Kayden is a stunt driver. One time, during a gig where she escaped from a building about to explode(!), she drove at a constant speed to get to the safe zone that was 160 meters away. After 3 seconds of driving, she was 85 meters away from the safe zone.
Let y represent the distance (in meters) from the safe zone after x seconds.
Complete the equation for the relationship between the distance and number of seconds.
y=, equals

Answer:

D

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 2, 3) and (x₂, y₂ ) = (4, 2) ← 2 points on the line

m = [tex]\frac{2-3}{4-(-2)}[/tex] = [tex]\frac{-1}{4+2}[/tex] = - [tex]\frac{1}{6}[/tex]

a) Coordinates of the midpoint: (2,1)

b) Gradient of the line PQ = -2/3

c) n = 13

What is the midpoint  of a line segment?

The midpoint is defined as the point which divides the line segment into two equal halves.

Given P = (-1,3) , Q = (5,-1)

Coordinates of the midpoint are given by

X' = (X1+ X2)/2

Y' = (Y1+ Y2)/2

(X1,Y1 ) and (X2,Y2) are the endpoints of the line segment.

Putting the values in the above formula X' = (-1+5)/2 = 2

Y' = (3-1)/2 = 1

hence midpoint  = (2,1)

The Slope or Gradient of the line is given by = (Y2-Y1)/X2-X1)

= (-1-3)/(5-(-1))

= -4/6 = -2/3

Gradient = -2/3

Distance between 2 points is given by the formula

[tex]\sqrt{(x_{1}-x_{2}) ^{2}+(y_{1}-y_{2}) ^{2} }[/tex]

[tex]\sqrt{(-1-5)^{2}+(3-(-1))^{2} }[/tex]

[tex]\sqrt{6^{2}+4^{2} }[/tex]

= [tex]2\sqrt{13}[/tex]

hence n = 13

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When he saved $80 in March, he saved $112 in April because he intended to save 140% more than he did.

In essence, percentages are fractions with a 100 as the denominator. We place the percent sign (%) next to the number to indicate that the number is a percentage. Percentage, a relative number showing hundredth parts of any amount, is a relative measure that indicates how many questions on a test you correctly answered out of 100 (75/100). Since one percent (symbolized as 1%) is equal to one tenth of anything, 100 percent stands for everything, while 200 percent refers to double the amount specified. By dividing the total by the amount you wish to convert to a percentage. You would divide 2 by 5 in this case as 2 divided by 5 equals 0.4. The result of multiplying 0.4 by 100 is 40, or 40%.

Here,

Amount of money he saved in march=$80

Amount of money he wish to save in April,

=140%*80

=$112

He saved $112 in April when he saved $80 in March and he wanted to save 140% more than what he saved in March.

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Answer:

-------------------------------

Find y:

The two expressions that represent the price of the item purchased after the discount is applied will be 1.2p and p + 0.2p

From the information, store offers a 20% discount to new customers. If the original price of an item is p dollars,

Let the original price = p

The new cost will be:

= p + (20% × p)

= p + 0.2p

= 1.2p

Therefore, the expression will be 1.2p.

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Answer: Positive

Step-by-step explanation:

Because the graph doesn't go down so it is not negative. It does not go straight up the y-axis so it does not a slope, it does not go straight through the x-axis so it is not undefined. So the answer is Positive

By using the properties of parallel lines, it can be proved that

[tex]\angle[/tex]1 [tex]\cong \angle[/tex]8 by the substitution property.

What are parallel lines?

Two lines are said to be parallel if on extending them indefinitely, they will never intersect

Given that e || f and g is a transversal,

We know that

[tex]\angle[/tex]4 [tex]\cong \angle[/tex]5 [by the alternate interior angles theorem]

We also know that

[tex]\angle[/tex]1 [tex]\cong \angle[/tex]4 and [tex]\angle[/tex]8 [tex]\cong \angle[/tex]5 by the vertically opposite angle

So [tex]\angle[/tex]1 [tex]\cong \angle[/tex]8 by the substitution property.

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Complete Question

Given that e parallel f and g is a transversal, we know that angle 4 is-congruent-to angle 5 by the alternate interior angles theorem. we also know that angle 1 is-congruent-to angle 4 and angle 5 is-congruent-to angle 8 by the ________. therefore, angle 1 is-congruent-to angle 8 by the substitution property. corresponding angles theorem alternate interior angles theorem vertical angles theorem alternate exterior angles theorem

The propagated error in the measurement of the side of the cube is 0.001.

We know that,

the volume of a cube is dependent on the length of the edge, s, which is given by the equation,

V = [tex]s^{3}[/tex].

With this we determine that the given cube has an edge of 27 = [tex]s^{3}[/tex]

⇒ s = 3 inches.

Now we can acquire the differential of the equation for the volume of the cube with the following equations.

V = [tex]s^{3}[/tex]

dV = d([tex]s^{3}[/tex])

dV = 3[tex]s^{2}[/tex] ds

We have given that volume of the cube is 0.027.

That is dV = 0.027 and s = 3

we simply plug in the given and then solve for ds to determine the error in the measurement of the edge of the cube.

dV = 3[tex]s^{2}[/tex] ds

0.027 = 3(3)²ds

0.027 = 27ds

0.001 = ds

Therefore, there is an error in measurement of the edge of the cube up to 0.001 inches.

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Answer:

-6.1,-2.5,-0.4,3.4

Step-by-step explanation:

If we used a number line and graphed all the numbers, we could visually see that -6.1 is the farthest from zero followed by -2.5,-0.4 and 3.4. Because we are doing the coldest temperature to warmest and not the other way around the answer would be -6.1,-2.5,-0.4,3.4

Hope this was helpful!

Using a midpoint Riemann sum with 3 subintervals of equal length to approximate [tex]\int^{70}_{10}v(t)dt[/tex] is 2020 and [tex]\int^{70}_{10}v(t)dt[/tex] means the distance in feet, traveled by rocket A from t=0 seconds to t=70 seconds.

From the given question,

An initial height of 0 feet at time t=0 seconds.

The velocity of the rocket is recorded for selected values of over the interval 0 < t < 80 seconds.

(a) Using a midpoint Riemann sum with 3 subintervals of equal length to approximate [tex]\int^{70}_{10}v(t)dt[/tex].

[tex]\int^{70}_{10}v(t)dt[/tex]

A midpoint Riemann sum with 3 sub intervals so, n=3

∆t= (70-10)/3

∆t = 60/3

∆t = 20

Intervals: (10, 30), (30,50), (50,70)

Midpoint:      20        40         60

Midpoint Riemann Sum

[tex]\int^{70}_{10}v(t)dt[/tex] = ∆t[v(20+v(40)+v(60)]

From the table

[tex]\int^{70}_{10}v(t)dt[/tex] = 20[22+35+44]

[tex]\int^{70}_{10}v(t)dt[/tex] = 20*101

[tex]\int^{70}_{10}v(t)dt[/tex] = 2020

(b) Now we have to explain the meaning of v(t)dt in terms of the rocket's flight [tex]\int^{70}_{10}v(t)dt[/tex].

It means the distance in feet, traveled by rocket A from t=0 seconds to t=70 seconds.

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Yes it is reasonable to save that the farm’s glass recycling could pay for their fuel oil.

Recycling is the process of turning trash into new products and materials. This idea frequently takes the recovery of energy from waste materials into account. The capacity of a substance to regain the qualities it had in its initial state determines how recyclable it is.

Both the environment and your community may benefit from recycling. It protects natural resources, minimizes greenhouse gas emissions, cleans up the air and water, and conserves energy.

In this question, there is a benefit to recycling. That is, the farm would be able to save more fuel. Hence it pays for the costs of fuel.

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The angles in the intersected lines are as follows:

When lines intersect angle relationships are formed such as vertically opposite angles, linear angles etc.

Angle a is vertically opposite to angle b.

Vertically opposite angles are congruent.

Therefore,

∠a ≅ ∠b

Hence,

x + 8 = 100(vertically opposite angles)

x = 100 - 8

x = 92

b + x + 8 = 180(sum of angles on a straight line)

b + 92 + 8 = 180

b = 180 - 100

b = 80 degrees.

Hence,

a = 80 degrees

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The domain of the relation is {-9, 1, 3, 8, 9}

All the values that go into a relation or a function are called the domain.

Given is a relation, (-3, -7), (8, -7), (1, 10), (-9, -8) and (9, -6)

The domain of a function or relation is the set of all possible independent values the relation can take.

Hence, the domain of the relation is {-9, 1, 3, 8, 9}

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Step-by-step explanation:

a=5( all of them)

b=5 (The last 5, the first two zeroes don't count)

c=2 ( The first two numbers)

Rules:

Non-zero digits are always significant

Any zeros between two significant digits are significant

A final zero or trailing zeros in the decimal portion ONLY are significant

If the zeroes are before a decimal but not in between two significant numbers, they are not significant

Answer:x=9/4 nine over 4 for improper fraction I hope this is helpful mark me brainlist if this sounds good

Step-by-step explanation:

7(x-1)=3x+2

Distribute through the parentheses

7x-7=3x+2

Move the variable to the left-hand side and change its sign

7x-7-3x=2

or Move the constant to the right-hand side and change its sign

7x-7-3x=2

Collect like terms

4x=2+7

And then Add the numbers

4x=9

Divide both sides of the equation by 4

x=9/4

Mixed number is 2 1/4

The relations which are functions as required to be identified in the task content are;

It follows from the task content that the relations which are functions among the given answer choices are to be identified.

Since the definition of a function is such that; a function is a special kind of relation in which case only one output value is assigned to each input values.

Put simply, a function has only one output value for each input value.

Therefore, it follows from the definition above that the relations which are functions among the given answer choices are as listed above.

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The measurement of the angles x, y, and z of the given triangles are;

x = 88°, y = 55° and z = 37°

We know that;

The sum of interior angles of any triangle is equal to 180 degree.

The sum of angles on a straight line is 180 degrees.

Thus;

x + y + z = 180°

Now, from the given diagram, we can see two pairs of parallel lines. This means that there will be some corresponding angles.

Thus;

y is a corresponding angle to 55° and as such we can say that;

y = 55°

Similarly, z° is a corresponding angle to 37° and as such we can say that;

z = 37°

Thus;

x + 55 + 37 = 180

x + 92 = 180

x = 180 - 92

x = 88°

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a. [tex]123.1(1.069)^3 \approx 150.4[/tex]

b. [tex]123.1(1.069)^{20} \approx 467.5[/tex]

The amounts of each solution needed are given as follows:

The percentage of paint when 5 liters of the thinned solution are added is of:

62%.

The variables to the system of equations are given as follows:

The painted needs 20 liters, hence:

x + y = 20.

The solution is 65%, hence:

0.5x + 0.75y = 0.65 x 20

0.5x + 0.75y = 13.

From the first equation, we have that:

x = 20 - y.

Hence the amount of liters of the 75% solution is obtained as follows:

0.5(20 - y) + 0.75y = 13.

0.25y = 3

y = 3/0.25

y = 12 liters.

Then the amount of liters of the 50% solution is of:

x = 20 - y = 20 - 12 = 8 liters.

When 5 liters of the 50% solutions are added, there would be 13 liters of the 50% solution, then the percentage would be of:

P = (0.5 x 13 + 0.75 x 12)/25 = 0.62 = 62%.

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Answer:

b = amount of boys

g = amount of girls

f = amount spent in first intermission

s = amount spent in second intermission

c = cake cost

x = coke cost

b = 16

g = 14

f = 76

s = 74

c = 2

x = 3

Step-by-step explanation:

cg + xb = f

xg + cb = s

f - 2 = s

b + g = 30

b > g

To solve for the variables, you just have to guess and check.

(2 x 14) + (3 x 16) = 76

(3 x 14) + (2 x 16) = 74

76 - 74 = 2

16 + 14 = 30

16 > 14

Answer:

First option

Step-by-step explanation:

Hope this helps

The expression that can be use to represent the amount owned on rental is 0.1x + 25y

Rick rents a car from a company that charges him $25 per day plus 10 cents per mile driven.

The expression that can be use to represent the amount owned on rental can be represented as follows:

let

x = number of miles driven

y = number of days

Let's convert cent to dollars

100 cents  = 1 dollars

10 cents = ?

cross multiply

amount in dollars = 10 / 100 = 0.1 dollars

Therefore,

the expression = 0.1x + 25y

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The speedup of a parallel algorithm will eventually reach some limit.

What is parallel algorithm?

An algorithm is a set of instructions that takes input from the user and, after doing some calculations, generates an output. A parallel algorithm is one that can carry out multiple operations simultaneously on various processing units and then combines all of the separate outputs to get the desired outcome.

An algorithm that can execute several instructions concurrently on various processing devices and then aggregate all of the individual outputs to produce the final result is known as a parallel algorithm.

Because a parallel algorithm's speedup is never equal to the number of processors, it ultimately reaches a limit beyond which it can no longer be accelerated. At that point, the algorithm will no longer be accelerated and the speedup will stop.

Hence, the speedup of a parallel algorithm will eventually reach some limit.

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The statement about the original and transformed triangles that must be true is The triangles are congruent.

Triangles are congruent when they have the same size and shape but face opposite directions. Triangles do not change size or shape as a result of translation and rotation.

This means that if a triangle is translated and then reflected, the result will still be congruent with the first triangle. If all three corresponding sides are equal and all three corresponding angles are equal in measure, two triangles are said to be congruent. These triangles can be moved, rotated, flipped, and turned to look exactly the same. So two triangles are congruent if all of their sides are the same—side, side, side.

In conclusion, the correct option is B.

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Answer:

15095.39

Step-by-step explanation:

[tex]13000(1+(0.03)/4)^{(4)(5)} \approx 15095.39[/tex]

Answer:

(-2,-4)

Step-by-step explanation:

3x+2=-2x-8

+2x.    +2x

5x+2=-8

   -2. -2

5x=-10

/5.  /5

x= -2

y=3(-2)+2

y=-6+2

y= -4

(-2,-4)

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The magnitude and the direction angle of the vector are given as follows:

The points that define the vector are given as follows:

m(-15, 16) and n(2,-6).

Considering m as the starting point and n as the endpoint, the vector is defined by the subtraction of the coordinates of n by the coordinates of m, hence:

v = (2 - (-15), -6 - 16) = (17, -22).

The magnitude of the vector is given by square root of the sum of the squares of the components, hence:

|v| = sqrt(17² + (-22)²) = 27.80.

The direction angle is the arc tangent of the division of the vertical component of the vector by the horizontal component of the vector, hence:

θ = arctan(-22/17)

θ = -52.3.

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Scatterplots are utilized to plot data of interest on a flat and an upward pivot in the endeavor to show the amount one variable is impacted by another.

A chart that shows two numerical variables. The results of these dependent parameters for each of the people are represented as points on the graph's horizontal directions, one for each variable.

At Stage Eight of linear regression, one of the two or more variables is considered the informative variable while the second variable is considered the can, therefore. In this instance, the response variable is represented on the vertical axis while the important point is plotted on the horizontal line (x-axis) (y-axis).

Scatterplots are utilized to plot data of interest on a flat and an upward pivot in the endeavor to show the amount one variable is impacted by another.

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