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2 years ago

Finish the polynomial by adding one number to make it a perfect square x^2+18x+

Mathematics

1 answer:

dsp732 years ago

6 0

Answer:

Step-by-step explanation:

${x}^{2} + 18x + {(( \frac{1}{2})(18)) }^{2}$

${x}^{2} + 18x + {9}^{2}$

${x}^{2} + 18x + 81$

${(x + 9)}^{2}$

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Mia uses 1/5 of a bag of gravel in the morning and 11/12 of a bag in the afternoon and how much gravel does she use in one day

wariber [46]

Answer:

She used 67/60 of a bag of gravel in one day.

Step-by-step explanation:

We must get a common denominator so we can add the two fractions.

Let's use 60!

1/5 = 12/60

11/12 = 55/60

Now we can add and get 67/60!

She used 67/60 of a bag of gravel in one day.

3 0

3 years ago

How long does it take for an investment to quadruple in value if it is invested at 11% compounded

defon

Let's assume we have $100 and an interest rate of 7%. For the $100 to quadruple it means that the future value would be $400. Thus, because we are talking about compounding daily we will set us the equation as follows:

100 * (1+1.07)x = 400

Then we will take 400 and divide it by 100 getting:

1.07X = 4

Now we have encountered a problem where we do not know exponent, so we will use logarithm to calculate such and transform our equation to: Log1.07(4)=X

Using our calculator we will find that it takes about 20.4895 days to quadruple the money invested under 7% interest rate compounded daily.

2nd: Using the same $100 but with the rate of 5.5% compounded continuously we will be using A=PERT formula

where:

P (principal) is equal to hypothetical $100

E (e) is a mathematical constant, which is approximately 2.718

R (rate) is the interest rate, in our case it is 5.5%

T (time) is the time required for money to grow

A (amount) is the final amount desired, which is 4 times larger of $100, thus $400

We have the following:

400 = 100 * e0.055t

400/100 = e0.055t

4 = e0.055t

Then we will apply natural log to both sides of the equations and get the following:

ln(4) = ln(e0.055t)

Since e is the base of ln(x) the equation simplifies to:

ln(4) = 0.055t

Using the calculator to find ln(4) we are getting:

1.38629 = 0.055t

Lastly find t

t = 1.38629/0.055

t = 25.20535202

Plug the answers back to the original equation to verify the answers.

1st part of the question answer: t = 20.4895

2nd part of the question answer: t = 25.20535202

3 0

3 years ago

Using the scale 1/2 inch = 100 miles, figure out the number

Wittaler [7]

Answer:

50 miles

Step-by-step explanation:

Multiply the given scale numbers by 1/2 to find your answer:

1/2 in = 100 mi

(1/2)(1/2 in) = (1/2)(100 mi) . . . . multiply the ratio values by 1/2

1/4 in = 50 mi

5 0

2 years ago

Use the information to answer the questions.

Anna71 [15]

Answer:

Part 1) The length of two sides and the measure of the included angle (Side-Angle-Side)

Part 2) $b^2=a^2+c^2-2(a)(c)cos(B)$

Part 3) $b=11.6\ in$

Step-by-step explanation:

we have

In the triangle ABC

$a=11\ in\\c=9\ in\\B=70^o$

Part 1) Which information about the triangle is given?

In this problem we have the length of two sides and the measure of the included angle (Side-Angle-Side)

see the attached figure to better understand the problem

Part 2) Which formula can you use ti find b?

I can use the law of cosines

$b^2=a^2+c^2-2(a)(c)cos(B)$

we have

$a=11\ in\\c=9\ in\\B=70^o$

substitute the given values

$b^2=11^2+9^2-2(11)(9)cos(70^o)$

$b^2=202-67.72$

$b=11.59\ in$

Part 3) What is b, rounded to the nearest tenth?

Remember that

To Round a number

a) Decide which is the last digit to keep

b) Leave it the same if the next digit is less than $5$ (this is called rounding down)

c) But increase it by $1$ if the next digit is $5$ or more (this is called rounding up)

In this problem we have

$11.59\ in$

We want to keep the digit $5$

The next digit is $9$ which is 5 or more, so increase the "5" by 1 to "6"

therefore

$b=11.6\ in$

4 0

3 years ago

Write an expression for the sequence of operations described below.

Aleks [24]

Answer:

g/(2 x 3)

Step-by-step explanation:

Your expression will be:

-Double 3 = multiply 3 by 2

-Divide g by the result (2 × 3)

g/(2 × 3)

6 0

3 years ago

Read 2 more answers