11. What must be true about p and q if the equation shows equivalent fractions​

Answer:

  4^-2

Step-by-step explanation:

The rules of exponents tell you ...

  (a^b)(a^c) = a^(b+c)

This means ...

  (4^6)(4^-8) = 4^(6-8) = 4^-2

To simplify the expression (4^6)(4^-8), add the exponents and rewrite the expression as 4^(-2). Then, use the rule that states any number raised to the power of -1 is the reciprocal of that number to rewrite 4^-2 as 1/(4^2) which equals 1/16.

To simplify the expression (4^6)(4^-8), we can use the rule that states when you multiply two powers with the same base, you add their exponents. In this case, 4^6 multiplied by 4^-8 will be equal to 4^(6 + (-8)). Simplifying the exponent, we have 4^(-2). Since any number raised to the power of -1 is the reciprocal of that number, we can rewrite 4^-2 as 1/(4^2) which is equal to 1/16.

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Answer:

x = 8

y = 10

Step-by-step explanation:

We are given the equations;

-3x + 4Y = 16

3x - y =14

We are required to solve the two equations simultaneously using elimination

In this case, we will eliminate one unknown;

We eliminate x by adding the two equations;

That is;

-3x + 4Y = 16

3x - y =14

.............................

     3y = 30

       y = 10

Solving for x

3x - (10) = 14

3x = 14 +10

  3x = 24

   x = 8

Therefore, the solution of the equation is x=8 and y=10

Answer: 2.125 ft

Step-by-step explanation:

17/8=2.125

In order words each hole needs to be 2 ft and 1 and 1/2 inches apart.

Answer:

11

Step-by-step explanation:

You will move the 7 to 18 but bc there is a equal sign you will change the positive sign to negative and just solve -7 plus 18 you will get 11 and that’s b

Answer:

Step-by-step explanation:

18 = 7/b

18b=7

b=7/18

Answer C seams like a likely answer ssa

Step-by-step explanation:

Answer:

Step-by-step explanation:

The correct fraction is simply 30/7, where 30 is the distance in miles and 7 is the number of days to complete it.

30/7 = 4.286miles daily but since you've asked to have this as a fraction, 30/7miles is good.

Final answer:

To achieve his goal of running 30 miles in a week, Raul should run 30 miles divided by 7 days, which is approximately 4 2/7 (⅔) miles every day.

Explanation:

If Raul wants to run 30 miles this week and he wants to run the same number of miles each day, we need to divide the total miles by the number of days in a week. There are 7 days in a week, so we will divide 30 miles by 7 days.

Using division: 30 miles ÷ 7 days = ⅔ miles per day. The fraction ⅔ represents the number of miles Raul plans to run each day to meet his goal of running 30 miles in a week.

Answer:

The answer is m = 5

Step-by-step explanation:

Let's solve the proportional equation, this way:

3/m-2 = 7/m+2

3 * (m + 2) = 7 * (m - 2) [Lowest common denominator (m + 2) * (m - 2)]

3m + 6 = 7m - 14

-4m = -14 - 6 (Like terms)

-4m = -20

m = -20/-4

m = 5

The answer is m = 5

Based on the number of people dying from both causes and their relationship with each other, we can calculate that the number of people dead from cancer was 300,000 and those from accidents was 60,000.

Assuming x number of people died from accidents, the number that died from cancer would be 5 times that:

= 5x

The number of people dead from accidents is:

360,000 = 5x + x

6x = 360,000

x = 60,000 people

The number dead from cancer is:

= 5x

= 5 × 60,000

= 300,000 people

In conclusion, 60,000 died from accidents and 300,000 people died from cancer.

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Final answer:

To solve the problem, we created two equations: c = 5a and c + a = 360,000. After substituting and solving these equations, we found that 300,000 people died from cancer and 60,000 from accidents.

Explanation:

The question refers to a situation where the number of people dying from cancer is five times the number who died from accidents, and the total deaths from these two causes amounted to 360,000. To solve this, we can set up a system of equations. Let ‘c’ be the number of cancer deaths and ‘a’ the number of accident deaths. We are given:

Substituting the first equation into the second, we get:

Then we substitute the value of ‘a’ back into the first equation to find ‘c’:

Therefore, 60,000 people died from accidents and 300,000 from cancer.

Answer:

A) The ratio of hypotenuse to base for the triangles is 0.75

Step-by-step explanation:

Here, the given  question is INCOMPLETE.

The following two triangles have the same angles, and are similar. What is the ratio of height to base for the triangles?

A) .75

B) 1.00

C) 1.25

D) 2.50

Here, given that the two triangles are similar.

In triangle one:

Height = 6 units , Base = 8 units

In triangle one:

Height = 3 units , Base = 4 units

Now,as the two given triangles are similar.

⇒Their corresponding sides are PROPORTIONAL.

[tex]\implies \frac{H}{h} = \frac{B}{b} = \frac{6}{8} = \frac{3}{4} = 0.75[/tex]

So, in both the triangles, the corresponding side ratio is 0.75.

Hence, the ratio of hypotenuse to base for the triangles is 0.75

Answer: Fills up something like how inflating a ballon fills it with air

Step-by-step explanation:

Hope it helped

Answer:

[tex]28[/tex]

Step-by-step explanation:

[tex] = \frac{14}{0.5} \ \\ \\ = \frac{14 \times 10}{5} \\ \\ = 14 \times 2 \\ = 28[/tex]

Answer:

[tex]28[/tex]........

Answer:

49.6 or 49 3/5

Step-by-step explanation:

62/100*80

Simplify the 62/100 (meaning to make it to its simplest terms as possible).

62/100= 31/50

Now we can solve:

31/50*80= 49.6 or 49 3/5

Answer:

Step-by-step explanation divide 62 by 100 and multiply by 80

= 49.6

Answer:

Explanation:

The ball is dropped from a height of 900 centimeters.

Since the heights form a geometric sequence, you can find a common ratio between consecutive terms. This is:

Hence, the ratio of the geometric sequence is 0.7, and taking bounce 1 as the start of the sequence, the general term of the sequence is:

            [tex]a_n=800(0.7)^{n-1}[/tex]

With that formula you can find any term:

             [tex]n=1,a_1=800(0.7)^{(1-1)}=800(0.7)^0=800\\ \\ n=2,a_{2}=800(0.7)^{(2-1)}=800(0.7)=560\\ \\n=5,a_{5}=800(0.7)^{(5-1)}=800(0.4)^4=192.08[/tex]

Rounding to nearest tenth of centimeter, the ball bounces 192.1 cm high on the 5th bounce.

Answer:

time  |   distance

2       | 50

1.5     | 37.5

t        | 25*t

2       | 50

12      | 300

d/25 | d

Step-by-step explanation:

The initial population is represented by [tex]P_{0}[/tex] which is the population at [tex]t=0[/tex], in other words [tex]P_{0}=20,000[/tex]

Suppose you have the following problem:

The population of Naguanagua in 2019 is estimated to be 20,000 people with an annual rate of increase of 4%. Which equation models the population of Naguanagua in t years?

Let:

[tex]P:Population \ of \ Naguanagua \\ \\ t:Number \ of \ years \ since \ 2019 \\ \\ r:Rate \ of \ increase[/tex]

So the population of Naguanagua can be modeled by the following equation:

[tex]P=P_{0}(1+r)^t \\ \\ P_{0}=20,000 \\ \\ r=4\%=0.04 \\ \\ \\ P=20,000(1+0.04)^t \\ \\ P=20,000(1.04)^t[/tex]

So the initial population is represented by [tex]P_{0}[/tex] which is the population at [tex]t=0[/tex], in other words [tex]P_{0}=20,000[/tex]

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Step-by-step explanation:

Given , The length of side of the square is 8 feet.

Since a circle is inscribed in the square. Then the diameter of the circle is equal to the length of side of the square .

Therefore the diameter of the circle is = 8 feet.

Radius of the circle is(r) = [tex]\frac{8}{2}[/tex] feet = 4 feet

The area of the circle is= 3.14 r²

                                       = 3.14 × 4² square feet

                                      = 50.24 square feet

The area of the square  is = side × side

                                          = 8×6 square feet

                                          =64 square feet

Therefore the area of remaining board = (64- 50.24)square feet

                                                                 =13.76 square feet

Answer:

15

Step-by-step explanation:

you work it out

Answer:

The inequality to determine the number of rotations is given by

 r ≤ 5.25

Therefore the maximum number of rotations possible is 5.

Step-by-step explanation:

i.) The bottom of Ignacio's desktop is  74.5 cm from the floor.

ii.) The tops of his legs are 49.3 cm from the floor.

iii.) the difference between the bottom of Ignacio's desktop and the top of his legs = 74.5  - 49.3 = 25.2 cm.

iv.) Each clockwise rotation of the knob on the chair raises Ignacio's legs by 4.8 cm.

v.) let the number of clockwise rotations be r.

vi.) therefore the inequality to determine the number of rotations is given by

  4.8r ≤ 25.2     therefore r ≤ 25.2/4.8    therefore r ≤ 5.25

Answer:

2:1

Step-by-step explanation:

Answer:60:30

Step-by-step explanation:

90-60=30 so 60 blue to 30 red is 60:30

Answer:

x=8.94 ; y = 1.58; z=2.02

Step-by-step explanation:

solve 10x+4y+12z = 120      →          5x+2y+6z = 60

         8x + 2y +32Z = 160   →           4x+y+16z = 80

To eliminate z multiply first equation by 16 and second equation by 6.

80x+32y+96z = 960

24x+6y+96z =   480

on subtractionwe get 56x+26y = 480

dividing by 2 we get, 28x + 13y = 240

Now we have a given equation 11x + 77y = 220 → x + 7y = 20

solving 28x + 13y = 240 and x + 7y = 20

28x + 13y =240

28x + 216y = 560

subtracting we get, 203y = 320

y = 1.58

x = 8.94

z = 2.02

Answer:

y=3/5*x, A(0,0), B(1,3/5), C(2,6/5)

Step-by-step explanation:

A(5,3)=(x1,y1)....x1=5, y1=3

m=3/5

y-y1=m(x-x1)

y-3=3/5(x-5)

y-3=3/5*x-3/5*5

y-3=3/5*x - 3

y=3/5*x-3+3

y=3/5*x

x=0, y=3/5*x, y=3/5*0=0 A(0,0)

x=1, y=3/5*1=3/5 B(1,3/5)

x=2, y=3/5*2=6/5 C(2,6/5)

Answer:

1

Step-by-step explanation:

Answer: if y is equal to 18 and x is equal to 72

Step-by-step explanation: 18*4=72

Answer:

9 3/4, 9 3/4, 9.5, 9.125

Step-by-step explanation:

*I converted to decimal form*

9 3/4= 9.75

9.75 is greater than both 9.5 and 9.125, so therefore it is first on the list.

Next, since 9.5 is greater than 9.125, it is arranged next on the list.

9.125 is the only number left, and is clearly the smallest out of all of the numbers shown.

We want to order the given set of numbers from greatest to lest.

The correct order is:

{9 3/4, 9 3/4, 9.5, 9.125}

Let's see how to get that.

The given set is:

{9.5, 9 3/4, 9.125, 9 3/4}

Here we can see that we have two times the mixed number (9 3/4).

This can also be written as:

9 + 3/4

And we know that 3/4 = 0.75

Then:

9 + 3/4 = 9.75

Then the mixed number is the largest number.

Then comes the 9.5, and finally the 9.125

Then the correct order is:

{9 3/4, 9 3/4, 9.5, 9.125}

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2[tex]\frac{3}{10\\}[/tex]

1) 216

2) 1

3) 450 ml

4)15 packs

5)12 sq m

Step-by-step explanation:

Step 1:

1) The series given is the cube of the first n natural numbers. Hence the nth term of the series can be obtained by n³.

Here we need the 6th term, so the cube of 6 is 216

Step 2 :

2 ) Area of the cube is given as 8000 cubic cm.

Hence side of the cube is 20 cm cube

The radius of the sphere is 20 cm as the diameter is given as 10 cm.

Hence number of spheres that can be placed in a cube of side 20 cm is 20/20 = 1

Step 3 :

3)

Total quantity of the mixture purchased from the chemist is 750 ml

Syrup and alcohol are in the ration 3:2

Hence the quantity of syrup in the mixture = 3/5 * 750 = 450 ml

Step 4 :

4)

Length and breadth of the given room is 17 m and 15 m

Hence its area is 17 * 5 = 85 sq m.

Size of the tiles is 1 sq m

So for covering 85 sq m we need 85/1 = 85 tiles

Since the tiles are bought in packs of 6 we need 85/6 packs which is approximately 15 packs of tiles.

Step 5 :

5)

Surface area of the given  box with length as l, breadth as b and width as w is

2lw+2 lh+2 wh

here we have l,b,w as 3,2,2

so surface area is 3*2*2 = 12 sq m  

Answer:

1) 216

2) 1

3) 450 ml

4)15 packs

5)12 sq m

Step-by-step explanation:

Step 1:

1) The series given is the cube of the first n natural numbers. Hence the nth term of the series can be obtained by n³.

Here we need the 6th term, so the cube of 6 is 216

Step 2 :

2 ) Area of the cube is given as 8000 cubic cm.

Hence side of the cube is 20 cm cube

The radius of the sphere is 20 cm as the diameter is given as 10 cm.

Hence number of spheres that can be placed in a cube of side 20 cm is 20/20 = 1

Step 3 :

3)

Total quantity of the mixture purchased from the chemist is 750 ml

Syrup and alcohol are in the ration 3:2

Hence the quantity of syrup in the mixture = 3/5 * 750 = 450 ml

Step 4 :

4)

Length and breadth of the given room is 17 m and 15 m

Hence its area is 17 * 5 = 85 sq m.

Size of the tiles is 1 sq m

So for covering 85 sq m we need 85/1 = 85 tiles

Since the tiles are bought in packs of 6 we need 85/6 packs which is approximately 15 packs of tiles.

Step 5 :

5)

Surface area of the given  box with length as l, breadth as b and width as w is

2lw+2 lh+2 wh

here we have l,b,w as 3,2,2

so surface area is 3*2*2 = 12 sq m  

Step-by-step explanation:

Answer:

y = -5

x = -2

Step-by-step explanation:

x+7y=-37

2x-5y=21

Multiply first equation by -2

-2 × (x + 7y) = -37 ➡ -2x -14y = 74

now add the equation up

2x-5y -2x -14y = 21 + 74 (-2x will eliminate 2x)

-19y = 95 divide both sides by 19

y = -5 we can find the value for x by using this information

x + 7y = -37 replace y by -5

x + 7×(-5) = -37

x = -2

Answer:

Ricky had 1199 hits.

Pedro had 1482 hits.

Step-by-step explanation:

State your variables

let "p" be the number of Pedro's base hits

let "r" be the number of Ricky's base hits

Create equations using information from the problem

p + r = 2681         [1]

p = r + 283          [2]

Substitute equation [2] in equation [1] replacing 'p'

p + r = 2681

r + 283 + r = 2681

Combine like terms to simplify

2r + 283 = 2681

Isolate '"r" to solve for Ricky's base hits.

2r + 283 - 283 = 2681 - 283            Subtract 283 on both sides

2r = 2398        

2r/2 = 2398/2               Divide both sides by 2

r = 1199              Number of Ricky's hits

Substitute r = 1199 into any equation to find "p". I will use [2].

p = r + 283

p = 1199 + 283         Add

p = 1482              Number of Pedro's hits

Therefore Ricky had 1199 hits and Pedro had 1482 hits.

Ricky had 1199 hits and Pedro had 1482 hits.

To solve this problem, we can set up a system of equations. Let x represent the number of hits Ricky had. Pedro had 283 more hits, so Pedro's number of hits would be x + 283.

Together, their hits add up to 2681, so we can write the equation:

x + (x + 283) = 2681

Combining like terms:

2x + 283 = 2681

Subtracting 283 from both sides:

2x = 2398

Dividing both sides by 2:

x = 1199

Ricky had 1199 hits and Pedro had x + 283 = 1199 + 283 = 1482 hits.

Answer:

(48 m^12)/n^8

Step-by-step explanation:

Simplify the following:

3 ((2 m^3)/(n^2))^4

Multiply each exponent in (2 m^3)/(n^2) by 4:

3×2^4 m^(4×3) n^(-2×4)

4 (-2) = -8:

3×2^4 m^(4×3) n^(-8)

4×3 = 12:

(3×2^4 m^12)/(n^8)

2^4 = (2^2)^2:

(3 (2^2)^2 m^12)/(n^8)

2^2 = 4:

(3×4^2 m^12)/(n^8)

4^2 = 16:

(3×16 m^12)/(n^8)

3×16 = 48:

Answer: (48 m^12)/n^8

Answer:

On the screen shot

Step-by-step explanation:

pretty basic. you can't evaluate it to a single digit if there are 2 variables. lmk which variable you are solving for.

Answer:

5 i think. im not good at math. sorry if wrong