Aidan bought 4 slices of pizza and a soda for a total of $7. If a soda costs $1, how much does a slice of pizza cost?

Answer:

x < 3 or x > 9

Step-by-step explanation:

given 6| x - 6 | + 7 > 25 ( subtract 7 from both sides )

6| x - 6 | > 18 ( divide both sides by 6 )

| x - 6 | > 3

Inequalities of the form | x | > a always have solutions of the form

x < - a OR x > a, hence

x - 6 < - 3 or x - 6 > 3 ( add 6 to both sides in both inequalities )

x < 3 or x > 9

Answer: x > 9 or x < 3

Step-by-step explanation:

Step 1: Isolate the absolute value expression.

6 | x - 6 | + 7 > 25

6 | x - 6 |  > 18      subtracted 7 from both sides

   | x - 6 |  > 3        divided both sides by 3

Step 2: Solve for x.

Note: the absolute value symbol makes the value positive, so the value inside could be positive or negative. We need to find both solutions.

If inside is negative

-(x - 6) > 3

 x - 6 < -3      divided both sides by -1 which flipped the inequality

     x < 3        added 6 to both sides

If inside is positive

+(x - 6) > 3

 x - 6 > 3      distributed +1, which didn't change the inequality

     x > 9        added 6 to both sides

Step 3: Graph the solution

←-------------o -3           9 o--------------→

Answer: a = 1, a = [tex]{\bold{-\dfrac{119}{125}}[/tex]

Step-by-step explanation:

In order to have the same root, the discriminant cannot be irrational.

(a + 3)x² - (11a + 1)x + a = 2(a - 5)

(a + 3)x² - (11a + 1)x + a = 2a - 10

(a + 3)x² - (11a + 1)x + a - 2a + 10 = 0

(a + 3)x² - (11a + 1)x  - (a - 10) = 0

a = a+3    b = -(11a+1)  c = -(a - 10)

Case 1:

b² - 4ac = 0

[-(11a + 1)]² - 4(a + 3)[-(a - 10)] = 0

121a² + 22a + 1 + 4a² - 28a - 120 = 0

125a² - 6a - 119 = 0

Use any method to solve the quadratic equation. I chose to use the factoring method.  

125a² - 6a - 119 = 0

125a² - 125a + 119a - 119 = 0

125a(a - 1) + 119(a - 1) = 0

(125a + 119)(a - 1) = 0

125a + 119 = 0          and        a - 1 = 0

              a = [tex]-\dfrac{119}{125}[/tex]    and             a = 1

Check:

(a + 3)x² - (11a + 1)x + a = 2(a - 5)

((1) + 3)x² - (11(1) + 1)x + (1) = 2((1) - 5)

  4x²      -       12x      + 1   = -8

4x² - 12x + 9 = 0

(2x + 3)² = 0

     x = [tex]-\dfrac{3}{2}[/tex]

Case 2: I am not sure how to do this one

[tex]ax^2+bx+c=0\\\\if\ \Delta=b^2-4ac>0\ then\ two\ solutions\qquad x_1=\dfrac{-b-\sqrt\Delta}{2a}\ and\ x_2=\dfrac{-b+\sqrt\Delta}{2a}\\if\ \Delta=b^2-4ac=0\ then\ one\ solution\\if\ \Delta=b^2-4ac<0\ then\ no\ real\ solution[/tex]

--------------------------------------------

[tex](a+3)x^2-(11a+1)x+a=2(a-5)\qquad\text{use distributive property}\\\\(a+3)x^2-(11a+1)x+a=2a-10\qquad\text{subtract 2 from both sides and add 10 to both sides}\\\\(a+3)x^2-(11a+1)x-a+10=0\\\\\Delta=[-(11a+1)]^2-4(a+3)(-a+10)\qquad\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\\Delta=(11a)^2+2(11a)(1)+1^2+(-4a-12)(-a+10)\\\\\Delta=121a^2+22a+1+4a^2-40a+12a-120\\\\\Delta=125a^2-6a-119[/tex]

[tex]\text{One solution if}\ \Delta=0.\\\\\Delta=0\iff125a^2-6a-119=0\\\\\Delta_a=(-6)^2-4(125)(-119)=36+59,500=59,536\\\\\sqrt{\Delta_a}=\sqrt{59,536}=244\\\\a_1=\dfrac{-(-6)-244}{2(125)}=\dfrac{-238}{250}=\dfrac{-238:2}{250:2}=-\dfrac{119}{125}\\\\a_2=\dfrac{-(-6)+244}{2(125)}=\dfrac{250}{250}=1\\\\Answer:\ \boxed{a=-\dfrac{119}{125}\ or\ a=1}[/tex]

We have two equilateral triangles and three rectangles.

The formula of an area of an equilateral triangle:

[tex]A_{\triangle}=\dfrac{a^2\sqrt3}{4}[/tex]

a - length of side

We have a = 14 ft. Substitute:

[tex]A_{\triangle}=\dfrac{14^2\sqrt3}{4}=\dfrac{196\sqrt3}{4}=49\sqrt3\ in^2[/tex]

The formula of an area of a rectangle:

[tex]A_{\boxed{\ }}=lw[/tex]

l - length

w - width

We have l = 10ft and w = 14 ft. Substitute:

[tex]A_{\boxed{\ }}=(10)(14)=140\ ft^2[/tex]

The Surface Area of the figure:

[tex]S.A.=3A_{\boxed{\ }}+2A_{\triangle}\\\\S.A.=3\cdot140+2\cdot49\sqrt3=(420+98\sqrt3)\ ft^2[/tex]

Answer:

a. 2 lb 11 oz, b. 7 T 1,992 lb 12 oz , c. 38 lb 14 oz

Step-by-step explanation:

The first thing we need to understand is the conversions.

1 T = 2,000 lb

1 lb = 16 oz

Knowing this, there are many ways to find out the answer, please see below the one I used; I converted all measure units to oz, subtracted the amounts, and finally converted the units back to their original ones.

a. 5 lb or (16 oz*5) - (2 lb or (16 oz*2) + 5 oz) = 80 oz - 37 oz = 43 oz = 2 lb 11 oz

b. (17 T or (2,000 lb*17) + 13 lb + 3 oz) - (9 T or (2,000 lb*9) + 20 lb + 9 oz) = (34,013 lb or (16 oz *34,013) + 3 oz) - (18,020 lb or (16 oz *18,020) + 9 oz) = 544,213  oz - 288,329  oz = 255,884  oz = 7 T 1992 lb 12 oz

c. (68 lb or (16 oz*68) + 13 oz) - (30 lb or (16 oz*30)+15) = 1,117 oz - 495 oz = 622 oz = 38 lb 14 oz

Answer:

A. 2 pounds 11 ounces

B. 7T 1,992 pounds 12 ounces

C. 38 pounds and 14 ounces

April sold 40 adult tickets and 35 child tickets.

To find the number of adult and child tickets sold, we can set up a system of equations based on the given information:

Let x be the number of adult tickets sold and y be the number of child tickets sold.

We can establish two equations:

To solve this system, we can use the method of substitution or elimination. Let's use the elimination method:

By multiplying equation 1 by 5, we get:

5x + 5y = 375 (equation 3)

Subtracting equation 3 from equation 2:

(8x + 5y) - (5x + 5y) = 495 - 375

Simplifying:

3x = 120

Dividing both sides by 3:

x = 40

Substituting the value of x into equation 1:

40 + y = 75

Solving for y:

y = 75 - 40

y = 35

Therefore, April sold 40 adult tickets and 35 child tickets.

The slope-intercept form:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

The formula of a slope:

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

substitute the coordinates of the points (8, 0) and (20, 12) to the formula:

[tex]m=\dfrac{12-0}{20-8}=\dfrac{12}{12}=1[/tex]

y = 1x + b = x + b

Put the coordinates of the point (8, 0) to the equation of a line:

0 = 8 + b      subtract 8 from both sides

-8 = b

Answer:

$1.10 per mile  PLEASE GIVE BRAINLIEST

Step-by-step explanation:

30 miles ÷ $33 = $1.10 per mile

Answer:

y = [tex]\frac{1}{2}[/tex] x - 2

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y-intercept )

rearrange 2x + y = - 6 into this form

subtract 2x from both sides

y = - 2x - 6 ← in slope-intercept form

with slope m = - 2

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-2}[/tex] = [tex]\frac{1}{2}[/tex]

y = [tex]\frac{1}{2}[/tex] x + c ← is the partial equation

to find c substitute (6, 1) into the partial equation

1 = 3 + c ⇒ c = 1 - 3 = - 2

y = [tex]\frac{1}{2}[/tex] x - 2 ← equation of perpendicular line

Answer:

5

Step-by-step explanation:

x + y + x + y + z = 5

The total amount of brown and white sugar that Lee needs is 4 1/2 cups of sugar

A fraction is written in the form of a numerator and a denominator where the denominator is greater than the numerator.

We have two types of fractions.

Proper fraction and improper fraction.

A proper fraction is a fraction whose numerator is less than the denominator.

An improper fraction is a fraction where the numerator is greater than the denominator.

Example:

1/2, 1/3 is a fraction.

3/6, 99/999 is a fraction.

1/4 is a fraction.

We have,

Lee needs 3/4 cup of white sugar for each batch of cookies, and she is making 2 batches, so she needs:

= 3/4 cup/batch x 2 batches

= 6/4 = 3/2 cups of white sugar

Lee needs 1 2/4 cups of brown sugar for each batch of cookies, and she is making 2 batches, so she needs:

= 1(2/4) cups/batch x 2 batches

= 3 cups of brown sugar

Therefore,

The total amount of brown and white sugar that Lee needs is:

= 3/2 cups of white sugar + 3 cups of brown sugar

= 4 1/2 cups of sugar

Thus,

The total amount of brown and white sugar that Lee needs is 4 1/2 cups of sugar

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Answer:

10 servings

Step-by-step explanation:

not very hard at all, all you have to do is do 4/(3/8) to get you 10.66, but since you need full servings, you leave out the decimal (logic) to get the answer

You can make 10 full servings of the recipe with 4 cups of raisins and have some leftover.

To determine how many full servings you can make with 4 cups of raisins when a recipe calls for 3/8 cup of raisins per serving, you can set up a division problem.

Divide the total amount of raisins, which is 4 cups, by the amount of raisins per serving, which is 3/8 cup.

You can convert 3/8 to a decimal by dividing the numerator (3) by the denominator (8).

This gives you 0.375.

Then, divide 4 by 0.375 to find the number of full servings.

The result is 10.67, which means you can make 10 full servings and have a little bit of raisins leftover.

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You have 4 cups of raisins. A recipe calls for 3/8 cup of raisins per serving. How many full servings can you make?

Answer:

five hundred seventeen billion nine hundred ninety-nine million nine hundred ninety-nine thousand nine hundred

Step-by-step explanation:

25.9 billion times 20=five hundred eighteen billion

then subtract one hundred from that to get the answer

Answer:

Step-by-step explanation:

5180000000

[tex]\text{Put c = -3 to the equation}\ F=\dfrac{9}{5}c+32.\\\\F=\dfrac{9}{5}(-3)+32=-\dfrac{27}{5}+32=-5.4+32=26.6\\\\Answer:\ \boxed{-3^oC=26.6^oF}[/tex]

Answer:

[tex](8,-12)[/tex]

Step-by-step explanation:

The two equations are:

[tex]\frac{1}{2}x+\frac{1}{3}y=0\\\frac{1}{4}x-\frac{1}{2}y=8[/tex]

We can solve the first equation for [tex]x[/tex] and then substitute into second equation to find the value of [tex]y[/tex].

[tex]\frac{1}{2}x+\frac{1}{3}y=0\\\frac{1}{2}x=-\frac{1}{3}y\\x=\frac{-\frac{1}{3}y}{\frac{1}{2}}\\x=-\frac{2}{3}y[/tex]

Now,

[tex]\frac{1}{4}x-\frac{1}{2}y=8\\\frac{1}{4}(-\frac{2}{3}y)-\frac{1}{2}y=8\\-\frac{2}{12}y-\frac{1}{2}y=8\\-\frac{2}{3}y=8\\y=\frac{8}{-\frac{2}{3}}\\y=-12[/tex]

Substituting [tex]y=-12[/tex] into the "solved for [tex]x[/tex]" version of first equation, we get the value of [tex]x[/tex]. So,

[tex]x=-\frac{2}{3}y\\x=-\frac{2}{3}(-12)\\x=8[/tex]

Hence the ordered pair is [tex](8,-12)[/tex] and this is the solution to the system of equations shown.

Answer:

(8,-12) the second option :)

Step-by-step explanation:

Chang spent $16 on fruit out of a total of $80 at the grocery store. In terms of percentages, this equals 20% of his total grocery bill spent on fruit.

The subject is about finding out what percentage of the total Chang spent on fruit at the grocery store. In order to solve this problem, we first need to know the total amount spent and how much was spent on one part, in this case, fruit.

Chang spent $16 on fruit and a total of $80 at the store. So, to find out the percentage spent on fruit, we divide the amount spent on fruit by the total amount spent, and then multiply by 100 to change the decimal to a percentage.

Here is the math: (16 ÷ 80) x 100 = 20%

So, Chang spent 20% of his total grocery bill on fruit.

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Answer:9090

it is simple you just need to multiply by 2

Answer:

9090

Step-by-step explanation:

meat to feed 22 pet dragons per day=4545

meet to feed 44 pet dragons per day=?

as number of pet dragons have doubled

so amount of feed will also be doubled

hence

meet to feed 44 pet dragons per day=4545*2=9090

Answer:

4

Step-by-step explanation:

Answer:

[tex]x=25[/tex]

Step-by-step explanation:

The given linear equation is

[tex]30=\frac{6}{5}x[/tex]

We multiply both sides by the reciprocal of [tex]\frac{6}{5}[/tex] which is [tex]\frac{5}{6}[/tex].

This will give us,

[tex]30\times \frac{5}{6} =\frac{5}{6}\times \frac{6}{5}x[/tex]

We cancel out common factors to get;

[tex]5\times \frac{5}{1} =x[/tex]

This implies that;

[tex]x=25[/tex]

Answer:

B) 21x-7  

Step-by-step explanation:

Let A = speed of Arabian horse and T = speed of thoroughbred.

Then

A = T – (4x + 2)

A = T – 4x - 2                Remove parentheses

A = 25x - 5 - 4x – 2     Combine like terms

A = 21x - 7

Answer:

5 is right 6 is right 7 is right ....

Step-by-step explanation:

actually they are all right triangles

Each of the triangle should be classified as follows;

5. Acute triangle.

6. Right triangle.

7. Obtuse triangle.

8. Obtuse triangle.

9. Obtuse triangle.

10. Acute triangle.

11. Right triangle.

12. Right triangle.

A triangle is classified as an acute triangle if the square of its longest side (c) is less than the sum of the squares of the two smaller sides (a + b).

Also, a triangle is classified as an obtuse triangle if the square of its longest side (c) is greater than the sum of the squares of the two smaller sides (a + b).

A triangle is classified as a right triangle if the square of its longest side (c) is equal to than the sum of the squares of the two smaller sides (a + b).

Part 5.

c² > a² + b²

15² > 11² + 12²

225 > 265 (False, it's an acute triangle).

Part 6.

c² > a² + b²

13² > 5² + 12²

169 > 169 (False, it's a right triangle).

Part 7.

c² > a² + b²

10² > 3² + 8²

100 > 73 (True, it's an obtuse triangle).

Part 8.

c² > a² + b²

20² > 9² + 12²

400 > 225 (True, it's an obtuse triangle).

Part 9.

c² > a² + b²

15² > 7² + 12²

225 > 193 (True, it's an obtuse triangle).

Part 10.

c² > a² + b²

10² > 8² + 7²

100 > 113 (False, it's an acute triangle).

Part 11.

c² > a² + b²

15² > 9² + 12²

225 > 225 (False, it's a right triangle).

Part 12.

c² > a² + b²

13² > 5² + 12²

169 > 169 (False, it's a right triangle).

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Answer: 9^-8

Step-by-step explanation:

To get single positive exponent,

9^-5 / 9^3

Since the exponent is same

So we can solve the coefficient like this

9^-5-3

So

9^-8

The problem 9⁻⁵ /9³ simplifies to -8 by subtracting the exponent in the denominator (3) from the exponent in the numerator (-5). To achieve a single positive exponent, take the reciprocal of the base, then the final answer becomes 1/9⁸.

The question pertains to the laws of exponents in mathematics. To be specific, you are asked to simplify the expression 9⁻⁵ /9³ into a single positive exponent. In this case, you should remember that division of the same base translates to subtraction of exponents, according to the exponent laws. Therefore, you simply subtract the exponent of the denominator (3) from the exponent of the numerator (-5).

Following the rule, -5 - 3 results in -8. So the expression simplifies to 9^-8. But, since we need a single positive exponent, we take the reciprocal of 9. Remember that changing the sign of an exponent is equivalent to taking the reciprocal of the base. Hence, the final answer = 9⁻⁸ becomes 1/9⁸.

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Answer:

Correct choice is C

Step-by-step explanation:

Consider segment AB with endpoints A(-2,1) and B(4,3).

1. Rotation counterclockwise of 90° has a rule

(x,y)→(-y,x),

then

2. x-axis reflection has a rule

(x,y)→(x,-y),

then

3. Rotation counterclockwise of 270° has a rule

(x,y)→(y,-x),

then

4. y-axis reflection has a rule

(x,y)→(-x,y),

then

Answer:

C) Rotation counter-clockwise of 90 degree → x-axis reflection → rotation counter-clockwise of 270 degree → y-axis reflection

Step-by-step explanation:

We are given the line segment AB with end points (-2,1) and (4,3).

It is provided that after applying rigid transformations the line segment AB maps onto itself.

So, according to the options,

1. Rotation counter-clockwise by 90 degree changes (x, y) into (-y, x)

i.e. (-2,1) → (-1,-2) and (4,3) → (-3,4)

2. X-axis reflection changes (x, y) into (x, -y)

i.e. (-1,-2) → (-1,2) and (-3,4) → (-3,-4)

3. Rotation counter-clockwise by 270 degree changes (x,y) into (y, -x)

i.e. (-1,2) → (2,1) and (-3,-4) → (-4,3)

4. Y-axis reflection changes (x,y) into (-x,y)

i.e. (2,1) → (-2,1) and (-4,3) → (4,3)

Hence, we see that after applying transformations to AB we are again obtaining the line AB as seen below in the figure.

So, option C is correct.  

Answer:

possible answrs addition, expanded form

Step-by-step explanation:

Answer:

E = {-5, -4, -3}

All circles are similar because they can be transformed into each other through a series of transformations without changing their core properties. These transformations include translation (shifting the position) and scaling (resizing).

All circles are similar because they maintain the same shape and can be scaled up or down without changing their properties. A sequence of transformations such as scaling (resizing) can carry one circle onto another. Here is how:

By performing these transformations, Circle A transforms into Circle B. This holds true for any two circles, thus all circles are always similar.

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Answer:

slope is undefined

Step-by-step explanation:

Answer:

Undefined

Step-by-step explanation:

The line is going straight down which means it cannot be negative or positive.

If you try to make the equation(y=mx + b), when you try to find the slope, you can't because (rise/run), there is no run. It is just a rise.

This means you cannot define the slope of the line.

[tex]24x=\boxed{2}\cdot\boxed{2}\cdot\boxed{2}\cdot3\cdot x\\\\8=\boxed{2}\cdot\boxed{2}\cdot\boxed{2}\\\\GCF(24x,\ 8)=\boxed{2}\cdot\boxed{2}\cdot\boxed{2}=8\\\\24x+8=8(3x+1)[/tex]

Answer:

o(30) = 59

Step-by-step explanation:

o(30)  means we want to let n = 30 in our function

o(n) =2n-1

o(30) = 2*30 -1

o(30) = 60 -1

o(30) = 59

Answer:

D

Step-by-step explanation:

given [tex]\frac{j^2}{2j}[/tex] × [tex]\frac{2j}{3g}[/tex]

the 2j on the denominator of the first fraction cancels with the 2j on the numerator of the second fraction, leaving the expression in simplified form as

= [tex]\frac{j^2}{3g}[/tex] → D