Suppose you want to determine the number of miles you can drive in your car. Your car gets 20 miles per gallon. The number of miles traveled varies directly with the number of gallons of gas the tank holds. Write a direct variation equation that represents the situation. Let y be the dependent variable and let x be the independent variable

Answer:

D.

Your doing it for a week..5 days, his cases are 12, but how many cases(c) does he need to sell minus his rent vs what his goal is.

Answer:

Step-by-step explanation:

12/5 is the answer.

Answer: 113.1

Step-by-step explanation:

first you have to multiply 4/3*pie or 3.14 times 3

4/3 x 3.14 x 3 = 113.1

Answer:

The answer is D. 4r^6.

<3

-Callie

Step-by-step explanation:

Answer:

D. 4r^6.

Step-by-step explanation:

Answer:

Step-by-step explanation:

(- 4 - 2)² + (- 4 - 1)² = AC²

(- 6)² + (- 5)² = AC²

36 + 25 = AC²

AC² = 61

AC = √61

AC ~ 7.81 unitário

I hope I helped you.

The distance between points A and C is calculated using the displacement vector ĐAC, resulting in a distance of 4.5 km.

The student's question, 'What is the distance between points A and C', pertains to the calculation of displacement in a vector context within the field of Mathematics. To determine the displacement vector ĐAC, we apply the given information that point C is located three-quarters of the distance from point A to point B. If the full displacement from A to B, denoted as ĐAB, has a magnitude of 6 km, the displacement vector from A to C, which is ĐAC, has a magnitude of 0.75 times 6 km, which equals 4.5 km.

The displacement vector ĐAC is parallel to ĐAB and in the same northeasterly direction, indicating that the distance from A to C is simply 4.5 km. The student can understand that the magnitude of displacement is different from the distance traveled if the path taken is not a straight line; however, in this instance, the path is straight, and therefore, the displacement coincides with the actual distance covered.

To summarize, the distance between points A and C is the magnitude of the displacement vector ĐAC, which is 4.5 km.

Answer:

C)  12/5

Step-by-step explanation:

Tan = Opposite / Adjacent

So

Tan(Z) = YX /YZ

Given: YZ = 5 and XZ = 13

so

(YZ)^2 = (XZ)^2   - (YZ)^2

= 13^2 - 5^2

= 169 - 25

= 144

YZ = 12

Tan(Z) = YX /YZ

Tan(Z) = 12/5

Answer:

[tex]A=\frac{5x^{2}}{6}[/tex]

Step-by-step explanation:

Let's solve this by using the Area formula for a triangle:

[tex]A=\frac{1}{2}bh[/tex]

Base: [tex]\frac{5}{3}x[/tex]

Height: [tex]x[/tex]

Solve for A (Area)

[tex]A=\frac{1}{2}(\frac{5}{3}x)(x)[/tex]

[tex]A=\frac{5x^{2}}{6}[/tex]

Since we do not have a given value for [tex]x[/tex], this is as far as we can condense the equation.

The area would be 5x^2/ 6x

See the image

Answer:

X + Y     and    x+0+(y+0)    are both correct

Step-by-step explanation:

Explanation is on the image  

Option A, x + y and B. x + 0 + (y + 0)

(x + 0) + y + 0 is equivalent to.

equation is the relationship between variable and represented as    is example of polynomial equation.

(x + 0) + y + 0
= x + 0 + (y + 0 )
= x + y

Thus both the option A. and B. is correct.

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Answer:

20cm

Step-by-step explanation:

Answer:

The correct answer is option 2

45 cm

Step-by-step explanation:

It is given a circle with circumference C = 180 cm

To find the length of arc ABC

From the figure we can see that the central angle of arc ABC = 90°

Therefore the arc length = (90/360) * Circumference

Arc ABC  = (90/360) * 180 = (1/4) * 180 = 45

Therefore arc length = 45 cm

The correct answer is option 2

Answer:

[tex]\large\boxed{f(-7b)=-35b+10}[/tex]

Step-by-step explanation:

[tex]\text{Put}\ v=-7b\ \text{to the function}\ f(v)=5v+10:\\\\f(-7b)=5(-7b)+10=-35b+10[/tex]

Put the answer into a calculator;

-√17 = -4.123105626

√17 = 4.123105626

Round to the nearest tenth by looking at the 2nd digit after the decimal point. If it is 5 or greater, round up, otherwise round down.

-√17 = 4.123105626

2 is less than 5, so we leave it as it is.

-√17  ≈ -4.12

√17 = 4.123105626

2 is less than 5, so we leave it as it is.

√17 = 4.12

v ≈ -4.12, 4.12

Answer:

C

Step-by-step explanation:

A proportional graph is a line. Every line has a slope. The slope is found by subtracting two points as a ratio. The line has points (0,0) and (2,6).

6-0 = 6

2 -0 = 2

The ratio is vertical over horizontal so 6/2 = 3.

The equation is y = 3x.

Answer:

C) [tex]y=3x[/tex]

Step-by-step explanation:

1) Checking the coordinate points (2,6), (4,12),  (6,18), (8,24). And since the Proportionality Constant is given by

[tex]k=\frac{y}{x}[/tex]

[tex]k=\frac{y}{x}=\frac{6}{2}=\frac{12}{4}=\frac{18}{6}=\frac{24}{8}=3[/tex]

Then k=3

2) A Proportional Function is given by:

[tex]y=kx[/tex]

Thus we can state that proportional function rule as:

[tex]y=3x[/tex]

Answer:

Each side is 25cm long.

Step-by-step explanation:

75/3=25 (This is because each side of an equilateral triangle is equal to each other.) (The perimeter is all sides added together.)

Answer:

equilateral traingle mean all sides are equal..so 75÷3

=25cm

Step-by-step explanation:

its equal....so we just simply just divide..

Answer:

jk(x) = -16x^2 -12x+10

Step-by-step explanation:

j(x) = -4x+2

k(x) = 5+4x

jk(x) = (-4x+2) (5+4x)

FOIL

-4x*5 +-4x*4x +2*5 +2*4x

Combine like terms

-20x-16x^2 +10+8x

-16x^2 -12x+10

jk(x) = -16x^2 -12x+10

Answer:

9

Step-by-step explanation:

The 4 part of the ratio represents 12 girls

Divide 12 by 4 to find the value of one part of the ratio

[tex]\frac{12}{4}[/tex] = 3 ← value of 1 part of the ratio, hence

Multiply the 3 part of the ratio by 3 to obtain number of boys

3 × 3 = 9 ← number of boys

Answer:9

Step-by-step explanation: it is 3 to 4 so you multiply 4 by 3 you get 12 you multiply 3 by 3 you get 9

Answer:

0 or undefined

Step-by-step explanation:

Answer:

The slope doesn't matter.

Step-by-step explanation:

Since the variable equals a constant, any y value would be perpendicular to x = 3.

So lines perpendicular to x = 3 would be,

Answer:

x^3 - 7x^2 + 4x + 30

Step-by-step explanation:

The equation is already simplified to its fullest if we're looking at factored form.

Otherwise, just multiply everything out using a punnett square.

Answer:

x^3 - 7x^2 + 4x + 30

Step-by-step explanation:

I just did this one hope this helps

4 · x^4 · x^4 · y

4 x^8 y

In words: four times x to the eighth times y

Step-by-step explanation:

the y-axis is the point (-x,y). Reflect over the y = x: When you reflect a point across the line y = x, the x-coordinate and y-coordinate change places. If you reflect over the line y = -x, the x-coordinate and y-coordinate change places and are negated (the signs are changed).

Answer:

The rule for reflection on the x-axis is (x,y) -> (x,-y)

The rule for reflection on the y-axis is (x,y) -> (-y,y)

Step-by-step explanation:

A reflection is a transformation that represents a turn of a figure. The figures can be reflected in a point, a line, or a plane.

A reflection copies each point of a figure to an image through a fixed line. The fixed line is called the reflection line.

[tex]\bf ~\hspace{10em}\textit{function transformations} \\\\\\ \begin{array}{llll} f(x)= A( Bx+ C)^2+ D \\\\ f(x)= A\sqrt{ Bx+ C}+ D \\\\ f(x)= A(\mathbb{R})^{ Bx+ C}+ D \end{array}\qquad \qquad \begin{array}{llll} f(x)=\cfrac{1}{A(Bx+C)}+D \\\\\\ f(x)= A sin\left( B x+ C \right)+ D \end{array} \\\\[-0.35em] ~\dotfill\\\\ \bullet \textit{ stretches or shrinks horizontally by } A\cdot B\\\\ \bullet \textit{ flips it upside-down if } A\textit{ is negative}[/tex]

[tex]\bf ~~~~~~\textit{reflection over the x-axis} \\\\ \bullet \textit{ flips it sideways if } B\textit{ is negative}\\ ~~~~~~\textit{reflection over the y-axis} \\\\ \bullet \textit{ horizontal shift by }\frac{ C}{ B}\\ ~~~~~~if\ \frac{ C}{ B}\textit{ is negative, to the right}\\\\ ~~~~~~if\ \frac{ C}{ B}\textit{ is positive, to the left}\\[/tex]

[tex]\bf \bullet \textit{ vertical shift by } D\\ ~~~~~~if\ D\textit{ is negative, downwards}\\\\ ~~~~~~if\ D\textit{ is positive, upwards}\\\\ \bullet \textit{ period of }\frac{2\pi }{ B}[/tex]

now, with that template in mind, let's take a look

[tex]\bf \begin{cases} f(x)=&2^x\\ g(x)=&f(x+k)\\ & f(x-5)\\ &2^{x-5} \end{cases}~\hspace{10em}g(x)=2^{\stackrel{A}{1}(\stackrel{B}{1}x\stackrel{C}{-5})}+\stackrel{D}{0} \\\\\\ \textit{horizontal shift by }\cfrac{C}{B}\implies \cfrac{-5}{1}\implies -5\qquad \qquad \textit{ of 5 units to the right}[/tex]

The graph of g(x) is shifted horizontally 5 units to the right of the graph of f(x).

The correct option is (b).

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable).

As per the given data:

We are given 2 functions, and we have to find out the shift in the graph.

f(x) = 2^x

g(x) = f(x+k)

When the value of k = -5 we have to find out the shift in the graph of g(x).

For finding out the shift in the graph of g(x):

g(x) = f(x+k)

By substituting the given value of f(x) = 2^x and k = -5:

g(x) = 2^(x-5)

When y = f(x) is changed to y = f(x - 5) the graph of f(x) shifts 5 units to the right horizontally.

Similarly, for g(x) = 2^(x-5) the graph will shift by 5 units to the right.

Hence, The graph of g(x) is shifted horizontally 5 units to the right of the graph of f(x).

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store a single drink cost $3/12 =25c

store b single drink cost $5.50/ 22 = 25c

store c single drink cost $4.75/18 = 26c

store d single drink cost $8/36 = 22c

hence store d offers the best buy

To determine the best buy among four stores selling soft drinks, compare the price per can or pack for each store. Store D offers the best buy with a cost of approximately $0.22 per can.

To determine which store offers the best buy, we need to compare the prices per can or pack of each store.

Therefore, Store D offers the best buy with a cost of approximately $0.22 per can.

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Answer:

20 + 8 + 0.1 + 0.09

Step-by-step explanation:

Answer:

20 + 8 + 0.1 + 0.09

20 wholes +8 wholes =28 then...

.1 tenth+.09 hundereths=.19 add..

28+.19=.  28.19

➷ Add 24 to both sides:

x^2 + 10x + 24

Find two values that multiply to make 24 but add to make 10

As you will notice, this is 6 and 4

Now factorize it:

(x + 4)(x + 6)

The values of x would be the opposite of what is in the parenthesis

Therefore x = -4 or x = -6

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

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Answer:

x= -6                    x=-4

Step-by-step explanation:

x2 + 10x = −24

Add 24 to each side

x2 + 10x+24 = −24+24

x2 + 10x +24=0

Factor

(x+6) (x+4) = 0

Using the zero product property

x+6 = 0             x+4 = 0

x+6-6 = 0-6      x+4-4 =0-4

x= -6                    x=-4

Bonsoir,

Combien fait 87$ augmenté de 200% ?

87 $ x 200/100 = 174 $ d'augmentation,  

174 + 87 = 261 $

Answer:

20 kg

Step-by-step explanation:

If we want any value in grams to be in kilograms, we divide it by 1000

in this example: 20000/1000

=20 kg

Answer:

5

Step-by-step explanation:

he can mow one lawn in 24 min

2 hours=120 min

120÷24=5

Answer:

2 sections.

Step-by-step explanation:

Given that number of students that had homework last night = 8

Given that number of students that had not homework last night = 4

Then total number of students = 8+4= 12

Then fraction of students that had not homework last night = 4/12

Alaina used that data to design a spinner with 6 congruent sections.

Then number of sections of Alaina's spinner the represents students who did not have homework = ( 6 section) ( 4/12 fraction)

= 6(4/12)

=24/12

=2

Hence final answer is 2 sections.

Answer:

The principal amount was $23,393.45

Step-by-step explanation:

The total amount paid on a 35 year loan was $98,000 at the rate of interest 4.1%

We will calculate Principal amount by this formula

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

Where A = amount (98,000)

           P = Principal amount (P)

           r = rate of interest 4.1% (0.041)

           n = number of compounding interest monthly (12)

           t = time (35 years)

[tex]98,000=P(1+\frac{0.041}{12})^{(12)(35)}[/tex]

[tex]98,000=P(1+0.003416)^{(420)}[/tex]

[tex]98,000=P(1.003416)^{(420)}[/tex]

98,000 = P(4.189386)

= 4.189386P = 98,000

P = [tex]\frac{98000}{4.189386}[/tex]

P = 23,392.4494 ≈ $23,392.45

The principal amount was $23,393.45

Answer:

$23,392

Step-by-step explanation:

Use the compound interest formula and substitute the values given: $98,000=P(1+.041/12)[tex]^{12(35)}[/tex]

Simplify using order of operations:

$98,000=P(1.003416667)[tex]^{420}[/tex]

P=$98,000(1.003416667)[tex]^{420}[/tex]

P≈$23,392

QUESTION 1

The given expression is

2+8

The greatest common factor of 2 and 8 is 2.

We can rewrite as: [tex]2+8=2\times1+2\times4[/tex]

Factor to get: [tex]2+8=2(1+4)[/tex]

QUESTION 2

Given: 9-3

Greatest common factor of 9 and 3 is 3.

Rewrite as: [tex]9-3=3\times3-3\times1[/tex]

Factor: [tex]9-3=3(3-1)[/tex]

QUESTION 3

Given: 30+25

Greatest common factor of 30 and 25 is 5.

Rewrite as: [tex]30+25=5\times6+5\times4[/tex]

Factor: [tex]30+25=5(6+4))[/tex]

QUESTION 4.

Given: 35-14

The greatest common factor of 35 and 14 is 7.

Rewrite as:  [tex]35-14=5\times7-2\times7[/tex]

Factor:  [tex]35-14=7(5-2)[/tex]

QUESTION 5

The given expression is 81-18.

The greatest common factor of 81 and 18 is 9.

Rewrite as: [tex]81-18=9\times9-9\times2[/tex]

Factor: [tex]81-18=9(9-2)[/tex]

QUESTION 6

Given: 60+100

The greatest common factor of 60 and 100 is 20.

Rewrite as : [tex]60+100=20\times3+20\times5[/tex]

Factor: [tex]60+100=20(3+5)[/tex]

QUESTION 7

Given: 28-20

The greatest common factor of 28 and 20 is 4.

Rewrite as: [tex]28-20=4\times7-4\times5[/tex]

Factor: [tex]28-20=4(7-5)[/tex]

QUESTION 8

Given: 72+48

The greatest common factor of 72 and 48 is 24.

Rewrite as: [tex]72+48=24\times3+24\times2[/tex]

Factor: [tex]72+48=24(3+2)[/tex]

QUESTION 9

The given expression is [tex]12x+18[/tex].

The greatest common factor of [tex]12x[/tex] and 18 is 6.

Rewrite as; [tex]12x+18=6\times2x+6\times3[/tex]

Factor; [tex]12x+18=6(2x+3)[/tex]

QUESTION 10

Given: [tex]4y+10[/tex]

The greatest common factor of [tex]4y[/tex] and 10 is 2.

Rewrite the expression as; [tex]4y+10=2\times2y+2\times5[/tex]

Factor:  [tex]4y+10=2(2y+5)[/tex]