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3 years ago

Need help with solving both of these questions for geometry homework.

Mathematics

1 answer:

faltersainse [42]3 years ago

8 0

Answer:

m<R = m<T = 80.5 deg

Step-by-step explanation:

Since WXYZ is a square, <WXZ is formed with a diagonal of the square and has measure 45 deg.

m<WXZ = 8x - 19 = 45

8x - 19 = 45

8x = 64

x = 8

Draw the kite. Make sure that segments QR and RS are not congruent. Fill in the given angle measures. Angles R and T are congruent opposite angles.

The sum of the measures of the interior angles of a convex, n-sided polygon is

180(n 2).

A kite is a quadrilateral, so n = 4.

180(4 - 2) = 180(2) = 360

The sum of the measures of the interior angles of a kite is 360 deg.

m<Q + m<R + m<S + m<T = 360

75 + m<R + 124 + m<T = 360

m<R + m<T + 199 = 360

m<R + m<T = 161

m<R = m<T, so we substitute m<T with m<R.

m<R + m<R = 161

2m<R = 161

m<R = 80.5

m<R = m<T = 80.5 deg

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A nurse collected data about the average birth weight of babies in the hospital that month. Her data is shown using the dot plot

mixer [17]

Answer:

The values of the box-plot are: B = {8.2, 8.3, 8.4, 8.5 and 8.9}.

Step-by-step explanation:

The data provided is as follows:

X Frequency

8 0

8.1 0

8.2 2

8.3 2

8.4 2

8.5 3

8.6 0

8.7 1

8.8 0

8.9 1

9 0

So, the actual data is:

S = {8.2 , 8.2 , 8.3 , 8.3 , 8.4 , 8.4 , 8.5 , 8.5 , 8.5 , 8.7 , 8.9 }

A boxplot, also known as a box and whisker plot is a method to demonstrate the distribution of a data-set based on the following 5 number summary,

Minimum (shown at the bottom of the chart)
First Quartile (shown by the bottom line of the box)
Median (or the second quartile) (shown as a line in the center of the box)
Third Quartile (shown by the top line of the box)
Maximum (shown at the top of the chart).

The data set is arranged in ascending order.

The minimum value is, Min. = 8.2

The lower quartile is,

$[\frac{n+1}{4}]^{th}\ obs.=[\frac{11+1}{4}]^{th}\ obs.=3^{rd }\ obs. =8.3$ ,

Q₁ = 8.3.

The median value is,

$[\frac{n+1}{2}]^{th}\ obs.=[\frac{11+1}{2}]^{th}\ obs.=6^{th}\ obs.=8.4$

Median = 8.4

The upper quartile is,

$[\frac{3(n+1)}{4}]^{th}\ obs.=[\frac{3(11+1)}{4}]^{th}\ obs.=9^{th }\ obs. =8.5$ ,

Q₃ = 8.5.

The maximum value is, Max. = 8.9.

So, the values of the box-plot are: B = {8.2, 8.3, 8.4, 8.5 and 8.9}.

5 0

3 years ago

PLEASE HELP 4 QUESTIONS 90 POINTS

kondor19780726 [428]

1. n^2 -8n +16 = 25

Subtract 25 from both sides

n^2 - 8n + 16 - 25 = 0

Simplify

n^2 - 8n - 9 =0

Factor

(n-9)(n+1) = 0

Solve for n

n-9 = 0, n = 9

n+1 = 0, n = -1

Solution: 9,-1

2. C = b^2/25

Multiply both sides by 25:

25c = b^2

Take square root of both sides

b = +/-√25c

Simplify:

b = 5√C, -5√C

3. d = 16t^2 +12t

subtract d from both side:

16t^2 + 12t -d =0

Use quadratic formula to solve:

t = (3 +/-√(9-4d))/8

4. 5w^2 +10w =40

Subtract 40 from both side:

5w^2 + 10w -40 = 0

Factor:

5(w-2)(w+4)=0

Divide both sides by 5:

(w-2)(w+4)=0

Solve for w:

w-2 = 0, w = 2

w+4=0, w = -4

Solution: 2,-4

4 0

3 years ago

Read 2 more answers

Solve the triangle. Round side lengths to the nearest tenth and angle measures to the nearest degree.

kirill115 [55]

Answer:

a=14.28

b=22.919

c=68°

6 0

2 years ago

The volume of the rectangular prism is 648 feet. The rectangular base is 6 feet by 9 feet. What is the height of the prism?

IrinaK [193]

Answer:

$h=12ft$

Step-by-step explanation:

The formula one would use for finding the volume of a rectangular prism is as follows:

Volume = length × width × height , $V=l*w*h$

With this in mind, let's plug in the given variables in the question for this formula.

$V=648ft^3$

$l=6ft$

$w=9ft$

$h=$ ?

We don't know the height, but that's just fine. We will plug in all our values and isolate $h$ .

$V=lwh\\648ft^3=(6ft)(9ft)h$

I'm leaving in units just because I want to show that units aren't just for show. They can be used when in doubt of how to go about your math.

$648ft^3=(6ft)(9ft)h\\648ft^3=(54ft^2)h\\\frac{648ft^3}{54ft^2}=\frac{(54ft^2)h}{54ft^2}$

Notice, that the units on the left side cancel out, leaving only the unit $ft$ left next to the solution. In the same way, the units on the right side cancel out too, leaving only $h$ , height.

$\frac{648ft^3}{54ft^2}=\frac{(54ft^2)h}{54ft^2}\\12ft=h$

If involving units only confuses you, like it does for me, you can remove them like so, you just need to know what units your solution uses instead of being able to come to the proper units by using math.

$V=lwh\\648=(6)(9)h\\648=54h\\\frac{648}{54}=\frac{54h}{54}\\12ft=h$

5 0

3 years ago

Please help!

erik [133]

For the answer to the question above,
1 + nx + [n(n-1)/(2-factorial)](x)^2 + [n(n-1)(n-2)/3-factorial] (x)^3

1 + nx + [n(n-1)/(2 x 1)](x)^2 + [n(n-1)(n-2)/3 x 2 x 1] (x)^3 

1 + nx + [n(n-1)/2](x)^2 + [n(n-1)(n-2)/6] (x)^3 

1 + 9x + 36x^2 + 84x^3 

In my experience, up to the x^3 is often adequate to approximate a route. 

(1+x) = 0.98 

x = 0.98 - 1 = -0.02 

Substituting: 

1 + 9(-0.02) + 36(-0.02)^2 + 84(-0.02)^3 

approximation = 0.834 

Checking the real value in your calculator: 

(0.98)^9 = 0.834 

So you have approximated correctly. 

If you want to know how accurate your approximation is, write out the result of each in full: 

1 + 9(-0.02) + 36(-0.02)^2 + 84(-0.02)^3 = 0.833728 

 (0.98)^9 = 0.8337477621 

So it is correct to 4

5 0

2 years ago

Read 2 more answers