Answer:
Sine (30°) = cosine(90-30) = cos(60°) = 1/2
Step-by-step explanation:
The value of the [tex]cos 60^0[/tex] is [tex]\dfrac{1}{2}[/tex].
Recall the relationship between the sine and cosine[tex]cos^2\theta= 1-sin^2\theta\\cos 2\theta = cos^2\theta - sin^2\theta[/tex]
How to find the cosine values?Given the value of [tex]sin30^0[/tex] is [tex]\dfrac{1}{2}[/tex].
Use the relation between the sine and cosine as-
[tex]\cos^230^0=1-\sin^230^0\\=1-\dfrac{1}{4}\\=\dfrac{3}{4}\\[/tex]
Use another relation [tex]\cos 2\theta = \cos^2\theta -\sin^2\theta[/tex] as-
[tex]\cos(2\times 30^0)=\cos^2{30^0}-\sin^2{30^0}\\=\dfrac{3}{4}-\dfrac{1}{4}\\=\dfrac{1}{2}[/tex]
Hence, [tex]\cos 60^0[/tex] is value is [tex]\dfrac{1}{2}[/tex].
Learn more about trigonometric functions here-
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what is a midsegment of a triangle?
Answer:
A midsegment of a triangle is a segment that connects the midpoints of two sides of a triangle
nd interest for a loan
To pay for an $18,900 truck, Joe made a down payment of $3600 and took out a loan for the rest. On the loan, he paid monthly payments of $338.67 for 4
years.
Answer: He will pay this amount, with interest, over a 4-year period payment that he must make After paying 20% as a down payment, they finance the Determine the monthly payments needed to amortize the loan and months, that payments can be made under each of the following options before the money runs out.
Step-by-step explanation:
pls help on number 6!!
Answer:
729 cubic feet
Step-by-step explanation:
write an equation of the line with slope -2 and passing through (3,1) in slope-intercept form
Answer:
y=-2x+7
Step-by-step explanation:
Hi there!
The form of slope-intercept form is given as y=mx+b, where m is the slope and b is the y intercept
We are given the slope (-2) and a point (3,1)
We can immediately substitute -2 as the slope in the equation
y=-2x+b
Now we need to find b
Because the line will pass through the point (3,1), we can use it to solve for b
Substitute 3 as x and 1 as y
1=-2(3)+b
multiply
1=-6+b
add 6 to both sides to isolate b
7=b
Substitute 7 as b into the equation
The line is y=-2x+7
Hope this helps!
Dave Bowers collects U.S. gold coins. He has a collection of 49 coins. Some are $10 coins, and the rest are $20 coins. If the face value of the coins is $690, how many of each denomination does he have?
How many $10 coins does he have?
How many $20 coins does he have?
There is a bag with only red marbles and blue marbles.
The probability of randomly choosing a blue marble is
7
8
.
There are 56 marbles in total in the bag and each is equally likely to be chosen.
Work out how many red marbles there must be.
Answer:
7
Step-by-step explanation:
The probability of choosing a blue marble is 7/8, or 49/56, which means that out of 56 marbles, 49 are blue. 56-49=7, so there are 7 red marbles. Hope this helps! :)
Pls help school almost over I need to pass
Answer:
B.
Step-by-step explanation:
6.4 times 10 to the 3rd power (6.4 times 10x10x10) is equal to 6400, therefor, B is the correct answer.
Consider the expression below. Assume the variable m represents an integer. 6m(3m + 21) Enter an expression in the box that uses the variable m and makes the equation true. (Simplify your answer completely. If no expression exists, enter DNE.) 6m(3m + 21) = 9 Given that m represents an integer, is 6m(3m + 21) divisible by 9?
Answer:
[tex](a)\ 6m(3m + 21) = 9(2m^2 + 14m)[/tex]
(b) Yes, it is divisible by 9
Step-by-step explanation:
Given
[tex]6m(3m + 21)[/tex]
Solving (a): Complete the blanks
[tex]6m(3m + 21) = 9 [\ ][/tex]
Expand the bracket
[tex]6m(3[m + 7]) = 9 [\ ][/tex]
[tex]6m*3(m + 7) = 9 [\ ][/tex]
Express 6m as 2m * 3
[tex]2m*3*3(m + 7) = 9 [\ ][/tex]
[tex]2m*9(m + 7) = 9 [\ ][/tex]
Rewrite as:
[tex]9 * 2m(m + 7) = 9 [\ ][/tex]
Multiply the bracket by 2m
[tex]9 * (2m^2 + 14m) = 9 [\ ][/tex]
Divide both sides by 9
[tex]2m^2 + 14m = [\ ][/tex]
Hence, the bracket will be filled with: [tex]2m^2 + 14m[/tex]
So:
[tex]6m(3m + 21) = 9(2m^2 + 14m)[/tex]
Solving (b): Is [tex]6m(3m + 21)[/tex] divisible by 9?
In (a), we have:
[tex]6m(3m + 21) = 9(2m^2 + 14m)[/tex]
The leading factor "9" implies that the expression is divisible by 9
What is the inverse of the function f(x) = 2x – 10
Answer:
y = 1/2x +5
Step-by-step explanation:
change f(x) to y
y = 2x - 10
then switch x and y
x = 2y - 10
then solve for y
add 10 to both sides and divide both sides by 2
Answer:
Step-by-step explanation:
One way to find the inverse is:
1. replace the symbol f(x) with y (for simplicy--stay tuned). Now you have
y = 2x -10
2. switch x and y. You get x = 2y - 10
3. Solve for y.
x + 10 = 2y
y = (x + 10)/2
4. Replace y with the symbol for the inverse function,
Another approach is to think about inverse operations in reverse order.
f(x): start with x
multiply by 2
subtract 10
Inverse: start with x
add 10 (addition is the inverse of subtraction)
divide by 2 (division is the inverse operation of multiplication)
Given m|n, find the value of x.
Answer:
x=150
Step-by-step explanation:
x+30=180[co-interior angle]
x=180-30
x=150
For numbers 6-10, how long does it take to travel:
11. A car travels 200 kilometers in 8 hours. Calculate the average speed of the car in:
a. Kilometer per hour
b. Kilometers per minute
This question have no choices specify your answers only
Answer:
A
Step-by-step explanation:
You divide distance over time so 200 divided by 8.
Rebecca walks nine dogs each week she gets paid $10 a week +2 for each dog she walks which expression can be used to find how much is Rebecca gets paid in one week
Answer:
F(x)= 2x + 10
Step-by-step explanation:
F(×) represent the total amount she will get that week.
The 2 represents her dog bonus, x how many dogs she walked.
10 is the bare minimum she makes each week and it never changes.
Answer for brainlest zzzz
Answer:
A = 42 cm²
Step-by-step explanation:
The area (A) of a triangle is calculated as
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )
Here b = 14 and h = 6 , then
A = [tex]\frac{1}{2}[/tex] × 14 × 6 = 7 × 6 = 42 cm²
Solve for x. A. x = 12 B. x = 4 C. x = 3 D. x = 1
Answer:
4=x
Step-by-step explanation:
1/5( 2x+92) = 5x
Multiply each side by 5
5*1/5( 2x+92) = 5x*5
( 2x+92) = 25x
Subtract 2x from each side
2x+92-2x = 25x-2x
92 = 23x
Divide by 23
92/23 = 23x/23
4=x
Answer:
x = 4
Step-by-step explanation:
1/5 ( 2x + 92 ) = 5x
[tex] \small \sf \frac{1}{5} × ( 2x + 92 ) = 5x \\ [/tex]
distribute 1/5 through the parantheses
[tex] \small \sf \frac{2}{5}x + \frac{92}{5} = 5x \\ [/tex]
multiply both side of equation by 5
[tex] \small \sf \frac{2}{5}x \times 5 + \frac{92}{5} \times 5 = 5x \times 5\\ [/tex]
2x + 92 = 25xMove all variables to the left hand side and change their sign
2x + 92 - 25x = 0combine like terms
2x - 25x + 92 = 0calculate
-23x + 92 = 0Move all the constant to the right side and change their sign
-23 x = - 92divide both side by -23x
-23x / -23 = -92/-23x = 4Find the area of this shape!!
Answer:
if you assume one box as 1 m^2
then area of the shape is 54 m^2
but i am not sure if this is correct answer
Joes Enough income has been increasing each year by the same dollar meal the first year his income was $22,000 in the fourth year his income was $24,100 in which year was his income 33,900
Answer:
In the 23rd year his income was of $33,900.
Step-by-step explanation:
Joe's income has been increasing each year by the same dollar amount.
This means that his salary after t years is given by:
[tex]S(t) = S(0) + at[/tex]
In which S(0) is the initial salary and a is the yearly increase.
The first year his income was $22,000
This means that [tex]S(0) = 22000[/tex]. So
[tex]S(t) = S(0) + at[/tex]
[tex]S(t) = 22000 + at[/tex]
In the fourth year his income was $24,100
S(4) = 24100, and thus, we use this to find a.
[tex]S(t) = 22000 + at[/tex]
[tex]24100 = 22000 + 4a[/tex]
[tex]4a = 2100[/tex]
[tex]a = \frac{2100}{4}[/tex]
[tex]a = 525[/tex]
So
[tex]S(t) = 22000 + 525t[/tex]
In which year was his income 33,900
This is t for which S(t) = 33900. So
[tex]S(t) = 22000 + 525t[/tex]
[tex]33900 = 22000 + 525t[/tex]
[tex]525t = 11900[/tex]
[tex]t = \frac{11900}{525}[/tex]
[tex]t = 22.67[/tex]
Rounding up, in the 23rd year his income was of $33,900.
The party planning committee has to determine the number of tables needed for an upcoming event. If a square table can fit 8 people and a round table can fit 6 people, the equation 150 = 8x + 6y represents the number of each type of table needed for 150 people.
The variable x represents the number of
Answer:
the answer is 25 round tables and you will need 18.75 square tables
Step-by-step explanation:
IT is right trust me
Answer: The variable x represents the number of
✔ square tables
.
The variable y represents the number of
✔ round tables
.
If y = 9, find the value of x. The committee needs
✔ 12
square tables. explanation:
3. What is the value of LC in the diagram?
A
4x
(2x
B
3x
С
O A. 90°
O B. 60°
O C. 80°
OD. 40°
Answer: B
Step-by-step explanation:
4x+3x+2x=180
9x = 180
x = 20
20x3 = 60
Given m||n find the value of x.
Answer:
x =17
Step-by-step explanation:
The angles are supplementary so they add to 180
6x-20 + 6x - 4 = 180
12x -24 = 180
Add 24 to each side
12x-24+24 = 180+24
12x = 204
Divide by 12
12x/12 =204/12
x = 17
Help I don’t know what I’m doing
Your slope is 6/4. I found this by locating two points where the line intercepts evenly at two points. One was on the y-axis(0,-3) and the other was at (5,3). I then calculated the slope- rise over run or y over x. Because this graphs in a straight line, it is a linear equation. Your equation formula is y = mx + b. M is your slope, and b is your y-intercept. y = 6/4x -3
A school is tracking its freshmen attendance for the first marking period. Shown below is a table summarizing the findings for the 284 members of the freshmen class.
(a) Find the mean and median number of days absent Round your mean to the nearest tenth
(b) What proportion of the population that has an absenteeism greater than 4 days?
Answer:
The median number of days absent is zero (0)
The mean number of days absent is 1.0 day
(b) The proportion of the population that has absenteeism greater than 4 days is 6.34 %
Step-by-step explanation:
total number of students, n = 284
The total number of students is even, the median number of days absent will in (n/2).
n/2 = 284/2 = 142
The cumulative frequency that falls in 148 students = 0 day
The median number of days absent is zero (0)
For mean:
Let the days absent = x
let the number of students = f
[tex]mean (\bar x) = \frac{\sum fx}{\sum f}\\\\\bar x = \frac{(158\times 0)+ (64\times 1)+(18\times 2)+(22\times 3)+(4\times 4)+(5\times 7)+(6\times 8)+(9\times 2)+(13\times 1)}{284} \\\\\bar x = \frac{296}{284} \\\\\bar x = 1.0 \ day[/tex]
(b) the number of students with absenteeism greater than 4 dyas;
= 7 + 8 + 2 + 1
= 18
The proportion of these students;
[tex]= \frac{18}{284} \\\\= 0.0634 \\\\= 6.34 \ \%[/tex]
Using statistical concepts, it is found that:
a) The mean number of days absent is of 1, while the median is of 0.b) 0.0634 = 6.34% of the population has an absenteeism greater than 4 days.Mean and Median:The mean is given the sum of the multiplication of each value and it's number of observations, divided by the number of observations.The median is the number of days absent for which the sum of the number of students will be half of the total number, that is, half of 284, which is 142.Question a:
Then, the mean is:
[tex]M = \frac{0(158) + 1(64) + 2(18) + 3(22) + 4(4) + 5(7) + 6(8) + 9(2) + 13(1)}{284} = 1[/tex]
158 > 142, hence, the median is 0.
Question b:
In the sample, there are 284 students.Of those, 7 + 8 + 2 + 1 = 18 were absent four more than 4 days, hence:[tex]p = \frac{18}{284} = 0.0634[/tex]
0.0634 = 6.34% of the population has an absenteeism greater than 4 days.
To learn more about mean and median, you can take a look at https://brainly.com/question/24732674
please help me please i really need help please
Step-by-step explanation:
right answer
...... y= 1/2x²
A spinner is divided into 8 equal sections where 3 are black, 4 are yellow, and I is red. If it is spun randomly, what is the probability of it landing either on a yellow or a red section?
Given:
A spinner is divided into 8 equal sections where 3 are black, 4 are yellow, and 1 is red.
To find:
The probability of it landing either on a yellow or a red section.
Solution:
We have,
Total number of sections = 8
Black sections = 3
Yellow sections = 4
Red sections = 1
Now,
Either yellow or red sections = 4 + 1
= 5
Now, the probability of it landing either on a yellow or a red section is:
[tex]\text{Required probability}=\dfrac{\text{Either yellow or red sections}}{\text{Total number of sections}}[/tex]
[tex]\text{Required probability}=\dfrac{5}{8}[/tex]
Therefore, the required probability is [tex]\dfrac{5}{8}[/tex].
The rule as a mapping for the translation of a rectangle is (x, y) = (x - 2, y + 7). Which describes this translation?
O a translation of 2 units down and 7 units to the right
O a translation
of 2 units down and 7 units to the left
O a translation of 2 units to the right and 7 units up
O a translation of 2 units to the left and 7 units up
Mark this and retum
Answer:
a translation of 2 units to the left and 7 units up
Step-by-step explanation:
Translation of points (x,y)
At point x, the function can be translated to the left or to the right.
(x-a) is the translation of the point a units to the left, and (x+a) is the translation of the point a units to the right.
At point x, the function can be translated up or down. y+a represents a shift of a units up, and y-a represents a shift of a units down.
(x, y) = (x - 2, y + 7)
x - 2: 2 units to the left.
y + 7: 7 units up
So the fouth option is correct.
the ratio of the measures of the angles in quadrilateral dogs is 5:8:12:15. find the measure of the largest angle.
Answer:
135º
Step-by-step explanation:
Total parts
5 + 8 + 12 + 15 = 40
Value of each part; 360º in a quadrilateral
360 / 40 = 9
Largest angle
15 * 9 = 135º
For the given function, find the vertical and horizontal asymptote(s) (if there are any).
f(x) = (x-5)/(x^2-1)
Answer:
See below for answers and explanations (as well as a graph attached)
Step-by-step explanation:
The function [tex]f(x)=\frac{x-5}{x^2-1}[/tex] can be written as [tex]\frac{x-5}{(x+1)(x-1)}[/tex], showing that there are 2 vertical asymptotes, which are at [tex]x=-1[/tex] and [tex]x=1[/tex] as they both make the denominator equal to 0.
Additionally, there would be a horizontal asymptote at [tex]y=0[/tex] since the degree of the numerator is less than the degree of the denominator.
See the attached graph.
3. In circle OJ, shown below, LK and MN are chords,
intersecting at point O. If LO=3, OK= 3, and MO =
1, what is ON?
M
K
(1) 1
(2) 3
(3) 6
(4) 9
9514 1404 393
Answer:
(4) 9
Step-by-step explanation:
The product of the segment lengths of each chord is the same.
LO×OK = MO×ON
ON = LO×OK/MO = 3×3/1
ON = 9
What is the result of subtracting the second equation from the first
I didn’t undertand the question... mayb ur attachment isnt added! Plz check!
anyone can help with this ?
Answer:
The first one : x^2 - 8x + 15 sq ft
Step-by-step explanation:
To find the ares you need to multipy L and W : (x - 3) x ( x - 5)
(x - 3) x ( x - 5)
(x times x) - ( 3x + 5x) + ( 5 x 3)
=x^2 - 8x + 15
If this helps you, please give brainliest!
Answer:
(x-3)(x-5)=x^2-5x-3x+15=x^2-8x+15
Step-by-step explanation:
Because the patio is a rectangle, so it's area is I.w=(x-3)(x-5)
The equation f = v + at represents the final velocity of an object, f, with an initial velocity, v, and an acceleration rate, a, over time, t.
Which is an equivalent equation solved for t?
Answer:
(f-v)/a = t
Step-by-step explanation:
f = v + at
Subtract v from each side
f-v = v-v + at
f-v = at
Divide each side by a
(f-v)/a = at/a
(f-v)/a = t
Answer:
f - v = a
t
Step-by-step explanation:
Equation:
f = v + at
subtract -v on both sides
f - v = at
divide t on both sides of the equation
f - v = a
t