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1) Adrianna wants to purchase GoodLife membership.When she visits the website, shedecides she wants to purchase a plan that charges $25 per month and has an initial cost of $90.What is the linear equation that represents how much Adrianna has to pay GoodLife

2) Anthony wants to purchase a Disney+ subscription.He visits the website anddecides to sign up for a plan that charges $17 per month. If the plan has no initial cost, what isthe linear equation? How much will he spend after 5 months?

3) :Sebastian wants to purchase a Premium Spotify subscription to listen to musicoffline and without ads. The plan that he chose is $10 per month and costs $15 up front. Write alinear equation to represent the cost. How much will Sebastian spend after 1 year?

Answer:

y = - 5x² - 10x + 2

Step-by-step explanation:

y = - 5(x + 1)² + 7 ← expand (x + 1)² using FOIL

  = - 5(x² + 2x + 1) + 7 ← distribute parenthesis by - 5

 = - 5x² - 10x - 5 + 7 ← collect like terms

 = -5x² - 10x + 2 ← in standard form

Answer: y = -5x² - 10x + 2

Step-by-step explanation:

Given quadratic function

y = -5 (x + 1)² + 7

Given requirement

Quadratic Standard Form: y = ax² + bx + c

Simplify the exponents

y = -5 (x + 1) (x + 1) + 7

y = -5 (x² + x + x + 1) + 7

y = -5 (x² + 2x + 1) + 7

Expand the parenthesis by distributive property

y = (-5) · x² + (-5) · 2x + (-5) · 1 + 7

y = -5x² + (-10x) + (-5) + 7

y = -5x² - 10x - 5 + 7

Combine like terms

[tex]\Large\boxed{y=-5x^2-10x+2}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

x=-2

Step-by-step explanation:

Solution Given:

3(x-3) = 5(2x + 1)

Opening bracket we get

3x-9=10x+5

keeping common value in same side

-9-5=10x-3x

-14=7x

x=-14/7

x= -2

Answer:

-2 =x

Step-by-step explanation:

3(x-3) = 5(2x + 1)

To solve for x

Distribute

3x -9 = 10x +5

Subtract 3x from each side

3x-9-3x = 10x -3x+5

-9 = 7x+5

Subtract 5 from each side

-9-5 = 7x+5-5

-14 = 7x

Divide by 7

-14/7 = 7x/7

-2 =x

The vertex of the function is a minimum and the coordinate of the vertex of the function is (0.2, -2.4)

The function is given as:

f(x) = 5x^2 + 2x - 3

Expand the function

f(x) = 5x^2 + 5x - 3x - 3

Factorize the function

f(x) = (5x - 3)(x + 1)

Set the function to 0

(5x - 3)(x + 1) = 0

Solve for x

x = 3/5 and x =-1

Hence, the x-intercept is 3/5 and -1

The vertex of the function is a minimum.

This is so because the leading coefficient of the function is positive

Here, we have:

f(x) = 5x^2 + 2x - 3

Differentiate and set to 0

10x + 2 = 0

Solve for x

x = -0.2

Substitute x = -0.2 in f(x) = 5x^2 + 2x - 3

f(0.2) = 5(0.2)^2 + 2(0.2) - 3

Evaluate

f(0.2) = -2.4

Hence, the vertex of the function is (0.2, -2.4)

To do this, we simply plot the x-intercept and the vertex.

And then connect the points

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The value of integration of y=16-[tex]x^{2}[/tex] from x=-1 to x=1 is 94/3.

Given the equation y=16-[tex]x^{2}[/tex] and the limit of the integral be x=-1,x=1.

We are required to find the value of integration of y=16-[tex]x^{2}[/tex] from x=-1 to x=1.

Equation is relationship between two or more variables that are expressed in equal to form.Equation of two variables look like ax+by=c.It may be linear equation, quadratic equation, or many more depending on the power of variable.

Integration is basically opposite of differentiation.

y=16-[tex]x^{2}[/tex]

Find the integration of 16-[tex]x^{2}[/tex].

=16x-[tex]x^{3}/3[/tex]

Now find the value of integration from x=-1 to x=1.

=16(1)-[tex](1)^{3}/3[/tex]-16(-1)-[tex](-1)^{3}/3[/tex]

=16(1)-1/3+16-1/3

=32-2/3

=(96-2)/3

=94/3

Hence the value of integration of y=16-[tex]x^{2}[/tex] from x=-1 to x=1 is 94/3.

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The solution of the given logarithmic equation is x = 28.1

Here we have the logarithmic equation:

4*ln(x - 8) = 12

And we want to solve this for x.

Remember the relations:

[tex]ln(e^x) = x\\e^{ln(x)} = x[/tex]

First, we divide both sides by 4:

[tex]ln(x - 8) = 12/4 = 3[/tex]

Then, if we apply the exponential equation to both sides of our equation, we get:

[tex]e^{ln(x - 8)} = e^{3}\\\\x - 8 = e^3\\\\x = e^3 + 8 = 28.1[/tex]

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The correctly matched quadratic functions are given as follows:

Quadratics are polynomial equations of the second degree, which means that they contain at least one squared term.

Quadratic equations are another name for it. The quadratic equation has the following general form: ax2 + bx + c = 0.

Recall that:
f(x) - a (x -c) (x - d)

where

Part A) First graph

We are given to know

The solutions or zeros of the first graph are

x=-1 and x=3

The parabola open up, so the leading coefficient a is positive, the function therefore, is equal to

The vertex is equal to the point (1, -4)

Substitute and solve for a

-4 = a(1-3)(1+1)

-4 = a(-2)(2)

a = 1

Hence, the function is equal to f(x) = (x-3) (x + 1)

Part B) Second Graph

We are also given to know that

The solutions or zeros of the first graph are

x=-3 and x=1

The parabola open down, so the leading coefficient a is negative

The function is equal to f(x) = a (x-1)(x+3)

Find the value of the coefficient a

The vertex is equal to the point (-1,8)

to solve for a, we must substitute:

8 = a(-1-1) (-1+3)

8 = a(-2)(2)

a = -2

Hence, the function is equal to: f(x) = -2 (x - 1) ( x + 3)

Part C)

We are given to know that the solutions or zeros of the first graph are

x=-2 and x=6

The parabola open up, so the leading coefficient a is positive

The function is equal to f(x)  = a(x-6) (x+2).

Find the value of the coefficient a

The vertex is equal to the point (2,-8)

We substitute and solve for a:

-8 = a(2-6) (2+2)

-8 = a(-4)(4)

a = 0.5

Hence, the function is equal to f(x) = 0.5(x - 6) (x + 2)

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By substitution, the value of x and y are 1 and 1 respectively.

3 / 8 x + 1 /3  y = 17 / 24

x + 7y = 8

x = 8 - 7y

Let's substitute the value of x in equation(ii)

3 / 8(8 - 7y) + 1 / 3 y = 17 / 24

3 - 21 / 8 y + 1 / 3 y = 17 / 24

1 / 3 y - 21 / 8 y = 17 / 24 - 3

8y - 63y/24 =  17 - 72/ 24

-55y / 24 = -55 / 24

cross multiply

-1320y = -1320

divide both sides by -1320

y = -1320 / -1320

y = 1

Hence,

x + 7(1) = 8

x = 8 - 7

x = 1

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Answer:

200,075

Step-by-step explanation:

90 times 2.5 = 225

225 divided by 3 = 75

75 + 200,000 = 200,075

Answer: 200075

Step-by-step explanation:

90 * 2.5 = 225

225 / 3 = 75

75 + 200,000 = 200,075

The values that exist two standard deviations above and below the mean are 681 and 265.

The given parameters exist:

Mean = 473

Standard deviation =104

The values above and below the mean exist calculated utilizing:

[tex]$x=\bar{x} \pm n \sigma$[/tex]

In this case n = 2.

So, we have, [tex]$x=\bar{x} \pm 2 \sigma$[/tex]

The value above is:

x = 473 + 2 [tex]*[/tex] 104 = 681

The value below is:

x = 473 - 2 [tex]*[/tex] 104 = 265

Therefore, the values that exist two standard deviations above and below the mean are 681 and 265.

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Answer:

Connect the arcs to make a perpendicular bisector

Answer:

Step-by-step explanation:

y=-1/2x+6

Answer:

[tex]z=\frac{t^{2}(m-3) }{4}[/tex]    or    [tex]z=\frac{1}{4}t^{2} (m-3)[/tex]

Step-by-step explanation:

[tex]t=\sqrt{\frac{4z}{m-3} }[/tex]

[tex]t^{2} =\frac{4z}{m-3}[/tex]

[tex]4z=t^{2} (m-3)[/tex]

[tex]z=\frac{t^{2}(m-3) }{4}[/tex]

Hope this helps

Based on the information given about the temperature, Daniela made her error on step 3 because it says: "Find the ratio of the differences of the means compared to the mean absolute deviation.

From the information given, it van be seen that Daniela recorded the low temperatures during the school day last week and this week and her results are shown in the table.

Here, she didn't find the difference between the today and last week means. She just put the mean as a whole.

Therefore, Daniela made her error on step 3 because it says: "Find the ratio of the differences of the means compared to the mean absolute deviation. This was the error.

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The equivalent expression to [tex](k o h)(x)[/tex]is [tex]\frac{1}{5 + x}[/tex]

Therefore  [tex](k o h)(x) = \frac{1}{5 + x}[/tex]

Given that the functions h is defined by h(x)=5+x

and k is defined by k (x) = [tex]\frac{1}{x}[/tex]

To find the composition of k and h that is: (k o h) (x)

Therefore

k (h(x)) = k (5+x)

k (h(x)) = [tex]\frac{1}{5+ x}[/tex]

The equivalent expression to is [tex]\frac{1}{5+ x}[/tex]

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Answer:

  24 m depth

Step-by-step explanation:

The quadratic function modeling depth will have zeros at x=1 and x=12, the distances in meters from the boat where the diver is at the surface.

The factored form of a quadratic function can be written as ...

  y = a(x -p)(x -q)

where p and q are zeros of the function. The value 'a' is a vertical scale factor.

Here, we are given y=0 at the surface, at points where x=1 and x=12. This means the function can be written as ...

  y = a(x -1)(x -12)

To find the value of 'a', we can use the maximum depth value. That depth will be halfway between the function zeros, at x = (1+12)/2 = 6.5

  -30.25 = a(6.5 -1)(6.5 -12)

  30.25 = 5.5²·a = 30.25a   ⇒   a=1

Then the function modeling the diver's depth in meters is ...

  y = (x -1)(x -12)

And the depth at x=4 will be ...

  y = (4 -1)(4 -12) = 3(-8) = -24 . . . . meters

The diver's depth is 24 meters when she is 4 m away from the boat.

Considering the dot plot, it is found that the tallest conifer is 3.25 inches taller than the shortest conifer.

It shows, with dots, the number of times that each of the measures appears in a data-set.

Researching this problem on the internet, and finding the dot plot, we have that:

The difference is:

9.5 - 6.25 = 3.25 inches.

Hence the tallest conifer is 3.25 inches taller than the shortest conifer.

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The profit is Rs.4800.

When, in a transaction, the selling price is greater than the cost price, it means we earn a profit. It is calculated with the help of the formula: Profit = Selling price - Cost price.

Given that,

S.P =$6000

C.P = $6000

If, 1$ = Rs.115.4 (in cost price)

  1$ = Rs.116.20 (in selling price)

Then,

C.P =  Rs. 115.40×6000

S.P = Rs.  116.20×6000

Then,

Profit = S.P-C.P

         =  116.20×6000 -115.40×6000

         =  (116.20-115.40)×6000

         = 0.80×6000

         =  Rs.4800

Hence, The profit is Rs.4800.

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The equation represents a population of 370 animals that decreases at an annual rate of 11% is [tex]p=370(0.89)^{t}[/tex].

It is defined as the function that rapidly decreases and the value of the exponential function is always positive. It denotes with exponent y = a^x

where a is a constant and a>1.

Given that,

A population of 370 animals that decreases at an annual rate of 11%

a = 370, r = 11%

p = [tex]a(1-r)^{t}[/tex]

 =  [tex]370(1-0.11)^{t}[/tex]

p  =  [tex]370(0.89)^{t}[/tex]

Hence, The equation represents a population of 370 animals that decreases at an annual rate of 11% is [tex]p=370(0.89)^{t}[/tex].

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Step-by-step explanation:

x^2 +4x +4 -7 is

y=x^2+4x-3

Answer: g(x)=(x+2)²-4.

Step-by-step explanation:

g(x)=f(x)+3

g(x)=(x+2)²-7+3

g(x)=(x+2)²-4.

The height of the cone in terms of y is h = 12x⁴y

The cylinder and the cone have the same volume.

Volume of a cylinder = πr²h

where

Therefore,

Volume of a cylinder = πx²y

volume of a cone = 1 / 3 πr²h

where

Therefore,

πx²y = 1 / 3 × π × (1 / 2x)² × h

πx²y = πh / 12x²

πx²y × 12x² / π = h

h = 12x⁴y

Therefore, the height of the cone in terms of y is h = 12x⁴y

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5. Alternate interior angles: ∠1 ≅ ∠5; ∠5 ≅ ∠7 and ∠4 ≅ ∠6

6. Alternate exterior angles: ∠3 ≅ ∠9 and ∠2 ≅ ∠8

7. Corresponding angles: ∠2 ≅ ∠6; ∠3 ≅ ∠7; ∠5 ≅ ∠9; ∠4 ≅ ∠8 and ∠1 ≅ ∠3

8. Vertical angles: ∠2 ≅ ∠4; ∠3 ≅ ∠5; ∠7 ≅ ∠9; and ∠6 ≅ ∠8 .

9.  ∠1 and ∠7.

If two lines that are cut across by a transversal are parallel, the following special angles are formed:

Given the image given, we can identify the following special angles:

5. Alternate interior angles: ∠1 ≅ ∠5; ∠5 ≅ ∠7 and ∠4 ≅ ∠6

6. Alternate exterior angles: ∠3 ≅ ∠9 and ∠2 ≅ ∠8

7. Corresponding angles: ∠2 ≅ ∠6; ∠3 ≅ ∠7; ∠5 ≅ ∠9; ∠4 ≅ ∠8 and ∠1 ≅ ∠3

8. Vertical angles: ∠2 ≅ ∠4; ∠3 ≅ ∠5; ∠7 ≅ ∠9; and ∠6 ≅ ∠8 .

9.  ∠1 ≅ ∠3 and ∠3 ≅ ∠7. So the two angles would be ∠1 ≅ ∠7.

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Answer:

There are two solutions:  
x = 0, y = -3  Point (0, -3)
x = 3, y = -6  Point (3, 6)

The solutions are at the intersections of the two individual graphs corresponding to each of the two equations (see attached figure)

Step-by-step explanation:

Use a graphing calculator or tool to plot each equation. The point of intersection of the two is the solution to the system of equations. See attached image

Algebraically

The first equation must be equal to the second equation for a unique value of y and x

[tex]y = x^2 - 3 = 3x -3\\x^2 - 3 = 3x - 3[/tex]

Subtract 3x - 3 from both sides giving

[tex]x^2 - 3 - (3x -3) = 0\\x^2 -3 -3x + 3 = 0\\x^2 - 3x = 0\\[/tex]

Factoring out x we get
[tex]x(x-3) = 0[/tex]

This means that x = 0 and also
x -3 = 0, or x = 3

Substituting for x = 0 in y = 3x-3 gives
y = 3.0 - 3 = -3
So x= 0, y = -3 is one solution (0,-3)

Substituting for x = 3 in the same equation gives
y = 3(3) - 3 = 6
So x = 3, y = 6 is another solution (3, 6)

Answer:

24.315°

Step-by-step explanation:

First use the pythagorean theorem to get the missing side since this is a right triangle.

a^2 + b^2 = c^2 →

b^2 = c^2 – a^2 →

b = (c^2 – a^2)^½

b = (17^2 – 7^2)^½

b = (289 – 49)^½

b = √240.

Then use the law of cosines to find the angle in between.

b^2 = a^2 + c^2 - 2ac * cos(B) →

b^2 - a^2 - c^2 = -2ac * cos(B) →

a^2 + c^2 – b^2 / 2ac = cos(B) →

cos^-1(a^2 + c ^2 – b^2 / 2ac) = C →

B = cos^-1(a^2 + c ^2 – b^2 / 2ac)

B = cos^-1(49 + 289 – √240 / 238)

B ≈ 75.685°.

A = 180 – B

A = 180 – 75.685

A = 24.315°

The first one , the second one ,the fourth one are true.

What is a commutative property in math?

This law simply states that with addition and multiplication of numbers, you can change the order of the numbers in the problem and it will not affect the answer.

1)  x + y = y + x  = a + c (b +  d ) i                                      true

2) ( xy )z = x (yz) = (a + bi)(c + di)( f + gi)                           true

3) x - y = a + bi - ( c - di ) = a - c + ( b- d )i

    y - x = c + di - ( a+bi) = c-a +(d-b)i                                  false

4) (x + y ) + z = x + ( y + z ) = a + c +f + (b +d + g)i                 true

5) (x - y ) - z = a + bi - ( c + di) - ( f + gi)

                    = a - c . f + ( b- d - g) i

         x - ( y - z ) = a + bi - ( c + di - f - gi )

                          = a - c + f + ( b - d + g ) i

{ put the hypothesis into the equation and get the proof }

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Answer:

Step-by-step explanation:

A square is made up of 4 sides that are equal in length. They can all be called "x" or "s" or whatever variable you want. The formula for the area of a square (and also the area of a rectangle) is Area = side × side.

If you called your sides "x", then the formula is A = x × x or A = x². Another way to note the area of either a square or a rectangle is to call the "bottom" the base and one of the sides the height and then the area formula looks like this:

A = b × h

or

A = length × width

They are all the same thing.

The amount saved in 10 years is = $1,04,461.13

The correct option is B.

An annuity is a series of payments that are distributed evenly over time.

One way to express the future value of an annuity of payment P for n years is,

Total salary is $65000

The interest rate is 5.32%

Trent save 8%  of his salary every year.

Company puts  4.6% of salary every year.

[tex]\text { Future Value }=\mathrm{P} \times \frac{\left(1+\frac{i}{n}\right)^{n t}}{\frac{i}{n}}[/tex]

Given:

Total salary is $65000

The interest rate is 5.32%

Trent save 8% of his salary every year.

Company puts  4.6%of salary every year.

The 8% of salary is calculated as:

[tex]\text { Amount } &=\frac{8}{100} \times 65000\\[/tex]

               [tex]&=\$ 5200[/tex]

The following information is available on the company's put:

[tex]\text { Amount } &=\frac{4.6}{100} \times 65000\\[/tex]

                [tex]&=\$ 2990[/tex]

Total amount as follows:

[tex]\begin{aligned}\text { Amount } &=5200+2990 \\&=\$ 8190\end{aligned}[/tex]

The future value can be obtained as follows

[tex]\begin{aligned}\mathrm{FV} &=8190 \times \frac{(1+0.053)^{10}-1}{0.053} \\&=8190 \times 12.75 \\&=1,04,461.13\ \\\end{aligned}[/tex]

Hence, the amount saved in 10 years is = $1,04,461.13

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The surface area of this pyramid with a regular pentagon as its base is equal to 851.09 square units.

In Mathematics, a complete circle has a magnitude of 360° and when it is divided by the 10 triangles, the angle formed at the center of the pentagon would always be equal to 36°.

Also, the length of the apothem of a pentagon can be calculated by using this formula:

a = s/2tan(36)

Where:

Substituting the given parameters into the formula, we have;

a = 10/2tan(36)

a = 10/1.45

a = 6.90 units.

Next, we would determine the slant height of this pyramid by applying Pythagorean theorem:

c² = a² + b²

c² = 6.9² + 13²

c² = 47.61 + 169

c² = 216.1

c = √216.1

c = 14.72 units.

For the surface area, we have:

Mathematically, the surface area of a pyramid with a regular pentagon as its base can be calculated by using this formula:

SA = 1.72l² × (5/2 × l × h)

SA = 1.72(14.72)² × (5/2 × 14.72 × 13)

SA = 372.69 + 478.4

SA = 851.09 square units.

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By working with percentages, we will see that they served 56 salmon filets.

Here we know that the restaurant served 70 specials in total, such that 80% of these were salmon filets.

So we just need to calculate what is the 80% of 70.

This is just given by:

70*(80%/100%) = 70*0.8 = 56

This means that they served 56 salmons filet.

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