Gas mileage is the number of miles you can drive on a gallon of gasoline. A test of a new car results in 560 miles on 20 gallons of gas. How far could you drive on 50 gallons of gas? What is the car’s gas mileage?

The division of 3.78 by 0.9 equals 4.2 after rounding to the nearest tenth. The given problem is an arithmetic division question typically encountered in mathematics. The keyword 3.78 is the number being divided by 0.9.

The division question posed: 3.78 divided by 0.9, is a simple arithmetic problem. To solve, we will perform the division calculation directly. First, we divide 3.78 (the dividend) by 0.9 (the divisor). This yields a quotient of approximately 4.2. Thus, 3.78 divided by 0.9 equals 4.2 when rounded to the nearest tenth. This division problem would be typically encountered in arithmetic, a branch of mathematics that deals with numbers and numerical computation.

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18.00 MOP equals to 2.26 US Dollars.

Step-by-step explanation:

Cost of taxi ride = 18.00 MOP

It is given that;

1 US Dollar = 7.98 MOP

It can also be written as,

7.98 MOP = 1 US Dollar

Therefore,

1 MOP = [tex]\frac{1}{7.98}\ US\ Dollars[/tex]

Now,

18.00 MOP = [tex]\frac{1}{7.98}*18.00\ US\ Dollars[/tex]

[tex]18.00\ MOP=\frac{18.00}{7.98}\ US\ Dollars\\18.00\ MOP= 2.26\ US\ Dollars[/tex]

18.00 MOP equals to 2.26 US Dollars.

Keywords: conversion, division

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Answer:

A'B'= 34 units long.

Step-by-step explanation:

The length A'B' will be 2 times the length of AB.

AD = sqrt( (8-0)^2 + (8- -7)^2 )

= sqrt 289

= 17

So A'B' = 34 .

Answer:

680$

Step-by-step explanation:

If this is a 64% discount, the price 244.80 is 36% of the original price

244.8 = 36%    -Divide by 36 on both sides

6.8 = 1%            - Times by a hundred

680 = 100%

The original price is 680$

To find the original price of the sofa given a 64% discount, divide the sale price by the discount percentage and subtract it from 100%.

To find the original price, we need to determine what the discount percentage represents in terms of the original price. Since the sale price is 64% of the original price, the discount is 100% - 64% = 36%. Let's represent the original price as x:

36% of x = $ 244.80

To solve this equation, we can convert 36% to the decimal form by dividing it by 100: 36/100 = 0.36. Now we can solve for x:

0.36x = $ 244.80

Dividing both sides of the equation by 0.36, we get:

x = $ 244.80 / 0.36 = $ 680

Therefore, the original price of the sofa was $ 680.

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Answer: 53, 54, 55, and 56

Step-by-step explanation: This problem states that the sum of 4 consecutive numbers is 218 and it asks us to find the numbers.

4 consecutive numbers can be represented as followed.

X ⇒ first number

X + 1 ⇒ second number

X + 2 ⇒ third number

X + 3 ⇒ fourth number

Since the sum of our 4 consecutive numbers is 218, we can set up an equation to represent this.

X + X + 1 + X + 2 + X + 3 = 218

On the left side of the equation, we can combine our x's and our numbers.

4x + 6 = 218

      -6     -6   ← subtract 6 from both sides of the equation

4x = 212

÷4    ÷4   ← divide both sides of the equation by 4

 X = 53

X ⇒ first number   = 53

X + 1 ⇒ second number   = 54

X + 2 ⇒ third number   = 55

X + 3 ⇒ fourth number   = 56

Therefore, our 4 consecutive numbers are 53, 54, 55, and 56.

Answer:

Step-by-step explanation:

Equation 1:  3a + 1o =5     3(1) + 1(2) = 5

Equation 2:  1a + 1o =3      2(1) + 1(2) = 3

Solution: apples are $1.00 each and oranges are $2.00 each

Answer:

y = 43x − 25

Step-by-step explanation:

Evaluate the function at x=1:

f(x) = 12x³ + 3x² + x + 2

f(1) = 12 + 3 + 1 + 2

f(1) = 18

Find the slope of the tangent line at x=1:

f'(x) = 36x² + 6x + 1

f'(1) = 36 + 6 + 1

f'(1) = 43

Point-slope form:

y − y₀ = m (x − x₀)

y − 18 = 43 (x − 1)

Convert to slope-intercept form:

y − 18 = 43x − 43

y = 43x − 25

Graph:

desmos.com/calculator/giumpkkphr

To find the linear approximation for the function f(x) = 12x^3 + 3x^2 + x + 2 at x = 1, we can use the equation for the linear approximation. First, we need to find the derivative of the function and then plug in the values into the formula. The linear approximation is f(1).

To find the linear approximation for the function f(x) = 12x^3 + 3x^2 + x + 2 at x = 1, we can use the equation for the linear approximation:

() ≈ () + '()( − )

First, we need to find '(), which is the derivative of the function. Taking the derivative of f(x) gives us:

'() = 36^2 + 6 + 1

Next, we plug in x = 1 into the first equation:

(1) ≈ (1) + '(1)(1 − 1)

Simplifying, we have:

(1) ≈ (1)

So, the linear approximation for f(x) at x = 1 is f(1).

Answer:

-4x

Step-by-step explanation:

Answer:

Adrian needs to pay $5 for all the fruit.

Step-by-step explanation:

Consider the provided information.

Grapes cost  $2.35 per pound, oranges cost $0.99 per  pound, and apples cost $1.65 per pound.

In order to find how much Adrian needs to pay we need to add $2.35, $0.99 and $1.65.

[tex]\$2.35 + \$0.99 + \$1.65=\$4.99[/tex]

Now round $4.99 to the nearest whole number.

[tex]\$4.99\approx\$5[/tex]

Hence, Adrian needs to pay $5 for all the fruit.

Answer:

The slope is -2.

Step-by-step explanation:

m=(y2-y1)/(x2-x1)=(8-6)/(1-2)=2/-1=-2

Answer:

The slope for the given points is - 2  , and  y- intercept is 5

Step-by-step explanation:

Given points as :

( - 1 , 7 )  and  ( 0 , 5 )

Now slope of line in points form as

Slope = m = [tex]\dfrac{y_2-y_1}{x_2-x_1}[/tex]

or, m =  [tex]\dfrac{5 - 7}{0 + 1}[/tex]

or, m = - 2

so, Slope of line is - 2

Now equation of line is given as

y - [tex]y_1[/tex] = m × ( x -  [tex]x_1[/tex] )

or, y - 7 = ( - 2 ) × ( x + 1)

or, y - 7 = - 2 x - 2

Or, equation of line is

y = - 2 x + 5

Now, for y - intercept , x = 0

So, from line equation

y = - 2 × 0 + 5

Or, y = 0 + 5

∴ y = 5

Hence The slope for the given points is - 2  , and  y- intercept is 5  Answer

Answer:

cot(x)

Step-by-step explanation:

csc(x) = 1/sin(x)

cos(x)*csc(x) = cos(x)*1/sin(x)

cos(x)*csc(x) = cos(x)/sin(x)

cos(x)*csc(x) = cot(x)

----

abbreviations

csc = cosecant

cos = cosine

sin = sine

cot = cotangent

To simplify cos x csc x, we can replace csc x with 1/sin x based on the trigonometric identity. This will give us cos x/sin x, which is the same as cot x based on the trig identities.

The question is asking us to simplify the expression cos x csc x. To do this, we can use the trigonometric identity sin = 1/csc, which tells us what csc x is in terms of sin x.

So if that is the case, we can rewrite csc x as 1/sin x and replace csc x in the original expression giving us cos x * (1/sin x) or equivalently cos x/sin x.

And if we look at our trigonometric identities again, we can find that cos x/sin x is the same as cot x, our final simplified expression.

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Answer:

19.5

is the correct answer

Answer:

The answer is 19.5

Step-by-step explanation

Have an amazing day :)

Answer:

None.

Step-by-step explanation:

18+36=54

A) 29+16=45

B) 6/3+12=2+12=14

C) 7(2+4)=7(6)=42

D) 2+36=38

Answer:

1.8=100x+b

Step-by-step explanation:

The formula y = mx + b sometimes appears with

different symbols.

For example, instead of x, we could use the

letter C. Instead of y, we could use the letter F.

Then the equation becomes

F = mC + b.

All temperature scales are related by linear

equations. For example, the temperature in

degrees Fahrenheit is a linear function of degrees Celsius.

Water freezes at: 0°C, 32°F

Water Boils at: 100°C, 212°F

After 14 weeks, both Megan and Conner will have saved the same amount.

Step-by-step explanation:

Amount Megan have = $50

Amount saved each week = $5.50

Amount Conner have = $18.50

Amount saved each week = $7.75

Let,

x be the number of weeks.

According to given statement;

M(x) = 50+5.50x    Eqn 1

C(x) = 18.50+7.75x   Eqn 2

For amount to be same;

Eqn 1 = Eqn 2

[tex]50+5.50x=18.50+7.75x\\50-18.50=7.75x-5.50x\\31.50=2.25x\\2.25x=31.50\\[/tex]

Dividing both sides by 2.25

[tex]\frac{2.25x}{2.25}=\frac{31.50}{2.25}\\x=14[/tex]

After 14 weeks, both Megan and Conner will have saved the same amount.

Keywords: functions, division

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An average of 291 backpacks were given out the past five years.

Step-by-step explanation:

Number of bags for last 5 years;

278, 310, 320, 242, 303

No. of terms = 5

Average = [tex]\frac{Sum\ of\ the\ terms}{No.\ of\ terms}[/tex]

[tex]Average=\frac{278+310+320+242+303}{5}\\Average=\frac{1453}{5}\\Average=290.6[/tex]

Rounding off to nearest whole number

Average = 291

An average of 291 backpacks were given out the past five years.

Keywords: average, addition

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Answer:

y = -0.5x -2

Step-by-step explanation:

We have to find a line perpendicular to the line y = -2x -3.

Let the required line will have slope m so ,

-2m = 1

m = -0.5.

So, the required line will have the slope -0.5.

Now, let the line be y = -0.5x + c.

This line is passing through (-2,-1), So putting this point in the line we will get

-1 = 1 + c

c = -2 .

So, the required line is

y = -0.5x -2.

Answer:

Angle C is 101 degrees

Step-by-step explanation:

Given triangle ABC,

Side BC =3

Side AB =16

Angle A=20

Also, Angle C is an obtuse angle.

To find Angle C:

As shown in figure,

By using basic trigonometry,

Angle A =20 and AB=13

BD =13sin20 and AD = 13cos20

Now, AD=AC+CD

CD=13cos20-3

CD=2.30506

And BD =13sin20=11.86828

In triangle BDC,

Tan(BCD) = [tex]\frac{BD}{CD}[/tex]

Tan(BCD) = [tex]\frac{11.86828}{2.30506}[/tex]

Tan(BCD) = [tex]\frac{11.86828}{2.30506}[/tex]=5.1487

Angle BCD = 79.00

Therefore, Angle BCA =180-Angle BCD=180-79=101.

Angle C is 101 degrees

The measure of angle C in triangle ABC is approximately 150.8° when rounded to the nearest tenth of a degree.

To find the measure of angle C, we can use the fact that the sum of the angles in any triangle is 180°. Given that angle A is 20° and angle C is obtuse, we can set up the following equation:

[tex]\[ \angle A + \angle B + \angle C = 180 \][/tex]

Since angle A is 20°, we can substitute this value into the equation:

[tex]\[ 20 + \angle B + \angle C = 180 \][/tex]

To find the measure of angle B, we can use the Law of Sines, which states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides of the triangle:

[tex]\[ \frac{a}{\sin(\angle A)} = \frac{b}{\sin(\angle B)} = \frac{c}{\sin(\angle C)} \][/tex]

We can use the sides AB and BC to find angle B:

[tex]\[ \frac{16}{\sin(20)} = \frac{3}{\sin(\angle B)} \][/tex]

Solving for[tex]\(\sin(\angle B)\)[/tex]:

[tex]\[ \sin(\angle B) = \frac{3}{16} \cdot \sin(20) \][/tex]

Now, we calculate the value of [tex]\(\sin(\angle B)\)[/tex]:

[tex]\[ \sin(\angle B) = \frac{3}{16} \cdot \sin(20) \approx \frac{3}{16} \cdot 0.3420 \approx 0.0649 \][/tex]

Taking the inverse sine [tex](sine) of \(\sin(\angle B)\)[/tex] gives us the measure of angle B :

[tex]\[ \angle B = \sin(0.0649) \approx 3.7 \][/tex]

Now we have the measures of angles A and B, so we can find angle C :

[tex]\[ 20 + 3.7 + \angle C = 180 \] \\[/tex]

[tex]\[ \angle C = 180 - 20 - 3.7\] \\[/tex]

[tex]\[ \angle C = 180 - 23.7 \] \\[/tex]

[tex]\[ \angle C = 156.3 \][/tex]

Since angle C is obtuse, we do not need to consider any other solutions for angle B that might be less than 90°. Therefore, the measure of angle C is approximately 156.3°, which rounds to the nearest tenth of a degree as 150.8°.

Answer:

y = x² + 2x + 5

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Here the vertex = (- 1, 4), thus

y = a(x + 1)² + 4

To find a substitute (0, 5) a point on the graph into the equation

5 = a(0 + 1)² + 4

5 = a + 4 ( subtract 4 from both sides )

a = 1, thus

y = (x + 1)² + 4 ← expand and simplify

  = x² + 2x + 1 + 4

  = x² + 2x + 5

The quadratic function to model the graph to the right is f(x) = x² + 2x + 5.

Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

As we know, the formula for the roots of the quadratic equation is given by:

[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]

The graph of the quadratic function is given in the picture.

As we know,

(y - h)² = 4a(x - k)

(h, k) is the vertex of the parabola:

Or

y = a(x - h)² + k

From the graph:

Here the vertex = (- 1, 4)

y = a(x + 1)² + 4

Plug x = 0, and y = 5 to find the value of a

5 = a(0 + 1)² + 4

a = 1

y = (x + 1)² + 4

f(x) = x² + 2x + 5

Thus, the quadratic function to model the graph to the right is f(x) = x² + 2x + 5.

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The perimeter of Jake window is 16x - 2 inches

Given that height of Jake window is 5x - 3 inches

Also given that width is 3x + 2 inches

To find: perimeter of Jake window

We know that, in general a window is of rectangular shape

The perimeter of rectangle is given as:

Perimeter of rectangle = 2(length + width)

Substituting the values we get,

Perimeter of rectangle = 2(5x - 3 + 3x + 2)

Perimeter of rectangle = 2(8x - 1) = 16x - 2

Hence, the perimeter of the window is 16x – 2 inches

Answer: 1/8

Step-by-step explanation: To write a percent as a fraction in lowest terms, first remember that a percent is a ratio that compares a number to 100.

So here, 12.5% can be written as the ratio 12.5 to 100 or 12.5/100.

To write 12.5/100 in lowest terms, first multiply the numerator and the denominator by 10 to get rid of the decimal. When we do this, we get the fraction 125/1000.

Now, we divide the numerator and the denominator of 125/1000 by the greatest common factor of 125 and 1,000 which is 125 and we end up with the equivalent fraction which is 1/8.

Therefore, 12.5% is equivalent to 1/8.

Answer:

3 minutes

5 minutes.

Step-by-step explanation:

It is given that, Amelia can wash 8 plates in 24 minutes.

So, if this rate remains constant then 1 plate will be washed in [tex] \frac{24}{8} = 3[/tex] minutes.

Again, it is given that, Amelia bakes 12 cookies in 60 minutes.

So, if this rate also remains constant then she will bake 1 cookie in [tex] \frac{60}{12} = 5[/tex] minutes. ( Answer )

Answer:

0

Step-by-step explanation:

5y-2=3

5y=3+2

5y=5

y=5/5=1

9y-9=9(1)-9=9-9=0

Answer:

D. [tex]\displaystyle (0,5, 0,5)[/tex]

Step-by-step explanation:

C(3, −3) and A(−2, 4)

Just by looking at the graph, we can CLEARLY see that answer choice D is EXACTLY halfway in between the two given endpoints.

I am joyous to assist you anytime.

Answer:

False

Step-by-step explanation:

Answer:

False

Step-by-step explanation:

The multiples of 16: 16,32,48,64,80,96,112,128,144,160,176,192,208,224,240,256,27

Factors of 24

The factors of 24.: 1,2,3,4,6,8,12,24,

Assuming that the correct expression is 2(x - 3)= 2(4x -12)

(2 * x) + (2 * −3) = (2 * 4x) + (2 * −12)

2x - 6 = 8x − 24

2x − 6 − 8x = 8x − 24 − 8x

−6x − 6 = −24

−6x − 6 + 6 = −24 + 6

−6x = −18

-6x/-6 = -8/-6

x = 3 (Answer)

______

Best Regards,

Wolfyy :)

Answer:

6 inches

Step-by-step explanation:

p=l+l+w+w

p=2+2+1+1

p=6

Answer:

6 in

Step-by-step explanation:

Answer:

2/3d=h

Step-by-step explanation:

2/3 is the amount it grows (in inches)

d represtenst the days

h represents height

2/3*6 = 4

Answer: 2/3

Step-by-step explanation: 2/3 is the amount it grows (in inches)

D= THE DAYS

H= THE HEIGHT

So... 2/3x6= 4

                   = 2/3