Which are steps that could be used to solve 0 = 9(x2 + 6x) – 18 by completing the square? Check all that apply.
18 + 81 = 9(x2 + 6x + 9)
18 + 9 = 9(x2 + 6x + 9)
18 + 36 = 9(22 + 6x + 36)
11 = (x + 3)2
07342 = (x + 6)2
199 = (x + 3)2

Answer:

8 slices

Step-by-step explanation:

To answer this question, we first need to know the area covered by the pizza.

Since it is circular in shape, we use the formula for the area of a circle.

Mathematically area of a circle = pi * r^2

Here, we were given the diameter but we know that D = 2r or r = D/2. This shows that the radius would be 14/2 = 7 inches

Now the area of the pizza is 22/7 * 7 * 7 = 22 * 7 = 154 square inch

Now we proceed to calculate the amount in calories present in the pizza;

That would be 154 * 14.04 = 2162.16 calories

one slice has 270 calories; The number of slices in 2162.16 calories would be 2162.16/270 = 8.008 which is approximately 8 slices

Answer:

16950

Step-by-step explanation:

Answer:

16950

PLEASE MARK BRAINLIEST IT TOOK A LING TIME TO FIGURE OUT!! THANK YOU!!

Answer:

An estimate of the probability that Jorge will make a profit is (5; 0.496)

Step-by-step explanation:

The total cost = 170x1 = $170

The payoff is $35 per $1 bet

The number of wins needed to make a profit = 170/35 = 4.86 \approx 5

Probability of winning, P(win), p = 1/38

n = 170

P(Jorge will make a profit) = P(at least 5 wins)

mean = np = 4.47

standard deviation = \sqrt{npq} = 2.09

P(X \geq 5) = 1 - P(X < 5)

P(X < A) = 1 - P(Z < (A - mean)/standard deviation)

After the application of continuity correction,

P(X \geq 5) = 1 - P(Z < (4.5 - 4.47)/2.09)

= 1 - P(Z < 0.01)

= 1 - 0.5040

P(X \geq 5 = 0.496

An estimate of the probability that Jorge will make a profit is (5; 0.496)

Answer:

probability that Jorge makes a profit is = 0.46412  

Step-by-step explanation:

Solution:-

- The number of bets made on number "3", N = 170

- He bets on each number "3", k = $1

- The winning pay-off odds : $ ( 35 : 1 )

- The probability of getting number "3" on a spin, p = 1/38

- The total amount paid (C) for n = 170 bets on number "3" are:

                 C = N*k

                 C = (170)*($1)

                 C = $170

- The probability of getting a number "3" on a spin is independent for each trial.

Denote:

- The amount received per win = $ 35

- The number of wins = r

- So the minimum "N" number of wins must be enough to match loss.

                 Amount Win = Amount Loss

                 r*$35 = C

                 r*$36 = C

                 r = $170 / 36

                 r = 4.7222 ≈ 5 wins

- So the minimum amount of wins required by r = 10 to make a profit.

- Let a random variable "X" denote the number of times Jorge spins to get number "3" - Number of wins. The probability to get a number "3" on each spin is independent for each trial. Therefore X follows Binomial distribution.

- So,                         X ~ B ( N , p )

                               X ~ B ( 170 , 1/38 )  

                               1 - p = 37 / 38

- So we need to determine that Jorge get number "3" at-least r = 5 times. Where the probability mass function for binomial distribution is given below:  

                              [tex]P ( X = r ) = ^NC_r * (p)^r * ( 1 - p )^(^N^ -^ r^ )[/tex]

So,

[tex]P ( X \geq 5 ) = 1 - P ( X \leq 4) = 1 - [ P ( X = 0 ) + P ( X = 1 ) + P ( X = 2 ) + P ( X = 3 ) + P ( X = 4 )]\\\\1 - [ (37/38)^1^7^0 + 170*(1/38)*(37/38)^1^6^9 + 170C2*(1/38)^2*(37/38)^1^6^8 + \\\\170C3*(1/38)^3*(37/38)^1^6^7 + 170C4*(1/38)^4*(37/38)^1^6^6 ]\\\\1 - [ 0.01074 + 0.04935 + 0.11271 + 0.17059 + 0.19249]\\\\= 1 - 0.53588\\\\= 0.46412[/tex]

- So the probability that Jorge makes a profit is = 0.46412                                        

Note:- The normal approximation to Binomial distribution may be a less cumbersome choice; however, care must be taken to verify the conditions for normal approximation i.e

                          N*p ≥ 10

With the given data, N = 170 , p = 1/38:

                          N*p = 170/38 = 4.4737 ≤ 10

Hence, the normal approximation is an invalid choice for the data given.

Answer:

The answer is 9 hours

Step-by-step explanation:

From the initial population of 180 cells, the number grows by 8% every hour for the first 9 hours.

This represents a increased population of 108% the previous population.

108% = 108/100 = 1.08

So the new population after n hours is

180 x 1.08^n

When population is 360

360 = 180 x 1.08^n

1.08^n = 2

Take log of both sides

n x Log1.08 = Log 2

n = Log 2/Log 1.08

n = 9

Answer:

B. 87

Step-by-step explanation:

The first thing is to calculate critical z factor

the alpha and the critical z score for a confidence level of 90% is calculated as follows:

two sided alpha = (100% - 98%) / 200 = 0.01

critical z factor for two sided alpha of .01 is calculated as follows:

critical z factor = z factor for (1 - .01) = z factor for (.99) which through the attached graph becomes:

critical z factor = 2.33

Now we have the following formula:

ME = z * (sd / sqrt (N) ^ (1/2))

where ME is the margin of error and is equal to 75, sd is the standard deviation which is 300 and the value of z is 2.33

N the sample size and we want to know it, replacing:

75 = 2.33 * (300 / (N) ^ (1/2))

solving for N we have:

N = (2.33 * 300/75) ^ 2

N = 86.86

Which means that the sample size was 87.

Answer:

a) reject H0

Step-by-step explanation:

The null and alternative hypotheses:

H0: the relative risk for moderate beer drinkers as compared to nondrinkers = 1

Ha: the relative risk for moderate beer drinkers as compared to nondrinkers ≠ 1

The level of significance, α = 0.1

Since the confidence interval for the relative risk of hypertension in moderate beer drinkers as compared to nondrinkers (0.47 to 0.90) does not contain the relative risk of 1,  the null hypothesis will be rejected at the specified level of significance, 0.1. Therefore, the conclusion is to reject H0.

Answer:A D E

Step-by-step explanation:

Answer:

Can i have breainliest.

Answer:

The volume of the sculpture is 12 cubic units

Step-by-step explanation:

The picture of the question in the attached figure

step 1

Find the volume of the L-shaped figure

The volume is given by

[tex]V=Bh[/tex]

where

B is the area of the base

h is the height of the figure

we have

[tex]h=1\ units[/tex]

The area of the base B is equal to the area of the complete square (3 units by 3 units)  minus the area of the interior square (2 units by 2 units)

[tex]B=3^2-2^2=5\ units^2[/tex]

so the volume of the L-shaped figure is equal to

[tex]V=(5)(1)=5\ units^3[/tex]

step 2

Find the volume of the sculpture

we know that

The volume of the sculpture is equal to the volume of the L-shaped figure, multiplied by two plus the volume of two unit cubes

so

[tex]V=2(5)+2(1)=12\ units^3[/tex]

Answer:

37.8metres

Step-by-step explanation:

The arc of the arrow can be modeled by the equation:

y=-0.02x²+0.65x+4

Where x is the horizontal distance (in meters) from Linda and y is the height (in meters) of the arrow.

The arrow hits the ground when its height (y) is zero.

Therefore, we determine the value(s) of x for which:

y=-0.02x²+0.65x+4=0

Using a calculator to solve the quadratic equation:

x=37.79 or -5.29

Since the distance cannot be a negative value, we ignore -5.29.

The distance from Linda when the arrow hits the ground is 37.8metres (to the nearest tenth)

Answer:

37.8 m

Step-by-step explanation:

Given:-

- The arc trajectory of the arrow is modeled by:

                    y = -0.02x^2 + 0.65x + 4

Where, x is the horizontal distance (in meters) from Linda

            y is the height (in meters) of the arrow

Find:-

How far from Linda does the arrow hit the ground? Round to the nearest tenth.

Solution:-

- We are to determine the range of the projectile trajectory of the arrow. The maximum distance "x_max" occurs when the arrow hits the ground.

- Set the trajectory height of arrow from linda , y = 0:

                   0 = -0.02x^2 + 0.65x + 4

- Solve the quadratic equation:

                   x = -5.29 m , x = 37.8 m

- The negative distance x lies at the back of Linda and hence can be ignored. The maximum distance travelled by the arrow would be = 37.8 m

Answer:

(2x + 3)(x + 5)

Step-by-step explanation:

2x² + 3x + 15 = 0

(2x + 3)(x + 5)

2x + 3 = 0

2x = -3

x = -3/2

x + 5 = 0

x = -5

Answer:

See the explaination

Step-by-step explanation:

Total No. of rolling each side of the 12-sided die= 12 x 12= 144 outcomes

No. of outcomes equals 10 are: (1, 9), (9, 1), (2, 8), (8, 2), (3, 7), (7, 3), (4, 6), (6, 4), (5, 5) = 9 outcomes.

No. of outcomes of rolling a No. >10: 144–9 = 135 outcomes.

Probability, Pr, of rolling a No. >10= 135/144

Pr (No. >10) = 0.9375 (to 4 dec. pl.)

Answer: I think you’re missing something on your question. But I think what your asking is how many numbers greater than 10. It should 2/12 or

Step-by-step explanation:

Answer:

she will finish the oatmeal in 15 days

Step-by-step explanation:

it takes 3 days to eat one cup. 3x5= 15.

hope this helps. :)

Answer:

It would take Jessica 15 days to finish the container.

Step-by-step explanation:

To work this out you would first multiply 1/3 by 3, which gives you 3/3 or 1. This shows that it would take Jessica 3 days to eat 1 cup of oatmeal. Then you would multiply 3 by 5, which is 15. This means that it would take Jessica 15 days to finish the container.

1)  Multiply 1/3 by 3.

[tex]\frac{1}{3} *3=\frac{3}{3} or 1[/tex]

2) Multiply 3 by 5.

[tex]3*5=15[/tex]

Answer:

Yes

Step-by-step explanation:

There are about 52 weeks in a year, 42,990 ÷ 52 = 826.73076 ,

1277 ÷ 12 = 106.41666

826.73076 - 106.41666 = 720.3141

720.3141 - 456 = 264.3141

Yes, one week's paycheck is enough to pay for his monthly auto loan and his monthly cost of insurance.

In mathematics, it deals with numbers of operations according to the statements.

There are 52 weeks in a year,
Income of 1 week = $42,990/52 = 826.73
So his income of Gary for 1 week is $826.73

he pays $1277 per year for auto insurance
There are 12 months in a calender year
Monthly auto insurance pay = 1277/12 = 106.42

Pay for monthly auto insurance is $106.42
and he currently has a $456 per month car loan payment

Total pay = 106.42 + 456 = $562.42
Here, their income of Gary for a week is greater than the total pay,

Thus,  yes, one week's paycheck is enough to pay for his monthly auto loan and his monthly cost of insurance.

Learn more about arithmetic here:

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Answer:

(x+3)(2x+7)

Step-by-step explanation:

Step  1  :

Equation at the end of step  1  :

 (2x2 +  13x) +  21

Step  2  :

Trying to factor by splitting the middle term

2.1     Factoring  2x2+13x+21

The first term is,  2x2  its coefficient is  2 .

The middle term is,  +13x  its coefficient is  13 .

The last term, "the constant", is  +21

Step-1 : Multiply the coefficient of the first term by the constant   2 • 21 = 42

Step-2 : Find two factors of  42  whose sum equals the coefficient of the middle term, which is   13 .

      -42     +     -1     =     -43  

      -21     +     -2     =     -23  

      -14     +     -3     =     -17  

      -7     +     -6     =     -13  

      -6     +     -7     =     -13  

      -3     +     -14     =     -17  

      -2     +     -21     =     -23  

      -1     +     -42     =     -43  

      1     +     42     =     43  

      2     +     21     =     23  

      3     +     14     =     17  

      6     +     7     =     13     That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  6  and  7

                    2x2 + 6x + 7x + 21

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

                   2x • (x+3)

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

                   7 • (x+3)

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

                   (2x+7)  •  (x+3)

            Which is the desired factorization

Final result :

 (x + 3) • (2x + 7)

- If you want this explained differently please let me know. Hope this helps!

1. baseball + basketball = 240

2. tennisball + soccerball = 500

3. soccerball - basketball + tennisball = 455

4. baseball + tennisball = 215

Subtract 1 from 4

5. tennisball - basketball = -25

Rearrange 3

6. soccerball + tennisball - basketball = 455

Substitute 5 into 6

7. soccerball - 25 = 455

Solve

soccerball = 480

Answer:

u have the answer tho right

Step-by-step explanation:

In mathematical terms, a whole pie is considered as 1 (or 1/1). If half (1/2) of it is eaten, what remains is the other half (1/2). So, the fraction that remains of the pie is 1/2.

When we talk about a pie in mathematics, we usually refer to it as a whole. If you've eaten half of the pie, essentially, you've consumed 1/2 of the pie. If that amount is subtracted from the whole pie (which is always considered as 1 or 1/1), what remains is the other half of the pie. Meaning, if you subtract 1/2 from 1 (or 1/1), you're left with 1/2 of the pie. Hence, if half of the pie is eaten, the fraction that remains is 1/2.

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Answer:

The answer to your question is  y = 2x + 1

Step-by-step explanation:

Data

line  y = 2x + 3

point  (-2, -1)

line parallel = ?

Process

1.- Find the slope of the original line.

The slope is the coefficient of the x, then the slope is 2

         y = 2x + 3

2.- Find the equation of the parallel line using the point slope equation

        y - y1 = m(x - x1)

-Substitution

       y + 1 = 2(x + 2)

-Simplification

       y + 1 = 2x + 2

       y = 2x + 2 - 1

-Result

       y = 2x + 1

Step-by-step explanation:

This is a cube

Formula surface area of a cube = s2 × 6

Where s is one side

Square of 8 = 64

64 × 6 = 384

Answer:

6

Step-by-step explanation:

you have to multiply it by joe mama

Answer:

A) 207 cm3

Step-by-step explanation:

9 x 23 = 207

Answer:

x=5

Step-by-step explanation:

2(x + 8) = x + 21

Distribute

2x+16 = x+21

Subtract x from each side

2x-x +16 = x-x+21

x +16 = 21

Subtract 16 from each side

x+16-16 =21-16

x =5

Answer:

a) 2

b) s₁    and   s₂

c)  First linear equation:     5*x₁  +  8*x₂ + 10*x₃ + s₁  = 173

   Second linear equation:   5*x₁  + 4*x₂  + 17*x₃  + s₂  = 254

Step-by-step explanation:

The problem statement, establishes two constraints, each one of them will need a slack variable to become a linear equation, so the answer for question

a) 2.

b)  The constraints are: s₁  and  s₂

c) First constraint

5*x₁  +  8*x₂ + 10*x₃ ≤ 173

We add slack variable  s₁   and the inequality becomes

5*x₁  +  8*x₂ + 10*x₃ + s₁  = 173

The second constraint is:

5*x₁  + 4*x₂  + 17*x₃ ≤ 254

We add slack variable  s₂   and the inequality becomes

5*x₁  + 4*x₂  + 17*x₃  + s₂  = 254

Answer:

A. Two slack variables are needed

B. S1 and s2 (option b)

C. Option d (5X1 + 8X2 + 10X3 + s1 = 173)

D. Option a (5X1 + 4X2 + 17X3 + s2 = 245)

E. Z is maximized at 173 when (X1, X2, X3) = (34.6, 0, 0)

Step-by-step explanation:

In a linear maximization problem like this, if we want to convert the inequality (constraint) into a linear equation, we add slack variables to the left hand side of each inequality.

Therefore we add s1 and s2 to the first and second inequality respectively.

[tex]5X1 + 8X2 + 10X3 \leq 173\\5X1 + 4X2 + 17X3 \leq 245[/tex]

Imputing the slack variables, we obtain as follows:

[tex]5X1 + 8X2 + 10X3 + s1 = 173\\5X1 + 4X2 + 17X3 + s2 = 245[/tex]

[tex]Maximize :\\Z = 5X1 + 3X2 + X3[/tex]

Subject to

[tex]5X1 + 8X2 + 10X3 \leq 173\\5X1 + 4X2 + 17X3 \leq 245\\With \\X1 \geq 0\\X2 \geq 0\\X3 > 0[/tex]

Solution :

[tex]5X1 + 8X2 + 10X3 + s1 = 173\\5X1 + 4X2 + 17X3 + s2 = 245\\-5X1 - 3X2 - X3 + Z = 0[/tex]

5X1 on the first equation is the pivot because the negative value of -5 is the highest and 173/5 is less than 245/5

We perform eq1 - eq2 on the first row and eq1 + eq3 on the third row to get X1 and clear the rest.

We

X1 = 173/5 = 34.6

X2 = 0 (inactive)

X3 = 0 (inactive)

s1 = 0 , s2 = -72/-1 = 72,

Z = 173/1 =173

Therefore the minimum value of Z is 173 when (X1, X2, X3) = (34.6, 0, 0)

Answer:

B) 5 (x minus 3)

C) 4 x + 3 y minus 15 minus 3 y + x

E) Negative 20 minus 3 x + 5 + 8 x

tep-by-step explanation:

5x minus 15

5x - 15

5(x - 3)

4 x + 3 y minus 15 minus 3 y + x

4x + 3y - 15 - 3y + x

5x - 15

Negative 20 minus 3 x + 5 + 8 x

-20 - 3x + 5 + 8x

5x - 15

Answer:

answers are b,c,e

Step-by-step explanation:

Final answer:

To find the volume of the cylinder with a given radius of 10 units and height of 13 units, we use the formula V = πr²h, which yields an approximate volume of 4085.48 cubic units using π as 3.1416. The nearest given option is C (1300 cubic units), although the calculated volume does not exactly match any of the provided choices.

Explanation:

To calculate the volume of a cylinder, we use the formula V = πr²h, where V represents the volume, r is the radius, and h is the height of the cylinder. Given the radius r as 10 units and the height x (which likely represents the height h in this context) as 13 units, we plug these values into the formula:

V = π(10²)(13) = π(100)(13) = 1300π cubic units.

Since π is approximately 3.1416, the volume is approximately:

V ≈ 1300(3.1416) ≈ 4085.48 cubic units.

As none of the multiple-choice options provided exactly match this calculated volume, this could indicate a typo or error in the question or options. However, if we use a rounded value of π as 3.14, then:

V ≈ 1300(3.14) ≈ 4082 cubic units.

The closest match to this calculated volume is option C (1300 cubic units). However, the student should verify the precision of π used in their classroom or the context of the question to ensure this match is consistent with their requirements.

Answer:

D) 69.1 ft

Step-by-step explanation:

Answer: a

Step-by-step explanation:

Answer:

x = 6

Well if there's one value of x that fits both of them your first step is to set them equal to each other.

26 - 2x = 3x - 4

Now lets solve it

      26 - 2x = 3x - 4

            +2x  +2x

              26 = 5x - 4

              +4          +4

              30 = 5x

           30/5 = 5x/5

                 6 = x

Answer:

Dimension of the Rectangle : 2W - 150 by W

Step-by-step explanation:

Given

Land Size = 150 metres

This land size represents the perimeter of the land

Let P = Perimeter

So, P = 150 m

To bisect the field into two equal halves means to divide length or width of the field into two equal halves

Let L = Length of the field

Let W = Width of the field

Assuming the length of the field is to be bisected., then the campground owner is left with 0.5L (i,e half of the length)

Perimeter of a rectangle is calculated by: 2(Length + Width)

P = 2(L + W) by substitution, becomes

150 = 2(0.5L + W) ----open bracket

150 = L + 2W ---- Male L the subject the formula

L = 2W - 150

The dimension of the largest area that can be enclosed id given by (L,W)

By substitution; the expression becomes

Dimension of the Rectangle : 2W - 150 by W

Answer:

Therefore the dimensions of the square should be 0.1528 inch by 0.1528 inch so, the box  has largest volume.

Step-by-step explanation:

Given that,

A box is being created out of a 15 inches by 10 inches sheet of metal.

The length of the one side of the squares which are cut out of the each corners of the metal sheet be x.

The length of the metal box be = (15-2x) inches.

The width of the metal box be =(10-2x) inches

The height of the metal box be =x inches

Then, the volume of the metal box= length×width×height

                                                         =(15-2x)(10-2x)x cubic inches

                                                         =(150x-50x²+4x³) cubic inches

∴ V= 4x³-50x²+15x

Differentiating with respect to x

V'=12x²-100x+15

Again differentiating with respect to x

V''=24x-100

For maximum or minimum value, V'=0

12x²-100x+15=0

Apply quadratic formula [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex], here a=12, b= -100 and c=15

[tex]x=\frac{-(-100)\pm\sqrt{(-100)^2-4.12.15}}{2.12}[/tex]

[tex]\Rightarrow x=\frac{100\pm\sqrt{9280}}{2.12}[/tex]

[tex]\Rightarrow x=0.1528,8.18[/tex]

For x= 8.18, The value of (15-2x) and (10-2x) will negative.

∴x=0.1528 .

Now, [tex]V''|_{x=0.1528}=24(0.1528)-100<0[/tex]

∴At x=0.1528 inch, the volume of the metal box will be maximum.

Therefore the dimensions of the square should be 0.1528 inch by 0.1528 inch so, the box  has largest volume.