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Vilka [71]
2 years ago
9

N JKL, mJ = 90, mK = 30, and mL = 60. Which of the following statements about JKL are true?

Mathematics
1 answer:
Leya [2.2K]2 years ago
3 0
KL=2*JL
I tried to find the rest of the question online, and I'm not sure if radicals couldn't show up or something, but attached is an image of the rules for a 30-60-90 triangle, so hopefully this helps.

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Laura owes $18,000 on her student loans. The interest rate on the bank loan is 2.5% and the interest rate on the federal loan is
Llana [10]

Answer:

The principal of the bank loan is $4,000

The principal of the federal lone is $14,000

Step-by-step explanation:

* Lets explain how to solve the problem

- Laura owes $18,000 on her student loans

- The interest rate on the bank loan is 2.5%

- The interest rate on the federal loan is 6.9%

- The total amount of interest she paid last year was $1,066

* Assume that the principle of the bank loan is $x and The principal of

 the federal loan is $y

∵ Her loan is 18,000

∴ x + y = 18,000 ⇒ (1)

- The interest is I = PRT, where P is the principal, R is the rate of interest

  in decimal ant is the time

# <u><em>The bank lone</em></u>

∵ P = $x

∵ R = 2.5/100 = 0.025

∵ T = 1

∴ <em>The interest of the bank lone</em> = x(0.025)(1) = <em>0.025 x</em>

# <u><em>The federal lone</em></u>

∵ P = $y

∵ R = 6.9/100 = 0.069

∵ T = 1

∴ <em>The interest of the federal lone</em> = 9(0.069)(1) = <em>0.069 y</em>

- The total interest is the sum of the interest of the bank lone and the

  interest of the federal loan

∵ The total interest is $1,066

∴ 0.025 x + 0.069 y = 1,066 ⇒ (2)

* We have system of equations

- Multiply equation (1) by -0.025 to eliminate x

∴ -0.025 x - 0.025 y = -450 ⇒ (3)

- Add equations (2) and (3)

∴ 0.044 y = 616

- Divide both sides by 0.044

∴ y = 14,000

- Substitute value of y in equation (1) to find x

∴ x + 14000 = 18000

- Subtract 18000 from both sides

∴ x = 4000

∵ x represents the principal of the bake loan and y represents the

  principal of the federal lone

* The principal of the bank loan is $4,000

* The principal of the federal lone is $14,000

3 0
2 years ago
a ball is thrown straight up from the top of a tower that is 280 ft high with an initial velocity of 48 ft/s . the height of the
poizon [28]
First find the time that the ball is level with the top of the building on its descent. You can do this by  solving 280 = -16^2 + 48t + 280 for t. This gives t = 3 seconds . 
Then when the ball reaches the ground the  time t is obtained by solving 0 = -16t^2 + 48t + 280  This gives t = 5.94 seconds.
Answer in interval notation is  (3, 5.94].
3 0
2 years ago
Read 2 more answers
A machine shop produces heavy duty high endurance 20-inch rods that are meant for use in a variety of military grade equipment.
QveST [7]

Answer:

The probability that a defective rod can be salvaged = 0.50

Step-by-step explanation:

Given that:

A machine shop produces heavy duty high endurance 20-inch rods

On occasion, the machine malfunctions and produces a groove or a chisel cut mark somewhere on the rod.

If such defective rods can be cut so that there is at least 15 consecutive inches without a groove.

Then; The defective rod can be salvaged if the groove lies on the rod between 0 and 5 inches i.e ( 20  - 15 )inches

Now:

P(X ≤ 5) = \dfrac{5}{20}

= 0.25

P(X ≥ 15) = \dfrac{5}{20}

= 0.25

The probability that a defective rod can be salvaged = P(X ≤ 5) + P(X ≥ 15)

= 0.25+0.25

 = 0.50

∴ The probability that a defective rod can be salvaged = 0.50

4 0
2 years ago
Choose the correct simplification of (3x3 + 2x2 − 5x) − (8x3 − 2x2)
zmey [24]
(3x³ + 2x² - 5x) - (8x³ - 2x²<span>) =
</span>3x³ + 2x² - 5x - 8x³ + 2x² =
-5x³ + 4x² - 5x
5 0
2 years ago
Read 2 more answers
A four-person committee is chosen from a group of eight boys and six girls. If students are chosen at random, what is the probab
Lapatulllka [165]

Answer: 0.07

Step-by-step explanation:

in the group, we can have only 4 persons.

we have 8 boys, and 6 girls.

We want to find the probability that in the comite we have only boys.

Ok, for the first selection, the probability of selecting a boy is equal to the number of boys divided the total number of the group ( 8 + 6 = 14) this is

p1 = 8/14.

For the second selection we do the same, but we already slected a boy, so now the number of boys is 7, and the total number of posibilities is 13.

p2 = 7/13.

for the third selection we do the same, in this case the probability is

p3 = 6/12

for the fourth selection the probability will be:

p4 = 5/11

The joint probability, of all the events happening at the same time, is equal to the product of the singular probabilities:

P = p1*p2*p3*p4 = (8/14)*(7/13)*(6/12)*(5/11) = 0.07

4 0
2 years ago
Read 2 more answers
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