Use the graph of the function y = -x² + 2x + 8 to
determine the solutions of the quadratic equation
0 = -x²+2x+8.
What are the solutions of the quadratic equation
0 = -x²+2x+8?
O-4 and 2
O-2 and 8
O-2 and 4
O4 and 8

Answer:

You need at least 90.5 points to get 200p

Step-by-step explanation:

200-109.5 = x

x = 90.5

Answer:

Step-by-step explanation:

OK so are you gonna do with this problem is going to take your 109.5 and you’re going to try to add to try to find 200 now you don’t want to go over 200 so it it can’t be 230 or anything through 200 so I can’t be 201 it Has to be 200 so you want to take 109.5 and add up until you get to 200 and then that will be your answer of what you added to get to 200 Hope this helps you good luck on your assignment

Answer:

Step-by-step explanation:

Item 1

<RSL is not ≅ < XYM

Item 2

< LST and < QRX are not supplementary (they are congruent)

Item 3

m < LST = 120 - there is no evidence for this.

Item 4

< JRS = <LST

so, If < LST =  120, then this can't be 195

Answer:

2

Step-by-step explanation:

one apple and another equals to 2.

Answer: 11

Step-by-step explanation: you put one and one together lol

\(y = 49x^2 - 1\implies \stackrel{y}{0}=49x^2 -1\implies 1=49x^2\implies \cfrac{1}{49}=x^2 \\\\\\ \sqrt{\cfrac{1}{49}}=x\implies \cfrac{\sqrt{1}}{\sqrt{49}}=x\implies \cfrac{1}{7}=x\)

Answer:

chatGPT

Step-by-step explanation:

Let's denote the speed of each car as v, and the distance that Car A travels as d. Then we can set up two equations based on the information given:

d = v * (12/60) (since Car A reaches its destination in 12 minutes)

d + 4 = v * (18/60) (since Car B travels 4 miles farther than Car A and reaches its destination in 18 minutes)

Simplifying the equations by multiplying both sides by 60 (to convert the minutes to hours) and canceling out v, we get:

12v = 60d

18v = 60d + 240

Subtracting the first equation from the second, we get:

6v = 240

Therefore:

v = 240/6 = 40

So the cars travel at a speed of 40 miles per hour.

The value of the unknown variable x in the equation x² + 5² = 13² is 12.

The use of numbers and words in the same mathematical equation is considered as an algebraic expression.

We can calculate the square of a number by multiplying the number by itself.

Therefore, the square of 5 is equal to 5 multiplied by 5 which is equal to 25.

While the square of 13 is equal to 13 multiplied by 13 which is equal to 169.

So to find the value of x, we can rearrange the given equation as:

x² = 13² - 5 ²

x² = 169 - 25

x² = 144

As x² is equal to 144, we can calculate the value of x by taking the square root of the value of 144.

Therefore,

x= √144

x= 12

Hence, the value of the unknown variable x in this equation is 12.

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Answer

C. 7y - 2x = 21

Expalnation

You must know that for two lines to be parallel to each other, they must have the same slope.

The standard form of equation of a line is expressed as y = mx+c

m is the slope of the line

Comparing to the given equation y = 2/7x – 5, you will see that

m = 2/7

This means that the equation that will be parallel to this line must also have a slope of 2/7.

Fromm the option given, we need to find the equation that has a slopw of 2/7.

Looking at option A

7x - 2y = -2

First we must write this in standard form y = mx+c as shown

To do this, we need to make y the subject of the formula:

7x - 2y = -2

-2y = -2-7x

-2y = -7x-2

Divide through by -2

-2y/-2 = -7x/-2 -2/-2

y = 7/2x + 1

The slope of this line is 7/2, this shows that the line is not parallel to the given line since their slope are different

Let us look at option C:

7y - 2x = 21

Rewrite the equation

7y = 21 +2x

Divide through by 7

7y/7 = 21/7 + 2/7 x

y = 3 + 2/7 x

y = 2/7 x + 3

We can see that the slope of this line is also 2/7 which is equivalent to the slope of the given line.

Hence the equation of the line parallel to y = 2/7x – 5 is 7y - 2x = 21

Answer:

c). 7y - 2x = 21.

Step-by-step explanation:

Given line is y = 2/7x - 5

Parallel lines have the same slope.

The equation is in slope-intercept form so,

the slope of the given line is 2/7.

We need to convert the given choices to slope / intercept form:

a) 7x = 2y = -2

2y = 7x + 2

y = 7/2x + 1

- so, it's not this one.

b) 2x + 7y = -42

7y = -2x - 42

y = -2/7x - 6 .  No.

c)  7y - 2x = 21

7y = 2x + 21

y = 2/7 + 3.

It's this one.

Answer:

240 tiles

Step-by-step explanation:

160/2 = 80

60/2 30

(80)*(30) = 240

Answer:

36

Step-by-step explanation:

80% of 45 is 36.

Have a FANTASTIC FRI-YAY!

The X and Y coordinates for point F and D are (179.194, 126.139) and (100.807, 61.184), respectively.

Given:

- Radius of point A to B is 53.457

- Length and width of the plate is 280 mm

To find

- X and Y coordinates for point F and D

Formula used:

- The coordinates of a point on the circumference of a circle with radius r and center at (a, b) are given by (a + r cosθ, b + r sinθ).

Explanation:

Let the center of the circle be O. Draw a perpendicular from O to AB, and the intersection is point E. It bisects AB, and hence AE = EB = 53.457/2 = 26.7285 mm.

By Pythagoras theorem, OE = sqrt(AB² - AE²) = sqrt(53.457² - 26.7285²) = 46.3383 mm.

The length of the plate = OG + GB = 140 + 26.7285 = 166.7285 mm.

The width of the plate = OD - OE = 280/2 - 46.3383 = 93.6617 mm.

The coordinates of A are (140, 93.6617).

To find the coordinates of F,

θ = tan⁻¹(93.6617/140) = 33.1508°.

So, the coordinates of F are (140 + 53.457 cos 33.1508°, 93.6617 + 53.457 sin 33.1508°) = (179.194, 126.139).

To find the coordinates of D,

θ = tan⁻¹(93.6617/140) = 33.1508°.

So, the coordinates of D are (140 - 53.457 cos 33.1508°, 93.6617 - 53.457 sin 33.1508°) = (100.807, 61.184).

Therefore, the X and Y coordinates for point F and D are (179.194, 126.139) and (100.807, 61.184), respectively.

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Answer:

w

Step-by-step explanation:

Monday = 4

Tuesday = 1/3 w  (where w is the miles walked on Wednesday)

Wednesday = w

Total = 24

4 + 1/3 w + w = 24

Combine like terms

4 + 4/3 w = 24

Subtract 4 from each side

4/3 w = 20

Multiply each side by 3/4

w = 20 *3/4

w = 15

In the equation when we start, we need to put the variable, not the solution

At the end we have the solution

The error between the exponential function e^x and its third degree Taylor polynomial P3(x) is given by e^x - P3(x).

Let's compute this error for various values of x:

For x = 0, we have e^0 - P3(0) = 1 - 1 = 0.

For x = 1, we have e^1 - P3(1) = e - (1 + 1 + 1/2 + 1/6) = e - 2.16667 ≈ -0.0803.

For x = -1, we have e^-1 - P3(-1) = 1/e - (1 - 1 + 1/2 - 1/6) = 0.581976 ≈ 0.582.

For x = 2, we have e^2 - P3(2) = e^2 - (1 + 2 + 4/2 + 8/6) = e^2 - 5.33333 ≈ 2.995.

For x = -2, we have e^-2 - P3(-2) = 1/e^2 - (1 - 2 + 4/2 - 8/6) = 0.133151 ≈ 0.133.

Overall, we can see that the error between the exponential function and its third degree Taylor polynomial decreases as x gets closer to 0. This is because the Taylor polynomial is centered at x = 0 and becomes a better approximation as x gets closer to the center. However, for larger values of x, the error can become quite significant.

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To find the z-value and p-value, we can use the information provided in the question and perform a hypothesis test.

Given:

Number of patients experiencing flulike symptoms (successes): \(\(x = 27\)\)

Total number of patients: \(\(n = 852\)\)

Percentage of drug users experiencing flulike symptoms: \(\(p = 2.8\% = 0.028\)\)

Significance level: \(\(\alpha = 0.1\)\)

We want to test the null hypothesis that the proportion of drug users experiencing flulike symptoms is equal to the known percentage of 2.8%:

\(H_0: p = 0.028\)

To calculate the z-value, we use the formula:

\(\[z = \frac{{\hat{p} - p}}{{\sqrt{\frac{{p(1-p)}}{{n}}}}}\]\)

where \(\(\hat{p}\)\) is the sample proportion, p is the known proportion, and n is the sample size.

Substituting the values into the formula, we have:

\(\[z = \frac{{\frac{{27}}{{852}} - 0.028}}{{\sqrt{\frac{{0.028(1-0.028)}}{{852}}}}}\]\)

Calculating the value, we find:

\(\[z \approx -1.162\]\)

To find the p-value, we use the z-value and consult a standard normal distribution table or use statistical software. Since the question mentions using technology, we will assume that a software or calculator output is available.

The p-value is the probability of observing a test statistic as extreme as the one obtained under the null hypothesis. In this case, we are conducting a one-tailed test, looking for evidence of fewer patients experiencing flulike symptoms.

Comparing the p-value with the significance level \(\(\alpha\)\), if the p-value is less than \(\(\alpha\)\), we reject the null hypothesis; otherwise, we do not reject the null hypothesis.

As the p-value is not provided in the question, we will proceed assuming it is available from the technology output. Given the instruction to round to three decimal places, we will assume the p-value is provided as \(\(p \approx 0.120\)\).

Comparing the p-value \((\(p \approx 0.120\))\) with the significance level \(\(\alpha = 0.1\)\), we observe that the p-value is greater than \(\(\alpha\)\). Therefore, we do not have enough evidence to reject the null hypothesis.

In summary:

The z-value is approximately -1.162, and the p-value is approximately 0.120. Since the p-value is greater than the significance level \(\(\alpha = 0.1\)\), we do not reject the null hypothesis.

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As per the probability, the project manager can estimate that the project will take 32.28 weeks to complete with a 90% confidence level.

To convert the project completion distribution to the standard normal distribution, the project manager needs to calculate the z-score, which represents the number of standard deviations away from the mean. The formula for the z-score is:

z = (x - μ) / σ

Where x is the completion time, μ is the mean of the distribution (30 weeks), and σ is the square root of the variance (√(2.78)).

Using a standard normal distribution table or calculator, the project manager can find the z-score corresponding to the 90th percentile, which is approximately 1.28.

To find the completion time that would be exceeded with a probability of only 10%, the project manager can use the inverse of the z-score formula:

x = z * σ + μ

Plugging in the values, the estimated completion time with a 90% confidence level is:

x = 1.28 * √(2.78) + 30 = 32.28 weeks

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Answer:

the smaller number minused by the bigger number.

Step-by-step explanation:

Hopefully this helps you :)

pls mark my answer brainlest ;)

Answer:

x=40°

Step-by-step explanation:

Since anges are vertical By Vertical Opposite angle property of Intersecting Lines

HOPE IT HELPS YOU.MARK ME AS BRAINIEST

Point estimate from the sample is 0.985, margin error is 0.003.

Confidence interval is defined as the interval which is the estimate for the parameter of the sample or population to be contained.

(a) To calculate point estimate or sample mean :

Point estimate is the mid point of the confidence interval.

Given that true mean weight of candy bars is 0.982 ounces to 0.988 ounces.

Point estimate = (0.982 + 0.988) / 2 = 1.97 / 2 = 0.985

(b) Margin error is the one half of the total width of the interval.

Margin error = (0.988 - 0.982) / 2 = 0.003

(c) The confidence level of 90% in this problem can be interpreted as , if we do the interval construction for many times, about 90% of the total constructed intervals has the true population mean of weight of fun size candy bars.

Hence the point estimate and margin error are 0.985 and 0.003 respectively.

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The total amount Jace will repay is $6120.

To calculate the total amount Jace will repay, we need to consider the principal amount borrowed, the interest rate, and the time period.

The formula for calculating simple interest is:

Interest = (Principal * Rate * Time) / 100

Given:

Principal amount (P) = $1800

Rate of interest (R) = 16%

Time period (T) = 15 months

Plugging in these values into the formula, we can calculate the interest amount:

Interest = (1800 * 16 * 15) / 100

= 4320

The interest amount is $4320.

To find the total amount Jace will repay, we need to add the principal amount and the interest amount:

Total amount = Principal + Interest

= 1800 + 4320

= 6120

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Answer:

90

Step-by-step explanation:

Measure of one arc = 90°

-> Measure of other arc = 360°- 90° = 270°

x° = 1/2 (270° - 90°)

-> x° = 1/2 * 180°

-> x° = 90°

-> x° = 90°

-> x = 90

Answer:

s= number of shirts

3/2= constant of proportionality

Step-by-step explanation:

Josh takes a load of dress shirts to the dry cleaners. The amount he pays for dry cleaning (

f. is given by the equation f=3/2s, where s is the number of shirts. What is the constant of proportionality in terms of the cost per shirt?

Given:

f= 3 / 2s

Where,

f= amount Josh paid for dry cleaning

s= number of shirts

3= constant of proportionality

2= amount paid per shirt

For example, if Josh took 3 shirts to the dry cleaner, the amount Josh will pay is

f= 3 / 2s

= 3 / 2(3)

= 3 / 6

= 1 / 2

f= 1 /2

The rate of change of the radius of the spherical balloon when the radius is 3 inches is 1/6π in/min.

The rate of change of the radius of the spherical balloon when the radius is 3 inches is 1/6π in/min.

Explanation:The volume V of a sphere of radius r is given by the formula

V = (4/3)πr³

Differentiating both sides of the equation with respect to time t (using the chain rule), we get

dV/dt = 4πr² (dr/dt)

We know that

dV/dt = 6 in³/min (given in the problem statement) and r = 3 in (given in the problem statement)

Therefore,6 = 4π(3²) (dr/dt)

dr/dt = 6 / (4π × 9)

dr/dt = 1 / (6π/4)

dr/dt = 4/6π

= 2/3π in/min

So, the rate of change of the radius of the spherical balloon when the radius is 3 inches is 1/6π in/min.

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The the function to estimate the average age of employee of a company is A(s)=0.285s + 59  , then the average age of employee in 2003 is 65.27 and in 2009 is 66.98

To estimate the average age of an employee in 2003, we need to find the value of A(s) when s = 22  ;

because the number of years between 2003 and 1981 is = 22 years ;

So , A(22) = 0.285×22 + 59 = 65.27  ;

The average age of an employee in 2003 is approximately 65.27.

To estimate the average age of an employee in 2009,

we need to find the value of A(s) when s = 28

because the number of years between 2009 and 1981 is = 28 years ;

So , A(28) = 0.285×28 + 59 = 66.98  ;

The Average age of employee in 2009 is approximately 71.48.

The given question is incomplete , the complete question is

The function​ A(s) given by ​A(s)=0.285s + 59  can be used to estimate the average age of employee of a company in the year 1981 to 2009. Let​ A(s) be the average age of an​ employee, and "s" be the number of year since​ 1981; that​ is, s=0 for 1981 and s=9 for 1990. What is the average age of the employee in 2003 and in​ 2009 ?

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Answer: x=1

Step-by-step explanation:

Assume that "log" is the base-10 logarithm

log (2x)+log (5)=1

log 10{10}(2x)+log (5)=1

Assume that "log" is the base-10 logarithm

\log 10{10}(2x)+\log (5)=1

\log 10{10}(2x)+\log10{10}(5)=1

Apply the logarithm product identity

\log 10{10}(2x)+\log 10{10}(5)=1

log 10{10}(2x x 5)}=1

The flux integral ∬S F · dS, where F(x, y, z) = (xy, yz, xz) and S consists of the upper hemisphere of radius r, can be evaluated using the Divergence Theorem.

The Divergence Theorem states that the flux integral of a vector field F over a closed surface S is equal to the triple integral of the divergence of F over the region V enclosed by S.

To apply the Divergence Theorem, we first calculate the divergence of the vector field F. The divergence of F is given by div(F) = ∂(xy)/∂x + ∂(yz)/∂y + ∂(xz)/∂z, which simplifies to y + z + x.

Next, we evaluate the triple integral of the divergence of F over the region V enclosed by the upper hemisphere of radius r and the plane z = 0. Using spherical coordinates, the region V can be defined by 0 ≤ θ ≤ π/2, 0 ≤ φ ≤ 2π, and 0 ≤ ρ ≤ r.

Integrating the divergence of F over V, we obtain the result (r^4)/4.

Therefore, the flux integral ∬S F · dS is equal to (r^4)/4.

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A standard bowling lane is approximately 60 feet long from the foul line to the head pin.

The metric system uses the terms kilometres (km), metres (m), decimeters (dm), centimetres (cm), and millimetres (mm) to describe length or distance.

A standard bowling lane is designed to be 60 feet in length from the foul line to the head pin. This distance is consistent across most bowling alleys and is a key measurement in the sport of bowling.

The 60-foot length is divided into specific sections that contribute to the overall structure of the lane. These sections include the approach area, the foul line, the lane itself, and the pin deck where the pins are set.

The approach area is the section where the bowler stands and prepares to release the ball. It usually spans around 15 feet, providing enough space for the bowler to take a few steps and build momentum before releasing the ball.

The foul line marks the boundary between the approach area and the actual lane. It is important for bowlers to release the ball before crossing the foul line; otherwise, it is considered a foul, and the resulting throw does not count towards the score.

Beyond the foul line is the lane, which is where the ball rolls towards the pins. The lane is typically around 41 to 42 inches wide, made of a specially coated wooden or synthetic surface that allows the ball to roll smoothly.

At the end of the lane is the pin deck, where the pins are arranged in a triangular pattern. The head pin, also known as the 1-pin, is positioned at the front of the triangle. When the ball reaches this area, it interacts with the pins, causing them to scatter or fall, resulting in a score.

Overall, the 60-foot length of a standard bowling lane provides enough distance for bowlers to exhibit skill and strategy in their throws while ensuring a fair and consistent playing field.

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Answer: D

Step-by-step explanation:

The solution to both A and C would total to about 0. Also, in B both numbers are positives, so that would also be out of the case. If you are looking for the least value, the answer would be D since -3/4 -3/4 would equal -1.5, (or -1 1/2). Therefore, your answer would be D.

Hope that helps :D

Answer:

D. -3/4 - 3/4

Step-by-step explanation:

A. 3/4 -3/4 = 0

B. 3/4 + 3/4 = 1 1/2

C. -3/4 + 3/4 = 0

D. -3/4 - 3/4 = -1 1/2

Answer:

a. The vertex is in quadrant IV and the graph opens down.

Step-by-step explanation:

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Answer:

mP = 35

Step-by-step explanation:

QR = 80

QS = 150

The measure of the angle formed by a secant and a tangent intersecting in the exterior of a circle is half the difference between the measures of the intercepted arcs.

This means that (150-80)/2 = mP

mP = 35 degrees

Hope this helps!

Answer:

the answer is 8!

Step-by-step explanation: