Answers
Answer: y=mx+b
Step-by-step explanation:
Related Questions
In Exercises 23-26, evaluate the trigonometric function by
memory or by constructing an appropriate triangle for the
given special angle.
23. (a) cos 60°
24. (a) cot 45°
25. (a) sin 45°
26. (a) sin 60°
(b) csc 30°
(b) cos 45°
(b) cos 30°
(b) tan 45°
27. (a) sin 10°
28. (a) tan 23.5°
29. (a) sin 16.35°
(c) tan 60°
(c) csc 45°
(c) tan 30°
(c) sec 30°
In Exercises 27-36, use a calculator to evaluate each
function. Round your answers to four decimal places. (Be
sure the calculator is in the correct angle mode.)
(b) cos 80°
(b) cot 66.5°
(b) csc 16.35°
23~29 Pls
Answers
In Exercises 23-26 and In Exercises 27-36 , the trigonometric function by memory and by constructing an appropriate triangle for the given special angle are mentioned below
What is trigonometry?Trigonometry is a branch of mathematics, which deals with the study of right angle triangles. Trigonometry is concerned with specified functions of angles and their applications to calculations.
There are 6 commonly used functions in trigonometry with their name and abbreviations-
sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), cosecant (cosec)
1. Exercises 23-26
23. (a) cos 60° = 0.5
24. (a) cot 45° = 0.7071
25. (a) sin 45° = 0.7071
26. (a) sin 60° = 0.8660
(b) cos 30° = 0.8660
(b) cos 45° = 0.7071
(b) cos 30° = 0.8660
(b) tan 45° = 1
27. (a) sin 10° = 0.9958
28. (a) tan 23.5° = 0.4348
29. (a) sin 16.35° = 0.2815
(c) tan 60° = 1.732
(c) cosec 45° = 1.4142
(c) tan 30° = 0.5773
(c) sec 30° = 1.1547
2. Exercises 27-36
(b) cos 80° = 0.1736
(b) cot 66.5° = 0.4348
(b) cosec 16.35° = 3.5523
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through: (4, 3), perpendicular to y=-2+1
Answers
The equation of the line that is perpendicular to y = -2x + 1 will be y = (1/2)x + 1.
What is a linear function?A straight line on the coordinate plane is represented by a linear function.
A linear function always has the same and constant slope.
The formula for a linear function is f(x) = ax + b, where a and b are real values.
As per the given line,
y = -2x + 1
The slope(m) intercept form of a line is given as,
y = mx + c
By comparing,
Slope m = -2
The product of the slopes of the two perpendicular lines is -1.
Slope of perpendicular line (m') x -2 = -1
m' = 1/2
Put m' = 1/2 and (4,3) into y = m'x + C.
3 = (1/2)4 + C
C = 1
Thus, line will be y = (1/2)x + 1
Hence "y = (1/2)x + 1 will be the equation for the line that is perpendicular to y = -2x + 1.".
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PLEASE HELP ASAP!!!!!!!!
Answers
Answer:
D. IT shows it is Exponential function i believe
Step-by-step explanation:
Which set of ordered pairs represents a function? (1 point) O ((0, 1), (1, 2), (2, 3), (3, 3)) O ((0, 1), (1, 2), (1, 3). (2.5)) O ((0, 0), (1, 2), (2, 4), (2, 6)) O ((0, 0), (0, 1), (2.0), (2,4))
Answers
Answer:
no
Step-by-step explanation:
the X corrdinate ( the first part of the ordered pair) has multiple repeating 0's.The numbers in the X cant repeat or its not a funtion
A new car is purchased for 24300 dollars. The value of the car depreciates at 15% per year. To the nearest year, how long will it be until the value of the car is 5600 dollars?
Answers
Answer:
9 years
Step-by-step explanation:
Losing 15 % means 85% remains
so multiply each year's value by .85 to find the current value
after 'n' years it will be 24300 * .85^n
when will it be 5600 ?
5600 = 24300 * .85^n
5600/24300 = .85^n
now you need to take the log of both sides and solve for 'n' years
log ( 5600/24300) / log(.85) = n = 9.031 = ~~ 9 years
the bearing of B from A is 162. Work out the bearing of A from B
Answers
Answer: 180°
Step-by-step explanation:
If given the bearing from B to A, the bearing from A to B can be found using interior angles. Subtract the bearing of B to A from 180° to find the missing interior angle, then use the fact that angles in a full turn add to 360° to find the bearing of A to B.
Six thousands four and twenty four thousandths in standard form
Answers
Answer:
6,004.024
Step-by-step explanation:
Answer:
The number 0.000380 converted to standard form is 3.80 x 10 -4 Note that we do not remove the trailing 0 because it was originally to the right of the decimal and is therefore a significant figure. Additional Resources See the Scientific Notation Calculator to add, subtract, multiply and divide numbers in scientific notation or E notation.
Step-by-step explanation:
find the valeu of r if 5(r-3)=20
Answers
The value of [tex]r[/tex] is [tex]7[/tex]
The given equation is
[tex]5(r-3)=20[/tex]
We will now open the bracket, [tex]5r-15=20[/tex]
Let's simplify,
[tex]5r=20+15\\5r=35\\r=\frac{35}{5} \\r=7[/tex]
The value of [tex]r=7[/tex]
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What percentage of the shape is blue?
Write your answer using a percent sign (%).
Answers
13/20=x/100
20x=1300
20x/20=x 1300/20=65
So x=65%
What is needed for HL congruence?
Answers
For HL congruence, two triangles need to have the same corresponding angles and corresponding sides. This means that the angles in one triangle must match the angles in the other triangle, and the side lengths must match respectively.
HL Congruence Between Two TrianglesHL congruence is a type of congruence between two triangles, which states that two triangles are congruent if they have the same corresponding angles and corresponding sides. The angles of one triangle must be equivalent to the angles of the other triangle, and the side lengths must match.
For example, if triangle ABC is congruent to triangle DEF, then angle A must be equal to angle D, angle B must be equal to angle E, and angle C must be equal to angle F.Learn more about Triangles: brainly.com/question/25215131
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Benito has a job that pays $14.15 per hour for a 40-hour work week. He is to be paid time and a half for every hour over 40 that he works in a week. What will his gross pay be for a week in which he works 49 hours?
Answers
Benito's gross pay for the week will be $757.07.
What are work and time?
In aptitude, work and time are related concepts that are used to calculate the rate of work being done.
Benito is to be paid time and a half for every hour over 40 that he works, so for a 49-hour work week, he will be paid for 49 - 40 = 9 hours of overtime.
His regular pay for the first 40 hours is $14.15 per hour * 40 hours = $566.
His overtime pay is $14.15 per hour * 1.5 = $21.23 per hour
His overtime pay for 9 hours is $21.23 per hour * 9 hours = $191.07
his gross pay for the week will be $566 + $191.07 = $757.07.
Hence, Benito's gross pay for the week will be $757.07.
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What is the solution to the equation 1/3x=6
Answers
[tex]\dfrac{1}{3} x=6[/tex]
Multiply both sides by 3:
[tex]3\times(\dfrac{1}{3} x)=3\times(6)[/tex]
[tex]\fbox{x = 18}[/tex]
1/3x = 6
Multiply both sides by 3:
3 * 1/3x = 3 * 6
x = 18
x = 18 would be your answer.
Hope this helps!
20÷5+4x7-4 help plis
Answers
Answer:
28 / Ounce of wed >;)
Step-by-step explanation:
Answer:
28
Step-by-step explanation:
PEMDAS (parenthesis, exponents, multiplication, division, addition, subtraction)
Multiply 4 and 7 (28), divide 20 by 5 (4), add those together (32) and then subtract 4 which will get you 28
Determine the ratio of surface area volume for each prism
Answers
1. The ratio of the surface area to volume of the cube = 3/ 5
2. The ratio of the surface area to volume of the cuboid = 113/ 62
Surface area and volume of a figure.
The surface area of a given figure is the area of the total external boundary of the figure. While the volume of a figure is the quantity of substance that can fill up the figure.
To solve the question, we have;
1. The surface area of a cube = 6a
where: a = length x length
= 10 * 10
a = 100 square centimeters
So that;
surface area of the cube = 6*100
= 600 sq cm
ii. Volume of a cube = l^3
= 10^3
volume of the cube = 1000 cubic centimeters
iii. The ratio of its surface area to volume = 600/ 1000
= 6/ 10 = 3/ 5
2. The surface area of a cuboid = 2a + 2b + 2c
= 2(a + b + c)
where a = b = c = length * width
a = length x width
= 4*2
a = 8 sq. m
b = length x width
= 6.2 x 4
b = 24.8 sq. m
c = length x width
6.2 x 2
c = 12.4 sq. m
Surface area of the cuboid = 2(8 + 24.8 + 12.4)
= 90.4 sq. m
ii. volume of a cuboid = length x width x height
= 6.2 x 4 x 2
= 49.6 cubic meters
iii. The ratio of surface area to volume of the cuboid = 90.4/ 49.6
= 113/ 62
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Determine the volume of the figure.
5.8 cm
4.6 cm
16.25 cm
10.1 cm
4.6 cm
5.8 cm
Answers
The volume of the figure is has been determined to be 597.632 cubic centimeters.
Volume of a figure.The volume of a figure is the amount of substance that it can conveniently contain considering its dimensions. Each figure has a given formula to determine its volume.
Considering the figure in the question, divide it into two parts.
So that,
i. volume of the first part = length x width x height
= 16.25 x 5.8 x 4.6
= 433.55
The volume of the first part is 433.55 cubic cm.
ii. volume of the second part = length x width x height
= (16.25 - 10.1) x 5.8 x 4.6
= 6.15 x 5.8 x 4.6
= 164.082
volume of the second part is 164.082
iii. Total volume of the figure = 433.55 + 164.082
= 597.632 cubic centimeters
The total volume has been determined to be 597.632 cubic centimeters.
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The first digits of data entries in most real-world data sets are not uniformly distributed. The most common first digit is 111, followed by 222, and so on, with 999 being the least common first digit. This phenomenon is known as benford's law.
Answers
The probability for the first digit of a random number of a data set to be greater than 7 is 0.097.
Here we are given a probability distribution table regarding Benford's law where all the probabilities about the occurrence of the first digit of a data set are given. As we can see that digit 1 has the highest probability with number 9, the least.
Here we need to find the probability that a randomly selected number, has a first digit greater than 7.
Here we don't have to think about Benford's law since the data already has given us the required distribution.
Hence P(D > 7) = P(D = 8) + P(D = 9)
= 0.051 + 0.046
= 0.097
Hence the probability for the first digit to be greater than 7 is 0.097.
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Correct Question
(Image Attached)
simplify -5.1m + 2.3m
Answers
Answer;
-2.8m
Step-by-step explanation;
It's just adding m terms, and yes it's adding decimals but you can do it in your head if your good at arithmetic if not your calculator is there to help you out dw
so -5.1m+2.3m is
-2.8mAnswer: -2.8
Step-by-step explanation:
it the answer
In this question, all measurements are in millimetres.
An equilateral triangle has side lengths of 4a + 2.
A square has side lengths of 2a + 7.
Given that the triangle has a larger perimeter than the square, work out the
smallest possible integer value that a could take.
+
Answers
The smallest possible integer value that 'a' could take is 6.
What is Perimeter?Perimeter is the total length of a shape's boundary.
Perimeter of equilateral triangle = 3a, where a is the side length
Perimeter of a square = 4b, where b is the side length
Let P₁ be the perimeter of equilateral triangle and P₂ be the perimeter of square.
Here,
Length of side of equilateral triangle = 4a + 2
P₁ = 3 (4a + 2)
Length of side of square = 2a + 7
P₂= 4 (2a + 7)
Given P₁ > P₂
3 (4a + 2) > 4 (2a + 7)
By distributive property,
12a + 6 > 8a + 28
12a - 8a > 28 - 6
4a > 22
a > 22/4
a > 5.5
Hence 6 is the smallest number which is an integer that 'a' could take.
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Geometry please help fast
Answers
Pythagorean Theorem:
a²+b²=c²
where a=leg 1, b=leg 2, and c=hypotenuse
The Pythagorean Theorem works to solve any side of a right triangle as long as we know t he length of 2 sides. So, let’s plug the values into the formula and solve for “a” (leg 1).
a²+(4)²=(4√5)²
Simplify:
a²+16=80
Solve for a:
Subtract 16 from both sides
a²=80-16
a²=64
Take the positive square root of both sides:
√a²=√64
a=8
So, leg 1 (a), or side 3 is equal to 8
Let’s check our work by plugging a=8 because into the formula:
(8)²+16=80
64+16=80
80=80
Thus, the 3rd side is 8
During the season, the number of goals Keon scored to
the number of goals Max scored was 3 to 4. If Max
scored 16 goals, how many goals did Keon score?
Answers
Keon scored 5 goals.
X
————————
Y
Formula of the Line
Answers
Answer:
y = 4x + 4
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept, where it crosses the y- axis )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 1, 0) and (x₂, y₂ ) = (- 2, - 4) ← 2 points on the line
m = [tex]\frac{-4-0}{-2-(-1)}[/tex] = [tex]\frac{-4}{-2+1}[/tex] = [tex]\frac{-4}{-1}[/tex] = 4
the line crosses the y- axis at (0, 4 ) ⇒ c = 4
y = 4x + 4 ← equation of line
Okay im learning algebra right now and this question hit my head
here, its asked which expression was equivalent to this 2v+6v+3c.
here are the answer 2v + 9c 8v + 3c 11vc 11+ v+ c
Answers
Answer:
8v+3c
Step-by-step explanation:
2v+6v+3c
2v and 6v have similar figures so you can add them together
so it becomes 8v+3c
c and v have nothing in common so you cannot simplify them more
If sec A = 15/7 and A + B = 90°, find the value of cosec B
Answers
The value of cosec B if A and B are complementary is 15/7
What are complementary angles?Two angles are called complementary when their measures add to 90 degrees. Since A+B = 90°, then A and B are complementary. Examples of complementary angles are 45 and 45, 30 and 60, 20 and 70 e.t.c
If sec A is 15/7
sec A= 1/cos A
therefore cos A = 7/15
if cos A = 7/15 , then from law of complementary angles
cos A = sin (90-A)
and 90-A = B
therefore cos A = sinB
if cos A = 7/15, then;
sin B = 7/15
then sinB = 1/cosec B
cosec B = 15/7
therefore the value of cosec B = 15/7
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What is the interest earned in a savings account for 12 months on a balance of $4000 of the interest rate is 1.5% APR compounded earlier
Answers
answer: 60.00
Based on the given conditions, formulate:: 4000x
((1.5%+1)12/12-1)
Evaluate the equation/expression:: 60
Round 60 to the required place rounding: 60.00
Aiden has $15.00 on his copy card. Each time he uses the card to make a photocopy, $0.06 is deducted from his card. Aiden wants to be sure that there will be at least $5.00 left on his card when he is finished. The inequality below relates x, the number of copies he can make, with his copy card balance. What is the maximum number of copies Aiden can make
Answers
Aiden can make up to 166 copies before his copy card balance reaches below $5.00 as each copy total costs $0.06.
1. 15.00 - 0.06x ≥ 5.00
2. Add 0.06x to both sides: 15.00 ≥ 0.06x + 5.00
3. Subtract 5.00 from both sides: 10.00 ≥ 0.06x
4. Divide both sides by 0.06: 166.67 ≥ x
5. Therefore, x ≤ 166.67, so Aiden can make a maximum of 166 copies.
Aiden's copy card balance is $15.00, and each copy he makes costs $0.06. To ensure that his card balance does not go below $5.00, he needs to calculate the max number of copies he can make. To do this, we set up an inequality, 15.00 - 0.06x ≥ 5.00, and solved it to get x ≤ 166.67, meaning Aiden can make a maximum of 166 copies.
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Please assist asap, it’s a 6 point question!
Answers
Answer: The equation of the perpendicular bisector of AB is 3x+7y-77=0
A line equation is an algebraic representation of a set of points that together form a line in a coordinate system. Multiple points that together form a line on the coordinate axis are represented as a set of x,y variables to form an algebraic equation called a one-line equation.
Equation of line⇒[tex](y-y1)=\frac{(y2-y1)}{(x2-x1)} (x-x1)[/tex]
Midpoint of line⇒[tex]\frac{(x1+x2)}{2}, \frac{(y1+y2)}{2}[/tex]
Step-by-step explanation:
Line CD⊥AB
Equation of AB⇒ [tex]\frac{y+10}{x-4} =\frac{15-1}{10-4} \\[/tex]
⇒ [tex]\frac{y+10}{x-4} =\frac{14}{6}[/tex]
⇒ [tex]\frac{y+10}{x-4} =\frac{7}{3}[/tex]
⇒ 3(y+10)=7(x-4)
⇒ 3y+30=7x-28
⇒ 7x-3y=30+28
⇒ 7x-3y=58
Midpoint of AB⇒ [tex]\frac{4+10}{2} , \frac{1+15}{2}[/tex]
⇒ [tex]\frac{14}{2}, \frac{16}{2}[/tex]
⇒ (7, 8)
Slope of CD⇒ [tex]\frac{-1}{slope of AB}[/tex]
Slope of AB⇒ [tex]\frac{-7}{-3}[/tex]
⇒ [tex]\frac{7}{3}[/tex]
Slope of CD⇒ [tex]\frac{-3}{7}[/tex]
Equation of CD⇒ [tex]y-8=\frac{-3}{7} (x-7)[/tex]
⇒ 7(y-8)=-3(x-7)
⇒ 7y-56=-3x+21
⇒ 3x+7y-56-21=0
⇒ 3x+7y-77=0
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What is the perpendicular slope to m=-2/3
Answers
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{ \cfrac{-2}{3}} ~\hfill \stackrel{reciprocal}{\cfrac{3}{-2}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{3}{-2} \implies {\Large \begin{array}{llll} \cfrac{3}{ 2 } \end{array}}}}[/tex]
Find the midpoint of the segment with the following endpoints?
(−1, 3) and (−9, −7)
Answers
Answer: To find the midpoint of a line segment, you can average the x-coordinates of the endpoints and average the y-coordinates of the endpoints.
The x-coordinates of the endpoints are -1 and -9, so the average of the x-coordinates is (-1 + (-9))/2 = -5
The y-coordinates of the endpoints are 3 and -7, so the average of the y-coordinates is (3 + (-7))/2 = -2
So the midpoint of the segment with endpoints (-1, 3) and (-9, -7) is (-5, -2)
Step-by-step explanation:
A line has the equation 2y + 3x – 4 = 0. Write the equation of a line parallel to the given line that has a y-intercept of 9.
Answers
Answer:
[tex]y=-\frac{3}{2}x+9[/tex]
Step-by-step explanation:
Parallel lines have the same slope, but different y-intercepts, so it helps to rewrite the equation in slope-intercept form:
[tex]2y+3x-4=0\\2y=-3x+4\\y=-\frac{3}{2}x+2[/tex]
Now, just simply change the y-intercept from 2 to 9 and you're done!
X by the power of 2 -36
Answers
The solutions of x²=-36 are 6i and -6i.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
X by the power of 2 is -36
This can be written as x²=-36
We need to find the value of x.
x²=-36
Take square root on both sides
x=√-36
x=√i²36
x=6i, -6i
Hence, the solutions of x²=-36 are 6i and -6i.
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