simplify this with all the steps

An equation that relates T to N can be written as T = 750 + 560N.

An equation can be defined as a mathematical expression which shows that two (2) or more thing are equal.

A function can be defined as a mathematical expression which can be used to define and represent the relationship that exist between two or more variables in a population (data set).

Since the total amount saved by using both plans (functions A and B) is represented by T, an equation that relates T to N can be written as follows:

T = A + B

Substituting the given parameters into the formula, we have;

T = (750 + 165N) + 395N

T = 750 + 165N + 395N

T = 750 + 560N.

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Complete Question:

Ann and her husband are each starting a saving plan. Ann will initially set aside $750 and then add $165 every month to the savings. The amount A (in dollars) saved this way is given by the function A=750+165N , where N is the number of months he has been saving. Her husband will not set an initial amount aside but will add $395 to the savings every month. The amount B (in dollars) saved using this plan is given by the function B=395N. Let T be total amount (in dollars) saved using both plans combined. Write an equation relating T to N.

Simplify your answer as much as possible.

Answer: (3, -7) and (3, -1)

Step-by-step explanation:

Distance formula: a^2 + b^2 = c^2

c is the distance between different points which is 5 in this case

a=3-(-1)

a=3+1

a=4 ==> distance between x-coordinates

4^2+b^2=5^2

16+b^2=25

b^2=9

b=3

Distance from -4 and y-coordinate of a different point is equaled to 3.

How to express this in the form of an equation?

|-4-y|=3    ==> where y is the y-coordinate of a different point

-4-y=3

-4+4-y=3+4

-y=7

y=-7  ==> (3, -7)

-4-y=-3

-4+4-y=-3+4

-y=1

y=-1  ==> (3, -1)

(3, -7) and (3, -1)

The number of people who can go to the amusement park is 3 people

89.50 = 7.75 + 27.25p

89.50 - 7.75 = 27.25p

81.75 = 27.25p

p = 81.75 / 27.25

p = 3

Therefore, the number of people who can go to the amusement park is 3 people.

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Answer: y = -55

Step-by-step explanation:

-57 = y -2

-57 + 2 = y

-55 = y

Answer:

1⁷/15

Step-by-step explanation:

2¾(3⅜-1½)

using the rule of BODMAS

change the fractions in the bracket into improper fraction

2¾(27/8-3/2)

find LCM of the fractions in the bracket

2¾(27-12)/8

2¾(15/8)

convert the other mixed fraction to an improper fraction

11/8(15/8)= 5.15625~ 5.2

if f(x)=2x+2

and f(x)= -1

2(-1) +2

-2 + 2 =0

the value would be 0

Answer:

Jajajjajjajj

Step-by-step explanation:

Answer:

It's a single number used to describe a set of numeric data.

2.25 kilometers on the ground is represented by 9cm on the map

According to the question, the scale on the map is in the ratio 1 : 25000

That is the     length on the map = length of the ground

                               1cm = 25000 cm

                                1 cm = 25000/100000 km

                                1 cm = 0.25 km

Now we have to find the length of the ground in kilometres which is represented by 9cm on the map

That is we have to find the ratio,  9cm : x km

As from above, we know that,

                          1cm = 0.25 km

                           9 cm = 0.25*9 km

                                    = 2.25 km

Hence 2.25 km on the ground is represented by 9 cm on the map

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y=mx+c, where m is slope. Here x=-2, x-intercept at (x,y)=(-2,0)

and there is no y intercept.

y=mx+c, where m is slope.

The x-intercept is the value of x when y=0.

Since x=-2 for all values of y

it follows that x=-2 when y=0.

The y-intercept is the value of y when x=0 (or alternately the solution point of the form 90,y)). since x neq 0 not matter what value is assigned to y, no such point exists (graphically x=-2 is a vertical line parallel to, and therefore never intersecting, the Y-axis).

Therefore  x-intercept at (x,y) is (-2,0) and there is no y intercept.

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Answer:

So the number is -48

Step-by-step explanation:

Lets say that the number is x

(x /6)+12=4

       x/6=-8

          x=-48

Answer:

r = (n - p)/c

Step-by-step explanation:

n = p + cr

Subtract p from both sides

n - p = p + cr - p

n - p = cr

Divide both sides by c.

(n - p)/c = cr/c

r = (n - p)/c

The true statements are

The original statement is given as:

If a number is negative, the additive inverse is positive

This can be represented as

If p, then q

i.e. if p → q

So, (a) is correct

For the inverse, we simply negate the hypothesis and the conclusion

i.e. if ¬p → ¬q ----(b) is correct

For the converse, we simply switch the hypothesis and the conclusion

i.e. if q → p ----(e) is correct

Hence, the true statements are (a), (b) and (e)

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Step-by-step explanation:

1.

the length of the terminal side from (0, 0) to (4, -7) is the radius of the circle, while

x = 4 = cos(theta)×radius

y = -7 = sin(theta)×radius

so,

sin(theta) = -7/radius

radius² = (4 - 0)² + (-7 - 0)² = 4² + 7² = 16 + 49 = 65

radius = sqrt(65)

sin(theta) = -7/ sqrt(65) = -0.868243142...

FYI

theta = -60.2551187...°

or 299.7448813...°

2.

tan(theta) = 3/2

so,

sin(theta)/cos(theta) = 3/2

2×sin(theta) = 3×cos(theta)

square both sides

4×sin²(theta) = 9×cos²(theta)

completing the square

4×sin²(theta) + 9×sin²(theta) = 9×cos²(theta) + 9×sin²(theta)

13×sin²(theta) = 9×(cos²(theta) + sin²(theta)) = 9

sin²(theta) = 9/13

sin(theta) = 3/sqrt(13)

to make it a rational denominator we multiply by

sqrt(13)/ sqrt(13)

and we get

sin(theta) = 3×sqrt(13)/13

3.

because the sum of all angles in a triangle is 180°.

one angle is theta.

then we have the 90° angle at the origin (or center of the circle).

and that leaves 180 - 90 - theta = 90 - theta for the third angle.

this triangle can be flipped with putting 90 - theta in place of theta.

the flipped triangle is equivalent to the original triangle (all angles and side lengths are identical between the 2 triangles).

the baseline (radius) is the same length in both triangles.

in that flipped triangle the side formerly sin(theta) is now cos(90-theta) and cos(theta) is now sin(90-theta).

Answer:

Get natural log on both sides and subtract 8 to subject the unknown x.

Step-by-step explanation:

                        [tex]\begin{aligned}\\e^{x+8} &= 15\\\\ln(e^{x+8}) &=\small ln(15)\\\\(x+8) ln(e)&=\small ln(15)\\\\x+8&=\small ln(15) \cdots\cdots\cdots[ ln(e) = 1]\\\\x&=\small ln(15) -8\end{aligned}[/tex]

Answer:

x = -5.29

Step-by-step explanation:

e^(x+8) = 15

==> take log of both sides

log(e) * (x+8) = log(15)

==> divide both sides by log e (log(15)/log(e) = 2.70805)

x + 8 = 2.70805

==> subtract both sides by 8

x = -5.29 (rounded to the nearest tenth)

Answer:  The answer would be D. I hope this is helpful :))

Answer:

[tex]84n-27[/tex]

Step-by-step explanation:

[tex]-9(1-10n) -2(3n+9)[/tex]

[tex]-9+90n-6n-18[/tex]

[tex]{84n-27}[/tex]

The set of statements is true; B. The number of stations airing the program increased by 82%. the equivalent expression that represents this situation is r+0.82r.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

IT is given that year ago, a radio program was aired on r stations across the country.

Also Today, the number of stations airing the radio program can be represented by the following expression; 0.82r

Therefore, the equivalent expression that represents this situation is r+0.82r

Hence, The set of statements is true; B. The number of stations airing the program increased by 82%. the equivalent expression that represents this situation is r+0.82r.

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The geometric mean between the pair of numbers, 18 and 1.5, is 3√3.

Geometric mean, like arithmetic mean, is a kind of average and a measure of central tendency.

To solve for the geometric mean, we multiply the numbers together and then take a square root (for two numbers), cube root (for three numbers) etc. In other words, geometric mean is the nth root of the product of n values.

The formula for the geometric mean is given by:

GM = n√x1 x2 . . . xn

Solving for the geometric mean between 18 and 1.5 using the formula:

GM = n√x1 x2 . . . xn

where n = 2, x1 = 18, and x2 = 1.5

GM = √(18)(1.5)

GM = √27

GM = 3√3

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Answer:

-48

Step-by-step explanation:

2 x 4 = 8

8 x -6 = -48

[tex]log_{5} \sqrt{14}[/tex] ≈ 0.82

The property of logarithms log ab = log a + log b , log a/b = log a - log b

[tex]log_{5} 2[/tex] ≈ 0.43

[tex]log_{5} 7[/tex] ≈ 1.21

We need to find,

[tex]log_{5} \sqrt{14}[/tex]

= 1/2[tex]log_{5} 14[/tex]

= 1/2[tex]log_{5} 2*7[/tex]     ( log ab = log a + log b)

= 1/2 ([tex]log_{5} 2[/tex] + [tex]log_{5} 7[/tex])  

=1/2( 0.43 + 1.21)

= 1/2 × 1.64

= 0.82

Hence logarithms of [tex]log_{5} \sqrt{14}[/tex] = 0.82

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Answer:

50 pounds of raspberries and 45 pounds of apples is sold

Solution:

Let  "a" be the number of pounds of raspberries sold

Let "b" be the number of pounds of apples sold

Cost of each pound of raspberry = $ 4

Cost of each pound of apple = $ 1.50

Austin made $267.50 from selling a total of 95 pounds of raspberries and apples

Therefore,

a + b = 95

b = 95 - a ------ eqn 1

Austin made $267.50. Therefore,

number of pounds of raspberries sold x Cost of each pound of raspberry + number of pounds of apples sold x Cost of each pound of apple = 267.50

4a + 1.50b = 267.50 --------- eqn 2

Substitute eqn 2 in eqn 1

4a + 1.5(95 - a) = 267.50

4a + 142.5 - 1.5a = 267.50

2.5a = 125

a = 50

Substitute a = 50 in eqn 1

b = 95 - 50

b = 45

Thus 50 pounds of raspberries and 45 pounds of apples is sold

Step-by-step explanation:

hope it helps u

Using quadratic equation, The equation for given value of zeros is equation is x² - 6x - 16 = 0.

f(x) = ax2 + bx + c, where a, b, and c are integers and an is not equal to zero, is a quadratic function.

A parabola is the shape of a quadratic function's graph. Although the "width" or "steepness" of a parabola can vary as well as its direction of opening, they always have the same fundamental "U" form. The three graphs in the image below are all parabolas.

The following must be true if those are the 0s:

-2 + 2 = 0

8 - 8 = 0

We would thus get the following equation if we were to include them in a quadratic-based one:

(x + 2)(x - 8) = 0

x² - 8x + 2x - 16 = 0

FOIL

Roughly speaking, x² - 6x - 16 = 0

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Answer:

f(x) = x2 − 6x − 16

Step-by-step explanation:

Write the zeros as solutions of two equations.

x  =  −2  x  =  8  

x + 2  =  0   x − 8  =  0  Rewrite each equation so that it equals 0.

Find the product of the two binomials.

(x + 2)(x − 8)  =  x2 − 8x + 2x − 16   Multiply.

=  x2 − 6x − 16  Simplify.

Rewrite the equation in function notation.

f(x) = x2 − 6x − 16

Therefore, the quadratic function with zeros of −2 and 8 is f(x) = x2 − 6x − 16.

The correct names for the given angle is ∠PHV.

How to name the any angle?

For naming any angle, the common vertex must come in the middle of the name.

But it could start with any of the end point.

Thus, the angle given can be named either ∠PHV or  ∠VHP.

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The difference is -3/4.

Given,

(5/2) - (13/4)

Solution:

Taking L.C.M,

(5/2) - (13/4) = 10/4 - 13/4

                    = -3/4

The difference is -3/4.

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Answer:

1215

Step-by-step explanation:

The radius of a cylinder having height of 5cm and volume 770 cm³ is 7 cm.

Volume of a cylinder is the space occupied by it in a three - dimensional space.

Volume of a cylinder is calculated using the formula:

[tex]V = \pi r^{2} h[/tex]

[tex]r = \sqrt{\frac{V}{\pi h} }[/tex]

where r is the radius of the base of the cylinder.

is a constant having value 3.14

h is the height of the cylinder. It is the perpendicular height from the base.

According to the given condition,

V = 770 cm³ and h = 5 cm.

Substituting these values in the equation above,

∴ r = 7 cm

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The correct expression and value is A. 9(n+8)-6, when n=5, the value is 111.

Firstly forming the expression using given information, starting the end of sentence. Breaking sentence into parts as follows -

1. the sum of a number and eight

2.  nine times the sum of a number and eight

3. six less than nine times the sum of a number and eight

Let the number be n.

So, equation according to 1. Sum = (n + 8)

Equation according to 2. 9(n + 8)

Equation according to 3. 9(n + 8) - 6

So, the expression is 9(n + 8) - 6

Now, keeping the value of n as 5 and finding the value of expression.

Value = 9(5 + 8 ) - 6

Firstly solving the bracket

Value = 9 × 13 - 6

Performing multiplication

Value = 117 - 6

Performing subtraction

Value = 111

Hence, the expression and value is A. 9(n+8)-6, when n=5, the value is 111

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The complete question is -

What is the expression and value of “six less than nine times the sum of a number and eight” when n = 5

A.9(n+8)-6, when n=5, the value is 111

B. 6-9(n+8), when n = 5, the value is 111

C. 9(n)+8-6, when n = 5 the value is 47

D.6-9(n), when n = 5, the value is 47

Answer:

The correct expression and value is A. 9(n+8)-6, when n=5, the value is 111.

Step-by-step explanation: