The line parallel to y=-7x-2 through (-4,6)

Answer:

a

Step-by-step explanation:

Given

2| x - 3 | + 5 = 17 ( subtract 5 from both sides )

2| x - 3 | = 12 ( divide both sides by 2 )

| x - 3 | = 6

The absolute value function always returns a positive value but the expression inside can be positive or negative, that is

x - 3 = 6 OR -( x - 3) = 6

x - 3 = 6 ( add 3 to both sides )

x = 9

OR

-( x - 3) = 6 ← distribute left side

- x + 3 = 6 ( subtract 3 from both sides )

- x = 3 ( multiply both sides by - 1 )

x = - 3

As a check

Substitute these values into the left side of the equation and if equal to the right side then they are the solutions.

x = 9 → 2|9 - 3| + 5 = 2|6| + 5 = (2 × 6) + 5 = 12 + 5 = 17 ← True

x = - 3 → 2|- 3 - 3| + 5 = 2| - 6 | + 5 = (2 × 6) + 5 = 12 + 5 = 17 ← True

Hence x = 9 or x = - 3 are the solutions → a

Answer:

$159.95

Step-by-step explanation:

Let price of trumphet be defined by [tex]x[/tex]

price of clarinet = $139.95

Number of clarinets sold = 19

Earning through clarinets' sale = [tex]19*139.95 = 2659.05[/tex]

Total earning of store = $4578.45

Earning through trumphets' sale = [tex]4578.45 - 2659.05 = 1919.40[/tex]

price of one trumohet = [tex]\frac{1919.40}{12} = 159.95[/tex]

price of clarinet = $159.95

Answer:64<84

Step-by-step explanation:

Answer:85.15

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

EFGH is a kite, so EF ≅ FG and EH ≅ HG.

The area of the kite consists of two area of triangles EFG and EHG.

1. Area of triangle EFG:

[tex]A_{\trangle EFG}=\dfrac{1}{2}\cdot EG\cdot h,[/tex]

where h is the height drawn from point F to the side EG.

1. Area of triangle EHG:

[tex]A_{\trangle EHG}=\dfrac{1}{2}\cdot EG\cdot H,[/tex]

where H is the height drawn from point H to the side EG.

3. Note that

[tex]EG \cong \text{rectangle's length}[/tex]

[tex]h+H\cong \text{rectangle's width}[/tex]

So,

[tex]A_{\text{kite }EFGH}\\ \\=A_{\triangle EFG}+A_{\triangle EHG}\\ \\=\dfrac{1}{2}\cdot EG\cdot (h+H)\\ \\=\dfrac{1}{2}\cdot \text{rectangle's length}\cdot \text{rectangle's width}\\ \\=\dfrac{1}{2}A_{\text{rectangle}}[/tex]

Thus, option C is true (the area of the kite doesn't depend on ratio in which points E and G divide the side)

Answer:

C.) The area of EFGH is always 1/2 of the area of the rectangle.

Step-by-step explanation:

Answer:

z=2x+3

z-3=2x

x=z-3/2

Represent it as N+3/2.

☺Happy to help!

Answer:

75

Step-by-step explanation:

Answer:75

Step-by-step explanation:

1/5=.2

15/.2=75

The answer would be {3, 5, 7, 9, 11, 13, 15}.

Answer:

The other answer is wrong the correct answer is {3, 5, 7, 9, 11, 13}

Step-by-step explanation:

Odyssey

Answer:

Any number plus 0 is the same as the first number.

Step-by-step explanation:

6 + 0 = 6, 8 + 0 = 8,9+ 0 = 9, 100 + 0 = 100.

Conclusion: Any number plus 0 is the number.

For example: x + 0 = x

x is the number.

Answer: 0

Step-by-step explanation:

100+0=100.

Just basic addition too. 100+0=100. That simple.

No other number can give off 100 like 0 can. 100 plus 0 just gives it the number itself.

Just like how 6+0=6. 6 is just being added to itself.

So, your answer for this is 0. No other number can give off a better answer than the 0 for this problem.

Bada bing bada boom! I hope this helps you!

Answer: No solution

Step-by-step explanation:

9-(-8)=20             given

9+8=20                the two negatives cancel out, making the eight positive

17=20                   this statement is not correct, so the answer is no solution

no solution

I'm not sure if there was supposed to be a variable in there somewhere, but I did my best to explain. Hope this helps!

Answer:

9 -( -8)= 9 + 8= 17 not 20

17 is the solution

Answer:

3 / 4

Step-by-step explanation:

[tex]\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill&1196.61\\ P=\textit{original amount deposited}\\ r=rate\to 2.25\%\to \frac{2.25}{100}\dotfill &0.0225\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &8 \end{cases}[/tex]

[tex]\bf 1196.61=P\left(1+\frac{0.0225}{4}\right)^{4\cdot 8}\implies 1196.61=P(1.005625)^{32} \\\\\\ \cfrac{1196.61}{(1.005625)^{32}}=P\implies 999.9969 \approx P[/tex]

To find the cost of a single cinema ticket, multiply the amount each friend paid, £6.15, by 4 to get the total cost for 3 paid tickets. Divide this total, £24.60, by 3 to find that the cost of one ticket is £8.20.

The question pertains to a group of 4 friends who buy cinema tickets using an offer where they buy 3 tickets and get 1 free. Since each friend pays £6.15, we need to determine the actual cost of a single ticket.

Under the offer, they are buying a total of 4 tickets for the price of 3. Therefore, we can calculate the cost of 3 tickets by multiplying £6.15 by 4, which gives us a total of £24.60. To find the cost of a single ticket, we divide the total cost of £24.60 by the number of tickets bought, which is 3.

Here is the calculation step:
Total cost for 4 friends = 4 × £6.15 = £24.60
Cost of a single ticket = [tex]\frac{24.60}{3}[/tex] tickets = £8.20

Therefore, the cost of one ticket without the offer is £8.20.

Answer: 9.25

Step-by-step explanation:

Answer:

−9.25

Step-by-step explanation:

Since the fraction is negative, the decimal equivalent is negative, too. Divide 74 by 8. The answer is −9.25.

Answer:

His car's speed rate to the nearest thousandth of an hour is 100.489

Step-by-step explanation:

First: This is the only step, round the speed rate to the nearest thousandth:

When rounding always look at the place value they're telling you to round to and the place value to the right of it. Since, the question wants us to round to the nearest thousandth, look at the thousandths place but more specifically the place value to its right. The thousandths is the third digit behind the decimal point and the one to its right would be the fourth.

100.4893

So, if the number to the thousandths' right is less than 5 turn that number into a zero and keep the rest of the number the same. If the number is greater than or equal to 5 round up by making the number in the thousandths place a digit bigger.

Since 3 is smaller than 5, we'll turn the 3 into a zero and keep the rest the same.

100.4890

Since the zero is behind the decimal point and it is the number farthest to the left we can take it out.

100.489

Thank you for reading

Topic: Rounding, Place Value

Answer:

c

Step-by-step explanation:

72

Final answer:

The angle of rotation for rotational symmetry of a regular pentagon is 72°, which is found by dividing the full rotation of 360° by the number of sides (5).

Explanation:

The angle of rotation for rotational symmetry of a regular pentagon is the angle you rotate the pentagon until it looks exactly the same as it did before the rotation. A regular pentagon has five sides that are all of equal length, and the amount of rotation required to bring one vertex to the position of the next is 360° divided by the number of sides. Therefore, the angle of rotation for a regular pentagon is 360°/5, which equals 72°.

Answer:

x = -7

Step-by-step explanation:

-6(8 + 7x) = -342

-48 + 42x = -342

42x = -294

x = -294/42

x = -7

Answer is provided in the image attached.

Answer:

y = -2

Step-by-step explanation:

You would use the Point-Slope Formula since we are given a point:

y - y₁ = m(x - x₁)

y + 2 = 0

y = -2

Because there was no rate of change [slope] given, it was automatically assumed to be a zero slope, which is a horizontal line.

I am joyous to assist you anytime.

Answer:

D

Step-by-step explanation:

y = -2/5x+4

Hope I helped all you have to do is subsitute the values for m and b!

Answer:72 miles

Step-by-step explanation:

You have to divide 5 by 1 then 360 by 5 and then get 72

Answer:

5/6 + 4/9 = 23 / 18

= 1 5/18

Step-by-step explanation:

Answer:

21 = n

Step-by-step explanation:

[tex]5 - \frac{1}{3}n = -2[/tex]

-5 - 5

________________

-⅓n = -7

____ __

-⅓ -⅓

21 = n

* Dividing by a fraction is the exact same as multiplying by its multiplicative inverse:

[tex]\frac{-7}{-\frac{1}{3}} = -7 \times -3 = 21[/tex]

I am joyous to assist you anytime.

Answer: zero and zero nineteenth thousandths

Step-by-step explanation:

The number 0.019 in expanded form is written as 0.010 + 0.009, which represents one-hundredth and nine-thousandths respectively.

The student is asking for the number 0.019 to be written in expanded form. Expanded form is a way to break down a number to show the place value of each digit. The number 0.019 in expanded form can be written as:

0.010 + 0.009

The first 0.010 represents one-hundredth and the second 0.009 represents nine-thousandths.

https://brainly.com/question/34236895

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Answer:

[tex]-7 + 8i[/tex]

Step-by-step explanation:

[tex](-11 + \sqrt{-4}) + (4 + \sqrt{-36}) = (-11 + 2\sqrt{-1}) + (4 + 6\sqrt{-1})[/tex]

We know [tex]\sqrt{-1}[/tex] is a complex number and is defined by [tex]i[/tex]

∴[tex](-11 + \sqrt{-4}) + (4 + \sqrt{-36}) = (-11 + 2i) + (4 + 6i) = -7 + 8i[/tex]

Answer:

5x^4 - 37x^3 - 6x^2 + 41x - 6

Step-by-step explanation:

Answer:

Because they are

Step-by-step explanation:

they ar4

Triangles are similar if their angles are congruent, supported by the AAA theorem. The similarity of triangles implies that the corresponding side lengths are proportional, which can be expressed algebraically or in words.

To justify that the triangles are similar, we look for congruent angles and proportional sides. The student indicated that the triangles have the same angles, which satisfies the AAA (Angle-Angle-Angle) similarity theorem. Because the angles are congruent, the sides are proportional, which means the ratios of corresponding sides are equal.

With words, we can express the relationship of corresponding lengths in similar triangles as the ratio of one triangle's side lengths to the other's. Algebraically, if we have corresponding sides a, b, and c from Triangle 1, and sides d, e, and f from Triangle 2, then a/d = b/e = c/f.

To solve for an unknown quantity, we algebraically isolate the variable in our equation, plug in the known values, calculate the answer, and then check to ensure the result is reasonable. For example, if we know sides a, b, d, and e, and we want to find side c, we would set up the proportion c/f = a/d, and after substituting the known values, we solve for c.

Answer:

The change in the index is - 69/50

Step-by-step explanation:

* Lets explain what is the rational number

- A rational number is a number that can be expressed as a fraction

 a/b where a and b are integers and b ≠ 0

- A rational number have numerator and denominator

- Whole numbers, integers, fractions, terminating decimals and

 repeating decimals are all rational numbers

- The rational numbers includes all positive numbers, negative

  numbers and zero that can be written as a fraction

- To convert a Decimal to a Fraction follow these steps:

# Write down the decimal divided by 1

# Multiply both top and bottom by 10 for every number right the

  decimal point

# Simplify (or reduce) the fraction

* Lets solve the problem

- A stock market index drops by 1.38 points

- We need to find the rational number represents the change in

 the index

∵ Drop means the stock is become less

∴ The value of change will be negative

∵ The stock is drops by 1.38

∴ -1.38 = -1.38/1

- Multiply up and down by 100 because there are 2 digits right the

 decimal point

∴ -1.38 = -138/100

- Divide up and down by 2

∴ -1.38 = - 69/50

∴ The change in the index is - 69/50 (-1.38)

Answer: [tex]\dfrac{69}{50}[/tex]

Step-by-step explanation:

A rational number is in the form of [tex]\dfrac{p}{q}[/tex] , where [tex]q\neq0[/tex]. and p and q are integers.

Given : A stock market index drops by 1.38 points.

To convert 1.38 into rational , we divide and multiply it by 100 ( 1.38 is decimal expression up to hundredth) , we get

[tex]1.38\times\dfrac{100}{100}=\dfrac{138}{100}[/tex]

Now , we divide  numerator and denominator by 2 , we get

[tex]\dfrac{69}{50}[/tex]

Hence, the rational number represent the change in the index is [tex]\dfrac{69}{50}[/tex].