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3 years ago

I have to find the length of the angle indicated for the trapezoid

Mathematics

1 answer:

Stels [109]3 years ago

6 0

That is not a trapezoid, it is a general quadrilateral. All 2-dimensional, 4-sided figures have an internal angle sum of 360 (triangles are 180). So if you assume angles P and Q are right, they are each equal to 90 degrees, for a total of 180.
Subtract: 360 - 180 = 180. We know that S + R must equal 180. If you subtract 180 - 65, you get 115, which is obtuse (greater than 90 degrees). This matches the drawing as the unknown angle is clearly greater than 90. So the answer is 115 degrees.

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Write the standard form of the equation of the circle with endpoints of a diameter at the points (7,2) and (-9,5).

lys-0071 [83]

Answer:

$(x+1)^2 + (y- 3.5)^2 =64$

Step-by-step explanation:

We are given that endpoints of a diameter at the points (7,2) and (-9,5).

Center of the circle is the mid point of diameter

So, first find the mid point of diameter

Formula : $x=\frac{x_1+x_2}{2} , y=\frac{y_1+y_2}{2}$

$(x_1,y_1)=(7,2)\\(y_1,y_2)=(-9,5)$

Substitute the values in formula

$x=\frac{7-9}{2} , y=\frac{2+5}{2}$

$x=-1 , y=3.5$

So, center of circle = (h,k )=(-1,3.5)

To find length of diameter :

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$(x_1,y_1)=(7,2)\\(y_1,y_2)=(-9,5)$

$d=\sqrt{(-9-7)^2+(5-2)^2}$

$d=\sqrt{265}$

Length of radius = r = $\frac{Diameter}{2}=\frac{\sqrt{256}}{2}$

Standard form of the equation of the circle : $(x -h)^2 + (y- k)^2 = r^2$

(h,k )=(-1,3.5)

$r=\frac{\sqrt{256}}{2}$

Equation of the circle : $(x+1)^2 + (y- 3.5)^2 =(\frac{\sqrt{256}}{2})^2$

Equation of the circle : $(x+1)^2 + (y- 3.5)^2 =64$

Hence the standard form of the equation of the circle with endpoints of a diameter at the points (7,2) and (-9,5) is $(x+1)^2 + (y- 3.5)^2 =64$

5 0

4 years ago

Please help me fast i will give first answer brainliest!!

Verdich [7]

Answer:

(-1,-18) is the coordinate of the vertex.

Step-by-step explanation:

We can obtain the vertex by taking the derivative and equating it to zero. I know this because the the slope of the tangent line at the vertex has to be equal to zero.

the derivative would be 4x + 4 = 0, where x = -1.

Plugging x into the original value we will end up with the y coordinate.

Hope this helps.

7 0

3 years ago

Read 2 more answers

A researcher is concerned that graduate students get less than the recommended 8 hours of sleep a night. She selects a random sa

dsp73

Answer:

H0 : μ = 8

H1 : μ < 8

Test statistic = - 7.51

conclude that there is statistical significance that student at the school get less than 8 hours of sleep on average.

Step-by-step explanation:

The hypothesis :

H0 : μ = 8

H1 : μ < 8

The test statistic :

(xbar - μ) ÷ (s/√(n))

Sample data :

1.75, 2, 2.25, 2.25, 2.5, 3, 3.5, 3.5, 3.5, 3.75, 4, 4.25, 4.5, 4.5, 4.5, 4.75, 5.25, 5.5, 5.75, 5.75, 5.75, 6, 6, 6, 6.25, 6.25, 6.25, 6.5, 6.5, 6.5, 6.75, 7, 7, 7, 7.5, 7.5, 7.75, 8, 8.25, 8.25, 8.25, 8.5, 8.75, 9, 9

Using calculator :

Sample mean, xbar = 5.71666

Sample standard deviation, s = 2.04

The test statistic :

(5.7166 - 8) ÷ (2.04/√(45))

-2.28 / 0.3041052

= - 7.5085

= - 7.51

Degree of freedom = 45 - 1 = 44

Pvalue(-7.51, 44) = 0.00001

α = 1% = 0.01

Since Pvalue < α ; we reject H0 and conclude that there is statistical significance that student at the school get less than 8 hours of sleep on average.

4 0

3 years ago

X delivery persons carry a total of B bags of groceries up the stairs. They can each carry y bags at a time, and they each make

True [87]

Answer:

B = 2xy

Step-by-step explanation:

pretty sure this is it

7 0

3 years ago

Read 2 more answers

What value of x makes this equation true?<br>10x-6=3(x+1/2)

valina [46]

Answer:

15/14

Step-by-step explanation:

3(x+1/2)

10x-6=3x+3/2

7x=3/2+12/2

7x=15/2

x=15/2*1/7

x=15/14

5 0

3 years ago