After a 35% reduction, you purchase a new bike for $282.75. What was the price of the bike before the reduction?

A) First write an equation you can use to answer this question. Use x as your variable and express any percents in decimal form in the equation.

B) Solve your equation in part [A] to find the original price of the bike.

Answer:

4 mph

Explanation :

Let us call x, the woman speed as she goes uphill

Now, we know that it took the woman 2 hours to go uphill; therefore, the distance covered is

4* (x)

shortly afterwards, when the woman returns she is walking at x + 2 mph; therefore, the distance she covers is

D = 4 (x +2 )

Since the uphill and the downhill distances ar the same, we have

4x = 2 (x +2 )

4x = 2x + 4

x = 2

Hence, going to the hill, the woman speed is 2 miles per goo

a) The opposite of the numbers 3, 7.5, and -2(2/3) will be 0.33, 0.133, and -0.375.

b) The sum of the given number and its opposite will be 7.928.

It is defined as the numbers in all real numbers which cannot be represented as rational numbers, in other words, the irrational number cannot be expressed in the form of p/q form.

A rational number is a sort of real number that has the form p/q and does not equal zero.

The given number is as,

3, 7.5, and -2(2/3)

a)

The opposite number is obtained as 1 by dividing the given number,

⇒ 1 / 3 = 0.33

⇒ 1 / 7.5 = 0.133

⇒ 1 / -2(2/3) = -0.375

b)

The sum of the given number and its opposite is,

= 3+0.33 + 7.5 + 0.133+ (-2(2/3) ) + (-0.375)

= 7.928

Thus, the opposite of the numbers 3, 7.5, and -2(2/3) will be 0.33, 0.133, and -0.375.and the sum of the given number and its opposite will be 7.928.

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Answer

(3x/4) - 9

Explanation

We are told to subtract (¼x + 5) from (x - 4)

We just simply do this step by step

(x - 4) - (¼x + 5)

Hope this Helps!!!

Answer:

126

Step-by-step explanation:

a+b=d

9x being d, 4x being a and 70 being b

4x+70=9x

70=5x

x=14

9(14)=126

Data:

Retail price: $4500

Pays cash: -10%

hire purshast: $675 + 24(212.50)

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

1. Find the 10% of 4500:

2. Substract the 10% to the retail price:

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

1. Add 675 and (24*212.50):

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

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

As the retail price 4500 is 100% which percent is 1725:

H=16.4

Step-by-step explanation:

1.2x4=4.8

3.9x4=15.6

so

4.1x4=16.4

If Angela spent $95 to buy 7 cakes for her office party, and she then cut each cake into quarters and each quarter into further 3 pieces, of which Kevin ate 5 pieces, then Angela had spent $5.65 on just the share of the cake that Kevin had.

As per the question statement, Angela spends $95 to buy 7 cakes for her office party, and she then cuts each cake into quarters and each quarter into further 3 pieces, of which Kevin ate 5 pieces.

We are required to calculate the amount Angela had spent on just the share of the cake that Kevin had.

To solve this question, first let us calculate the total number of pieces, did Angela cut all the 7 pieces of the cake into.

Considering one piece, that it was first cut into a quarter and then each quarter into further 3 pieces, one single piece out of original 7 pieces was cut into a total of [(4 * 3) = 12] pieces.

Therefore, all the 7 original pieces were altogether cut into a total of

[(7 * 12) = 84] pieces.

Now, since Angela spent $95 to buy the original 7 pieces,

Or, Angela actually spent $95 to buy 84 pieces of cake,

Then, 1 piece of the 84 costs $(95/84) = $1.13.

Now, since Kevin ate 5 such pieces of the 84, those 5 pieces cost

$(1.13 * 5) = $5.65.

Therefore, Angela had spent $5.65 on just the share of the cake that Kevin had.

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Answer: 35.9166 mm (the square root of 1290)

Step-by-step explanation:

The number of miles that Luke ran on Thursday will be 3 miles.

From the information given, it was illustrated that Luke ran 4 miles on Wednesday and then ran 3/4 as much as much as he did on Thursday.

It should be noted that the distance that he ran on Thursday will be:

= 3/4 × Distance on Wednesday

= 3/4 × 4

= 3 miles.

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Luke ran 4 miles on Wednesday. Luke ran 3/4 as much as much as he did on thursday than he did on wendsday how many miles did luke run on thrurday

Answer: slope = 4/7

Step-by-step explanation:

you can plug the coordinates into the slope formula. y2 - y2/x2 -x1.

Answer:

Everybody hates somebody sometimes.

Or Not everybody loves somebody sometime

Step-by-step explanation:

The initial speed to the waterpark is 40 miles/hr.

The return speed is 60 miles/hr.

Given,

t = 3hr

Return speed = s +20m

Return time = 3 -1 = 2hrs

Solution:

s = d/t

s = d/3

d = 3s----1

s + 20 = d/t - 1

s + 20 = d/3-1

s + 20 = d/2

2s + 40 = d------2

Equating equations 1 and 2,

3s = 2s + 40

s = 40 miles/hr

The initial speed to the waterpark is 40 miles/hr.

Return speed = s +20

= 40+20

= 60 miles/hr

The return speed is 60 miles/hr.

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Solution

For this case we have the following:

x intercept 4: (4,0)

y intercept 2: (0,2)

Then we can find the slope like this:

then the equation is given by:

y= -1/2 x+ 2

and we can use x= 1 and we have y= 3/2

x= 2 , y= 1

Then two other points could be:

(1,3/2) and (2,1)

Surface Area of rectangular pyramid is lw + l√[(w ÷ 2)² + h²] + w√[(l ÷ 2)² + h²].

The area of ​​a rectangular pyramid is equal to the sum of the areas of the sides and faces of the rectangular pyramid. A quadrilateral pyramid is a three-dimensional shape with only a rectangular base and triangles on either side of the base.

The area of ​​the base of the rectangle is calculated by multiplying the length of the rectangle by the width of the rectangle.

The area of ​​a rectangle with a pyramidal formula is determined by observing the width, length, and height of the base,

S.A. = lw + l√[(w ÷ 2)² + h²] + w√[(l ÷ 2)² + h²],

where l is the length of the bottom of the rectangle, w is the width of the bottom of the rectangle, and h is the height.

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Answer: -37

Step-by-step explanation:

1110800. Equity Account will be after stock dividends

Similar to a cash dividend, however instead of cash, stocks are given out. A stock dividend will increase the number of shares outstanding while lowering the stock price.

In this issue, there are 460000 shares outstanding at a price of $30, which equals 13800000

Equity's total market value is $13800000.

Each shareholder will get a 20% increase in stock, and the number of existing shares will increase as a result of the 20% stock dividend.

Shares outstanding after dividend announcement total 460000 + 46000 ×20% =552000.

The number of outstanding common shares will rise to 552000 as a result of the issuance of 92000 more shares.

Common stock only contains the par value; for example, if the market price of a share is $30 and the par value is $1, the excess amount of $29×92000:2668000 is added to the capital surplus account. It will total 861000 + 2668000=3529000.

Due to the absence of any monetary transactions, the total owners' equity is unaltered.

The retained earnings will be decreased by 92000 × 30 = 2760000, resulting in 3870800 – 2760000=1110800.

Equity Account will be after stock dividends.

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Answer:

(g ◦ h) (x) = 16x² + 12x -4

Step-by-step explanation:

We have

g(x) = x² − 5x

h(x)= 4x + 4

(g ◦ h) (x) = g(h(x))

h(x) = 4x + 4

g(h(x)) = g(4x + 4)

= (4x + 4)² - 5(4x+4)         //substitute 4x + 4 wherever there is an s-term in

(4x + 4)² = 16x² + 32x + 16

5(4x + 4) = 20x + 20

(4x + 4)² - 5(4x+4)  = 16x² + 32x + 16 -(20x + 20)

= 16x² + 32x + 16 - 20x - 20

= 16x² +(32x - 20x) + (16-20)

= 16x² + 12x -4

Explanation

The vertical asymptote

for the given function

According to the formula

The denominator will be undefined when

The vertical asymptotes are

For the horizontal function

Since the denominator degree is higher than the numerator

Then

The horizontal asymptote is

For the oblique asymptote

Since the degree of the numerator is not one degree greater than the denominator, then there are no slant asymptotes.

There are no oblique asymptote

we have

S= 4*(pi)*r^2​

solve for r

That means ------> isolate the variable r

step 1

Divide by 4*(pi) both sides

so

S/(4*pi)=r^2

step 2

Square root both sides

so

Answer:

D. An infinite number of real solutions

Step-by-step explanation:

3(2x + 1) = 2(3x + 5) - 7

6x + 3 = 6x + 10 - 7

6x + 3 = 6x + 3

I hope this helps!

Generally, the equation representing the simple interest on a deposited amount is;

where ;

I is the simple interest

R is the rate

T is the time

We have other varaints of this formula, depending on the term missing

All we have to is to make the missing term the subject of the equation and input the other given values to get the missing term

We can have the variants of this formula as follows

a) Missing Principal

b) Missing Rate

c) Missing Time

Answer:

D. -87 + 33i

Step-by-step explanation:

(7 + 5i)(-6 + 9i)

7(-6 + 9i) + 5i(-6 + 9i)

-42 + 63i + -30i + 45i²

-42 + 33i + 45(-1)

-42 + 33i - 45

-87 + 33i

I hope this helps!

The length of segment CD is 7 units. The length of segment AE is 20.5 units. The m∠BCD is 45 degrees.

A parallelogram is always a quadrilateral but a quadrilateral can or cannot be a parallelogram.

Given that parallelogram ABCD, has m∠ABC = 135° and the length of diagonal AC is 41 units.

The measure of length of side AD is 35 units and length of side AB is 7 units.

WE know that the opposite side of a parallelogram are same. Thus,

The length of segment CD = AB = 7 units.

Also, the length of diagonal AC =  41 units. Then;

The length of segment AE = 1/2 AC = 41/2 = 20.5 units.

Therefore, m∠BCD + m∠ABC  = 180

m∠BCD + 135  = 180

m∠BCD  = 180 - 135

m∠BCD = 45 degrees.

Hence, The length of segment CD is 7 units. The length of segment AE is 20.5 units. The m∠BCD is 45 degrees.

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Answer:

45

7

20.5

Step-by-step explanation:

Given:

Aim:

We need to write the given expression in scientific notation.

Explanation:

Final answer:

ANSWER

EXPLANATION

Now, imagine you are to divide something into 100 equal sections;

the 12th section of those sections is the twelve hundredths.

To represent this as a fraction we have 12/100.

Hence, the twelve hundredths as a fraction is 12/100.

Answer:

Step-by-step explanation:

Set up a proportion. x stands for hours that we need to find out.

[tex]\frac{6hrs}{74score} = \frac{xhrs}{98score}\\ 6(98)=74(x)\\588= 74x\\588/74=x\\8=x[/tex]

**the answer was 7.9 BUT I rounded it to 8.

Lisa would need to study for 8 hours to get a score of 98.

Answer:

Hot dogs cost £3 and fry's cost £2.

Total cost £5.

Step-by-step explanation:

Let a hot dog cost £x and a portion of fry's cost £y.

Then:

12x + 8y = 52

8x + 12y = 48

Simplifying these 2 equations we get:

3x + 2y = 13 ---------- (A)

2x + 3y = 12...............(B)

multiply the first equation by 2 and the second by 3:

6x + 4y = 26  

6x + 9y = 36

Subtracting:

0 - 5y = -10

y = -10/-5 = 2.

Now, substituting in equation  (A):

3x + 2(2) = 13

3x = 9

x = 3.

Answer:

Step-by-step explanation:

Using division, If you have 7/8 of a cup of tomato sauce and you must fill small containers with exactly 1/4 of a cup of tomato sauce, then number of containers can fill completely is 3 containers

The total  quantity of tomato sauce that you have = 7/8 of a cup

The quantity of tomato sauce with you must fill small containers = 1/4 of a cup

To find the number of containers that you can fill completely, you have to use division

Number of containers can fill completely = The total  quantity of tomato sauce that you have / The quantity of tomato sauce with you must fill small containers

= 7/8 ÷ 1/4

= 7/8 × 1/4

= 7/2

= 3.5

≈ 3 containers

Hence, using division, if you have 7/8 of a cup of tomato sauce and you must fill small containers with exactly 1/4 of a cup of tomato sauce, then number of containers can fill completely is 3 containers

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SOLUTION

Step1:Write out the formula

Step2; write out the parameters

Step3: Substitute into the formula and simplify

Step4: simplify the expression above

Then the rate becomes

Therefore the rate is 20.49