Answer:
C. 196 in3
No explanation needed
The line l is tangent to the circle with equation x² + y2 = 169 at the point P.
By thinking about the radius or otherwise, determine the gradient of the line l.
Given:
The equation of a circle is
[tex]x^2+y^2=169[/tex]
A tangent line l to the circle touches the circle at point P(12,5).
To find:
The gradient of the line l.
Solution:
Slope formula: If a line passes through two points, then the slope of the line is
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Endpoints of the radius are O(0,0) and P(12,5). So, the slope of radius is
[tex]m_1=\dfrac{5-0}{12-0}[/tex]
[tex]m_1=\dfrac{5}{12}[/tex]
We know that, the radius of a circle is always perpendicular to the tangent at the point of tangency.
Product of slopes of two perpendicular lines is always -1.
Let the slope of tangent line l is m. Then, the product of slopes of line l and radius is -1.
[tex]m\times m_1=-1[/tex]
[tex]m\times \dfrac{5}{12}=-1[/tex]
[tex]m=-\dfrac{12}{5}[/tex]
Therefore, the gradient or slope of the tangent line l is [tex]-\dfrac{12}{5}[/tex] .
i need help w this plss
Answer:
Line a and Line b are parallel. The slopes are equal
Line b is perpendicular to line c. The slopes are different
Step-by-step explanation:
The standard form of an equation is y =- mx+C
m is the slope
Two lines are parallel if they have the same slope and perpendicular if the product of their slope is -1
For Line a: 4x-3y = 2
Rewrite
-3y = -4x+2
y = 4/3 x - 2/3
Slope of line a is 4/3
Line b: y = 4/3x + 2
mx = 4/3x
m = 4/3
slope of line b is 4/3
Line c = 4y+3x = 4
4y = -3x + 4
y = -3/4 x + 1
Slope of line c is -4/3
Since line a and b have the same slope, they arer parallel
mb * mc = 4/3 * -3/4
mb*mc = -1
Since the product of slope of line b and c is -1, they are perpendiclar
the ratio of dogs to cats at the local shelter is 2 to 5.there are 20 dogs at the shelter.what is the total number of dogs and cats at the shelter?
20:50 or if you have to add it 70
What is / are the coefficients in this expressions? 3a+7-8n
Answer:
3 and 8
Step-by-step explanation:
3 and 8 are the only numbers that have a variable, or the letter beside it
June was thinking of a number. June doubles it, then adds 18 to get an answer of 90.7. What was the original number?
Answer:
36.35
Step-by-step explanation:
2x×18=90.7
2x=72.7
x=36.35
ANSWER ASAP PLEASE
A right rectangular prism has a height of 2 1/2 inches. Its length is 1/3 inch and its width is 3 feet. What is its volume?
Answer: 30 inches (2.5 feet)
Step-by-step explanation:
2 1/2 x 1/3 x 36
Solve: 2.4y - 3.2 = 4
A y = 0.5
B y = 1.6
C y = 2
D y = 3
Answer:
y=3 you have to use PEMDAS
Answer:
y=3
Step-by-step explanation:
Combine multiplied terms into a single fraction
2.4y-3.2=4
12y/5 -3.2=4
Add 3.2 to both sides of the equation
12y/5- 3.2+3.2=4+3.2
Simplify
add the numbers 12y/5=7.2
Solution
y=3
Write 245,800,000 in scientific notation.
Answer:
2.485x10^8
Step-by-step explanation:
Kevin just put 20.26 gallons of fuel into his car. There were 3.9 gallons in the car to begin with. How much fuel is in Kevin's car now?
HELPP
Answer:
24.16
Step-by-step explanation:
-3.5(x+9). URGENT : SHOW ALL STEPS PLEASE
Answer:
-3.5x - 31.5
Step-by-step explanation:
-3.5(x+9)
= -3.5x + -3.5(9)
= -3.5x - 31.5
Select the quadrant in which the terminal side of the angle falls.
210° terminates in quadrant
390° terminates in quadrant
Answer:
The answer is below
Step-by-step explanation:
Select the quadrant in which the terminal side of the angle falls.
210° terminates in quadrant
-150° terminates in quadrant
390° terminates in quadrant
Solution:
The x and y axis divides the cartesian plane into four equal parts known as the four quadrants.
Angles between 0° and 90° are in the first quadrant, angles between 90° and 180° are in the second quadrant, angles between 180° and 270° are in the third quadrant while angles between 270° and 360° are in the fourth quadrant.
a) Since 210 degrees is between 180° and 270°, hence it terminates in the third quadrant.
b) -150° = 360 - 150 = 210°. Since 210 degrees is between 180° and 270°, hence it terminates in the third quadrant.
c) 390° = 390° - 360° = 30°.
Since 30 degrees is between 0° and 90°, hence it terminates in the first quadrant.
Answer:
a. quadrant III
b. quadrant III
c. quadrant I
Step-by-step explanation:
correct on edge 2022
Help! Will mark brainliest to whoever puts the answer first!
Answer:
1 and 6 (alternate exterior angle)
2 and 5(corresponding angle)
4 and 5(co interior angle)
3 and 5(alternate interior angle)
exterior angle theorem
A) 110°
B) 34°
C) 23°
D) 30°
Answer:
D) 30°
Step-by-step explanation:
By exterior angle theorem:
? = 70° - 40°
? = 30°
Please due today are 11:59
A student need to fill a tank with 9 liters of water. How many 1/3 liters will it take to fill the tank?
Answer:
Number of [tex]\frac{1}{3}[/tex] liters required to fill the tank = 27
Step-by-step explanation:
Amount of water needed to fill the tank = 9 liters
Measure of water to fill a vessel = [tex]\frac{1}{3}[/tex] liters
Number of [tex]\frac{1}{3}[/tex] liters vessels required to fill the tank = [tex]\frac{9}{\frac{1}{3}}[/tex]
= 9 × [tex]\frac{3}{1}[/tex]
= 27
Therefore, number of [tex]\frac{1}{3}[/tex] liters required to fill the tank = 27
how many zeros are in f(x) = 3x^4 + x + 2
i know its 4... but i dont know how to solve the question
so please help me solve the question and show how there are 4 zeroes
Answer:
The power of the polynomial determines the number of zeroes it has in this case power is 4 so 4 zeroes. Whereas in 5^3+4 it has 3 zeroes as its power is 3. U can find the zero by trial and error method.
Hope this helps.
Step-by-step explanation:
Plssss help meeee I need help??
Answer:
The y-intercept will be moved 11 units downward.
Step-by-step explanation:
Select the correct answer.
620
530
х
What is the value of x in this triangle?
Answer:
65
Step-by-step explanation:
The front of Jane’s house is similar in shape to the front of Spot’s doghouse. The base of the doghouse is 4 feet and the height is 4.4 feet. If the height of Jane’s house is 22 feet, what is the length of its base? I
A: 21.6 ft
B: 20 ft
C: 24.2 ft
Answer:
21.6
Step-byit just the answerr
HELPP
The coast guard is out to sea and gets notification that two ships need help. One ship is directly west of the coast guard, and the other is directly south, as shown in the image below. The two ships are 6 miles from each other. Which ship is currently closer to the coast guard?
Answer:
Ship one is closer to the coast guard
In parallelogram DEFG if FH=16 find FD.
Answer:
32
Step-by-step explanation:
16x2
4.
I got 1,386.18 as my answer
Use the formula d = rt. Find t for r = 45.9 m/h and d = 647.19 m.
A. 14.1 h
B. 0.07 h
C. 601.29 h
D. 29,706 h
The volume of a rectangular prism can be found by multiplying the three side lengths. A bookcase in the shape of a rectangular prism has dimensions (b+8) ft, b ft, and (b+3) ft. Find the volume of the bookcase
Answer:
(b³+11b²+24)ft³
Step-by-step explanation:
Volume of the rectangular prism = Length * Width * Height
Given the dimension
Length = b+8 ft
Width = b ft
Height = (b+3)ft
Volume of the rectangular prism = b(b+8)(b+3)
Volume of the rectangular prism = b(b^2+3b+8b+24)
Volume of the rectangular prism = b(b^2+11b+24)
Volume of the rectangular prism = b(b^2)+b(11b)+1(24)
Volume of the rectangular prism = b^3+11b^2+24
Hence the Volume of the rectangular prism is (b³+11b²+24)ft³
Graph the system of equations, and determine the
solution.
X + 5y = 10
2x + 10y = 50
Use the graphing tool to graph the system,
Answer:
First one is 2. The second one is 5.
Step-by-step explanation:
Complete the table of values for x + y =6
Answer:
-2 -1 0 1 2 3
8 7 6 5 4 3
Step-by-step explanation:
Help plsssssssssssss
Answer:
CStep-by-step explanation:
use the number then do ÷
1/8 + 3/4 in its simplist form
Rewrite 3/4 to have the same denominator as 1/8.
3/4 = 6/8
Now you have 1/8 + 6/8 = 7/8
The answer is 7/8
HELP ILL GIVE BRAINLIEST
In a class of 40 students, 75% of the students
turned in their assignments. How many
students did NOT turn in their assignments?
Answer:
10 students didnt turn in work
Step-by-step explanation:
10. its like saying 100 divided by 25
The square root of 150 lies between which two consecutive integers?
O 10 and 11
O 11 and 12
O 12 and 13
O 149 and 151
Answer:
12^2 = 144 and 13^2 = 169
So, the answer is 12 and 13
Step-by-step explanation:
The perimeter of the triangle is 202cm. Using that find the value of x
Answer:
x = 13
Step-by-step explanation:
3x + 12 + 5x + 16 + 4x + 18 = 202
combine like terms
12x + 12 + 16 + 18 = 202
12x + 46 = 202
-46 -46
12x = 156
divide by 12
x = 13
Hope this helped! Have a nice rest of ur day! Plz mark as brainliest!!!
-Lil G
Add all the sides together (don´t forget parenthesis) Put the x´s with the x´s and the same with the other numbers. The subtract additional numbers from the total. The divide what left from the number in front of the x.
(3x + 12) + (5x + 16) + (4x + 18) = 202
8x + 28 + (4x + 18) = 202
12x + 46 = 202
- 46 -46
12x = 156
/12 /12
x = 13