An equilateral triangle is dilated by a scale factor of 3. If a side of the original triangle is 6, what is the measure of a side of the new triangle?

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:

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:

5.61

Step-by-step explanation:

just subtract 9.39 from 15.00

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:

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

The answer should be

x= -9

Answer:

x = -9

Step-by-step explanation:

1/3 (x+3) = 2/3x + 4

1/3x + 1 = 2/3x + 4

subtract 1/3x from both sides

1 = 2/3x - 1/3x +4

1 = 1/3x + 4

subtract 4 from both sides

1 -4 = 1/3x

-3 = 1/3x

multilply by 3 (to cancel out the 1/3)

-9 = x

x = -9

YaY!!!! u got it!!! =)

Answer:

5 & 1

Step-by-step explanation:

Factors are numbers that, when multiplied, will give the number that is given in the question. In this case:

5 * 1 = 5

5 & 1 are factors

~

Answer:

5= 1,5 so easy question

Answer:

5.5 servings

Step-by-step explanation:

4+7=11

11/2=5.5 sevings

Answer:

6k+31

Step-by-step explanation:

19-6( -k -2)

= 19 +6k+12

=6k+31

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 legend says 1 inch = 30 yards.

Multiply the total inches by 30 yards:

4 inches x 30 yards = 120 total yards.

Answer:

1 inch = 30 yards

If you’re trying to figure out how many yards is 4 inches, you multiply 30 by 4. Your answer should be 120 yards  

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:

Dawn can make 1482 packages

Step-by-step explanation:

for each package Dawn need  5 cookies so for 7414 cookies she can make

7414 ÷ 5 = 1482.8

so she can make 1482 packages.

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:

You can estimate to the nearest 10th.

Example:8.4

Step-by-step explanation:

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:  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:

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:

(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.

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.

Answer:

About 0.12

Step-by-step explanation:

There are 3 people who prefer merchant D out of n = 25 total

Divide: 3/25 = 0.12

Optionally, you can multiply both top and bottom of 3/25 by the value 4 and it leads to 3/25 = 12/100 = 12% = 0.12

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]

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.

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.

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:

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: Woops I meant 2 cannot be repeated because x-values cannot be the same. So it is C.

A function CAN have the same y-values such as (3,4) and (6,4). But a function CANNOT have the same x-values like (7,10) and (7,1) because it would be a straight line.