Answer:
Option B is the correct answer
Step-by-step Explanation:
[tex] \sin 45 \degree = \frac{x}{2} \\ \\ \frac{1}{ \sqrt{2} } = \frac{x}{2} ..( \because \: \sin 45 \degree =\frac{1}{\sqrt 2}) \\ \\ \huge \purple{ \boxed{ x = \frac{ \sqrt{2} }{2}}} \\ \\ [/tex]
Using the trigonometric ratio sine, we find that x = [tex]\sqrt{2}[/tex], making option D to be correct.
The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec). These trigonometric ratios deduce a relationship between angles of right angle triangle ( other than the right angle ) and the sides of the triangle : base, perpendicular, hypotenuse.
We have used trigonometric ratio sine here.
sin[tex]\theta[/tex] = [tex]\frac{perpendicular}{hypotenuse}[/tex]
In the given question,
from the point of view of angle 45° which is marked in the figure,
base = y
perpendicular = x
hypotenuse = 2
Using, sin[tex]\theta[/tex] = [tex]\frac{perpendicular}{hypotenuse}[/tex]
sin 45 = [tex]\frac{2}{x}[/tex]
[tex]\frac{1}{\sqrt{2} } = \frac{x}{2} \\\\x = \frac{2}{\sqrt{2} } = \sqrt{2}[/tex]
Learn more about trigonometric ratios here
https://brainly.com/question/23130410
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A grocer's shop sells carrots, onions and cucumbers.
The ratio of carrots to onions is 3:4
The ratio of onions to cucumbers is 6:5.
Work out the ratio of carrots to cucumbers.
Write the ratio in its simplest form.
Type your answer without using any spaces. You do not need to show any working.
Answer: 3:4
Step-by-step explanation:
There is a list of seven numbers. The average of the first four numbers is 5, and the average of the last four numbers is 8. If the average of all seven numbers is 6 4/7 , find the number common to both sets of four numbers.
Answer:
Number common to both sides=6
Step-by-step explanation:
Average of first four numbers=5
4*5=20
Average of the last four numbers=8
4*8=32
Average of all seven numbers=6 4/7
7*6 4/7
Find the number common to both sets of four numbers
Solution
4*5=20
4*8=32
32+20=52
7 * 6 4/7
=7*46/7
=46
Number common to both sides=52-46
=6
Just divide and check,
(x^2 + 7x + 10) ÷ (x + 2)
Answer:
x+5
Step-by-step explanation:
so first you would divide by x (which means you would multiply x+2 by -x)
x^2 + 7x + 10
-x^2 - 2x
5x + 10
then you would divide by 5 (which means you would multiply x+2 by -5)
5x + 10
5x +10
0
So then to check it you would multiply x+5 by x+2
(x+5)(x+2)
x^2 + 2x + 5x + 10
then simplify to get
x^2 + 7x + 10
PLEASE HELP ME!! explain this to me I am so confused.
Answer:
2
Step-by-step explanation:
sec∅ is equal to 1/cos∅ or (hypotenuse over adjacent).
With that in mind:
sec∅ = 2/1
sec∅ = 2
Answer:
B. 2
Step-by-step explanation:
We need to find the value of secant for this triangle.
Remember the trigonometric functions: secant = hypotenuse / adjacent, where the hypotenuse is the longest side (2 in this case), and the adjacent is the side right next to the labelled angle but is not the hypotenuse (1 in this case).
Plugging the values into the equation yields:
sec(θ) = hypotenuse / adjacent
sec(θ) = 2 / 1 = 2
The answer is thus B.
~ an aesthetics lover
Find the solution to the equation graphically. 10x - 10 = x + 10
Answer: x = [tex]2\frac{2}{9}[/tex]
Step-by-step explanation:
10x - 10 = x + 10
Subtract(x)
9x - 10 = 10
Add(10)
9x = 20
Divide(9)
x = [tex]2\frac{2}{9}[/tex]
Hope it helps <3
Answer:
x = 20/9
Step-by-step explanation:
10x - 10 = x + 10
Subtract x on both sides.
Add 10 on both sides.
10x - x = 10 + 10
Combine like terms.
9x = 20
Divide 9 on both sides.
x = 20/9
PLEASE HELP ME IS FOR TOMMOROW
Answer:
65°
Step-by-step explanation:
The missing angle is x°
tan x° = [tex]\frac{opposite }{adjacent}[/tex]
tan x° = [tex]\frac{850}{400\\}[/tex]
tan x° = 2.125
Using a calculator insert
tan^(-1)(2.125) ≈ 65° (after rouding the the nearest unit)
1. Solve.
a) (x + 3)(x - 5) = 0
b) 5(x - 6) (x - 9) = 0
c) (2x + 1) (3x - 5) = 0
d) 2x(x - 3) = 0
Step-by-step explanation:
2x × 3x +(-5×1)=6x-6=o
Answer: A: x=-3, 5
Step-by-step explanation: Use the quadratic equation or solving system method to get x=-3,5 the other questions are similar!
A researcher finds that the average preschool-aged child drinks two cups of milk per day. Assuming these data are normally distributed, the z score for any score more than the average cups per day in this example will be ______. Group of answer choices
Answer choices :
less than 0
greater than 0
exactly equal to 0
There is not enough information to answer this question.
Answer: greater than 0
Step-by-step explanation: For a normally distributed data, that is a data which is symmetrical whereby the majority of the values cluster at the center of the distribution. In general, for a normal distribution, the mean is 0 and the standard deviation is 1. Where the mean measures the average and refers to the center of the distribution and the standard deviation measures how spread out the data is.
Z - scores are used to standardize values with values above the average having z-scores greater than 0, those below average having values less than 0 and average value having a z-score of exactly 0.
I NEED HELP PLEASE, THANKS! :)
Answer: A
Step-by-step explanation:
The standard form of a cosine equation is: y = A cos (Bx - C) + D where
Amplitude (A) is the distance from the center to the maxPeriod (P) is the length of the function = 2π/B Phase Shift is the distance the max is moved from the y-axis = C/BCenter (D) is the imaginary line between the max and minPlot the points (see graph below).
A = 28
[tex]\dfrac{1}{2}P=6\quad \rightarrow \quad P=12\\\\\\P=\dfrac{2\pi}{B}\qquad \rightarrow \qquad 12=\dfrac{2\pi}{B}\qquad \rightarrow \qquad \large\bold{B=\dfrac{\pi}{6}}[/tex]
Phase Shift = 7 = C/B
[tex]7=\dfrac{C}{\frac{\pi}{6}}\qquad \rightarrow \qquad \large\bold{C=\dfrac{7\pi}{6}}[/tex]
D = 49
Input the values of A, B, C, and D into the standard form of a cosine equation to get:
[tex]\large\boxed{y=28\cos \bigg(\dfrac{\pi}{6}x-\dfrac{7\pi}{6}\bigg)+49}[/tex]
Brian rolls 2 fair dice and adds the results from each. Work out the probability of getting a total that less than 1.
Answer: The probability of getting a total less than 1 is 0%
Step-by-step explanation: The minimum roll for any pair of fair dice is 2. Already greater than 1.
It seems like a trick question, but in probability, you have to consider that some events are impossible!
Select the correct answer.
If the range of the function ºf(x) = x/4' is {28, 30, 32, 34, 36}, what is its domain?
Answer:
A is right. domain = {112, 120, 128, 136, 144}
Step-by-step explanation:
The range is the y-coordinate while the domain is the x-coordinate
y = x/4
x = 4y
domain = {4(28), 4(30), 4(32), 4(34), 4(36)}
= {112, 120, 128, 136, 144}
The cost for 3.5 pounds of shrimp is $14.63.
Find the unit price in dollars per pound.
If necessary, round your answer to the nearest cent.
Answer:
$4.18 dollars per pound
Step-by-step explanation:
We can find the price in dollars per pound by dividing the cost by the number of pounds:
14.63/3.5 = 4.18
This means the price in dollars per pound is $4.18
A 4cm ladder rest against a vertival wall with it's foot 2 m from the wall. How far up the wall does the ladder reach?
The table below gives input and output values for the function h(x) = a^x.
Answer:
It's the first one.
hope it helps :)
Step-by-step explanation:
can someone help me plz
Answer:
7 cm
Step-by-step explanation:
The area of a right triangle is given by
A = 1/2 bh
21 = 1/2 y* 6
21 = 3y
Divide each side by 3
21/3 = 3y/3
7 = y
The base is 7 cm
Area formula: A = bh/2
We have a height of 6, a base of y, and a area of 21.
Fill in and solve:
21 = y * 6 / 2
21 = 6y/2
21 = 3y
7 = y
Therefore, the base is 7
Best of Luck!
A pilot wants to arrive at her destination as soon as possible. Air traffic is busy, so she can take off 10 minutes later than expected and will be able to travel three times faster than expected if she waits. Create an equation to represent her total travel time, including wait time, where x is the number of minutes the flight was expected to take.
Answer:
y = x/3 + 10
Step-by-step explanation:
Let y be the number of minutes the flight takes
She can take off 10 minutes later than expected. She will be able to travel at a speed three times than expected.
Let her expected speed be s, therefore, she can travel at 3s.
x = number of minutes the flight was expected to take.
In terms of distance and speed:
x = d / s ______(1)
where d = total distance traveled
The time for the flight (minus waiting time) is now the division of the distance she traveled and her speed, i.e.:
t = d / 3s
From (1):
=> t = x / 3
The time she spent waiting is 10 minutes.
Therefore, the total time that the flight takes (plus waiting time) is:
y = t + 10
=> y = x/3 + 10
What is the solution to -2(8x - 4) < 2x+5
Answer: x>1/6
Step-by-step explanation:
For this problem, you solve it as if it had an equal sign.
-2(8x-4)<2x+5 [distribute -2]
-16x+8<2x+5 [combine like terms by adding and subtracting on both sides]
3<18x [divide both sides by 18]
x>1/6
A baby was born on October 1
1
. The table gives the weight of the baby on three different dates. Which graph best represents the baby's weight on these days?
Answer:
The second one or the one in the middle.
Explanation:
Although the weight is good. We are more focused on the Time in months.
The first graph represents that the weight on October 1 was taken when the baby was a month old. Which is inaccurate.
The second is accurate because it's says that the baby was a newborn when the weight was taken in October 1st. And after exactly 2 months he was weighted again. And another time a month and a half later.
And then the third represents that the baby was weighted every month on the same date. Which is also inaccurate.
Hope this helps you out! : )
Answer:
its the one in the middle
Step-by-step explanation:
I got it right on imagine math !!
Can you please help me I really need help please help me thank you
Answer:
a) x = 17/8
b) x = 23
c) x = -8/11.
Step-by-step explanation:
a)
-3x + 5 = 5x - 12
Add 3x to both sides:
5 = 8x - 12
Add 12 to both sides:
17 = 8x
Divide both sides by 8:
17/8 = 8x/8
x = 17/8.
---------------------
b)
6(x-3)-4(x+2) = 20
Distribute:
6x - 18 - 4x - 8 = 20
Combine like terms:
2x - 26 = 20
Add 26 to both sides:
2x = 46
Divide both sides by 2:
x = 23.
---------------------
c)
-2/5(x + 3) = 1/3(x - 2)
Distribute:
-2/5x - 6/5 = 1/3x - 2/3
Add 2/5x to both sides by creating a common denominator:
-6/15x - 6/5 = 5/15x - 2/3
-6/5 = 11/15x - 2/3
Add 2/3 to both sides. Create common denominator:
-18/15 = 11/15x - 10/15
-8/15 = 11/15x.
Divide both sides by 11/15:
[tex]\frac{-8}{15}* \frac{15}{11} = \frac{-8}{11} = x[/tex]
x = -8/11.
plz answer..................................
Answer:
840π
Step-by-step explanation:
To calculate the surface area of a cylender, do S=2(π)*radius*height.
2(π)*12*35 = 840 π
CAN I GET SOME HELP ASAP PLEASE
Answer:
11.2 - B to C12 - B to A8.8 - A to CYou have to multiply all the sides by 4.
B to C = 2.8*4
2.8 * 4 = 11.2
B to A = 3*4
3*4 = 12
A to C = 2.2*4
2.2*4 = 8.8
Hope this helped!
Of a certain road 7.264km are down hill, 3.873km are up hill and 6.89 are level.what is the length of the road pls urgent tnx
Answer:
18.027
Step-by-step explanation:
7.264+3.873+6.89
18.027
13 At the beginning of 2009, Mr Veale bought a company.
The value of the company was £50 000
Each year the value of the company increased by 2%.
(a) Calculate the value of the company at the beginning of 2017
Give your answer correct to the nearest £100
Answer:
£58,800
Step-by-step explanation:
The answer can be calculated using
FV=p(1+r/n)^nt
P=£50,000
r=2%=0.02
n=12
t=2009 to 2017=8 years
FV=p(1+r/n)^nt
=50,000(1+0.02/12)^12*8
=50,000(1+0.0017)^96
=50,000(1.0017)^96
=50,000(1.1771)
=58,855
FV=58,855
To the nearest £100=£58,800
Stevie and Michael share their profit in a ratio 3:5. Stevie gets £120 more than Michael. How much profit did they make altogether?
Answer:
£480
Step-by-step explanation:
we can multiply both terms of ratio with same number without changing the ratio.
Example
a:b = ax: bx (here we have multiplied both terms with x)\
Given
Stevie and Michael share their profit in a ratio 3:5
Let the profit for Stevie and Michael be 3x and 5x
Given Stevie gets £120 more than Michael
Profit for Steve = 120 + profit for Michael
3x = 120 + 5x
3x-5x = 120
=> -2x = 120
=> x= -120/2 = -60
As we see profit is negative , hence it cannot be solution.
It can be solved if Stevie and Michael share their profit in a ratio 5:3
(note: in ratio , bigger number should have bigger term in ratio)
Let the profit for Stevie and Michael be 3x and 5x
Given Stevie gets £120 more than Michael
Profit for Steve = 120 + profit for Michael
5x = 120 + 3x
5x-xx = 120
=> 2x = 120
=> x= x120/2 = 60
Profit for stevei = 5x =5*60 = 300
Profit for Michael = 3x = 3*60 = 180
Total profit for them together = 300 + 180 = 480 Answer.
I need help ASAP bsnbssbbsb
Answer:
Option A and C
Step-by-step explanation:
An isosceles triangle have:
=> Two equal angles
=> Two sides with the same length
Answer:
A & C
Step-by-step explanation:
The triangle is an isosceles triangle. The two base angles are equal. Two sides of the triangle are same in length. All the angles in the triangle shown are less than 90 degrees.
ADDISON RAE mixed L of water with 1 L vegetable oil. Which fluid will be floating? Why? The total volume is 2 L. If water’s density is 1 g/cm^3 and the oil’s density is 0.9 1 g/cm^3, what is the density of the mixture? How about 1.9L of water and 0.1 L of the same oil?
Answer:
The FitnessGram Pacer Test is a multistage aerobic capacity test that progressively gets more difficult as it continues. The 20 meter pacer test will begin in 30 seconds. Line up at the start. The running speed starts slowly but gets faster each minute after you hear this signal bodeboop. A sing lap should be completed every time you hear this sound. ding Remember to run in a straight line and run as long as possible. The second time you fail to complete a lap before the sound, your test is over. The test will begin on the word start. On your mark. Get ready!… Start
245 x 20 remander2/13
a) Find the value of
Write your answer correct to the nearest 10.
b) Find the value of square root of 58 - 29 + 38
Write your answer correct to 2 decimal places.
Answer:
1) 245 x 20 remander2/13 = 4940
2) square root of 58 - 29 + 38
= 8.19
Step-by-step explanation:
245 x 20 remander2/13= 245* 20 2/13
245 x 20 remander2/13= 245 * 262/13
245 x 20 remander2/13= (245*262)/13
245 x 20 remander2/13 =64190/13
245 x 20 remander2/13= 4937.69
245 x 20 remander2/13 = 4940
square root of 58 - 29 + 38
= √(58-29+38)
square root of 58 - 29 + 38
= √(96-29)
square root of 58 - 29 + 38
= √(67)
square root of 58 - 29 + 38
= 8.185
square root of 58 - 29 + 38
= 8.19
Which number sentence is NOT true? A. B. |-3| = -3 C. D. HELP PLEASE ILL GIVE BRAINLIEST!!!
Answer:
it looks like the question is not complete but anything in a bracket like(-3) since tjere is no number in front of it or anything to divide it if the number is alone there is no need for the bracket
Answer:
A
Step-by-step explanation:
work out the shaded area
Answer:
70 [tex] {cm}^{2} [/tex]Step-by-step explanation:
Shaded area:
Area of big rectangle - Area of small rectangle
[tex] = 10 \times 12 - (10 - 5) \times (12 - 2)[/tex]
Calculate the difference
[tex] = 10 \times 12 - 5 \times 10[/tex]
Calculate the product
[tex] = 120 - 50[/tex]
Calculate the difference
[tex] = 70 \: {cm}^{2} [/tex]
Hope this helps...
Best regards!!
Shubham, Ashish, and Vinay participated in a long jump competition on their sports day. Shubham jumped 41 m 2 , while Ashish jumped 3 m less than Shubham. On the 4 other hand, Vinay jumped 11m more than Ashish. How 4 long was Vinay's jump?
Answer:
Vinay jumped = 49m
Step-by-step explanation:
Given:
Shubham jumped = 41m
Ashish jumped = 3m less than Shubham
Vinay jumped = 11m more than Ashish
Find:
Length of Viney's jump
Computation:
Ashish jumped = Shubham jumped - 3m
Ashish jumped = 41m - 3m
Ashish jumped = 38m
Vinay jumped = Ashish jumped + 11m
Vinay jumped = 38m + 11m
Vinay jumped = 49m