Answer: [tex]\cos(\theta) = \frac{8\sqrt{113}}{113}\\\\[/tex]
=================================================
Work Shown:
x^2+y^2 = r^2
(8)^2+(-7)^2 = r^2
113 = r^2
r = sqrt(113)
The distance from (0,0) to (8,-7) is exactly sqrt(113) units.
This is the exact length of the hypotenuse of the right triangle.
Next, we do the following steps:
[tex]\cos(\text{angle}) = \frac{\text{adjacent}}{\text{hypotenuse}}\\\\\cos(\theta) = \frac{x}{r}\\\\\cos(\theta) = \frac{8}{\sqrt{113}}\\\\\cos(\theta) = \frac{8\sqrt{113}}{\sqrt{113}*\sqrt{113}}\\\\\cos(\theta) = \frac{8\sqrt{113}}{\sqrt{113*113}}\\\\\cos(\theta) = \frac{8\sqrt{113}}{\sqrt{113^2}}\\\\\cos(\theta) = \frac{8\sqrt{113}}{113}\\\\[/tex]
Side note: cosine is positive in quadrant Q4.
A corollary needs which of the following geometric terms to be proven true?
A. Theorem
B. Identity
C. Common notion
D. Inverse
Answer:
B. Identity
Step-by-step explanation:
can anyone help for me in this questions
Answer:
Step-by-step explanation:
Note : any number or variable with it's power 0 is considered as one.
Last one is the solution to find the two ration numbers between 2/5 and 3/4 (question which u asked just before this question).
Select the correct answer.
What is the domain of y= tan x?
Answer:
π/2 + n*π
Step-by-step explanation:
All real numbers except π/2 + n*π
Answer:
Step-by-step explanation:
For some problems, stating the domain actually means to identify what x CANNOT be as opposed to what x IS. This occurs with tangent and cotangent functions along with rational functions.
As far as the tangent function goes, look at your unit circle. Your unit circle gives you 2 values for each angle, the first value reflects the cosine of the angle and the second value reflects the sine of the angle. This is because cosine is directly related to the x values and sine is directly related to the y values; cos goes into the "x" position and sin goes into the "y" position inside the brackets just like x and y go into parenthesis for coordinates. Anyway, a ratio is undefined if the denominator equals 0, right? And since tangent is the same as sin/cos, tangent is undefined when cos is 0. This occurs at [tex]\frac{\pi}{2}+k\pi[/tex] . That means that tangent does NOT exist at pi over 2 and every integer of pi you add in after. Let's look at a couple of examples of how that domain "works". Adding in an integer means adding in 1, 2, 3, etc. If the domain of tangent is undefined at [tex]\frac{\pi}{2}+k\pi[/tex], then let's let k = 1, and
[tex]\frac{\pi}{2}+1\pi=\frac{\pi}{2}+\frac{2\pi}{2}=\frac{3\pi}{2}[/tex] . Now let k = 2:
[tex]\frac{\pi}{2}+2\pi=\frac{\pi}{2}+\frac{4\pi}{2}=\frac{5\pi}{2}[/tex]. Now let k = 3:
[tex]\frac{\pi}{2}+ 3\pi=\frac{\pi}{2}+\frac{6\pi}{2}=\frac{7\pi}{2}[/tex]. And it continues like that.
You can see when you graph the tangent function in radian mode on your calculator that these values where tangent is undefined show up as asymptotes. Use your unit circle and your graphs to determine the domain of trig functions.
The sides of a square field are 24 meters. A sprinkler in the center of the field sprays a circular area with a diameter that corresponds to a side of the field. How much of the field is not reached by the sprinkler? Round your answer to the nearest hundredth. Use 3.14 for π.
Answer:
A
Step-by-step explanation:
i took the test
The two triangles illustrated below are similar. What are the values of x and y?
Answer:
[tex]{ \bf{by \: relations : }} \\ { \tt{ \frac{28}{7} = \frac{x}{8} }} \\ \\ { \tt{x = \frac{28 \times 8}{7} }} \\ x = 32 \\ \\ { \tt{y = 83 \degree}}[/tex]
Một người gửi tiết kiệm tại ngân hàng một số tiền là 120 triệu đồng vào đầu mỗi năm theo thể thức lãi kép kỳ hạn một năm với lãi suất cố định 6,5%/ năm.
a) Hỏi sau 3 năm, số tiền gốc cộng lãi mà người đó nhận được là bao nhiêu ?
b) Hỏi sau bao nhiêu năm thì tổng số tiền nhận được lần đầu vượt quá 1,1 tỷ đồng.
Answer: lil t j
Step-by-step explanation:
I’m not a goat but I fit the description we walk around with then bands in my pocket
A researcher wants to calculate the average variability from the mean of the scores in their normally-distributed data set. For each participant, they calculate a deviation score. The researcher then sums all the deviation scores together and is surprised to find that the average deviation from the mean in the group is zero. Which of the statements below is FALSE about this scenario?
A. Deviation scores can be used to calculate sum of squares, variability, and then standard deviation.
B. Approximately the deviation scores will be positive and half will be negative.
C. Deviation scores are calculated by subtracting the participant score from the mean.
D. Average deviation from the mean in the group must be squared to be meaningful.
Answer:
D. Average deviation from the mean in the group must be squared to be meaningful.
Step-by-step explanation:
The average variability from mean is not calculated with mean square of the selected group. The deviation scores calculated by subtracting participant score from the mean.
Which of the following is most likely next in the series?
Answer:
B.
Step-by-step explanation:
Judging by the picture, it appears that you are correct. The pattern seems to go as follows:
1. Blue (with one line)
2. Red (with two lines)
3. Blue (with three lines)
This means that your final step should be red with four lines, and we can eliminate D as there is no sign that the line should branch off that way (based on the pattern that we already have). Hope this helps and please let me know if you still need help!
A volleyball team wins 105 games, which is 70% of the games played. How many games were played?
The total number of games played is
Answer:
70/100 = 105/X ---> 70X = 10,500 ---> X = 150 games played.
Step-by-step explanation:
i don't know what to do so can someone help me
Answer:
1. 8r+7
2. 8 ( r-t)
3. 2(3r+5t)
Step-by-step explanation:
See Image below:)
Solve the equation on the interval (0,2pi). Write your answer in exact simplest form.
[tex]cos6x-5sin3x+2=0[/tex]
9514 1404 393
Answer:
x ∈ {π/18, 5π/18, 13π/18, 17π/18, 25π/18, 29π/18}
Step-by-step explanation:
Using the trig identity ...
cos(2x) = 1 -2sin²(x)
we can rewrite the equation as ...
(1 -2sin²(3x)) -5sin(3x) +2 = 0
2sin²(3x) +5sin(3x) -3 = 0 . . . . . standard form
(sin(3x) +3)(2sin(3x) -1) = 0 . . . . factored form
There are no real values of x that will make the first factor zero. The second factor is zero when ...
sin(3x) = 1/2
3x = arcsin(1/2) +2nπ or (2n+1)π -arcsin(1/2)
x = 1/3(π/6 +2nπ) or 1/3((2n +1)π -π/6)
x = (12n+1)π/18 or (12n+5)π/18
x ∈ {π/18, 5π/18, 13π/18, 17π/18, 25π/18, 29π/18}
What is a demand schedule?
А.
a chart that shows the demand for a type of product at various prices
B.
a graph that shows the demand for a product at a single price point
C.
a chart that shows the demand for a product at various prices
Answer:
Answer is C
Step-by-step explanation:
In demand when the price goes up the quantity goes up and when the price goes down the quantity also goes down
In Supply when the price goes up the quantity goes down and when the price goes down the quantity goes up
Demand Schedule is a Chart
Demand Curve is a graph
Supply Schedule is a Chart
Supply Curve is a graph
Hope this helps
Step-by-step explanation:
[tex]hope \: it \: helps[/tex]
A metallurgist has one alloy containing 24% aluminum and another containing 60% aluminum. How many pounds of each alloy must he use to make 44 pounds of a third alloy containing 47% aluminum?
Answer:
15 8/9 pounds of 24%
28 1/9pounds of 60%
Step-by-step explanation:
x = pounds of 24%
44 - x = pounds of 60%
24x + 60(44 - x) = 47(44)
24x + 2640 - 60x = 2068
-36x + 2640 = 2068
-36x = -572
x = 15 8/9
44 - x = 28 1/9
Rounded
15 8/9 pounds of 24%
28 1/9pounds of 60%
HELP PLEASE!!! 5-6! Help!!!
Answer:
Step-by-step explanation:
5
x + y = 5 => x = 5 - y
y - 4 = - x
=> y - 4 = - ( 5 - y)
=> y - 4 = - 5 + y
=>4 = 5 , not true
So, no solution => system is inconsistent
6
option b
Explanation just as above.
3^4 +3 • 5= _. (Input whole numbers only.) Numerical Answers Expected! Please explain.
Answer:
96
Step-by-step explanation:
81+15=96
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\mathsf{3^4 +3 \times5}\\\\\\\mathsf{3^4}\\\mathsf{= 3\times3\times3\times3}\\\mathsf{=9\times9}\\\mathsf{= \bf 81}\\\\\\\mathsf{81+5\times3}\\\\\mathsf{3\times5=\bf 15}\\\\\\\\\mathsf{81+15}\\\mathsf{= \bf 96}\\\\\\\boxed{\boxed{\large\textsf{Answer: \huge \bf 96}}}\huge\checkmark[/tex]
[tex]\large\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
can someone answer this please
Answer:
ArcAB should be 182.
Step-by-step explanation:
You are not going to believe this, because the diagram is very misleading. AC is the same as the central angle. The central angle is twice m<ABC.
The central angle = 2*91 = 182
Simplify -4 + (-3) + 6.
Answer:3/6 in simplest fraction form is 1/2.
Step-by-step explanation:EASY and my chanel is FireFlameZero if u can check dat out
27. Find the length of the segment LK. (G.CO.C.10)
Show your work! (2pts)
J
1
3x
L
K
X + 6
Click to add speaker notes
Answer:
9
Step-by-step explanation:
the only thing we can say for sure is that JL is splitting the triangle and also its baseline IK in half.
so, both sides of the baseline must be equal :
3x = x + 6
2x = 6
x = 3
=> LK = x + 6 = 3 + 6 = 9
PLS HELP! The picture is down below
With a certain medical insurance policy, the customer must first pay an annual $250deductible, and then the policy covers 70% of the cost of x-rays. The first insurance claims for a specific year submitted by a person are for two x-rays. The first x-ray cost $700, and the second x-ray cost $950. How much, in total, will he need to pay for these x-rays?
I got $345, but it's wrong.
Answer:
$495 (745 if you include the $250 deductible)
Step-by-step explanation:
70% of 700 is 490
700 - 490 = 210
70% of 950 is 665
950 - 665 = 285
210 + 285 = $495
Answer:
495
Step-by-step explanation:
70% of 700= 490
700 - 490= 210
70% of 950= 665
950 - 665= 285
Add them together
210 + 285= 495
The reason you might have gotten 345 is because you subtracted 495 with 250 but 250 is how much he has to pay for the medical insurance, not how much he also get off
PLZZZZZZZZZZZZZZZZZZZZZ HELP MEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
Task #2 EZ Coasters
Emma and Zeke own an on-line business, EZ Coasters, that sells cork beverage coasters, which can be bought plain or with logos. The price for both types of coasters is $3.00 each. There is also a one-time set-up charge of $25 for coasters with a logo.
1) Write an equation describing the relationship between:
a) The number of plain coasters bought and the cost of the coasters.
b) The number of coasters with a logo bought and the price of the coasters.
c) Is either coaster relationship proportional? Explain in writing how you know.
d) Explain what the unit rate of the line described by each equation means in the context of the coasters.
2) EZ Sales also sells plain natural sandstone coasters for $4.00 each.
a) Write the equation describing this relationship.
b) Indicate whether or not it is a proportional relationship and explain why?
c) Will the graph of this equation ever intersect the graph of the equations for either of the other two EZ Coasters? Explain in typing how you made your decision.
Answer:
7
Step-by-step explanation:
I need help finding x please?
[tex]\large\mathfrak{{\pmb{\underline{\blue{To\:find}}{\blue{:}}}}}[/tex]
The value of [tex]x[/tex].
[tex]\large\mathfrak{{\pmb{\underline{\orange{Solution}}{\orange{:}}}}}[/tex]
[tex]\longrightarrow{\green{x\:=\: 25° }}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
We know that,
[tex]\sf\purple{Sum\:of\:angles\:on\:a\:straight\:line\:=\:180°}[/tex]
➪ 125° + [tex]x[/tex] + 30° = 180°
➪ [tex]x[/tex] + 155° = 180°
➪ [tex]x[/tex] = 180° - 155°
➪ [tex]x[/tex] = 25°
Therefore, the value of [tex]x[/tex] is 25°.
Now, the three angles of the triangle are 125°, 25° and 30°.
[tex]\large\mathfrak{{\pmb{\underline{\pink{To\:verify}}{\pink{:}}}}}[/tex]
✒ 125° + 25° + 30° = 180°
✒ 180° = 180°
✒ L. H. S. = R. H. S.
[tex]\boxed{Hence\:verified.}[/tex]
[tex]\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{ヅ}}}}}[/tex]
23.
Rewrite the equation of the circle (x + 2)2 + (y + 5)2 = 9 in general form.
A. x2 + y2 + 4x + 5y +20 = 0
B. x2 + y2 + 4x+10y+38 = 0
C. x2 + y2 +4x+10y+20 = 0
D. x2 + y2 +2x+10y+20= 0
Answer:
The answer is C .
Step-by-step explanation:
Here's your answer in image
Answer:
The answer is C
Step-by-step explanation:
Your Answer is in the above image
Find the product of −2+5i and its conjugate. The answer is a+bi where
Answer:
29
Step-by-step explanation:
The given complex number is -2+5i
We need to find the product of −2+5i and its conjugate.
The conjuagate of -2+5i is -2-5i
So, it will become,
[tex](-2+5i)(-2-5i)[/tex]
We know that,
[tex](a-b)(a+b)=a^2-b^2[/tex]
Here, a = -1 and b = 5i
[tex](-2+5i)(-2-5i)=(-2)^2-(5i)^2\\\\=4-25i^2\\\\=4-25(-1)\ \ (As\ i^2=-1)\\\\=4+25\\\\=29[/tex]
So, the values of a+bi is equal to 29.
A grande with a counter weight is shown in the figure. Find the horizontal distance between points A and D.
Step-by-step explanation:
the answer is in the above image
The girls in Lana’s troop set a goal to sell 1,000 boxes of cookies this year. There are 13 girls in the troop. At least how many boxes of cookies should each girl sell to reach their goal?
Answer:
76.92 boxes each or round up to 77
Step-by-step explanation:
1000 ÷ 13 = 76.92
Write a polynomial that represents the area of the above football field.
Answer:
36x² + 24x + 300 ft²
Step-by-step explanation:
→ Area of rectangle = Length × Width
→ Area of rectangle = (12x + 8) ft × (3x + 15) ft
→ Area of rectangle = 12x(3x + 15) + 8(3x + 15) ft²
→ Area of rectangle = 36x² + 180 + 24x + 120 ft²
→ Area of rectangle = 36x² + 24x + 300 ft²
Dennis collected a total of 1712 stamps over the past 16 years At this rate how many stamps would he collect in 21 years
2,247
Step-by-step explanation:
you take 1712 and divide that by 16 which is 107 and then you multiply 107 by 21 thus you get 2,247.
3 Connor is painting a superhero with this belt buckle shown. What is the area of the belt buckle in square Inches? 9 inches 2.5 inches 4 inches 5 inches 15 inches 2.5 mches The area in square Inches is:
HELP PLSSS
Answer:
87.5 square inches
Step-by-step explanation:
(For Diagram,Please Find in Attachment)
Given, in diagram of the belt Knuckle there are 4 Triangles (2 are of same dimensions & another 2 are of same dimensions) and a Rectangle .
Now For Area of belt Knucle, We have to First Calculate the area of 4 triangles and Area of Rectangle.
∴ Area of 2 Triangle with given dimensions ( height = 2.5 inches & base = 9 inches )
Area = 2×(1/2×b×h) ⇔ 2×(1/2×9×2.5)
Area= 22.5 square inches
∴ Area of another 2 triangle with given dimensions ( height = 5 inches & base = 4 inches )
Area = 2×(1/2×b×h) ⇔ 2×(1/2×4×5)
Area= 20 square inches
∴Area of Rectangle with given dimensions ( Length = 9 inches & Width = 5 inches )
Area= length × Width ⇔ 9×5 ⇒ 45 square inches
Now, Area of belt Knucle=Sum of Area of 4 Triangles + Area of Rectangle
Area of belt Knucle = 87.5 square inches
Given f(x)=10-2x, find f(7)
Answer:
-4
Step-by-step explanation:
f(x) = 10 - 2x
substitute 7 in place of x
f(7) = 10 -2*7
=10 - 14
=-4
therefore the value of f(7) is -4.