Can the distributive property be used to rewrite
4x (6 - 3)?

The factors of the given model are (x+2) and (x+7)

Given the representation of the model expressed as;

[tex]x^2+9x+14[/tex]

To get the factors, we will factorize the given quadratic function as shown:

[tex]g(x) = x^2+2x+7x+14[/tex]

Group the functions to have;

[tex]g(x) = (x^2+2x) + (7x+14)\\[/tex]

Factor out the GCF from both parenthesis:

[tex]g(x) = x(x+2)+7(x+2)\\g(x)=(x+2)(x+7)[/tex]

Hence the factors of the given model are (x+2) and (x+7)

Learn more on factorization here: https://brainly.com/question/25829061

Answer:

5.93

Step-by-step explanation:

6 x 9.45 = 56.7

10 x 6.95 = 69.5

14 x 5.50 = 77

9 x 3.10 = 27.9

56.7 + 69.5 + 77 + 27.9 = 231.1

6 + 10 + 14 + 9 = 39

231.1 / 39 = 5.925 = 5.93

First find the areas of the two separate rectangles where:

Area of rectangle = length x width

Area of the small rectangle = x(x–4)

Area of small rectangle = [tex]x^{2} -4x[/tex]

Area of big rectangle = (x–2)(2x+x)

Area of big rectangle = (x–2)(3x)

Area of big rectangle = [tex]3x^{2} -6x[/tex]

The total area of the compound shape is 36, therefore:

[tex]3x^{2} -6x +x^{2} -4x=36[/tex]

[tex]4x^{2} -10x-36=0[/tex] (collecting like-terms and by bringing the +36 to the other side)

By dividing this by 2, you get:

[tex]2(2x^{2} -5x-18)=0[/tex]

[tex]2x^{2} -5x-18=0[/tex]

To find the length of AB (x), solve the quadratic by either factorising, completing the square or by using the quadratic formula, etc to solve for x.

[tex]2x^{2} -5x-18=0[/tex]

[tex](2x-9)(x+2)=0[/tex]

[tex]x=\frac{9}{2}[/tex]

[tex]x=-2[/tex]

However, a length cannot be negative, so x must be [tex]\frac{9}{2}[/tex] or 4.5cm, so length AB = 4.5cm.

Hope this helps :)

Answer:

Bank A: 24 years, Bank B: 28 years

Step-by-step explanation:

Answer: The variable that will be eliminated when the equations are combined after the multiplication is y.

Step-by-step explanation: Happy to help :D

Answer:

  A.  (f-g)(x) = -7x -3

Step-by-step explanation:

(f -g)(x) = f(x) -g(x) = (-3x -5) -(4x -2)

  = -3x -5 -4x +2

  = -3x -4x -5 +2

  (f -g)(x) = -7x -3

Answer:

12

Step-by-step explanation:

plug in -7 where x is

5 - (-7) = 12

Answer:

12

Step-by-step explanation:

plug in -7 where x is

5 - (-7) = 12

It's pretty simple!

I hope this helps you

Answer:

  112

Step-by-step explanation:

It appears that the relation is f(a, b) = a(a+b).

  f(3, 4) = 3(3+4) = 21

  f(2, 5) = 2(2+5) = 14

  f(7, 7) = 7(7+7) = 98

  f(8, 6) = 8(8+6) = 112

__

The symbol "+" has apparently been repurposed from its usual meaning in math. It is being used as an infix operator with two arguments. We have shown the relation above as a function f with two arguments (a, b). In our definition ...

  f(a, b) = a(a+b)

the symbol "+" has its usual meaning.

_____

Additional comment

This sort of question requires a little bit of "out of the box" thinking. It helps immensely if you're familiar with your addition and multiplication facts. Then you are in a position to recognize how the outputs may be related to the inputs.

See below

[tex]\\ \sf\Rrightarrow y=-x+2[/tex]

[tex]\\ \sf\Rrightarrow y=x+1[/tex]

Now

[tex]\\ \sf\Rrightarrow -x+2=x+1[/tex]

[tex]\\ \sf\Rrightarrow -2x=-1[/tex]

[tex]\\ \sf\Rrightarrow x=0.5[/tex]

Put in eq(2)

[tex]\\ \sf\Rrightarrow y=0.5+1[/tex]

[tex]\\ \sf\Rrightarrow y=1.5[/tex]

[tex](1)... \frac{x}{5} = 2 \\ x = 5 \times 2 \\ x = 10 \\ (2).. \frac{a}{3} + 1 = 3 \\ \frac{a + 3}{3} = 3 \\ a + 3 = 9 \\ a = 9 - 3 = 6 \\ (3) \: \: \frac{p}{4} - 1 = 2 \\ \frac{p - 4}{4} = 2 \\ p - 4 = 8 \\ p = 8 + 4 = 12[/tex]

[tex](4) \frac{2x}{5} = 7 \\ 2x = 35 \\ x = \frac{35}{2} = 17.5[/tex]

Based on the information the cost of the product is $40,000.

Given:

Percentage earn=5% or 0.05

Amount earned=$2,000

Let x represent the cost of the product

Hence:

Formulate

.05x = $2000  

Divide both sides by .05

x=$2,000/.05

x=$40,000

Inconclusion  the cost of the product is $40,000.

Learn more about cost here:https://brainly.com/question/824281

Answer:

x = 8

Step-by-step explanation:

Since the figures are similar then the ratios of corresponding sides are in proportion , that is

[tex]\frac{JK}{AB}[/tex] = [tex]\frac{KL}{BC}[/tex] , substitute values

[tex]\frac{x}{4}[/tex] = [tex]\frac{6}{3}[/tex] = 2 ( multiply both sides by 4 to clear the fraction )

x = 8

Answer:

4200

Step-by-step explanation:

Answer: 4,200 meters

Step-by-step explanation:

[tex]\frac{28}{100} * 15 = 4.2 km = 4200 m[/tex]

this is your answer hope it's helpful for you

Answer:

7. Consecutive Interior Angles that are Supplementary

8. Alternate Exterior Angles that are Congruent

9. Alternate Exterior Angles that are Congruent

10. Alternate Exterior Angles that are Congruent

11. Same Side Exterior Angles that are Supplementary

12. Consecutive Interior Angles that are Supplementary

Step-by-step explanation:

Not sure if I even got them in the correct order, my apologies. The picture provided was a bit hard to read.

Correct me if I am incorrect.

The data plan that has the cheapest deal is given by the ratio of the data

plan price to the GB allocated.

The given phone data plans are;

[tex]\begin{tabular}{|l|cl|}&Prepaid Single Phone Plan&Prepaid Family Plan\\ a&\$30 for 1 GB &\$30 for 1 GB\\b& \$35 for 6 GB & \$40 for 6 GB\\ c&\$45 for 16 GB&\$50 for 16 GB\\d & \$65 for Unlimited Data & \$70 for Unlimited Data\end{array}\right][/tex]

The price per GB are;

Plan a = $30 ÷ 1 = $30 per GB

Plan b = $35 ÷ 6 = $5.8[tex]\overline 3[/tex] per GB and $40÷ 6 = $6.[tex]\overline 6[/tex] per GB for Family Plan

Plan c = 45 ÷ 16 = $2.8125 per GB and $3.125 per GB

Plan d = $65 for Unlimited Data = 65 ÷ ∞ ≈ 0;  $70 for Unlimited Data = 0

Therefore, the plan with the cheapest price per GB from the given option is option B. Prepaid Single Phone Plan $45 for 16 GB.

Learn more about ratios here:

https://brainly.com/question/10705874

$23, a $20 bill plus $3 tip

Answer:

Step-by-step explanation:

The relevant relation is "the exterior angle is equal to the sum of the remote interior angles." That means ...

  (4x +8)° = (2x +3)° +51° . . . equation to solve for x

  2x = 46 . . . . . . . . . . . . . divide by °, subtract 8+2x

  x = 23 . . . . . . . . . . . . divide by 2

Then the exterior angle is ...

  (4x +8)° = (4(23) +8)° = 100°

_____

Additional comment

Instead of solving for x, we can solve for (2x+3). We can do that by subtracting 5+2x from both sides to get 2x+3 = 49. Then the exterior angle is the sum 49+51 = 100 degrees. (We don't actually care about the value of x.)

Answer:

it's d

.

hope I helped! I need to write more words so I can send this

Answer:

The answer is A

Step-by-step explanation:

|6x + 3| = 27

6x + 3 = 27

6x + 3 = -27

6x = 24

6x = -30

x = 4

x = -5

So:

x = 4, -5

Answer:

She will still need about 450$

Step-by-step explanation:

So from what I have learned, she will need to work in order to get the money, but even when she is working, she may have expenses to pay and she may not make it, but she will because she can do loans and when she earns the money from loans, then she can pay, then she may have left over money she can use while on trip.

Answer:

0.65

Step-by-step explanation:

the number is greater than 0.5 and less than 7, that would usually be 0.6 but since it has two decimal places, it can be 0.61 to 0.68 since 0.69 would be the largest

Answer:91.6

Step-by-step explanation:

The height of the tree if the point on the ground is 28 feet from the tree is 91.5 ft.

The angle of elevation is given 73°. The distance between the point on the ground and the tree is 28 feet.

In mathematics, the trigonometric function is a function that deals with the sides of the right-angled triangle and angles.

sin, cos, tan, cosec, sec, and cot are the basic function of trigonometric.

We know that tan Ф = perpendicular / Base

tan 73° = h / 28

tan 73° × 28 = h

3.27 × 28 =h

h = 91.5 ft

Therefore, the height of the tree if the point on the ground is 28 feet from the tree is 91.5 ft.

Learn more about a trigonometric function;

brainly.com/question/6904750

the answer for 135 times 12 is 1620

Answer:

1620

Step-by-step explanation:

u can time 12 by 135 or divide them

Answer:

21.00845

Step-by-step explanation:

πD = 66m

D = 66x 7/22

D = 21m is your answer brainlist me plz

The correct option is D.[tex]0< x\leq 20[/tex] and [tex]0< y\leq 60[/tex].

Given,  [tex]x[/tex] represent the number of male birds and  [tex]y[/tex] represent the number of female birds.

The flock needs to have exactly three times more females than males to thrive.  

So, in equation form we have,

[tex]y=3x[/tex]........(1)

Since, The zoo only has room for a maximum of 20 male birds.

So, we can write the inequality for [tex]x[/tex] as,

[tex]0< x\leq 20[/tex]......(2)

Since The maximum number of male birds is 20, so for [tex]x=20[/tex]

y will be,

[tex]y=3\times 20\\[/tex]

[tex]y=60[/tex]

Hence, The maximum number of female birds is 60.

So, we can write the inequality for [tex]y[/tex] as,

[tex]0< y\leq 60[/tex]

Hence the required constraints are [tex]0< x\leq 20[/tex] and [tex]0< y\leq 60[/tex].

For more details on Inequality follow the link:

https://brainly.com/question/19491153

Answer:d

Step-by-step explanation: did the test

Answer:

e

Step-by-step explanation:

e

Answer:

x=2

Step-by-step explanation:

5x=3x+4

5x-3x=4

2x=4

x=4/2

x=2

All the best for ur exams .........Mine are going on too btw.......