Use the Law of Cosines to determine the indicated angle 0. (Assume a = 65.01, b = 36.38, and c = 42.05. Round your answer to two decimal places.)
Answers
a = 65.01, b = 36.38, and c = 42.05.
And it is required to find the measure of angle 0 which will be the angle B
Using the law of cosine
[tex]\begin{gathered} b^2=a^2+c^2-2\cdot a\cdot c\cdot\cos B \\ \cos B=\frac{a^2+c^2-b^2}{2\cdot a\cdot c}=\frac{65.01^2+42.05^2-36.38^2}{2\cdot65.01\cdot42.05}=0.854 \\ \end{gathered}[/tex][tex]\angle\emptyset=\angle B=\cos ^{-1}0.854=31.31[/tex]the answer is rounded to two decimals
Related Questions
what does the g in 5 = g/8 ?
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Given data:
The given expression is 5=g/8.
The given expression can be written as,
[tex]\begin{gathered} 5=\frac{g}{8} \\ g=40 \end{gathered}[/tex]Thus, the value of g is 40.
what expression is equivalent to 5+3×4+1 A (5 + 3) x 4 + 1 B 5+ (3 x 4) + 1 C 5 + 3x (4 + 1) D (5 + 3) (4 + 1)
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answer: B
how to solve (s + 5)(s - 5)
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Here, we want to solve an expansion
To get this, we simply multiply the terms in the first bracket with the terms in the second, before we proceed to collect like terms
We have this as follows;
[tex]\begin{gathered} (s+5)(s-5)\text{ = s(s-5)+5(s-5)} \\ =s^2-5s+5s-25 \\ =s^2-25 \end{gathered}[/tex]The quadrilateral is a kite.Find the values of x and y.х621°y
Answers
Remember that in a kite, the greater diagonal bisect the small diagonal
so
that means
x=6
Find the value of y
Remember that
the greater diagonal divide the kite into two congrient triangles
therefore
y=21 degrees
answer is
x=6
y=21 degrees
I need help finding my equation for the question. I’m very confused
Answers
1)
The ratio of cookies to hours spent cooking = C : H
= 300 : 4
= 75 : 1
2)
How many hours does it take to bake 225 cookies
[tex]\begin{gathered} =\text{ }\frac{225}{75}\text{ } \\ =\text{ 3 hours} \end{gathered}[/tex]Given PQRS is a parallelogram, find the value of x and the value of y* Р 0 (4y + 7) 13x + 15 19x - 9 (10y - 37) S R 4 5 6 7 10 14 15 None of these y= horollalaram find the msc. (do not enter units) * 3 points
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If PQRS is a parallelogram, we know that:
- PS and QR have the same length.
-
Then, we can calculate x as:
[tex]\begin{gathered} PS=QR \\ 13x+15=19x-9 \\ 13x-19x=-9-15 \\ -6x=-24 \\ x=\frac{-24}{-6} \\ x=4 \end{gathered}[/tex]And we can calculate y as:
[tex]\begin{gathered} m\angle Q+m\angle R=180\degree \\ (4y+7)+(10y-37)=180 \\ 14y-30=180 \\ 14y=180+30 \\ 14y=210 \\ y=\frac{210}{14} \\ y=15 \end{gathered}[/tex]Answer: x=4 and y=15
A dinner party is being organized with the option of 7 dinner choices to serve at the venue. Since catering is expensive thehost asks everyone attending to rank each dish. The top ranked dish will be served at the venue. What is the probability thatyour favorite dish is the chosen dish served at the venue?• Write your answer as an exact fraction which is reduced as much as possible.
Answers
Given:
Total number of dinner choices = 7
Let's find the probability that your favorite dish is the chosen dish at the venue.
Given that you are to choose just one dish.
Probability can be said to be a measure of the likeklihood of an event to occur.
The probability of an event is a number between 0 and 1.
To find the probability, apply the formula below:
[tex]\begin{gathered} P(\text{fav)}=\frac{\text{Number of favorite dish}}{\text{Total number of dishes}} \\ \\ P(\text{fav)}=\frac{1}{7} \end{gathered}[/tex]Therefore, the probability the that your favorite dish is the chosen dish at the venue is
[tex]\frac{1}{7}[/tex]ANSWER:
[tex]\frac{1}{7}[/tex]Point C is located at (4, -2). It is translated 3 units to the left and 4 units up. Graph the location of the translated point.
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Answer:
Step-by-step explanation: Refer to the photo taken.
Grandma Meyer uses the recipe to make a soup.A.Draw a bar diagram to find how much vegetable stock and cream are needed.B. Find how many cups of soup will be made with all the ingredients. Explain your work.
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Prior to plotting our chart, we need to convert these mixed fractions to decimals. Since denominators are 4, we can easily multiply both sides of the fraction by 25 to give the fraction in terms of 100 and thus, easily convert to decimal.
[tex]ChickenBroth\colon2\frac{3}{4}=\text{ 2 + (}\frac{3\times25}{4\times25}\text{)= 2 + }\frac{75}{100}=\text{ 2 + 0.75 = 2.75}[/tex][tex]Water\colon1\frac{1}{4}=\text{ 1 + (}\frac{2\times25}{4\times25}\text{)= 2 + }\frac{50}{100}=\text{ 2 + 0.5 = 1.5}[/tex][tex]Cream\colon1\frac{1}{4}=\text{ 1 + (}\frac{1\times25}{4\times25}\text{)= 1 + }\frac{25}{100}=\text{ 1 + 0.25 = 1.25}[/tex][tex]Vegetablestock\colon2\frac{3}{4}=\text{ 2 + (}\frac{3\times25}{4\times25}\text{)= 2 + }\frac{75}{100}=\text{ 2 + 0.75 = 2.75}[/tex]B.
The number of cups of soup will be a total of the ingredient,
[tex]\begin{gathered} \text{Total = 2.75 + 1.5 + 1.25 + 2.75 = 8.25} \\ To\text{ get back as mixed fractions,} \\ (8\text{ + }\frac{25}{100})\text{ + (8 +}\frac{1}{4}\text{) = 8}\frac{1}{4} \end{gathered}[/tex]Complete the squareto find the vertexof this parabola.2y +6y+8 x+1=0(121)
Answers
Given,
The equation of the parabola is y^2+6y+8x+1=0
Required:
The vertex of the parabola.
The equation of the parabola is taken as:
[tex]\begin{gathered} y^2+6y+8x+1=0 \\ y^2+6y+1=-8x \\ y^2+6y+9-9+1=-8x \\ (y+3)^2-9+1=-8x \\ (y+3)^2-8=-8x \\ (y+3)^2=8-8x \\ -8x=(y+3)^2-8 \\ x=\frac{-(y+3)^2}{8}+1 \end{gathered}[/tex]The standard form of the equation is,
[tex]x=a(y-k)^2+h[/tex]Here, h and k are the vertex of the parabola.
On comparing the standard form with given vertex form of the parabola.
[tex](h,k)=(1,-3)[/tex]Hence, the vertex of the parabola is (1, -3).
The price of an online Maths website subscription is decreased by 81% and
now is $24.89.
Find the original price
Answers
The value of a quantity after reducing it to some percentage can be found by taking the difference of the old value and the percent of the old value. The original price is $226.27.
What is percentage?A percentage is a value that indicates 100th part of any quantity.
To convert percentage into a fraction it is divided by 100.
Given that,
The percentage of decrease in price = 81%
The new price is $24.89.
Since the new price is obtained by substracting the decrease percentage from the original price. The expression for the original price is given as,
Suppose the original price be P.
P - 81% of P = 24.89
=> P - (89 / 100) × P = 24.89
=> (11 / 100) × P = 24.89
=> P = 226.27
Hence, the original price is given as $ 226.27.
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What is the perimeter of the figure below?34 mm40 mm88 mm96 mmI probably doing
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The perimeter is the sum of the length of the sides that form a boundary of the figure.
That is
[tex]\text{ The Perimeter =}8+2+4+6+12+8[/tex]Therefore
[tex]\text{ The Perimeter =}40\text{ mm}[/tex]The perimeter is 40 mm
Suppose you have a standard deck of 52 carts. What is the probability that if you select a card at random that it does not have a face value of 9? Round your answer to two decimals
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A deck of cards has 13 face values: Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, and King. These face values are present for four different suits (Clubs, Diamonds, Hearts, and Spades) for a total of 52 cards.
An event's probability in an experiment with equally likely outcomes is defined by the following formula, where P (event) means the probability of the event occurring and is founding by dividing the number of outcomes in the event by the number of outcomes in the sample space:
[tex]P(event)=\frac{Number\text{ }of\text{ outcomes in the event}}{Number\text{ of outcomes in the sample space}}[/tex]The probability of not getting the event is given to be:
[tex]P^{\prime}(event)=1-\frac{Number\text{ }of\text{ outcomes in the event}}{Number\text{ of outcomes in the sample space}}[/tex]Since there are 4 cards with a face value of 9, the probability of getting a 9 is:
[tex]P(9)=\frac{4}{52}=\frac{1}{13}[/tex]Therefore, the probability of not getting a 9 is given to be:
[tex]\begin{gathered} P^{\prime}(9)=1-\frac{1}{13} \\ P^{\prime}(9)=\frac{12}{13} \end{gathered}[/tex]In two decimal places, the probability that the card picked does not have a face value of 9 is 0.92.
If 10 is increased to 15, the increase is what percent of the original number? (This is known as the percent change.)Answer = Write your resulting percent in decimal form with three decimal places of accuracy. Example: Write 2% as 0.02. Write 5.66% as 0.057.
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we have the following:
[tex]\begin{gathered} \frac{10}{100}=\frac{15}{x} \\ x=\frac{100\cdot15}{10} \\ x=150 \end{gathered}[/tex]15 represents 150%, therefore:
[tex]150-100=50[/tex]The percentage with respect to the original is 50%.
[tex]\frac{50}{100}=0.5[/tex]form decimal = 0.5
I don’t understand how I’m supposed to do this problem I know it’s three times X but I got to figure out what X is this
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We need to solve the following equation:
[tex]3x+9=-36[/tex]Solving an equation is the same as finding the value of x.
In order to do so, we need to apply a sequence of the same operations on both sides of the equation, until we isolate the variable x on the left side of the equation, and find its value.
First, let's isolate 3x on the left side. We need to subtract 9 from both sides:
[tex]\begin{gathered} 3x+9-9=-36-9 \\ \\ 3x+0=-45 \\ \\ 3x=-45 \end{gathered}[/tex]Now, to end with x on the left side, we need to divide both sides by 3:
[tex]\begin{gathered} \frac{3x}{3}=-\frac{45}{3} \\ \\ \frac{3}{3}x=-15 \\ \\ 1x=-15 \\ \\ x=-15 \end{gathered}[/tex]Answer: B) x = -15
How would you do number 5 would you use a formula I’m confused
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N 5
we have that
Triangle ABC is a right triangle
so
Applying the Pythagorean Theorem
AB^2=AC^2+BC^2
substitute given values
AB^2=^2+9^2
AB^2=36+81
AB^2=117
AB=√117Type SSS, SAS, ASA, AAS, or HL tojustify why the two larger triangles arecongruent.BСAB = DCAD
Answers
In triangle ABC and DCB
AB=DC
Hypotenuse of both the triangles are equal
BC = CB
Both of you come to school.
According to the HL triangle congurency
Two right triangles are congruent if the hypotenuse and one corresponding leg are equal in both triangles.
Thus, triangles are congurent by HL method
In ABCD, the measure of ZD=90°, CB = 37, BD = 12, and DC = 35. What is the valueof the sine of ZB to the nearest hundredth?
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First we need to draw the triangle:
now that we have the triangle we have to remember that the sine function is defined as:
[tex]\sin \theta=\frac{\text{opp}}{\text{hyp}}[/tex]Then, in this case we have:
[tex]\begin{gathered} \sin B=\frac{35}{37} \\ \sin B=0.95 \end{gathered}[/tex]Therefore the sine of B is 0.95 to nearest hundreth
at the given number in the indicated base
Answers
Consider the equation -3x+4y=-12 A line parallel to the above line would have a slope of ()/(frac{3}{4}) what would A line perpendicular to the above line have a slope of?
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1) Perpendicular lines have reciprocal and opposite slopes. But to properly check it, we need to rewrite the Standard form to the Slope-intercept
So let's rewrite it:
[tex]\begin{gathered} -3x+4y=-12 \\ 4y=-12+3x \\ y=-\frac{12}{4}+\frac{3}{4}x \\ y=\frac{3}{4}x-3 \end{gathered}[/tex]2) Now, we can clearly see the slope. So now, we can tell that a perpendicular line would be reciprocal and opposite to the slope so we can tell that a perpendicular line will be:
[tex]m=-\frac{4}{3}[/tex]i was wondering if i could get help on my geometry i’ve been struggling
Answers
We need to count the units to go from A to A'
ANSWER
7 units to the left
Solve:y = 3xx = -2y + 70
Answers
Equation1: y = 3x
Equation 2: x = -2y + 70
To solve this system, we will use the value of x of the second equation into the fist equation:
y = 3x = 3(-2y + 70) = -6y + 210
y = -6y + 210
y + 6y = 210
7y = 210
y = 210/7 = 30
y = 30
Now, we will tusethe value of y into the second equation to find the value of x:
x = -2y + 70 = -2(30)+80 = -60 + 70 = 10
x = 10
Answer:
x = 10
y = 30
Find anexpression which represents the sum of (8x + 10y) and (-4x - 3y) insimplest terms.
Answers
The sum of the two expressions is given as:
[tex](8x+10y)+(-4x-3y)[/tex]Expanding the parentheses using the symbols:
[tex]8x+10y-4x-3y[/tex]Collecting like terms,
[tex]8x-4x+10y-3y[/tex]Simplifying:
[tex]4x+7y[/tex]The simplest term is given as (4x + 7y)
14 + 35=7(2+_) I don't understand it I need help please
Answers
The equation is given as
14 + 35 = 7 (2 + _)
We shall represent the dash as letter y (the unknown variable)
14 + 35 = 7 (2 + y)
49 = 7 (2 + y)
Divide both sides of the equation by 7 (to eliminate it from the right side of the equation)
Mrs. Thompson hosts an annual art contest for kids, and she keeps a record ofthe number of entries each year.Art contest entriesYear Number of entries201128201227332013201420152735According to the table, what was the rate of change between 2013 and 2014?entries per yearSubmit
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We were given a table that describes teh relationship between the year of an art contest entry, and the number of entries for that year. From these datapoints we need to calculate the rate of change between the years of 2013 and 2014.
The rate of change describes how the function is increasing or decreasing for a particular point. For our case, since the two datapoints are only one year apart, we can subtract the number of entries, and that should give us the desired result. This is done below:
[tex]\begin{gathered} \text{rate}=27-33 \\ \text{rate}=-5 \end{gathered}[/tex]The function rate of change between 2013 and 2014 was -5 entries per year.
Solve the system using the addition method 5x-2y=32x-y=0What is the y-valueA. 3B. 6C. -3D. none of the above
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First, we multiply the first equation by "2":
[tex]\begin{gathered} 2\times\lbrack5x-2y=3\rbrack \\ 10x-4y=6 \end{gathered}[/tex]Then, we multiply the second equation by "-5":
[tex]\begin{gathered} -5\times\lbrack2x-y=0\rbrack \\ -10x+5y=0 \end{gathered}[/tex]The two new equations are:
[tex]\begin{gathered} 10x-4y=6 \\ -10x+5y=0 \end{gathered}[/tex]We add both equations and solve for y. The steps are shown below:
[tex]\begin{gathered} 10x-4y=6 \\ -10x+5y=0 \\ ----------- \\ y=6 \end{gathered}[/tex]The correct answer is y = 6.
AnswerBI NEED HELP ASP ;-;. On the day of the test, the teacher instructed the students to take out no less than 2 pencils from their backpacks.
Determine which inequality represents this scenario.
2 ≥ p
2 ≤ p
2 > p
2 < p
Answers
The inequality that represents the given situation perfectly is (B) 2 ≤ p.
What exactly is inequality?An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made.Make use of the following steps to solve an inequality: Step 1: Remove fractions by multiplying all terms by the fractions' lowest common denominator. Step 2 Combine like terms on both sides of the inequality to simplify. Step 3 Obtain the unknown on one side and the integers on the other by adding or subtracting quantities.So, the inequality that perfectly represents the given situation:
The teacher asks, to take out no less than 2 pencils.So, inequality can be:
2 = p and 2 < pCombine: 2 ≤ p
Therefore, the inequality that represents the given situation perfectly is (B) 2≤p.
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Correct question:
On the day of the test, the teacher instructed the students to take out no less than 2 pencils from their backpacks.
Determine which inequality represents this scenario.
A 2 ≥ p
B 2 ≤ p
C 2 > p
D 2 < p
How to solve precalc logarithmic question - 50 points
Answers
The predicted value for the logarithm ㏒ ₐ 3⁴ is equal to 4 · g.
What is the predicted value associated to a logarithm in accordance with logarithm properties?
In this problem we have the definitions of three logarithms and we are asked to find the predicted value related to at least one of the logarithms described in the statement, this can be done by means of logarithm properties. Herein we proceed to use the following logarithm property related to logarithms of a power:
㏒ ₐ b = n · ㏒ ₐ bⁿ
First, define the logarithm described in the statement of the problem:
㏒ ₐ 3⁴
Second, use the logarithm property for a power in the given expression:
4 · ㏒ ₐ 3
Third, substitute the logarithm ㏒ ₐ 3 defined in the statement of the problem:
4 · g
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perform the indicated operation 5/17 • 3/8 I really need explanation on how to do the problem when I need to do it alone
Answers
To multiplicate two fractions, you have to multiply their numerator and denominator, like this:
[tex]\frac{5}{17}\times\frac{3}{8}=\frac{15}{136}[/tex]The numbers trading cards owned by 10 middle-school students are given below.(NOTE THAT THESE ARE ALREADY ORDERED FROM LEAST TO GREATEST)Suppose that the number 355 from the list changes to 415. Answer the following.
Answers
Answer:
(a) It increases by 8
(b) It stays the same
Explanation:
First, we need to calculate the mean and median of the original data. This data is
335, 393, 425, 453, 489, 542, 556, 563, 623, 661
Then, the mean is the sum of all the values divided by the number of values, so
[tex]\begin{gathered} \text{ mean = }\frac{335+393+425+453+489+542+556+563+623+661}{10} \\ \\ \text{ mean = }\frac{5040}{10} \\ \\ \text{ mean=504} \end{gathered}[/tex]The median is the value that divides the set into two sets of equal sizes. In this case, these numbers are 489 and 542 because there are 4 numbers before 489 and 4 numbers after 542
335, 393, 425, 453, 489, 542, 556, 563, 623, 661
Then, the median is
[tex]\begin{gathered} \text{ median = }\frac{489+542}{2} \\ \\ \text{ median=}\frac{1031}{2} \\ \\ \text{ median=515.5} \end{gathered}[/tex]Now, we need to calculate the mean and median when 335 is changed to 415. So, the new data set is
393, 415, 425, 453, 489, 542, 556, 563, 623, 661
Then, the mean is
[tex]\begin{gathered} \text{ mean = }\frac{393+415+425+453+489+542+556+563+623+661}{10} \\ \\ \text{ mean =}\frac{5120}{10} \\ \\ \text{ mean = 512} \end{gathered}[/tex]And the median is 515.5 because the numbers in the middle are the 489 and 542
393, 415, 425, 453, 489, 542, 556, 563, 623, 661
Therefore, we can say that:
The mean increased by 8 because 512 - 504 = 8
The median stays the same
So, the answers are
(a) It increases by 8
(b) It stays the same