Kelsey has saved $35 towards the cost of A $390 video game in the weeks to come she plans to save in additional $10 per week use unit analysis to represent them out just saved after W weeks and identify the units for the expression

ANSWER

The line that is parallel to [tex]y=4x-6[/tex] through [tex](12,10)[/tex] is  [tex]y=2x-14[/tex].

EXPLANATION

The equation that is parallel to the line [tex]y=4x-6[/tex] has a slope that is equal to the slope of this line.

By comparing this equation to the general slope intercept form,

[tex]y=mx+c[/tex],this line has slope [tex]m=2[/tex].

Hence the line parallel to this line also has slope [tex]m=2[/tex].

Let [tex]y=mx+b[/tex] be the equation of the line parallel to the line

[tex]y=4x-6[/tex]

We can substitute [tex]m=2[/tex] to obtain;

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

If the line passes through the point [tex](12,10)[/tex],then this point must satisfy its equation.

We substitute [tex]x=12[/tex] and [tex]y=10[/tex] to obtain;

[tex]10=2(12)+b[/tex]

We this equation for [tex]b[/tex].

[tex]\Rightarrow 10=24+b[/tex]

[tex]\Rightarrow 10-24=b[/tex]

[tex]\Rightarrow -14=b[/tex]

We substitute this value of  [tex]b=-14[/tex] in to [tex]y=2x+b[/tex] to get;

[tex]y=2x+-14[/tex].

Hence the equation of the line that is parallel to [tex]y=4x-6[/tex] through [tex](12,10)[/tex] is  [tex]y=2x-14[/tex].

9)

[tex]\frac{24z^{5}y^{4}}{3z^{-2}y^{5}} = \frac{24}{3}*\frac{z^{5}}{z^{-2}}*\frac{y^{4}}{y^{5}} = \frac{8}{1} *\frac{z^{5+2}}{1}*\frac{1}{y^{5-4}} = \frac{8z^{7} }{y}[/tex]

11)

(a²b)³ = a²⁽³⁾b¹⁽³⁾ = a⁶b³

12)

The exponent tells you how many places to move the decimal. The positive/negative sign tells you which direction to move the decimal (negative is left, positive is right).

8.4 x 10⁻⁵ move the decimal 5 places to the left   =  0.000084

$60

$45 is 75% of the original price. 75/3 is 25, so divide 45/3=15. $15 is 1/4 of the original price. 15*4=60

The original price of the pair of shoes is $60.

To find the original price of a pair of shoes, we can use the given information that the sale price is $45 after a 25% discount.

Let's assume the original price of the shoes is "x" dollars.

The discount of 25% means that the sale price is equal to 75% (100% - 25%) of the original price.

Mathematically, we can express this as:

Sale price = Original price * (Discount percentage in decimal form)

$45 = x * (0.75)

To find the original price (x), we divide both sides of the equation by 0.75:

$45 / 0.75 = x

x = $60

Therefore, the original price of the pair of shoes is $60.

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Positive, 72 minus negative 9 is the same thing as 72+9, which equals 81. So the answer is positive

Hanna walks a total of 3 1/6 miles before and after school.

To find how many miles Hanna walks before and after school, we can add the distances she walks to school and to work.

Distance to school = 1 2/3 miles

Distance to work = 1 1/2 miles

To find the total distance Hanna walks before and after school, add the two distances:

Total distance = 1 2/3 + 1 1/2

To add these fractions, we need to convert them to have a common denominator, which is 6:

1 2/3 = (3/3 + 2/3) = 5/3

1 1/2 = (3/2)

Now, we can add the fractions:

Total distance = 5/3 + 3/2

To add these fractions, we need to have a common denominator, which is 6:

Total distance = (5/3) * (2/2) + (3/2) * (3/3)

Total distance = 10/6 + 9/6

Now, add the fractions:

Total distance = 19/6

We can simplify this fraction:

Total distance = 3 1/6 miles

So, Hanna walks a total of 3 1/6 miles before and after school.

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Answer:

Domain is -3

Step-by-step explanation:

Given that coordinate of a graph is (-3, -2)

We have to find out the domain.

We know that if A and B are two sets, a mapping from A to B is the subset of cartesian product AxB.

Domain is the set of values of A which have images in B.

Use the above definition.

We have A = {-3,...} and B = {-2,....}

The mapping is from -3 to -2

Hence domain is -3

$78

$65x.20=13

65+13=$78

Solution: The numerical expression is [tex]8\times (9+11.3)[/tex] and the value of this expression is 162.4.

Explanation:

The sum of 9 and 11.3 is written as [tex](9+11.3)[/tex].

The product of 8 means the expression should multiply by 8.

According to the given information the the product of 8 and the sum of 9 and 11.3 is written as [tex]8\times (9+11.3)[/tex].

To evaluate the value of the expression first we have to add 9 and 11.3 after that multiply the result by 8.

[tex]8\times (9+11.3)=8\times (20.3)\\8\times (9+11.3)=162.4[/tex]

Therefore, the numerical expression is [tex]8\times (9+11.3)[/tex] and the value of this expression is 162.4.

Answer:

162.4

Step-by-step explanation:

To write the numerical expression for the product of 8 and the sum of 9 and 11.3 we need to follow these steps:

Sum of 9 and 11.3 is given as follows:

[tex](9+11.3)[/tex]

Now the product of 8 and the sum of 9 and 11.3 is:

[tex]8(9+11.3)[/tex]

So the required expression is:

[tex]8(9+11.3)[/tex]

Solving the above expression we get:

[tex]8(9+11.3)=8(20.3)=8 \times 20.3=162.4[/tex]

C.

Combine like terms when adding f(x) and g(x) 2x^2 + x^2 and 1 + (-7) = 3x^2 - 6

Y=.25x+176.10 Y is the monthly cost and B would be the cost of the insurance every month. X is the amount of miles driven since the .25 stays constant but the amount of miles you drive in a month is different every month, Hence, needs to be a variable that can be adjusted,

A - The value of b, $176.10, represents the fixed costs like insurance and car payments, which remain constant regardless of the number of miles driven. B - It serves as the baseline monthly cost for driving the car.

(a) To model the monthly cost of driving the car (y) in terms of the number of miles driven (x), you can use the equation y = mx + b, where:

y represents the monthly cost of driving the car.

x represents the number of miles driven.

m represents the cost per mile for gasoline, oil, and routine maintenance, which is $0.25 in this case.

b represents the fixed costs, including insurance and car payments, which are $176.10 per month.

So, the values for m and b in this scenario are:

m = 0.25 (the cost per mile)

b = 176.10 (the fixed monthly costs)

Therefore, the equation to model the monthly cost of driving the car is:

y = 0.25x + 176.10

(b) The value of b, which is 176.10 in this equation, represents the fixed costs associated with driving the car. In this case, it includes the monthly insurance and car payment expenses. These are costs that do not depend on how many miles you drive.

Instead, they remain constant every month. So, b represents the baseline or starting point for the monthly cost of driving the car. Even if you were to drive zero miles in a month, you would still have to pay these fixed costs.

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Answer:

y=-0.7

Step-by-step explanation:

−(7y+0.6)=3.6−y

-7y+-0.6=3.6−y

-6y+-0.6=3.6

-6y=4.2

y=-0.7

To solve the linear system by graphing, convert the equations to slope-intercept form, plot the lines, and find the point of intersection.

To solve the given linear system by graphing, we need to graph both equations on the same coordinate plane and find the point of intersection.

Step 1: Convert both equations into slope-intercept form, y = mx + b.

Step 2: Plot the y-intercepts (b values) of both equations and use the slopes (m values) to draw the lines.

Step 3: The point where the lines intersect is the solution to the system of equations. In this case, the solution is x = 6 and y = 0.

[tex]3x^2+4y^2\\\\\text{Put the values of x=2, y=1 and z=-3 to the expression:}\\\\3(2^2)+4(1^2)=3(4)+4(1)=12+4=16[/tex]

Substituting the provided values of x and y into the equation 3x^2 +4y^2 gives a final result of 16.

The question is asking for the value of the mathematical expression 3x^2 +4y^2 when x is 2 and y is 1. To find this, we substitute the values of x and y into the expression.

Therefore, the value of 3x^2 +4y^2 when x=2 and y=1 is 16.

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First we know that,

3x+15=5x-65 because of vertical angle thr.

y=y because of reflex property

there are 360 degrees in a circle so..

3x+15+5x-65+2y=360

3x+15=5x-65

x=40

so each 2 of the angles are...(40*3+15)=135

Then your new equation is

135+135+2y=360

2y=90

y=45

Hope this helps :)

Answer:

c

Step-by-step explanation:

Use Pythagorean Theorem (a² + b² = c²) to find the lengths of the sides. You can also use the distance formula.

6² + 14² = d²

36 + 196 = d²

232 = d²

15.23 ≅ d

2² + 5² = d²

4 + 25 = d²

29 = d²

5.39 ≅ d

Next, use the Perimeter formula:

P = 2L + 2w

  = 2(15.23) + 2(5.39)

  = 30.46 + 10.78

  = 41.24

For #6, Use the Area formula:

A = L x w

  = 5.39 x 41.24

  = 222.28

to solve  for the dimensions (x+7)(x+2)=66,

we can first use the foiling method to simplify the left side.

x^2 + 2x + 7x + 14 = 66

x^2 + 9x + 14 = 66

now, subtract 66 from both sides.

x^2 + 9x - 52 = 0

now, split this into two parentheses.

(x + 13)(x - 4)

since the root of -13 would give you negative values, x=4. This means that the dimensions of the rectangle are 11 and 6.

The dimensions of the rectangle is 11 by 6 inches

The dimensions are given as:

x + 7 and x + 2

The area is given as:

Area = 66

The area of a rectangle is:

Area = Length * Width

So, we have:

(x + 7) * (x + 2) = 66

Express 66 as 11 * 6

(x + 7) * (x + 2) = 11 * 6

By comparison, we have:

x + 7 = 11 and x + 2 = 6

Solve for x

x = 4 and x = 4

Substitute 4 for x in x + 7 and x + 2

x + 7 = 4 + 7 = 11

x + 2 = 4 + 2 = 6

Hence, the dimensions of the rectangle is 11 by 6 inches

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The volume of any prisma no matter wich one side it have got the following formula:

V=Ab*h where Ab is the base area and h is called height.

From our data we know the volume (6k^2-13K+5) and we know the base area (2k-1). Inserting this data in the general formula we got:

6k^2-13K+5=(2k-1)*h, solving for our unknown variable the height h

h=6k^2-13K+5/2k-1

factoring numerator :

h=(3k-5)(2k-1)/2k-1 simplifying

h=3k-5

The answer is 3k-5

Remark

The Volume = B * h

V = 6k^2 - 13k + 5

B = 2k - 1

h = ??

The volume will factor into (2k - 1)(3k - 5)

You can tell that one of the factors is 2k - 1 because that is the given amount for the base. You need only find the other factor. 3k is needed to multiply 2k to 6k^2.

- 1 needs - 5 to get the answer to 5

So the other factor is 3k - 5

Solution

V/b = h

(6k^2 - 13k + 5)/(2k - 1)

(3k - 5)(2k - 1) / (2k - 1)   The (2k - 1)s Cancel out

Answer

B = 3k - 5 Second one down.

To solve the equation x²−12x=−6, Lamar should first move the constant to the other side and complete the square, leading to x = 6 ±√30. This equation, which is a type of quadratic or second-order polynomial, may have two solutions, a typical characteristic of such equations.

The equation presented is x²−12x=−6. To solve this equation by completing the square, we first move the constant term to the other side, which leads to x² - 12x = -6, or x² - 12x + 36 = -6 + 36. We added 36 on both sides because (12/2)² = 36, which is a step in completing the square for the equation. Thus, we have (x-6)² = 30. Now, solve for x: x - 6 = ±√30, so x = 6 ±√30.

This method, known as completing the square, is a typical approach to solving quadratic equations. The general quadratic equation ax²+bx+c = 0 can also be solved using the quadratic formula -b ± √(b² - 4ac) / 2a. With both methods, remember that a quadratic equation will usually have two solutions, as it is a second-order polynomial.

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7x+9

5x+2x= 7x

5+4=9

7x + 9 is the result when combining like terms.

Answer:

7x+9

Step-by-step explanation:

Add the numbers

5x + 4 + 2x + 5

5x+9+2x

Combine like terms

5x+9+2x

7x+9

Solution:

7x+9

Step 1. Take out the constants

3/9 y^2y^4

Step 2. Simplify 3/9 to 1/3

1/3 y^2y^4

Step 3. Simplify

y^2y^4/3

Step 4. Use the Product Rule

y^2 + 4/3

Step 5. Simplify 2 + 4 to 6

y^6/3

For every 7 animals, you have 5 dogs to 2 cats. So divide 98 by 7 and you get 14 groups of 7.

Multiple 14 times 5 dogs and you get 70

Multiple 14 times 2 cats and you get 28

70 + 28 = 98.

So she pays 6 lb of chicken for $39 then $39/6 = $6.30 is the price per pound.

11lb + 6lb = 17lb total of  chicken then multiply it by the price per pound

17($6.50) = $110.50

Final answer:

Stacey will pay $71.50 for 11 more pounds of chicken.

Explanation:

To figure out how much Stacey will pay for 11 more pounds of chicken, we can use the given information that she bought 6 pounds of chicken for $39.

Therefore, Stacey will pay $71.50 for 11 more pounds of chicken.