Answer:
see explanation
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
(a)
given the equation of L1 is
2x - y = 3 ( subtract 2x from both sides )
- y = - 2x + 3 ( multiply through by - 1 )
y = 2x - 3 ← in slope- intercept form
with slope m = 2
• Parallel lines have equal slopes
then slope of L2 is m = 2
given the equation of L2 is
kx + 2y = 3 ( subtract kx from both sides )
2y = - kx + 3 ( divide through by 2 )
y = - [tex]\frac{k}{2}[/tex] + [tex]\frac{3}{2}[/tex] ← in slope- intercept form
with slope m = - [tex]\frac{k}{2}[/tex]
since slope of L1 and L2 are equal, both 2 , then
- [tex]\frac{k}{2}[/tex] = 2 ( multiply both sides by 2 to clear the fraction )
- k = 4 ( multiply both sides by - 1 )
k = - 4
----------------------------------------------
(b)
given the slope of a line is m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{2}[/tex]
Then
for L2 to be perpendicular to L1
- [tex]\frac{k}{2}[/tex] = - [tex]\frac{1}{2}[/tex] ( multiply both sides by - 1 )
[tex]\frac{k}{2}[/tex] = [tex]\frac{1}{2}[/tex] , thus
k = 1
James earned a total of $68 last week. He earned $48 washing cars and won x dollars in an art contest. Which equation can be used to find the number of dollars James won in the art contest?
Answer:
Step-by-step explanation:
since $68 is your total, let's use the example z=y+x
z is our total, and we know that he made a total of $68, therefore z is the number 68.
We also know that James made a total of $48 washing cars, which gives us the answer 48 as y. So in order to find x, we would need to subtract 68 and 48, which is called using the communtative property. Thsi answer would give us the remaining amount of money we do not yet know.
So 68-48= 20. therefore James made $20 at the art contest.
What is the radius of 6 inches
Answer:
28.27 sq. units or 9π sq.
Step-by-step explanation:
Sam tries to draw lines of reflection through a rectangle so that the rectangle can be reflected onto itself. How many lines of reflection can sam draw? enter the answer in the box.
Therefore the solution of this question is Sam can draw 2 lines of reflection.
What is line of reflection?If a figure is reflected in a line or a point, the image and preimage are consistent. A reflection converts each point in a figure into an image along a predetermined line. Line of Reflection refers to the fixed line.
To determine the quantity of lines that will reflect a rectangle back onto itself.
Due to the fact that the line of reflection is the perpendicular bisector of the segment connecting a point with its image. The perpendicular bisector of a side must be the line of reflection if one side of the rectangle is to map to itself.
A rectangle has two distinct perpendicular bisectors of its sides, leading to two lines of reflection that map a rectangle to itself.
Therefore Sam can draw 2 lines of reflection.
To know more about line of reflection , visit
https://brainly.com/question/17370055
#SPJ4
A polygon has vertices at (-5, 3), (-1, 3), (1, 0), and (-3, 0). Which represents a geometric translation of the give
polygon 4 units to the right and 5 units down?
Answer:
(-1, 3), (3, 3), (5, 3), (1, 0)
Step-by-step explanation:
A translation of 4 units to the right means adding 4 to every x-coordinate.
The new coordinates are:
(-1, 3), (3, 3), (5, 3), (1, 0)
suppose the continuous random variable, x, is uniformly distributed between 2 and 10. what is the probability that x is either less than 3 or greater than 8?
The probability that x is either less than 3 or greater than 8 is 0.375 .
In the question ,
it is given that ,
a continuous random variable X , is uniformly distributed between 2 and 10 ,
So , alpha(α) = 2 and beta(β) = 10 .
the probability that x is either less than 3 or greater than 8 can be calculated by :
P(X < 3 or X > 8) = 1 - (8 - 3)/(β - α)
= 1 - (8 - 3)/(10 - 2)
= 1 - 5/8
On simplifying further ,
we get ,
= 0.375
Therefore , the probability P(X < 3 or X > 8) is = 0.375 .
Learn more about Probability here
https://brainly.com/question/13796457
#SPJ4
The points L(5,0) , M(-4,0) and N(5,-4) form a triangle find the perimeter of the triangle . Round your answer to the nearest tenth if necessary .
Answer:
9.1 units
Step-by-step explanation:
See diagram below ....using pythagorean theorem
In Michael’s closet he can choose from a yellow, green, or orange shirt, navy or gray shorts, and tennis shoes or sandals. Create a table to represent the various clothing options.
The table is attached below.
What are table entries?
Entities are gathered at tables. A group of properties makes up an entity. Each object may contain up to 252 name-value pairs for its properties.
From the information given, we can make a table to display all the options available for Michael to choose clothing options.
The table is attached as follows:
To learn more about tables, visit the following link:
https://brainly.com/question/16411173
#SPJ1
There are 12 clothing options for Michael to choose from in his closet. By the fundamental principle of counting, the possible number of options is calculated.
What is the fundamental principle of counting?The fundamental principle of counting states that an operation/event can be performed in 'm' ways and a second operation/event can be performed in 'n' ways. Then there are (m × n) ways for the two operations to be performed together.
Calculation:It is given that,
Michael is having three shirts - yellow, green, and orange; two pairs of shorts: navy, gray and two footwear: tennis shoes and sandals.
So, we can write
the number of shirts = 3
the number of shorts = 2
the number of footwear = 2
Then, according to the fundamental principle of counting, all these are multiplied to get the total number of ways that he can wear them together.
I.e., 3 × 2 × 2 = 12
Therefore, there are 12 combinations for him to choose one among these.
Learn more about the fundamental principle of counting here:
https://brainly.com/question/10275154
#SPJ1
I need help with this geometry please i don’t understand. Just #1 please
Answer:
a) CE=PR
b) TR=FE
c) <F=<T
d) <P=<C
e) RPT=ECF
Step-by-step explanation:
Mr. Reynolds, the gym teacher, divided a class of 16 students into 2 equal teams. How many students were on the team?
Answer:
8
Step-by-step explanation:
16 divided by 2 is 8.
Answer: 8 students
Step-by-step explanation: 16/2=8
function rule to find f(11).
the next question is more point go check it out after you answer this question!!!!!
The solution for f(11) in the function when the function f(x) = 12|x + 8| is 228
How to determine the solution for f(x) in the function?From the question, we have the following equation that can be used in our computation:
f(x) = 12|x + 8|
The above equation is an absolute value equation
An absolute value equation has the following representation
f(x) = a|x - h| + k
So, we have the following representation
f(x) = 12|x + 8|
Also from the question, we have
f(11)
This means that the value of x is 11, and we calculate f(x) when x = 11
Substitute the known values in the above equation, so, we have the following representation
f(11) = 12|x + 8|
So, we have the following equation
f(11) = 12|11 + 8|
There are constants to add or subtract to both sides of the equation
Also, there are factors to multiply or divide from both sides of the equation
So, we have the following representation
f(11) = 12|19|
Solving further, we have
f(11) = 12 * 19
Evaluate the products
f(11) = 228
Hence, the solution is 228
Read more about functions at
brainly.com/question/28277110
#SPJ1
Which equation models the relationship between the two variables in the table below?
2343H
5
-7
-10
-13
y=-2z
y=-3z+2
1=-3z
IN
y=-2z-3
Answer:
2nd equation
Step-by-step explaination:
1st. -7≠-2(3)
2nd. Sastifies all
3rd. -10≠-3(4)
4th. -4≠-2(2)-3
Arrange the steps in the correct order to solve the equation,
3(22-5) - 4 = 10
Add 4 to each side of the
equation:
3/22 - 5) = 14
Use the Exponential Property and
write in decimal form:
(2 - 5)log2 = log4. 67
log4. 67
Find the value of Toga
and substitute
2-5 = 2. 23
Simplify
23. 625
Take the log of each side:
log(22+ - 5) = log('9).
2 - 5 - 1034. 87
Divide each side by log 2
Tog?
Add 5 to each side of the
equation
2+ = 2. 23 +5
Divide both sides of the equation
The correct order to solve the equation is given below .
In the question ,
it is given that ,
the equation is 3*([tex]2^{2 t - 5}[/tex]) - 4 = 10 ,
Step(1) , adding 4 to each side of the equation ,
3*([tex]2^{2 t - 5}[/tex]) = 14
Step(2) , dividing both sides of the equation by 3 ,
we get , ([tex]2^{2 t - 5}[/tex]) = 14/3 .
Step(3) , taking log on each side ,
log([tex]2^{2 t - 5}[/tex]) = log(14/3)
Step(4) , Using the Exponential Property and writing 14/3 in decimal form ,
we get ,
(2t - 5)*log(2) = log(4.67)
Step(5) , Dividing each side by log(2) ,
we get , 2t-5 = log(4.67)/log(2) .
Step(6) , Add 5 to each side of equation
we get , 2t = 2.23 + 5 ;
Step(7) , Simplifying we get ,
we get , t = 3.625 .
Therefore , the the solution of the given equation is t = 3.625 .
The given question is incomplete , the complete question is
Arrange the steps in the correct order to solve the equation,
3*([tex]2^{2 t - 5}[/tex]) - 4 = 10 .
Learn more about Equations here
https://brainly.com/question/7102383
#SPJ4
Vincent is completing his math homework about the process of Completing the Square to solve quadratic equations. His work is shown below.
solve: x²-3x+7=0
step 1: x²-3x = -7
step 2: x²-3x+9=-7 +9
step 3: (x-3)² = 2
step 4: X-3= = √2
x=3 = √2
Did Vincent make a mistake as he solved the quadratic using Completing the Square? If so, in what
step did he first make a mistake? (Step numbers are labeled in blue on the left)
Answer:
Step-by-step explanation:
He made a mistake in step one turning the 7 into a -7
[tex]x^{2}[/tex] - 3x + 7 = 0
Solving:
[tex]1x^{2}[/tex] - 3x + 7 = 0 ← If the term doesn't have a coefficient, it is considered that the coefficient is 1.
[tex]1x^{2}[/tex] + (-3x) + 7 = 0 ← Identify the coefficients a, b, and c of the quadratic equation.
a = 1, b = -3, c = 7
x = - (-3) ±√[tex](-3)^{2}[/tex] - 4 x 1 x 7
2 x 1
x = 3 ± √[tex](3)^{2}[/tex] - 4 x 7
2
x = 3 ± √9 - 4 x 7
2
x = 3 ±√9 - 28
2
x = 3 ± √-19
2
The square root of a negative number does not exist in the set of real numbers.
x = ∉ R
find the slope of the line through (1,-1) and (6,2
Answer:3/5
Step-by-step explanation:
(y2-y1)/(x2-x1)
(2-(-1))/(6-1)=3/5
i’m so lost and i really need help :’). this is 9th grade algebra
Answer:
1 and 2 are functions, 3 is not a function.
Step-by-step explanation:
One x-value can lead to one y-value. If the x-value leads to more than one y-value like #3, then the relation is not a function.
If each input value leads to only one output value, classify the relationship as a function. If any input value leads to two or more outputs, do not classify the relationship as a function.
a. Prove ABD is congruent to CBD.
b. Determine whether all four triangles in the diagram are congruent.
c. Explain your reasoning.
Answer:
a. The proof is in your picture
b. Yes
c. All four triangles are congruent by the HL theorem
Step-by-step explanation:
Given AB≅CB in ∆ABC with BD⊥AC, you want to show ∆ABD≅∆CBD, and you want to know if these are congruent to ∆CEG and ∆FEG.
a. Left trianglesYour picture correctly shows a proof that ∆ABD≅∆CBD by the HL postulate.
b. Right trianglesSides CE and FE are marked congruent to each other and sides AB and CB. The altitudes BD and EG of these isosceles triangles are marked as congruent. Hence all four triangles, ∆ABD, ∆CBD, ∆CEG, and ∆FEG are congruent by the HL theorem.
c. All trianglesThe same HL theorem reasoning applies to all of the triangles.
__
Additional comment
The distance from the light to the stage is said to be the same for both lights. That would be measured perpendicular to the stage, and is the shortest such distance. We are assuming that BD and EG are those perpendicular distances, as we see no markings on the diagram indicating right angles.
Two fair number cubes have faces labeled with the numbers 1 through 6. The two cubes will be rolled simultaneously. What is the probability that at least one of the cubes will have the face labeled 5 showing and that the sum of the showing faces will be greater than 8 ?.
The probability that at least one of the cubes will have the face labeled 5 showing and that the sum of the showing faces will be greater than 8 is 5/36.
What is the probability?A probability is a numerical representation of the possibility or chance that a specific event will take place. Probabilities can be written as percentage between 0 and 1.
Number of sample spaces that are labeled 5 and display a sum more than 8 / total sample space gives the likelihood that at least one of the cubes will have the face labeled 5 showing and that the sum of the faces showing will be greater than 8.
When two cubes are rolled, the total sample space is 36.
The sample space that is labelled 5 and has a sum greater than 5 are: (4,5) , (5, 4) , (5, 5), (5, 6) , (6,5) = 5
The probability = 5/36
To know more about probability check the link:
brainly.com/question/11234923
#SPJ4
Rotate triangle P 90° clockwise about the point (2, -1).
54
3
2
1
-5 -4 -3 -2 -1 0
-1
2345
-4
1 2 3 4 5
P
Answer:
p=12345
Step-by-step explanation:
Answer:
see attached
Step-by-step explanation:
You want the graphed triangle rotated 90° CW about the point (2, -1).
RotationAfter rotation 90° CW, points will be as far to the south and west of the center of rotation as they are east and south in the original image. This is shown by the blue triangle in the attachment.
please help me i’ve got midterms and i’ve been stuck on this for like 45 minutes Dx
Answer:
f(x) = ³√(x–1) + 4
f-¹(x) = (x + 1)³ + 4
Step-by-step explanation:
i hope this helped
Answer the question and help a brother out
Answer:
25
Step-by-step explanation:
first add the degrees: 50+30+25=105, then 180-105 is 75, 75=3s, s is 25
(im not sure completely im only in 7th grade)
help me pleaseeeeeeeeeeeeeeeeeeeeee!!!!!!!!!!!!!!!!
Answer: omg never seen somthing dat complex :O
Step-by-step explanation:
Consider the system of equations
5x+3y=30
−5x−2y=−25
Part A: Solve the system. Show your work.
_______
Part B: Use the solution to your equation to find the value of x – y. Show your work.
x−y = _____
By solving the two equations, the values of x , y and x-y are found to be 1, 25/3 and -22/3 respectively.
Given two equations are;
5x+3y=30..........(1)
−5x−2y=−25.........(2)
Now , from (2)
−5x−2y=−25
⇒ 5x +2y = 25 (multiply both sides with '-' sign)
⇒ y = [tex]\frac{(25 -5x)}{2}[/tex]
Solving the system;
substitute the above vale of y in eq (1)
5x + 3y = 30
⇒ 5x + 3 ( [tex]\frac{(25 -5x)}{2}[/tex]) = 30
⇒ 5x + ([tex]\frac{(75 - 15x)}{2}[/tex]) = 30
⇒ [tex]\frac{10x+75-15x}{2}[/tex] = 30
⇒ -5x + 75 = 60
⇒ -5x = -5
⇒ x = 1
∴ x = 1
Now substitute the value of x in (1)
5x + 3y = 30
⇒ 5 × 1 + 3y = 30
⇒ 3y = 25
⇒ y = 25/3
∴ y = 25/3
Now using the value of x and y , we can find the value of x - y
x - y = 1 -25/3 = (3 - 25)/ 3 = -22/3
∴ x - y = -22/3
Learn more about solving equation here;
https://brainly.com/question/22688504
#SPJ1
i need help with this question
Answer: it’s B
Step-by-step explanation: Look at the graph clearly
and you will see the value of x and y
Aaliyah is going to invest in an account paying an interest rate of 5% compounded continuously. How much would Aaliyah need to invest, to the nearest hundred dollars, for the value of the account to reach $181,000 in 19 years?
Based on the given parameters, the value of the money to invest initially is $99341.383
How to determine the amount of investment?The given parameters about the compound interest are
Amount, A = $181000
Interest Rate, R = 5%
Time, t = 19 years
Number of times, n = 365 i.e. continuously
To calculate the amount, we have:
A = P + CI
Where
C = P(1 + R)^t
So, we have
A = P(1 + R)^t
This can be rewritten as
A = P(1 + R/n)^nt
Substitute the known values in the above equation
181000 = A * (1 + 5%/365)^(12*365)
So, we have
A = 181000 /[(1 + 5%/365)^(12*365)]
Evaluate the expression
A = 99341.383
Hence, the amount of the investment is $99341.383
Read more about compound interest at:
brainly.com/question/13825593
#SPJ1
in 2016, a 1952 Willie Mays rookie card from Topps sold for $478,000! Currently, a toaster may cost $25. How many toasters could you buy with the money spent on the willie Mays rookie card?
Answer: 19120 Toaster
Step-by-step explanation: We just need to take $478000 divided by 25, equal to 19120 Toaster!
J53)
a) what i the x-coordinate of every point along thi line?
b) ue your anwer to ue part a) to write the equation of the line
The abscissa or x-coordinate of any point on Y-axis is zero.
Which line is the x-coordinate?
Two parallel lines, known as axes (pronounced AX-eez), that are perpendicular to each other make up a coordinate grid. Typically, the term "x-axis" refers to the horizontal axis. The y-axis is the common name for the vertical axis.
The ordinate and abscissa are other names for the x-axis and y-axis, respectively. These two axes can be used to find or represent any point on the coordinate plane as an ordered pair of the form (x,y).
The equation of a line is typically written as y=mx+b where m is the slope and b is the y-intercept.
In order to represent the equation in y-intercept (y=mx+b) form, the slope and y-intercept must be included. The slope is the ratio of the y-to-x change. Draw a sloping triangle connecting the two spots you find on the line.
To learn more about equation visit:https://brainly.com/question/29657992
#SPJ4
is 0.04x=y proportional
Which best describes Nosaira’s work and answer?
Her work is correct, but there is one solution rather than no solution.
Her work is correct and her interpretation of the answer is correct.
Her work is incorrect. She distributed incorrectly.
Her work is incorrect. She moved terms across the equals sign incorrectly.
Answer: A
Step-by-step explanation:
Write an equation in slope-intercept form of the line that is parallel to the one given and passes through the given point
(1,3); y=7x+5
What is the equation for the line in slope-intercept form?
Answer:
y = -2x - 4
Step-by-step explanation:
y = mx +b is the slope intercept form of a line. The m is the slope and the b is the y intercept.
The y intercept is where the line crosses the y axis. It crosses at the point (0,-4). The -4 is where the line crosses the y axis. It is the b.
The slope is the change in y over the change in x. To go from point (0,-4) to the point (-2,0) You go up 4 units and the left 2 units. Up is positive and left is negative. 4/-2 which simplifies to -2. This is your m.