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musickatia [10]
3 years ago
5

Show that the two triangles given beside are similar and calculate the lengths of sides PQ and PR.

Mathematics
1 answer:
Rina8888 [55]3 years ago
5 0

9514 1404 393

Answer:

  • ΔABC ~ ΔPQR
  • PQ = 8
  • PR = 14

Step-by-step explanation:

Angles A and P are marked congruent; angles B and Q are marked congruent, so the triangles are similar by the AA similarity postulate. The similarity statement can be written ...

  ΔABC ~ ΔPQR by AA similarity

__

The ratio of sides of PQR to ABC is the ratio QR/BC = 12/6 = 2. That is, each side in the larger triangle is 2 times the length of the corresponding smaller side.

  PQ = 2·AB = 2·4 = 8

  PR = 2·AC = 2·7 = 14

The side lengths of interest are ...

  PQ = 8, PR = 14

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3 years ago
A company placed $500,000 in three different investment plans.
Paha777 [63]

Answer:

B. $200,000

Step-by-step explanation:

Let x be the amount placed at 5.5%

3x is the amount placed at 5%

This leaves the rest for the 4.5 %   500000- x - 3x = 500000-4x

Assuming simple interest

I = PRT where I is interest, P is principle, rate is rate and t  is time

Interest for the 5.5% for 1 year is

I = x * .055 * 1 = .055x

Interest for the 5.% for 1 year is

I = 3x * .05 * 1 = .15x

Interest for the 4.5% for 1 year is

I = 500000-4x * .045 * 1 = 22500 - 0.18 x

Add the interest together to get the income for 1 year

.055x+  .15x+22500 - 0.18 x=25,000

Combine like terms

0.025x+22500=25000

Subtract 22500

.025x =2500

Divide by .025

x =100000  

short term notes is 100000

3*x = 300000 = government bonds

The rest is utility bonds 500000- 100000-300000 = 100000

We want how much more in government bond than utility bond

300000 -100000 = 200000

8 0
3 years ago
Read 2 more answers
A 20-ounce bag of potato chips costs $3.80. What is the unit rate of the chips?
melisa1 [442]
To find the unit rate you would need to find the cost per ounce of potato chips. To find this you would simply divide. $3.80/20 = .19

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3 0
3 years ago
On a winter morning, the temperature before sunrise was -10℉. The temperature then rose by 1℉ each hour for 7 hours before dropp
Artemon [7]

Answer:

The temperature after 10 hours is -9 ºF.

Step-by-step explanation:

This statement can be translated mathematically as follows. The temperature after 10 hours from sunrise is:

T = -10\,^{\circ}F + \left(1\,\frac{^{\circ}F}{h} \right)\cdot (7\,h)+ \left(-2\,\frac{^{\circ}F}{h} \right)\cdot (3\,h)

T = -9\,^{\circ}F

The temperature after 10 hours is -9 ºF.

6 0
3 years ago
Cans of frozen orange juice are weighed to ensure they are not underfilled. Cans are independent, and the probability that a can
olga2289 [7]

Answer: 0.999986176

Step-by-step explanation:

To solve this, the probability distribution formula for selection will be used

Where P(x=r) = nCr * p^r * q^n-r

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P(x=3) = 3C3 * 0.024^3 * 0.976^0

P(x=3) = 1 * 0.000013824 * 1

P(x=3) = 0.000013824.

Then, probability that all three cans are not overfilled becomes :

1 - 0.000013824. = 0.999986176,

7 0
3 years ago
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