Given the table of values below from a quadratic function, write an equation of that function.
X | 0 | 1 | 2 | 3 | 4 |
———————————
Y | 4 | 10 | 12 | 10 | 4 |

Answer:

Step-by-step explanation:

You want the amounts in each of two accounts, one earning 8% interest, and the other, with an initial balance that is $450 greater, earning 12% interest. The total interest earned is $176.

Let x represent the initial balance in the 12% account. Then the initial balance in the 8% account is (x -450). The total interest earned is ...

  0.08(x -450) +0.12(x) = 176

  0.20x - 36 = 176 . . . . . simplify

  0.20x = 212 . . . . . . add 36

  x = 1060 . . . . . .  divide by 0.2

  x -450 = 610

The 8% account had $610 invested; the 12% account had $1060 invested.

The number of solutions of the system of equations in this problem is given as follows:

Infinitely many solutions.

The system of equations for this problem is defined as follows:

Writing the second equation in standard format like the second, we have that:

x/3 + y = -2.

Multiplying by 3:

x + 3y = -6.

The two equations are equal, meaning that the system has an infinite number of solutions, and the two equations are the same on the graph.

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Answer:

Multiply row 1 by 1/7

The resulting matrix is
[tex]\begin{pmatrix}1&-\frac{4}{7}&\frac{8}{7}\\ -12&7&-13\end{pmatrix}[/tex]

Step-by-step explanation:

Original matrix is
[tex]\begin{pmatrix}7&-4&8\\ -12&7&-13\end{pmatrix}[/tex]

Multiplying any one row by a nonzero scalar is a valid matrix operation. This will not affect the final solution of the matrix

So all we have to do is to multiply row 1 by 1/7 and you get a 1 in row 1, column 1

[tex]R_1 \times \dfrac{1}{7} \longrightarrow \begin{pmatrix}1&-\frac{4}{7}&\frac{8}{7}\\ -12&7&-13\end{pmatrix}[/tex]

The length of the shortest side is 0.28ft

The scale factor is a measure for similar figures, who look the same but have different scales or measures.

Scale factor = dimension of new shape / dimension of old shape

Perimeter of new rectangle = 12 inches = 1 feet

perimeter of the old = 2(28+32)

= 100feet

scale factor = 1/100

therefore the dimension of the shortest length is

1/100 = x/28

100x = 28

x = 28/100

x = 0.28ft

The shortest length of scale drawing is 0.28feet.

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A mathematics topic that van be looked into is how linear algebra, graph theory and optimization can be used on the airline industry.

In this case, to solve the scheduling issues faced by airlines such as planning flights, assigning planes and crews to routes - mathematical techniques can be employed.

By leveraging Linear Algebra, operators can simulate the flow of aircrafts and passengers while Graph Theory can help model flight schedules and aircraft routes.

Simultaneously using Optimization techniques in the problem-solving process can work to streamline various operations resulting in reduced costs and improved efficiency which can increase profit margins.

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You can express sin195° as -sin15° by using the trig identities.

We will be applying trig identities to solve this question

sin195°:

Recall that:

    sin(x + 180°) = -sin(x)

then:

    sin(195°) = sin(15° + 180°) = -sin(15°)

Therefore,

   sin(195°) = -sin(15°).

cos75°:

Recall that:

   cos(x) = sin(90° - x)

then:

   cos(75°) = sin(90° - 75°) = sin(15°)

Therefore,

   cos(75°) = sin(15°)

tan345°:

Recall that:

   tan(x + 180°) = tan(x)

then:

   tan(345°) = tan(15° + 330°) = tan(15°)

Therefore,

   tan(345°) = tan(15°)

sin105°:

Recall that:

    sin(x + 90°) = cos(x)

then:

    sin(105°) = cos(15°)

Therefore,

   sin(105°) = cos(15°).

sin225°:

Recall that:

    sin(x + 180°) = -sin(x)

then:

    sin(225°) = sin(45° + 180°) = -sin(45°)

Therefore,

   sin(195°) = -sin(15°).

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Lee's TV costs $4.05 to operate for a month of 30 days.

To calculate the cost of operating Lee's TV for a month, we need to find out the total number of kilowatt-hours (kWh) of electricity consumed by the TV during that time.

First, let's find out how many watts Lee's TV consumes in a day:

250 watts/hour x 3 hours/day = 750 watts/day

To convert this to kilowatts, we divide by 1000:

750 watts/day ÷ 1000 = 0.75 kilowatts/day

Now, we can calculate the total number of kilowatt-hours consumed by the TV in a month:

0.75 kilowatts/day x 30 days = 22.5 kilowatt-hours

Finally, we can calculate the cost of operating the TV for a month:

22.5 kilowatt-hours x 18 cents/kilowatt-hour = $4.05

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The height of 3 meter to the left of the center of arch is -2.7 meters which is found by the evaluation of the given equation when x = -3.

We can solve it through

The Height at x = -3 meters on the left of the center = [tex](1/10)(-3^2 - 36) [by Substituting x = -3]= (1/10)(9 - 36)= (1/10)(-27)= -2.7 meters[/tex]

At the end height of the arch at 3 meters to the left of the center when x = -3 is -2.7 meters. This negative value means the point is actually below the ground level at that position. So the height is -2.7 meters where - insists negative value.

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The missing statement about base angles of the isosceles trapezoid is ∠TPR ≅ ∠ TAR.

The base angles of isosceles trapezoids are congruent.

In an isosceles trapezoid, the base angles (the angles formed by one of the bases and a leg) are congruent.

Since the opposite angles in an isosceles trapezoid are congruent, the base angles must also be congruent.

In the given diagram, we will identify the base angles as follows;

∠TPR ≅ ∠ TAR

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Answer:

only child

Step-by-step explanation:

A point that represent a striking deviation in the box plot above include the following: C. P.

In Mathematics and Statistics, a box plot can be defined as a type of chart that can be used to graphically or visually represent the five-number summary of a data set with respect to locality, skewness, and spread.

Based on the information provided about the data set, the five-number summary for the given data set include the following:

In conclusion, we can logically deduce that point P represent a striking deviation in the box plot because it is an outlier (it is significantly far from all of the other data points).

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The area of the parallelogram is A = 72 units²

Given data ,

Let the parallelogram be represented as ABCD

Now , the height of the parallelogram is = 12 units

The base of the parallelogram = 6 units

And , area of parallelogram A = base x height

On simplifying , we get

A = 12 x 6

A = 72 units²

Hence , the area is A = units²

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The solution to the system of equations, y = 2x -1 and y = x + 3 is: x = 4 and y = 7.

Given the system of equations as:

y = 2x - 1 ---> eqn. 1

y = x + 3 --> eqn. 2

Substitute y for (x + 3) into equation 1:

x + 3 = 2x - 1

Combine like terms:

x - 2x = -3 - 1

-x = -4

x = 4

Substitute x = 4 into equation 1:

y = 4 + 3

y = 7

The solution is: x = 4 and y = 7.

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The segments AB and CD on item 1 are classified as follows:

Perpendicular.

The slope, given by change in y divided by change in x, determines if the lines are parallel, perpendicular, or neither, as follows:

The slope of segment AB is given as follows:

m = (3 - 13)/(0 - (-2))

m = -10/2

m = -5.

The slope of segment CB is given as follows:

m = (3 - 0)/(10 - (-5))

m = 3/15

m = 1/5.

The multiplication of these slopes is given as follows:

-5 x 1/5 = -1.

As the multiplication of the slopes is of -1, the segments are perpendicular.

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The graph of y = (x + 3)² is a transformation of the graph y = x². It is shifted left 3 units.

The equation of the function is given as

y = x²

The transformed function is

y = (x + 3)²

This means that the parent function is y = x²

When compared, we can see that

x in y = x² is x + 3 in y = (x + 3)²

This means that y = x² is shifted left by 3 units to form y = (x + 3)²

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The relation that is not a function is relation 3, and the other 3 are functions.

A relation is a function if each point on its domain is mapped into a single point in the range.

So if you see an input that is mapped into two different outputs, then it is not a function.

Then the relation 3 is not a function, because h is mapped to different things, meaning that we have the same input being mapped to different outpouts. While the other 3 relations are all functions.

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Answer: If y varies inversely as x, then:

y = k/x

where k is a constant of proportionality. To find k, we can use the initial condition that y = 6 when x = 8:

6 = k/8

Solving for k, we get:

k = 48

Now we can use this value of k to find y when x = 2:

y = 48/2 = 24

Step-by-step explanation:

The area and the circumference of the circle is 1074.6 m² and 116.18 m respectively.

Given that a circle has a diameter of 37 m, we will find the circumference of and the area of the circle,

Radius = diameter /2

Radius = 18.5 m

Circumference = π × diameter

= 3.14 × 37

= 116.18 m

Area = π × radius²

= 3.14 × 18.5²

= 1074.6 m²

Hence, the area and the circumference of the circle is 1074.6 m² and 116.18 m respectively.

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The value of the expression is 13. 75

An algebraic expression is described as an expression that is known to consist of certain variables, terms, their coefficients, factors and also their constants.

Algebraic expressions are also known to be made up of some arithmetic operations such as;

From the information given, we have that;

14 minus 25%

This is represented as;

14 - 25%

Find the percent

14 - 25/100

Divide the values

14 - 0.25

13. 75

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Answer:

1) Let x be the distance from Alberto to the base of the building. Using trigonometry, we have:

tan(70) = 40 / (x + 6)

x + 6 = 40 / tan(70)

x = 40 / tan(70) - 6

x ≈ 11.1 feet

Therefore, Alberto is about 11.1 feet away from the base of the building.

2) Let h be the height of the building. Using trigonometry, we have:

tan(θ) = h / (100 + 1.55)

h = (100 + 1.55) tan(23)

h ≈ 42.9 feet

Therefore, the height of the building is about 42.9 feet.

3)  Let θ be the angle of elevation for each ramp. Using trigonometry, we have:

sin(θ) = 22 / 122

θ = sin⁻¹(22/122)

θ ≈ 10.3 degrees

Therefore, the measure of the angle of elevation for each ramp is about 10.3 degrees.

4) Let d be the distance from the boat to the base of the lighthouse. Using trigonometry, we have:

tan(28) = 40 / d

d = 40 / tan(28)

d ≈ 78.5 feet

Therefore, the distance from the base of the lighthouse to the boat is about 78.5 feet.

5) Let x be the distance from General Han Xin's position to the palace. Using trigonometry, we have:

tan(35) = x / 800

x = 800 tan(35)

x ≈ 595.4 meters

Therefore, the palace is about 595.4 meters away from General Han Xin's position.

6) Let h be the height of the clouds. Using trigonometry, we have:

tan(80) = h / 165

h = 165 tan(80)

h ≈ 702.4 meters

Therefore, the clouds are about 702.4 meters high.

Step-by-step explanation:

Answer:

x = 15

Step-by-step explanation:

3x+1+4x-3 = 103

7x = 105

x = 15

Answer:

Step-by-step explanation:

Yes, the student is correct. To write a percent as a fraction, we can write the number before the percent symbol as the numerator and 100 as the denominator. For example, 25% can be written as 25/100, which can be simplified to 1/4. This is because percent means "per hundred," so 25% means 25 per hundred, which can be expressed as a fraction with a denominator of 100.

Step-by-step explanation:

Similar triangle ratio:

15  is to 10    as  AB is to 6

15/10 = AB / 6

6 * 15/10 =   AB  =  9   units

Answer:

  (b)  The data has a possible range of 19, which is a wide spread. This might mean that there is a large difference in the number of water-skiing trips taken by the students.

Step-by-step explanation:

You want the best description of the spread of data shown in the histogram.

The least data value that can be represented on the chart is 6. The greatest value the chart can represent is 25. This means the possible range of data values is ...

  range = max - min = 25 -6 = 19

This possible spread of 19 might mean there is a large difference in the number of trips taken by students, choice B.

__

Additional comment

The range must be at least 21 -10 = 11 trips, not an answer choice. The most common number appears to be in the range 16-20, so will likely not be 10. (This is referred to as the "mode range", as we cannot tell from the grouped data what the actual mode is.)

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One of the fractions is 7/8 and can be written as

Information made available in the question includes

Mathematically this is written as

assuming the number is x

5/5 < x < 13/8

For fractions greater than five eighths but lesser than thirteen eighths is seven eighths (7/8) within the two.

This fraction can be expressed in three unique forms which include:

decimal notation of 0.875,

percent representation at 87.5%, and

fraction form = 7/8

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The amount of the interest, payment to principal, and new principal for the first payment is solved

Given data ,

Let the loan amount = $ 210,000

Let the interest rate r = 6.5 %

Let the monthly payment be = $ 1,362.06

Now , On calculating the monthly interest rate

Monthly interest rate = 0.065 / 12 = 0.00542 or 0.542%

Calculate the interest amount

Interest amount = 0.00542 x $210,000 = $1,138.20

Calculate the payment to principal

Payment to principal = $1,362.06 - $1,138.20 = $223.86

Calculate the new principal balance

New principal balance = $210,000 - $223.86 = $209,776.14

Hence , for the first payment, the amount of interest is $1,138.20, the payment to principal is $223.86, and the new principal balance is $209,776.14

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The number that represents the phrase is -40.

Let's use algebra to solve the problem.

If we let "a number" be represented by the variable x, we can write the first part of the sentence as "Seventeen more than a number" which can be written as:

x + 17

The problem also says that this expression is equal to negative twenty-three.

We can write that as:

x + 17 = -23

To solve for x, we need to isolate it on one side of the equation. We can do this by subtracting 17 from both sides:

x + 17 - 17 = -23 - 17

x = -40

Therefore, the number is -40.

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Answer:

80 cm³

Step-by-step explanation:

Volume = w x l x h = width x length x height

You already know the area of the base:  w x l = 8 cm², so the volume is:

V = 8 cm² x 10 cm = 80 cm³