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A quadratic equation is graphed to the left. Which of the following equations could be paired with the graphed equation to create a system of equations whose solution set is comprised of the points (2,-4)and (-4,2)?

Theo's base salary  using a simultaneous equation approach is $2,996.22 .

In order to determine the base salary of Theo, we can express the two earnings and sales amounts using simultaneous equation, that we would solve to arrive at the base salary

Bear in mind that total earnings are determined as base salary plus commission

Let X be the base salary

Let R be the rate of commission

commission =sales*rate of commission

When earnings were $3,835.25 and sales is $12,850, we have the below equation:

X+(12,850*R)=3,835.25

X+12850R=3,835.25  .................... equation (1)

When earnings were $3,641 and sales is $9,875, we have the below equation:

X+(9,875*R)=3641

X+9875R=3641 .........................  equation (2)

subtract equation 2 from 1

2975R=194.25

R=194.25/2975

R=commission rate=6.52941176470588%

substitute for R in equation 1 to arrive at X(base salary)

X+(12850*6.52941176470588%)=3,835.25

X=3,835.25-(12850*6.52941176470588%)

X=base salary=$2,996.22

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Based on the information, Christian would have $5525.5 of annuity.

According to given information, the number of coffees per week is 3 then, per month is 3x4 = 12

For each coffee is $4.5. Then monthly expenditure for coffees is 12 x 4.5 = $54

Rate of interest r = 1.6% = 1.6/100 = 0.016 and for monthly compounding r = 0.016/12 = 0.00133

n = number of payments = 8 x 12 = 96

We can use the formula for finding the future value as below

FV = C x [ ( 1 + r )n-1 ] / ( r )

FV = 54 x [ ( 1 + 0.00133 )96 – 1 ] / (0.00133)

= 54 x [ (1.13609 - 1)] / (0.00133)

= 54 x 0.13609 / (0.00133)

= 54 x 102.3233

= 5525.5

Therefore Christian would have $5525.5 of annuity.

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The ratio of major to minor arc = 2 : 1

What is a Circle?

A circle is the locus of a point such that its distance from a fixed point (center) is always constant.

Calculation

The length of an arc (L) with center angle θ is given by:

                                          L = (θ/360) * 2πr

where r is the radius.

Putting the values in the above formula.

For the major arc:

L = (240/360) * 2πr

For the major arc:

l = ((360-240)/360) * 2πr

l = (120/360) * 2πr

The ratio of major to minor arc = [(240/360) * 2πr] / [(120/360) *2πr] = 2 : 1

The ratio of major to minor arc = 2 : 1.

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Answer:c

Step-by-step explanation:

Point [tex](1,5)[/tex] is a solution of the equation [tex]g(x)=3x+2[/tex] and point [tex](1,5)[/tex] is not a solution of equation [tex]f(x)=|x-1|+1[/tex]

Why point [tex](1,5)[/tex] is solution of the equation [tex]g(x)=3x+2[/tex] ?

If point [tex](1,5)[/tex] is solution of the equation then they must satisfy the equation.

So we need to check one by one

[tex](x,y)=(1,5)[/tex]

equation [tex]g(x)=3x+2[/tex]

We can write as

[tex]y=3x+2\\5=3*1+2\\5=5[/tex]

So  point [tex](1,5)[/tex] is solution of this equation.

Equation [tex]f(x)=|x-1|+1[/tex]

We can write as

[tex]y=|x-1|+1\\5=|1-1|+1\\5=0+1\\5\neq 1[/tex]

So point [tex](1,5)[/tex] is not solution of equation [tex]f(x)=|x-1|+1[/tex]

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As a percentage, the relative frequency of plastics recycling in New Mexico in 2008 compared to plastics recycled in all three states combined is approximately 11%.

A relative frequency measures the proportion of events that occur within a class out of the total number of observations.

When using relative frequency, the results are usually displayed in percentages, proportions, and fractions.

Year    State                   Recycled Plastics                 Relative

                                       (thousands of tons)            Frequency

2008  New Mexico                   500                        0.111  (500/4,500)

2008  New York                     1,500                        0.333 (1,500/4,500)

2008  Texas                          2,500                        0.566 (2,500/4,500)

Total                                       4,500                        1

Thus, the relative frequency of plastics recycling in New Mexico in 2008 compared to plastics recycled in all three states combined is approximately 11%.

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Answer: 9%

Step-by-step explanation:

just did the question

The slope of diagonal PS is  -1 and the slope of diagonal QR is 1 based on the information about the coordinate plane.

Step 1: Calculate the slope of the diagonals.

The slope of diagonal PS is  -1

The slope of diagonal QR is 1

Step 2: Calculate the midpoint of the diagonals.  

The midpoint of PS is (2,2)

The midpoint of QR is  (2,2)

The diagonals of the square are perpendicular bisectors because the diagonals are perpendicular and share the same midpoint

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Answer:

1. The slope of diagonal PS is -1.

2. The slope of diagonal QR is 1.

3. The midpoint of PS is (2,2).

4. The midpoint of QR is (2,2).

5. The diagonals of the square are perpendicular bisectors because the diagonals are perpendicular and share the same midpoint.

Step-by-step explanation: I just did it on edge 2023. Hope this helps!

Answer:

31

Step-by-step explanation:

C= 2πr  We will used 3.14 for pi and the radius is 5

C = 2(3.14)(5)

C =31.4 Then round to the nearest whole number which would be 31.  31.4 is closer to 31 than 32

the operation:

[tex]2*10^1 - 4*10^0 = 20 - 4 = 16[/tex]

Gives a square number.

A perfect square is the product of a number and itself.

As you can see in the example, 16 is a square number. Then let's try to get 16.

To get 16 we can use the difference:

20 - 4

So the first therm needs to be equal to 20, and the second equal to 4.

To write 20 in scientific notation we have:

[tex]2*10^1[/tex]

To write 4 in in scientific notation:

[tex]4*10^0[/tex]

Then the operation:

[tex]2*10^1 - 4*10^0 = 20 - 4 = 16[/tex]

Gives a square number.

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Answer:

[tex]-\frac{345}{37}[/tex]

Step-by-step explanation:

Just follow the order of operations

210÷[5+16÷2{6−18÷(7+2)}]−15  

= 210÷[5+16÷2{6−18÷9}]−15   (calculate 7+2)

= 210÷[5+16÷2{6−2}]−15 (calculate 18÷9)

= 210÷[5+16÷2{4}]−15  (calculate 6-4)

= 210÷[5+16÷2×4]−15

= 210÷[5+8×4]−15  (calculate 16÷2)

= 210÷[5+32]−15  (calculate 8×4)

= 210÷[37]−15  (calculate 5+32)

= 210÷37−15

= 210÷37−(15×37)÷37  (put on the same denominator)

= 210÷37−555÷37  (calculate 15×37)

= (210−555)÷37

=-345÷37   (calculate 210-555)

Answer:

x - 3 > 15

Step-by-step explanation:

The value of positive integers in the set are 16.

According to the statement

we have given that the there is a set of numbers from 1 to n and we have to find that the how many integers in this set. and there is one condition that the numbers in the set are less than or equal to 24.

So, For this purpose,

Since [tex]$1 + 2 + \cdots + n = \frac{n(n+1)}{2}$[/tex]

the condition is equivalent to having an integer value for [tex]$\frac{n!} {\frac{n(n+1)}{2}}$.[/tex]

This reduces, when [tex]$n\ge 1$[/tex], to having an integer value for [tex]$\frac{2(n-1)!}{n+1}$[/tex]

This fraction is an integer unless n+1 is an odd prime. There are 8 odd primes less than or equal to 24,

so there are 24-8 = 16.

So, The value of positive integers in the set are 16.

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The expression equivalent to -7(y - 2) is -7y + 14

Given the expression; -7(y - 2)

We expand the expression by multiplying each element inside the parentheses the element out i.e -7

-7(y - 2)

[ -7 × y and -7 × -2 ]

-7y + 14

Therefore, the expression equivalent to -7(y - 2) is -7y + 14.

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The property A*B = (A' + A") * ( B'+B") is equal to each other.

According to the statement

We have given that the a and b is the positive integers and we have to prove that the product of all positive divisors of a equals the product of all positive divisors of b.

And in this statement

Now we use Distributive property

Here A and B is the positive integer and

A' and A" are the divisors of A and B' and B" are the divisors of B.

Now,

A = A' + A" and B = B'+B"

Now, Multiply both with each other then

A*B = (A' + A") * ( B'+B")

then

A*B = (A' B'+ A'B") + ( A"B'+A'B")

by this way it is equal to each other

Hence proved.

So, The property A*B = (A' + A") * ( B'+B") is equal to each other.

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Answer: [tex]x=8, y=2\sqrt 2[/tex]

Step-by-step explanation:

By the Pythagorean theorem, x=8.

So, by the geometric mean theorem,

[tex]y^2 = (6)(2)=8\\\\y=2\sqrt{2}[/tex]

Answer:

[tex]\huge\boxed{\sf 7x + 10\ cm}[/tex]

Step-by-step explanation:

= 5 + 2x + 2x + 5 + 3x

Combine like terms

= 2x + 2x + 3x + 5 + 5

= 7x + 10 cm

[tex]\rule[225]{225}{2}[/tex]

Answer:

7x + 10

Step-by-step explanation:

Perimeter is the sum of all the sides together, the distance around a shape.

3x + 5 + 2x + 2x + 5

Organize so the variables are on one side

3x + 2x + 2x + 5 + 5

Combine like terms:

7x + 10

Your answer would be: 7x + 10

I hope it helps! Have a great day!

bren~

If the sales had dropped 23% then music store had sold 551 units in the second quarter.

Given that a music store had sold 715 units in first quarter and sales had dropped by 23%.

We are required to determine the sales in the second quarter.

Percentage is the number or ratio expressed in terms of 100. It is expressed as %.

Sales in first quarter=715 units

Decrease in sales=23%

In units ,decrease=715*23%

=715*23/100

=164.45

Sales of second  quarter=715-164.45

=550.55

After rounding we will get 551.

Hence if the music store sold 715 units in first quarter then the units sold by music store in second quarter 551 units.

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Answer:

  7.7 km

Step-by-step explanation:

This question is asking you to find the third side of a triangle in which two sides and an angle not between them are given. The law of sines provides the necessary relationships.

The Law of Sines tells you that triangle side lengths are proportional to the sine of the opposite angle. For this triangle TPJ, the relation is ...

  t/sin(T) = p/sin(P) = j/sin(J)

We are given T=68°, p=5.2 km, t=7.5 km, and we are asked to find the length of j, the TP distance.

We know the sum of angles in a triangle is 180°, and the sine of an angle is equal to the sine of its supplement. This lets us fill in the Law of Sines equation like this:

  7.5/sin(68°) = 5.2/sin(P) = j/sin(68°+P) . . . . . solve for j

This can be solved in two steps. First, we find angle P, then we use that to find length j.

  sin(P) = 5.2/7.5 × sin(68°) ≈ 0.642847

  P = arcsin(0.642847) ≈ 40.0045°

Now, we can find j:

  j = 7.5 × sin(68° +40.0045°)/sin(68°) ≈ 7.693 . . . km

The distance from the tower to the plane is about 7.7 km.

__

Additional comment

We have used T, P, and J to refer to the vertices at the tower, plane, and jet.

The triangle can also be solved using the Law of Cosines. In that case, the missing side will be the solution to a quadratic equation with irrational coefficients.

Snow reaches at a 15 inches after 16 hours. and 8 inches melt in next 6 hours.

According to the statement

we have a given that there was 1 inch snow on the ground before the snowstorm starts.

then snow fell at constant rate of 3 inches every 2 hours until the snow level reaches at 12 inch had fallen

It means after that there was 13 inch snow on the ground.

and in 1 hour only 1.5 inches snow increases

and if snow takes 2 hours to increase at 3 inches then

it takes 10 hours to reach at 12 inches.

So, snow falls for 10 hours to increase at 12 inches.

And then the snow falls at constant rate of 1 inch per hour for 2 hours.

It means now snow reaches at a 15 inches after 16 hours.

Then sun melt the snow at a 4 inches per 3 hours and sun came for 6 hours then

it means now the level of snow reduced and came at the 7 inches.

because sun reduced 8 inches snow in 6 hours.

So, this is the data collected by a person.

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Answer:

1 1/2

Step-by-step explanation:

When you are subtracting a negative number is is the same as adding a positive.  So the problem is really 5/8 + 7/8, since the denominators are the same, just add the numerators to get 12/8  divide the top and bottom by 4 to get 3/2 or 1 1/2, if I divide 3 by 2.

Answer:

x = -8, 1.

Step-by-step explanation:

x^2 + 7x - 8 = 0

(x + 8)(x - 1) = 0

x = -8, 1.

Answer:

-8 and 1

Step-by-step explanation:

Quadratic expression.

A quadratic expression is an expression with 2 as the highest power of the unknown.

Solving the question:

[tex]x {}^{2} + 7x - 8 \\ x {}^{2} + 8x - x - 8 \\ x(x + 8) - 1(x + 8) \\ (x - 1)(x + 8) \\ x = 1 \: or \: x = - 8[/tex]

The matricial equation of the degenerate parabola is [tex]\left[\begin{array}{c}x'\\y'\end{array}\right] = \left[\begin{array}{c}\frac{ \sqrt{2} }{2}\cdot x + \frac{1}{8}\cdot x^{2}+1 \\\-\frac{\sqrt{2}}{2}\cdot x + \frac{1}{8}\cdot x^{2} + 1 \end{array}\right][/tex].

A parabola is degenerated when its axis of symmetry is not parallel to any orthogonal axis (i.e. x, y). First, we have to find an "equivalent" parabola whose axis of symmetry is parallel to the y-axis and whose vertex is along that axis.

Direction of the degenerate parabola

[tex]\tan \theta = \frac{2 - 1}{2 - 1}[/tex]

tan θ = 1

θ = 45°

This means that the degenerate parabola must be rotated 45° clockwise (- 45°) around the origin with respect to the "equivalent" parabola.

Distance from the vertex to the focus

[tex]p = \sqrt{(2 - 1)^{2}+(2 - 1)^{2}}[/tex]

[tex]p = \sqrt{2}[/tex]

Vertex of the "equivalent" parabola

[tex](h', k') = (0, \sqrt{2})[/tex]

Equation of the "equivalent" parabola

[tex]y = \frac{1}{4\cdot p}\cdot x^{2} + k'[/tex]

[tex]y = \frac{1}{4\sqrt{2}}\cdot x^{2}+\sqrt{2}[/tex]

Now we apply following rotation formula:

[tex]\left[\begin{array}{c}x\\y\end{array}\right] = \left[\begin{array}{cc}\cos (-45^{\circ})&-\sin (-45^{\circ})\\\sin (-45^{\circ})&\cos (-45^{\circ})\end{array}\right] \cdot \left[\begin{array}{c}x\\\frac{1}{4\sqrt{2}}\cdot x^{2}+\sqrt{2}} \end{array}\right][/tex]

[tex]\left[\begin{array}{c}x'\\y'\end{array}\right] = \left[\begin{array}{c}\frac{ \sqrt{2} }{2}\cdot x + \frac{1}{8}\cdot x^{2}+1 \\\-\frac{\sqrt{2}}{2}\cdot x + \frac{1}{8}\cdot x^{2} + 1 \end{array}\right][/tex]

A representation of the degenerate parabola is shown in the figure attached below.

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Answer:

see image

Step-by-step explanation:

see image. We can use the given info and definition of isosceles (congruent sides) and reflexive property (something is congruent to itself) to prove (i) by SSS.

The using "Corresponding Parts of Congruent Triangles are Conguent" (CPCTC) to get more info to prove (ii) by SAS

The graph of the quadratic function f(x)=x² - 5x + 12 is a parabola which opens up.

An equation is an expression that shows the relationship between two or more numbers and variables.

The standard form of a quadratic equation is:

y = ax² + bx + c

The graph of a quadratic equation is a parabola.

The graph of the quadratic function f(x)=x² - 5x + 12 is a parabola which opens up.

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The equation of the first circle is (x + 1)^2 + (y - 1)^2 = r^2 and the equation of the second circle is (x + 1)² + (y - 1)² = 16

The points are given as:

P(3, 0) and Q(0, 5)

The midpoint of PQ is

Midpoint = 0.5(3 + 0, 0 + 5)

Midpoint = (1.5, 2.5)

Calculate the slope of PQ

m = (y2 - y1)/(x2 - x1)

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

m = -5/3

A line perpendicular to PQ would have a slope (n) of

n = -1/m

This gives

n = -1/(-5/3)

n = 0.6

The equation is then calculated as:

y = n(x - x1) + y1

Where

(x1, y1) = (1.5, 2.5)

So, we have:

y = 0.6(x - 1.5) + 2.5

y = 0.6x - 0.9 + 2.5

Evaluate the sum

y = 0.6x + 1.6

Hence, the equation of the perpendicular bisector of PQ is y = 0.6x + 1.6

We have:

y = x + 2

Substitute y = x + 2 in y = 0.6x + 1.6

x + 2 = 0.6x + 1.6

Evaluate the like terms

0.4x = -0.4

Divide

x = -1

Substitute x = -1 in y = x + 2

y = -1 + 2

y = 1

Hence, the center of the circle is (-1, 1)

We have:

Center, (a, b) = (-1, 1)

Point, (x, y) = (0, 5) and (3, 0)

A circle equation is represented as:

(x - a)^2 + (y - b)^2 = r^2

Where r represents the radius.

Substitute (a, b) = (-1, 1) in (x - a)^2 + (y - b)^2 = r^2

(x + 1)^2 + (y - 1)^2 = r^2

Substitute (x, y) = (0, 5) in (x + 1)^2 + (y - 1)^2 = r^2

(0 + 1)^2 + (5 - 1)^2 = r^2

This gives

r^2 = 17

Substitute r^2 = 17 in (x + 1)^2 + (y - 1)^2 = r^2

(x + 1)^2 + (y - 1)^2 = r^2

Hence, the circle equation is (x + 1)^2 + (y - 1)^2 = r^2

The equation of the second circle is

2x² + y² + ax + by - 14 = 0

Rewrite as:

2x² + ax + y² + by = 14

For x and y, we use the following assumptions

2x² + ax = 0    and  y² + by = 0

Divide through by 2

x² + 0.5ax = 0    and  y² + by = 0

Take the coefficients of x and y

k = 0.5a                   k = b

Divide by 2

k/2 = 0.25a           k/2 = 0.5b

Square both sides

(k/2)² = 0.0625a²           (k/2)² = 0.25b²

Add the above to both sides of the equations

x² + 0.5ax +0.0625a² = 0.0625a²    and  y² + by + 0.25b² = 0.25b²

Express as perfect squares

(x + 0.25a)² = 0.0625a² and (y + 0.5b)² = 0.25b²

Add both equations

(x + 0.25a)² + (y + 0.5b)² = 0.0625a² + 0.25b²

So, we have:

2x² + ax + y² + by = 14 becomes

(x + 0.25a)² + (y + 0.5b)² = 0.0625a² + 0.25b²+ 14

Comparing the above equation and (x + 1)^2 + (y - 1)^2 = r^2, we have:

0.25a = 1 and 0.5b = -1

Solve for a

a = 4 and b = -2

This means that the value of a is 4 and b is -2

We have:

a = 4 and b = -2

Substitute these values in (x + 0.25a)² + (y + 0.5b)² = 0.0625a² + 0.25b²+ 14

This gives

(x + 0.25*4)² + (y - 0.5*2)² = 0.0625*4² + 0.25*(-2)²+ 14

(x + 1)² + (y - 1)² = 16

The equation of the first circle is

(x + 1)² + (y - 1)² = 17

The radii of the first and the second circles are

R = √17

r = √16

√17 is greater than √16

Since they have the same center, and the radius of the first circle exceeds the radius of the second circle, then the second circle lies inside the first circle.

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The possible outcomes are WH, BH, BH, BH, RH, RH, WL, BL, BL, BL, RL, RL

The given parameters are:

Coin = Head (H) and Tail (T)

Marble = W, B, B, B, R, R

See attachment for the tree diagram

From the tree diagram, we have the following possible outcomes

WH, BH, BH, BH, RH, RH, WL, BL, BL, BL, RL, RL

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Answer:

The system of equations y=14-2x and 6x+3y=42.

Step-by-step explanation:

Please see attachment to see the answer as a graph.

Hope this helps!

The central angle formed between the ends of the ribbon is 98.6°.

The circumference will be:

= πd

= 3.14 × 15 = 47.1

Ribbon = 60 - 47.1 = 12.9

Length of arc = x/360 × πd

12.9 = x/360 × 3.14 × 15

x = 98.6°

The angle is 98.6°

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Using the law of sines, it is found that 1 triangle can be formed with the given conditions.

Suppose we have a triangle in which:

The lengths and the sine of the angles are related as follows:

[tex]\frac{\sin{A}}{a} = \frac{\sin{B}}{b} = \frac{\sin{C}}{c}[/tex]

Hence, for this problem, we have that the relation is:

[tex]\frac{\sin{64^\circ}}{10} = \frac{\sin{G}}{9}[/tex]

[tex]\sin{G} = 0.9\sin{64^\circ}[/tex]

[tex]\sin{G} = 0.8089[/tex]

[tex]G = \arcsin{0.8089}[/tex]

G = 54º

A triangle can have one angle of 64º and another of 54º, hence 1 triangle can be formed with the given conditions.

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