x^2=6x+1

1) rewrite the equation by completing the square

2) what are the solutions to the equation?

Answer:

To begin to answer this question, you will want to determine the equation for the volume of a rectangular prism. In this case, the equation is length times width times height or:

V = l * w * h

In the question, you are given several pieces of information that you can then plug into the equation. For example, you know the volume is 21,904 ft3 because they tell you that directly. You also know that the pool is 8 feet deep. I consider the depth to be the same as the height. With that information, you now have the equation:

21,904 ft3 = l * w * (8ft)

You are also told that the length is 2 times the width. Written as an equation, you would say that

l = 2w

Now, you can substitute that 2w for l to get the equation:

21,904 ft3 = (2w) * w * 8ft

We know that when you multiply a variable times itself, you get a squared variable, so 2w * w = 2w2 and that

21,904 ft3 = 2w2 * 8ft

Now, you can solve the equation to find w. At this point, it is easiest to drop the units of feet on the numbers to do the math. As long as all your numbers are in the same units (i.e. feet), you are good to go. Start by dividing each side by 8 to get

2738 = 2w2

Then divide both sides by 2 to get

1369 = w2

Finally, for this portion, take the square root of 1369 to get

w = 37 feet.

But you're not done yet. You know the width, and you know that l = 2w. Plug the value for w (37) into this equation to get the length, which is 74 feet.

The final answer is that the width of the pool is 37 feet and the length is 74 feet.

You can check your answer by plugging the length, width, and height (depth) into the equation for volume to see if you get 21,904ft3.

If you take 8 ft x 37 ft x 74 ft, you get 21,904 ft3 and you know that you answer is correct.

Step-by-step explanation:

Answer:

307.916cm^3

Step-by-step explanation:

[tex]volume \: of \: a \: cone \: = \frac{1}{3}\pi \: r {}^{2} h \\ v = \frac{1}{3} \times 3.142 \times 3.5 {}^{2} \times 24 = 307.916cm {}^{3} [/tex]

Answer:

The first step that we are going to do is to solve the area of the top rectangle.  We are given a width of 15 cm and a length of 25 cm so we can just multiply them against each other to get the area.

[tex]Area = l * w[/tex]

[tex]Area = 25\ cm * 15\ cm[/tex]

[tex]Area = 375\ cm^2[/tex]

The second side that we are going to solve for is the bottom rectangle.  We are given a width of 12 cm and a length of 25 cm so lets just multiply them against each other to get the area.

[tex]Area = l * w[/tex]

[tex]Area = 25\ cm * 12\ cm[/tex]

[tex]Area = 300\ cm^2[/tex]

The next area that we are going to determine is the back rectangle which has a width of 9 cm and a length of 25 cm so lets just multiply them against each other to get the area.

[tex]Area = l * w[/tex]

[tex]Area = 25\ cm * 9\ cm[/tex]

[tex]Area = 225\ cm^2[/tex]

The final area that we have to determine are the side triangles.  After determining the area of one triangle we will have to multiply it by 2 to get the area for both of the triangles.  We are given a base of 12 cm and a height of 9 cm so lets just use the formula to find the area.

[tex]Area = \frac{1}{2}* b*h[/tex]

[tex]Area = \frac{1}{2}* 12\ cm*9\ cm[/tex]

[tex]Area = 54\ cm^2[/tex]

Multiply it by two to get the area for both of the triangles.

[tex]Area = 54\ cm^2 * 2[/tex]

[tex]Area = 108\ cm^2[/tex]

Finally, we are onto the last part which is to add up all of the areas and get the surface area after we combine everything.

[tex]Area_{total}=375\ cm^2 + 300\ cm^2 + 225\ cm^2 + 108\ cm^2[/tex]

[tex]Area_{total}=1008\ cm^2[/tex]

Therefore, our final answer is option B, 1008 [tex]cm^2[/tex]

Hope this helps!

Answer:

10

Step-by-step explanation:

Answer:

sorry but I do know that it is A or B hope this helps.

The rate of change of the given simple index over 1 day is -0.9%.

When something has a constant rate of change, one quantity changes in relation to the other.

Given that;

Stock A opens on Monday with 10000 shares at $5.50 per share.

Stock B opens on Monday with 8000 shares at $6.25 per share.

Stock A opens on Tuesday at $5.80 per share, and stock B opens on Tuesday at $6.65 per share.

Total value of the simple index at Monday is;

= (10000×5.50) + (8000×6.25)

= 55,000 + 50,000

= 105,000

The total value of the simple index at Tuesday is;

= (10000×5.80) + (8000×6.65)

= 58,000 + 53,200

= 111,200

The rate of change of this simple index over 1 day is;

= (111,200-105,000)/(10000-8000) -1

= 6,200/2000 - 1

= 3.1 - 1

= 2.1

Hence, the rate of change of the given simple index over 1 day is -0.9%.

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When Digitalis knows that it'll sell many of the processors, it's expected to make money since there's a higher probability that it's not defective.

Since the processor is sold for $3300 and a profit of $429 is made, the selling price will be:

= $3300 - $429

= $2871

In this case, there's a 13% chance that it's defective and 87% that's it's not defective. Therefore, it's expected to make money since there's a higher probability that it's not defective.

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→ The formula to convert a fraction to a decimal is ( "a ÷ b" ) .

→ where ( a ) is the NUMERATOR and ( b ) is the DENOMINATOR of the fraction .

The fraction to decimal formula states that:

• you just need to divide the numerator by denominator to get the decimal equivalent of the fraction ..

• convert 25/100 to decimal ?

→ Just divide 25 by 100 = 0.25

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Step-by-step explanation:

to convert a fraction to decimal ,well just divide numerator ....by the denominator

we 'll divide 1 by 4.1 divided by 4 equal to zero to keep dividing we ' ll add a decimal point and a zero after 1.

Answer:

t = 8 days i saw it on a website if i recall its the answer

Step-by-step explanation:

speed = distance/time

4 P = 1 House / 10 Days

P = 1 House / 40 Days

Let T = Time it takes for five painters.

5 P = 1 House / T

5(1/40) = 1 /T

1/8 = 1 /T

T = 8 Days

Answer :

[tex]\boxed{D) \sqrt{119} \: cm}[/tex]

Solution :

In the above figure, the line that is drawn from the centre of the given circle to the targent PQ is perpendicular to PQ.

And So, OP ⊥ PQ

Using Pythagoras theorem in triangle ΔOPQ we get ,

[tex]\Longrightarrow\: OQ^2 = OP^2 + PQ^2[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

[tex]\Longrightarrow\: (12)^2 = 5^2+PQ^2[/tex]

[tex]\: \: \: \: \: \: \: \: \: \: \: \: [/tex]

[tex]\Longrightarrow\: PQ^2 = 144-25[/tex]

[tex]\: \: \: \: \: \: \: \: \: \: \: \: [/tex]

[tex]\Longrightarrow\: PQ^2 = 119[/tex]

[tex]\: \: \: \: \: \: \: \: \: \: \: \: [/tex]

[tex]\Longrightarrow\: PQ = \sqrt{119} [/tex]

[tex]\: \: \: \: \: \: \: \: \: \: \: \: [/tex]

So, option D) √119 cm is the length of PQ.

We will see that there are 284.2 kilograms of helium inside the ballon.

In this problem, we know the volume of helium and the density of helium.

Remember that:

density = mass/volume.

Then we can write:

mass = density*volume.

Replacing the two in the right, we get:

mass = (1,592 m³)*( 0.1785 kg/m³) = 284.2kg

Then we can conclude that there are 284.2 kilograms of helium in the ballon.

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The domain of the given relation will be { - 1,2,3,4}.

The domain of the function is defined as the set of all the possible values of the function.

So here we have the ordered pairs given as:-

{ (-1,- 6), (2, - 6), (3,5), (4,0), (4,7)}

Here the possible values for the input of the functions are { - 1,2,3,4}.

Therefore the domain of the given relation will be { - 1,2,3,4}.

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Answer:

62

Step-by-step explanation:

all you do for this is take 496 and divide it by 8, which gives you 62, if you still need help explain I can reply with a step by step of showing how to divide

Step-by-step explanation:

it seams like this question is wrong

Answer:

B

Step-by-step explanation:

You are going to add 9 to 27 because you are counting by nines on the bottom.

Answer:

16.97

Step-by-step explanation:

Therefore b= 16.97

Answer: 64 m^3

Step-by-step explanation:

V=1/3*a^2*h

V = 1/3*64*3

V=64 m^3

Answer:

64 m³

Step-by-step explanation:

Formula

[tex]\textsf{Volume of a square based pyramid}=\dfrac{1}{3}a^2h[/tex]

where:

Given:

Substituting the given values into the formula:

[tex]\begin{aligned}\implies \textsf{Volume}& =\dfrac{1}{3} \cdot 8^2 \cdot 3\\\\& = \dfrac{3}{3} \cdot 64\\\\& = 1 \cdot 64\\\\& = 64\:\sf m^3\end{aligned}[/tex]

Answer:  [tex]y = 850(0.943)^t[/tex]

Reason:

The exponential of the form [tex]y = a*b^x[/tex] has 'a' as the initial term and b as the growth or decay factor.

a = 850 is the starting amount

b = 1 + r = 1 + (-0.057) = 0.943 is the decay factor

If the sample loses 5.7% of its mass each year, then it keeps the remaining 94.3% of it.

Answer:

5 given as -1 and 8 positive 8 cross by axis

Put u=17

Answer:

59.5.

Step-by-step explanation:

h = 3.5u

When u = 17,

h = 3.5*17

= 59.5

Answer:

Slope is 3.

Step-by-step explanation:

Slope formula

[tex]m = \frac{\text{rise}}{\text{run}} = \frac{\text{change in y}}{\text{change in x}} = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

m ... slope

Two points on the line are (x1, y1) and (x2, y2).

Now let's insert the coordinates of points (6,9) and (4,3) in the slope formula.

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}\\\\m = \frac{9 - 3}{6 - 4}\\\\m = \frac{6}{2}\\\\m = 3[/tex]

You could also do [tex]m = \frac{3-9}{4-6}[/tex] and would get the same result.

Since the customers can choose among 5 drinks, 4 main dishes, and 5 sides. there 100 different combo meals are possible.

Since order is not important we use combination to solve the problem

This is the number of ways in which x objects can be selected out of n objects. It is given mathematically as ⁿCₓ = n!/x!(n - x)!

Now, given that the customer can choose among 5 drinks, 4 main dishes, and 5 sides.

There are ⁵C₁ ways of choosing the drinks.

So, ⁵C₁ = 5!/1!(5 - 1)!

= 5!/1!/4!

= 5

There are ⁴C₁ ways of choosing the main dishes.

So, ⁴C₁ = 4!/1!(4 - 1)!

= 4!/1!/3!

= 4

There are ⁵C₁ ways of choosing the sides.

So, ⁵C₁ = 5!/1!(5 - 1)!

= 5!/1!/4!

= 5

So, total number of ways of choosing the combo meals is

⁵C₁ × ⁴C₁ × ⁵C₁ = 5 × 4 × 5

= 100 ways.

So, there 100 different combo meals are possible.

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Answer: The answer is 100

Step-by-step explanation:

Answer:

12.025

Step-by-step explanation:

h=v/(π*r square)

divide the volume of a cylinder by the amount of the radius squared multiplied by π(pi)

340÷(π×3square)

giving you 12.025

(original in calculator=12.02504014)

but it is 12.025

Answer:

√645^3=16,380.9. Mathematically correct

Answer:

The mean of the data is 70

Step-by-step explanation:

Hope this helps you! :D

Answer:

70

Step-by-step explanation:

Mean-

Add all the numbers to the total = 350

Divide by the amount of numbers (125, 15, 30, 110,70 = 5 numbers)

350/5 = 70

Answer:

B) [tex]f(x)=-3(x+1)^2+2[/tex]

Step-by-step explanation:

Notice that the graph of the parabola opens downward. This tells us that the leading coefficient of the function must be negative. Hence, we can rule out answers A and D.

Also, notice that our vertex is [tex](h,k)\rightarrow(-1,2)[/tex], which when we plug into vertex form, we get [tex]y=a(x-h)^2+k\rightarrow y=a(x-(-1))^2+2\rightarrow y=a(x+1)^2+2[/tex].

This means that B is the correct function that represents the graph.

Answer:

15.7 lbs (please mark brainliest)

Step-by-step explanation:

2.6+x+x=34

2x=31.4

x=15.7

Answer: 14.4

Step-by-step explanation: I took 34 and divided it by 2 then subtracted 2.6 from 17 which gave me 14.4. If it's wrong, sorry.

Apple be A and blueberries be B

So

As per Venn diagram

#1

P(A)=12/24

P(B)=7/24

Add

#2.

n(AUB)

E=8+16=24

P(AUB)=16/24=2/3

Answer:

[tex]\sf a) \quad P(contains\:apple)+P(contains\:blueberry)=\dfrac{5}{6}[/tex]

[tex]\sf b) \quad P(contains\:apple\:or\:blueberry)=\dfrac{11}{15}[/tex]

c)    Not mutually exclusive events

Step-by-step explanation:

From inspection of the Venn diagram:

[tex]\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}[/tex]

Let A = contains apple

Let B = contains blueberry

[tex]\implies\sf P(A)=\dfrac{15}{30}=\dfrac{1}{2}[/tex]

[tex]\implies\sf P(B)=\dfrac{10}{30}=\dfrac{1}{3}[/tex]

Part (a)

[tex]\begin{aligned} \implies \sf P(A)+P(B) & =\sf \dfrac{1}{2}+\dfrac{1}{3}\\\\ & = \sf \dfrac{3}{6}+\dfrac{2}{6}\\\\ & = \sf \dfrac{5}{6}\end{aligned}[/tex]

Part (b)

[tex]\textsf{Addition Law}: \quad\sf P(A\:or\: B) = P(A)+P(B)-P(A\:and\:B)[/tex]

Given:

[tex]\sf P(A)+P(B)=\dfrac{5}{6} \quad \textsf{(from part a)}[/tex]

[tex]\sf P(A\:and\:B)=\dfrac{3}{30}\quad \textsf{(where the circles overlap)}[/tex]

[tex]\begin{aligned}\implies \sf \sf P(A\:or\: B) &= \sf P(A)+P(B)-P(A\:and\:B)\\\\& =\sf \dfrac{5}{6}-\dfrac{3}{30}\\\\ & =\sf \dfrac{25}{30}-\dfrac{3}{30}\\\\ & =\sf \dfrac{22}{30}\\\\ & = \sf \dfrac{11}{15}\end{aligned}[/tex]

Or, we can simply read P(contains apple or blueberry) from the Venn diagram.  

P(A or B) is the total of the numbers inside the circles divided by the total number of smoothies:

[tex]\sf P(A\:or\:B) = \dfrac{12+3+7}{30}=\dfrac{22}{30}=\dfrac{11}{15}[/tex]

Part (c)

For two events, A and B, where A and B are mutually exclusive:

[tex]\sf P(A \: or \: B)=P(A)+P(B)[/tex]

Given:

[tex]\sf P(A)+P(B)=\dfrac{5}{6} \quad \textsf{(from part a)}[/tex]

[tex]\sf P(A\:or\:B)=\dfrac{11}{15} \quad \textsf{(from part b)}[/tex]

[tex]\sf As\:\dfrac{11}{15}\neq \dfrac{5}{6} \implies P(A \: or \: B)\neq P(A)+P(B)[/tex]

Therefore, choosing a smoothie containing apple and choosing a smoothie containing blueberry are NOT mutually exclusive events.