6 sqrt (x-2) +4 < 28

How do you solve? Btw.. x-2 is under sqrt sign.

Answer: Width= 7 in.

               Length= 10 in.

Step-by-step explanation:

[tex]l=w+3[/tex]

The perimeter of the rectangle is 34 inches.

[tex]2(w+l)=34[/tex]

substitute

[tex]2(w+w+3)=34[/tex]

[tex]2(2w+3)=34[/tex]

distributive property [tex]a(b+c)=ab+ac[/tex]

[tex]2\cdot 2w+2\cdot 3=34[/tex]

[tex]4w+6=34[/tex]

[tex]4w+6-6=34-6[/tex]

[tex]4w=28[/tex]

divide 4 on both sides

[tex]w=7[/tex]

Width is 7 inches

substitute w=7 in equation [tex]l=w+3[/tex]

[tex]l=7+3[/tex]

[tex]l=10[/tex]

Length is 10 inches

Answer:

313/7

Step-by-step explanation:

Here, we are interested in turning the wordings of the statement to numeric values.

We take it one at a time.

Sum of 35 and 1/5(35) = 35 + 7 = 42

This is added to 1/7(11 + 8)

= 1/7(19) = 19/7

So we have;

42 + 19/7 = (294 + 19)/7 = 313/7

Answer:

[tex]\huge \boxed{430=2 \times 5 \times 43}[/tex]

Step-by-step explanation:

Using factor tree,

Answer:

[tex]\large\boxed{2, 5, 43}[/tex]

Step-by-step explanation:

                                                          430

                                                      /             \

                                                  215              2

The 2 cannot be factorized anymore, so I will put a small box around it.

                                                          430

                                                      /             \

                                                  215            [tex]\boxed{2}[/tex]

                                                  /  \                

                                             43     5

5 and 43 cannot be factorized any smaller.

                                                          430

                                                      /             \

                                                  215            [tex]\boxed{2}[/tex]

                                                  /  \                

                                             [tex]\boxed{43}[/tex]     [tex]\boxed{5}[/tex]

The prime factorization is the numbers in the boxes, which are 2, 5, and 43.

[tex]\large\boxed{2, 5, 43}[/tex]

Hope this helps :)

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

If the formatting is not showing up correctly, please refer to the images of my answer below instead.

Answer:

(a) and (a)

Step-by-step explanation:

In both questions the denominator of the rational functions cannot be zero as this would make them undefined. Equating the denominators to zero and solving gives the values that x cannot be.

Given

[tex]\frac{x-3}{(3-x)(2+x)}[/tex]

solve (3 - x)(2 + x) = 0

Equate each factor to zero and solve for x

3 - x = 0 ⇒ x = 3

2 + x = 0 ⇒ x = - 2

x = 3 and x = - 2 are excluded values → (a)

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

Given

[tex]\frac{-9x+3}{6x^2+10x-4}[/tex]

solve

6x² + 10x - 4 = 0 ← in standard form

(x+ 2)(6x - 2) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 2 = 0 ⇒ x = - 2

6x - 2 = 0 ⇒ 6x = 2 ⇒ x = [tex]\frac{1}{3}[/tex]

x = [tex]\frac{1}{3}[/tex] and x = - 2 are excluded values → (a)

Answer:

x≥5

Step-by-step explanation:

3(x+15)≤5(x+2)+15

3x+45≤5x+10+15

3x+35≤5x+25

3x-5x≤25-35

-2x≤-10

x≥5

{x:xEx:6,7,8,9,10....}

Hope this helps ;) ❤❤❤

Answer:

-5

Step-by-step explanation:

The coefficient is the number attached to the variable.

Answer:

scale factor = [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

Compare the ratio of corresponding sides, image to original.

scale factor = [tex]\frac{3}{9}[/tex] = [tex]\frac{1}{3}[/tex]

Answer:

3.

Step-by-step explanation:

3x3 =9

1.2 x3=9

Answer:

−5 < x < 10

Step-by-step explanation:

−6 < x − 1 < 9

Add 1 to all sides

−6+1 < x − 1+1 < 9+1

−5 < x < 10

Answer:

B

Step-by-step explanation:

Add one to everything

-5 < x < 10

Best of Luck!

Answer:

Compression, stirring, and friction all increase heat

Step-by-step explanation:

I did a lesson on it and got it right

Answer:

Step-by-step explanation:

(a+2,b)=(4,5)

Since the points are equal we can equate them to find a

Comparing a + 2 to 4

We have

a + 2 = 4

Send 2 to the right side of the equation

a = 4 - 2

We have the final answer as

Hope this helps you

Step-by-step explanation:

Here,

according to the question,

(a+2, b)=(4,5)

since, they are equal, equating with their corresponding elements we get,

(a+2)=4

or, a= 4-2

Therefore, the value of a is 2.

Also you can find value of b in same way,

b=5.

Therefore, the value of a abd b are 2 and 5 respectively.

Hope it helps...

Answer:

x= 3.43

Step-by-step explanation:

First, use the distributive property and multiply 3 by x and 3 by 2:

3x + 6

next use the distributive property again and multiply 4 by x and -5:

4x - 20

Combine Like terms: 3x + 6 + 4x - 20

3x + 4x = 7x

6 - 20 = -14

Now Add 14 to both sides: 7x - 14 = 10

10 + 14 = 24

Now divide 7 by both sides: 7x = 24

24 / 7 = 3.428571429 = 3.43

Answer:

x=24/7 or 3 3/7

Step-by-step explanation:

3(x+2) + 4(x-5)=10   parenthesis first

3x+6+4x-20=10

7x-14=10               addition on both sides

7x-14+14=10+14

7x=24

x=24/7

check the answer:

3(x+2) + 4(x-5)=10

3(24/7+2)+4(24/7-5)=10

72/7+6+96/7-20=10

168/7-14=10

24-14=10

10=10 correct

Answer:

1.0625

Step-by-step explanation:

Answer:

3 / 19

Step-by-step explanation:

Given the following :

ratio of college graduates with a graduate degree to non-college graduates = 1:8

ratio of college graduates without a graduate degree to non-college graduates is 2:3

If college graduate with a degree = A

College graduate without a degree = B

Non-college graduate = C

College graduate to non college graduate = A:C

College graduate without degree to non college graduate = B:C

A:C = 1:8 - - - (1) ; B:C = 2:3 - - - (2)

Combining the two ratios :

To do so : the proportion of non college graduate should be the same in both ratios

To do this, multiply (1) by 3 and (2) by 8

A:C = 3 : 24

B:C = 16 : 24

combining both, we have :

A:B:C = 3:16:24

If one random college graduate is picked, what is the probability that they hold a graduate degree?

Total proportion of college graduate : (college graduates with degree + college graduates without degree)

A + B = (3 + 16) = 19

Proportion who hold a graduate degree = A = 3

Probability = require outcome / Total possible outcomes

Thus :

P = A / (A +B)

= 3/19

Answer:

STEP 1: Find the circumference:

Circumference = 2πr

Circumference = 2π(14) = 28π cm

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

STEP 2: Find the length of the arc:

Length of the arc = 36/360 x 28π

Length of the arc = 8.8 cm

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

Answer: The length of the arc is 8.8 cm

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

hope it helpssss

Mark it as brilliant answer plzzz

ФωФ

Answer:

27°

Step-by-step explanation:

arc length = circumference × fraction of circle

let x be the central angle, then

2πr × [tex]\frac{x}{360}[/tex] = 6.6

2 × [tex]\frac{22}{7}[/tex] × 14 × [tex]\frac{x}{360}[/tex] = 6.6

88 ×[tex]\frac{x}{360}[/tex] = 6.6 ( multiply both sides by 360 )

88x = 2376 ( divide both sides by 88 )

x = 27

Thus central angle is 27°

Answer:

Step-by-step explanation:

Angle 1 and angle 4 are Alternative angles:

Alternative angles are pair of angles on the inner side of each of those two lines but on opposite sides.

∠2-∠2=180  ,∠2=180-62=118

∠4+118=180  ⇒∠4=180-118 ⇒∠4=62 degrees

  ∠1=∠4                  alternative angles        

Answer:

a) ¿cuanto dinero aporto el tercer amigo?

= $ 8,000

b) ¿Cual de los tres hizo el mayor aporte?

El segundo amigo hizo la mayor contribución.

c)¿cuanto mas puso en relación con que el que aporto menos?

El tercer amigo hizo la menor contribución

Step-by-step explanation:

De la pregunta, se nos dice:

Dinero total requerido: $ 72,000

El primer amigo contribuyó: 1/3 si el dinero era necesario

Por lo tanto, el primer amigo contribuyó:

1/3 × $ 72 000 = $ 24 000

El segundo amigo contribuyó con 5/6 del resto

La fracción que representa el resto = 1 - 1/3 = 2/3

Por lo tanto, el segundo amigo contribuyó = 5/6 de 2/3 = 5/6 × 2/3 = 5/9

La fracción de la cantidad de dinero que contribuyó el segundo amigo = 5/9

Por lo tanto, la cantidad que contribuyó el segundo amigo =

5/9 × $ 72 000 = $ 40 000.

a) ¿cuanto dinero aporto el tercer amigo?

Esto se calcula como:

$ 72,000 - ($ 24,000 + $ 40,000)

$ 72 000 - $ 64 000

= $ 8,000

Por lo tanto, el tercer amigo aportó $ 8,000.

b) ¿Cual de los tres hizo el mayor aporte?

Del cálculo anterior:

El primer amigo = $ 24,000

Segundo amigo = $ 40,000

Tercer amigo = $ 8,000

Por tanto, el segundo amigo hizo la mayor contribución.

c) ¿cuanto mas puso en relación con que el que aporto menos?

Del cálculo anterior:

El primer amigo = $ 24,000

Segundo amigo = $ 40,000

Tercer amigo = $ 8,000

Por lo tanto, el tercer amigo hizo la menor contribución.

Answer:

[tex]\huge\boxed{Option \ C}[/tex]

Step-by-step explanation:

∠CAD is the central angle and ∠CBD is the inscribed/circumference angle which means that

∠CAD = 2(∠CBD)

So, If ∠CBD = 55° then ∠CAD = 110°

Answer:

-0.4 or 2.3

Step-by-step explanation:

simple

each box is 0.1 unit

Answer:

Step-by-step explanation:

The answer is where the graph cuts the x-axis.

I can't see it very well but it looks like x = -0.4 and 2.3.

Answer:

Step-by-step explanation:

77; The formula to calculating the area of a trapezoid is (a+b)/2 * c. a+b are the 2 parallel lines, and c is the height or the altitude. So, it is (10+12)/2 * 7, which is 22/2 * 7 = 11*7=77 :)

Answer:

LM = 2(MP)

Step-by-step explanation:

The radius KN is perpendicular to LM meaning that the line is split in half at the crossing. Review properties of circles to see why this is true.

Since we know this, we can say LM = LP + MP. And LP = MP.

So we can say LM = 2(MP).

Cheers

Step-by-step explanation:

The question has asked you to have another concepts or facts that can be used to find the other angles and measure of side length.

by looking the fig we can determine various sides and angles as all are joined together.

Answer:

60.1508310

Step-by-step explanation:

60 tens=60.

1 tenth=1.0

83 hundredth=83.00

150 thousandth=150.000

Tenth=1 decimal place

Hundredth=2 decimal place

Thousandth=3 decimal place

150.000

83.00

1.0

1508310

60.1508310

Answer:

-3

Step-by-step explanation:

First we need to distribute the -4.

-6x+20+4x=26

-2x+20=26

subtract 20 on both sides

-2x=6

divide out -2

x=-3

Answer:

Step-by-step explanation:

y = -2/3x + 4

y = 2/3x

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

4/3x = 4

4x = 12

x = 3

y = 2/3(3)

y = 2

(3,2) one solution

option 3

Answer:

[tex]x=-40[/tex]

Step-by-step explanation:

You need to find the value of x. To do this, you need to isolate the variable:

[tex]7x=80+9x[/tex]

Move the 80 to the left side of the equation using the reverse operation of '+', which is subtraction:

[tex]7x-80=80-80+9x\\\\7x-80=9x[/tex]

Now move the coefficient, 7x, to the right side of the equation using the reverse operation of addition (because it's a positive number), which is subtraction:

[tex]7x-7x-80=9x-7x\\\\-80=2x[/tex]

Now isolate the variable using reverse operations. The coefficient can also be seen as [tex]2*x[/tex] , so the opposite of multiplication is division. Divide by 2, remembering to do the same on both sides of the equation to keep it stable:

[tex]-\frac{80}{2}=\frac{2x}{2}\\\\ -40=x[/tex]

The value of x is -40.

:Done

Answer:

Twenty-seven and a half million metric tons of apples are eaten fresh.

Step-by-step explanation:

The amount of metric tons of apples that are eaten fresh is equal to the half of the total amount of metric tons. That is:

[tex]m = \frac{55,000,000\,m-ton}{2}[/tex]

[tex]m = 27,500,000\,m-ton[/tex]

Twenty-seven and a half million metric tons of apples are eaten fresh.

Answer:

y = 7 when x = -5

Step-by-step explanation:

First go to x = -5

Then go up to where you meet the green line

The y value is 7

y = 7 when x = -5

Answer:

Ok, when we have an equality, like:

A = B

That says that A is the same as B.

Then if a multiply, divide, add or subtract (or do a lot of other operations) in both sides of the equality, the equality does not change.

I suppose that we start with something like:

(4/3)*x = 2

(i will work with this, because you did not post the actual equations)

the thing that Carrie did is:

She multiplies both sides by 3, and get:

3*(4/3)*x = 2*3

4*x = 6

Now she divides bot sides by 4

4*x/4 = 6/4

x = 6/4 = 3/2.

Now, a simpler step is considerin (4/3) as a number A, then we have:

A*x = 2

Now we divide both sides by A.

A*x/A = 2/A

x = 2/A

and we have A = (4/3) then 1/A = (3/4)

x = 2*(3/4) = 3/2

Answer:

933

Step-by-step explanation:

female : male

x : 1000

x : 4000

1000 x 4 = 4000

3732 : 4000

3732 ÷ 4 = 933

When [tex]\theta[/tex] terminates in quadrant III, both [tex]\cos\theta[/tex] and [tex]\sin\theta[/tex] are negative, and

[tex]\sin^2\theta+\cos^2\theta=1\implies\cos\theta=-\sqrt{1-\sin^2\theta}=-\dfrac{12}{13}[/tex]

When [tex]\varphi[/tex] terminates in quadrant II, [tex]\cos\varphi[/tex] is negative and [tex]\sin\varphi[/tex] is positive, so

[tex]1+\tan^2\varphi=\sec^2\varphi\implies\sec\varphi=-\dfrac{17}{15}[/tex]

which gives

[tex]\cos\varphi=\dfrac1{-\frac{17}{15}}=-\dfrac{15}{17}[/tex]

[tex]\tan\varphi=\dfrac{\sin\varphi}{\cos\varphi}=-\dfrac8{15}\implies\sin\varphi=\dfrac8{17}[/tex]

Now,

[tex]\sin(\theta+\varphi)=\sin\theta\cos\varphi+\cos\theta\sin\varphi=-\dfrac{21}{221}[/tex]