AE = EC and BF = FC. EF = 8 and DF = 10. AB = [?]

y = 5x + 4 is the equation of the line whose slope is 5 and y intercept is (0,4)

Solution:

Given that we have to write the equation of the line whose slope is 5 and y intercept is (0,4)

The equation of line in slope intercept form is given as:

y = mx + c -------- eqn 1

Where, "m" is the slope of line and "c" is the y - intercept

Given that,

Slope = m = 5

Also, y intercept is (0,4)

Therefore, c = 4

Substitute c = 4 and m = 5 in eqn 1 to get equation of line

y = 5x + 4

Thus the equation of line is found

Answer:

16 ft and 8 ft

Step-by-step explanation:

x + 1/2 x=24

2/2 x + 1/2 x= 24

3/2 x=24

3 x= 48

x=16

1/2x=16/2=8

Answer:

The cost for full day car rental will be $100.

Step-by-step explanation:

A bike shop charges x dollars to rent a bike for half a day. It charges (x + 40) dollars to rent a bike for a full day.

On that day the shop made a total of $600 from the bike rentals. If there were 5 half day and 3 full day rental, then we can write

5x + 3(x + 40) = 600

⇒ 8x = 600 - 120

⇒ 8x = 480

⇒ x = $60

Therefore, the cost for full day car rental will be $(x + 40) = $100. (Answer)

Answer:

5 3.00 for 4 is 1.50 each so add 3.00 +1.50 is 4.50

The value of k is 8

Solution:

Given that,  points (9, 9) and (10, k) fall on a line with a slope of -1

To find: value of "k"

The slope of a line with points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is given as:

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

Here given that,

slope = m = -1

[tex](x_1, y_1) = (9, 9)\\\\(x_2, y_2) = (10, k)[/tex]

Substitute the values in formula, and solve to get value of k

[tex]m = \frac{k-9}{10-9}\\\\-1 = \frac{k-9}{10-9}\\\\-1 = \frac{k-9}{1}\\\\k-9 = -1\\\\k = -1+9\\\\k = 8[/tex]

Thus the value of k is 8

Answer:

225

Step-by-step explanation:

75/100×300=225

Your answer is True!

Some other examples of an element in the set of natural numbers are 2, 3, 4, 5, etc.

Hope this helps you!

~sofia

The numbers are -3 and 2

Step-by-step explanation:

Let x be the first number and y be the second number

then according to given statements the linear equations will be:

"Four times a number minus twice another number is -16"

[tex]4x-2y = -16\ \ \ Eqn1[/tex]

"The sum of the two numbers is -1"

[tex]x+y = -1\ \ \ Eqn2[/tex]

From equation 2:

[tex]y = -x-1[/tex]

Putting y = -x-1 in equation 1

[tex]4x-2(-x-1) = -16\\4x+2x+2 = -16\\6x +2 = -16[/tex]

Subtracting 2 from both sides

[tex]6x+2-2 = -16-2\\6x = -18[/tex]

Dividing both sides by 6

[tex]\frac{6x}{6} = \frac{-18}{6}\\x = -3[/tex]

Putting x = -3 in equation 2:

[tex]x+y = -1\\-3+y = -1\\y = -1+3\\y = 2[/tex]

Hence,

The numbers are -3 and 2

Keywords: Linear equations, variables

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Answer:

48

Step-by-step explanation:

Answer:48

Step-by-step explanation:

first you should find the hourly rate so you take 34 and divide it by 4 to get 8.5 which will be the hourly rate

then you take 8.5 and multiply it by 10 to get how much she'll earn for 10 hours of working

the answer for how much will she earn in 10 hours is $85.

Answer:

Unpaid balance = $ 250.22

Finance charge = $ 3.13

New balance = $ 348.60

Step-by-step explanation:

Calculate the unpaid balance, finance charge, and new balance using the unpaid balance method.Note: interest rate is given as a monthly rate.

Previous balance = $410.22

Payments/credits = $160.00

subtract 410-160 to get unpaid balance

Unpaid balance = $ 250.22

Monthly rate = 1.25%

multiply 250 by monthly rate (decimal) .0125 to get finance charge

Finance charge = $ 3.13

New purchases = $95.25

add unpaid balance and finance charge and new purchases to get new balance

New balance = $ 348.60

Final answer:

To calculate the unpaid balance, finance charge, and new balance using the unpaid balance method, subtract the payments/credits from the previous balance, add the finance charge, add the new purchases, and calculate the new balance.

Explanation:

To calculate the unpaid balance, finance charge, and new balance using the unpaid balance method, follow these steps:

Start with the previous balance.

Subtract the payments/credits.

Add the finance charge.

Add the new purchases.

Calculate the new balance.

For example, with a previous balance of $410.22, payments/credits of $160.00, and new purchases of $95.25, the equation would be: unpaid balance = previous balance - payments/credits = $410.22 - $160.00 = $250.22. The finance charge would then be calculated by multiplying the unpaid balance by the monthly interest rate. Finally, the new balance would be the unpaid balance plus the finance charge and new purchases.

Answer:

Step-by-step explanation:

$3307.50

The fifth term of the geometric sequence is 640, so the correct option is D.

Here we have a geometric sequence, such that the terms are given by:

[tex]A_n = 40*(-2)^{(n-1)}[/tex]

To get the 5-th term, we just need to replace n by 5 on the above rule, so we can write:

[tex]A_5 = 40*(-2)^{(5-1)} = 40*(-2)^4 = 640[/tex]

Then the value of the 5-th term is 640, which means that the correct option is D.

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Hope this will help u..............

Option A and Option B are correct answers.

Step-by-step explanation:

Option a: Diego's teacher writes a test worth 100 points. There are 6 more multiple choice questions than short answer questions.

Reason:

Let x denote the multiple choice questions.

Let y denote the short answer questions.

It is given that there are 6 more multiple choice questions than short answer questions and writing it as equations,

[tex]y=x+6[/tex]

Also, given that Diego's teacher writes a test worth 100 points and writing it as equations,

[tex]x+y=100[/tex]

Option b: Lin and her younger cousin measure their heights. They notice that Lin is 6 inches taller, and their heights add up to exactly 100 inches.

Reason:

Lin is represented by the variable y.

Her younger cousin is represented by the variable x.

It is given that Lin is 6 inches taller and writing it as equation, we get,

[tex]y=x+6[/tex]

Also, given that their heights add up to exactly 100 inches and thus, writing it as equation, we get,

[tex]x+y=100[/tex]

Thus, Option a and Option b represent the same system of equations. Hence, both story can be represented by the system of equations.

The story that can be represented with the system of equations is story B.

Description of simultaneous equations

Simultaneous equations are a set of two or more equations that have to be solved together in order to determine the needed values.

If Lin is 6 inches taller than her cousin, if Lin's height is represented with y and her cousin's height is represented with x, then the equation is: y = x + 6. If the sum of their ages is 100, this can be represented with: x + y = 100.

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Answer:

-1

Step-by-step explanation:

9/3+4(6-7)

3+4(-1)

3+(-4)

3-4

-1

Answer:

-1

Step-by-step explanation:

Just did the test

Answer: 18 ft

Step-by-step explanation:

The length of one side is 18 feet.

A closed shape's perimeter is the sum of the lengths of its outside boundaries. The lengths of all the sides are added to determine the measurement.

Given:

An equilateral triangle has a perimeter of 54 feet.

Let x be the side of an equilateral triangle.

Then,

3x = 54

x = 54/3

x = 18

Therefore, 18 feet are the length of one side.

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Answer:

Clara drew the figure correctly and correctly identified the four-sided figure as a quadrilateral.

Step-by-step explanation:

To plot the vertices of the figure, Clara needs to take the first coordinate of each point and mark it on the x-axis and the second coordinate should be marked on the y-axis. Then she has to draw vertical and horizontal lines through the x-coordinate and y-coordinate. These two lines intersect at the point which has those coordinates. Following these steps, Clara drew the figure correctly.

Connecting all consecutive vertices, she got a figure with four sides - this is exactly the quadrilateral.

Hence, Clara drew the figure correctly and correctly identified the four-sided figure as a quadrilateral.

Answer:

A

Step-by-step explanation:

Answer:

one solution

Step-by-step explanation:

the numbers aren't the same, the variables don't repeat

40 kilograms alloy of 20 % copper and 60 kilograms of alloy of 70 % copper is combined to get 100 kg of 50 % copper alloy

Solution:

Th final alloy is 100 kg

Let "x" be the alloy of 20 % copper

Then, (100 - x) is the alloy of 70 % copper

Therefore,we can say,

"x" kilograms alloy of 20 % copper and (100 - x) kilograms of alloy of 70 % copper is combined to get 100 kg of 50 % copper alloy

Therefore, we frame a equation as:

[tex]x \times 20 \% + (100-x) \times 70 \% = 100 \times 50 \%\\\\x \times \frac{20}{100} + (100-x) \times \frac{70}{100} = 100 \times \frac{50}{100}\\\\0.2x + (100-x) \times 0.7 = 0.5 \times 100\\\\0.2x + 70 - 0.7x = 50\\\\-0.5x = -20\\\\x = 40[/tex]

Thus 40 kilograms of 20 % copper

Then, 100 - x = 100 - 40 = 60

60 kilograms of 70 % copper is used

Answer:

Step-by-step explanation:

y = -x + 1

2y = -2x + 2......reduce by divide everything by 2 and u get y = -x + 1

same line......infinite solutions....CONSISTENT and  DEPENDENT

Final answer:

The system of equations represented by y = -x + 1 and 2y = -2x + 2 is both consistent and dependent, as the equations are essentially the same, representing the same line with infinitely many solutions.

Explanation:

To determine whether the system of equations is consistent and independent, consistent and dependent, or inconsistent, we need to assess if they have one unique solution, infinitely many solutions, or no solutions at all. The two equations given are y = -x + 1 and 2y = -2x + 2.

Consistency: To see if the equations are consistent, they must at least have one solution. By looking at the second equation, we can simplify it by dividing every term by 2, yielding y = -x + 1, which is identical to the first equation. This implies that both equations actually represent the same line.

Dependence: Given that both equations are the same, they have an infinite number of solutions where the two lines would intersect if they were different. Since they are the same line, the system is considered dependent.

Therefore, the system of equations is both consistent and dependent, as both equations are the same, representing the same line and thus having infinitely many solutions.

Answer:

80

Step-by-step explanation:

you multiply 16 x 5 = 80

The solution is 4368 ways

The number of ways 16 colored markers in bucket can be arranged by Kelly if she chose 5 of them is 4368 ways

What are Combinations?

The number of ways of selecting r objects from n unlike objects is:

ⁿCₓ = n! / ( ( n - x )! x! )

where

n = total number of objects

x = number of choosing objects from the set

Given data ,

Let the equation be represented as A

Now , the value of A is

The number of colored markers n = 16 markers

The number of markers Kelly chooses x = 5 markers

The number of ways Kelly can choose 5 markers from 16 markers is calculated by Combinations

And , the combination is given by

¹⁶C₅ = 16! / ( 16 - 5 )! ( 5! )

On simplifying the equation , we get

¹⁶C₅ = 16! / 11! x 5!

¹⁶C₅ = ( 16 x 15 x 14 x 13 x 12 ) / ( 5 x 4 x 3 x 2 x 1 )

The value of ¹⁶C₅ = 4368 ways

Therefore , the value of A is 4368 ways

Hence , The number of ways 16 colored markers in bucket can be arranged by Kelly if she chose 5 of them is 4368 ways

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Answer:

the zeros as  x = 5 or x = -6 . SO the correct option is Option B.

Step-by-step explanation:

i) the zeros of any expression of f(x) is found by equating f(x) to zero and then solving for x.

ii) therefore to find the zeros ( or roots) of the given expression we can write f(x) = [tex]x^{2} + x - 30 = 0[/tex]

iii) therefore [tex]x^{2} + x - 30 = 0[/tex]   ⇒  [tex]x^{2} + 6x - 5x - 30 = 0[/tex]  .... from visual observation

 therefore we can write [tex]x( x + 6) -5(x + 6) = 0[/tex]    ⇒ [tex](x - 5)(x + 6) = 0[/tex]

 therefore either x - 5 = 0, or, x + 6 = 0 if the above equation is to be true.

iv) therefore solving for x we get the zeros as  x = 5 or x = -6. So the correct option is Option B.

Answer:

Therefore the zeros of

[tex]f(x)=x^{2}+x-30[/tex]

are

[tex]x=-6\ and\ x= 5[/tex]

Step-by-step explanation:

Given:

[tex]f(x)=x^{2}+x-30[/tex]

To Find:

Zeros of the  function.

Solution:

Zeros of Polynomial or function:

Zeros of the polynomial means while substituting the value of X in the polynomial you will get the value of the polynomial or function equals to Zero.

Hence to find a value of zeros , the value of function should be zero.

Therefore,

f(x) =0

[tex]x^{2}+x-30=0[/tex]

To find the value of 'x' we need to factorize the above quadratic equation.

First is to remove the factor of -30 such that  when you add the factors you should get one.

-30 = 6 × -5

6 - 5 = 1

Hence by splitting the middle term we get

[tex]x^{2}+6x-5x-30=0\\x(x+6)-5(x+6)=0\\(x+6)(x-5)=0\\x+6=0\ or\ x-5=0\\x=-6\ or\ x=5[/tex]

Therefore the zeros of

[tex]f(x)=x^{2}+x-30[/tex]

are

[tex]x=-6\ and\ x= 5[/tex]

Answer:

The sum of the two equations is 8x + 5 and the value of x is -5/8

Step-by-step explanation:

Let's add these two equations and solve for x:

2x + 6 + 6x - 1 = 0

8x + 5 = 0

8x = -5

x = -5/8

The sum of the two equations is 8x + 5 and x =  -5/8

Answer:

Sum = 8x + 5

Step-by-step explanation:

It is required to add the following equations

2x+6    &   6x-1

So, the sum of the equations

= (2x + 6) + ( 6x - 1 ) ⇒ Combine like terms.

= ( 2x + 6x ) + ( 6 - 1 )

= 8x + 5

So, the result of adding the equations 2x+6 and 6x-1 is 8x + 5

Answer:

river c is 2850 and river d is2650

Step-by-step explanation:

Answer:

Step-by-step explanation:

I would look at it by taking the 100 off of the 5500. Leaving you with 5400 you would then Divide that by two since there is two rivers being described. So River d is 2700 miles long and then river c is 2800. Hope it helps :)