Answers
Answer:
m₁×m₂ = -1
m₁ = 3 and m₂ = -1/3
3×-1/3 = -1
-1 = -1
Hence proved, the given two lines are perpendicular.
Step-by-step explanation:
You can prove that the two lines are perpendicular if the following condition holds true.
m₁×m₂ = -1
Where m₁ is the slope of line 1 and m₂ is slope of line 2
So first you have to find out the slope of each line.
You are given 2 equations
y = 3x + 5 eq. 1
6y + 2x = 1 eq. 2
You have to write these equations in slope-intercept form to find out their slopes.
The slope-intercept form is given by
y = mx + b
Comparing the general form with eq. 1
y = 3x + 5
We notice that the slope is m₁ = 3
Now convert the eq. 2 into slope-intercept form
6y + 2x = 1 eq. 2
6y = -2x + 1
y = (-2x + 1)/6
y = -1/3x + 1/6 eq. 2
Comparing the general form with eq. 2
y = -1/3x + 1/6
We notice that the slope is m₂ = -1/3
Now we have slopes of both lines so let us test whether they are perpendicular or not
m₁×m₂ = -1
m₁ = 3 and m₂ = -1/3
3×-1/3 = -1
-1 = -1
Hence proved, the given two lines are perpendicular.
Related Questions
What’s the error mica make?
Answers
Step-by-step explanation:
She should have added 2 to the 3, not 1 because on the right side, she added 1, but that was being multiplied by 2 so to balance the equation she should add 2 to the 3. Hope this helps!
What is 3/4 + 1/5 equal to?
Answers
Answer:
[tex]19/20[/tex]
Step-by-step explanation:
[tex]3/4+1/5[/tex]
[tex]15/20 + 4/20[/tex]
[tex]19/20[/tex]
Answer:
[tex] = \frac{19}{20} [/tex]
Step-by-step explanation:
[tex] \frac{3}{4} + \frac{1}{5} \\ \frac{15 + 4}{20} \\ = \frac{19}{20} [/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
A gym offers three levels of membership based on the number of visits per month, as represented by the table. Kaleigh wants to know how much she will pay for her gym membership. Which graph represents the total monthly cost at the gym as a function of the number of visits Kaleigh plans to make each month?
Answers
Answer:
graph one
Step-by-step explanation:
Let
x ----> the number of visit per month
y ----> the total cost
we know that
Observing the table
1) For the interval of x equal to ----> [0,12] (close circle both points)
The domain is all whole numbers greater than or equal to 0 visits and less than or equal to 12 visits
The value of y is
y=5x+15
For x=0 ----> y=$15
For x=12 ----> y=5(12)+15=$75
The range is the interval ----> [15,75] (close circle both points)
All real numbers greater than or equal to $15 and less than or equal to $75
2) For the interval of x equal to ---->(12,16] (open circle at left and close circle at right)
The domain is all whole numbers greater than 12 visits and less than or equal to 16 visits
The value of y is
y=4x+32
For x=12 ----> y=4(12)+32=$80
For x=16 ----> y=4(16)+32=$96
The range is the interval ----> (80,96] (open circle at left and close circle at right)
All real numbers greater than $80 and less than or equal to $96
3) For the interval of x equal to ---->(16,24] (open circle at left and close circle at right)
The domain is all whole numbers greater than 16 visits and less than or equal to 24 visits
The value of y is
y=3x+42
For x=16 ----> y=3(16)+42=$90
For x=24 ----> y=3(24)+42=$114
The range is the interval ----> (90,114] (open circle at left and close circle at right)
All real numbers greater than $90 and less than or equal to $114
please mark me brainliest!
The graph that represents the total monthly cost at the gym as a function of the number of visits in a month is shown by option A)
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Based on the number of visits each month, a gym provides three different levels of membership.
Let the monthly visits be 'a' and the overall expense be 'b'. The following will be the appropriate graph showing the total monthly cost of the gym as a function of monthly visits:
A) For the interval of a = [0,12]
The value of b is given by:
b = 5a + 15
when a = 0 in the above equation.
b = $15
when a = 12 in the above equation.
b = 60 + 15
b = $75
The interval of b = [15,75]
B)
For the interval of a = [12,16]
The value of b is given by:
b = 4a + 32
when a = 12 in the above equation.
b = 48 + 32
b = $80
when a = 16 in the above equation.
b = 64 + 32
b = $96
The interval of b = [80,96]
C)
For the interval of a = [16,24]
The value of b is given by:
b = 3a + 42
when a = 16 , we get
b = 48 + 42
b = $90
when a = 24 in the above equation , we get
b = 72 + 42
b = $114
The interval of b = [90,114]
Hence , the graph is represented by graph A
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There are 32 students in Mrs. Nyer's class. This is 8% of the students in the
school. How many students are in the school?
Answers
WILL MARK BRAINIEST ASAP PLEASE HELP!!!!!!!!!!!!!!11111 What is the coefficient of the c-term of the algebraic expression 14 a minus 72 r minus c minus 34 d? -34 -1 0 1
Answers
Answer:
The correct answer would be -1
Step-by-step explanation:
Answer:
-1 I believe
Step-by-step explanation:
Question of the day
Fill in the table of values below for the equation y=x+3
Х
у
Answers
x | y
———-
0 | 3
1 | 4
Slope: 1
Y-intercept: 3
Answer:
yuuurrrppp
Step-by-step explanation:
determine the slope of a line that passes through A(-4, 7) and B(6,3)
Answers
Answer:
-2/5
Step-by-step explanation:
The slope is found by
m= (y2-y1)/(x2-x1)
= (3-7)/(6 - -4)
= -4/(6+4)
- 4/(10)
= -2/5
Answer:
[tex]m=\frac{-2}{5}[/tex]
Step-by-step explanation:
Use the formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Plug in the numbers (coordinates) given, like so:
[tex]m=\frac{3-7}{6+4}[/tex]
[tex]m=\frac{-4}{10}[/tex]
Simplify:
[tex]m=\frac{-2}{5}[/tex]
A recipe requires 1/3 cup of sugar for every 3/4 cup of flour. How many cups of sugar are required for every cup of flour?
Answers
Answer:
4/9 cup of sugar
Step-by-step explanation:
[tex]\frac{1}{3} cup of sugar= \frac{3}{4} cup of flour[/tex]
[tex]? cup of sugar=1 cup of flour[/tex]
so crisscross them and finally you'll get
1/3*4/3=4/9
For 1 cup of flour, 4/9 cups of sugar is needed.
What are ratios and proportion?Ratio is a quantitative relation between two amounts showing the number of times one value contains or is contained within the other. A statement expressing the equality of two ratios A:B and C:D is called a proportion. We can express proportion as -
A : B ∷ C : D
AND
A x D = B x C
Product of extremes equal to product of means.
Given is a recipe that requires 1/3 cup of sugar for every 3/4 cup of flour.
Now -
For 1/3 cup of sugar = 3/4 cup of flour is needed.
For 1 cup of flour = (1/3)/(3/4) cups of sugar = 1/3 x 4/3 = 4/9 cups of sugar is needed.
Therefore, for 1 cup of flour, 4/9 cups of sugar is needed.
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There are already 1,600 gallons of water in a swimming pool. If water is filling the pool at a rate of 25 gallons per minute, which expression indicates the amount of water, in gallons, in the swimming pool after m minutes?
Answers
The expression that indicates the amount of water, in gallons, in the swimming pool after m minutes is 1600 + 25m.
What is an expression?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.
In this case, there are already 1,600 gallons of water in a swimming pool and water is filling the pool at a rate of 25 gallons per minute.
Let m = number of minutes
The expression will be:
1600 + (25 × m)
1600 + 25m
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A square has a perimeter of 44cm. Calculate the area of the square.
The most relevant aka correct answer will get brainiest :)
Answers
Answer:
p = 44cm
perimeter of a square = 4l
44/4 = 11
area = l²
area = 11²
area = 121cm²
Step-by-step explanation:
A person invests 6500 dollars in a bank. The bank pays 7% interest compounded
quarterly. To the nearest tenth of a year, how long must the person leave the money
in the bank until it reaches 20100 dollars?
A= P(1 + -]nt
Answers
Answer:
t=16.2 years
Step-by-step explanation:
A=p(1+r/n)^nt
A=$20100
P=$6500
r=7%=0.07
n=4
t=?
t=ln(A/P)/n {ln(1+r/n)}
=ln(20100/6500) / 4{ln(1+0.07/4)}
=ln(3.0923)/4{ln(1+0.0175)}
=ln(3.0923)/4{ln(1.0175)}
=1.1289/4(0.0174)
=1.1289/0.0696
=16.23
To the nearest tenth
t=16.2 years
Of the 650 students at westMoreland junior high ,80% will attend the field trip . How many students will attend the field trip ?
Answers
Answer:
520
Step-by-step explanation:multiply 650 by 80 amd then divide by 100
or simply multiply 650 by 0.8
520 number of students will attend the field trip.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given that there are 650 students at westMoreland junior high.
80% of the students will attend the field trip.
We need to find the students will attend the field trip.
We need to find what is 80% of the 650.
firstly let us convert 80% to decimal by dividing 80 with 100.
80/100=0.8
Now multiply 0.8 with 650
0.8×650
Zero point eight × Six hundred fifty.
520
Hence, 520 number of students will attend the field trip.
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Find the perimeter of a triangle with side lengths of
√80
√20, and √45
Answers
The exact answer is=
20.125
Make x the subject of Y=4x+3
Answers
The value of x from the expression is,
⇒ x = 1/4 (Y - 3)
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The equation is,
⇒ Y = 4x + 3
Now, We can solve the expression for the value of x as;
⇒ Y = 4x + 3
Subtract 3, we get;
⇒ Y - 3 = 4x + 3 - 3
⇒ Y - 3 = 4x
Divide by 4;
⇒ (Y - 3) / 4= 4x/4
⇒ (Y - 3)/4 = x
⇒ x = 1/4 (Y - 3)
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Which is a better statistical question A:how many points per game did your team score? B:how many games did your team play this year?
Answers
Answer:
A
Step-by-step explanation:
B would be just a number, but for A you need to connect data points and actually do some statistics.
(would really, reallly appreciate the brainliest)
Answer:
A - how many points per game did your team score?
Solve 2y - 3 = 4y +6.
I
y=
Answers
Answer:
-9/2
Step-by-step explanation:
Begin by subtracting 2y from both sides
(2y - 2y) - 3 = (4y - 2y) + 6
-3 = 2y + 6
Then, subtract 6 from both sides
(-3 - 6) = 2y + (6 - 6)
-9 = 2y
Finally, divide by 2 on each side
(-9/2) = (2y/2)
y = -9/2
Which of the sequences is an arithmetic sequence?
I need help!!!!
Answers
the answer is (A) is arithmetic
Which table represents exponential growth?
Answers
Answer:
You haven't linked any tables?
Step-by-step explanation:
Is 6.584 a rational
number?
Answers
Answer:
Step-by-step explanation:
To get rid of the decimal point in the numerator, we count the numbers after the decimal in 6.584, and multiply the numerator and denominator by 10 if it is 1 number, 100 if it is 2 numbers, 1000 if it is 3 numbers, and so on.
Therefore, in this case we multiply the numerator and denominator by 1000 to get the following fraction: 6584 / 1000
Then, we need to divide the numerator and denominator by the greatest common divisor (GCD) to simplify the fraction.
The GCD of 6584 and 1000 is 8. When we divide the numerator and denominator by 8, we get the following: 823 / 125
Therefore, 6.584 as a fraction is as follows: 823 / 125
Which equations could you solve using the addition property of equality? Check all that apply. 4 + y = 100 y – 4 = 100 4y = 100 4 + 100 = y 100 = y – 5
Answers
Answer:
y-4=100 and 100=y-5
Step-by-step explanation:
Because the addition property of equality is: The property stating that adding the same number to both sides of an equation does not change the equation.
Equations are used to represent equal expressions
The equivalent equation of y + 4 = 100 is 4 + y = 100
How to determine the equationsThe equation is given as:
y + 4 = 100
Rewrite the equation as follows:
4 + y = 100
Hence, the equivalent equation of y + 4 = 100 is 4 + y = 100
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16:07:48
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Question: 1/20
The graph of which equation would be a circle with a center at
(2.3) and a radius of 7 ?
A. (x + 2y = (y - 3) = 7
B. (x - 2) = (y + 3) = 7
C. (x - 2y + (y + 3)2 = 49
D. (x - 2) - (y - 3)2 = 49
OB
Whats the correct choice?
Answers
Answer:
A. ( x + 2y = ( y - 3 ) = 7
maaf kalo salah
Scott traveled and left his home on his bicycle and went 2 miles to the beach. The trip took him 15 minutes. He returned home the same way at a speed of 6 miles per hour. How many hours did it Scott take to get back home?
Answers
It took him 20 minutes to get home going 6 mph.
Factor the given quadratic function x2 + 9x = 36.
Answers
Answer:
(x + 12)(x - 3)
Step-by-step explanation:
[tex] {x}^{2} + 9x = 36 \\ {x}^{2} + 9x - 36 = 0 \\ {x}^{2} + 12x - 3x - 36 = 0 \\ x(x + 12) - 3(x + 12) = 0 \\ (x + 12)(x - 3) = 0[/tex]
La base de una cartulina rectangular mide 8 cm de altura si le recortamos 3 cm a su altura el area de la nueva cartulina seria 126 cm calcula las dimenciones de la cartulina inicial
Answers
Answer:
[tex]w=8cm\\h=18.75cm[/tex]
Step-by-step explanation:
Let:
[tex]w=Width\\h=Initial\hspace{3}height\\h_m=Modified\hspace{3}height\\\\Where:\\\\h_m=h-3[/tex]
The area of the cardboard can be calculated using the formula to find the area of a rectangle:
[tex]A=w*h[/tex]
The area of the new cardboard would be:
[tex]A=w*h_m\\\\Where:\\\\w=8\\h_m=h-3\\A=126[/tex]
So:
[tex]126=8*(h-3)\\\\126=8h-24[/tex]
Solving for h:
[tex]126+24=8h\\\\150=8h\\\\h=\frac{150}{8} =\frac{75}{4} =18.75cm[/tex]
Therefore, the dimensions of the initial cardboard are:
[tex]w=8cm\\h=18.75cm[/tex]
Translation:
Sea:
[tex]w=Ancho\\h=Altura\hspace{3}inicial\\h_m=Altura\hspace{3}modificada\\\\Donde:\\\\h_m=h-3[/tex]
El área de la cartulina se puede calcular usando la fórmula para encontrar el área de un rectángulo:
[tex]A=w*h[/tex]
El área de la nueva cartulina sería:
[tex]A=w*h_m\\\\Donde:\\\\w=8\\h_m=h-3\\A=126[/tex]
Entonces:
[tex]126=8*(h-3)\\\\126=8h-24[/tex]
Resolviendo para h:
[tex]126+24=8h\\\\150=8h\\\\h=\frac{150}{8} =\frac{75}{4} =18.75cm[/tex]
Por lo tanto, las dimensiones de la cartulina inicial son:
[tex]w=8cm\\h=18.75cm[/tex]
Pls help me Is hard for me
Answers
Answer:
15
Step-by-step explanation:
3 yards in a ft, so 15 yards in 5 ft.
Answer:
15 feet.
Step-by-step explanation:
1 yard = 3 feet
5 yards = x feet
[tex]x=5 \times 3[/tex]
[tex]x=15[/tex]
PLEASE HELP GIVING BRAINLIEST TO ONLY CORRECT ANSWER
Answers
Answer:
I think option 3 but not sure
Step-by-step explanation:
Theoretical probability is what we expect to happen, where experimental probability is what actually happens when we try it out. The probability is still calculated the same way, using the number of possible ways an outcome can occur divided by the total number of outcomes.
Find the area of a circle with a diameter of 6.
Either enter an exact answer in terms of it or use 3.14 for I and enter your answer as a decimal.
units2
Answers
Answer:
A = 9pi
Step-by-step explanation:
The area of a circle is given by
A = pi r^2
We know the diameter
r = d/2 = 6/2 = 3
A = pi (3)^2
A = 9pi
Answer:
[tex]28.26 \: \: {units}^{2} [/tex]
Step-by-step explanation:
[tex]area \\ = \pi {r}^{2} \\ = 3.14 \times 3 \times 3 \\ = 28.26 \: \: {units}^{2} [/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
In a random survey of 226 college students, 20% reported being "only" children (no siblings). The standard deviation is 2%.
Determine the confidence interval that is likely to contain the percent of all students nationwide who are only children.
Answers
Answer:
The confidence interval that is likely to contain the percent of all students nationwide who are only children is (0.1505,0.2554)
Step-by-step explanation:
Total number of students = n = 226
We are given that 20% reported being "only" children (no siblings).
Number of students being "only" children (no siblings) [tex]= 20\% \times 226=\frac{20}{100} \times 226=45.6\sim46[/tex]
So, x = 46
[tex]p=\frac{x}{n}=\frac{46}{226}=0.203[/tex]
Z at 95% is 1.96
Formula for confidence interval for sample proportion :
[tex]CI=p \pm Z \times \sqrt{\frac{p(1-p)}{n}}[/tex]
Substitute the values in the formula :
[tex]CI=0.203 \pm 1.96 \times \sqrt{\frac{0.203(1-0.203)}{226}}\\CI=(0.1505,0.2554)[/tex]
Hence the confidence interval that is likely to contain the percent of all students nationwide who are only children is (0.1505,0.2554)
Point A is the midpoint of side XZ and point B is the
midpoint of side YZ.
What is AX?
2 units
4 units
6 units
5x - 7
O 8 units
2x-2
X+1
B
A
Markandeur
Save and Exit
Et
Answers
Answer:
Option (2)
Step-by-step explanation:
Given question is incomplete; here is the complete question.
Point A is the midpoint of side XZ and point B is the midpoint of side YZ.
Triangle XYZ is cut by line segment AB. Point A is the midpoint of side XZ and point B is the midpoint of side YZ. The length of XY is (5x - 7), the length of AB is (x + 1), and the lengths of XA and ZA are (2x - 2). The lengths of YB and BZ are congruent.
What is AX ?
2 units
4 units
6 units
8 units
From the figure attached,
XYZ is a triangle having A and B as the midpoints of the sides XZ and YZ.
By the theorem of midpoints,
AB = [tex]\frac{1}{2}\text{(XY)}[/tex]
Since AB = (x + 1) and XY = (5x - 7)
(x + 1) = [tex]\frac{1}{2}(5x-7)[/tex]
2x + 2 = 5x - 7
5x - 2x = 2 + 7
3x = 9
x = 3
Therefore, side AB = 3 + 1 = 4 units
Side XY = (5x - 7)
= 15 - 7
= 8 units
Side XA = 2(x - 1)
= 4 units
Therefore, Option (2) will be the answer.
Guillermo is a professional deep water free diver. His altitude (in meters relative to sea level), xxx seconds after diving, is modeled by g(x)=\dfrac{1}{20}x(x-100)g(x)= 20 1 x(x−100)g, left parenthesis, x, right parenthesis, equals, start fraction, 1, divided by, 20, end fraction, x, left parenthesis, x, minus, 100, right parenthesis How many seconds after diving will Guillermo reach his lowest altitude?
Answers
Answer: 140
Step-by-step explanation:
Answer: 50
Step-by-step explanation:
Khan academy answer