2
A payment increases from $700 to $945. What is the percent increase in the
payment? Show your work.

The required equation of the hyperbola is expressed as

[tex]\frac{x^2}{10}- \frac{y^2}{15}=1 \\[/tex]

The standard form for calculating the equation of a parabola along the x-axis is expressed as:

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

(h, k) is the center

(k±c, h) are the foci

[tex]x=h\pm\frac{a^2}{c}[/tex] is the directrix

From the question given, we can see that foci = (±5, 0)

k±c, h = ±5, 0

k = 0

h = 0

c = 5

From the directrix,

[tex]x=h\pm\frac{a^2}{c}\\x =0\pm\frac{a^2}{5}\\\pm2 = \pm\frac{a^2}{5}\\a^2 = 10\\[/tex]

Also, we need to know that;

a²+b² = c²

10 + b² = 5²

b² = 25 - 10

b² = 15

Substituting the gotten values into the equation of a hyperbola;

[tex]\frac{(x-0)^2}{10}- \frac{(y-0)^2}{15} =1\\\frac{x^2}{10}- \frac{y^2}{15} =1\\[/tex]

This gives the required equation of the hyperbola

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Answer:

The answers are between C and D

Step-by-step explanation:

It can't be A or B because they create a horizontal hyperbola, when the directrices are vertical.

From 12 different letters, 3326400 arrangements can be made using the letters in the word CARELESSNESS.

When the order of the arrangements counts, a permutation is a mathematical approach that establishes the total number of alternative arrangements in a collection. Choosing only a few items from a collection of options in a specific sequence is a common task in arithmetic problems.

Among the 12 letters in CARELESSNESS,

there are 4 S’s, 3 E’s, and 1 each of C, A, R, L, N.

There are 12! = 479,001,600 arrangements (permutations) of the 12 letters,

most of which are identical because of repeated letters.

In order that each permutation be distinct, repeat letters have to be accounted for.

4 S’s be in 4! = 24 ways,

3 E’s, in 3! = 6 ways.

And 1! = 1 way.

Distinct permutations as requested,

thus = 12!/(3!)(4!)(1!)

       = 3326400.

Therefore, 3326400  different 12-letter arrangements can be made using the letters in the word CARELESSNESS.

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Exact Answer:     x = 16/3

Approximate Answer:      x = 5.333

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

Work Shown:

base = 3x-1

height = x

area of triangle = (base*height)/2

40 = x*(3x-1)/2

40*2 = 3x^2 - x

80 = 3x^2 - x

0 = 3x^2 - x - 80

3x^2 - x - 80 = 0

Now apply the quadratic formula

[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(-1)\pm\sqrt{(-1)^2-4(3)(-80)}}{2(3)}\\\\x = \frac{1\pm\sqrt{961}}{6}\\\\x = \frac{1\pm31}{6}\\\\x = \frac{1+31}{6} \ \text{ or } \ x = \frac{1-31}{6}\\\\x = \frac{32}{6} \ \text{ or } \ x = \frac{-30}{6}\\\\x = \frac{16}{3} \ \text{ or } \ x = -5\\\\x \approx 5.333 \ \text{ or } \ x = -5\\\\[/tex]

A negative height doesn't make sense, so we ignore x = -5

The only solution is x = 16/3 which approximates to x = 5.333

Answer:

67% (rounded)

Step-by-step explanation:

Since there is 1-6,

There is 3,4,5,6 which is 4/6 chance being above 2.

2/3 = 66.6%  

Answer:1/36

Step-by-step explanation:

Answer:

c=-18 d=2

Step-by-step explanation:

[ 6 8 -11 15 ]-[c+2 3 -5 d-4 ]=[ 22 5 -6 17]

The equation tells that when the two matrices are subtracted we get the resultant matrix.

Each element of the first matrix corresponds to each element of the second matrix

From above

6- (c+2)= 22

6- c-2= 22

4-c= 22

-c= 22-4

-c= 18

c= -18

And

15-( d-4)= 17

15- d+4= 17

19-d= 17

-d= 17-19

-d= -2

d= 2

Answer:

D

Step-by-step explanation:

c= -18

d= 2

Answer:

Where are the answers

Step-by-step explanation:

Answer:

65 degrees

Step-by-step explanation:

90 + 90 + 115 + x = 360

x= 65

Answer:

AB = 7

Step-by-step explanation:

The polygon pictured is a hexagon, which means that it has 6 equal side lengths. The perimeter is 42. AB is the length of one side.

Perimeter = 6 x length of one side

If you plug everything you know in the equation, you would get...

42 = 6 x length of one side

42 ÷ 6 = 7

So, 7 is the length of AB, since in a hexagon, all sides are the same length.

The length of side AB  is 7.

A regular polygon is a closed shape that has straight sides of equal length and interior angles of equal measure.

This means that all of the sides and angles of a regular polygon are congruent (i.e., have the same size).

We have,

The given polygon is a hexagon since it has 6 faces.

Now,

The six faces are equal in length.

So,

6 faces length = 42

Now,

Each face = x

And,

6x = 42

x = 42/6

x = 7

Thus,

The length of AB  is 7.

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Answer:

m1= 82

m2=98

m3=82

Step-by-step explanation:

Angle m4 is supplementary with angle m1 so their values add up to 180

180-98=82

Angle m3 is opposite of m1 and is the same value, it is also supplementary to m4 so you can find the value that way as well.

Angle m3 is opposite of m4 so it is the same value.  It is supplementary to m1 and m3, so it must be 98 through that logic as well.

Answer:

A. the control group in an experiment

Step-by-step explanation:

Researchers give one group a new cold medicine and compare them with to a group that takes no medicine. The group that is not given any medicine is the control group in an experiment.

Researchers are those who do research on something i.e. systematics and deep investigation into something.

Control Group is that group in research which does not take any medication or untreated group.

During the research while a new type of medicine is to be tested, the group that receives the medication or being tested is called the experimented group and the group that does not receive the treatment  is called the control group.

Hence, we can say that the group that is not given any medicine is the control group in an experiment.

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Answer:

y=2x+2

Step-by-step explanation:

Answer: 7

Step-by-step explanation:

Answer: D

Step-by-step explanation:

Plug in 0 for each variables in the equation and see which one holds true

Hope this helps

Answer:

113.1 in

Step-by-step explanation:

C = πd

d = 36

C = 36π = 113.1 in

Answer:

d. 3,200

Step-by-step explanation:

If the total population consists of 32,000 people, a sample of the population selected will consist of a number equal or less than 32,000 people.

From the given options, the only option that matches the above explanation is "D" which is less than 32,000 people.

Therefore, the correct answer choice is D. 3,200.

Answer:

n = 8

Step-by-step explanation:

The angles are vertical angles and so they are equal

9n = 8n+8

Subtract 8n from each side

9n - 8n = 8n+8-8n

n = 8

Answer:

A series can be represented in a compact form, called summation or sigma notation. The Greek capital letter, ∑ , is used to represent the sum. The series 4+8+12+16+20+24 can be expressed as 6∑n=14n . The expression is read as the sum of 4n as n goes from 1 to 6 .

Step-by-step explanation:

I hope it's help u

Answer:

the answer is B

Step-by-step explanation:

i got your back

Answer:

D

Step-by-step explanation:

Using the tangent ratio in the right triangle

tanθ = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{7}{4}[/tex] , then

θ = [tex]tan^{-1}[/tex] ([tex]\frac{7}{4}[/tex] ) ≈ 60° ( to the nearest degree )

Answer:

Option. A

Step-by-step explanation:

Have a great day!

Answer: A

Step-by-step explanation: there's 8 spaces on the spinner

Given:

The figure of a circle.

To find:

The measure of arc AD and measure of each arc.

Solution:

The measure of arc is equal to the central angle of that arc.

The central angle of arc AD is 105 degrees. So,

[tex]m(arc(AD))=105^\circ[/tex]

The central angle of arc BC is 35 degrees. So,

[tex]m(arc(BC))=35^\circ[/tex]

The central angle of arc CD is 50 degrees. So,

[tex]m(arc(CD))=50^\circ[/tex]

The central angle of a complete circle is 360 degrees. So,

[tex]m(arc(AD))+m(arc(BC))+m(arc(CD))+m(arc(AB))=360^\circ[/tex]

[tex]105^\circ+35^\circ+50^\circ+m(arc(AB))=360^\circ[/tex]

[tex]190^\circ+m(arc(AB))=360^\circ[/tex]

[tex]m(arc(AB))=360^\circ-190^\circ[/tex]

[tex]m(arc(AB))=170^\circ[/tex]

Therefore, the measure of arc AD is 105°, the measure of arc BC is 35°, the measure of arc CD is 50° and the measure of arc AB is 170°

Answer:

c

Step-by-step explanation:

dfghfghj

Answer:

3/4, 4/5, 2/3. 3/5, 2/3

Step-by-step explanation:

What is 4/8 + 1/4 simplified

4/8 + 1/4

4/8 + (1/4)*2/2 (find the common denominator in our case it is 8)

4/8 + 2/8

6/8

or, 3/4 (I simplified the fraction to lowest term)

what is 3/5 + 2/10 simplified  

3/5 + 2/10

3/5 + 1/5

4/5

what is 1/3 + 3/9 simplified

1/3 + 3/9

1/3 + 1/3

2/3

what is 2/10 +2/5 simplified

2/10 + 2/5

1/5 + 2/5

3/5

what is 3/6 + 2/12 simplified

3/6 + 2/12

3/6 + 1/6

4/6

2/3

Answer:

[tex]11^2 *11^10 \\13^6 *13^4\\14^9 * 14^10\\2^4*2^4\\7^8*7^6\\3^3*3^9[/tex]

Step-by-step explanation:

Please Mark Brainliest for helping

Answer:

take 20 degree as reference angle

let hypotenuse be x

using cos rule

cos 20=adjacent/hypotenuse

0.93=7/x

0.93*x=7

x=7/0.93

x=7.5

Step-by-step explanation:

Answer:

Let the three consecutive numbers be x,x+1,x+2 . The numbers are: 23,24,and25 and the smallest one is 23

Step-by-step explanation:

Answer: (x-1) + (x) + (x+1) = 72; smallest number is 23.

Step-by-step explanation:

The numbers are consecutive, meaning they sit next to each other on a number line. For example 4, 5, 6.

Because they are three consecutive numbers, their average will be the value of the middle one. For example the average of 4, 5, 6 is 5.

Knowing this, we can divide 72 by three to get the value of the middle number.

72/3 = 24, so the middle number is 24.

The numbers that fall either side of 24 on the number line are 23 and 25, so the three consecutive numbers are 23, 24, 25.

You can also set up and solve the equation: (x-1) + (x) + (x+1) = 72 because the numbers are consecutive.

To solve, combine like terms. The (-1) and (+1) cancel out and the equation becomes 3x = 72.

72/3 = 24, so x = 24, and the smallest term, (x-1) = 23.

Answer:

= 5^-8 . 5^-10

= 5^(-8 ) + (-10)

=5^-18

Answer:

5^-18

Step-by-step explanation:

[tex](5^{-8})(5^{-10}) = 5^{-8-10} = 5^{-18}[/tex]