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3 years ago

Find the simple interest on a $340 loan at a 12% annual interest rate for 5 years *

Mathematics

2 answers:

Lady_Fox [76]3 years ago

5 0

Answer: $204

Step-by-step explanation:

Formular for simple interest (I) is: Principal(P) x Rate (R) x Time (T)

From the question, P= $340

R= 12% = 12/100 = 0.12

T= 5 years

Therefore, simple interest (I) =

340 x 0.12 x 5

I = $204

I hope this is clear, please mark as brainliest

Inessa [10]3 years ago

4 0

$340 (principle) *5 (time) *0.12 (rate) =204

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The surface area of the top surface of the water in a circular swimming pool is about 206 square feet. Estimate the radius of th

nataly862011 [7]

Area=pi (radius^2) Plug in numbers. 206=3.14 (r^2) Divide both sides by 3.14 65.61=r^2 Then square root both sides. 8.1ft =r Then round to the nearest foot. r=8ft

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3 years ago

A container holds 24 pints of lemonade. How much is this in gallons?

krok68 [10]

Answer:

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2 years ago

Write as a product 27a^3−(a−b)^3

jarptica [38.1K]

Answer:

(2a +b)·(13a^2 -5ab +b^2)

Step-by-step explanation:

The factorization of the difference of cubes is a standard form:

(p -q)^3 = (p -q)(p^2 +pq +q^2)

Here, you have ...

p = 3a
q = (a-b)

so the factorization is ...

(3a -(a -b))·((3a)^2 +(3a)(a -b) +(a -b)^2) . . . . substitute for p and q

= (2a +b)·(9a^2 +3a^2 -3ab +a^2 -2ab +b^2) . . . . simplify a bit

= (2a +b)·(13a^2 -5ab +b^2) . . . . . . collect terms

6 0

3 years ago

In right △ABC, the altitude CH to the hypotenuse AB intersects angle bisector AL in point D. Find the sides of △ABC if AD = 8 cm

tangare [24]

Answer:

$AC=8\sqrt{3}\ cm\\ \\AB=16\sqrt{3}\ cm\\ \\BC=24\ cm$

Step-by-step explanation:

Consider right triangle ADH ( it is right triangle, because CH is the altitude). In this triangle, the hypotenuse AD = 8 cm and the leg DH = 4 cm. If the leg is half of the hypotenuse, then the opposite to this leg angle is equal to 30°.

By the Pythagorean theorem,

$AD^2=AH^2+DH^2\\ \\8^2=AH^2+4^2\\ \\AH^2=64-16=48\\ \\AH=\sqrt{48}=4\sqrt{3}\ cm$

AL is angle A bisector, then angle A is 60°. Use the angle's bisector property:

$\dfrac{CA}{CD}=\dfrac{AH}{HD}\\ \\\dfrac{CA}{CD}=\dfrac{4\sqrt{3}}{4}=\sqrt{3}\Rightarrow CA=\sqrt{3}CD$

Consider right triangle CAH.By the Pythagorean theorem,

$CA^2=CH^2+AH^2\\ \\(\sqrt{3}CD)^2=(CD+4)^2+(4\sqrt{3})^2\\ \\3CD^2=CD^2+8CD+16+48\\ \\2CD^2-8CD-64=0\\ \\CD^2-4CD-32=0\\ \\D=(-4)^2-4\cdot 1\cdot (-32)=16+128=144\\ \\CD_{1,2}=\dfrac{-(-4)\pm\sqrt{144}}{2\cdot 1}=\dfrac{4\pm 12}{2}=-4,\ 8$

The length cannot be negative, so CD=8 cm and

$CA=\sqrt{3}CD=8\sqrt{3}\ cm$

In right triangle ABC, angle B = 90° - 60° = 30°, leg AC is opposite to 30°, and the hypotenuse AB is twice the leg AC. Hence,

$AB=2CA=16\sqrt{3}\ cm$

By the Pythagorean theorem,

$BC^2=AB^2-AC^2\\ \\BC^2=(16\sqrt{3})^2-(8\sqrt{3})^2=256\cdot 3-64\cdot 3=576\\ \\BC=24\ cm$

3 0

2 years ago

In trapezoid RTUW, V is the midpoint of segment UW, and S is the midpoint of segment RT. Find UT.

andrezito [222]

The line VS is middle line of that trapezoid, so you know that it is

VS= (WR+UT)/2

so we will get that it is:

<span>40= (x^2+2 +2x^2+3)/2
x = 5

Therefore,

x^2 + 2
5^2 + 2
25 +2
27 <----- OPTION 2

Hope this answers the question.</span>

8 0

2 years ago