Solve the triangle. (Do not round until the final answer. Round angles to the nearest degree and side lengths to the nearest tenth of a unit.)C=___∠A=___∠B=___
Answers
Explanation
to solve this we need to use the cosine law
Law of cosines says
[tex]\begin{gathered} a^2=b^2+c^2-2bc\cdot\cos (A) \\ b^2=a^2+c^2-2ac\cdot\cos (B) \\ c^2=a^2+b^2-2ab\cdot\cos (C) \end{gathered}[/tex]then
Step 1
find c
Let
[tex]\begin{gathered} b=8 \\ a=5 \\ \angle C=67 \end{gathered}[/tex]now, let's find c
[tex]\begin{gathered} c^2=a^2+b^2-2bc\cdot\cos (C) \\ \text{replace} \\ c^2=5^2+8^2-2\cdot5\cdot8\cdot\cos (67) \\ c^2=25+64-31.25849028 \\ c^2=57.74 \\ \text{square root in both sides} \\ \sqrt{c^2}=\sqrt{57.74} \\ c=7.598 \\ \text{rounded} \\ c=7.6 \end{gathered}[/tex]Step 2
now,let's find the angle A
[tex]\begin{gathered} a^2=b^2+c^2-2bc\cdot\cos (A) \\ replace \\ 5^2=8^2+7.6^2-2\cdot8\cdot7.6\cdot\cos (A) \\ 25=64+57.76-121.6\text{ cos(A)} \\ 25=121.76-121.6(\cos A) \\ \text{subtract 121.76 in both sides} \\ 25-121.76=121.76-121.6(\cos A)-121.76 \\ -96.76=-121.6(\cos A) \\ \text{divide both sides by -121.6} \\ \frac{-96.76}{-121.6}=\frac{-121.6(\cos A)}{-121.6} \\ 0.795=\cos \text{ (A)} \\ Inverse\text{ cosine} \\ \cos ^{-1}(0.795)=\cos ^{-1}(\cos \text{ (A))} \\ 37.276=\text{ A} \\ \text{rounded} \\ A=37\~\text{ =A} \end{gathered}[/tex]Step 3
Finally,let's find angle B
we can use the formula as we did in step 2 to find angle A, but also we can use this fact:
the sum of the internal angles in a triangle equals 180 ,so
[tex]\angle A+\angle B+\angle C=180[/tex]replace and solve for angle C
[tex]\begin{gathered} \angle A+\angle B+\angle C=180 \\ 37+\angle B+67=180 \\ 104+\angle B=180 \\ \text{subtract 104 in both sides} \\ 104+\angle B-104=180-104 \\ \angle B=76 \end{gathered}[/tex]
Related Questions
A microwave company claims that their microwaves can pop popcorn in under 2.25 minutes. After 134 randomly chosen microwaves were sampled, it was found that the mean time to pop popcorn was 2.5 minutes, with a standard deviation of .25 minutes. Using the information provided, determine if this claim should be rejected?A. Reject the null hypothesis. There is not enough evidence to oppose the microwave company's claim.B. Reject the null hypothesis. There is enough evidence to oppose the microwave company's claim.C. Fail to reject the null hypothesis. There is not enough evidence to oppose the microwave company's claim.D. Fail to reject the null hypothesis. There is enough evidence to oppose the microwave company's claim.
Answers
ANSWER
A. Reject the null hypothesis. There is not enough evidence to oppose the microwave company's claim.
EXPLANATION
The claim is that the microwave can make popcorn in under 2.5 minutes. Hence, the statistical hypotheses are:
[tex]\begin{gathered} H_0\colon\mu\ge2.25 \\ H_1\colon\mu<2.25 \end{gathered}[/tex]where H0 = null hypothesis
H1 = the hypothesis we are interested in proving
The level of significance of the test is not given, hence, we can assume that the level of significance of the test is 5%:
[tex]\alpha=5\%=0.05[/tex]Since the sample size is n = 134, we can use the approximation to the standard normal distribution to calculate the test statistic:
[tex]z=\frac{\bar{x}-\mu}{\frac{S}{\sqrt[]{n}}}[/tex]For the given sample:
[tex]\begin{gathered} n=134 \\ \bar{x}=2.5\text{ min} \\ S=0.25 \\ \mu=2.25\text{ min} \end{gathered}[/tex]Hence, we have that:
[tex]\begin{gathered} z=\frac{2.5-2.25}{\frac{0.25}{\sqrt[]{134}}} \\ z=\frac{0.25}{\frac{0.25}{11.5758}} \\ z=0.25\cdot\frac{11.5758}{0.25} \\ z=11.5758 \end{gathered}[/tex]Now, we have to find the p-value.
If the p-value is greater than the significance level, the decision is to not reject the null hypothesis.
If the p-value is less than the significance level, the decision is to reject the null hypothesis.
For any z-score value greater than 3, the accumulated probability is 0.99999 and for any value below -3, the accumulated probability is 0.
We have that the z-score is 11.5758. This means that:
[tex]\begin{gathered} P(z>11.58)=1-P(z<11.57)=1-0.99999 \\ \Rightarrow P(z>11.58)=0.00001 \end{gathered}[/tex]As we can see, the p-value is less than the significance level, so the decision is to reject the null hypothesis.
This means that the alternative hypothesis:
[tex]H_1\colon\mu<2.25[/tex]is right (or stays) and so, the claim of the company is right.
Hence, the correct answer is option A.
Find the value of xOptions are 110, 80, 35, 40
Answers
The sum of all angles in a triangle is 180º. Therefore:
[tex]\begin{gathered} 180=\text{ 30 + \lparen3x-10\rparen + x} \\ 180=\text{ 30 +3x -10 + x} \\ 180\text{ = 20 + 4x} \\ 180\text{ - 20 = 4x} \\ 160=\text{ 4x} \\ \\ \frac{160}{4}=\text{ x} \\ \\ 40=\text{ x} \end{gathered}[/tex]X will be 40º.
please help me answer the question in the image. thank you for any help and explanations you can give me!
Answers
We can solve this type of question using trigonometric functions. Here, we use sine of the angle of take-off with the horizontal runway.
[tex]\begin{gathered} \sin 10^o=\frac{500}{c} \\ c=\frac{500}{\sin 10^o} \\ c=\frac{500}{0.1736} \\ c=2880.18 \end{gathered}[/tex]Thus, the distance that the plane has traveled is equal to 2880 ft.
what is 13579 x2468?
Answers
to muliply the given number is,
[tex]13579x2468?=33512972[/tex]The answer is 33512972.
the part of Ray and Kelley's roller coaster is a curved pattern that can be represented by a polynomial function. I will upload the complete question. because it is to much to type.
Answers
Thus, the answer is Kelsey is the one who is correct. Because the number of intercepts is different from the number of zeroes.
1) Examining the question, we take into consideration that not all intercepts are zeroes of the polynomial.
In a third-degree polynomial function, there is another kind of intercept. The y-intercept.
2) So, we can tell that there is no way for both of them to be correct.
3) Thus, the answer is Kelsey is the one who is correct. Because the number of intercepts is different from the number of zeroes.
2 - (32/f) use f = 8
Answers
Answer:
f = -2
Step-by-step explanation:
2-(32/8) = -2
-8 I think or -2
This is what I think it is
A biker is making a turn around the corner. The biker's speed remained constant at 12 miles per hour during the entire turn. Which of the following statements describes the forces on the biker?
The forces were balanced to keep the biker with a constant speed.
The forces were unbalanced as the biker made the turn.
The forces were balanced due to the biker's inertia.
The forces were unbalanced due to the action-reaction pair required to turn.
Answers
The forces were balanced due to the biker's inertia. Option C.
Objects that move in circles or along circular orbits experience a centripetal force. That is there is a physical force pushing or pulling an object toward the center of the circle. The centripetal force that causes the car to spin in a circle is generated by the friction between the tires and the road surface. A minimum coefficient of friction is required. Otherwise, the car will travel a curve with a larger radius and leave the lane.
As the motorcycle climbs the loop friction forces act along the direction of travel to prevent gravity from slowing it down. As the motorcycle descends the loop friction forces act against the direction of motion preventing acceleration due to gravity. Whenever the velocity increases at the same rate, we are moving with constant acceleration. Centripetal force supports the circular motion. One idea is that if the road is smooth the car can't make a circle.
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Answer: The forces were balanced due to the biker's inertia.
Step-by-step explanation:
option c
(x^4)+(5x^2)+4=1 i need help on how to do this
Answers
Find the area of a square with a side length x when x is equal to the given value. Are the area of a square and the length of its side directly proportianal? Justify your answer. x=3 in.
Answers
Answer:
9 in
It is portions because the area will always be the square of a side
Step-by-step explanation:
all sides of a square are the same so we can just multiply 3 by 3 to make 9.
Hopes this help please mark brainliest
Answer: The answer is 9 inches
Step-by-step explanation:
The answer is nine inches but the sides are not proportional.
(123*7+38*101)/(90-15*6)
Answers
Figure it out ur self
please put answers for sin, cos, tan, cot, sec, and csc
Answers
If we measure the angle in the clockwise direction:
Therefore, this point is:
[tex](-1,0)[/tex]Since the cosine and sine functions are given by:
[tex]\begin{gathered} \sin (\theta)=\frac{opposite}{_{\text{ }}hypotenuse} \\ \cos (\theta)=\frac{adjacent}{_{\text{ }}hypotenuse} \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} \sin (-\pi)=\frac{0}{1}=0 \\ \cos (-\pi)=\frac{1}{-1}=-1 \end{gathered}[/tex]Since:
[tex]\begin{gathered} \cot (\theta)=\frac{adjacent}{_{\text{ }}opposite}\to\cot (-\pi)=-\frac{1}{0}=_{\text{ }}undefined \\ \csc (\theta)=\frac{hypotenuse}{_{\text{ }}opposite}\to\csc (-\pi)=\frac{1}{0}=_{\text{ }}undefined \end{gathered}[/tex]Therefore, we can conclude that cotangent and cosecant are undefined for - π
[tex]\begin{gathered} \tan (\theta)=\frac{opposite}{_{\text{ }}adjacent}=\frac{0}{-1}=0 \\ \sec (\theta)=\frac{hypotenuse}{_{\text{ }}adjacent}=\frac{1}{-1}=-1 \end{gathered}[/tex]
Which pairs of non- overlapping angles share a ray to make a right angle? Select all that apply.
Answers
From the figure the pairs of angles that share a ray to make a right angle are:
[tex]\begin{gathered} \measuredangle EGK\text{ and }\measuredangle KGF \\ \measuredangle\text{FGJ and }\measuredangle JGH \end{gathered}[/tex]Answer: Option 1 and Option 4.
Determine whether or not the following correspondences specify a function, and explain your reasoning in writing
Answers
Recall that a relation is a function if for every value on the domain there is only one value on the range.
(a) Notice that for every value on the domain, there is only one value on the range:
For the value 0 in the domain, there is the value 5 in the range.
For the value 1 in the domain, there is the value 6 in the range.
For the value 2 in the domain, there is the value 7 in the range.
For the value 3 in the domain, there is the value 7 in the range.
Therefore the relation represented by the given graph in a) is a function.
(b) Notice that for the value 3 in the domain there are two values in the range, 6 and 7, therefore, the relation represented by the graph in b) is not a function.
Answer:
(a) Function.
(b) Not a function.
PLEASE HELP IM SICK AND I DONT UNDERSTAND.DUE IN 30 MINS!!!!!!
Answers
The value of x is -12 and the pair of interior angles are: 130 and 50 degrees.
Given, a transversal is passed by the parallel lines.
Hence consecutive interior angles are formed.
Each pair of internal angles on the same side of a transversal are supplementary, or they add up to 180°, if the transversal meets two parallel lines.
therefore, x+142 + x + 62 = 180°
arrange the variables one side
2x + 142 + 62 = 180
add the constants.
2x + 204 = 180
2x = 180-204
2x = -24
x = -12
interior angle 1 = x+142
= -12+142
= 130°
interior angle 2 = x+62
= -12+62
= 50°
Hence the value of x is -12.
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I need help with this practice Can you solve, please explain step-by-step, *as I am new to this branch/topic of math*
Answers
Explanation
This is Algeba, an aspect of Math
We are told to find th correct optionthat satisfies the condition of a and b
Given that
a =5 and b =8
To go about this, we will simply substitute a = 5 and b=8 into each of the equation and cross-check the value with 104
Let us check for the first option
[tex]\begin{gathered} 8+a+8+b \\ 8+5+8+8=29 \\ since\text{ 29 is not equal to 104, then this is a wrong answer} \end{gathered}[/tex]Option B
[tex]\begin{gathered} 8+a+8b \\ 8+5+8(8)=8+5+64=77 \\ since\text{ 77 is not equal to 104, then this is wrong also} \end{gathered}[/tex]Option C
[tex]\begin{gathered} 8a+8+b=8(5)+8+8=40+16=56 \\ since\text{ 56 is not equal to 104, then this is also wrong} \end{gathered}[/tex]Option D
[tex]\begin{gathered} 8a+8b=8(5)+8(8)=40+64=104 \\ \\ 104\text{ is EQUAL to 104} \\ This\text{ is correct} \end{gathered}[/tex]Therefore, the anser is
A friend lends you $260, which you agree to repay with 3% interest.How much will you have to repay?How much of that was interest?
Answers
To answer this question we will use the following formula to compute the x% of y:
[tex]y\times\frac{x}{100}.[/tex]Since you have to repay with 3% interest, then you have to pay 103% of the original amount.
The 103% of 260 is:
[tex]260\times\frac{103}{100}=267.80.[/tex]Now, notice that the interest is the difference between the original amount and the above result:
[tex]I=267.80-260=7.80.[/tex]Answer:
How much will you have to repay? $267.80.
How much of that was of interest? $7.80.
Consider this scenario and then answer the next three questions: A land owner wants a good approximation of the width of his stream from point D to point C. At high point B, he lays a carpenter’s square (used to make right angles) so that he can sight along BC and BA. AD = 9.3 ft and BD = 15.7 ft.1) State the corresponding proportional sides between similar triangles ABC and ADB. 2) Calculate the length of segment AB. Round the answer to the nearest tenth. (Hint: Use Pythagorean Theorem)3) Answer the following questions about the previous scenario: (a) Write an algebraic expression to represent the length from A to C. (b) Write a proportion to find the distance across the stream. (c) What is the length across the stream?
Answers
1) Let's consider both triangles ABC and ADB:
Then the proportional sides between similar triangles is:
[tex]\frac{AB}{AD}=\frac{BC}{BD}=\frac{AC}{AB}[/tex]2)Since we have that AD=9.3 and BD=15.7, using the pythagorean theorem we get the following:
[tex]\begin{gathered} AB^2=AD^2+DB^2 \\ \Rightarrow AB^2=(9.3)^2+(15.7)^2=86.5+246.5=333 \\ \Rightarrow AB=\sqrt[]{333}=18.2 \\ AB=18.2 \end{gathered}[/tex]Therefore, AB=18.2 ft
3)a)the best way to represent the length from A to C is with the pythagorean theorem:
[tex]AC=\sqrt[]{AB^2+BC^2}[/tex]b)The proportion to find the distance across the stream is the segment DC, then:
[tex]\frac{AD}{BD}=\frac{DB}{DC}[/tex]c)We can find the length by using the values for AD, BD and DB that we previously got:
[tex]\begin{gathered} AD=9.3 \\ BD=15.7 \\ \Rightarrow\frac{9.3}{15.7}=\frac{15.7}{DC} \\ \Rightarrow DC\cdot(\frac{9.3}{15.7})=15.7 \\ \Rightarrow DC=\frac{15.7}{(\frac{9.3}{15.7})}=26.5 \\ DC=26.5 \end{gathered}[/tex]Finally, we have that the length across the stream is 26.5 ft
slove using elimination-2x-5y=12x+2y=-10
Answers
We have the following:
[tex]\begin{gathered} -2x-5y=1 \\ 2x+2y=-10 \end{gathered}[/tex]solving using elimination:
[tex]\begin{gathered} -2x-5y=1 \\ + \\ 2x+2y=-10 \\ -2x+2x-5y+2y=1-10 \\ -3y=-9 \\ y=\frac{-9}{-3} \\ y=3 \end{gathered}[/tex]Now, for x:
[tex]\begin{gathered} -2x-5\cdot3=1 \\ -2x-15=1 \\ -2x=16 \\ x=\frac{16}{-2} \\ x=-8 \end{gathered}[/tex]Therefore:
x = -8 and y = 3
k(-1,3)5-2 -14321(0, 1)y1.1, 3) (2, 3)1 2613VXAnalyze the graph of the exponential decay function.The initial value isThe base, or rate of change, isThe domain isD
Answers
The general expression for an exponential function is the following:
[tex]y=ab^x[/tex]where b represents the base of the function.
In this case, notice that the graph of the function passes through the points (0,1) and (1,1/3), then, with these points we can find the values of a and b:
[tex]\begin{gathered} (0,1): \\ 1=ab⁰\Rightarrow a=1 \\ (1,\frac{1}{3}): \\ \frac{1}{3}=b¹\Rightarrow b=\frac{1}{3} \end{gathered}[/tex]therefore, we have that:
the initial value is a = 1
the base is b = 1/3
the domain of the function is all real numbers.
What is the solution of 0.2x - 4 - 2x < -0.4 and 3x + 2.7 <3
Answers
Answers:
1) x > - 2
2) x < 0.1
Explanatt
The given inequalities are:
1) 0.2x - 4 -2x < -0.4
2) 3x + 2.7 < 3
Solution to number 1:
0.2x - 4 - 2x < -0.4
Collect like terms
0.2x - 2x < -0.4 + 4
-1.8x < 3.6
Divide both sides by 1.8
[tex]\begin{gathered} \frac{-1.8x}{1.8}<\frac{3.6}{1.8} \\ -x\text{ < }2 \\ x\text{ > -2} \end{gathered}[/tex]Solution to number 2:
3x + 2.7 < 3
Collect like terms
3x < 3 - 2.7
3x < 0.3
Divide both sides by 3
[tex]\begin{gathered} \frac{3x}{3}<\frac{0.3}{3} \\ x\text{ < 0.1} \end{gathered}[/tex]Where are the minimum and maximum values for f(x) = sin x + 1 on the interval [0, 2π]?A. min:z =OB. min:x=OC. min:z =max:x= = 0, 2πOD. min:z = 0, π, 2π max: z =Reset Selectionmax: 1 =2 2max:z = 0, π, 2π
Answers
Given the function:
[tex]f(x)=sinx+1[/tex]Let's find the minimum and maximum values over the interval [0, 2π].
Let's first find the derivative of the function:
[tex]f^{\prime}(x)=cosx[/tex]Now set the derivative to 0 and solve for x:
[tex]\begin{gathered} cosx=0 \\ \\ \text{ Take the inverse cosine of both sides:} \\ x=cos^{-1}(0) \\ \\ x=\frac{\pi}{2} \end{gathered}[/tex]The cosine function is positive in quadrants I and IV, to find the reference angle(minimum), subtract the first solution from 2π:
[tex]\begin{gathered} x=2\pi-\frac{\pi}{2} \\ \\ x=\frac{2(2\pi)-\pi}{2} \\ \\ x=\frac{4\pi-\pi}{2} \\ \\ x=\frac{3\pi}{2} \end{gathered}[/tex]Plug in the values in the function to determine the minimum and maximum:
[tex]\begin{gathered} f(\frac{\pi}{2})=sin(\frac{\pi}{2})+1=1+1=2 \\ \\ \\ f(\frac{3\pi}{2})=sin(\frac{3\pi}{2})+1=-1+1=0 \end{gathered}[/tex]Therefore, we have the following:
Minimum occurs at: x = 3π/2
Maximum occurs at: x = π/2
ANSWER:
[tex][/tex]Evaluate. Write your answer as a
decimal or whole number.
(0.07)² =
Answers
Answer:
(0.07)^2
= (7 / 100)^2
= 7^2 / 100^2
= 49 / 10000
= 0.0049
A spring is oscillating vertically according to the equation y=3cos(2t-pi) where y is the displacement in feet and t is time in seconds. At what time will the spring be 2 ft. high? Round your answer to the nearest tenth.
Answers
we have the equation
[tex]y=3cos(2t-pi)[/tex]For y=2 ft
substitute in the given equation
[tex]\begin{gathered} 2=3cos(2t-p\imaginaryI) \\ cos(2t-p\mathrm{i})=\frac{2}{3} \end{gathered}[/tex]Solve for t
using a calculator
2t-pi=0.84
2t=0.84+pi
2t=3.98
t=1.99 -----------> round to one decimal place
t=2.0 sec
The answer is option CIn 1995, the standard bus fare in Chicago was $1.50. In 2008, the standard bus fare was $2.40.Find the percent increase. Round to the nearest tenth of a percent
Answers
Given that:
- The standard bus fare was $1.50 in 1995.
- The standard bus fare was $2.40 in 2008.
You need to use the following formula, in order to find the percent increase:
[tex]PercentageIncrease=\frac{Final\text{ }Value-Initial\text{ }Value}{|Initial\text{ }Value|}\cdot100[/tex]In this case, you can identify that:
[tex]\begin{gathered} Final\text{ }Value=2.40 \\ Initial\text{ }Value=1.50 \end{gathered}[/tex]Therefore, substituting values into the formula and evaluating, you get:
[tex]\begin{gathered} PercentageIncrease=\frac{2.40-1.50}{|1.50|}\cdot100 \\ \\ PercentageIncrease=\frac{0.9}{1.50}\cdot100 \end{gathered}[/tex][tex]\begin{gathered} PercentageIncrease=0.6\cdot100 \\ \\ PercentageIncrease=60\text{ \%} \end{gathered}[/tex]Hence, the answer is:
[tex]PercentageIncrease=60\text{ \%}[/tex]Rochelle needs to pack a picture frame that measures 7 3/8 inches on each side will it be into a box that measures 7.4 inches on each side
Answers
A picture frame that is 7 3/8 inches wide on each side needs to be packed into a box that is 7.4 inches wide on each side. It would not consequently fit.
Given that,
A picture frame that is 7 3/8 inches wide on each side needs to be packed into a box that is 7.4 inches wide on each side.
Picture frame length is 7 3/8, or 7.4 inches.
Box length is 7.4 inches.
Therefore, it is clear from the about that the box's length is shorter than the picture frame's length.
It would not consequently fit.
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Veronica owes a clothing store $1800, but until she makes a payment, she pays 4% interest per month.What is Veronica's monthly interest payment?
Answers
The interest Veronica has to pay monthly is:
1,800 * 0.04 = I think you can calculate this, Km.
At a sale this week, a table is being sold for $400. This is a 36% discount from the original price.
What is the original price?
Answers
Using the concept of Percentage, the original price of the table is $625.
What is Percentage?A Percentage means a ratio with the second part being 100. Percentage refers to parts per hundred. The term is derived from the Latin phrase per centum, which means "per hundred." In mathematics, the symbol % stands for percent.
Example: 50% means 50 out of every 100. So if 50% of 200 students are girls, then there are 100 students who are girls.
We know that,
Table was sold at $400.
Discount given is 36% then the table is sold at,
100% - 36% = 64%
Let the original price be p then,
64% of p = 400
That gives,
p = [tex]\frac{40000}{64}[/tex]
p = 625
Hence, The original price of the table is $625.
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HELP MEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
is (8, -44) a solution of the eqution y = -7x + 6
Answers
Answer:
It is NOT a solution to the equation
Step-by-step explanation:
To solve this, plug (8, -44) into the equation. Remember that 8 is x and -44 is y:
y = -7x
-44 = -7 (8)
-7 x 8 = -56
-44 ≠ -56
2(x + 4) = - 3(x + 5)
Answers
Solving for x:
[tex]\begin{gathered} 2(x+4)=-3(x+5)\rightarrow2x+8=-3x-15 \\ \rightarrow2x+3x=-15-8\rightarrow5x=-23 \\ \rightarrow x=-\frac{23}{5} \end{gathered}[/tex]I need help please!!!! I need the answer like right now please!! Thank you!!!
Answers
For example (Calculator);
$9.60 x 25% = $2.40
The answer above would go on the third column.
Because the first three are examples of markup, you add that $2.40 with the original price and that answer goes on the last column.
The bottom three, you'd repeat the process, but rather than adding the discount and original, you are subtracting.
Let me know if I need to elaborate a little more and I hope this helped a bit!
