Annika’s older sister cousin borrowed 800$ to repair her car she will pay off the loan after 2years by paying back the principal plus 4.5% simple interest for each year. How much will she pay in interest?

The vertex of the function f(x) = x^2 + 12x is (-6, -36).

The concept that will be used here is the concept of Standard equation of a curve in vertex form.

The standard equation can be written as

f (x) = ax^2 + bx + c

Then the Vertex is the (h,k)

Then the X-coordinate of the vertex  can be written as (h = -b/2a) where  k = f(h)

If we compare the given equation with the standard form, then we have

a = 1, b = 12 and c = -10

Then we can input the values into the  (h = -b/2a)

h =[ -12/2(1)] = - 6

Then we can substitute the value of h in f (x) which is f(x) = x2 + 12x

k = f(h)= f (-6) =[ (-6)2 + 12 (-6)]

= [36 - 72] = -36

In conclusion the vertex is (-6, -36).

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Step-by-step explanation:

using Pythagoras theorem.

37,

x² = 6² + 8²

x = √6²+8² = 10ft

38.

13²=12²+x²

169 = 144 + x²

√169 - 144 = x = 5cm

hope it helps. :)

Answer:

x = 10 and x = 5

Step-by-step explanation:

using Pythagoras' identity

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides.

(36)

x² = 6² + 8² = 36 + 64 = 100 ( take square root of both sides )

x = [tex]\sqrt{100}[/tex] = 10

(38)

13² = x² + 12²

169 = x² + 144 ( subtract 144 from both sides )

25 = x² ( take square root of both sides )

[tex]\sqrt{25}[/tex] = 5 = x

x = 5

Answer:

a) See attached (sorry if its a bit unneat, use 5 points for more accuracy while drawing. 3 points is generally accepted though.)

b) 80 mins

c) 4000 meters, 40 minutes

Step-by-step explanation:

First, lets define the literal meaning of the questions.

A) Graph the function (I will explain how to do below)

B) What is the absolute value of the distance of the x-intercepts?

C) What is the y value of the vertex (maximum/ minimum value). What is the x value of the vertex?

Lets solve these problems. To graph a quadratic equation by hand, first you must find the vertex. Formula for the x-value of the vertex:

[tex]\frac{-b}{2a}[/tex]

Because a quadratic equation is in the form:

[tex]ax^2 + bx + c = 0[/tex]

We can find the values of a and b.

Values of a and b in this equation:

a: -2.5

b: 200

Plug into the vertex formula (shown above), -b/2a

[tex]\frac{(-)(200)}{(2)(-2.5)}[/tex]

Simplify.

[tex]\frac{-200}{-5}[/tex]

Simplify.

-200/-5 = 40

Now we have 40, the x value of the vertex. Plug 40 back into the x values of the problem (t in this word problem) to find the y value of the vertex.

The equation:

[tex]h=-2.5t^2+200t[/tex]

Plug in 40 to the t values.

[tex]h = -2.5(40)^2 + 200(40)[/tex]

Simplify.

[tex]h = -4000 + 8000[/tex]

Add.

h = 4000

Now, we have the values of the vertex.

Values of vertex:

x: 40

y: 4000

This means that when the x-value is 40, the y-value is 4000. In this case, it means 40 minutes in, the altitude of the plane is 4000 meters.

On a graph, draw a point at x-value 40 and y-value 4000. This will be needed when we draw the graph.

We need at least 3 points to graph a quadratic equation (this applies to all parabolas.)

This part is a bit hard to explain, but you will get it with this example. Since we need 3 points, we need to solve for 2 more points like we just did. But what x-values do we use? For the vertex, we knew the x value was -b/2a!

Solve for x-values that have an equivalent absolute distance from the x value of the vertex.

For example, in this case, the x value of the vertex is 40.

If we were to pick the x value of 38 for the 2nd point, we would have to use the 42 for the 3rd point as they are both 2 away from 40.

|40-38| = 2

|40-42| = 2

I will use the x values of 38 and 42 to graph this. Lets do the same thing we did to find the y value of the vertex. Plug the x values into the equation individually.

Equation:

[tex]h=-2.5t^2+200t[/tex]

Plug in 38 to the x values (in this case its called t.)

[tex]h = -2.5(38)^2 + 200(38)[/tex]

Simplify.

h = -3610 + 7600

Add.

h = 3990

This means when the x value of the parabola is 38, the y value is 3990. In this case, it means after the plane has flown for 38 minutes, the altitude of the plane is 3990.

Now lets find what the y-value of the parabola would be when the x-value is 42 (when we've did this, we can graph it.)

But here is a little trick to speeden things up. If the absolute value of the difference of the x-value of the vertex (40 in this case) and the x value of the point we just found (38 in this case) is the same as the absolute value of the difference of the 3rd point we need to graph (42 in this case), which is always true if you followed the steps above, the y value is the same!

So, this means, when:

Point 2:

x: 38

y: 3990

Point 3:

x: 42

y: 3990

The y-value of the 3rd point we need to find is 3990.

Now we can graph it using our points.

Point 1 (Vertex):

x: 40

y: 4000

Point 2:

x: 38

y: 3990

Point 3:

x: 42

y: 3990

I'll just use paint to draw this, draw the points, label them, and connect the points with a parabola.

Now lets answer b using the definitions.

Because we need to find the x intercepts, lets use the quadratic formula.

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

Ignore the A's, its a bug.

If you need to know how to use the quadratic equation, DM me. Otherwise, I will just write the x-intercepts.

x-intercepts:

0,80

Because it is asking for the distance between Toronto and Montreal in minutes, subtract 0 from 80.

80-0=80

B) 80 minutes

The maximum height of the aircraft is the y value of the vertex and the time that the aircraft reaches this height is the x-value of the intercept.

(Vertex):

x: 40

y: 4000

C) 4000 meters, 40 minutes

Answer:

a)  See attached.

b)  80 minutes

c)  Maximum height = 4000 m

    Time = 40 minutes

Step-by-step explanation:

Given function:

[tex]h=-2.5t^2+200t[/tex]

where:

The function is quadratic, which means the graph of the function is a parabola.  

Axis of Symmetry

A parabola has perfect symmetry.

For a quadratic in the form  [tex]ax^2+bx+c[/tex], its axis of symmetry is:

[tex]\boxed{x=-\dfrac{b}{2a}}[/tex]

Therefore, the axis of symmetry for the given function is:

[tex]x=-\dfrac{200}{2(-2.5)}=40[/tex]

Vertex

As the leading coefficient is negative, the parabola opens downwards.

Therefore, the vertex is the maximum point of the parabola.

The axis of symmetry is the x-value of the vertex.

Substitute t = 40 into the given function to find the y-value of the vertex:

[tex]\implies h(40)=-2.5(40)^2+200(40)[/tex]

[tex]\implies h(40)=4000[/tex]

Therefore, the vertex of the function is (40, 4000).

x-intercepts

To find the x-intercepts of the function, set the function to zero and solve for t:

[tex]\implies -2.5t^2+200t=0[/tex]

[tex]\implies -2.5t(t-80)=0[/tex]

Therefore:

[tex]\implies -2.5t=0 \implies t=0[/tex]

[tex]\implies t-80=0 \implies t=80[/tex]

Therefore, the x-intercepts are (0, 0) and (0, 80).

Graphing the function

Draw a coordinate plane where the axis scale is:

Plot:

Draw a curve, symmetric about the axis of symmetry, that passes through the vertex and the x-intercepts.

When the aircraft is in Toronto and Montreal, the height of the aircraft is zero.

The time at which the height of the aircraft is zero is t = 0 and t = 80 (from part a).  Therefore, the time it takes to fly from Toronto to Montreal is the difference between the two times:

[tex]\implies 80-0=80\; \sf minutes[/tex]

The maximum height of the aircraft is the y-value of the vertex of the parabola.

Therefore, as the vertex of the parabola is (40, 4000), the maximum height of the aircraft is 4000 m.  

The maximum height is reached 40 minutes after the aircraft leaves Toronto.

Answer:

I hope this will help. Tip: reuse the formula!

The expression that represents the sum of the arithmetic series that has a first term of -12, a common difference of +7 and a number of terms of 5 is the option with the following;

An arithmetic series one that consists of the sum of an arithmetic sequence, such that each term of the series is obtained from the previous term by the addition or subtraction of a constant.

The series in the question is; -12 + (-5) + 2 + 9 + 16

The series in therefore a series of an arithmetic sequence

The equation of the series when the first term is -12 can therefore be presented as follows;

-12 + 7·k

Where;

-12 is the first term, 7 is the common difference, n is the number of terms, and k = n - 1

The above values for the terms of the series is obtained by using values of k that range from k = 0 to k = 4

The expression that represents the series is therefore the option;

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Answer:

slope is the coefficient of x

so it is 6

good luck!!

Answer:

-11r

Step-by-step explanation:

4r - 9r = -5r

-5r - 11r = -16r

-16r + 7r = -11r

The value of f(-5) = -130

A cubic equation is an equation with degree three. All cubic equations have either one real root and two imaginary roots or three real roots. When polynomials have degree three, they are referred to as cubic polynomials.

A Cubic polynomial function is a polynomial function with the highest degree of exponents as 3. A cubic polynomial function has the following standard form:

Ax3 + bx2 + cx +d = 0

For the given question the cubic equation will be:

2x3 + bx2 + cx - 5 = 0

Given

Leading coefficient (a) = 2

Constant (T) = -5

f(1) = 0

f(2) = 9

Therefore the equation formed will be:

2x3 + bx2 + cx - 5 = 0

Now f(1) = 0

2(1)3 + b(1)2 + c(1) - 5 = 0

2 + b + c -5 = 0

b + c = 3  

b = 3-c -----(1)

On solving f(2) = 3

2(2)3 + b(2)2 + c(2) - 5 =3

16 + 4b + 2c – 5 =3

4b +2c = 3 – 11

4b + 2c = -8  ----(2)

Now substitute the b value in equation (2)

4(3-c) + 2c = -8  

12 – 4c +2c = -8

-2c = -20

C =10

Now substitute the c value in equation (1)

b= 3 – c

b = 3 -10

b = -7

Now substitute the b and c values in the cubic equation

2x3 - 7x2 + 10x - 5 = 0

Now calculate f(-5)

2(-5)3 - 7(-5)2 + 10(-5) - 5

= -250 + 175 – 50 -5

= -130

Therefore the value of f(-5) = -130

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Answer: 1. 3

5. -3

Step-by-step explanation:

Annie paid a total of $2.6 for 1.2 pounds of strawberries

In this question, we have the following parameters:

Unit cost per pound = $2.13 per pound

Number of pounds = 1.2 pounds

The amount paid for the number of pounds is represented by the equation

Amount paid = Unit cost per pound x Number of pounds

Substitute the known values in the above equation So, we have the following equation

Amount paid = 2.13 * 1.2

Evaluate the products

Amount paid = 2.556

Approximate

Amount paid = 2.6

Hence, the amount is $2.6

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Answer:

2.56

Step-by-step explanation:

The surface area of a triangular prism = 108cm2

The volume of the triangular prism = 48cm3

The space occupied by a two-dimensional flat surface is called the area. It is measured in square units. The area occupied by a three-dimensional object by its outer surface is called the surface area.

Given that

The Triangle legs are 3 and 4 feet long, the hypotenuse is 5 feet long, and the prism height is 8 feet tall.

We have to determine the surface area and volume of each triangular prism

here a = 3ft b = 4ft  c = 5ft and height  h = 8ft

Surface area of triangular prism = ab + h(a+b+c)

= 3x4 + 8(3+4+5)

= 12 + 8(12)

= 12 + 96

= 108cm2

Volume of triangular prism = ½(abh)

= ½ (3x4x8)

=1/2(96)

= 96/2

= 48cm3

Therefore

The surface area of a triangular prism = 108cm2

The volume of the triangular prism = 48cm3

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Answer:

A = 0.25*j + 1

Step-by-step explanation:

Answer:

[tex]A = 18 + \frac{j}{4}[/tex]

Step-by-step explanation:

A = 18 + j/4

A = Amount in $

Starting amount is 18 and a 1/4 dollar is earned for every cup of juice sold.

Answer:

soda: 97

Hot dogs: 56

Step-by-step explanation:

S-sodas

H- hot dogs

S+H=153

41+H=S

Substitute equation

(41+H)+H=153

41+2H=153

-41.        -41

2H=112

/2.   /2
H=56

S+56=153

 -56.  -56

S=97

Hopes this helps please mark brainliest

Applying the corresponding angles theorem, the measure of ∠HIJ = 33°.

If two triangles are similar to each other, their corresponding angles would be equal. Also, based on the corresponding angles theorem, corresponding angles are equal to each other.

Triangles IHJ and FGH are similar to each other, therefore, angles HFG and HIJ are corresponding angles.

Therefore:

The measure of angle HFG = the measure of angle HIJ

m∠HFG = 57 − 6x

m∠HIJ = −4x + 49

Thus:

57 − 6x = -4x + 49

Combine like terms

4x - 6x = -57 + 49

-2x = -8

Divide both sides by -2

-2x/-2 = -8/-2

x = 4

m∠HIJ = −4x + 49 = -4(4) + 49

m∠HIJ = 33°

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Complete Question:

In the diagram below of triangle FGH, I is the midpoint of FH and J is the midpoint of GH. If m∠HFG = 57 − 6x, and m∠HIJ = −4x + 49, what is the measure of ∠HIJ?

Answer:

x = 4

Step-by-step explanation:

Yes, y=x has an inverse.

Yes, y=x passes the horizontal line test.

If it didn't pass the horizontal line test, it would not have an inverse.

The amount of cookies baked was 28 cookies

let the number of pumpkin cookies be x

half of them on a plate for your brother and you

= x - x/2 = x/2

Your dog Gobbles ate six

= x/2 - 6

Your brother ate half of what was left

= (x/2 - 6)) / 2

= x/4 - 3

you ate the last four means that what was left is equal to 4

x/4 - 3 = 4

x - 12 = 16

x = 16 + 12

x = 28

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Answer:

1/5

Step-by-step explanation:

these fractions are proper fractions

Answer: 1/

Step-by-step explanation:

Question:

Write a linear function f with f (- 1/2) = 1 and f (0) = -4

The linear function f with f (- 1/2) = 1 and f (0) = -4 would be ; y = -5x -4.

What is a linear equation?

A linear equation is an equation in which each term has at max one degree. Linear equations in variables x and y can be written in the form

y = mx + c

Linear equation with two variables, when graphed on the cartesian plane with axes of those variables, give a straight line.

We are asked to write the linear function f with f (- 1/2) = 1 and f (0) = -4

Let the equation in variables x and y can be written in the form y = mx + c

So f (- 1/2) = 1

this gives, 1 = -1/2m+c      -----------eq 1

Also f (0) = -4

This gives -4 = c.            --------------eq2

Now Putting the value of c in the equation in eq1 we get m=0.

So 1 = -1/2m+c  

1 = -1/2m - 4

m = -5

Then we get;

y = -5x -4.

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The largest possible value of N is 42, which is equal to the sum of numbers of one group and product of numbers of other group.

We have provided the following informations,

total number = 10 and possible numbers are,

S = {1, 2,3,4,5,6,7,8,9,10}

Now, we have to split the 10 numbers into two groups. The conditions for group making are

maximum possible sum of numbers from S is 55.

because given numbers are in A.P and sum of A 10 terms is 55 in A.P.

but according to question, t the maximum possible value of N which follow the conditions is 42.

we can splits the set S elements in two groups such that one is P={6,7} and other one Q={ 1,2,3,4,5,8,9,10}

sum of numbers of Q is 42 and product of second group (P) = 42

No other value of N greater than 42 is possible for N .

Hence, 42 is largest possible value of N.

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Answer: 11 cows and 19 chickens

Step-by-step explanation:

Answer:

$90

Step-by-step explanation:

180x5 equal 00

$18x5 equals $90

The value that the linear equation predicts for the year 2001 is 4652.15

The discrepancy between the actual and anticipated value is 2173.85

Given data;

Here, we present the dataset from the United Nations, which contains information on the number of kilowatt-hours of wind energy generated globally. The data set provides statistics on the US for 25 years, from 1990 to 2014, in millions of kilowatt-hours.

The linear equation for the first 11 years of data, from 1990 to 2000, must be determined.

To determine how much the actual value and anticipated value for the year 2001 differ in Quantity, we must first forecast the value for the year 2001 using our fitted equation with y-intercept.

It will be written as y = m(x) + c.

where,

The dependent variable is y. (in our example is quantity)

The independent variable is x. (in our example is the year)

'm' is equal to the slope of the variable X.

'C' is a constant.

The fitted equation is provided as follows:

Quantity = 186.87 (year) - 369274.72

Now that the value for the year 2001 has been provided,

Quantity = -1868.87 -369274.72 

Quantity = 4652.15

The value that the linear equation predicts for the year 2001 is 4652.15.

The precise figure for 2001 is 6806.

For the year 2001, the discrepancy between the actual and anticipated values is

6806 - 4652.15 = 2173.85

The distinction is 2173.85.

(2173.85/6806)*100 is the percentage difference.

As a result, the difference between the actual value and the forecasted value for the year 2001 is 31.94%.

Hence,

The value that the linear equation predicts for the year 2001 is 4652.15

The discrepancy between the actual and anticipated value is 2173.85

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Answer: (2x+1)(x−3) ( 2 x + 1 ) ( x - 3 )

Step-by-step explanation:

To write a polynomial in standard form, simplify and then arrange the terms in descending order. Expand (2x+1)(x−3) ( 2 x + 1 ) ( x - 3 ) using the FOIL Method.

The 20th term of the given arithmetic progression is 119.

An arithmetic progression is a set of integers with a fixed difference between any two succeeding numbers (A.P.).

3,6,9,12,15,18, and 21 are A.P. examples.

So, the formula for the nth term:

a+(n-1)d, where d is the common difference

Now, take out the equation:

6th term = 35

a+(6-1)d= 35

a+5d=35 ....(1)

13th term = 77

a+12d= 77 .....(2)

Then, subtract equation (1) from equation (2):

a+12d-(a+5d)= 77-35

a+12d-a-5d= 42

7d=42

d=6

Calculate from equation (1):

a= 35-5d= 35-5(6)= 35-30 = 5

20th term= a+19d= 5+19(6)= 119

Therefore, the 20th term of the given arithmetic progression is 119.

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Answer:

Step-by-step explanation:

There is only one line of symmetry:

because the one that is vertical is not representing symmetry.

Step-by-step explanation:

AC is the combination of AB and BC.

so, AB + BC = AC

(2n - 1) + (4n + 5) = 10n - 12

2n - 1 + 4n + 5 = 10n - 12

6n + 4 = 10n - 12

4 = 4n - 12

16 = 4n

n = 4

Answer:

Each piece will be 4.9 inches long

Step-by-step explanation:

All you have to do is divide 14.7 by three as the rope itself is cut into 3 equal parts

therefore: 14.7/ 3= 4.9