What are the zeros of the parabola represented by the function - 2x2 = -5x + 3?

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Based on the information, the length of JI is twice the length of the radius and it's 2.34.

We know that the tangent GH is perpendicular to the radius at the point of tangency. This means that the radius is also perpendicular to the secant JIH.

We can use the Pythagorean theorem to find the length of the radius. The radius is the hypotenuse of a right triangle with legs of length 0.866 and 0.5.

The radius is ✓(0.866² + 0.5²) - ✓1.366 = 1.17

The length of JI is twice the length of the radius, or 2×1.17=2.34.

Rounded to the nearest tenth, the length of JI is 2.3.

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Answer: 24 units

Step-by-step explanation:

If you are multiplying a shape by a scale factor, the dimensions are also multiplied by the scale factor.

QR= x

Q'R'= (1/2)(X)

12=(1/2)(X)

(2)12= 1/2x(2)

24=X

If you're multiplying QR by 1/2 you would get 12. 12 is a half of QR. Therefore, QR is 24.

2.54 x 10 = 25.4

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The system of statements, in standard form, modeling the relationships between amount of yoys (x) and amount of quects (y) is x ≥ 17, x ≥ 7y, and x + 7y ≤ 28.

The system of statements, in standard form, modeling the relationships between amount of yoys (x) and amount of quects (y) is calculated as follows;

She expected to sell at least 17 yoys, the equation  becomes;

x ≥ 17

She expected to sell at least $7 per quect, the equation becomes;

x ≥ 7y

She expected to make no more than $28.

x + 7y ≤ 28

The statements combined in standard form becomes;

x ≥ 17, x ≥ 7y, and x + 7y ≤ 28

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The equation that models the relationship between the models to show Ethan's employee benefits is y = 14 + 3(x - 1).

The number of paid vacation days Ethan earned was 35 paid vacation days .

Ethan will reach the maximum number of paid vacation days in 7 years.

Let x represent the number of years he has worked for this employer and y represent the number of paid vacation days he has earned.

The equation that models the relationship between x (years worked) and y (paid vacation days earned) is:

y = 14 + 3(x - 1)

Using the equation from part a, we can find out how many paid vacation days Ethan has earned after eight years:

y = 14 + 3(8 - 1)

y = 14 + 3(7)

y = 14 + 21

y = 35

To determine when Ethan will reach the maximum number of paid vacation days, we can set y equal to 30 and solve for x:

30 = 14 + 3(x - 1)

16 = 3(x - 1)

16/3 = x - 1

x = 16/3 + 1

x = 16/3 + 3/3

x = 19/3

x = 7

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The TIV Telephone Company wants to determine if the mean length of current long-distance calls is different from the average length of 12.44 minutes in 1999. A sample of 150 calls yielded a mean length of 13.71 minutes and a standard deviation of 2.65 minutes. Using a 5% significance level, we will test the hypothesis.

A. The null hypothesis (H0) is that the mean length of current long-distance calls is equal to 12.44 minutes. The alternative hypothesis (Ha) is that the mean length is different from 12.44 minutes.

B. To calculate the test statistic, we will use the formula:

t = (sample mean - hypothesized mean) / (sample standard deviation / √n)

Substituting the given values:

t = (13.71 - 12.44) / (2.65 / √150)

t ≈ 3.244

C. The rejection region for a two-tailed test at a 5% significance level consists of extreme values in both tails of the t-distribution. Since we have a large sample size, we can use the standard normal distribution. The critical values are ±1.96.

D. Since the test statistic falls outside the rejection region (|t| > 1.96), we reject the null hypothesis.

E. To calculate the p-value, we compare the absolute value of the test statistic to the critical value(s) for the given significance level. The p-value is the probability of obtaining a test statistic as extreme or more extreme than the observed value, assuming the null hypothesis is true. In this case, the p-value is very small, less than 0.001.

In conclusion, based on the test results, we reject the null hypothesis and conclude that the mean length of current long-distance calls is significantly different from 12.44 minutes.

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Answer:

We get x=3 and y=21

The ordered pair will be: (3,21)

Step-by-step explanation:

We need to use the substitution method to solve the system of equations.

\(y = 10x-9\\y = x + 18\)

For substitution method we substitute the value of x or y from one equation to other.

Let:

\(y = 10x-9--eq(1)\\y = x + 18--eq(2)\)

Putting value of y from equation 2 into equation 1

\(y=10x-9\\Put\:y=x+18\\x+18=10x-9\\x-10x=-9-18\\-9x=-27\\x=\frac{-27}{-9}\\x=3\)

So, we get value of x=3

Now, for finding value of y, We substitute the value of x

Find value of x from equation 2

\(y=x+18\\x=y-18\)

Now, putting value of x in equation 1

\(y=10x-9\\Put\:x=y-18\\y=10(y-18)-9\\y=10y-180-9\\y-10y=-189\\-9y=-189\\y=\frac{-189}{-9}\\y=21\)

So, we get value of y=21

So, We get x=3 and y=21

The ordered pair will be: (3,21)

Answer:

1. Find the prime factorization of each number.

2. Write each number as a product of primes, matching primes vertically when possible.

3. Bring down the same numbers in each column and the remaining numbers in each column.

4. Multiply the factors to get the LCM.

for example the lcm of 24 and 36

= 24 = (2 × 2 × 2 × 3) = 2^3 × 3^1

 and 36 = (2 × 2 × 3 × 3) = 2^2 × 3^2

LCM(24, 36) = 2^2 × 3 × 2 × = 72

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Answer:

The x-axis is always the the horizontal axis which represents the independent variable

The y-axis is always the vertical axis which represents the dependent variable

Hope this helps!

Answer:

I am only answering this so you can give the other girl brainliest.

Step-by-step explanation:

Answer: B -3

Step-by-step explanation

-3/4 my teacher would say rise over run, run means x axes and rise is y axes to get 2 to 8 you need 6 if you times -3/4 by 2 you would get -6/8 6 is x +2 from (5,2) you would get 8 so (m,8) then -8 +5 is -3 creating (-3,8)

Answer:

42

Step-by-step explanation:

42/6=7

Answer:

42

Step-by-step explanation:

I hope this helps!

Answer:

The price of a drink is $7.25

Step-by-step explanation:

Let d represent the price of a drink

let p represent the price of a popcorn

6p+12d=118.50  equation 1

p+6d=48.75    equation 2

multiply both equation 1  by 2

multiply equation 2 by 4

12p+24d=237   equation 3

4p+24d=195 equation 4

subtract equation 4 from 3

8p=42

p=42/8

p=$5.25

Substitute for p in equation 1

(6*5.25 )+12d=118.50

31.5 +12d=118.50

12d=118.50-31.5 0

12d=87

d=87/12

d=$7.25

Answer:

3.3

Step-by-step explanation:

I think so I don't know

The simplest and most straightforward measure of variability is the range. The range is calculated by subtracting the smallest value in a dataset from the largest value.

It provides a basic understanding of how spread out the data points are. However, the range has limitations as it only considers the extreme values and does not take into account the distribution of the remaining data points.

Therefore, while the range is a simple measure of variability, it is often supplemented or replaced by more robust measures such as the variance and standard deviation, which provide a more comprehensive understanding of the dispersion of data.

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The rate at which the top of the ladder is slipping down at the instant when the bottom of the ladder is 15 feet from the base of the building is -75/8 feet per second

The length of the ladder = 17

Consider the length of the base as x and the height is h

The rate at which the ladder is sliding = 5 feet per second

dx/dt = 5

Apply the Pythagorean theorem

x^2 + h^2 = 17^2

h^2 = 289 - x^2

h = \(\sqrt{289-x^2}\)

The rate of change of height with respect to x is

dh/dx = - x / (289 - x^2)^(1/2)

dh/dt = dh/dx × dx/dt

Substitute the values in the equation

= - 15 / (289 - 15^2)^(1/2) × 5

= -15/8 × 5

= -75/8 feet per second

Therefore, the rate of change of height when x = 15 is -75/8 feet per second

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The total number of minutes used by John over the cell phone is 718.

A linear equation in two variable has the general form as y = ax + by + c, where a, b and c are integers and a, b ≠ 0.

It can be represented as a straight line on a graph.

Given that,

The monthly plan of the cell phone company is $40.

The charge per minute for every minute over 700 minutes is $0.45.

The total charge paid is $48.10.

Suppose John uses x minute over 700 minutes.

Then, as per the problem the following equation can be made for John's expense,

40 + 0.45x = 48.10

=> 0.45x = 48.10 - 40

=> x = 8.10/0.45

=> x = 18

Thus, total number of minutes used is given as  700 + 18 = 718 minutes.

Hence, John must have used 718 minutes during the month.

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Answer:

\(-9.5\) is the best answer.

Step-by-step explanation:

Given the expression

\(x + (-y)\)

putting x=1.2 and y=-10.72 in the expression

\(x\:+\:\left(-y\right)=1.2\:+\:\left(-10.72\right)\)

                \(=-9.52\)

Therefore, -9.5 is the best answer.

The statement about systematic errors that is true is: They can occur when a selection bias is present.

Systematic errors can be defined as a type of error that affects the accuracy of the results of an experiment or study. It is mostly caused by the tools, materials, or a particular problem with the instrument used in the experiment. A systematic error can be of different types, including the following:

Scale Error: Scale errors occur due to calibration issues. They can occur due to a problem with the measuring instruments, which may not provide accurate readings during an experiment.

Selection Bias: It occurs when a researcher deliberately selects a certain group of individuals or data that are not representative of the general population. This can lead to inaccurate results for the study.

Resolution Error: This error is common when researchers do not choose the correct measurement tools to measure the variables of interest.

Therefore, option A is correct. This is because systematic errors can occur when a selection bias is present.

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There is no sufficient evidence to indicate the true standard deviation is less than 4000.

What is the standard deviation?

The standard deviation is a statistic that expresses how much variation or dispersion there is in a set of values. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the set mean.

given that n = 16

x = 60139.7

s = 3718.06

∝ = 0.05

To test the hypothesis

H0 : = 4000

H1 :  < 4000 (claim)

test statistics

x² = ((n-1)s²) / H0²

  = (15 * 13823970.16) / (16000000)

  = 12.96

P- value = P [x² < 12.96]           DF = n-1 = 15

            = 0.3946

0.1 < P-value <0.5

Hence, there is no sufficient evidence to indicate the true standard deviation is less than 4000.

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Answer:

Option (3)

Step-by-step explanation:

Coordinates of a point (h, k) which divides a line with ends \((x_1,y_1)\) and \((x_2,y_2)\) in the ratio of m : n are,

h = \(\frac{mx_2+nx_1}{m+n}\)

k = \(\frac{my_2+ny_1}{m+n}\)

If the ends of line AB are A(-5, -4) and B(5, 1) and a point (h, k) divides this line into two parts in the ratio of 3 : 2

h = \(\frac{3\times (5)+2(-5)}{3+2}\)

h = 1

k = \(\frac{3(1)+2(-4)}{3+2}\)

k = -1

Therefore, coordinates of the point (h, k) are (1, -1).

Option (3) will be the answer.

Statistics computed for larger random samples tend to be less variable compared to statistics computed for smaller random samples.

This statement is based on the concept of the Central Limit Theorem (CLT) in statistics. According to the CLT, as the sample size increases, the distribution of the sample mean approaches a normal distribution regardless of the shape of the population distribution. This means that the variability of the sample mean decreases as the sample size increases.

The variability of a statistic is commonly measured by its standard deviation or variance. When working with larger random samples, the individual observations have less impact on the overall variability of the statistic. As more data points are included in the sample, the effects of outliers or extreme values tend to diminish, resulting in a more stable and less variable estimate.

In practical terms, this implies that estimates or conclusions based on larger random samples are generally considered more reliable and accurate. Researchers and statisticians often strive to obtain larger sample sizes to reduce the variability of their results and increase the precision of their statistical inferences.

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Answer:

√241 or 15.5242

Step-by-step explanation:

We're gonna use the distance formula: √(x₁ - x₂)² + (y₁ - y₂)²

√(-9 - 6)² + (3 - (-1))²

√(-15)² + (4)²

√225 + 16

√241

The required value of x is 22 degrees for the given figure.

Adjacent angles are a sort of additional angle. Adjacent angles share a common side and vertex, such as a corner point. Their points do not overlap in any manner.

As we know that supplementary angles are defined as when pairing of angles addition to 180° then they are called supplementary angles.:

According to the given figure, it can be written as follows:

2x + 24 + 6x - 20 = 180

8x + 4 = 180

8x = 180 - 4

8x = 176

x = 176/8

x = 22

Therefore, the required value of x is 22 degrees for the given figure.

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The complete question is as follows:

Find the value of x for the below figure.

The area of the sector as shown in the diagram is 13.1 cm².

A sector is said to be a part of a circle made of the arc of the circle along with its two radii.

To calculate the area of the sector, we use the formula below

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the area of the sector is 13.1 cm².

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The range of the given function would be -

Range → {-2, 3, 5, 6}

An function in mathematics defines a relationship between one variable (the independent variable {x})  and another variable (the dependent variable {y}). Example → y = f{x} = ax + b.

Given is the graph of the function as shown in the image.

Range represents the set of values along the {y} - axis. So, we can write the range as -

Range → {-2, 3, 5, 6}

Therefore, the range of the given function would be -

Range → {-2, 3, 5, 6}.

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The permutation combination is 120 for 3 different topping pizzas are available.

Permutation Combination:

A variety of ways to select objects from a set, usually forming a subset without replacement. The selection of this subset is called a permutation if the order of selection is a factor, and a combination if the order is not a factor. The French mathematicians Blaise Pascal and Pierre de Fermat, in the 17th century, used many chances in his game of combinatorics and probability by considering the ratio of the number of required subsets to the number of all possible subsets stimulated the development of the theory.

The concepts of permutations and combinations and their differences can be illustrated by examining all the different ways of selecting pairs of objects from five identifiable objects such as the letters A, B, C, D and E.

According to the Question:

Given that :

Number of different toppings = 10

Number of Pizzas = 03

therefore,

The permutation  combination are :

                = 10!/7! 3!

                = 15 × 8

                = 120.

Therefore, there are 120 different combinations of toppings.

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Answer:

rectangle

Step-by-step explanation:

Isaac has a 1/40 chance of winning the raffle, or a 2.5% chance. This indicates that he has a 2.5% probability of having his ticket chosen out of the 40 tickets that were sold.

Isaac has a 1/40 chance of winning the raffle, or a 2.5% chance. This indicates that he has a 2.5% probability of having his ticket chosen out of the 40 tickets that were sold. This is because there is only one raffle winner and it is impossible to predict which ticket will be picked.

It's also crucial to remember that his odds of winning are entirely independent of those of any other ticket holder; nobody else's ticket will affect the outcome of the raffle. As a result, Isaac has the same chance of winning as any other ticket holder. It's also vital to remember that regardless of how many tickets are sold, the likelihood of winning stays the same. Therefore, regardless of how many raffle tickets are sold, there is a 2.5% chance of winning.

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