Answer:
C) y+6=3/2(x-2)
Step-by-step explanation:
y-y1=m(x-x1)
m=slope & (x1, y1) is a point on the line
m=(y2-y1)/(x2-x1)
m=(-3-(-6))/(4-2)
m=(-3+6)/2
m=3/2
y-(-6)=3/2(x-2)
y+6=3/2(x-2)
Option 3
The point slope form of the given points (2, -6) and (4, -3) is [tex]y+6=\frac{3}{2}(x-2)[/tex]
Solution:Given that two points are (2, -6) and (4, -3)
We have to find the point slope form
The point-slope of the line is given as:
[tex]y - y_1 = m(x - x_1)[/tex]
Where m is the slope of the given line.
So now to write the given points in point intercept form we need to find the slope, m
The slope of line is given as:
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]\text { Here } x_{1}=2 ; y_{1}=-6 ; x_{2}=4 ; y_{2}=-3[/tex]
Plugging in the values, we get
[tex]m=\frac{-3-(-6)}{4-2}=\frac{3}{2}[/tex]
So, the slope of the given line is [tex]\frac{3}{2}[/tex]
Now, we need to find the point slope form. For that purpose we can use either of the points, but since in the answer options they have used the 1st point we will do so too.
Therefore, the point slope form is:
[tex]\begin{array}{l}{y-(-6)=\frac{3}{2}(x-2)} \\\\ {y+6=\frac{3}{2}(x-2)}\end{array}[/tex]
From the given options we can see that the correct answer is option 3.
5 ft
3 ft
3 ft
2 ft
2 ft
2 ft
3 ft
4 ft
find the area
Answer:
multiply all together
Step-by-step explanation
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:
- Suppose y varies directly as x. If y = -7 when x = -14, find x when y = 10.
Answer:
[tex]x=20[/tex]
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]
in this problem
For x=-14, y=-7
Find the value of the constant of proportionality k
[tex]k=y/x[/tex]
substitute
[tex]k=-7/-14=0.5[/tex]
so
The linear equation is
[tex]y=0.5x[/tex]
Find x when the value of y=10
substitute the value of y in the equation
[tex]10=0.5x[/tex]
solve for x
Multiply by 2 both sides
[tex]x=20[/tex]
Final answer:
In direct variation relationship 'y = kx', using the given y = -7 when x = -14, the constant of variation 'k' is found to be 0.5. To find x when y = 10, we use 'y = kx' to get x = 20.
Explanation:
The student's question revolves around the concept of a direct variation, which is a fundamental topic in algebra. The direct variation relationship between two variables 'x' and 'y' can be expressed as 'y = kx', where 'k' is the constant of variation. To determine the constant 'k', we can use the given condition, which states that when x = -14, y = -7. This equation simplifies to 'k = y/x', so 'k = (-7)/(-14)' which equals 0.5.
Now, we need to find 'x' when y is 10. Using the direct variation equation 'y = kx' and our calculated 'k' value of 0.5, we can set up the equation '10 = 0.5x'. Solving for 'x', we get 'x = 10/0.5' which simplifies to 'x = 20'. Thus, when y equals 10, the corresponding value of x is 20.
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
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
Find a numerical value of one trigonometric function of x for cos^2x+ 2sin x-2=0
Answer:
x = 90°
Step-by-step explanation:
We are given a trigonometric function of x from which we have to a solution for x.
The function is [tex]\cos^{2} x + 2\sin x - 2 = 0[/tex]
⇒ [tex]1 - \sin^{2} x + 2\sin x - 2 = 0[/tex]
{Since we know the identity [tex]\sin^{2} \alpha + \cos^{2} \alpha = 1[/tex]}
⇒ [tex]\sin^{2} x - 2 \sin x + 1 = 0[/tex]
⇒ [tex](\sin x - 1)^{2} = 0[/tex]
{Since we know the formula (a - b)² = a² - 2ab + b²}
⇒ [tex](\sin x - 1) = 0[/tex]
⇒ [tex]\sin x = 1 = \sin 90[/tex]
⇒ x = 90° (Answer)
To solve cos^2 x + 2sin x - 2 = 0, we convert cos^2 x to 1 - sin^2 x and solve the quadratic equation sin^2 x - 2sin x + 1 = 0, finding that sin x equals 1. Thus, the numerical value of the trigonometric function is sin x = 1.
To find a numerical value of one trigonometric function of x for the equation cos2x + 2sin x - 2 = 0, let's start by expressing everything in terms of sin x:
Using the Pythagorean identity, we know that cos2x = 1 - sin2x. So, we can write:
(1 - sin2x) + 2sin x - 2 = 0
Simplifying, we get:
1 - sin2x + 2sin x - 2 = 0
-sin2x + 2sin x - 1 = 0
This is a quadratic equation in terms of sin x. Let's solve it:
sin2x - 2sin x + 1 = 0
We recognize this as a perfect square trinomial:
(sin x - 1)2 = 0
So, we have:
sin x - 1 = 0
Therefore:
sin x = 1
So, the numerical value of one trigonometric function of x from the given equation is sin x = 1.
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
#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.
Evaluate x-2 for x=8
Answer:
6
Step-by-step explanation:
8-2=6
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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1/8% is what as a decimal
Answer:
[tex]\large\boxed{\dfrac{1}{8}\%=\dfrac{1}{800}}[/tex]
Step-by-step explanation:
[tex]p\%=\dfrac{p}{100}\\\\\dfrac{1}{8}\%=\dfrac{\frac{1}{8}}{100}=\dfrac{1}{8}\cdot\dfrac{1}{100}=\dfrac{1}{800}\\\\\text{other method}\\\\\text{Convert the fraction to the decimal:}\\\\\dfrac{1}{8}=0.125\to\dfrac{1}{8}\%=0.125\%\\\\0.125\%=\dfrac{0.125}{100}=\dfrac{0.125\cdot1000}{100\cdot1000}=\dfrac{125}{100000}=\dfrac{125:125}{100000:125}=\dfrac{1}{800}[/tex]
9-4 (3+6*2)=__+1=
(need answer asap please)
Write 5 over 15 in simplest form.
Answer: 1/3
Step-by-step explanation:
5/15 divided both by 5 is 1/3
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
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
Hiroto’s texting plan costs $20 per month, plus $0.05 per text message that is sent or received. Emilia’s plan costs $10 per month and $0.25 per text. Using the graph below, which statement is true?
Hiroto’s plan costs more than Emilia’s plan when more than 50 texts are sent.
Both plans cost the same when 22 texts are sent.
Emilia’s plan costs more than Hiroto’s plan when more than 22 texts are sent.
Both plans cost the same when 50 texts are sent.
Answer:
it's D
Step-by-step explanation:
y= .05x+20
x=50
y=.05(50)+20
2.5+20
y=22.5
y=.25x+10
x=50
y=.25(50)+10
12.5+10
y=22.5
what is a equivalent fraction of 10/25, 6/8, 3/5, 1/10
Answer:
Step-by-step explanation:
10/25=20/50=40/100
6/8=3/4=12/16
3/5=6/10=60/100
1/10=10/100
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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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:
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
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.
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
Ginger adds 15 mL of vitamin C drops to her guinea pig's water everyday. A bottle
of vitamin C drops holds 350mL and costs $4.85. About how much does she spend
on vitamin C drops each year?
A- $70 to $90
B- $50 to $70
C- more than $90
D- less than $50
it is d
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
First find how many bottles Ginger will need.
15 mL x 365 day = 5475 mL for 1 yr
5475 mL / 350mL = 16 bottles
Then find the price for the 16 bottles.
16 bottles x $4.85 = $77.60
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%
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:
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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If 4 quarts of paint are needed for a 75-foot fence, how many quarts are needed for an
825-foot fence?
Answer:
44 quarts of paint
Step-by-step explanation:
Given,
75-foot fence needs = 4 quarts.
We have to use the unitary method to determine how many quarts will be needed for the fencing system. Hence,
75-foot fence needs = 4 quarts of paint
1-feet fence needs = (4/75) quarts of paint
825-foot fence needs = (4 x 825)/75 quarts of paint
= 3,300/75 quarts of paint
= 44 quarts of paint
Therefore, we need 44 quarts of paint for 825-foot fence.
To determine how many quarts of paint are needed for an 825-foot fence, we can set up a proportion and solve for the unknown quantity.
Explanation:To determine how many quarts of paint are needed for an 825-foot fence, we can use the concept of ratios. Since we know that 4 quarts of paint are needed for a 75-foot fence, we can set up a proportion:
4 quarts of paint / 75 feet = ? quarts of paint / 825 feetTo solve for the unknown quantity, we can cross-multiply and solve for the missing value:
4 quarts of paint * 825 feet = ? quarts of paint * 75 feetDividing both sides of the equation by 75, we get:
? quarts of paint = (4 quarts of paint * 825 feet) / 75 feetBy performing the calculation, we find that quarts of paint is approximately 44 quarts. Therefore, 44 quarts of paint are needed for an 825-foot fence.
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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
Suppose the graph of y=f(x) includes the points (1,5), (2,3), and (3,1).
Based only on this information, there are two points that must be on the graph of y=f(f(x)). If we call those points (a,b) and (c,d), what is ab+cd?
Answer: 17
================================
How I got that answer:
(2,3) and (3,1) have '3' in common in that the y value of the first pairs with the x value of the second.
If you picture a chain, then you start with x = 2, move to y = 3, then move to x = 3 and then y = 1
2 ---> 3 ---> 3 ---> 1
So f(f(2)) = f(3) = 1
If g(x) = f(f(x)), then we know (2,1) is on the graph of g(x)
-------------------------
Repeat for (3,1) and (1,5)
3 ---> 1 ---> 1 ---> 5
f(3) = 1
g(x) = f(f(x)) = f(f(3)) = f(1) = 5
We know that (3,5) is on the graph of g(x)
-------------------------
The two points on g(x) are: (2,1) and (3,5)
Comparing that to (a,b) and (c,d) we can see
a = 2, b = 1, c = 3, d = 5
a*b + c*d = 2*1 + 3*5 = 2 + 15 = 17