Answers
In this question, we are presented with two triangles are required to find he missing sides in them. the missing side in the first triangle is equal to 8 and the missing sides in the second triangle are 8.660, 5 and 60 for the adjacent, opposite and the second angle respectively
Trigonometric RatioIn the first triangle, we need to use trigonometric ratio to find the missing side in the triangle
Data;
Angle = 45hypothenuse = [tex]8\sqrt{2}[/tex]adjacent = xTo find the adjacent side, we need to use cosine rule on this problem.
[tex]cos\theta = \frac{adjacent}{hypothenuse} \\cos45 = \frac{x}{8\sqrt{2} } \\x = 8[/tex]
The adjacent side is equal to 8 units
In the second triangle, we also need to use trigonometric ratio, but let's write down our data
angle = 30hypothenuse = 10opposite = ?adjacent = ?We can use both cosine and sine rule here or use one and use Pythagoras's theorem to find the other side.
[tex]cos \theta = \frac{adjacent}{hypothenuse} \\cos 30 = \frac{x}{10} \\x = 8.660[/tex]
The adjacent side is equal to 8.660, let's find the opposite side using sine rule
[tex]sin\theta = \frac{opposite}{hypothenuse} \\sin 30 = \frac{y}{10} \\y = 5[/tex]
And lastly, the value of the other angle is
[tex]90 + 30 + z = 180\\z = 180 - 120\\\\z = 60[/tex]
From the calculations above, the missing side in the first triangle is equal to 8 and the missing sides in the second triangle are 8.660, 5 and 60 for the adjacent, opposite and the second angle respectively
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Related Questions
She would also like to tour genoa as well, which would cost her €60.85. if the conversion rate of us dollars to euros at the time of kari’s visit is 1:0.6859, how will this affect her budget? round all dollar values to the nearest cent. a. kari can see genoa and have $60.33 left in her budget. b. kari can see genoa and have $41.38 left in her budget. c. kari has almost exactly enough left in her budget to see genoa. d. kari cannot afford to see genoa, because it would put her $84.48 over budget.
Answers
The conversion rate will affect her budget as C. Kari has almost exactly enough left in her budget to see Genoa.
How to illustrate the budget?From the information given, it should be noted that a trip to Genoa will cost her €60.85.
This will be converted to dollars which will be:
= 60.85/0.6859
= 88.72
Therefore, out of the $585 budget, only $88.72 is used.
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Keisha has two dogs. The larger dog weighs 1.2 pounds more than the smaller dog. The combined weight of the two dogs is 13.6 pounds. What is the weight, in pounds, of the smaller dog?
Answers
Answer:
x = 6.2
Step-by-step explanation:
let ‘x’ denotes the weight of a smaller dog.
“1.2″ + x” be the weight of the larger dog
combined weight = 13.6
smaller dog weight =
x+x+1.2 = 13.6
2x + 1.2 = 13.6
2x = 13.6–1.2
2x = 12.4
x = 12.4/2
x = 6.2 pounds.
Hope you understood it, Happy Learning.
Joe has 7/8 yards of string. What is the maximum number of 1/16 yards of string Joe can be cut from the string? 11 points
Answers
Answer:
14
Step-by-step explanation:
7/8 = 14/16
Which statement BEST describes the graph of f(x - 6)?
A. The graph of f(x) is shifted up 6 units.
6
B. The graph of f(x) is shifted left 6 units.
C. The graph of f(x) is shifted right 6 units.
D. The graph of f(x) is shifted down 6 units.
Answers
Answer:
B. f(x) is shifted left by 6 units
Step-by-step explanation:
when we talk about translations, we know they happen along the X axis, y axis or sometimes both, in this case we see that were subtracting x by six units, so we are moving left along the x axis
ways to remember this is:
-you count up x the RIGHT way going right
-you count UP y
and of cource by process of ellimination we know that decreasing X goes left and decreasing y goes down
ALSO NOTE: x always goes horizontally and y always goes vertically
Translate the following sentence into an equation: "Seven added to eight times a number is three less than
twice the number."
?
Answers
[tex]let\ x\ be\ the\ unknown\ number[/tex]
[tex]8x+7=2x-3[/tex]
first choose a variable to represent the number.
when something is "..." times a number, we are multiplying that number by that value.
"seven added to eight times a number" means that we are multiplying the number by eight (8x) and then adding seven to it (+7).
"is" usually means 'equals to' so we put an equal sign there.
"three less than twice the number" means that we are multiplying the number by two (2x) and then subtracting three from it (-3).
An equation form of given statement is, 7 + 8m = 3 - 2m where m is any real valued number.
What is an equation?"It is a mathematical statement which consists of equal symbol between two mathematical expressions."
For given question,
We have been given a statement.
We need to translate given statement into a equation.
Seven added to eight times a number is three less than twice the number.
Let 'm' be any real number.
We can rewrite above statement as,
Seven plus to eight times 'm' is three minus twice 'm'.
⇒ 7 + 8 × m = 3 - 2 × m
So, we get an equation,
⇒ 7 + 8m = 3 - 2m
Therefore, an equation form of given statement is, 7 + 8m = 3 - 2m where m is any real valued number.
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Solve for x.
X=
x +19 7x +9
Answers
Step-by-step explanation:
X+7x=9-19
8x=-10
X=-10÷8
X=1.25
What is the area of triangle ABC?
C
12
60°
60°
A
D
B
Answers
Answer:
Area of the triangle is 36√3
Step-by-step explanation: Hope this will help
The hypotenuse of each 30 - 60 - 90 triangle is 12
The base length is 6 + 6 = 12 because the triangle is equilateral and the
altitude of the triangle divides the base into two equal parts and the altitude (DC) is the height of the triangle.
Now you have two 30 - 60 - 90 triangles with the hypotenuse of 12, the short leg = 6 and you need to find the length of DC.
Finding DC .
a² + b² = c²
6² + b² = 12² 0r the long leg = short leg times √3
36 + b² = 144 6√3
b² = 108
b = 6√3
Area of a triangle = 1/2bh
= 1/2(12)(6√3)
= 6(6√3) = 36√3
HELP PLEASE, I'LL GIVE BRAINLIEST.
if x + yi = (1 + i)⁴ , then x + y = ......
a) 4
b) - 4
c) 2
d) - 2
an explanation for future reference would be greatly appreciated <333
Answers
x + yi = (1 + i)⁴
then -4 + 4 = x
All of the following are equivalent to 1.75 except _____. 14/8, 1 75/100, 1 3/4, 4/7
Answers
Solve -2x + 7 < -41 how do you solve this
Answers
Answer:
x>21
Step-by-step explanation:
-2x + 7 < -41 Subtract 7 from both sides
-2x<-48 Divide by negative 2
x>21 When you divide by a negative you have to flip the sign
Answer:
x<28
Step-by-step explanation:
-2x+7<-41
-2x<-48 subtract 7 from both sides
x>24 divide by -2 to both sides
3. The Wang family has a take-home income of $45 000 per year. If they budget 22% for rent, how much rent would they budget for the year? How much for each month?
Answers
Answer:
Step-by-step explanation:
45000 x %22 = 9900 per year
9900/12=825 per month
Find the greatest common factor of 12y4 and 7y3.
Answers
Answer:
24
Step-by-step explanation:
12*2=24
7*3=24
3*7=24
4*6=24
Hope this helps!
For this problem, a non-integer answer should be entered as a fraction in simplest form using / as the fraction bar. malik randomly picked two numbers from 1 to 9 (including 1 and 9). the same number could be picked more than once. the first of the two numbers he picks is odd and less than 5. what is the probability that the sum of the two numbers malik picks is less than 5, given that the first number is odd and less than 5?
Answers
Based on the numbers that Malik can pick and the condition of the sum being less than 5, the probability of this happening is 2/9.
What is the probability that Malik's number are less than 5 when added?The first number that Malik picked is an odd number less than 5 which makes it with 1 or 3.
In order for the two number to be less than 5 when added, the numbers to be picked have to be:
1 and 21 and 33 and 11 and 1These are 4 possibilities out of a total of 18 possibilities so the probability is:
= 4 / 18
= 2 / 9
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Answer:
See image
Step-by-step explanation:
Plato
What is the sum of the following equation: (9+5)*43x(23,550-32)*655
Answers
Answer:
1,012,632....I'm sure that's is answerA cube has a surface area of 96 square inches. If 16 cubes are combined to make a rectangular prism, what is the volume of the rectangular prism?
Answers
Answer:
1536
Step-by-step explanation:
What is the constant of proportionality shown in the table?
Answers
The constant of proportionality shown in the table that shows the cost and the number of books is 3.
What is the constant of proportionality ?When there is a direct proportional relationship, it means that as the value of one variable increases, the value of the other variable also increases. As the number of books increases, the cost increases.
Direct proportion: y = kx
Where:
y = dependent variable k = constant of proportionality x = independent variablek = y/x
6/2 = 3
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Answer:3
Step-by-step explanation:
A survey was taken of a random sampling of residents of New York City and Los Angeles to compare how many
of them own a car
Answers
Answer:
The survey represents quantitative data and there is greater percentage of LA residents who own cars than NYC residents who do.
QUESTION 1 [10] The accompanying diagram shows the graph of f(x) = a* B 1.1. Write down the coordinate of A; explain. 1.2. How can we tell that: 0 < a < 1? 1.3. Determine a if B is the point (4;). (3) (2) 1.4. Determine the equation of the graph obtained if the graph above is reflected about the y-axis 1.5. Write down the coordinates of the point of intersection of the two graphs. (2 (2) (1)
Answers
The Coordinate of A is (0, 1) and the equation of the graph with B coordinate is ¹/₂^(ˣ) - (¹/₂)x
How to interpret Graph Functions?The equation of the accompanying graph is;
f(x) = aˣ
1) We want to write the coordinate of A. Thus;
f(0) = a⁰ = 1
Thus;
Coordinate of A = (0, 1)
2) The way we can tell that: 0 < a < 1 is; From figure number and inverse functions.
3) If B is the point (4, ¹/₁₆), then;
f(4) = a⁴ = ¹/₁₆
a = ⁴√(¹/₁₆)
a = ¹/₂
4) The equation of the graph with B coordinate is;
y - ax
⇒ ¹/₂^(ˣ) - (¹/₂)x
5) To get the coordinates of the point of intersection of the two graphs is;
¹/₂^(ˣ) - (¹/₂)x = ¹/₂^(ˣ)
⇒ (¹/₂)x = 0
x = 0
Thus, the coordinate of the intersection is; (0, 0)
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Anthony wants to find out the percentage of students at his school who are vegetarians. Which of the following is the most representative group of students for him to surve
A. 50 students at a icecream parlor
B. 5 students at a icecream parlor
C. 50 students at a hamburger restaurant
D. 5 students at a hamburger restaurant
Answers
Answer:
A
Step-by-step explanation:
You wont find vegatarians at a hamburger restaurant but you wilk find non vegetarians at a icecream parlor
Alice and Amy decide to meet at a party. From a corner of the party hall, Amy spots Alice at the corner of the hall diagonally opposite her. If the party hall is a rectangle that measures 100 feet by 60 feet, what is the shortest distance Amy has to walk to reach Alice? Round your answer to the nearest foot.
A.
40 feet
B.
80 feet
C.
117 feet
D.
160 feet
Answers
Answer:
C) 117 Feet
Step-by-step explanation:
The question is ultimately asking for the hypotenuse of the rectangle. We can calculate that with a^2 + b^2 = c^2.
100^2+60^2=c^2
10000+3600=c^2
c^2=13600
c=116.6190379
Round --> 117
Thus the answer, C).
6 cm
6 cm
What is the area?
Answers
Answer:
= 18 [tex]cm^{2}[/tex]
Step-by-step explanation:
As the triangle is right angled:
formula
= [tex]\frac{1}{2}[/tex] base x height
= [tex]\frac{1}{2}[/tex] 6 x 6
=[tex]\frac{1}{2}[/tex] x 36
=[tex]\frac{36}{2}[/tex]
= 18 [tex]cm^{2}[/tex]
Find the volume of the composite solid. Round your answer to the nearest tenth.
A composite solid is shown with a cone placed atop a cylinder. The height of the cone is 6 feet and the diameter of its base is 16 feet. The diameter of the circular bases of the cylinder are the same as the diameter of the cone. The height of the cylinder is 4 feet.
The volume is about
cubic feet.
Answers
Answer:
1206.4 ft³
Step-by-step explanation:
The volume of the composite figure is the sum of the volumes of its parts. Each part has its own volume formula.
__
formulasThe formula for the volume of a cone is ...
V = 1/3Bh . . . . where B is the area of the base, and h is the height
The formula for the volume of a cylinder is ...
V = Bh . . . . where B is the area of the base, and h is the height
The formula for the area of a circle is ...
A = πr² = π(d/2)² = (π/4)d²
Combining the volume formulas for a figure with the same base area, we have ...
V = B(cylinder height) + 1/3B(cone height)
V = B(cylinder height + 1/3×cone height) . . . . where B is the base area
composite volumeUsing 16 ft for the diameter, and 4 ft and 6 ft for the heights of the cylinder and cone, respectively, we have ...
V = (π/4)(16 ft)²(4 ft + 1/3×6 ft) = 64π(4 +2) ft³ = 384π ft³
The volume is about ...
384π ft³ ≈ 1206.4 ft³
Distribute to create an equivalent expression with the fewest symbols possible.
(1 - 25 +4h) - 5 =
Answers
Answer:
4h - 29
Step-by-step explanation:
[tex](1-25+4h)-5\\=(-24+4h)-5\\=(4h-24)-5\\=4h-24-5\\=4h-29[/tex]
You could also write this solution as [tex]-29+4h[/tex], but I just think [tex]4h-29[/tex] looks nicer :)
Honorable Quinn with 6 children earns 613 200 naira per month. Calculate:
a. tax allowance
b. taxable income
c. amount of tax paid
d. income after tax is paid
Answers
Find the volume of the cone. Round your answer to the nearest tenth. A cone is shown. Its height is 3 meters and the diameter of the base is 6 meters. The volume of the cone is about a cubic meters.
Answers
Answer:
The answer to this question should be 28.3
chosen at random from a bag comtaining 8 marbles: 4 blue 3 green and 1 red. define a probability distribution for this experiment on the sample space{B,G,R}
Answers
Answer:
1/2, 3/8, 1/8
Step-by-step explanation:
the radio of giving blue marbles is 4/8=1/2
the radio of giving green marbles is 3/8
the radio of giving red marbles is 1/8
Answer:
the probability of you getting a B marble is 1/2 for a R marble its 1/8 and for a G marble its 3/8.
Step-by-step explanation:
Which sets of ordered pairs represent a function? Select all that apply.
A. (1,1), (1,2), (1,3), (1.4)
B. (1,1), (2,2), (3,3), (4,4)
C. (1,1), (2,1), (3,1), (4,1)
D. (1,4), (2,4), (1,3), (2,3)
E. (1,4), (2,2), (3,1), (4,3)
Answers
Answer:
B, C, and E
Step-by-step explanation:
In order for a function to be a function, an ordered pair cannot be on the same x coordinate
Help ASAP NEED ANSWER NOW
Answers
Answer:
A.
Step-by-step explanation:
bc, it's high preasured. meaning its going 2b snowy.
Solve: 4+1.8x = 8 (1+0.1x)
A. There are infinitely many solutions.
B. x = -3
C. x = -4
D. x = 4
Answers
[tex]4+1.8x=8+0.8x\\\\4+1.0x=8\\\\1.0x=4\\\\x=4\\[/tex]
the answer is x = 4.
Round to the nearest two decimal places
Answers
98.01 = 42.25 + b^2
Sqrt of 55.76 = b
b = 7.46726
≈ 7.47
Hope this helps :)