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2 years ago

What is the measure of the secant AB

Mathematics

1 answer:

cricket20 [7]2 years ago

6 0

A secant is a line that intersects a circle in exactly two points. When a tangent and a secant, two secants, or two tangents intersect outside a circle than the measure of the angle is formed is one-half the positive difference of the measures of the intercepted arcs.

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The following data show the midterm and final exam scores in an English writing class. Student 1 2 3 4 5 6 7 8 9 10 11 12 Midter

tester [92]

Answer:

The co variance of the midterm and final exam scores is 58.76.

Step-by-step explanation:

The formula to compute the sample co variance is:

$Cov(x,y)=\frac{\sum(X-Mean\ of\ X)(Y-Mean\ of\ Y)}{n-1}$

The values are computed in the table below.

Compute the co variance as follows:

$Cov(x,y)=\frac{\sum(X-Mean\ of\ X)(Y-Mean\ of\ Y)}{n-1}\\=\frac{646.33}{12-1}\\ =58.76$

Thus, the co variance of the midterm and final exam scores is 58.76.

7 0

2 years ago

An excavating company charges $300 an hour for the use of a backhoe and $500 an hour for the use of a bulldozer. (part of an hou

Fed [463]

We have that

Cost use of a backhoe----------------------$300 an hour

<span> Estimate for equipment rental each week---------------------$18,400</span>

Total hours operator per week--------------------------------------40

<span> 40*300</span>=$12000---------------------it is the cost per week to use a backhoe

$12000<$18400 is ok

<span> The maximum of hours that I can rent </span>a backhoe <span> are 40 hours, since it is the limit of the operator and it do not overcome the total budget </span>

4 0

2 years ago

In parallelogram ABCD , diagonals AC⎯⎯⎯⎯⎯ and BD⎯⎯⎯⎯⎯ intersect at point E, AE=x2−16 , and CE=6x .

MAXImum [283]

Answer:

<h3>AC=96 units.</h3>

Step-by-step explanation:

We are given a parallelogram ABCD with diagonals AC and BD intersect at point E.

$AE=x^2-16.$ , and CE=6x .

<em>Note: The diagonals of a parallelogram intersects at mid-point.</em>

Therefore, AE = EC.

Plugging expressions for AE and EC, we get

$x^2-16=6x.$

Subtracting 6x from both sides, we get

$x^2-16-6x=6x-6x$

$x^2-6x-16=0$

Factoriong quadratic by product sum rule.

We need to find the factors of -16 that add upto -6.

-16 has factors -8 and +2 that add upto -6.

Therefore, factor of $x^2-6x-16=0$ quadratic is (x-8)(x+2)=0

Setting each factor equal to 0 and solve for x.

x-8=0 => x=8

x+2=0 => x=-2.

We can't take x=-2 as it's a negative number.

Therefore, plugging x=8 in EC =6x, we get

EC = 6(8) = 48.

<h3>AC = AE + EC = 48+48 =96 units.</h3>

5 0

2 years ago

If ABCD is a square and AB = 10, what is the measure of CE to the nearest hundredth?

andrey2020 [161]

Answer:

$AC=14.14\ units$

Step-by-step explanation:

<em><u>The correct question is </u></em>

If ABCD is a square and AB = 10, what is the measure of AC? (rounded to the nearest hundredth)

see the attached figure to better understand the problem

we know that

All four sides of the square are congruent and all four interior angles are equal to 90°.

AB=BC=CD=AD

In the right triangle ACD

Applying the Pythagorean Theorem

$AC^2=CD^2+AD^2$

we have that

$CD=AD=AB=10\ units$

substitute the given value

$AC^2=10^2+10^2$

$AC^2=200$

$AC=\sqrt{200}\ units$

$AC=14.14\ units$

6 0

2 years ago

Jackie took out a $9,000 personal loan with a 4.5% interest rate that she will pay back in 3 years. She will make monthly paymen

gayaneshka [121]

Answer:

Total cost of repayment is $10,852.92

Step-by-step explanation:

Firstly, we need to calculate the interest attached to this loan repayment

To calculate this, we use the formula for simple interest

Mathematically,

I = $\frac{PRT}{100}$

where P is the amount borrowed which is $9,000

R is the rate which is 4.5%

T is the time which is 3 years

Plugging these values, we have

I = (9000×4.5×3)/100 = $1,215

Now we were also told in the question that she will make a monthly repayment of $267.72

Now the number of months in 3 years is 36 months. Total monthly repayment = 267.72 × 36 = $9637.92

Adding the interest amount, we have 9637.92 + 1215 = $10,852.92

7 0

2 years ago