Based on the length sir the segments in the hyperbola below, how long is the transverse axis?

Answer:

mother age 37

sons age 12

The equation 2•x² + 4•y² + 8•x - 16•y + F = 0, at a value of F is the graph of an ellipse when we have;

a. A value of F that results in the equation of an ellipse is; F = 23

b. A point on the ellipse is ((-2), 2.5)

The equation of an ellipse can be presented as follows;

[tex] \frac{(x - h) ^{2} }{ {a}^{2} } + \frac{(y - k) ^{2} }{ {b}^{2} } = 1[/tex]

The given equation can be presented as follows;

2•x² + 4•y² + 8•x - 16•y + F = 0

Collecting like terms, gives;

2•(x² + 4•x) + 4•y² - 16•y + F = 0

Adding a constant value to both sides, we get;

2•(x² + 4•x + 4) + 4•y² - 16•y + 16 + F = 24

2•(x + 2)•(x + 2) + (2•y - 4)•(2•y - 4) + F = 24

2•(x + 2)² + 4•(y - 2)² + F = 24

2•(x + 2)² + 4•(y - 2)² + F - 23 = 24 - 23 = 1

When F = 23, we have;

2•(x + 2)² + 4•(y - 2)² + 23 - 23 = 1

Which gives;

[tex] \mathbf{\frac{(x + 2) ^{2} }{ \left( {\frac{1}{ \sqrt{2} }} \right)^{2}} + \frac{(y - 2) ^{2} }{ \left( {\frac{1}{ 2} } \right)^{2}} } = 1[/tex]

Where;

b) A point on the ellipse can be found as follows;

When x = -2

2•((-2) + 2)² + 4•(y - 2)² = 1

0 + 4•(y - 2)² = 1

y - 2 = √(1/4) = 1/2

A point on the ellipse is therefore;

When y = 2

2•(x + 2)² + 4•(2 - 2)² = 1

2•(x + 2)² + 0 = 1

2•(x + 2)² = 1

(x + 2)² = 1/2

x + 2 = √(1/2)

x = √(1/2) - 2

Another point on the ellipse is therefore;

((√(1/2) - 2), 0)

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Option C. The correct statement about spatial relationshipo is that Spatial terms such as above, below, behind, and under are used to describe objects in space.

These are the types of relationships that are used to relate objects to the location of somethings else. It makes use of words like under, above etc.

It is one of the knowledge that children need in the preoperational stage to learn how to use logical operations.

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Answer:

10

Step-by-step explanation:

[tex]\boxed{\textsf{If }y=x^n,\: \textsf{then }\dfrac{\text{d}y}{\text{d}x}=nx^{n-1}}[/tex]

Given equation:

[tex]2y=x^3+2x^2[/tex]

Isolate y by dividing both sides by 2:

[tex]\implies y=\dfrac{1}{2}x^3+x^2[/tex]

Differentiate with respect to x:

[tex]\implies \dfrac{\text{d}y}{\text{d}x}=3 \cdot \dfrac{1}{2}x^{3-1}+2 \cdot x^{2-1}[/tex]

[tex]\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{3}{2}x^2+2x[/tex]

Finally, substitute x = 2 into the differentiated equation:

[tex]\begin{aligned} \implies \dfrac{\text{d}y}{\text{d}x} & =\dfrac{3}{2}(2)^2+2(2)\\\\ & = \dfrac{3}{2}(4)+4\\\\ & = \dfrac{12}{2}+4\\\\ & = 6+4\\\\ & = 10\end{aligned}[/tex]

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The value of x from the figure is 70°

It is important to note that alternate angles are equal and angles in a triangle sum up to 180°

We then have that,

x + 50 + 60 = 180 °

x + 110 = 180°

Make 'x' subject

x = 180 - 110

x = 70 °

Thus, the value of x from the figure is 70°

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The correct trigonometry formula to solve for x in the right angled triangle is sin(62°) = 18 / x

An equation is an expression that shows the relationship between two or more variables and numbers.

Trigonometric ratio is used to show the relationship between the sides and angles of a right angled triangle.

Hence:

sin(62°) = 18 / x

The correct trigonometry formula to solve for x in the right angled triangle is sin(62°) = 18 / x

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Answer:

-42

Step-by-step explanation:

Assuming you want the dot product,

(8)(-6)+(2)(3)= -42

Answer:

20% increase

Step-by-step explanation:

To find the percent increase, use this formula

New value - original value

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

original value

114-95

-----------

95

19

---- = .2

95

.2 is 20%, so it is a20% increase

Based on the information, it can be inferred that payment option A means a payment of $450, while option B means a payment of $300.

The payment options contemplated by the employer are distributed as follows:

Option A

Option B

Note: This question is incomplete because there is some information missing. Here is the missing information:

Complete the tables to show how much money would be received for both payment options, each week, for 6 weeks.

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I don’t have an answer but by any chance did you complete the assignment?

The amount of time between interest payments is know as period.

Period is the time between when interests are paid. Period can vary depending on the terms of the investment. Periods can be yearly, quarterly, semi-annually, biweekly or weekly.

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Answer:

Step-by-step explanation:

Hello : let A(0,-6) B(8,-8)

the slope is : (YB - YA)/(XB -XA)

(-8+6)/(8-0) = -2/8=-1/4

an equation is : y=ax+b a is a slope

y = (-1/4)x +b

the line through point A (0;-6) : -6 = (-1/4)(0)+b

b = -6            the equation is : y =(-1/)4x-6

The linear equation graphed is given by:

y - 5 = 3(x - 1).

A linear function is modeled by:

y = mx + b

In which:

In point-slope form, considering a point [tex](x_0, y_0)[/tex], the equation is:

[tex]y - y_0 = m(x - x_0)[/tex]

The line goes through points (0,2) and (1,5), hence the slope is:

m = (5 - 2)/(1 - 0) = 3.

Since the line goes through point (1,5), the equation is:

y - 5 = 3(x - 1).

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When calculating the total area of this unknown figure, you should use (π - r²)/4 for the area of both the semicircle (half circle) and the larger square.

By critically observing this unknown figure, we can logically deduce that it comprises a semicircle, squares, a rectangle and a triangle. Thus, its total area should be calculated by adding the area of each of the geometric figures together.

Total area = A₁ + A₂ + A₃ + A₄

However, you should take note that the diameter of the semicircle (half circle) is equal to the side length of the larger square.

Area of a semicircle = πr²/4

Thus, the total area of both the semicircle (half circle) and the larger square is given by:

Area = πr²/4 - d²

Note: d = 2r

Area = πr²/4 - (2r)²

Area = πr²/4 - 4r²

Area = (π - r²)/4 sq. units.

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Answer:

C

Step-by-step explanation:

For lines AC and EF, line FC is a transversal.

Angles ACF and EFC are same side interior angles.

Since their measures add to 180°, then the lines are parallel.

Answer: Choice C

By evaluating the quadratic function, we will see that the differential quotient is:

[tex]\frac{f(2 + h) - f(2)}{h} = 8 + h[/tex]

Here we have the quadratic function:

[tex]f(x) = x^2 + 4x + 5[/tex]

Evaluating the quadratic equation we get:

[tex]\frac{f(2 + h) - f(2)}{h}[/tex]

So we need to replace the x-variable by "2 + h" and "2" respectively.

Replacing the function in the differential quotient:

[tex]\frac{(2 + h)^2 + 4*(2 + h) + 5 - (2)^2 - 4*2 - 5}{h} \\\\\frac{4 + 2*2h + h^2 + 8 + 4h - 4 - 8 }{h} \\\\\frac{ 2*2h + h^2 + 4h }{h} = \frac{8h + h^2}{h}[/tex]

If we simplify that last fraction, we get:

[tex]\frac{8h + h^2}{h} = 8 + h[/tex]

The third option is the correct one, the differential quotient is equal to 8 + 4.

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Using the Factor Theorem and limits, the end behavior of g(x) is that the function decreases to the left and increases to the right.

The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:

[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]

In which a is the leading coefficient.

Considering the table, the roots are given as follows:

[tex]x_1 = -4, x_2 = 5, x_3 = 12[/tex]

Hence the function is:

f(x) = a(x + 4)(x - 5)(x - 12).

f(x) = a(x² - x - 20)(x - 12)

f(x) = a(x³ - 13x² - 32x + 240).

When x = 0, y = 1, hence the leading coefficient is found as follows:

240a = 1

a = 0.004167

Then:

f(x) = 0.004167(x³ - 13x² - 32x + 240).

The end behavior is given by the limits of f(x) as x goes to infinity, hence:

Hence the end behavior is that the function decreases to the left and increases to the right.

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Given that, y varies indirectly as the square of x, the value of y when x equal 8 is 2.

Indirect variation is expressed as;

y ∝ 1/x

Given that;

y ∝ 1/x²

y = k/x²

Where k is the proportionality constant.

Given that;

First, we determine the proportionality constant.

y = k/x²

8 = k/4²

8 = k/16

k = 128

Now, we find y when x = 8

y = k/x²

y = 128 / 8²

y = 128 / 64

y = 2

Given that, y varies indirectly as the square of x, the value of y when x equal 8 is 2.

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Answer:

D = 50t

Step-by-step explanation:

we see, with every additional hour the distance increases by 50.

that means in general that the number of hours are multiplied by 50 to get the distance.

in other words, this just calculates for a vehicle going constantly 50 miles per hour the distance it is traveling.

Answer:

Well a sovial reason is that no one would no what order yo do it in, which would cause arguments

Answer:

without the order of operations, maths literally doesn't work.

Step-by-step explanation:

like whilst some equations don't rely on a particular order for solving, if you for example, don't solve brackets first, then try to multiply them by something else basically the equation breaks and you get the wrong answer. So... kids remember your BODMAS :)

The area of QOR from the given diagram is 2π square centimeters

A sector is said to be a part of a circle made of the arc of the circle along with its two radii.

The formula for calculating the area of a sector is expressed as;

A = r²β/2

where

r is the radius of the circle

β is the angle subtended

Given the following parameters

<QOR = 180 - <POQ

<QOR = 180 - 135

<QOR = 45 degrees

Determine the radius

L = rβ

π = r(π/4)

1 = r/4

r =  4

Determine the area of QOR

Area = 4²(π)/8

Area = 2π

Hence the area of QOR from the given diagram is 2π square centimeters

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The total value of the investment is $107,032.16.

The total interest earned is $53,032.16

The inheritance would last the tenure of the university.

The formula that can be used to determine the future value of the 18-year annuity is: annuity factor x amount deposited yearly

Annuity factor = {[(1+r)^n] - 1} / r

Where:

$3000 x [(1.075^18 - 1) / 0.075] = $107,032.16

Amount deposited in the course of 18 years = (3000 x 18) = 54,000

Interest earned = 107,032.16 - 54,000 = $53,032.16

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The percentage of the can that is not occupied by tennis​ balls is 33.33%.

Given:

Radius of cylinder=3.4cm

First step

Height of cylinder=3.4×2×6

Height of cylinder=40.8 cm

Second step

Volume of cylinder=(3.4)^2×40.8

Volume of cylinder=471.648

Volume of tennis=6×4/3×(3.4)^3

Volume of tennis=314.432

Third step

Percentage=471.648-314.432/471.648×100

Percentage=33.33%

Therefore the percentage of the can that is not occupied by tennis​ balls is 33.33%.

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The correct set of data are 15, 16, 16, 17, 19, 20, 21, 23, 32, 42.

According to the question

Using the key: 2|4 = 24, the following are the set of data represented by the stem-and-leaf plot showing:

Row one, 1| 5 6 6 7 9 :

This means there are 5 data set for the first row which are:

15, 16, 16, 17, 19

Row two, 2|0 1 3 :

There are 3 data here, which are:

20, 21, 23

Row 3, 3|2: = 32

Row 4, 4|2: = 42

So, The correct set of data are 15, 16, 16, 17, 19, 20, 21, 23, 32, 42.

Correct option is C.

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The time it takes between when the rock was dropped and when it landed is 1.33 seconds.

The time it takes the rock to land on the ground from where it is dropped can be determined by using the function given.

The height of the function when it hits the ground will be zero, so the function can be written as:

[tex]\mathbf{h(t) =36t^2 -64}[/tex]

[tex]\mathbf{0 =36t^2 -64}[/tex]

64 = 36t²

[tex]\mathbf{t^2 = \dfrac{64}{36}}[/tex]

t² =1.778

[tex]t = \sqrt{1.778}[/tex]

t = 1.333 seconds

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Answer:

19

Step-by-step explanation:

4(4)+3

16+3=19

Answer:

19

Step-by-step explanation:

4x+3

4(4)+3

16+3

19

hope it helps

Using trigonometric identities, the simplified expression, without quotients, is given as follows:

A. [tex]\cos{\beta}\cot{\beta}[/tex]

The cosecant of an angle is given by one divided by the sine of the angle, hence:

[tex]\csc{\beta} = \frac{1}{\sin{\beta}}[/tex]

The sine and the cosine of an angle are related as follows:

[tex]\sin^2{\beta} + \cos^2{\beta} = 1[/tex]

[tex]\cos^2{\beta} = 1 - \sin^2{\beta}[/tex]

The cotangent of an angle is:

[tex]\cot{\theta} = \frac{\cos{\theta}}{\sin{\theta}}[/tex]

The expression given is:

[tex]\csc{\beta} - \sin{\beta}[/tex]

Simplifying the cosecant:

[tex]\csc{\beta} - \sin{\beta} = \frac{1}{\sin{\beta}} - \sin{\beta} = \frac{1 - \sin^{2}\beta}{\sin{beta}}[/tex]

Then, applying the last two identities in the subsection above to remove the quotient, the simplified expression will be found as follows:

[tex]\frac{1 - \sin^{2}\beta}{\sin{beta}} = \frac{\cos^2{\beta}}{\sin{\beta}} = \frac{\cos{\beta}}{\sin{\beta}} \times \cos{\beta} = \cos{\beta}\cot{\beta}[/tex]

Hence option A is correct.

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Answer:

x² + 1 = 0

a = 1

b = 0

c = 1

[tex]x1.2 = \frac{ - b± \sqrt{ {b}^{2} - 4ac } }{2a} [/tex]

[tex]x1.2 = \frac{ - 0 ±\sqrt{ {0}^{2} - (4.1.1) } }{2.1} [/tex]

[tex]x1.2 = \frac{0± \sqrt{0 - 4} }{2} [/tex]

[tex]x1.2 = \frac{± \sqrt{ - 4} }{2} [/tex]

There is no real solution because the discriminant is negative

Note.

Formula diskriminan

√b² - 4ac.

if the diskrimanan is negatif, so the quadratic equatoin dont have solution

The value of x is 22

Based on the description in the question,

The angles 5x -40 and 5x are angles on a straight line

So, we have:

5x - 40 + 5x = 180

Evaluate the like terms

10x = 220

Divide by 10

x = 22

Hence, the value of x is 22

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Answer:

7 : 20

Step-by-step explanation:

2km = 2000m

Then the ratio of 700m to 2 km​ is :

700 / 2000

Then the ratio in simplest form is :

7 / 20