You bought groceries last week. You used coupons and saved 25% on your grocery bill. You saved $8.80. How much was your bill before coupons?

Answer:

y=-5/2x-1/2

Step-by-step explanation:

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Answer:   [tex]\bold{a)\ \overline{CD}=6\qquad b)\ \overline{AD}=\dfrac{32}{3}\qquad c)\ \overline{AC}=\dfrac{50}{3}\qquad d)\ \overline{OB}=\dfrac{25}{3}}[/tex]

Step-by-step explanation:

a) First, use the Pythagorean Theorem to find CD:

8² + (CD)² = 10²     →     CD = 6

d) Next, find OB.  Notice that both OB and OC are the radius of the circle.

Using the Segment Addition postulate, we know the radius (r) = CD + DO  →  DO = r - 6

Use the Pythagorean Theorem for ΔOBD to find OB:

(DO)² + (BD)² = (OB)²

(r - 6)² + 8² = r²

r² - 12r + 36 + 64 = r²

   -12r + 100        = 0

             100        = 12r

              [tex]\dfrac{25}{3}\quad = r[/tex]              

c) Now, find AC. Notice that AC is the diameter.

Diameter = 2r

               = 2(OB)

               [tex]=2\bigg(\dfrac{25}{3}\bigg)\qquad =\dfrac{50}{3}[/tex]  

b) Lastly, find AD. Using the Segment Addition Postulate, we know that

AD + CD = AC   →   AD = AC - CD

                                      [tex]= \dfrac{50}{3}-6\qquad \rightarrow \quad \dfrac{50}{3}-\dfrac{18}{3}\qquad =\dfrac{32}{3}[/tex]

===========================================================

Explanation:

For me, it helps to graph everything on the same xy coordinate system. Start with the given graph and plot the points shown in the table. You'll get what you see in the diagram below.

The blue point C in that diagram is on the red parabola. This point is the x intercept as this is where both graphs cross the x axis. Therefore, they have a common x intercept.

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Side notes:

Answer:

maximum point: (0, 4)

x-intercepts: (2, 0), (-2, 0)

y-intercepts: (0, 4)

Answer:

150°

Step-by-step explanation:

to find the individual angle of a REGULAR dodecagon (which means that all sides are equal), you'd use the equation I(individual angle)= (n-2)×180/n

N is number of sides. The number of sides on a dodecagon is 12. So, substitute N for 12

I= (12-2)×180/12 which simplifies to 10×180/12

10×180= 1800

1800/12 = 150

so, an individual interior angle of a dodecagon is 150°

Step-by-step explanation:

-12 +7

=-5 .

Therefore, 5-19-5

= -19.

In all, -12+7 can not be 5-19 or 19

Answer:

Proved;

See Explanation

Step-by-step explanation:

Given:

Shape: Parallelogram

Sides: b and c

Required:

Show that P = 2b + 2c

Let P represents the perimeter of the parallelogram.

There are 4 sides in a parallelogram where 2 sides are opposite and parallel

Given that two of the side of the parallelogram is b and c; this implies that the next two sides are also b and c.

This means that the sides of the parallogram are b,c,b,c

The perimeter of any shape is calculated by adding the lengths of the shape;

This means that

[tex]P = b + c + b + c[/tex]

Collect like terms

[tex]P = b + b + c + c[/tex]

[tex]P = 2b + 2c[/tex] ------ Proved

Answer:

9

Step-by-step explanation:

2n+4=22

2n=18

n=9

Answer: 15 degrees

Step-by-step explanation:

180 degrees - 165 degrees = 15 degrees

The root index of 5 start root 13 cubed End root is [tex]13^\frac{3}{5}[/tex].

If 'n' is a positive integer that is greater than 1, and 'a' is a real number then "n √a = [tex]a^\frac{1}{n}[/tex]  where 'n' is root index, 'a' is base and '√' is radical".

According to the question,

5 start root 13 cubed end root can be written in root index form.

If 'n' is a positive integer that is greater than 1, and 'a' is a real number then "n √a = [tex]a^\frac{1}{n}[/tex]  where 'n' is root index, 'a' is base and '√' is radical".

= [tex]13^\frac{3}{5}[/tex].

Hence, the root index of 5 start root 13 cubed End root is [tex]13^\frac{3}{5}[/tex].

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Answer: D

Step-by-step explanation:

you're welcome

Answer:

SA =64 pi units ^2

Step-by-step explanation:

The surface area of a sphere is given by

SA = 4 pi r^2

SA = 4 * pi * 4^2

SA =64 pi

SA =200.96

Answer:

x = 1.6

Step-by-step explanation:

4x + 6x - 6 = 10

10x - 6 = 10

      +6    +6

      10x = 16

      10x/10 = 16/10

           x = 1.6

Answer:

8.25 pounds

Step-by-step explanation:

When you multiply 12 and 11 you get 132. So then you would have to divided the total amount of ounces by 16 to get the amount of pounds

Answer:

x= 9

Step-by-step explanation:

(3x + 4) and 50 are complementary angle

=> (3x + 4) + 50 = 90

-> 3x+4 = 40

-> 3x = 36

-> x= 9

Answer: C

Step-by-step explanation:

Answer:

23/34

Step-by-step explanation:

This is guessing you only have fiction books.

Answer:

The speed of the boat in calm water is 12.8 miles per hour.

Step-by-step explanation:

While going downstream the speed of the boat is "x + 2", where x is the speed in calm water, while going upstream the speed of the boat is "x - 2". He made a trip that had two legs, each with a distance of 50 miles, therefore, the sum of the times it took him to complete each leg must be equal to the total time of the trip.

[tex]speed = \frac{distance}{time}\\\\time = \frac{distance}{speed}[/tex]

For the upstream:

[tex]time_{up} = \frac{50}{x - 2}[/tex]

For the downstream:

[tex]time_{d} = \frac{50}{x + 2}[/tex]

The sum of each of these times must be equal to "8 h", therefore:

[tex]8 = time_{up} + time_{d}\\\\8 = \frac{50}{x - 2} + \frac{50}{x + 2}\\\\8 = \frac{50*(x+2) + 50*(x - 2)}{(x-2)*(x+2)}\\\\8*(x-2)*(x+2) = 50*x + 100 + 50*x - 100\\\\8*(x^2 - 4) = 100*x\\\\8*x^2 - 100*x - 32 = 0\\\\x^2 - 12.5*x - 4 = 0\\\\x_{1,2} = \frac{-(-12.5) \pm \sqrt{(-12.5)^2 - 4*(1)*(-4)}}{2}\\\\x_{1,2} = \frac{12.5 \pm \sqrt{156.25 + 16}}{2}\\\\x_{1,2} = \frac{12.5 \pm \sqrt{172.25}}{2}\\\\x_{1,2} = \frac{12.5 \pm 13.124}{2}\\\\x_1 = 12.812\\\\x_2 = -0.312[/tex]

Since the speed can't be negative in this context, the only possible answer is 12.812 mph.

Answer:

12.8

Step-by-step explanation:

Answer:

Neither, they have a solution

Step-by-step explanation:

Use a sheet of graphing paper and graph the equation using the y-intercept and slope.

Answer:

C

Step-by-step explanation:

[tex]\frac{y^{3/4} }{y^{1/2} }[/tex]   Original expression

[tex]y^{\frac{3}{4}-\frac{1}{2} }[/tex]   Division Property of Exponents

[tex]y^{\frac{3}{4}-\frac{2}{4} }[/tex]   Find a common denominator (4)

[tex]y^{\frac{1}{4} }[/tex]   Simplify

[tex]\sqrt[4]{y}[/tex]   Rewrite as a radical expression (an exponent of 1/4 is equivalent to the 4th root of the expression)

Answer:

4. [tex]11.333...[/tex]

Answer:

Answer is  (4) -11.333

Step-by-step explanation:

multiply : 2x /12-4/3= 4x /15 -1/5

bring variable on one side :

2x/12 -4x/15= 4/3 - 1/5

common denominator : -6x/60=17/15

simplify : -x/10= 17/15

x= - 170/15= -11.3333

Answer:

242 integers

Step-by-step explanation:

We have to find the number of integers between 17 and 2678 which are the multiple of 11.

Divide 17 by 11 = [tex]\frac{17}{11}=1.55[/tex]

Smallest multiple of 11 which is greater than 11 = 2nd multiple = 22

Divide the largest number 2678 by 11 = [tex]\frac{2678}{11}=243.45[/tex]

Largest multiple of 11 which is less than 2678 = 443rd multiple

                                                                            = 243 × 11

                                                                            = 2673

Therefore, number of integers between 17 and 2678 multiple of 11

= 243 - 2 + 1

= 242 integers

Answer:

f(2) = -6

Step-by-step explanation:

f(x) = 3x - 12

Let x =2

f(2) = 3*2 -12

     = 6-12

       = -6

Answer:

48

Step-by-step explanation:

Total points = 60

% = 80%

Therefore no. of points right = 80/100×60 = 48

For the box and whiskers plot for the following set of data the value of Min is 3, Q1 is 6, Med is 12, Q3 is 14.5 and Max is 17.

Box and wishkers plot is the way of representation of data which gives the graphical image of the data set to understand better. In this the data is represented with the help of quartile.

The minimum and the maximum values in the box plot is plotted at the end points.

The following set of data which i s given in the problem.

3, 4, 5, 6, 6, 7, 7, 12, 13, 14, 14, 15, 15, 16, 17

The minimum value in the given data is 3. Thus, the min is 3.

First quartile appears at 6. Thus, the value of Q1 is 6.

The middle value of the given data is 12 which appears at the center of all the values. Thus the med is 12.

Second quartile appears at 14.5. Thus, the value of  second quartile Q2 is 6.

The minimum value in the given data is 17 as shown in the image attached below. Thus, the min is 17.

Hence, for the box and whiskers plot for the following set of data the value of Min is 3, Q1 is 6, Med is 12, Q3 is 14.5 and Max is 17.

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Answer:

5x^4+14x^2+1

Step-by-step explanation:

Hope that helps

Answer:

A. x

C. x – 5

D. x + 2

Step-by-step explanation:

From the question above, we are asked to find the factors of an algebraic expression that is given as:

x³ - 3x² - 10x

We would use the step of factorisation

Step 1

x(x² - 3x- 10)

The first factor of the algebraic expression has been obtained = x

Step 2

We factorise x² - 3x - 10

x² +2x - 5x - 10

(x²+2x) - (5x - 10)

x(x + 2) -5(x + 2)

(x + 2)(x - 5)

Step 3

x³ - 3x² - 10x

x(x² - 3x- 10)

(x)(x + 2)(x - 5)

Therefore, the factors of the algebraic expression are:

(x), (x + 2), (x - 5)

Answer:

First Part is C

The second part is 0,2,4

Step-by-step explanation:

Edge said so

The graph of the solution is option (C) [tex]x\geq -3[/tex] is the correct answer.

An inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is the condition of being unequal. It is used most often to compare two numbers on the number line by their size.

For the given situation,

The expression is [tex]-3x-3\leq 6[/tex].

The graph below shows the inequality of the expression.

The solution of the expression is

[tex]-3x-3\leq 6[/tex]

⇒ [tex]-3x\leq 6+3[/tex]

⇒ [tex]-3x\leq 9[/tex]

Divide both sides by -3. Then the inequality will also get changed.

⇒ [tex]\frac{-3}{-3}x\geq \frac{9}{-3}[/tex]

⇒ [tex]x\geq -3[/tex]

Hence we can conclude that the graph of the solution is option (C) [tex]x\geq -3[/tex] is the correct answer.

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Answer: -105

Step-by-step explanation:

21 times -5 will be -105

Answer:

Step-by-step explanation: