Determine the next step for solving the quadratic equation by completing the square.

0 = –2x2 + 2x + 3
–3 = –2x2 + 2x
–3 = –2(x2 – x)
–3 +
= –2(x2 – x +
)
StartFraction negative 7 Over 2 EndFraction = –2(x – StartFraction 1 Over 2 EndFraction)2
StartFraction 7 Over 4 EndFraction = (x – StartFraction 1 Over 2 EndFraction)2
The two solutions are
Plus or minus StartFraction StartRoot 7 EndRoot Over 2 EndFraction.

The length of the longer side of the rectangle is 8.78cm

The formula for calculating the area of a rectangle is expressed as:

A = lw

For a semicircle;

A = πr²/2

r is the radius

Area of the figure = lw + πr²/2

Substitute the given paramters

41.4 = 4w +  π(2)²/2

41.4 = 4w + 6.28
4w = 41.4 - 6.28

4w = 35.12

w = 35.12/4

w=  8.78 cm

Hence the length of the longer side of the rectangle is 8.78cm

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Answer: 24 days

Step-by-step explanation:

Takes her 4 days to read 1/2 of a 200 page book, or 100 pages.

4 days = 100 pages

X days = 600 pages

24 days = 600 pages

The linear equation that represents the given rule is f(x) = 221x + 447.

To find the linear equation, we need to determine the slope and y-intercept. Looking at the given rule, we can observe that the values of f(x) increase by 221 as x increases by 1. This indicates that the slope of the line is 221.

Now, we need to find the y-intercept. From the given rule, we can see that when x is 0, f(x) is 447. Therefore, the y-intercept is 447.

Combining the slope and y-intercept, we can write the linear equation as f(x) = 221x + 447. This equation represents the given rule, where f(x) is determined by multiplying x by 221 and adding 447 to it.

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Answer:

A rotation ____on the coordinate plane________ a figure around a fixed point called the center of

___rotation_____________.

Here, QRS represents the proportion of longest triangle to middle-length sides. 26/36 = 13/18 QUT: 12/16 = ¾ ≠ 13/18

Students should be taught that whereas a triangle can have many various side lengths and angles, a square must have all of its sides be the same length and all of its angles must be right angles.

Hence, a square cover must contain a minimum of 4 corner-power points. Nevertheless, each triangles may include one corners in its inside or twin vertex on edges (score of 1) for a not more than one point. Three triangles only cover a square with a maximum of three corner-power points.

\(QRS: 26/36 = 13/18\)

\(QUT: 12/16 = 3/4 not equal 13/18\)

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5) By AAA congruency rule, ΔVWU ≅ ΔMNU.

6) By SAS congruency rule, ΔCAB ≅ ΔUAV

If any twο sides and the angle included between the sides οf οne triangle are equivalent tο the cοrrespοnding twο sides and the angle between the sides οf the secοnd triangle, then the twο triangles are said tο be cοngruent by SAS rule.

5) ∠V ≅ ∠V = 36°

∠VUW ≅ ∠NUM

then according to angle sum property

∠VWU ≅ ∠MNU

Then,

ΔVWU ≅ ΔMNU

By AAA congruency rule, ΔVWU ≅ ΔMNU.

6) 77 ≅ 66 (common side)

42 ≅ 36 (common side)

∠CAB ≅ ∠UAV (common angle)

Then,

ΔCAB ≅ ΔUAV

By SAS congruency rule, ΔCAB ≅ ΔUAV

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Answer:

No, this is not proportional.

Step-by-step explanation:

This is simple to solve. Choose a pair from the table, like 10 and 9.9, and divide the pounds by the price. For this, I got 1.01. We have to do the same for another one. I chose 4 and 3.96, and got 1.11. Since these are different, this is not proportional.

*If it was the same, try doing this with all of the pairs just to make sure it is proportional

Hope I helped!!!

Answer:

4:3

Step-by-step explanation:

Got the same question. the answer is 4:3

The solution to the systems of equations graphically is (2, 4)

From the question, we have the following parameters that can be used in our computation:

y = 2x

y = -x + 6

Next, we plot the graph of the system of the equations

See attachment for the graph

From the graph, we have solution to the system to be the point of intersection of the lines

This points are located at (2, 4)

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Answer:

The sum is;

Step-by-step explanation:

Solution:

Option c) The centers will roughly be equal, and the variability of simulation A will be less than the variability of simulation B

According to the information given in the question,

A true proportion of 0.325 represents that the two simulations will be conducted for sampling proportions from a population

Simulation A -

Sample size - 100

Trials - 1500

Simulation B -

Sample size - 50

Trials - 2000

Now due to the relation of simulation A and simulation B, they are closely equal-

The total sample size of simulation A= 1500 x 100

= 150000

The total sample size of simulation B = 2000 x 50

= 100000

From the above calculations of simulations A and B, we can see that while comparing the,

Sample Size = Simulation A > Simulation B

Variability = Simulation B < Simulation B

Therefore, option c) The centers will roughly be equal, and the variability of simulation A will be less than the variability of simulation B is correct.

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In a recent survey, the proportion of adults who indicated mystery as their favorite type of book was 0.325. Two simulations will be conducted for the sampling distribution of a sample proportion from a population with a true proportion of 0.325. Simulation A will consist of 1,500 trials with a sample size of 100. Simulation B will consist of 2,000 trials with a sample size of 50. Which of the following describes the center and variability of simulation A and simulation B?

A) The centers will roughly be equal, and the variabilities will roughly be equal.

B) The centers will roughly be equal, and the variability of simulation A will be greater than the variability of simulation B.

C) The centers will roughly be equal, and the variability of simulation A will be less than the variability of simulation B.

D) The center of simulation A will be greater than the center of simulation B, and the variability of simulation A will roughly be equal to the variability of simulation B.

E) The center of simulation A will be less than the center of simulation B, and the variability of simulation A will be greater than the variability of simulation B.

Answer:

The correct option is;

x³ + 4·x² + 3·x  < x³ + 13·x² + 54·x + 72.

Step-by-step explanation:

The given parameters are;

The basic plan of the decorator = x wall-color options, x + 1 ceiling-colr options, and x + 3 floor options

The gold plan of the decorator = All of the basic plan options plus 3 additional options in each category

Therefore, the gold plan of the decorator = (x + 3) wall-color options, (x + 1 + 3) ceiling-color options, and (x + 3 + 3) floor options

The total number unique layouts offered by the basic plan = x × (x + 1) × (x + 3) = x³ + 4·x² + 3·x

Also, the total number unique layouts offered by the gold plan = (x + 3) × (x + 1 + 3) × (x + 3 + 3) = (x + 3) × (x + 4) × (x + 6)  = x³ + 13·x² + 54·x + 72

Which gives;

The comparison between the total number of unique layouts offered by the basic and gold plans  as x³ + 4·x² + 3·x  < x³ + 13·x² + 54·x + 72.

The 95% confidence interval for the mean heart rate of Chicago Marathon finishers five minutes after completing the race is (128.74, 135.26) beats per minute for variance.

To find the 95% confidence interval for the mean heart rate of Chicago Marathon finishers five minutes after completing the race, we can use the following formula:

\(CI = x +- (t * (s / \sqrt{n} ))\)

where:
- CI is the confidence interval
- x is the sample mean (132)
- t is the t-value corresponding to the 95% confidence level
- s is the square root of the sample variance (the sample standard deviation)
- n is the sample size (41)

Step 1: Calculate the sample standard deviation
\(s = \sqrt{s^2} = \sqrt{105}\)≈ 10.25

Step 2: Find the t-value for a 95% confidence level with 40 degrees of freedom (n - 1)
Using a t-table or calculator, we find that the t-value is approximately 2.021.

Step 3: Calculate the margin of error
Margin of Error =\(t * (s / \sqrt{n} ) = 2.021 * (10.25 / \sqrt{4} )\) ≈ 3.26

Step 4: Calculate the confidence interval
CI = x ± Margin of Error = 132 ± 3.26
CI = (128.74, 135.26)

So, the 95% confidence interval for the mean heart rate of Chicago Marathon finishers five minutes after completing the race is (128.74, 135.26) beats per minute.

Answer:

41

Step-by-step explanation:

how all work! 1) Find two consecutive odd integers with a sum of 80. Let x= first consecutive integer 39. Let x+2= second. 41. 2x=78 x+x+2= 80. 2x+2=80.

X= 39 & 41

Answer:

(-2, -4)

Step-by-step explanation:

Start at point O which has coordinates (0, 0). Go 2 units left. Go 4 units down. Now you are at point I.

Answer: (-2, -4)

Answer:

x=-3

Step-by-step explanation:

5x+7+3x=-8+3x

Combine like terms

8x+7 = 3x-8

Subtract 3x from each side

8x+7-3x = 3x-8-3x

5x+7 = -8

Subtract 7 from each side

5x+7-7 = -8-7

5x = -15

Divide each side by 5

5x/5 = -15/5

x = -3

In a normal distribution, x = 3 and z = 0.67. This tells us that x = 3 is 0.67 standard deviations to the right of the mean.

Here's why:

In a normal distribution, the z-score is the number of standard deviations from the mean.

The formula for converting a value to a z-score is:

z = (x - μ) / σ

where z is the z-score, x is the value, μ is the mean, and σ is the standard deviation.

In this case, we know that x = 3 and z = 0.67.

We don't know the mean or standard deviation, but we can use algebra to rearrange the formula and solve for them.

Here's how:

z = (x - μ) / σ

0.67 = (3 - μ) / σ

multiply both sides by σ:

0.67σ = 3 - μ

subtract 3 from both sides:-

-2.33 = -μ + σ

divide both sides by -1:-

2.33 = μ - σ

so the mean is 2.33 standard deviations to the left of the value x = 3.

Therefore, x = 3 is 0.67 standard deviations to the right of the mean.

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Answer-

yes

Step-by-step explanation:

yes, because no matter what value you plug in for x, you'll always get the same y.

For instance, if you plug in 3 as the value for x, y will always be 1.  This is true for every x, so this is a function.

The perimeter is the total distance around the outer boundaries of a shape. It is used to measure the size of an area by adding the lengths of all the sides of the shape together.

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Hey there!

The correct answer is 30 miles per gallon.

If he can drive 270 miles on 9 gallons, we want to find the unit rate, or miles per gallon. We can do this by dividing 270 by 9. To make it easier, we will take off the zero, and do 27/9, which is 3. Now we add the 0 back on, which gives us 30. Therefore, his average mileage is 30 miles per gallon.

Have a terrificly amazing day! :D

Answer:

30 miles per gallon

Step-by-step explanation:

1. 30 miles per gallon since 360/12 = 30

2. 270 / 9 = 30

The values in the question obtained by reading the attached graph are as follows;

Question 7

Question 8

Question 9

Question 10

A graph is a pictorial representation of the relationship between two or more variables on a coordinate plane by locating each point according to the magnitude of the variable and the axis that bears the variable's parameters.

Question 7;

The cost rate of each cab, which can be found from the cab equations are as follows;

The points on the graph of The Red Cabs are; (0, 2), and (3, 8)

The slope of the graph of The Red Cabs is; (8 - 2)/(3 - 0) = 2

The equation of the graph of The Red Cabs is therefore;

y - 2 = 2 × x

The equation for the cost of The Red Cabs is; y = 2·x + 2

Points on the graph of The Green Cabs are; (0, 5), and (3, 8)

The slope = (8 - 5)/(3 - 0) = 1

The equation is therefore;

y - 5 = x

The equation for the cost of The Green Cabs is; y = x + 5

The cost of traveling 2 miles on the The Red Cabs is; x = 2

y = 2 × 2 + 2 = 6

The cost of traveling 2 miles on The Green Cabs is; x = 2

y = 2 + 5 = 7

The Red Cabs is more affordable when traveling 2 miles

Question 8

From the graph, the cost of The Red Cabs when traveling 6 miles is $14

The cost of The Green Cabs when traveling 6 miles is $11

The Green Cabs cost less when traveling for 6 miles and should be called

Question 9

The point when the cost are the same for both taxis is specified by the point of intersection of the two graphs, which is the point (3, 8)

The point (3, 8) corresponds to a distance of 3 miles at a cost of $8

Therefore;

Question 10

The cost of traveling with The Red Cabs for 8 ,miles from the graph is $18

The cost of traveling with The Green Cabs for 8 miles is $13

The difference in the cost between the two companies is therefore;

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Answer:

yes it is a function because the x does not repeat itself

Step-by-step explanation:

Answer:

196π

Step-by-step explanation:

14^2=196

196×π

=196π

They rode 15 miles before replacing each horse.

Let's assume that each rider rode a different number of horses, denoted as x, y, and z respectively. Since they used a total of 16 horses, we have the equation x + y + z = 16.

Since they rode the same number of miles on each horse, let's denote the distance traveled by each horse as d. Therefore, the total distance covered by all the horses can be calculated as 16d.

We are given that the three riders rode a total of 240 miles. Therefore, we have the equation xd + yd + z*d = 240.

From the given information, we have two equations:

x + y + z = 16 (Equation 1)

xd + yd + z*d = 240 (Equation 2)

Since we need to find the number of miles they rode before replacing each horse, we need to find the value of d. To solve this system of equations, we can substitute one variable in terms of the others.

Let's assume x = 16 - y - z. Substituting this into Equation 2, we get:

(16 - y - z)d + yd + z*d = 240

Simplifying, we have:

16d - yd - zd + yd + zd = 240

16d = 240

d = 240/16

d = 15

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Answer:

10 lattes and 23 cappuccinos were sold.

Step-by-step explanation:

Given that one day, a café sells 3 more than twice the number of cappuccinos as they do lattes, and they sold a total of 33 cappuccinos and lattes together, to determine which equation could be used to find the number of lattes that were sold at the coffee the following calculation must be carried out:

Latte = X

Cappuccino = 2X + 3

X + 2X + 3 = 33

3X + 3 = 33

3X = 33 - 3

X = 30/3

X = 10

Latte = 10

Cappuccino = 2 x 10 + 3 = 23

Therefore, 10 lattes and 23 cappuccinos were sold.

Answer:

FDE = 116 degrees

Step-by-step explanation:

If FDE and CDE are supplementary, then their total would be 180 degrees. Thus, we can set up the following equation:

CDE + FDE = 180

3x + 10 + 6x + 8 = 180

9x + 18 = 180

9x = 162

x = 18

Now that we know "x = 18", we can find the measurement of FDE:

FDE

6x + 8

6(18) + 8

116

Answer:

It will not be enough money to pay for the fruit

Step-by-step explanation:

Reason:

3+3.87+2.23+2.37= $11.47

$11.47-10= $1.47

hes missing $1.47

the answer is 30°

EXPLAINATION:

since the angle is a right angle triangle one of it's angles is 90°, and all the angles of a triangle always add up to 180°

so, 90° + 60° + x = 180

150° + x = 180°

so x = 180° - 150° = 30°

hence, the other acute angle is 30°.

Answer:

C ≈ 54

Step-by-step explanation:

The circumference (C) is calculated as

C = πd ( d is the diameter )

Here d = 18 , then

C = π × 18 ≈ 3 × 18 = 54

Answer:

2.5 X z = 10

z stands for the unknown number that is multiplied by 2.5 to equal 10