Complete the square to slice the quadratic equations

1. x2(x square) -10x = -100

2. x2(x square) +7x-16=0

The product of the values can be obtained by multiplying as follows:

1. 8 * 15 * 19 = 2280

2. 7 * -4 * 12 =  -41

To find a product simply means to multiply the figures in order to arrive at a value. The question asks that we get the product of some values. To get these values, we are to multiply the numbers given to arrive at the answers.

It is possible to multiply two, three, or more values at the same time. So, another word that is used in place of multiplication is "product" as is the case in the question given.

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Answer:

√17 good luck

Step-by-step explanation:

The function c(x) = √x is a continuous and increasing function over the interval [0, ∞), which means that its minimum and maximum values on the given domain interval [1/121, 17] will occur at its endpoints.

At x = 1/121, we have c(1/121) = √(1/121) = 1/11.

At x = 17, we have c(17) = √17.

Therefore, the minimum value of c(x) on the given domain interval is 1/11, and the maximum value is √17.

The volume of the figure is 76 ft³.

In geometry, a prism is a three-dimensional solid object that has two parallel bases that are congruent polygons, and rectangular faces connecting the bases. The rectangular faces are also called lateral faces or sides, and the edges where the bases and lateral faces meet are called lateral edges. The number of sides in the bases and the shape of the bases determine the name of the prism.

To find the volume of the figure, we can break it down into two rectangular prisms and add their volumes.

The first rectangular prism has dimensions 6 ft x 2 ft x 3 ft, so its volume is:

V1 = 6 ft x 2 ft x 3 ft = 36 ft³

The second rectangular prism has dimensions 4 ft x 2 ft x 5 ft (8 ft - 3 ft), so its volume is:

V2 = 4 ft x 2 ft x 5 ft = 40 ft³

The total volume of the figure is the sum of these volumes:

V = V1 + V2 = 36 ft³ + 40 ft³ = 76 ft³

Therefore, the volume of the figure is 76 ft³.

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We can use the proportion of people carrying bags from the sample of 50 people to estimate the number of visitors who purchased something out of the total 4,800 visitors to the mall.

The proportion of people carrying bags in the sample is:

37/50 = 0.74

This means that 74% of the sample of 50 people were carrying bags.

To estimate the number of visitors who purchased something out of the total 4,800 visitors, we can multiply the proportion by the total number of visitors:

0.74 x 4,800 = 3,552

Therefore, we can predict that approximately 3,552 visitors out of the total 4,800 visitors purchased something on that day.

Answer:

The total number of gallons of milk sold is equal to the total number of gallons of orange juice sold. This is because there are 2 quarts in a half-gallon, so the 14 half-gallon containers of milk sold is equal to 28 quarts. Therefore, the total amount of milk sold is the same as the total amount of orange juice sold, which is 28 gallons.

Answer:

see the attachment

Step-by-step explanation:

These are the two complex solutions to the equation [tex]x^{2} - 6x = -18[/tex] is[tex]x = 3 + 3i or x = 3 - 3i[/tex].

A linear formalism is a statement that two numbers or values are equal, such as 6 x 4 = 12 x 2. 2. A noun that counts. When two or more components must be taken into account together in order to comprehend or explain the whole situation, this is known as an equation.

The concept of an equation in algebra is a statistical statement that demonstrates the equality of two mathematical expressions. For instance, the formula 3x + 5 = 14 consists of the two numbers 3x + 5 and 14, which are separated by the 'equal' sign.

we have a = 1, b = -6, and c = 18

[tex]x = (-(-6) +- \sqrt{-6^{2} } - 4(1)(18))) / 2(1)[/tex]

[tex]x = (6 +/- \sqrt{36-72} / 2[/tex]

[tex]x = (6 +/- \sqrt{36} / 2[/tex]

[tex]\sqrt{-36} = \sqrt{36} * \sqrt{-1} = 6i[/tex]

Therefore, the solutions are:

[tex]x = (6 + 6i) / 2 or x = (6 - 6i) / 2[/tex]

Simplifying:

[tex]x = 3 + 3i or x = 3 - 3i[/tex]

These are the two complex solutions to the equation [tex]x^{2} - 6x = -18[/tex].

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Answer: 16.642

Step-by-step explanation:

I hope this helped you! A brainilist is highly appreciated and helpful! <3

Answer: 16.642

Step-by-step explanation:

10 + 6.034 = 16.034

16.034 + 0.608 = 16.642

Two parallel lines have the same slope, so we need to find the slope of the first line y = (1/4)x - 2, and then use it to find the equation of the parallel line that passes through (4, -2).

The slope of the first line is 1/4, so the slope of the parallel line will also be 1/4.

Using the point-slope form of the equation, we can write the equation of the parallel line as:

y - (-2) = (1/4)(x - 4)

Simplifying this equation, we get:

y + 2 = (1/4)x - 1

Subtracting 2 from both sides, we get:

y = (1/4)x - 3

Therefore, the equation of the line that is parallel to y = (1/4)x - 2 and passes through (4, -2) is y = (1/4)x - 3, which is option D.

Answer:

y + 13 = - [tex]\frac{2}{3}[/tex] (x + 11)

Step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

here m = - [tex]\frac{2}{3}[/tex] and (a, b ) = (- 11, - 13 ) , then

y - (- 13) = - [tex]\frac{2}{3}[/tex] (x - (- 11) ) , that is

y + 13 = - [tex]\frac{2}{3}[/tex] (x + 11)

Answer: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8

Step-by-step explanation:

The mean absolute deviation gives an idea of how spread out the data is from the mean, indicating that the stem lengths of the tomato plants are varying considerably.

The absolute deviation is a measure that quantifies the average deviation of data points from a central point, which can be any point in the data set such as the mean, median, or mode.

Typically, the mean is used as the central point. The formula to calculate the mean absolute deviation (MAD) involves finding the average of the absolute deviation (distance) of each data point from the mean of the data set.  

Here we have

Melinda planted 18 tomato seeds on the same day. She then measured each plant 7 weeks later and determined that the mean stem length was 8 inches with a mean absolute deviation (MAD) of 2.4 inches

In this situation, the MAD of 2.4 inches means that on average, the stem length of each tomato plant deviated from the mean stem length of 8 inches by 2.4 inches.

Therefore,

The mean absolute deviation gives an idea of how spread out the data is from the mean, indicating that the stem lengths of the tomato plants are varying considerably.

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Answer:

Answer is option  D

Step-by-step explanation:

Hope this helps:)

Answer:

hope this helps

Step-by-step explanation:

The 95% confidence interval for the mean SAT scores is CI = (526.2, 549.8)

It is a statistical tool used in inferential statistics to estimate the unknown population parameter based on the sample data.

To find the 95% confidence interval for the mean SAT scores, we can use the formula: CI

where:

sample mean (538)

population standard deviation (96)

n = sample size (250)

z = z-score for the desired confidence level (95% confidence corresponds to a z-score of 1.96)

Plugging in the values, we get:

CI = 538 ± 1.96*(96/√250)

Simplifying, we get:

CI = 538 ± 11.8

Rounding to the nearest tenth, the 95% confidence interval for the mean SAT scores is:

CI = (526.2, 549.8)

For example, a 95% confidence interval for a population mean means that if we were to repeat the sampling process multiple times and calculate a 95% confidence interval each time, about 95% of the intervals would contain the true population mean.

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The answer of the given question is (a)  95% of the sample means will fall within the interval from 0.9448 to 0.9512. (b) The sampling distribution of X is approximately normal with μ = 0.9480 and σ = 0.0060/√35.  (c)  We used the central limit theorem to answer part (b).

The central limit theorem is a fundamental concept in statistics that states that for a sufficiently large sample size, the distribution of the sample mean will be approximately normal, regardless of the distribution of the population from which the sample is drawn. This means that if we take repeated random samples from a population, the distribution of the means of those samples will approach a normal distribution, even if the population itself is not normally distributed.

(a) We can use the formula for the confidence interval of a mean:

σ is the population standard deviation, n is the sample size, and z is the critical value from the standard normal distribution corresponding to the desired confidence level. For a 95% confidence level, z = 1.96.

Substituting the given values, we get:

CI = 0.9480 ± 1.96*(0.0060/√35)

CI = (0.9448, 0.9512)

Therefore, 95% of the sample means will fall within the interval from 0.9448 to 0.9512.

(b) The sampling distribution of X is approximately normal with μ = 0.9480 and σ = 0.0060/√35. This is because the central limit theorem states that for a sufficiently large sample size (n[tex]\geq[/tex]30), the sampling distribution of the sample mean will be approximately normal, regardless of the distribution of the population.

(c) We used the central limit theorem to answer part (b).

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Step-by-step explanation:

So this will be an upside down parabola....the leading coefficient (for x^2 ) will be negative ...

Vertex at   60,90   <=====given

 Vertex form   y = a (x-h) ^2 + k

                        y = a ( x -60)^2 + 90    to find 'a' substitute in a point on the parabola...I'll use   0,0

                       0 = a ( 0-60)^2 + 90    shows a = - 1/40

so the equation is   y =  -1/40 ( x -60)^2 + 90  

           (  or expanded to y=   -1/40 x^2 + 3x )

Solve for 'x' when y = 6 ft  ( to keep from hitting your head)

      6 = -1/40x^2 +3x

      0 = -1/40 x^2 + 3x - 6      Use Quadratic Formula to find x = ~ 2 feet

The total cost of 2 burgers and 3 fries, considering a system of equations, is given as follows:

$17.

The costs are obtained by a system of equations, for which the variables are given as follows:

3 burgers and 6 fries, which cost $30, hence:

3x + 6y = 30

x + 2y = 10

x = 10 - 2y.

3 burgers and 2 fries, which cost $18 in total, hence:

3x + 2y = 18

1.5x + y = 9

Replacing the first equation into the second, the value of y is given as follows:

1.5(10 - 2y) + y = 9

2y = 6

y = 3.

Then the value of x is given as follows:

1.5x + 3 = 9

x = 6/1.5

x = 4.

Then the cost, in dollars, of 2 burgers and 3 fries, is given as follows:

2 x 4 + 3 x 3 = $17.

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Answer:

yes

Step-by-step explanation:

4p+ 3p= 7p

7p+7n=14pn

Rolling a dice and flipping a coin are two independent events. Spinning two spinners each round are independent events. Grabbing an S out of the scrabble bag and then grabbing an M are two dependent events. Pulling a candy, eating it, and then pulling another out of a bag are dependent events.

What is meant by events?

In probability theory, an event is a set of outcomes or results that can occur when performing a random experiment. An event can consist of a single outcome or multiple outcomes, and it is defined as a subset of the sample space of the random experiment.

1.Rolling a dice and flipping a coin are two independent events. The probability of rolling any particular number on a dice is 1/6, and the probability of flipping heads on a coin is 1/2. Since the outcome of rolling a dice does not affect the outcome of flipping a coin and vice versa, these events are considered independent.

2.Spinning two spinners each round are independent events. The probability of each spinner landing on a particular section is fixed, and the outcome of one spinner does not affect the outcome of the other spinner. Therefore, these events are considered independent. The probability of the first spinner landing on a specific section and the second spinner landing on another specific section at the same time is the product of their individual probabilities.

3.Grabbing an S out of the scrabble bag and then grabbing an M are two dependent events. In the beginning, there are 12 S tiles and 9 M tiles in the bag. The probability of drawing an S tile is initially 12/21 or 4/7. If an S tile is drawn first, the number of S tiles in the bag decreases to 11, and the probability of drawing an M tile on the second draw becomes 9/20. Therefore, the probability of drawing an S tile and then an M tile is (4/7) x (9/20) = 18/70 = 9/35.

4.Pulling a candy, eating it, and then pulling another out of a bag are dependent events. Initially, there are a certain number of candies in the bag. After one candy is drawn and eaten, the number of candies in the bag decreases, affecting the probability of drawing a specific candy on the second draw. Therefore, these events are considered dependent.

Therefore, Rolling a dice and flipping a coin are two independent events. Spinning two spinners each round are independent events. Grabbing an S out of the scrabble bag and then grabbing an M are two dependent events. Pulling a candy, eating it, and then pulling another out of a bag are dependent events.

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to follow the order of operations or PEMDAS (parentheses, exponents, multiplication and division, and addition and subtraction) to ensure that we get the correct answer. [tex]231 3/25 \times 0.75 = 4348.5 / 75.[/tex]

To solve this multiplication problem, we can first convert the mixed number 231 3/25 to an improper fraction:

[tex]231 3/25 = (25 \times 231 + 3) / 25 = 5778/25[/tex]

Then, we can multiply this fraction by 0.75:

[tex]5778/25 \times 0.75 = (5778 \times 0.75) / 25[/tex]

To simplify this fraction, we can multiply the numerator and denominator by 3:

[tex](5778 \times 0.75 \times 3) / (25 \times 3) = 4348.5 / 75[/tex]

Therefore, [tex]231 3/25 x\times 0.75 = 4348.5 / 75.[/tex]

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The missing numbered angle is  80 degrees.

In the given diagram, we can see that angles A and B form a linear pair (they are adjacent angles whose sum is 180 degrees). So we can write:

A + B = 180 degrees

Substituting the given value of angle A, we get:

(3x + 10) + B = 180 degrees

Simplifying this equation, we get:

3x + B = 170 degrees

We are also given that angle C is a complementary angle to angle B, which means that angle C + angle B = 90 degrees. We can substitute the value of angle B from the above equation to get:

C + (3x + B) = 90 degrees

Simplifying this equation, we get:

C + (3x + 170 - 3x) = 90 degrees

Simplifying further, we get:

C + 170 = 90 degrees

Subtracting 170 from both sides, we get:

C = 80 degrees

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Answer:

[tex]225 \: {m}^{2} [/tex]

Step-by-step explanation:

I added a photo of my notes

This figure is formed from a rectangle and a trapezoid

Since the opposite sides of a rectangle are equal, we can find the its area:

A (rectangle) = 9 × 17 = 153 m^2

In order to find the area of a trapezoid, we have to know the length of its altitude:

H = 15 - 9 = 6 m

We know the lengths of both bases, now we can find the area:

A (trapezoid) = 0,5(7 + 17) × 6 = 0,5 × 24 × 6 = 12 × 6 = 72 m^2

Now add these two areas together and we'll get the total area of this figure:

A = 153 + 72 = 225 m^2

Answer:

b-4/5×2 =g

Step-by-step explanation:

if u wrote down the equation correctly

Option A : The lines that best approximate the directrices of the ellipse are x= -4.6 and x = 4.6, which are the closest to x = -5 and x = 5.

The directrices of an ellipse are lines that are equidistant from the two foci. In this case, the foci of the ellipse are located at (-5,0) and (5,0). The distance between the foci is 2c, where c is the distance from the center to a focus, and can be found using the equation [tex]c^2 = a^2 - b^2[/tex], where a and b are the lengths of the major and minor axes, respectively.

From the given diagram, we can see that the length of the major axis is 10 and the length of the minor axis is 8. Therefore, a = 5 and b = 4. The value of c can be found as follows:

[tex]c^2 = a^2 - b^2[/tex]

[tex]c^2 = 5^2 - 4^2[/tex]

[tex]c^2 = 9[/tex]

c = 3

Therefore, the directrices are the vertical lines that pass through (-5,-3) and (5,-3) and are equidistant from the foci. These lines are given by x = -5 and x = 5.

Therefore, the lines that best approximate the directrices of the ellipse are A. x= -4.6 and x = 4.6, which are the closest to x = -5 and x = 5.

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Which lines best approximate the directrices of the ellipse? Round to the nearest tenth.

A. x= -4.6 and x = 4.6

B. x = -3.5 and x = 3.5

C. y=-4.6 and y = 4.6

D. y = -3.5 and y = 3.5

Option D is correct. The Standard Deviation of the number of residents in the sample who were born in colorado is 7.75

How to find Standard Deviation of a given sample ?

Let x be the standard deviation for the sample, n =250

p = probability of success, q = probability of failure = 1 - p

q = 1 - 0.40 = 0.60

[tex]x = \sqrt{n \times p \times q}\\= \sqrt{250 \times 0.40 \times 0.60}\\= \sqrt{60}\\=7.75[/tex]

Therefore, Option D is correct. Standard Deviation is 7.75.

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option (d) the standard deviation of the number of residents in the sample who were born in Colorado is approximately 7.75.

The standard deviation of a binomial distribution is given by the formula:

σ = √(np(1-p))

binomial distribution with parameters n = 250 and p = 0.4—where n is the sample size and p is the probability of success—can be used to approximate the distribution of the number of Colorado residents who were born in Colorado in a sample of 250 residents.

Substituting n = 250 and p = 0.4, we get:

σ = √(250 x 0.4 x 0.6) ≈ 7.75

Therefore, the standard deviation of the number of residents in the sample who were born in Colorado is approximately 7.75.

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Answer: 57

It won't let me show the steps, since I've already edited my answer once...

Answer:

f(x) = 4+10/x

Step-by-step explanation:

f(x)x-5 = 4x+5

add 5 to both sides

f(x)x = 4x+10

divide both sides by x

f(x) = 4+10/x

still not sure if its the right problem...

As a result, the triangle's base angle is roughly 72 °

What is isosceles triangle?

An isosceles triangle in geometry is a triangle with two equal-length sides.. Sometimes it is said that it must have exactly two sides that are the same length, and other times it must have at least two sides that are the same length, with the latter version adding the equilateral triangle as an exception.

Let x represent the size of one of the triangle's base angles.

Hence, we may apply the following equation to determine x:

angle = ((b/2)/h) arccos

where h is the height and b is the length of the base of one of the equal sides.

B in this instance equals 23 feet, while h is 8 feet.

Filling up the formula with these values:

angle = ((23/2)/8) arccosine

angle ≈ 72°

Consequently, one of the triangle's base angles is roughly 72 °

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