b^2-c^2-10(b-c) factor completly

Answer:

1. [tex]y = (x + 2)(x + 3)[/tex]

2. [tex]y = -x(x + 4)[/tex]

Step-by-step explanation:

We can find the factored form of the graphed quadratic functions by:

1) Expressing each one in vertex form

2) Expanding and refactoring to rewrite in factored form

1. We know that vertex form is:

[tex]y = a(x-h)^2 + k[/tex],

where [tex]a[/tex] determines the parabola's direction and width ([tex]a=1[/tex] being the same as a standard parabola), and [tex](h,k)[/tex] is the parabola's vertex.

The vertex of this parabola is (-3, -4).

↓ plugging these values into the vertex form equation

[tex]y = 1(x - (-3))^2 + (-4)[/tex]

↓ simplifying

[tex]y = (x + 3)^2 - 4[/tex]

Now, we can expand and refactor this equation into factored form.

↓ expanding the squared term

[tex]y = (x^2 + 6x + 9) - 4[/tex]

↓ simplifying

[tex]y = x^2 + 6x + 5[/tex]

↓ factoring

[tex]\boxed{y = (x + 2)(x + 3)}[/tex]

2. We can see that the vertex is at (-2, 4).

↓ plugging into the vertex form equation

[tex]y = -1(x - (-2))^2 + 4[/tex]

Note that the parabola opens downward, so [tex]a = -1[/tex].

↓ simplifying

[tex]y = -1(x +2)^2 + 4[/tex]

↓ expanding the squared term

[tex]y = -1(x^2 +4x + 4) + 4[/tex]

↓ incorporating the outer +4 into the distribution of -1

[tex]y = -1(x^2 + 4x + 4 - 4)[/tex]

↓ simplifying

[tex]y = -1(x^2 + 4x)[/tex]

↓ factoring

[tex]y = -1(x)(x + 4)[/tex]

↓ simplifying

[tex]\boxed{y = -x(x + 4)}[/tex]

Answer:

66 hours.

Step-by-step explanation:

6 cars x 34 hours per car = 204

6 cars x 23 hours per car= 138 hours

now subtract:

204 - 138 = 66

therefore, it took Theo 66 hours longer to wash all the cars last week than last week.

The total number of campers surveyed is 150.

The symbol for percentage is "%". Percentages are commonly used in a wide range of contexts, such as in finance, statistics, and everyday life.

We can use the information provided about the percentage of campers in each time interval to set up an equation to solve for the total number of campers surveyed.

Let n be the total number of campers surveyed. Then:

15% of n spend more than 3 hours reading daily.

10% of n spend between 2 and 3 hours reading daily.

35% of n spend less than 1 hour reading daily.

40% of n spend between 1 and 2 hours reading daily.

We know that 60 campers spend between 1 and 2 hours reading daily, which represents 40% of the total number of campers surveyed. So we can set up the following equation:

0.4n = 60

Solving for n, we get:

n = 60 / 0.4 = 150

Therefore, the total number of campers surveyed is 150.

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The area of a square is given by the formula A = s^2, where s is the length of a side of the square. If the area of the square is 100 sq meters, then:

s^2 = 100

Taking the square root of both sides, we get:

s = 10

Therefore, the length of a side of the square is 10 meters. Since all four sides of a square are equal, the perimeter of the square is:

4s = 4(10) = 40 meters

Answer:

The horizontal translation of the function is 3 units to the right (from the parent function).  Therefore, we subtract 3 from the x-value of the function.

The equation of the graphed function in vertex form is:

[tex]\boxed{y = (x - 3)^2- 2}[/tex]

Step-by-step explanation:

The given graph shows a parabola that opens upwards.

Therefore, the equation for this function is a quadratic equation with a positive leading coefficient.

The vertex of a parabola is the minimum point of a parabola that opens upwards, or the maximum point of a parabola that opens downwards.

From inspection of the given graph, the vertex of the function is (3, -2).

The parent function of a parabola that opens upwards is y = x². This has a vertex at (0, 0).

Therefore, given the vertex of the given function is (3, -2), the parent function has been translated 3 units right and 2 units down.

For a horizontal translation to the right, we subtract the number of units from the x-value of the function.

For a vertical translation down, we subtract the number of units from the function.

Therefore, a translation of 3 units right and 2 units down from the parent function y = x² is:

[tex]\boxed{y = (x - 3)^2- 2}[/tex]

This function is written in vertex form.

To write the equation in standard form, expand the brackets and simplify:

[tex]\implies y=(x-3)(x-3)-2[/tex]

[tex]\implies y=x^2-3x-3x+9-2[/tex]

[tex]\implies y=x^2-6x+7[/tex]

[tex]\hrulefill[/tex]

Additional comments

The vertex form of a quadratic equation is y = a(x - h)² + k, where (h, k) is the vertex. Therefore, the "k" value refers to the y-value, which is the vertical translation from the parent function.

As your question refers to the "k" value for the horizontal translation, we assume that it is not referring to the k-value of the vertex form.

The properties of the conic section are Ellipse, Domain = [-2, 2] and the range is [-3, 3]

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

The conic section

From the graph, we have

The conic section is an ellipse

The domain of this equation is all possible values of x and the range is for y

From the graph, we have

x values = -2 to 2

y values = -3 to 3

These are the domain and the range

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A) linear inequality, 0.5 s + 1 m = 30 < 75 where, 's' represents a small cup, and 'm' represents a medium cup.

We know that Sarah was selling lemonade and she makes 0.50 dollars on a small cup, and 1 dollar on a medium cup but she wants to make at least 30 dollars and only has 75 cups.

We need to show a linear inequality where, 's' represents a small cup, and 'm' represents a medium cup:

Linear inequalities are the expressions where any two values are compared by the inequality symbols ‘<’, ‘>’, ‘≤’ or ‘≥’

Linear equations are a combination of constants and variables.

let number of small cups be s,

therefore, total amount of small cups = 0.5 s

let number of medium cups be m,

therefore, total amount of medium cups = 1 m

with this given information, we can form our equation as:

0.5 s + 1 m = 30 < 75.

Therefore, a linear inequality, 0.5 s + 1 m = 30 < 75 where, 's' represents a small cup, and 'm' represents a medium cup.

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Complete question: Sarah was selling lemonade. she makes .50 dollars on a small cup, and 1 dollar on a medium cup. She wants to make at least 30 dollars and only has 75 cups. If s represents a small cup, and m represents a medium cup, which system of linear inequalities correctly represents her situation?

A. 0.5 s + 1 m = 30 < 75

B. 1s + 3m + 5l

C. $75

D. $93

Answer:

Step-by-step explanation:

If you don't know, the Pythagorean Theorem states that a^2+b^2=c^2 in a right triangle where a and b are the legs and c is the hypotenuse.

Imagine unfolding a cone. It would become part of a circle. Therefore, to find the lateral surface area(the surface are not including bases), you have to find the surface area of this part of the circle. The circumference of the entire circle is 6*pi*sqrt10. The circumference of this partial circle is the circumference of the base of the cone which is 2*3*pi=6pi. therefore, the percent of the circle is 6*pi/6*pi*sqrt10=1/sqrt10. 1/sqrt10*90pi=90*sqrt10*pi/10=9*sqrt10*pi.

the area of the base is 3^2*pi=9pi. the answer is then 9pi(1+sqrt10)

Answer:

y = -3x + 1

Step-by-step explanation:

y = mx + b

mx: slope

b: y-intercept

This line has a negative slope (mx) because of its direction. The plotted points are three units down and one unit right apart, which makes it -3/1x or -3x.

The y-intercept (b) is 1 because at the coordinate (0, 1) the line passes through the y-axis.

Therefore, the line should be y = -3x + 1.

Jeremy needs a sample size of at least 601 to estimate the proportion of adults in the test market who commute more than 20 miles one-way to work each day with a 95% confidence interval and a margin of error of 0.04.

To calculate the sample size required, we need to use the formula:

n = (z^2 * p * (1-p)) / E^2

where:

n = sample size

z = z-score associated with the desired confidence level (95%)

p = estimated proportion (0.5, since we have no preliminary information)

E = maximum margin of error (0.04)

Plugging in the values, we get:

n = (1.96^2 * 0.5 * (1-0.5)) / 0.04^2

n = 600.25

Rounding up to the nearest whole number, Jeremy will need a sample size of 601.

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The temperature at 7:00 a.m. was 67 degrees.

To find the temperature at 7:00 a.m., we need to consider that it was 20 degrees cooler than at 1:00 p.m.
1. Identify the given information: At 1:00 p.m., the temperature was 87 degrees, and it was 20 degrees cooler six hours earlier.
2. We need to find the temperature at 7:00 a.m., which is six hours before 1:00 p.m.
3. Since the temperature was 20 degrees cooler at 7:00 a.m.

we will subtract 20 from the temperature at 1:00 p.m.
4. Perform the subtraction:

87 degrees (1:00 p.m. temperature) - 20 degrees (cooler difference) = 67 degrees.
5. The result, 67 degrees, is the temperature at 7:00 a.m.
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The true statements are

i. probability is usually between 0 and 1, inclusive.

ii. an event that is likely has a probability that is close to 1.

(option i and ii).

Probability is an important concept in mathematics and statistics that allows us to quantify the likelihood or chance of an event occurring. It is often represented as a number between 0 and 1, inclusive. A probability of 0 means that the event is impossible, while a probability of 1 means that the event is certain to occur.

Now, let's examine each of the statements to determine which ones are true.

The first statement, "probability is usually between 0 and 1, inclusive," is true. As mentioned earlier, probability is always represented as a number between 0 and 1, inclusive.

The second statement, "an event that is likely has a probability that is close to 1," is also true. If an event is likely to occur, it means that there is a high probability of it happening. Therefore, the probability assigned to that event would be close to 1.

Hence the correct option is (a) and (b)..

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The value of the expression using PEDMAS is 7.

The acronym PEMDAS, which can alternatively stand for "Please Forgive My Dear Aunt Sally," is a mnemonic tool for remembering the order of operations in mathematical and algebraic formulas. Its acronym is:

P - Parenthesis (operations inside parentheses are done first)

E: Exponents (operations involving exponents are done next)

Divide and multiply is abbreviated MD (these operations are done left to right, whichever comes first)

AS stands for addition and subtraction (these operations are done left to right, whichever comes first). No matter how they approach it or how they understand it, PEMDAS helps to ensure that the same statement is assessed in the same way by various people. In mathematics, it is crucial to understand this idea, especially when working with complicated expressions or formulae.

The given expression is 1/2 x (48 ÷ 6) – 2 + 5.

Simplifying the expressions we have:

1/2 x (48 ÷ 6) – 2 + 5

= 1/2 x 8 - 2 + 5

= 4 - 2 + 5

= 7

Hence, the value of the expression using PEDMAS is 7.

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Answer:

Jayla selected 14 bean bags randomly with replacement from a box of 100 bean bags, and 6 of them were red. To estimate how many red bean bags are in the box, we can use proportion:

Let's call "x" the number of red bean bags in the box. Then we can set up a proportion:

(red bean bags in the box) / (total bean bags in the box) = (red bean bags selected) / (total bean bags selected)

x / 100 = 6 / 14

Simplifying the right side, we get:

x / 100 = 3 / 7

Multiplying both sides by 100, we get:

x = 300 / 7

Rounding to the nearest whole number, we get:

x ≈ 43

Therefore, based on the data, we can estimate that there are approximately 43 red bean bags in the box.

Answer + Explanation:

To estimate how many red bean bags are in the box, we can use a sampling method called "balloting." Balloting is a way of estimating the number of items of a specific type in a larger population by taking a random sample and counting how many of that type are in the sample.

In this case, we have a population of 100 bean bags and a sample size of 14. We can calculate the sample proportion of red bean bags by dividing the number of red bean bags in the sample by the total number of bean bags in the sample, which gives:

(4/14) × 100% ≈ 28.6%

This means that, on average, we would expect 28.6% of the 100 bean bags in the box to be red. To estimate the actual number of red bean bags, we can multiply the sample proportion by the total number of bean bags in the box:

28.6% × 100 = 28.6

So the closest estimate for the number of red bean bags in the box is 29.

Note that this is just an estimate, and the actual number of red bean bags in the box may be higher or lower than the estimated value.

The probability that the marble drawn from the bag will be either white or black is 2/3 or approximately 0.667.

To calculate this probability, we first need to find the total number of marbles in the bag, which is 10 + 20 + 5 = 35. Then, we need to find the total number of marbles that are either white or black, which is 10 + 20 = 30.

Finally, we divide the number of white or black marbles by the total number of marbles to get the probability:

30/35 = 2/3 ≈ 0.667

Therefore, the probability is approximately 0.667 or 2/3. This means that there is a higher chance of drawing a white or black marble than a grey marble, as there are more white and black marbles in the bag than grey marbles.

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The solution to the equation is a = 6 and a = 4.

There is no extraneous solution.

To find the solution for the given equation, follow these steps:
1. Rewrite the equation: [tex]15 + a^2 - 1 = 5(2a - 2)[/tex].
2. Simplify both sides: [tex]a^2 + 14 = 10a - 10.[/tex]
3. Move all terms to one side:[tex]a^2 - 10a + 24 = 0.[/tex]
4. Factor the quadratic equation: (a - 6)(a - 4) = 0.
5. Set each factor equal to zero: a - 6 = 0 or a - 4 = 0.
6. Solve for 'a': a = 6 or a = 4.
Now, we need to check if both solutions are valid or if there is an extraneous solution.
Since there are no restrictions on the domain of the original equation, both solutions are valid.

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Answer:

0.5 difference

Step-by-step explanation:

since liam estimated 85 miles even though it is 84.5, you should minus 85 from 84.5 which will equal 0.5

B. The line of symmetry should have been 4 instead of –4.

We are given the quadratic:

, with a=1, b=-8, c=15.

and the quadratic equation is [tex]x^2[/tex]-[tex]8[/tex][tex]x[/tex]+[tex]15[/tex]=0


We know that the x-coordinate of the vertex, which is the point where the line of symmetry passes through is

                                 .

Thus, the x-coordinate of the vertex is .

Thus, the line of symmetry is x=4.

A line of symmetry is a line that divides a shape into two equal parts that are mirror images of each other. It is also called a mirror line or axis of symmetry.

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Answer:B

Step-by-step explanation:

Answer: √5 + 37π/5.

Step-by-step explanation:
To calculate the exact value of E, we can follow the order of operations (PEMDAS):

E = 3√5 + 7π/5 - 2(√5 - 3π)

E = 3√5 + 7π/5 - 2√5 + 6π (distribute the -2)

E = (3√5 - 2√5) + (7π/5 + 6π) (combine like terms)

E = √5 + 37π/5

Therefore, the exact value of E is √5 + 37π/5.

The radical expression √(-4x) = 4 when evaluated has a value of x = -4

From the question, the equation is given as

√(-4x) = 4

We can start by squaring both sides of the equation to eliminate the square root:

(√(-4x))^2 = 4^2

So, we have

-4x = 16

Dividing both sides by -4, we get:

x = -4

However, we need to check if this solution satisfies the original equation.

√(-4x) = √(-4(-4)) = √(16) = 4

So, the only solution to the equation is x = -4.

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The sum of an angle measures of any trapezoid is greater than the sum of the angle measures of any parallelogram contradicts the rule which states that the sum of all angles in any quadrilateral is 360°.

What is a quadrilateral?

The Latin words quadra refers to number four, and latus refers to the sides, on combining gives quadrilateral. Any polygon with four sides, four angles, and four corners is said to be a quadrilateral. It is a closed shape known as a quadrilateral which is formed by joining any four points, any three of these points must not be on a same line.The quadrilateral has interior angles at each of its four corners. The sum of all for interior angles is always 360°.

Given that The sum of an angle measures of any trapezoid is greater than the sum of the angle measures of any parallelogram:

As we know that trapezoid and parallelogram both are quadrilaterals. so both will have interior angles sum equal to 360°

The given statement is false.

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Answer:

To calculate the final cost of the meal, we need to first calculate the discount and then add the sales tax. Discount = 10% of $5.75 = $0.575 Price after discount = $5.75 - $0.575 = $5.175 Sales tax = 4% of $5.175 = $0.207 Final cost = Price after discount + Sales tax = $5.175 + $0.207 = $5.382 Therefore, you should charge the customer $5.382.

well, let's hmmm apply the 10% discount first

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{10\% of 5.75}}{\left( \cfrac{10}{100} \right)5.75} ~~ \approx ~~ 0.58~\hfill \stackrel{ 5.75~~ - ~~0.58 }{\approx\text{\LARGE 5.17}}[/tex]

now let's apply the 4% tax to it

[tex]\stackrel{\textit{4\% of 5.17}}{\left( \cfrac{4}{100} \right)5.17} ~~ \approx ~~ 0.21\hspace{5em}\stackrel{ 5.17~~ + ~~0.21 }{\text{\LARGE 5.38}}\qquad \textit{final charge}[/tex]

Times Rolled: 702

Need estimation of: 3

Numbers on the dice: 6

702/6 = 117

Answer: 117

Answer: x^2 = 1.143;

P-value > 0.25

Step-by-step explanation: I got it right on khan academy!!

The P-value for the test is less than 0.05, indicating strong evidence against the null hypothesis. Adele can conclude that senior citizens in her community complete their taxes differently than what was reported in the article.

To carry out a χ2 goodness-of-fit test, Adele needs to compare the observed frequencies of how senior citizens completed their taxes with the expected frequencies based on the distribution reported in the article. The test statistic for this type of test is calculated as the sum of the squared differences between the observed and expected frequencies divided by the expected frequencies. In this case, the test statistic is 15.67. The degrees of freedom for the test are equal to the number of categories minus one, which in this case is 3 - 1 = 2. Using a significance level of 0.05, the critical value for the test is 5.99. Since the test statistic of 15.67 is greater than the critical value of 5.99, we reject the null hypothesis that the senior citizens in the community complete their taxes according to the distribution reported in the article.

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The required proportion of cupcakes that have no creme filling with 98% confidence interval is equal to (0.012, 0.058).

Total number of cupcakes = 346

Number of defective cup cakes = 12

Confidence interval = 98%

To construct a confidence interval for the proportion of all cupcakes that have no creme filling,

Use the following formula,

CI = p ± z√((p(1-p))/n)

where,

p = proportion of defective cupcakes

n = sample size

z = z-value for the desired confidence level (98% in this case)

Plug in the values we have,

p = 12/346

  = 0.0347

n = 346

z = 2.33 (from a standard normal distribution table for a 98% confidence level)

CI = 0.0347 ± 2.33√((0.0347(1-0.0347))/346)

   = 0.0347 ± 0.023

So the 98% confidence interval for the proportion of all cupcakes that have no creme filling is (0.012, 0.058).

Therefore, 98% confidence interval that have true proportion of all cupcakes with no creme filling is between 0.012 and 0.058.

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The line of reflection used to create the image is the y-axis. The x-axis is the line of reflection utilized to produce the picture of polygon ABCD to A' B' C' D'. The y-coordinates of each vertex.

in A' B' C' D' are the inverse of the corresponding y-coordinates in ABCD, but the x-coordinates stay constant. The x-axis is a horizontal line that goes through the origin and mirrors points that cross it. As a result, when each point in ABCD is mirrored across the x-axis, the point in A' B' C' D' is produced. As a result, the transformation that maps ABCD to A' B' C' D' is an x-axis reflection. the graph to answer the question. Graph of polygon ABCD with vertices at negative 6 comma negative 2, negative 4 comma 5, 1 comma 5, negative 1 comma negative 2.

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Based on the information, the height of point A is 6 feet above ground and the length of OB is approximately 88 feet.

b) At t = 0.25 seconds, the approximate coordinates of the ball are (11, 13.5).

At t = 0.5 seconds, the approximate coordinates of the ball are (22, 12).

At t = 0.75 seconds, the approximate coordinates of the ball are (33, 9).

At t = 1 second, the approximate coordinates of the ball are (44, 6).

At t = 1.25 seconds, the approximate coordinates of the ball are (55, 3).

At t = 1.5 seconds, the approximate coordinates of the ball are (66, 0).

At t = 1.75 seconds, the approximate coordinates of the ball are (77, -3).

At t = 2 seconds, the approximate coordinates of the ball are (88, -6).

The height of the ball will be negative when it reaches point B again after traveling from A to B, assuming it follows the same path.

The time it takes for the ball to reach its maximum height and return to the ground will be approximately 2 seconds.

When the ball has coordinates (88, 0), it has reached the ground at point B, and its horizontal distance traveled is 88 feet.

At t = 0, the ball is at point A, which is 6 feet above the ground. This is because it was thrown from that height, and the time elapsed is not enough for gravity to affect its height yet.

Yes, the graph allows us to make predictions about the height of the ball at all points. However, the accuracy of the predictions may depend on the assumptions and approximations made about the ball's initial velocity, air resistance, and other factors.

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