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3 years ago

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Which equation represents this number sentence? Two more than one-third of a number is 8. a. (2+1/3)n=8 b. 2+1/3n+8=0 c. 2=1/3n

+8 d. 2+1/3n=8

1 answer:

Rina8888 [55]3 years ago

5 0

Answer:

d

Step-by-step explanation:

let the number be n then one third of the number is

$\frac{1}{3}$ n and 2 more than this is

2 + $\frac{1}{3}$ n = 8 ( is 8 means = 8 ) → d

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Which equation represents a circle that contains the point (-5, 3) and has a center at (-2, 1)? Distance formula: vaa -02 (x - 1

natali 33 [55]

Given:

The center of the circle = (-2,1).

Circle passes through the point (-5,3).

To find:

The equation of the circle.

Solution:

Radius is the distance between the center of the circle and any point on the circle. So, radius of the circle is the distance between the points (-2,1) and (-5,3).

$Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$r=\sqrt{(-5-(-2))^2+(3-1)^2}$

$r=\sqrt{(-5+2)^2+(2)^2}$

$r=\sqrt{(-3)^2+(2)^2}$

On further simplification, we get

$r=\sqrt{9+4}$

$r=\sqrt{13}$

The standard form of a circle is:

$(x-h)^2+(y-k)^2=r^2$

Where, (h,k) is the center of the circle and r is the radius of the circle.

Substitute h=-2, k=1 and $r=\sqrt{13}$ .

$(x-(-2))^2+(y-1)^2=(\sqrt{13})^2$

$(x+2)^2+(y-1)^2=13$

Therefore, the equation of the circle is $(x+2)^2+(y-1)^2=13$ .

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3 years ago

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earnstyle [38]

Answer:

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3 years ago

What is the recursive rule for the sequence?

adoni [48]

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4 years ago

Which is a factor of 144 − 49x2?<br><br> 12 - 7x2<br> 72 – 7x2<br> 12 – 7x<br> 72 + 7x

Vinil7 [7]

Answer:

(12-7x)

Step-by-step explanation:

144 − 49x²

by observation, we can see that 144 = 12² and 49 = 7²

hence we can rewrite the equation

144 − 49x²

= 12² - 7²x²

= 12² - (7x)²

recall that the expression x² - y² = (x+y)(x-y)

hence,

12² - (7x)²

= (12 + 7x)(12-7x)

(12-7x) appears in the expression above, hence 12 -7x is a factor

5 0

3 years ago

Read 2 more answers

You deposit $200 in an account earning 3.5% simple interest how long will it take for the balance of the account to be $221

Rus_ich [418]

It takes 3 years for the balance of account to be $ 221

<em><u>Solution:</u></em>

From given information,

Principal = $ 200

Rate of interest = 3.5 %

Amount after "n" years = $ 221

To find: number of years

In simple Interest,

Simple interest = amount earned - principal

Simple interest = 221 - 200 = 21

Thus simple interest earned is $ 21

<em><u>The formula for simple interest is given as:</u></em>

$simple\ interest = \frac{ p \times n \times r}{100}$

Where,

p is the principal

n is the number of years

r is the rate of interest per annum

Substituting the given values in formula,

$21 = \frac{200 \times n \times 3.5}{100}\\\\21 = 2n \times 3.5\\\\n = \frac{21}{7}\\\\n = 3$

Thus it takes 3 years for the balance of account to be $ 221

7 0

4 years ago