Question 5 of 15
What would be the best first step in solving this system
x²-3x + 2y = -4
y = 3x + 2

Step-by-step explanation:

[tex] - 32 + 45 = 13 \\ t_{n} = ( a_{1} + (n - 1)d) \\ \\ d = 13 \: \: a_{1} = - 45[/tex]

[tex] t_{n} = - 45 + (n - 1)13 = = = > \\ - 45 + 13n - 13 = = = > \\ t_{n} = 13n - 58[/tex]

and now

[tex]124 = 13n - 58 = = = > \\ 182 = 13n = = = > n = 14[/tex]

The number of terms in the sequence: –45, –32, –19, –6, ..., 124 = 9.

The common difference is -45 - (-32)= 13

                                                  d = 13.

AP is a sequence of numbers in order, in which the difference among any two consecutive numbers is a constant cost. it's also referred to as mathematics series.

using arithmetic progress:-

last term = (n-1)d

first term(a) = –45

    term = a + (n-1)d

there is a difference of 13, so the sequence will be

–45, –32, –19, –6,7, 20, 33, 46, 59, 72, 85, 98, 111, 124.

∴ number of terms = 9

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Answer:

2n^3 + 6n^2 + 8n

Answer: It's 2n^3 + 6n^2 + 8n

Step-by-step explanation:

We kindly invite to check the image attached below to see the representation of the exponential function. This function shows exponential growth.

In this occasion we must plot the graph of exponential functions of the form:

y = a · bˣ     (1)

Where:

First, we need to follow this procedure to create the graph of the curve on Cartesian plane:

Therefore, we build the exponential curve with the help of a graphing tool (i.e. Desmos), whose result is shown in the image attached below.

From (1) we must understand that exponential functions report growth for b > 1 and decay for 0 < b < 1. Thus, the exponential function y = 3ˣ shows exponential growth according to graphical and analytical findings.

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As x increases, y value decreases.

The rate of change for y as a function of x is decreasing, therefore the function is a decreasing function.

For all values of x, the function value y, decreases to 0.

The y intercept of the graph is the function value y=8

When x=1, the function value y=5.

From the given graph, it is clear that the curve is decreasing for all values of x. Hence, the rate of change of the give curve is decreasing.

Therefore, the giving function is called as decreasing function.

Since, the function is decreasing for all values of x, the value of y decreases to 0.

Form the graph, it is clear that the y-intercepts is at y=8.

Also, the value of y at x=1 is 5 from the graph.

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If [tex]x[/tex] and [tex]y-1[/tex] have the same sign, then either

[tex]x>0,y>1 \implies 2|x| + 3|y-1| = 2x + 3(y-1)=6 \implies 2x + 3y = 9[/tex]

or

[tex]x<0,y<1 \implies 2|x| + 3|y-1| = -2x - 3(y-1) = 6 \implies 2x + 3y = -3[/tex]

If [tex]x[/tex] and [tex]y-1[/tex] have opposite sign, then

[tex]x>0,y<1 \implies 2|x| + 3|y-1| = 2x - 3(y-1) = 6 \implies 2x -3y = 3[/tex]

or

[tex]x<0,y>1 \implies 2|x| + 3|y-1| = -2x + 3(y-1) = 6 \implies 2x-3y = -9[/tex]

This is to say that the region has boundaries given by these two sets of parallel lines, so we can equivalently describe the region with the set

[tex]R = \left\{(x,y) \mid -3\le2x+3y\le9 \text{ and } -9\le2x-3y\le3\right\}[/tex]

The area of [tex]R[/tex] is given by the double integral

[tex]\displaystyle \iint_R dx\,dy[/tex]

To compute the area, change the variables to

[tex]\begin{cases}u = 2x + 3y \\ v = 2x - 3y\end{cases} \implies \begin{cases}x = \frac14(u+v) \\ y = \frac16(u-v)\end{cases}[/tex]

The Jacobian for this transformation is

[tex]J = \begin{bmatrix} x_u & x_v \\ y_u & y_v \end{bmatrix} = \begin{bmatrix}1/4 & 1/4 \\ 1/6 & -1/6\end{bmatrix}[/tex]

with determinant [tex]\det(J) = -\frac1{12}[/tex]. Then the integral transforms to

[tex]\displaystyle \iint_R dx\,dy = \iint_R |J| \, du \, dv = \frac1{12} \int_{-3}^9 \int_{-9}^3 dv\, du[/tex]

which is 1/12 the area of a square with side length 12. Hence the integral evaluates to

[tex]\displaystyle \iint_R dx\,dy = \frac1{12}\times12^2 = \boxed{12}[/tex].

Based on the transformed function of y = sin(x) and the given parameters, the value that is closest to the amplitude of the transformed function is 54

The amplitude of the function is calculated

Amplitude = Highest  - Lowest

From the graph, we have the following points

Highest = 84

Lowest = 30

Substitute the known values in the above equation

Amplitude = 84 - 30

Evaluate the difference

Amplitude = 54

Based on the transformed function of y = sin(x) and the given parameters, the value that is closest to the amplitude of the transformed function is 54

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The steps in evaluating each of the following expressions is shown below.

An expression is a mathematical equation which shows the relationship that exist between two or more numerical quantities or variables.

15 - 35/7 - 2 + 3 - 4

15 - (35/7) - 2 + 3 - 4 (bracket and division)

15 - 5 - 2 + 3 - 4 (regroup)

15 + 3 - 5 - 2 - 4 (subtract and add)

18 - 11 = 7.

10 + 2(9 - 5) - 16/18

10 + (2 × 4) - 8/9 (bracket and division)

10 + 8 - 8/9 (add)

18 - 8/9 (subtract)

162/9 - 8/9 = 17 1/9 or 154/9.

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Complete Question:

Show your steps in evaluating each of the following expressions. The steps count 4 points each, the answer is 1 point.

A. 15 - 35/7 -2 + 3 -4

B. 10 + 2(9 - 5) - 16/18

At the DVD rental store, Jamie found 6 DVDs that she wanted, but can only rent 4. Jamie can make 15 possible choices, as per combinations of DVDs.

Number of Possible Combinations:

Given Information is as follows,

Total number of DVDs that Jamie wanted, n = 6

Number of DVDs Jamie can rent at a  time, x =4

The Combinations formula is given as,

ⁿCₓ = n! / (n-x)! x!

Here, n = 6 and x = 4

Substituting these values of n and x in the Combinations formula, we get,

⁶C₄ = 6! / (6-4)! 4!

⁶C₄ = 6! / 2! 4!

⁶C₄ = 6×5×4! / 2! 4!

⁶C₄ = 6×5 / 2

⁶C₄ = 3×5

⁶C₄ = 15

Thus, Jamie can make 15 possible combinations of DVDs.

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The option B is a correct option which is y = 26x and y = -0.030(x-500)2 15,900 represent the quadratic and linear function.

According to the statement

we have given that Vertex

(h,k) = (500, 15900)

And One of the points on the graph

(x,y) = (0,8400)

FIRST PART: we have to find the quadratic function

We can find the quadratic function by parabola's equation formula

y = a (x - h)² + k  -(1)

Input the numbers to the formula, to find the value of a

y = a (x - h)² + k

8400 = a(0 - 500)² + 15900

8400 = a (500)² + 15900

8400 = 250000a + 15900

-250000a = 15900 - 8400

-250000a = 7500

a = 7500/-250000

a = 0.03

Now,

Submit a to the formula (1)

y = a (x - h)² + k

y = 0.03 (x - 500)² + 15900

this is the quadratic equation.

SECOND PART: Find the linear function

the total cost = cost each helmet × the number of helmet

y = 26x

So,

The option B is a correct option which is y = 26x and y = -0.030(x-500)2 15,900 represent the quadratic and linear function.

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Disclaimer: This question was incomplete. Please find the full content below.

Question: A company plans to sell bicycle helmets for $26 each. The company's business manager estimates that the cost, y, of making x helmets is a quadratic function with a y-intercept of 8,400 and a vertex of (500, 15900)

x= number of helmets

y = amount in dollars

Which system models this situation?

a) y = 26x and y = 8,400(x-500)2+15,900

b) y = 26x and y = -0.030(x-500)2+15,900

c) y = x/26 and y = -0.030(x-500)2+15,900

d) y = x/26 and y =8,400(x-500)2+15,900

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Answer:

B. y = 26x and y = -0.030(x-500)2+15,900

Step-by-step explanation:

Answer:

C.  b^8.

Step-by-step explanation:

b^10/b^2     We subtract the exponents:-

= b^(10-2)

= b^8.

b^8

Step-by-step explanation:

b^10/b^2 ,. b^10-2 ;. b^8

circumference of the mirror = 175.84 cm

area of the mirror = 2461.76 cm²

The measure needed to find the amount of wire round the mirror is the circumference.

The measure needed to find the amount of glass needed is the area.

The circumference and area of a circle can be found as follows:

circumference of the mirror = 2πr

circumference of the mirror = 2 × 3.14 × 28 = 175.84 cm

area of the mirror = πr²

area of the mirror = 3.14 × 28²

area of the mirror = 2461.76 cm²

The measure needed to find the amount of wire round the mirror is the circumference.

The measure needed to find the amount of glass needed is the area.

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The blue marble is predicted to be picked 120 times, in the experiment of picking a marble from a bag containing 3 red and 2 blue marbles and performing this experiment 300 times, using the theoretical probability.

The theoretical probability of any event is the ratio of the number of favorable outcomes to the event, to the total number of possible outcomes in the experiment.

If we have an event A, the number of favorable outcomes to event A as n, and the total number of possible outcomes in the experiment as S, then the theoretical probability of event A is given as:

P(A) = n/S.

In the question, we are given that Ellen has a bag with 3 red marbles and 2 blue marbles in it. She is going to randomly draw a marble from the bag 300 times, putting the marble back in the bag after each draw.

We are asked the predict the number of times that the marble picked will be blue using the theoretical probability.

Let the event of picking a blue marble be A.

The number of favorable outcomes to event A (n) = 2 {The total number of blue marbles in the bag}.

The total number of possible outcomes in the experiment of picking a ball (S) = 5 {The total number of marbles in the bag}.

Thus, the theoretical probability of event A is,

P(A) = n/S = 2/5 = 0.4.

To predict the number of times marble picked was blue, we multiply the time's the experiment was performed by the theoretical probability of picking a blue ball.

Thus, the predicted number of times = 300 * 0.4 = 120.

Thus, the blue marble is predicted to be picked 120 times, in the experiment of picking a marble from a bag containing 3 red and 2 blue marbles and performing this experiment 300 times, using the theoretical probability.

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Answer:

x = 20

Step-by-step explanation:

x°

2x°

(x + 10)°

little box on the bottom left means this is a right angle which is 90°

add up all the angles and make it equal to 90°

( x° + 2x° + (x + 10)° ) = 90°

4x + 10 = 90

4x = 80

x = 20

Since we can see the "square" at the bottom left corner of the angle, the square indicates that the angle is a right angle (which measures 90°).

We can also see three smaller angles forming the right angle. Therefore, the sum of the measure of the smaller angles = 90°.

According to the diagram, the measures of the smaller angles are x°, 2x°, and (x + 10)° respectively. Then we get the following equation:

[tex]\implies x + 2x + (x + 10) = 90\°[/tex]

Here, we had the equation: [tex]\underline{x + 2x + (x + 10) = 90\°}[/tex]

[tex]\implies x + 2x + x + 10 = 90\°[/tex]              [tex]\text{(Ope} \text{ning the parentheses)}[/tex]

[tex]\implies 4x + 10 = 90\°[/tex]                             [tex]\text{(Combining like terms)}[/tex]

[tex]\implies 4x + 10 - 10 = 90 - 10[/tex]          [tex]\text{(Subtracting 10 on both sides)}[/tex]

[tex]\implies 4x = 80[/tex]                                    [tex]\text{(Simplifying both sides)}[/tex]

[tex]\implies \dfrac{4x}{4} = \dfrac{80}{4} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \text{(Dividing 4 on both sides)}[/tex]                            

[tex]\implies \boxed{x = 20}[/tex]                                      [tex]\text{(Simplifying both sides)}[/tex]

Therefore, the value of x, in the diagram provided, is 20.

Answer:

5 cm

Step-by-step explanation:

When two chords are equidistant from the center of the circle, the two chords have equal length. Therefore, the length of chord AB, 4x - 6, is equal to the length of chord CD, 6x - 12.

4x - 6 = 6x - 12

6 = 2x

x = 3

Now that we know x = 3, we can substitute the value back into the original expression, 4x - 6, to find the length of chord AB.

AB = 4x - 6 = 4*3 - 6 = 12 - 6 = 6 cm

When measuring the distance between a line and a point, we create a segment through the point perpendicular to the line. In Geometry, we also learn that the perpendicular bisector of a chord in a circle contains the center of the circle.

In this case, the gray line perpendicularly bisects segment AB. PX is 4 cm long and AX is 3 cm long (because AX is half the length of AB). Notice that triangle AXP is a right triangle, so we can use Pythagorean Theorem to find AP.

[tex]AP^{2} = AX^{2} +PX^{2}[/tex]

[tex]AP = \sqrt{3^{2} +4^{2} }[/tex]

[tex]AP =\sqrt{9+16}[/tex]

[tex]AP = \sqrt{25}[/tex]

[tex]AP = 5[/tex]

Answer:

[tex]y = -\frac{1}{2} x+4[/tex]

Step-by-step explanation:

Standard form for equation of line: y = mx + c

where m = gradient or slope

c = y-intercept

From the question we know that,

x = 2

y = 3

m = - 0.5

We will substitute these values into the equation to find c.

3 = (-0.5)(2) + c

3 = - 1 + c

c = 3 + 1 = 4

Therefore the equation of this line is [tex]y = -\frac{1}{2} x+4[/tex]

Answer:

13

Step-by-step explanation:

Given x = 2, y = 3 and z = 4. We'll evaluate the value of x² + y² with given condition.

First, remind that we are only given the expression of x-term and y-term only and therefore, z-term is not included - it's not to be considered.

Substitute x = 2 and y = 3 in the expression:

[tex]\displaystyle{2^2+3^2 = 4+9}\\\\\displaystyle{4+9 = 13}[/tex]

Hence, the value of x² + y² when x = 2 and y = 3 is 13.

Please let me know if you have any questions!

The value of the quantity after 1.2 minutes, to the nearest hundredth, is 313.56

A quantity is a measurable attribute of a particular thing or group of objects. One quantity might be more than, less than, or equal to another quantity when comparing them. Quantity is a notion that is used frequently in both mathematics and the sciences.

A quantity cannot be a property that cannot be compared. The conventional format for presenting a quantity is as the product of a magnitude and a unit.

According to the question,

Initial value of the quantity=310

Rate of growth= 8.5% per second

Value of the quantity after 1.2 minutes,

=[tex]310(1+\frac{8.5}{100}) ^{1.2*60}[/tex]

=[tex]310(\frac{108.5}{100})^{72}[/tex]

=313.56

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Answer:

141008.06

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

to find the intersection equate g(x) and h(x) , that is

(x + 7)(x - 5) = x - 5 ← expand left side using FOIL

x² + 2x - 35 = x - 5 ( subtract x - 5 from both sides )

x² + x - 30 = 0 ← in standard quadratic form

(x + 6)(x - 5) = 0 ← in factored form

equate each factor to zero and solve for x

x + 6 = 0 ⇒ x = - 6

x - 5 = 0 ⇒ x = 5

substitute these values into either g(x) or h(x) for corresponding values of y

substituting into h(x)

h(- 6) = - 6 - 5 = - 11 ⇒ (- 6, - 11 )

h(5) = 5 - 5 = 0 ⇒ (5, 0 )

Answer:

Ans: (4,-1)

Step-by-step explanation:

Lets keep:

2x+y=7 --- equation 1

x - 2y=6 ----- equation 2

equation 2 x 2: 2x - 4y=12 -------equation 3

now subtract equation 1 from equation 3

  2x - 4y = 12

(-) 2x + y = 7

----> -5y = 5 [ Divide both sides by -5 ]

------> y= -1

Substitute y= -1 into eqaution 1

----> 2x + -1 = 7 [ add 1 to both side]

----> 2x = 8 [Divide by 2 on both sids]

----> x=4

Ans: (4,-1)

Answer:

Step-by-step expl

2.73 A,16.3 V

The vertices of the parabolae are:

Parabolae are represented by quadratic equations. In this problem we have parabolae in standard form and we need to determine its vertex form to find the needed information. Now we summarize the forms of quadratic equations:

Standard form

y = a · x² + b · x + c     (1)

Vertex form

y - k = C · (x - h)²     (2)

Please notice that (x, y) = (h, k) represents the vertex of the parabola.

To change quadratic equations from standard form into vertex form we need to apply algebraic handling:

y = x² + 6 · x + 8

y + 1 = x² + 6 · x + 9

y + 1 = (x + 3)²

(h, k) = (- 3, - 1)

y = x² - 2 · x - 8

y + 9 = x² - 2 · x + 1

y + 9 = (x - 1)²

(h, k) = (1, - 9)

y = - x² + 8 · x - 15

y = - 1 · (x² - 8 · x + 15)

y - 1 = - 1 · (x² - 8 · x + 16)

y - 1 = - 1 · (x - 4)²

(h, k) = (4, 1)

y = - 4 · x² + 6 · x

y = - 4 · [x² - (3/2) · x]

y + (- 4) · (9/16) = - 4 · [x² - (3/2) · x + 9/16]

y - 9/4 = - 4 · (x - 3/4)²

(h, k) = (3/4, 9/4)

y = x² + 6 · x + 11

y - 2 = x² + 6 · x + 9

y - 2 = (x + 3)²

(h, k) = (- 3, 2)

y = - x² + 36

y - 36 = - x²

(h, k) = (0, 36)

y = - x² + 7 · x - 10

y = - (x² - 7 · x + 10)

y + (- 1) · (9/4) = - (x² - 7 · x + 49/4)

y - 9/4 = - (x - 7/2)²

(h, k) = (7/2, 9/4)

y = x² - 10 · x + 24

y + 1 = x² - 10 · x + 25

y + 1 = (x - 5)²

(h, k) = (5, - 1)

y = 2 · x² - 4 · x - 1

y = 2 · (x² - 2 · x - 1/2)

y + 2 · (3/2) = 2 · (x² - 2 · x + 1)

y + 3 = 2 · (x - 1)²

(h, k) = (1, - 3)

y = - 4 · x² - 2 · x

y = - 4 · [x² + (1/2) · x]

y + (- 4) · (1/4) = - 4 · [x² + (1/2) · x + 1/4]

y - 1 = - 4 · (x + 1/2)²

(h, k) = (- 1/2, 1)

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The function that has a domain of all real numbers is:

A. [tex]y = 2x^{\frac{1}{3}} - 7[/tex].

The domain of a function is the set that contains all possible input values for the function.

If a function has an even root, equivalent to an exponent of [tex]\frac{1}{n}[/tex] with n even, the domain is only positive values, while if the exponent is odd, the domain is all real values.

Researching the problem on the internet, the function with odd exponent is:

A. [tex]y = 2x^{\frac{1}{3}} - 7[/tex].

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Answer:

  h(x) = 2x² -8x -10

Step-by-step explanation:

In the US, a quadratic is in standard form when the terms are listed in order of decreasing degree.

In the UK, a quadratic is in standard form when it is written in vertex form.

__

The only function with terms in order of decreasing degree is ...

  h(x) = 2x² -8x -10

All of the functions except the last are written in vertex form:

__

Additional comment

Since the question asks about one function, we assume it is from the perspective of the US understanding of standard form. The point here is that "standard form" may vary from one tradition to another. (The "standard form" for numerical values varies by tradition, as well.)

Rearranging the equation so q is the independent variable is; q = -1.6r

We are given the expression;

-7q + 12r = 3q - 4r

Since we want to make q the subject, let us rearrange the equation with variables having q on the left and others on the right side to get;

-7q - 3q = -4r - 12r

-10q = -16r

q = 16r/10

q = -1.6r

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Answer:

the answer is D- 9/k

Answer:

D- 9/k

Step-by-step explanation:

Answer:

31

Step by step:

You need to do it in reverse:

Devidng Becomes multiplying so its 3.8x10=38

Then same for this + = - do its 38-7=31

So answer is 31

Answer:

7.8g/cm

Step-by-step explanation:

Considering the logarithmic loudness equation, the relative intensity of 120 decibels is of [tex]R = 10^{12}[/tex].

The equation is:

[tex]L = 10\log{R}[/tex]

In which:

For this problem, we have that L = 120, hence the relative intensity is found as follows:

[tex]120 = 10\log{R}[/tex]

[tex]\log{R} = 12[/tex]

[tex]R = 10^{12}[/tex]

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