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Answer:

x =10

Step-by-step explanation:

3x + 10 = 6x -20

3x - 6x + 10 = -20

-3x + 10 = -20

-3x = -20 -10

-3x = -30

x = -30/-3

x = 10

Check:

3(10) + 10 = 6(10) - 20

30 + 10 = 60 - 20

40 = 40

Answer:

[tex]a=7,\\b=3[/tex]

Step-by-step explanation:

The area of a rectangle is equal to [tex]A=l\cdot w[/tex], where [tex]l[/tex] is the length of the rectangle and [tex]w[/tex] is the width of the rectangle. In a rectangle, opposite sides are equal.

Therefore, we can write the following system of equations:

[tex]\begin{cases}a\cdot (9+b)=84,\\a\cdot b=21\end{cases}[/tex]

Expand the first equation:

[tex]9a+ab=84[/tex]

Substitute the second equation into the first ([tex]ab=21[/tex]):

[tex]9a+21=84,\\9a=63,\\a=\boxed{7}[/tex]

Solving for [tex]b[/tex]:

[tex]7b=21,\\b=\frac{21}{7}=\boxed{3}[/tex]

Answer:

Step-by-step explanation:

Hope this helps u!!

Given:

The equation is:

[tex]2y=3x-6[/tex]

To find:

The x-intercept and y-intercept of the graph of the given equation.

Solution:

We have,

[tex]2y=3x-6[/tex]

Substitute [tex]y=0[/tex] to find the x-intercept.

[tex]2(0)=3x-6[/tex]

[tex]0+6=3x[/tex]

[tex]\dfrac{6}{3}=x[/tex]

[tex]2=x[/tex]

So, the x-intercept of the graph of the given equation is 2.

Substitute [tex]x=0[/tex] to find the y-intercept.

[tex]2y=3(0)-6[/tex]

[tex]2y=-6[/tex]

[tex]y=\dfrac{-6}{2}[/tex]

[tex]y=-3[/tex]

So, the y-intercept of the graph of the given equation is -3.

Therefore, the x-intercept is 2 and the y-intercept is -3.

Answer:

The length of the rectangular plot is 30 m

Step-by-step explanation:

Mathematically, the area of a rectangle is the product of its length and width

Let us have the length as x m ; for the length to be 9/2 of the breadth, it means the breadth is 2/9 of the length

so we have the breadth as 2/9 * x = 2x/9

The product of the two equals the area which is 200 square meters

thus, we have it that;

x * 2x/9 = 200

2x^2 = 9 * 200

x^2 = 1800/2

x^2 = 900

x = √900

x = 30 m

Answer:

A. The prevalence of Type II diabetes

Step-by-step explanation:

A. The prevalence of Type II diabetes

B. The number of sugary drinks consumed by a child during a day

C. Both the prevalence of Type II diabetes and the number of sugary drinks consumed by a child during a day

D. There is no dependent variable

The prevalence of Type II diabetes depends on number of sugary drinks consumed by a child each day

If

x = The prevalence of Type II diabetes

y = number of sugary drinks consumed by a child each day

Then,

x depends on y

The dependent variable is The prevalence of Type II diabetes

Answer:

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Answer:

y=-3/4x+3

Step-by-step explanation:

the slope is -3/4

in this case, y=mx+b

so y=-3/4x+b

b is the y intercept, so it would be 3

altogether, y=-3/4x+3

Answer:

See Explanation

Step-by-step explanation:

Given two variables (say x and y); the constant of proportionality is the ratio between these to variables.

Illustration; y is directly proportional to x

The above statement can be represented as:

[tex]y\ \alpha\ x[/tex]

When converted to an equation, you get

[tex]y\ =k x[/tex]

k, in the above equation, represents the constant of proportionality

Divide both sides by x to solve for k

[tex]k = \frac{y}{x}[/tex]

Take for instance: [tex]y = 3x[/tex]

Divide both sides by x

[tex]\frac{y}{x} = 3[/tex] --- 3 is the constant of proportionality

Answer:

following k is l

before k is j

Sum j + k + l

Step-by-step explanation:

I think there may be something missing from your question.

Answer:

um, K=1?  I think you are missing stuff from your question cuz all you gave us was K. So, before K is 0 and after is 2

Step-by-step explanation:

If K were to equal one, It Would go 0, 1(K), 2

So The Sum Could Be Three ( 3 )

Answer:

x^2+7x+6

Step-by-step explanation:

Answer:

a=5 days, 3 hours

b= 3 people

Answer:

x = 74.4

Step-by-step explanation:

tan = opp/adj

tan42 = 67 / x

x = 67/tan42

use calculator

x = 74.411038493555922

rounded

x = 74.4

Answer: 30.26%

Step-by-step explanation:

Answer:

Answer:

15 is the missing side (hypotenuse)h

Step-by-step explanation:

A^2+b^2=c^2

9^2+12^2=c^2

81+144=c^2

225=c^2

15=c

Answer:

b=77

c = 103

Step-by-step explanation:

b and 77 are vertical angles and vertical angles are equal

b= 77

c and 77 are supplemental angles and supplemental angles add to 180

c+77 =180

c = 180-77

c =103

[tex] \large \sf \star \: \blue{Answer} \: \star[/tex]

[tex] \small \sf \mapsto\: b = \fbox{77 °} [/tex]

[tex] \small \sf \mapsto \: c = \fbox{ 103 °}[/tex]

Here,

And,

So, b + c = 180 °

77° + c = 180 ° ... { b = 77 -( vertical angle )}

subtract 77 from each sides

77 - 77 + c = 180 ° - 77 °

c = 103 °

Answer:

Diameter, D = 2.65 cm

Step-by-step explanation:

Given the following data;

Circumference of circle = 8.34 cm

To find the length of its diameter;

Mathematically, circumference of a circle is equal to;

C = πD

Where;

Substituting into the formula, we have;

8.34 = 3.142 * D

[tex] D = \frac {8.34}{3.142} [/tex]

Diameter, D = 2.65 cm

Answer:

322.0 ft

Step-by-step explanation:

d = ∅r

d = 4.1 π * 25

d = 322.013246993

Rounded

322.0 ft

Answer:

Step-by-step explanation:

since EG bisects angle DEF

31 = x + 15

31 - 15 = x

x = 16 degree

6x - 4 = 56

6x = 56 + 4

x = 60/6

x = 10

Answer:

8. 16

9. 10

abcdefghijklmnopqrstyvwxyz

Answer:

7/26

Step-by-step explanation:

let the other fraction be x

according to the question,

1/13 +x =9/26

x = 9/26 - 1/13

take lcm of the denominator . lcm=26

x = 9*1 - 1*2/26

x = 9-2/26

x=7/26

Answer:

6) 62.5%

7) 54

8) B

Step-by-step explanation:

For number 6, just add 96 and 160 and then do 160/(96+160), which is equal to 0. 625, or 62.5%.

for number 7, x is always equal to 1/3 of y, so if x is 18, we know that 18 is 1/3 of y. 18x3 is equal to 54, which is your answer.

For number 8, you can see that B is right because it uses the greatest common factor of 32 and 48, which is 16. All the other answers can be simplified more.

Answer:

6. C) 62.5%

7. D) 54

8. B) 16(2c + 3d)

Step-by-step explanation:

160 + 96 = 256

[tex]\frac{160}{256}=\frac{160/32}{256/32}=\frac{5}{8}[/tex]

5 ÷ 8 = 0.625

0.625 × 100

62.5%

GCF = 32

The factors of 160: 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, 160

The factors of 256: 1, 2, 4, 8, 16, 32, 64, 128, 256

The GCF is 32.

1:3 = 7:21 = 9:27 = 13:39 = 18:y

[tex]\frac{1}{3}: \frac{18}{y}[/tex]

1 × y = 18 × 3

y = 54

GCF(32, 48)

32 = 2 × 2 × 2 × 2 × 2

48 = 2 × 2 × 2 × 2 × 3

GCF = 2 × 2 × 2 × 2

GCF = 16

16(2c + 3d)

Answer:

the answer is D

1.step by step explanation :

[tex]4 {x}^{2 } - 25 {y}^{2}{z}^{2} [/tex]

[tex] \sqrt{4 {x}^{2} } - \sqrt{25 {y}^{2} } {z}^{2} [/tex]

2x-5yz

Answer:

a right angle

b acute angle

c obtuse angle

d obtuse angle

e acute

f obtuse

Answer:

$28080 per year

Step-by-step explanation:

15$ per hour for the first job and she does it for 10 hours each week, this means, 15*10 which is 150. So we have 150 for the 1st job every week.

2nd job, 13$ per hour. She does that for 30 hours a week so we have 13*30 which is 390$ per week.

The two jobs together are 150 per week and 390 per week which means 540$ per week. Now` if we want to find how much she makes in a year, the are 52 weeks in a year, so multiply 540$ *52=$28080

So she makes $28080 per year

Answer:

[tex]a_{n}[/tex] = 4 [tex](-5)^{n-1}[/tex]

Step-by-step explanation:

There is a common ratio r between consecutive terms , that is

r = - 20 ÷ 4 = 100 ÷ - 20 = - 5

This indicates the sequence is geometric with nth term ( explicit formula )

[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]

where a₁ is the first term and r the common ratio

Here a₁ = 4 and r = - 5 , then

[tex]a_{n}[/tex] = 4 [tex](-5)^{n-1}[/tex]

Answer:

x = 6

Step-by-step explanation:

Given

- 6 + 8x = 42 ( add 6 to both sides )

8x = 48 ( divide both sides by 8 )

x = 6