A cyclist's speed is 1.5 times faster than a walker's speed. they simultaneously start at the same point and after 1.5 hours the distance between them is 12.5 miles. what are their speeds?

The solution of each of the given exponents are;

1) 10x⁸y⁴/(-6x⁴y⁵) = -5x⁴/3y

2) (-4x³ * x² y⁴)/(-2x³y⁴) = 2x²

3) (3n⁴)² = 9n⁸

4) (5x⁶y⁰)² = 25x¹²

The Laws of Exponents are;

Thus;

1) 10x⁸y⁴/(-6x⁴y⁵) = -(10/6)x⁸⁻⁴y⁴⁻⁵

= -5x⁴/3y

2) (-4x³ * x² y⁴)/(-2x³y⁴)

= (-4/-2)(x⁵⁻³)(y⁴⁻⁴)

= 2x²

3) (3n⁴)² = 3² * n⁴*²

= 9n⁸

4) (5x⁶y⁰)²

= 5²x⁶*²y⁰*²

= 25x¹²

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Answer:

4/ 25x¹²

Step-by-step explanation:

Because y^0 will cancel any thing!

So we have left 5x^6 times 5x^6

Same base so add square root of ^6 = 5x^12

Given,

Decrement of 17 inches takes  1 year.

So, Decrement of 1  inches takes [tex]\frac{1}{17}[/tex] year.

therefore, decrement of 255 inches will take [tex]\frac{255}{17}[/tex] years, which is, 15 years.

So, the answer is 15 years.

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you take out a loan for $702 at an annual interest rate of 6% compounded quarterly for 2 years what is the total amount that you will have at the end of the two-year ​

we know that

The compound interest formula is equal to

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

where

A is the total amount at the end of two years

P is the loan

r is the rate of interest  in decimal

t is Number of Time Periods

n is the number of times interest is compounded per year

in this problem we have

P=$702

r=6%=6/100=0.06

t=2 years

n=4

substitute the given values in the formula

therefore

the answer is

Answer:

|-17| = 17, so -3 + |-17| = -3 + 17 = 14

The equation that passes through the given point 2x-3y=0.

Let the point which they pass be the origin (0,0).

From the given equation we get [tex]y= 2/3x + 19[/tex]

On comparing this with the general equation that is [tex]y= mx+c[/tex]

We get [tex]m= 2/3[/tex]

Thus as we know the equation of line is [tex]y-y1 = x-x1[/tex]

Substituting the values in this equation we get;

[tex]y-0= 2/3(x-0)[/tex]

On cross multiplying we get

[tex]3y=2x[/tex] or [tex]2x-3y=0[/tex]

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Answer:

Step-by-step explanation:

Answer:

lol doofus

Step-by-step explanation:

Answer:

(5x)(-1.2x+5)

=-6x^2+25x

Step-by-step explanation:

Answer:it is x=24

because you cant divide a negative and negative to get a negative you will get a postive if you divide -24/-3 but 24/-3 is -8

Step-by-step explanation:

For this question, notice that:

This are 3 different ways to name

Answer: The answer is B.

Step-by-step explanation: The scale on the y-axis could be changed to 100–120.

The teacher has set up 7 workstations in each classroom

Total pounds of clay = 7/8 pounds

Pound of clay put at each workstation = 1/16

Fractions: A numerical value that designates a portion of a whole is used to represent fractions. A fraction is a component or section taken from a whole, which can be any number, a certain amount, or an object.

Finding the number of workstations:

Number of workstations = Total clay available/Clay set up at each workstation

=(7/8)/(1/16)

=7/8*16/1

= 14 workstations

There are two classes in which these workstations are divided

so, each class will have 7 workstations

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Answer:

168 straberries was rotten

Step-by-step explanation:

Answer: Did you get the help you needed?

Step-by-step explanation:

The coordinates after dilation is

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).

Given coordinates of triangle (-3, 6), (0, 3) and (-3, 3)

As, the figure dilated by factor 4/3

Then the coordinates after dilation is

(-3 x 4/3, 6 x 4/3) = (-4 , 8)

(0 x 4/3, 3 x 4/3) = (0, 4)

(-3 x 4/3, 3 x 4/3) = (-4, 4)

Hence, the coordinates are:

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The quantity of space inside a form is measured by its volume.
The volume as a function of side length(x) is: V(x) = 4x³ - 40x² + 100x

What is volume functions?
A three-dimensional space's volume can be calculated. It is frequently quantified numerically by different imperial units or SI-derived units. Volume and length have a mutually reliant relationship.

Given, length of the cardboard = 10 units
Width of the cardboard = 10 units
When side length(x) is removed from the cardboard, the dimension of the box becomes:
Length of the new cardboard = (10 - 2x) units
Width of the new cardboard = (10 - 2x) units
Height of the new cardboard = x units
Therefore, volume of the new cardboard box, V(x)
= Length*Width*Height
= x*(10 - 2x)*(10 - 2x) cubic units
= 100x² - 20x² - 20x² + 4x³
= 4x³ - 40x² + 100x

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For the transformation of parent function f(x)=|x| to the  g(x)=|x|+4, the transformation occurred is 4 units upward.

The function transformation / translation principles are as follows: f (x) + b raises the function b units.

The given parent function is; f(x)=|x|

The transformed function is; g(x)=|x|+4

Thus, from the 1st rule of the transformation we can say that the function has shifted 4 units to upward.

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Answer: 14 mile/s2

Step-by-step explanation:

Answer:

4^-1 = 0.25

Step-by-step explanation:

Answer:

160

Step-by-step explanation:

360-170-30=160 subtract all angles from 360

Answer:

140°

Step-by-step explanation:

oh, come on, this is like "you have 8 apples as a mixture of red and green apples. 5 apples are red, how many are green ?".

it is the same here.

the total angle is 170°.

now we know a part of it is 30°.

how large is the rest ?

well, it is 170 - 30 = 140°

The ways in which the linear systems are similar to quadratic systems includes:

The linear system means the model based on the use of a linear operator and, they exhibit features and properties that are much simpler than the nonlinear case. The quadratic system of equations consists of only quadratic equations.

The linear & quadratic systems are solved by graphing and substitution. In the linear systems, we get the lines and in quadratic systems, we get curves. In conclusion, the point of intersection of two lines or curves are the solutions of the respectively system.

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Let N be the nickels and Q be the quarters, since Charlie found 35 coins, we can write

Now, we know that a nickel is worth 5 cents and a quarter is worth 25 cents, then we can write

Then, the answer is option a.

well, let's keep in mind that whenever the x-coordinate is the same, we have a vertical line, so, Check the picture below.

The bonus based upon the given formula is $2606.15 approximately

Given,

Annual salary = $48,000

Yearly sales = $76,000

Bonus is given according to the formula:

2 weeks salary + 1 percentage commission

Here,

Annual salary is given as $48,000

We have to find the weekly salary:

There is 52 weeks in a year.

So, salary for one week = Annual salary / number of weeks =  48000/52 = $923.077

Now, salary for two weeks = 923.077 × 2 = $1846.154

Rate of annual commission is 1%

The commission amount:

1% of yearly sales = 1% of 76000 = (1/100) × 76000 = $760

So,

The bonus amount = 2 weeks salary + 1 percentage commission

The bonus amount = 1846.154 + 760

The bonus amount = 2606.154

Therefore, the bonus given based upon the given formula is $2606.154

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Answer:

tilly

its remy on the 4th quesiton

cricket loves burger clown

officer keys

gloria who works at coffee shop

because bill was going to lose the farm back in the country

Good Ol' Joe

because she let the cows out of the stables

here is your answers

Answer:

y = 32

Step-by-step explanation:

With this problem, we will use the direct variation form, y = kx.

k = proportionality constant.

Substitute the known inputs of x = 8 and y = 16 into the direct variation form:

y = kx turns into 16 = k(8)

Get k by itself by dividing 8 on both sides:
16/8 = k

2 = k

Now that we know the k value is 2, we input everything we know into the direct variation form if x were equal to 16

k = 2

x = 16

y = kx:

y = 2(16), making y equal to 32

Answer: Area= [tex]\frac{bh_{b} }{2}[/tex]

Example:

Let the base be 3 and the height([tex]h_{b\\}[/tex]) 4

So,

Area= [tex]\frac{3*4}{2\\}[/tex]-->[tex]\frac{12}{2}[/tex]=6

the rate from the plane to the radar station increasing 3 minutes later is 19.81 km/min

A plane flying with a constant speed of 14 km/min passes over a ground radar station at an altitude of 4 km and climbs at an angle of 45 degrees. At what rate is the distance from the plane to the radar station increasing one minutes later?

speed (Δs₁)= change in distance(Δd₁) /(Δt₁)change in time

mathematically,

(Δd₁) /(Δt₁) = Δs₁

= 14 km/min = (Δd₁) /(Δt₁)

and will are to find the speed after passes the radar

=Δs₂  km/min = (Δd₂) /(Δt₂)

to find distance d₁ and d₂ with respect to angle 45 degree at 4km

sin 45 = opp/hyp = 4/d₁

d₁ = 4/sin45 = 5.66km

tan 45 == opp/adj = 4/d₂

d₂ =4/tan45 =  4km

for one minute increment,

=1 x d₁ x Δs₁ = 1 x d₂ Δs₂

= 1x5.66x14 = 1x 4 xΔs₂

= 79.24 = 4Δs₂

speed =Δs₂ = 19.81km/min

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The most appropriate choice for complementary angle will be given by:

∠A = 27°

What are complementary angles?

Two angles are said to be complementary if the sum of the two angles is 90°

Here,

∠A = (2x + 5)°

∠B = (4x + 19)°

∠A and ∠B are complementary

(2x + 5) + (4x  + 19) = 90

6x + 24 = 90

6x = 90 - 24

6x = 66

x = [tex]\frac{66}{6}[/tex]

x = 11

∠A = 2 x 11 + 5

     = 22 + 5

     = 27°

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Complete Question

∠ A and ∠B complementary angles. If m∠A =  (2x + 5)°  and m∠B  = (4x + 19)°, then find the measure of ∠A.

The change in distance between the two after 15 minutes is 3.566 mi/h

Velocity is defined as the rate of change in displacement (distance) with time. It's a vector quantity so it has both magnitude and direction. Velocity is given by the formula:

Velocity = distance / time

If one walks east at 4 mi/h and the other walks northeast at 5 mi/h, then after 15 minutes, their distance are:

distance = velocity * time

distance₁ = 4 mi/h (15 mins)(1 hour/60 mins)

distance₁ = 1 mile east

distance₁ = 5 mi/h (15 mins)(1 hour/60 mins)

distance₁ = 1.25 mile northeast

Using trigonometric function and Pythagorean theorem, we can determine the distance between the two people. (Refer to the attached picture.)

d² = (1.25 sin 45°)² + (1.25 cos 45° - 1)²

d² = 0.795

d = 0.891 mi

After 15 mins, the distance is 0.891 mi and the change in distance in mi/h is

(0.891 mi / 15 mins)(60 mins / hour) = 3.566 mi/h

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