Which is an equivalent expression using a positive exponent?
(3/5)^-8 ÷ (3/5)^-4
(3/5)^4
(3/5)^12
(5/3)^32
(5/3)^4

Answer:

400

Step-by-step explanation:

yw

Answer:

1. 26 2/3

2. 13/5

3. 2000,3000,4000

Answer: $2.96

Step-by-step explanation:

$18.75 - $3.95 = $14.80

$14.80 / 5 = $2.96

Answer:

4 seconds

===========================

Given is the

quadratic function

, which has a graph of parabola.

It has two

x-intercepts

, with the greater one representing the

projectile on the ground, at h(t) = 0

.

Let's

solve

the equation:

- 16t² + 32t + 128 = 0

t² - 2t - 8 = 0

t² - 2t + 1 - 9 = 0

(t - 1)² = 9

t - 1 = 3 and t - 1 = - 3

t = 4

and t = - 2

The root with the greater value is

t = 4

, which represents the time we need.

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \:4 \:\: sec [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

height of an object projected in air with time is represented by the given equation :

[tex]\qquad\displaystyle \tt \rightarrow \: h(t) = - 16 {t}^{2} + 32t + 128[/tex]

The height when the object hits the ground will be 0

so, just equate the equation with 0, and we will get the value of t (time) when the projectile will be back to ground.

[tex]\qquad\displaystyle \tt \rightarrow \: - 16 {t}^{2} + 32t + 128 = 0[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: - 16( {t {}^{2} - 2t}^{} - 8) = 0[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: t {}^{2} - 2t - 8 = 0[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: t {}^{2} - 4t +2 t - 8 = 0[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: t(t - 4) + 2(t - 4) = 0[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: (t - 4)(t + 2) = 0[/tex]

So,

[tex]\qquad\displaystyle \tt \rightarrow \: t = 4 \: \: \: \: or \: \: \: \: t = - 2[/tex]

but since time can't be negative, t = 4 seconds

The object will be back on ground after 4 seconds.

The transformation has a horizontal shift right by 4 units and vertical shift upwards by 3 units.

What do you mean by transformation of a function ?

The modification of a graphed function to create a different version of the parent function is known as transformation.

For the given condition :

The function is y = (x - 4)² + 3.

The above function is transformed from the parent function which is y = x².

We know that , the horizontal shift depends on the value of h. The horizontal shift and it is described as:

y = f (x + h)

Then , the graph of function will be shifted to left by h units.

and

y = f (x - h)

Then , the graph of function will be shifted to right by h units.

If we compare both functions i.e., y = (x - 4)² and y = f (x - h), their is a difference of -1 , it meant shift is right by 4 units.

Now , we know that , the vertical shift depends on the value of k. The vertical shift is described as:

y = f(x) + k

Then , the graph of function will be shifted up by k units.

and

y = f(x) - k

Then , the graph of function will be shifted down by k units.

Here , if we compare functions i.e., y = (x - 4)² + 3 and y = y = f(x) - k ,  we find out that the graph of function will be shifted upwards by 3 units.

Therefore , the transformation has a horizontal shift right by 4 units and vertical shift upwards by 3 units.

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Answer:

x = - 1 / 24

Step-by-step explanation:

-6 ( 6x - 1 ) + 9 = 36x + 18

First, solve the brackets.

-36x + 6 + 9 = 36x + 18

Then, subtract 36x by both sides.

-36x - 36x + 6 + 9 = 18

-72x + 15 = 18

Now, Subtract 15 by both sides.

-72x = 18 - 15

-72x = 3

Now divide both sides -72 by both sides.

x = - 3 / 72

x = - 1 / 24

The expanded form of this number 14.702 will be  (1 × 10) + (4 × 1) + (7/10) + (2/1000)

It should be noted that expanded form simply means breaking down of the number given into different units.

Therefore, based on the information illustrated. This will be:

14.702 will be:

= (1 × 10) + (4 × 1) + (7/10) + (2/1000)

= 10 + 4 + 0.7 + 0.002

Note that your options aren't written well.

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

Where m is the slope and b is the y-intercept. These values are given, then the equation of the line is:

To graph it, we need to know the coordinates of at least two points on the line.

Whan x=0, then y is:

Thus, the first point is (0,-4).

When x=1, then y is:

The second point on the line is (1,0).

If we draw these points in the coordinate plane, we can draw a line that passes through them, and this will be the graph of the line.

It looks like this:

Based on the gross pay for Melika Yasin, and the fact she claims no allowances and is married, the amount withheld from her pay for Federal Income Tax is $43.

Melika Yasin had a gross pay of $355.00 for the week. This amount is more than $350 but less than $360.

Melika Yasin therefore falls into the bracket of "At least $350 but less than $360."

She also claims no allowances in this bracket. This means that the amount that would be withheld for Federal Income Tax according to the table would be $43.

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Answer:

8.00340909

Step-by-step explanation:

since 21129 was walked in one hour the in two hours 42258 wouldve been walked so that means mark walked a little over 8 miles

hope this helped

have a good day^^

The tables that represent a proportional relationship are :

x 1 2 3 4 5

y 4 5 6 7 8

b 2 3 8 9 14

c 4 6 16 18 28

Two variables have a proportional relationship when the ratios of the rate of change of the variables are constant.

Ratio = change in the value of y / change in the value of x

First table:

(5 - 4) / (2 - 1) = 1

(6 - 5) / (3 - 2) = 1

(7 - 6) / (4 - 3) = 1

(8 - 7) / (5 - 4) - 1

Second table:

(5 - 3) / (3 - 2) = 2

(6 - 5) / (4 - 3) = 1

(8 - 6) / (5 - 4) = 2

(9 - 8) / (6 - 5) = 1

Third table:

(6 - 4) / (3 - 2) = 2

(16 - 6) / (8 - 3) = 2

(18 - 16) / (9 - 8) = 2

(28 - 18) / (14 - 9) = 2.

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Before taxes, the tie will cost $11.25

Discounts are price cuts made by store owners on goods or services that would otherwise be sold for the indicated price. Usually, this portion of the rebate is given to increase sales or get rid of extra inventory. The List Price, sometimes referred to as the Marked Price, is the cost of a product as declared by the seller or manufacturer, excluding any discounts.

The final price at which a product is actually sold is the selling price, which includes any discounts or price drops from the list price. Off or reductions are frequent terms used to describe discounts. Note that the marked price of the item is always used to calculate the discount (list price).

Discount = List Price - Selling Price

Discount (%) = (Discount/List Price) × 100

According to the question,

List price = $15.00

Discount % = 25 %

Cost of the tie before taxes = [tex]List \: price \:\frac{ (100 - Discount \%)}{100}[/tex]

⇒ [tex]\text{\$15.00}\: \frac{(100-25)}{100}[/tex]

⇒ [tex]\text{\$15.00}\: \frac{75}{100}[/tex]

⇒ [tex]\text{\$15.00}\: \frac{3}{4} = \text\:{\$15.00 \times 0.75}[/tex]

⇒ $11.25

Therefore, before taxes, the tie will cost $11.25

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Answer:

D.

Step-by-step explanation:

7.99 is the basic fixed cost per month. this is charged, even if there are no songs (x = 0) downloaded.

and so, 1.75 is the cost per downloaded song in addition to the basic fixed cost. so, yes, the number of downloaded songs has to be multiplied by the cost for a single song to get the total.

and so, 1.75 is the change in the total cost for every automakers download (every time x is increased by 1).

We need to know how to write linear equation to solve the problem. The number of hours when they make the same amount is 2 hours.

Linear equation is when a value of one variable is dependent on only one other variable. In the given question we know that Greg charges a flat fee of $140 and another $25 for every hour and Greg charges a flat fee of $100 and $45 for every hour. We need to find out the number of hours when both of them have the same amount, we can consider number of hours to be x and form equations accordingly.

140+25x=100+45x

20x=40

x=2

Therefore both of them will make the same payment when number of hours is 2.

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The approximate total of weight of the litter of  6 kittens 0.675kg

What is Weight ?

The force exerted on an object by gravity is known as its weight. The gravitational force acting on the item is referred to as weight in several common textbooks. Some people refer to weight as a scalar quantity that measures the gravitational force's strength.

Given,

The weight of one newborn kitten = 1/4 pounds
The value of pound in kilograms = 1pound = 0.45kg
convert the weight from  pound to kilograms = 1/4 x 0.45

                                                                              = 0.1125kg

Now, to find out total weight of litter of 6 kitten in kilograms

= 0.1125 x 6

= 0.675kg

Hence, The approximate total weight of the litter of 6 kittens in kilograms is 0.657kg
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The area of the rectangles A,B, C are 8 cm , 3cm and 15 cm , whereas  the area of the enlarged rectangle A,B,C are  32 cm ,12 cm and 60cm  

The relation between the area of the both original and the enlarged is the area of the enlarged rectangle is 4 times the area of the original rectangle.The problem we are dealing with is area what is referred to as the amount of space occupied by a two-dimensional figure, it is the amount that measures the number of unit squares that surround the surface of a closed figure. The standard unit of the region is square units which are generally spoken to as square inches, square feet. For the area of the rectangle we multiply the length of the rectangle by the width of the rectangle.

Area= l x b

for rectangle A : 4 x2 = 8 cm, for  B : 3 x 1 = 3 cm and for C: 5 x 3 = 15 cm  

As  we increase each dimension by 2 times:

For the enlarged rectangle A : 8 x4 = 32 cm ,B : 6 x 2 = 12 cm and C: 10 x 6 = 60 cm  .

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The amount of cash that as kept in the bank is $937500.

Let's have x represent the amount of cash.

One portion of it pays 0.5%, so 0.005x; the other portion pays 3.5%, so 0.035x. This gives us:

0.005x + 0.035x = 37500

Combining like terms:

0.040x = 37500

Solve for x:

x = (37500)/(0.04)

x = 937500

Therefore, the company started with $937,500.

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The absolute value of (-8) would be 8 on number line.

The absolute value of any number represented on number line is given as the distance of the number from zero on a number line, when counted on whichever side it is present that is either negative or positive. In mathematical notation, absolute value is defined as the modulus of the number, enclosed in two straight lines. For example: |-8| or |8| would have absolute value 8 even though both the numbers are represented on negative and positive side of zero respectively on the number line. The absolute value of any number which is also a real number is the non-negative value of that number irrespective of its sign. Number line figure is attached below.

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The number of green marbles in the bag is 10

From the question, we have the following parameters:

The given parameters can be represented using the following ratio

Ratio = Green marble : Orange marble

So, we have

Green marble : Orange marble = 2 : 3

When there are a total number of 15 orange marbles in a bag, then we have

Green marble : 15 = 2 : 3

Multiply ratio by 5

Green marble : 15 = 10 : 15

By comparison, we have

Green marble = 10

Hence, there are 10 green marbles in the bag

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Total number of possible outcomes:

From those 36 possible outcomes the next 10 sum of at least 9 ( a number greather than or equal to 9):

Then, the probability of obtaining a sum of at least nine when rolling a pair of dice is:

Answer:

y < 3

Step-by-step explanation:

Answer: 2/3

Step-by-step explanation:

1) First locate two points.

First, locate two points on the graph. For this example, I will choose (-2,0) and (1,2)

2) Find the distance between these two points.

We can find that from starting from (-2,0), we go right 3 and up 2. You can easily do this on paper by drawing a triangle.

3) Using the numbers we have before, find the rate.

To find the rate, we can use rise/run. Which will become 2/3.

Hello!

To find the slope of the line:

 ==> must find two points on the line

    (x₁, y₁): (-2,0)

    (x₂, y₂):(1,2)

 [tex]Slope = \dfrac{2-0}{1--2} =\dfrac{2}{3}[/tex]    <== Answer

Hope that helps!

Considering Justin's serve, it is found that:

a) The ball traveled 21.4 feet, which means that Justin's estimate is correct.

b) An assumption regarding the angle of Justin's serve was made.

c) The Pythagorean Theorem was used to solve this mathematical problem.

The Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle(triangle which has an angle of 90º between the two legs) with the length of the hypotenuse h, stating that the hypotenuse squared is the sum of the legs squared, according to the following rule:

[tex]h^2 = l_1^2 + l_2^2[/tex]

Assuming that the ball was served at an angle of 90º, the situation can be summarized as follows:

Hence the Pythagorean Theorem is applied and the distance is calculated as follows:

d² = 7.5² + 20²

d = sqrt(7.5² + 20²)

d = 21.4 feet.

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Answer:

while using a calculator we need it for solving problems and practice and analysis of reference to be able to answer

Step-by-step explanation:

according to which unit are we calculating

A square has 4 congruent side lengths. This means that each side will be the same length. Therefore, we can set the two lengths equal to each other.

[tex]S=S[/tex]

[tex]7x-15=2x[/tex]

Isolating a variable: rearranging an equation so that the variable is by itself

3 Step Solving process:

1. Collect like terms

2. Perform inverse operations

3. Simplify if necessary

[tex]7x-2x-15=0[/tex]

[tex]5x=15[/tex]

[tex]\frac{5x}{5}=\frac{15}{5}[/tex]

[tex]x=3[/tex]

The value of x =  3

The perimeter can be found by adding all of the side lengths. A square has 4 sides.

a + a + a + a = P

However, we know that a square has congruent sides so we can manipulate this formula:

4a = P - where a is equal to the side length

Using a previous equation we know that a side length is equal to 2x and we know the value of x, to be 3. Therefore, a side length must be 6.

we can now input the value of the side length into the formula.

[tex]4(6)=P[/tex]

[tex]24=P[/tex]

The perimeter of the square is 24.

Answer:

Step-by-step explanation:

[tex]3\sqrt{20} + 4\sqrt{5}[/tex]

1st: Split up the numbers under the radical into possible factors.

[tex]3\sqrt{5*4} + 4\sqrt{5}[/tex]

2nd: Take out the perfect square (in this case 4)

[tex]3*2\sqrt{5} + 4\sqrt{5}[/tex]

3rd: simplify

[tex]6\sqrt{5} + 4\sqrt{5}[/tex]

4th: Combine like terms

[tex]10\sqrt{5}[/tex]

Answer:

[tex]\sf 10\sqrt{5}[/tex]

Step-by-step explanation:

      Prime factorize 20 and simplify 3√20

[tex]\sf 3\sqrt{20} = 3\sqrt{2*2*5}=3*2*\sqrt{5}=6\sqrt{5}[/tex]

[tex]\sf 3\sqrt{20}+4\sqrt{5}=6\sqrt{5}+4\sqrt{5}[/tex]

                   [tex]\sf = 10\sqrt{5}[/tex]

(i) When sinФ=2/3 → It lies in Ist and IInd quadrants and the suitable graph is not provided here.

(ii) when cosФ=-1/2 → It lies in IInd and IIIrd quadrants and the suitable graph is A and D.

(iii) when cotФ=3/4 → It lies in Ist and IIIrd quadrants and the suitable graph is E.

(iv) when cosecФ=3/2 → It lies in the Ist quadrant and the suitable graph is not provided here.

What is Quadrant?

(i) When sinФ=2/3

Ф=sin^(-1)(2/3)

Ф=41.81°,138.18°

So it lies in Ist and IInd quadrant.

A suitable graph is not provided here.

(ii) when cosФ=-1/2

Ф=cos^(-1)(-1/2)

Ф=120°,240°

So it lies in IInd and IIIrd quadrant.

A suitable graph is A and D.

(iii) when cotФ=3/4

Ф=cot^(-1)(3/4)

Ф=53.13°,233,13°

So it lies in Ist and IIIrd quadrant.

A suitable graph is E.

(iv) when cosecФ=3/2 or sinФ=2/3

Ф=sin^(-1)(2/3)

Ф=0.729°

So it lies in Ist quadrant.

A suitable graph is not provided here.

(i) When sinФ=2/3 → It lies in Ist and IInd quadrants and the suitable graph is not provided here.

(ii) when cosФ=-1/2 → It lies in IInd and IIIrd quadrants and the suitable graph is A and D.

(iii) when cotФ=3/4 → It lies in Ist and IIIrd quadrants and the suitable graph is E.

(iv) when cosecФ=3/2 → It lies in the Ist quadrant and the suitable graph is not provided here.

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Answer:70 cm

Step-by-step explanation:a^2+b^2=c^2

Answer: No, at least one segment length is not preserved, making this a nonrigid transformation.

Step-by-step explanation: A rigid transformation implies that both the shape and size are not changed. The second answer is right because the length of segment JK (2 units) is not preserved when mapped onto J'K' (5 units).

The null hypothesis should not be rejected. There is insufficient evidence that the true diameter differs from 0.5 inches.

We are given that,

n = 15

t-value = 1.66

Significance level;α = 0.05

So, DF = n - 1 = 15 - 1 = 14

In the attached one-sample t-table, we can see that the p-value of 0.06

corresponds to a t-value of 1.66 and a DF of 14

Due to the P-value of 0.06, it is greater than the significance level of 0.05. Based on the results, we are not rejecting the null hypothesis. There is insufficient evidence to conclude that the true diameter in active attachment is different from 0.5

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