which of the following is a solution to the equation 16=4x-4?
a.-5
b.-4
c.5
d.16

let's firstly convert the mixed fractions to improper fractions and then multiply.

[tex]\bf \stackrel{mixed}{5\frac{3}{7}}\implies \cfrac{5\cdot 7+3}{7}\implies \stackrel{improper}{\cfrac{38}{7}}~\hfill \stackrel{mixed}{2\frac{2}{7}}\implies \cfrac{2\cdot 7+2}{7}\implies \stackrel{improper}{\cfrac{16}{7}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{38}{7}\cdot \cfrac{16}{7}\implies \cfrac{(38)(16)}{(7)(7)}\implies \cfrac{604}{49}\implies 12\frac{20}{49}[/tex]

Answer:

Step-by-step explanation:

94 dollars

Answer:

The discount would be $94.50 but the final price would be $220.25.

Hope this helps!

Step-by-step explanation:

The given table:

X       Y

3    − 2

6    − 4

9   − 6

12  − 8

To find, the constant ratio, [tex]\dfrac{y}{x}[/tex] = ?

The constant ratio, [tex]\dfrac{y}{x}[/tex] = [tex]\dfrac{-2}{3}[/tex],

The constant ratio, [tex]\dfrac{y}{x}[/tex] = [tex]\dfrac{-4}{6}[/tex] = [tex]\dfrac{-2}{3}[/tex],

The constant ratio, [tex]\dfrac{y}{x}[/tex] = [tex]\dfrac{-6}{9}[/tex] = [tex]\dfrac{-2}{3}[/tex] and

The constant ratio, [tex]\dfrac{y}{x}[/tex] = [tex]\dfrac{-6}{9}[/tex] = [tex]\dfrac{-2}{3}[/tex]

Thus, the required option A) yes; [tex]\dfrac{-2}{3}[/tex] is correct.

Answer:

36 batches

Step-by-step explanation:

we know that

Each bath of cookies used 2/9 cup of sugar

so

using proportion

Find out how many batches of cookies Melinda makes for 8 cups of sugar

[tex]\frac{1}{(2/9)}\ \frac{bath}{cups}=\frac{x}{8}\ \frac{bath}{cups}\\\\x=8/(2/9)\\\\x=36\ batches[/tex]

Answer:

5 years = 89,940

10 years = 107, 856

Step-by-step explanation:

75000 * 1.037 ^ 5 for the 5 years one

Then do the answer (89940) and times by 1.037 ^ 5. For 10 years

You do it to the power of 5 because you are adding on another 5 years

a) ASA congruency

b)SAS congruency

c)SSS congruency

d) Not congruent

Step-by-step explanation:

Step 1:

a)

Angle PRQ = Angle RQS

Angle PRQ = Angle QRS (since PQ is parallel to RS , these form corresponding angles and hence are equal.

QR is the common Side

Hence 2 angles are same and the side which is included are same.Hence the 2 given triangles are congruent.

Step 2 :

b)

Angle IGH = Angle EDF

Side IG = DF and Side GH = DE

Here 2 of the sides of the triangle are same and the Angle which is included are same.

Hence the given triangles are equal

Step 3:

c)

In the given triangles the three sides re equal. Hence as per the side Side Side postulate the triangles are equal.

Step 4:

d) 2 angles are equal but the equal Side is not included and hence the two triangles are not congruent

The blank is -8

Step-by-step explanation:

Let us revise some rules of indices:

∵ [tex]4^{3}[/tex] × [tex]4^{-6}[/tex] = [tex]4^{5}[/tex] × [tex]4^{x}[/tex]

∵ All bases are equal

∴ Use the first and third rule above to find x

∵  [tex]4^{3}[/tex] × [tex]4^{-6}[/tex] = [tex]4^{3+-6}[/tex]

∴  [tex]4^{3}[/tex] × [tex]4^{-6}[/tex] = [tex]4^{-3}[/tex] ⇒ L.H.S

∵  [tex]4^{5}[/tex] × [tex]4^{x}[/tex] = [tex]4^{5+x}[/tex] ⇒ R.H.S

Equate L.H.S and R.H.S

∴  [tex]4^{-3}[/tex] =  [tex]4^{5+x}[/tex]

Equate the indices of the two sides

∴ -3 = 5 + x

- Subtract 5 from both sides

∴ -8 = x

∵ x represents the blank

∴ The blank = -8

The blank is -8

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Four to the power of three times four to the power of negative six is equal to four to the power of five times four to the power of negative eight.

To solve for the missing exponent, we can use the following properties of exponents:

Multiplying exponents with the same base: When multiplying powers with the same base, we add their exponents.

Negative exponents: A number raised to a negative exponent is equal to its reciprocal raised to the positive exponent.

Applying these properties:

4^3 * 4^-6 = 4^(3 - 6) = 4^-3 (since 4^-6 = 1/4^6)

4^5 * 4^x = 4^(5 + x)

Setting these equal to find x:

4^-3 = 4^(5 + x)

Therefore, x = -3 - 5 = -8.

Answer:

Multiply by 5

-250, 1250

Step-by-step explanation:

2 x -5 = -10

-10 x -5 = 50

50 x -5 = -250

-250 x -5 = 1250

Answer:

C. and A.

Step-by-step explanation:

4. 5(x + 3) - 2x

5x + 15 - 2x

3x + 15

5. -6x + 2.5(x - 1) - 5x

-6x + 2.5x - 2.5 - 5x

-8.5x - 2.5

Answer:

Akira needs 45 square inches of  gold foil to cover the chair free including the bottom​

Step-by-step explanation:

Total surface  =  surface area of the base square + area of 4 triangles

Step 1: The surface area of the base square

surface area of the base = surface area of the square =  [tex]s^2[/tex]

where s is the side length

The the surface area of the base  = [tex]3^2[/tex] = 9 square inches

Step 2: The surface area of the side triangles

The area of the triangle = [tex]\frac{1}{2}\times \text{side length} \times \text{slant height}[/tex]

On substituting the values,

The area of the triangle =[tex]\frac{1}{2} \times 3 \times 6[/tex]

The area of the triangle = [tex]\frac{18}{2}[/tex]

The area of the triangle = 9 square inches

Now the area of 4 triangles  =  4 x 9  = 36 square inches

Thus the total surface area  =  9 + 36 = 45 square inches

The amount of gold foil needed to cover a trophy in the shape of a square pyramid can be calculated using the surface area formula for square pyramids, which considers the base area and the slant height.

To calculate the amount of gold foil needed to cover the trophy, we need to find the surface area of the square pyramid trophy. The surface area of a square pyramid is calculated by the formula: Surface Area = base area + 1/2 * Perimeter of base * slant height. If we know the length of the base (which is a square here), the slant height, we can substitute them into this formula to get the surface area. This is the amount of gold foil Akira used to cover her trophy, assuming the gold foil perfectly fits the trophy shape with no overlap.

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Answer:

D

Step-by-step explanation:

When Y is a function of X, the graph is a v shape.

The volunteers gave 1368 fliers in total.

Step-by-step explanation:

Given,

Fliers given by volunteers in first neighborhood = [tex]\frac{21}{38}[/tex]

Remaining fliers = 612

Fraction of remaining fliers = [tex]1-\frac{21}{38}=\frac{38-21}{38}[/tex]

Fraction of remaining fliers = [tex]\frac{17}{38}[/tex]

Let,

x be the total fliers given by volunteers.

[tex]\frac{17}{38}\ of\ x=612[/tex]

[tex]\frac{17}{38}x=612[/tex]

Multiplying both sides by [tex]\frac{38}{17}[/tex]

[tex]\frac{38}{17}*\frac{17}{38}x=612*\frac{38}{17}\\\\x=\frac{23256}{17}\\\\x=1368[/tex]

The volunteers gave 1368 fliers in total.

Keywords: fraction, division

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Answer:

4+ x/2 =6

Step-by-step explanation:

Let  the number be X

half of the number is 1/2 multiply X= X/2

Four increased by half the number is 4+X/2

Therefore, Four increased by half of anumber is equal to six is written as

4+ x/2 =6

Total area is 102.3 yd²

Step-by-step explanation:

Total area = area of the parallelogram + area of the right triangle

Calculate the area of the parallelogram.

Base = 11 yd, Height = 6.2 yd

⇒ Area of the parallelogram = Base × Height = 11 × 6.2 = 68.2 yd²

Calculate the area of the right triangle.

Height = 6.2 yd, Base = 11 yd (Since opposite sides of a parallelogram are equal)

⇒ Area of the triangle = 1/2 × base × height = 1/2 × 11 × 6.2 = 34.1 yd²

Calculate the total area.

⇒ Total area = 68.2 + 34.1 = 102.3 yd²

Answer:

a) $30

b) $8

Step-by-step explanation:

Wayne's savings to Stef's savings were in the ratio 5:6.

Let, Wayne's saving is 5x and Stef's saving is 6x.

Now, given that after spending $28 each the ratio became 1:4.

So, we can write the equation as

[tex]\frac{5x - 28}{6x - 28} = \frac{1}{4}[/tex]

⇒ 20x - 112 = 6x - 28

⇒ 14x = 84

⇒ x = 6

a) Therefore, Wayne's savings before he spends $28 is $(5 × 6) = $30

b) And, Stef's savings after she spends $28 will be $(6x - 28) = $(6 × 6 - 28) = $8 (Answer)

Answer:

yes

Step-by-step explanation:

well plug it in: y=6x -> y=6(3/9) and solve, yes if theres a slope of 1

Answer:

5x + 15 = -5x - 15

10x = -30

x = -3

y = 5(-3) + 15 = -15 + 15 = 0

(-3,0)

Step-by-step explanation:

Answer:

300.

Step-by-step explanation:

256 is closer to 300 than it is to 200 so it rounds to 300.

Answer:300

Step-by-step explanation:

Answer:

∠A = 45°

Step-by-step explanation:

The sum of angles in a triangle = 180°.

That means in the triangle ABC, ∠A + ∠B + ∠C = 180°.

Given ∠B = 90° and ∠C = 45°.

⇒ ∠A + 90° + 45° = 180°

⇒ ∠A = 180 - 90 - 45

⇒ ∠A = 45° is the required answer.

Answer:

6km

Step-by-step explanation:

Area of circle = πr²

Where r = radius,  π= 3.14, A = 28.26km²

A = 3.14 x r²

3.14 r2 = 28.26

Divide both sides by 3.14

r²= 28.26/3.14

r² = 9

Square root both sides

r= √9

r= 3

Radius = 3km

Note : Diameter = 2 x radius

Diameter = 3 x 2

Diameter = 6km

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Answer:the answer is B

Step-by-step explanation:

The function that represents the exponential growth is

f(x) = 4 x [tex]1.05^n[/tex].

Option B is the correct answer.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

An exponential growth function.

Rate of change = 5%

This means,

There is a growth per year of 5%.

The function can be represented as,

f(x) = a [tex](1 +0.05)^n[/tex]

f(x) = a x [tex]1.05^n[/tex]

Where 100% = 1 and 5% = 0.05

Let a = 4

f(x) = 4 x [tex]1.05^n[/tex]

Thus,

The exponential growth function is

f(x) = 4 x [tex]1.05^n[/tex]

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Answer:

1st triangle = 1

2nd triange= 3

3rd triangle = 9

4th triangle = 27

A triangle exists a three-sided polygon with three vertices and three edges. The number of triangles in the given figure exists 1, 3, 9, and 27.

A triangle exists a three-sided polygon with three vertices and three edges. It exists one of the major fundamental geometric forms.

The number of shaded triangles in each of the triangles exists shown below, thus, the number of triangles in each triangle can are:

1st triangle = 1

2nd triangle = 3

3rd triangle = 9

4th triangle = 27

Therefore, the number of triangles in the given figure exists 1, 3, 9, and 27.

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Answer:

$19.60

Step-by-step explanation:

$98 is made each week.

80% is saved, and the rest is spend on lunch, so 20% is spent on lunch.

20%=.20

98•.20=19.6

$19.60 is spend on lunches each week.

Answer:

Option B

Step-by-step explanation:

The function in the graph is an exponential growth function.

Therefore its equation is [tex]g(x)=3^x[/tex]

A transformation that shrinks this graph is of the form: [tex]f(x)=k*3^x[/tex] where [tex]0\:<\:k\:<\:1[/tex]

From the given options, we must have [tex]k=\frac{1}{2}[/tex]

This implies that:

[tex]f(x)=\frac{1}{2} (3)^x[/tex]

Answer:

B

Step-by-step explanation:

Answer:

$8.60

Step-by-step explanation:

Answer:

$8.60

Step-by-step explanation:

Answer:

[tex]\frac{104}{5}[/tex] weeks or [tex]20\frac{4}{5}[/tex] weeks

Step-by-step explanation:

To do this we can set up a proportion

[tex]\frac{52}{1} *\frac{2}{5}[/tex]

This will tell us how many weeks are in 2/5 of a year

Let's evaluate this

[tex]\frac{104}{5}[/tex]

We cannot simplifiy this anymore, so we will leave it as an improper fraction, or a mixed number as shown below

[tex]20\frac{4}{5}[/tex] weeks

[tex]\text{We're trying to find how many weeks Ben has lived in London}\\\\\text{We know that there are 52 weeks in a year}\\\\\text{We also know that he's been in London for 2/5 of a year, or 40\%}\\\\\text{To find your answer, you could multiply 52 by 0.40}\\\\52*0.40= 20.8\\\\\boxed{\text{Ben has been in London for 20.8 weeks}}[/tex]

Answer:

Step-by-step explanation:

Answer:

9%

Step-by-step explanation:

It is simple because you just count to get to 24 and that is the percentage.

Answer:

x=8

NR=5 units

BI=10 units

Step-by-step explanation:

In  a rectangle BRIA

AN=5 units

NR=x-3

We have to solve for x , NR and BI.

We know that

Diagonals of rectangle bisect to each other.

BI and AR are the diagonals of rectangle BRIA and intersect at point N.

AN=NR

[tex]5=x-3[/tex]

[tex]x=5+3=8[/tex]

[tex]x=8[/tex]

Substitute the value of x

NR=8-3=5

By property of rectangle

BI=AR=AN+NR=5+5=10 unit

BI=10 units

Answer:

The total number of fliers they gave out is 1368.

Step-by-step explanation:

Given:

Volunteers for a political campaign gave out 21/38 of their fliers. They gave out the remaining 612 fliers in another neighborhood.

Now, to find the total number of fliers they gave out.

Let the total number of fliers be [tex]x.[/tex]

Number of fliers they gave out for a political campaign:

[tex]\frac{21}{38}\ of\ x[/tex]

[tex]=\frac{21}{38} \times x[/tex]

[tex]=\frac{21x}{38}[/tex]

Number of fliers remaining they gave out in another neighborhood = 612.

Now, to get the total number of fliers by putting an equation:

[tex]x-\frac{21x}{38} =612[/tex]

[tex]\frac{38x-21x}{38} =612[/tex]

[tex]\frac{17x}{38} =612[/tex]

Multiplying both sides by 38 we get:

[tex]17x=23256[/tex]

Dividing both sides by 17 we get:

[tex]x=1368.[/tex]

Therefore, the total number of fliers they gave out is 1368.