Answer:
∠45°
Step-by-step explanation:
When looking at a unit circle, the only acute angle (an angle between
0° and 90°) that consists of an equal sine and cosine is 45°. This is because:
[tex]sin 45 = \frac{\sqrt{2} }{2}[/tex]
[tex]cos45 = \frac{\sqrt{2} }{2}[/tex]
45° is the only acute angle that contains an equal sine and cosine.
Answer:
45 degrees
Step-by-step explanation:
Since Sin(90-x) = Cos(x), we can find that the angle at which 90-x=x is 45 degrees. This corresponds to [tex]\frac{\pi }{4}[/tex] radians
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
The difference of the range and the interquartile range of the data set represented by the box plot is _______.
Answer:
10
Step-by-step explanation:
The range is the largest number minus the smallest number
34 - 16 =18
The interquartile range is the right side of the box minus the left side of the box
29-21 = 8
Range - IQR = 18-8 = 10
Answer:
10
Step-by-step explanation: i got it right on test
Fifteen percent of the students at Central High take Spanish, 12% take French, and 4% take both. If a student is selected at random, what is the
probability that the student takes Spanish or French?
A 31%
B.27%
C. 23%
D. 19%
Answer:
C. 23%
Step-by-step explanation:
C. The probability that the student takes Spanish or French is 23%
What is mutually exclusive events ?
If two events can not occur together at same time, then the events are called mutually exclusive.
If two events are mutually exclusive, then,
P(A∪B) = P(A)+P(B)
And If two events are not mutually exclusive, then,
P(A∪B) = P(A)+P(B)-P(A∩B)
What is the required probability ?In central high school,
15% of the students take Spanish language = P(A) (say)
12% of the students take French language = P(B) (say)
& 4% of the students take both the languages = P(A∩B)
Since some of students take both languages, so this is not mutually exclusive.
The probability that the student takes Spanish or French is P(A∪B).
∴ P(A∪B) = P(A)+P(B)-P(A∩B)
= 15%+12%-4%
= [tex]\frac{15}{100}+\frac{12}{100}-\frac{4}{100}[/tex]
= [tex]\frac{15+12-4}{100}[/tex]
= [tex]\frac{23}{100}[/tex] = 23%
Hence, Required probability is 23%
Learn more about mutually exclusive events here :
https://brainly.com/question/3550010
#SPJ2
Using the image below, identify the angles that are vertical angles, list the angles that are linear pairs, and then solve for , , and .
Answer:
Step-by-step explanation:
y and 76 are vertically opposite angles
x and z are vertically opposite angles
Linear pairs.
If sum of two adjacent angles are 180, then they are linear pair.
x & 76 are linear pairs
y & z are linear pairs
z & 76 are linear pairs
x and y are linear pairs
Solutions:
y = 76 { vertically opposite angles are equal}
x + 76 = 180 { linear pair}
x = 180 - 76
x = 104
z = x {Vertically opposite angles are equal}
z = 104
Translate the following expression
20 decreased by 17
Question 7 options:
17 - 20
20 - 17
20 + 17
17 + 20
Answer:
20 - 17
Step-by-step explanation:
Decreased means subtract
20 - 17
The correct translation of the expression "20 decreased by 17" is "20 - 17."
Given is a verbal expression we need to convert it into algebraic form,
To reach this conclusion, we need to understand the phrase "decreased by" means subtraction.
When we say "20 decreased by 17," it implies that we are subtracting 17 from 20. In mathematical terms, this can be represented as 20 - 17.
Let's analyze the other options:
17 - 20: This option represents 17 subtracted by 20, which is the opposite of the original expression and doesn't match the given phrase.
20 + 17: This option represents the addition of 20 and 17, which doesn't align with the original expression. We are looking for subtraction, not addition.
17 + 20: This option also represents addition, and as mentioned before, the original expression involves subtraction, not addition.
Therefore, the correct answer is 20 - 17.
Learn more about Expression click;
https://brainly.com/question/28170201
#SPJ6
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. The measure of angle 0 is 7pie/6 the measure of its reference angle is __ degree and sin 0 is __ .
I need help on this.
Step-by-step explanation:
Russia is 0.35 20 Russia I said the answer is the answer is 0.35 CC 0.3522
Solve the equation to this problem
Answer:
x = - 6/7
Step-by-step explanation:
To start, 1x is just 1 times x, which you can just write as x.
x+3 = 8x+9
Then, you can bring x over to the other side of the equation, meaning it becomes -x. You can also think about subtracting x from both sides so it cancels out on the left.
3 = 8x+9-x
Next, do the same for the 9, so your equation looks like this:
3-9 = 8x-x
Just simplify it:
-6 = 7x
Finally, divide -6 by 7 to find x.
So, x = -6/7
what is the equation of a line that passes through the point (1,3) and is parallel to a line with a slope of -2?
Answer:
Step-by-step explanation:
y - 3 = -2(x - 1)
y - 3 = -2x + 2
y = -2x + 5
Given the formula for an arithmetic sequence f(8) = f(7) + 5 written using a recursive formula, write the sequence using an arithmetic explicit formula.
Answer choices
f(8) = f(1) + 5
f(8) = f(1) + 7
f(8) = f(1) + 35
f(8) = f(1) + 40
Answer:
f(8) = f(1)+35
Step-by-step explanation:
f(8) = f(7) + 5
We are adding 5 each time
f(7) = f(6)+5
f(6) = f(5) +5
f(5) = f(4)+5
f(4) = f(3) +5
f(3)=f(2)+5
f(2)=f(1)+5
f(8) = f(7) + 5
Replacing
f(8) = f(6)+5 + 5
f(8) = f(5)+5+5 + 5
f(8) = f(4)+5+5+5 + 5
f(8) = f(3)+5+5+5 + 5+5
f(8) = f(2)+5+5+5+5 + 5+
f(8) = f(1)+5+5+5+5+5 + 5+5
f(8) = f(1)+35
Answer:
f(8) = f(1)+35
Step-by-step explanation:
Patrick has a gas-powered boat that averages 5 miles per gallon of gasoline, and the tank holds 4 gallons. At 2 p.m., he left the dock. At 3 p.m., he was 6 miles west and 8 miles south of the dock. If he continues at this rate, in how many more hours will the tank be out of gasoline? Round to the nearest tenth if necessary.
Answer:
1 hour
Step-by-step explanation:
Let's assume that Patrick is travelling on a straight line throughout the whole path in order to minimize the distance.
The number of miles that he can travel on a full tank is:
[tex]m = 5\ mpg*4\ gallons\\m=20\ miles[/tex]
The distance travelled by Patrick in one hour (from 2p.m. to 3p.m.) is:
[tex]d^2=6^2+8^2\\d=\sqrt{100}\\ d=10\ miles[/tex]
If he is travelling at 10 miles per hour, and he could travel for a total of 20 miles, then the time remaining before the tank runs out of gasoline is:
[tex]t=\frac{20-10}{10}\\ t=1\ h[/tex]
If he continues at this rate, the gas will last for 1 more hour.
9x + 2+ 5x = 23 +7
SOLVE pLEASE
Answer:
2
Step-by-step explanation:
14x + 2 = 30
14x = 28
x = 2
Answer:
x =2
Step-by-step explanation:
9x + 2+ 5x = 23 +7
Combine like terms
14x +2 = 30
Subtract 2 from each side
14x +2-2 = 30-2
14x = 28
Divide each side by 14
14x/14 = 28/14
x = 2
Which linear equation includes the points
(6,0) and
(0, – 4)?
Answer:
y= (2/3)x - 4
Step-by-step explanation:
To answer this you'll want to use the slope intercept form of a line:
y= mx + b
So to solve essentially you just have to find the values for m and b
- m represents the slope of the line
- b is the y-intercept (the point where the line crosses the y-axis)
You can figure that b = -4 because the line will cross the y-axis when x = 0, and you are given the point on the line (0,-4), where x is equal to 0.
Now to find the slope of the line, since you are given two points on the line you will want to use the slope equation:
slope = [tex]\frac{y1-y2}{x1-x2}[/tex]
So you can assign each of the two points a number (1 or 2) where its values are equal to (x1, y1) or (x2, y2). It does not matter which point gets which number.
In this example:
We will assign the point (6,0) to be (x1, y1),
and we will assign the point (0, -4) to be (x2, y2)
So we end up with the following:
m= [tex]\frac{0- (-4)}{6-0}[/tex]
m= [tex]\frac{0+4}{6}[/tex]
m= [tex]\frac{4}{6}[/tex]
Simplify the fraction:
m = [tex]\frac{2}{3}[/tex]
From there you just substitute in for m and b into the slope intercept equation
Find the missing side length, and enter your answer in the box below. If
necessary, round your answer to 2 decimal places,
Answer:
c = 50
Step-by-step explanation:
Using Pythagoras' identity in the right triangle
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is
c² = 48² + 14² = 2304 + 196 = 2500 ( square root both sides )
c = [tex]\sqrt{2500}[/tex] = 50
What is the name of a savings account that offers higher interest rates, but in which a person's money must stay deposited for a specific amount of time? A. Money market account B. CD C. Savings account
Answer:
CD
Step-by-step explanation:
Apex
The name of the savings account that offers higher interest rates, but in which a person's money must stay deposited for a specific amount of time is B. CD.
Money market account, Certificates of deposits (CD) and the regular savings account are all different types of savings account.
Regular savings account has only lower interest rate while both CD and Money market account have higher interest rates.
And the money must be stayed in the account for a fixed period of time in CD accounts. This is not required in the money market accounts.
Thus, CD is the correct answer.
Learn more about Savings Account here :
https://brainly.com/question/30064097
#SPJ7
Simplify the expression. sin2x + sinx + cos2x - 1 sinx sinx - 1 sinx - 2
Answer:
-1
Step-by-step explanation:
Evaluate for x=0
sin((2)(0))+sin(0)+cos((2)(0))−1(sin(0))(sin(0))−1(sin(0))−2
sin((2)(0))+sin(0)+cos((2)(0))−1(sin(0))(sin(0))−1(sin(0))−2
= −1
Answer:
sinx
Step-by-step explanation:
sin^2 + cos^2 = 1 (pythagorean identity)
therefore we take the square sin and cos out to make a 1
sin2x + sinx + cos2x - 1 sinx sinx - 1 sinx - 2
left with sinx -1 +1 =
sinx because the 1s cancel out
The areas of the squares formed by the side lengths of the triangles are given for each triangle below. Which triangles are right triangles? Check all that apply. (Figures are not drawn to scale.)
3 squares form a triangle. The squares have areas 6 inches squared, 10 inches squared, 8 inches squared.
4 squares form a triangle. The squares have areas 9 inches squared, 25 inches squared, 16 inches squared.
5 squares form a triangle. The squares have areas 25 inches squared, 169 inches squared, 144 inches squared.
6 squares form a triangle. The squares have areas 7 inches squared, 25 inches squared, 24 inches squared.
7 squares form a triangle. The squares have areas 64 inches squared, 225 inches squared, 289 inches squared.
8 squares form a triangle. The squares have areas 10 inches squared, 26 inches squared, 24 inches squared.
Answer:
Well, Your best choice will be is B, and D.
Step-by-step explanation:
Because, Choice B.
9 + 16 = 25
. So, Choice B is the right answer.
Then, Choice D.
64 + 255 = 289. So, Choice D. is the right answer.
Good Luck!~
[tex]^{Brazts[/tex]
Answer:
b and d
Step-by-step explanation:
edinuity
XYZ Music Store sells new CDs, n, for $12.25, and used CDs, u, for $5.75. The
store earned $765 revenue last month. The store sold 22 more used CDs than
new CDs. Which system of equations represents this scenario?
Answer:
B.
Step-by-step explanation:
12.25 for n CD's
5.75 for u CD's
the total is 765
22 are more sold for more used than new
Answer: B) 12.23n + 5.75u = 765: u = n + 22
Step-by-step explanation: took the quiz.
Apply the 30-60-90 triangle theorem to find the length of the longer leg of a triangle of the length of the shorter leg is 4 inches.
3square root 4
7 inches
4 square root 2
8 square root 3
Answer:
4sqrt(3) inches
Step-by-step explanation:
The ratio of the lengths of the legs of a 30-60-90 triangle is:
short leg : long leg : hypotenuse
1 : sqrt(3) : 2
The long leg is sqrt(3) times the length of the short leg.
Here, the short leg measures 4 inches.
long leg = sqrt(3) * short leg
long leg = 4sqrt(3) inches
Find the area of the shaded segment. Round your answer to the nearest square centimeter. 24 cm2 23 cm2 21 cm2 22 cm2
This question is incomplete because it lacks the appropriate diagram. Find attached to this answer the complete diagram
Question:
Find the area of the shaded segment. Round your answer to the nearest square centimeter.
a) 24 cm²
b) 23 cm²
c) 21 cm²
d) 22 cm²
Answer:
d) 22 cm²
Step-by-step explanation:
We have Area and a Triangle in that diagram.
In other to find the shades segment , we have to find the Area of the triangle and the Area of the sector
Step 1
Area of a Triangle
= 1/2 × a × b × sin θ
Where θ = 120°
a = 6 cm
b = 6 cm
Area of the triangle = 1/2 × 6 × 6 × sin 120°
= 15.59 cm²
Step 2
Area of the sector
The formula is given as
Area = πr²θ/360
r = radius = 6cm
Area = π × 6² × 120/ 360
Area = 37.699111843cm²
Approximately = 37.70 cm²
Step 3
The Area of the shaded segment = Area of the sector - Area of the triangle
= 37.70cm² - 15.59cm²
= 22.11 cm²
Approximately to the nearest square centimeter
= 22 cm²
Pedro paid $25 for some books. He then saw a week later that the books were on sale for $20. What was the percent of discount on the books?
Answer:
20%
Step-by-step explanation:
25x.20=5
25-5=20
What's the steepest ladder you would personally be willing to climb? The shallowest?
Answer:
Personally, the steepest ladder I would be willing to climb would be a ladder with 2 meters long, that's it, because I don't like hights.
On the other hand, the shallowest ladder would be the nearest to the ground level possible, because, as I said before, I don't like being to far away from ground level.
(The question asked a personal perspective)
Calculate the slope of the line that goes through the points (2, 0) and (−4, 6)
The answer is -1
look at the attached picture
Hope it will help you
Good luck on your assignment
Answer:
m = - 1. (Slope)
Step-by-step explanation:
To find the slope of a line, you will need to use the slope formula: [tex]m = \frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex]
Plug in the 'x' and 'y' value of each coordinate into the equation:
[tex]m = \frac{0-6}{2-(-4)}[/tex]
Simplify this:
[tex]m = \frac{-6}{6}[/tex]
m = -1.
Therefore, the slope of the line is m = -1.
Which of the following options have the same value as 30%t of 81?
Choose 3 answers:
So the right options are:
option Aoption BOption DPlease see the attached picture for full solution
Hope it helps
Good luck on your assignment
2) Jose recently saw an ad online for a new version of his tablet. The projected price is $450, and the phone will be out on the market in about one year. Jose wants to purchase a new phone but is wondering if he should wait a year. With a 2.75% inflation, what amount would he pay to purchase a laptop today that is the same value as the one he saw online?
A.) $437.63
B.) $462.38
C.) $455.25
D.) $425.36
Answer:437.63
Step-by-step explanation:
Answer:
437.96
Step-by-step explanation:
:)
The surface area of a cube is 302.46 m^2. The length of each side of the cube = ______ m.
7.1
50.4
6.7
plz help thanx
Answer:
7.1 m
Step-by-step explanation:
A cube has 6 congruent square faces.
Given the surface area = 302.46 m² then the area of one face is
302.46 ÷ 6 = 50.41 m²
The area of a square = s² ( s is the side length ), thus
s² = 50.41 ( take the square root of both sides )
s = [tex]\sqrt{50.41}[/tex] = 7.1 m
The length of each side of the cube is 7.1 m
4) Explain how you can convert from percent to decimal and decimal to percent with two examples.
Answer:
To convert from a decimal to percent, multiply a decimal by 100 and add the percent sign.
Example: 0.10 becomes 0.10 x 100 = 10%
Example: 0.22 becomes 0.22 x 100 = 22%
To convert from a percent to a decimal, divide a percent by 100 and remove the percent sign.
Example: 10% becomes 10/100 = 0.10
Example: 22% becomes 22/100 = 0.22
Hope this helps!
:)
4p + 8 (p - 4) – 7 ( q - 4) =
So the answer is 12p-7q-4
please see the attached picture for full solution
hope it helps
Good luck on your assignment
Answer:
12p - 7q - 4
Step-by-step explanation:
In the absence of instructions here, I can only assume that you want to simplify this expression.
4p + 8p - 32 - 7q + 28 = 12p - 7q - 4
Helen needs to buy 6 packs of tea.
Each tea pack costs $8.
This table shows the offers available in two shops
Offer
Shop
А
3 for the price of 2
Buy one, get one half price
B
Which shop is cheaper for Helen?
Solve for a. 5+2a=−9
Answer:
a = - 7
Step-by-step explanation:
Given
5 + 2a = - 9 ( subtract 5 from both sides )
2a = - 14 ( divide both sides by 2 )
a = - 7
Answer:
a = -7
Step-by-step explanation:
5 + 2a = -9 {Subtract 5 form both sides}
5 + 2a - 5 = -9 - 5
2a = -14
Divide both sides by 2
2a/2 = -14/2
a = -7
Which of the following equations best represents the relationship in the table?
a. y = -4x + 2
b. y = -5x + 2
c. y = -5x + 6
d. y = -4x - 4
Answer: A y= -4x + 2
Step-by-step explanation:
y= mx + b
when x is 0, y is 2 which you make the y intercept (b) 2
going from x=0 to x=1, the y coordinate moves down 4, so the slope would be -4
:)