What is the name of each of the two blue points in the hyperbola below?
A. Focus
B. Center
C. Vertex
D. Directrix

See attachment for the axis of symmetry and maximum point.

To plot the axis of symmetry:

Therefore, the maximum value occurs at the vertex, given by (h,k)=(-2,8).

So, see attachment for the axis of symmetry and maximum point.

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Answer:

372 in^3.

Step-by-step explanation:

The volume of the first prism =  9*6*3

= 162 in^3.

Volume of second prism

=  10*7*3

= 210 in^3.

Total vol = 162 + 210

= 372 in^3.

The required volume of the composite prism is 372 cubic inches,

Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.

here,
To determine the volume of the composite prism,
As we can see there is two rectangular prisms,
Calculate the volume of two individual prisms and add their volume to the composite volume of the figure.

The volume of the first prism
= lenght × width × height
=  9 × 6 ×3 = 162 in³

The volume of the second prism
= lenght × width × height
=  10 × 7 ×3 = 210 in³

The total volume of the composite figure = 162 + 210 = 372 in³.

Thus, the required volume of the composite prism is 372 cubic inches,

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The rate of the current is 6 mile/hour.

In this context, the rate is tantamount to speed o velocity in a linear motion. The S.I unit will be mile per hour.

Given that a boat takes 10 hours to sail a distance of 100 nautical miles with the current. The rate at which the boat move will be

The rate R1 = 100/10

R1 = 10 mile/hour

And when it moves against the current, it takes the boat 25 hours to sail the same distance. The rate at which the boat move will be

The rate R2 = 100/25

R2 = 4 mile/hour

The rate of the current R will be the difference between the two calculated rate. That is,

R = R1 - R2

R = 10 - 4

R = 6 mile/hour

Therefore, the rate of the current is 6 mile/hour.

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Answer:

60

Step-by-step explanation:

Since this angle is unknown, let's just represent it with the variable "x". So the supplement angle of "x" is essentially, the value of the angle that we need to add to "x" to get 180. In other words let's just say that the supplement angle is "y". This means that: [tex]x+y=180[/tex]. If we subtract x from both sides we can represent "y" or the supplement angle as: [tex](180-x)[/tex].

Since it's 660 less than 6 times it's own supplement let's first multiply the supplement by 6

[tex]6(180-x) = 1,080-6x[/tex]

Now let's subtract 660 from it, since it's 660 less

[tex](1,080 - 6x) - (660) = 420 - 6x[/tex]

This value should be equal to the angle, which is represented as "x". So let's set it equal to x

[tex]420-6x=x[/tex]

Add 6x to both sides

[tex]420=7x[/tex]

Divide both sides by 7

[tex]60 = x[/tex]

The variable used to predict another variable in a regression analysis (usually x) is called the independent variable.

The regression analysis is used to determine the effect on the dependent variable with every one unit change in the independent variable.

The dependent variable is also known as response.

and the independent variable is also known as predictor.

In case of simple linear regression there is only one independent variable and in cases of multiple linear regression there are more than one independent variables.

The general form of simple linear regression is:

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

The general form of multiple linear regression is:

[tex]y=c+m_1x_1+m_2x_2+...+m_nx_n[/tex]

The dependent variable are usually denoted by the letter "y" and the independent variables are usually denoted by the letter "x".

Therefore, the variable used to predict another variable in a regression analysis (usually x) is called the independent variable.

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Step-by-step explanation:

its 29 9x4=29 9+4=13 13+4=17

Answer:

[tex]a.(fog)(x) = 7x + 7 \\ b.(gof)(x) = 7x + 1 \\ c.(fog)(4) = 35 \\ d.(gof)(4) = 29[/tex]

Step-by-step explanation:

Greetings !

a. (fog)(x)= f[g(x)] = 7(x+1)

b. (gof)(x) = g[f(x)] =7x+1

c. (fog)(4)=7(4)+7=28+7=35

d. (gof)(4)= 7(4)+1=28+1=29

(fog)(x)

(gof)(x)

(fog)(4)

(gof)(4)

According to Sturge's rule, number of classes or bins recommended to construct a frequency distribution is k ≈ 7

Sturge's Rule: There are no hard and fast guidelines for the size of a class interval or bin when building a frequency distribution table. However, Sturge's rule offers advice on how many intervals one can make if one is genuinely unable to choose a class width. Sturge's rule advises that the class interval number be for a set of n observations.

Given,

n = 66

We know that,

According to Sturge's rule, the optimal number of class intervals can be determined by using the equation:

[tex]k=1+log_{2} n[/tex]

Here, n is equal to 66 and by substituting the value to the equation we get:

[tex]k=1+log_{2} (66)[/tex]

k = 7.0444

k ≈ 7

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========================================

Work Shown:

|3x-12| ≥ 6

3x-12 ≥ 6 or 3x-12 ≤ -6  ..... see note below

3x ≥ 6+12 or 3x ≤ -6+12

3x ≥ 18 or 3x ≤ -6+12

3x ≥ 18 or 3x ≤ 6

x ≥ 18/3 or x ≤ 6/3

x ≥ 6 or x ≤ 2

x ≤ 2 or x ≥ 6

----

Note: if |A| ≥ B, then A ≥ B or A ≤ -B where B is some positive number.

Example: |x| ≥ 5 means either x ≥ 5 or x ≤ - 5

Answer:

The answer is C

Step-by-step explanation:

Answer:

Step-by-step explanation:

the weight of the substance after 28 years is 8 grams.

We have that the half life of a substance is defined as the time required for the substance to decrease by half

The formula for calculating the half - life of a material is given as;

[tex]N(t) = N0 (\frac{1}{2} )^\frac{t}{t^\frac{1}{2} }[/tex]

Where

Substitute into the formula

N(t) = 128 × (0. 5) ^28/ 7

N (t) = 128 × ( 0. 5) ^ 4

N(t) = 128 × 0. 0625

N(t) = 8 grams

Thus, the weight of the substance after 28 years is 8 grams.

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625 ml is the amount of smoothie is left for Ahmed to drink.

According to the statement

we have given that the

Ahmed made a 625 ml fruit smoothie in his blender and out of this he gave

320 milliliters of the smoothie to his brother and we have to find that the

How much smoothie is left for Ahmed.

So, For this purpose,

The total smoothie = 625 ml

Smoothie he gave to his brother = 320 ml

Now, we have to find the Amount of smoothie left for ahmed.

So, Smoothie left for ahmed = 625 ml - 320 ml

Smoothie left for ahmed = 305 ml

So, 625 ml is the amount of smoothie is left for Ahmed to drink.

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Disclaimer: This question was incomplete. Please find the full content below.

Question:

Ahmed made a fruit smoothie in his blender, shown below. He gave 320 milliliters of the smoothie to his brother. How much smoothie is left for Ahmed to drink? check the image below.

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Answer:

Step-by-step explanation:

To graph by hand I would first convert both equations into y=mx+b.

We start with:

[tex]\left \{ {{2x-2y=4} \atop {x+2y=8}} \right.[/tex]

Solve for y for 2x-2y=4

[tex]2x+2y=4\\2y=4-2x\\y=2-x[/tex]

Solve for y for x+2y=8

[tex]x+2y=8\\2y=8-x\\y=4-\frac{x}{2}[/tex]

Giving the new but equal system of equations:

[tex]\left \{ {{y=2x-x} \atop {y=4-\frac{x}{2} }} \right.[/tex]

From this point on you can graph the two functions to find where the two lines intersect, thats your solution.

I've gone ahead and graphed it on desmos for you

The answer is 38cm.

The formula used is perimeter of rectangle so in this case it will be 2(PQ+QR).

So,

=2×(12+7)

=2×19

=38cm

Answer:

a) √80 ≈ 9

b) √27 ≈ 5

c) √110 ≈ 10

d) √0.03 ≈ 0.2

e) √0.12 ≈ 0.3

Step-by-step explanation:

80 is close to 81

Therefore, √80 can be estimated as √81

√81 = 9

[tex]\Large\boxed{\sqrt{80}\approx9 }[/tex]

27 is close to 25

Therefore, √27 can be estimated as √25

√25 = 5

[tex]\Large\boxed{\sqrt{27}\approx5 }[/tex]

110 is close to 100

Therefore, √110 can be estimated as √100

√100 = 10

[tex]\Large\boxed{\sqrt{110}\approx10 }[/tex]

0.03 is close to 0.04

Therefore, √0.03 can be estimated as √0.04

√0.04 = 0.2

[tex]\Large\boxed{\sqrt{0.03}\approx0.2 }[/tex]

0.12 is close to 0.09

Therefore, √0.12 can be estimated as √0.09

√0.09 = 0.3

[tex]\Large\boxed{\sqrt{0.12}\approx0.3 }[/tex]

Hope this helps!! :)

Please let me know if you have any questions

There are 91 such ways in whih the volunteers can be assigned if two of them cannot be assigned from 14 volunteers.

Given that a school dance committee has 14 volunteers and each dance requires 3 volunteers at the door, 5 volunteers on the floor and 6 on floaters.

We are required to find the number of ways in which the volunteers can be assigned.

Combinations means finding the ways in which the things can be choosed to make a new thing or to do something else.

n[tex]C_{r}[/tex]=n!/r!(n-r)!

Number of ways in which the volunteers can be assigned is equal to the following:

Since 2 have not been assigned so left over volunteers are 14-2=12 volunteers.

Number of ways =14[tex]C_{12}[/tex]

=14!/12!(14-12)!

=14!/12!*2!

=14*13/2*1

=91 ways

Hence there are 91 such ways in whih the volunteers can be assigned if two of them cannot be assigned.

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The temperature at 9 AM is approximately 10 degrees. Neither of the answers are correct. (Correct choice: E)

Sinusoids are expressions with trascendent functions, to be more specfic, trigonometric functions, whose form is described below:

T(t) = A · sin (2π · t / T + C) + B       (1)

Where:

The temperature amplitude and the middle temperature can be found by the following expressions:

A = (t' - t'') / 2      (2)

B = (t' + t'') / 2      (3)

Where t' and t'' are maximum and minimum temperatures, in degrees.

Then, we proceed to find each constant of the sinusoidal model:

A = (45 - 7) / 2

A = 38 / 2

A = 19

B = (45 + 7) / 2

B = 52 / 2

B = 26

We assume a period of 24 hours (T = 24).

If we know that t = 0, T = 24, A = 19, B = 26, T(t) = 7, then the angular phase is:

7 = 19 · sin [(π / 12) · 0 + C] + 26

- 19 = 19 · sin C

sin C = - 1

C = π

T(t) = 19 · sin (π · t / 12 + π) + 26

Then, the temperature at 9 AM is: (t = 4)

T(4) = 19 · sin (π · 4 / 12 + π) + 26

T(4) ≈ 9.545

The temperature at 9 AM is approximately 10 degrees. Neither of the answers are correct. (Correct choice: E)

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Answer:

1 is the closest to 28/31

Step-by-step explanation:

0 is technically 28 spaces away and 1/2 is around 13 spaces away but 1 is only 3. :)

The distance from Balloon A to Balloon B, d ≈ 1,052 feet

What is distance ?

The given parameters are;

The angle at which Balloon A rises, x° = 50° above horizontal

The angle at which Balloon B rises, y° = 78° above horizontal

The (vertical) distance of Balloon A to the ground, h = 1,000 ft.

The required parameter;

The distance from Balloon A to Balloon B, d

We find the distances of the balloons from Charlie and the angle between the balloon strings, θ, then apply cosine rule

Let,

The height of the balloon strings are equal

The distance of Balloon A to the ground, h₁ = The distance of Balloon B to the ground, h₂ = 1,000 ft.

The distance of the Balloon A  from Charlie, l₁, is given as follows;

l₁ × sin(x°) = h₁

∴ l₁ = h₁/(sin(x°))

Which gives;

l₁ = 1,000 ft./(sin(50°)) ≈ 1,305.41 ft.

l₁ ≈ 1,305.41 ft.

For Balloon B, we get;

h₁ = h₂ = 1,000 ft.

∴ l₂ = 1,000 ft./(sin(78°)) ≈ 1,022.34 ft.

l₂ ≈ 1,022.34 ft

The angle between the balloon strings, θ = 180° - (x° + y°)

∴ θ = 180° - (50° + 78°) = 52°

The angle between the balloon strings, θ = 52°

By cosine rule, we have;

d = √(l₁² + l₂² - 2 × l₁ × l₂ × cos(θ))

∴ d = √(1,305.41² + 1,022.34² - 2 × 1,305.41×1,022.34 × cos(52°)) ≈ 1,052 feet

Therefore, the distance from Balloon A to Balloon B, d ≈ 1,052 feet

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Answer:

D

Step-by-step explanation:

slope = rise / run

slope = (5 - 3) / (-2 - 2)

slope = 2 / -4

slope = -2 / 4

slope = -1/2

The value of the vector will be -53. The correct option is C.

In mathematics and physics, the term "vector" is used informally to describe certain quantities that cannot be described by a single number or by a set of vector space elements.

The dot product, also known as the scalar product, is an algebraic operation that takes two sequences of integers of equal length and outputs a single number.

The given vectors are u=2i-9j and v=-5i+7j, the dot product of the vectors will be calculated as below:-

u.v = ( 2i-9j ).( -5i+7j)

u.v = -10i² + 17 (i.j) -45(i.j) -63j²

Substitute i² = 1, j² = 1 and (i.j) = 0 in the above equation.

u.v = -10 + 63

u.v = 53

Therefore, the value of the vector will be -53. The correct option is C.

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[tex]\frac{-2x^{2} +25 }{(x-2) (x-5)} ,x\neq 2,x\neq 5[/tex]  is the difference.

What is an expression?

⇒ An expression is a combination of numbers, variables, and functions (such as addition, subtraction, multiplication or division, etc.)

Calculation :

⇒   [tex]\frac{3x^{2} }{(x^{2} -7x+10)}- \frac{5x} {x-2}[/tex]

⇒   [tex]\frac{3x^{2} }{(x-2)(x-5)}- \frac{5x} {x-2}[/tex]

⇒1/(x-2) [(3x²-5x{x-5})/(x-5)]

⇒1/(x-2) [(3x²-5x²+25x)/(x-5)]

⇒1/(x-2) [ (-2x²+25x)/(x-5)]

⇒[tex]\frac{-2x^{2} +25x }{(x-2)(x-5)}[/tex]

at x=2 and x=5 the denominator becomes zero If the denominator of a fraction is zero, the expression is not a legal fraction because its overall value is undefined.

⇒   [tex]\frac{-2x^{2} +25 }{(x-2) (x-5)} ,x\neq 2,x\neq 5[/tex] is the difference

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Correct option is  B)

Cross-multiplication is helpful in Solving proportions.

Solving proportions is simply a matter of stating the ratios as fractions, setting the two fractions equal to each other, cross-multiplying and solving the resulting equation.

Method I: Draw a double-sided number line, label the parts, set up a proportion and solve.

Method II: Using any method, calculate unit rate and then calculate how many pounds you can get for $30. Method III: Graph a point to represent the original ratio.

The product of the means is equal to the product of the extremes.

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I understand the the question you are looking for is :

Cross-multiplication is helpful in:

a. quadratic equations

b. solving proportions

c. linear equations

d. word problems

please select the best answer from the choices provided a b c d

The value of the f(-8) from the given f(x) is 1/53.

According  to the statement

we have given that the value of f(x) and with the value of this we hav eto find the value of f(-8).

So, For this purpose,

The given value of f(x) :

The function f(x) is

f(x) = 1 / x^2 -11

Now we find the value of the f(-8) then

For this put Put x is -8 in the f(x) then the equation become

f(x) = 1 / x^2 -11

f(-8) = 1 / (-8)^2 -11

f(-8) = 1 / 64 -11

f(-8) = 1 / 53.

here the value becomes 1/53.

So, The value of the f(-8) from the given f(x) is 1/53.

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Answer:

They are all true

Step-by-step explanation:

1. 3² +4² = 5²

3x3 + 4x4 = 5x5

  9   +  16  =  25

25 = 25

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

2. 6² + 8² = 10²

36 + 64 = 100

100 = 100

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

3. 9² + 12² = 15²

81 + 144 = 225

225 = 225

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

4. 5² +12² =13²

25 + 144 = 169

169 =169

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

Answer:

Step-by-step explanation:

Simplify both sides of the equation:

4 (2 + a) = 24

( 4 )( 2 ) + ( 4 )( a )  =  24   (Distribute)

8 + 4a = 24

4a  +  8 = 24

subtract 8 from both sides:

4a + 8 − 8 = 24 − 8

4a = 16

Divide both sides by 4:

4 a/4     =     16/4

a  =  4

Multiple bracket out first:

4 x 2 =8

4 x a = 4a

8 +4a = 24

-8

4a. = 16

÷4

a = 4

Hope this helps!

The answer is y - 3 = -1/2 (x - 2).

First, let's find the slope.

Then, the point slope form will be :

Answer: y=-0,5x+4.

Step-by-step explanation:

[tex]A(-4;6)\ \ \ \ B(2;3)\\Straight \ line\ equation\ is:\\\displaystyle\\\boxed {\frac{x-x_1}{x_2-x_1} =\frac{y-y_1}{y_2-y_1}} \\\frac{x-(-4)}{2-(-4)}=\frac{y-6}{3-6} \\ \frac{x+4}{2+4}=\frac{y-6}{-3} \\\frac{x+4}{6}=\frac{y-6}{-3} \\ Multiply\ the\ left\ and\ right\ sides\ of\ the\ equation \ by\ -3:\\\frac{-(x+4)}{2} =y-6\\-0,5x-2=y-6\\y=-0,5x+4.[/tex]