A cylindrical roller 2.5 m in length, 1.5 m in radius when rolled on a road was found to cover the area of 16500 m2 . How many revolutions does it make ?

Question 1:

For this case we must solve the following system of equations by the method of elimination:

[tex]8x-6y=-20\\-16x+17y=30[/tex]

We multiply the first equation by 2:

[tex]16x-12y = -40[/tex]

We have the equivalent system:

[tex]16x-12y = -40\\-16x + 17y = 30[/tex]

We add the equations:

[tex]5y = -10[/tex]

We divide between 5 on both sides of the equation:

[tex]y = - \frac {10} {5}\\y = -2[/tex]

We find the value of the variable "x":

[tex]8x-6 (-2) = - 20\\8x + 12 = -20\\8x = -20-12\\8x = -32[/tex]

We divide by 8 on both sides of the equation:

[tex]x = - \frac {32} {8}\\x = -4[/tex]

Thus, the solution of the system is:

[tex](x, y): (- 4, -2)[/tex]

Answer:

[tex](x, y): (- 4, -2)[/tex]

Question 2:

For this case we must solve the following system of equations by the method of elimination:

[tex]-4y-11x = 36\\20 = -10x-10y[/tex]

We multiply the first equation by 10:

[tex]-40y-110x = 360[/tex]

We multiply the second equation by -4:

[tex]40y + 40x = -80[/tex]

We have the equivalent system:

[tex]-40y-110x = 360\\40y + 40x = -80[/tex]

We add the equations:[tex]-70x = 280[/tex]

We divide by -70 on both sides of the equation:

[tex]x = \frac {280} {- 70}\\x = -4[/tex]

We find the value of the variable "y":

[tex]-4y-11 (-4) = 36\\-4y + 44 = 36\\-4y = 36-44\\-4y = -8[/tex]

We divide between -4 on both sides of the equation:

[tex]y = - \frac {8} {- 4}\\y = 2[/tex]

Thus, the solution of the system is:

[tex](x, y): (- 4,2)[/tex]

Answer:

[tex](x, y): (- 4,2)[/tex]

The three important tools of Federal Reserve's monetary policies are as follows:

Step-by-step explanation:

The monetary policies of the United States's central bank, Federal Reserve are the acts of the entity to influence money and raise the country's economy. These policies also helps in looking over the aspects of how the money and credits draw affects on credit rates and the overall performance of the U.S. Economy.

The three prime tools of the Federal reserve's monetary policies are the Open Market Operations, Discount Rates and the Reserve Requirements.

Open Market operations

This involves in purchase and selling process of government securities. The primary dealer with which the Reserve deals compete on the basis of prices and thus the dealer gets decided with whom the reserve deal for the day.

Discount Rates

This is the discount rate charged to depository institutions for short term loans by the Federal Reserve.

Reserve Requirements

This is the money or deposit amount the Reserve Bank must sustain in its vault or depository.

the answer about be am number one child so yeah

Answer:

288inches²s

step-by-step explanation:

from metrics

12inches = 1feet

converting

lenght = 3 * 12 = 36 inches

Area of the rectangle = 36 * 8 = 288inches²

Answer:

Step-by-step explanation:

Slope m = 5/6

The points (-2,1)

So; y1 = 1 and x1 = -2

The equation is y - y1 = m(x - x1)

y - 1 = 5/6(x + 2)

Multiply each term by 6

6y - 6 = 5(x + 2)

6y - 6 = 5x + 10

6y = 5x + 10 + 6

6y = 5x + 16

- 5x + 6y = 16

Multiplying by minus

5x - 6y = -16

Answer:

5x - 6y = -16

Step-by-step explanation:

5/6 = (y - 1)/(x - 2)

cross multiplying,

5x + 10 = 6y - 6

5x - 6y = -16

Answer: -9

Step-by-step explanation: When you're asked to multiply positives and negatives together, the rules are simple.

A positive times a positive is a positive.

A positive times a negative is a negative.

A negative times a positive is a negative.

A negative times a negative times a negative is a positive.

So for the problem you see here, we will use rule 2 which I have highlighted in bold above which states that a positive times a negative is a negative.

So (+3)(-3) = -9

The value is 0

PEDMAS is simply defined as a mathematical acronym that is used to represent the different arithmetic operations.

These letters represents;

From the information given, we have the expression

(3)-3

expand the bracket, we get;

3 - 3

Subtract the values, we have;

0

Learn about PEDMAS at: https://brainly.com/question/345677

#SPJ6

Answer:

Part 1) The sum of the two angles equals 70 degrees

Part 2) The complementary angle is 19 degrees and the supplementary angle is 109 degrees

Step-by-step explanation:

Part 1) we know that

The sum of the interior angles in any triangle must be equal to 180 degrees

so

In the triangle JKL

[tex]m\angle JKL+m\angle KLJ+m\angle LJK=180^o[/tex]

we have

[tex]m\angle JKL=110^o[/tex]

substitute

[tex]110^o+m\angle KLJ+m\angle LJK=180^o[/tex]

[tex]m\angle KLJ+m\angle LJK=180^o-110^o[/tex]

[tex]m\angle KLJ+m\angle LJK=70^o[/tex]

therefore

The sum of the two angles equals 70 degrees

Part 2) we know that

If two angles are complementary, then their sum is equal to 90 degrees

If two angles are supplementary, then their sum is equal to 180 degrees

step 1

Find the complementary

Let

c ----> the complementary angle

[tex]m\angle c+71^o=90^o[/tex]

[tex]m\angle c=90^o-71^o=19^o[/tex]

step 2

Find the supplementary

Let

s ----> the supplementary angle

step 1

Find the complementary

Let

c ----> the complementary angle

[tex]m\angle s+71^o=180^o[/tex]

[tex]m\angle s=180^o-71^o[/tex]

[tex]m\angle s=109^o[/tex]

therefore

The complementary angle is 19 degrees and the supplementary angle is 109 degrees

Devin buys his clothes in Illinois, so he would pay the sales tax rate of Illinois, which is 6.25%. Therefore, the correct answer is D. 6.25%.

Certainly! Devin buys his clothes in Illinois, where the sales tax rate is 6.25%. This means that for every dollar he spends on clothes, he pays an additional 6.25 cents as tax.

To calculate how much tax Devin pays on a $100 purchase, you can use the formula:

[tex]\[ \text{Tax Amount} = \text{Purchase Amount} \times \text{Tax Rate} \][/tex]

Substitute the values:

[tex]\[ \text{Tax Amount} = \$100 \times 0.0625 \][/tex]

[tex]\[ \text{Tax Amount} = \$6.25 \][/tex]

So, if Devin buys clothes worth $100 in Illinois, he would pay $6.25 as sales tax, which corresponds to the 6.25% tax rate of Illinois.

Answer:

The answer is x = 1

Step-by-step explanation:

Let¿'s solve for x in the equation:

(x + 5)/4 = (2x + 1)/2

x + 5 = 2 * (2x + 1)

x + 5 = 4x + 2

-3x = 2 - 5

-3x = -3

x = 1

Proof of x = 1

1 + 5/4 = 2 + 1/2

6/4 = 3/2

3/2 = 3/2 (Dividing by 2 at the left side)

We proved that x = 1 is correct

Answer:

The order of the sides of the triangle from shortest to longest:

BC , AC and AB

Step-by-step explanation:

ΔABC, m∠A = 41° and m∠B = 62°

So, m∠C = 180° - ( m∠A + m∠B)

              = 180° - ( 41° + 62°)

              = 180° - 103° = 77°

Arranging the angles from the smallest to the greatest

∠A , ∠B and ∠C

We should know that

The shortest side is opposite to the smallest angle and vice verse.

So, the sides of the triangle in order of shortest to longest is as following:

BC , AC and AB

Answer:

The Law of Cosines (also called the Cosine Rule) says: c2 = a2 + b2 . We know angle C = 37º, and sides a = 8 and b = 11. The Law of .Answer: c = 6.67

explanation:

hope this helped

Step-by-step explanation:

Given Will ran the diagonal distance across a square field measuring 40 yards each sides .

∴The distance covered by Will was =[tex]\sqrt{40^{2}+40^2 }[/tex] yards

                                                         = [tex]40\sqrt{2}[/tex] yards=56.56 yards

Again James ran diagonal distance across a rectangle field with a length of 25 yards and a width of 35 yards.

So,distance covered by James was =[tex]\sqrt{25^2+35^2}[/tex] yards

                                                             =[tex]5\sqrt{74}[/tex] yards = 43.01 yards

∴Will ran longer distance.

∴Will ran 13.55 yards more than James.

To calculate the longer distance Will ran compared to James, find the diagonal distances each ran. Will ran approximately 13.56 yards longer.

To determine how much longer Will ran compared to James, we need to calculate the diagonal distances for each run.

Will ran 56.57 - 43.01 ≈ 13.56 yards longer than James. Thus, Will ran around 13.56 yards longer than James, as determined by subtracting the diagonal of the rectangular field from that of the square field. This calculation offers a quantitative measure of the difference in running distances, providing insight into their comparative performances.

Answer:370

Step-by-step explanation:

You have to multiply .26 by 500 because it says of. Of means to multiply. You get 130 and subtract that from 500

Answer:

Step-by-step explanation:

[tex]-2\sqrt{-24}=-2\sqrt{24i}=-2\sqrt{2*2*2*3*i}\\\\=-2*2\sqrt{2*3*i}=-4\sqrt{6i}[/tex]

Answer:

0.9

Step-by-step explanation:

i) 1 nickel is equal to 5 cents

ii) 36 nickels will equal to = 36 × 5 = 180 cents

iii) 1 dime is equal to 10 cents

iv) 20 dimes will equal to = 20 × 10 = 200 cents

v) the ratio of 36 nickels to 20 dimes will equal to

  =  36 nickels ÷ 20 dimes

 = 180 cents ÷ 200 cents

 = [tex]\frac{9}{10}[/tex]

 = 0.9

To express the comparison of 36 nickels to 20 dimes as a ratio in lowest terms, calculate the value of nickels and dimes in pennies, then simplify the ratio. By converting to pennies and reducing, the ratio of 36 nickels to 20 dimes is 9:10.

The question asks to write the comparison of 36 nickels to 20 dimes as a ratio reduced to lowest terms. To compare the value of nickels and dimes, we must know their value in pennies, the smallest unit of US currency. Since 1 nickel is worth 5 pennies and 1 dime is worth 10 pennies, we can express 36 nickels and 20 dimes in terms of pennies.

36 nickels = 36 x 5 pennies = 180 pennies

20 dimes = 20 x 10 pennies = 200 pennies

Now, we write the comparison as a ratio:

180 pennies : 200 pennies

Next, we reduce this ratio to lowest terms by dividing both numbers by their greatest common divisor, which is 20 in this case:

180 ÷ 20 : 200 ÷ 20

9 : 10

Therefore, the ratio of 36 nickels to 20 dimes reduced to lowest terms is 9:10.

Answer:

1. We can see that salesperson's weekly income is the sum of her constant weekly salary ($760) and a commission which is variable and depends on her weekly sales.

So, if we say that y is her weekly income and x is her weekly sales, we can write this as:

y = 760 + 0.075x

Note that we had to change percentage to decimal number dividing it by 100.

2  Since for each value of x there is only one corresponding value of y, we can say that this is a function. For any value of x we input there is only one solution we get - that is the main feature of function and a way to tell if something is really a function.

Since this is a function, it can also be written as:

f(x) = 760 + 0.075x

3. Domain of a function is, basically, set of all values of x for which the function can work. That practically means that, since x is weekly sale, it can not be negative (one cannot make -$500 sale, for example). However, it is possible that she doesn't make a sale one week, making it possible for x to be 0. Also, the value of her sales doesn't have to be integer (it is quite possible that she makes $673.50 sale).

All this means that appropriate domain for this function are positive real numbers including 0.

Answer:

the first one is 5. 5 and second is 5

Step-by-step explanation:

sorry i couldnt do the others

Answer:

Step-by-step explanation:

6) In rectangle, diagonals are equal.

KM = LN

6x + 16 = 49

6x = 49 - 16

6x = 33

x = 33/6

x = 5.5

7) 2x + 4 =  5x - 11

2x - 5x = -11 -4

-3x = -15

x = -15/-3

x = 5

In  rhombus,diagonals make two congruent triangles

So, ∠ACD = ∠ACB

8) In Rectangle, diagonals are equal and bisect each other

x + 10 = 3x - 18

x - 3x =  -18 -10

-2x = -28

x = -28/-2

x = 14

9) a + 36 = 180   { sum of co interior angles is 180}

a = 180 - 36 = 144

a = 144

113 + b = 180    { sum of co interior angles is 180}

b = 180 - 113

b = 67

10)  4th figure

Answer:

2x+4

Step-by-step explanation:

Distribute:

=(2)(x)+(2)(−6)+(2)(8)

=2x+−12+16

Combine Like Terms:

=2x+−12+16

=(2x)+(−12+16)

=2x+4

Final answer:

The simplified expression of 2(x-6)+2(8) is 2x + 4 after distributing the 2 and combining like terms.

Explanation:

To simplify the expression 2(x-6)+2(8), you need to distribute the 2 into the parentheses and then combine like terms. Distributing the 2 into the first set of parentheses gives us 2x - 12.

For the second set, multiplying 2 by 8 gives us 16. So the expression becomes 2x - 12 + 16. Adding together the numerical terms (-12 + 16) gives us 2x + 4. Therefore, the simplified expression is 2x + 4.

Answer:

No, the books had more sales by 5/6 being bigger (Greater Than) than 3/4.

By converting both fractions to have a common denominator of 12, it becomes clear that there were more books than toys for sale, as 10/12 (books) is greater than 9/12 (toys).

To determine whether there were more toys or books for sale, we need to compare the fractions ⅓ (representing toys) and ⅗ (representing books). To compare these fractions, they must have a common denominator. The least common denominator for 4 and 6 is 12. Converting both fractions to have the denominator of 12, you would get:

When comparing 9/12 (toys) to 10/12 (books), it is clear that there were more books than toys for sale since 10/12 is greater than 9/12.

Answer:

Therefore we can say that 98 boxes will be needed to hold all the paperweights.

Step-by-step explanation:

i) there are 1657 souvenir paperweights that need to be packed in boxes.

ii) each box will hold 17 paperweights

iii) therefore the number of boxes that will be needed are

   = [tex]\dfrac{total\hspace{0.15cm} number\hspace{0.15cm} souvenir\hspace{0.15cm} paperweights}{number\hspace{0.15cm} of\hspace{0.15cm} paperweights\hspace{0.15cm} per\hspace{0.15cm} box}[/tex]  = [tex]\dfrac{1657}{17}[/tex] = 97.471

iv) Therefore we can say that 98 boxes will be needed to hold all the paperweights.

Answer:

34 is the answer

Step-by-step explanation:

Answer:

the answer is 70/2+(5-6) i think. Sorry if it is wrong

Step-by-step explanation:

The solution is x = 1 and x = -3

Solution:

Given that we have to solve the given equation by factoring

Given equation is:

[tex]x^2=2x + 3\\\\x^2 - 2x - 3 = 0[/tex]

[tex]\text{Consider the form } x^2+bx+c[/tex]

Find a pair of integers whose product is c and and whose sum is b

[tex]\text{Compare } x^2-2x-3 = 0 \text{ with } x^2+bx +c\\\\\text{We get } b = -2 \text{ and } c = -3[/tex]

Now find, a pair of integers whose sum is -2 and product is -3

The integers that satisfies this condition is -1 and 3

When we add - 1 and 3 we get 2

When multiply -1 and 3 we get -3

Thus the pair of integers are -1 and 3

Write the factored form using these integers.

[tex](x-1)(x+3) = 0[/tex]

The Zero Product Property states that if ab = 0, then either a = 0 or b = 0, or both a and b are 0

Set the factors equal to 0

[tex]x - 1 = 0 \text{ and } x + 3 = 0[/tex]

x = 1 and x = -3

Thus the solution is x = 1 and x = -3

Answer:

Answer: 8

Step-by-step explanation:

Good morning ☕️

Answer:

Step-by-step explanation:

Thé amount of data that is available at the beginning of the cycle

= 8 × 1.5 + 6 = 12 + 6 = 18

:)

420 gallons of 90% antifreeze must be mixed with 60 gallons of 10% antifreeze to get mixture that is 80% antifreeze

Solution:

Let "x" be the gallons of 90% antifreeze

The, final mixture would contain (x + 60) gallons

Then by given question, we can say,

"x" be the gallons of 90% antifreeze must be mixed with 60 gallons of 10% antifreeze to get 80 % of (x + 60) gallons

Thus we frame a equation as:

[tex]x \times 90 \% + 60 \times 10 \% = (x + 60) \times 80 \%[/tex]

Solve the above equation for "x"

[tex]x \times \frac{90}{100} + 60 \times \frac{10}{100} = (x + 60) \times \frac{80}{100}\\\\0.9x + 6 = (x+60) \times 0.8\\\\0.9x + 6 = 0.8x + 48\\\\\text{Combine the like terms }\\\\0.9x - 0.8x = 48 - 6\\\\0.1x = 42\\\\x = \frac{42}{0.1} = 420[/tex]

Thus, 420 gallons of 90% antifreeze is used

Answer:

(1/5)(10/3) = 10/15 = 2/3 mile

The friend lives [tex]$\frac{2}{5}$[/tex] of a mile away.

To solve this problem, we need to calculate the total distance based on the speed at which the bike is ridden and the time it takes to reach the friend's house.

First, we determine the speed at which the bike is ridden, which is given as [tex]$\frac{1}{5}$[/tex] of a mile per minute.

Next, we calculate the time it takes to reach the friend's house, which is [tex]$3\frac{1}{3}$[/tex] minutes. To work with this mixed number easily, we convert it to an improper fraction. [tex]$3\frac{1}{3}$[/tex] minutes is the same as [tex]$\frac{10}{3}$[/tex] minutes because [tex]$3\frac{1}{3} = 3 + \frac{1}{3} = \frac{9}{3} + \frac{1}{3} = \frac{10}{3}$[/tex].

Now, we can find the total distance by multiplying the speed by the time:

[tex]\[ \text{Distance} = \text{Speed} \times \text{Time} \][/tex]

[tex]\[ \text{Distance} = \frac{1}{5} \text{ mile/minute} \times \frac{10}{3} \text{ minutes} \][/tex]

When we multiply these two fractions, we multiply the numerators together and the denominators together:

[tex]\[ \text{Distance} = \frac{1}{5} \times \frac{10}{3} \][/tex]

[tex]\[ \text{Distance} = \frac{1 \times 10}{5 \times 3} \][/tex]

[tex]\[ \text{Distance} = \frac{10}{15} \][/tex]

We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 5:

[tex]\[ \text{Distance} = \frac{10 \div 5}{15 \div 5} \][/tex]

[tex]\[ \text{Distance} = \frac{2}{3} \][/tex]

Therefore, the friend lives [tex]$\frac{2}{5}$[/tex] of a mile away.

Answer:

dude what? provide the image or something at least

This equation means what would f(x) be if x was -2. F(x) is another way to write y. So this equation can be rewritten as y = 2(-2) - 3.

y = -4 - 3

y = -7

Answer:

2(-2)-3 =-4-3 =-7

Step-by-step explanation:

Answer:

Option A

[tex]m\angle LQR=126^o[/tex]

Step-by-step explanation:

step 1

Find the value of b

we know that

[tex]m\angle MQR=m\angle LQX[/tex] ----> by vertical angles

substitute the given values

[tex](-3b+63)^o=(90-12b)^o[/tex]

solve for b

[tex]12b-3b=90-63\\9b=27\\b=3[/tex]

step 2

Find the measure of angle LQR

we know that

[tex]m\angle LQR+m\angle MQR=180^o[/tex] ---> by supplementary angles (form a linear pair)

[tex]m\angle MQR=(-3b+63)^o[/tex]

substitute the value of b

[tex]m\angle MQR=(-3(3)+63)=54^o[/tex]

substitute in the expression above

[tex]m\angle LQR+54^o=180^o[/tex]

[tex]m\angle LQR=180^o-54^o=126^o[/tex]

The unit rate is $4.25 per day for lunch.

To find the unit rate of how much it costs to buy lunch for one day, we divide the total cost by the number of days. In this case, the total cost is $21.25 for 5 days of lunch.

Here's the calculation to find the unit rate:

Divide the total cost by the number of days: $21.25 / 5 = $4.25

Hence, the unit rate is $4.25 per day for lunch.

Answer:

If we sketch the line of best fit, we can determine that the slope is positive. 3) ... Based on the trend, predict the number of hybrid cars sold if the price of gas is $4.00 a gallon. A) ... 2 10 5 16 6 15 20 12 28 30 28 35 37 32 45 39 56 52 60 65 ... B). C). D). Explanation: Scatterplot A correctly shows Natalie's data.

Step-by-step explanation:

Answer: ≈ 8%

Step-by-step explanation:

Total number of students = total number of boys + total number of girls

Total number of students = 88 + 75

Total number of students =  163

10.2% of the boys have blue eyes , this means that 10.2% of 88 have blue eyes

[tex]\frac{10.2}{100}[/tex] x 88 = 8.976

Since we are dealing with humans , therefore , this means that 9 boys have blue eyes.

Also , 5.3% of the girls have blue eyes means that 5.3% of 75 have blue eyes. That is

[tex]\frac{5.3}{100}[/tex] x 75 = 3.975 , therefore : 4 girls have blue eyes.

In total , 13 students have blue eyes

Therefore , to calculate the % of students that have blue eyes , we have :

13/163 x 100 = 7.975460123

Therefore : ≈ 8% of the students have blue eyes