2x + 4y = 12
y= 2x-3
What is the solution to the system of equations?
• (-1,8)
(8, -1)
• (5. 3

Answer:

Yes there is GCF > 1 ⇒ (GCF = 4)

The completely factored form is 4(x - 2)(x² + 2x + 4)

Step-by-step explanation:

* Lets find the greatest common factor of the two terms

- The binomial is 4x³ - 32

- The terms of the binomial are 4x³ and 32

- The greatest common factor of 4 and 32 is 4 because both of them

  can divided by 4

∵ 4x³ ÷ 4 = x³

∵ 32 ÷ 4 = 8

∴ The greatest common factor GCF is 4

∴ 4x³ - 32 = 4(x³ - 8)

* Yes there is GCF > 1

# x³ - 8 is the difference of two cubs, it can factorize it into two

  brackets

- The first bracket has cube root of x³ and cube root of 8

- The second bracket comes from the first bracket it has three terms

# The 1st term is square the 1st term in the first bracket

# The 2nd term is the product of the 1st term and the 2nd term of the

  1st bracket with opposite sign of the 2nd term in the 1st bracket

# The 3rd term is the square of the 2nd term in the 1st bracket

* Lets do these steps with x³ - 8

∵ The first bracket = (∛x³ - ∛8)

∵ ∛x³ = x and ∛8 = 2

∴ The first bracket = (∛x³ - ∛8) = (x - 2)

- Lets make the 2nd bracket from the 1st bracket

∴ The second bracket = (x² + (x)(2) + 2²)

∴ The second bracket = (x² + 2x + 4)

∴ The factorization of x³ - 8 = (x - 2)(x² + 2x + 4)

* The completely factored form is 4(x - 2)(x² + 2x + 4)

Answer:

....Yes it is 4                                                                                                                       ....4(x-2)

Step-by-step explanation:

the screenshot shows proof :))

Answer:

x^3(2x+1)(2x-1)

Step-by-step explanation:

first take common then use formula of a^2-b^2

Answer:

The factor of the provided expression are: [tex]x^3(4x-1)(4x+1)[/tex]

Step-by-step explanation:

Consider the provided expression.

[tex]16x^5-x^3[/tex]

Here the Greatest common factor in the above expression is x³.

The above expression can be written as:

[tex]x^3(16x^2-1)[/tex]

[tex]x^3((4x)^2-1^2)[/tex]

Now use the difference of the square property: [tex]a^2-b^2=(a+b)(a-b)[/tex]

By using the above property we can rewrite the provided expression as shown:

[tex]x^3(4x-1)(4x+1)[/tex]

Hence, the factor of the provided expression are: [tex]x^3(4x-1)(4x+1)[/tex]

Answer:

[tex]\large\boxed{(g\circ f)(2)=1296}[/tex]

Step-by-step explanation:

[tex]f(x)=-x+8,\ g(x)=x^4\\\\(g\circ f)(x)=g\bigg(f(x)\bigg)\\\\(g\circ f)(x)=\bigg(-x+8\bigg)^4\\\\(g\circ f)(2)\to\text{put x - 0 to the equation of the function:}\\\\(g\circ f)(2)=(-2+8)^4=(6)^4=1296[/tex]

Answer:

[tex]18g + 7 - 12g - 3 = 6g + 4[/tex]

Step-by-step explanation:

[tex]18g+7-12g-3\\=18g-12g+7-3\\=6g+7-3\\=6g+4[/tex]

The third angle would have to be either an obtuse angle or a right angle.

The third angle can either be an acute angle or obtuse angle

The sum of an interior angle of a triangle is 180 degrees

Acute angles are angles that are less than 90 degrees. If the two angles of a triangle are acute, the two angles can be 30 and 45 degrees

If the third angle is m<C

m<C = 180 - (30 + 45)

m<C = 180  - 75

m<C = 105 degrees

Since the angle is greater than 90 and less than 180, hence it is an Obtuse angle.

Similarly, if the two angles of a triangle are acute, the two angles can be 30 and 89 degrees

If the third angle is m<D

m<D = 180 - (30 + 90)

m<D = 180  - 119

m<D = 61 degrees

Since the angle is less than 90degrees, hence it is an acute angle.

This shows that the third angle can either be an acute angle or obtuse angle

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Answer:

Step-by-step explanation:89

Answer:

The last choice.

Step-by-step explanation:

That would be the last one, with a minimum value of -4.

Answer:

IV graph

Step-by-step explanation:

Given is a picture consisting of 4 parabolas with first 3 open up and last one open down.

We are to find the minimum value vertex

Seeing the graph we can write coordinates of vertex as where they turn their direction.

Hence vertices are

Graph           Vertices        y value

I                      (0,5)               5

II                     (0,0)               0

III                    (1,2.5)             2.5

IV                   (0,-4)              -4

Of the 4 y values, IV graph has the minimum value vertex

[tex]8 - 4 \frac{2}{5} < 3 \frac{3}{4} \\ 3 \frac{3}{5} < 3 \frac{3}{4} [/tex]

The value of the rational expression when x is -2 or -1 is 0 and 3, respectively.

To find the value of the rational expression when x is -2 or -1, we substitute these values into the expression. Plugging in -2, we have (-2)^2 - 4/((-2)+2)((-2)+1) = 0.

Next, plugging in -1, we have (-1)^2 - 4/((-1)+2)((-1)+1) = 3.

Therefore, the value of the rational expression when x is -2 or -1 is 0 and 3, respectively.

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Answer:

D:Spring A is 3 m longer than spring B because 15 – 12 = 3.

Step-by-step explanation:

In this question, you should remember the Hooke's Law in physics.

The Hooke's Law simply explains that the extension that occurs on a spring is directly proportional to the load applied on it.

The mathematical expression for this law is

[tex]F=-kx[/tex]

where;

F= force applied on the spring

x = the extension on the spring

k= the spring constant which varies in spring.

The question will need you to calculate the extension on the springs A and B then compare the values obtained.

In spring A

Force, F=60N and spring constant ,k=4 N/m

To find the extension x apply the expression;

[tex]F=-kx\\\\60=-4*x\\\\60=-4x\\\\\frac{60}{-4} =\frac{-4x}{-4} \\\\\\-15=x[/tex]

Here the spring extension is 15 m

In spring B

Force, F=60N and spring constant , k=5N/m

To find the extension x apply the same expression

[tex]F=-kx\\\\60=-5*x\\\\60=-5x\\\\\\\frac{60}{-5} =\frac{-5x}{-5} \\\\\\-12=x[/tex]

Here the extension on the spring is 12 m

Compare

The extension on spring A is 3 m longer than that in spring B because when you subtract the value of spring B from that in spring A you get 3m

[tex]=15m-12m=3m[/tex]

Answer:

D)Spring A is 3 m longer than spring B because 15 – 12 = 3.

trust

Answer: OPTION A.

Step-by-step explanation:

Find the length scale factor by dividing the known length of the larger triangle by the known length of the smaller triangle:

[tex]lenght\ scale\ factor=\frac{35}{25}=\frac{7}{5}[/tex]

Then, the  area scale factor is:

[tex]area\ scale\ factor=(\frac{7}{5})^2=\frac{49}{25}[/tex]

To find the area of the the larger triangle, multiply the area of the smaller triangle by the area scale factor. Then:

[tex]A_{(larger)}=(270ft^2)(\frac{49}{25})=529.2ft^2[/tex]

So, the option that shows an approximation of the area of the larger triangle is the option A:

[tex]A_{(larger)}[/tex]≈[tex]530ft^2[/tex]

Answer:

C - AC equals AD times AB over AE

Step-by-step explanation:

If Hiro is creating a larger scaled replica of a triangular canvas, then Hiro will get two similar triangles ABE (the small one) and ACD (the large one). Similar triangles have proportional corresponding sides, so

[tex]\dfrac{AC}{AB}=\dfrac{AD}{AE}[/tex]

From this proportion:

[tex]AC=\dfrac{AD\cdot AB}{AE}[/tex]

So, option C (AC equals AD times AB over AE) is correct option

Answer:

D   sin 85         sin 31

    ---------- =     ----------

      b                  9.3

Step-by-step explanation:

We can use the law of sins

sin B        sin A         sin C

---------- = ----------- = ----------

b                   a            c

We do not know angle C, but we can calculate it

The angles of a triangle add to 180

A + B + C = 180

64+ 85 + C = 180

149 + C = 180

C = 180-149

C =31

sin B         sin C

---------- = ----------

b                  c

We know B =  85, C = 31, b = unknown and c = 9.3

sin 85         sin 31

---------- = ----------

b                  9.3

the correct answer would be D

The value of larger and smaller angles are 135 and 45 degrees respectively.

Two angles are supplementary if their sum is 180 degrees.

Since, given that One angle measures three times the measure of a smaller angle.

Let us consider that one angle is 3x and other is x.

                   [tex]3x+x=180\\\\4x=180\\\\x=180/4=45[/tex]

Larger angle is, [tex]3x=3*45=135[/tex]

Smaller angle is, [tex]x=45[/tex]

Learn more about the Supplementary angle here:

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Answer:

x=5

Step-by-step explanation:

3/2 = 3/2x - 6/5x

Get a common denominator of 10 for the fractions with x

3/2 = 3/2 *5/5 x - 6/5 *2/2 x

3/2 = 15/10x - 12/10x

3/2 = 3/10 x

Multiply each side by 10/3 to isolate x

10/3 * 3/2 = 10/3 * 3/10 x

10/2 = x

5 =x

Answer:

One solution; x = -[tex]\frac{6}{7}[/tex]

Step-by-step explanation:

12x + 6 = 5x

12x - 5x = -6

7x = -6

x = -[tex]\frac{6}{7}[/tex]

Answer:

Step-by-step explanation:

[tex]\text{The formula of a perimeter of a rectangle:}\\\\P=2(l+w)\\\\l-length\\w-width\\\\\text{We have}\ l=(w+24)\ in,\ P=128\ in\\\\\text{Substitute:}\\\\128=2(w+24+w)\qquad\text{divide both sides by 2}\\\\64=2w+24\qquad\text{subtract 24 from both sides}\\\\40=2w\qquad\text{divide both sides by 2}\\\\20=w\to w=20\ in\\\\l=20+24=44\ in[/tex]

Answer:

reciprocals

Step-by-step explanation:

Let's actually find the slopes.  Then we can better compare them.

8x - 9y = 5 → - 9y = 5 - 8x → slope is m = (-8) / (-9), or 8/9.

9x - 8y = 1  →  - 8y = 1 - 9x  → slope is (-9) / (-8), or 9/8

These two slopes are reciprocals (but not negative reciprocals).

Answer:

reciprocals, but not negative reciprocals

Step-by-step explanation:

8x - 9y = 5

9y = 8x - 5

y = 8/9x - 5/9

m1 = 8/9

9x - 8y = 1

8y = 9x - 1

y = 9/8x - 1/8

m2 = 9/8

[tex]\bf (\stackrel{x_1}{6}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{-5}~,~\stackrel{y_2}{3}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{3-4}{-5-6}\implies \cfrac{-1}{-11}\implies \cfrac{1}{11}[/tex]

Answer:

1/11

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

The Answer IS: 2480 I just did the question

Step-by-step explanation:

Answer:

2.5

Step-by-step explanation:

because half of 5 is 2.5

Answer:

the answer should be 1

Step-by-step explanation:

4[(-3+z)2-2(-3+z)]+1

4(-6+2z+6-2z)+1

-24+8z+24-8z+1

the 24's and 8's cancel out leaving 1

To find g(h(-3+z)), we first find h(-3+z) by substituting -3+z into h(a), it becomes z^2-8z+15. Then, substitute this into g(a) to get g(h(-3+z)), which results in 4z^2-32z+61.

In the field of Mathematics, to solve the problem g(h(-3+z)), we need to substitute h into g. It means that every 'a' in g(a) will be replaced by what h(-3+z) is equal to. To find h(-3+z), we substitute -3+z into h(a) in place of a. Therefore, h(-3+z) equals to (-3+z)^2-2(-3+z). After simplifying, it becomes z^2-6z+9+6-2z=z^2-8z+15. Next, we substitute this into g(a) to get g(h(-3+z))=4[z^2-8z+15]+1=4z^2-32z+61. Hence, the solution to the problem g(h(-3+z)) is 4z^2-32z+61.

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Answer:

10

Step-by-step explanation:

f(x) = 3x + 1

f(3)= 3 * 3 + 1 + 10

Answer:

42

Step-by-step explanation:

This means 0.84 divided by 0.02

which equals to 42

the points mean that there is a zero

if a number has been written in that format of  "point" then "number" without any number before the point, it means there is  a zero there

if you need anything else clarified please do so in the comment section i would like to help more

           Hope this helps and if it does mark as branliest answer thx

Note that perimeter of rectangle [tex]P=2l+2w[/tex]

So we have to solve for width or w.

[tex]P=2l+2w[/tex]

[tex]30=2\times10+2w[/tex]

[tex]w=5[/tex]

Width of a rectangle is 5 units.

Hope this helps.

r3t40

Answer:

your answer would be just x

Step-by-step explanation:

you just subtract the exponents

The expression x^-8/x^-7 simplifies to 1/x. This is due to the rule for dividing exponential expressions with the same base, which involves subtracting the exponents.

To solve x^-8/x^-7, we need to understand the rule for division of expressions with exponents which is: x^a / x^b  = x^(a-b).

When you divide exponential expressions with the same base, you subtract the exponents.

In our case, x^-8 / x^-7 = x^(-8 - -7). This simplifies to x^-1 or x^-1 = 1/x. So, the result is 1/x.

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Answer:

function

Step-by-step explanation:

hoped this helped;)

Answer:

Step-by-step explanation:

Not a function.  The number of people has little direct connection with the total number of watches owned.

Final answer:

To solve probability questions, you need to understand the basic concepts and formulas.

Explanation:

To solve probability questions, you need to understand the basic concepts and formulas.

Answer:

2 sets of possible solutions:

x=3, y = 5

and

x=-1, y = -3

Step-by-step explanation:

Using the graphical method, (see attached)

you can graph both equations and find their intersection points.

From the attached plot, you can see that the graphs intersect at (3,5) and (-1,-3)

Alternatively, you can solve this numerically by solving the following system of equations. You will get the same answer.

y = 2x + 1 ------------------- eq. (1)

y = x² - 4 ------------------- eq. (2)