Answer:
- 12 /13
Step-by-step explanation:
Given that:
Cot(θ) = 5 /12 ;
Recall ; cot θ = 1 / tan θ ; tan θ = sin θ / cos θ
Hence ;
tan θ = 1 / cot θ
tan θ = 1 ÷ (5 / 12)
tan θ = 1 * 12 /5 = 12/5
Tan θ = opposite / Adjacent = 12 /5
Sin θ = opposite / hypotenus
Hypotenus = √(opposite² + adjacent²)
Hypotenus = √12² + 5²
Hypotenus = √(144 + 25)
Hypotenus = √169
Hypotenus = 13
Hence,
Sin θ = opposite / hypotenus = 12 / 13
pi < theta < 3pi/2 lies in the 3rd quadrant ; SinΘ will be negative ;
Sin θ = - 12 /13
Answer:
A
Step-by-step explanation:
Ed2021
1. The circle C has centre (5,k), where k is a constant. The line y = 2x + 1 is tangent to C at point
A (3,7). Find the equation of C.
Answer:
[tex](x-5)^2+(y-6)^2=5[/tex]
Step-by-step explanation:
Equation of the Circle
A circle centered at (h,k) and radius r can be written with the equation:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
We are given the center (5,k), thus:
[tex](x-5)^2+(y-k)^2=r^2[/tex]
We know the point (3,7) belongs to the circle. This means the distance between the center and this point is the radius.
Given two points (x1,y1) and (x2,y2), the distance between them satisfies:
[tex]d^2=(x_2-x_1)^2+(y_2-y_1)^2[/tex]
Calculating the radius, we have:
[tex]r^2=(7-k)^2+(3-5)^2[/tex]
[tex]r^2=(7-k)^2+4\qquad\qquad [1][/tex]
Now we use the fact that the line y=2x+1 and the circle are tangent at (3,7). The radius and the line are perpendicular at that point. Two perpendicular lines with slopes m1 and m2 satisfy the condition:
[tex]m_1\cdot m_2=-1[/tex]
The line y=2x+1 has a slope of m1=2, thus the slope of the segment from (5,k) to (3,7) has a slope of -1/2:
The slope is calculated as:
[tex]\displaystyle \frac{7-k}{3-5}=-\frac{1}{2}[/tex]
Operating:
[tex]\displaystyle \frac{7-k}{-2}=-\frac{1}{2}[/tex]
Multiplying by -2
[tex]\displaystyle 7-k=1[/tex]
Solving:
k=6
From [1] the radius is:
[tex]r^2=(7-6)^2+4[/tex]
[tex]r^2=1+4[/tex]
[tex]r^2=5[/tex]
Finally, substituting into the equation of the circle:
[tex]\mathbf{(x-5)^2+(y-6)^2=5}[/tex]
The graph can be seen in the figure below.
Answer:
Step-by-step explanation:
What’s the answer
What are the slope and the y-intercept of the linear function that is represented by the graph
During a 60-minute period, a traffic engineer counted 66 trucks and cars that crossed a bridge. The ratio of trucks to cars that travel across the bridge is usually 3:8. The equation 3 8 = t 66 − t 3 8 = t 66 − t can be used to predict the number of trucks, t, the engineer should have counted. How many trucks should the engineer have counted?
Answer:
18
Step-by-step explanation:
t = Number of trucks counted
c = Number of cars
Ratio of trucks to cars = [tex]\dfrac{t}{c}=\dfrac{3}{8}[/tex]
Total number of cars and truck = 66
[tex]t+c=66[/tex]
Divide the left and right side by the number of cars
[tex]\dfrac{t+c}{c}=\dfrac{66}{c}\\\Rightarrow \dfrac{t}{c}+1=\dfrac{66}{c}\\\Rightarrow \dfrac{3}{8}+1=\dfrac{66}{c}\\\Rightarrow \dfrac{11}{8}=\dfrac{66}{c}\\\Rightarrow c=66\times \dfrac{8}{11}\\\Rightarrow c=48[/tex]
Total number of cars is 48
so
[tex]t=66-c\\\Rightarrow t=66-48\\\Rightarrow t=18[/tex]
Total number of trucks counted is 18.
can someone please help.....
a fruit Shop sells dried fruit by the pound the cost for X pounds of raisins is represented by the equation y= 3.5x, where y is the total cost for X pounds. the cost for 4 pounds of dried cranberries is $18 Graph both proportional relationship on the grid to the right which fruit has the lower unit price? Explain.
y=4.5x the equation for cranberries
Step-by-step explanation:
So the easiest way to solve this would be take the $18 and divide it by the 4 pounds you then get the unit price per pound which is $4.5 a pound
You have put ₹ 2500 in your bank account. After some years, you observe that you have received interest and the amount now is ₹ 4100. What is the percentage of increase?
Answer:
64%
Step-by-step explanation:
The first step is to calculate the increase
= 4100-2500
= 1600
Therefore the percentage increase can be calculated as follows
= increase/original number × 100
= 1600/2500 × 100
= 0.64 × 100
= 64%
Hence the percentage increase is 64%
6. When rounded to the nearest hundredth, log, 7 =1.77. Which of the following represents the value of
log, 63 to the nearest hundredth? Hint: write 63 as a product involving 7.
Note: Consider the base of all is 3 instead of comma.
Given:
Consider the given value is [tex]\log_37=1.77[/tex].
To find:
The value of [tex]\log_363[/tex].
Solution:
Using properties of logarithm, we get
[tex]\log_363=\log_3(9\times 7)[/tex]
[tex]\log_363=\log_3(3^2\times 7)[/tex]
[tex]\log_363=\log_3(3^2)+\log_3(7)[/tex] [tex][\because \log ab=\log a+\log b][/tex]
[tex]\log_363=2+ \log_3(7)[/tex] [tex][\because \log_aa^x=x][/tex]
[tex]\log_363=2+1.77[/tex] [tex][\because \log_37=1.77][/tex]
[tex]\log_363=3.77[/tex]
Therefore, the value of [tex]\log_363[/tex] is 3.77.
Applying logarithm properties, it is found that:
[tex]\log_3{63} = 3.77[/tex]
We want to find [tex]\log_3{63}[/tex], considering that [tex]63 = 7 \times 9 = 7 \times 3^2[/tex], we have that:
[tex]\log_3{63} = \log_3{(7 \times 3^2)}[/tex]
The first property applied is:
[tex]\log{a \times b} = \log{a} + \log{b}[/tex]
Hence:
[tex]\log_3{63} = \log_3{(7 \times 3^2)} = \log_3{7} + \log_3{3^2}[/tex]
The next property is:
[tex]\log_a{a^b} = b[/tex]
Hence:
[tex]\log_3{7} + \log_3{3^2} = 1.77 + 2 = 3.77[/tex]
A similar problem is given at https://brainly.com/question/2620660
Order the numbers from least to greatest.
Put the lowest number on the left.
1.001 1.101 0.113
Answer:
I think this is answer:
0.113-1.001-1.101
Step-by-step explanation:
HEELLLPP MEEEE PLZZZZ!!!!!
Use the distance formula to find base and height.
It takes Mark 1 hour to get to work each day. Mark drives from home 20 minutes to the train station at a constant rate of 42 mph. He then takes the train, traveling at a constant 60 mph, the remaining distance to work. How far does Mark live from his work place? A. 108 mi. B. 80 mi. C. 62 mi. D. 54 mi.
PLEASE HELP QUICK
Answer:D.54
Step-by-step explanation: it takes 20 minutes in the car which is 1/3 of an hr so 42/3= 14 then that leaves 40 minutes left for the train which is 2/3 of 60 and 60/3=20 and 20x2= 40 so 40+14=54
Answer:
D. 54
Step-by-step explanation:
Give the guy above brainliest
Find the distance from point A(−1, 7) to the line y=3x. Round your answer to the nearest tenth.
Answer:
The distance from the point to the line is approximately 3.2 units
Step-by-step explanation:
Distance From a Point to a Line
Is the shortest distance from a given point to any point on an infinite straight line. The shortest distance occurs when the segment from the point and the line are perpendiculars.
If the line is given by the equation ax + by + c = 0, where a, b and c are real constants, the distance from the line to a point (x0,y0) is
[tex]\displaystyle d= \frac{|ax_0+by_0+c|}{\sqrt{a^2+b^2}}[/tex]
The line is given by the equation:
y=3x. We need to transform it into the specified form.
Subtracting 3x:
y - 3x = 0
Comparing with the general form of the line, we have
a=-3, b=1, c=0
The point (xo,yo) is (-1,7), thus:
[tex]\displaystyle d= \frac{|-3\cdot (-1)+1\cdot 7+0|}{\sqrt{(-3)^2+1^2}}[/tex]
[tex]\displaystyle d= \frac{|3+7|}{\sqrt{9+1}}[/tex]
[tex]\displaystyle d= \frac{|10|}{\sqrt{10}}[/tex]
[tex]\displaystyle d= \frac{10}{\sqrt{10}}[/tex]
[tex]d\approx 3.2[/tex]
The distance from the point to the line is approximately 3.2 units
PLEASE HELP ASAP GIVING 15 POINTS AND MARKING BRAINLIEST THE FIRST PHOTO IS THE GRAPH THE SECOND IS THE ANSWER CHOICES PLEASE HELP!!!
Pls help i will mark brainliest シ♡︎
Answer:
D:95 mm Hg
Step-by-step explanation:
Using the linear model, y=x+95, x represents the age and y represents the blood pressure.
For a newborn, x=0 this gives us
> y=0+95 = 95<
Answer: 1mm hg per year
Step-by-step explanation:
OK y'all, one more, help please !!
Answer:
1) B
2) A
3) H
4) E
Step-by-step explanation:
Complete the following statement.
24 ft = in.
Answer:
288
Step-by-step explanation:
1 foot= 12 inches
24x12=288
Answer:288
Step-by-step explanation:24x12=288 hope this helps
빠IHO
4. Find 39% of 65.
What is the answer
URGENT! What is the value of x?
Enter your answer in the box.
(MAKE SURE IT’S THE CORRECT ANSWER)
Answer:
48 degrees
Step-by-step explanation:
Need help with this pls
Answer:
hi
Step-by-step explanation:
hi
Part A: In your own words, describe the relationship between the temperature of the city and the number of ice cream cones sold.
Part B: Describe how you can make the line of best fit. Write the approximate slope and y-intercept of the line of best fit. Show your work, including the points that you use to calculate slope and y-intercept.
Answer:
Part A: The higher the temp the more ice cream sold.
Part B
Step-by-step explanation:
The cost of a school banquet is $85 plus $12 for each person attending. Write an equation that gives the total cost of the number of people attending.
A. Y=85x-12
B. Y=12x+85
C. Y=85x+12
D. Y=12x-85
Answer: I think that the answer is B
Step-by-step explanation:
Which of the following shows 2.736 correctly rounded to the tenths place?
2.74
2.7
2.8
3
Answer:
2.7
Step-by-step explanation:
The 3 does not round up the 7, so it stays as 2.7
Answer:
2.7
Step-by-step explanation:
the tenths place is the first number after the decimal. When rounding numbers 5 and higher can increase the number next to it by 1. So 2.736 becomes 2.74 then becomes 2.7 as the 4 is not able to round the number since it is below 5.
No rush on this one:)
The price of a shirt decreases by 13$. Which integer represents the decrease in the shirt’s price?
Answer:
-13
Step-by-step explanation:
-13 since it's going down in price
Plz help!! Ty
A (2-7)
B. (1-6)
C. (5,0)
D. (0,-7.5)
Answer:
i have a feeling it is C because the lines intersect at (5,0)
What are some reasons to live I could use them right now
Answer:
mom will be sad
Step-by-step explanation:
YOU ARE A BEATIFUL AND AMAZING PERSON DONT DIE ON ME LIKE THIS
Which ordered pairs are NOT a solution of y = 2x + 1? Select all that apply. (3, 7) (3, 7) (0, 1) (0, 1) (-1, 1) (-1, 1) (-3, -5) (-3, -5) (-2, 3)
Answer:
The ordered pairs are;
(-1,1) and (-2,3)
Step-by-step explanation:
Here, we want to select which ordered pair is not a solution to the given equation
The one that will not be a solution will be a point at which if we insert the x-value into the equation, we do not get the y-value at that point
For (3,7
2(3) + 1 = 7
For 0,1
2(0) + 1 = 1
For (-1,1)
= 2(-1) + 1 = -2 + 1 = -1
This is wrong
(-3,-5)
= 2(-3) + 1 = -6 + 1 = -5
(-2,3)
= 2(-2) + 1 = -4 + 1 = -3
This is wrong also
The last time Aiden played baseball, he hit the ball 35% of the times he was at bat. Based on this information, how many times will Aiden hit the ball the next time he plays baseball if he is at bat 20 times?
Answer:
the number of times will Aiden hit the ball is 7
Step-by-step explanation:
The computation of the number of times will Aiden hit the ball is shown below:
She hit 35% of the times
i.e.
= Given percentage of number of times
= 35% of 20
= 35 ÷ 100 × 20
= 0.35 × 20
= 7
Hence, the number of times will Aiden hit the ball is 7
We simply applied the above formula so that the correct value could come
The same is to be considered
A certain cookie recipe calls for 2 cups of flour to make one batch of cookies. Which graph best
represents the relationship between the amount of flour and the number of batches of cookies that
can be made using this recipe?
Answer:
1 cup of flower makes 1/2 a batch of cookies
Step-by-step explanation:
2 divided by 2 is 1
1 divided by 2 is 1/2
Solve for x in the equation
4*+2=1
Answer:
x=(-1)/4
Step-by-step explanation:
4x=1-2
4x=(-1)
x=(-1)/4
15. Which expression has the greatest value?
A. 142-(-172)
B. 1 12+ -1 12
C. -142 - (-14)
D. 142
Answer:
i think that its D
Step-by-step explanation:
hopes this helps
Tilly and Lilly worked together on a job. Tilly earned twice as much as Lilly, and together they earned $510. How much did each person earn? Use the 5D Process, showing all your work.
Answer:
Lilly earns $170
Tilly earns $340
Step-by-step explanation:
Given that
Tilly earned twice as much as Lilly
If Lilly's earning = x, then Tilly's earning = 2x
Total amount they both earned = $510
x + 2x = $510
3x = $510
3x / 3 = $510 /3
x = $170
Hence,
Lilly earns x = $170
Tilly earns, 2x = 2* 170 = $340