How to find the area of a triangle using trig

Answer:

The shortest segment from the point to the line is perpendicular to the line.

Step-by-step explanation:

See the attached image.  The blue segments go from the point to the line, but they are longer than the shortest such segment (red).

Answer:

y = - 15.57x² + 179.32x + 0.20

510

Step-by-step explanation:

The quadratic model obtained using a quadratic regression solver with Coefficient rounded to the nearest hundredth is :

y = - 15.57x² + 179.32x + 0.20

Where, height = y

x = time

Using the model obtained ; the height, to the nearest foot, at a time, x = 6.4 seconds.

y = - 15.57x² + 179.32x + 0.20

y = - 15.57(6.4^2) + 179.32(6.4) + 0.20

y = 510.1008

y = 510

The quadratic model obtained using a quadratic regression solver with Coefficient rounded to the nearest hundredth is :

height = y

x = time

                          Using the model obtained;

The height, to the nearest foot, at a time, x = 6.4 seconds.

Thus, the correct answer is 510.

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Answer:

Step-by-step explanation:

The missing diagram showing the trapezoids is attached in the diagram below.

There are three stages by which trapezoid A must be transformed into trapezoid B.

We can see three fundamental differences as follows:

As a result, we will perform the following transformations: 

Answer:

The image's not clear!

Step-by-step explanation:

Answer:

The answer is 30 (C)

Answer:

Third Grade!

Step-by-step explanation:

Hope you have a good day <3

Answer:

it's third grade:)

Step-by-step explanation:

just follow the line from 150 and when you see the grade level that meets it exactly there's your answer!

Answer:

y=x+3

Step-by-step explanation:

when you connect all the dots it makes a straight linear line. then you can use the format y=mx+b

y is the y value

m is the slope (change in y divided by change in x or, rise over run)

x is the x value

b is the y intercept (the y value where the line will touch the y axis/vertical line)

to make the equation

y=mx+b

y and x are variables so you dont need to write them

the slope is rise/run just pick two points such as the first point (0,3) and the second point (1,4)

between these points it changes one unit to the right (1) and one unit up vertically meaning 1/1

=1

when the slope is 1 you get

y=1x+b which is just y=x+b

then the y intercept

the first dot is touching the y axis line and it's y value is 3

y=x+3

hope this helps

Answer:

sin X=30 degree

cos X=30 degree

tan X=30 degree

cot X=30 degree

sec X=30 degree

Step-by-step explanation:

Answer:

153:20

Step-by-step explanation:

765000/100000

=153/20

9514 1404 393

Answer:

  (c)  (0, 6)

Step-by-step explanation:

Conventionally, an "ordered pair" is a pair of items in parentheses, separated by a comma. The items don't have to be numbers. (0, 6) is an ordered pair.

__

Comments on the other answer choices

Curly braces are usually used as delimiters of a set, not an ordered pair.

Three items do not constitute a "pair." Rather, they are a "triple."

Items without any particular indicator of grouping are usually not considered a "pair."

Answer:

yes it does. good job on your A.

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

Answer:

x > [tex]\frac{1}{5}[/tex]

Step-by-step explanation:

[tex]\frac{5(9-x)}{3+1}<11[/tex]

Add 3 and 1 to get 4.

[tex]\frac{5(9-x)}{4}<11[/tex]

Use the distributive property to multiply 5 by 9−x.

[tex]\frac{45-5x}{4}<11[/tex]

Subtract  45/5 from both sides.

[tex]-\frac{5}{4}x<11-\frac{45}{4}[/tex]

Since 44/4 and 45/4 have the same denominator, subtract them by subtracting their numerators.

[tex]-\frac{5}{4} x<-\frac{1}{4}[/tex]

Multiply both sides by -4/5, the reciprocal of -5/4. Since -5/4 is negative, the inequality direction is changed.

[tex]x>-\frac{1}{4} (-\frac{4}{5} )[/tex]

Multiply -1/4 times -4/5 by multiplying numerator times numerator and denominator times denominator.

[tex]x>\frac{-(-4)}{4 x 5}[/tex]

[tex]x>\frac{1}{5}[/tex]

Answer:

B  160 ft^2

Step-by-step explanation:

Right away you can eliminate A and C as area in square feet suppose to be. A=bh A= 20 x 8=160 ft^2

Answer:

650,000 cm²

Step-by-step explanation:

10x6.5=65 METERS squared.  They want it in CENTIMETERS squared.

65m² = 650,000cm²

Answer:

32.5[tex]m^{2}[/tex]

Step-by-step explanation:

The coloured triangle with the blank triangle area =

(14m x 6.5m)÷2 = 45.5[tex]m^{2}[/tex]

The blank triangle area =

[(14-10m) x 6.5m]÷2 = 13[tex]m^{2}[/tex]

Therefore:

The coloured triangle area =

(45.5 - 13)[tex]m^{2}[/tex]

=32.5[tex]m^{2}[/tex]

Answer:

x=√154 over 7 , −√154 over 7

Step-by-step explanation:

Answer:

the answer is that x=positive or negative square root of 22 over square root of 7

Step-by-step explanation:

Answer:

The 95% confidence interval estimate of the population mean  is (7.38, 8.46).

Step-by-step explanation:

Before building the confidence interval, we need to find the mean and standard deviation of the sample.

In this sample, there are 50 values.

Mean of the sample:

Sum of all values divided by the number of values.

With the help of a calculator, the mean is of 7.92.

Standard deviation:

Square root of the division of the sum of the difference squared between each value and the mean by the number of the values.

With the help of a calculator, the standard deviation is of 1.8958.

Confidence interval:

We have the confidence interval for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 50 - 1 = 49

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 49 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.01

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 2.01\frac{1.8958}{\sqrt{50}} = 0.54[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 7.92 - 0.54 = 7.38

The upper end of the interval is the sample mean added to M. So it is 7.92 + 0.54 = 8.46

The 95% confidence interval estimate of the population mean  is (7.38, 8.46).

Answer:

Option D

Step-by-step explanation:

[tex]60+45+75=180[/tex]

[tex]Triangle ~has ~the~ sum ~of ~angle =180[/tex]

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hope it helps...

have a great day!!

Answer:

D will be your answer!!

Step-by-step explanation:

hope it helps

Answer:

D. (-2, -11)

Step-by-step explanation:

Since -2 - 9 = -11, it fits into the equation x - 9 = y, with -2 being "x" and -11 being "y".

And out of all the options, D is the only one that works.

Answer:

Radius of cylinder = 2 inch (Approx.)

Step-by-step explanation:

Given:

Volume of cylinder = 75.4 in³

Height of cylinder = 6 inches

Find;

Radius of cylinder

Computation:

Volume of cylinder = πr²h

Volume of cylinder = (3.14)r²(6)

75.4 = (18.84)r²

(Radius of cylinder )² = 75.4 / 18.84

(Radius of cylinder )² = 4.002123

(Radius of cylinder) = 2

Radius of cylinder = 2 inch (Approx.)

Answer:

m∡x = 95°

m∡y = 147°

m∡z = 128°

Step-by-step explanation:

m∡z = 180-52 = 128

measure of third angle in left triangle = 180-(45+50) = 85°

m∡x = 180-85 = 95°

measure of top angle in right triangle = 180-(95+52) = 33°

m∡y = 180-33 = 147°

Answer:

9

Step-by-step explanation:

you can always use guess-and-check:

124 seems rather high

(6)P(2) = 6!/4! = 6x5 ≠ 72

(9)P(2) = 9!/7! = 9x8 = 72

Answer:

i think the value of n is 12

Answer:

5 x Square root:2

Step-by-step explanation:

Answer:

Table of values

[tex]x \to y[/tex]

[tex]0 \to -5[/tex]

[tex]1 \to -2[/tex]

[tex]2 \to 1[/tex]

[tex]3 \to 4[/tex]

[tex]4 \to 7[/tex]

[tex]5 \to 10[/tex]

See attachment for graph

Step-by-step explanation:

Given

[tex]y = 3x - 5[/tex]

Solving (a): Make a table

Considering the values of x from 0 to 5, we have:

When [tex]x = 0[/tex]

[tex]y = 3x - 5 \to 3 * 0 - 5 = -5[/tex]

When [tex]x = 1[/tex]

[tex]y = 3x - 5 \to 3 * 1 - 5 = -2[/tex]

When [tex]x = 2[/tex]

[tex]y = 3x - 5 \to 3 * 2 - 5 = 1[/tex]

When [tex]x = 3[/tex]

[tex]y = 3x - 5 \to 3 * 9 - 5 = 4[/tex]

When [tex]x = 4[/tex]

[tex]y = 3x - 5 \to 3 * 4 - 5 = 7[/tex]

When [tex]x = 5[/tex]

[tex]y = 3x - 5 \to 3 * 5 - 5 = 10[/tex]

So, we have:

[tex]x \to y[/tex]

[tex]0 \to -5[/tex]

[tex]1 \to -2[/tex]

[tex]2 \to 1[/tex]

[tex]3 \to 4[/tex]

[tex]4 \to 7[/tex]

[tex]5 \to 10[/tex]

Solving (b): The graph

See attachment

Answer:

[tex] 35m [/tex]

Step-by-step explanation:

Given :-

And we need to find the length of the rectangle . We can use the formula to find the perimeter of rectangle , as ,

Perimeter of rectangle :-

[tex]\implies Perimeter = 2( l + b)[/tex]

[tex]\implies 120m = 2 ( x + 25m) \\\\\implies x + 25m =\dfrac{120m}{2}\\\\\implies x + 25m = 60m \\\\\implies x = 60m - 25m \\\\\implies x = 35m [/tex]

Hence the length of the rectangle is 35 m .

Answer:

A. 9.8ft

Step-by-step explanation:

work out arc length using this formula

[tex]2\pi \: \times r \times \frac{\theta}{360} [/tex]

r is the radius, 7 in this case and theta(the symbol above 360) is the angle, 80 in this case

9514 1404 393

Answer:

Step-by-step explanation:

Let s represent the FCI for soccer. The given values tell us ...

  s + (s +7.47) = 108.09

  2s = 100.62 . . . . . . . . . . subtract 7.47

  s = 50.31

  s+7.47 = 57.78

The FCI for soccer was $50.31; the FCI for hockey was $57.78.

Step-by-step explanation:

I feel there is important information lost in the way you provided the problem statement.

e.g. "... also equal to ?"

equal to what ?

sin x = what ?

so, I can only guess some things.

answer C is definitely correct for any angle up to 180 degrees.

answer A is only correct for an angle of 45 or 225 degrees, where sin(x) and cos(x) are both 1/sqrt(2) or both -1/sqrt(2).

answer B is always wrong (459 degrees is no special number, this is a full circle of 360 degrees and then additional 99 degrees there is no special relationship between sine and cosine for 99 degrees, so sine and cosine cannot have the same value for any x).

answer D is always wrong, as there is always a 30 degree difference between the arguments for sine and cosine, and that can never lead to an equal value.

answer E is also always wrong, as these 45 degrees difference also block equal values.