Answers
Let's assume
reference angle =B
so,
opposite =b
adjacent=a
now, we can use tan
[tex]tan(B)=\frac{b}{a}[/tex]
now, we can solve for b
Multiply both sides by a
[tex]a*tan(B)=a*\frac{b}{a}[/tex]
[tex]b=a*tan(B)[/tex]
so, option-A...............Answer
Related Questions
5 quarts of water are needed for every 2 pounds of chicken, how much water do you need per pound
Answers
Verify the equation below with each of the values listed for x to find a solution.
5 = 3x + 4
Answers
Answer:
123123131231231312312
Step-by-step exp13123123123lanation:
jkbbhivbyuiiyu1312312
What is the solution of the equation when solved over the complex numbers? X2+24=0.
Answers
Answer:
[tex]x=+-2i\sqrt{6}[/tex]
Step-by-step explanation:
[tex]x^2+24=0[/tex]
To solve for x we need to get x alone
Subtract 24 from both sides
[tex]x^2+24=0[/tex]
[tex]x^2=-24[/tex]
Now take square root on both sides to remove the square
[tex]x^2=-24[/tex]
[tex]\sqrt{x^2} =\sqrt{-24}[/tex]
[tex]x=+-2\sqrt{-6}[/tex]
square root of -1 is 'i'
[tex]x=+-2i\sqrt{6}[/tex]
Answer:
Step-by-step explanation:
2i√6 and -2i√6 :))
In the inequality, what are all the possible values of x? 2 − 3(2x + 1) < 6x(2 − 4) A) x ≥ 1 6 B) x ≤ 1 6 C) x ≥ − 1 6 D) x ≤ − 1 6
Answers
2 - 3(2x + 1) < 6x(2 - 4)
2 - 6x - 3 < 12x - 24x
-1 - 6x < -12x
-1 < -6x
Dividing by -6 both sides gives you;
1/6 < x or;
Final answer is x > 1/6
Answer:
A) x ≥ 1 6
: )
A coral reef grows 0.12 m every week how much does it grow in 5 weeks
Answers
Final answer:
To calculate the growth of a coral reef over 5 weeks at a rate of 0.12 meters per week, you multiply the weekly growth by 5, resulting in a total growth of 0.6 meters.
Explanation:
If a coral reef grows 0.12 meters every week, we can calculate its growth over 5 weeks by multiplying the weekly growth rate by the number of weeks.
Perform the calculation: 0.12 m/week × 5 weeks = 0.6 meters.
Therefore, a coral reef grows 0.6 meters in 5 weeks.
Suppose each square on the grids below is 1 cm by 1 cm. Estimate the area of the figure.
about 30 cm2
about 40 cm2
about 20 cm2
about 10 cm2
Answers
Answer:
About [tex]20cm^2[/tex]
Step-by-step explanation:
In the given image each of the square has side 1 cm by 1 cm.
If we could count the whole squares in the image we can see that there are about 14 whole squares, then there are 6 squares which are nearly half occupied so that makes about 3 whole squares. And then there are almost 12 squares whose quarter area is enclosed by the lines so that makes about 3 whole squares.
So the total area of the given figure is about [tex]20 cm^2[/tex].
Answer:
Option "C" would be the correct answer
Find f(6) if f(x) = x2 ÷ 3 + x.
4
10
18
Answers
f(x) = x2 ÷ 3 + x
f(6)
Replace X with 6 then follow order of operations.
6^2 / 3 + 6
6^2 = 36:
36 / 3 + 6
36 /3 = 12:
Add:
12 + 6 = 18
The answer is 18
What does the degree of a polynomial expression tell you about its related polynomial function? Explain your thinking. Give an example of a polynomial expression of degree three. Provide information regarding the graph and zeros of the related polynomial function.
Answers
The polynomial degree relates to the number of "zeros" or points of intersection of the polynomial function (curve in the (x,y) plane) with the x axis (that is, points where y=0). These zeros can sometimes be coinciding but that phenomenon aside, you will see N such intercepts with the x axis for a polynomial expression of N-th degree.
Example of a polynomial of 3rd degree is: x^3 + 2 x^2 - x - 2
You can factor it to (x-1)(x+1)(x+2) to see that the zeros are +1, -1, and -2. The plot is attached as an image - note the intercepts. Lmk if you have questions.
A degree in a polynomial function is the greatest exponent of that equation, which determines the most number of solutions that a function could have and the most number of times a function will cross the x-axis when graphed or we can also say that degree of polynomial determines the number of zeroes of that polynomial function.
Let us take an example of polynomial expression of degree three,
For e.g. [tex]x^{3}+2x^{2} -x-2=0[/tex] ...(1)
By hit and trial method we have to solve it .
Firstly, we put [tex]x = +1[/tex] in above equation ,
We get , [tex]1+2-1-2=0[/tex]
Thus, x = +1 is first zero of the equation.
Now ,we put [tex]x = -1[/tex] in equation...(1) ,
We get,
[tex]-1+2-(-1)-2=0[/tex]
i.e. x = -1 is also second zero of the equation.
Then, we put [tex]x = -2[/tex] in equation...(1) ,
We get ,
[tex]-8+8-(-2)-2=0[/tex]
Thus, the third zero of the equation is x = -2.
Therefore there are three zeroes of the polynomial function are x = -1, +1 and -2.
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which equation is the quadratic regression equation for the data shown in the table?
x 3 6 5 10 5 4 7 2 9
y 7 2 4 5 3 5 1 12 2
y=3x∧2 + 6x+5
y=0.392x - 5.583x
y=0.392x∧2 - 5.583x + 21.167
y= -0.006x∧2 - 0.431x + 0.407
Answers
Answer-
Quadratic regression equation [tex]y=0.392x^2 - 5.583x + 21.167}[/tex]
Solution-
Quadratic Regression Equation,
[tex]ax^2+bx+c[/tex]
[tex]a=\frac{(\sum x^2y\sum xx)-(\sum xy\sum xx^2)}{(\sum xx\sum x^2x^2)-({\sum xx^2)}^2}[/tex]
[tex]b=\frac{(\sum xy\sum x^2x^2)-(\sum x^2y\sum xx^2)}{(\sum xx\sum x^2x^2)-({\sum xx^2)}^2}[/tex]
[tex]c=\frac{\sum y}{n}-b\frac{\sum x}{n}-a\frac{\sum x^2}{n}[/tex]
Where,
[tex]\sum xx=\sum x^2-\frac{(\sum x)^2}{n}[/tex]
[tex]\sum xy=\sum xy-\frac{\sum x\sum y}{n}[/tex]
[tex]\sum xx^2=\sum x^3-\frac{\sum x\sum x^2}{n}[/tex]
[tex]\sum x^2y=\sum x^2y-\frac{\sum x^2\sum y}{n}[/tex]
[tex]\sum x^2x^2=\sum x^4-\frac{(\sum x^2)^2}{n}[/tex]
Calculating the values from the table,
a= 0.392
b= -5.583
c= 21.167
∴ Quadratic regression equation,
[tex]y=0.392x^2 - 5.583x + 21.167[/tex]
A line segment has endpoints at (4, –6) and (0, 2). What is the slope of the given line segment? What is the midpoint of the given line segment? What is the slope of the perpendicular bisector of the given line segment? What is the equation, in slope-intercept form, of the perpendicular bisector?
Answers
slope = - 2, midpoint = (2, - 2 )
the slope m is calculated using the ' gradient formula '
m = ( y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (4, - 6 ) and (x₂, y₂ ) = (0, 2 )
m = [tex]\frac{2+6}{0-4}[/tex] = [tex]\frac{8}{-4}[/tex] = - 2
calculate midpoint using midpoint formula
{[tex]\frac{1}{2}[/tex] (4 + 0 ), [tex]\frac{1}{2}[/tex] (- 6 + 2 )] = (2, - 2 )
gradient of perpendicular bisector = - [tex]\frac{1}{-2}[/tex] = [tex]\frac{1}{2}[/tex]
equation in slope-intercept form is
y = mx + c ( m is slope and c the y-intercept )
partial equation is y = [tex]\frac{1}{2}[/tex] x + c
to find c substitute ( 2, - 2) into the partial equation
- 2 = 1 + c ⇒ c = - 3
y = [tex]\frac{1}{2}[/tex] x - 3 in slope-intercept form
Answer:
-2
(2,-2)
1/2
y=(1/2)x-3
Step-by-step explanation:
It’s correct on edge.
Jules reads that 1 pint is equivalent to 0.473 liters. He asks his teacher how many liters are in a pint . His teachers responds that there about 0.47 liters on a pint. He asks his parents they say they are about 0.5 liters in a pint. Jules says they are both correct . How can that be true explain your answer
Answers
The parents are looking at the number in the hundredths place, and, seeing if they can round it up, since, it's a 5, and 5 or higher, you round up, they round it up to 0.5 liters.
I hope this helps!
Two cars are driving towad each other along a straight road. Their separation distance is l - (r1 + r2)t, where l is their original separation distance and r1 and r2 are their speeds. Will the cars meet? When? What if they are going in the same direction and not driving toward one another? Will they meet then?
Answers
If they are going in the same direction, assuming they are both driving at a constant speed, they will never meet. One car will be constantly on the other’s tail, but since one car is constantly moving away from the other, they will never meet unless the first car (moving away from the other) stops or slows down enough so the other one catches up, or the car “chasing” the other speeds up enough to crash into the other.
Carlos is using a number line to add another integer to –4. He begins by showing –4 on the number line, as shown below. Carlos adds the other integer on the number line and says that the sum is negative.Which is true of the number Carlos added to –4?
Answers
y=–3x + 6y=9 What is the solution to the system of equations? (–21, 9) (9, –21) (–1, 9) (9, –1)
Answers
ANSWER
The solution is [tex](-1,9)[/tex]
EXPLANATION
We want to solve the simultaneous equations
[tex]y=-3x+6---(1)[/tex]
and
[tex]y=9--(2)[/tex].
We substitute equation (2) in to equation (1), to obtain
[tex]9=-3x+6[/tex]
This has now become a linear equation in a single variable [tex]x[/tex].
We solve for x by grouping like terms.
[tex]9-6=-3x[/tex]
[tex]3=-3x[/tex]
We divide through by negative 3 to get;
[tex]-1=x[/tex].
Hence, the solution is [tex](-1,9)[/tex]
What is the sum of the angle measures in a decagon?
1,800°
1,440°
1,260°
210°
Answers
Use the formula (n - 2) * 180 to find the sum of the interior measures of a polygon.
n stands for the number of sides that the polygon has, so substitute 10 for n since a decagon has 10 sides.
(10 - 2) * 180, start by solving inside the parentheses and subtracting 10 and 2.
(8) * 180, multiply.
B. 1,440 is your answer.
Contestants in a dance-a-thon rest for the same amount of time evey hoir. A couple rests for 25 minutew in 5 hours. How long did they rest in 8 hours?
Answers
If each couple rests for [tex] k [/tex] minutes every hour, the time spent resting, [tex] r [/tex], after [tex] h [/tex] hours is given by
[tex] r = kh [/tex]
We know that a couple spent 25 minutes resting in 5 hour. So, the rate is
[tex] 25 = 5k \iff k = \dfrac{25}{5}=5 [/tex]
So, every couple rests 5 minutes per hour.
This means that, after 8 hours, the couples rest
[tex] r = 5\cdot 8 = 40 [/tex]
minutes.
If you finish one year of collage does it raise your income for the rest of your life?
Answers
The expression below is the factorization of what trinomial? -1(x - 6)(x + 8) apex question
Answers
Then, apply the FOIL method (first, outside, inside, last). This will give you: -x^2-8x+6x+48.
Last, CLT (combine like terms), to give you the trinomial: -x^2-2x+48
You could get this answer on PhotoMath (an app)
Final answer:
The trinomial factorization -1(x - 6)(x + 8) corresponds to the trinomial -x² - 2x + 48.
Explanation:
The trinomial factorization you are asking about is -1(x - 6)(x + 8). To find out the trinomial it factors from, you need to multiply the two binomials together and then multiply by -1. Let's do this step by step:
Multiply the binomials using the FOIL method, which stands for First, Outer, Inner, Last. This gives us the following intermediate step: (x - 6)(x + 8) = x(x) + x(8) - 6(x) - 6(8)
Simplify the intermediate step: x² + 8x - 6x - 48
Combine like terms: x² + 2x - 48
Finally, multiply the entire expression by -1 to give the final trinomial: -x² - 2x + 48.
Thus, the trinomial factorization -1(x - 6)(x + 8) corresponds to the trinomial -x² - 2x + 48.
Sten had some apples in his basket. He ate 3 and then put 3 in each of 4 bags. How many apples did Sten start with in his basket?
Answers
3 * 4 + 3 = 12 + 3 = 15
Answer: He had 15 apples.
The county fair charges $2.50 per ticket for the rides. Henry bought 15 tickets for the rides and spent a total of $55.50 at the fair. Henry spent his money only on ride tickets and fair admission. The price of the fair admission is the same for everyone. Use x to represent the number of ride tickets and y to represent the total cost.
Find the cost of admission to the fair. Explain how you found the cost of admission.
Write a linear equation that can be used to determine the cost for anyone who only pays for ride tickets and fair admission.
Explain what the coefficient of x and the constant of your linear equation represents.
Answers
Answer:
Admission to the fair = $ 18
[tex]y = 2.50x +18[/tex].
Where the coefficient of x represents the cost of each ticket and the constant represents the cost of admission to the fair.
Step-by-step explanation:
The total money Henry spent was $ 55.50
If Henry only spent the money on the tickets for the rides and at the entrance to the fair, then we know that:
Bought 15 tickets at 2.5 $
Therefore the price of the admission to the fair is the total expense ($ 55.50) minus the expense in the tickets for the rides ($ 2.50 * 15)
55.50 - 15 * 2.50 = 18
So:
Admission to the fair = $ 18
Ticket for the rides = $ 2.50
So if we call y at the total cost and x the number of tickets for the rides:
[tex]y = 2.50x +18[/tex].
This is a linear equation that represents the total cost.
Where the coefficient of x represents the cost of each ticket and the constant represents the cost of admission to the fair.
To find the cost of admission to the fair, set up a linear equation using the given information: 2.5x + y = 55.50. The coefficient of x (2.5) represents the cost of each ride ticket, while the constant (55.50) represents the total expenditure that includes both the ride tickets and the admission fee.
Explanation:To find the cost of admission to the fair, we can set up a linear equation based on the given information. Let's denote the cost of the admission as y and the number of ride tickets as x. We are given that the county fair charges $2.50 per ticket, so the cost of the ride tickets would be 2.5x. Additionally, we know that Henry bought 15 ride tickets and spent a total of $55.50, so we have the equation 2.5x + y = 55.50.
The linear equation that can be used to determine the cost for anyone who only pays for ride tickets and fair admission is 2.5x + y = 55.50.
In this equation, the coefficient of x (2.5) represents the cost of each ride ticket, while the constant (55.50) represents the total expenditure that includes both the ride tickets and the admission fee.
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Given a line segment with end points A (0,0) and B (6,8), find point C (x,y) that the triangle vertices A, B and C has an area of 25 square units?
Answers
Answer:
C(6.25 , 0)
Step-by-step explanation:
Draw the diagram
A is at (0,0)
B is at (6,8)
Draw a line from A to B.
Put a large dot where (0,6) is. Call this D
Draw BD
Draw another line from (0,0) to just beyond (6,0) Call this C. Draw in BC
What You Have Drawn
The height of the triangle is BD and it is 8. That comes from B which is (6,8)
Solve
Formula
Area = 1/2 * B * H
Area = 25
H = 8
Area = 1/2 B * H
25 = 1/2 * B * 8 Switch sides
1/2 * B * 8 = 25 Combine factors on the left.
4 B = 25 Divide both sides by 4
4B/4 = 25/4
B = 6.25
What that means is that AC is 6.25 units long and is on the x axis
C is C(6.25,0)
The question is in the attached below , thank you for helping me .
Answers
JKLM is a parallelogram. - Given
JM is a parallel to KL. - Definition of bisect
Given - LN bisects <KLP.
<2 ~= <3 - Definition of bisect
<1 ~= <3 - Transitive Property of Congruence
Solve for x. 14+x>18 Enter your answer, as an inequality, in the box.
Answers
14+x > 18 ---> Subtract 14 from both sides
18-14 = 4
x>4 -----> This is your answer!
Tip: If you ever multiply or divide by a negative you must flip the inequality sign the other direction. This did not happen in this one, but it is just a tip for other questions :D
Hope this helped!
x > 4 is your answer
Working alone it would take laura 45 minutes to mow the lawn kelly would take 1 hour 15 minutes if they work together the girls believe it will take 1 hour to mow the lawn which is the best described of the solution
Answers
Answer:
31.5 minutes only
Inverse proportion
Step-by-step explanation:
It takes 45 minutes for Laura to mow the lawn.
For Kelly it takes 1 hour 45 minutes or 60+45 = 105 minutes
In one minute Laura can mow 1/45 of the lawn.
Similarly in one minute Kelly can mow 1/105 of the lawn
Together in one minute they can mow the sum
= [tex]\frac{1}{45} +\frac{1}{105}[/tex]
Take lcd for 45 and 105 and make them equivalent fractions with same denominator
LCD of 45 and 105 is 15(3) (7) = 315
[tex]\frac{1}{45} +\frac{1}{105}=\frac{7+3}{315}=\frac{10}{315}\\=\frac{2}{63}[/tex]
In other words it would take 63/2 = 31.5 minutes only to lawn if they work together.
The situation here is the problem on inverse proportion. If no of people increase, work time would decrease.
A train leaves Roseville heading east at 6:00 am at 40 miles per hour. Another eastbound train leaves on a parallel track at 7:00 am at 50 miles per hour. What times will it be when the two trains are at the same distance away from Roseville?
Answers
Answer:
At 11:00 am the both trains will be at same distance away from Roseville
Step-by-step explanation:
The first train was 40 miles away from Roseville at 7:00 am
After some time t the both trains will be at the same distance away from Roseville.
We will make equation for that situation
d- distance v1= 40mph and v2= 50mph - velocity
d = v1*t + 40 = v2*t => v2*t - v1*t = 40 => t (v2-v1) = 40 -> t = 40/ (v2-v1)
t = 40/(50-40) = 40/10= 4h t = 4h
7:00 am * 4h = 11:00 am
Good luck!!!
Find the prime factorization of 210
A.) 2 X 3 X 5 X 7
B.) 2 X 3 X 35
C.) 2 X 7 X 15
Answers
To prime factorization would be A: 2 X 3 X 5 X 7
Because if your do 2 X 3 it would be 6
Then you do 5 X 7 it would be 35
And 6 X 35 would be 210
AND THAT IS FACTORING THE PROBLEM
[tex]210:2=105\\\\105:5=21\\\\21:3=7\\\\7:7=1\\\\210=2\cdot3\cdot5\cdot7[/tex]
Answer: A)
If f(x) = 2x + 7 and g(x) = x2 2, what is [f o g](3)?
Answers
Answer:
The value [fog](3) is 29.
Step-by-step explanation:
The given functions are
[tex]f(x)=2x+7[/tex]
[tex]g(x)=x^2+2[/tex]
We have to find [fog](3).
[tex](f\circ g)(x)=f(g(x))[/tex]
[tex](f\circ g)(3)=f(g(3))[/tex]
[tex](f\circ g)(3)=f(3^2+2)[/tex] [tex][\because g(x)=x^2+2][/tex]
[tex](f\circ g)(3)=f(11)[/tex]
[tex](f\circ g)(3)=2(11)+7[/tex] [tex][\because f(x)=2x+7][/tex]
[tex](f\circ g)(3)=22+7[/tex]
[tex](f\circ g)(3)=29[/tex]
Therefore the value [fog](3) is 29.
What is the known and unknown in 6 multiple by 2 are are 12 devided by 6
Answers
12 ÷ 6 =. 2
6 × 2 = 12
totally answer
he work shows how to use long division to find (x2 + 3x –9) ÷ (x – 2). What will be the remainder over the divisor?
Answers
Explanation of how to find the remainder using long division with a polynomial expression.
Explanation:Long Division Example:
We are given (x² + 3x – 9) ÷ (x – 2). To find the remainder using long division, we need to divide x² + 3x - 9 by x - 2 step by step.
Start by dividing x² by x, which gives x. Multiply x by (x - 2) to get x² - 2x.
Subtract x² - 2x from x² + 3x to get 5x. Bring down the -9.
Repeat the process: divide 5x by x to get 5. Multiply 5 by (x - 2) to get 5x - 10.
Subtract 5x - 10 from 5x - 9. The remainder is 1, which is the value over the divisor x - 2.
There are about 25.4 millimeters in one inch. Write this number in scientific notation.
Answers
Answer:
I inch = 25.4mm
Step-by-step explanation:
i inch =25.4mm
= 2.54×10^1
25.4 millimeters in scientific notation can be written as [tex]2.54 \times 10^1 \text {milimeters}[/tex]
The value "25.4 millimeters" must be expressed as a decimal number between 1 and 10, multiplied by a power of 10, in order to be written in scientific notation.
We may write the given number, 25, as follows:
[tex]2.54 \times 10^1[/tex]
In scientific notation, the decimal point is placed after the first non-zero digit, and in this case it is 2. The exponent 1 indicates that we move the decimal point one place to the right to get the original value.
Therefore, 25.4 millimeters in scientific notation is [tex]2.54 \times 10^1\text{millimeters }[/tex]
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