Answer:
-3x + 8y - 96 = 0
Step-by-step explanation:
Standard form is ax + by + c = 0.
Converting from standard to slope-intercept form:
ax + by + c = 0
by = -ax - c
y = -a/b x - c/b
Compare the conversion formula to y = 3/8 x + 12.
In the equation, the slope is 3/8, which is the result of -a/b.
a= -3 and b=8
In the equation, 12 is a result of -c/b.
If b is 8:
-c/b = 12
-c/8 = 12
-c = 96
c = -96
Test a= -3 and b=8 and c= -96 in standard form converts to y=3/8 x+ 12
ax + by + c = 0
-3x + 8y - 96 = 0
-3x + 8y = 96
8y = 3x + 96
y = 3/8 x + 96/8
y = 3/8 x +12
This is correct. Therefore a= -3, b=8 and c= -96.
The standard form is -3x + 8y - 96 = 0
Point A(2, 2) and point B(4, −3) are located on the grid. Which measurement is closest to the distance between point A and point B in units?
A) 5.2 units
B) 5.4 units
C) 5.6 units
D) 5.8 units
Answer:
b
Step-by-step explanation:
ABC has coordinates of A (-8,-8), B (4,-2), and C (2,2). Find the coordinates of its image after a dilation centered at the origin with a scale factor of 1.5
A. A(–5.33, –5.33), B(2.67, –1.33), C(1.33, 1.33)
B. A(–12, –12), B(6, –3), C(3, 3)
C. A(–12, –8), B(6, –2),C(3, 2)
D. A(–8, –8), B(4, –2), C(2, 2)
The coordinates of the image after dilation are
A (-12 , -12) , B (6 , -3) , C (3 , 3) ⇒ answer B
Step-by-step explanation:
A dilation is a transformation that produces an image that is the
same shape as the original, but in a different size
When you dilate a figure, with
The center of dilation is the origin The scale factor of dilation is kThen the coordinates of each point of the figure is multiplied by k
to find the image of the figure after dilation
∵ ABC has coordinates of A (-8 , -8), B (4 , -2), and C (2 , 2)
∵ ABC is dilated by scale factor 1.5
∵ The center of dilation is the origin
- Multiply the coordinates of points A, B, and C by 1.5
∴ The image of point A = (-8 × 1.5 , -8 × 1.5) = (-12 , -12)
∴ The image of point B = (4 × 1.5 , -2 × 1.5) = (-6 , -3)
∴ The image of point C = (2 × 1.5 , 2 × 1.5) = (3 , 3)
The coordinates of the image after dilation are
A (-12 , -12) , B (6 , -3) , C (3 , 3)
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Grace is comparing cell phone plans. A prepaid phone plan costs $0.20 per minute and has no monthly fee. A contracted phone plan costs $50 per month and $0.02 per minute. How will the graphs of the monthy costs of the two cell phone plans compare where x represents minutes purchased in a month?
The prepaid phone plan will have a steeper line and lower y-intercept.
The contracted phone plan will have the same steepness and a higher y-intercept.
The prepaid phone plan will have a less steep line and the same y-intercept.
The contracted phone plan will have a steeper line and same y-intercept.
Answer:
The prepaid phone plan will have a steeper line and lower y-intercept.
I hope this is right
Step-by-step explanation:
prepaid phone plan y = .20x
contracted phone plan y = .02x + 50
The prepaid and the contracted plans are illustrations of linear functions, where the prepaid phone plan has a steeper line and lower y-intercept.
We have:
Prepaid
[tex]Rate = 0.20[/tex]
[tex]Monthly = 0[/tex]
Contracted
[tex]Monthly = 50[/tex]
[tex]Rate = 0.02[/tex]
For both plans, the cost function (y) is:
[tex]y =Monthly + Rate \times x[/tex]
Where:
[tex]x \to[/tex] Number of minutes
[tex]Rate \to[/tex] Steepness
So, we have:
Prepaid
[tex]y =0 + 0.20 \times x[/tex]
[tex]y =0.20x[/tex]
The y intercept (i.e. when x = 0) is
[tex]y = 0.20 \times 0 = 0[/tex]
The steep of the function is 0.20The y-intercept is 0Contracted
[tex]y = 50 + 0.02 \times x[/tex]
[tex]y = 50 + 0.02x[/tex]
The y intercept is:
[tex]y = 50 + 0.02 \times 0 = 50[/tex]
The steep of the function is 0.02The y-intercept is 50By comparing the steepness and the y-intercepts,
The prepaid plan is steeper (0.20 > 0.02)The prepaid plan has a smaller y-intercept (0 < 50)Hence, (a) is correct
See attachment for the graphs of both plans
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Neptune has a gravitational pull 1.2 times that on earth if an object weights 15.3 pounds on earth how much would it weigh on Neptune
Answer:
the object would weigh 18.36
since it is 1.2 times as much you multiply the weight of the object on earth by 1.2 and that's the answer
Step-by-step explanation:
5xy —9cs (-)-3xy + cs simplify
Answer:
Step-by-step explanation:
2 • (xy - 4cs)
The y-intercept is 4 and the line is parallel to the line whose equation is 6x+y=5
Answer:
[tex]\displaystyle 6x + y = 4[/tex]
Step-by-step explanation:
In the Linear Standard Formula [Ax + By = C], C represents the y-intercept, and since the instructions say "parallel line", you keep your '6' the same, and just alter 5 to 4.
* Parallel Lines have SIMILAR RATE OF CHANGES [SLOPES], which was why 6 remained the way it was.
I am joyous to assist you anytime.
#1
Suppose g(a) = 7.6 cos(0.5a).
a. What is the argument of the cosine function? (Enter an expression.)
Answer:
[tex]0.5a[/tex]
Step-by-step explanation:
We have been given a trigonometric function [tex]g(a)=7.6\text{ cos}(0.5a)[/tex]. We are asked to find the argument of the cosine function.
We know that a trigonometric equation is solved for an unknown angle and that unknown angle is known as the argument of the trigonometric function. For example: [tex]\text{cos}(\theta)=0[/tex]. In this equation [tex]\theta[/tex] is the argument of the equation.
Upon looking at our given function, we can see that [tex]0.5a[/tex] is the argument.
The graph represents this system of equations y equals 4 - x y equals x - 2 what is the solution to the system of equations
The solution to the system of equations is (3,1)
Step-by-step explanation:
The system of equations represented by graph are:
[tex]y=4-x\\y=x-2[/tex]
Solving the system of equations
Let:
[tex]y=4-x\,\,\,eq(1)\\y=x-2\,\,\,eq(2)[/tex]
Putting value of y from eq(2) into eq(1):
[tex]x-2=4-x\\Simplifying:\\x+x=4+2\\2x=6\\x=6/2\\x=3[/tex]
So, Value of x = 3
Putting value of x into eq(2)
[tex]y=x-2\\y=3-2\\y=1[/tex]
So, value of y= 1
So, The solution to the system of equations is (3,1)
Keywords: System of equations
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Jacob has $1,000 in a checking account and withdraws $40 each week. His account requires a minimum balance of more than $400. Write an inequality to model the number of weeks, x, that he can withdraw $40 to maintain the minimum balance requirement.
Answer:
[tex]1000-40x>400[/tex]
Step-by-step explanation:
Let's call B the balance of Jacob's checking account. Each week he withdraws $40 from his actual balance of $1000, so if x is the number of weeks, the account's balance is
B=1000-40x
The balance must be more than $400, which means
[tex]1000-40x>400[/tex]
That is the inequality to model the situation. If we wanted to know the limit for x, we can solve the inequality. Operating:
[tex]1000-400>40x[/tex]
600>40X
[tex]x<\frac{600}{40}[/tex]
Or x<15
Which means Jacob can withdraw $40 14 times at most to maintain the minimum balance requirement
Please help lol it’s my hwwwwwwwww
Answer:
8/27 is the solution and the alternative form is 0.296 or 2/3 to the power of 3
what does x = -6(4x+3) = 6(-4x-3)
Answer:
Infinitely many solutions
Step-by-step explanation:
-6(4x+3)=6(-4x-3)
-24x-18=-24x-18
infinitely many solutions
if y varies inversely as x² and x varies directly as z. find the relationship connecting y and z if c is a constant
Answer:
y = c/z²
Step-by-step explanation:
(1) y ∝ 1/x²or
y = a/x² where a is a constant
x ∝ z or x = bz, where b is a constant
Substitute x into (1)
y ∝ a/(bz)² = a/(b²z²) = (a/b²)/z²
a is a constant and b is a constant, so a/b² is a constant.
Let c = a/b². Then
y = c/z²
Marquise is 9 years old. In two years, Marquise will be 1/3 of his mother’s age. What is his mother’s age?
Answer:
33
Step-by-step explanation:
9+2=1/3x
11=1/3x
x=11/(1/3)=(11/1)(3/1)=33/1=33
25(M-2)=650 what is M ?
Answer:M=24
Step-by-step explanation:
There are 2 ways to do this
---------------------------------------------------
Method 1) Divide both sides by 25, then add 2 to both sides
25(M-2) = 650
M-2 = 650/25
M-2 = 26
M = 26+2
M = 28
---------------------------------------------------
Method 2) Distribute the 25 through to each term inside the parenthesis. Then isolate for M by adding 50 to both sides, and then dividing both sides by 2.
25(M-2) = 650
25M - 50 = 650
25M = 650+50
25M = 700
M = 700/25
M = 28
---------------------------------------------------
Either way the answer is 282 Construct a rational function that will help solve the problem. Then, use a calculator to answer the question.
An open box with a square base is to have a volume of 500 cubic inches. Find the dimensions of the box that will have
minimum surface area. Let x = length of the side of the base.
Show your work:
Answer:
Dimension of box:-
Side of square base = 10 in
Height of box = 5 in
Minimum Surface area, S = 300 in²
Step-by-step explanation:
An open box with a square base is to have a volume of 500 cubic inches.
Let side of the base be x and height of the box is y
Volume of box = area of base × height
[tex]500=x^2y[/tex]
Therefore, [tex]y=\dfrac{500}{x^2}[/tex]
It is open box. The surface area of box, S .
[tex]S=x^2+4xy[/tex]
Put [tex]y=\dfrac{500}{x^2}[/tex]
[tex]S(x)=x^2+\dfrac{2000}{x}[/tex]
This would be rational function of surface area.
For maximum/minimum to differentiate S(x)
[tex]S'(x)=2x-\dfrac{2000}{x^2}[/tex]
For critical point, S'(x)=0
[tex]2x-\dfrac{2000}{x^2}=0[/tex]
[tex]x^3=1000[/tex]
[tex]x=10[/tex]
Put x = 10 into [tex]y=\dfrac{500}{x^2}[/tex]
y = 5
Double derivative of S(x)
[tex]S''(x)=2+\dfrac{4000}{x^3}[/tex] at x = 10
[tex]S''(10) > 0[/tex]
Therefore, Surface is minimum at x = 10 inches
Minimum Surface area, S = 300 in²
9-4 (3+6*2)=__+1=
(need answer asap please)
-(-7 (to the 3 power) )
It is 343 Or -343?
Thank you
Answer:
343
Step-by-step explanation:
-(-7^3)=-(-7*-7*-7)=-(-343)=343
Answer:
Step-by-step explanation:
-(-7 to the power 3)
=-(-7×-7×-7)= -(-343)
=343
what is the slope of the line that contains the points (-2,5) and 6,-3)
Answer:
slope = - 1
Step-by-step explanation:
Calculate the slope m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (- 2, 5) and (x₂, y₂ ) = (6, - 3)
m = [tex]\frac{-3-5}{6+2}[/tex] = [tex]\frac{-8}{8}[/tex] = - 1
Find the range and standard deviation for the set of numbers.
111, 122, 134, 146, 150, 159, 193
Answer:
For this set of numbers, we have a range of 82, a mean of 145, a variance of 618.86 and a standard deviation of 24.88.
Step-by-step explanation:
1. Let's find the range for the set of numbers given:
Don't forget that range is a measure of dispersion and is the difference between the lowest and highest values in this set of numbers.
Range = 193 - 111
Range = 82
2. For calculating the standard deviation, we should calculate first the mean and the variance, this way:
Mean = Sum of all the terms / Number of the terms of the set
Mean = (111 + 122 + 134 + 146 + 150 + 159 + 193)/ 7
Mean = 1,015/7
Mean = 145
Now, we proceed to calculate the variance this way:
Variance= Sum of the squared distances of each term in the set from the mean/ Number of terms of the set or sample
Let's calculate the squared distances of each term in the set from the mean:
111 - 145 = - 34 ⇒ - 34² = 1,156
122 - 145 = - 23 ⇒ - 23² = 529
134 - 145 = - 11 ⇒ - 11² = 121
146 - 145 = 1 ⇒ 1² = 1
150 - 145 = 5 ⇒ 5² = 25
159 - 145 = 14 ⇒ 14² = 196
193 - 145 = 48 ⇒ 48² = 2,304
Now replacing with the real values:
Variance = (1,156 + 529 + 121 1+ 25 + 196 + 2,304)/7
Variance = 4,332/7
Variance = 618.86 (Rounding to two decimal places)
Finally, we can calculate easily the standard deviation:
Standard deviation = √Variance
Standard deviation = √ 618.86
Standard deviation = 24.88 (Rounding to two decimal places)
Carol buys a house for £234 900
She pays a 10% deposit
Work out the deposit made by carol
Answer:
23,490
Step-by-step explanation:
10% = 0.1
234900 x 0.1 = 23490
HELP!!!! What is-15=(3x-10)-5x
Answer:
x = 2.5Step-by-step explanation:
[tex]-15=(3x-10)-5x\\\\-15=3x-10-5x\qquad\text{combine like terms}\\\\-15=(3x-5x)-10\\\\-15=-2x-10\qquad\text{add 10 to both sides}\\\\-15+10=-2x-10+10\\\\-5=-2x\qquad\text{divide both sides by (-2)}\\\\\dfrac{-5}{-5}=\dfrac{-2x}{-2}\\\\2.5=x\to x=2.5[/tex]
Answer:
exact form x=5/2 decimal form2.5 mixed number form 2 1/2
Step-by-step explanation:
If 30 percent of a certain number is 240 what is 50 percent the number
Answer:
400
Step-by-step explanation:
0.30 * x = 240
x = 240/0.30 = 800
0.50 * 800 = 400
Answer:
The value of 50 % of number is 400 .
Step-by-step explanation:
Given as :
Let The number be x
According to statement
30 percent of a number is 240
I.e 30 % of x = 240
Or, [tex]\frac{30}{100}[/tex] × x = 240
Or, 0.3 × x = 240
So. x = [tex]\frac{240}{0.3}[/tex]
∴ x = 800
SO, The number is 800 .
Now again 50 percent of that number = y
I.e y = 50 % of x
or, y = 50 % of 800
Or, y = [tex]\frac{50}{100}[/tex] × 800
Or, y = 0.5 × 800
∴ y = 400
Hence The value of 50 % of number is 400 . Answer
Write 5 over 15 in simplest form.
Answer: 1/3
Step-by-step explanation:
5/15 divided both by 5 is 1/3
Which exponential function has an initial value of 2? f(x) = 2(3x) On a coordinate plane, an exponential function approaches y = 0 in quadrant 2 and increases into quadrant 1. It crosses the y-axis at (0, 0.5) and goes through (2, 2). f(x) = 3(2x) A 2-column table has 5 rows. The first column is labeled x with entries negative 2, negative 1, 0, 1, 2. The second column is labeled f (x) with entries one-eighth, one-fourth, one-half, 1, 2.
Answer:
The correct answer is A. f(x)= 2(3^x)
Step-by-step explanation:
The exponential function y = 2(3)ˣ, has an initial value of 2
Exponential functionAn exponential function is in the form:
y = abˣ
where y, x are variables, a is the initial value of y and b is the multiplicative rate of change
Given the exponential function y = 2(3)ˣ, has an initial value of 2
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Which value is needed in the expression below to create a perfect square trinomial?
x2+8x+______
Answer:
Step-by-step explanation:
The answer is 16
A 9-sided die is rolled. The die's faces are labeled with the numbers 1 through 9, and each number is equally likely to be rolled. Find the probability of rolling an even
number
Final answer:
The probability of rolling an even number on a 9-sided die is 4/9.
Explanation:
To find the probability of rolling an even number on a 9-sided die, we need to determine the number of favorable outcomes (even numbers) and divide it by the total number of possible outcomes.
In this case, there are 4 even numbers on the die: 2, 4, 6, and 8. The total number of possible outcomes is 9 (since there are 9 sides on the die).
Therefore, the probability of rolling an even number is 4/9.
Train A and Train B leave the station at 2 P.M. The graph below shows the distance covered by the two trains. Compare the speeds of the two trains.
Answer:
Train b is moving faster than a by 45 units an hour
Step-by-step explanation:
EASY MATH FROM THE BEGINNING OF 6th GRADE MATH BUT THIS WAS A REVIEW FROM BACK IN 5TH GRADE!!!!GETS BRAINILIST!!The figure below shows the quotient of fraction 1 over 2 divided by fraction 1 over 6. Rectangle divided into six equal parts, where the first part is shaded dark representing one-sixth, the next two parts are shaded light to complete the one-half, and the last three parts are not shaded. The quotient is ____. Numerical Answers Expected! Answer for Blank 1:
Answer:
=3
Step-by-step explanation:
Okay so you 1/2 divided by 1/6
Answer:
3
Step-by-step explanation:
1/2÷ 1/6
=
1/2×6/1
=
1 × 6
2 × 1
=
6/2
=
6 ÷ 2
2 ÷ 2
= 3
Just Divide 1/6 by 1/2
the sum of one-half t and one third s
Answer:
5/6
Step-by-step explanation:
Add the fractions by finding the common denominator.
1/2 + 1/3
3/6 + 2/6
5/6
there are 125 students in your class 75 of them are girls what percent all boys percent
Answer:
40%
Step-by-step explanation:
125 - 75= 50
50 ÷ 125 = 0.4
0.4 = 40%