Answer:
A. [tex] y_1 = -m(x_2 - x_1) + y_2 [/tex]
Step-by-step explanation:
Given, slope formula = [tex] m = \frac{y_2 - y_1}{x_2 - x_1} [/tex]
To find an equivalent equation, let's make [tex] y_1 [/tex] the subject of the formula.
[tex] m = \frac{y_2 - y_1}{x_2 - x_1} [/tex]
Cross multiply
[tex] 1(y_2 - y_1) = m(x_2 -x_1) [/tex]
[tex] y_2 - y_1 = m(x_2 - x_1) [/tex]
Subtract [tex] y_2 [/tex] from both sides
[tex] y_2 - y_1 - y_2 = m(x_2 -x_1) - y_2 [/tex]
[tex] - y_1 = m(x_2 - x_1) - y_2 [/tex]
Divide both sides by -1
[tex] \frac{- y_1}{-1} = \frac{m(x_2 -x_1) - y_2}{-1} [/tex]
[tex] y_1 = -m(x_2 - x_1) + y_2 [/tex]
94. Juan is practicing archery using a simple circular target with a radius of 18 inches. The target's a bullseye has a circumference of 18pi inches. What is the area of the portion of the target that is not part of the bullseye?
Answer: 763.02 in^2
Step-by-step explanation:
For a circle of radius R, we know that:
The area is:
A = pi*R^2
the circumference is:
C = 2*pi*R
where pi = 3.14
We know that the circumference of the bullseye is 18*pi, then the radius of this circle is:
2*pi*R = 18*pi
2*R = 18
R = 18/2 = 9
The radius of the bullseye is 9 inches.
Now, the area of the target that is not part of the bullseye is equal to the difference between the area of a circle of radius 18in (the total target area) and a circle of radius 9in (the bullseye area)
This is:
A = pi*(18in)^2 - pi*(9in)^2 = 3.14*( (18in)^2 - (9in)^2) = 763.02 in^2
Solve for the variable. You may use the hangers to help you.
40 = 2f + 12
f
f
40
12
Answer:
i don't know what the hangers are for but the calculation is given below
Step-by-step explanation:
40 = 2f + 12
40 - 12 = 2f
28 = 2f
28/2 = f
14 = f
therefore f = 14
I just learned this kind of confused :(
Answer:
9.4247
Step-by-step explanation:
c= πd, c=(3.14)d , 3 is the diameter so we put it in the d spot. So c=(3.14)3 and you multiply those together to get the circumference.
2.) Which is equivalent to 3 (а- 9)?
За - 9
OOption 2
оза + 9
оза - 27
Answer:
3a-27
Step-by-step explanation:
Distribute the 3
3 x a is 3a
3 x 9 is 27
Multiple Choice: What method can be used to prove the triangles below are congruent? * Angle Side Angle (ASA) Angle Angle Side (AAS) Option 1 Option 2 Not Congruent Hypotenuse Leg (HL)
Answer:
angle side angle
Step-by-step explanation:
What is the circumference of a circle with radius 2.1 cm? Use > (inserts wavey = sign) 3.14.
Step-by-step explanation:
The formula for the circumference of a circle is 2*pi*radius
Circumference = 2(3.14)(2.1)
= 13.188cm
HELP!! Mr. Posey is buying a baseball bat that normally cost $160. It is now on sale for 24% off. If sales tax is 10%, how much will he pay for the baseball bat?
Answer:
he will pay $133.10
Step-by-step explanation:
If you could help I would really appreciate it, but if not that’s fine. Thank you.
Answer:
Option C is correct answer.
Step-by-step explanation:
We need to draw the graph of piece wise function
[tex]f(x)\[ \begin{cases} -2-x & if\:x\leq 1 \\ -3+2x & if\: x>1 \end{cases}\][/tex]
So, for drawing the graph, we will find values of f(x) for both the given equations.
First finding f(x) for [tex]-2-x \:\: if\:x\leq1[/tex]
The value of x must be less than or equal 1
x f(x)
1 -3
0 -2
-1 -1
-2 0
-3 1
-4 2
The graph will start from closed circle because x ≤ 1
Now, finding values of f(x) for [tex]-3+2x\: if\:x>1[/tex]
The value of x must be greater than 1
x f(x)
2 1
3 3
4 5
5 7
The graph will start from open circle because x> 1
Now, plotting these numbers we will get graph of Option C.
Option C is correct answer.
Select the correct answer.
You're given three angle measurements of 30°, 70°, and 80°.
How many triangles can you construct using these measurements?
A. 0
B. 1
C. 2
D. Infinitely many
Answer:
The answer is not 1 or 0
I think its D. infinitely many
Step-by-step explanation:
How long does it take for an investment to quadruple in value if it is invested at 11% compounded
continuously? Type the exact answer as your answer (no decimal approximations).
Let's assume we have $100 and an interest rate of 7%. For the $100 to quadruple it means that the future value would be $400. Thus, because we are talking about compounding daily we will set us the equation as follows:
100 * (1+1.07)x = 400
Then we will take 400 and divide it by 100 getting:
1.07X = 4
Now we have encountered a problem where we do not know exponent, so we will use logarithm to calculate such and transform our equation to: Log1.07(4)=X
Using our calculator we will find that it takes about 20.4895 days to quadruple the money invested under 7% interest rate compounded daily.
2nd: Using the same $100 but with the rate of 5.5% compounded continuously we will be using A=PERT formula
where:
P (principal) is equal to hypothetical $100
E (e) is a mathematical constant, which is approximately 2.718
R (rate) is the interest rate, in our case it is 5.5%
T (time) is the time required for money to grow
A (amount) is the final amount desired, which is 4 times larger of $100, thus $400
We have the following:
400 = 100 * e0.055t
400/100 = e0.055t
4 = e0.055t
Then we will apply natural log to both sides of the equations and get the following:
ln(4) = ln(e0.055t)
Since e is the base of ln(x) the equation simplifies to:
ln(4) = 0.055t
Using the calculator to find ln(4) we are getting:
1.38629 = 0.055t
Lastly find t
t = 1.38629/0.055
t = 25.20535202
Plug the answers back to the original equation to verify the answers.
1st part of the question answer: t = 20.4895
2nd part of the question answer: t = 25.20535202
PLEASE HELP ME
Solve for X and Z
9514 1404 393
Answer:
x = 1z = 11Step-by-step explanation:
If we assume that the segment marked (2x+1) is a midsegment, then it is half the length of the parallel base:
2(2x+1) = 8x-2
4x +2 = 8x -2 . . . . eliminate parentheses
4 = 4x . . . . . . . . . . add 2-4x to both sides
1 = x . . . . . . . divide by 4
__
The above assumption makes the two segments marked with z-expressions be the same length:
3z = z +22
2z = 22 . . . . . . subtract z
z = 11 . . . . . . . . . divide by 2
The values of X and Z are 1 and 11, respectively.
1. Gold is an element. What does an element of gold contain? (S8P1.a) DOK 5 point
1
one kind of compound
O a single type of atom
O a simple mixture of different atoms
O one mixed substance of two different metals
What is x ?
-2x + 7x - 62 = 83
Answer:
x = 29
Step-by-step explanation:
Giving 40 points
Solve each system by substitution
Step-by-step explanation:
[tex] \underline{ \underline{ \text{Given}}} : [/tex]
-4x - y = 19 -------- Equation ( i ) x - 2y = -7 ----------- Equation ( ii )[tex] \underline{ \underline{ \text{To \: find}}} : [/tex]
Value of x & y[tex] \underline {\underline{ \text{ Solution}}} : [/tex]
From equation ( i ) :
-4x - y = 19
-y = 19 + 4x
-y = - ( -19 - 4x )
y = -4x - 19 ------ Equation ( iii )
Substituting the value of y from equation ( iii ) in equation ( ii ) , we get :
[tex] \tt{x - 2y = - 7 }[/tex]
⇾ [tex] \tt{x - 2( - 4x - 19) = - 7}[/tex]
⇾ [tex] \tt{x + 8x + 38 = - 7}[/tex]
⇾ [tex] \tt{9x = - 7 - 38}[/tex]
⇾ [tex] \tt{9x = - 45}[/tex]
⇾ [tex] \tt{x = \frac{ - 45}{9}} [/tex]
⇾ [tex] \boxed{ \tt{x = - 5}}[/tex]
Substituting the value of x in equation ( i ) , we get :
⇾ [tex] \tt{ - 5 - 2y = - 7}[/tex]
⇾ [tex] \tt{ - 2y = - 7 + 5}[/tex]
⇾ [tex] \tt{ - 2y = - 2}[/tex]
⇾ [tex] \tt{y = \frac{ - 2}{ - 2}} [/tex]
⇾ [tex] \boxed{ \tt{y = 1}}[/tex]
The possible solution of the system is ordered pair ( x , y ) = ( -5 , 1 ) .
[tex] \red{ \boxed{ \boxed { \tt{Our \: final \: answer : \boxed{ \tt{( - 5 \:, 1 \: )}}}}}}[/tex]
Hope I helped ! ツ
Have a wonderful day / night ! ♡
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my head is empty for now, i rly can't with online classes
so anyone wanna help me?
Answer:
The Y intercept is (0,7)
Step-by-step explanation:
If it is a y intercept, there will be a number in the y coordinate. For example, (x,y) if the point said (7,0) that would be the x intercept. Because it it (0,7) and in the y place that makes it a y intercept. I hope this helped :)
I REALLY NEED HELP ON THIS!!! The graph below shows the amount of snowfall recorded in New York during that time. Write an equation to represent the relationship between amount of snow accumulated and time.
Answer:
Y=.5x
Step-by-step explanation:
For every hour you gain half an inch of snow so for every 2 hours you gain one inch of snow. Hope ths helps
Which statements are true? Select all that apply.
9514 1404 393
Answer:
A, B, D
Step-by-step explanation:
The figure is symmetrical about the horizontal centerline, so triangles, angles, and segments above that line are congruent with corresponding segments below that line. Choices A, B, D are true statements.
__
There is nothing in the figure to indicate that ΔFGK is isosceles, so statement C cannot be considered to be true.
Solve for x.
And solve for Z
From Tales theorem: [tex]\dfrac{8x-2}{2x+1}=\dfrac{3z+z+22}{3z}[/tex]
Solving for x:[tex]\dfrac{8x-2}{2x+1}=\dfrac{4z+22}{3z}\\\\(8x-2)(3z)=(2x+1)(4z+22)\qquad\qquad\{divide\ both\ sides\ by\ 2\}\\\\(4x-1)(3z)=(2x+1)(2z+11)\\\\12xz-3z=2x(2z+11)+1(2z+11)\\\\12xz-2x(2z+11)=3z+2z+11\\\\x(12z-4z-22)=5z+11\\\\x(8z-22)=5z+11\qquad\qquad\{divide\ both\ sides\ by\ (8z-22)\}\\\\x=\dfrac{5z+11}{8z-22}[/tex]
Solving for z:[tex]\dfrac{8x-2}{2x+1}=\dfrac{4z+22}{3z}\\\\(8x-2)(3z)=(2x+1)(4z+22)\qquad\qquad\{divide\ both\ sides\ by\ 2\}\\\\(4x-1)(3z)=(2x+1)(2z+11)\\\\(12x-3)(z)=(2x+1)(2z)+(2x+1)(1)\\\\(12x-3)(z)-(4x+2)(z)=(2x+1)\\\\\ [(12x-3)-(4x+2)](z)=(2x+1)\\\\(12x-3-4x-2)(z)=(2x+1)\\\\(8x-5)(z)=(2x+1)\qquad\qquad\{divide\ both\ sides\ by\ (8x-5)\}\\\\z=\dfrac{2x+1}{8x-5}[/tex]
Pierre had $42 before he paid his club dues. Evaluate the expression 42 − d for d = 25 to find how much money Pierre had left after he spent $25 on dues
Answer:Pierre has $17 left
Step-by-step explanation:
Amount of money before dues = $42
according to the expression 42-d, d represents dues= $25
Amount left = Amount of money before dues - Amount of dues
= $42- $25
=$17
Pierre has $17 left after he spent $25 on dues.
BlacIf w = -2 and v = -8, which of the following expressions shows the values correctly substituted in for the variables in the expression w2 - v + 1?
(-2) 2 - (-8) + 1
(-2) 2 - (8) + 1
-2 2 - (-8) + 1
-2 2 - 8 + 1
Answer:
-2² - (-8) + 1
Step-by-step explanation:
The values given are:
w = -2 and v = -8
Expression given:
w² - v + 1
When we substitute, we put a certain value in place of another. In an equation, variables are used as placeholders.
For this problem:
w = -2
v = -8
So;
-2² - (-8) + 1
Answer:
Given that w=-2 and v=-8
The expression is w²-v+1
Now putting the value of w=-2 and v=+8 in the given expression, we get
(-2)²-(-8)+1
Hence, (-2)²-(-8)+1 is the right answer.
20x^2/12x+8 simplified
Which one is linear
7x (6 x t) and (7 x 6) x t
If your question is which propperty is used in that opperation
Answer: The commutative property of multiplication
Step-by-step explanation: The comutative property of multiplication says that the order in which elements are multiplied the result is the same.
2. Solve the equation for x.
14 - x = 5x - 4
Answer:
x=3
Step-by-step explanation:
14-x=5x-4
Add the x from the left side to the right
14=6x-4
and the 4 to the left side
16=6x
6x=18
x=3
Answer:
x = 3
Step-by-step explanation:
If we substitute x for 3 it will give u the following expression:
14 - 3 = 5 x 3 - 4
If we solve both these expressions they will both give us: 11
This will prove the equation correct
Suppose a city with a population of 400,000 has been growing at a rate of 3% per year what will the population be in the next 19 years
Solve this equation. Please show work.
log(4m-10)=1
Answer:
m=5
Step-by-step explanation:
1. Convert the logarithm into exponential form using the fact that [tex]log_{a}[/tex](x)=b is equal to x=[tex]a^{b}[/tex] so ... 4m-10=[tex]10^{1}[/tex]
2. Any expression raised to the power of 1 equals itself so ... 4m-10=10
3. Move the constant to the right-hand side and change its sign so ... 4m=10+10
4. Add the numbers so ... 4m=20
5. Divide both sides of the equation by 4 so ... m=5, m>[tex]\frac{5}{2}[/tex]
6. Check if the solution is in the defined range so ... m=5
z=2 = 27
_____ __
4 12
Answer:
hmmmmmm
i believe that the answer is _
because of _
(i helped w/ your other one lol)
Step-by-step explanation:
Please help, pic attached!
Answer:
(y − 9) (y − 2)
Step-by-step explanation:
Factor y^2 − 11y + 18 using the AC method.
(y − 9) (y − 2)
The “AC” method or factoring by grouping is a technique used to factor trinomials. A trinomial is a mathematical expression that consists of three terms.
what is the value or |-12.7| and |11.1/4| ?
Answer:
12.7, because the absolute value gets rid of the negative integer, and shows it true value which is positive 12.7.
Step-by-step explanation: Have a Happy Thursday :)
the difference of a number t and 9
t-9 or 9-t