Answer:
The 1st, 2nd and 5th options are correct.
Step-by-step explanation:
The equation of a line can be written in the form of y=mx+c, where m is the gradient and c is the y-intercept.
①Rewrite the given equation into the form of y=mx+c to find the gradient.
[tex]- \frac{5}{3} x = \frac{1}{4} y - 8 \\ \frac{1}{4} y = - \frac{5}{3} x + 8 \\ y = - \frac{20}{3} x + 32[/tex]
Thus, the gradient of the given equation is [tex] - \frac{20}{3} [/tex].
② Find gradient of unknown line.
The product of the gradients of perpendicular lines is -1.
Let m be the gradient of the unknown line.
[tex]- \frac{20}{3} m = - 1 \\ m = - 1 \div ( - \frac{20}{3} ) \\ m = - 1 \times ( - \frac{3}{20} ) \\ m = \frac{3}{20} [/tex]
③Substitute the value of m into the equation.
[tex]y = \frac{3}{20} x + c[/tex]
④ Find the value of c by substituting a pair of coordinates.
When x= -7, y= 3,
[tex]3 = \frac{3}{20} ( - 7) + c \\ 3 = - \frac{21}{20} + c \\ c = 3 + \frac{21}{20} \\ c = 4 \frac{1}{20}[/tex]
Thus, the equation of the line is [tex]y = \frac{3}{20} x + 4 \frac{1}{20} [/tex].
Thus, the 4th option is incorrect.
Writing c as an improper fraction,
[tex]y = \frac{3}{20}x + \frac{81}{20} [/tex]
Thus, the 1st option is correct.
-3 from both sides of the equation:
[tex]y - 3 = \frac{3}{20} x + \frac{21}{20} [/tex]
Factorise 3/20 out of the right hand side:
[tex]y - 3 = \frac{3}{20} (x + 7)[/tex]
Thus, the 2nd option is correct.
The 3rd option is incorrect as factorising -20/3 out would leave us with -0.0225 as the coefficient of x.
Let's look at the 5th option.
[tex]y = \frac{3}{20} x + 4 \frac{1}{20} [/tex]
×20 on both sides:
[tex]20y = 3x + 81[/tex]
-20y on both sides:
[tex]3x - 20y + 81 = 0[/tex]
-81 on both sides:
[tex]3x - 20y = - 81[/tex]
Thus, the 5th option is also correct.
Prasitha has two buildings A and B. A is 10 feet shorter than the twice the height of B. The distance between the buildings is 120 feet and the height of B is 60 feet. Find the distance between their tops.
Answer:
The distance between their tops is 130 feet
Step-by-step explanation:
The given parameters are;
The height of A, [tex]h_A[/tex] = 2 × The height of B - 10
The distance between the two buildings, d = 120 feet
The height of B, [tex]h_B[/tex] = 60 feet
Therefore, we have;
The height of A, [tex]h_A[/tex] = 2 × The height of B - 10 = 2 × 60 - 10 = 110 feet
The height of A, [tex]h_A[/tex] = 110 feet
By Pythagoras theorem, the distance between their tops = √(([tex]h_A[/tex] - [tex]h_B[/tex])² + d²)
Substituting the values gives;
The distance between their tops = √((110 - 60)² + 120²) = 130
The distance between their tops = 130 feet.
A health insurance policy requires that each
person covered pay the first $300 of a bill and
then 0.2 times the rest of the bill. Fran is
covered by this policy and had to pay $500.
What was her total bill?
Use the elimination method to solve the system of equations. Choose the correct ordered pair. 2y = x + 2 x - 3y= -5 O A. (2, 2) O B. (4,3) O C. (6,4) O D. (8,5)
Answer:
(4,3)
Step-by-step explanation:
2y = x + 2
x - 3y = -5
Rearrange the second equation to equal y.
x - 3y = -5
x + 5 = 3y
(x+5)/3 = y
Substitute into the first equation.
2y = x +2
2[(x+5)/3] = x + 2
(2x + 10)/3 = x + 2
2x + 10 = 3(x + 2)
2x + 10 = 3x + 6
10 - 6 = 3x - 2x
4 = x
Therefore, the correct ordered pair is (4,3) since x is equal to 4.
D=
R=
Function?
Find the domain and range of each relation. Then, determine if the relation is a function.
Answer:
Step-by-step explanation:
D = { - 4 , 0 , 2 , 7 }
R = { - 8 , - 1 , 3 }
Yes the relation is a function.
Is the relation in the mapping below a function? Explain.
Domain
1,3,5,7
Range
2,4,6
Answer: No
Step-by-step explanation:
The range and the Domain aren’t equal
The points in each table lie on a line. Find the slope of the line.
O 1/2
O 1
O 2
O None of the above
Answer:
1
Step-by-step explanation:
Given table:
x -1 1 3 5
y -2 0 2 4
Unknown:
Slope of the line = ?
Solution:
Each x and y pair on the table lies on the line. Therefore, we can use them to find the slope;
Slope = [tex]\frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]
let us take;
x₁ = -1 x₂ = 3
y₁ = -2 y₂ = 2
Insert the parameters and solve;
Slope = [tex]\frac{2 - (-2)}{3- (-1)}[/tex] = [tex]\frac{4}{4}[/tex] = 1
The slope of the line is 1
Graph the system of inequalities . Which two quadrants does the solution lie in?
someone help a brotha out
Answer:
Quads 1 and 2
Step-by-step explanation:
Option A or quadrants 1 and 2 is the correct answer:)
The temperature has been dropping 2 degrees every hour and the current temperature is -15°F. How many hours ago was the temperature 0°F?
Answer: 6 1/2
Step-by-step explanation:
six and 1 half of a hour
Which of the following is equivalent to 5x − 6y = 8?
A. y = -5/6x
B. y = 6/5x + 2
C. y = 5/6x - 4/3
D. y = 8/11x
Answer:
b
Step-by-step explanation:
1)
Which number is NOT in the solution set of x + 8 > 15?
A)
6
B)
8
C)
10
D)
12
Answer:
A) 6
Step-by-step explanation:
x + 8 > 15
x > 15 - 8
x > 7
8, 10, and 12 are all greater than 7. 6 is NOT
Answer: is A because 6+8=14 when the rest of the choices are bigger then 15
How many solutions exist for the given equation? (x + 12) = 4x - 1 o zero infinitely many
A cuboid with a volume of 925cm^3 has dimensions.
4cm, (x + 1) cm and (x + 11) cm.
Show clearly that x^2 + 12x - 220 = 0
Solve the equation by factorising, making sure you show the factorisation.
State both values of x on the same line.
Finally, find the dimensions of the cuboid, writing all three on one line.
Answer:
Step-by-step explanation:
Volume of the cuboid = Length * Width * Height
Given
Length = 4cm
Width = (x+1)cm
Height = (x-11)cm
Volume of the cuboid = 4(x+1)(x+11)
Volume of the cuboid = 4(x^2+11x+x+11)
Volume of the cuboid = 4(x^2+12x+11)
Volume of the cuboid = 4x*2+48x+44
925 = 4x*2+48x+44
4x*2+48x+44-925 = 0
4x*2+48x-881 = 0
Divide through by 4
x^2 + 12x - 220.25 = 0
Factorize using the general formula;
x = -12±√12²-4(-220.25)/2
x = -12±√144+881/2
x = -12±√1025/2
x = -12±32/2
x = 12+32/2
x = 20/2
x = 10
Hence the dimension of the cuboid is 4cm, (10+1)cm and (10+11)cm
Dimension is 4cm by 11cm by 21cm
Can anyone help me with this plzz?
===========================================================
Explanation:
Check out figure 1 in the attached images below. In this figure, I've plotted the function y = 6/(2x-3) on a 2D grid system. The function curve is in blue. Then I've plotted (2,0) and (3,0) on the x axis. Point A is somewhere between those endpoints. Point A is also on the x axis. Directly above A is point B such that B is on the blue function curve.
The distance from A to B is found by subtracting the y values of each point.
The y coordinate of A is y = 0. The y coordinate of B is y = 6/(2x-3)
Therefore, the distance from A to B is 6/(2x-3) units. This will form the radius of each cylindrical slice as figure 2 shows. Note the color coding to help see how the 2D view corresponds to the 3D view. The xy plane has been laid flat on the floor. So we're viewing the function curve at a downward angle now. Each of those gray cylinders combine to form an approximate 3D volume. The more cylinders we have, and the finer the cuts, the more accurate the total volume.
So it comes down to finding the volume of each cylindrical slice and adding up the volumes. This is effectively what integral calculus is all about.
------------------------------------
Since the radius of each cylinder is y = 6/(2x-3), this means r = 6/(2x-3) is plugged into the formula
V = pi*r^2*h
which is the volume of a cylinder formula
The height of each cylinder is delta x, which we'll use dx for short. So this is where the dx comes from in integrals.
This is what the integral will look like
[tex]\displaystyle V = \int_{2}^{3} \pi*\left(\frac{6}{2x-3}\right)^2dx[/tex]
which turns into
[tex]\displaystyle V = 36\pi\int_{2}^{3}\frac{1}{(2x-3)^2}dx[/tex]
after a bit of algebra. We're able to factor the 36pi out because it's a constant
From here we use u-substitution. Let u = 2x-3
This leads to du/dx = 2 which can be solved to dx = du/2
Since u = 2x-3, the lower endpoint x = 2 leads to
u = 2x-3 = 2*2-3 = 1
and x = 3 leads to
u = 2x-3 = 2*3-3 = 3
So the interval 2 < x < 3 turns into 1 < u < 3
After using u-sub, making the proper replacements, and integrating, we get
[tex]\displaystyle V = 36\pi\int_{2}^{3}\frac{1}{(2x-3)^2}dx\\\\\\\displaystyle V = 36\pi\int_{1}^{3}\frac{1}{u^2}\frac{du}{2}\\\\\\\displaystyle V = 36\pi*\frac{1}{2}\int_{1}^{3}\frac{1}{u^2}du\\\\\\\displaystyle V = 18\pi\int_{1}^{3}u^{-2}du\\\\\\\displaystyle V = 18\pi\left[-u^{-1}+C\right]_{1}^{3}\\\\\\\displaystyle V = 18\pi\left[-\frac{1}{u}+C\right]_{1}^{3}\\\\\\[/tex]
Let's evaluate that to get the following
[tex]\displaystyle V = 18\pi\left[-\frac{1}{u}+C\right]_{1}^{3}\\\\\\\displaystyle V = 18\pi\left[\left(-\frac{1}{3}+C\right)-\left(-\frac{1}{1}+C\right)\right]\\\\\\\displaystyle V = 18\pi\left(-\frac{1}{3}+1\right)\\\\\\\displaystyle V = 18\pi\left(\frac{2}{3}\right)\\\\\\\displaystyle V = 12\pi\\\\\\[/tex]
So the 3D volume formed by rotating that region (under the curve from x = 2 to x = 3) is exactly 12pi cubic units
The speed of an object can be found by taking the distance it travels and dividing it by the time it takes to travel that distance. An object travels 100 feet in 2.5 seconds. Let the speed, , be measured in feet per second.
Write an equation to represent the relationship between the three quantities (speed, distance, and time).
speed = [tex]\frac{distance}{time}[/tex]
speed = [tex]\frac{100}{2.5}[/tex]
speed = 40 feet per second
i need help asap !!!
Answer:-15/28
Step-by-step explanation:
2/1*x5/7x-3/8=-30/56 ÷2=-15/28
On a spelling quiz, Lily got 16 out of 20 questions correct. Select all the expressions that show the ratio of Lily’s correct answers to incorrect answers.
Answer:
ACD
Step-by-step explanation:
VNQLW3M2L,Q;KJ52KQ
Answer correctly please !!!!!!!!!!!!!!!! Will mark brainliest !!!!!!!!!!!!!!!!!!!!!
Please help me!Find the slope of the line on the graph.
Write your answer as a fraction or a whole
number, not a mixed number or decimal.
Enter the correct answer
Answer:
[tex]m=-\frac{3}{2}[/tex]
Step-by-step explanation:
First, look at the graph and pick out two points that we can use for the slope equation. I see (0,2) and (-2,5) as two possibilities. Now, we just plug them into the slope equation. Remember that the slope equation is
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
(the '2' and '1' are subscripts, not exponents)
Let's call our first point (0,2) x1 and y1. (-2,5) can be the second point.
If we plug this into the equation:
[tex]m=\frac{5-2}{-2-0}[/tex]
Now we just simplify and get
[tex]m=\frac{3}{-2}[/tex]
Our slope is [tex]-\frac{3}{2}[/tex].
I hope this helps!
Laura checked her outdoor thermometer and noticed that the temperature rose from 31 degrees in the morning to 45 degrees in the afternoon. What is the approximate percent increase for the day so far?
A. The percent increase is approximately 31%.
B. The percent increase is approximately 45%.
C. The percent increase is approximately 68%.
D. The percent increase is approximately 82%.
Answer:
C
Step-by-step explanation:
If you find the difference between 45 and 31, you find the increase. Take that and make it a percentage of 68. I hope this helped! Have a great day.
What is 400,000 in scientific notation?
O A) 40 x 104
OB) 400 x 103
OC) 4 x 106
OD) 4 x 105
Answer:
4 x 10⁵
so that i think will be OD)
___________ is the measure of the value of a section of the stock market and is computed from the price of selected stocks.
Answer:
stock index
Step-by-step explanation:
Answer:
stock index is the measure of the value of a section of the stock market and is computed from the price of selected stocks. (Please mark me brainliest)
Step-by-step explanation:
what is the measure of <x
Answer:
X=17
Step-by-step explanation:
73+x=90 90-73=17
A small town has two local high schools. High School A currently has 850 students and is projected to grow by 35 students each year. High School B currently has 700 students and is projected to grow by 60 students each year. Let AA represent the number of students in High School A in tt years, and let BB represent the number of students in High School B after tt years. Write an equation for each situation, in terms of t,t, and determine after how many years, t,t, the number of students in both high schools would be the same.
An equation for each situation, in terms of t, is y = 850e^35t and
y = 700e^70t
The required equation will be in the form y = Ae^kt
where:
k is the growth constantA represents the number of students in High School A in t years.B represents the number of students in High School B after t years.If High School A currently has 850 students and is projected to grow by 35 students each year, hence;
A = 850k = 35 (growth factor)Substituting into the formula, we will have:
y = 850e^35t
If High School B currently has 700 students and is projected to grow by 60 students each year, hence;
A = 700k = 60 (growth factor)Substituting into the formula, we will have:
y = 700e^70t
An equation for each situation, in terms of t, is y = 850e^35t and
y = 700e^70t
Learn more on exponential function here: https://brainly.com/question/12940982
please tell me the answer
Answer: D
Step-by-step explanation:
I solved it:)
If m <2 = 120', what is m<7?
m<7=120'
Step-by-step explanation:
m<2 = m<6 because m and l are parallel and m<6 =m<7 because they are vertically opposite angles (v.o.a)
Answer:
m<7=120
Step-by-step explanation:
2 and 7 are alternate exterior angles and because l and m are parallel lines then m<2=m<7
What's 6+2x^2 in factored form?
Answer:
2 ( x^2 + 3 )
Step-by-step explanation:
if the cost of 8 mobile set is rs 40,000.how many mobile sets can be purchased for Rs 100,000
Answer:
20 mobile sets.
Step-by-step explanation:
Every mobile set costs:
40000 / 8
= 5000 Rs.
Therefore, for 100,000 Rs, the number of mobile sets that can be purchased is:
100,000 / 5000
= 20 mobile sets.
Hope this helped!
will give brainliest
I don't understand algebra 2!!! at all idk why
break it down please help
Answer:
1/5... 1 on top 5 on bottom
Step-by-step explanation:
sub in the values:
[tex]\frac{5+y}{6x}[/tex] will now be [tex]\frac{5+7}{6(10)}[/tex]
now add:
[tex]\frac{12}{60}[/tex]
simplify:
1/5
If using the method of completing the square to solve the quadratic equation x squared -20x+24=0, which number would have to be added to “complete the square”
Oksuru k diyaf ramincok ani kasilm asiyla olusan bir refle kstir.
Kiran's family is having people over to watch a football game. They plan to serve sparkling water and pretzels. They are preparing 12 ounces of sparkling water and 3 ounces of pretzels per person. Including Kiran's family, there will be 10 people at the gathering.
A bottle of sparkling water contains 22 ounces and costs $1.50. A package of pretzels contains 16 ounces and costs $2.99. Let LaTeX: nn represent number of people watching the football game, LaTeX: ss represent the ounces of sparkling water, LaTeX: pp represent the ounces of pretzels, and LaTeX: bb represent Kiran's budget in dollars. Which equation best represents Kiran's budget?