Answers
Answer:
x = 1 [tex]y=\frac{\sqrt{3}}{2}[/tex]Step-by-step explanation:
From the given right-angle triangle
The angle = ∠60°
The adjacent to the angle ∠60° is 1/2. The opposite to the angle ∠60° is y.The hypotenuse = x
Determining the value of x:
Using the trigonometric ratio
cos 60° = adjacent / hypotenuse
substituting adjacent = 1/2 and hypotenuse = x
[tex]cos\:60^{\circ }=\:\:\frac{\frac{1}{2}}{x}[/tex]
[tex]\cos \left(60^{\circ \:}\right)=\frac{1}{2x}[/tex]
[tex]\frac{1}{2}=\frac{1}{2x}[/tex] ∵ cos (60°) = 1/2
[tex]2x=2[/tex]
Dividing both sides by 2
[tex]\frac{2x}{2}=\frac{2}{2}[/tex]
Simplify
[tex]x=1[/tex]
Thus, the value of hypotenuse x is:
x = 1
Determining the value of y:
Using the trigonometric ratio
sin 60° = opposite / hypotenuse
As we have already determined the value of hypotenuse x = 1
substituting opposite = y and hypotenuse = 1
sin 60° = y/1
y = 1 × sin 60°
[tex]y=\frac{\sqrt{3}}{2}[/tex] ∵ [tex]\sin \left(60^{\circ \:}\right)=\frac{\sqrt{3}}{2}[/tex]
Therefore, the value of y is:
[tex]y=\frac{\sqrt{3}}{2}[/tex]
Summary:
x = 1 [tex]y=\frac{\sqrt{3}}{2}[/tex]Related Questions
write the equivalent fraction by division 30 by 42
Answers
Answer:
5/7
Step-by-step explanation:
5/7 is the simplified fraction for 30/42 by using the GCD or HCF method
Given the system below, describe how you would find the solution. You can either use complete sentences to tell how you would graph and what the result would be or you can create a graph on paper and submit a picture of it as your answer. Please make sure you are clear about what the solution is to the system.
x + 2y= -2
-x + 4y= -16
Answers
Answer:
y= -3 x=4
Step-by-step explanation:
Solve for each variable. Once youve done that, you have the underlined answers. Plug in one variable into the opposite equation. I put x's underlined value into y's equation. Solve for y again using x's value. Y equals -3. Plug this number into x's underlined value to find that x equals 4.
Between which two values would 50% of the data lie? Select all that apply. 15 and 40 15 and 45 40 and 50 45 and 50 45 and 60
Answers
Answer:
The answer is:
(2). 15 and 45
(3). 40 and 50
(5). 45 and 60
Step-by-step explanation:
Hope this helps! Also can i have brainliest?
Find the slope and y-intercept 15 POINTS
−5 − y = −3x
Answers
anybody know how to work on decay rate? I'll give brainliest. THIS IS DUE SOON SO PLEASE HELP
Answers
Answer:
28%
Step-by-step explanation:
In the function the .72 means that each unit of time 72% of the value is retained. This means that 28% percent of the value is lost or decays because 1-0.72=0.28 or 28 percent.
How many 2/7 s are in 3?
Answers
Answer: 11 is the answer.
there are 11 2/7's in 3 with a remainder of 1/7, 11 1/7.
Step-by-step explanation:
Answer:
10.5 or 21/2
Step-by-step explanation:
The question is asking how many 2/7 are in 3. So let make 3 a equivalent fraction that has 7 as it denomanater. 7/7 is 1, 14/7 is 2, so 21/7 is 3. Now let divide 21/7 by 2/7. flip 2/7 around to 7/2 then multiply by 21/7 which equals
[tex]\frac{147}{14}[/tex] which equals 10.5 or 21/2.
Sissy wants to enlarge a picture of a constellation so that she can put it on the wall in her daughter’s room. What will be the area of the enlarged picture on the wall?
24 in.2
108 in.2
224 in.2
486 in.2
Answers
Answer: 486 in
Just did this on edge
The enlargement transformation applied to the rectangular figure gives
a rectangle that is enlarged and similar to the figure.
Correct response:
The area of the enlarged picture is 486 in.²The given dimensions of the picture are;
Height, [tex]\overline{MN}[/tex] = 6 in.
Width, [tex]\overline{LP}[/tex] = 4 in.
The length of QL' = 12 + 42 = 54
By similar triangles, we have;
[tex]\dfrac{\overline{L'P'}}{\overline{LP}} = \mathbf{ \dfrac{\overline{QL'}}{\overline{QL}}}[/tex]
Which gives;
[tex]\dfrac{\overline{L'P'}}{6} = \mathbf{ \dfrac{54}{12}}[/tex]
[tex]\overline{L'P'} = \dfrac{54 }{12} \times 6 = \mathbf{27}[/tex]
Given that an enlargement gives similar figures, we have;
[tex]\dfrac{\overline{L'P'}}{\overline{LP}} = \mathbf{\dfrac{\overline{L'M'}}{\overline{LM}}} = Scale \, factor \ of \ the \ enlargement[/tex]
Therefore;
[tex]\dfrac{27}{6} = \dfrac{\overline{L'M'}}{4}[/tex]
Which gives;
[tex]\overline{L'M'} = \dfrac{27}{6} \times 4 = \mathbf{ 18}[/tex]
The area of the enlarged picture is, A = [tex]\overline{L'M'}[/tex] × [tex]\overline{L'P'}[/tex]
Which gives;
A = 27 × 18 = 486
The area of the enlarged picture on the wall is A = 486 in.²
Learn more about scale factors and enlargement transformation here:
https://brainly.com/question/14215765
https://brainly.com/question/2839518
Chanelle deposits $7,500 into the bank. She does not withdraw or deposit money for 6 years. She earns 6% interest during that time. a. How much interest will she have earned at the end of 6 years? She will earn $2,700 interest b. What will the balance be when she is finally able to withdraw her money?
Answers
Answer: a. $2700
b. $10200
Step-by-step explanation:
a. The interest she would have earned at the end of the 6 years can be gotten using the formula
= PRT/100
= $7500 × 6% × 6
= $7500 × 6/100 × 6
= $7500 × 0.06 × 6
= $2700
b. Her balance when she wants to withdraw the money would be:
= $7500 + $2700
= $10200
Please Answer!
Which expression is equivalent to the given expression?
4(a−3)=
−8a
4a−12
4a−3
−4(a+3)
Answers
because 4(a-3) what’s in () can’t be done so you go to the next step in pemdas and multiply and then you write it out and your done
Answer: The answer is 4a−12
what is true of the data in the dot plot? Check all that apply.
Number of Minutes Shelly Spent Waiting for the Bus Each Morning
A dot plot going from 10 to 15. 10 has 2 dots, 11 has 4 dots, 12 has 0 dots, 13 has 3 dots, 14 has 6 dots, 15 has 1 dot.
The center is 13.
The center is 14.
The peak is at 14.
It has two clusters.
It is skewed left.
The spread is from 13 to 15.
The person waited for the bus 16 times.
Answers
Answer:
True answers
The center is 13
The peak is at 14
It has two clusters
It is skewed left
The person waited for the bus 16 times
Step-by-step explanation:
Edge2021
Answer:
A, C, d, e, g
Step-by-step explanation:
3 mm
4 mm
What is the length of the hypotenuse?
C =
millimeters
Answers
The function f(x) = 2x^2 + 3 represents the rate of a boat traveling with the current in miles per hour.The function g(x) = x+2 represents the time the boat traveled in hours. Solve (f x g) (2), and then interpret the answer (f x g)(2) = 15, the distance in miles the boat traveled
(F times G) (2) = 15, the distance in miles the boat traveled
(F time G) (2) = 15, the number of boats
(F times G) (2) = 44, the distance in miles the boat traveled
(F times G) (2) = 44, the number of boats
Answers
Answer:
Step-by-step explanation:
Answer:
The distance travelled by the B737-400 aircraft in 5 hours is 2,000 miles
Step-by-step explanation:
Average speed = 400 miles per hour
Distance = 400t
t= 5
Total distance = 400t at t hours
Total distance when t = 5 hours
Total distance travelled = 400t
= 400 × 5
= 2,000 miles
Total distance travelled = 2,000 miles
The distance travelled by the B737-400 aircraft in 5 hours is 2,000 miles
use This for your explanation byeeeeeeee
Help me please! This is very confusing.
Answers
Answer: 60°
Step-by-step explanation:
Answer: x=60
Step-by-step explanation:
120+120= 240
360-240= 120
120/2= 60
can you list these measurements from least to greatest. 2.6cm 3cm 2.7cm
Answers
Answer:
3cm, 2.7cm, 2.6cm
Step-by-step explanation:
3 is higher than 2.7 and 2.6
Grace earns $7 for each car she
washes. She always saves $25 of her
weekly earnings. This week, she
wants to have at least $65 in
spending money. At least how many
cars must she wash?
Answers
These two triangles are similar. What is the length of side a and b? Help ASAP pleasee! Look at the screenshot Please, Thank you! :)
Answers
Answer:
do you have 12 as an answer?
Phillip wanted to leave a 15% tip. He thought to himself that 15% = 10% plus half of 10%. Which of the following equations will help Phillip estimate the tip on a $36.00 bill correctly?
A.
$3.60 + $1.80 = $5.40
B.
$3.60 + $3.60 = $7.20
C.
$3.60 + $0.36 = $3.96
D.
$1.80 + $1.80 = $3.60
Answers
Answer: D
Step-by-step explanation:
7.
The pair of figures is similar. Find x. Round to the nearest tenth if necessary.
A. 34 cm
B. 9.8 cm
C. 21.9 cm
D. 29.6 cm
Answers
Answer:
Choice B
Step-by-step explanation:
When two shapes are similar their sides are always going to be proportional. So here we will set up a proportion to solve this.
[tex]\frac{23}{40}=\frac{x}{17}[/tex]
Now we cross multiply
[tex]391=40x[/tex]
After we got an equation we solve it
[tex]x=9.775[/tex]
Since we got a decimal we will have to round it to the place they instruct for us, on this one it is 9.8 cm so it is choice b.
The required value of x is 9.8 cm. For the two similar triangles.
Two similar triangles are given. value of x to be determined.
Similar triangles are those triangles that have similar properties,i.e. angles and proportionality of sides.
Here, if triangles are similar then their ratio of sides is also equal.
x/23=17/40
x = 0.425*23
x = 0.425 * 23
x = 9.8 cm
Thus, The required value of x is 9.8 cm. For the two similar triangles.
Learn more about similar triangles here:
brainly.com/question/25882965
#SPJ2
if 3(x-1) -5(x-4)=8 find the value of x-5 whole 1/2
Answers
Step-by-step explanation:
3(x-1) -5(x-4) = 8
3x-3 -5x+20 = 8
3x -5x -3 +20 = 8
-2x + 17 = 8
17 -8 = 2x
9 = 2x
2x = 9
x = 9/2
3(x-1)-5(x-4)=8
We move all terms to the left:
3(x-1)-5(x-4)-(8)=0
We multiply parentheses
3x-5x-3+20-8=0
We add all the numbers together, and all the variables
-2x+9=0
We move all terms containing x to the left, all other terms to the right
-2x=-9
x=-9/-2
x=4+1/2
A bottle contains 1.7 L of water. A second bottle contains 450 mL of water. What is the total number of mL of water in both bottles?
Answers
Answer:
2150 mL
Step-by-step explanation:
1L=1000mL - convert
1.7mL=1700mL - convert problem numbers
1700+450mL - addition
2150mL- answer
Need help on this? Please help
Answers
parallel: g(x) = -5/3x + 1
perpendicular: h(x) = 3/5x - 5
neither: j(x) = 2x + 3
PLEASE HELP ILL GIVE U BRAINLIEST!
Answers
Answer:
part a) 112/350 = x/100
Step-by-step explanation:
part b) the answer is 32%
What is the slope of the line
Answers
Answer:
Positive, Upward Slope.
Step-by-step explanation:
Answer:
the slope of a line shows how steep a straight line is, or the direction of a straight line
(2k^3 - 7k^2 + 3k) - (-4k^2 + 5k) in polynomial standard form PLEASE HELP
Answers
Answer:
2 k 3 − 3 k 2 − 2 k
Step-by-step explanation:
Answer: ...
2k^3−3k^2−2k
PLEASE HELP I WILL GIVE BRAINLIEST!! EASY 35 POINTS!!!!!!
1. What is the rise between the points (0,0) and (8, 12)?
2. What is the run between the points (0,0) and (8, 12)?
3. What is the slope of the line?
Answers
Answer:
rise: 12 run:8 slope: 3/2
Step-by-step explanation:
1. It rises 12 points up (positive)
2. it runs 8 points to the right ()
3. the slope is rise/run= 12/8
4. simplify=3/2positive
What tropism does this experiment represent?
The straw scrunched up and expanding represents is a representation of
Correct answer:
turgor pressure
.
Answers
ESTIMATE THE QUOTIENT (Use rounding): 59.67 ÷ 11.1 =
Answers
Answer:
59.67 rounds to 60, 11.1 rounds to 10, so 60 divided y 10 equals 6
Step-by-step explanation:
hope this helps
PLEASE HELP ME WITH THIS I WILL GIVE BRAINLIEST
Answers
Answer:
The area of the large rectangle can be represented in two ways. Either the sum of each of the areas of the individual smaller rectangles, which is what the first equation represents, as its the base multiplied by the height (a) of each rectangle.
The second equation is a simplified version of the first one, and can be explained in three ways:
Each of the terms in the earlier equation had a common factor of a, which could be taken outside the parentheses.
or
Since the height is the same for each of the smaller rectangles, you can just multiply the height times the sum of the three smaller rectangle's widths
or
The width of the large rectangle is just the sum of each of the smaller widths, so the sum of those multiplied by a will give the area of the large rectangle.
Hope this helps!
show me a Graph x=−4.
Answers
Answer:
The graph of line x = -4 is also attached below.
The graph indicates that no matter what the value of y is, the x-value remains the same. Hence, the line is vertical with undefined slope,
Step-by-step explanation:
Given the line
x=−4
The given line x=-4 represents the vertical. We know that the slope of a vertical line is undefined. Thus, the slope of x=-4 is undefined.
As the line is vertical, meaning no matter what the value of y is, the x-value remains the same.
The graph of the line x = -4 is also attached below.
The graph indicates that no matter what the value of y is, the x-value remains the same. Hence, the line is vertical with undefined slope,
Ms. Hall found a mistake as she was grading Ethan’s paper. Each step should represent an equivalent expression. Which step shows the mistake that Ms. Hall found?
Expression: (1/2)exponet 2 x 8 – 3
Step 1:1/4 x 8 – 3
Step 2: 1/4 x 5
Step 3: 5/4
Step 4: 1/4