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2 years ago

26. The first half of a play is 35 minutes longer than the second half of the play. If

1 answer:

7 0

155-35= 120 (you subtract 35 so you get the number if both plays lasted the same time )
120/2= 60 (you get the amount of time one play lasted without extra 35 minutes)
60+35=95 (then add 35 minutes to one play because 1 one is longer than the other one)

the first half of the play is 95 minutes long.

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Find the area of triangle ABC with vertices A(2,1), B (12,2), C (12,8). Hence, or otherwise find the perpendicular distance from

Lapatulllka [165]

<h2>The area of a triangle is =54 square units</h2><h2>The perpendicular distance from B to AC is = $\frac{108}{\sqrt{149} } units$ </h2>

Step-by-step explanation:

Given a triangle ABC with vertices A(2,1),B(12,2) and C(12,8)

$x_1=2,y_1=1,x_2=12,y_2=2,x_3=12 and y_3=8$

The area of a triangle is= $\frac{1}{2} [x_1(y_2-y_3) +x_2 (y_3- y_1)+x_3(y_1-y_2)]$

= $|\frac{1}{2} [2(2-8+12(8-1)+12(1-2)]|$

= $|-54|$ = 54 square units

The length of AC = $\sqrt{(x_1-x_3)^{2} +(y_1-y_3)^2}$

= $\sqrt{(2-12)^{2} +(1-8)^2}$

= $\sqrt{149}$ units

Let the perpendicular distance from B to AC be = x

According To Problem

$\frac{1}{2} \times x \times \sqrt{149} = 54$

⇔ $x =\frac{108}{\sqrt{149} }$ units

Therefore the perpendicular distance from B to AC is = $\frac{108}{\sqrt{149} } units$

5 0

2 years ago

Last year, Josh had $20,000 to invest. He invested some of it in an account that paid 7% simple interest per year, and he invest

Ilya [14]

Answer: $12000 was invested at 7% while $8000 was invested at 9%.

Step-by-step explanation:

Based on the information given in the question, let the amount that was invested at 7% be n.

Therefore,

0.07n + 0.09(20000 - n) = 1560

0.07n + 1800 - 0.09n = 1560

-0.02n = 1560 - 1800

-0.02n = -240

n = 240/0.02

n = 120

Therefore, $12000 was invested at 7% while $8000 was invested at 9%.

3 0

2 years ago

1. Consider the data set 1,2,3,4,5,6,7,8,9.

ivanzaharov [21]

Answer: a) Mean = 5, Median = 5

b) Mean = 15, Median = 5

c) Due to presence of outlier i.e. 99.

Step-by-step explanation:

Since we have given that

1,2,3,4,5,6,7,8,9

Here, n = 9 which is odd

So, Mean would be

$\dfrac{1+2+3+4+5+6+7+8+9}{9}=\dfrac{45}{9}=5$

Median = $(\dfrac{n+1}{2})^{th}=\dfrac{9+1}{2}=5^{th}=5$

If 9 is replaced by 99,

1,2,3,4,5,6,7,8,99

So, mean would be

$\dfrac{1+2+3+4+5+6+7+8+99}{9}=\dfrac{135}{9}=15$

Median would be same as before i.e. 5

The mean is neither central nor typical for the data due to outlier i.e. 99

Hence, a) Mean = 5, Median = 5

b) Mean = 15, Median = 5

c) Due to presence of outlier i.e. 99.

5 0

2 years ago

In triangle ABC, BD bisects Angle ABC and AD is similar to CD. Tell what kind of triangle ABC must be

Anestetic [448]

A right triangle. Hope this helps.

7 0

2 years ago

What is the rule? 100 cm 1 m, 250 cm ? M, 1500 cm ? M

kirza4 [7]

There are 100 cm(centimeters) in a m(meter).
So, to solve this, we divide 250 by 100. this gives us 2.5meters.
1500÷100=15meters
The rule is m=cm÷100.

4 0

2 years ago