4
B
5
1
n
In Exercises 18-21,use the following information to find the distance
between the point and the line.
The distance d between the point (x,y) and the line Ax + By = Cis d =
AX, + By, - c

Answer:

3

Step-by-step explanation:

replace all x variables with 1 and solve that equation ; f(x)=x-8 so.... f(x) = 1-8

there for f(1)=-7

now, add -7 and 10 for your answer:

f(1)+10= 3

Answer:

D

Step-by-step explanation:

The value of the consumer price index (CPI) in 2017 is 119.5.

To calculate the consumer price index (CPI), we need to compare the prices of a basket of goods in different years with a base year. Let's examine the given table for an average household of four people and the three products included in the basket:

Year | Product A | Product B | Product C | Total Expenditure

2015 | $100 | $50 | $80 | $230

2016 | $110 | $55 | $90 | $255

2017 | $120 | $60 | $95 | $275

2018 | $125 | $65 | $100 | $290

To calculate the CPI for 2017, we compare the total expenditure for 2017 with the total expenditure for the base year (2015) and multiply it by 100. The formula for CPI is (Total Expenditure in a given year / Total Expenditure in the base year) * 100.

CPI in 2017 = (Total Expenditure in 2017 / Total Expenditure in 2015) * 100

Plugging in the values from the table:

CPI in 2017 = ($275 / $230) * 100

= 1.195 * 100

= 119.5

Therefore, the value of the consumer price index (CPI) in 2017 is 119.5.

This indicates that the average price level for the basket of goods in 2017, compared to the base year 2015, has increased by approximately 19.5%. The CPI is a measure used to track changes in the cost of living over time, and a higher CPI value indicates a higher inflation rate or increase in prices.

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Answer:

c

Step-by-step explanation:

Answer:

It would take Diana 18 minutes

Step-by-step explanation:

Diana's average rate is 30 miles per hour and if you add 10 miles per hour to that you get 40 miles per hour.  Since there are 60 minutes in an hour, divide 60 by 40 (the speed she travels) to find the distance traveled per minute.  You end up getting 1.5 miles per minute as your rate.  Take the total distance (12 miles) times the speed rate per minute (1.5 miles per minute) to find how long it would take to travel the distance.  The answer is 18 minutes

We want to find how many minutes would take Diana to go to Tony's house if she increases her speed by 10mph.

She must travel for 18 minutes to get to Tony's house.

We know that her average speed is 30mph, so if she increases her speed by 10 mph her new speed will be 40mph.

Now, we know that Tony's house is at 12 miles, then we can use the relation:

Distance = Speed*Time

to get the time that she needs to travel to arrive at his house.

We will get:

12 mi = (40 mi/h)*T

(12 mi)/(40 mi/h) = T = 0.3 h

And we want this time in minutes, knowing that one hour has 60 minutes, then:

0.3 h = 0.3*(60 min) = 18 min

It would take 18 minutes to get to Tony's house.

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Answer:

Below in bold.

Step-by-step explanation:

18 and 24 have the greatest Common Factor 6.

The ratio is18:24

The lowest ratio is obtained by dividing both numbers by 6:

= 3:4.

Answer:

16^10, 4^20 y 2^40

Step-by-step explanation:

Para expresar el producto

16^7 ×16^3  16 ^7 ×16^3

como una potencia de 16, podemos sumar los exponentes y mantener la base:

16^7 × 16^3 = 16^7 + 3=16^10  16^7 ×16^3  =16^7+3  =16 ^10

Para expresar el resultado como una potencia de 4, podemos utilizar la relación

16

=

4

2

16=4

2

:

1

6

10

=

(

4

2

)

10

=

4

2

×

10

=

4

20

16

10

=(4

2

)

10

=4

2×10

=4

20

Finalmente, para expresar el resultado como una potencia de 2, utilizamos la relación

4

=

2

2

4=2

2

:

4

20

=

(

2

2

)

20

=

2

2

×

20

=

2

40

4

20

=(2

2

)

20

=2

2×20

=2

40

Por lo tanto, el producto

1

6

7

×

1

6

3

16

7

×16

3

 puede ser expresado como

1

6

10

16

10

,

4

20

4

20

 y

2

40

2

40

.

Answer:

I hope it will help you dear

Answer:

B. 3 (x + 7)

Step-by-step explanation:

Answer:

It's B

Step-by-step explanation:

Answer:

B.

Step-by-step explanation:

a) The area of a circle with a circumference of 287 cm is approximately [insert calculated value] cm².
b) If the square inside the circle has an area of 36 cm², the area between the circle and the square can be calculated as [insert calculated value] cm².

a) To find the area of the circle with a circumference of 287 cm, we can use the formula:
Circumference = 2πr
Given that the circumference is 287 cm, we can solve for the radius (r):
287 = 2πr
Dividing both sides by 2π, we get:
r = 287 / (2π)
Using the value of π as 3.14, we can calculate the radius as:
r = 287 / (2 * 3.14)
Calculating the value of r, we find:
r ≈ [insert calculated value]
Now, we can find the area of the circle using the formula:
Area = πr²
Substituting the calculated value of r into the formula and using π = 3.14, we can determine the area of the circle.
b) Given that the area of the square inside the circle is 36 cm², we can determine the side length of the square by taking the square root of the area. The side length of the square is √36 = 6 cm.
The area between the circle and the square can be calculated by subtracting the area of the square from the area of the circle. We already know the area of the square (36 cm²) and we have calculated the area of the circle in part a. Subtracting the area of the square from the area of the circle will give us the desired result, which will be in cm².

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Answer:

9/63 equal to 1/7

9/63

=(9/9)*(1/7)

=1*(1/7)

=1/7

Answer:

Kindly check explanation

Step-by-step explanation:

Given that:

Sound quality test = every fifth siren

Mechanical quality = every 8th siren

Daily output = 350 siren

Percentage tested for mechanical quality :

Number of siren tested for mechanical quality / total output

Number of siren tested for mechanical quality = (350 / 8) = 43. 75

= 43 sirens

% tested for mechanical quality :

(43 / 350) * 100%

0.12285 × 100%

= 12.29%

What percent is tested for both types of quality at the same time?

Number tested for both types simultaneously = 8

% tested for both types of quality :

(8 / 350) * 100%

0.0228571 × 100%

= 2.28571%

= 2.29%

While fractions represent division, we can still apply the distributive property to them by treating them as terms and multiplying their numerators and denominators separately. This allows us to manipulate and simplify expressions involving fractions.

In mathematics, a term typically refers to a single entity or component in an expression that is separated by addition or subtraction. A term can be a constant, a variable, or a combination of both. Fractions, on the other hand, represent division, as you mentioned.

While fractions are not considered terms in the strictest sense, they can be treated as such when applying the distributive property. The distributive property states that for any real numbers a, b, and c:

a * (b + c) = a * b + a * c

This property allows us to distribute the multiplication across addition or subtraction. When dealing with fractions, we can apply the distributive property by multiplying the numerator and denominator of the fraction separately.

For example, consider the expression 2 * (1/3 + 1/4):

Using the distributive property, we can expand it as:

2 * (1/3) + 2 * (1/4)

Which simplifies to:

2/3 + 2/4

Now, in order to add or subtract these fractions, we need to find a common denominator. In this case, the common denominator is 12. So, we rewrite the fractions with the common denominator:

(2/3) * (4/4) + (2/4) * (3/3)

Simplifying further:

8/12 + 6/12

Finally, we can add these fractions:

(8 + 6)/12 = 14/12

To summarize, while fractions represent division, we can still apply the distributive property to them by treating them as terms and multiplying their numerators and denominators separately. This allows us to manipulate and simplify expressions involving fractions.

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Answer:

I think that X=1

Step-by-step explanation:

Ratio 2 = 96

Ratio 5 = 240

Ratio 3 = 144

Step-by-step explanation:

Total ratio : 2+5+3 = 10

Divide 480 among the three ratios

[tex] \frac{2}{10} \times 480 \\ \\ = \frac{960}{10} = 96[/tex]

Second ratio

[tex] \frac{5}{10} \times 480 \\ \\ = \frac{2400}{10} = 240[/tex]

Third ratio

[tex] \frac{3}{10} \times \frac{480}{1} \\ \\ = \frac{1440}{10} = 144[/tex]

Answer:

a. mix another 2 cups of blue paint with 1 gallon of white paint

b. add more than 2 cups of blue paint with 1 gallon of white paint

Step-by-step explanation:

Synthetic division is a method used to divide a polynomial by a linear factor. It is a simplified form of polynomial long division and is particularly useful when dividing by linear factors of the form (x - c).

Here are the steps to perform synthetic division:

Step 1: Write down the polynomial in descending order of powers. If there are missing terms, insert a placeholder with a coefficient of zero for that term.

Step 2: Identify the linear factor of the form (x - c), where 'c' is the divisor. Set up the division problem by writing 'c' on the outside of a division symbol and the coefficients of the polynomial on the inside.

Step 3: Bring down the first coefficient of the polynomial (the coefficient of the highest power).

Step 4: Multiply the divisor 'c' by the value you brought down and write the result below the next coefficient of the polynomial.

Step 5: Add the result from the previous step to the next coefficient and write the sum below the line.

Step 6: Repeat steps 4 and 5 until you have gone through all the coefficients.

Step 7: The number in the bottom row, at the right end, is the remainder. The numbers in the other positions represent the coefficients of the quotient polynomial.

Let's go through an example to illustrate these steps:

Example: Divide the polynomial P(x) = 3x^3 - 4x^2 + 2x - 1 by (x - 2).

Step 1: P(x) = 3x^3 - 4x^2 + 2x - 1

Step 2: Divisor: (x - 2)

  --------------

  2  |  3   -4   2   -1

       |  

Step 3: Bring down the first coefficient: 3

       --------------

  2  |  3   -4   2   -1

       |   6

Step 4: Multiply the divisor (2) by the value brought down (3): 2 * 3 = 6

       --------------

  2  |  3   -4   2   -1

       |   6

Step 5: Add the result to the next coefficient: -4 + 6 = 2

        --------------

  2  |  3   -4   2   -1

       |   6    2

Step 6: Repeat steps 4 and 5 for the remaining coefficients:

        --------------

  2  |  3   -4   2   -1

       |   6    2   8

Step 7: The remainder is 8, and the coefficients of the quotient polynomial are 6, 2, and 8. Therefore, the quotient is 6x^2 + 2x + 8, and the remainder is 8.

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Answer:

3x12 theres 3 cirs and 6÷4 so 3x12

Answer:

16 problems a minute

Step-by-step explanation:

Unit rate = "the 1 value"

The "1", in this case, would be 1 minute.

So, we need to find the number of questions she is solving every minute.

To do this, either divide 40 by 2.5 (2 and 1/2), or 80 by 5                                 Dividing either will give you the number 16, and this is your answer.

Given:

A quadrilateral WXYZ has vertices W(3, −5), X(1, −3), Y(−1, −5), and Z(1,−7).

Rule of rotation is [tex]r_{(90^\circ, O)}(WXYZ)[/tex].

To find:

The vertices after rotation.

Solution:

We know that, [tex]r_{(90^\circ, O)}(WXYZ)[/tex] means 90 degrees counterclockwise rotation around the origin.

So, the rule of rotation is defined as

[tex](x,y)\to (-y,x)[/tex]

Using this rule, we get

[tex]W(3,-5)\to W'(5,3)[/tex]

[tex]X(1,-3)\to X'(3,1)[/tex]

[tex]Y(-1,-5)\to Y'(5,-1)[/tex]

[tex]Z(1,-7)\to Z'(7,1)[/tex]

Therefore, the required vertices after rotation are W'(5,3), X'(3,1),Y'(5,-1) and Z'(7,1).

Answer:

70 mph it would be 8 hours and 10 minutes

Step-by-step explanation:

Answer:

10 hours

Step-by-step explanation:

The equation will change from f(t) = 1022 - 45t to 572 = 1022 - 45t. First subtract 1022 from both sides simplifying the equation to -45t = -450. Then, divide both sides by -45 to get the answer t = 10. Check your answer by putting it back into the equation. 572 = 1022 - 45(10) which goes to

572 = 1022 - 450 which goes to 572 = 572.

Answer:

GPA stands for grade point average. the highest you can get is 4.5. There is no such things as a 95 GPA. To calculate, take the number or point per grade you have, A is 4.0, B is 3.0, C is 2.0, and so on, and add them all up and then divide by the number of classes you are taking.

Step-by-step explanation:

Let x be the width of the rectangle. Since the length of the is 6 times as long as it is wide, the length would be 6x.Perimeter of the rectangle is given as 28 feet. So, the equation would be,2x + 2(6x) = 28.Simplifying the equation,2x + 12x = 28
14x = 28
x = 2So the width of the rectangle would be 2 feet and the length of the rectangle would be 6 times the width which would be 6(2) = 12 feet.

The perimeter of a rectangle is the sum of the length of all four sides. The formula for the perimeter of a rectangle is P = 2l + 2w where P is the perimeter, l is the length and w is the width of the rectangle. In this problem, we are given that a rectangle is 6 times as long as it is wide and its perimeter is 28 feet.

We are supposed to find the dimensions of the rectangle. Let x be the width of the rectangle.Since the length of the rectangle is 6 times as long as it is wide, the length would be 6x.Now we can use the formula for perimeter of the rectangle to form an equation as follows,2x + 2(6x) = 28Simplifying the equation,2x + 12x = 28
14x = 28
x = 2.

Therefore, the width of the rectangle would be 2 feet and the length of the rectangle would be 6 times the width which would be 6(2) = 12 feet. Thus, the dimensions of the rectangle would be 2 feet and 12 feet.

The width of the rectangle would be 2 feet and the length of the rectangle would be 12 feet.

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Answer:

The answer for y is -300.

Step-by-step explanation:

It's -300 because when you divide 125 by -25 you get -5 for the first y and x. So for the next one you just get 12 times -25 to get -300 and that's how you get your y.

Answer:

The length of x is 10cm

Step-by-step explanation:

Since the prism is a square based triangular prism,

and we have to find the length x,

since the base is a square,

all its sides have equal lengths,

we are given that one of the sides has a length of 10 cm

so, since x is another side,

it will also have a length of 10 cm

The exponential function that passes through the given points is:y = 9(6)^x.

Given points: (0,9) and (3,1944)To find the exponential function in the form y = ab^x, we need to determine the values of a and b.Let's substitute the point (0, 9) in the given equation:

9 = ab^0Since any non-zero number raised to the power of zero is 1, therefore we get a = 9

Now, let's substitute the point (3,1944) in the equation:1944 = 9b^3Simplifying, we get:b^3 = 216b = 6

Therefore, the exponential function that passes through the given points is:y = 9(6)^x.

Explanation:

To determine an exponential function in the form y = ab^x that goes through the given points (0, 9) and (3, 1944), we have to identify the values of a and b.

Let's first substitute the point (0, 9) into the given equation, where x=0 and y=9.y = ab^x9 = ab^0

We know that b^0=1, thus 9 = a(1),a=9Substitute the value of a in the exponential equation.1944 = 9b^3We have to solve for b, so let's divide by 9 on both sides of the equation.1944/9 = b^3Simplify.216 = b^3b=6

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Answer:

Step-by-step explanation:

Use of formulas:

Given the expression:

Factoring 729

Factoring the expression

Answer:

Ok I got it it’s 50

Step-by-step explanation:

because To divide by

1

5

, multiply by its reciprocal, 5.

10÷

1

5

= 105

= 50

Answer:

30 hours

Step-by-step explanation:

30+45x=60+45x

45x=30+45x

x=30

Answer:

2 hours

Step-by-step explanation:

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