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Choose one of the following.

Parallel lines have ____________________.

A. one solution
B. 10 solutions
C. infinitely many solutions
D. no solution

Using linear functions, the system of inequalities that matches the graph is given by:

A linear function is modeled by:

y = mx + b

In which:

Given two points, the slope is given by change in y divided by change in x. For the first line, the points are:

(-1, -3) and (0,0).

Hence the slope is:

m = (0 - (-3))/(0 - (-1))

m = 3.

When x = 0, y = 0, hence the y-intercept is of b = 0 and the line is given by:

y = 3x.

Everything to the right of the solid line is shaded, hence the values that are equal(line is solid) or greater than the line compose the inequality, as follows:

y ≥ 3x.

For the second line, the points are:

(-2,3) and (1,-3).

Hence the slope is:

m = (-3 - 3)/(1 - (-2)) = -6/3 = -2.

Then:

y = -2x + b.

When x = -2, y = 3, hence:

3 = -2(-2) + b

b = -1.

Hence the line is:

y = -2x - 1.

Everything to the right of the dashed line is shaded, hence the inequality is:

y > -2x - 1.

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Answer:

The area is 12.57

The Circumference is 12.57

Step-by-step explanation:

Ruguru need $15 more to rent a car for 3 days.

Given,

Number of days Ruguru wants to rent a car = 3 days

The amount Ruguru has with him = $115

The cost for the rental of the car:

C = 25 + 35D

Where,

D is the number of days

Now,

Lets find the total rent of the car for 3 days

C = 25 + 35D

C = 25 + 35 × 3

C = 25 + 105

C = 130

The total rent of a car for 3 days is $130

We have to find the amount needed by Ruguru to rent a car for 3 days.

That is,

Total rent - Amount Ruguru has = Amount needed

130 - 115 = 15

Therefore,

Ruguru need $15 more to rent a car for 3 days.

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It will take 53 minutes to read 42 pages in a novel

Given,

The time taken to read 8 pages in a novel = 10 minutes

Therefore, the time taken to read 1 page = 10 ÷ 8 = 1.25 minutes

Now,

We have to find the time taken to read 42 pages of a novel.

Time to read 42 pages = 42 × 1.25

Time taken = 52.5 minutes

We can round it to nearest tenth, that is 53 minutes.

That is, the time taken to read 42 pages in a novel is 53 minutes.

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Answer: 3.5

Step-by-step explanation:

If your trying to solve for X the answer would be 3.5 because you calculate 2 to the power of 1 and get 2 which then by now your equation should look along the lines of 3×2X+1−4^1 X=8

Calculate 4 to the power of 1 and get 4 then you Subtract 1 from both sides.

and then Subtract 1 from 8 to get 7. Combine all terms containing X which would make the equation come down to a standard form which then means you would have to divide both sides by 2, by dividing by 2 undoes the multiplication by 2. You should get 7/2 which then = 3 and 1/2 converted into 3.5

The Height of the frame having area of 560cm² is 50cm.

By splitting a rectangle into two equal-sized right triangles, the formula for calculating the area of a rectangle may be obtained. For instance, a diagonal is drawn from vertex A to vertex C in the rectangle ABCD that is supplied.

The rectangle is split into two identical right-angled triangles by the diagonal AC.

(ABCD) Area = b × h

Given,

The area of the frame = 560cm²

Width of the frame = 11 1/5

Length = ?

Area of the rectangle = Length × Breadth

560 = 11 1/5 × L

⇒ L = 560 × 5/56

⇒ L = 50cm

The frame is 50cm tall.

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Correct question -

Claire is making a frame to display a drawing she made. The frame is 11 1/5 cm wide. The frame has a rectangular shape and an area of 560cm². How tall is the frame?

Answer:

[tex]x\leq 120[/tex]

---------------------------

Hope this helps!

Have a great day and God bless! :)

The measure of angle FLH is 31x  + 4

See attachment for the image that completes the question

The given parameters are

m∠FLG = 14x + 5°

m∠HLG = 17x − 1 °

The measure of FLH is calculated as

FLH = m∠FLG +  m∠HLG

This gives

FLH = 14x + 5 + 17x - 1

Collect the like terms

FLH = 14x + 17x  + 5 - 1

Evaluate the like terms

FLH = 31x  + 4

Hence, the measure of FLH is 31x  + 4

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Answer: Height is equal to approximately 3.56.

Step-by-step explanation:

3 * [tex]\frac{V}{\pi r^{2} }[/tex]

    2. INSERT Volume and Radius

3 * [tex]\frac{98}{\pi 5.13^{2} }[/tex]

    3.CALCULATE Height

Answer:

3.6cm=h

Step-by-step explanation:

v=1/3πr^2h

input your values

98=1/3×22/7×5.13×5.13×h

98=(22*5.13*5.13*h)/21

cross multiply

98*21=22*5.13*5.13*h

2058=22*5.13*5.13*h/22*5.13*5.13

3.6cm=h

hope it helps, please mark brainliest

The decimal fraction is 0.28 and reduced fraction is 7/25.

In mathematics, the fraction is generally a term which define the small part of something or amount of something. A fraction has generally two parts a numerator and a denominator.

The general syntax for fraction is : [tex]\frac{x}{y}[/tex]

where, x is the numerator part

           y is the denominator part

The fraction has two types of notations:

In the question given,

Total number of samples = 1214

Adults who answered peanut butter = 28%

Now, the decimal fraction  = 28 / 100 = 0.28

and, the reduce fraction  = 28/100 = (7)(4) / (25)(4) = 7/25

Hence, The decimal fraction is 0.28 and reduced fraction is 7/25.

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The recursive definition of f is f(1) = - 2, f(n) = f(n - 1) + 2. (Correct choice: A)

A recursive formula is a formula to find the value of an element in terms of previous elements of the same series. According to the statement, a sequence is defined by f(n) = - 4 + 2 · n. To derive the recursive definition, we must use algebra properties on the following difference:

Δf = - 4 + 2 · (n + 1) - (- 4 + 2 · n)

Δf = 2

n = 1

f(1) = - 4 + 2 · 1

f(1) = - 2

Then, the recursive definition of f is f(1) = - 2, f(n) = f(n - 1) + 2.

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The range of the data provided in the boxplot given the minimum number and the maximum number is 2.

A box plot is used to study the distribution and level of a set of scores. The box plot consists of two lines known as the whiskers and a box. The left whisker represents the lowest number in the dataset. The right whisker represents the highest number in the dataset. The difference between these numbers is the range.

The box can be used to determine the first quartile, median and the third quartile. These values can be determined using the lines on the box.

The range of a data set is the difference between the highest number and the lowest number. Range is used to measure the variance of a dataset.

Range = highest number - lowest number

7.5 - 5.5 = 2

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Answer:11 cups

Step-by-step explanation:

Srry if im wrong :)

[tex]\stackrel{3x}{R\rule[0.35em]{10em}{0.25pt}} A\stackrel{5x-12}{\rule[0.35em]{10em}{0.25pt}T} \\\\\\ 3x~~ = ~~5x-12\implies 3x+12=5x\implies 12=2x\implies \cfrac{12}{2}=x\implies \boxed{6=x} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{\LARGE RT}}{3(6)~~ + ~~5(6)-12\implies 18+18\implies \text{\LARGE 36}}[/tex]

Answer:

There is an outlier. The outlier is 20. 20 should be removed because a dice only has 6 faces, and there is no side numbered 20.

Step-by-step explanation:

A quotient is an answer in the division. The divisor (denominator) and the quotient are the factors. The dividend (numerator) is the amount being divided — it doesn’t matter whether the dividend is larger or smaller than the divisor.

In elementary school, we refer to this process only in terms of fractions, so many people don’t realize that fractions are just division. If your fraction is proper, you will get a decimal number or simplified equivalent fraction. If the numerator (multiple) is the larger number, then the quotient will represent the other factor after dividing.

For example, in the equation x + 5 = 10, x is the unknown variable, and you want to find some number, which when added to 5 would result in 10.

Quotients are answers to a division problem.

For example, the quotient of 8÷2 would be 4.

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Using a linear function, it is found that Tamara will need to order a new bag after 46 days.

A linear function is modeled according to the following rule:

y = mx + b

In which:

The slope and the intercept in the context of this problem are given as follows:

Hence the weight of the bag after d days is given by:

W(d) = 20 - 0.4d.

He needs to order a new bag when W(d) = 1.6, hence:

1.6 = 20 - 0.4d.

0.4d = 18.4

d = 18.4/0.4

d = 46 days.

Hence she needs to order the new bag in 46 days.

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When Kenneth opened her account, her account balance was 30.

A function is an expression that assigns each input value, say x, a unique output value, say y. Mathematically, a function can be represented as-

F(x) = x + a

Here, we are given that Kenneth's bank account is modeled by the following equation-

f(x) = 13x + 30

here, x =  number of weeks

and  f(x) = total amount

When Kenneth must've opened his account, the number of weeks would've been zero.

⇒ x = 0

Substituting the value of x = 0 in f(x), we get-

f(0) = 13(0) + 30

f(0) = 0 + 30

f(0) = 30

Thus, when Kenneth opened her account, her account balance was 30.

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The volume will be 1004.5 ft³.

It should be noted that the volume is calculated as:

= Length × Width × Height

= 12.25 × 10 × 8.2

= 1004.5 ft³

Therefore, the volume will be 1004.5 ft³.

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 hi!

lets try and further analyze this.

The integer -2 would be graphed directly on the "-2" point on the line. also marking positive 2 (2) as for that's its opposite. Positive 3 (3) would be marked on the 3 and so would -3. Then -5 and positive 5 (5) and lastly -1 and positive 1 (1).

hope this helps!

side note: for actually graphing the point just use a filled in dot indicating where you mark it.

Answer:

48x^2 - 48x + 38

Step-by-step explanation:

To get the composite function first understand the process of which a function inside another operates.

First solve one step at a time by trying to evaluate the inside before evaluating the outside using substitution.

For instance, h(g(f(x))) is the h function of g function of f.

Since f(x) is the inner component of the composite function, replace the x of g with the value of f(x).

Such that g(x) = 3x^2 + 5 → 3(f(x))^2 + 5 →

3(2x - 1)^2 + 5 → 3(2x - 1)(2x - 1) + 5 [foil] → 3(4x^2 - 4x + 1) + 5 → 12x^2 - 12x + 3 + 5 →

12x^2 - 12x + 8

Thus g(f(x)) = 3(f(x))^2 + 5 = 12x^2 - 12x + 8.

Finally to compute h(g(f(x))), using the process from the first composite function, same can be applied here:

Since h(x) = 4x + 6 →

h(g(f(x))) =

h(12x^2 - 12x + 8) =

4(12x^2 - 12x + 8) + 6 [distribute] →

48x^2 - 48x + 32 + 6 [combine like terms] →

48x^2 - 48x + 38

Answer:

n=-2/3

Step-by-step explanation:

2/3n + 3/2n = -13/4

Make 2/3n and 3/2n into 4/6n and 9/6n so you can add them together.

13/6n = -13/4

Divide both sides by 13/6

n=-2/3

^ i hope thats what you were asking for :)

Answer: -32+5√6

Step-by-step explanation:

(3√3 - 5√2) (2√3 + 5√2)=

(3√3 * 2√3) + (3√3 * 5√2) - (5√2 * 2√3) - (5√2 * 5√2) =

(3*2*√3*√3) + (3*5*√3*√2) - (5*2*√2*√3) - (5*5*√2*√2)=

6*3 + 15*√(3*2) - 10*√(2*3) - 25*2=

18+15√6-10√6-50=

18-50+(15-10)*√6=-32+5√6

Answer:

0.10x + 0.13y = 10780

x + y = 100000

x = 74000 --------------10%

y = 26000 --------------13% (more risky)