value to satisfy the new inequality.

It should be noted that inequality provides an interval to the solution.

This is illustrated graphically. Let's illustrate this with an example, suppose a =1, b = 3

a - b < 0.

1 - 3 < 0

-2 < 0

If a stays the same value, b will be greater than 1.

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The cube can contain 1000 cm^3 of water

The side length is given as:

L = 10 cm

The amount of water it can contain is calculated as;

V =L^3

So, we have:

V = 10^3

Evaluate

V = 1000

Hence, the cube can contain 1000 cm^3 of water

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Given the diameter of the circular garden, the area of the garden is 28.36 yd².

The area of a circle is expressed as; A = πr²

Given that;

A = πr²

A = 3.14 × (3yd)²

A = 3.14 × 9yd²

A = 28.36 yd²

Given the diameter of the circular garden, the area of the garden is 28.36 yd².

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Answer:

2

Step-by-step explanation:

Select two points that the red line goes through like (0,-10) and (2,-6).  If I start at the bottom left of the red line, I can see that I am moving to the right and up.  That means that the slope will be positive.  As my x is increasing so is my y.  Starting at point (0,-10) 2 space, but each space counts as 2, so I really move up 4.  Then I check to see how much I moved right.  It is only one space, but again, I am counting by 2s, so I really moved 2 units to the right.  

The fraction would be 4/2 which just equals 2/1  or 2.  

The metallurgist would need 46.875 lb of an alloy containing 30 % copper and 3.125 lb of an alloy containing 62 % copper to produce 50 lb of a third alloy.

In this question we must prepare a third alloy by using correct quantity of two alloys with different copper concentrations. Required weights can be determined by applying concept of weighted average:

(32/100) · (50 lb) = (30/100) · x + (62/100) · (50 - x)

32 · 50 = 30 · x + 62 · (50 - x)

32 · 50 = 30 · x + 62 · 50 - 62 · x

32 · x = 30 · 50

x = 46.875

The metallurgist would need 46.875 lb of an alloy containing 30 % copper and 3.125 lb of an alloy containing 62 % copper to produce 50 lb of a third alloy.

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Answer: 54

Step-by-step explanation:

So I helped 54 customers in 7.5 hours yesterday.

Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression for some number of times.

Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.

Given:

You helped 3.6 customers per half hour yesterday.

That means,

for one hour:

Using multiplication

(3.6) x 2 per 1/2 x 2 hours

7.2 per hour.

Therefore,

if n hours so,

(7.2) per n hours

Here, n = 7.5

(7.2) x (7.5) per 7.5 hours

54 customers per 7.5 hours.

Therefore, I helped 54 people in 7.5 hours.

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The missing values of the right angle triangle are; a = 28 yds; c = 47 yds; ∠B = 54°

From the attached image of the right angle ABC, we see that;

∠A = 36°

b = 38 yd

∠C = 90°

Using trigonometric ratios, we have;

a/38 = tan 36

a = 38 * tan 36

a = 27.61 yd ≈ 28 yds

Similarly;

38/c = cos 36

c = 38/cos 36

c = 46.97 yds ≈ 47 yds

∠B = 180 - (36 + 90)

∠B = 54°

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Answer:

Step-by-step explanation:

(0,2)

Answer:

Step-by-step explanation

So, the graph goes through the points, (-3,0) and (2,0). 3 points on the graph can be (-3,0), (2,0), and (4,3)

The future values of Ashley's periodic deposits under the five scenarios are stated in the deposit table as follows:

Item     Initial       Periodic      Deposit    Interest    Future Value    Interest

         Deposit     Deposit        Period        Rate                                    ($)

a.      $10,000     $10,000     6 months        5%        $61,774.51      $1,774.51

b.     $10,000     $10,000     3 months        5%      $30,502.78       $502.78

c.      $10,000    $10,000     6 months        5%        $51,774.51     $1,522.42

d.    $20,000    $10,000      6 months       5%        $72,201.71     $2,201.71

e.   $10,000     $10,000     6 months       5%/6%  $60,803.78       $803.78

The future value of a periodic investment represents the present value of cash flows compounded at an interest rate into the future.

The future value is computed using the FV formula or factor.

It can also be computed using an online finance calculator as follows:

Periodic Deposit = $10,000

Investment period = 6 months

Interest rate = 5% compounded monthly

N (# of periods) = 6 months

I/Y (Interest per year) = 5%

PV (Present Value) = $0

PMT (Periodic Payment) = $10,000

Results:

FV = $61,774.51

Sum of all periodic payments = $60,000 ($10,000 x 6)

Total Interest = $1,774.51

c) Interest on $10,000 for 3 months is $1,522.42 ($1,774.51 - $252.09).

d)                             Future Value      Interest

5% with $20,000   $82,285.04    $2,285.04

5% with  $10,000     (10,083.33)          (83.33)

Total for 6 months   $72,201.71     $2,201.71

e)                            Future Value       Interest

5% for 3 months    $30,502.78       $502.78

6% for 3 months     $30,301.00       $301.00

Total for 6 months $60,803.78      $803.78

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The factor of the polynomial expression 4x^3 – 12x^2 + 4x by using GCF method is  4x(x^2 - 3x + 1).

The factors of a given number are those numbers that are divisible by the given number without a remainder.

By using the GCF method in an algebraic, i.e. the factors of the algebraic equation will be dependent on the greatest common factor.

From the given information, we are to factorize the following expression by using the GCF method as follows.

1.

4x^3 – 12x^2 + 4x

Here; the common expression in all the three variables is 4x. So, we have:

= 4x(x^2 - 3x + 1)

Option A is correct

2.

9x^4 + 4x^3 - 27x^2 + 12x

The common expression here is (x); So,

= x(9x^3 +4x^2 - 27x + 12)

Option B is correct

3.

x^2 - 3x + 4

This polynomial expression cannot be factored.

Option F is correct.

4.

17x^5 + 51x^2 - 34

= 17(x^5 + 3x^2 - 2)

Option D is correct.

The factorization of a quadratic equation (polynomial expression) in the form (ax^2 + bx + c) by grouping results into two factors that if multiplied together result back into the original equation.

Given that:

5.

x^2 – 2x + 1

Factors are two numbers that if the multiplied result in (ac) and if added it gives us (b)

By grouping, the polynomial expression is:

= (x - 1)(x - 1)

Option A is correct

6.

x^2 + 2x - 15

= (x + 5) (x - 3)

Option C is correct

7.

x^2 – 3x – 18

=(x + 3)(x - 6)

Option B is correct

8.

8x^2 + 47x + 28

= This polynomial expression cannot be factored in as it contains rational numbers.

Option A is correct.

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[tex]\large\displaystyle\text{$\begin{gathered}\sf 9|x-8| < 36 \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf Divide \ both \ sides \ by \ 9. \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf Solve \ Absolute \ Value. \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf We \ know \ x-8 < 4 \ and \ x-8 > -4 \end{gathered}$}[/tex]

         [tex]\large\displaystyle\text{$\begin{gathered}\sf x-8 < 4 \ (Condition \ 1) \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf x-8+8 < 4+8 \ (Add \ 8 \ to \ both \ sides) \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf x < 12 \end{gathered}$}[/tex]

           [tex]\large\displaystyle\text{$\begin{gathered}\sf x-8 > -4 \ (Condition \ 2) \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf x-8+8 > -4+8 \ (Add \ 8 \ to \ both \ \ sides) \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf x > 4 \end{gathered}$}[/tex]

[tex]\underline{\boldsymbol{\sf{Answer}}}[/tex]

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf x < 12 \ and \ x > 4 \end{gathered}$} }[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf Therefore,\bf{\underline{the \ correct \ option}} \ \end{gathered}$}\large\displaystyle\text{$\begin{gathered}\sf is \ \bf{\underline{"A"}}. \end{gathered}$}[/tex]

Answer:

12

Step-by-step explanation:

3x^2

because the information provided states that x = -2, that is what we are going to replace x with.

3(-2)^2

the next step is to evaluate the power because that is next in PEMDAS.

(-2)^2 = 4

that leaves us with:

3 * 4 = 12      ( the " * " represents the multiplication sign)

hope this helps!

Answer:

D. 5/72

Step-by-step explanation:

The non-zero digits are 1 through 9.

There are 9 different non-zero digits.

p(A) = 1/9

There are 5 odd digits.

p(B) = 5/8

p(A and B) = p(A) × p(B) = 1/9 × 5/8 = 5/72

I think the answer is

A: 1/18

The missing number is 20.

Subtraction is the mathematical operation that is used to find the difference between two or more numbers.

In order to find the missing number, subtract the total number of people who like science and mathematics from the total number of people who like science

38 - 18 = 20

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The monthly payments for each add-on interest loan is $29.7.

Simple interest is a way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific duration of time. Contrary to compound interest, where we add the interest of one year's principal to the next year's principal to compute interest, the principal amount under simple interest remains constant.

According to the question,

Principal (P) = $1150

Rate of Interest(R) = 6%

Time (T) = 4 years

The interest is calculated as follows:

SI = (P × R × T)/100

SI = (1150 × 6 × 4)/100

SI=$ 276

Amount (A) = P + SI

A = $(1150 +276)

A = $1426

Monthly payment with interest = A/(4×12)

= $ 1426/48

= $29.7

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