Complete the square to transform the quadratic equation into the form (x –p)2= q.X2-8x -10 = 18

Factor 3x^3−12x

3x^3−12x

=3x(x+2)(x−2)

Answer:

3x(x+2)(x−2)

3x^3 - 12x //Common factor: 3x

3x (x^2 - 4)

3x (x - 2) (x + 2)

Answer: C

//Hope this helps.

Answer:

The radius is increased by 1.2599 times the original size.

Step-by-step explanation:

The volume is 3 dimensional whereas the radius is one dimensional.

Therefore the factor for the  radius will be the cube root of the factor for the volume.

So the radius is increased by 1.2599.

Answer:

Option C

Step-by-step explanation:

The first number is - 3, then we have a blank and the third number is - 1 1/8

In order for the numbers to be arranged from least to greatest, the number in the center should be greater than -3, and lesser than -1 1/8

Note that for negative numbers, the larger the constant, the smaller the number. i.e. -5 is smaller than -4.

So from the given options, the only number that is greater than -3 and lesser than -1 1/8 is - 2 1/4

So, option C gives us the correct answer to have the numbers ordered from least to greatest.

Answer:

96sqrt(3)

Step-by-step explanation:

Simplest and most intuitive way is to find area of 1 triangles and multiply it by 6.

Area of one triangle:

base = 8 and a = 4sqrt(3)

Area of 1 trangle = ba/2

Area of base of hexagon = 6 times that.

Answer:

The correct answer is "Study of tree rings and associated geology shows that the Earth is more than 12,429 years old"

Step-by-step explanation:

While tress have been growing long enough to prove the earth is more than 12,000 years old, it is not able to prove much longer than that. Luckily geology is able to show is that Earth is over 4.6 billions years old. As a result, the above is the only true statement.

The age of the Earth is approximately 4.5 billion years, as determined by radioactive dating methods and supported by other geological evidence. Although not directly determining the Earth's age, the study of tree rings provides valuable information about climate conditions in specific periods.

The scientific study of tree rings, known as dendrochronology, can provide valuable information about the Earth's climate in different periods. However, it doesn't directly determine the overall age of the Earth.

Conversely, radioactive dating methods, like uranium-238 dating or rubidium-strontium dating, have been used to determine the Earth's age by dating the oldest rocks and minerals on Earth's crust. For example, the Jack Hills zircons from Australia were found by uranium-lead dating to be nearly 4.4 billion years old.

Using these dating methods in connection with the study of tree rings and other geological evidence, scientists have estimated that the age of the Earth is approximately 4.5 billion years.

This age is significantly older than what could be derived from tree rings alone, as the oldest living trees, like the Methuselah tree, are estimated to be just over 4,800 years old.

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Answer:

B

Step-by-step explanation:

first you wanna multiply and sehow many mutiplesof 4 will go into 8.

The equal amount of bird food put into the 4 feeders is 7 / 32 pounds.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Mia has 7/8 pounds of bird food. She puts an equal portion into 4 bird feeders.

The amount of bird food for each feeder will be calculated as,

Bird food = (7/8) / (4)

Bird food = [ 7/ (8 x 4 )]

Bird food =  7 / 32 pounds

Therefore, the equal amount of bird food put into the 4 feeders is 7 / 32 pounds.

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Step-by-step explanation:

Inverse is x · y = k

Since k = 20, then you are looking for x,y coordinates whose product is 20.

Answer:

The following are possible solutions:

[tex]\left\begin{array}{c|c|c}\underline{\quad x\quad }&\underline{\quad y\quad }&\underline{\qquad k\qquad }\\1&20&1\cdot 20=20\\2&10&2\cdot 20=20\\4&5&4\cdot 5=20\\10&2&10\cdot 2=20\\20&1&20\cdot 1=20\end{array}\right[/tex]

(See attached for graph)

Answer:

M = 4S

In three years

M + 3 = 3(S + 3)

So you put the 4S in to substitute for the M.

4S + 3 = 3(S + 3)

4S + 3 = 3S + 9

S = 6

If the son is 6, the father must be 24.

We can check this by adding three to both ages. Then, the son will be 9 and the father will be 27, which is three times 9.

Step-by-step explanation:

Answer:

10 × 4 – (5 – 3) + 2

10 × 4 – 2 + 2

40 – 2 + 2

38 + 2

40

Step-by-step explanation:

To solve;

10 × 4 – (5 – 3) + 2

We use BODMAS

We start by removing brackets, to get

10 × 4 – 2 + 2

Then we proceed to multiplication to get;

40 – 2 + 2

Then subtraction to get;

38 + 2

The answer is 40

The correct answer to evaluate  is  10 × 4 – (5 – 3) + 2 is 40

The correct way to evaluate the expression 10 × 4 – (5 – 3) + 2 is as follows:

10 × 4 – (5 – 3) + 2

= 40 – (5 – 3) + 2

= 40 – 2 + 2

= 38 + 2

= 40

Therefore, the correct evaluation is 40.

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Answer:

Choice B is correct

Step-by-step explanation:

The eccentricity of the conic section is given as 4 and thus the conic section is a hyperbola. Hyperbolas are the only conic sections with an eccentricity greater than 1.

Next, the directrix of this hyperbola is located at y = -6 implying that the hyperbola will be opening upwards. Consequently, the polar equation of this hyperbola will be of the form;

[tex]r=\frac{k}{1-4sin(theta)}[/tex]

The value of k in the numerator is the product of eccentricity and the absolute value of the directrix;

k= 4*6 = 24

The polar equation is thus given by alternative B

Answer:

b on edge

Step-by-step explanation:

Answer:

W = 16 in

Step-by-step explanation:

P = 2L + 2W

56 = 2(12) + 2W

56 = 24 + 2W

56-24 = 2W

32 = 2W

W = 32/2

W = 16 in

Best regards

it should be the radius

Answer:

A) 3 1/3

Step-by-step explanation:

5 x 2 = 10

10/3= 3 with a remainder of 1. That gives you 3 1/3

Answer:

Step-by-step explanation:

IF you calculate it right it is 3.3333333 or 3 1/3

Answer:

10.1

Step-by-step explanation:

i divided the numbers now mark brainliest if its wrong or right

Find the midpoint of the chord:

9 / 2 = 4.5 cm

Now we can find the radius:

Radius = √(4.5^2 + 3.7^2)

Radius = √(20.25 + 13.69)

Radius = √33.94

Radius = 5.8 cm

Answer:

<1:88

<2:65

<3:115

Step-by-step explanation:

Since we know that a line and the inside of a triangle equals 180 than we can use that to identify the missing angles.Using what we know about a line we can subtract 92 from 180 and we get 88, knowing that angle 1(<1)is the only angle that rest on that line than we know that <1 is 88.(to check this you can add 92 plus 88 and you get 180)Then switching hands,we can now figure out the interior missing angle 2(<2).There are two ways you can do this,Add all the interior angles together and then subtract from 180(88+57=145 then 180-145=35)or you can subtract all the known interior angles and then the answer is your missing angle(180-57-88=35).Now switching again, in order to find <3 then you have to find which number falls on the angle which we are looking for.Which would be 35 or <2.Now all you have to do is subtract 180-35=145

Part B:

I agree with the other person below⬇⬇⬇

Answer:

Step-by-step explanation:

(A) From the given figure, we have

[tex]{\angle}1+92^{\circ}=180^{\circ}[/tex] (Linear pair)

⇒[tex]{\angle}1=180^{\circ}-92^{\circ}[/tex]

⇒[tex]{\angle}1=88^{\circ}[/tex]

Thus, the measure of [tex]{\angle}1[/tex] is [tex]88^{\circ}[/tex].

Also, using the angle sum property in the given triangle, we get

[tex]{\angle}1+{\angle}2+57^{\circ}=180^{\circ}[/tex]

⇒[tex]88^{\circ}+{\angle}2+57^{\circ}=180^{\circ}[/tex]

⇒[tex]{\angle}2+145^{\circ}=180^{\circ}[/tex]

⇒[tex]{\angle}2=35^{\circ}[/tex]

Thus, the measure of [tex]{\angle}2[/tex] is [tex]35^{\circ}[/tex].

And, [tex]{\angle}2+{\angle}3=180^{\circ}[/tex]

⇒[tex]35^{\circ}+{\angle}3=180^{\circ}[/tex]

⇒[tex]{\angle}3=145^{\circ}[/tex]

Thus, the measure of [tex]{\angle}3[/tex] is [tex]145^{\circ}[/tex].

(B) Exterior angle theorem states that the exterior angle is equal to the sum of the two interior angles, thus from the given figure, we have

[tex]{\angle}1+{\angle}2=123^{\circ}[/tex]

Therefore, the relationship between the measure of [tex]{\angle}1[/tex] and  [tex]{\angle}2[/tex] to exterior angle is [tex]{\angle}1+{\angle}2=123^{\circ}[/tex].

Answer:

Step-by-step explanation:

Question 1:

For this case we must find the derivative of the following function:

[tex]f (x) = \frac {7} {x}[/tex] evaluated at [tex]x = 1[/tex]

We have by definition:

[tex]\frac {d} {dx} [x ^ n] = nx ^ {n-1}[/tex]

So:

[tex]\frac {df (x)} {dx} = - 1 * 7 * x ^ {- 1-1} = - 7x ^ {- 2} = - \frac {7} {x ^ 2}[/tex]

We evaluate in [tex]x = 1[/tex]

[tex]- \frac {7} {x ^ 2} = - \frac {7} {1 ^ 2} = - 7[/tex]

ANswer:

Option A

Question 2:

For this we must find the derivative of the following function:

[tex]f (x) = 4x + 7\ evaluated\ at\ x = 5[/tex]

We have by definition:

[tex]\frac {d} {dx} [x ^ n] = nx ^ {n-1}[/tex]

The derivative of a constant is 0

So:

[tex]\frac {df (x)} {dx} = 1 * 4 * x ^ {1-1} + 0 = 4 * x ^ 0 = 4[/tex]

Thus, the value of the derivative is 4.

Answer:

Option A

Question 3:

For this we must find the derivative of the following function:

[tex]f (x) = 12x ^ 2 + 8x\ evaluated\ at\ x = 9[/tex]

We have by definition:

[tex]\frac {d} {dx} [x ^ n] = nx ^ {n-1}[/tex]

So:

[tex]\frac {df (x)} {dx} = 2 * 12 * x ^ {2-1} + 1 * 8 * x ^ {1-1} = 24x + 8 * x ^ 0 = 24x + 8[/tex]

We evaluate for [tex]x = 9[/tex]we have:

[tex]24 (9) + 8 = 224[/tex]

Answer:

Option D

Question 4:

For this we must find the derivative of the following function:

[tex]f (x) = - \frac {11} {x}\ evaluated\ at\ x = 9[/tex]

We have by definition:

[tex]\frac {d} {dx} [x ^ n] = nx ^ {n-1}[/tex]

So:

[tex]\frac {df (x)} {dx} = - (- 1 * 11 * x ^ {- 1-1}) = 11x ^ {- 2} = \frac {11} {x ^ 2}[/tex]

We evaluate for [tex]x = 9[/tex] and we have:

[tex]\frac {11} {9 ^ 2} = \frac {11} {81}[/tex]

ANswer:

Option D

Question 5:

For this case we have by definition, that the derivative of the position is the velocity. That is to say:

[tex]\frac {d (s (t))} {dt} = v (t)[/tex]

Where:

s: It's the position

v: It's the velocity

t: It's time

We have the position is:

[tex]s (t) = 1-10t[/tex]

We derive:

[tex]\frac {d (s (t))} {dt} = 0- (1 * 10 * t ^ {1-1}) = - 10 * t ^ 0 = -10[/tex]

So, the instantaneous velocity is -10

Answer:

-10

Answer:

The required expression is 24 - 4x

Step-by-step explanation:

Given,

Initial number of stickers she has = 24,

Also, the number of stickers she used for a card = 4,

⇒ the number of stickers she used for x cards = 4x,

So, the number of stickers she left after decorating x cards = Initial number of stickers - the number of stickers used for x cards,

= 24 - 4x

Which is the required expression.

The cost per package depends on the weight of the package.

We know that a dependent variable is one which depends on some other variable or the value of the variable is calculated corresponding to the independent variable.

Generally we consider the values on the y-axis or the vertical axis as the dependent values because they are dependent upon the x-value or the value on the horizontal axis.

Here from the graph we may observe that the cost of the package depends on the weight of the package.

The cost per package depends on the weight of the package.

We know that a dependent variable is one which depends on some other variable or the value of the variable is calculated corresponding to the independent variable.

Generally we consider the values on the y-axis or the vertical axis as the dependent values because they are dependent upon the x-value or the value on the horizontal axis.

Here from the graph we may observe that the cost of the package depends on the weight of the package.

Answer:

Option B. [tex](x-4)^{2}=44[/tex]

Step-by-step explanation:

we have

[tex]x^{2}-8x-10=18[/tex]

Group terms that contain the same variable, and move the constant to the opposite side of the equation

[tex]x^{2}-8x=18+10[/tex]

[tex]x^{2}-8x=28[/tex]

Complete the square. Remember to balance the equation by adding the same constants to each side

[tex]x^{2}-8x+16=28+16[/tex]

[tex]x^{2}-8x+16=44[/tex]

Rewrite as perfect squares

[tex](x-4)^{2}=44[/tex]

Answer:

b

Step-by-step explanation:

Answer:

Shifted horizontally to the right 3 units, and shifted vertically down 2 units

Step-by-step explanation:

The parent graph of this equation is y = |x|

There are 2 translations to this graph for the equation y = |x - 3| - 2

The "x - 3" part shifts the graph to the right 3 units

The -2 shifts the graph vertically down 2 units

See below for the parent graph, and the graph of the equation we are working with

The graph of function y = |x - 3| - 2 is shown in figure.

A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.

Given that;

The equation is,

⇒ y = |x - 3| - 2

Now,

Since, The equation is,

⇒ y = |x - 3| - 2

Clearly, The equation y = |x - 3| - 2 is the translation of y = |x| with 3 units right and 2 units up.

Thus, The graph of function y = |x - 3| - 2 is shown in figure with 3 units right and 2 units up translation of y = |x|.

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Answer:

A total of zero softballs will fit into the container

Step-by-step explanation:

step 1

Find the dimensions of the base  of the prism

we know that

The volume of the prism is equal to

[tex]V=Bh[/tex]

where

B is the area of the base

h is the height of the prism

In this problem we have

[tex]V=99\ in^{3}[/tex]

[tex]h=11\ in[/tex]

substitute in the formula and find the area of the base B

[tex]99=B(11)[/tex]

[tex]B=99/11=9\ in^{2}[/tex]

the length side of the square base is the square root of the area

so

[tex]\sqrt{9}=3\ in[/tex]

we have that

The diameter of the softball 3.8 inches will fit (11/3.8=2.89 )  2 times  in the length of the container

The diameter of the softball 3.8 inches will fit  0 times  in the width of the container

so

A total of 0 times of softballs will fit  in the width of the container

therefore

A total of zero softballs will fit into the container

Answer:

Zero softballs with a diameter of 3.8 inches will fit into the container as length of the container is less the diameter of the softball.

Zero softballs can fit in length and zero softballs will fit in width.

Step-by-step explanation:

Length of the square base in rectangular pyramid = s

Breadth of the square base in rectangular pyramid = s

Height of the square base in rectangular pyramid ,l = 11 inches

Volume of the square base in rectangular pyramid ,V=[tex]99 inches^3[/tex]

Volume of the cuboid =  l × b × w

V= s × s × l

[tex]99 inches^3=s^2\times 11 inches[/tex]

s = 3 inches

Softballs with a diameter of 3.8 inches.

But the length of the container is less the diameter of the softball which means not even single ball will not be able to get into the container. So zero softballs can fit in length and zero softballs will fit in width.

Answer:    14  15-pound weights

Step-by-step explanation:

15 × 14= 210

Julio should put 14 fifteen-pound weights on the bar to achieve a total weight of 210 pounds.

Julio wants to have a total of 210 pounds on the barbell. Since each weight he will add is 15 pounds, we simply need to divide the total desired weight by the weight of one plate to determine the number of plates required.

Here is the calculation:

Therefore, Julio should put 14 fifteen-pound weights on the bar to reach a total of 210 pounds.

Answer:

Option B. 36

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form [tex]y*x=k[/tex] or [tex]y=k/x[/tex]

The graph of the figure represent an inverse variation

so

In this problem

Constant=Height*Width

Take any point in the graph

example -----> the point (4,9)

Constant=4*9=36

Answer:

8

Step-by-step explanation:

So a square is equal on all sides if I'm correct so. The area is pretty much the length x width. So 8 times 8 equals 64.

Hope this helps, have a good day

s = 8cm (Answer A)

Step-by-step explanation:

The area of a square, A, is the square of the length of any one side:

A = s².

If A = 64 cm², then 64 cm² = s².

Taking the square root of both sides yields s = 8cm (Answer A)

Answer:

Choice D is correct

Step-by-step explanation:

The first step is to write the polar equation of the conic section in standard form by dividing both the numerator and the denominator by 2;

[tex]r=\frac{3}{1-cos(theta)}[/tex]

The eccentricity of this conic section is thus 1, the coefficient of cos θ. Thus, this conic section is a parabola since its eccentricity is 1.

The value of the directrix is determined as;

d = k/e = 3/1 = 3

The denominator of the polar equation of this conic section contains (-cos θ) which implies that this parabola opens towards the right and thus the equation of its directrix is;

x = -3

Thus, the polar equation represents a parabola that opens towards the right with a directrix located at  x = -3. Choice D fits this criteria

Answer: Yes. On average, it takes about 455 days for 1 person to throw away 1 ton of garbage, so just over 1 year.

Step-by-step explanation: The average person throws away 4.4 pounds of trash daily. So, the way to figure this out is 2,000 divided by 4.4 to find out the number of days it would take to throw away 2,000 pounds of trash.

79-y=2y+22

Add y on both sides

79=3y+22

Subtract 22 from both sides

57=3y

Divide by 3 on both sides

19=y

Wouldn't he be making $1,000 a week again? Since it was reduced by 10% but then raised by 10%.....

Answer:

x = 69  and  y = [tex]23\sqrt{3}[/tex]

Step-by-step explanation:

Firstly the hypotenuse is the side opposite the 90 degree angle. So hypotenuse is [tex]46\sqrt{3}[/tex]

Since the angle given is 30 degree, with respect to this angle, the side length y is opposite and the side length x is adjacent.

Now, we can use trigonometric ratios to solve for x and y. Sine is defined as  [tex]sin\theta=\frac{Opposite}{Hypotenuse}[/tex] and Cos is defined as  [tex]Cos\theta=\frac{Adjacent}{Hypotenuse}[/tex]

Hence, we can write:

[tex]Sin(30)=\frac{y}{46\sqrt{3} }\\y=46\sqrt{3}*Sin30 \\y=46\sqrt{3}*\frac{1}{2}\\y=23\sqrt{3}[/tex]

Also, we can figure out:

[tex]Cos(30)=\frac{x}{46\sqrt{3} }\\Cos(30)*46\sqrt{3}=x\\ x=\frac{\sqrt{3} }{2}*46\sqrt{3} \\x=\frac{46*3}{2}\\x=69[/tex]

2nd answer choice is right.

ANSWER

[tex]x = 69,y = 23 \sqrt{3} [/tex]

EXPLANATION

Recall and use the mnemonics SOH CAH TOA.

We use the cosine ratio to find x.

[tex] \cos(30 \degree) = \frac{adjacent}{hypotenuse} [/tex]

[tex] \cos(30 \degree) = \frac{x}{46 \sqrt{3} } [/tex]

[tex] \frac{ \sqrt{3} }{2} = \frac{x}{46 \sqrt{3} } [/tex]

Cross multiply,

[tex]2x = 46 \sqrt{3} \times \sqrt{3} [/tex]

[tex]2x = 46(3)[/tex]

[tex]x = 23(3)[/tex]

[tex]x = 69[/tex]

We use the sine ratio, to find y.

[tex] \sin(30 \degree) = \frac{opposite}{hypotenuse} [/tex]

[tex]\sin(30 \degree) = \frac{y}{46 \sqrt{3} } [/tex]

[tex] \frac{1}{2} = \frac{y}{46 \sqrt{3} } [/tex]

Solve for y.

[tex] \frac{1}{2} \times 46 \sqrt{3} = y[/tex]

[tex]23 \sqrt{3} = y[/tex]

Therefore,

[tex]x = 69,y = 23 \sqrt{3} [/tex]

Answer:

384√3 in²

Step-by-step explanation:

Given in the question a regular 6 sided polygon

To find it's area you have to use the following formula

Perimeter = the sum of the lengths of all the sides

Suppose length of one side = x

Apothem = a segment that joins the polygon's centre to the midpoint of any side that is perpendicular to that side = 8√3

Since the polygon have 6 sides so

perimeter = 6x

x = 2(8)

x = 16

perimeter = 6(16) = 96 in

plug values in the formula of area

384√3 in²

Answer:

= 384√3 In²

Step-by-step explanation:

The polygon is a hexagon ; thus the angle subtended by each side at the center will be given by;

θ = 360/6

 = 60°

Therefore; we can calculate the length of each side;

Tan θ = opp/Adj

Tan θ = x /8√3

 Tan 30 = x /8√3

Therefore; 1/√3 =x /8√3

x = 8√3× 1/√3

   = 8

The length of each side is 8 × 2 = 16 In

The area of the polygon will be;

Area of one triangle multiplied by the number of a triangle;

= 1/2 × 16 × 8√3 ×6