Solve x^2+12x=-11by completing the square which is the solution set of the equation A={-11,-1} B={-11,1} C={11,-1} D={11,1}

Answer:

[tex]=\left(x+4\right)\left(x-9\right)[/tex]

Step-by-step explanation:

[tex]x^2-5x-36\\\mathrm{Break\:the\:expression\:into\:groups}\\=\left(x^2+4x\right)+\left(-9x-36\right)\\\mathrm{Factor\:out\:}x\mathrm{\:from\:}x^2+4x\mathrm{:\quad }x\left(x+4\right)\\\mathrm{Factor\:out\:}-9\mathrm{\:from\:}-9x-36\mathrm{:\quad }-9\left(x+4\right)\\=x\left(x+4\right)-9\left(x+4\right)\\\mathrm{Factor\:out\:common\:term\:}x+4\\=\left(x+4\right)\left(x-9\right)[/tex]

Answer:

15

Step-by-step explanation:

Let's call Leah's age l and Rachel's age r. We can write:

l = 3r - 2 (1)

l + 3 = 2(r + 3) + 7 (2)

Substituting (1) into (2) we get:

(3r - 2) + 3 = 2(r + 3) + 7

3r + 1 = 2r + 13

r = 12

In 3 years Rachel will be 12 + 3 = 15 years old.

Answer:

5

Step-by-step explanation:

t(1) = [tex]1^{2} + 4 = 5[/tex]

Answer:

54 · 0.45

Step-by-step explanation:

This expression will give you 45% of 54, since 54 will be multiplied by the decimal equivalent to 45%

Answer:

0.45 · 54

Step-by-step explanation:

In math, 45% is equal to 0.45, because percents are out of a hundre. ’of’ is just another way of putting a multiplicative sign, so it would be 0.45 · 54

Answer:

99,7 % of all values will be in the interval ( -2 ; 34)

Step-by-step explanation:

Empirical Rule for the normal distribution with mean X,  implies that the intervals :

X ± σ             will contain  68 % of all values

X ± 2σ           will contain  95 % of all values

X ± 3σ           will contain  99,7 % of all values

Therefore in the interval    X  - 3σ   ;   X + 3σ

X - 3*6    =  X  -18  =  16 - 18 = -2

And

X + 3*6  = X + 18   = 16 + 18 = 34

99,7 % of all values will be in the interval ( -2 ; 34)

Answer:

Yes. The graph of the parent function has been dilated by a scale factor other than 1.

Step-by-step explanation:

Let the parent function of the absolute value function is,

f(x) = |x|

This function passes through (0, 0) and slope = 1 or -1.

After transformation vertex (0, 0) becomes (-2, 3) and a point through which this function passes through is (-1, 0)

Slope of the function = [tex]\frac{3-0}{-2+1}[/tex]

                                   = -3

Since slope of the transformed function is less than the parent function. (-3 < -1)

Therefore, parent function will be dilated by a scale factor other than 1.

Answer:

edge answer

Step-by-step explanation:

Yes, the graph has been dilated.

Using the standard form of the equation, substitute in the values: h = –2, k = 3, x = –1, and y = 0.

Solve the equation to get a = –3.

Graphically, the parent function follows the pattern of right 1, up 1. Moving 1 unit to the right from the vertex, you can move down 3 units to get to the point (–1, 0), so it has been horizontally compressed.

Hi there u have not given us the figure please correct the answer and I will send my answer.Is it a cylinder cuboid cube or?

Answer:

dA/dt = k1(M-A) - k2(A)

Step-by-step explanation:

If M denote the total amount of the subject and A is the amount memorized, the amount that is left to be memorized is (M-A)

Then, we can write the sentence "the rate at which a subject is memorized is assumed to be proportional to the amount that is left to be memorized" as:

Rate Memorized = k1(M-A)

Where k1 is the constant of proportionality for the rate at which material is memorized.

At the same way, we can write the sentence: "the rate at which material is forgotten is proportional to the amount memorized" as:

Rate forgotten = k2(A)

Where k2 is the constant of proportionality for the rate at which material is forgotten.

Finally, the differential equation for the amount A(t) is equal to:

dA/dt = Rate Memorized - Rate Forgotten

dA/dt = k1(M-A)  - k2(A)

Answer:

Lucy's percentage profit = 33.33% based on Sales Value

and 50% based on Cost.

Step-by-step explanation:

a) Calculations:

7kg = 7,000g of nuts

Cost of 7,000g = £10

350g = 20 bags (7,000/350)

Sales value = £15 (20 x 75p)

Profit = Sales value minus Cost

Profit = £5 (£15 - £10)

Profit percentage based on sales = Profit/Sales x 100 = 5/15 x 100 = 33.33%

Profit percentage based on cost = Profit/Cost x 100 = 5/10 x 100 = 50%

b) Profit is the excess of sales over cost.  There are two ways to express it in percentages.  Profit can be expressed as a percentage of the cost (Markup).  It can also be expressed as the percentage of the sales value (Margin).

Answer:

Step-by-step explanation:

  The recommended number of volunteers is five (5)

  Since the the distance of the race is 5km,

and the safety committees recommends 1 volunteer per kilometre.

Hence ten (10) volunteers is more than enough

Answer:

96

Step-by-step explanation:

Exterior angles add up to 360

360 - 134-130 = 96

x = 96

Answer:

$34,816.60

Step-by-step explanation:

The computation of the maximum amount of cash should willing to pay for the copy machine by using the present value is shown below:

Present value is

[tex]= Incremental\ cash\ flows \times PVIFA\ factor[/tex]

where,

Incremental cash flows is $14,000 per year

Discount rate is 10%

And, the number of years is three years

PVIFA factor for 10% at 3 years is 2.4869

Refer to the PVIFA factor table

Now placing these values to the above formula

So, the present value is

[tex]= \$14,000 \times 2.4869[/tex]

= $34,816.60

Answer:

The table shows the heights of the winners and runner-ups of 8 presidential elections. Find the line of regression that predicts the runner-up's height given the winner's height. Determine if the regression line is a good predictor of heights for the winners and runner-ups of presidential elections.

Winner: 69.5; 73; 73; 74; 74.5; 74.5; 71; 71

Runner-Up: 72; 69.5; 70; 68; 74; 74; 73; 76

a. y = 95.4 - 0.321x; no, because the r-value is low.***

b. y = -0.321 + 95.4x; no, because the r-value is low.

The regression line is NOT a good predictor of heights for the winners and runner-ups of presidential elections because the r-value is low

Given that:

The data given for the winners are:

69.5; 73; 73; 74; 74.5; 74.5; 71; 71

The runners up are:

72; 69.5; 70; 68; 74; 74; 73; 76

With this, we can see that a. y = 95.4 - 0.321x; no, because the r-value is low.

Read more about lines of regression here:

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Answer:

Step-by-step explanation:

Let X denote the dimension of the part after grinding

X has normal distribution with standard deviation [tex]\sigma=0.002 in[/tex]

Let the mean of X be denoted by [tex]\mu[/tex]

there is an upper specification of 3.150 in. on a dimension of a certain part after grinding.

We desire to have no more than 3% of the parts fail to meet specifications.

We have to find the maximum [tex]\mu[/tex] such that can be used if this 3% requirement is to be meet

[tex]\Rightarrow P(\frac{X- \mu}{\sigma} <\frac{3.15- \mu}{\sigma} )\leq 0.03\\\\ \Rightarrow P(Z <\frac{3.15- \mu}{\sigma} )\leq 0.03\\\\ \Rightarrow P(Z <\frac{3.15- \mu}{0.002} )\leq 0.03[/tex]

We know from the Standard normal tables that

[tex]P(Z\leq -1.87)=0.0307\\\\P(Z\leq -1.88)=0.0300\\\\P(Z\leq -1.89)=0.0293[/tex]

So, the value of Z consistent with the required condition is approximately -1.88

Thus we have

[tex]\frac{3.15- \mu}{0.002} =-1.88\\\\\Rrightarrow \mu =1.88\times0.002+3.15\\\\=3.15[/tex]

Answer:

you could buy a pair of shoes and a belt still have 95 dollars to spend

Answer:

To find the second-shortest side we'll multiply 9 by √3 which is 9√3 and for the hypotenuse we'll do 9 * 2 = 18.

Answer:

75%

Step-by-step explanation:

Divide 3 by 4 to get 0.75. Round to 75%.

Answer:

75%

Step-by-step explanation:

Divide 3 by 4 to get 0.75 and multiply by 100 to convert from a decimal to a percentage. The answer will be 75%.

Hope this helps!!! PLZ MARK BRAINLIEST!!!

Answer:

When we expand we get -9 - 33i + 30i². Since i² = -1 we can write this as -9 - 33i + 30 * (-1) = -9 - 33i - 30 = -33i - 39.

Answer:

-21-33i

Step-by-step explanation:

(-3+6i)(-3+5i)=9-15i-18i+30i²=9-33i+30(-1)=-21-33i

Answer:

The percentage of employees with 8 or more years at the company that reported that email is their preferred method of communication is 30.48%. I suppose there was a small typing mistake in option B.

Step-by-step explanation:

The proportion is the number of desired outcomes divided by the number of total outcomes.

The percentage is the proportion multiplied by 100.

In this question:

210 employees with 8 of more year.

Of those, 64 have the email as their preferred method of communication.

64/210 = 0.3048

0.3048*100 = 30.48%

The percentage of employees with 8 or more years at the company that reported that email is their preferred method of communication is 30.48%. I suppose there was a small typing mistake in option B.

In this exercise we have to use the percentage knowledge to calculate the number of employees of the company over the years, in this way we find that this corresponds to:

The percentage of employees with 8 or more years at the company that reported that email is their preferred method of communication is 67,9%. Is D.

They are using the data informed in the text, we have:

So doing the percentage calculation we have that;

[tex]210-64=146\\(146*100)/210=67,19\%[/tex]

See more about Percentage at brainly.com/question/8011401

Answer:

66.67%

Step-by-step explanation:

They do not say that I estimate a value of 350 chips but in reality there were 210 chips in total, we have that the error formula is:

Percentage error (%) = (estimated value - actual value) / actual value × 100 (in absolute value)

replacing:

Percentage error (%) = | 350 - 210 | / 210 × 100

Percentage error (%) = 140/210 * 100

Percentage error (%) = 66.67

Which means that the percentage error is 66.67%

Answer: c) ABCDA, $960

Step-by-step explanation:

The nearest Neighbor Algorithm states to choose the next vertex based only on the weights of the neighbor of that vertex.

Starting at A: Options are B = 220, C = 240, D = 310

Choose B because it has the smallest value.

From B: Options are C = 200, D = 210

Choose C because it has the smallest value.

From C: There is only one option --> D = 230 (we cannot choose A because it was our starting point and we haven't touched every vertex, yet).

From D: We touched all of the vertices so return to the starting point, A = 310

A → B → C → D → A --> 220 + 200 + 230 + 310 = 960

Notice that if we looked at the entire circuit first, this is NOT the optimum path. But this is the result using the Nearest Neighbor Algorithm.

Answer:

Answer choice 3

Step-by-step explanation:

Option 3 is correct one

∠TQS ≅ ∠RSQ

⇒ ΔTQS ≅ ΔRSQ

⇒ QR≅ST and QT≅RS

QRST is parallelogram by definition

Answer:

Option 3

Step-by-step explanation:

Angle TQS is congruent to angle RSQ and can be proved by alternating interior angle theorem.

Triangle TQS is congruent to triangle RSQ.

Line QR is congruent to line ST.

Line QT is congruent to line RS.

Answer:

600 cubic feet of water

Step-by-step explanation:

If the pool is filled 4 feet and the pool is 5 feet deep, that leaves 1 foot of depth left to fill. This makes the volume equation 30 x 20 x 1 which equals 600.

Answer:

x>4/3 and x<1

Step-by-step explanation:

8x-4 < -12

8x<-12+4

x<8/8

x<1

8x+7> 23

8x>23-7

x>12/8

simplify : x>4/3

Question:

A 5-card hand is dealt from a perfectly shuffled deck of playing cards.

What is the probability that the hand is a two of a kind?

A two of a kind has two cards of the same rank (called the pair). Among the remaining three cards, not in the pair, no two have the same rank and none of them have the same rank as the pair. For example, {4♠, 4♦, J♠, K♣, 8♥} is a two of a kind.

Answer:

P(two of a kind) = 42.3%

Step-by-step explanation:

The probability that the hand is a two of a kind is given by

P(two of a kind) = No. of ways to produce two of a kind/Total no. of ways to deal 5-hand cards

There are total 52 cards in a standard deck of playing cards.

Total number of ways to deal 5-card hand is given by

Total number of ways = ₅₂C₅

Total number of ways = 2595960

So there are 2595960 different ways of dealing 5-card hands

Now we will find out the number of ways to produce two of a kind.

The number of ways to select the rank of two matching cards is given by

Rank of matching cards = ₁₃C₁ = 13

Since the matching cards must be of same rank.

The number of ways to select the rank of remaining 3 cards is given by

Rank of remaining 3 cards = ₁₂C₃ = 220

Since the remaining ranks are now 12.

The number of ways to select the suits of two matching cards is given by

Suits of two matching cards = ₄C₂ = 6

The number of ways to select the suits of 1st non-matching card is given by

Suits of 1st non-matching card = ₄C₁ = 4

The number of ways to select the suits of 2nd non-matching card is given by

Suits of 2nd non-matching card = ₄C₁ = 4

The number of ways to select the suits of 3rd non-matching card is given by

Suits of 3rd non-matching card = ₄C₁ = 4

Finally, the probability is

P(two of a kind) = No. of ways to produce two of a kind/Total no. of ways to deal 5-hand cards

P(two of a kind) = (₁₃C₁ × ₁₂C₃ × ₄C₂ × ₄C₁ × ₄C₁ × ₄C₁) / ₅₂C₅

P(two of a kind) = (13 × 220 × 6 × 4 × 4 × 4) / 2595960

P(two of a kind) = 1098240/2595960

P(two of a kind) = 0.423

P(two of a kind) = 42.3%

Answer:

The break-even point is when x is equal to 3.75

Step-by-step explanation:

At the break-even point, total cost function is equal to the total revenue function. In that regard, break-even is when;

C = 12x + 30 is equal to R = 20x.

thus, 12x + 30 = 20x

then, 12x - 12x + 30 = 20x - 12x

therefore, 30 = 8x

then, 30/8 = 8x/8

finally, x = 15/4 or 3.75

A stuffed animal business has a total cost of production C=12x+30 and a revenue function R=20x, the Break even point is (3.75,75)

Given :

A stuffed animal business has a total cost of production C=12x+30 and a revenue function R=20x.

Break even point occurs when revenue = cost

R=C

Replace the expression and solve for x

[tex]R=C\\20x=12x+30\\20x-12x=30\\8x=30\\divide \; by \; 8\\x=\frac{15}{4}\\x=3.75[/tex]

Now we find out y using Revenue

[tex]R= 20x\\R=20(3.75)\\R=75[/tex]

So y is 75

Break even point is (3.75,75)

Learn more : brainly.com/question/15281855

Answer:

Step-by-step explanation:

the event of drawing a spade card

Answer:

a) The cumulative distribution function would be given by:

x         0         1       2        3      4      5

F(X)  0.05   0.15  0.30  0.55  0.9    1

b) [tex] P(1 \leq X \leq 4) = F(4) -F(0) =0.9-0.05 = 0.85 [/tex]

And replacing we got:

[tex]P(1 \leq X \leq 4) =0.85[/tex]

Step-by-step explanation:

For this case we have the following probability distribution function given:

x        0       1       2       3       4       5

P(X)  0.05  0.1  0.15  0.25  0.35  0.1

We satisfy the conditions in order to have a probability distribution:

1) [tex] \sum_{i=1}^n P(X_i)=1[/tex]

2) [tex] P(X_i) \geq 0, i=1,2,..,n[/tex]

Part a

The cumulative distribution function would be given by:

x         0         1       2        3      4      5

F(X)  0.05   0.15  0.30  0.55  0.9    1

Part b

For this case we want to find this probability:

[tex] P(1 \leq X \leq 4) = F(4) -F(0) =0.9-0.05 = 0.85 [/tex]

And replacing we got:

[tex]P(1 \leq X \leq 4) =0.85[/tex]

Answer: Option 3.

Step-by-step explanation:

A rotation around the side AB, means that the side AB remains fixed in the place, and we rotate the vertex C creating in this way a solid figure.

Now, this figure will Create a cone with height AB, and where the radius of the base will be BC. (Where AB is the length of the side AB in the original triangle, and BC is the length of the side BC on the original triangle)

The correct option is option 3.