Which number line represents the solution set for the inequality -4(x+3) ≤ -2 - 2x?

Answer:

- 24x + 9

Step-by-step explanation:

Differentiate each term using the power rule

[tex]\frac{d}{dx}[/tex] ( a[tex]x^{n}[/tex] ) = na[tex]x^{n-1}[/tex]

Given

f(x) = - 12x² + 9x, then

f'(x) = (2 × - 12)x + (9 × 1) [tex]x^{0}[/tex]= - 24x + 9

Answer:x^2+2x+3

Step-by-step explanation:

I’m assuming you meant 2x^4+4x^3+6x^2...

So you can pull out 2x^2 from all of the polynomials...

And this equation isn’t able to be simplified anymore. Hope this helps!

The polynomial 2x^4 + 4x^3 + 6x^2 is factored by first finding the GCF 2x^2, resulting in 2x^2(x^2 + 2x + 3). The quadratic inside the parentheses cannot be factored further with real coefficients.

To factor the polynomial 2x^4 + 4x^3 + 6x^2, we first look for the greatest common factor (GCF) that can be factored out. In this case, each term has at least a factor of 2 and an x^2. Factoring out the GCF, we get:

2x^2(x^2 + 2x + 3)

Now, we look at the quadratic inside the parentheses to see if it can be factored further. However, the quadratic x^2 + 2x + 3 does not factor neatly over the integers because the discriminant, b^2 - 4ac, is negative (2^2 - 4(1)(3) = 4 - 12 = -8). Since we are only looking for real coefficients and not complex ones, we conclude that the quadratic cannot be factored further, and so the polynomial is fully factored as 2x^2(x^2 + 2x + 3).

Answer:

Step-by-step explanation:

We will check whether the given pair x = 3 and y = 2 is the solution of the first equation.

4(3) - 5(2) = 12 - 10 = 2 CORRECT

Put x = 3 and y = 2 to the equation 6x + 7y = Q:

Q = 6(3) + 7(2)

Q = 18 + 14

Q = 32

Answer:

-7

Step-by-step explanation:

Lets count back.

1,0,-1,-2,-3,-4,-5,-6

We are going back, so -7

Answer:

[tex](5\pi-11.6)\ ft^{2}[/tex]

Step-by-step explanation:

we know that

The area of the shaded region is equal to the area of the sector minus the area of the triangle

step 1

Find the area of the circle

the area of the circle is equal to

[tex]A=\pi r^{2}[/tex]

we have

[tex]r=5\ ft[/tex]

substitute

[tex]A=\pi (5)^{2}[/tex]

[tex]A=25\pi\ ft^{2}[/tex]

step 2

Find the area of the sector

we know that

The area of the circle subtends a central angle of 360 degrees

so

by proportion find out the area of a sector by a central angle of 72 degrees

[tex]\frac{25\pi}{360}=\frac{x}{72}\\ \\x=72*25\pi /360\\ \\x=5\pi\ ft^{2}[/tex]

step 3

Find the area of triangle

The area of the triangle is equal to

[tex]A=\frac{1}{2}(2.9+2.9)(4)= 11.6\ ft^{2}[/tex]

step 4

Find the area of the shaded region

Subtract the area of the triangle from the area of the sector

[tex](5\pi-11.6)\ ft^{2}[/tex]

Answer:

a.$247

Step-by-step explanation:

39×5=195

195+52=247

Answer:

The answer is $247 (Option A)

Step-by-step explanation:

Pamela will have the car for 5 days.

The cost per renting is variable, and it increases as the days do.

5*$39= $195

And the LDW (Loss Damage Waiver) is an only once cost of $52

You can get the total rental cost by adding both of them:

$195+$52= $247 (Option A)

Answer:

r<280

Step by step explanation:

Subtract 28 from both sides of the equation r+28<308.

r+28 subtracted by 28 leaves us with r<.

308-28 is 280.

Hence the equation becomes r<280.

The expression or inequality is 28 > r < 308 which represents 28 greater than r is less than 308.

It is defined as the combination of constants and variables with mathematical operators.

The question is incomplete.

The complete question is:

Write the expression for the word expression "28 greater than r is less than 308"

It is given that:

The statement is:

28 greater than r is less than 308:

Here r is the real number.

Inequality can be defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.

28 > r < 308

Thus, the expression or inequality is 28 > r < 308 which represents 28 greater than r is less than 308.

Learn more about the expression here:

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Answer:

Draw a line across  the points (6,0) and (0,3)

Step-by-step explanation:

This is the equation of a line, so it is enough to find two points (x,y), locate them and draw a straight line passing trough then,

Having said that, lets start.

The first easy point to find is the one that makes y=0, so we have the following equation: 0=-1/2 x +3, which gives that x=6, this point is (6,0)

The other easy point to find is the one that makes x=0, so we have the following equation y=-1/2 * 0 +3, which gives that y=3, this point is (0,3)

We have two points (6,0) and (0,3)

Answer:

1

Step-by-step explanation:

(f °g)(3) = f(g(3)) = f(-13) = 1

Answer:

y = 7.5x and y = 5.5x + 10

Step-by-step explanation:

this is for if you get the graph or not!

Answer:

5 classes

37.50 monthly cost for both gyms

Step-by-step explanation:

2022 edge

Answer:

the answer is A. f(x +1) = -2f(x)

Step-by-step explanation:

every new number in the sequence is multiplied by -2, making it -2f(x).

Answer:

(D) f(x+1)=2f(x)

Step-by-step explanation:

Answer:

[tex]y=\frac{1}{2}x+\frac{5}{2}[/tex]

Step-by-step explanation:

We are going to find the slope by lining up the points vertically and subtract, then put 2nd difference over first.

Also you could just use [tex]\frac{y_2-y_1}{x_2-x_1}[/tex].  It is the same thing.

(  5  ,   5)

-(  1  ,   3)

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

  4      2

So the slope is 2/4 or 1/2 after reducing.

The point-slope form a line is

[tex]y-y_1=m(x-x_1)[/tex] with a point on the line [tex](x_1,y_1)=(1,3)[/tex] given and with slope [tex]m=\frac{1}{2}[/tex] given.

[tex]y-3=\frac{1}{2}(x-1)[/tex]

We are going to solve this for y and simplify what we can because our goal is y=mx+b; this is slope-intercept form.  It is called that because it tells us the slope,m, and the y-intercept,b.

Distribute:

[tex]y-3=\frac{1}{2}x-\frac{1}{2}[/tex]

Add 3 on both sides:

[tex]y=\frac{1}{2}x-\frac{1}{2}+3[/tex]

Simplify:

[tex]y=\frac{1}{2}x+\frac{5}{2}[/tex]

Answer:

c) -20x^2+14x+12

all real numbers

Step-by-step explanation:

So (fg)(x)=f(x)g(x)=(-4x-2)(5x-6).

Need find the expression in standard form we need to use foil:

First:  (-4x)(5x)=-20x^2

Outer: (-4x)(-6)=24x

Inner:  (-2)(5x)=-10x

Last:  (-2)(-6)=12

--------------------------Add like terms:

-20x^2+14x+12

Polynomials have domain all real numbers.

There are no restrictions on what x can be.  For every number you plug in, you will get a number back.  

Answer:

c.-20x^2 + 14x + 12; all real numbers

Step-by-step explanation:

f(x) = -4x - 2

g(x) = 5x - 6

Therefore, -20x^2 + 14x + 12; all real numbers.

Answer:

x ≥ 4

Step-by-step explanation:

Given

- 4(8 - 3x) ≥ 6x - 8 ← distribute parenthesis on left side

- 32 + 12x ≥ 6x - 8 ( subtract 6x from both sides )

- 32 + 6x ≥ - 8 ( add 32 to both sides )

6x ≥ 24 ( divide both sides by 6 )

x ≥ 4

Answer:

x ≥ 4

Step-by-step explanation:

4(8 - 3x) ≥ 6x - 8  distribute parenthesis on left side

32 + 12x ≥ 6x - 8 (subtract 6x from both sides)

32 + 6x ≥ - 8 (add 32 to both sides)

6x ≥ 24 (divide both sides by 6)

= x ≥ 4

In Mathematics, quadratic functions such as y=ax^2 and cubic functions such as y=ax^3, will have their vertex at the origin, represented by (0,0). These functions show this characteristic because there are no shifts involved in the equation.

In Mathematics, there are different functions that can have their vertex at the origin (0,0). For instance, when we speak of quadratic functions, a function in the form of y = ax^2 will have its vertex at the origin as it's a parabola that opens upward or downward.

Similarly, for the case of cubic functions, a function in the form of y = ax^3 will have the vertex at the origin.

Important to note is that, for all these cases, the vertex is at the origin because there are no horizontal or vertical shifts involved in the equation. That is, the h & k in (x-h)^2+k and (x-h)^3+k are both zero.

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Answer:

2[tex]w^{3}[/tex]-6[tex]w^{2}[/tex]+4w=240

Step-by-step explanation:

The length and height are given in terms of the width. Width =w; Length =(2w−4); Height =(w−1); and the Volume is equal to the product of the three. Therefore, we can set up the equation as follows:

w×(2w−4)×(w−1)=240

To finish, we distribute and combine like terms:

(2[tex]w^{2}[/tex]−4w)×(w−1)=240

2[tex]w^{3}[/tex]−2[tex]w^{2}[/tex]−4[tex]w^{2}[/tex]+4w=240

2[tex]w^{2}[/tex]−6[tex]w^{2}[/tex]+4w=240

Therefore, 2[tex]w^{3}[/tex]−6[tex]w^{2}[/tex]+4w=240 is our equation for the dimensions of the dumpster in terms of w.

To find the dimensions of the dumpster given its volume and relationships between dimensions, we express the length and height in terms of the width and substitute these into the volume equation to get 240 = (2W - 4)(W)(W - 1).

The student has been given a problem involving the volume of a rectangular prism, representative of a dumpster, which mathematically belongs to the subject of geometry. The volume is given as 240 cubic feet, and the relationships between the dimensions (length, width, and height) are provided. The length L is described as 4 feet less than twice the width W, and the height H is 1 foot less than the width (W). We can express this information in terms of equations:

L = 2W - 4

H = W - 1

The volume V of a rectangular prism is found using the formula V = LWH. Substituting the given expressions in terms of W into the volume equation, we get:

V = (2W - 4)(W)(W - 1)

Since the volume is given as 240 cubic feet, we can write the equation as:

240 = (2W - 4)(W)(W - 1)

This is the equation in terms of the width W that could be used to find the dimensions of the dumpster.

Answer:

[tex]574.62\ in^3[/tex]

Step-by-step explanation:

First we calculate the volume of the cylinder.

[tex]V=\pi r^2*l[/tex]

Where r is the radius and l is the length of the cylinder.

We know that:

[tex]r = \frac{diameter}{2}[/tex]

[tex]r = \frac{4}{2}[/tex]

[tex]r = 2\ in[/tex]

Then:

[tex]V=3.14* 2^2*48[/tex]

[tex]V=602.88\ in^3[/tex]

Assuming that the cannon balls are spherical then the volume of the 2 spheres is:

[tex]V=2*\frac{4}{3}\pi r^3[/tex]

[tex]V=2*\frac{4}{3}(3.14)(\frac{3}{2})^3[/tex]

[tex]V=2*\frac{4}{3}(3.14)(\frac{3}{2})^3[/tex]

[tex]V=28.26\ in^3[/tex]

So the space left inside the cannon is

[tex]V=602.88\ in^3 - 28.26\ in^3\\\\V=574.62\ in^3[/tex]

Answer:

(0,7)

Step-by-step explanation:

This equation you are given is in slope-intercept form, the form y=mx+b.

It is called slope-intercept from because it gives us the slope and the y-intercept.

The slope is m.

The y-intercept is b.

If we compare y=8x+7 to y=mx+b, we should make the conclusion that m=8 and b=7.

This tells the slope is 8 while the y-intercept is 7.

The y-intercept is 7 is sometimes required to be represented by a point.  Since it is the y-intercept, the x is 0 so the point that represents the y-intercept is (0,7).

Answer:

0,7

Step-by-step explanation:

Answer:

Your slope of the line is -3/10.

Step-by-step explanation:

Use the following equation:

m (slope) = (y₂ - y₁)/(x₂ - x₁)

Let:

(x₁ , y₁) = (-2 , 7)

(x₂ , y₂) = (18 , 1)

Plug in the corresponding numbers to the corresponding variables:

m = (1 - 7)/(18 - (-2))

Simplify. First solve the parenthesis, then divide:

m = (-6)/(18 + 2)

m = -6/20

Simplify.

m = (-6/20)/(2/2) = -3/10

Your slope of the line is -3/10.

~

Answer:

[tex]\displaystyle \frac{-3}{10}[/tex]

Step-by-step explanation:

Slope formula:

[tex]\displaystyle \frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]\displaystyle\frac{1-7}{18-(-2)}= \frac{-6}{20}=\frac{-6\div2}{20\div2}=\frac{-3}{10}=-\frac{3}{10}[/tex]

Therefore, the slope is -3/10, and the correct answer is -3/10.

Step-by-step explanation:

Write a proportion.  3 laps is to 2 km as 5 laps is to x km.

3 / 2 = 5 / x

Cross multiply:

3x = 10

Divide:

x = 10/3

x = 3⅓

Madison will have run 3⅓ kilometers.

Answer:

A. 30

Step-by-step explanation:

30*.08=24

Answer:

-18a⁷b⁷ + 42a²b⁵

Step-by-step explanation:

  (3a⁵b⁶ - 7b⁴)(-6a²b)

= (3a⁵b⁶)(-6a²b) – (7b⁴)(-6a²b)     Distributed the 6a²b term

= -18a⁷b⁷ - (-42a²b⁵)                     Multiplied and added exponents

= -18a⁷b⁷ + 42a²b⁵                       Removed parentheses

Step-by-step explanation:

To prove that two sides are parallel on a graph, we must show that their slopes are the same. Plotting this on Desmos, we get the first image attached.  Finding the slopes of each line, we get

[tex]TOP\\\frac{5-3}{6-1} =2/5\\BOTTOM\\\frac{-1-(-1)}{7-2} =2/5\\RIGHT\\-4\\LEFT\\-4[/tex]

As the top slope is the same as the bottom, and the right is the same as the left, this is a parallelogram.

To prove that two sides are congruent, we must find their lengths. The distance formula is

[tex]\sqrt(x_{1}+x_{2})^2+(y_{1}+y_{2})^2 } \\[/tex]

Finding the distances, we get

TOP: [tex]\sqrt{29}[/tex]

BOTTOM: [tex]\sqrt{29}[/tex]

RIGHT:[tex]\sqrt{17}[/tex]

LEFT:[tex]\sqrt{17}[/tex]

As the lengths are the same, the sides are congruent

For this case we must find the roots of the following equation:

[tex]3x ^ 2-4x + 2 = 0[/tex]

We have that the roots will come from:

[tex]x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2 (a)}[/tex]

Where:

[tex]a = 3\\b = -4\\c = 2[/tex]

Substituting the values:

[tex]x = \frac {- (- 4) \pm \sqrt {(- 4) ^ 2-4 (3) (2)}} {2 (3)}\\x = \frac {4 \pm \sqrt {16-24}} {6}\\x = \frac {4 \pm \sqrt {-8}} {6}\\x = \frac {4 \pm \sqrt {-1 * 8}} {6}\\x = \frac {4 \pmi \sqrt {2 ^ 2 * 2}} {6}\\x = \frac {4 \pm2i \sqrt {2}} {6}\\x = \frac {2 \pmi \sqrt {2}} {3}[/tex]

We have two complex roots:

[tex]x_ {1} = \frac {2 + i \sqrt {2}} {3}\\x_ {2} = \frac {2-i \sqrt {2}} {3}[/tex]

Answer:

[tex]x_ {1} = \frac {2 + i \sqrt {2}} {3}\\x_ {2} = \frac {2-i \sqrt {2}} {3}[/tex]

Answer:

(2,4)

Step-by-step explanation:

We have the system:

y=x+2

y=3x-2.

This is already setup for substitution.

I'm going to replace my first y with what the second y equals.

That is, I'm going to write 3x-2=x+2.

Time to solve the following for x:

3x-2=x+2

Subtract x on both sides:

2x-2= 2

Add 2 on both sides:

2x. = 4

Divide both sides by 2:

x. = 2

Now that we know x=2 and we have an equation that relates x to y: either y=x+2 or y=3x-2, doesn't matter which we use, we can find y.

So we y=x+2 with x=2 which means y=2+2=4.

So the solution, the intersection, is (2,4).

Answer:

(2, 4 )

Step-by-step explanation:

Given the 2 equations

y = x + 2 → (1)

y = 3x - 2 → (2)

Substitute y = 3x - 2 into (1)

3x - 2 = x + 2 ( subtract x from both sides )

2x - 2 = 2 ( add 2 to both sides )

2x = 4 ( divide both sides by 2 )

x = 2

Substitute x = 2 into (1) for the corresponding value of y

y = x + 2 = 2 + 2 = 4

As a check

Substitute x = 2 into the 2 equations and check validity

(1) → y = 2 + 2 = 4 ← Correct

(2) → y = (3 × 2) - 2 = 6 - 2 = 4 ← Correct

Solution is (2, 4 )

Answer:

161 is 4.6% of 3500

Step-by-step explanation:

Divide:

 161

-------- = 0.046

3500

Now multiply this result by 100%:  4.6%.

161 is 4.6% of 3500.

Answer:

4.6%

Step-by-step explanation:

To find what percent number A is of number B, divide A by B and multiply by 100.

To find what percent 161 is of 3500, divide 161 by 3500 and multiply by 100.

percent = 161/3500 * 100 = 0.046 * 100 = 4.6%

161 is 4.6% of 3500

Answer:

1 Ounce = 28.3495231 Grams

Step-by-step explanation:

Answer:

28.38 grams to the nearest hundredth.

Step-by-step explanation:

By proportion there is 454 / 16

= 28.38 grams in an ounce.

Answer:

A

Step-by-step explanation:

Given

x³ - 4x² - 3 divided by x + 1

Write the coefficients of the polynomial in descending order, including a zero for any terms not included in the polynomial.

In this case a 0 is required to denote the x- term

Division by ( x + h) is evaluated for x = - h, hence

division by x + 1 is evaluated for x = - 1, hence

- 1 | 1  - 4  0  - 3 ← is the required synthetic division → A