Solve x2 +7=71
giving the positive and negative solutions.

Answer:

The center of the circle is at the point (2, -3), and its radius is 4 units

Step-by-step explanation:

The equation of the circle in standard form can be obtained by completing the square for both x and y terms as follows:

7x^2 - 28x + 7y^2 + 42y - 35 = 0

7(x^2 - 4x) + 7(y^2 + 6y) = 35

7(x^2 - 4x + 4 - 4) + 7(y^2 + 6y + 9 - 9) = 35

7[(x - 2)^2 - 4] + 7[(y + 3)^2 - 9] = 35

7(x - 2)^2 + 7(y + 3)^2 - 112 = 0

7(x - 2)^2 + 7(y + 3)^2 = 112

Dividing by 112 on both sides, we get:

(x - 2)^2 + (y + 3)^2 / 16 = 1

Therefore, the equation of the circle in standard form is (x - 2)^2 + (y + 3)^2 / 16 = 1.

The center of the circle is at the point (2, -3), and its radius is 4 units.

Since it doesn't make sense for Timothy to have negative money, we can conclude that there is no solution to this problem.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

Let's assume that Timothy has x dollars when he enters the first store.

According to the problem, he spends 1 dollar more than half of what he has.

So, the amount he spends in the first store is:

1/2 * x + 1

After spending this amount, he will have:

x - (1/2 * x + 1) = 1/2 * x - 1

dollars left.

He then goes to the second store and spends 1 dollar more than half of what he has left, which is:

1/2 * (1/2 * x - 1) + 1 = 1/4 * x + 1/2

After spending this amount, he will have:

1/2 * x - 1 - (1/4 * x + 1/2) = 1/4 * x - 3/2

dollars left.

He repeats this process for each of the five stores.

Therefore, the amount of money Timothy has left after visiting all five stores is:

1/4 * x - 3/2 - (1/4 * x + 1/2) - (1/4 * x + 1/2) - (1/4 * x + 1/2) - (1/4 * x + 1/2) = -5/4 * x - 5

Since he has spent all his money, the amount of money he has left must be 0:

-5/4 * x - 5 = 0

Solving for x, we get:

x = -20

However, since it doesn't make sense for Timothy to have negative money, we can conclude that there is no solution to this problem.

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Answer:

Let's start by finding how much money Mary has left after buying the gift cards:

$250 - $130 = $120

Now, to find the greatest number of candy bars Mary can buy, we need to divide the amount of money she has left by the cost of each candy bar:

$120 ÷ $1.50 = 80

So Mary can buy up to 80 candy bars with the rest of her money.

We can check which inequality represents this situation by plugging in the numbers:

130 + 1.50x ≤ 250

where x represents the number of candy bars Mary buys.

If we subtract 130 from both sides, we get:

1.50x ≤ 120

Finally, if we divide both sides by 1.50, we get:

x ≤ 80

This matches our answer, so the correct inequality is:

D. 130 +1.50x ≤ 250

Answer:

D. 130 +1.50x ≤ 250

Step-by-step explanation:

250 - 130 = 120
1.50x = 120

Answer:

c

Step-by-step explanation:

So what you need to do is split who is part of each:

1/2:

Wife:$?

1/2:

Daughter:$40,000

Butler:$?

Charity:$6,000

This makes it much easier to see as you know the charity and Butler received the same amount. You take your total (x) and do a simple equation of x=$40,000+6,000+6,000 as you know the butler must have also received the $6,000 the charity did. You will get x=$52,000 and you know that is half of the estate as he gave the other half to his wife. This is the same as knowing the butler and charity received the same amount as halves are equal to each other. SO now all you have to do is add $52,000+$52,000=$104,000 getting your answer.  

The complete table:

c                       1       2       3

28 - c³ + 6       33    26      7.

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. In other terms, a "polynomial function of degree 2" is a quadratic function.

Given:

A quadratic expression is 28 - c³ + 6.

Let A = 28 - c³ + 6.

When c = 1,

then A = 28 - 1³ + 6 = 28 - 1 + 6 = 33

When c = 2,

then A = 28 - 2³ + 6 = 28 - 8 + 6 = 26

When c = 3,

then A = 28 - 3³ + 6 = 28 - 27 + 6 = 7.

Therefore, all the required values are given above.

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The equation of the line shown is y = 2x.

In Mathematics, a proportional relationship can be defined as a type of relationship that generates equivalent ratios and it can be modeled or represented by the following mathematical expression:

y = kx

Where:

Next, we would determine the constant of proportionality (k) as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = 2/1 = 4/2

Constant of proportionality, k = 2.

Therefore, the required equation is given by:

y = kx

y = 2x

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the answer is r6 because of the end result

The solution of the linear equation y =  15 x + 9 and y = 1/2 x - 20 is

x = -2

y = -21

The linear equation can be solved by graphical method to give the solution. The graph is attached

(-2, 21)

Using elimination method we have

y =  15 x + 9

y = 1/2 x - 20

subtracting will result to

0 = 14.5x + 29

-14.5x = 29

isolating x

x = 29 / -14.5

x = -2

substituting x = -2 into y =  15 x + 9

y =  15 (-2) + 9

y = -30 + 9

y = -21

Hence the solution is x = -2 and y = -21

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Answer:

Rhombus and Square

Step-by-step explanation:

Perpendicular Diagonals mean that the diagonals intersect each other at a 90 degree angle always.

Rectangles do not intersect at a 90 degree angle, and parallelograms don't ALWAYS intersect at that angle.
However, rhombuses and squares do.

In the equation, the ordered pair for x = 5 is (5, 5.5), the ordered pair for x = 10 is (10, 8), the ordered pair for x = 20 is (20, 13).

A linear equation has the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept. The line's rate of change, or how steeply it rises or descends as we go down the x-axis, is indicated by the slope. The line's intersection with the y-axis, or the value of y when x is equal to 0, is represented by the y-intercept.

The given equation is:

y=0.50x + 3

Substituting the different values of x we find the required ordered pair as follows:

When x = 5:

y = 0.50(5) + 3 = 5/2 + 6/2 = 11/2 = 5.5

When x = 10:

y = 0.50(10) + 3 = 5 + 3 = 8

When x = 20:

y = 0.50(20) + 3 = 10 + 3 = 13

Therefore, the ordered pair for x = 5 is (5, 5.5), the ordered pair for x = 10 is (10, 8), the ordered pair for x = 20 is (20, 13).

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Answer:

The model represents the division of the larger rectangle (3.5 units wide) into 4 equal parts, and shading 1 part of it.

This means that the division is 3.5 divided into 4 parts, with each part being equal to the smaller rectangle with a width of 0.875.

Therefore, the expression represented by the model is:

B. 3.5 divided by 0.875

Step-by-step explanation:

The probability is approximately 0.129

To calculate the probability that Cindy will get at least 48 orange Stattles in her next 14 ounce bag, we need to use the binomial probability formula:

P(X >= 48) = 1 - P(X < 48)

Where

To calculate P(X < 48), we need to use the binomial probability formula:

P(X = x) = (nCx) * p^x * q^(n-x)

Where

nCx is the binomial coefficient, which can be calculated using the formula:

nCx = n! / (x! * (n-x)!)

where ! denotes the factorial function.

We can use a cumulative binomial distribution table or a binomial calculator to find the probability of getting less than 48 orange Stattles in a 14 ounce bag. For example, using an online calculator, we find that:

P(X < 48) = 0.871

Therefore, the probability that Cindy will get at least 48 orange Stattles in her next 14 ounce bag is:

P(X >= 48) = 1 - P(X < 48) = 1 - 0.871 = 0.129

So, the probability is approximately 0.129 or 12.9%.

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Answer: To draw a trend line that models the given data set, we first need to plot the points on a graph. We can use a scale of 1 unit on the x-axis and 5 units on the y-axis to plot the points as follows:

(1, 27.5)    ●

(4, 35)      ●

(7, 42.5)    ●

(10, 50)     ●

(13, 57.5)   ●

We can see that the points roughly form a straight line. To find the equation of the trend line, we can use linear regression, which involves finding the line that best fits the data.

Using a calculator or software, we can find that the equation of the trend line is:

y = 3.5x + 24

This means that for every increase of 1 unit in x, y increases by 3.5 units. The y-intercept of the trend line is 24, which represents the value of y when x = 0.

We can plot the trend line on the same graph as follows:

     |                          

  60 |-●-                        

     |  |                        

  55 |-●-----                  

     |    |                    

  50 |-●-------                

     |      |                  

  45 |-●--------              

     |        |                

  40 |-●----------            

     |          |              

  35 |-●------------          

     |            |            

  30 |-●--------------        

     |              |          

  25 |-●-----------------      

     |                |        

     --------------------      

        1   4   7   10  13      

The dots represent the original data points, and the line represents the trend line.

Step-by-step explanation:

Answer:

70%

Step-by-step explanation:

100%-30%=70%

fxbhctcybyvybuninuvtxectb

the positive value of "x" for the given quadratic equation will be 5.

ax²+bx+c=0, with a not, equals 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated.

Given a quadratic equation, √(4x² - 4x + 1) = 9

Simplifying the value of the given equation  to calculate the value of the variable "x",

Equation,

=> √(4x² - 4x + 1) = 9

Square both sides

=> (4x² - 4x + 1) = 81

=> 4x² - 4x - 80 = 0

Divide by 4 into both sides of the equation,

=> x² - x -20 = 0

Simplifying the equation using the factorization method,

=> x² - 5x + 4x - 20 = 0

=> x(x - 5) + 4(x - 5) = 0

=> x = -4

=> x = 5

Therefore, the positive value of "x" for the given quadratic equation will be 5.

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The pair of complementary angles is the one in the last option:

BFC and DFE

Two angles A and B are complementary if their measures add upto 90°, on the diagram we can see that the angles defined are:

AFB = 40°

BFC = 60°

CFD = 50°

DFE = 30°

Now just see which pairs of these angles add up to 90 degrees, these pairs are complementary angles.

Then the sets of complementary angles are:

AFB and CFD

BFC and DFE

So the correct option  is the last one.

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The quantity provides the best measure of the television show’s popularity is the number of streams per episode.

We anticipate that independent variables will have an impact on dependent variables. What occurs as a result of the independent variable is referred to as a dependant variable.

The dependant variable is what changes as a result of the independent variable, which is what you modify.

The most accurate indicator of a television show's popularity on a streaming service is the number of streams each episode.

This is because, rather than just the length of the episodes or the number of episodes every season, the number of streams directly represents the number of viewers who are actively choosing to watch the show.

The number of streams also considers re-watchability and binge-watching, which are further indicators of how popular a show is.

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Answer:

159

Step-by-step explanation:

So first you work on the (3 + 5) which is 8 but don't forget the ^2 so 8^2 is 64. Then you work on your next term which is 10^2 which is 100. So now our equation is 100 + 64 -5 and you can solve this by going left to right. So 100 + 64 is 164 then - 5 is 159.

Answer: 320

Step-by-step explanation:

Multiply each time by 2 so 10*2=20 then 40, 80, 160, and 320

The correct option is D. For the circumcenter A of the triangle ∆RST, the length of AT is equal to 23.

The circumcenter of a triangle is the point where the perpendicular bisectors of the sides of the triangle intersect. This point is equidistant from the three vertices of the triangle and is the center of the circumcircle, which is the circle passing through all three vertices of the triangle.

Hence;

AS = AR = AT

3x - 7 = 2x + 3

3x - 2x = 7 + 3 {collect like terms}

x = 10

so;

AS = 3(10) - 7

AS = 30 - 7

AS = 23 and AT also is = 23.

Thus , for the circumcenter A of the triangle ∆RST, the length of AT is equal to 23.

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Since odds in favor of a certain horse finishing in second place are given as 49 to 51 so number of outcomes in favor is m = 49

and number of outcomes not in favor n = 51

and total outcomes are m+n = 49 +51 = 100

The probability of a certain horse finishing in second place is 49 /100 = 0.49.

The number of favourable outcomes to all possible outcomes of an event is the ratio, which is known as probability. For an experiment with 'n' number of outcomes, the symbol x can be used to indicate the number of excellent outcomes. The probability of an event can be calculated using the following equation:

x/n, where Probability is Favorable Outcomes/Total Results (Event)

The number of outcomes in favour is m = 49, the number of outcomes not in favour is n = 51, and the total outcomes are m+n = 49 + 51 = 100 because the chances in favour of a particular horse placing in second place are provided as 49 to 51.

The likelihood that a certain horse will place second is 49/100, or 0.49.

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The complete question is:

For a certain are given as to. Express the indicated degree of likelihood as a probability value between 0 and 1 inclusive.

Wyatt's paycheck for the week would be $550.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

To calculate Wyatt's paycheck, we need to determine his total earnings for the week.

His earnings from his base salary are simply $250.

To calculate his earnings from commission, we need to determine 3% of his sales.

3% of $10,000 is:

0.03 * 10000 = $300

So Wyatt's earnings from commission would be $300.

Adding his base salary and commission together, we get:

$250 + $300 = $550

Therefore, Wyatt's paycheck for the week would be $550.

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Answer:

737 cooks are required to prepare a meal for 737 people in 5 hours

Step-by-step explanation:

According to the given information, 10 cooks can prepare a meal for 536 people working for 8 hours each.

Let's calculate the total work done by the 10 cooks in 8 hours.

Total work done = Number of cooks * Hours worked

Total work done = 10 * 8 = 80

Now, let's calculate the work done by one cook in one hour.

Work done by one cook in one hour = Total work done / (Number of cooks * Hours worked)

Work done by one cook in one hour = 80 / (10 * 8) = 1

Therefore, one cook can prepare food for 1 person in 1 hour.

Now, let's calculate the number of cooks required to prepare a meal for 737 people in 5 hours.

Total work required = Number of people * Hours required

Total work required = 737 * 5 = 3685

Number of cooks required = Total work required / (Hours worked * Work done by one cook)

Number of cooks required = 3685 / (5 * 1) = 737

Therefore, 737 cooks are required to prepare a meal for 737 people in 5 hours.

Answer: 54%

Step-by-step explanation:

divide 1.89 by 3.49 then multiply by 100

(x+2 (x+4)

I factored using the AC method.

The highest height of the ball, to the closest foot, is stated to be around 88 feet.

Velocity may be referred to as the speed when something moves toward a particular location. as the rate of a car driving northwest on a highway or the pace at which a rocket takes off.

The function h(t) = −16t² + v0t + h0 models the vertical motion of the ball, where t is time in seconds, v0 is the initial velocity in feet per second, and h0 is the initial height in feet.

In this case, the beginning height is 4 feet, and the velocity of the fluid equals 75 feet per second. As a result, the following outlines the function h(t) which it simulates the ball's vertical motion:

h(t) = -16t² + 75t + 4

The point of the concave function h must be located in order to determine the ball's peak (t) = -16t² + 75t + 4.

The t-coordinate of the vertex is given by t = -b/2a, where a = -16 and b = 75. Substituting these values, we get:

t = -75 / (2 x (-16)) = 2.34375

We enter this t quantity into the procedure h(t) to get the maximum height:

h(2.34375) = -16(2.34375)² + 75(2.34375) + 4 = 87.74

To the nearest foot, the ball therefore achieves a peak of 88 feet.

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The quantitative quality that is transferred to a physical system or a body is known as energy, and it is evident in the production of heat and light as well as in the performance of work.

What is Work?

Work, It is defined as the energy that is applied to or removed from an object by applying force along a displacement. A constant force acting in the same direction as the motion, the work is simply equal to product of the force's magnitude and the distance traveled.

The total price of high-energy lamp is a whole-number multiple of 4. The total price of the low-energy lamp is a whole number multiple of 5.

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Complete Question :

An electrician has $120 to spend on interior light fixtures. The

wholesale price for a 13-watt low-energy lamp is $4. The price for a

high-energy lamp is $5.

How does the total price of the high energy lamp relate to the low energy lamp? how does the total price for the low energy lamps relate to the high energy lamps?

A graphing calculator's tvm solver will calculate the monthly payment for a 25-year loan which comes to

N=300; I%=6.7; PV=-175000; PMT=; FV=0; P/Y=12; C/Y=12; PMT:END

A TVM solver needs the loan amount as the Present Value (PV), zero as the Future Value (FV), and N as the actual number of payments (25×12 = 300) in order to determine the loan payment.

The annual interest rate is considered by solvers to be I%. The monthly interest rate is used an HP-12C financial calculator.

Here C contains the list of numbers required to calculate the monthly payment for this $175,000 loan at a 6.7% interest rate.

Cash flow typically has a negative sign for amounts paid and a positive sign for quantities received.

Here the available options indicate that the loan amount is negative while the payment amount is positive. Also, we anticipate receiving the loan amount and making the installments.

We are Given the aforementioned standards, the indicators, in this case, are the opposite of what we typically anticipate.

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