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2 years ago

Geometry: The base of a triangle is 12 in. Its height is (x + 6) in. Its area is no more

Mathematics

1 answer:

larisa [96]2 years ago

3 0

Answer:

The area of a triangle= bh/2. Substitute

12(x+6)/2 ≤ 72

12(1/2x+3) ≤ 72

6x+36 ≤ 72

6x ≤ 72-36

6x ≤ 36 Divide both sides by 6

x ≤ 6

x|x ≤6 (read: x, where x is equal or smaller than 6)

Step-by-step explanation:

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The Henley's took out a loan for $195,000 to purchase a home. At a 4.3% interest rate

ella [17]

Interest paid after 30 years is $494,546.99.

Solution:

Principal (P) = $195,000

Interest rate (r) = 4.3%

Time (t) = 30 years

n = number of times interest calculated per year

n = 1

Compound interest formula:

$$A=P\left(1+\frac{r}{n}\right)^{n t}$

where A is the final amount

$$A=195000\left(1+\frac{4.3\%}{1}\right)^{1\times 30}$

$$A=195000\left(1+\frac{4.3}{100}\right)^{30}$

$$A=195000\left(\frac{100+4.3}{100}\right)^{30}$

$$A=195000\left(\frac{104.3}{100}\right)^{30}$

A = 689546.99

Interest = Amount - Principal

= 689546.99 - 195000

= 494546.99

Interest paid after 30 years is $494,546.99.

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3 years ago

The discriminant of a quadratic equation is negative. One solution is 3+4i . What is the other solution?

Fiesta28 [93]

I believe the correct answer from the choices listed above is option B. <span>The discriminant of a quadratic equation is negative. One solution is 3+4i . The other would be 3-4i. Hope this answers the question. Have a nice day.</span>

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3 years ago

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For a segment of a radio show, a disc jockey can play 10 records. there are 14 records to select from, in how many ways can the

mixas84 [53]

The formula of combination is

$nCr= \frac{n!}{(n-r)!r!}$

We have $n=14$ and $r=10$

$14C10= \frac{14!}{(14-10)!10!} = 1001$

Hence, there are 1001 ways of arranging 10 records from 14 records

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3 years ago

A right triangle has a perimeter of 24 cm and a hypotenuse of 10 cm. Find the length of the other two sides.

jekas [21]

Answer:

One of the sides is 6 cm and the other is 8 cm

Step-by-step explanation:

Let's call the unknown sides a and b. From the perimeter information (24 cm) we have:

a + b + hypotenuse = 24

a + b + 10 = 24

a + b = 14

b = 14 - a

So now we can right the Pythagorean theorem as follows:

$a^2 + b^2 = hypotenuse^2\\a^2 + (14-a)^2=10^2\\a^2+ 14^2-28\,a+a^2=100\\2\,a^2-28\,a +96=0\\2\,(a^2-14\,a+48)=0\\2\,(a^2-6\,a-8\,a+48)=0\\2(a\,(a-6)-8\,(a-6))=0\\2\,(a-6)\,(a-8)=0$

and from this expression in factor form to be zero a must be 6 or a must be 8.

Therefore the solutions are a = 6 (and therefore b = 14 - 6 = 8)

or a = 8 (and therefore b = 14 - 8 = 6)

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3 years ago

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