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3 years ago

Find the midpoint of the line segment joining the points (-1,-1) and (-3,12)

Mathematics

2 answers:

Lyrx [107]3 years ago

6 0

the answer is (-2, 11/2)

maxonik [38]3 years ago

5 0

Answer:

(−2, 11/2)

Step-by-step explanation:

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Can I please have help with question 2) a and b

Ulleksa [173]

Answer:

$\frac{10\sqrt{6} }{3}$ and $\frac{11\sqrt{3} }{3}$

Step-by-step explanation:

(a)

A = $\frac{1}{2}$ × 4 $\sqrt{2}$ × $\frac{5}{\sqrt{3} }$

= 2 $\sqrt{2}$ × $\frac{5}{\sqrt{3} }$

= $\frac{10\sqrt{2} }{\sqrt{3} }$ × $\frac{\sqrt{3} }{\sqrt{3} }$ ← rationalise the denominator

= $\frac{10\sqrt{6} }{3}$ units²

(b)

Using Pythagoras' identity in the right triangle

let hypotenuse be h , then

h² = (4 $\sqrt{2}$ )² + ( $\frac{5}{\sqrt{3} }$ )²

= 32 + $\frac{25}{3}$

= $\frac{96}{3}$ + $\frac{25}{3}$

= $\frac{121}{3}$ ( take the square root of both sides )

h = $\sqrt{\frac{121}{3} }$ = $\frac{11}{\sqrt{3} }$ × $\frac{\sqrt{3} }{\sqrt{3} }$ ← rationalise the denominator

h = $\frac{11\sqrt{3} }{3}$

7 0

3 years ago

The following annual expenses for car insurance, vacation, and home repairs for the Clark family are $1130, $700, and $468, resp

eimsori [14]

Answer:

A) $192

Step-by-step explanation:

Given:

Yearly expense of Car insurance = $1130

Yearly expense of Vacation = $700

Yearly expense of home repairs = $468

we need to find the monthly allowance of Clark family.

First we find the total annual expense of Clark family.

Total Annual expense is equal to sum of Yearly expense of Car insurance and Yearly expense of Vacation and Yearly expense of home repairs.

Framing in equation form we get;

Total annual expense = $\$1130 + \$700+\$468 = \$2298$

Now we know that;

Number of months in a year = 12 months.

Total Monthly allowance will be equal to Total annual expense divided by Number of months in year.

Framing the equation we get;

Total Monthly allowance = $\frac{\$2298}{12}= \$191.5$

Rounding to nearest dollar we get;

Total Monthly allowance of Clark family is $192.

6 0

3 years ago

Read 2 more answers

Which is the slope of the line that passes through the points (2, 8) and (4, 6)?

kotegsom [21]

Slope: (y2-y1)/(x2-x1)
(6-8)/(4-2) = -2/2 = -1
The slope is -1

6 0

3 years ago

Read 2 more answers

If you place a cup of 210 degree Fahrenheit coffee on a table in a room that is 68 degrees fareinheit, and ten minutes later, it

Lana71 [14]

Newton's Law of Cooling

Tf=Ts+(Ti-Ts)e^(-kt) where Tf is temp at time t, Ts is temp of surroundings, Ti is temp of object/fluid. So we need to find k first.

200=68+(210-68)e^(-10k)

132=142e^(-10k)

132/142=e^(-10k)

ln(132/142)=-10k

k=-ln(132/142)/10

k≈0.0073 so

T(t)=68+142e^(-0.0073t) so how long until it reaches 180°?

180=68+142e^(-0.0073t)

112=142e^(-0.0073t)

112/142=e^(-0.0073t)

ln(112/142)=-0.0073t

t= -ln(112/142)/(0.0073)

t≈32.51 minutes

8 0

3 years ago

-12 = 4x + 1<br> solve<br> algebra

Eddi Din [679]

Answer:

$x=-\frac{13}{4}$

Step-by-step explanation:

$-12=4x+1\\4x=-12-1\\x=-\frac{13}{4}$

4 0

3 years ago