Solve for x in the equation x^2 + 10x + 12 = 36. x = –12 or x = 2 x = –11 or x = 1 x = –2 or x = 12 x = –1 or x = 11

OK, so this is assuming we are considering that the first three kids to solve ARE NOT in the first day.

So we have 3 kids and it doubles

Day 1 : 6

Day 2 : 12

Day 3 : 24

Day 4 : 48

Day 5 : 96

Day 6 : 192

Day 7: 384

So it should take 7 days or a week to solve all the problems.

The equation:

(3 * 2)^x = 384

Answer:

It will take 7 days for all the class to complete the problems.

Step-by-step explanation:

We are given that 3 students solve math problems everyday.

Also, the number of students doubles each day.

So, we get the pattern,

Days (S)                             Number of students                      

1                                                     3                                                 =  3

2                                                    3 × 2                                           =  3 × 2¹  

3                                                    3 × 2 × 2                                     =  3 × 2²

4                                                    3 × 2 × 2 × 2                               =  3 × 2³

5                                                    3 × 2 × 2 × 2 × 2                         =  3 × 2⁴

6                                                    3 × 2 × 2 × 2 × 2 × 2                   =  3 × 2⁵

As, there are total 384 students in the class.

We get the equation as, [tex]3(2)^S=384[/tex]

On solving, we have,

[tex]3(2)^S=384[/tex]

i.e. [tex]2^S=\frac{384}{3}[/tex]

i.e. [tex]2^S=128[/tex]

i.e. [tex]S\log 2=\log 128[/tex]

i.e. [tex]S\times 0.301=2.107[/tex]

i.e. [tex]S=\frac{2.107}{0.301}[/tex]  

i.e. S = 7

Hence, it will take 7 days for all the class to complete the problems.

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

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:

The slope of the given linear function is -4.

Step-by-step explanation:

We have been given the linear equation [tex]y=-4x-9[/tex]

The slope intercept form of a line is given by [tex]y=mx+b[/tex]

Here, b is y-intercept and m is the slope.

On comparing, the given equation with the slope intercept form, we get

b = -9

m = -4

It means that the y-intercept is -9 and the slope of the line is -4.

Therefore, the slope of the given linear function is -4.

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:

5.5 servings

Step-by-step explanation:

4+7=11

11/2=5.5 sevings

The jaguar will run 32 miles farther than the giraffe after both run for 4 hours, calculated using the equation: Distance = Speed x Time.

To calculate how much farther the jaguar will run compared to the giraffe, we can start by writing an equation for the distance each animal travels. Distance is equal to speed multiplied by time, which can be expressed as:

D = s *t

For the jaguar traveling at 40 miles per hour for 4 hours, the distance would be:

D_jaguar = 40 miles/hour*4 hours = 160 miles

For the giraffe traveling at 32 miles per hour for 4 hours, the distance would be:

D_giraffe = 32 miles/hour *4 hours = 128 miles

To find out how much farther the jaguar runs, subtract the distance run by the giraffe from the distance run by the jaguar:

Additional distance = D_jaguar - D_giraffe = 160 miles - 128 miles = 32 miles

The jaguar will run 32 miles farther than the giraffe.

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

[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:

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

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

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

Answer:

For the first picture, the y-intercept is the height the pebble was dropped from. The x-intercept is the amount of seconds it took for the pebble to hit the ground.

For the second picture, the y-intercept is the height of the soccer ball (ground level). The x-intercept is the amount of seconds it took for the soccer ball to hit the ground.

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

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]

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.

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:

Answer:

You can estimate to the nearest 10th.

Example:8.4

Step-by-step explanation:

Answer:

The simple answer: 48

Step-by-step explanation:

Finding the area of a triangle in most cases is simple, multiply the two sides that are not the hypotenuse (the noticeably longer side) then divide the product by two. In this case the perimeter is included because you are given one side and the hypotenuse. With simple 12+14=26 and 34-26=8 you have the other side you need. So 12 times eight equals 96 divide that by two and you have the answer 48.

To solve this, turn everything into decimals. Once you've done that, it reads this way:

Which quantities are proportional to 15?

9

15 -- aka 90/6

15 -- aka 15/1

22.5

30

The only provided quantities that are proportional are 90/6 and 15/1.

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.  

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

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:

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:

5.61

Step-by-step explanation:

just subtract 9.39 from 15.00

[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:

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.

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.