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3 years ago

Solve the inequality -5(3x+4)<6-3x

1 answer:

7 0

$-5(3x+4) -26\ \ \ \ |:12\\\\x > -\dfrac{26}{12}\\\\x > -\dfrac{26:2}{12:2}\\\\x > -\dfrac{13}{6}\to x\in\left(-\dfrac{13}{6},\ \infty\right)$

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Solve for x. The triangles in each pair are similar. <br>

KatRina [158]

Answer:

Step-by-step explanation:

You need to pay very close attention to the triangle similarity statement. This says that triangle NML is similar to triangle NVU. But if you look at the way that triangle NVU is oriented in its appearance, it's laying on its side. We need to set it upright so that angle N is the vertex angle, angle V is the base angle on the left, and angle U is the base angle on the right. When we do that we see that sides NV and NM are corresponding and exist in a ratio to one another; likewise with sides VU and ML. Setting up the proportion:

$\frac{NV}{NM}=\frac{VU}{ML}$

Filling in:

$\frac{12}{36} =\frac{9}{9x}$

Cross multiply to get

324 = 108x

and x = 3

3 0

3 years ago

Harry church borrowed 17,500.00 at 6.5% exact interest. He had to pay back a maturity value of 17,873.97 to pay off the loan. Wh

kirill [66]

Answer:the term of the loan is approximately 4 months

Step-by-step explanation:

The term of the loan means the period for which the loan was given.

We would apply the formula for simple interest which is expressed as

I = PRT/100

Where

P represents the principal

R represents interest rate

T represents time in years

I = interest after t years

From the information given

P = 17500

R = 6.5%

I = total amount paid - principal

I = 17,873.97 - 17,500.00 = 373.97

Therefore

373.97 = (17500 × 6.5 × T)/100

373.97 = 1137.5T

T = 373.97/1137.5

T = 0.32 years

Converting to months, it becomes

0.32 × 12 = 3.84

Approximately 4 months.

3 0

3 years ago

A table with a round top is cut in half so that it can be used against a wall.after it is cut,the edge along the wall is 6 feet

MrRissso [65]

Answer:

The area of the table after it is cut is 12 or 36 because

Step-by-step explanation:

6 times 2= 12 and 6 times 6= 36 so year

4 0

3 years ago

The length of a rectangle is 5959 inches greatergreater than twice the width. if the diagonal is 2 inches more than the length,

lorasvet [3.4K]

Length: 2w + 59

width: w

diagonal: (2w + 59) + 2 = 2w + 61

Length² + width² = diagonal²

(2w + 59)² + (w)² = (2w + 61)²

(4w² + 118w + 3481) + w² = 4w² + 122w + 3721

5w² + 118w + 3481 = 4w² + 122w + 3721

w² + 118w + 3481 = 122w + 3721

w² - 4w + 3481 = 3721

w² - 4w - 240 = 0

a = 1, b = -4, c = -240

w = $[-(b) +/- \sqrt{(b)^{2} - 4(a)(c) }]/2(a)$

= $[-(-4) +/- \sqrt{(-4)^{2} - 4(1)(-240) }]/2(1)$

= $[4 +/- \sqrt{(16 + 960) }]/2$

= $[4 +/- \sqrt{(976) }]/2$

= $[2 +/- 4\sqrt{(61) }]/2$

= $1 +/- 2\sqrt{(61) }$

since width cannot be negative, disregard 1 - 2√61

w = 1 + 2√61 ≈ 16.62

Length: 2w + 59 = 2(1 + 2√61) + 59 = 2 + 4√61 + 59 = 61 + 4√61 ≈ 92.24

Answer: width = 16.62 in, length = 92.24 in

7 0

3 years ago

In New York State's Quick Draw lottery, players choose between one and ten numbers that range from 1 1 to 80 . 80. A total of 20

amid [387]

Answer:

Step-by-step explanation:

7 0

3 years ago