7.
Find all solutions to the following triangle. (Round your answers for angles A, C, A', and to the nearest minute. Round your answers for sides a and a'to two decimal places. If either triangle is not
possible, enter NONE In each corresponding answer blank.)
B = 65° 20', b = 5.38 inches, c = 4.88 inches
First triangle (assume C greater than or equal to 90°):
A= ____ degrees ____’
C=____ degrees ____’
a= ____ in

Answers

Answer 1

The measures of the angles and the lengths of the sides of the triangle can

be found using sine rule.

The correct responses are;

A = 59 degrees 9'C = Nonea = 5.083 in.

Reasons:

The given parameter are;

∠B = 65°20', b = 5.38 inches, c = 4.88 inches

∠C ≥ 90°

By sine rule, we have;

[tex]\dfrac{5.38}{sin(65^{\circ} 20')} = \mathbf{ \dfrac{4.88}{sin(\angle C)}}[/tex]

[tex]sin(\angle C) = \mathbf{ \dfrac{sin(65^{\circ} 20') \times 4.88}{5.38}}[/tex]

[tex]\angle C = arcsin \left(\dfrac{sin(65^{\circ} 20') \times 4.88}{5.38} \right) \approx \mathbf{ 55.517 ^{\circ}}[/tex]

∠C = 55.517° < 90°, therefore, the correct response is; None

[tex]\dfrac{sin(65^{\circ} 20')}{5.38} = \dfrac{4.88}{sin(\angle C)}[/tex]

∠A = 180° - 65°20' - 55.517° = 59.15° = 59°9'

∠A = 59°9'

Therefore;

[tex]\dfrac{5.38}{sin(65^{\circ} 20')} = \mathbf{ \dfrac{a}{sin(59.15^{})}}[/tex]

[tex]a = \dfrac{5.38 \times sin(59.15^{\circ}) }{sin(65^{\circ} 20')} \approx \mathbf{ 5.083}[/tex]

a ≈ 5.083 inches

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https://brainly.com/question/15018190


Related Questions

what is the area of a rectangle if 1 base is 14 in, the 2nd base is 3.5 in and the height is 8 in?​

Answers

Check the picture below.

notice, we have three pair of sides, let's add them all up to get the area

[tex]\stackrel{\textit{left and right}}{2(8\cdot 14)}+\stackrel{\textit{front and back}}{2(3.5\cdot 8)}+\stackrel{\textit{top and bottom}}{2(3.5\cdot 14)}\implies 378~in^2[/tex]

Will the answer to the subtraction problem below be odd or even?
5291 - 4070 = ?

Answers

Answer:

1221

Step-by-step explanation:

here you go ...........

even because the answer is 1221

What is 1/3÷1/2 math answers?

Answers

Step-by-step explanation:

If you like my answer than please mark me brainliest thanks

what is 7 1/2 inches as a decimal of 1 foot

Answers

Answer:

7 1/2 inches as a decimal of 1 foot is 0.625ft

Answer:

7 1/2 inches = 0.625 ft

Step-by-step explanation:

7 1/2 inches = 7.5 inches

1 ft = 12 inches

7.5/12 = 0.625

7 1/2 inches = 0.625 ft

There are 20 school days in a month. About how many miles does Manuel walk each month? Write an equation to show your work.

Answers

Answer:

he  walks at lest 5 miles

Step-by-step explanation:

3. Find the difference between the two expressions.
(3/5x - 5y) - (4/5x + 2y

Answers

Answer:

[tex]^{-1}/_{5}x-7y[/tex]

Step-by-step explanation:

Our equation is

[tex](^{3}/_{5}-5y)-(^{4}/_{5}+2y)[/tex]

now we distribute the - and we get

[tex]^{3}/_{5}-5y-^{4}/_{5}-2y[/tex]

[tex]Combine[/tex] [tex]like[/tex] [tex]terms[/tex]

and now we have [tex]^{-1}/_{5}x-7y[/tex]

Any athlete who fails the Enormous State University's women's soccer fitness test is automatically dropped from the team. Last year, Mona Header failed the test, but claimed that this was due to the early hour. (The fitness test is traditionally given at 5 AM on a Sunday morning.) In fact, a study by the ESU Physical Education Department suggested that 46% of athletes fit enough to play on the team would fail the soccer test, although no unfit athlete could possibly pass the test. It also estimated that 37% of the athletes who take the test are fit enough to play soccer. Assuming these estimates are correct, what is the probability that Mona was justifiably dropped

Answers

Using conditional probability, it is found that there is a 0.7873 = 78.73% probability that Mona was justifiably dropped.

Conditional Probability

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened. [tex]P(A \cap B)[/tex] is the probability of both A and B happening. P(A) is the probability of A happening.

In this problem:

Event A: Fail the test.Event B: Unfit.

The probability of failing the test is composed by:

46% of 37%(are fit).100% of 63%(not fit).

Hence:

[tex]P(A) = 0.46(0.37) + 0.63 = 0.8002[/tex]

The probability of both failing the test and being unfit is:

[tex]P(A \cap B) = 0.63[/tex]

Hence, the conditional probability is:

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.63}{0.8002} = 0.7873[/tex]

0.7873 = 78.73% probability that Mona was justifiably dropped.

A similar problem is given at https://brainly.com/question/14398287

Please help!

Find the equation of this line.

Answers

Answer:

y = 1/3x + 2

Step-by-step explanation:

Slope - Intercept Form = y = mx + b

y - intercept = b = 2 (point of intersection of the y-axis)

m = slope

Slope = Change in Y/Change In X

You can see that as the graph goes up by 1, it goes to the right 3, so slope = 1/3

Equation : y = mx + b

Equation : y = 1/3x + 2

-Chetan K

Answer:

Step-by-step explanation:

Equation : y = mx + b

Equation : y = 1/3x + 2

Don’t totally understand it

Answers

Answer:

A.1 B.2 E.5 F.6

Step-by-step explanation:

Hope it helps brainliest awnser pls

A tire manufacturer is interested in testing the fuel economy for two different tread patterns. Tires of each tread type are driven for 1000 miles on each of 18 different cars. In a separate experiment, 18 cars were outfitted with tires with tread type A, and another 18 were outfitted with tires with tread type B. Each car was driven 1000 miles. The cars with tread type A averaged 23.95 mpg, with a standard deviation of 1.79 mpg. The cars with tread type B averaged 22.19 mpg, with a standard deviation of 1.95 mpg. Let μX represent the population mean mileage for tread type A and let μY represent the population mean mileage for tread type B.


Required:

Find a 99% confidence interval for the difference μXâμY. Round the answers to three decimal places.

Answers

Using the t-distribution, it is found that the 99% confidence interval for the difference is (0.058, 3.462).

We are given the standard deviation for the samples, hence, the t-distribution is used to solve this question.

The standard errors are given by:

[tex]s_A = \frac{1.79}{\sqrt{18}} = 0.4219[/tex]

[tex]s_B = \frac{1.95}{\sqrt{18}} = 0.4596[/tex]

For the distribution of differences, the mean and the standard error are given by:

[tex]\overline{x} = \mu_A - \mu_B = 23.95 - 22.19 = 1.76[/tex]

[tex]s = \sqrt{0.4219^2 + 0.4596^2} = 0.6239[/tex]

The interval is given by:

[tex]\overline{x} \pm ts[/tex]

The critical value for a two-tailed 99% confidence interval with 18 + 18 - 2 = 34 df is t = 2.7284.

Then:

[tex]\overline{x} - ts = 1.76 - 2.7284(0.6239) = 0.058[/tex]

[tex]\overline{x} + ts = 1.76 + 2.7284(0.6239) = 3.462[/tex]

The 99% confidence interval for the difference is (0.058, 3.462).

For more on the t-distribution, you can check https://brainly.com/question/16162795

pls help me solve the missing answers thanks!

Answers

Answer: I'll give you formula

Step-by-step explanation: circumference = 2 x π x radius

radius = diameter÷2      area = π × radius²

3/4 ÷ a = 1/4. Solve for a

Answers

Answer:

a = 3

Step-by-step explanation:

ok so first you do the reciprocal of division which is multiplication. So its gonna be 3/4 x 1/a = 1/4

you multiply the fractions 3/4 x 1/a and get 3/4a = 1/4

then you cross multiply and you get 12=4a

swap sides so its going to be 4a = 12

divide both sides by 4 and you get a = 3

A store sells 5 T-shirts for $48.05. What is the unit cost per T-shirt?

Answers

Answer:

$9.61 per shirt

Step-by-step explanation:

You take the total cost of $48.05 and divide it by the number of t-shirts which is 5.

48.05/5 = 9.61

Ty'Sean went to the bowling alley and spent $14.50. If his rental shoes cost $4.50 and he played in 5 games, what was the price per game?

Answers

Answer:

$2 each

Step-by-step explanation:

$14.50-$4.50=$10.00

10.00/5 games =$2 each

Convert 95°F to degrees Celsius.
If necessary, round your answer to the nearest tenth of a degree.
Here are the formulas.
C=- (F-32)
-F
9
F==C+32

Answers

Answer:

35 degrees celsius

(Score for Question 2: of 27 points) 2. Two sidewalks in a park are represented by lines on a coordinate grid. Two points on each of the lines are shown in the tables. Sidewalk 1 х y 2 17 0 5 Sidewalk 2 х у 1 20 3 26 (a) Write the equation for Sidewalk 1 in slope-intercept form. (b) Write the equation for Sidewalk 2 in point-slope form and then convert to slope-intercept form. (c) Is the system of equations consistent independent, coincident, or inconsistent? Explain. a. Note: Review 2.11 Strange Solutions and 5.05 Classifying Systems if you're not sure where to start. (d) Use the substitution or elimination method to solve your system, and explain which one you picked. If the two sidewalks intersect, what are the coordinates of the point of intersection?


PLS HURRRRRRY i need this answer the real one and step by step pls if u dont know it dont try​

Answers

Answer:

Step-by-step explanation:

From the question, I couldn't really tell what the chart looks like, so I am guessing it looks like this:

Sidewalk 1:

x  |  y

2  |  17

0  | 5

Sidewalk 2:

x  |  y

1  |  20

3  | 26

Part a.

Now, we have to write the equation for sidewalk 1 in slope-intercept form.

Slope-intercept form is represented as this: [tex]y=mx+b[/tex], where m is the slope and b is the y-intercept. Because this is true for all values on the line, we can plug in values of the chart for Sidewalk 1.

[tex]17=2m+b\\5=0m+b[/tex]

Subtracting the second equation from the first, we have

[tex]12=2m[/tex], and [tex]m = 6[/tex].

Now, we can just plug 6 back into the first equation to get:

[tex]17=2(6)+b[/tex]  to get [tex]17 = 12 + b[/tex], and then [tex]b = 5[/tex].

Now, we can just rewrite slope intercept form for Sidewalk 1 to have

[tex]y=6x+5[/tex].

Part b.

Point-slope form is represented as [tex]y-y_1=m(x-x_1)[/tex], where x and y are the coordinates of one point, and x1 and y1 are the coordinates of another point on the line. Because the chart represented for Sidewalk 2 includes a point, namely [tex](1, 20)[/tex] and [tex](3, 26)[/tex], we can plug this in and solve for the slope:

[tex]26-20=m(3-1)[/tex]

This is it in point-slope form. Because the second part of the question asks us to convert to slope-intercept form, we must solve for the slope, or m.

Expanding, we have [tex]26-20=3m-m[/tex]

Combining like terms, we have [tex]6 = 2m[/tex], and then [tex]3 = m[/tex]. Now, we need to plug a point and the slope back into point-slope form, not needing another point. We choose [tex](1, 20)[/tex], even though [tex](3, 26)[/tex] works just as well.

[tex]y-20=3(x-1)[/tex]

Expanding, we have [tex]y-20=3x-3[/tex]

Adding 20 to both sides, we have [tex]y=3x+17[/tex]

Part c. and d.

We see that both equations do not have the same slope, so then they are not parallel, meaning they don't have no solutions. If they have a solution, we can set them equal to each other.

[tex]3x+17=6x+5[/tex]

Subtracting 3x, we have [tex]17=3x+5[/tex]

Subtracting 5, we have [tex]12 = 3x[/tex]

Dividing by 3, we have [tex]x = 4[/tex].

Because there is no x = x, or anything like that, the solution does not have infinite solutions and therefore has one solution, meaning it is consistent independent.

solve using quadratic formula
6x^2-x=2

Answers

[tex]6x^2-x=2\implies 6x^2-1x-2=0 \\\\[-0.35em] ~\dotfill\\\\ ~~~~~~~~~~~~\textit{quadratic formula} \\\\ \stackrel{\stackrel{a}{\downarrow }}{6}x^2\stackrel{\stackrel{b}{\downarrow }}{-1}x\stackrel{\stackrel{c}{\downarrow }}{-2}=0 \qquad \qquad x= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a}[/tex]

[tex]x = \cfrac{ -(-1) \pm \sqrt { (-1)^2 -4(6)(-2)}}{2(6)}\implies x = \cfrac{1\pm\sqrt{1+48}}{12} \\\\\\ x = \cfrac{1\pm\sqrt{49}}{12}\implies x = \cfrac{1\pm 7}{12}\implies x = \begin{cases} \frac{8}{12}\to &\frac{2}{3}\\[1em] -\frac{6}{12}\to &-\frac{1}{2} \end{cases}[/tex]

GIVING OUT BRAINLIEST!!

Answers

Answer:

Jill plz tell if i am right

Step-by-step explanation:

give me schoology website

Một người tiêu dùng có thu nhập I = 1.200 đ dùng để mua hai sản phẩm X và Y với giá tương ứng là PX = 100đ/sp và PY = 300đ/sp. Mức thoả mãn được thể hiện qua hàm số:

TUX = -1/3X2 + 10X

TUY = -1/2Y2 + 20Y

a. Hãy xác định phương án tiêu dùng tối ưu của người này?

b. Tính tổng hữu dụng tương ứng đạt được?

Answers

gak bisa bahasa inggris.

Step-by-step explanation:

maap.

PLEASE LOOK AT THE PHOTO !Number 32 please help me and thank you
❤️❤️❤️

Answers

Answer: 4 1/4 hours

Explanation: 2.5 + 1.75 = 4.25

4.25 = 4 1/4

1. 543.5 = _______ ft _________ in

Answers

Answer:

uważam że nie wiem ale bym wiedział tylko muszę wiedzieć

Rewrite 1/4 barrel 2/5 hour as a unit rate ​

Answers

Answer:

5/8

Step-by-step explanation:

1/4÷2/5=1/4×5/2=5/8 barrel/Hour

Elijah has a muffin and a banana. To find the banana's weight, Elijah uses a balance scale twice and the scale is balanced both times as shown below. How much does the banana weigh? please help me I don't get it

Answers

Answer:

the scale is balanced both times as shown below.

No scale is shown

Step-by-step explanation:

y/x dy/dx=(1+x^2)^-1/2(1+y^2)^1/2

Answers

Answer:

(1+y)^(3/2)-3(1+y)^(1/2)=(1+x)^(3/2)-3(1+x)^(1/2)+c

Step-by-step explanation:

This is separable.

Multiply x dx on both sides and divide both sides by (1+y)^(1/2) to obtain:

y/(1+y)^(1/2)=(1+x)^(-1/2) x dx

Using law of exponents to get rid of negative exponent by finding reciprocal:

y/(1+y)^(1/2)=x/(1+x)^(1/2) dx

Let u=(1+y)^(1/2).

Then u^2=1+y.

Differentiate: 2 u du=dy

[Let v=(1+x)^(1/2).]

Plug in our substitution:

(u^2-1) 2u du/u=(v^2-1) 2v dv/v

Simplify:

(u^2-1) 2 du=(v^2-1) 2 dv

Integrate both sides:

(u^3/3-u) 2+L=(v^3/3-v) 2+K

Divide both sides by 2:

u^3/3-u +L/2=v^3/3-v+K/2

K/2-L/2 is just a constant value C:

u^3/3-u=v^3/3-v+C

Use substitution again to put back in terms of x and y:

((1+y)^(1/2))^3/3-(1+y)^(1/2)=((1+x)^(1/2))^3/3-(1+x)^(1/2)+C

Simplify the exponent part a bit:

(1+y)^(3/2)/3-(1+y)^(1/2)=(1+x)^(3/2)/3-(1+x)^(1/2)+C

I don't like the division by 3 so multiply both sides by 3:

(1+y)^(3/2)-3(1+y)^(1/2)=(1+x)^(3/2)-3(1+x)^(1/2)+3C

3C is still just an unknown constant, c.

(1+y)^(3/2)-3(1+y)^(1/2)=(1+x)^(3/2)-3(1+x)^(1/2)+c

6/11 = q/3


Pls help me!

Answers

q=18/11

Step by step:

Times both sides by 3 to cancel out the 1/3.

6/11(3)=q

18/11=q

I need help on this
Here it is

Answers

Solution:

2. Barlow School: (4 / 9) * 873 = 388 of the students are boys.

873-388 = 485 of the students are girls.

The b(boy) to g(girl) ratio at Barlow School is 388b:485g


1. Willow School: (2 / 3) * 630 = 420 of the students are girls.

630-420 = 210 of the students are boys.

The b(boy) to g(girl) ratio at Willow School is 420g:210b

3. 388 - 210 = 178


Answer: Barlow School has the greater number of boys by 178 students.

Read the excerpt from "Healthy Eating."

If anything gets in the way of our good eating, it's lifestyle. When you get home from work late, why spend an hour in front of the stove when you can spend two minutes at the microwave? And doesn't that oatmeal box claim to be a good source of calcium for our kids, never mind the small print listing 14 grams of sugar? A small soda at the movies could satisfy a family of four. Even schools have vending machines.

What does the author think is responsible for people's poor eating habits?

A They do not know how to correctly read the nutrition information on food packages.
B They do not know how to prepare healthy meals that are both inexpensive and quick.
C They often choose foods that are quick and convenient instead of ones that are healthy.
D They spend time thinking about work and entertainment instead of thinking about food.

Answers

Step-by-step explanation:

Find the critical points, relative extrema, and saddle points of the function. (If an answer does not exist, enter DNE.) f(x, y) = 25 − (x − 5)2 − y2

Answers

Take the first partial derivatives of f(x, y):

∂f/∂x = -2 (x - 5) = 10 - 2x

∂f/∂y = -2y

The critical points occur where both derivatives are zero:

10 - 2x = 0   ===>   x = 5

-2y = 0   ===>   y = 0

So there is only critical point at (5, 0), which takes on a value of f(5, 0) = 25.

Compute the Hessian matrix for f :

[tex]H(x, y) = \begin{bmatrix}\frac{\partial^2f}{\partial x^2} & \frac{\partial^2f}{\partial x\partial y} \\ \frac{\partial^2f}{\partial y\partial x} & \frac{\partial^2f}{\partial y^2}\end{bmatrix} = \begin{bmatrix}-2&0\\0&-2\end{bmatrix}[/tex]

Since det(H(x, y)) = 4 > 0 for all x, y, the critical point (5, 0) is a relative minimum.

f has no saddle points.

What is the equation in slope-intercept form for the line that passes through the points (-6, 4) and (12, 13)​

Answers

Answer: y= 1/2x + 7

Step-by-step explanation:

answer fully /// /////////////////////

Answers

Answer:

Step-by-step explanation:

Yes, but like they say in Vegas, you're trying to make your point the hard way.

8 * (8 - 4)              So the distributive property is means remove the brackets.

8*8 - 4*8               What you have done is multiply the numbers on either side of the - sign by 8. It is a good practice NOT to destroy the minus sign just yet.

64 - 32

32                          The answer is 32. That's how the distributive property works

With this question only It might be easier to do what is inside the brackets first. That's making your point the easy way.

8*(8-4) = 8* 4 = 32

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