Calculus help please, thank you

Answer:

4 miles per gallon. Answer choice B is correct.

Step-by-step explanation:

To find the gas mileage for each car, we need to divide the distance traveled by the amount of gasoline used.

For Mitra's car, the gas mileage is:

gas mileage = distance traveled / amount of gasoline used

gas mileage = 469.8 / 14.5

gas mileage = 32.4 miles per gallon

For Adira's car, the gas mileage is:

gas mileage = distance traveled / amount of gasoline used

gas mileage = 355 / 12.5

gas mileage = 28.4 miles per gallon

To find the difference in gas mileage, we can subtract the gas mileage for Adira's car from the gas mileage for Mitra's car:

difference = gas mileage for Mitra's car - gas mileage for Adira's car

difference = 32.4 - 28.4

difference = 4 miles per gallon

Therefore, the difference in gas mileage between the two cars is 4 miles per gallon. Answer choice B is correct.

Answer:204

Step-by-step explanation:

pemdas

6x[2--32]=6×[34]=204

Here are five combinations of nickels and dimes that add up to 80 cents:

4 dimes and 4 nickels

3 dimes and 7 nickels

2 dimes and 12 nickels

1 dime and 16 nickels

8 dimes and 4 nickels

The value of x if the object is a square with a perimeter of 94 cm is 23.5 cm

From the question, we have the following parameters that can be used in our computation:

The permieter of object A is 94cm

Assuming the object is a square

So, we have

4x = 94

Divide both sides by 4

So, we have

x = 94/4

Evaluate

x = 23.5

Hence, the value of x is 23.5cm

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Step-by-step explanation:

Note that the perimeter of the trapezoid shown is 23 units. Thus, the statement is false.

To derive the perimeter we  must know the following:


a = base = 5

b = base = 8

d = side = 4
c is the hypotenuse" = (h x base of the right triangle) = (4x3)/2 = 6

Thus, Perimeter of the trapezoid = a + b + c + d =

5 + 8 + 4 + 6

= 23 units.

Thus, the statement that the perimeter of the trapezoid shown is 22 units is false.

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Full Question>

Use the trapezoid shown to mark each statement below as true or false. if false, please rewrite the statement correctly in the space below the statement!

Q: The perimeter of the trapezoid shown is 22 units.

True false?

Answer:

25000

Step-by-step explanation:

Answer:

x= -13/15

Step-by-step explanation:

x(15x +13)

x =0

15x + 13 = 0

15x = -13

x =-13/15

Answer: 84 in

Step-by-step explanation:

A = h(b)/2

h= 7

b= 24

24x7= 168

168/2= 84

The equation that could be used to find the distance that the tornado traveled is: log d = 0.7

We are told that The wind speed near the center of a tornado is represented by the equation S = 93 log d + 65,

where:

d is the distance, in miles, that the tornado travels.

S is the wind speed, in miles per hour.

When S = 130, we have:

130 = 93 log d + 65

93 log d = 130 - 65

93 log d = 65

log d = 65/93

log d = 0.7

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This prompt has to do with the analysis of random outcomes. See the attached tables and graphs accordingly.

An exhaustive depiction of all possible marble combinations that may arise out of a chance experiment involving two random selections has been depicted in this table.

The table enlists five different-colored marbles available in a bag and elaborates its varying conclusions based on two distinct selections.

The columns indicate colors, whereas each result depicts two correlated choices made during an experiment's progression to illustrate randomness accurately.

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Answer:

V = 3 × 2 × 6 = 36 cubic centimeters

Answer:

Bozo's rate of reading in words per minute is 75 (300 words / 4 minutes = 75 words/minute).

Step-by-step explanation:

Mark Brainliest!!

Answer: 75 words per minute

Step-by-step explanation:

     We will divide 300 words by 4 to find the rate of words per minute since the original rate is words per four minutes.

                       300 / 4 = 75 words per minute

Matching of the statements with their respective linear equations are:

1) The line contains (0, -8) and a slope of 3/2: y = ³/₂x - 8

2) A line that contains the point (0, -2) and (4, 0): 2y - x = -4

3) y-intercept is (0, -2) and slope is -3/4: y = -³/₄x - 2

4) A line that has a slope of 5/3 and a y-intercept of -4: 5x + 3y = -12

The formula for the equation of a line in slope intercept form is:

y = mx + c

where:

m is slope

c is y-intercept

1) The line contains (0, -8) and a slope of 3/2

The only option that even has a slope of 3/2 is option B with the equation: y = ³/₂x - 8

2) A line that contains the point (0, -2) and (4, 0)

The only one that fits this is option C with the equation:

2y - x = -4

3) y-intercept is (0, -2) and slope is -3/4.

This means the only equation that matches it is:

y = -³/₄x - 2

4) A line that has a slope of 5/3 and a y-intercept of -4.

This means the only equation that matches it is:

5x + 3y = -12

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Answer:

15.43 + 12.85 + 21.3 = 49.58

Rounding to the nearest whole number, the sum is 50.

Step-by-step explanation:

Answer:

15.43 + 12.85 + 21.3 = 49.58

Step-by-step explanation:

The amount that Katherine, who is going to invest in an account paying an interest rate of 5.8% compounded monthly, would need to invest, to the nearest ten dollars for the future value of the account for the account to reach $960 in 26 years, is $380 (present value).

The future value is the present value compounded at an interest rate.

The present value is the future value discounted at an interest rate.

The future value and the present value can be computed using an online finance calculator.

N (# of periods) = 192 months (16 years x 12)

I/Y (Interest per year) = 5.8%

PMT (Periodic Payment) = $0

FV (Future Value) = $960

Results:

Present Value (PV) = $380.38

Total Interest = $579.62

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Evaluating the square root expression -2√(2r + 5) = 6 gives r = 2

From the question, we have the following expression that can be used in our computation:

-2 square root of 2r +5=6

Express properly

So, we have

-2√(2r + 5) = 6

Divide by -2

√(2r + 5) = -3

So, we have

2r + 5 = 9

Subtract 5 from both sides

2r = 4

Divide

r = 2

Hence, the solution is 2

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The surface area of each square pyramid, we used the formula Surface Area = Base Area + 4 x (1/2 x Base x Height of Face) is 1049.2, 1285.8 and 2100mm². The cost to cover each pyramid was $1.05, $1.29 and $2.10

To calculate the surface area of each pyramid, we need to use the formula

Surface Area = Base x Height of face + 2 x ((Base/2) x Slant Height)

For the small pyramid, we have

Surface Area = 20 x 25 + 2 x ((20/2) x 26.46)

Surface Area = 500 + 2 x 10 x 26.46

Surface Area = 1049.2 mm²

Cost to cover the small pyramid

Cost = Surface Area x 0.001

Cost = 1049.2 x 0.001

Cost = $1.05

For the medium pyramid, we have

Surface Area = 20 x 40 + 2 x ((20/2) x 42.43)

Surface Area = 800 + 2 x 10 x 42.43

Surface Area = 1285.8 mm²

Cost to cover the medium pyramid

Cost = Surface Area x 0.001

Cost = 1285.8 x 0.001

Cost = $1.29

For the large pyramid, we have

Surface Area = 30 x 40 + 2 x ((30/2) x 50)

Surface Area = 1200 + 2 x 15 x 50

Surface Area = 2100 mm²

Cost to cover the large pyramid

Cost = Surface Area x 0.001

Cost = 2100 x 0.001

Cost = $2.10

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The strongest classification of the quadrilateral with the given vertices is rhombus.

The vertices of the quadrilateral is given as,

E(5, 4), F(9, 2), G(5, 0) and H(1, 2).

Find the adjacent sides EF and FG whether they are equal.

Using the distance formula,

EF = √(9 - 5)² + (2 - 4)²  = √(16 + 4) = √20

FG = √(5 - 9)² + (0 - 2)² = √(16 + 4) = √20

Adjacent sides are equal.

So they are either square or rhombus.

Find the lengths of the diagonals whether they are equal.

EG = √(5 - 5)² + (0 - 4)²  = √(0 + 16) = 4

FH = √(1 - 9)² + (2 - 2)²  = √(64 + 0) = 8

Diagonals are not equal.

So it is a rhombus.

Hence the quadrilateral is a rhombus.

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Answer:

Sure, here are the answers to your questions:

**A) The value of $f(-5)$ is $-2$.**

To find the value of $f(-5)$, we can simply substitute $x=-5$ into the equation $f(x)=-2x^2-8x+14$. This gives us:

$$f(-5)=-2(-5)^2-8(-5)+14=-2(25)+40+14=-50+54=4$$

**B) The vertex of the parabola is $(2,6)$.**

To find the vertex of the parabola, we can complete the square. This involves adding and subtracting $\left(\dfrac{{b}}{2}\right)^2$ to both sides of the equation, where $b$ is the coefficient of the $x$ term. In this case, $b=-8$, so we have:

$$\begin{aligned}f(x)&=-2x^2-8x+14\\\\ f(x)+20&=-2x^2-8x+14+20\\\\ f(x)+20&=-2(x^2+4x)\\\\ f(x)+20&=-2(x^2+4x+4)\\\\ f(x)+20&=-2(x+2)^2\end{aligned}$$

Now, if we subtract 20 from both sides, we get the equation of the parabola in vertex form:

$$f(x)=-2(x+2)^2-20$$

The vertex of a parabola in vertex form is always the point $(h,k)$, where $h$ is the coefficient of the $x$ term and $k$ is the constant term. In this case, $h=-2$ and $k=-20$, so the vertex of the parabola is $(-2,-20)$. We can also see this by graphing the parabola.

[Image of a parabola with vertex at (-2, -20)]

**C) The $y$-intercept is the point $(0,14)$.**

The $y$-intercept of a parabola is the point where the parabola crosses the $y$-axis. This happens when $x=0$, so we can simply substitute $x=0$ into the equation $f(x)=-2x^2-8x+14$ to find the $y$-intercept:

$$f(0)=-2(0)^2-8(0)+14=14$$

Therefore, the $y$-intercept is the point $(0,14)$.

**D) The two values of $x$ that make $f(x)=0$ are $2.5$ and $-3.5$.**

To find the values of $x$ that make $f(x)=0$, we can set the equation $f(x)=-2x^2-8x+14$ equal to zero and solve for $x$. This gives us:

$$-2x^2-8x+14=0$$

We can factor the left-hand side of the equation as follows:

$$-2(x-2)(x-3)=0$$

This means that either $x-2=0$ or $x-3=0$. Solving for $x$ in each case gives us the following values:

$$x=2\text{ or }x=3$$

However, we need to round our answers to two decimal places. To do this, we can use the calculator. Rounding $x=2$ and $x=3$ to two decimal places gives us the following values:

$$x=2.5\text{ and }x=-3.5$$

Therefore, the two values of $x$ that make $f(x)=0$ are $2.5$ and $-3.5$.

Answer:

x = 3

Step-by-step explanation:

4x + 2x - 3 = 15 ← collect like terms on left side

6x - 3 = 15 ( add 3 to both sides )

6x = 18 ( divide both sides by 6 )

x = 3

Answer:

x=3

Step-by-step explanation:

You can start of by adding 4x and 2x because they both share the same variable "x". Now you have 6x-3=15. Using the addition property of equality, you can add 3 on both sides of the equation to cancel it out. You are left with 6x=18. Divide both sides by 6 and that leaves you with x=3

The calculated value of the side length b is 17.32 meters

From the question, we have the following parameters that can be used in our computation:

Angle B = 60 degrees

Length a = 10 meters

The side length b is calculated as

tan(60) = b/a

So, we have

tan(60) = b/10

Make b the subject

b = 10 * tan(60)

Evaluate

b = 17.32

Hence, the side length b is 17.32 meters

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The exact value of tan2θ in simplest radical form is  -21/√7.

The value of tan2θ at the given quadrant is calculated as follows;

From Pythagorean identity, we know that;

sin² θ + cos² θ = 1

cos² θ is calculated as follows;

(3/4)² + cos² θ = 1

9/16 + cos² θ = 1

cos² θ = 1 - 9/16

cos² θ = 7/16

cos θ = √(7/16)

The value of tan θ is calculated as follows;

tan θ = sin θ / cos θ = 3/4 x 4/√7 = 3/√7

Now, we will find tan 2θ;

tan 2θ = 2tan θ / (1 - tan² θ)

tan 2θ = 2(3/√7) / (1 - (3/√7)²)

tan 2θ = (6/√7) / (-2/7)

tan 2θ = -21/√7

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Answer:

3 × 2 × 1 + 3 + 8 + 6 + 7 - 9 - 9 ÷ 7 × 0 × 1

= 6 + 3 + 8 + 6 + 7 - 9 - 0

= 31 - 9

= 22

Therefore, the value of the expression is 22

Answer:

Step-by-step explanation:

considering that it is not an equation but an algebraic expression we solve it like this

10 + 6k6k =

10 + 36k²

The angle of incline of the tram is 19.4 degree.

According to the question:

h=(10450-6311)ft

= 4139 ft

We know that, sinθ=Opposite/Hypotenuse

So, sinθ=h/12463

sinθ= 4139/12463

sinθ= 0.3321

Solve the trigonometric equation by isolating the function and then taking the inverse. Use the period to find the full set of all solutions.

θ=19.39

θ≈19.4°

Therefore, the angle of incline of the tram is 19.4 degree.

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movies 1.75 each

games 5.75 each

The area of the given rectangle is 34 squared units.

Determining the area of a rectangle with the coordinates

can be achieved through using the distance formula to calculate the magnitude of its sides and then applying the formula for the area pf rectangle we find the area.

Length of Side AB:

= square root of [(3 - (-5))^2 + (5 - 3)^2]

= square root of 68

Length of Side BC:

= square root of [ (4-3)^2 + (1 - 5)^2]

= square root of 17

Area of this rectangle  

= side AB × Side BC

= square root[68] x square root[17]

= square root of [68 times 17]

= square root of 1156

= 34 Square Units

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The length of the worktable is 82 inches and the width is 32 inches.

To find the length and width of the worktable, we can use a system of equations. Let's denote the width of the table by w.

Since the length is 18 inches more than twice the width, we can write:

Length = 2w + 18

The perimeter of the table is the sum of all its sides, which in this case is the sum of the length and the width, each multiplied by 2:

Perimeter = 2(length + width)

Perimeter = 2(2w + 18 + w)

Perimeter = 2(3w + 18)

Perimeter = 6w + 36

We know that the perimeter is 228 inches, so we can set up an equation:

6w + 36 = 228

Solving for w, we get:

w = 32

Now that we know the width, we can use the equation for the length to find:

Length = 2w + 18

Length = 2(32) + 18

Length = 82

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