The x and y intercepts of a line are when [tex]y=0[/tex] and [tex]x=0[/tex] respectively.
c and d are the x and y intercepts because they represent C/A and B/A in the standard linear equationThe x and the y intercepts are related to c and d because they represent the values of the equation when y and x equals 0 respectively.The given equation is:
[tex]\frac xc + \frac yd = 1[/tex]
(1) Why c and d are the intercepts
We have:
[tex]\frac xc + \frac yd = 1[/tex]
Multiply through by cd
[tex]cd \times \frac xc + cd \times \frac yd = cd \times1[/tex]
[tex]dx + cy = cd[/tex]
A linear equation is represented as:
[tex]Ax + By = C[/tex]
Where:
[tex]\frac CA \to[/tex] x intercept
[tex]\frac BA \to[/tex] y intercept
So, by comparing [tex]Ax + By = C[/tex] to [tex]dx + cy = cd[/tex]
[tex]\frac CA \to d \to[/tex] The x-intercept
[tex]\frac CB \to c \to[/tex] The y-intercept
(b) How the intercepts are related to c and d?
In (a) above, we have:
[tex]\frac CA \to d \to[/tex] The x-intercept
[tex]\frac CB \to c \to[/tex] The y-intercept
When [tex]x = 0[/tex]
We have:
[tex]dx + cy = cd[/tex]
[tex]d \times 0 + cy = cd[/tex]
[tex]cy = cd[/tex]
Divide by c
[tex]y = d[/tex] ---- the y-intercept
When [tex]y = 0[/tex]
We have:
[tex]dx + cy = cd[/tex]
[tex]dx + c \times 0 = cd[/tex]
[tex]dx = cd[/tex]
Divide by d
[tex]x =d[/tex] ---- the x-intercept
Read more about intercepts at:
https://brainly.com/question/13593488
Plz solve it
Factorize: no w
Answer:
here we can go for two solution
Type the correct answer in each box
The general form of the equation of a circle is x^2+y^2+8x+22y+37=0
The equation of this circle in standard form is (x+__)^2+(y+__)^2=__. The center of the circle is at the point (__,__).
Answer:
We know that the equation of the circle in standard form is equal to (x-h)² + (y-k)² = r² where (h,k) is the center of the circle and r is the radius of the circle.
We have x² + y² + 8x + 22y + 37 = 0, let's get to the standard form :
1 - We first group terms with the same variable :
(x²+8x) + (y²+22y) + 37 = 0
2 - We then move the constant to the opposite side of the equation (don't forget to change the sign !)
(x²+8x) + (y²+22y) = - 37
3 - Do you recall the quadratic identities ? (a+b)² = a² + 2ab + b². Now that's what we are trying to find. We call this process "completing the square".
x²+8x = (x²+8x + 4²) - 4² = (x+4)² - 4²
y²+22y = (y²+22y+11²)-11² = (y+11)²-11²
4 - We plug the new values inside our equation :
(x+4)² - 4² + (y+22)² - 11² = -37
(x+4)² + (y+22)² = -37+4²+11²
(x+4)²+(y+22)² = 100
5 - We re-write in standard form :
(x-(-4)²)² + (y - (-22))² = 10²
And now it is easy to identify h and k, h = -4 and k = - 22 and the radius r equal 10. You can now complete the sentence :)
Solve for x. A. 19 B. 17 C. 15 D. 11
Answer:
B. 17
Step-by-step explanation:
By the property of intersecting secants outside of a circle, we have:
7 (7 + x) = 8 (13 + 8)
49 +7x = 8*21
7x = 168 - 49
7x = 119
x = 119/7
x = 17
what is the general form to find square roots
Answer:
see below (I hope this helps!)
Step-by-step explanation:
Square roots are usually in the form a√b where a and b are any rational number.
Find the radius of a circle that has an area of 6.76 cm². Use it for pi.
Answer:
radius = 1.47 cmStep-by-step explanation:
Area of a circle = πr²
where
r is the radius
From the question
Area = 6.76 cm²
To find the radius substitute the value of the area into the above formula and solve for the radius
That's
[tex]6.76 = \pi \: {r}^{2} [/tex]
Divide both sides by π
We have
[tex] {r}^{2} = \frac{6.76}{\pi} \\ r = \sqrt{ \frac{6.76}{\pi} } [/tex]
r = 1.46689291
We have the final answer as
radius = 1.47 cm
Hope this helps you
PLEASE HELP!!! The data set shows the ages of people riding a bus.
What is the mode for this data set?
18 16 11 45 33 11 33 14 18 11
A. 11, 18, and 33
B. 17
C. 21
D. 11
Step-by-step explanation:
The number which is repeated more times will be mode...
So...
11 is Answer
HELPPP PLZZZZ DUE SOONnnn
Answer:
x = 7, EF = 10, FG = 12
Step-by-step explanation:
EF = 4x - 18
FG = 3x - 9
EG = 22
EG = 22
EF + FG = 22
4x - 18 + 3x - 9 = 22
4x + 3x - 18 - 9 = 22
7x = 22 + 18 + 9
7x = 49
x = 7
EF = 4x - 18
EF = 4*7 - 18
EF = 28 - 18
EF = 10
FG = 3x - 9
FG = 3*7 - 9
FG = 21 - 9
FG = 12
16-32)
What is the equation of the line that is perpendicular to
the given line and passes through the point (3, 0)?
O 3x + 5y = -9
O 3x + 5y = 9
O 5x - 3y = -15
O 5x - 3y = 15
Answer:
the fourth option : 5x - 3y = 15
Step-by-step explanation:
the slope of the original line is given by the coordinate differences between the 2 points on the line.
remember, the slope is the factor of x in the line equation and is the ratio y/x indicating how many units y is changing, when x changes a certain number of units.
so, to go from (-3. 2) to (2, -1) x changes 5 units and y -3 units.
therefore, the slope is -3/5.
the slope of a perpendicular line simply switched x and y. and the sign of the slope.
therefore the slope of the perpendicular line is 5/3.
and the line equation is
y = (5/3)x + c
to get c we need the point on the line (3, 0).
0 = (5/3)×3 + c = 5 + c
c = -5
y = (5/3)x - 5
3y = 5x - 15
3y - 5x = -15 or (after multiplying both sides by -1)
5x - 3y = 15
Which graph represents a function?
Answer:
The first one is the only function
Step-by-step explanation:
You cannot have points on the same y gridline
If it is a function is has to pass the pencil test
Answer:
[tex]\boxed{Graph A.}[/tex]
Step-by-step explanation:
Hey there!
Well graph A is correct because if you do the vertical line test which decides is the graph is a function or not you can see that all the graph expect A have the vertical line go through 2 points.
Hope this helps :)
A random number generator chooses 2 numbers between 1 and 5. This table demonstrates all possible outcomes. 1 2 3 4 5 1, 1 1, 2 1, 3 1, 4 1, 5 2 2, 1 2, 2 2, 3 2, 4 2, 5 3 3, 1 3, 2 3, 3 3, 4 3, 5 4 4, 1 4, 2 4, 3 4, 4 4, 5 5 5, 1 5, 2 5, 3 5, 4 5, 5 What is the probability that the computer will pick two 5s?
Answer as a fraction = 1/25
Answer in decimal form = 0.04
Answer in percent form = 4%
Explanation:
There are 5*5 = 25 different outcomes, of which only one outcome has 5,5. The probability of picking two 5s is 1/25 = 0.04 = 4%
Answer:
4%
Step-by-step explanation:
(-6x)(½y)(-⅓z) what is the product?
Answer:
xyz
Step-by-step explanation:
[tex](-6x)(\frac{1}{2}y)(-\frac{1}{3}z) = (-6)*\frac{1}{2}*(-\frac{1}{3}) * xyz = \frac{6}{6} xyz = xyz[/tex]
Question 20 of 33
What is the surface area of the sphere shown below with a radius of 7?
1.72
A. 495 sq. units
B. 65x sq, units
C. 457 sq. units
D. 1965 sq. units
SERNAT
Answer:
The surface area of the sphere 1s 615.75 sq. unit.
Step-by-step explanation:
The surface area of a sphere [tex]A_s[/tex] = 4·π·r²
Given that the radius of the sphere = 7, we have
The surface area of the sphere = 4 × π × 7^2 = 615.75 sq. unit
The surface area can also be derived from the volume of the sphere by differentiation as follows;
Volume of a sphere, V = 4/3·π·r³
(The volume of the sphere is 4/3·π·7³ = 1436.76 cube unit)
dV/dr = d(4/3·π·r³)/dr = 3×4/3·π·r² = 4·π·r²
The surface area of the sphere = 615.75 sq. unit.
AB = 3.2 cm
BC= 8.4 cm
The area of triangle ABC is 10 cm²
Calculate the perimeter of triangle ABC.
Give your answer correct to three significant figures.
Answer:
Therefore, perimeter of the given triangle is 18.300 cm.
Step-by-step explanation:
Area of the triangle ABC = [tex]\frac{1}{2}(\text{AB})(\text{BC})(\text{SinB})[/tex]
10 = [tex]\frac{1}{2}(3.2)(8.4)(\text{SinB})[/tex]
Sin(B) = [tex]\frac{10}{3.2\times 4.2}[/tex]
B = [tex]\text{Sin}^{-1}(0.74405)[/tex]
B = 48.08°
By applying Cosine rule in the given triangle,
(AC)² = (AB)² + (BC)²-2(AB)(BC)CosB
(AC)² = (3.2)² + (8.4)² - 2(3.2)(8.4)Cos(48.08)°
(AC)² = 10.24 + 70.56 - 35.9166
(AC)² = 44.88
AC = [tex]\sqrt{44.8833}[/tex]
AC = 6.6995 cm
Perimeter of the ΔABC = m(AB) + m(BC) + m(AC)
= 3.200 + 8.400 + 6.6995
= 18.2995
≈ 18.300 cm
Therefore, perimeter of the given triangle is 18.300 cm
What is the simplest form of 20 over 315?
Answer:
4/63
Step-by-step explanation:
20/315 = (20÷5)/(315÷5)
Find each of the following products
a) 6x * (-2y)
Answer ) -12xy
Step-by-step explanation:
6x × (-2y) = -12xy thank youQuestion 3 Multiple Choice Worth 2 points)
04.04
The swimming team has competed in 45 races this season. They have won 30 races so far. How many races will the team need to win today for the team to have a 75%
Success rate?
8
10
12
15
Answer:
Total number of matches need to win = 15
Step-by-step explanation:
Given:
Total number of race completed = 45
Total races win = 30
Success rate = 75% = 0.75
Find:
Total number of matches need to win
Computation:
Assume, extra number of matches = y
Extra number of win matches = x
So,
(30 + x) / (45 + y) = 0.75
Assume y = x
So,
(30 + x) / (45 + x) = 0.75
30 + x = 33.75 + 0.75 x
x = 15
Total number of matches need to win = 15
Two students use different methods to solve this multiplication problem:
3/4*-4 2/9
Read each of their methods below and then enter numbers to correctly complete their
work.
Answer/Step-by-step Explanation:
Given, [tex]\frac{3}{4}*-4\frac{2}{9}[/tex]
Ivy solves this problem by writing each number as a fraction and then multiplies as shown below:
[tex] \frac{3}{4}*-4\frac{2}{9} = \frac{3}{4}* -\frac{38}{9} [/tex]
[tex] = \frac{3}{4}*-\frac{38}{9} = -\frac{3*38}{4*9} = -\frac{1*19}{2*3}[/tex]
[tex]= -\frac{19}{6}[/tex]
Fabian solves this problem by writing the mixed number as a sum and applies the distributive method of multiplication as shown below:
[tex] \frac{3}{4}*-4\frac{2}{9} = \frac{3}{4}(-4 + -\frac{2}{9}) [/tex]
[tex] = \frac{3}{4}*-4 + \frac{3}{4}*-\frac{2}{9} [/tex]
[tex] = -\frac{3}{1} + \frac{1}{2}*-\frac{1}{3} [/tex]
[tex] = -3 + (-\frac{1}{6}) [/tex]
[tex] = -3 - \frac{1}{6} = -3\frac{1}{6} [/tex]
A dripping tap loses water at a rate of 5mL a minute.
How long does it take to lose one litre?
1 liter = 1000mL
Divide 1000mL by mL per minute:
1000 / 5 = 200 minutes ( 3 hours and 20 minutes)
Solve for x. 3x-91>-87 AND 17x-16>18
Answer & Step-by-step explanation:
For this problem, we have two inequalities to solve for x.
3x - 91 > -87
17x - 16 > 18
Now that we know what our inequalities are, we will solve them as if we are solving for the value of x.
3x - 91 > -87
Add 91 on both sides.
3x > 4
The solution for the first inequality is 3x > 4
Now let's do the second inequality.
17x - 16 > 18
Add 16 on both sides.
17x > 34
Divide by 17 on both sides.
x > 2
The soultion for the second inequality is x > 2
Answer:
The answer is x>2
Step-by-step explanation:
"A die is rolled and a number less than 5 comes up"
Which letter from A to G best represents the probability of the event?
Answer:
4/6
Step-by-step explanation:
Im pretty sure***
but if a dice has 6 sides, and you have to get something less than 5, which is 1-4, which is 4 numbers, so 4 out of 6 total is 4/6
For the function f(x) = -12x + 7, find the
matching value for x when f(x) = 17. Write
your answer as a fraction.
Answer:
[tex]\large\boxed{x=-\frac{5}{6}}[/tex]
Step-by-step explanation:
f(x) is the same value as y. Therefore, y = 17. We can place this into slope intercept form (except with a defined value for y) and solve for x.
Start by subtracting 7 from both sides. Then, divide by -12 to solve for x. Finally, simplify the fraction.
17 = -12x + 7
10 = -12x
-10/12 = x
-5/6 = x
[tex]\large\boxed{x=-\frac{5}{6}}[/tex]
pls help me asap !!!!
Answer:
9--7
Step-by-step explanation:
3. A doctor treated 2,000 patients over a period of time. If he worked for
5 hours a day and spent 15 minutes pach patient, how many days
did the doctor spend to treat all the patients?
Answer:
100 days
Step-by-step explanation:
the doctor works 5 hrs per day, which means 20 patients per day, in 100 days he will be able to treat 2000 patients
The coordinate grid shows the graph of four equations:
Which set of equations has (3, 1) as its solution?
A and B
C and D
B and D
A and D
Answer:
A and D
Step-by-step explanation:
All you need to do is locate the point (3,1) on the graph and figure out which two lines are intersecting it. In this case it is A and D so that is your solution.
plssss help i want it now
Find an equation of the line: Through the point (2, −4) with a y-intercept of −2 Through the points (4,2) and (3,1) Through the point (3,2) with a slope of −2
Answer and Step-by-step explanation: Equations of line through points and slope can be determined by:
[tex]y-y_{0}=m(x-x_{0})[/tex]
m is slope
Point (2,-4) and y-intercept = -2Y-intercept is point (0,-2)
m = [tex]\frac{y_{a}-y_{b}}{x_{a}-x_{b}}[/tex]
m = [tex]\frac{-4-(-2)}{2-0}[/tex]
m = - 1
Equation:
[tex]y+2=-1(x-0)[/tex]
[tex]y=-x-2[/tex]
Points (4,2) and (3,1)m = [tex]\frac{2-1}{4-3}[/tex]
m = 1
Equation:
[tex]y-2=(x-4)[/tex]
[tex]y=x-2[/tex]
Point (3,2) and slope = -2m = -2
Equation:
[tex]y-2=-2(x-3)[/tex]
[tex]y=-2x+6+2[/tex]
[tex]y=-2x+8[/tex]
Need help ! Help needed very much !
Answer:
x/2 > 5
Step-by-step explanation:
Quotient means division
x/2
is more than means greater
x/2 > 5
Find an equation for the nth term of the arithmetic sequence. 9, 11, 13, 15, ...
Answer:
2n+7
Step-by-step explanation:
First lets find the common difference which is 2, now we can use this formula to find the nth term.
an = a1 + (n - 1 ) d
an= 9+(n-1)2
=9+2n-2
=2n+7
To check let's insert n=5, 2(5)=10+7=17.
15+2=17!
11) MZHGF = 16x + 4, m EGF = 110°,
and MZHGE = 3x + 11. Find x.
G
H
F
E
=======================================================
Explanation:
The smaller angles HGE and EGF combine to form the largest angle HGF.
This is an example of the angle addition postulate.
(angle HGE) + (angle EGF) = angle HGF
(3x+11) + (110) = 16x+4
3x+121 = 16x+4
121-4 = 16x-3x
117 = 13x
13x = 117
x = 117/13
x = 9 which is the final answer
We can stop here.
--------------------
Extra info (optional section)
Use this x value to find each angle shown below
angle HGE = 3x+11 = 3*9+11 = 27+11 = 38 degreesangle HGF = 16x+4 = 16*9+4 = 144+4 = 148 degreesThen notice how,
(angle HGE)+(angle EGF) = 38+110 = 148
which is exactly the measure of angle HGF
This confirms that the equation
(angle HGE) + (angle EGF) = angle HGF
is true for that x value of x = 9. Therefore, the answer is confirmed.
9514 1404 393
Answer:
11) x = 9°
13) x = -12°
Step-by-step explanation:
11) ∠HGE +∠EGF = ∠HGF
(3x +11) +(110°) = (16x +4)
117° = 13x . . . . . . . . . . . . . . . subtract 3x+4, collect terms
9° = x . . . . . . . . . . . . divide by 13
__
13) ∠BCF +∠FCD = ∠BCD
(x +78) +(x +41) = 95°
2x = -24°
x = -12°
In right triangle ABC, AB = 3 and AC = 9. What is the measure of angle B to the nearest degree?
Answer:
90 degrees
Step-by-step explanation:
see image
make x A
y B
z C
AB=3 (given)
AC=9 (given)
measure of angel B or y, is 90
if
x= A
y= C
z= B
then the hypotenuse would be shorter than one of the legs
3<9
so B has to be the right angle (90 degrees)