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3 years ago

Determine whether the given number is a solution of the given equation.

Mathematics

2 answers:

Mandarinka [93]3 years ago

4 0

Answer:

Substituting x with 9

9-11

= -2

Yes, it is a solution.

Vanyuwa [196]3 years ago

4 0

Yes, it is (9)-11=-2

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Summer has an offer to buy an item with a sticker price of $13,200 by paying $460 a month for 36 months. What interest rate is S

AysviL [449]

Answer:

the annual interest rate is 7.583%

Step-by-step explanation:

We are given

Summer has an offer to buy an item with a sticker price of $13,200

so, we have

P=13200

paying $460 a month for 36 months

so, we can find total amount

$A=460\times 36$

$A=16560$

Let's assume

annual interest is r

total time =36 months

so, total number of years =3

Since, it is compounded monthly

so, n=12

now, we can use formula

$A=P(1+\frac{r}{n} )^{nt}$

now, we can plug values

$16560=13200(1+\frac{r}{12} )^{36}$

now, we can solve solve for r

$(1+\frac{r}{12} )^{36}=\frac{16560}{13200}$

$r=0.07583$

So, the annual interest rate is 7.583%

6 0

3 years ago

Read 2 more answers

THe question asked what is 0.35 written as a ratio?

Masja [62]

Step 1: 0.35 = 35⁄100
Step 2: Simplify 35⁄100 = 7⁄20
answer: 7/20

5 0

4 years ago

Match the following items.

Veseljchak [2.6K]

Answer:

1. h

2. k

3. d

4. j

5. m

6. n

7. a

8. l

9. e

10. c

11. f

12. i

13. g

14. b

Step-by-step explanation:

1. a quotient of two quantities -> h. fraction

2. a quotient that involves variables -> k. algebraic fraction

3. numbers that would result in division by zero -> d. exclusions

4. multiply the numerators and multiply the denominators for a new fraction -> j. multiplication of fractions

5. multiply by the reciprocal of the divisor -> m. division of fractions

6. the denominators must be the same -> n. addition of fractions

7. contains a fraction in the numerator, denominator, or with the denominator -> a. complex fractions

8. a new fraction resulting from the interchanging of the numerator and denominator -> l. reciprocal

9. the dividend of a fraction -> e. numerator

10. the divisor in a fraction -> c. denominator

11. the lowest common multiple of denominators -> f. lowest common denominator

12. a combination of integral and fractional expressions -> i. mixed expression

13. an equation that contains fractions -> g. fractional equation

14. a statement that two fractions are equal -> b. proportion

8 0

3 years ago

If cos() = − 2 3 and is in Quadrant III, find tan() cot() + csc(). Incorrect: Your answer is incorrect.

nydimaria [60]

Answer:

$\tan(\theta) \cdot \cot(\theta) + \csc(\theta) = \frac{5 - 3\sqrt 5}{5}$

Step-by-step explanation:

Given

$\cos(\theta) = -\frac{2}{3}$

$\theta \to$ Quadrant III

Required

Determine $\tan(\theta) \cdot \cot(\theta) + \csc(\theta)$

We have:

$\cos(\theta) = -\frac{2}{3}$

We know that:

$\sin^2(\theta) + \cos^2(\theta) = 1$

This gives:

$\sin^2(\theta) + (-\frac{2}{3})^2 = 1$

$\sin^2(\theta) + (\frac{4}{9}) = 1$

Collect like terms

$\sin^2(\theta) = 1 - \frac{4}{9}$

Take LCM and solve

$\sin^2(\theta) = \frac{9 -4}{9}$

$\sin^2(\theta) = \frac{5}{9}$

Take the square roots of both sides

$\sin(\theta) = \±\frac{\sqrt 5}{3}$

Sin is negative in quadrant III. So:

$\sin(\theta) = -\frac{\sqrt 5}{3}$

Calculate $\csc(\theta)$

$\csc(\theta) = \frac{1}{\sin(\theta)}$

We have: $\sin(\theta) = -\frac{\sqrt 5}{3}$

So:

$\csc(\theta) = \frac{1}{-\frac{\sqrt 5}{3}}$

$\csc(\theta) = \frac{-3}{\sqrt 5}$

Rationalize

$\csc(\theta) = \frac{-3}{\sqrt 5}*\frac{\sqrt 5}{\sqrt 5}$

$\csc(\theta) = \frac{-3\sqrt 5}{5}$

So, we have:

$\tan(\theta) \cdot \cot(\theta) + \csc(\theta)$

$\tan(\theta) \cdot \cot(\theta) + \csc(\theta) = \tan(\theta) \cdot \frac{1}{\tan(\theta)} + \csc(\theta)$

$\tan(\theta) \cdot \cot(\theta) + \csc(\theta) = 1 + \csc(\theta)$

Substitute: $\csc(\theta) = \frac{-3\sqrt 5}{5}$

$\tan(\theta) \cdot \cot(\theta) + \csc(\theta) = 1 -\frac{3\sqrt 5}{5}$

Take LCM

$\tan(\theta) \cdot \cot(\theta) + \csc(\theta) = \frac{5 - 3\sqrt 5}{5}$

6 0

3 years ago

Drag the tiles to the correct boxes to complete the pairs.

Contact [7]

1) (3.8 * 10^3) * (9.4 * 10^-5) = 0.3572 = 3.6 * 10^-1

2) (4.2 * 10^7) * (7.4 * 10^-2) = 3.1 * 10^6

3) (8.6 * 10^-6) * (7.1 * 10^9) / (4.1 * 10^ -2) * ( 2.8 * 10 ^-7) = 5.3 * 10^-6

4) 4.2 * 10^-1

Sorry for not putting my work for number 4. Hope this helps!

3 0

2 years ago