Answer:
[tex]\cos(A + B) = \frac{23}{265}[/tex]
Step-by-step explanation:
Given
[tex]\tan A=\frac{28}{45}[/tex]
[tex]\cos B=\frac{3}{5}[/tex]
Required
[tex]\cos(A+B)[/tex]
In trigonometry:
[tex]\cos(A+B) = \cos\ A\ cosB - sinA\ sinB[/tex]
We need to solve for cosA, sinA and sinB
Given that:
[tex]\tan A=\frac{28}{45}[/tex] and the tangent of an angle is a ratio of the opposite side (x) to the adjacent side (y),
So, we have:
[tex]x =28[/tex] and [tex]y = 45[/tex]
For this angle A, we need t calculate its hypotenuse (z).
Using Pythagoras,
[tex]z^2 = x^2 + y^2[/tex]
[tex]z = \sqrt{x^2 + y^2[/tex]
[tex]z = \sqrt{28^2 + 45^2[/tex]
[tex]z = \sqrt{2809[/tex]
[tex]z = 53[/tex]
From here, we can calculate sin and cos A
[tex]\sin A= \frac{opposite}{hypotenuse}[/tex] and [tex]\cos A= \frac{adjacent}{hypotenuse}[/tex]
[tex]\sin A= \frac{x}{z}[/tex]
[tex]\sin A= \frac{28}{53}[/tex]
[tex]\cos A= \frac{y}{z}[/tex]
[tex]\cos A= \frac{45}{53}[/tex]
To angle B.
Give that
[tex]\cos B=\frac{3}{5}[/tex] and the cosine of an angle is a ratio of the adjacent side (a) to the hypotenuse side (c),
So, we have:
[tex]a = 3[/tex] and [tex]b = 5[/tex]
For this angle B, we need to calculate its opposite (b).
Using Pythagoras,
[tex]c^2 = a^2 + b^2[/tex]
[tex]5^2 = 3^2 + b^2[/tex]
[tex]25 = 9 + b^2[/tex]
Collect like terms
[tex]b^2 = 25 - 9[/tex]
[tex]b^2 = 16[/tex]
[tex]b = \sqrt{16[/tex]
[tex]b = 4[/tex]
From here, we can calculate sin B
[tex]\sin B= \frac{opposite}{hypotenuse}[/tex]
[tex]\sin B = \frac{b}{c}[/tex]
[tex]\sin B = \frac{4}{5}[/tex]
Recall that:
[tex]\cos(A+B) = \cos\ A\ cosB - sinA\ sinB[/tex]
and
[tex]\cos B=\frac{3}{5}[/tex] [tex]\sin B = \frac{4}{5}[/tex] [tex]\sin A= \frac{28}{53}[/tex] [tex]\cos A= \frac{45}{53}[/tex]
[tex]\cos(A + B) = \frac{45}{53} * \frac{3}{5} - \frac{28}{53} * \frac{4}{5}[/tex]
[tex]\cos(A + B) = \frac{135}{265} - \frac{112}{265}[/tex]
[tex]\cos(A + B) = \frac{135-112}{265}[/tex]
[tex]\cos(A + B) = \frac{23}{265}[/tex]
The value of [tex]\cos (A+B)[/tex] is [tex]-\frac{96}{265}[/tex].
Trigonometrically speaking, the sine, cosine and tangent of an angle are described by the following formulas:
[tex]\sin \theta = \frac{y}{\sqrt{x^{2}+y^{2}}}[/tex] (1)
[tex]\cos \theta = \frac{x}{\sqrt{x^{2}+y^{2}}}[/tex] (2)
[tex]\tan \theta = \frac{y}{x}[/tex] (3)
Where:
[tex]\theta[/tex] - Angle, in sexagesimal degrees.[tex]x[/tex] - Adjacent leg.[tex]y[/tex] - Opposite leg.And we have the following trigonometric identity for the cosine of the sum of angles:
[tex]\cos (A+B) = \cos A\cdot \cos B - \sin A \cdot \sin B[/tex] (4)
By (1) and (2), we rewrite (4):
[tex]\cos (A+B) = \frac{x_{A}\cdot x_{B}}{\sqrt{x_{A}^{2}+y_{A}^{2}}\cdot \sqrt{x_{B}^{2}+y_{B}^{2}}} - \frac{y_{A}\cdot y_{B}}{\sqrt{x_{A}^{2}+y_{A}^{2}}\cdot \sqrt{x_{B}^{2}+y_{B}^{2}}}[/tex]
If we know that [tex]x_{A} = 28[/tex], [tex]y_{A} = 45[/tex], [tex]x_{B} = 3[/tex] and [tex]y_{B} = 4[/tex], then the cosine for the sum of angles is:
[tex]\cos (A+B) = \frac{28\cdot 3}{\sqrt{28^{2}+45^{2}}\cdot \sqrt{3^{2}+4^{2}}}-\frac{45\cdot 4}{\sqrt{28^{2}+45^{2}}\cdot \sqrt{3^{2}+4^{2}}}[/tex]
[tex]\cos (A+B) = -\frac{96}{265}[/tex]
The value of [tex]\cos (A+B)[/tex] is [tex]-\frac{96}{265}[/tex].
We kindly invite to check this question on trigonometric identities: https://brainly.com/question/24836845
I need help please help yo
Answer:
28/35
Step-by-step explanation:
Soh-Cah-Toa
Sin = Opposite/Hypotenuse
Cos = Adjacent/Hypotenuse
Tan = Opposite/Adjacent
Leah would like to earn at least $120 per month. She babysits for $5 per hour and works at an ice cream shop for $8 per hour. Leah cannot work more than a total of 20 hours per month. Let x represent the number of hours Leah babysits and let y represent the number of hours Leah works at the ice cream shop. How did you determine the pair(s) (x, y) that Leah could work to meet the given conditions in item 15?
Answer:
Babysitting= 13.3 hours
Icecream shop= 6.6 hours
Step-by-step explanation:
Step one:
let the hours for babysitting be x
and the hours for icecream shop be y
we are told that Leah would like to earn $120 monthly
She babysits for $5 per hour and
works at an ice cream shop for $8 per hour
5x+8y=120---------------1
Leah cannot work more than a total of 20 hours per month
x+y≤20-------------2
The system of equation for the situation is
5x+8y=120
x+y≤20
x=20-y
put x=20-y in eqn 1
5(20-y)+8y=120
100-5y+8y=120
3y=120-100
3y=20
y=20/3
y=6.6 hours
put y=6.6 in eqn 2
x+6.6≤20
x≤20-6.6
x=13.3hours
sqrt((1, 476 + 274(341 - 48))/2)
Write the sentence as an inequality.
A number (x) plus 10 is less than 34.
Answer:
X + 10 < 34
Step-by-step explanation:
X is the variable and variable represent a number in equations. Then this < is considered to be the less than symbol. The rest should be easy when you get the understanding.
The newspaper in Haventown had a circulation of 80,000 papers in the year 2000. In 2010, the circulation was 50,000. With x=0 representing the year 2000, the graph below models this scenario. What number will complete the point-slope equation that models this scenario?
y−50,000=[_______](x−10)
Answer:
Step-by-step explanation:
sup
can you guys help me please the things are
A
B
or C
Answer:
I don't really know about this sorry sorry
Answer:
✨ B
Step-by-step explanation:
✨Hope this helps✨
A toy maker wants to re-create the Wright Brothers 1903 airplane. The actual plane was 21 feet long. The toy maker wants to use a scale model of 3 feet = 2 inches. How long will the replica plane be?
Answer:
[tex]x = 14ft[/tex]
Step-by-step explanation:
Given
[tex]Actual\ Length = 21ft[/tex]
Model:
[tex]3\ ft = 2\ in[/tex]
Required
Determine the length of the replica
Represent the model as a ratio:
[tex]Ratio = 3\ in:2\ ft[/tex]
Convert to fraction
[tex]Ratio = \frac{3\ in}{2\ ft}[/tex]
Represent the actual lengths as a ratio
[tex]Ratio = 21\ ft : x[/tex]
Where x is the length of the replica
Convert to fraction
[tex]Ratio = \frac{21\ in}{x}[/tex]
Equate both ratios (because they are in proportion)
[tex]\frac{3\ in}{2\ ft} = \frac{21\ in}{x}[/tex]
[tex]\frac{3}{2\ ft} = \frac{21}{x}[/tex]
Cross Multiply:
[tex]3 * x = 21 * 2\ ft[/tex]
[tex]3x = 42\ ft[/tex]
Solve for x
[tex]x = \frac{42ft}{3}[/tex]
[tex]x = 14ft[/tex]
Hence, the length of the replica is 14ft
HI my name is summer im a F my email is summerander12 is yall what to ch at you dont have to i really dont care
Answer:
yes
Step-by-step explanation:
ok thus is a help for help tho
Help me please and thank you! try your best i will mark brainlist who is first and accurate.
Answer:
the first
Step-by-step explanation:
if it's perpendicular so is the gradient so y= -5/6 + 12
*I'm so sorry if I'm wrong
A) Find the distance of line segment PR. Round answer to the nearest tenth. B) Find the distance around the park (perimeter).
Answer:
A. [tex] PR = 80.6 yd [/tex]
B. Perimeter = 190.6 yd
Step-by-step explanation:
A. Distance between P(10, 50) and R(80, 10):
[tex] PR = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]
[tex] PR = \sqrt{(80 - 10)^2 + (10 - 50)^2} [/tex]
[tex] PR = \sqrt{(70)^2 + (-40)^2} [/tex]
[tex] PR = \sqrt{4,900 + 1,600} [/tex]
[tex] PR = \sqrt{6,500} [/tex]
[tex] PR = 80.6 yd [/tex] (nearest tenth)
B. Distance around the park = Perimeter = PR + PQ + QR
PR = 80.6 yd
PQ = |50 - 10| = 40 yd
QR = |80 - 10| = 70 yd
Perimeter = 80.6 + 40 + 70
Perimeter = 190.6 yd
Mark sold 218 tickets for the school play and made $1,363. Adult tickets are $8 and
student tickets are $5. How many adult tickets did Mark sell?
Answer: 91
Step-by-step explanation:
Let adults tickets be a
Let students ticket be b.
The information in the question can be presented as an equation as:
a + b = 218 .......... i
8a + 5b = 1363 ......... ii
Multiply equation i by 5
Multiply equation ii by 1
5a + 5b = 1090 ........ iii
8a + 5b = 1363 ....... iv
Subtract iii from iv
3a= 273
a = 273/3
a = 91
Number of adult's ticket sold = 91
2 angles whose non shared sides are opposite rays are defined as
Using mixed numbers, write a problem in which an estimate is enough to solve the problem.
explain:
Estimating Differences of Fractions and Mixed Numbers
Estimating Differences of Fractions and Mixed NumbersRecall that estimation is a method for finding an approximate solution to a problem. Even when you are asked to find an exact ko, estimation is a useful way to get an idea of a reasonable solution to a problem. Once you have found an exact answer, you can check your answer against the estimate.
, estimation is a useful way to get an idea of a reasonable solution to a problem. Once you have found an exact answer, you can check your answer against the estimate.When working with fractions and mixed numbers, you can use the fraction benchmarks of 0,
, estimation is a useful way to get an idea of a reasonable solution to a problem. Once you have found an exact answer, you can check your answer against the estimate.When working with fractions and mixed numbers, you can use the fraction benchmarks of 0, 12
, estimation is a useful way to get an idea of a reasonable solution to a problem. Once you have found an exact answer, you can check your answer against the estimate.When working with fractions and mixed numbers, you can use the fraction benchmarks of 0, 12, and 1 to help you to estimate differences.
, estimation is a useful way to get an idea of a reasonable solution to a problem. Once you have found an exact answer, you can check your answer against the estimate.When working with fractions and mixed numbers, you can use the fraction benchmarks of 0, 12, and 1 to help you to estimate differences.Here are the steps for estimating the differences of fractions and mixed numbers using benchmarks.
Solve-1 + 8 =
10 - 3a.
Answer:
a = 1
Step-by-step explanation:
Original Equation:
-1 + 8 = 10 - 3a
Add 1 to both sides
8 = 11 - 3a
Subtract 11 from both sides
-3 = -3a
Divide both sides by -3
a = 1
Hope this helps :)
Please consider Brainliest :)
Answer:
a = 1
Step-by-step explanation:
-1 + 8 = 10 - 3a
7 = 10 - 3a
-10 -10
-3 = -3a
---- -----
-3 -3
1 = a
The price of the radio was $14. The sales tax was 3.5%.
What was the total cost of the radio, including the sales
tax?
Answer:
14.49
Step-by-step explanation:
14 * 0.035 = 0.49
14 + 0.49 = 14.49
Baylee received a 36% on her puppy test. How many tricks did she get right if there were a total of 25 questions?
Help Geometry help pleasseeee??
formula
perimeter:c²=a2+b2
area:A=length x width
A cyclist estimates that he will bike 80 miles this week. He actually bikes 75.5 miles. What is the percent error of the cyclist's estimate? Round the percent to the nearest hundredth if necessary.
Answer:
The percent error of the cyclist's estimate is 5.63%
Step-by-step explanation:
Percentages
The cyclist estimates he will bike 80 miles this week, but he really bikes 75.5 miles.
The error of his estimate in miles can be calculated as the difference between his estimate and the real outcome:
Error = 80 miles - 75.5 miles = 4.5 miles
To calculate the error as a percent, we divide that quantity by the original estimate and multiply by 100%:
Error% = 4.5 / 80 * 100 = 5.625%
Rounding to the nearest hundredth:
The percent error of the cyclist's estimate is 5.63%
A ladder is 8 meters long. It leans against a wall with one end on the ground, 6 meters from the wall. The other end reaches a windowsill. Calculate the height of the window sill above the ground.
Answer:
[tex]\sqrt{28[/tex]
Step-by-step explanation:
a^2 + b^2 = c^2.
if you draw out the triangle, you can substitute numbers into an equation.
6^2 + b^2 = 8^2
36 + b^2 = 64
b^2 = 64 - 36
b^2 = 28
b = [tex]\sqrt{28}[/tex]
can someone tell me how to do this????
Question: Reflective symmetry over y = (3/5)x ?
Answer: No
-------
Question: Reflective symmetry over y = (5/3)x ?
Answer: No
================================================
Explanation:
For any parallelogram that's a square, we'll have four lines of symmetry: The two diagonals and two extra lines of symmetry for the opposite pairs of sides.
In this case, we don't have a square (we can prove this by finding the lengths of each side of the parallelogram), so we move on.
--------------
If the parallelogram is a rectangle, then we'll have two lines of symmetry: one for each pair of opposite sides.
However, we don't have a rectangle either. We can prove this by finding the slopes of the blue lines of the parallelogram, and finding they are not perpendicular slopes.
So we move on.
---------------
The last case is a parallelogram that isn't a rectangle. So it's not a square either. That's what we have here. For parallelograms of this nature, there are no lines of symmetry. We cannot fold it along any line to have it match up with itself.
So that's why the answer is "no" to both of these questions.
Answer:
No and No.
Step-by-step explanation:
Miles has 10 red marbles, 3 blue marbles and 5 green marbles. He randomly chooses a marble out of a bag 150 times. Make a prediction of how many times Miles will pull a green marble
A Close to but not exactly 30
B Close to but not exactly 300
C Close to but not exactly 90
D Close to but not exactly 45
Answer:
D
Step-by-step explanation:
Name the set of numbers that √7 belongs.
Answer:
Thats A radical number
Step-by-step explanation:
Since its. Sqare root with a never ending decimal (not perfect)
Help! Solve for r.
12=r-(34-2)
Write two hundred thousand and fifty seven in figures
In which group on the Periodic Table does the atom pictured belong?
A)
4
B)
6
16
D
14
Find the slope and the y-intercept of the graph of y=−45x−2.
Answer:
Slope: -45
Y-intercept: -2
Step-by-step explanation:
The expression is written in slope-intercept form or y=mx+b.
mx is the slope and b is the slope intercept
A rectangle has a length of x inches and a width 2 inches less than the length. If the dimensions were doubled, what would be the area, in square inches , of the new rectangle in terms of x
Answer:
Option (4)
Step-by-step explanation:
Area of a rectangle = Length × width
If the dimensions of the given rectangle is doubled,
Area of the new rectangle = 2(Length) × 2(width)
= 4(Length × width)
= 4(x)(x - 2)
= 4[x² - 2x]
= 4x² - 8x
Therefore, Option (4) will be the correct option.
Find the distance between the pair of points (2,-5) and (3,-7).
Answer:
2.24Step-by-step explanation:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\(2,-5)\quad\implies\quad x_1=2\,,\ \ y_1=-5\\\\(3,-7)\quad\implies\quad x_2=3\,,\ \ y_2=-7\\\\d=\sqrt{(3-2)^2+(-7+5)^2}= \sqrt{1^2+(-2)^2}=\sqrt{1+4}=\sqrt5=2.236....\approx2.24[/tex]
About 5% of the population has a particular genetic mutation. 400 people are randomly selected. Find the standard deviation for the number of people with the genetic mutation in groups of 400.
Answer:
20
Step-by-step explanation:
(5/100) * (400/1)
cancel the zeros
4 * 5= 20
I alway get this wrong idk how pls help
Answer:
C
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
the total earned is d
you earn $4 after each hour (x), so you multiply
xoxo, your highness...