Answers
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Explain the formula to use
Using the cosine rule which states that:
\(z^2=x^2+y^2-2xy\cos Z\)STEP 2: Write the given sides
\(x=4,y=6,Z=41^{\circ},z=?\)STEP 3: Find the value of z
\(\begin{gathered} By\text{ substitution,} \\ z^2=4^2+6^2-2(4)(6)\cos41 \\ z^2=16+36-48cos41 \\ z^2=52-36.22605985 \\ z^2=15.77394015 \\ z=\sqrt{15.77394015} \\ z=3.971641997 \\ z\approx4.0 \end{gathered}\)Hence, the indicated length is 4.0
Related Questions
1.What must be true about a circle with a circumference of 16 π?the radius is 16the diameter is 16the diameter is πthe radius is πQUESTION 21.If the radius of circle P is 4, then thediameter is 4.circumference is 4 π.diameter is 8.circumference is 16 π.QUESTION 31.π isequal to 5.26.always equal to the radius of a circle.twice the diameter of a circle.a circle's circumference divided by its diameter.1.If a circle has a center of R and a point on the circle labeled T, then RT isthe diameter.a chord.the radius.twice the diameter.1.Find the circumference of a circle with a diameter of 3. Use π = 3.14.9.4218.843.141.05QUESTION 61.If the circumference of circle A is 16 π, then the length of a chord in circle A istwice the diameter.twice the circumference.equal to the circumference.16 inches or less.QUESTION 71.If a circle has a circumference of 10 π, then the ratio of the circle's circumference to its diameter isπ.10.10 π.2 π.QUESTION 81.If the radius of a circle is 3.14, then the circumference equals3.14 π2 (3.14) π(3.14) (3.14) ππ.QUESTION 91.If the circumference of a circle is 16 π, then the radius of the circle equals816π4QUESTION 101.A circle is to the circumference as a square is to thearea.perimeter.volume.diameter.
Answers
The area of a circle with radius r is given by the formula:
\(A=\pi r^2\)If the radius is 8 inches, substitute r=8in:
\(\begin{gathered} A=\pi(8in)^2 \\ =3.14\times64in^2 \\ =200.96in^2 \end{gathered}\)Therefore, the area of the circle in square inches, is:
\(200.96\)9. A company is looking to hire a painter. One painter states that their fee can be determined by
using the expression 50x + 100 where x is the number of hours it takes to paint. A second painter
states that their fees can be determined by using the expression 40x + 125. The company wants
to know when the fee would be the same for each painter. What number of hours makes the
equation 50x + 100 = 40x + 150 true?
Answers
What are the two equations to set up to solve the equation |2x−3|=11
Answers
The two equations to set up to solve |2x−3|=11 are 2x − 3 = 11 and 2x − 3 = -11
Hence, option C)2x − 3 = 11 and 2x − 3 = -11 is the correct answer.
What are the two equations to set up to solve the equation |2x−3|=11?Given the equation in the question;
| 2x − 3 | = 11
To solve the equation, we have to remove the absolute value term and this will create the a ± on the right side of the equation.
Note that; |x| = ±x
Hence;
| 2x − 3 | = 11
2x − 3 = ±11
The solution of the equation is the result of both the positive and negative portions of the of the solution.
2x − 3 = 11 and 2x − 3 = -11
Therefore, the two equations to set up to solve |2x−3|=11 are 2x − 3 = 11 and 2x − 3 = -11
Hence, option C)2x − 3 = 11 and 2x − 3 = -11 is the correct answer.
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A cloth bag contains 6 cards numbered 1 through 6. Two cards are drawn without replacement. What is the probability that the sum of the numbers on the two drawn cards is 7
Answers
Answer: \(\dfrac15\)
Step-by-step explanation:
Given : A cloth bag contains 6 cards numbered 1 through 6. Two cards are drawn without replacement.
Favorable outcome: sum of the numbers on the two drawn cards is 7
Since 1+6 = 7 , 2+5=7, 4+3 = 7
So, sum of 7 can be obtained as (1, 6), (2, 5), (3, 4), (4, 3), (5, 2) and (6, 1)
Probability of getting (first 1, second 6) = \(\dfrac16\times\dfrac15=\dfrac{1}{30}\)
Probability of getting (first 2, second 5) = (\(\dfrac16\times\dfrac15=\dfrac{1}{30}\)
Probability of getting (first 3, second 4) =\(\dfrac16\times\dfrac15=\dfrac{1}{30}\)
Probability of getting (first 4, second 3) = \(\dfrac16\times\dfrac15=\dfrac{1}{30}\)
Probability of getting (first 5, second 2) = \(\dfrac16\times\dfrac15=\dfrac{1}{30}\)
Probability of getting (first 6, second 1) =\(\dfrac16\times\dfrac15=\dfrac{1}{30}\)
Required probability =\(6\times\dfrac{1}{30}=\dfrac15\)
Hence, the required probability = \(\dfrac15\)
David was asked to solve the problem below:
If a = 5x - 4 and b = 3x, what is the value of a - b?
David used the steps below to solve the problem
Step 1: a - b
Step 2: (5x-4) - 3x
Step 3: 5x-4-3x
Step 4: -2x
Determine whether David's solution is correct. If he is correct, show the work that proves he is
correct. If he made an error, explain what he should have done instead, and provide the correct
solution.
Answers
Answer:
not correctStep 4: 2x -4Step-by-step explanation:
You want to know if David's solution of -2x for (5x-4) -(3x) is correct, and what David should have done.
SolutionDavid's solution is correct up to Step 4.
At that point, it appears as though David treated -4 as if it were -4x. The constant cannot be combined with x terms. Step 4 should have been ...
Step 4: (5 -3)x -4 = 2x -4
David's incorrect solution should have been 2x -4.
Find the number of years necessary for an investment to double at each of these rates of simple interest. Round to the nearest tenth if necessary.
Interest Rate: 11%
Answers
It would take approximately 6.5 years for an investment to double at a simple interest rate of 11%.
According to given information :To find the number of years necessary for an investment to double at a simple interest rate of 11%, we can use the following formula:
n = 72 / r
where n is the number of years required for the investment to double, and r is the interest rate.
Plugging in the values, we get:
n = 72 / 11
n ≈ 6.5 years (rounded to the nearest tenth)
Therefore, it would take approximately 6.5 years for an investment to double at a simple interest rate of 11%.
What is simple interest ?Simple interest is a type of interest that is calculated on the principal amount of a loan or investment. It is a fixed percentage of the original amount borrowed or invested, and it is not compounded over time.
The formula for calculating simple interest is:
I = P * r * t
where I is the interest, P is the principal amount, r is the interest rate, and t is the time period.
For example, if you borrow $1,000 for two years at a simple interest rate of 5%, the interest you would pay is calculated as follows:
I = 1,000 * 0.05 * 2
I = $100
So, you would have to pay back the $1,000 principal plus $100 in interest, for a total of $1,100.
Simple interest is commonly used in short-term loans or investments, and it is usually easier to calculate and understand than compound interest, which takes into account the effect of earning interest on previously earned interest.
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What is the degree of the polynomial, y^2+7x^14-10x^2?
Answers
The degree of the polynomial is 14
How to determine the degree of the polynomial?The polynomial is given as:
y^2+7x^14-10x^2
Here, we assume that the variable of the polynomial is x
The highest power of x in the polynomial y^2+7x^14-10x^2 is 14
Hence, the degree of the polynomial is 14
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30
A restaurant used 231 eggs last week. Of these, 46 were brown in color. The remaining
eggs were white in color. Which equation can be used to solve for w, the number
of white eggs used last week?
A 231 +46w=0
B 46+ w = 231
C w = 231 +46
D 231 = 46w
Answers
D 231 = 46w can be used to solve for w, the number of white eggs used last week.
How to determine open interval on which the function is increasing?
Answers
Answer:
To find when a function is increasing, you must first take the derivative, then set it equal to 0, and then find between which zero values the function is positive. Now test values on all sides of these to find when the function is positive, and therefore increasing.
Seth is using the figure shown below to prove Pythagorean Theorem using triangle similarity:
In the given triangle ABC, angle A is 90° and segment AD is perpendicular to segment BC.
The figure shows triangle ABC with right angle at A and segment AD. Point D is on side BC.
Which of these could be a step to prove that BC2 = AB2 + AC2?
possible answers -
By the cross product property, AB2 = BC multiplied by BD.
By the cross product property, AC2 = BC multiplied by BD.
By the cross product property, AC2 = BC multiplied by AD.
By the cross product property, AB2 = BC multiplied by AD.
Answers
The correct step to prove that \(BC^2 = AB^2 + AC^2\) is:
By the cross product property, \(AC^2 = BC \cdot AD\).
To prove that \(BC^2 = AB^2 + AC^2\), we can use the triangle similarity and the Pythagorean theorem. Here's a step-by-step explanation:
Given triangle ABC with right angle at A and segment AD perpendicular to segment BC.
By triangle similarity, triangle ABD is similar to triangle ABC. This is because angle A is common, and angle BDA is a right angle (as AD is perpendicular to BC).
Using the proportionality of similar triangles, we can write the following ratio:
\($\frac{AB}{BC} = \frac{AD}{AB}$\)
Cross-multiplying, we get:
\($AB^2 = BC \cdot AD$\)
Similarly, using triangle similarity, triangle ACD is also similar to triangle ABC. This gives us:
\($\frac{AC}{BC} = \frac{AD}{AC}$\)
Cross-multiplying, we have:
\($AC^2 = BC \cdot AD$\)
Now, we can substitute the derived expressions into the original equation:
\($BC^2 = AB^2 + AC^2$\\$BC^2 = (BC \cdot AD) + (BC \cdot AD)$\\$BC^2 = 2 \cdot BC \cdot AD$\)
It was made possible by cross-product property.
Therefore, the correct step to prove that \(BC^2 = AB^2 + AC^2\) is:
By the cross product property, \(AC^2 = BC \cdot AD\).
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Devi invested a principal of $2750 in her bank account with an interest rate of 1.5%. How much simple interest did she earn in 3 years?
Answers
To calculate the simple interest, we use the following formula:
(Principal) • (interest rate) • (time) = simple interest
Plugging the values in, we will find that:
$2,750 (our principal) • 0.015% (our interest rate represented by a decimal) • 3 (our time period in years) = $123.75 (our simple interest)
Ultimately, Devi made an investment and in 3 years earned a simple interest of $123.75.
what is 8888888888888 times 668999000? due
Answers
Answer:
5.9466578e+21
\(Well,\;I\;Dont\;See\;Why\;Your\;Teacher\;Gave\;You\;This...\;\;But,\;Here\;You\;Go.\)
\(8888888888888 * 668999000\;\;Equals\;The\;Following..\)
\(5.94665778*10^2^1\)
Which expression uses the associative to make it easier to evaluate 14 (1/7 x 2/5)?
A. 7 (1/14 x 2/5)
B. (14 x 5/2) 1/7
C. 14 (2/5 x 1/7)
D. (14 x 1/7) 2/5
Answers
Answer:
D- (14×1/7) 2/5
Step-by-step explanation:
Hope it can help you lovelots
Solve the inequality.
a/-8 + 15 < 23
Answers
Answer:
The answer is a < (-64)
Step-by-step explanation:
a/-8 + 15 < 23
a/-8 + 15 – 15 < 23 – 15
a/-8 < 8
(a/-8) × (-8) < 8 × (-8)
a < -64
Thus, The answer is a < (-64)
-TheUnknownScientist 72
Charles drew a plan for a rectangular piece of material that he will use for a blanket. Three of the vertices are (−2.2,−2.3), (−2.2,1.5), and (1.5,1.5). What are the coordinates of the fourth vertex?
Answers
The coordinates of the fourth vertex are (-2.2, 1.5).
Understanding how to estimate coordinatesTo find the coordinates of the fourth vertex, we can use the fact that opposite sides of a rectangle have equal length and are parallel to each other.
First, we can find the length of one of the sides of the rectangle. Let's take the side connecting the points (-2.2, -2.3) and (-2.2, 1.5):
length = |1.5 - (-2.3)| = 3.8
Since this is a rectangle, the length of the side opposite to this one must also be 3.8. We can find this side by taking the points (-2.2, 1.5) and (1.5, 1.5):
width = |1.5 - (-2.2)| = 3.7
Now we know the length and width of the rectangle, so we can find the coordinates of the fourth vertex. Let's call this point (x, y).
Since the fourth vertex is opposite to the point (-2.2, -2.3), the x-coordinate of the fourth vertex must be the same as the x-coordinate of (-2.2, -2.3):
x = -2.2
Similarly, since the fourth vertex is opposite to the point (1.5, 1.5), the y-coordinate of the fourth vertex must be the same as the y-coordinate of (1.5, 1.5):
y = 1.5
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please tech me how to solve
Answers
Students at two high schools were asked about their plans after graduation. The table displays the results for 300 students at Henderson High School. The bar graph displays the results for 300 students at Johnson High School. Which Statement about the results from Henderson High School and johnson high school must be true?
Answers
Armed force and other for Henderson high school is greater than
Johnson High School.
The mode for each school is college.
Options F and G are the correct answer.
We have,
The number of students in Henderson High School.
Work = 96
College = 114
Armed forced = 48
Other = 42
The number of students in Johnson High School.
Work = 30
College = 40
Armed forced = 15
Other = 15
From the information,
The number of students in Work for Henderson High School is greater than Johnson High School.
Now,
Henderson High School:
Armed force and other = 48 + 42 = 90
Mode = college
Johnson High School.
Armed force and other = 15 + 15 = 30
Mode = college
Thus,
Armed force and other for Henderson high school is greater than
Johnson High School.
The mode for each school is college.
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Help me with this please
Answers
Answer:
That's called a parabola
Step-by-step explanation:
Since it's graphed in a "U" shape
Does anyone know which is bigger for a poster Size: 22.375" x 34" or Size: 14.725" x 22.375"
Answers
Answer:
22.375" × 34" is the bigger size for a poster
please help me work through this if you can, thank you!
Answers
Given:
\(C=\frac{x^4}{4}-\frac{4}{3}x^3-\frac{35}{2}x^2+150x\)Let's solve for the following:
• (a). Find C'(x).
Here, we are to find the derivative of C(x).
Apply the sum rule:
\(\begin{gathered} C^{\prime}=\frac{d}{dx}(\frac{x^4}{4})+\frac{d}{dx}(-\frac{4}{3}x^3)+\frac{d}{dx}(-\frac{35}{2}x^2)+\frac{d}{dx}(150x) \\ \\ C^{\prime}=x^3-4x^2-35x+150 \end{gathered}\)• (b). The critical numbers of C(x).
The critical numbers will be the points where the graph changes direction.
Using the derivative, let's solve for x.
\(x^3-4x^2-35x+150=0\)Factor the left side using the rational root test:
\((x-5)(x^2+x-30)=0\)Now factor using the AC method:
\(\begin{gathered} (x-5)((x-5)(x+6))=0 \\ \\ (x-5)(x-5)(x+6)=0 \end{gathered}\)Equate each factor to zero and solve for x:
\(\begin{gathered} x-5=0 \\ \text{ Add 5 to both sides:} \\ x-5+5=0+5 \\ x=5 \\ \\ \\ x-5=0 \\ x-5+5=0+5 \\ x=5 \\ \\ \\ x+6=0 \\ x+6-6=0-6 \\ x=-6 \end{gathered}\)Therefore, the critical numbers of C(x) are:
x = -6, 5
• (C). Increasing interval.
Use the critical points to find the increasing and decreasing intervals.
Using interval notation, the increasing interval is:
\((-6,5)\cup(5,\infty)\)• D. Decreasing interval:
Using interval notation, the decreasing interval is:
\((-\infty,-6)\)ANSWER:
(a). C'(x) = x³ - 4x² - 35x + 150
(b). x = -6, 5
(c). Increasing: (-6, 5) U (5,∞)
Decreasing: (-∞, -6)
1 is subtracted from 8 times a certain number.the result is 15.find the number
Answers
Answer:
number is 2
Step-by-step explanation:
let the number be n then 8 times the number is 8n, subtract 1 from this and
8n - 1 = 15 ( add 1 to both sides )
8n = 16 ( divide both sides by 8 )
n = 2
that is the number is 2
somebody helppppppppppppppppppppppppp....
Answers
Answer:
55
Step-by-step explanation:
It is 55 minutes more because 1 1/2 hrs = 90 minutes and when you add 20 plus quarter of an hour it equal to 35. SO than you subtract 35 from 90 and you get 55 which is the more minutes .
Suppose 27 gallons of water came out of a pipe in 9 minutes.what was the rate in gallons per minute
Answers
Answer:
Rate = 56 gal / 7 min
= 8 gal / min
Step-by-step explanation:
Hope this helps pls leave a heart c:
In 2004 5,545 woman were participating in college lacrosse and in 2008 6,830 woman joined was is the rate of change
Answers
Answer:
321.25 per year
Step-by-step explanation:
In 2004 they had 5,545
In 2008 they had 6,830
Subtract them both and you get 4 years, 1285 people
Divide 1285 by 4 and get 321.25 per year.
The Choir Booster Club had a budget of $1,300.00 at the start of the school year. They spend $225.30 on t-shirts, $482.25 on lost uniforms, and $135.68 on a holiday party. How much does the booster club have left in their budget?
A. $1,543.23
B. $1,074.70
C. $543.27
D. $456.77
Answers
Which of the following would a scale be used to measure?
the distance between two points on a trail
the volume of water a fish tank can hold
the weight of a fish after it is caught
the length of a piece of wood for building a treehouse
Answers
The scale that can be used to measure is the length of a piece of wood for building a treehouse
What is measurement scale?Measurement is the comparison of an unknown quantity with a known quantity. Scaling is the assignment of objects to numbers
A measurement scale is used to qualify or quantify data variables during measurement.
The scale that can be used to measure is the length of a piece of wood for building a treehouse
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if a to b ratio, b to c ratio, c to d ratio, are given, then express a to d in terms of given ratios
Answers
The ratio of a to d can be expressed by multiplying the ratio of a to b, b to c, and c to d. Therefore, a to d = (a to b) x (b to c) x (c to d).
The ratio of a to d can be determined by using the given ratio of a to b, b to c, and c to d. To begin, the ratio of a to b can be expressed as a:b, the ratio of b to c can be expressed as b:c, and the ratio of c to d can be expressed as c:d. Then, the ratio of a to d can be determined by multiplying the ratios of a to b, b to c, and c to d. This can be written as (a:b) x (b:c) x (c:d). Therefore, the ratio of a to d can be expressed as (a:b) x (b:c) x (c:d). For example, if the ratio of a to b is 2:3, the ratio of b to c is 4:5, and the ratio of c to d is 6:7, then the ratio of a to d would be (2:3) x (4:5) x (6:7) or 24:35.
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A salesman earns 3% commission for everything he sells. Yesterday, he sold a large screen television for $2,400 and a video game system for $500. How much money did the salesperson make on commission?
Answers
500 x 0.03 = $15
Total commission = $87
Help me please (I have to write something to send a question)
Answers
Answer:
yshannmm
Step-by-step explanation:
yes
HELPP!!
Ryan collects rainwater in a barrel for his garden. The barrel is filled with 15 gallons of water. Ryan used 6.8 gallons to water his garden in June and 5 and one-eighth gallons in July. How much water is left in the barrel?
1.) 3.075 gallons
2.) 5.125 gallons
3.) 5.178 gallons
4.) 16.675 gallons
Answers
Subtracting the initial amount of water from the amount used, the remaining amount of water is given by:
1.) 3.075 gallons.
How to find the remaining amount of water in the barrel?
To find the remaining amount of water in the barrel, we have to subtract the initial amount by the amount used.
We have that:
The initial amount was of 15 gallons.The amount used was of: 6.8 + 5 + 1/8(relative to the one-eight) = 11.925 gallons.Hence the remaining amount is:
15 - 11.925 = 3.075 gallons.
Which means that option 1 is correct.
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Answer: 3.075 gallons
Step-by-step explanation: