A women went shopping and spent 2/3 of all the money she had. Then she lost 3/5 of what she had left after shopping. how much money did she have in the begining if she has $10.00 left

The correct option is (C) The slope of f(x) is greater than the slope of g(x). The y-intercept of f(x) is equal to the y-intercept of g(x).

Given that the following table represents  the linear function f(x), and the equation represents the linear function g(x) :

x                   0                     2                          4

f(x)                1                      9                         17

and g(x) = 3x + 1 .........(1)

We have to compare the y-intercepts and slopes of the linear functions f(x) and g(x) and choose the answer that best describes them.

From the graph, we note that (0, 1), (2, 9) and (4, 17) are three points on the line graph of function f(x).

We know that, the slope of any line having two points (a, b) and (c, d) on it is given by

m = d-b/c-a

So, the slope of the line of f(x) is

m = 9-1/2-0

m = 8/2

⇒ m = 4

Since the line of f(x) passes through the point (0, 1), so its equation will be

f(x) -1 = m(x-0)

⇒ f(x) -1 = 4(x-0)

⇒ f(x) -1 = 4x

⇒ f(x) = 4x+1 ........... (2)

The slope-intercept form of the equation of a line is y = mx + c, where m is the slope and c is the y-intercept of the line.

Comparing equation (2) and (1) with the slope-intercept form, we get

slope of f(x) = 4  and  y-intercept of f(x) = 1 and

slope of g(x) = 3  and  y-intercept of g(x) = 1.

Thus, the slope of f(x) is greater than the slope of g(x). The y-intercept of f(x) is equal to the y-intercept of g(x).

Option (C) is CORRECT.

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Answer:

C. 5/12

Step-by-step explanation:

Let's solve your equation step-by-step.

3/5a= 1/4

Step 1: Multiply both sides by 5/3.

(5/3)*(3/5a)=(5/3)*(1/4)

a = 5/12

Answer:

y = 2016 - 112x

Step-by-step explanation:

because he is paying 112 dollars each month for 18 months

y= 2016 -112x

for instance, he paid it for 6 months we would say

y = 2016 - 112(6)

y = 2016 - 672

y = 1334

so, y = 2016 - 112x

Answer:

780 ≥ 58.53x + 566.83

Step-by-step explanation:

He has $780 that he can spend, so the total must be less than or equal to 780.

Let x = number of biking outfits.

Costs:

Bicycle: $490.50

Reflectors: 4 × $14.98 = $59.92

Gloves $16.44

Outfits: $58.53x (The cost of x outfits is 58.53x)

The total he spends is:

490.5 + 59.92 + 16.44 + 58.53x =

= 58.53x + 566.86

This total has to be less than or equal to $780.

58.53x + 566.86 ≤ 780

This can be written as

780 ≥ 58.53x + 566.83

marshal just stoopid.. that simple

anyway marshal divided it by 100 instead of 104, the answer of it divided by 104 is 243.547509615

Answer:

Point form:

(2, 9)

Equation form:

x = 2,y = 9

Step-by-step explanation:

244140625 x^{54} value of the Algebraic functions .

What is Algebraic functions?

Evaluate the exponent

= [tex]\frac{5^{7} . 125^{3} }{25^{2} } . x^{54}[/tex]

Evaluate the exponent

= [tex]\frac{78125 . 125x^{3} }{25^{2} } . x^{54}[/tex]

Multiply the numbers

= [tex]\frac{78125 . 1953125 }{25^{2} } . x^{54}[/tex]

Evaluate the exponent

= [tex]\frac{152587890625}{25^{2} } . x^{54}[/tex]

Cancel terms that are in both the numerator and denominator

= [tex]\frac{152587890625}{625} . x^{54}[/tex]

= [tex]\frac{152587890625}{625} . x^{54}[/tex]

= 244140625 x^{54}

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The simplification of difference of the given two rational expressions [tex]\frac{x-1}{x+5}-\frac{x+3}{x^{2} +6x+5}[/tex]  is equal to [tex]\frac{x^{2}- x-4}{(x+5)(x+1)}[/tex]. Restriction on the variables is given by x≠ -5,  x≠ -1.

As given in the question,

Given expression is [tex]\frac{x-1}{x+5}-\frac{x+3}{x^{2} +6x+5}[/tex]

Simplify the given two rational expressions by factorizing them,

[tex]\frac{x-1}{x+5}-\frac{x+3}{x^{2} +6x+5}\\\\= \frac{x-1}{x+5}-\frac{x+3}{x^{2} +5x +x+5}\\\\= \frac{x-1}{x+5}-\frac{x+3}{(x+5)(x+1)}\\\\= \frac{x^{2} -1-(x+3)}{(x+5)(x+1)}\\\\= \frac{x^{2}- x-4}{(x+5)(x+1)}[/tex]

Restriction on the variables is given by  x≠ -5,  x≠ -1.

Therefore, the  simplification of difference of the given two rational expressions [tex]\frac{x-1}{x+5}-\frac{x+3}{x^{2} +6x+5}[/tex]  is equal to [tex]\frac{x^{2}- x-4}{(x+5)(x+1)}[/tex]. Restriction on the variables is given by x≠ -5,  x≠ -1.

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The simplied form of the given fraction will be -3 11/40.

There is a fraction, containing numerator(upper value) and denominator(lower value).  When the numerator is less than the denominator, the fraction is called proper fraction, otherwise it is called improper fraction. A proper fraction is also called fraction which is less than 1 an improper fraction is ≥ 1. A mixed fraction contains a sum of whole number and a proper fraction.

WE have been given an expression as;

−3/8+(−2 9/10)

Then first we will solve the mixed fraction;

−2 9/10 = -29/10

Now solve the fraction;

−3/8+-29/10

-131/40

In mixed number form:

-3 11/40

Hence, The simplied form of the given fraction will be -3 11/40.

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Answer:

Option 2 [tex]x[/tex] = 15, [tex]y[/tex] = 3

Step-by-step explanation:

Vertical angles are equivalent. Thus [tex]4x+10y[/tex] = 90. To solve for [tex]x[/tex], we set [tex]6x[/tex] = 90, since adjacent angles equal 180. This gives us 15 as x. Plugging 15 into the first equation we get that y is equal to 3.

The term is 0.04

The geometric sequence given is

0.004, __, 0.4, 4....

Now let us find the value of r which is the factor between the terms, called the common ratio.

r = [tex]\frac{0.04}{0.004}[/tex] = [tex]\frac{0.4}{0.04}[/tex]

 = 10

General form= [tex]a_{n}[/tex] =[tex]a_{1}[/tex]×[tex]r^{n-1}[/tex]

The geometric series

           [tex]a_{n}[/tex] = 0.004× [tex]10^{n-1}[/tex]

Therefore to find the second number of the sequence is

          [tex]a_{2}[/tex]  = 0.004 × [tex]10^{2-1}[/tex]

               = 0.004 × 10

               = 0.04

Therefore the missing term of a geometric sequence is 0.04.

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Answer: 2 quarts of pure antifreeze are needed.

Step-by-step explanation:

We have proved that , the ΔXWZ is congruent to ΔZYX i.e., ΔXWZ ≅ ΔZYX

It is given that XY ║ WZ and XW ║ YZ.

We have to prove that ΔXWZ is congruent to ΔZYX i.e., ΔXWZ ≅ ΔZYX.

What is the SSS rule of congruency of triangles ?

SSS axiom states that if two triangles have three pairs of congruent sides, then the triangles are congruent.

As per the question ;

XY ║ WZ and XW ║ YZ

So , using this data we can conclude that ;

XY = XW and WZ = YZ

The two triangles are ΔXWZ and ΔZYX

So ,

XY = XW (from given data)

and

WZ = YZ (from given data)

and

XZ = XZ (common)

∴ Both triangles are congruent to each other ;

i.e.,

ΔXWZ ≅ ΔZYX

by using the SSS axiom.

Thus , the ΔXWZ is congruent to ΔZYX i.e., ΔXWZ ≅ ΔZYX

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Answer:

From the Soldier's point of view, the American Civil War was not a continuous battle. Instead, it was long monotonous marches and long residency in camps punctuated by the terror and chaos of combat. When winter set in and the campaigning season came to a close, most Soldiers counted on a long, cold stay in a winter camp. The four log cabins at the center of the Army Heritage Trail represent the types of buildings which Soldiers in both the Union and the Confederate Armies spent the long dreary months of winter. The cabins are modeled after images from the USAHEC collection, including the Army of the Potomac's winter camp at Brandy Station and the Confederate camp at Centerville

Answer:

Needs alot of steps which you can try

Step-by-step explanation:

Sum of interior angles=exterior angle

Eg, left side 60°+90° = the exterior (big angle outside triangle)

All of the lines are straight so you can find angles using (angles on a straight line) so 180°- the angle known when your solving

There is also opposites angles which are equal, you can search it up

4 cups of pasta are used per cup of sauce.

Given,

Greta uses 3 cups of pasta for every 3/4 cup of sauce.

We need to find how much pasta she uses per cup of sauce.

Example:

12 apples = 2 basket ____(1)

For 5 baskets:

We need to make 2 baskets = 5 baskets.

We can divide by 2 and multiply 5 on both sides on (1).

5/2 x 12 apples = 5/2 x 2 baskets

30 apples = 5 baskets.

We have,

3 cups of pasta = 3/4 cup of sauce

We need to make 3/4 cup of sauce as 1 cup of sauce.

Multiply 4/3 on both sides.

4/3 x 3 cups of pasta = 4/3 x 3/4 cup of sauce

4 cups of pasta = 1 cup of sauce

Thus 4 cups of pasta are used per cup of sauce.

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The slope of the given problem is 14

It is a problem of linear regression Line

y = a +by

where a = ∑Y - b ∑X / N  

and b = N ∑XY - (∑X×∑Y)/ ( N∑x²- (∑X)  

      Month(X) Temperature (y)  X²              XY

               1                   42                        1                  42

               2                  56                        4                 112

               3                  70                         9                210

               4                  84                        16               336

Total        10               252                     30               700

Number of observation (n) = 4

So, b = 4(700) - (10)(252) / ( 120 - 10²)

         = 2800-2520/20

        = 280/20

         = 14

b = 14

Now a=  252 - (14)10/ 4

          =112 /4

         = 28

So, The linear regression line is

         y= 28 + 14x

Slope = 14

The slope here is positive which means increase in period or moving forward in month is increasing the average temperature of the month.

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Answer:

24

Step-by-step explanation:

3a/6 = 12

3a = 6 * 12

3a = 72

a = 72/3

a = 24

Check:

3*24/6 = 12

72/6 = 12

Answer -

1/2x + 5 = 7

1x/2 + 5 = 7

1x/2 + 5 = 7

x/2 + 5 = 7

x/2 + 5 = 7

x/2 + 2.5/2 = 7

X = 4

The solution of the given system of equations is (1, 3)

We can solve a system of equations using:

- graphical method

- elimination method

- substitution method

The given system of equations:

y = 4 - x    ....... (1)

3x + y = 6  ....... (2)

To use elimination method, add x to both sides of equation (1)

x + y = 4 ....... (3)

Substract equation (3) from equation (2)

3x + y = 6

x + y = 4   –

2x       = 2

 x       = 1

Substitute x = 1 into equation (1)

y = 4 - x

  = 4 - 1 = 3

Thus the solution is (1,3)

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From the given vertices, the area of the polygon is 28.

The rectangle is a quadrilateral.  The classification for quadrilaterals is given by the length of sides and angles. For a rectangle,  the opposite sides are equal and parallel and their interior angles are equal to 90°.

A rectangle is a geometric figure that has 4 sides called: base and height. Due to its characteristics, the rectangle presents two bases (B) and two heights (H).

The area of a rectangle is given by the multiplication between the base and the height.

First, you should plot the points, then see image 1.

From the figure, it is possible to see that the bases ( AB and CD) = 5-3=2

and heights (AC and BD) =-7-(-7)=7+7=14. Thus,

A= B*H= 2*14=28

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The amount of you swam is +15 feet and your friend swam is -6 feet.

Given that you move forward 15 feet and your friend is not a strong swimmer, so he moves back 6 feet.

The arithmetic operators means performing an addition, subtraction, multiplication, division, exponentiation, and modulus operations.

It is given that you move the forward that means you move in positive direction.

So, you move forward means you move +15 feet.

It is also given that your friend is not a strong swimmer, so he moves back that means he move in negative direction.

So, your friend moves backward means he move -6 feet.

Hence, you move forward 15 feet is +15 feet and your friend is not a strong swimmer, so he moves back 6 feet is -6 feet.

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The sum of an infinite geometric series is twice its first term then the common ratio(r) be 1/2.

An infinite geometric series is the outcome of an unlimited geometric sequence. This series wouldn't have a finish. It is possible to calculate the sum of all finite geometric series. The terms in the sequence will grow steadily larger, but adding the larger numbers together will not provide a solution if the common ratio of an infinite geometric series is greater than one.

Given: S = 2a₁

a₁ be the first term

r be the common ratio

Let the equation be S = a₁/1-r

2a₁ = a₁/1-r

substitute the values in the above equation, we get

2 = 1/1-r

2 - 2r = 1

2r = 1

The value of r = 1/2

Therefore, the common ratio(r) be 1/2.

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Answer: x = -10

Step-by-step explanation:

Answer:

(- 10, 10 )

Step-by-step explanation:

6x + 5y = - 10 ( subtract 6x from both sides )

5y = - 10 - 6x → (1)

3x + 5y = 20 → (2)

substitute 5y = - 10 - 6x into (2)

3x - 10 - 6x = 20

- 3x - 10 = 20 ( add 10 to both sides )

- 3x = 30 ( divide both sides by - 3 )

x = - 10

substitute x = - 10 into (2) and solve for y

3(- 10) + 5y = 20

- 30 + 5y = 20 ( add 30 to both sides )

5y = 50 ( divide both sides by 5 )

y = 10

solution is (- 10, 10 )

Answer: 22

Step-by-step explanation: 143 divided by 6.50 = 22, therefore our answer is 22

Answer:

Solutions below.

Step-by-step explanation:

a) To solve this question, we can use the formula.

Average Cost per Bracelet = Total Price ÷ Number of Bracelets.

Toy Barn

Average Cost = $5.40 ÷ 6 = $0.90 per bracelet

Dollar Deals

Average Cost = $10.50 ÷ 11 = $0.95 per bracelet (rounded off to 2 decimal places)

b) The better deal comes with a lower price per bracelet, in this case, Toy Barn has a better deal.

The simplified value of the expression 1/2 / ( x² - y²) - 5/2(x² - y²) is -2/x² + 2/y²  .

Like terms in an algebraic expression is defined as those terms that have same variable and that variable has the same power .

For Example : 5y,2y are like terms .

In the given question 1/2 / ( x² - y²) - 5/2(x² - y²) the first term is a complex fraction,

[tex]=\frac{\frac{1}{2} }{(x^{2}-y^{2} ) } -\frac{5}{2(x^{2} -y^{2}) }[/tex]

Simplifying the complex fraction we get ,

= 1/2(x² -y²) -5/2(x² -y²)

= 1/(2x² - 2y²) -5/(2x² -2y²)

On further simplifying

= 1/2x² -1/2y²- 5/2x²  +5/2y²

On combining the like terms of x² and y².

= 1/2x² - 5/2x² -1/2y²  +5/2y²

taking LCM of like terms as 2x² and 2y².

=(1-5)/2x²+(-1+5)/2y²

= (-4)/2x² + 4/2y²

=-2/x² + 2/y²

Therefore , the simplified value of the expression 1/2 / ( x² - y²) - 5/2(x² - y²) is -2/x² + 2/y²  .

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The coordinates of N so that MN is 1/3 of MP are:

(0,7/4)

In geometry line segment is a part of a line that is bounded by two end points, and contains every point on the that is between end points.

Given, coordinates of M(-3,-2)

and coordinates of P(9,13)

so we have,

x₁ = -3

y₁ = -2

x₂ = 9

y₂ = 13

Also we know that MN is 1/3 of MP

⇒ MN/MP = 1/3 = mn

here, m= 1 and n=3

Let the coordinates of N be (x,y)

Therefore,

(x,y)  = (nx₁+mx₂)/(m+n) , (ny₁+my₂)/m+n

⇒ (x,y) = (3(-3)+1(9)/1+3) , (3(-2)+1(13)/1+3)

⇒ (x,y) = (-9+9/4) , (-6+13/4)

⇒ (x,y) = (0,7/4)

Thus the coordinates of N so that MN is 1/3 of MP is (0,7/4)

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