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3 years ago

LM has the end points (-2, -4) and (4, -6) what are the coordinates for the midpoint of the LM

Mathematics

1 answer:

DanielleElmas [232]3 years ago

5 0

(-2 +4)/2 = 2/2 = 1
(-4-6)/2 = -10/2 = -5
midpoint = (1, -5)

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If triangle ABC is dilated by a scale factor of 2 with a dilation center of A, what will be the coordinates of point b’?

mojhsa [17]

Answer:

In the given figure the sides of triangle measures as follows:

AB= 4 units,

BC= 6 units,

Since triangle ABC is right angled triangle, to find AC we will have to use Pythagorean theorem,

AB² + BC² = AC²

Plugging the values of AB and BC to find AC,

4² + 6² = AC²

16+36=AC²

AC = 7.48

Now if the triangle is dilated by a scale factor of 2, each side will be multiplied by 2 to get the new triangle A'B'C'

side A'B' = 2* AB = 2*4= 8 units

side B'C' = 2* BC = 2*6 =12 units

side A'C' = 2*AC = 2*7.48 = 14.96 units

Perimeter of triangle = sum of three sides

Perimeter of triangle A'B'C' = A'B' + B'C' + A'C'= 8+12 + 14.96 = 34.96 units.

Perimeter of triangle ABC = AB+BC + AC = 4+6+7.48 = 17.48 units.

Perimeter of triangle A'B'C' = 2* Perimeter of triangle ABC

The perimeter of new triangle A'B'C' is 34.96 units which is twice that of triangle ABC.

Answer : A) The perimeter of A'B'C' is 2 times the perimeter of ABC.

8 0

3 years ago

A group of five friends are sharing 2 pounds of trail mix write a division problem and a fraction to represent this problem

KiRa [710]

2/5 or 2 divided by 5. 2 pounds are divided up by 5 friends.

3 0

3 years ago

The mean of five numbers is 25, what is their sum?

zubka84 [21]

125 is the answer.

A mean of vie numbers is 25. If it is 25, the numbers must be 25. So, since there is 5 of 25, multiply 25 by 5. Then, the answer would be 125.

There is also another way to do it. Set-up your equation.

x/5=25.

Now flip it to make the equation a multiplication problem.

25×5=x

Once you solve the equation, you should get 125 is the answer.

3 0

3 years ago

A physicist examines 25 water samples for nitrate concentration. The mean nitrate concentration for the sample data is 0.165 cc/

xz_007 [3.2K]

Answer:

The 80% confidence interval for the the population mean nitrate concentration is (0.144, 0.186).

Critical value t=1.318

Step-by-step explanation:

We have to calculate a 80% confidence interval for the mean.

The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.

The sample mean is M=0.165.

The sample size is N=25.

When σ is not known, s divided by the square root of N is used as an estimate of σM:

$s_M=\dfrac{s}{\sqrt{N}}=\dfrac{0.078}{\sqrt{25}}=\dfrac{0.078}{5}=0.016$

The degrees of freedom for this sample size are:

$df=n-1=25-1=24$

The t-value for a 80% confidence interval and 24 degrees of freedom is t=1.318.

The margin of error (MOE) can be calculated as:

$MOE=t\cdot s_M=1.318 \cdot 0.016=0.021$

Then, the lower and upper bounds of the confidence interval are:

$LL=M-t \cdot s_M = 0.165-0.021=0.144\\\\UL=M+t \cdot s_M = 0.165+0.021=0.186$

The 80% confidence interval for the population mean nitrate concentration is (0.144, 0.186).

6 0

3 years ago

Solve the inequality x/5-3<0

Kisachek [45]

Answer:

x < 15

Step-by-step explanation:

$\frac{x}{5}$ - 3 < 0 ( add 3 to both sides )

$\frac{x}{5}$ < 3 ( multiply both sides by 5 to clear the fraction )

x < 15

7 0

3 years ago