Rewrite the function by completing the square.
h (x)=x^2+3x−18

Answer:L*W

Step-by-step explanation:

if you look at the pattern you will see that

[tex]2x^2-10x=0\\2x(x-5)=0\\2x=0 \vee x-5=0\\x=0 \vee x=5[/tex]

Answer:

Here

2x^2 - 10x = 0

2x^2 = 0 + 10x

2x^2 = 10x

x^2 = 10x ÷ 2

x^2 = 5x

2x^2 - 10x = 0

x^2 - 5x = 0

Step-by-step explanation:

first find the value of x and then put the value and slove

The GDP at FC from the following data: GDP at MP = Rs. 2,000 billion Indirect taxes = Rs. 300 billion Subsidies = Rs. 100 billion​ is: Rs. 1,800 billion.

Using this formula to determine the GDP at FC

GDP at FC = GDP at MP - Indirect taxes + Subsidies

Where:

GDP at MP (Market Price) = Rs. 2,000 billion

Indirect taxes = Rs. 300 billion

Subsidies = Rs. 100 billion

Let plug in the formula

GDP at FC = 2,000 billion - 300 billion + 100 billion

GDP at FC = 1,800 billion

Therefore the GDP at factor cost (FC) is Rs. 1,800 billion.

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Answer:

Arc EG = 23.21 units

Step-by-step explanation:

Arc length:

Arc length could be found by the below mentioned formula.

         [tex]\boxed{\bf Arc \ length =\dfrac{\theta }{180}*\pi r}[/tex]

r - radius of circle = 19 units

Ф - central angle of arc = 70°

                             [tex]\sf arc \ EG = \dfrac{70}{180}*3.14*19\\\\[/tex]

                                         = 23.21 units

The probability of 12 women jurors being chosen is approximately 0.000342 or 0.0342%.

To calculate the probability of selecting 12 women jurors out of a pool of 26 men and 29 women, we need to consider the total number of possible combinations and the specific combination of interest.

The total number of ways to choose 12 individuals from a pool of 55 (26 men + 29 women) is given by the combination formula:

C(55, 12) = 55! / (12! * (55-12)!) = 22579284062370.

The number of ways to choose 12 women from a pool of 29 is given by the combination formula:

C(29, 12) = 29! / (12! * (29-12)!) = 7726160.

Therefore, the probability of selecting 12 women jurors is the ratio of the number of ways to choose 12 women to the total number of possible combinations:

P(12 women jurors) = C(29, 12) / C(55, 12) ≈ 7726160 / 22579284062370 ≈ 0.000342.

Hence, the probability of 12 women jurors being chosen is approximately 0.000342 or 0.0342%.

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Reema should use 3 hooks, with a distance of 7 inches between each hook, and each hook will be positioned 5 3/8 inches from the left edge of the wood.

To determine the number of hooks Reema should use, we first need to calculate the available space on the wood for the hooks.

The total length of the wall is 4 feet, which is equivalent to 48 inches. Reema wants to center the coat rack, so she will have an equal amount of space on either side.

Therefore, each side will have (48 - 28 1/4) / 2 = 9 3/8 inches of space.

Next, we need to determine the distance between the hooks.

Reema wants about 7 or 8 inches of space between each hook.

Let's choose 7 inches for consistency.

Since there will be (n - 1) spaces between n hooks, the total space taken by the spaces will be 7 [tex]\times[/tex] (n - 1) inches.

Now, let's subtract the space taken by the spaces from the available space on the wood: 9 3/8 - 7 [tex]\times[/tex] (n - 1) = 9 3/8 - 7n + 7 inches.

Reema wants the first and last hooks to be no less than 1 3/4 inches from either end of the wood.

Therefore, we subtract twice this distance from the remaining space: 9 3/8 - 7n + 7 - 2 [tex]\times[/tex] (1 3/4) = 9 3/8 - 7n + 7 - 3 1/2 inches.

Now we have the expression 9 3/8 - 7n + 7 - 3 1/2 inches representing the remaining space.

We want this value to be greater than or equal to zero, as it should not be negative.

Simplifying the expression, we have 18 7/8 - 7n - 3 1/2 inches ≥ 0.

Now we can solve this inequality to find the range of values for n, the number of hooks.

We can then determine the distance between the hooks by dividing the remaining space by the number of spaces, and the distance of each hook from the left edge of the wood by adding the space taken by the spaces to the distance between the hooks.

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The statement "The cup of flour has a mass of exactly 121.8 grams" is not true.

Since the baking scale measures mass to the tenth of a gram, it means it can measure values such as 121.7 grams, 121.8 grams, and 121.9 grams. However, it does not have the capability to measure beyond the tenths place, so it cannot determine whether the exact mass of the cup of flour is exactly 121.8 grams. Therefore, the statement claiming an exact mass is not true.

The other statements are all true:

[tex]\huge{\mathcal{\colorbox{black}{\textcolor{lime}{\textsf{I hope this helps !}}}}}[/tex]

♥️ [tex]\large{\textcolor{red}{\underline{\texttt{SUMIT ROY (:}}}}[/tex]

Answer:

Step-by-step explanation:

A baking scale measures mass to the tenth of a gram, up to 650 grams. A cup of flour is placed on the scale and results in a measure of 121.8 grams. [ Which of the following statements is not true? a.The exact mass of the cup of flour must be between 121.7 and 121.9 grams.

The relationship between Calorie and weight is very weak and insignificant.

Comparing the relationship between Calorie and Weight using the correlation coefficient, the coefficient value obtained is 0.0086 which is very weak.

There is no obvious pattern linking an increase in calorie to Weight or decrease in association between the two variables.

Therefore, we can conclude that a very weak and insignificant relationship exists between Calorie and weight for the given data.

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The minimum y-value of g(x) is -3 and g(x) has the smallest possible y-value.

The function  f(x) = 32 - 3 is a constant function, as there is no variable term involving x. It simplifies to f(x) = 29.

Regardless of the value of x, the function f(x) will always have a y-value of 29.

Therefore, option A is incorrect because there is no minimum y-value for f(x); it is a constant.

g(x) = 7x² - 3 is a quadratic function in the form of ax² + bx + c, where a = 7, b = 0, and c = -3.

The coefficient a (7) is positive, indicating that the parabola opens upward.

Since there is no linear term (bx), the vertex of the parabola is located at the point (0, -3), which corresponds to the minimum y-value of the function.

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The area of the composite figures are:

The total area of Shape A is = 115.5 in²

and, total area of Shape B is = 51ft².

Here, we have,

from the given diagram we get,

Shape A.)

Part 1: it is a rectangle,

l= 13 and w = 7

so, area = 91 in²

Part 2: it is a triangle,

b = 7 and h = 7

so, area = 1/2 *7 * 7 = 24.5 in²

So, The total area of Shape A is = 115.5 in²

now, Shape B.)

part 1 : it is a rectangle,

l=4 and w = 6

so, area = 24 ft²

part2: it is a square,

side = 3

so, area = 9 ft²

part 3: it is a trapezium,

a = 6, b = 3, h =4

so, area = 1/2 * (6+3) * 4 = 18ft²

So, total area of Shape B is = 51ft².

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Answer:

[tex]\overline{LP}=77[/tex]

Step-by-step explanation:

Given [tex]\Delta LMQ\sim\Delta LNP[/tex], then [tex]\overline{LN}=\overline{LM}+\overline{MN}=8+14=22[/tex]. This will help us find [tex]\overline{LQ}[/tex] since we know the length of [tex]\overline{QP}[/tex]:

[tex]\displaystyle \frac{\overline{LM}}{\overline{LM}+\overline{MN}}=\frac{\overline{LQ}}{\overline{LQ}+\overline{QP}}\\\\\frac{8}{8+14}=\frac{\overline{LQ}}{\overline{LQ}+49}\\\\\frac{8}{22}=\frac{\overline{LQ}}{\overline{LQ}+49}\\\\8(\overline{LQ}+49)=22\overline{LQ}\\\\8\overline{LQ}+392=22\overline{LQ}\\\\392=14\overline{LQ}\\\\28=\overline{LQ}[/tex]

Therefore:

[tex]\overline{LP}=\overline{LQ}+\overline{QP}=28+49=77[/tex]

The amount of money that Jane Doe get to take home after taxes in 2017 is A. $48500

Based on the W-2 form above, Jane Doe's gross pay was $50,000. She had $6,835 in federal income tax withheld, $725 in state income tax withheld, and $1,000 in FICA taxes withheld. This means that her net pay was $48,500.

Net pay = Gross pay - Total taxes withheld

Net pay = $50,000 - ($6,835 + $725 + $1,000)

Net pay = $48,500

Therefore, amount of money that Jane Doe get to take home after taxes in 2017 is A. $48500

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The exact value of cos(θ/2) is:

[tex]cos(\frac{\theta }{2}) = \right-\sqrt{\frac{1}{122} }[/tex]

To find the exact value of cos(θ/2), we can use the half-angle formula for cosine:

[tex]cos(\frac{\theta }{2}) = \right\pm\sqrt{\frac{1+cos\theta}{2} }[/tex]

First, let's find the value of cos(θ) using the given information about θ:

Given:

tan(θ) = 11/60

θ lies in the 3rd quadrant (π < θ < 3π/2)

In the 3rd quadrant, both sin(θ) and cos(θ) are negative.

tan(θ) = opposite/adjacent

Also, in the 3rd quadrant, both opposite and adjacent are negative.

Thus,

opposite = -11

adjacent = -60

hypotenuse = √[(-60)² + (-11)²]   (Pythagoras theorem)

hypotenuse = 61

cos(θ) = adjacent/hypotenuse

cos(θ) = -60/61

Finally, we can substitute these values into the half-angle formula for cosine:

[tex]cos(\frac{\theta }{2}) = \right\pm\sqrt{\frac{1+(\frac{-60}{61})}{2} }[/tex]

[tex]cos(\frac{\theta }{2}) = \right\pm\sqrt{\frac{\frac{1}{61} }{2} }[/tex]

[tex]cos(\frac{\theta }{2}) = \right\pm\sqrt{\frac{1}{122} }[/tex]

Since the cos(θ/2) is negative. Therefore, the exact value of cos(θ/2) is:

[tex]cos(\frac{\theta }{2}) = \right-\sqrt{\frac{1}{122} }[/tex]

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Por lo tanto, la parcela mide 18 metros de largo y 12 metros de ancho.

Llamemos "largo" (L) a una de las dimensiones de la parcela y "ancho" (A) a la otra dimensión.

Según la información dada, sabemos que la suma del largo y el ancho es de 30 metros:

L + A = 30 ---(1)

También se nos dice que la diferencia entre el largo y el ancho es de 6 metros:

L - A = 6 ---(2)

Podemos resolver este sistema de ecuaciones utilizando el método de sustitución o de eliminación. En este caso, resolveremos utilizando el método de sustitución.

De la ecuación (2), podemos despejar L en términos de A:

L = A + 6

Sustituyendo este valor de L en la ecuación (1), obtenemos:

(A + 6) + A = 30

2A + 6 = 30

Restamos 6 de ambos lados de la ecuación:

2A = 30 - 6

2A = 24

Dividimos ambos lados de la ecuación por 2:

A = 12

Ahora que conocemos el valor de A, podemos encontrar el valor de L sustituyendo en la ecuación (2):

L = A + 6

L = 12 + 6

L = 18

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Answer:

To calculate Mr. Chi's total tax bill, we need to find the amount of sales tax charged by each entity and add them together.

The state sales tax on the sale of a house is 3.2%, which means Mr. Chi will owe 0.032 x $289,300 = $9,267.20 in state sales tax.

The county sales tax on the sale of a house is 2.6%, which means Mr. Chi will owe 0.026 x $289,300 = $7,520.80 in county sales tax.

The city sales tax on the sale of a house is 1.8%, which means Mr. Chi will owe 0.018 x $289,300 = $5,207.40 in city sales tax.

Therefore, Mr. Chi's total tax bill will be $9,267.20 + $7,520.80 + $5,207.40 = $21,995.40.

The tangent from the external point are equal, so the x value is 3 units.

7) The measure of the arc XW is 180-105=75

8) The measure of the arc VWY is 105+75+85 = 265

9) We know that, tangent from the external point are equal

In circle C, AB=AD

26=8x+2

8x=24

x=24/8

x=3 units

10) 9x-3=7x+5

9x-7x=5+3

2x=8

x=8/2

x=4

Therefore, the tangent from the external point are equal, so the x value is 3 units.

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1. The price of a pair of gloves (x) is $8.50, and the price of a hat (y) is $6.50.

2. Aaliyah invested $7,200 in the mutual fund that rose 6% and $2,800 in the mutual fund that rose 9%.

1. Let's assume the price of a pair of gloves is represented by 'x' and the price of a hat is represented by 'y'.

From the given information, we can establish the following equations based on Cody and Tor's purchases:

Equation 1: 2x + 4y = 43.00 (Cody's purchase)

Equation 2: 2x + 2y = 30.00 (Tor's purchase)

To solve this system of equations, we can use a method like substitution or elimination.

Using the substitution method, we can rearrange Equation 2 to express x in terms of y:

2x = 30.00 - 2y

x = 15.00 - y

Now, we substitute this value of x into Equation 1:

2(15.00 - y) + 4y = 43.00

30.00 - 2y + 4y = 43.00

2y = 43.00 - 30.00

2y = 13.00

y = 6.50

Substituting this value of y back into Equation 2 to find x:

2x + 2(6.50) = 30.00

2x + 13.00 = 30.00

2x = 30.00 - 13.00

2x = 17.00

x = 8.50

Therefore, the price of a pair of gloves (x) is $8.50, and the price of a hat (y) is $6.50.

2. Let's assume Aaliyah invested an amount represented by 'x' in the mutual fund that rose 6% and an amount represented by 'y' in the mutual fund that rose 9%.

From the given information, we can establish the following equations based on the rise in investment:

Equation 1: 0.06x + 0.09y = 684 (rise in investment)

Equation 2: x + y = 10,000 (total investment)

To solve this system of equations, we can use a method like substitution or elimination.

Using the substitution method, we can rearrange Equation 2 to express x in terms of y:

x = 10,000 - y

Now, we substitute this value of x into Equation 1:

0.06(10,000 - y) + 0.09y = 684

600 - 0.06y + 0.09y = 684

0.03y = 84

y = 2800

Substituting this value of y back into Equation 2 to find x:

x + 2800 = 10,000

x = 10,000 - 2800

x = 7200

Therefore, Aaliyah invested $7,200 in the mutual fund that rose 6% and $2,800 in the mutual fund that rose 9%.

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Answer:

Step-by-step explanation:

To find the diameter of the cylinder, we can use the formula for the volume of a cylinder:

Volume = π * radius^2 * height

Given:

Volume = 20π cm^3

Height = 5 cm

We can rearrange the formula to solve for the radius:

radius^2 = Volume / (π * height)

radius^2 = (20π) / (π * 5)

radius^2 = 4

radius = 2

Now, we can find the diameter by multiplying the radius by 2:

diameter = 2 * radius

diameter = 2 * 2

diameter = 4

Therefore, the diameter of the cylinder is 4 cm.

The value of the missing segment n using the product of intersecting chord theorem is 14cm

The product of the segments of two intersecting chords are equal.

The segments of the chords ;

Chord 1 = 4 and n

Chord 2 = 7 and 8

The principle can be related Mathematically thus ;

4 × n = 7 × 8

4n = 56

Divide both sides by 4

4n/4 = 56/4

n = 14

Therefore, the value of n in the question is 14cm

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the answer to this question is

m=1

Answer: y<-x+3

Step-by-step explanation:

Slope-Intercept Form formula is y=mx+b.

1. Rearrange the variables (subtract x).  x+y<3  --> y<-x+3.

2. y<-x+3 is the final answer!

Very Simple!

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Based on the results, the below  list shows a comparison of the overall performance of the portfolios, from best to worst:

Portfolio 2, Portfolio 1, Portfolio 3

Portfolio 1:

total investment=$1250+$575+$895+$800+$1775

total investment = $5295

weighted average ROR= (12.6%*$1250/$5295 + 2.8%*$575/$5295 + 10.4%*$895/$5295 +1.8%*$800/$5295 - 5.6%*$1775/$5295)

weighted average ROR = 3.23%

Portfolio 2:

total investment = $950 + $2025 + $1185 + $445 + $625

total investment = $5230

weighted average ROR= ( 12.6%*$950/ $5230 + 2.8% *$2025/ $5230 + 10.4%*$1185/ $5230 + 1.8%* $445/ $5230 - 5.6%*$625/ $5230)

weighted average ROR = 5%

Portfolio 3:

total investment = $900 + $2350 + $310 + $1600 + $2780

total investment = $7940

weighted average ROR = (  12.6%*$900/$7940 + 2.8% *$2,350/$7940 + 10.4%*$310/ $7940 + 1.8%* $1600 / $7940 −5.6% *$2780/$7940)

weighted average ROR = 1%

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The theoretical probability of selecting the letter T is 1/4.

Probability is the possibility of happening an event.

Given the four letters M, A, T, and H.

Note that the letter T occurs 1 time, therefore, the probability of selecting the letter T is:

[tex]\sf P=\dfrac{1}{4}[/tex]

Hence, the theoretical probability of selecting the letter T is 1/4.

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Answer:

Step-by-step explanation:

Willis’s mistake is that he used the differences of 6, 10 and 14 instead of the differences of 7, 17 and 31. For a linear function, the y values should have a constant rate of change and not the differences.

Answer:

Para encontrar el valor de la expresión 6 - (3x + 1) + 2x^2 cuando x = 4, sustituimos el valor de x en la expresión y evaluamos:

6 - (3x + 1) + 2x^2

= 6 - (3 * 4 + 1) + 2 * 4^2

= 6 - (12 + 1) + 2 * 16

= 6 - 13 + 32

= -7 + 32

= 25

Por lo tanto, cuando x = 4, el valor de la expresión 6 - (3x + 1) + 2x^2 es igual a 25.

Step-by-step explanation:

Answer:

Step-by-step explanation:

To find the radius of the cylinder, we can use the formula for the volume of a cylinder:

Volume = π * radius^2 * height

Given:

Volume = 627.8 cm^3

Height = 19.5 cm

π (pi) = 3.14

Substituting the given values into the formula:

627.8 = 3.14 * radius^2 * 19.5

Simplifying the equation:

627.8 = 60.93 * radius^2

To solve for the radius, we can divide both sides of the equation by 60.93:

radius^2 = 627.8 / 60.93

radius^2 = 10.29

Taking the square root of both sides:

radius ≈ √10.29

Rounding to the nearest tenth:

radius ≈ 3.2

Therefore, the approximate radius of the cylinder is 3.2 cm.

Answer:

3.2

Step-by-step explanation:

The volume of a cylinder is:

Vol = pi•r^2•h

Fill in what is given.

627.8 = pi•r^2•19.5

use 3.14 for pi.

627.8 = 3.14•r^2•19.5

simplify.

627.8 = 61.23r^2

divide by 61.23

10.253 = r^2

sqrt both sides

sqrt10.253 = r

3.2 = r