Answer:
cosФ = [tex]\frac{1}{\sqrt{65}}[/tex] , sinФ = [tex]-\frac{8}{\sqrt{65}}[/tex] , tanФ = -8, secФ = [tex]\sqrt{65}[/tex] , cscФ = [tex]-\frac{\sqrt{65}}{8}[/tex] , cotФ = [tex]-\frac{1}{8}[/tex]
Step-by-step explanation:
If a point (x, y) lies on the terminal side of angle Ф in standard position, then the six trigonometry functions are:
cosФ = [tex]\frac{x}{r}[/tex]sinФ = [tex]\frac{y}{r}[/tex]tanФ = [tex]\frac{y}{x}[/tex]secФ = [tex]\frac{r}{x}[/tex]cscФ = [tex]\frac{r}{y}[/tex]cotФ = [tex]\frac{x}{y}[/tex]Where r = [tex]\sqrt{x^{2}+y^{2} }[/tex] (the length of the terminal side from the origin to point (x, y)You should find the quadrant of (x, y) to adjust the sign of each function∵ Point (1, -8) lies on the terminal side of angle Ф in standard position
∵ x is positive and y is negative
→ That means the point lies on the 4th quadrant
∴ Angle Ф is on the 4th quadrant
∵ In the 4th quadrant cosФ and secФ only have positive values
∴ sinФ, secФ, tanФ, and cotФ have negative values
→ let us find r
∵ r = [tex]\sqrt{x^{2}+y^{2} }[/tex]
∵ x = 1 and y = -8
∴ r = [tex]\sqrt{x} \sqrt{(1)^{2}+(-8)^{2}}=\sqrt{1+64}=\sqrt{65}[/tex]
→ Use the rules above to find the six trigonometric functions of Ф
∵ cosФ = [tex]\frac{x}{r}[/tex]
∴ cosФ = [tex]\frac{1}{\sqrt{65}}[/tex]
∵ sinФ = [tex]\frac{y}{r}[/tex]
∴ sinФ = [tex]-\frac{8}{\sqrt{65}}[/tex]
∵ tanФ = [tex]\frac{y}{x}[/tex]
∴ tanФ = [tex]-\frac{8}{1}[/tex] = -8
∵ secФ = [tex]\frac{r}{x}[/tex]
∴ secФ = [tex]\frac{\sqrt{65}}{1}[/tex] = [tex]\sqrt{65}[/tex]
∵ cscФ = [tex]\frac{r}{y}[/tex]
∴ cscФ = [tex]-\frac{\sqrt{65}}{8}[/tex]
∵ cotФ = [tex]\frac{x}{y}[/tex]
∴ cotФ = [tex]-\frac{1}{8}[/tex]
-
y=2/3x + 2 and passes through the point (12, 6).
Find an equation perpendicular to the line
A. y=-3/2x + 21
B. y=-3/2x +24
C. y= 2/3x + 14
D. y= 2/3x + 8
Answer:
B. y = -3/2x + 24
Step-by-step explanation:
The perpendicular slope is -3/2x to find the y-intercept use the point given
Plug in
6 = -3/2(12) + b (b = y-intercept)
6 = -18 + b (add 18 on both sides)
24 = b (so)
y = -3/2x + 24
Carrie has $500 in her bank account. She plans to add $245 a week to her account. Jose has $710 in his bank account. He plans to add $230 a week. How many weeks will it take untill carrie & jose have an equal ammount of money saved up is neither of them spent any of their savings?
Answer:
14 weeks
Step-by-step explanation:
14 times 245= 3430+ 500=3930 (carrie)
14 times 230= 3220+ 710= 3930 (jose)
Two sides of a triangle are equal in length. The length of the third side exceeds the length of one of the other sides by 3 centimetres. The perimeter of the triangle is 93 centimetres. Find the length of each side of the triangle
Answer:
it must be 30, 30, 33
Step-by-step explanation:
first, divide 93 by 3, since a triangle has 3 sides, you would get 31, yet if you took away that three in 93, it'd be 30. For that one that exceeds the others by 3, add the three to one of the thirds, and the other two are just the same, so when it said, "exceeds the length of one of the other sides," It didn't really change anything, because the other side is just as long.
−20=−4x−6x Find the value of x
Answer:
[tex]\huge\boxed{x=2}[/tex]
Step-by-step explanation:
[tex]-20=-4x-6x\qquad|\text{combine like terms}\\\\-20=-10x\qquad|\text{divide both sides by (-10)}\\\\\dfrac{-20}{-10}=\dfrac{-10x}{-10}\\\\2=x\to x=2[/tex]
A Norman window has the shape of a rectangle surmounted by a semicircle. If the perimeter of the window is 8 ft, find the value of x so that the greatest possible amount of light is admitted.
Answer: x = 2
If x is the width of the window, the value for x that results in the greatest area-- presumably admitting the greatest amount of light.
Step-by-step explanation:
Initial calculations to find a starting value for w.
Determine dimensions that will have a sum of 8 as the perimeter. The length of the arc plus three sides of the rectangle.
The length of the arc is half the circumference of the circle, the width is the diameter. So, modifying the equation: C= πd, a = πw/2
Three sides of a rectangle (presumably a square for the initial calculation) 3w
Initial equation: 3w + πw/2 = 8 Substitute 3.14 for π and solve for w
2(3w) + 2(3.14w/2) = 2(8) multiply all terms by 2 to eliminate denominator
6w + 3.14w = 16 combine like terms
9.14w = 16 divide both sides by 9.14
w ≈ 1.75
Calculate the area using this value:
Area of semicircle: πr²/2 r= 1.75/2
3.14(.875)²/2 ≈ 1.203
Area of rectangle 1.75 × 1.75 = 3.0625
Total Area with width 1.75 : 4.265 ft²
Increasing the width to 2
The length of the arc becomes 3.14 This is twice the area of the semicircle.
3.14/2 = 1.57
The height of the rectangle reduces to 1.43
1.43 × 2 = 2.86
Total area with width of 2 ft 2.86 + 1.57 = 4.43 ft²
So 2 ft seems to be the optimal width.
Walt multiples 25 times 16 using partial products what did walt do wrong
Answer:
first what the full question and if 25*16/2=200
Step-by-step explanation:
Help me find the slope of this problem ??
The formula to put in E176 that will give me the sum of all the units sold by the indicated sales rep and product is:
Question attached
Answer :
There is no such formular
Explanation:
there is no such Formula I'm the options given. However the total product units sold by the sales representative for the period can be calculated in the excel sheet by adding up the cells with the units sold(cells F179,F180... to F186) and inserting the formula in the cell under total units sold by sales representative. So any change of figures in the cells added would reflect in the total units cell E176, if there is an additional figure for units sold in another cell, we could add this cell to formula in E176
Solve for x.
x-4/5= -1/3
Answer:
x = 1 2/15
Step-by-step explanation:
What are the scale factor of ABC dilated to XYZ plz help
====================================
Explanation:
The order is important for ABC and XYZ so we can see what letters pair up.
A pairs with X since they are the first lettersB pairs with Y since they are the second lettersC pairs with Z since they are the third lettersBased on that, we can see that AB pairs with XY as they are the first two letters of ABC and XYZ respectively.
Divide the length XY over AB and reduce
XY/AB = 10/15 = 2/3
We could also divide XZ over AC
XZ/AC = 14/21 = 2/3
and we get the same ratio
Write the equation of a line with slope 2 and y-intercept −1.
Answer:
y =
Answer: y = 2x - 1
Step-by-step explanation: The form of the equation of a line is y = mx + b, where m is the slope and b is the y-intercept. Just plug in the values, and you have your answer!
8. Fay Teng's expenditures for the past 3 months were: August,
$1,735.50; September, $1,829.42; and October, $1,793.88.
What is her average monthly expenditure?
9. You use the utility company's budget plan for paying your
home heating bills. You pay $75 a month for 9 months. Your
actual bills are: September, $28.95; October, $16.15; November,
$68.46; December, $109.34; January, $115.26; February. $94.19;
March $75.66; April, $51.97; and May, $49.16. Compute the
average for the 9 months.
ght The McGraw-e Companies, Inc. All rights
=$75.66 all in all and $67.99 dollars
4.8(x-1.75)= -9.6 but without the distributive property
HELP! Will be giving branliest!!!!!!
A is the right anwer to your Question because of the Hours and weeks
____ is 22 more than 88
Answer:
110
Step-by-step explanation:
88+22=110
Claire wants to determine how her math score 690 on a standardized college entrance exam compared to her mother score 680 what she took the exam 20 years earlier the year Clair took the exam the mean math score was 510 with a standard deviation of 110 points on Claires mother took the exam the mean math score was 490 with a standard deviation of 100 points who has the better relative performance
Answer:
Claires mother did better because her z score was greater than Claires
Step-by-step explanation:
I j took the quiz
Claire's mother did better because her z-score was greater than that of Claires.
What is Z -score?A Z-score is defined as the fractional representation of data point to the mean using standard deviations.
As per the given information, the solution would be as
Here is Claire's data:
ц₁ = 510
σ₁ = 110
X₁ = 690
⇒ z-score = (X₁-ц₁ )/σ₁
Substitute the values,
⇒ z-score = (690 - 510)/110
⇒ z-score = 180/110
⇒ z-score = 1.636
Here is Claire's mother's data:
ц = 490
σ₂ = 100
X₂ = 680
⇒ z-score = (X₂-ц )/σ₂
Substitute the values,
⇒ z-score = (680 - 490)/100
⇒ z-score = 190/100
⇒ z-score = 1.9
So Claire's mother's z-score > Claire's z-score
Therefore, Claire's mother did better because her z-score was greater than that of Claires.
Learn more about the z-score here:
brainly.com/question/13793746
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Susan's grandpa was fibbing again: "your grandma and I, together, we are over 150
The students can make 6 tickets from each sheet of paper. How many sheets of paper. How many sheets of paper are needed for 125 tickets?
Answer:
21 sheets of paper
Step-by-step explanation:
If its basically 6 tickets to a piece of paper then you just divide 125 tickets by 6 and get 20.833.... Then your round to the nearest sheet which is 21.
Hope this helps!
Answer:
Approx. 21 sheets of paper
Step-by-step explanation:
1 sheet of paper is used to make 6 tickets
6 tickets = 1 sheet
If 1 sheet is used to make 6 tickets. The number of sheets used to make 125 tickets will more.
if
6 tickets = 1 sheet
125 tickets = (125÷6) × 1
= 20.83333333333
what is -1(9)
Ignore theses it said it was too short
why is 1+1 = 2 and not 8? Why did someone came up with 2? How do you approach 2 from 1+1? Who even invented numbers? Why is math a thing? Why are we conditioned to know that 1+1 =2?
Let x be a continuous random variable that is normally distributed with a mean of 25 and a standard deviation of 6. Find the probability that x assumes a value between 29.0 and 55.0. Use Table IV in Appendix C to compute the probabilities. Round your answer to four decimal places.
Answer:
i think it is between 22 and 35
Step-by-step explanation:
MATH what is 9x1 9x2 9x3 9x4 9x5 9x6 9x7 9x8 9x9 9x10
EASY MATH 10 POINT
Answer:
9
18
27
36
45
54
63
72
81
90
Step-by-step explanation:
I just take the last numer of the times 9 and subtract 1 and put whatever equals 9.
example 9x7=63
7-1=6+3 so 63
Sorry if it does not make sense
What is the measure of ZRIA?
R
PA
N
999
.
A. 55
B. 30°
O C. 95°
D. 60°
The measure of angle RIA is 55 degrees, option A is correct.
What is Coordinate Geometry?A coordinate geometry is a branch of geometry where the position of the points on the plane is defined with the help of an ordered pair of numbers also known as coordinates.
We have to find the measure of angle RIA
The opposite angle of RIA is LIK
Let us find the measure of LIK
∠FIL+∠LIK+∠KIN=180
30+∠LIK+95=180
∠LIK + 125 =180
Subtract 125 from both sides
∠LIK = 180 - 125
=55 degrees
∠LIK is equal to ∠RIA
∠RIA = 55 degrees
Hence, the measure of angle RIA is 55 degrees, option A is correct.
To learn more on Coordinate Geometry click:
brainly.com/question/27326241
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Which is true when you rent?
ОА.
You build equity in your house.
ОВ.
You are responsible for any repairs.
Ос.
You pay fewer up-front costs.
You are responsible for any repairs.
f(x) = x + 7, g(x) = x - 7
(a) (f + g)(x) =
(b) (f-g)(x)=
(c) (fg)(x)=
(d) (f/g)(x)=
a) 2x
b) 14
c) x^2 -49
d) -1
- 8n - 8 = -72
I don’t know how to do this
Answer:
n=8
Step-by-step explanation:
Add 8 to both sides of the equals sign, then bring down -8n, add -72+8, You'll get -64, lastly you divide -64 and -8, and you'll get your answer
what is 78756567.998 divided by 76454
Answer:
1,030.11703766971
Step-by-step explanation:
Just use a calculator (windows + r and then type calc if your on windows or search up calculator)
can anyone help me
Answer:
A
Step-by-step explanation:
I need to find the missing angle for this triangle
Answer:
44 degrees
Step-by-step explanation:
Because a right angle triangle if added all angles will=to 180 degrees
so 46+90=136
180-136=44
Answer:
44
Step-by-step explanation:
You add 46 to the 90 degree angle (right angle) and get 136. Then, because the angles of a triangle add up to 180 degrees all the time, you would do 180-136 and get 44.
30=Five-sixthsY solve for Y
Given :-
A linear Question is given to us .The equⁿ is [tex]\sf 30 = \dfrac{5}{6}y[/tex]To Find :-
The value of y .Solution:-
Taking the given equⁿ :
[tex]\bf \implies30=\dfrac{5}{6}y[/tex]
[tex]\bf \implies 30\times 6=5y[/tex]
[tex]\bf\implies y=\dfrac{\cancel{30}\times6}{\cancel5}[/tex]
[tex]\underline{\boxed{\red{\bf{\longmapsto \qquad y \qquad = \qquad 36 \qquad}}}}[/tex]
[tex]\boxed{\green{\bf\pink{\dag}\: Hence\:the\:value\:of\:y\:is\:36.}}[/tex]
Some rules :-
On transposing numbers or variables,
Plus changes to minus.Minus changes to plus .Multiply changes to divide.Divide changes to multiply.