standard equation for hyperbola with vertices (-2, 1), (2, 1) and foci (-3, 1) (3,1)

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Given:

The equation is:

[tex]\ln(3x^2-1)=\ln(191)[/tex]

To find:

The solution for the given equation.

Solution:

We have,

[tex]\ln(3x^2-1)=\ln(191)[/tex]

On comparing both sides, we get

[tex]3x^2-1=191[/tex]

[tex]3x^2=191+1[/tex]

[tex]3x^2=192[/tex]

Divide both sides by 3.

[tex]x^2=\dfrac{192}{3}[/tex]

[tex]x^2=64[/tex]

Taking square root on both sides, we get

[tex]x=\pm \sqrt{64}[/tex]

[tex]x=\pm 8[/tex]

Therefore, the solutions of the given equation are -8 and 8.

Answer:

m=5

c=-7

Step-by-step explanation:

m is slope

c is the intercept on the y axis

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The slope of the line through each pair of points (16,1), (17,7) is 6.

A line's slope serves as a gauge for its steepness. Between any two locations on the line, it is the ratio of the vertical change to the horizontal change.

The slope of a line can be positive, negative, zero, or undefined.

In algebraic equations, the letter "m" frequently stands in for slope. In slope-intercept form, a line's equation is written as y = mx + b, where m denotes the line's slope and b its y-intercept.

To find the slope of the line that passes through two points (x1, y1) and (x2, y2), you can use the following formula

m = (y2 - y1) ÷ (x2 - x1)

where m is the slope of the line and (x1, y1) and (x2, y2) are the coordinates of the two points.

In this case, the slope of the line through the points (16,1) and (17,7) is:

m = (7 - 1) ÷ (17 - 16) = 6 ÷ 1 = 6

So the slope of the line is 6.

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Hi there!

[tex]\large\boxed{35 \text{ units}^2}[/tex]

Find the area of the parallelogram using the formula:

A = b × h

Thus:

A = 7 × 5 = 35 units²

Answer:

Step-by-step explanation:

I believe that the answer is 85

Answer: #4 x >l 11

Hope this helps

Step-by-step explanation:

Answer:

-2[tex]t^{3}[/tex] + 5t - 1

Step-by-step explanation:

(7[tex]t^{3}[/tex] + 3t - 1) + (-9[tex]t^{3}[/tex] + 2t)

7[tex]t^{3}[/tex] - 9[tex]t^{3}[/tex] + 3t + 2t - 1  Combine like terms

-2[tex]t^{3}[/tex] + 5t - 1

Like terms have to have the same variable and the same exponents to be like terms.

Answer: A line segment is a part of a line having two endpoints.

Im not sure if you meant to put a picture there. So, a line segment is a piece or part of a line having two endpoints. Unlike a line, a line segment has a definite length.

Answer:

x = 26

Step-by-step explanation:

m<RTS = 4x - 14 (given)

Based on the inscribed angle theorem, the measure of the inscribed angle in a semicircle = right angle (90°)

Therefore,

4x - 14 = 90

4x - 14 + 14 = 90 + 14 (addition property of equality)

4x = 104

4x/4 = 104/4

x = 26

Answer:332

Step-by-step explanation:

Let x be the number

Using algebra

(x÷4)+75=158

(x÷4)=158-75

(x÷4)=83

x=83×4

x=332

Check

(332÷4)+75=158

The value of the quantity after 96 months, to the nearest hundredth is 1146.66

The standard expression for an exponential equation is expressed as:

P(t) = P0e^rt

Given the following parameters

Po = 800

rate r = 4.5% = 0.045

time t = 8 years

Substitute

P(8) = 800e^0.045(8)
P(8) = 1146.66

Hence the value of the quantity after 96 months, to the nearest hundredth is 1146.66

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Answer:

Step-by-Step:5 cars and 14 bikes

Answer: obtuse

Step-by-step explanation:

64+47=111

111>39

Answer:

Step-by-step explanation:

First of all I'm going to presume it means an eight-grader chosen at random from the instrument players, if this is incorrect the question should have specified the total amount of students.

You have to add the amount of students of each of instrument to get the total:

5+9+10+9=33

then it says to not include the drum playing students so it goes from

[tex]\frac{33}{33}[/tex] to [tex]\frac{33-10}{33}[/tex] so its [tex]\frac{23}{33}[/tex] which we must now turn to a percentage.

so you divide the 23 by the 33:

23/33=0.6969....

then you multiply by 100 as it's a percentage:

0.6969...×100=69.6969...

and finally we round it do the nearest integer/whole number:

70 (we look at the tenths digit and it's a 6 so it's rounded up)

Answer:

B

Step-by-step explanation:

Answer:

3357

Step-by-step explanation:

'Substitution Property of Equality'  illustrates the statement "If AC = 14, then BD + AC = BD + 14" from the question.

What is property of equality?

The equality characteristics define the relationship between two equal quantities. If a mathematical operation is applied to one side of an equation, it must also be applied to the opposing side to keep the equation balanced.

The Substitution Property of Equality states that if we know that two expressions are equal, we can substitute one of them for the other in any equation.

In this statement, it is stated that "If AC = 14, then BD + AC = BD + 14." Here we substitute 14 for AC in BD + AC = BD + 14. Which means that if we know that AC = 14, we can substitute 14 for AC in any equation, and the equation will still be true.

Therefore, given statement illustrates the Substitution Property of Equality.

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Therefore , As a result 5, 10, and 15 make up the reasonable domain for the function 2 (l + w) = 64..

A connection between a group of sources and one output for each input is referred to as a function. A function is, to put it simply, a collection of equation  connected to a single, unique output. In mathematics, a function is a statement, rule, or law that describes the connection between two variables (the dependent variable). One input leads to one output when a rule of this type is used. by Alex Federspiel, the photographer. This statement gives an example of y=x2. There is just one output for y from any input for x. According to our definition, y is a function of x since x is the input value.

Here,

We have the following for the rectangle's perimeter:

2 ( l + w ) = 64

Here,

W = width, and L = length.

We must determine the length and breadth values necessary to make the rectangle's perimeter 64.

Now,

2 ( l + w ) = 64

l + w = 32

Thus, the sum of the length and breadth measurements must equal 32.

The possible widths are 5, 10, 15, 20, and 25.

Now,

l + 5 = 32

l = 27

l + 10 = 32

l = 22

l + 15 = 32

l = 17

l + 20 = 32

l = 12

l + 25 = 32

l = 7

We think about

The domain has widths of 5, 10, 15, 20, and 25.

The range for length is: 27, 22, 17, 12, and 7.

Values for width and length are used as the x- and y-axes, respectively.

Below is a graph of the data.

The following is the reasonable domain for the aforementioned situation:

5, 10, 15, 20, and 25

Below is a graph of the function 2 (l + w) = 64.

Therefore , As a result, 5, 10, and 15 make up the reasonable domain for the function 2 (l + w) = 64.

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The answer of x is 100 degree.We can find by using percentage formula.

Percentage is a value or ratio that shows a fraction of 100. Percent means per 100. It does not have any units.If we have to calculate percent of a number then we  divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.

The formula used to calculate percentage is: (value/total value)×100%.The most basic application of percentages is to compare one quantity against another. When we want to talk about data in this way we use it with the word, "of." To use this data as an example, we would say, for example, "25% of people prefer cake," as in this example.

Now we have

100 = x of 100%

100= x * 100/100

100=  x

Hence we can calculate value of x.

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Answer:

she can edit 4 commericals in 144 minutes.

Step-by-step explanation:

144 divided by 36 is 4

Answer:

180

Step-by-step explanation:

you have to add 36/144 to get your answer our welcome.

9514 1404 393

Answer:

  $6749.29

Step-by-step explanation:

The balance is given by ...

  A = Pe^(rt)

  A = $5000·e^(0.10·3) ≈ $6749.29

Edgar will owe $6749.29.

The equation includes equal to sign and the inequality includes the sign of greater than and equal to sign.

Inequality is defined as the relation which makes a non-equal comparison between two given functions.

when we have to solve an equation, it does not has an equal sign and inequalities.

When we have to solve an inequality equations usually are exact answers.

The equation includes equal to sign and the inequality includes the sign of greater than and equal to sign.

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Answer:

[tex]V = 864cm^3[/tex]

Step-by-step explanation:

Given

[tex]r = 6[/tex]

[tex]\pi = 3[/tex]

Required

The volume of the sphere

This is calculated as:

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

So, we have:

[tex]V = \frac{4}{3} *3 *6^3[/tex]

[tex]V = \frac{4}{3} *3 *216[/tex]

This gives:

[tex]V = 4 *216[/tex]

[tex]V = 864[/tex]

Explanation:

The zeros in 0.00798516 are not considered significant because they are not between nonzero values.

If we had something like 1.207, then that zero would be considered significant.

The first three significant values we come across in 0.00798516 are 7, 9 and 8 in that order. The next digit 5 meets the criteria of "5 or larger", which means the 798 bumps up to 799. Erase everything to the right of that.

Therefore, 0.00798516 rounds to 0.00799 when rounding to 3 significant figures.

Answer: 0.00799

0.00798516 rounded off to three significant figures is 0.00799

hope that helps...

Answer:

C. y = 11.76(0.7)×

Step-by-step explanation:

I calculated it logically

The exponential equation that models the data is  y = 16.8×1.7ˣ.

A relation is a function if it has only One y-value for each x-value.

y = a.rˣ is the exponential function.

We can see that the y-values are decreasing, which means that the growth factor must be between 0 and 1.

Additionally, we can divide the y-value for each x by the y-value for the previous x to get an estimate of the growth factor.

Using this method, we find that the growth factor is approximately 0.85, which means that a possible equation is y = a × 0.85ˣ.

To find the value of a, we can substitute one of the data points into the equation.

Lets use the point (-2, 24), we get:

24 = a × 0.85⁻²

a = 24 / 1.551

a = 15.456

Therefore, the exponential equation that models the data is  y = 16.8×1.7ˣ.

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The coordinates of the vertices of the square with height x is given as follows:

A square is a figure for which all the four side lengths are congruent, that is, they have the same measure.

The side length of the square in this problem is given as follows:

x.

As the height is equals to the base.

The vertex J represents the origin, hence it has coordinates given as follows:

J(0,0).

Then the remaining coordinates of the square are given as follows:

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Answer:

2x^3+5x^2−28x−15

Step-by-step explanation:

The equation to represent the height of a glass slab is y=11x+2.

The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.

From the given table, we have (2, 24) and (4, 46).

Substitute (x₁, y₁)=(2, 24) and (x₂, y₂)=(4, 46) in m=(y₂-y₁)/(x₂-x₁)

= (46-24)/(4-2)

= 22/2

= 11

Substitute m=11 and (x, y)=(2, 24) in y=mx+c, we get

24=11(2)+c

c=2

Substitute m=11 and c=2 in y=mx+c, we get

y=11x+2

Therefore, the equation to represent the height of a glass slab is y=11x+2.

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Answer:

x < [tex]\frac{11}{2}[/tex]

Step-by-step explanation:

=> 10x - 5 < 8x + 6

Subtract 8x from the left and right side of the inequality sign:

=> 2x - 5 < 6

Now, add 5 on both sides of the inequality:

2x < 11

now divide 2 on both sides:

x < [tex]\frac{11}{2}[/tex]

Hope this helps!