Model the unknown number problem by writing an algebraic expression. Then complete the statements. The class was divided into three equal groups. The number of students in class is represented by . The words “divided into three equal groups” means division by 3 . The correct algebraic expression is .

Answer:

[tex]p = 4 \times 6 + 3 \times 5 - 19 = 20[/tex]

Step-by-step explanation:

Number of packs available with Alena initially = 4

Number of gums in each pack = 6

Total number of gums initially present with Alena can be found by multiplying the number of packs with the number of packs.

i.e. number of gums initially present with Alena = 4 [tex]\times[/tex] 6 = 24

Number of packs available with Hugh initially = 3

Number of gums in each pack = 5

Total number of gums initially present with Hugh can be found by multiplying the number of packs with the number of packs.

i.e. number of gums initially present with Hugh = 3 [tex]\times[/tex] 5 = 15

Total number of gums present initially = 24 + 15 = 39

Number of gums left with Alena and Hugh = 19

The number of gums chewed can be found by subtracting the number of gums left with them from the number of gums initially present with them.

i.e. Number of gums chewed, [tex]p[/tex] = 39 - 19 = 20

The equation that can be used is:

[tex]p = 4 \times 6 + 3 \times 5 - 19 = 20[/tex]

Answer: D. 53    [tex]a_{4}=53[/tex]

Step-by-step explanation:

[tex]a_{1}=4\\a_{2}=2(a_{1})+3\\a_{3}=2(a_{2})+3\\a_{4}=2(a_{3})+3[/tex]

[tex]a_{2}=2(a_{1})+3\\a_{2}=2(4)+3\\a_{2}=8+3\\a_{2}=11[/tex]

[tex]a_{3}=2(a_{2})+3\\a_{3}=2(11)+3\\a_{3}=22+3\\a_{3}=25[/tex]

[tex]a_{4}=2(a_{3})+3\\a_{4}=2(25)+3\\a_{4}=50+3\\a_{4}=53[/tex]

Answer:

It's simple the answer is 8%

Step-by-step explanation:

$. 36/ $4.50 × 100 = 8%

Answer:

8%

Step-by-step explanation:

Sales price x sales tax rate = sales tax

4.50 x sales tax rate = .36

sales tax rate = .36/4.50

sales tax rate = .08 or 8%

Answer:

m = -2 and n = 10

Step-by-step explanation:

If the polynomial mx^3 - 3x^2 + nx + 2 is divided by x + 3, the remainder is -1. Then;

x+ 3 = 0

x = -3

Substitute x =-3 into the polynomial and equate to -1

-1 = m(-3)³-3(-3)²+n(-3) + 2

-1 = -27m - 27 - 3n + 2

27m + 3n = -25 + 1

27m + 3n = -24 ... 1

Similarly, if it is divided by x - 2, the remainder is -4, then;

-4 =  m(2)³-3(2)²+n(2) + 2

-4 = 8m - 12- 2n + 2

8m -2n = -4 + 10

8m + 2n = 6 ... 2

Solve 1 and 2 simultaneously

27m + 3n = -24 ... 1 * 2

8m + 2n = 6 ... 2 * 3

______________________

54m + 6n = -48

24m + 6n = 12

54m - 24m = -48 - 12

30m = -60

m = -60/30

m = -2

Get n by substituting m = -2 into 1

From 1:  27m + 3n = -24

27(-2) + 3n = -24

-54 + 3n = -24

3n = -24 +54

3n = 30

n = 30/3

n = 10

Hence m = -2 and n = 10

Answer:

33.33%

Step-by-step explanation:

Percent change equation is:

(x2 - x1) / x1 * 100%

where x1 is initial and x2 is final

This is an right angle ∆ and the side lengths containing a right angle are 9 and 11.

By Pythagoras theoram,

[tex] {p}^{2} + {b}^{2} = {h}^{2} [/tex]

where p is the perpendicular, b is the base and h is the hypotenuse.

Plugging the values,

[tex] {9}^{2} + {11}^{2} = {h}^{2} [/tex]

Then,

[tex]h = \sqrt{ {9}^{2} + {11}^{2} } [/tex]

[tex]h = 14.12(approx.)[/tex]

The x of the right angled ∆ = 14.12

Answer:

the top angle is 11 and the angle on the left is 9 so the X will be rounded to the nearest hundreth since it's the biggest angle so 11×9=109 so yea I THINK its 100 since it's rounding

Answer:

Step-by-step explanation:

remember when we divide 2 fraction, we will multiply the first one with the reciprocal of the second

(5/12)*(- 6/1)=-30/12= - 5/2= -2 1/2

look at the image to figure out how to solve this!!

good luck, and have a good day :]

Answer:

See Explanation

Step-by-step explanation:

The question is incomplete as the radius of the sphere is missing.

The volume of a sphere is:

[tex]V = \frac{4}{3}\pi r^3[/tex]

Substitute 3.14 for [tex]\pi[/tex]

[tex]V = \frac{4}{3}* 3.14* r^3[/tex]

[tex]V = \frac{4* 3.14}{3}* r^3[/tex]

[tex]V = \frac{12.56}{3}* r^3[/tex]

[tex]V = 4.187* r^3[/tex]

At this point, assume that r = 3.

The expression becomes:

[tex]V = 4.187* 3^3[/tex]

[tex]V = 4.187* 27[/tex]

[tex]V = 113.05[/tex]

Answer:

1. 1 cup  of yellow 17.5 cups of blue 2. 4 cups of yellow 70 cups of blue

3. 2 cups of yellow 40 cups of blue 4. 2 cups of yellow 30 cups of blue

Step-by-step explanation:

1. to get same shade keep ratios the same but divide by 2 for smaller amount

2/2 = 1 and 35 /2 = 17.5

2. similar to 1. except multiply by 2

3. use same yellow amount but more blue

4. use same yellow but less blue

Answer:

5,4

Step-by-step explanation:

Answer:

x=28

Step-by-step explanation:

sum of all angles im a triangle = 180°

(2x+5) + (4x+10) + (x-31) = 180

7x=196

x=28

Answer:

x = 28°

Step-by-step explanation:

Sum of a triangle is equal to 180°. Firstly you need to form an equation. Add all the angles which equals to 180°.

2x + 5 + 4x + 10 + x - 31 = 180°

Now simply and find the value of x. Add all the x terms and whole numbers.

7x + 5 + 10 - 31 = 180°

7x + 15 - 31 = 180°

7x - 16 = 180°

7x = 180° + 16

7x = 196

x = 196 ÷ 7

x = 28°

So the angles are:

Angle A = 2x + 5

2 x 28 + 5 = 61°

Angle B = 4x + 10

4 x 28 + 10 = 122°

Angle C = x - 31

28 - 31 = -3°

Answer:

We conclude that -1 = 0 is false, therefore the system of equations has no solution.

Step-by-step explanation:

Given the system of equations

y = – 4x + 6

y = – 4x + 5

solving the system of the equations

[tex]\begin{bmatrix}y=-4x+6\\ y=-4x+5\end{bmatrix}[/tex]

Substitute y = -4x+5

[tex]\begin{bmatrix}-4x+5=-4x+6\end{bmatrix}[/tex]

Refine – 4x + 5 = – 4x + 6

-1 = 0

FALSE!

NO SOLUTION!

We conclude that -1 = 0 is false, therefore the system of equations has no solution.

Answer:

Hydrogen = 13.4

Oxygen = 85.76

Carbon =  26.8

Step-by-step explanation:

H= 13.4

When you multiply by 1/10 all you have to do is move the decimal point to the LEFT.

So... 134←. = 13.4

_______________________________________________________

O= 85.76

134×[tex]\frac{16}{25}[/tex]=85.76

________________________________________________________

C= 26.8

134×[tex]\frac{1}{5}[/tex]=26.8

Answer:

x,y,z=4,3,-4

Step-by-step explanation:

2x+4y-6x=44   =    x+2y-3z=22

x+2y-3z=22

x+2y+3z=-2

x+2y-3z=22

3x-4y+4z=-16

x+2y-3z=22         ------>

                                         2x+4y=20

x+2y+3z=-2          ------>

x+2y-3z=22                      ------>

                                                        13x-4y=40

3x-4y+4z=-16                    ------->

2x+4y=20

13x-4y=40

y=3

x=4

4+2x3-3z=22

z=-4

(x,y,z)=(4,3,-4)

2x4+4x3-6x(-4)=44

4+2x3+3x(-4)=-2

44=44

-2=-2

-16=-16

(x,y,z)=(4,3,-4)

I am so sorry if it is incorrect I  tried :<

Step-by-step explanation:

[tex] \underline{ \underline{ \text{Solution}}} : [/tex]

[tex] \sf{4x - 3y = 19}[/tex] ••••• equation ( i )

[tex] \sf{2x + 3y = 23}[/tex] ••••• equation ( ii )

The coefficients of y are the same in both equation but the sign of 3y of equation ( i ) differs from the equation ( ii ). So , we add one equation from the other to eliminate 3y.

Adding equation ( i ) and ( ii ) , we get :

[tex] \sf{4x \: \cancel{ - 3y}} = 19[/tex]

[tex] \sf{2x \: \cancel{ \: + 3y}} = 23[/tex]

_________________

[tex] \sf{6x \: \: \: \: \: = \: \: \: 42 }[/tex]

Solve for x :

⟿ [tex] \sf{ \frac{6x}{6} = \frac{42}{6}} [/tex]

⟿ [tex] \boxed{ \sf{x = 7}}[/tex]

Now , substituting the value of x in equation ( ii ) , we get ( Remember : you can substitute the value of x in any of the equation ) :

[tex] \sf{2x + 3y = 23}[/tex]

⟿ [tex] \sf{2 \times 7 + 3y = 23}[/tex]

⟿ [tex] \sf{14 + 3y = 23}[/tex]

⟿ [tex] \sf{3y = 23 - 14}[/tex]

⟿ [tex] \sf{3y = 9}[/tex]

⟿ [tex] \sf{ \frac{3y}{3 } = \frac{9}{3}} [/tex]

⟿ [tex] \boxed{ \sf{y = 3}}[/tex]

[tex] \red{ \boxed{\boxed{ \tt{☥ \: Our \:final \: answer :x = 7 \: and \: y = 3}}}}[/tex]

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✑[tex] \underline{ \underline{ \sf{learn \: more }}}: [/tex]

https://brainly.com/question/20487855?exp=27-1

Hope I helped ! ツ

Have a wonderful day / night ♡

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Answer:

46. f(g(x)) =doesn't exist

because from the range of g(x) there is none in the domain of f(x)

48.f(g(x)) = {(0,2), (1,1)}

Answer:

3 seven point touchdowns

Step-by-step explanation:

x=5 pointn

y=7point

x+y=13

5x+7y=71

solve

multiply first equaiton by -5 and add

-5x-5y=-65

5x+7y=71 +

0x+2y=6

2y=6

divide 2

y=3

sub

x+y=13

x+3=13

x=10

10 five point touchdowns

3 seven point touchdowns

Answer: D (5.5,4.3)

Step-by-step explanation:

Answer:

D: 5.5, 4.3

Step-by-step explanation:

yes

Answer:

x = 3

Step-by-step explanation:

3x - X - 9 = 3(2 - x)  (Given)

2x - 9 = 3(2 - x) (combine like terms)

2x - 9 = 6 - 3x (distributive property of equality)

5x = 15 (addition property of equality)

x = 3 (division property of equality)

Ace

Answer:

B

Step-by-step explanation:

3x6 is 18 so therefore its B

Answer:

0.45

Step-by-step explanation:

you have to divide 5.40 by 12

Answer:

The cube of [tex](x+2)^3 \:is\:\mathbf{(x+2)(x^2-2x+4)}[/tex]

Step-by-step explanation:

We need to find cube of [tex](x+2)^3[/tex]

It can be found using formula: [tex](a+b)^3=(a+b)(a^2-ab+b^2)[/tex]

In the question given:

We have a = x and b = 2

Now finding cube using the above formula:

[tex](x+2)^3\\=(x+2)(x^2-(x)(2)+(2)^2)\\=(x+2)(x^2-2x+4)[/tex]

So, the cube of [tex](x+2)^3 \:is\:\mathbf{(x+2)(x^2-2x+4)}[/tex]

Answer:

the answer is 60/100 60%

Step-by-step explanation:

it's a I know this because I'm in the 8th

Step-by-step explanation:

it's a

Answer:

It would take the apprentice 14 hours to make the fireplace on his own.

Step-by-step explanation:

Let x represent the hours it takes the bricklayer to make a fireplace on his own and x + 10 represent the hours it takes the bricklayer's apprentice to make a fireplace on his own.

7/(x + 10) + 2/x = 1

7/(x+10) represents the fraction of the fireplace the bricklayer's apprentice made (total amount of time the bricklayer's apprentice worked on the fireplace/time it takes the bricklayer's apprentice to make a fire place on his own) while 2/x represents the fraction of the fireplace the bricklayer made (total amount of time the bricklayer worked on the fireplace/time it takes the bricklayer to make a fire place on his own). The 1 on the right side of the equation represents the number of fireplaces they made in that time.

Multiply both sides of the equation by x(x + 10) to get rid of the denominators:

x(x + 10)[7/(x + 10) + 2/x] = x(x + 10)1

x(x + 10)[7/(x + 10)] + x(x + 10)(2/x) = x(x + 10)

7x + 2(x + 10) = x² + 10x

7x + 2x + 20 = x² + 10x

Gather all the terms to one side of the equation:

x² + 10x - 7x - 2x - 20 = 0

x² + x - 20 = 0

Factoring the simplified equation:

(x + 5)(x - 4) = 0

Solving for each factor:

When x + 5 = 0,

x = -5

When x - 4 = 0,

x = 4

Since a negative solution wouldn't make sense for this question, it would take the bricklayer 4 hours to complete the fireplace on his own.

Substituting x = 4 into x + 10 to find out how long it would take the apprentice to make the fireplace on his own:

x + 10 = 4 + 10 = 14

Therefore, it would take the apprentice 14 hours to make the fireplace on his own.

Answer:

6

Step-by-step explanation:

add 18 on both sides

7w = 42

divide by 7 on both sides

w = 6

Answer:

Step-by-step explanation:

7w-18=24

7w= 24+18

w=42:7

w=6

Answer:

Step-by-step explanation:

.