3. "the product of a number and 5.”

Answer:

\(y=3x-8\)

Step-by-step explanation:

Answer:

around 45 minutes

Step-by-step explanation:

it takes about 15 minutes to do 1 mile, do the correct math, it'll take about 45 minutes to do 3 miles

The average price of the pickup truck increased by 80%.

To find the percentage increase in the average price of the pickup truck, we need to calculate the difference between the 2012 and 1991 prices, divide that difference by the 1991 price, and then multiply by 100 to get the percentage increase.

First, we need to find the difference between the two prices:

$35,100 - $19,500 = $15,600

Next, we divide the difference by the 1991 price:

$15,600 / $19,500 = 0.8

Finally, we multiply by 100 to get the percentage increase:

0.8 x 100 = 80%

Therefore, the average price of the pickup truck increased by 80%.

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Answer:

Step-by-step explanation:

A rational number is a nonrepeating fraction. To convert, we need to put 71,625 over 1000.

We divide 1000 by 125.

This simplifies to 573/8.

Then we get the whole number part of the mixed number.

Answer: The function that represents exponential decay is:

D. f(x) = 268(0.86)^x

This function has a base of 0.86, which is less than 1. As x increases, the value of the function decreases exponentially. This is the characteristic of exponential decay, where the value of a quantity decreases at a constant percentage rate over time.

Option A, f(x) = 0.25(1.06), represents exponential growth, as the base (1.06) is greater than 1.

Option B, f(x) = 18 + 0.9x, represents linear growth, as the value of the function increases linearly with x.

Option C, f(x) = 412 + 1.03x, also represents linear growth, as the value of the function increases linearly with x.

Step-by-step explanation:

Answer:

c = 13

Step-by-step explanation:

Answer: the answer would be 169

Step-by-step explanation:

\(5x^{2} +12x^{2} = 169\)

Answer:

The y-intercept of this line is 2.

Step-by-step explanation:

To find where this line reaches the y axis, you simply need to assign the value 0 to x, and solve for y:

\(2x + 3y = 6\\2(0) + 3y = 6\\3y = 6\\y = 6/3\\y = 2\)

So the y intercept of that line is 2

Answer:

4,368 / 42

Step-by-step explanation:

I can tell without answering the problems because if you have a larger amount to divide by, it would lead to people having a higher amount. Meanwhile having a smaller amount to divide by.

Answer:

She can paint 17 statues

Step-by-step explanation:

Sorry I don’t really know how to show my work

Answer:

140/8

simplified: 35/2

decimal: 17.5

Step-by-step explanation:

honestly, I don't know how to show my work but I hope this helps.

Answer:

The pentagon MNPQR has a perimeter of 22 units.

Step-by-step explanation:

Geometrically speaking, the perimeter of the pentagon is the sum of the lengths of each side, that is:

\(p = MN + NP + PQ + QR + RM\) (1)

\(p = \sqrt{\overrightarrow{MN}\,\bullet \, \overrightarrow{MN}} + \sqrt{\overrightarrow{NP}\,\bullet \, \overrightarrow{NP}} + \sqrt{\overrightarrow{PQ}\,\bullet \, \overrightarrow{PQ}} + \sqrt{\overrightarrow{QR}\,\bullet \, \overrightarrow{QR}} + \sqrt{\overrightarrow{RM}\,\bullet \, \overrightarrow{RM}}\) (1b)

If we know that \(M(x,y) = (2,4)\), \(N(x,y) = (5,8)\), \(P(x,y) = (8,4)\), \(Q(x,y) = (8,1)\) and \(R(x,y) = (2,1)\), then the perimeter of the pentagon MNPQR is:

\(p =\sqrt{(5-2)^{2}+(8-4)^{2}} + \sqrt{(8-5)^{2}+(4-8)^{2}}+\sqrt{(8-8)^{2}+(1-4)^{2}}+\sqrt{(2-8)^{2}+(1-1)^{2}}+\sqrt{(2-2)^{2}+(4-1)^{2}}\)\(p = \sqrt{3^{2}+4^{2}} + \sqrt{3^{2}+(-4)^{2}}+\sqrt{0^{2}+(-3)^{2}}+\sqrt{(-6)^{2}+0^{2}}+\sqrt{0^{2}+3^{2}}\)

\(p = 22\)

The pentagon MNPQR has a perimeter of 22 units.

The pentagon MNPQR has a perimeter of 22 units.

Geometrically speaking, the perimeter of the pentagon is the sum of the lengths of each side, that is:

p = MN + NP + PQ + QR + RMp=MN+NP+PQ+QR+RM (1)

p = \sqrt{\overrightarrow{MN}\,\bullet \, \overrightarrow{MN}} + \sqrt{\overrightarrow{NP}\,\bullet \, \overrightarrow{NP}} + \sqrt{\overrightarrow{PQ}\,\bullet \, \overrightarrow{PQ}} + \sqrt{\overrightarrow{QR}\,\bullet \, \overrightarrow{QR}} + \sqrt{\overrightarrow{RM}\,\bullet \, \overrightarrow{RM}}p=

MN

∙

MN

+

NP

∙

NP

+

PQ

∙

PQ

+

QR

∙

QR

+

RM

∙

RM

(1b)

If we know that M(x,y) = (2,4)M(x,y)=(2,4) , N(x,y) = (5,8)N(x,y)=(5,8) , P(x,y) = (8,4)P(x,y)=(8,4) , Q(x,y) = (8,1)Q(x,y)=(8,1) and R(x,y) = (2,1)R(x,y)=(2,1) , then the perimeter of the pentagon MNPQR is:

p =\sqrt{(5-2)^{2}+(8-4)^{2}} + \sqrt{(8-5)^{2}+(4-8)^{2}}+\sqrt{(8-8)^{2}+(1-4)^{2}}+\sqrt{(2-8)^{2}+(1-1)^{2}}+\sqrt{(2-2)^{2}+(4-1)^{2}}p=

(5−2)

2

+(8−4)

2

+

(8−5)

2

+(4−8)

2

+

(8−8)

2

+(1−4)

2

+

(2−8)

2

+(1−1)

2

+

(2−2)

2

+(4−1)

2

p = \sqrt{3^{2}+4^{2}} + \sqrt{3^{2}+(-4)^{2}}+\sqrt{0^{2}+(-3)^{2}}+\sqrt{(-6)^{2}+0^{2}}+\sqrt{0^{2}+3^{2}}p=

3

2

+4

2

+

3

2

+(−4)

2

+

0

2

+(−3)

2

+

(−6)

2

+0

2

+

0

2

+3

2

p = 22p=22

The pentagon MNPQR has a perimeter of 22 units.

Answer:

15 + -7 OR 15 - 7

Step-by-step explanation:

Answer:

Step-by-step explanation:

Sin (90 + Ф ) =Cos Ф

135° = 90 + 45

Sin 135° = Sin (90 + 45)

             = Cos 45°

             \(= \dfrac{1}{\sqrt{2}}\)

The perimeter 2a+g unit and area a*g/2 unit² of the rectangle.

What is a rectangle?

Rectangles are quadrilaterals having four right angles in the Euclidean plane of geometry. Various definitions include an equiangular quadrilateral,

The area of rectangle is A = a*b

here given is b = g/2unit

The area will be a*g/2 unit²

The perimeter of the rectangle is 2(a+b)

perimeter will be 2(a+g/2) = 2a+g unit

hence the perimeter and area of the rectangle are a*g/2 unit² and 2a+g unit respectively.

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If the scale factor between the sides is 5, the scale factor between the surface areas will be 25, and the scale factor between the volumes will be 125.

When the scale factor between the sides of a shape is given, the scale factors between the surface areas and volumes can be determined by considering the relationship between the dimensions.

Let's denote the scale factor between the sides as "k."

For surface area:

The surface area of a shape is determined by the square of its linear dimensions. Therefore, the scale factor for the surface area will be k^2. In this case, if the scale factor between the sides is 5, the scale factor between the surface areas will be 5^2 = 25.

For volume:

The volume of a shape is determined by the cube of its linear dimensions. Hence, the scale factor for the volume will be k^3. Given that the scale factor between the sides is 5, the scale factor between the volumes will be 5^3 = 125.

Therefore, if the scale factor between the sides is 5, the scale factor between the surface areas will be 25, and the scale factor between the volumes will be 125.

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Answer:

x=18

Step-by-step explanation:

see answer

Based on triangle DEF, the missing side lengths include the following:

10. d = 5.1423 units, e = 6.1284 units.

11. e = 17.2516 units, f = 21.6013 units.

12. d = 24.7365 units, f = 26.8727 units.

In order to determine the missing side lengths, we would apply cosine ratio because the given side lengths represent the adjacent side and hypotenuse of a right-angled triangle.

cos(θ) = Adj/Hyp

Where:

Part 10.

By substituting the given side lengths cosine ratio formula, we have the following;

cos(40) = e/8

e = 8cos40

e = 6.1284 units.

d² = f² - e²

d² = 8² - 6.1284²

d = 5.1423 units.

Part 11.

E = 53°, d = 13.

cos(53) = 13/f

f = 13/cos(53)

f = 21.6013 units.

e² = f² - d²

e² = 21.6013² - 13²

e = 17.2516 units.

Part 12.

D = 67°, E = 10.5.

cos(67) = 10.5/f

f = 10.5/cos(67)

f = 26.8727 units.

d² = f² - e²

d² = 26.8727² - 10.5²

d = 24.7365 units.

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The graph of the given function is attached below.

A relationship between a group of inputs and one output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.

The graph of the function y = -2log2(x+3) + 2 is a downward-sloping curve that approaches the x-axis as x approaches infinity.

The curve is defined only for positive values of x, as the logarithm is undefined for negative values.

As x increases, the logarithm term inside the parentheses becomes larger in magnitude, causing the value of y to decrease rapidly.

The curve approaches the x-axis but never touches it, as the logarithm term will never reach zero.

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The dimensions that will result in a solid with maximum volume are approximately x = 12.02 centimeters and h = 5.01 centimeters.

Let the side of the square base be x, and let the height of the rectangular solid be h. Then, the surface area of the solid is given by:

Surface area = area of base + area of front + area of back + area of left + area of right

Surface area = x² + 2xh + 2xh + 2xh + 2xh = x² + 8xh

We are given that the surface area is 433.5 square centimeters, so we can write: x² + 8xh = 433.5

We want to find the dimensions that will result in a solid with maximum volume. The volume of the solid is given by:

Volume = area of base × height = x² × h

We can use the surface area equation to solve for h in terms of x:

x² + 8xh = 433.5

h = (433.5 - x²)/(8x)

Substituting this expression for h into the volume equation, we get:

Volume = x² × (433.5 - x²)/(8x) = (433.5x - x³)/8

To find the maximum volume, we need to find the value of x that maximizes this expression. To do this, we can take the derivative of the expression with respect to x, set it equal to zero, and solve for x:

d(Volume)/dx = (433.5 - 3x²)/8 = 0

433.5 - 3x² = 0

x² = 144.5

x = sqrt(144.5) ≈ 12.02

We can check that this is a maximum by computing the second derivative of the volume expression with respect to x:

d²(Volume)/dx² = -3x/4

At x = sqrt(144.5), this is negative, which means that the volume is maximized at x = sqrt(144.5).

Substituting x = sqrt(144.5) into the expression for h, we get:

h = (433.5 - (sqrt(144.5))²)/(8×sqrt(144.5))

h = 433.5/(8×sqrt(144.5)) - sqrt(144.5)/8

h = 5.01

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The dimensions of the rectangular solid that will result in a maximum volume are approximately.\(6.34 cm \times 9.03 cm \times 9.03 cm.\)

Let's assume that the length, width, and height of the rectangular solid are all equal to x, so the base of the solid is a square.

The surface area of the rectangular solid can be expressed as:

\(SA = 2xy + 2xz + 2yz\)

Substituting x for y and z, we get:

\(SA = 2x^2 + 4xy\)

We are given that the surface area is 433.5 square centimeters, so:

\(2x^2 + 4xy = 433.5\)

Simplifying, we get:

\(x^2 + 2xy - 216.75 = 0\)

Using the quadratic formula to solve for y, we get:

\(y = (-2x\± \sqrt (4x^2 + 4(216.75)))/2\)

\(y = -x \± \sqrt (x^2 + 216.75)\)

Since the base of the rectangular solid is a square, we know that y = z. So:

\(z = -x \± \sqrt(x^2 + 216.75)\)

The volume of the rectangular solid is given by:

\(V = x^2y\)

Substituting y for\(-x + \sqrt (x^2 + 216.75),\) we get:

\(V = x^2(-x + \sqrt(x^2 + 216.75))\)

Expanding and simplifying, we get:

\(V = -x^3 + x^2\sqrt(x^2 + 216.75)\)

The dimensions that will result in a solid with maximum volume, we need to find the value of x that maximizes the volume V.

We can do this by taking the derivative of V with respect to x, setting it equal to zero, and solving for x:

\(dV/dx = -3x^2 + 2x\sqrt(x^2 + 216.75) + x^2/(2\sqrt (x^2 + 216.75)) = 0\)

Multiplying both sides by \(2\sqrt (x^2 + 216.75)\) to eliminate the denominator, we get:

\(-6x^2\sqrt (x^2 + 216.75) + 4x(x^2 + 216.75) + x^3 = 0\)

Simplifying, we get:

\(x^3 - 6x^2\sqrt (x^2 + 216.75) + 4x(x^2 + 216.75) = 0\)

We can solve this equation numerically using a graphing calculator or computer software.

\(The solution is approximately x = 6.34 centimeters.\)

Substituting x = 6.34 into the expression for y and z, we get:

\(y = z \approx 9.03 centimeters\)

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Answer:

8/10 is 0.8

73/100 is 0.73

Answer: We started with 36 dried meals

Step-by-step explanation: Let x be the number of dried meals we started with. After the first night, we had x - x/3 = 2x/3 meals left. After the second day, we had 2x/3 - 4 meals left. After the second night, we had (2x/3 - 4) - (2x/3 - 4)/3 = 4x/9 - 8/3 meals left. After the third day, we had (4x/9 - 8/3) - 4 meals left. After the third night, we had ((4x/9 - 8/3) - 4)/2 meals left. This was equal to 4, so we can set up an equation and solve for x:

((4x/9 - 8/3) - 4)/2 = 4

Multiplying both sides by 2, we get:

(4x/9 - 8/3) - 4 = 8

Adding 4 to both sides, we get:

4x/9 - 8/3 = 12

Multiplying both sides by 9, we get:

4x - 24 = 108

Adding 24 to both sides, we get:

4x = 132

Dividing both sides by 4, we get:

x = 33

However, if x = 33, then the number of dried meals we had left after the third night would be ((4*33/9 - 8/3) - 4)/2 = 4.666… This is not a whole number, so it means that we either had more or less than 4 meals left. Since we ate the four remaining meals and headed home, we know that we had exactly 4 meals left. Therefore, x cannot be 33. The closest integer to 33 that satisfies the equation is 36.

Hope this helps, and have a great day! =)

Answer:

  33 meals

Step-by-step explanation:

You want to know the number of meals you started with if 4 were left after half those at the end of the third day were destroyed, 4 were eaten on the third day after 1/3 those at the end of the second day were destroyed, 4 were eaten on the second day after 1/3 of the starting number were destroyed.

Assume we started with x meals. The sequence of events seems to be ...

  1/3 were destroyed overnight, so 2/3x remained

  4 were eaten next day, so (2/3x -4) remained

  1/3 were destroyed overnight, so 2/3(2/3x -4) remained

  4 were eaten on the third day, so 2/3(2/3x -4) -4 remained

  1/2 were destroyed, so 1/2(2/3(2/3x -4) -4) remained

The number remaining was 4.

Undoing the layers of the expression, we have ...

  1/2(2/3(2/3x -4) -4) = 4

  2/3(2/3x -4) -4 = 8 . . . . . . . multiply by 2

  2/3(2/3x -4) = 12 . . . . . . . . . add 4

  2/3x -4 = 18 . . . . . . . . . . . . . multiply by 3/2

  2/3x = 22 . . . . . . . . . . . . . . . add 4

  x = 33 . . . . . . . . . . . . . . . . . . multiply by 3/2

You started with 33 meals.

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Given DataMass, m = 74.0 kg, Acceleration, a = 1.36 m/s²

Initial velocity, u = 0

Distance covered before constant velocity, s = 34 m

Distance remaining, s' = 100 - 34 = 66 m

Formula Used The equation for calculating distance is given by: s = ut + (1/2)at²

Where,s = Distance

u = Initial velocity

a = Acceleration

t = Time , The equation for calculating time is given by:t = √((2s)/

a)Calculation Acceleration remains constant, so the equation for calculating time will be:

t = √((2s)/a)t = √((2(34))/1.36)t = 5.11 s

Now, for calculating the remaining time taken by the sprinter to complete the race, we need to find the final velocity of the sprinter. The equation used is given by:v² - u² = 2as'

Where,v = Final velocity, u = Initial velocity, a = Accelerations' = Distance remaining

v² = u² + 2as'v² = 0 + 2(1.36)(66)v² = 179.52v = 13.4 m/sNow, we can calculate the time taken by the sprinter for the remainder of the race.t' = s'/vt' = 66/13.4t' = 4.93 s

The total time taken by the sprinter for the race is given by:Total time taken, t_total = t + t' = 5.11 + 4.93 ≈ 10.04 s

Therefore, the time taken by the sprinter to complete the race is approximately 10.04 seconds.

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Answer:

(x-2) (x+1) (x+4)

Step-by-step explanation:

x^3+3x^2-6x-8

Rearranging the terms,

(x^3 - 8) + (3x^2 - 6x)

a^3 - b^3 = (a-b) (a^2 + ab + b^2)

(x^3 - 8) = (x^3 - 2^3) = (x-2) (x^2 + 2x + 4)

(3x^2 - 6x) = 3x(x-2)

So, x^3 + 3x^2 -6x -8

= (x-2) (x^2 + 2x +4) + 3x(x-2)

(x-2) is the common factor,

= (x-2) ( x^2 +2x+4 + 3x)

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

= (x-2) (x^2 + 4x + x + 4)

= (x-2) (x(x+4) +1(x+4))

= (x-2) (x+1) (x+4)

Its C.

Negative x Negative is positive, so its not A or D.

Positive x Positive is Positive, so its not B either.

C is your option because Positive x Negative is Negative, and vice verca.

Answer:

C

Step-by-step explanation:

this is because a negative number multiplied with a negative number gives you a positive, a positive number multiplied with a positive number gives you a positive but a negative number multiplied with a positive gives you a negative so the answer is C.

for more information watch videos about the rules of positive and negative numbers.

Given:

x, y and z are integers.

To prove:

If \(3x-y+5z\) is even, then at least one of x, y or z is even.

Solution:

We know that,

Product of two odd integers is always odd.          ...(i)

Difference of two odd integers is always even.          ...(ii)

Sum of an even integer and an odd integer is odd.      ...(iii)

Let as assume x, y and z all are odd, then \(3x-y+5z\) is even.

\(3x\) is always odd.          [Using (i)]

\(5z\) is always odd.          [Using (i)]

\(3x-y\) is always even.       [Using (ii)]

\((3x-y)+5z\) is always odd.       [Using (iii)]

\(3x-y+5z\) is always odd.

So, out assumption is incorrect.

Thus, at least one of x, y or z is even.

Hence proved.

Answer:

  tan(α) = 1/tan(90°-α)

Step-by-step explanation:

The tangent of one is the reciprocal of the tangent of the other.

__

In a right triangle, ...

  tan = opposite/adjacent

For the two complementary acute angles in such a triangle, opposite and adjacent are swapped. That is the tangent of one is the inverse of the tangent of the other. (That inverse is also known as the cotangent.)

  tan(α) = cot(90°-α) = 1/tan(90°-α)

The angle x in the diagram is 98 degrees.

When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate interior angle, alternate exterior angles, vertically opposite angles, same side interior angles etc.

Therefore, let's find the angle of x using the angle relationships as follows:

The size of the angle x can be found as follows:

82 + x = 180(same side interior angles)

Same side interior angles are supplementary.

Hence,

82 + x = 180

x = 180 - 82

x = 98 degrees

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I'm assuming your trying to find the weight of the math book so here it is:

Answer:

4 5/36

Step-by-step explanation:

You'd have to do 18 7/8 - 14 7/9 but you can't subtract them yet because they don't have common denominators. So, you have to multiply the 7/8 by 9 and the 7/9 by 8. Then you would get 63/72 and 56/72. Then you put that into the equation and get, 18 63/72 - 14 53/72. If you subtract those, you get the answer, 4 10/72. Which can be simplified as 4 5/36.

Answer:

3²/₃ m

Step-by-step explanation:

Since h(x)= −(x−11)(x+3) represents the height of the hovercraft after x seconds, at the time of takeoff, x = 0.

So, the height at takeoff is h(0) = −(0 − 11)(0 + 3)

= -(-11)/3

= 11/3 m

= 3²/₃ m

Answer: 33 seconds

Step-by-step explanation: Khan Academy