Answer:
[tex]y=\frac{1}{5}x+\frac{12}{5}[/tex]
Step-by-step explanation:
The slope of a line that is perpendicular to another will have an opposite-reciprocal slope. So, if the slope was -2, then the perpendicular slope would be [tex]\frac{1}{2}[/tex] .
[tex]y=-5x+11[/tex]
This is written in slope-intercept form:
[tex]y=mx+b[/tex]
m is the slope and b is the y-intercept. Find the opposite-reciprocal of the slope, -5:
[tex]y=\frac{1}{5} x+b[/tex]
Now we need to find the y-intercept. For this, substitute the given points for its appropriate value:
[tex](3_{x},3_{y})\\\\3=\frac{1}{5}(3)+b[/tex]
Solve for b:
Simplify multiplication:
[tex]\frac{1}{5}*\frac{3}{1}=\frac{3}{5}[/tex]
Insert:
[tex]3=\frac{3}{5}+b[/tex]
Subtract b from both sides:
[tex]3-b=\frac{3}{5}+b-b\\\\3-b=\frac{3}{5}[/tex]
Subtract 3 from both sides:
[tex]3-3-b=\frac{3}{5}-3\\\\-b=\frac{3}{5}-3[/tex]
Simplify subtraction:
[tex]\frac{3}{5}-3\\\\\frac{3}{5}-\frac{3}{1}\\\\\frac{3}{5}-\frac{15}{5}=-\frac{12}{5}[/tex]
Insert:
[tex]-b=-\frac{12}{5}[/tex]
Multiply both sides by - 1 to simplify b (it can be seen as -1b):
[tex]-b*(-1)=-\frac{12}{5}*(-1)\\\\b=\frac{12}{5}[/tex]
Insert:
[tex]y=\frac{1}{5}x+\frac{12}{5}[/tex]
:Done
There are four activities on the critical path, and they have standard deviations of 1, 2, 4, and 2 days. The standard deviation of the critical path is
Answer:
The standard deviation of the critical path = 5
Step-by-step explanation:
The formula for the standard deviation of a critical path is given as:
Standard deviation of a path
=√(sum of variances of activities on path)
Variance = (Standard deviation)²
In the above question, we are given:
Standard deviation of 1, 2, 4 and 2 days
Standard deviation of a critical path
=√(sum of variances of activities on path)
= √1² + 2² + 4² + 2²
= √1 + 4 + 16 + 4
= √25
= 5
In the following questions, look at different ways to represent the relation given by the equation y = x2 - 1. The table below shows some values for the given equation. Find the values of a and b.
Question: In the following questions, look at different ways to represent the relation given by the equation y = x2 - 1. The table below shows some values for the given equation. Find the values of a and b.
Answer:
a= 3
b= 0
The value of a and be will be three and zero respectively.
What is an equation?The equation in mathematics is the relationship between the variables and the number and establishes the relationship between the two or more variables.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
We are given the quadratic equation as;
y = x² - 1
From the given table;
At x = -2, y = (-2)² - 1 = 3
At x = -1, y = 0
At x = 0, y = -1
At x = 1, y = 0
Now, from the values above, we can say that the first graph is the correct one that shows some values for the given equation.
Therefore, values of a and be will be three and zero respectively.
The complete question is given below:-
In the following questions, look at different ways to represent the relation given by the
equation y = x2 - 1.
The table below shows some values for the given equation. Find the values of a and b.
a =
b =
The table is attached with the answer.
Read more about Quadratic Function Graphs at; brainly.com/question/1523847
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need help ASP .find the universe function of f(x)=1/2x+3
Answer:
f (1) = 1/ 2(1) + 3
= 1/2 + 3
= 1/5
5 5/6+(-1/6)+2 2/3+(-2 2/3)
Answer:
17/3 or 5 2/3 or 5.6 repeating
Step-by-step explanation:
z
Answer:
5(5/6)+(-1/6)+2(2/3)+(-2)(2/3)
(35/6)-(1/6)+(8/3)-(8/3)
find the least common multiple which is 3
therefore 70-3+16-16
the answer is 67
graph: y-3= 1/2(x+2)
Answer:
slope: 1/2
y-intercept: 4
I need help on this plz i don’t understand the question
We know that the area of a circle in terms of π will be πr². However the area with respect to the diameter will be a different story. The first step here is to find a function relating the area and diameter of any circle --- ( 1 )
For any circle the diameter is 2 times the radius,
d = 2r
Therefore r = d / 2, which gives us the following formula through substitution.
A = π(d / 2)² = πd² / 4
Hence the area of a circle as the function of it's diameter is A = πd² / 4. You can also say f(d) = πd² / 4.
Now we can substitute " d " as 4, solving for the area ( A ) or f(4) --- ( 2 )
f(4) = π(4)² / 4 = 16π / 4 = 4π - This makes the area of circle present with a diameter of 4 inches, 4π.
Factorise the following expression using grouping.
11x - 55 - 5a + ax
11x - 55 - 5a + ax
11 (x - 5) - a ( 5 + x )
Answer:
11 (x - 5) - a ( 5 + x )
Comparing Amounts of Debt
Quick
Check
Jack's bank statement shows a debt of $25. Sort the account balances to show which are greater than Jack's debt
and which are less than Jack's debt
Account balance: -$30
Greater than Jack's Debt
Less than Jack's Debt
Account balance: $30
Account balance: $15
Account balance. -$10
Account balance: -550
Account balance: $5
Answer: Grater than jacks debt -$50 , -$30
less that jacks debt: $15 , -$10 , $30 , $5.
srry if its wrong but this is how i got it right
hopefully im right .......................... bye.
∩⁽° ⁻ °⁾∩
Answer:
Grater than jacks debt -$50 , -$30
less that jacks debt: $15 , -$10 , $30 , $5.
srry if its wrong but this is how i got it right
hopefully im right .......................... bye.
Step-by-step explanation:
Frank needs to fill juicecups for his little sister's birthday party there are 35 juice cups in each juice cup holds 12 fluid ounces the juice comes in a 1 gallon bottle how many 1 gallon bottles of juice will Frank need to purchase
Answer:
He would need 3.3 gallons
Step-by-step explanation:
1 gallon = 128 ounces
35 * 5 = 420
420 / 128 = 3.28
you design a new app for cell phones. your revenue for x downloads is given by f(x)=3x. your profit is $20 less than 90% of the revenue for x downloads create a function p to model the profit. find the profit for 90 downloads
Answer:
The Break Even point is the point at which the cost=revenue 14,980+20x=30x 14,980=10x 1,498=x a. 1,498 units must be sold to break even. At $20 per unit, the dollar amount will be $29,960 b. The profit function is P(x)=R(x)-C(x) So P(x)=30x-(14,980+20x) If you want to solve for this equation just enter the value of x we found for the break even point to get the answer.
Hoped I helped
The profit for 90 downloads will be;
⇒ P = $223
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;
Your revenue for x downloads is given by,
⇒ f(x) = 3x
And, Your profit is $20 less than 90% of the revenue for x downloads create a function p to model the profit.
Now,
Since, Your revenue for x downloads is given by,
⇒ f(x) = 3x
And, Your profit is $20 less than 90% of the revenue for x downloads create a function p to model the profit.
Hence, We can formulate;
⇒ P = 90% of f (x) - 20
⇒ P = 90/100 × 3x - 20
⇒ P = 270x/100 - 20
⇒ P = 2.7x - 20
So, The profit for 90 downloads will be;
⇒ P = 2.7 × 90 - 20
⇒ P = $223
Thus, The profit for 90 downloads = $223
Learn more about the mathematical expression visit:
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Circle the equivalent expressions: A. 3(2p + 2) B. 12p C. p(3 + 3) + 6 D. 5p + 6 E. 2p + 4p + 6 F. 3 + 6p + 3
Answer:
a,e,f
Step-by-step explanation:
a. 6p+6
b.12p
c.6p
d.5p+6
e.6p+6
f.6p+6
Find the value of 5 · 2 ^3
Answer:
40
Step-by-step explanation:
[tex]5. {2}^{3} = 5.8 = 40 \\ [/tex]
If you have 3/12 of an orange, how many fourths do you have?
Answer:
1/4
Step-by-step explanation:
you would have one fourth because you divide 3 and 12 by 4 and you get 1/4
3/3=1
12/3=4
Find the midpoin, M, of AB
Answer:
11
Step-by-step explanation:
The midpoint of AB is half the distance from A to B. Here that distance is 22. Thus, the midpoint of AB is 11.
Answer:
Hey there!
The answer is 11. We can use the midpoint formula, but since this is a number line, we can easily see that 11 is half of 22.
Let me know if this helps :)
An autonomous car is programmed to travel forty kilometers at an average speed of 40 km/hr. During the first 20 km, an average speed of 40 km/hr is maintained. During the next ten kilometers, however, the car averages only twenty km/hr. To drive the remaining ten kilometers and average 40 km/hr, the autonomous car must drive
Answer:
To cover the remaining ten kilometres and average 40 km/hr, the autonomous car must drive at infinite speed (light speed)
Step-by-step explanation:
The average speed = (The total distance)/(The total time taken)
The given parameters are;
The required average speed of the autonomous car = 40 km/hr
The average speed of the car during the first 20 km = 40 km/hr
The average speed of the car during the next 10 km = 20 km/hr
Therefore, we have;
The time taken = Distance/Speed
The time taken by the car during the first 20 km = 20 km/40 km/hr = 0.5 hour
The time taken by the car during the next 10 km = 10 km/20 km/hr = 0.5 hour
Therefore, the amount of time elapsed = 0.5 hour + 0.5 hour = 1 hour
The distance covered = 30 km
Which gives;
To drive the remaining distance of 10 km the car has 0 hour left,
The speed of the remaining 10 km must therefore be 10/0 = Infinite (speed).
To cover the remaining ten kilometres and average 40 km/hr, the autonomous car must drive at infinite speed.
Please someone help me ASAP.
Answer:
£13
Step-by-step explanation:
Set up a system of equations where s represents the cost of one shirt and j represents the cost of one jumper:
2s + j = 29
s + j = 21
Multiply the bottom equation by -2 to solve by elimination by cancelling out the s variables:
2s + j = 29
-2s - 2j = -42
-j = -13
j = 13
One jumper will cost £13
Which expression is equivalent to 36 + 12? 9(4+3) 10(26+2) 12(3+1) 6(30+6)
Answer:
12(3 + 1)
Step-by-step explanation:
if you distribute the 12:
12 x 3 = 36
12 x 1 = 12
= 36 + 12
Help me answer the following question.
Answer:
160 m
Step-by-step explanation:
you can approach this question with the thinking of simple math. First, you have the value of -85 rose by 30 means +30 and descending 105 means -105.
So, the calculation you will get is -85+30-105=-160. The negative means going down as the direction.
pls solve with workings
Answer:
2a). Height = 2 cm
2b). Surface area = 395.84 cm²
Step-by-step explanation:
2a). Volume of the cylinder = 308 cm³
Radius of the base of the cylinder = 7 cm
Formula to get the volume of a cylinder = πr²h
308 = π(7)²h
h = [tex]\frac{308}{49\pi }[/tex]
h = 2 cm
Therefore, height of the cylinder will be 2 cm.
2b). Formula to calculate the surface area of the cylinder = [tex]2\pi r(r + h)[/tex]
By substituting the values in the given formula,
S.A. = 2π(7)(7 + 2)
= 395.84 cm²
Therefore, Surface area of the cylinder is 395.84 cm².
As of Sunday evening, José has collected 172 clothing items and Biruk has collected 1 clothing item for the clothing charity drive. José says he will collect 6 items per day. Biruk says he will collect 15 items per day. How many days from Sunday will it take until they have collected the same total number of clothing items for the charity drive?
Answer:
It will take 19 days from Sunday.
Step-by-step explanation:
You can use the equation 172 + 6d = 1 + 15d for this equation. 172 and 1 are how many items Jose and Biruk started with. 6d and 15d represent how many items they get a day. Here's how you can solve the equation:
172 + 6d = 1 + 15d
-6d -6d
172 = 1 + 9d
-1 -1
171 = 9d
÷9 ÷9
19 = d (write it as d = 19)
(When you type the answer, be sure to always put the letter first.)
ASAP.....!help........!!
Answer:
360
Step-by-step explanation:
First, we need to solve the numbers in the parentheses.
(14-2)^2 = (14 - 2)(14 - 2) = 196 -56 +4 = 144 (Use FOIL)
Then, we multiply that by 5.
144 * 5 = 720
Finally, we divide by two to get our answer.
720 ÷ 2 = 360
Answer:
360.
Step-by-step explanation:
Step 1:
Combine and Determine sums of certain numbers: 12 = 22•3
(12)2 = (22•3)2 = 24 • 32 =
--5 • (24•32) /2
Step 2:
Simplify: 24•32) /2 =
--5 • 72
Step 3:
Multiply: 360
What is the answer to this problem 30 + (16/2)
Answer:
Brainliest!
Step-by-step explanation:
30+8
=38
16/2 = 8
Answer:
38
Step-by-step explanation:
16/2 = 8
30 + 8 = 38
Your favorite local college football team, the UCF Knights, won 35 of out 39 games over a period of 4 years. If they keep their winning pace, predict how many games you would expect them to win over the next 78 football games?
Answer:
They will win 70 games
Step-by-step explanation:
if for 39 games they won 35 of them,
for 78 they will win X
39*X= 78* 35
39X= 2730
X= 70
Name a fourth point in plane UVX
Answer:
The correct option is;
W
Step-by-step explanation:
The number of points that defines a plane in a Euclidean space in all dimensions is either three points which are not on the same line, or two colinear points and a third point not on the line
The given points of the plane are UVX, which gives the plane as being diagonal to the cube and perpendicular to the side face of the cube.
The fourth point in plane UVX is therefore W.
I need to find the value of x and y. HELP PLEASE
Answer:
The answer is option C
Step-by-step explanation:
Since the triangle is a right angled triangle we can use trigonometric ratios to find x and y
For xIn order to find x we use tan
tan∅ = opposite/ adjacent
From the question
The opposite is 4
The adjacent is x
Substitute the values into the above formula
That's
[tex] \tan(30) = \frac{4}{x} \\ x \tan(30) = 4 \\ x = \frac{4}{ \tan(30) } [/tex]We have the answer as
[tex]x = 4 \sqrt{3} [/tex]For yIn order to find y we use sine
sin ∅ = opposite / hypotenuse
From the question
The opposite is 4
The hypotenuse is y
So we have
[tex] \sin(30) = \frac{4}{y} \\ y \sin(30) = 4 \\ y = \frac{4}{ \sin(30) } [/tex]We have the answer as
y = 8Hope this helps you
Simplify the expression to a polynomial in standard form: (x−3)(x 2 −7x−2)
Answer:
-5x²+13x+6
Step-by-step explanation:
(x-3)*(2x-7x-2)
(x-3)*(-5x-2)
-5x²-2x+15x+6
-5x²+13x+6
can u do question b pls
Answer: a) $481.62 b) $16,569.76
Step-by-step explanation:
The formula for compound interest is: [tex]A = P(1 + r)^t[/tex] where
A is the accrued amount (balance)P is the principle (initial deposit)r is the rate (convert percentage into a decimal)t is the time (number of years)Given: P = 3000, r = 1.15% (0.015), t = 10
[tex]A = 3000(1 + 0.015)^{10}\\\\\\A = 3000(1.015)^{10}\\\\\\A = 3,481.62[/tex]
Interest Earned = accrued amount - principle
= 3,481.62 - 3,000
= 481.62
******************************************************************************************
I couldn't remember the formula so I created a table:
[tex]\begin{array}{c||l|c||r}\underline{Jan\ 1}&\underline{Interest\ Earned}&\underline{Deposit}&\underline{Balance}\\2019&0&3000&3,000.00\\2120&3000(1.015)&1200&4,245.00\\2121&4245(1.015)&1200&5,508.68\\2122&5508.68(1.015)&1200&6,791.31\\2123&6791.31(1.015)&1200&8,093.17\\2124&8093.17(1.015)&1200&9,414.57\\2125&9414.57(1.015)&1200&10,755.79\\2126&10755.79(1.015)&1200&12,117.13\\2127&12117.13(1.015)&1200&13,498.88\\2128&13498.88(1.015)&1200&14,901.37\\2129&14901.37(1.015)&1200&16,324.89\\\end{array}[/tex]
2130 || 16324.89(1.015) | 0 || 16,569.76
A particle is moving along a projectile path at an initial height of 160 feet with an initial speed of 144 feet per second. This can be represented by the function H(t) = −16t2 + 144t + 160. What is the maximum height of the particle?
Answer:
The maximum height of the particle is 484 m.
Step-by-step explanation:
Given that,
A particle is moving along a projectile path at an initial height of 160 feet with an initial speed of 144 feet per second. This can be represented by the function :
[tex]H(t) = -16t^2 + 144t + 160[/tex] ....(1)
We need to find the maximum height of the particle. For maximum height put [tex]\dfrac{dH}{dt}=0[/tex]
So,
[tex]\dfrac{d(-16t^2+144t+160)}{dt}=0\\\\-32t+144=0\\\\t=4.5\ s[/tex]
Put t = 4.5 s in equation (1) as :
[tex]H(t) = -16(4.5)^2 + 144(4.5)+ 160\\\\H(t)=484\ m[/tex]
So, the maximum height of the particle is 484 m.
Answer:
484 feet
Step-by-step explanation:
First, look at H(t) = −16t^2 + 144t + 160 as ax^2 + bx + c
Second, write out a=, b=, c=, which are a=-16, b=144, c=160
Third, plug a, b, & c into the equation for vertex which is t= -b/(2a) or t=-144/[2*(-16)], t=4.5.
Fourth, plug t=4.5 into the original equation H(t) = −16t^2 + 144t + 160, so H(4.5)=−16((4.5)^2) + 144(4.5) + 160 = -324 + 648 +160 = 484 feet
order the following from least to greatest: 2/5, 6%, 6, -5/4, 0, 25%
Answer:
-5/4 0 6% 2/5 25% 6
Step-by-step explanation:
converting all to decimal -
.4, .06, 6, -1.25, 0, .25
Ok so we need to turn these all into the same type of number.
I'm going to turn it into decimals.
2/5 = 4/10 = 40/100 = 0.40
6%=0.06
6=6.00
-5/4 = -125/100 = -1.25
0 = 0.0
25% = 0.25
So now we order from least to greatest.
0.4, 0.06, 6, -1.25, 0, 0.25
Since -1.25 is a negative number, it goes first.
All of them except for -1.25 and 0 are positive numbers so 0 goes next.
Now you could ignore the decimal point; 40, 6, 600, 25
From least to greatest it is; 6, 25, 40, 600
So the final order from least to greatest is; -1.25, 0, 0.06, 0.25, 0.4, 6
Or; -5/4, 0, 6%, 25%, 2/5, 6
♡ Hope this helped! ♡
❀ 0ranges ❀
The parallel sides of a trapezoid have lengths 9 cm and 12 cm. Draw one diagonal, dividing the trapezoid into two triangles. What is the ratio of their areas?
Answer:
Ratio of triangle = 3 : 4
Step-by-step explanation:
Given:
Parallel sides = 9 cm , 12 cm
Find:
Ratio of triangle
Computation:
Assume height = h
Area of triangle = [1/2]bh
Area of triangle (1) = [1/2](9)h
Area of triangle (1) = 4.5 h
Area of triangle (2) = [1/2](12)h
Area of triangle (2) = 6 h
Ratio of triangle = 4.5 h / 6 h
Ratio of triangle = 3 : 4