Elaine is 8 years younger than her brother Tyler. The sum of their ages is 34. Define a variable and then write and solve an equation to find Elaine’s and Tyler’s ages.

Answer:

2 < x < 3

Step-by-step explanation:

4x - 4 < 8    AND    9x + 5 > 23

4x < 12  AND   9x > 18

x < 3 AND x > 2 so the answer is 2 < x < 3.

  Solve  :    9x-28 = 0

Add  28  to both sides of the equation :

                     9x = 28

Divide both sides of the equation by 9:

                    x = 28/9 = 3.111

Answer:

[tex] \sqrt[5]{a^{3} b^{2}c}[/tex]

Step-by-step explanation:

Rationalization factor of [tex] \sqrt[5]{a^2 b^3 c^4} [/tex]

[tex] = \sqrt[5]{a^{5-2} b^{5-3}c^{5-4}}\\

= \sqrt[5]{a^{3} b^{2}c^{1}}\\

= \sqrt[5]{a^{3} b^{2}c}\\ [/tex]

Answer:

r= square root of A /π

Step-by-step explanation:

to find the radius with the area

use the formula square root of area/pi

Answer:

Step-by-step explanation:

We need to add the measurements together to get the answer.

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[tex]\frac{4}{5} + \frac{1}{4} + \frac{1}{4} + \frac{3}{5}[/tex]

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Since [tex]\frac{1}{4}[/tex] and

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[tex]\frac{3}{5} + \frac{4}{5}[/tex] = [tex]\frac{7}{5}[/tex] and [tex]\frac{1}{4} + \frac{1}{4} = \frac{2}{4} = \frac{1}{2}[/tex]

7/5 + 1/2 (we need to find a common denominator to add these)

14/10 + 5/10 = 19/10 or 1 9/10 hours

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Answer:

19/10 hours or 1 [tex]\frac{9}{10}[/tex] hours.

Step-by-step explanation:

jog = 4/5 hours

lifting = 1/4 hours

stretching = 1/4 hours

cycling = 3/5 hours

total hours for that week = 4/5 + 1/4 + 1/4 + 3/5 = 19/10 hours or 1 [tex]\frac{9}{10}[/tex] hours.

Answer:

15.25 cm²

Step-by-step explanation:

Step 1: find the width of the rectangle, AE.

[tex] cos(60) = \frac{EA}{8} [/tex]

[tex] 8*0.5 = EA [/tex]

[tex] 4 = EA [/tex]

[tex] EA = 4 cm [/tex]

Step 2: Find the area of the rectangle

[tex] Area_{rectangle} = length * width = 8*4 = 32 cm^2 [/tex]

Step 3: Find the area of the sector.

Take π as 3.14

[tex] Area_{sector} = \frac{30}{360}*3.14*8^2 [/tex]

[tex] Area_{sector} = \frac{30}{360}*3.14*8^2 = 16.75 cm^2 [/tex]

Step 4: Find the area of the shaded region.

Area of shaded region = [tex] Area_{Rectangle} - Area_{sector} = 32 - 16.75 = 15.25 cm^2 [/tex]

Answer:

It would be 5.

Step-by-step explanation:

3 - 5 is -2, because it goes like this:

-5  -4  -3  -2  -1  0  1  2  3  4  5 (just count down)

Answer:

Step-by-step explanation:

let the rate of travel of bicycle=x m/h

rate of travel of motor scooter=2x+2

time taken by motor scooter to travel 12 mi=12/(2x+2) hrs.

time taken by bicycle to travel 5 mi=5/x

as time is same

[tex]\frac{12}{2x+2}=5/x\\12x=5(2x+2)\\12x=10x+10\\12x-10x=10\\2x=10\\x=10/2=5\\rate~ of~ travel~ of~bicycle=5 m/h\\rate~ of~ travel~ of~ motor~ scooter=2x+2=2 \times 5+2=12 ~m/h[/tex]

Answer: 2^6

Step-by-step explanation:

First, when we have:

x^n

this means that we are multiplicating x by itself n times.

Now, in this case we have:

6 factors of 2 would mean that we have:

(2)*(2)*(2)*(2)*(2)*(2)

2 multiplied by itself 6 times.

This is equal to:

(2)*(2)*(2)*(2)*(2)*(2) = 2^6

Answer:

5041

Step-by-step explanation:

Hence the least number that should be subtracted from 5045 to make it a perfect square is 4 . So the perfect square number is = 5045 - 4 = 5041

Answer:

40

Step-by-step explanation:

94 + 125 - 17 / 5

Answer:

√29

Step-by-step explanation:

We have points (3,4) and (5,9), so the distance:

Answer:

3

Step-by-step explanation:

[tex]3+11t-9u\\\\\rightarrow\boxed{t = 9; u = 11}\\\\3+11(9)-9(11)\\\\3+99-99\\\\102-99\\\\\boxed{3}[/tex]

Hope this helps.

Answer:

Quadrant I

Step-by-step explanation:

Reflection is a type of solid transformation in which an object or a point is flipped with respect to a reference point or plane to produce its image. It changes the orientation of an object, but not its shape and size.

Reflecting the point X across x-axis produces an image in quadrant II. Now, reflecting it across the y-axis would fix its image now in quadrant I.

Therefore, reflecting point X across the x-axis and then y-axis would produce its image in quadrant I.

1)Option B is the correct option.

231

2)Option A is the correct option.

6336

3)Option B is the correct option.

307 (not sure)

Step-by-step explanation:

According to rules of Proportionality :

[tex]a = k \frac{b}{ {c}^{2} } [/tex]

(A) When (a = 10, b = 8, c = 2)

K = 5

(B) When (b = 20, c = 5)

[tex]a = 5 \times \frac{20}{25} = 4[/tex]

Answer:

right angles and supplementary

Answer:

Each team has 8 players. That means that the x players will be separated into x / 8 teams.

Hope this helps!

Answer:

Rational

Step-by-step explanation:

A surd is an irrational number. An irrational number refers to any number that can not be written in the form a/b where a and b are integers.

Given √3600, which can be written as √36 × √100 = 6 ×10 = 60.

Hence √3600 is a rational number.

Answer:

11.9 in.

Step-by-step explanation:

√142=11.9in

Answer:

y = 14 [tex](6)^{x}[/tex]

Step-by-step explanation:

For an exponential function of the form y = a[tex]b^{x}[/tex]

Use the given points to find a and b

Using (0, 14 ), then

14 = a[tex]b^{0}[/tex] ( [tex]b^{0}[/tex] = 1 ) , thus

a = 14

y = 14[tex]b^{x}[/tex]

Using (3, 3024 ) , then

3024 = 14 b³ ( divide both sides by 14 )

216 = b³ ( take the cube root of both sides )

b = [tex]\sqrt[3]{216}[/tex] = 6 , thus

y = 14 × [tex]6^{x}[/tex] ← exponential function

Answer:

The nth term for the given sequence can be written as:

[tex]a_n=6\,n+1[/tex]

Step-by-step explanation:

Notice that this arithmetic sequence is created by adding to each term a common difference of 6 units:

7 + 6 = 13

13 + 6 = 19

19 + 6 = 25

Then, using the general expression for the nth term of an arithmetic sequence of first term "[tex]a_1[/tex]"  and common difference "d" we can write the nth term as:

[tex]a_n=a_1+(n-1)\,d[/tex]

which in this case translates as:

[tex]a_n=a_1+(n-1)\,d= 7\,+(n-1)\,6=7+6\,n-6=6\,n+1[/tex]

Answer:

Step-by-step explanation:

7,  13,  19,   25, .......

Arithmetic sequence.

First term = a = 7

Common difference = d = second term -  first term

            d = 13 - 7 = 6

nth term [tex]a_{n}=a+(n-1)d\\[/tex]

[tex]a_{n} = 7 +(n-1)*6\\\\\\a_{n}=7 + 6n - 6\\\\\\a_{n} = 1 + 6n[/tex]

Answer:

x = 4

Step-by-step explanation:

8x – 13 = 3x + 7

add 13 to both sides

8x = 3x + 20

subract 3x from both sides

5x = 20

divide by 5 on both sides

x = 4  

Answer:

Below

Step-by-step explanation:

The end behavior of a function is how it grows when it reaches both plus and - infinity.

To do that we will calculate:

● lim h(x) x=> +infinity = lim-4x+4 x=> +inf = lim -4x x=> +inf

-4 is negative so the limit will be -infinity

● lim (-4x+4) x=> -inf = lim (-4x) x=> -inf

-4 is negative, x is negative then -4x is positive. So the limit will be + inf

Answer:

-30x +20

Step-by-step explanation:

-5(6x-4)

Distribute

-5*6x -5*-4

-30x +20

Answer:

-30x + 20

Step-by-step explanation:

I think you need to expand the brackets

you will need to times -5 with 6x

then times -5 with -4

Answer:

7) a = 60; b = 100

8) c = 20

9) d = 45

Step-by-step explanation:

7)

a + 120 = 180

a = 60

b + 80 = 180

b = 100

8)

5c + 4c = 180

9c = 180

c = 20

9)

3d + d = 180

4d = 180

d = 45

Answer:

¼ hours or 15 minutes

Step-by-step explanation:

let the time it will for laura to catch up with Tony be 't'

Distance = speed × time

Distance corvered by Laura in time (t) = Distance corvered by Tony in time (t) + Distance between Tony and Laura

6×t = 4×t + ½

6t = 4t + ½

2t = ½

t = ¼ hours or 15 minutes

BRAINLIEST PLEASE

Answer:

15 minutes

Step-by-step explanation:

Let Tony is running x distance when Laura catch up him.

Then Laura is running x + 0.5 miles distance .

This motion takes the t time.

Using the equation of the motion ,

s = ut

s - Distance u - velocity t - Time

For Tony's motion

x = 4 × t --------*

For Laura's motion

x + 0.5 = 6 × t ------**

** - * --->

x + 0.5 - x = 6t - 4t

0.5 = 2t

t = 0.25 hours

t = 15 minutes

Answer:

18 quarters

Step-by-step explanation:

4.50/.25=18

Answer:

He has 18 quarters

Step-by-step explanation:

Each dollar is equivalent to 4 quarters, and max has $4. Therefore max has 16 quarters. Then you add the 50 cents, which is equivalent to 2 quarters. Now you add the 16to the 2 and you get 18. Max has 18 quarters.