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2 years ago

7

Sofia's family took a road trip to Mount Rushmore. Sofia slept through the last 65% of the trip. If the total length of the trip

was 840 miles, how many miles had they travelled when Sofia fell asleep?

1 answer:

zhuklara [117]2 years ago

7 0

Sofia slept 546 miles and was awake for 45% which is 294 of the miles.

You can find this by finding 1%, and that would be 8.4. (You get 1% from dividing 100 from the 100% number.) Then you multiply it by 65 so now you get 546.

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Which point lies on a circle with a radius of 5 units and center at P(6,1)?

ryzh [129]

Answer:

Option B. $R(2,4)$

Step-by-step explanation:

we know that

If a ordered pair lie on the circle. then the ordered pair must satisfy the equation of the circle

step 1

Find the equation of the circle

we know that

The equation of the circle in center radius form is equal to

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

where

r is the radius of the circle

(h,k) is the center of the circle

substitute the values

$(x-6)^{2}+(y-1)^{2}=5^{2}$

$(x-6)^{2}+(y-1)^{2}=25$

step 2

Verify each case

case A) $Q(1, 11)$

substitute the value of $x=1, y=11$ in the equation of the circle and then compare the results

$(1-6)^{2}+(11-1)^{2}=25$

$25+100=25$ ------> is not true

therefore

the ordered pair Q not lie on the circle

case B) $R(2,4)$

substitute the value of $x=2, y=4$ in the equation of the circle and then compare the results

$(2-6)^{2}+(4-1)^{2}=25$

$16+9=25$ ------> is true

therefore

the ordered pair R lie on the circle

case C) $S(4,-4)$

substitute the value of $x=4, y=-4$ in the equation of the circle and then compare the results

$(4-6)^{2}+(-4-1)^{2}=25$

$4+25=25$ ------> is not true

therefore

the ordered pair S not lie on the circle

case D) $T(9,-2)$

substitute the value of $x=4, y=-4$ in the equation of the circle and then compare the results

$(9-6)^{2}+(-2-1)^{2}=25$

$9+9=25$ ------> is not true

therefore

the ordered pair T not lie on the circle

7 0

3 years ago

Ryan deposited $6,700 into an account at the Town Bank, earning 3.4% interest compounded annually. He made no deposits or withdr

Nonamiya [84]

Answer: The amount of money in his account after 4 years = $7,658.73

Step-by-step explanation:

If interest is compounded annually, then formula to compute amount :

$A=P(1+r)^n$ , where P+ principal value, r= rate of interest, n= time ( in years).

As per given,

P= $6700 , r = 3.4% =0.034, n =4

$A=6700(1+0.034)^4\\\\=6700(1.034)^4\\\\=6700(1.14309455234)\approx7658.73$

Hence, the amount of money in his account after 4 years = $7,658.73

6 0

2 years ago

An account earns annual simple interest. find the balance of the account.

I am Lyosha [343]

y=2000(1+.09^2)^1/2

y=2000(1.09^2)1/2

y=2000(1.1881)^1/2

y=2000(1.09)

y=$2180

3 0

3 years ago

Simplify: 2⁶X5⁴X3¹²/2²x5²x3⁴

Sholpan [36]

Step-by-step explanation:

2⁶X5⁴X3¹²/2²x5²x3⁴

2⁴ × 5²×3⁸

4 0

2 years ago

Read 2 more answers

A doctor's office has a computer file showing the heights of 100 male patients of one of the doctors of the practice. the height

kumpel [21]

A) Yes. we don't have enough information so this can not be determined.
B) No, it would just be an outlier.

7 0

2 years ago