The graph of the function f(x) = (x + 6)(x + 2) is shown. Which statements describe the graph? Check all that apply.

this is the answer to your equation

The solutions to the equation x² = -63 in simplified, rationalized form are:

x = 3√7 * i

x = -3√7 * i

Isolate x²: In this case, x² is already isolated on one side of the equation.

Apply the Square Root Property: Take the square root of both sides of the equation to eliminate the exponent on x²:

√(x²) = √(-63)

Simplify and Introduce Imaginary Unit: Recall that the square root of a negative number is an imaginary number. We introduce the imaginary unit 'i,' defined as √(-1):

x = ±√(63) * √(-1)

x = ±√63 * i

Simplify and Rationalize: √63 cannot be simplified further, but we can rationalize it by multiplying both the numerator and denominator by √3:

x = ±√63 * i * √3 / √3

x = ±3√7 * i

No, they do not represent the same quantity. Explained in attached sheet.

The unit rate in the equation 64t = 384 is 64.

The unit rate in the equation 64t = 384 is 64.

To find the unit rate, we divide the total value by the number of units. In this case, the total value is 384 and the number of units is 64. When we divide 384 by 64, we get the unit rate of 6.

Therefore, the unit rate in the equation is 64.

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The unit rate in the equation 64t = 384 is 6.

The unit rate in the equation 64t = 384 is 6.

To find the unit rate, divide both sides of the equation by 64:

t = 384/64 = 6.

Therefore, the unit rate is 6, which means that Steve drove at a constant rate of 6 hours to reach the beach.

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Answer:

[tex]\large\boxed{b)\ y=\dfrac{3}{4}x-1}[/tex]

Step-by-step explanation:

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

m - slope

b = y-intercpt → (0, b)

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have the points (4, 2) and (0, -1) - y-intercept → b = -1.

(we see this already which equation. Only in b) y-intercept is b = -1).

Anyway, calculate the slope:

[tex]m=\dfrac{-1-2}{0-4}=\dfrac{-3}{-4}=\dfrac{3}{4}[/tex]

Finally we have the equation:

[tex]y=\dfrac{3}{4}x-1[/tex]

Answer:

A. $24.11

Step-by-step explanation:

Take $210 out of the $250 he gave the cashier

250 - 210 = 40

So you have his exact change without the tax though. so take what he RECIVED away from what he was suppose to recive which is 40. So.....

40 - 15.89 = 24.11

$24.11

Hope this helps!

Answer:

a.) is 36 square meters

b.) 400 square meters

Step-by-step explanation:

to find the Volume you must multiply the length, width, and the hight. so to find a.) V = lwh

6 x 2 x 3 = 36

36 square meters.

and you can use the same formula for b.)

Hope this helps!

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Volume of a) 36 cubic meter

Volume of b) 400 cubic feet

Let, Length of the rectangular solid = l unit

Width of the rectangular solid = w unit

And height of the rectangular solid = h unit

Then volume of rectangular solid = l × w × h cubic unit

Given, Length of the rectangular solid = 6 meters

Width of the rectangular solid = 2 meters

And height of the rectangular solid = 3 meters

∴ Volume of the rectangular solid = (6×2×3) cubic meter

                                                        = 36 [tex]m^{3}[/tex]

Given, Length of the rectangular solid = 5 feet

Width of the rectangular solid = 10 feet

And height of the rectangular solid = 8 feet

∴ Volume of the rectangular solid = (5×10×8) cubic feet

                                                        = 400 cubic feet

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Option B is correct since both the lines given in option B have same slope so both the lines do not intersect each other and hence have no common solution.

The given equations are of the form

ax + by = c ......(1)

Slope for the equation of line is given by [tex](\dfrac{-a}{b} )[/tex]

We can  clearly see that in option B the lines given are

4x + 2y = 12 .......(2)

20x + 10y = 30....... (3)

Slope of equation (2)

[tex](\dfrac{-4}{2} )= -2[/tex]

Similarly slope of equation (3)

[tex](\dfrac{-20}{10} )= -2[/tex]

Which concludes that both are parallel to each other.

Since parallel lines can not have any common solution so  they never intersect each other. Hence option B is correct.

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Answer: OPTION C

Step-by-step explanation:

By definition you know that:

[tex]\sqrt[n]{a^n}=a[/tex]

and by the exponents properties you also know that:

[tex]a^n*a^m=a^{(n+m)}[/tex]

Now, descompose 18 into its prime factors:

18=2*3*3=2*3²

Rewrite the expression and simplify (Keep on mind that: [tex]\sqrt{x^4}=x^{(\frac{4}{2})}=x^{2}[/tex]). Then, you obtain:

[tex]\sqrt{2*3^2*x^4*y*y^2}=3x^2y\sqrt{2y}[/tex]

Answer:

C. [tex]3x^2y\sqrt{2y}[/tex].

Step-by-step explanation:

The given radical expression is  [tex]\sqrt{18x^4y^3}[/tex].

We can rewrite this radical expression to obtain;

[tex]\sqrt{2\times9 \times (x^2)^2\times y^2\times y}[/tex].

This will give us;

[tex]\sqrt{2y} \times \sqrt{9(x^2)^2 y^2}[/tex].

[tex]3x^2y\sqrt{2y}[/tex].

The correct choice is C

[tex]\bf (\stackrel{x_1}{1}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{-5}~,~\stackrel{y_2}{-7}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-7-6}{-5-1}\implies \cfrac{-13}{-6}\implies \cfrac{13}{6}[/tex]

The slope of the line is [tex]\frac{13}{6}[/tex].

A slope of a line is the change in y coordinate with respect to the change in x coordinate.

If [tex]P(x_{1} ,y_{1} )[/tex] and [tex]Q(x_{2} ,y_{2} )[/tex] are the two points on a straight line, then the slope formula is given by:

Slope, m = Change in y-coordinates/Change in x-coordinates

[tex]m = \frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]

According to the given question.

We have a two points (1, 6) and (-5,-7).

Therefore, the slope of the line from these points is given by

[tex]slope = \frac{-7-6}{-5-1} = \frac{-13}{-6} =\frac{13}{6}[/tex]

Hence, the slope of the line is [tex]\frac{13}{6}[/tex].

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Answer:

(x - 7)(x + 6)

Step-by-step explanation:

Consider the factors of the constant term ( - 42) which sum to give the coefficient of the x- term ( - 1)

The factors are - 7 and + 6, since

- 7 × 6 = - 42 and - 7 + 6 = - 1

x² - x - 42 = (x - 7)(x + 6)

Answer:

Factor x²−x−42 using the AC method.

Step-by-step explanation:

What is the factored form of the following expression?

x^2 - x - 42

STEPS:

x²-x-42

Break the expression into groups:

=(x²+6x)+(-7x-42)

Factor out x from x²+6x: x(x+6)

Factor out -7 from -7-42: -7(x+6)

=x(x+6)-7(x+6)

Factor out common term x+6

Answer:

3 times 10

Step-by-step explanation:

Answer:

35 ft²

Step-by-step explanation:

We set up a system of linear equations describing this rug and then solve it:

Perimeter:  P = 2L + 2W

L = (1  2/5)W = 1.4W

Going back to the Perimeter equation, and knowing that P here is 24 ft, we have:

24 ft = 2(1.4W) + 2W, or 2.8W + 2W, or 4.8W.

Solve for W (width) by dividing both sides of this equation by 4.8:

W = 24 ft  / 4.8  = 5

The width of the rug is 5 ft; the length is 1.4(5 ft), or 7 ft.

Thus the area of the rug is A = L * W, or A = (7 ft)(5 ft) = 35 ft²

Answer:

number 16 is correct nice job!  number 17 is J=PM/300

Step-by-step explanation:

For 16 the answer is option D

For 17 the correct option is D

See the attached figure

Answer:

-2

Step-by-step explanation:

slope is equal to:       y2-y1

                                _______ =

                                   x2-x1

  6-2            4

______ = _____ = -2

-7-(-5)          -2

have a good day!!!!!!!!!

The total cost of the regular price for a group of x people is represented by the equation C = 22x, while the total cost of the group special is represented by C = 18x + 24.

Equations for Total Cost

1. Total Cost of Regular Price: Ms. Chen can calculate the total cost for x people with the regular price by using the equation C = 22x. Here, C represents the total cost, and x is the number of people in the group.

2. Total Cost of Group Special: To calculate the total cost for x people with the group special, Ms. Chen would use the equation C = 18x + 24. C is still the total cost, x is the number of people, and 24 represents the additional fee for the private room.

By comparing the results of both equations for a specific number of people, Ms. Chen can determine which option is more cost-effective.

Answer:

-3/4 g =x

Step-by-step explanation:

g=-4x/3

Multiply each side by 3

3g = -4/3 x *3

3g = -4x

Divide each side by -4

3/-4 g = -4x/-4

-3/4 g =x

Answer:

7.25

Step-by-step explanation:

2 7/8 + 3 2/8 * 1 1/8 = 7.25

Answer:

7 1/4

Step-by-step explanation:

exact form is 29/4 but if you wanted to simplify it the mixed number form is 7 1/4

Answer:

its A i just took the test

Step-by-step explanation:

Answer: The correct answer is 24 square units.

Step-by-step explanation:

Answer:

it is 5/6

Step-by-step explanation:

it's easy. There are 5 numbers that are greater than 2.

Answer: the answer is 2/3 i took the test

Answer:

Step-by-step explanation:

f(x) = - 4x + 3

x = - 5

f(- 5) = - 4.(- 5) + 3

f(- 5) = 20 + 3

f(- 5) = 23

Alternative D

I hope I helped you.

Answer:

the answer is D

Step-by-step explanation:

Answer:

1. Area = 113.1 square units

2. Area = 28.27 square units

3. Area of Shaded = 22.27 square units

Step-by-step explanation:

1.

Area of the circle is given by the formula   [tex]A=\pi r^2[/tex]

where A is the area and r is the radius

In our case the radius is 6 units, thus we have:

[tex]A=\pi r^2\\A=\pi (6)^2\\A=\pi *36\\A=113.1[/tex]

Area = 113.1 square units

2.

When we have the angle given in radians, the area of sector is given by the formula   [tex]A=\frac{1}{2}r^2\theta[/tex]

Where  [tex]\theta[/tex]  is the central angle ( in our case [tex]\theta = \frac{\pi}{2}[/tex] and r is the radius (it is 6)

Plugging in these info into the formula we have area of sector:

[tex]A=\frac{1}{2}r^2\theta\\A=\frac{1}{2}(6)^2(\frac{\pi}{2})\\A=\frac{1}{2}*36*\frac{\pi}{2}\\A=28.27[/tex]

Area = 28.27 square units

3.

Area of shaded region = Area of Sector - Area of Triangle

We know area of sector is 28.27

Since the angle is 90 degrees, we have a right triangle, we can use the pythagorean theorem to find the height of the triangle, CE.

Thus

[tex]DC^2+CE^2=DE^2\\3^2+CE^2=5^2\\9+CE^2=25\\CE^2=25-9\\CE^2=16\\CE=4[/tex]

The area of triangle is  [tex]A=\frac{1}{2}bh[/tex]

where b is the base (in our case it is DC = 3 ) and h is the height (in our case it is CE, which is 4). Plugging into the formula we have the area of triangle as:

[tex]A=\frac{1}{2}bh\\A=\frac{1}{2}(3)(4)\\A=6[/tex]

Area of Shaded = 28.27 - 6 = 22.27 square units

Answer:

<3 and <6 are Vertical angle and is the correct answer

Step-by-step explanation:

1) Vertical angle is The angles opposite each other when two or more line intersect each other or crosses each other.

Hopes this helps.

Answer:

Step-by-step explanation:

Vertical angles: each of the pairs of opposite angles made by two intersecting lines.

The vertical angles from the picture:

∡1 and ∡4

∡2 and ∡5

∡3 and ∡6

The Answer is hundredths

this is an example, but it's not drawn accurately and not to scale

use a protractor and ruler for yours

Answer:

You can make 11 recipes with 7 1/2 cups of walnuts

Answer:

Step-by-step explanation:

11 1/4 but it says the number of full recipes so it would be 11

x=4.80989686

by simplifying both sides of the equation, then isolating the variable.

Answer:

x= - 9

Step-by-step explanation:

This problem bothers on the law of indices

Given the expression

3^4x=27^x-3

We can also simplify it using the law

3^4x= 3^3(x-3)

Equating the powers we have

4x= 3(x-3)

Opening bracket

4x= 3x-9

Collecting like terms we have

4x-3x=-9

x=-9

Indices are used to show numbers that have been multiplied by themselves. They can also be used to represent roots, such as the square root, and some fractions. The laws of indices enable expressions involving powers to be manipulated more efficiently than writing them out in full.

Answer:

You can make one triangle with these lengths

Step-by-step explanation:

we know that

The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side

Verify if the lengths satisfy the triangle inequality theorem

1) 2+1 > 2

3 > 2 ------> is true

2)2+2 > 1

4 > 1 -----> is true

so

The lengths  satisfy the triangle inequality theorem

therefore

You can make one triangle with these lengths

False, .0034 is 1/10 of .034

The statement that 0.034 is 1/10 of 0.0034 is incorrect. In fact, 0.034 is 10 times larger than 0.0034. Thus, it's correct to say 0.0034 is 1/10 of 0.034.

No, the statement that 0.034 is 1/10 of 0.0034 is not correct. When comparing the two numbers, we can see that 0.034 is actually 10 times larger than 0.0034, not 1/10. To confirm this, we can perform the division operation: 0.034 ÷ 0.0034 = 10. Therefore, we can say that 0.0034 is 1/10 of 0.034, but not the other way around.

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Answer:

Step-by-step explanation:

(1/4) (2-5x+6)

=(1/4)(8-5x)

= 8/4 - 5x/4

=1/2 - 5x/4

Bred has a total of 771 ways to paint the wall, taking into account that he can use at most two colors for the stripes or just one.

The subject matter pertains to the field of combinatorics, a branch of mathematics dealing with combinations and permutations. The task requires finding the number of ways to paint 8 stripes on a wall using up to 2 colors from a selection of 3 colors, namely: blue, red, and white. Since we have more paint than stripes, the limiting factor in this problem is the number of stripes, not the quantity of paint.

As Bred can use at most two colors for the stripes, the combinations we can have with two colors are: blue and red, blue and white, red and white. In each of these combinations, there are 2^8 (or 256) ways to paint 8 stripes (exploration of all binary possibilities). So, for three combinations, it will be 3*256 = 768 ways.

Now, let's look at the single color options. He can also paint the stripes all in one color, but since he has only three colors, he has three ways for this.

Hence, in total, Bred has 768 (from two-color combinations) + 3 (from single color option) = 771 ways to paint a wall.

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