What is the area of this triangle?

The value of x equals quantity of (3 ± √23)/2.

A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax² + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term.

Here, given equation;

  x² - 3x = -8

    x² - 3x + 8 = 0

 x² - 2 X 3/2 x + 8 = 0

 x² - 2.3/2 x + (3/2)² - (3/2)² + 8 = 0

 (x - 3/2)² - 9/4 + 8 = 0

 (x - 3/2)² + 23/4 = 0

  (x - 1.5)² = -5.75

  x - 1.5 = ±√(-5.75)

 x = 1.5 ± i√(5.75)

  x = (3 ± i√21)/2

Thus, x equals quantity of 3 plus or minus I square root of 23 all over 2.

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Answer: K

Step-by-step explanation:

The subtraction with the negatives can cancel out, resulting in a possible positive answer.

Answer:

k

Step-by-step explanation:

K      you CAN get a positive number....

        example  :

     -3   - (-5)   = -3 + 5 = + 2

The correct answers are option 1, Option 3 and option 4 which are:-

2(x² + 6x + 9) = 3 + 18

2(x² + 6x) = 3

x+3 = ±√21/√2

The polynomial having a degree of two or the maximum power of the variable in a polynomial will be 2 is defined as the quadratic equation and it will cut two intercepts on the graph at the x-axis.

We will check all three options one by one:-

2(x² + 6x + 9) = 3 + 18

2x² +  12x + 18 = 3 + 18

2x² + 12x -3 = 0

We are getting the original equation so it is correct.

2(x² + 6x) = 3

2x² + 12x = 3

2x² + 12x - 3 = 0

This is also right.

x+3 = ±√21/√2

Squaring on both the sides:-

( x + 3 )² = 21 / 2

x² + 6x + 9 = 21 / 2

2x² + 12x + 18 = 21

2x² + 12x = 21 - 18

2x² + 12x -3 = 0

This is also right

Therefore the correct answers are option 1, Option 3 and option 4 which are:-

2(x² + 6x + 9) = 3 + 18

2(x² + 6x) = 3

x+3 = ±√21/√2

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Answer:

A, C, D

A: 2(x2 + 6x + 9) = 3 + 18

C: 2(x2 + 6x) = 3

D: x + 3 = Plus or minus StartRoot StartFraction 21 Over 2 EndFraction EndRoot

Step-by-step explanation:

Got 100% on quiz

Answer:

485.5

Step-by-step explanation:

180.65+135.60+169.25

The Arrangement that will be the first to have a red and blue ribbon is the 15th arrangement.

The least common multiple that is divisible by both a and b is the smallest positive integer, lowest common multiple, or smallest common multiple of two numbers a and b, generally indicated by LCM.

Given the florist places a red ribbon on every third Arrangement and a blue ribbon on every fifth Arrangement. Therefore, to find the arrangement that will have both a red and a blue ribbon, you need to take the LCM of 3 and 5.

Since the LCM is 15, therefore, the Arrangement that will be the first to have a red and blue ribbon is the 15th arrangement.

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answer is this in decimal form if this is what ur looking for 4.21900462…

hope it helps....

Answer:

17.8

Step-by-step explanation:

Answer:

2-2/3 hours

Step-by-step explanation:

1/4 + 2/3 + 1-3/4 = 1/4 + 2/3 + 7/4. Use common is 12, so we get 3+8+21/12 = 32/12. Simplify equal 8/3 or 2-2/3 hours!

Answer:

Mr. Harry has 5 children.... I know what you were going for...

The answer is -0.18

when you convert 43% to decimal, it is 0.43

And the z-score of 0.43 is closest to -0.18

Hope it helps!

The correct answer is option C which is the ratio of the difference in the means of the two teams to the mean absolute deviation of Team B will be 0.25.

Mean is defined as the ratio of the sum of the number of the data sets to the total number of the data.

The difference between the mean times is about 16 times the mean absolute deviation of the data set.

59.32 - 59.1 = 0.22

2.4 - 1.5 = 0.9

0.22 / 0.9 = 0.25

Therefore the correct answer is option C which is the ratio of the difference in the means of the two teams to the mean absolute deviation of Team B will be 0.25.

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Answer:

x = 7/2

Step-by-step explanation:

1/5 (10x+30)-14= - 1/3 (6x-18)

10x + 30/5 - 14 = -6x + 18/3

(2*5)x+2*3*5/5-14 = -(2*3)x-2*3^2/3

x = 7/2

El costo en la opción uno es menor que el de la opción dos, asi que la primera es la más conveniente.

En la primera opción, el par de zapatos cuesta $90, y el segundo par tiene un descuento del 25%.

Entonces el costo por 2 pares es:

C = ($90 + $90)*(1 - 25%/100%)

Donde le aplicamos un descuento del 25% al total del costo de los dos zapatos, resolviendo esto obtenemos:

C = ($180)*(0.75) = $135.

En la segunda opcion tenemos que los pares cuestan $90, pero esta vez le aplicamos un descuento del 40% al segundo par.

C = $90 + $90*(1 - 40%/100%) =

C = $90 + $90*(0.6) = $144

Así, vemos que en la primera opción el costo es menor, entonces esa es la mejor opción.

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Answer:

1,260

Step-by-step explanation:

[tex]\implies C(9,4)*C(5,3)*C(2,2)[/tex]

[tex]\implies 9!/4!(9-4)!*5!/3!(5-3)!*2!/2!(2-2)![/tex]

[tex]\implies 9!/4!5!*5/3!2! *2!0![/tex]

[tex]\implies (9 * 8 * 7 * 6 / 4 * 3 * 2 * 1) * (5 * 4 / 2 * 1) * 1[/tex]

[tex]\implies 1260[/tex]

Therefore, 1,260 committees can be formed.

Answer: -35/16

Step-by-step explanation:

[tex]f(8)=-5\\\\f(-8)=30\\\\\frac{f(8)-f(-8)}{8-(-8)}=\frac{-5-30}{16}=\boxed{-\frac{35}{16}}[/tex]

Answer:

The slope of the line passing through is -6.

Using the normal distribution, it is found that 7.64% of of sample means are greater than 8.8 hours.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The parameters are given as follows:

[tex]\mu = 8.4, \sigma = 1.77, n = 40, s = \frac{1.77}{\sqrt{40}} = 0.2799[/tex]

The proportion of sample means greater than 8.8 hours is one subtracted by the p-value of Z when X = 8.8, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{8.8 - 8.4}{0.2799}[/tex]

Z = 1.43

Z = 1.43 has a p-value of 0.9236.

1 - 0.9236 = 0.0764.

7.64% of of sample means are greater than 8.8 hours.

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The slope of the line is

[tex]\frac{-1-4}{-1-0}=5[/tex]

So, the equation of the line in point-slope form is [tex]\boxed{y+1=5(x+1)}[/tex]

distance = speed * time

the first bus speed = x

second bus = x - 12

the sum of distance = 765 miles

first distance = 6x

second distance = 6 (x -12)

6x + 6(x-12) = 765

x + x -12 = 127.5

2x = 139.5

x = 69.75 mi/h which is the faster bus

the second bus speed = 57.75 mi/h

Answer:

Step-by-step explanation:

Comment

An x intercept occurs when y = 0. So the table shows three of them.

Answer

There are 3 x values when y = 0. They are

Answer: A. [tex](-1, 0)[/tex]

Step-by-step explanation:

The x-intercept is every point where y=0. To see this, we should look at the table's f(x) section to find any zeroes.

According to the table and this knowledge, one x-intercept of this continuous function is [tex](-1, 0)[/tex].

I hope this helps! Pls mark brainliest!! :)

The standard form of the circle equation 4x² + 8x + 4y² + 32y +52 = 0 is (x + 1)² + (y + 4)² = 2²

It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)

We have an equation that represents the circle:

4x² + 8x + 4y² + 32y +52 = 0

Divide by 4 on both the sides:

x² + 2x + y² + 8y + 13 = 0

x² + 2x + 1 - 1 + y² + 8y + 4² - 4² + 13 = 0

x² + 2x + 1 + y² + 8y + 4² - 1 - 16 + 13

(x + 1)² + (y + 4)² = 4

(x + 1)² + (y + 4)² = 2²

Thus, the standard form of the circle equation 4x² + 8x + 4y² + 32y +52 = 0 is (x + 1)² + (y + 4)² = 2²

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Answer:

3x^{2} -16x-19

Step-by-step explanation:

If we are going to be simplying this problem, then we need to take it step by step.

Start off by using the distributive property, and then combining like terms. Keep in mind the square, and make sure that gets sorted out correctly.

Answer:

(3x - 19) • (x + 1)

Step-by-step explanation:

STEP

1

:

Equation at the end of step 1

((3•((x-5)2))+14•(x-5))-24

STEP

2

:

Equation at the end of step 2

(3 • (x - 5)2 + 14 • (x - 5)) - 24

STEP

3

:

Trying to factor by splitting the middle term

Factoring 3x2-16x-19

The first term is, 3x2 its coefficient is 3 .

The middle term is, -16x its coefficient is -16 .

The last term, "the constant", is -19

Step-1 : Multiply the coefficient of the first term by the constant 3 • -19 = -57

Step-2 : Find two factors of -57 whose sum equals the coefficient of the middle term, which is -16 .

-57 + 1 = -56

-19 + 3 = -16 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -19 and 3

3x2 - 19x + 3x - 19

Step-4 : Add up the first 2 terms, pulling out like factors :

x • (3x-19)

Add up the last 2 terms, pulling out common factors :

1 • (3x-19)

Step-5 : Add up the four terms of step 4 :

(x+1) • (3x-19)

Which is the desired factorization

Answer:

D. f and h

Step-by-step explanation:

The function f is a liner function because for every increase in x, there is a proportional increase in f(x). This can be seen when the x value goes from 2 to 4, so a 2 unit increase, the f(x) value increases by 3. Since this is true for every interval of 2 in f(x) -- increase x by 2 results in an increase in 3 of f(x) -- then f(x) is a linear function.

The same principle can be applied to h(x), with each 4 unit increase in x, the h(x) value increase by 36.

The function g(x) is not a linear function because for each unit increase of x, there is not a proportional increase (or decrease) in g(x). As seen in the table, g(2)-g(1)= 8-4= 4. For g(x) to be a linear function, every other one unit increase in x should result in a 4 unit increase in g(x0. But this does not occur. g(3)-g(2)= 16-8= 8 , g(4)-g(3)= 32-16= 16, 8 and 16 are not equal to four so g(x) cannot be a linear function.

Answer:

175

Step-by-step explanation:

Average queue length = (arrival rate * service time) / (1 - arrival rate * service time)

For the given problem, the average queue length is:

Average queue length = (50 * 35) / (1 - 50 * 35)

= 175

The complete statement is divide factors of ± 8 by factors of ± 1

The polynomial is given as:

4x^3 + x^4 - 7x^2 - 8x - 8

Rewrite properly as:

x^4 + 4x^3 - 7x^2 - 8x - 8

The first term in the above equation is 1 i.e. 1x^4, while the last term is 8

To determine the possible rational roots, we divide the factors of the last term i.e. 8 by the factors of the first term i.e. 1

Hence, the complete statement is divide factors of ± 8 by factors of ± 1

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Using it's concept, the sample space for the experiment is given as follows:

{(H,1), (H,2), (H,3), (H,4), (H,5), (H,6), (T,1), (T,2), (T,3), (T,4), (T,5), (T,6)}

The sample space is the set that contains all possible outcomes for an experiment.

In this problem:

Hence the sample space is given as follows:
{(H,1), (H,2), (H,3), (H,4), (H,5), (H,6), (T,1), (T,2), (T,3), (T,4), (T,5), (T,6)}

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Answer:

all real number {x | x is a real number}

Answer:

1000 balls

(there are infinitely many solutions to this question; you can scale up 1000, use a different total, etc.)

Step-by-step explanation:

there are, of course, multiple possible numbers,

but the easiest way is to go with 1000, because we can say 375 / 1000 and 400 / 1000

(0.4 + 0.275 + 0.225 = 1)

400 out of 1000 balls are red (400/1000 = 4/10 = 0.4)

375 out of 1000 balls are green (375/1000 = 3.75/10 = 0.375)

225 out of 1000 balls are yellow (225/1000 = 2.25/10 = 0.225)

the question never gave detail as to if the answer should be the lowest number of possible balls, so this value is possible.

So, a possible number of balls in this bag is 1000.

Answer: Option 4

Step-by-step explanation:

Similar triangles have congruent angles, so this means that the sines, cosines, and tangents should be the same.

Thus, the side lengths of the triangle we want to find should be multiples of  [tex]1, \sqrt{15}, 4[/tex].

Between options 2 and 4, we know that the Pythagorean theorem is not satisfied by option (2), thus we should eliminate it.

This leaves us with option (4)

98% of confidence intervals for the Population proportion of people who captured after appearing on the 10 most wanted list

(0.6625, 0.7388).

A confidence interval is the mean of your estimate plus and minus the variation in that estimate.

Given sample, n= 782

As, 548 were not captured.

x= 548

So, p= 548/ 782

     p = 0.7007

q= 1- 0.7007 = 0.2993

98% of confidence intervals for the Population proportion of people who captured after appearing on the 10 most wanted list

Now,

α = 1 - 0.98 = 0.02

α/2 = 0.02/2 = 0.01

For confidence level of 98% , z is 2.33

Now,

(0.70007 - 2.33√ (0.7007(0.2993))/782 , 0.70007 + 2.33 √(0.7007(0.2993))/782

= (0.6625, 0.7388)

Hence, 98% of confidence intervals for the Population proportion of people who captured after appearing on the 10 most wanted list

(0.6625, 0.7388).

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