After an outbreak of a mysterious disease the average wait time at a hospital increased by 70%. Before the outbreak, the average wait time at the hospital with M minutes. Which of the following expressions could represent the average time at the hospital after the outbreak? Choose two answers:

Answers

Answer 1

Answer:

[tex]\frac{170}{100}m[/tex]

[tex]1.7m[/tex]

Step-by-step explanation:

Here,

Before the outbreak, the average wait time at the hospital was m minutes,

Also, after outbreak it is increased by 70 %,

So, the average wait time at the hospital after the outbreak = The average wait time before outbreak + 70 % of the average wait time before outbreak

= m + 70 % of m

[tex]=m+\frac{70m}{100}[/tex]

[tex]=\frac{100m+70m}{100}[/tex]

[tex]=\frac{170m}{100}[/tex]

[tex]=1.7m[/tex]

Hence, the expressions could represent the average time at the hospital after the outbreak would be,

[tex]\frac{170}{100}m[/tex]

[tex]1.7m[/tex]


Related Questions

Ryan has 4 cups of grape juice and Kelsey has 7 cups of lemonade they want to combine what they have to make punch how many 1/2 cup servings of punch can they make

Answers

Answer:

5.5 servings

Step-by-step explanation:

4+7=11

11/2=5.5 sevings

Rewrite the set E by listing its elements. Make sure to use the appropriate set notation. E= { x | x is an interger and -5 ≤ x < -2

Answers

Answer:

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



So I copied this off from my teacher she was showing this on the board but I need help showing my work on this so that she doesn’t know I copied it which I think she wouldn’t but you never know

Answers

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

You work at a fruit market. Bananas cost 50¢ a pound. A customer hands you a bunch of bananas that weighs 3 pounds. How much should you charge for the bunch of bananas?

Answers

3 pounds of bananas cost $1.50

Answer:  I should charge 150¢ for the bunch of bananas.  

Step-by-step explanation:  Given that I work at a fruit market and bananas cost 50¢ a pound.

A customer hands me a bunch of bananas that weighs 3 pounds.

We are to find the price that I should charge for the bunch of bananas.

We will be using the UNITARY method to solve the given problem.

Also, we know that

100 ¢ = $1.

Cost of 1 pound of bananas =  50¢

Therefore, the cost of 3 pounds of bananas is given by

p = (50 × 3)¢ = 150¢ = $1.50.

Thus, I should charge 150¢ for the bunch of bananas.  

At 10:00 AM, Gavin rented a mountain bike. He returned the bike at 3:00 PM, having gone 30 miles. He paid $33 for the rental. Find the rental rate, in dollars per mile.
$6.60/mile
$1.10/mile
$6.00/mile
$0.92/mile

Answers

Answer:

$1.10 per mile  PLEASE GIVE BRAINLIEST

Step-by-step explanation:

30 miles ÷ $33 = $1.10 per mile


Write a polynomial function with zeros -7, -1, 4

Answers

Answer:

(x+7)(x+1)(x-4)

Step-by-step explanation:

A zero is is the x-intercept of the function. It is also known as the root. From the equation, the zero or root comes from the factors. When the factors are set equal to 0, we solve for x and the zero is the result. We will reverse this by taking the opposite value of the zero and placing into a factor expression. Remember the factor has the form x+a.

-7: x+7

-1: x+1

4: x-4

We write them together. (x+7)(x+1)(x-4). With more information we could find the leading coefficient and so forth.

Solve the following subtraction problems. Remember to borrow as necessary.
a. 5 lb. – 2lb. 5 oz.
b. 17 T. 13 lb. 3 oz. – 9 T. 20 lb. 9 oz.
c. 68 lb. 13 oz. – 30 lb. 15 oz.

Answers

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

What is the greatest common factor for both terms: 24x + 8

Answers

[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]

Find the surface area of the figure below.

Answers

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]

The quotient of 12 times an unknown number and 13 is 6 what is the unknown number?

Answers

Answer:

unknown number is 13/2

Step-by-step explanation:

Let unknown number be 'x'

given that quotient of 12 times x and 13 is 6

i.e. 12 x/13 =6

multiply 13 both sides

12x = 6 * 13

divide 12 on both sides

x= (6*13)/12

x=13/2

1/2x + 1/3y = 0
1/4x -1/2 y = 8
What is the solution of the system shown?
(-8, 12)
(8, -12)
(8, 12)

Answers

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:

find o(30) where o(n) =2n-1

Answers

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


Identify the slope of the line shown in the graph below: slope = -1
Slope = 0
Slope = undefined
Slope = 1

Answers

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.

7.3 back side help me

Answers

Answer:

11. x=4.5

12. x=16

13. x=15

14. x=15

15. x=10

EH=9

16. Corry is 6 feet tall.

17. The Ferris Wheel is 15 m tall.

18. The mural is 150 inches long.

19. A 15 foot ladder would touch the building at a height of 10 feet.

Step-by-step explanation:

11. x/7.5=6/10

Simplifying the fraction on the right side of the equation:

x/7.5=3/5

Solving for x: Multiplying both sides of the equation by 7.5:

7.5(x/7.5)=7.5(3/5)

x=1.5(3)

x=4.5

12. x/20=(27-15)/15

x/20=12/15

Simplifying the fraction on the right side of the equation:

x/20=4/5

Solving for x: Multiplying both sides of the equation by 20:

20(x/20)=20(4/5)

x=4(4)

x=16

13. x/6=(14-4)/4

x/6=10/4

Simplifying the fraction on the right side of the equation:

x/6=5/2

Solving for x: Multiplying both sides of the equation by 6:

6(x/6)=6(5/2)

x=3(5)

x=15

14. x/20=12/(12+4)

x/20=12/16

Simplifying the fraction on the right side of the equation:

x/20=3/4

Solving for x: Multiplying both sides of the equation by 20:

20(x/20)=20(3/4)

x=5(3)

x=15

15. [(x+5)+9]/(x+5)=12/6

(x+5+9)/(x+5)=2

(x+14)/(x+5)=2

Solving for x: Multiplying both sides of the equation by (x+5):

(x+5)(x+14)/(x+5)=(x+5)2

x+14=2(x+5)

Eliminating the parentheses applying the distributive property:

x+14=2(x)+2(5)

Multiplying:

x+14=2x+10

Grouping the x's on the right side of the equation: Subtracting x both sides of the equation:

x+14-x=2x+10-x

Subtracting:

14=x+10

Solving for x: Subtracting 10 both sides of the equation:

14-10=x+10-10

4=x

x=4

EG=x+5→EG=4+5→EG=9

EH/HF=EG/GD

Replacing the known values:

EH/9=9/9

EH/9=1

Solving for EH: Multiplying both sides of the equation by 9:

9(EH/9)=9(1)

EH=9

16. Corry's height / Corry's shadow = Giraffe's height / Giraffe's shadow

Replacing the given values:

Corry's height / 4 feet = 18 feet / 12 feet

Simplifying the fraction on the right side of the equation:

Corry's height / 4 feet = 3/2

Solving for Corry's height: Multiplying both sides of the equation by 4 feet:

4 feet (Corry's height / 4 feet) =4 feet (3/2)

Corry's height = 2 feet (3)

Corry's height = 6 feet

17. Ferris Wheel's height / Ferris Wheel's shadow =

Man's height / Man's shadow

Replacing the given values:

Ferris Wheel's height / 20 m = 1.8 m / 2.4 m = 18/24

Simplifying the fraction on the right side of the equation:

Ferris Wheel's height / 20 m = 3/4

Solving for Ferris Wheel's height: Multiplying both sides of the equation by 20 m:

20 m (Ferris Wheel's height / 20 m) =20 m (3/4)

Ferris Wheel's height = 5 m (3)

Ferris Wheel's height = 15 m

18. Mural's length / Mural's width =

Photographer's length / Photographer's width

Replacing the given values:

Photographer's length / 120 inches = 5 inches / 4 inches = 5/4

Solving for Photographer's length: Multiplying both sides of the equation by 120 inches:

120 inches (Photographer's length / 120 inches) = 120 inches (5/4)

Photographer's length = 30 inches (5)

Photographer's length = 150 inches

19. Height 15-foot ladder touch the building / 15 feet =

Height 9-foot ladder touch the building / 9 feet


Height 15-foot ladder touch the building / 15 feet = 6 feet / 9 feet = 6/9

Simplifying the fraction on the right side of the equation:

Height 15-foot ladder touch the building / 15 feet = 2/3

Solving for Height 15-foot ladder touch the building: Multiplying both sides of the equation by 15 feet:

15 feet (Height 15-foot ladder touch the building / 15 feet) = 5 feet (2/3)

Height 15-foot ladder touch the building = 5 feet (2)

Height 15-foot ladder touch the building = 10 feet

The stem and leaf plot below displays a set of data recorded in the North Pole.

Stem:
-3, -2, -1, 0, 1, 2, 3

Leaf:
5,2,2,1,0,7,7,7,5,3,2,0,-9,-6,-4,-1,-1,0,3,6,1,2,5

Which box plot closely resembling the data set within the stem and leaf plot, represents a data set with outliers?

Answers

Answer:

plot B

Step-by-step explanation:

-3

-2 goes with 5,2,2,1,0

-1 goes with 7,7,7,5,3,2,0

0 goes with -9,-6,-4,-1,-1,0,3,6

1 goes with 1,2

2 goes with 6

3


This means there should be no data  in our box and whisker plot until a whisker starts at -25.  This eliminates plot A

We will also stop our last whisker at 26 .  This eliminates plot C

We have 23 data points.  So the median point is 12

The 12th point is -10

The middle of our box should be at -10  This eliminates plot D

Our answer is plot B

Given that line segments are taken to line segments of the same length during rigid transformations, which transformation maps the line segment AB onto itself?
The line is -2,1 and 4,3
A) rotation counterclockwise of 90° → x-axis reflection → rotation counterclockwise of 270° → x-axis reflection
B) rotation counterclockwise of 90° → y-axis reflection → rotation counterclockwise of 270° → y-axis reflection
C) rotation counterclockwise of 90° → x-axis reflection → rotation counterclockwise of 270° → y-axis reflection
D) rotation counterclockwise of 180° → x-axis reflection → rotation counterclockwise of 270° → y-axis reflection

Answers

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

A(-2,1)→C(-1,-2);B(4,3)→D(-3,4).

2. x-axis reflection has a rule

(x,y)→(x,-y),

then

C(-1,-2)→E(-1,2);D(-3,4)→F(-3,-4).

3. Rotation counterclockwise of 270° has a rule

(x,y)→(y,-x),

then

E(-1,2)→G(2,1);F(-3,-4)→H(-4,3).

4. y-axis reflection has a rule

(x,y)→(-x,y),

then

G(2,1)→A(-2,1);H(-4,3)→B(4,3).

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.  

what is the equation of a line that passes through the point (6,1) and perpendicular to the line whose equation is 2x+y= - 6 ?

Answers

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


What value correctly fills in the blank in the equation 16 + 12 = 4 ´ ( __ + 3) to show the sum of the two areas of flowers?

Answers

Well, the last part if your sentence, "to show the sum of the two areas of flowers?", is irrelevant to the equation. Let's focus on just the equation: 16 + 12 = 4(_ + 3). Though I have no idea what the apostrophe means, I'll assume you meant to put an '*' or asterisk, meaning multiply. Firstly, whenever you have a variable, or a number you want to solve for, replace the blank with a letter like x. It would look like this: 16 + 12 = 4(x + 3). Using PEMDAS or Parentheses, Exponents, Multiply, Divide, Addition, Subtraction, let's address our parentheses. To solve the parentheses, simply multiple 4 with both x and 3 like so: 4(x + 3) = 4x + 12. Our equation will come out something like this: 16 + 12 = 4x + 12. Next, we can subtract 12 from both sides to simplify our equation: 16 = 4x. From there, divide both sides by 4 and you will get: 4 = x or x = 4. That's your answer! If you have any questions, feel free to ask.

Answer:

4

Step-by-step explanation:

The speed of an Arabian horse is "4x + 2" miles per hour slower than a thoroughbred horse with a speed of "25x − 5" miles per hour. Find a single expression that represents the speed of an Arabian horse. A) 21x − 3 B) 21x − 7 C) 29x − 3 D) 29x − 7
PLS AWNSER THIS WERE GOING TO LEEVE AT 855

Answers

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

j^2 over 2j times 2j over 3g

Answers

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


Use the formula F = 9/5c + 32 to convert -3 degrees Celsius to degrees Fahrenheit

Answers

[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]

what is 25.9 billion times 20 and then divided by 100? will mark brainliest.

Answers

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

Amara needs 4545 kilograms of meat to feed her 22 pet dragons each day. Each pet dragon eats the same amount of meat.
How many kilograms of meat does Amara need to feed 44 pet dragons each day?

Answers

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


what is the estimate of 8.36

Answers

Answer:

You can estimate to the nearest 10th.

Example:8.4

Step-by-step explanation:


state of each triangle is acute, obtuse, or right

Answers

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.

How to determine and classify each of the triangles?

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).

Read more on triangles here: https://brainly.com/question/31186179

#SPJ6

How many variable terms are in the expression 3x^3y+5x^2-4y+z+9

Answers

Answer:

5

Step-by-step explanation:

x + y + x + y + z = 5

pls someone should kindly help me with this

Answers

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.

Case 1: Discriminant = zeroCase 2: Discriminant = perfect square

(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]

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[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]

if a line includes the points (8,0) and (20,12). What is its equation in slope-intercept form?

Answers

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: y = x - 8

Marjorie baked 100 cupcakes for a bake sale. She sold each cupcake for $0.50. The function P(c) = 0.50c represents the amount, in dollars, that she earned from the bake sale by selling c cupcakes. What domain and range are reasonable for the function?

Answers

Answer:

The answer in the procedure

Step-by-step explanation:

we have

P(c)=0.50c

where

P(c) ---> is the amount in dollars that Marjorie earned from the bake sale

c ----> is the number of cupcakes

The domain of the function are the number of cupcakes sold

so

The domain is the interval -----> [0,100]

All positive integers greater than or equal to 0 and less than or equal to 100

Find the range

For c=0

P(0)=0.50(0)=$0

For c=100

P(0)=0.50(100)=$50

The range is the interval -----> [0,50]

All real numbers multiples of 0.50 greater than or equal to 0 and less than or equal to 50

The domain for the function is c ≥ 0, and the range is P(c) ≥ 0.

Domain: The domain for the function P(c) = 0.50c, where c represents the number of cupcakes sold, would be all non-negative integers since Marjorie cannot sell a negative number of cupcakes. So, the domain is c ≥ 0.

Range: The range for the function would be all the possible earnings that Marjorie can make from selling cupcakes. Since each cupcake is sold for $0.50, the earnings can be any non-negative real number. Therefore, the range is P(c) ≥ 0.

when f(x) = x-7/2 , what is the value of (f^0 f^-1) (3)

Answers

Answer:

[tex](f o f^{-1})(3) = 3[/tex]

Step-by-step explanation:

[tex]f(x) = \frac{x-7}{2}[/tex]

We need to find (fof^-1)(3)

First we find f^-1(x)

Replace f(x) with y

[tex]y = \frac{x-7}{2}[/tex]

Now replace x  with y and y with x

[tex]x = \frac{y-7}{2}[/tex]

Multiply by 2 on both sides

2x = y -7

Now add 7 on both sides

2x + 7 = y

Replace y with f^-1(x)

f^-1(x) = 2x+ 7

Now we find (fof^-1)(3)

[tex](f o f^{-1})(3) = f(f^{-1}(3))[/tex]

First we find f^-1(3)

f^-1(x) = 2x+ 7

f^-1(3) = 2(3) + 7 = 6 + 7 = 13

Now we plug in 13 for x  and find out f(13)

[tex]f(x) = \frac{x-7}{2}[/tex]

[tex]f(13) = \frac{13-7}{2}= 3[/tex]

So , [tex](f o f^{-1})(3) = f(f^{-1}(3))= 3[/tex]

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