Miranda and Lily both bought a used car on the same day. Miranda's used car has 5,132 miles on it already, and she drives 525 miles per month. Lily's car has 4,789 miles on it already, and she drives 723 mile per month.

Answer:

g(8)=17

Step-by-step explanation:

Given :
g(a)=a²+2a-63

Substitute a = 8 :

g(8)=8^2+2(8)-63

= 64+16-63

=17

Answer:

you can ask questions for clarification

Answer:

y = 15/4 mm

x = 36/5 mm

Step-by-step explanation:

In similarity triangles, the corresponding sides are in same ratio.

          [tex]\sf \dfrac{3}{y}=\dfrac{4}{5}\\\\\bf Cross \ multiply,\\\\ y*4 = 3*5\\\\ y =\dfrac{15}{4}\\\\\boxed{y = \dfrac{15}{4}}[/tex]

                               [tex]\sf \dfrac{x}{9}=\dfrac{4}{5}\\\\x = \dfrac{4}{5}*9\\\\x = \dfrac{36}{5}\\\\\boxed{x = \dfrac{36}{5} \ mm}[/tex]

Answer:

[tex]3x + y = 3 \\ 3 = x - y \\ 3 = x[/tex]

Answer:

y = -3x - 4

Step-by-step explanation:

We are given the equation 3x + y = 3, and we want to find an equation of the line that is parallel to 3x + y = 3.

This same line also passes through the point (1, -7).

Parallel lines have the same slopes. This means that we'll first need to find the slope of 3x + y = 3.

The equation is written in standard form, which is ax+by=c, where a, b, and c are free integer coefficients, but a and b cannot be 0. a is usually non-negative as well.

There is a shortcut into finding the slope when the equation is in standard form; the slope of the line is -a/b, where a is the coefficient in front of x and b is the coefficient in front of y).

The coefficient in front of x is 3, and 1 in front of y.

Substitute 3 as a, and 1 as b in -a/b. Don't forget about the - in front of a!

-3/1 = -3

This means the slope of the line is -3.

It is also the slope of the line parallel to it.

We can write the equation of the line we are trying to solve for in standard form, too. However, we could also write it in slope-intercept form.

Slope-intercept form is given as y=mx+b, where m is the slope and b is the y intercept.

As we are already given the slope, we can immediately plug that into the formula.

Replace m with -3.

y = -3x + b

Now we need to find b.

As the equation passes through the point (1, -7), we can use its values to help solve for b.

Substitute 1 as x and -7 as y.

-7 = -3(1) + b

Multiply.

-7 = -3 + b

Add -3 to both sides

-4 = b

Substitute -4 as b into the equation

y = -3x - 4

Answer:

16x⁶+y⁶

Step-by-step explanation:

(4x^3+y^3) (4x^3+y^3)

= 16x^6+y^6

The fraction is 47/200. The decimal is 0.235.

A percentage can be written in a fraction form by putting 100 on the denominator. For example, the fraction corresponding to x % is x/100.

For converting a percentage into a decimal first it should be converted into fractions as fractions can only be converted into decimal.

For example, the decimal for the fraction 50% is 0.5, which is given by writing 50% as 50/100 = 0.5 after putting decimal on 2 places left to 50.

So here the given percentage is 23.5%.

The corresponding fraction is 23.5/100 = 235/1000 = 47/200 after eliminating the decimal on the numerator and simplifying.

Now the corresponding decimal is, 0.235. Since 1000 is in the denominator for 235/1000, we can simply find the decimal by putting decimal point on 3 places left to 235.

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Answer:

$4,000 in the 10% per year account

$11,000 in the 12% per year account

Let the age of Maisie be x

From the first statement, Ellie is six years older than Maisie implying:

From the second statement, Zoe is twice as old as Eli implying:

From the last statement, the sum of their ages is 50 implying:

Solving for x:

We open the bracket and collect like terms

Hence, Zoe's age is:

Answer:

Zoe's age = 28

Answer:

r = - 8

Step-by-step explanation:

calculate the slope m using the slope formula , then equate to 3

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 5, r ) and (x₂, y₂ ) = (2, 13 )

m = [tex]\frac{13-r}{2-(-5)}[/tex] = [tex]\frac{13-r}{2+5}[/tex] = [tex]\frac{13-r}{7}[/tex]

then equating gives

[tex]\frac{13-r}{7}[/tex] = 3 ( multiply both sides by 7 )

13 - r = 21 ( subtract 13 from both sides )

- r = 8 ( multiply both sides by - 1 )

r = - 8

John's driving at a speed of 40 miles per hour

Given that,

Dale and John leave their home traveling in different directions on a straight road. Dale drives 20 miles per hour faster than John. After 30 minutes they are 50 miles apart.

a. Define a variable for Dale's rate: x mph

Write an expression for John's rate: x-20 mph

-------

b. Write and solve an equation to find Dale rate. Then find John's rate.

They are separating at the rate of x + x-20 = 2x-20 mph.

-------

Equation:

time*speed = distance

0.5(2x-20) = 50 miles

x-10 = 50

x = 60 miles

x = 60

----

John's rate = x-20 = 40 mph

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Answer:

Here is your Answer and I'm from South Africa

The pearson's coefficient of skewness is found as the 1.065.

Pearson skewness:

The skewness of the a data set is calculated by subtracting the mean from the median and dividing by the standard deviation.

In this case:

The mean is 95, the median is 77, as well as the standard deviation is 16.9. So,

Pearson skewness = (95 - 77)/16.9

Pearson skewness = 1.065.

Thus, the pearson's coefficient of skewness is found as the 1.065.

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Answer:-2

Step-by-step explanation: Substitute the given y-value into 4x−3y=18 and solve for x

The teacher requires 1.5 gallons of paint for the whole class

Quantity of paint available with the teacher = 1 gallon

Fractions: In mathematics, a fraction is represented by a number that identifies a portion of a whole. A fraction is a component or section taken from a whole, which can be any number, a certain amount, or an object.

Portion of the class covered by 1 gallon of paint = 2/3 class

Let x represent the whole class

Formulating the equation:

The portion of the class covered out of the whole class*Total class = Paint required for the portion of the class

So, for 2/3x = 1

x = 3/2

x = 1.5 gallon

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Answer:

a -7

b 18

c -13

d -5

e 0

f -7

g 0

h -6

Step-by-step explanation:

too lazyy

If we look at the series, one third of the current term gives the numerical value of the next term.

If we need to express it algebraically, we can write the following equation.

Therefore, our common multiplier can be found as follows. Because this sequence is a geometric sequence.

In geometric sequences, any term can be written in terms of the first term. Below is an example.

Since we know the numerical values of the first term and the common factor of the series, we can easily find the seventh term.

Answer:

$189

Step-by-step explanation:

you would take 27 × 7 and multiply the two numbers, then get your answer.

Answer:

$12.25

Step-by-step explanation:

The unit rate would be[tex]\frac{21}{12}[/tex] 1.75 a can

7 x 1.75 = 12.25

After the discount the net price is $7053.75 and the trade discount is 35.875% .

The term discount designates a sum or a percentage subtracted from an item's usual selling price.

The given marked price of the article is 11000

Price after first discount of 5% = 11000 - 5% of 11000 = 10450

Price after second discount of 10% = 10450 - 10% of 10450 = 9405

Price after third discount of 25% = 9405 - 25% of 9405 = 7053.75

Therefore the net price is 7053.75.

Therefore the trade discount is = ( 11000 - 7053.75 ) ÷ 11000 = 0.35875

Trade discount percentage = 35.875%

Hence after the discount the net price is $7053.75 and the trade discount is 35.875% .

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Answer:

3.1

Step-by-step explanation:

Answer:

both angles 1 and 2 measure 135°

Step-by-step explanation:

angle 1 = angle 2 = 135°

Hope this helps

The equation that represents the line is y = -2x -3 which passes through the points (0, -3) and (1, -5).

A straight line is a combination of endless points joined on both sides of the point.

The slope 'm' of any straight line is given by:

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

From the graph:

The two points are:

(0, -3) and (1, -5)

The equation of the line:

y - (-5) = [-5 - (-3)]/[1] (x - 1)

y + 5 = -2(x - 1)

y = -2x -3

Thus, the equation that represents the line is y = -2x -3 which passes through the points (0, -3) and (1, -5).

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The value of b for the given line is 1

The set of points that make up a line in a coordinate system are represented algebraically by a line's equation. An equation of a line is an algebraic expression that represents the many points that together make up a line in the coordinate axis as a set of variables, x, and y. We may determine whether a given point lies on a line using the equation of any line.

Given that : y = 3x + b; (2, 7)

y =3x + b

7 = 6 + b

1 = b

The value of b for the given line is 1

The line's equation is a linear equation of degree one.

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The least common multiple for 12 and 15 is 60, the least common multiple for 6 and 15 is 30, and the least common multiple for 9 and 15 is 45.

In mathematics, the term "least common multiple" is used to refer to a multiple of two or more numbers share and that is the smallest number possible.

Mulitiply the numbers given by 1, 2, 3, 4, etc. until your find the first common number.

Lets use the numbers given

12 x 1 = 12        15 x 1 = 15

12 x 2 = 24       15 x 2 = 30

12 x 3 = 36       15 x 3 = 45

12 x 4 = 48       15 x 4 = 60

12 x 5 = 60

Based on this, the least common multiple is 60

6 x 1 = 6          15 x 1 = 15

6 x 2 = 12       15 x 2 = 30

6 x 3= 18

6 x 4 =24

6 x 5 =30

Based on this, the least common multiple is 30

9 x 1 = 9           15 x 1 = 15

9 x 2 = 18         15 x 2 = 30

9 x 3= 27         15 x 3 = 45

9 x 4 =36

9 x 5 =45

Based on this, the least common multiple is 45

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Answer: 21

Step-by-step explanation:

The Equation of perpendicular bisector line l is found to be [tex]y = 2x+ 11[/tex]

Given Line XY is formed by points  X(-9, -7) and Y(-3,5) therefore, it passes through these two respective points.

Let the slope of this line be n

The Slope of line passing through X and Y points is given by

n = [tex](y_{2} - y_{1} )/(x_{2} -x_{1} )[/tex]

⇒ n = {5 - (-7) }/ {(-3) - |(-9)}

⇒ n = 12/6

⇒ n = 2               (equation 1 )

Given that line l is perpendicular bisector of XY

Let the slope of l  = m

We know that the product of the slopes of any two perpendicular lines is -1

Therefore, n x m = -1

⇒ m = -1 \ n

putting the value of n from the above equation 1 we get

⇒ m = - 1/2

Additionally, because l is the perpendicular bisector hence it goes through the mid point of the line XY

Mid point of two lines = [tex](x_{2} + x_{1} )/2[/tex] and [tex](y_{2} + y_{1} )/2[/tex]

Mid point of XY = [tex]\frac{-9 + (-3)}{2}[/tex] and [tex]\frac{-7 + (5)}{2}[/tex]

                          = (-6, -1)

The equation of perpendicular bisector l is given my the following formula:

[tex]y = nx + c[/tex]

here we have n = slope of line

we have n = 2 from equation 1

∴ y = 2x + c (equation 2)

Also equation (2) is satisfied by the point (-6,-1)

Hence we can express it as:

-1 = 2(-6) + c

⇒ c = 11

Therefore the required equation of perpendicular bisector l is

[tex]y = 2x + 11[/tex]

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If a trader is given a 15 percent discount on the factory price of certain goods, the factory price being ¢45000000, then

(I) The discount amount will be ¢6750000

(II) The final amount that the trader will have to pay to buy the goods will be ¢38250000.  

As per the question statement, a trader is given 15 Percent discount on goods bought from a factory and the original price of the item bought from the factory is ¢45000000.

We are required to calculate the discount amount, and the final amount that the trader will have to pay to buy the goods.

To solve this question, we simply need to calculate 15 percent of 45000000, and then subtract the calculated discount amount from ¢45000000.

Therefore, 15 percent of ¢45000000 = ¢[(15/100) * 45000000]

                                                   = ¢(15 * 450000)

                                                   = ¢6750000

That is, on 15 percent discount on the factory price of certain goods, the factory price being ¢45000000, the discount amount is ¢6750000.

And, considering the discount of ¢6750000 on the factory price of ¢45000000, the final amount that the trader will have to pay to buy the goods = ¢(45000000 - 6750000)

           = ¢38250000.

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