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3 years ago

Which expression helps you find the length x of a side of a rectangle that has a diagonal of 15 units and a width of 9 units?

2 answers:

6 0

15²-9²= x² use Pythagoras' theorum and square the two smaller sides to get the square of the hypotenuse (the diagonal) then rearrange this to get the above calculation

Setler79 [48]3 years ago

6 0

The diagonal of rectangle is 15 units and a width is 9 units.

Let the length of rectangle is x units.

Relation of sides of rectangle and diagonal

Sum of square of length of side of rectangle is equal to square of length of diagonal.

Using pythagoreous theorem:

$x^2+9^2=15^2$

$x^2=15^2-9^2$

$x^2=(15+9)(15-9)$

$x^2=24\times 6$

$x^2=144$

$x=\sqrt{144}$

$x=12$

Above all are possible expressions to find x.

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Terrence records the numbers of e-mail he receives per day. During one week, he receives 7, 3, 10, 5, 5, 6, and 6 e-mails.

Mazyrski [523]

Answer:

mean:6, median:6, mode:5 and 6,

Step-by-step explanation:

Mean is average, mode, is the number that occurs most frequently, median is the middle number.

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2 years ago

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Need help with this problem!!

Nezavi [6.7K]

Answer:

Area:

4 x 4 = 16

Finding area of semi circle:

4 is your diameter so half of it is your radius which is 2 since half of 4 is 2!

2^2<---your radius being squared = 4

4(radius squared) x 3.14(pi) = 12.56

12.56 divided by 2 since its a semi circle is = 6.28

6.28 + 16 = 22.28 is your area

Perimeter is:

4 + 4 + 4 (all sides of a square are equal therefore one or two given lengths will be all the sides) = 12

Circumference:

Radius is 2,

2(you just always have to multiply this number when finding circumference) x 3.14(pi) x 2(radius), 2 x 3.14 x 2 = 12.56

12.56 divided by 2 = 6.28

6.28 + 12 = 18.28 is your perimeter.

Just a refresh:

Circumference Formula:

2(always use this number when finding circumference) x pi(3.14 or 22/7 depending on what they tell you to use for pi) x radius

Area of a Circle Formula:

Radius squared x pi(3.14 or 22/7 whatever they tell you to use for pi)

Another thing you should remember:

Whenever it gives you 1/4 of a circle or 1/3 or a semi circle or any fraction, REMEMBER TO DIVIDE BY THAT DENOMINATOR TO WHAT YOU GET FROM EITHER CIRCUMFERENCE OR AREA OF A CIRCLE!

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2 years ago

You need a 30-year, fixed-rate mortgage to buy a new home for $225,000. your bank will lend you the money at an apr of 5.5 perce

bulgar [2K]

Loan amount, P = 225000
interest = 5.5%/12 per month
Monthly payment, A = 1000

At the end of 30 years,
Future value of loan (with zero repayment)
F1=225000*(1+.055/12)^(30*12)
=1167162.264

Future value of repayment, A=1000 per month
F2= $\frac{A((1+i)^n-1)}{i}$
= $\frac{1000((1+.055/12)^{360}-1)}{.055/12}$
=913611.893

Therefore balloon payment
= F1-F2
=1167162.264-913611.893
=253550.37 (to the nearest cent)

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2 years ago

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erik [133]

Answer:

X =3

Step-by-step explanation:

X = 3 is the correct answer

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2 years ago

By cutting away identical squares from each corner of a rectangular piece of cardboard and folding up the resulting flaps, an op

lozanna [386]

Answer:

1.81 inch by 8.38 inch by 6.38 inch

Smallest Value=1.81 inch

Largest Value=8.38 inch

Step-by-step explanation:

The cardboard is 12 in. long and 10 in. wide

Let the length of the square cut off=x

Length of the box=12-2x

Width of the box=10-2x

Height of the box=x

Volume of the box=lwh

V=x(12-2x)(10-2x)

The dimensions of the box that will yield maximum volume occurs at the point where the derivative of V=0.

$V^{'}=4\,\left( 30 - 22\,x + 3\,x^{2}\right)$

Thus:

4(30-22x+3x²)=0

Since 4≠0

3x²-22x+30=0

Solving for x using a calculator gives:

x=1.81 or x=5.52

x cannot be 5.52 inch since the width is 10 inch and removing 2(5.52) from the width gives a negative result.

When x=1.81 inch

Length of the box=12-2x=12-2(1.81)=8.38inch

Width of the box=10-2x=10-2(1.81)=6.38 inch

Therefore, the dimensions at which the Volume is maximum are: 1.81 inch by 8.38 inch by 6.38 inch

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2 years ago