Solve the triangle. A = 52°, b = 10, c = 7 (5 points)

Answers

Answer 1

The solutions to this triangle are:

7.944.1 degrees83.7 degrees

How to solve for the triangle

Using the law of cosine we would have

a²=b²+c²-2bc cos A

a² =100+49-2(10)(7)cos 52

This would give us

=149 -140 x (0.6157)

=62.82

We take the square root of 62.82 =

7.93 or 7.9

We have to use the sine law to find the other side

7.9/sin 52=10.057

10.06=7/sin C

such that

sin C = sin(0.6958)

=44.1°

10.06=10/sin B

cross multiply

sin B=10/10.06

= sin⁻¹0.9940

Then B = 83.7°

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Related Questions

A triangle has vertices as D(4,5), E(1,8) and F (1,2). Show that the height from D is also the median from D.

Answers

The x-coordinate of the altitude on EF is the same as the point D(4, 5) and by calculation, the height from D (1, 5) is also median from D (1, 5)

How can the height and median be calculated?

The height from D is perpendicular to EF

The slope of EF = (8 - 2)/(1 - 1) = ∞

Therefore, the side EF is parallel to the y-axis.

Therefore, the coordinates of the point of intersection of the altitude from D and the line EF is (1, 5)

The median is the midpoint of the side EF

The coordinates of the midpoint is found as follows;

[tex] \mathbf{ \left(1 + \frac{1 - 1}{2}, \: 1 + \frac{8 - 2}{2}\right)} = (1 ,5)[/tex]

Therefore;

The height from D is also the median from D.

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PLEASE HELP, kinda forgot how to do it

Answers

Answer:

20

Step-by-step explanation:

Rise over run

Answer:

m = 20

Step-by-step explanation:

In an interview of 45 students, 12 liked Mathematics and Science, 5 liked Mathematics and English, 25 liked Mathematics; 23 liked Science; 4 liked all three subjects; 15 liked English; 10 liked Science and English. How many students did not like any of the subjects?​

Answers

Answer:

Step-by-step explanation:

plus 18 and subtract 4

Can someone help me out on these geometry fill in the blanks questions? Just questions 2,3,4.. it’s urgent

Answers

2.) 3&4
3.) 1&3
4.) 2&4

is 2x 2 times or 2x mean 2 x or 1x+1x or 0x+2?

Answers

Answer:

Generally x means times so the best and not dummest option is 2 times

2x and 2 x is the same the 2 x is spaced out a little

Step-by-step explanation:

What else would need to be congruent to show that triangle ABC is congruent to DEF by AAS?

Answers

Answer:

B

Step-by-step explanation:

In order the angles <C and <F are shared, then <B and <E, then the side equaling 10. This together proves that this triangle is congruent because of AAS (angle,angle,side) a triangle congruency rule.

The amount of water in a leaky bucket is given by the linear function , where y is in ounces and x is in minutes. Find and interpret the slope and y-intercept of the linear equation.

Answers

The y-intercept = 127 and the slope = -10

How to determine the y-intercept and the slope?

The function is given as:

y = 127 - 10x

A linear function is represented as:

y = c + mx

Where

c = the y-intercept

m = slope

This means that:

y-intercept = 127

slope = -10

The y-intercept implies that, the initial amount of water is 127 ounces and the slope implies that the water leaks by 10 ounces per minute

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Complete question

The amount of water in a leaky bucket is given by the linear function y = 127 - 10x, where y is in ounces and x is in minutes. Find and interpret the slope and y-intercept of the linear equation.

Li invests money in a savings account. She wants to know the amount of simple interest that she will earn in 6 years at 3.75 percent. What additional information does she need to find this amount?

Answers

Answer:

She needs the starting amount of money to create an equation.

Step-by-step explanation:

The formula that she can use when she has the starting amount or the y-intercept is this one: f(t)=P(1+b)^t.

t=time

b=percent

P=starting value

The formula with the information given is: f(6)=P(1+3.75)^6

Hope this helps!

If not, I am sorry.

Answer:

Principal

Step-by-step explanation:

Since, the amount in the simple interest is,

Where, P is the principal amount,

r is the annual rate,

t is the time ( in years ),

Here, r = 3.75 %, t = 6 years,

Thus, By the above explanation,

It is clear that, we need the value of P, that is, principal to find the amount.

For which value of b can the expression x2 + bx + 18 be factored?

Answers

An expression is defined as a set of numbers, variables, and mathematical operations. The value of b for which the expression x² + bx + 18 can be factored is 9.

What is an Expression?

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The value of b for which the given expression x² + bx + 18 can be factored is 9. This will make the expression factored as (x+3) and (x+6).

Thus, the value of b for which the expression x² + bx + 18 can be factored is 9.

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Point X is the incenter of ΔABC.
Triangle A B C has point X as its incenter. Lines are drawn from the points of the triangle to point X. Lines are drawn from point X to the sides of the triangle to form right angles. Line segments X F, X G, and X E are formed.

If EX = 4z + 1, XF = 2z + 7, and mABC = 44°, find the following measures.

GX =

Answers

Not sure about this one, please show a picture of your problem!

Michell is making a sign for her sister's birthday. The sign says "HAPPY BIRTHDAY" in all capital letters. If each letter is 4/5 inches long estimate the length needed to spell out “HAPPY BIRTHDAY."
ps.also add 4/5 for the space between the two words..................... Thanks

Answers

Answer:

5/4 is the correct answer for this question

(a) sin x° = 0.8
Given that x is an obtuse angle, find x.
(b) cos 127° = -cos yo
Given that y is an acute angle, find y.

Answers

The value of x is 126.87° and the value of y is 53°.

What is an obtuse and an acute angle?

An obtuse angle is an angle that is greater than 90° but lesser than 180° while an acute angle is an angle between 0-90°.

From the given information:

sin x° = 0.8

x = sin⁻¹ (0.8)

x = 53.13°

x + 53.1° = 180°

x = 180° -53.13°

x = 126.87°

If cos 127° = -cos y°,

-cos y = -0.6018

cos y = 0.6018

y = cos⁻¹ (0.6018)

y = 53°

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A triangle is translated by using the rule (x,y) →(x-4.y+1). Which describes how the figure is moved?
O four units left and one unit down
O four units left and one unit up
O one unit right and four units down
O one unit right and four units up

Answers

Answer:

Four units left and one unit up.

Step-by-step explanation
Adding -4 to each x-coordinate shifts the figure to the left 4 units.

Adding +1 to each y-coordinate shifts the figure up 1 unit.

The figure is moved ...

 four units left and one unit up

Answer:

2nd option

Step-by-step explanation:

x-4 = 4 left

y+1 = 1 up

2nd option

What is the logarithmic form of 13² = 169?

Answers

The logarithmic form of  13² = 169 is ㏒₁₃ 169 = 2

How to determine the logarithmic form

Using the logarithmic rule , we have that

㏒ₙn = bⁿ

Given 13² = 169

It is important to  note that it can be written either in the logarithmic form or in the index form.

In this case, we have written in the index form as .

㏒₁₃ 169 = 2

Thus, the logarithmic form of  13² = 169 is ㏒₁₃ 169 = 2

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117 Mr. Turtle, Mrs. Squirrel and Ms. Pigeon work at the Magic Forest's post office. Mr. Turtle can
deliver a package from the Southern Glade to the Northern Glade in 3 days, while Ms. Pigeon can
deliver it in 30 minutes. How much time will the same job take Mrs. Squirrel, if the ratio of Mr.
Turtle's time to the Mrs. Squirrel's time is the same as the ratio of Mrs. Squirrel's time to Ms.
Pigeon's time?

Answers

The proportion shows that the time taken to do the same job by Mrs. Squirrel is 6 hours.

How to calculate the value?

From the information given, the ratios are:

Turtle / Squirrel = Squirrel / Pigeon

3/x = x/(1/48)

x² = 1/16

x = 1/4

The number of days will be:

= 1/4 × 24

= 6 hours.

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What is a disadvantage of debt consolidation?
OA. You can have payments that are lower.
B. You can spread payments over a longer time.
о C. You can have a lower interest rate.
о D. You can pay more money in the long term.

Answers

A disadvantage of debt consolidation is you can pay more money in the long term.

What is debt consolidation?


Debt consolidation is when a person takes out a new loan in order to pay off an existing loan. Debt consolidation increases the money you pay in the long term because you would still have to pay for the new debt incurred.

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If I went to bed at around 1:20 AM, and woke up at 8 AM, around how many hours of sleep did I get?

Answers

Answer:

you would get about 6:20 of sleep

you would have gotten at least 6 hours of sleep and 20 mins

Step-by-step explanation:

Select the correct answer from each drop-down menu.
The endpoints of the longest chord on a circle are (4, 5.5) and (4, 10.5).
The center of the circle is at the point (-4, 6.75)(4, 8)(4, 9.25)(4, 16), and its radius is 1.252.53.756.25 units. The equation of this circle in standard form is (x - 4)^2 + (y - 8)^2 = 2.5(x + 4)^2 + (y + 8)^2 = 2.5(x - 4)^2 + (y - 8)^2 = 6.25(x + 4)^2 + (y + 8)^2 = 6.25.

Answers

The correct options regarding the circle with endpoints of the longest chord at (4, 5.5) and (4, 10.5) are:

The center is (4,8).The radius is of 2.5 units.[tex](x - 4)^2 + (y - 8)^2 = 6.25[/tex]

What is the equation of a circle?

The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

The center is the midpoint of the chords, hence:

[tex]x_0 = \frac{4 + 4}{2} = 4[/tex].[tex]y_0 = \frac{5.5 + 10.5}{2} = 8[/tex].

The radius is half the distance between the chords, hence:

[tex]r = 0.5\sqrt{(4-4)^2 + (10.5 - 5.5)^2} = 0.5 = 2.5[/tex].

Hence the equation is:

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

[tex](x - 4)^2 + (y - 8)^2 = 2.5^2[/tex]

[tex](x - 4)^2 + (y - 8)^2 = 6.25[/tex]

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Problem Set
Show instructions
Question 4 (1 point)
Given a triangle with sides of length 5 and 8, find the range of possible values for the third side. (Note: left
hand side of inequality in Blank 1 and right hand side in Blank 2)
Blank 1:
Blank 2:
____

Answers

Answer:

3 < x < 13

Step-by-step explanation:

Triangle Inequality Theorem

The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

Let x be the length of the unknown side.

Therefore, x will either be the longest side or one of the shorter sides.

Therefore:

   x < 5 + 8

⇒ x < 13

And:

   8 < 5 + x

⇒ 3 < x

So the range of possible values of the third side is greater than 3 and less than 13:   3 < x < 13

The table shows data from a survey about the number of times families eat at restaurants during a week. The families are either from Rome, Italy, or New York, New York:
High Low Q1 Q3 IQR Median Mean σ
Rome 21 1 1.5 7.5 6 4.5 6.5 6.6
New York 20 1 3.5 7.5 4 5 6.5 5.2

Which of the choices below best describes how to measure the center of these data?
Both centers are best described by the mean.

Both centers are best described by the median.

The Rome data center is best described by the mean. The New York data center is best described by the median.

The Rome data center is best described by the median. The New York data center is best described by the mean.

Answers

Choices for the measure of center that is best are: C. Rome data center is best described by the mean while that of New York data is best described by the median.

What are the Measures of Center?

The measures of center include the mean and the median. Mean is best for a symmetrical data distribution while median is good for a skewed data distribution with an outlier.

The data for New work has an outlier, while that of Rome does not. Therefore, the best choices for the measure of center is: C. Rome data center is best described by the mean while that of New York data is best described by the median.

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What is the measure of the corresponding central angle for XY in radians?

Answers

Answer:

4 radians

Step-by-step explanation:

Arc Length (Radians) = rθ

Given Arc Length XY  = 40cm and radius, r = 10cm,

we will substitute these 2 values into the formula to find θ.

(10)θ  = 40

θ = 40 / 10

= 4 radians

Answer:

A

Step-by-step explanation:

the length of arc XY is calculated as

arc = circumference of circle × fraction of circle

      = 2πr × [tex]\frac{0}{2\pi }[/tex] ( r is radius and Θ is central angle )

here arc = 40 and r = 10 , then

2π × 10 ×[tex]\frac{0}{2\pi }[/tex] = 40

20π × [tex]\frac{0}{2\pi }[/tex] = 40 ( cancel 20π and 2π by 2π )

10Θ = 40 ( divide both sides by 10 )

Θ = 4 radians

Briefly explain how multiple regression enhances the two primary purposes of regression analysis.

Answers

The statistical goal of multiple regression analysis is to build a linear equation model that identifies the optimal weighted linear combination of independent variables in the study in order to optimally predict the reference variable.

Regression analysis is usually performed for one of two purposes. Predicting the value of the dependent variable of a person whose information about the explanatory variable is available, or estimating the effect of the explanatory variable on the dependent variable.

In multiple regression analysis, researchers can determine the strength of the relationship between the outcome (dependent variable) and multiple predictors, and the importance of each predictor in the relationship, often the effect of other predictors. It can be evaluated by statistically eliminating it.

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PLEASE HELP!!

Triangle not drawn to scale
Given: m & B = 18°, b = 9, and c = 20. Find
m & Co to nearest whole number.

Answers

Answer:

43°

Step-by-step explanation:

Calculating for the measure of angle C using

sine rule

[tex] \frac{sin18}{9} = \frac{sinc}{20} \\ sinc = \frac{sin18 \times 20}{9} \\ sinc = 0.6867 \\ c = \csc(0.6867) \\ c = 43.3869 \\ c = 43 \: degrees[/tex]

Solve the following linear system by elimination. Check your solution:
1. x + 5y =4
2. 4x + 12y = 8

Answers

Answer:

(- 1, 1 )

Step-by-step explanation:

x + 5y = 4 → (1)

4x + 12y = 8 → (2)

multiplying (1) by - 4 and adding to (2) will eliminate x

- 4x - 20y = - 16 → (3)

add (2) and (3) term by term to eliminate x

0 - 8y = - 8

- 8y = - 8 ( divide both sides by - 8 )

y = 1

substitute y = 1 into either of the 2 equations and solve for x

substituting into (1)

x + 5(1) = 4

x + 5 = 4 ( subtract 5 from both sides )

x = - 1

As a check

substitute these values into the left side of both equations and if equal to the right side then they are the solution.

- 1 + 5(1) = - 1 + 5 = 4 = right side

4(- 1) + 12(1) = - 4 + 12 = 8 = right side

(- 1, 1 ) is the solution to the system of equations

Substituting the equation y = 4x + 1 into the equation 2y = -x – 1 will produce the equation ________.

a.)
7x = -3

b.)
7x = 1

c.)
9x = -3

d.)
9x = 1

Answers

Answer:

C.

Step-by-step explanation:

This is substitution method in solving simulteanous equations.

given y = 4x + 1

we will substitute y into 2y = -x-1

[tex]2(4x + 1) = - x - 1 \\ 8x + 2 = - x - 1 \\ 8x + x + 2 = - 1 \\ 9x + 2 = - 1 \\ 9x = - 1 - 2 \\ 9x = - 3[/tex]

Therefore the answer is C.

SOLVING

[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]

Substituting the equation given into another equation will produce another equation. But which one?

[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]

[tex]\bf{2y=-x-1}[/tex] | substitute the required equation

[tex]\bf{2(4x+1)=-x-1}[/tex] | solve in terms of x

[tex]\bf{8x+2=-x-1}[/tex] | carry on solving

[tex]\bf{9x+2=-1}[/tex] | carry on solving

[tex]\bf{9x=-3[/tex]

[tex]\cline{1-2}[/tex]

[tex]\bf{Result:}[/tex]

                 [tex]\bf{=The\;third\;option}[/tex]

[tex]\LARGE\boxed{\bf{aesthetics\not1\theta 1}}[/tex]

What is the system of inequalities associated with the following graph?


A) {y>−2
{x+y≥1


B){y<−2
{x+y≥1


C){y<−2
{x+y<1

D){y< -2
{x+y> 1

Answers

Answer: C

Step-by-step explanation:

[tex]y=-2[/tex] is dotted and shaded below, so it represents [tex]y < -2[/tex].

Also, [tex]x+y=1[/tex] is shaded above, so it represents [tex]x+y < 1[/tex].

Does dy/dx in a graph mean the value of f'(x), or the slope of f'(x) at the point?

Answers

dydx and f'(x) are the same thing just in different notations

Write at least 1 full sentence explaining the steps you would take to evaluate an expression.

Answers

The step you would take to evaluate an expression is to follow the order of operation

What are expressions?

Expressions are mathematical statements that involve variables, terms, coefficients and mathematical operators

How to determine the steps?

Different expressions require different ways of solving

However, the general guide is that the order of operation must be followed

The order of operation is represented by the acronym BEDMAS

Which means

Bracket

Exponent

Division

Multiplication

Addition

Subtraction

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6.Find by suitable rearrangement
a)4x2984x250
b) 495+114+205
factor of 13965

Answers

The solutions by suitable arrangement are:

2984000814

How to find the suitable arrangement

a)4x2984x250

By suitable arrangement, we would arrange this as

(4 x 250) x 2984

= (1000 * 2984)

= 2,984,000

b. b) 495+114+205

By suitable arrangement we would have:

(495 + 205) + 114

= 814

c. The factors of 13965 are all of the numbers that can divide this number.

They are: 1, 3, 5, 7, 15, 19, 21, 35, 49, 57, 95, 105, 133, 147, 245, 285, 399, 665, 735, 931, 1995, 2793, 4655, and 13965

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NEED HELP ASAP!!
This graph shows the total number of patients seen by a doctor over the course of a 5-day workweek.

What are the domain and range of this relationship??

Answers

Using the domain and range concepts, we have that:

The domain is: {0, 1, 2, 3, 4, 5}.The range is: {0, 12, 24, 36, 48, 60}.

What are the domain and the range of a function?

The domain of a function is the set that contains all the values of the input. In a graph, it is given by the values of x.The range of a function is the set that contains all the values of the output. In a graph, it is given by the values of y.

Hence, considering the given graph:

The domain is: {0, 1, 2, 3, 4, 5}.The range is: {0, 12, 24, 36, 48, 60}.

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The set of natural numbers x that satisfy x+8=3 Kendra lifts a box using a force of 80 N. She lifts the box a height of 0.5meters in 2 seconds. How much work does she do on the box?A. 80 JB. 40 JC. 160 JD. 120 J Show work how you know its a function or not a function for each problem. PLEASE SOMEONE HELP ME OUT A pea plant with purple flowers of unknown genotype is test crossed with a white-flowered pea plant (ff), and half of the offspring have purple flowers and half the offspring have white flowers. What is the genotype of the purple flower The ratio of the numerator to the denominator of a certain fraction is one to four. If three is added to the numerator andsubtracted from the denominator, the new fraction reduces to one-third. What is the original fraction?A 12/45B 15/45C 12/48 Belief in the utility of research is a critically important factor in the process of becoming a competent counselor Group of answer choices True False Discount points paid increases the yield of: Select one: a. Brokers. b. Lenders. c. Sellers. d. Buyers. Read the passage from "Cruel Tribute.Years passed by. Every spring when the roses began to bloom seven youths and seven maidens were put on board of a black-sailed ship and sent to Crete to pay the tribute which King Minos required. In every house in Athens there was sorrow and dread, and the people lifted up their hands to Athena on the hilltop and cried out, "How long, O Queen of the Air, how long shall this thing be?"In the meanwhile the little child at Troezen on the other side of the sea had grown to be a man. His name, Theseus, was in everybody's mouth, for he had done great deeds of daring; and at last he had come to Athens to find his father, King Aegeus, who had never heard whether he was alive or dead; and when the youth had made himself known, the king had welcomed him to his home and all the people were glad because so noble a prince had come to dwell among them and, in time, to rule over their city.In this excerpt, the sequence of events creates suspense bystarting the story in the middle of things.describing a setting that causes anticipation.slowing down the plot to focus on an important character.speeding up the plot to move the story forward and build tension. What is the central idea of After Love by Sara Teasdale? Sasha made a model of a clipper ship. If her model has a length of 18 inches, and the original ship has a length of 160 feet and a width of 32 feet, what should be the width of her model? How do the images of travel in part 46 of "Song of Myself" contribute to the poems theme?They suggest that human life is impermanent.They show that growth involves a steady movement forward.They remind readers that the poem is about journeying within ones self.They suggest expansiveness, or extending ones reach outward. Prokaryotic organisms/cells have which of the following characteristics?A. division by mitosisB. nucleusC. cellular membraneD. multicellularE. Call of the choices are correct How did Liberia differ from most other African countries in its experiencewith European imperialism? compute 1 + 2 + 3 +....+ 99 + 100 + 99 + 98 +...+ 3 + 2 + 1 Which detail best reveals the theme that joy comes from within? If the methane contained in 2.50 L of a saturated solution at 25 C was extracted and placed under STP conditions, what volume would it occupy? this sentence is in the passive form:A wonderful splash was created by the boy.Choose the option that makes it activeA. the splash, which was wonderful, was created by the boy.B. The boy created a wonderful splash.C. The splash,which was created by the boy,was wonderfulD. A wonderful spalsh,which was created by the boy,was in the pool Write a short story including adventures and characters I need help on a questionAs we know that the three most common household fuse values are 3A,5A and 13A. Make a list of yourhousehold electrical appliances. Divide them into 3 groups according to their power consumption to decide what fuse should be fitted in the plug for each of them. 1.Effective communicators are aware of other person's frames of___and views of the ___