What are the zeros of f(x) = x² + x - 30?
OA. x=-15 and x = 2
OB. x= -6 and x = 5
OC. x = -2 and x = 15
D. x = -5 and x = 6
SUB

The triangle  DAE and FCE is congruent by the vertical angle theorem property.

What is congruency ?

Congruence of triangles is a term used in geometry to describe the relationship between two triangles that have exactly the same size and shape. In other words, if two triangles are congruent, all of their corresponding sides and angles are equal. When two triangles are congruent, they can be superimposed on each other, and all parts of one triangle will coincide with the corresponding parts of the other triangle.

The concept of congruence is essential in geometry, as it allows us to prove various theorems and make deductions about the properties of triangles. Two triangles can be shown to be congruent if any of the following conditions are met:

Side-Side-Side (SSS) Congruence: If the three sides of one triangle are equal to the three sides of another triangle, then the triangles are congruent.

Side-Angle-Side (SAS) Congruence: If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the triangles are congruent.

Angle-Side-Angle (ASA) Congruence: If two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the triangles are congruent.

Angle-Angle-Side (AAS) Congruence: If two angles and a non-included side of one triangle are equal to two angles and the corresponding non-included side of another triangle, then the triangles are congruent.

Knowing these congruence criteria, we can use them to prove theorems and solve problems in geometry involving triangles.

The reflexive property is a fundamental concept in mathematics, and it applies to many different areas of study, including geometry. In the context of geometry, the reflexive property is related to congruence of triangles.

The reflexive property of congruence states that any geometric figure is congruent to itself. In the case of triangles, this means that any triangle is congruent to itself. In other words, every triangle is identical to itself, and all of its corresponding sides and angles are equal.

The reflexive property of triangles is used frequently in proofs and demonstrations in geometry. For example, if we want to show that a given triangle is congruent to another triangle, we can use the reflexive property to show that the two triangles are congruent to themselves. Then, we can use other methods, such as the SSS or SAS criteria, to show that the two triangles are congruent to each other.

Overall, the reflexive property is a key concept in geometry that allows us to reason about congruence and to prove various theorems and results related to triangles and other geometric figures.

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By answering the presented question, we may conclude that So, the equation of the line that passes through the point ([tex]12,19[/tex]) with slope [tex]-2/3[/tex] is: [tex]y = (-2/3)x + 27[/tex]

what is slope?

In mathematics, slope is the steepness of a line or curve. It is a measure of how much a function's y-value fluctuates when the x-value changes. A line's slope is commonly symbolised by the letter m and may be computed as follows: [tex]m = (y2 - y1) / (x2 - x1) (x1, y1)[/tex] and [tex](x2, y2)[/tex] are any two points on the line. The slope of a line might be positive, negative, zero, or unknown. A positive slope means the line ascends from left to right, whereas a negative slope means the line drops from left to right.

The point-slope form

[tex]y-y1=m(x-x1)[/tex]

[tex]y-19=(-2/3)(x-12)[/tex]

[tex]y-19=(-2/3)x+8\\y=(-2/3)x+27[/tex]

So, the equation of the line that passes through the point [tex](12,19)[/tex]  with slope [tex]-2/3[/tex] is:

[tex]y = (-2/3)x + 27[/tex]

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a) The predicted GPA for a student with Verbal SAT score of 500 is 2.9805.

b) The residual for this student is -0.2805.

To calculate the predicted GPA for a student with Verbal SAT score of 500, we need to plug in the value of 500 into the regression equation:

GPA = 2.0336 + 0.0018929 × VerbalSAT

Thus, the predicted GPA for a student with Verbal SAT score of 500 is

GPA = 2.0336 + 0.0018929 × 500 = 2.9805

To calculate the residual for this student, we subtract the predicted GPA from the actual GPA

Residual = Actual GPA - Predicted GPA

Residual = 2.7 - 2.9805 = -0.2805

Therefore, the residual for this student is -0.2805.

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I have solved the question in general, as the given question is incomplete.

The complete question is:

A straight line linear regression analysis was carried out, using Verbal SAT score, VerbalSAT (values can range from 0 to 800), to predict grade point average in college, GPA, for first-year BU students (GPA values can range from 0 to 4). The sample size is 345 first-year BU students. The following are the least squares estimates of the coefficients of the linear regression model and the estimates of their standard error: Variable DF Parameter Standard Estimate Error 1 2.0336 0.1621 Intercept VerbalSAT (Slope) 1 0.0018929 0.0002709 . . Calculate the predicted GPA and the residual for a student with Verbal SAT score of 500. GPA was 2.7 for this student.

The best interpretation of the correlation coefficient is:

There is a weak positive association between the number of minutes played and the number of tokens used.

What is the correlation coefficient?

A correlation coefficient is a number between -1 and 1 that tells you the strength and direction of a relationship between variables.

The correlation coefficient is 0.363 for these data. Since the correlation coefficient is positive,

we know that there is a positive association between the number of minutes played and the number of tokens used.

However, since the correlation coefficient is less than 0.5, we can conclude that the association is weak.

Therefore, the best interpretation of the correlation coefficient is:

There is a weak positive association between the number of minutes played and the number of tokens used.

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Answer: 8

Step-by-step explanation: 5x8=40

When adding one identical room to a pair of houses, the price increase for a house with 4000 sqft compared to a house with 1000 sqft is $150,000.

What is the basis of this problem?

We have two houses, one with a 4000 square foot floor plan and another with a 1000 square foot floor plan. Both of them are identical, and each of them is expected to receive an additional identical room. We must determine how much the price of the house with the 4000 square foot floor plan will increase compared to the house with the 1000 square foot floor plan when both of these are completed.

Let's start by identifying the amount of money needed to construct each house. The amount of money needed to construct the house with the 4000 square foot floor plan is $300,000, and the amount of money required to build the house with the 1000 square foot floor plan is $150,000.The cost of building per square foot in this case is therefore $75/sqft.

As a result, the price for a 4000 sqft house is: $75/sqft × 4000 sqft = $300,000On the other hand, the cost of constructing a 1000 sqft house is:$75/sqft × 1000 sqft = $75,000When each house gets an additional identical room, the increase in the cost of the room is $50,000. As a result, the price of the house with the 4000 square foot floor plan will increase by 4 times, or $200,000, whereas the price of the house with the 1000 square foot floor plan will increase by one, or $50,000. As a result, the price of a 4000 sqft house will be $300,000 + $200,000 = $500,000, whereas the price of a 1000 sqft house will be $150,000 + $50,000 = $200,000.

When we compare these two values, we obtain the following outcome: Suppose you add 1 identical room to a pair of houses. The two houses are identical except for square footage.

When we compare the two values, we get the following result: $500,000 - $200,000 = $300,000

Therefore, the price increase for a house with 4000 sqft compared to a house with 1000 sqft is $150,000.

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For the probability of 90% that it will take at least 68.195 minutes long to assemble an electronic component.

As we have the time it takes to assemble an electronic component is normally distributed.

Mean time, [tex] \mu[/tex] = 17.2 minutes

Standard deviations, [tex] \sigma[/tex]

= 3.1 minutes

We have to determine probability is 90% that it will take at least how long to assemble a component. Now, from the standard normal distribution table value of Z - score for 90% is equals to the 1.645.

Using the Z- score formula in normal distribution, [tex]Z = \frac{ X - \mu}{\sigma }[/tex]

=> 1.645 = ( X - 17.2 )/3.1

=> X - 17.2 = 31 × 1.645

=> X = 17.2 + 50.995

=> X = 68.195

Hence, the required at least the long to assemble a component is equals to the 68.195.

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In the given information, we can see that the populace of the United States has expanded consistently over time, with a few variances.

 Here is a chronological chart of the US population data:

Year   Population (millions)

1790  3.9

1800  5.3

1810   7.2

1820   9.6

1830   12.9

1840   17.1

1850   23.2

1860   31.4

1870   38.6

1880   50.2

1890   63.0

1900   76.2

1910   92.2

1920   106.0

1930   123.2

1940   132.2

1950   151.3

1960   179.3

1970   203.3

1980   226.5

1990   248.7

2000  281.4

2010  308.7

From the time chart, we can see that the populace of the United States has expanded consistently over time, with a few variances.

The slant is up, with the populace developing quicker in later a long time.

The time chart moreover permits us to see the rate of populace development over time. We can see that the population has expanded from less than 4 million in 1790 to more than 300 million in 2010.

We are able moreover to see the rate of populace development over diverse periods, such as fast populace development. within the middle of the twentieth century.

In general, the time chart of US populace information gives a visual representation of statistic patterns over time and permits us to effortlessly distinguish designs and changes within the populace.

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The histogram provided displays the frequency of grades earned on a Spanish test.

Which of the below best illustrates the data's shape and why?

Based on the given information, the shape of the data is not symmetric because the grades are not evenly distributed in each of the intervals.

The data appears to be skewed to the left because there are fewer students who received higher grades than those who received lower grades. Additionally, the mode of the data is in the 71-80 interval, which is the highest point in the histogram.

Therefore, the correct answer is:

"Because there is a large amount of data, the data is skewed, with the average grade being in the middle i.e, option c"

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The solution to the system of equations is x = 6, y = 22.

What is solution?

We can start by setting the two expressions for y equal to each other:

x² - 3x + 16 = 9x - 20

Next, we can rearrange the equation into standard quadratic form:

x² - 12x + 36 = 0

Now we can factor the quadratic:

(x - 6)² = 0

This equation has only one solution, x = 6. To find the corresponding value of y, we can substitute x = 6 into either of the original equations:

y = 6² - 3(6) + 16 = 22

Therefore, the solution to the system of equations is x = 6, y = 22.

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Answer: Assuming the field is rectangular, the distance between the two corners diagonally can be calculated using the Pythagorean theorem, which states that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.

In this case, the length and width of the field form the two sides of the right triangle, and the diagonal is the hypotenuse.

So, using the Pythagorean theorem:

Diagonal^2 = Length^2 + Width^2

Diagonal^2 = 80^2 + 60^2

Diagonal^2 = 6400 + 3600

Diagonal^2 = 10000

Diagonal = √10000

Diagonal = 100 yards

Therefore, the soccer player will have to kick the ball 100 yards to reach the opposite corner of the field.

Step-by-step explanation:

The function is an exponential function of the form y = a * b^x, where "a" is the initial value and "b" is the common ratio.

Using the given table, we can see that:

- The initial value is y(0) = -2, so a = -2.

- To find the common ratio, we can divide any term by the previous term. For example:

 - b = y(1)/y(0) = (-10)/(-2) = 5

 - b = y(2)/y(1) = (-50)/(-10) = 5

 - and so on.

Since we get the same value of b for all the ratios, we can conclude that the common ratio is b = 5.

Therefore, the equation for the function shown in the table is: y = -2 * 5^x.

a. The height of the golf ball at the instant it is hit is 0 feet.

b. The height of the golf ball 2.8 seconds after it is hit is approximately 62.72 feet.

c. It takes 4 seconds for the golf ball to hit the ground after it is hit.

a) To find the height of the golf ball at the instant it is hit, we need to evaluate the function h when t = 0.

Substituting t = 0 into the given equation, we get:

h = -16(0)² + 64(0) = 0

Therefore, the height of the golf ball at the instant it is hit is 0 feet.

b) To find the height of the golf ball 2.8 seconds after it is hit, we need to evaluate the function h when t = 2.8.

Substituting t = 2.8 into the given equation, we get:

h = -16(2.8)² + 64(2.8) ≈ 62.72

Therefore, the height of the golf ball 2.8 seconds after it is hit is approximately 62.72 feet.

c) To find how long it takes the ball to hit the ground after it is hit, we need to find the value of t when the height is 0.

Setting h = 0 in the given equation, we get:

0 = -16t² + 64t

0 = t(-16t + 64)

t = 0 or t = 4

Since the golf ball was hit upwards, we are only interested in the positive value of t, which is t = 4.

Therefore, it takes 4 seconds for the golf ball to hit the ground after it is hit.

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The question is -

The height in feet of a golf ball hit into the air is given by h = − 16t² + 64t, where t is the number of seconds elapsed since the ball was hit, and represents the golf ball height, in feet.

a) what is the height of the golf ball at the instant it is hit?

b) what is the height of the golf ball 2.8 seconds after it is hit?

c) how long does it take the ball to hit the ground after it is hit?

Answer:

80%

Step-by-step explanation:

We Know

There are 260 students at the rally.

208 students are wearing purple.

What percent are wearing purple?

We Take

208 divided by 260, time 100 = 80%

So, 80% students wearing purple.

Since 3 has the highest frequency, the mode is 3.Now, the curve is positively skewed if mean is bigger than mean.

Total number is a term used to refer to the sum of two or more individual elements. It is commonly used in the context of mathematics and can refer to the result of addition, subtraction, multiplication, or division. For example, the total number of apples in a basket could be five, the total number of days in a week could be seven, and the total number of people in a family could be four. In any case, the total number is the sum of all the individual elements that are being considered.

Presented to us is a distribution:

{4.5, 3, 1, 2, 4, 3, 6, 4.5, 4, 5, 2, 1, 3, 4, 3, 2}

We must determine the mean.

Mean is equal to the sum of all observations divided by the total number of observations.

Mean = 52/16

Mean = 3.25

We now determine the mode, which is the observation with the highest frequency, or how frequently it has occurred.

observations per unit of time

4.5 2

3 4

1 2

2 3

4 3

6 1

5 1

Since 3 has the highest frequency, the mode is 3.
Now, the curve is positively skewed if mean is bigger than mean.

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Complete questions as follows-
What is the mean of the given distribution, and which type of skew does it exhibit?
{4.5, 3, 1, 2, 4, 3, 6, 4.5, 4, 5, 2, 1, 3, 4, 3, 2}

WHAT IS THE MEAN? and WHAT TYPE OF SKEW EXHIBITS? negative, positive, symmetric, zero etc..

We can estimate the expected number of clutch plates with

wear of more than 203 mm as:

[tex]0.7 \times \text{total number of clutch plates}[/tex]

To estimate the average wear and variance, we first calculate the sample

mean and sample variance:

Sample mean:

[tex]\bar{x} = \frac{1}{n}\sum_{i=1}^{n}[/tex]

[tex]x_i = \frac{204.5 + 231.1 + 157.5 + 190.5 + 261.6 + 127.0 + 216.6 + 172.7 + 243.8 + 291.0}{10} = 213.3[/tex]

Sample variance:

[tex]s^2 = \frac{1}{n-1}\sum_{i=1}^{n}[/tex]

[tex](x_i - \bar{x})^2 = \frac{(204.5 - 213.3)^2 + (231.1 - 213.3)^2 + ... + (291.0 - 213.3)^2}{9} = 3415.5[/tex]

To estimate the proportion of clutch plates with wear of more than 203

mm, we first need to calculate the sample proportion:

[tex]{number of linings with wear more than 203 mm}{\text{total number of linings}} = \frac{7}{10} = 0.7[/tex]

To estimate the proportion for a large set of clutch plates, we assume

that the sample proportion is equal to the population proportion.

Therefore, we can estimate the expected number of clutch plates with

wear of more than 203 mm as:

[tex]0.7 \times \text{total number of clutch plates}[/tex]

However, we don't know the total number of clutch plates in the

population, so we cannot provide a specific estimate.

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Answer:

I can’t see it

Step-by-step explanation:

Step-by-step explanation:

10^2   +    10^6    +   10^1    =    10 ^(2+6+1)  = 10 ^9

Answer:

A addition

Step-by-step explanation:

You would simply everything in the parentheses first and then multiply that by 1.  Lastly, you would add 8.

Helping in the name of Jesus.

It will take Mindy 1 week tο save $150.

The slοpe οf a line is the measure οf its steepness, defined as the ratiο οf the vertical change (rise) οver the hοrizοntal change (run) between any twο pοints οn the line.

Part A:

Tο create a graph that can be used tο mοdel the number οf dοllars Mindy saves in x weeks, we can use a linear equatiοn in slοpe-intercept fοrm:

y = mx + b

where y is the tοtal amοunt saved after x weeks, m is the slοpe (the cοnstant rate at which Mindy saves mοney), and b is the initial amοunt saved (which is 0 in this case).

Using the infοrmatiοn given, we can find the slοpe οf the line as fοllοws:

m = (change in y) / (change in x)

m = ($900 - $0) / (6 weeks - 0 weeks)

m = $150 per week

Sο the equatiοn fοr the line is:

y = $150x

We can graph this line by plοtting the pοints (0,0) and (6, $900), and then drawing a straight line cοnnecting them.

Part B:

The slοpe οf the line represents the cοnstant rate at which Mindy saves mοney each week. In this case, the slοpe is $150 per week, which means that Mindy is saving $150 every week.

Part C:

Tο use the line tο predict the number οf weeks it will take Mindy tο save $150, we can plug in the value fοr y (which is $150) intο the equatiοn and sοlve fοr x:

$150 = $150x

x = 1

Sο it will take Mindy 1 week tο save $150.

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Answer:

sin(cos⁻¹(x+1)) = √(1 - (x+1)²)

Step-by-step explanation:

Answer:

Step-by-step explanation:

5p+10 equals big 5

Answer:

p = 0.8; q = 0,6

Step-by-step explanation:

5p + 10q = 10

2p - q = 1

5p + 10q = 10

q = 2p - 1

5p + 10 ( 2p - 1 ) = 10

5p + 20p - 10 = 10

25p = 20

p = 0,8

q = 2 x 0,8 - 1

q = 0,6

Answer:

[tex]\frac{1}{8}[/tex]

Step-by-step explanation:

Since there are four answer choices for question one, the chance of picking the correct answer is [tex]\frac{1}{4}[/tex]. However, there is also another question. That question is a true-or-false question, meaning that there is only two options. Therefore, the probability of picking the correct answer is [tex]\frac{1}{2}[/tex]. To find the probability of picking both correctly, you multiply the two together. [tex]\frac{1}{4} * \frac{1}{2} = \frac{1}{8}[/tex], so the answer is [tex]\frac{1}{8}[/tex].

Answer:

Using the inscribed angle theorem, we know that the measure of an inscribed angle is equal to half the measure of the central angle that intercepts the same arc. So, we need to find the central angle measure for each of the inscribed angles.

For angle a, the central angle measure is 80°, so the measure of angle a is (1/2)*80° = 40°.

For angle b, the central angle measure is 120°, so the measure of angle b is (1/2)*120° = 60°.

For angle c, the central angle measure is 40°, so the measure of angle c is (1/2)*40° = 20°.

For angle d, the central angle measure is 140°, so the measure of angle d is (1/2)*140° = 70°.

For angle e, the central angle measure is 80°, so the measure of angle e is (1/2)*80° = 40°.

For angle f, the central angle measure is 60°, so the measure of angle f is (1/2)*60° = 30°.

Therefore, the degree measures of the angles are:

a = 40°

b = 60°

c = 20°

d = 70°

e = 40°

f = 30°

Step-by-step explanation: Did try my best

Answer:

50%

Step-by-step explanation:

There are 4 cards.  4 and 6 are not odd, which is 2 cards.

P(not odd) = number of cards that are not odd/ total number of cards

                   = 2/4 = 1/2 = .5 = 50%

There are 848 different combinations of games that you can attend if you want to go to at least 4 games out of the 10 scheduled games.

If you want to attend at least 4 games out of the 10 scheduled games, there are several different combinations that you can attend.

To calculate the total number of combinations, we can use the combination formula

nCr = n! / r! × (n-r)!

where n is the total number of games (10), and r is the number of games you want to attend (4).

First, let's calculate the number of combinations of attending exactly 4 games

10C4 = 10! / 4! × (10-4)! = 210

This means that there are 210 different combinations of attending exactly 4 games out of the 10 scheduled games.

Next, let's calculate the number of combinations of attending 5, 6, 7, 8, 9, or all 10 games

10C5 = 10! / 5! × (10-5)! = 252

10C6 = 10! / 6! × (10-6)! = 210

10C7 = 10! / 7! × (10-7)! = 120

10C8 = 10! / 8! × (10-8)! = 45

10C9 = 10! / 9! × (10-9)! = 10

10C10 = 10! / 10! × (10-10)! = 1

So the total number of different combinations of attending at least 4 games is

210 + 252 + 210 + 120 + 45 + 10 + 1 = 848

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