Which equation could be solved using this application of the quadratic formula?
-3√32-4(1)(24)
2(1)
H=
O A.
O B.
O C.
C.
O D.
x² + 6x + 24 = 3x
3x² + 3x + 24 = 3
x² + 3x - 24 3
-
x² + 3x + 24 = 3

The potential values for the equation -2a + 3b, for given inequalities 4 < a < 5 and 2 < b < 4 are: (-8 + 3b), (-10 + 3b), (-2a + 6), and (-2a + 12), where 'a' and 'b' can take any value within their respective provided ranges.

In mathematics, inequalities are mathematical expressions or statements that compare the relative magnitude of two or more numbers or quantities. They are used to depict connections such as "greater than," "less than," "greater than or equal to," "less than or equal to," and "not equal to" between numbers or mathematical expressions.

Some generally known types of inequalities in mathematics are:

For given problem,

Given that 4 < a < 5 and 2 < b < 4, we can consider the extreme values of 'a' and 'b' within these ranges to find the possible values of the expression.

So, the four potential values for the expression -2a + 3b, where 4 < a < 5 and 2 < b < 4, are:

-8 + 3b, -10 + 3b, -2a + 6, and -2a + 12

where 'a' and 'b' can take any value within their respective given ranges.

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Answer: -4 and 4

Step-by-step explanation:

use the lowest value for a and the highest for b

The intersection points in the function is (-4, 61)

To find the intersection points of two functions, we can set them equal to each other and solve for x. Substituting x = -4, we have:

4(-4)² + 3(-4) + 3 = (-4)³ + 7(-4)² - 3(-4) + d

Simplifying, we get:

64 - 12 + 3 = -64 + 112 + 12 + d

d = -77

So the two functions intersect at x = -4 and y = 61. Therefore, the only intersection point is (-4, 61).

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Answer:

C

Step-by-step explanation:

+) L = 3W + 6

+) L×W = (3W + 6)×W = 3W² + 6W ≤ 250

Answer:

Step-by-step explanation:

The GCF of 42 and 50 is 2.

Thus, for the given similar triangles-

11. ΔCAG ≈ Δ CEF (Angle-Angle similarity)

12. ΔACB ≈ ΔCED (Angle-Angle similarity)

13. ∠ACB = ∠ECD = 92° (vertical angles)

17. BC = √32

Congruent triangles and similar triangles are two distinct but closely related concepts. Similar triangles are any two or more triangles having the identical proportions of their corresponding sides, an equal pair with corresponding angles, and their similar shape.

For the given values:

11. ΔCAG ≈ Δ CEF (Angle-Angle similarity)

∠ACG = ∠ECF (vertical angles)

∠GAC= ∠CEF (alternate interior angles)

12. ΔACB ≈ ΔCED (Angle-Angle similarity)

∠ACB = ∠ECD (vertical angles)

∠BAC = ∠CED (alternate interior angles)

13. m∠ECD = ?

In Δ ACB

53 + 45 + ∠ACB = 180

∠ACB = 180 - 98

∠ACB = 92

∠ACB = ∠ECD = 92° (vertical angles)

17. BC = ?

BC² = GB² + GC²

BC² = 4² + 4²

BC = √32

14. m∠ECF = m∠GCA  (vertical angles)

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Complete question:

For the following figure- Determine:

11. ΔCAG ≈

12. ΔACB ≈

13. m∠ECD = ?

17. BC = ?

The correct answer is C. 0.3, which is equivalent to 3/10.

What are fractions?

A fraction is a mathematical representation of a quantity that expresses a part of a whole or a ratio between two quantities.

To find the total fraction of the diagram that is shaded, we need to add the fractions representing the shaded areas of the two squares.

Given that one square is shaded 2/12 and the other shaded square is 2/15, we can add these fractions:

2/12 + 2/15

To add fractions, we need to find a common denominator. The least common multiple (LCM) of 12 and 15 is 60, so we can use 60 as the common denominator for both fractions:

(2/12) + (2/15) = (2/12) * (5/5) + (2/15) * (4/4)

= 10/60 + 8/60

Now we can add the numerators:

= (10 + 8)/60

= 18/60

= 3/10

So, the total fraction of the diagram that is shaded is 3/10.

Hence, the correct answer is C. 0.3, which is equivalent to 3/10.

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The other three roots of the polynomial are:

1) -2i

2) 1 + i

3) 1 - i

The polynomial with a root 2i and exactly 2 real roots is F(x)=x³-x² + 4x-4

Polynomials are sums of k-xⁿ terms, where k can be any number and n can be any positive integer.

3x+2x-5, for example, is a polynomial.

Given the polynomial function below

F(x)=x³-x² + 4x-4

Group

F(x)=(x³-x²) + (4x-4)

f(x) = x²(x-1)+4(x-1)

f(x) = (x²+4)(x-1)

If f(x) = 0

x²+4 = 0 and x -1. = 0

x² = -4 and x = 1

x = ±2i and -1

Hence polynomial with a root 2i and exactly 2 real roots is F(x)=x³-x² + 4x-4

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complete question:

Which of the following options is a polynomial with a root 2i and exactly 2

real roots?

A. F(x)=x²-x²³ +2x² - 4x-8

B. F(x)=x²-x² + 4x-4

C. F(x)=x²-x³-6x² +4x+8

OD. F(x)= x³ + x² + 4x+8

The answer of the given question based on the Critical value is , , the critical value to for the confidence level c = 0.99 and sample size n = 22 is 2.819.

What is Critical value?

In statistics,  critical value is  value that is used to determine whether to reject  null hypothesis in hypothesis test. It is based on chosen level of significance, which is the maximum probability of making a Type I error (rejecting  true null hypothesis). The critical value is determined by sampling distribution of the test statistic, which is often a t-statistic or z-statistic, depending on the test and the characteristics of the population being studied.

To find the critical value t for a 99% confidence level and a sample size of 22, we need to use a t-distribution table or a calculator.

Using a t-distribution table with 21 degrees of freedom (n-1), we find that  critical value for a 99% confidence level is approximately 2.819.

Therefore, critical value for confidence level c = 0.99 and sample size n = 22 is 2.819 (rounded to nearest thousandth).

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[tex]7.24 * 10^4 - 7.21 * 10^3[/tex] in scientific notation is [tex]6.519 * 10^4[/tex].

What is scientific notation?

Scientific notation is a way of expressing a number as a number between 1 and to multiplied by a power of 10.

To subtract these two numbers, we need to make sure they have the same exponent. We can do this by rewriting [tex]7.21 * 10^3[/tex] as [tex]0.721 * 10^4[/tex] (since [tex]7.21 * 10^3 = 0.721 * 10^4[/tex]).

Now we can perform the subtraction:

[tex]7.24 * 10^4 - 0.721 * 10^4 = 6.519 * 10^4[/tex]

Therefore, [tex]7.24 * 10^4 - 7.21 * 10^3[/tex] in scientific notation is [tex]6.519 * 10^4[/tex].

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Answer:

-9/2

Step-by-step explanation:

f(x) = 3/2x + b

f(2) = 0

Find out what the variable b is.

3/2(2) + b = 0

3 + b = 0

Subtract 3 from both sides.

b = -3

f(-1) = 3/2(-1) - 3

f(-1) = -4.5

-4.5 = -9/2

Answer:

$4500

Step-by-step explanation:

Find out 25% of $6000. 25/100 × 6000 = 1500

6000 - 1500 = 4500

The formula for the surface area of a cylinder is:

SA = 2πr² + 2πrh

where r is the radius of the base, h is the height, and π is approximately 3.14.

Plugging in the values given, we get:

SA = 2π(3²) + 2π(3)(7)

SA = 2π(9) + 2π(21)

SA = 18π + 42π

Adding these two terms, we get:

SA = 60π

So the surface area of the cylinder is 60π square meters. If you want a numerical approximation, you can use a calculator and round to an appropriate number of decimal places.

Briana and her mother will need to measure and cut the fabric for the quilt. They will need to decide on a pattern and color scheme for the quilt. They will need to sew the pieces of fabric together to create the quilt top. They will need to layer the quilt top with batting and backing fabric and then quilt the layers together. Finally, they will need to bind the edges of the quilt.

Thickness of 10 dollar bill is 1.1×10⁻³meters

Thickness of 1.25 × 10³ dollar bill  is 1.375×10⁻¹meters

Thickness of 137 dollar bill is1.507 ×10⁻²meters

Thickness is the measure of the distance between opposite surfaces of an object. In other words, it is the distance between two parallel planes that bound an object or material. Thickness is often used to describe the dimension of a flat or sheet-like object, such as paper, fabric, or metal, as well as the distance between the front and back surfaces of a three-dimensional object, such as a book or a wall. Thickness can be measured in units such as millimeters, inches, or micrometers.

The thickness of a one-dollar bill is 1.1 × 10⁻⁴ meters

Thickness of 10 dollar bill=10×1.1 × 10⁻⁴

=1.1×10⁻³meters

Thickness of 1.25 × 10³ dollar bill=1.25 × 10³ ×1.1 × 10⁻⁴

=1.375×10⁻¹meters

Thickness of 137 dollar bill=137 ×1.1 × 10⁻⁴

=1.507 ×10⁻²meters

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From given sample space, No. of toothpicks each student will get is 51.

What exactly is a sample space?

In mathematics, a sample space is the set of all possible outcomes of an experiment or a random phenomenon. It is denoted by the symbol "S" and is a fundamental concept used in calculating probabilities. For example, when flipping a coin, the sample space is {heads, tails}. When rolling a fair six-sided die, the sample space is {1, 2, 3, 4, 5, 6}. The sample space for a more complex event may involve multiple variables and outcomes.

Now,

Total Toothpicks = 918

Total students = 18

then

Toothpicks per student = 918/18=51

Hence,

           No. of toothpicks each student will get is 51.

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The surface area equation for a triangular prism is SA = bh + pl

You have been given most of your information, but you need to find the perimeter. The problem has given you the lengths needed to find the perimeter, so add the lengths together to get the perimeter!

P = a + b + c

P = 21 + 17  17

P = 55

Now you have all your information. Plug into the Surface area equation to find the surface area of the triangular prism:

SA= bh + pl

SA = (16)(15) + (55)(21)

SA= 240 + 1155

SA= 1395 cm ²

*connected parenthesis indicated multiplication*

The surface are of this triangular prism is 1395 square centimeters

The correct direction and angle of rotation between triangle ABC in quadrant 4 and polygon A' B' C' in quadrant 3 is: 90° clockwise rotation.

A transformation in geometry is a procedure that modifies the location, scale, or orientation of a shape. Translations, rotations, reflections, and dilations are examples of common transformations.

Rotations are transformations that involve rotating a shape around a fixed point called the center of rotation. The direction of rotation can be either clockwise or counterclockwise, and the angle of rotation is the amount of rotation in degrees.

A' is located to the left of A, which indicates a clockwise rotation.

B' is located below B, which also indicates a clockwise rotation.

C' is located to the right of C, which indicates a clockwise rotation as well.

The correct response is a 90° clockwise rotation since all of the relevant vertices of polygon A' B' C' are turned clockwise in relation to triangle ABC. I regret if the prior replies left you perplexed.

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Answer:

(A) 90° clockwise rotation

Step-by-step explanation:

Took the test (FLVS) got it right. ;)

Okay, let's walk through this step-by-step:

The initial balance of the savings account: $312.50

The final balance after 9 years: $1250

Let's call the interest rate r.

We know the final balance is the initial balance times (1 + r)^9

(because of continuous compounding over 9 years)

So:

312.50 = (1 + r)^9

312.50 / (1 + r)^9 = 1250

Solving for r:

(312.50 / 1250)^(1/9) = 1 + r

0.2504 = 1 + r

0.7596 = r

Converting to a percentage:

0.7596 * 100% = 75.96%

Rounding to the nearest whole percent: 76%

So the interest rate is 76%.

Does this make sense? Let me know if you have any other questions!

Required frequency table is

Movie Number of students

1) Action 6

2) Comedy 4

3) Horror 7

4) Drama 5

5) Romance 8

What is frequency table?

A frequency table is a statistical tool used to organize data by counting the number of occurrences of each unique item or value in a dataset. It is a way to summarize and present data in a concise and structured manner, making it easier to understand and analyze.

For example, if you have a dataset of students' grades, you can create a frequency table by listing all the possible grades (e.g., A, B, C, D, F) and counting how many times each grade appears in the dataset. The resulting table will show the frequency or number of times each grade was earned by the students.

Frequency tables can be used to display both qualitative (categorical) and quantitative (numerical) data. For categorical data, the frequency table will show the count or percentage of occurrences of each category. For numerical data, the frequency table will show the number of times each value or range of values appears in the dataset

Based on the data you provided, here is a frequency table for the movie genres:

Movie Number of students

1) Action 6

2) Comedy 4

3) Horror 7

4) Drama 5

5) Romance 8

In the table, the movie genres are listed in the left column, and the number of times each genre appears in the survey results is listed in the right column.

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Correct question is " You survey the students in your class to find out what kinds of movies they like to watch. The students were given the following choices: Comedy (C), Horror (H), Drama (D), Action (A), Romance (R). The following were the results of your survey: C, C, R, R, D, R, H, H, C, A, A, R, A, A, A, R, R, H, H, H, C, H, A, R, D, D, D, D, H, R a. Make a frequency table for the movie genres."

We can estimate that there are approximately 134 glass beads in the bin.

What is probability?

Probability is a measure of the likelihood of an event occurring.

To estimate the number of glass beads in the bin, we can use the proportion of glass beads in the handful that Jasper selected.

There are 15 beads in the handful, and 4 of them are glass. So, the proportion of glass beads in the handful is:

4/15 ≈ 0.267

We can assume that the proportion of glass beads in the bin is similar to the proportion in the handful. Therefore, we can estimate the number of glass beads in the bin as:

0.267 x 500 ≈ 134

Therefore, we can estimate that there are approximately 134 glass beads in the bin.

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The density of nitrogen in the space will be 3.13 kg/m³

Density is the ratio of mass to volume of a substance. It is measured in kg/m³.

The volume of the shade part = volume of the cone- volume of the hemisphere

volume of the hemisphere = 2/3 πr³

= 2/3 × 3.14 × 40³

= 401920/3

= 133973.33m³

volume of the cone = 1/3 πr²h

= 1/3 × 3.14 × 40²× 500

= 2512000/3

= 837333.33 m³

volume of the shaded part = 837333.33-133973.33 = 703360m³

The density of the space = 2200000/703360

= 3.13kg/m³.

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The probability of both rolls being more than 4 is 0.25, written to two decimal places.

Probability is the measure of how likely it is that a certain event will occur. It is expressed as a number between 0 and 1, where 0 indicates that the event is impossible and 1 indicates that the event is certain to occur. Probability is calculated by taking the number of outcomes that are favorable to the event divided by the total number of possible outcomes.

Let X1 be the outcome of the first roll and X2 be the outcome of the second roll.
We want the probability that X1 > 4 and X2 > 4.
Since each of the 6 outcomes are equally likely and the two rolls are independent of each other, we can calculate the probability as the product of the probabilities of each event.
The probability of X1 > 4 is 3/6, and the probability of X2 > 4 is also 3/6.
Therefore, the probability that both rolls are more than 4 is:
P(X1 > 4 and X2 > 4) = (3/6) * (3/6) = 0.25
The probability of both rolls being more than 4 is 0.25, written to two decimal places.

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The area of the poster in square meters is 0.014 m².

It should be noted that to convert the area from square centimeters to square meters, we need to divide by 10,000 (since 1 square meter is equal to 10,000 square centimeters).

The area of the poster is:

14 cm × 10 cm = 140 cm²

To convert this to square meters, we divide by 10,000:

140 cm² ÷ 10,000 = 0.014 m²

Therefore, the area of the poster in square meters is 0.014 m².

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Heather has a rectangular poster that is 14 centimeters long and 10 centimeters wide. What is the area of the poster in square meters? Do not round your answer. Be sure to include the correct unit in your answer.

The area of the figure is 51 cm², which is option C.

In mathematics, area refers to the measure of the size of a two-dimensional surface or shape. It is typically expressed in square units, such as square meters (m²) or square centimeters (cm²), and can be calculated for a variety of geometric shapes, including squares, rectangles, triangles, circles, and more complex shapes such as trapezoids or polygons.

To find the area of the figure, we need to identify the shape of the figure. From the given information, we know that the figure has a top side, a height, and a base. We are also told that the base is divided into two parts by a perpendicular, and one of the parts is labeled as 4 cm, while the other part from the perpendicular to the right vertex is 6.2 cm.

Based on this information, we can draw the figure as a trapezoid, where the top side is the shorter base, the height is the vertical distance between the two bases, and the longer base is the sum of the two parts of the base.

Using the given information, we can calculate the longer base:

longer base = 4 cm + 6.2 cm = 10.2 cm

Now we can use the formula for the area of a trapezoid to find the area of the figure:

A = (1/2)h(b₁ + b₂)

where h is the height, b₁ is the shorter base, and b₂ is the longer base.

Plugging in the given values, we get:

A = (1/2)(5 cm)(10.2 cm + 10.2 cm) = 51 cm²

Therefore, the area of the figure is 51 cm² , which is option C.

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Complete Question:

A four-sided figure has one side labeled 10.2 cm, a height of 5 cm, and a portion of the base from the perpendicular to a vertex labeled 4 cm. The portion of the base from the perpendicular to the right vertex is labeled 6.2 cm. What is the area of the figure?

Answer:

18gall

Step-by-step explanation:

If the group is too large to survey everyone, you may consider using a sampling technique to select a representative subset of the group for the survey.

Here are some common sampling techniques you could use:

When selecting a sampling technique, it's important to consider the size of the group, the available resources, and the research question. It's also important to ensure that the sampling technique is unbiased and representative of the group being studied.

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Therefore, the maximum height the ball will attain is 221.875 feet.

We are given the equation for the height of a projectile as a function of time:

[tex]h(t) = -16t^2 + v0t + h0[/tex]

where v0 is the initial velocity, h0 is the initial height, and t is the time. We are also given that a tennis ball machine serves a ball vertically into the air from a height of 2 feet, with an initial speed of 120 feet per second. Therefore, we can plug in the values of v0 and h0 into the equation:

[tex]h(t) = -16t^2 + 120t + 2[/tex]

To find the maximum height, we need to find the vertex of this parabola. The x-coordinate of the vertex is given by:

[tex]t = -b/2a[/tex]

where a = -16 and b = 120. Substituting these values, we get:

[tex]t = -120/(2(-16)) = 3.75 seconds[/tex]

To find the corresponding maximum height, we can plug this value of t back into the equation:

[tex]h(3.75) = -16(3.75)^2 + 120(3.75) + 2 = 221.875 feet[/tex]

Therefore, the maximum height the ball will attain is 221.875 feet.

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The linear regression equation that represents the given set of data is y = 442.86x + 1150, where x represents the number of years since 2005 and y represents the profit in thousands of dollars.

Data in math is information that is organized and analyzed to help draw conclusions and make predictions. It can be numerical, or it can be non-numerical, such as words or images. Data can be collected through experiments, surveys, or other methods. Data analysis helps mathematicians to uncover patterns, relationships, and trends that could not be seen through traditional methods. Data can be used to solve problems, make decisions, or create models to help explain the behavior of a system.

x y
0 1150
1 1550
2 1850
3 2150
4 2500

Linear regression equation:
y = 442.86x + 1150

Projected profit for 2016 (in thousands of dollars):
7,427.

The linear regression equation that represents the given set of data is y = 442.86x + 1150, where x represents the number of years since 2005 and y represents the profit in thousands of dollars. Using this equation, the projected profit for 2016 (in thousands of dollars) can be calculated to be 7,427. This shows that the company's profits are expected to increase steadily over time.

It is important to note that the linear regression equation is just a model of the data and may not accurately predict the actual profits in 2016. Other factors such as economic conditions, competition, and market trends can all affect a company's profits and should be taken into consideration when making any predictions.

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