[tex]\bf \qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \textit{we know that } \begin{cases} y=8\\ x=4 \end{cases}\implies 8=k4\implies \cfrac{8}{4}=k\implies 2=k \\\\[-0.35em] ~\dotfill\\\\ ~\hfill y=2x~\hfill[/tex]
For this case we have that by definition, a direct variation is represented as:
[tex]y = kx[/tex]
Where:
k: It is the constant of proportionality
So:
[tex]k = \frac {y} {x}[/tex]
Substituting the values we have:
[tex]k = \frac {8} {4}[/tex]
Finally, the proportionality constant is:
[tex]k = 2[/tex]
Answer:
[tex]y=2x[/tex]
when simplified, which of the following expressions has a coefficent of -3?
A) -2m + 5m
B) 2m + 5m
C) 5m - 2m
D) -5m + 2m
Can i get an explanation too?
Answer: The answer is: -5m + 2m
Step-by-step explanation:
Because -5 + 2 equals -3
Hope it helps
God bless you guy!
Please help!! Find P(A/A^c)
A.1
B.0
C. 1/2
D. Unknown
Answer: b
Step-by-step explanation:
trust!!!
(100 Points)last one i promise lol
Answer:
40.35
Step-by-step explanation:
First find the discount
97 * 60%
97 *.6 = 58.2
Subtract the discount to find the new price
97-58.20 =38.80
Next find the tax
38.80 * 4%
38.80 * .04
1.55
We add the tax to the sales price
38.8+1.55
40.35
Can someone help me
Answer: D
Step-by-step explanation:
W is the total number of oranges.
W/5 is the oranges being divided equally for 5 friends
. Which points are on the graph of the function rule f(x) = 10 - 4x?
(2, -18), (0, -10), (-2,-2)
(-2, 18), (0, 10), (2, 2)
(18, -2), (10,0), (2, 2)
(-18, 2), (-10,0), (-2,-2)
Answer:
(-2, 18), (0, 10), (2, 2)
Step-by-step explanation:
All you do is plug each coordinate into the equation to confirm the authentication.
I am joyous to assist you anytime.
Answer:
(-2, 18), (0, 10), (2, 2)
Step-by-step explanation:
You're welcome ;)
Which figures are shown
Answer:
Point D, Segment CD, Ray CD
Step-by-step explanation:
What us the slope of the line (-7,2) and (5,8)
Final answer:
The slope of the line passing through the points (-7,2) and (5,8) is calculated using the slope formula and is found to be 0.5.
Explanation:
The student asked about the slope of the line passing through two points, (-7,2) and (5,8). To find the slope, one should use the slope formula: slope (m) = (y2 - y1) / (x2 - x1). Plugging in the values from the points, we have m = (8 - 2) / (5 - (-7)) = 6 / 12 = 0.5. Therefore, the slope of the line is 0.5.
What type of data is best represented by a bar graph?
A. Data that are compared using bars
B. Parts of a total amount
C. Each response shown by an X or a dot
D. Change in data over time
A bar graph is most suitable for comparing data across different categories or groups, as each bar corresponds to a particular group and the height or length of the bar shows the quantity of data for that group.
Explanation:The type of data that is best represented by a bar graph is generally data that is being compared across different categories or groups, which corresponds to option A. This is because each bar in a bar graph represents a particular group or category, and the height or length of the bar corresponds to the quantity of data for that group. For example, if you conducted a survey to find out the favorite fruit of students in a class and the choices were apples, bananas, oranges, and grapes, a bar graph would be a suitable way to present this categorical data.
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Which data sets have outliers? Check all that apply.
14, 21, 24, 25, 27, 32, 35
15, 30, 35, 41, 44, 50, 78
16, 32, 38, 39, 41, 42, 58
17, 23, 28, 31, 39, 45, 75
18, 30, 34, 38, 43, 45, 68
Answer:
the answer is c and e
Step-by-step explanation:
just took it
The datasets that have outliers are (c) 16, 32, 38, 39, 41, 42, 58, (d) 17, 23, 28, 31, 39, 45, 75 and (e) 18, 30, 34, 38, 43, 45, 68
What are data sets?Data sets are simply collections of related data elements
What are outliers?Outliers are data elements that are relatively far from other data elements in the dataset
If a value is too small or too high from other elements, then the dataset has an outlier
By the method of observation, we can conclude that the following datasets have outliers
16, 32, 38, 39, 41, 42, 5817, 23, 28, 31, 39, 45, 7518, 30, 34, 38, 43, 45, 68Hence, the datasets that have outliers are (c), (d) and (e)
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In 2001, a company marketed 730,000 units of its product. In 2001 its yearly volume was 50% of its volume for 2004. The 2004 volume represents how many units for each of the 365 days of 2004?
Answer:
4000 units
Step-by-step explanation:
In 2001 the total number of marketed units= 730,000
If this number represents 50% of what was marketed in 2004, then the total number of units marketed in 2004 was:
(100/50)× 730,000=1460000
To get the number for each of the 365 days in 2004 we divide the total for 2004 by 365
1460000/365= 4000 units
Answer: 4,000 units per day.
Step-by-step explanation:
You know that in 2001 its yearly volume was 50% of its volume for 2004.
Therefore, if in 2001 the company marketed 730,000 units of its product, in 2004 the volume is:
[tex]Yearly\ volume_{(2004)}=(730,000\ units)(2)=1,460,000\ units[/tex]
Let be "x" the number of units for each of the 365 days of 2004, you can find its value by dividing the 2004 volume by 365.
The result is:
[tex]units=\frac{1,460,000\ units}{365}=4,000\ units.[/tex]
what expression is equivalent to 25 X 9y3
Answer:
D
Step-by-step explanation:
Use exponents property:
[tex]\dfrac{x^a}{x^b}=x^{a-b}[/tex]
1. Note that
[tex]\dfrac{x^9}{x^6}=x^{9-6}=x^3[/tex]
and
[tex]\dfrac{y^3}{y^{11}}=y^{3-11}=y^{-8}=\dfrac{1}{y^8}[/tex]
2. Now
[tex]\sqrt{25}=5\\ \\\sqrt{64}=8\\ \\\sqrt{x^3}=x\sqrt{x}\\ \\\sqrt{\dfrac{1}{y^8}}=\dfrac{1}{y^4}[/tex]
So
[tex]\sqrt{\dfrac{25x^9y^3}{64x^6y^{11}}}=\dfrac{\sqrt{25}\sqrt{x^3}}{\sqrt{64}\sqrt{y^8}}=\dfrac{5x\sqrt{x}}{8y^4}[/tex]
because [tex]x>0,\ y>0[/tex]
Answer: Last option.
Step-by-step explanation:
You need to remember the Quotient of powers property:
[tex]\frac{a^m}{a^n}=a^{(m-n)}[/tex]
Applying this property, we know that:
[tex]\sqrt{\frac{25x^9y^3}{64x^6y^{11}} }=\sqrt{\frac{25x^3}{64y^8}}[/tex]
Descompose 25 and 64 into their prime factors:
[tex]25=5*5=5^2\\64=8*8=8^2[/tex]
Since:
[tex]\sqrt[n]{a^n}=a[/tex]
And according to the Product of powers property:
[tex](a^m)(a^n)=a^{(m+n)}[/tex]
You can simplify. So, the equivalent expression is:
[tex]\sqrt{\frac{5^2x^2*x}{8^2y^8}}=\frac{5x\sqrt{x} }{8y^4}[/tex]
3x - y = 2
y = x - 1
When the expression x - 1 is substituted into the first equation for y, the resulting equation is
Answer:
see explanation
Step-by-step explanation:
Given
3x - y = 2
Substitute y = x - 1 into the equation
3x - (x - 1) = 2
3x - x + 1 = 2 ← simplify left side
2x + 1 = 2 ← required equation after substitution
Given.
3x - y = 2
Substitute x - 1 for variable y.
3x - x - 1 = 2 ← Resulting equation
find the gradient of the line joining (3,7) and (6,9). Hence, find the acute angle it makes with the positive x-y axis
Answer:
33.7 degrees
Step-by-step explanation:
As we go from (3,7) to (6,9), x increases by 3 and y increases by 2. Thus, the gradient (slope) of the line connecting these two points is
m = rise / run = 2/3. Using the slope-intercept formula y = mx + b, we obtain
7 = (2/3)(3) + b, or 7 = 2 + b, so we see that b = 5 and y = (2/3)x + 5. The y-intercept is (0, 5).
Next we find the x-intercept. We set y = (2/3)x + 5 = to 0 and solve for x:
(2/3)x = -5, or (3/2)(2/3)x = -5(3/2), or x = -15/2, so that the x-intercept is
(-15/2, 0). This line intersects the x-axis at (-15/2, 0).
Now look at the segment of this line connecting (-15/2, 0) and (0, 5). Here x increases by 15/2 and y increases by 5, and so the tangent of the acute angle in question is
tan Ф = 5 / (15/2) = 10 / 15 = 2/3.
Using the inverse tangent function, we get Ф = arctan 2/3, or approx.
33.7 degrees.
I believe you meant "the acute angle it makes with the positive x-axis."
Final answer:
The gradient of the line is 2/3, and the acute angle it makes with the positive x-axis is found by taking the arctan of the gradient. which is approximately 33.69 degrees.
Explanation:
The gradient of the line joining two points, (x1, y1) and (x2, y2), is calculated using the formula:
Gradient = (y2 - y1) / (x2 - x1)
Substituting the given points (3,7) and (6,9) into the formula, we get:
Gradient = (9 - 7) / (6 - 3) = 2 / 3
The gradient is 2/3. To find the acute angle θ the line makes with the positive x-axis, we use the formula:
Tan(θ) = Gradient
So, θ = arctan(Gradient)
θ = arctan(2/3)
Calculating θ will give us the acute angle. which is approximately 33.69 degrees.
What is the percent of change from 35 to 62? round to the nearest percent.
In order to change from 35 to 62, we have to add 27. So, the question becomes: which percentage of 35 is 27?
To answer this question, we set this simple equation
[tex]27 = 35\cdot\dfrac{x}{100}[/tex]
And solving for x we have
[tex]x = \dfrac{2700}{35} \approx 77.14[/tex]
So, if you change from 35 to 62, you have an increase of about 77%
The percentage change is 77.14%
The following information can be gotten from the question:
Old number = 35
New number = 62
Increase in number = 62 - 35 = 27
Percentage change will be:
= (Increase in number / Old number) × 100
= 27/35 × 100
= 2700/35
= 77.14%
In conclusion, the percentage change is 77.14%
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A company needs to package 2400 pencils. A box in the shape of a rectangular prism can hold 60 pencils. A cylindrical container can hold 80 pencils. Each box cost the company $0.50, while each cylindrical container $0.75
Answer: A
Step-by-step explanation:
2,400 divided by 60 will give you 40. 40 multiplied by 0.50 give you $20.00.
2,400 divide by 80 will give you 30 but 30 multiplied but 0.75 gives you $22.50.
$22.50 minus $20.00 gives you $2.50
Let’s solve to answer the question.
Divide the amount of pencils the company needs by the amount of pencils the box holds.
2,400/60=40.
Now multiply it by the price.
40*.5=$20.
Repeat.
2400/80=30
30*.75=22.5
The cylindrical containers cost less.
Hope this helps!
What is the relationship between the volume of a cone
and the volume of a cylinder? Explain.
Hello There!
The volume of a cylinder is pi * r^2 * h. It's a circle times the height.
The volume of a cone is (1/3) * pi * r^2 * h. So it is one third of the volume of a cylinder with the same dimensions.
Answer:
The volume of a cone is one-third the volume of a cylinder.
Step-by-step explanation:
Which expression is equivalent to (2x2 + 4x - 7)(x-3)?
ОО
O A. x(2x2 + 4x - 7) - 3
O B. -3x(2x2 + 4x - 7)
O c. x/2x2 + 4x + 7) + 3(2x2 + 4x - 7)
O D. (2x2 + 4x - 7)(x) + (2x2 + 4x 7)(-3)
Answer:
D
Step-by-step explanation:
It isn't the most efficient way to solve the problem, but the other 3 are incorrect.
expression (2 x 2 + 4 x - 7)(x) + (2 x 2 + 4 x 7)(-3) is equivalent to (2 x 2 + 4 x - 7)(x-3).
What is a linear equation?
A linear equation has one or two variables. No variable in a linear equation is raised to a power greater than 1.No variable is used as the denominator of a fraction. A linear equation is defined as an equation that is written in the form of ax+by=c. When solving the system of linear equations, we will get the values of the variable, which is called the solution of a linear equation.
solving this we will get the valve of Y if x is given.
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What is the solution for the equation (x-5)^2+3(x-5)+9=0 Use u substitution and the quadratic formula to solve?
Answer:
Here is the answer.
x= 1/2(7+3i√3) and 1/2(7-3i√3)
What is (f+g)(x)
f(x)=-x^2-3
g(x)=3x
Answer:
[tex]\large\boxed{(f+g)(x)=-x^2+3x-3}[/tex]
Step-by-step explanation:
[tex](f+g)(x)=f(x)+g(x)\\\\f(x)=-x^2-3\\\\g(x)=3x\\\\\text{Substitute:}\\\\(f+g)(x)=(-x^2-3)+(3x)=-x^2+3x-3[/tex]
Which graph represents the function h(x) = –(x + 6)3 – 3?
Answer:
Step-by-step explanation:
Please, if you're indicating exponentiation, use the symbol " ^ " to indicate it. Thanks.
The parent function here is f(x) = x^3.
g(x) = (x + 6)^3 has the same graph as does
f(x) = x^3, except that the entire graph of x^3 is translated 6 units to the left.
h(x) = -(x + 6)^3 has the same graph as
does g(x), except that the entire graph of g(x) is reflected in the x-axis.
The graph of h(x) = h(x) = –(x + 6)3 – 3 is the same as that of h(x) except that the entire graph is translated downward by 3 units.
Answer: B
Step-by-step explanation:
Determine 8th term in the
geometric sequence whose first
term is -10 and whose common
ratio is 2.
Answer:
- 1280
Step-by-step explanation:
The n th term of a geometric sequence is
[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]
here a₁ = - 10 and r = 2, hence
[tex]a_{8}[/tex] = - 10 × [tex]2^{7}[/tex] = - 10 × 128 = - 1280
Hi! I need help with this problem.
Answer:
B 70
Step-by-step explanation:
7 |H| + 4 G
H = -6 and G = 7
| H| = 6
7*6 + 4*7
42+28
70
If f(x) = 3x-2 and g(x)= x^2 +1, find (f+g)(x).
Answer:
It's choice D.
Step-by-step explanation:
(f + g)(x) = f(x) + g(x)
= 3x - 2 + x^2 + 1
= x^2 + 3x - 1.
Answer:
D. x^2+3x-1
Step-by-step explanation:
You have:
f(x) = 3x-2
g(x)= x^2 +1
Then:
(f+g)(x)=f(x)+g(x)
(f+g)(x)=(3x-2)+(x^2+1)
(f+g)(x)=3x-1+x^2 (-2+1=-1)
(f+g)(x)=x^2+3x-1 (ordering terms)
A camera manufacturer spends $1,800 each day for overhead expenses plus $9 per camera for labor and materials. The cameras sell for $18
each. a. How many cameras must the company sell in one day to equal its daily costs? b. If the manufacturer can increase production by 50
cameras per day, what would their daily profit be?
Amount of money spent per day = $1800
Cost of overhead expenses per day for labor and materials = $9
Selling price of each camera = $18
a. Let us assume the number of cameras manufactured per day = x dollars
Then
Cost of cameras sold in 1 day = 18x
So
18x = 1800 + 9x
18x - 9x = 1800
9x = 1800
x = 200
From the above deduction, we can conclude that the number cameras sold per day is 200
b. Daily selling amount of 250 cameras = 250 * 18
= 4500 dollars
Daily manufacturing price of 250 cameras = 1800 + (9 * 250)
= 4050 dollars
Then
Daily profit = 4500 - 4050
= 450 dollars
60. George made a payment of $37.50 on a
bill of $73.94. How much did he still owe?
George still owes $36.44 after making a payment of $37.50 on his original bill of $73.94. This is calculated by subtracting the payment from the original bill amount.
Explanation:George made a payment of $37.50 on a bill of $73.94. To determine how much he still owes, we subtract the payment he made from the original bill.
Original bill: $73.94
Payment made: $37.50
To calculate the remaining balance:
Subtract the payment made from the original bill: $73.94 - $37.50.This equals $36.44.Therefore, George still owes $36.44 on his bill.
I’m If Linda age is decreased by 36, the result is twice Linda’s age. how old is linda?
Answer:
x=lindas age
3 times lindas age (3 time x or 3x) is decreased by 36 (-36), the result (=) is twice lindas age (2 times x or 2x)
now we have
3x-36=2x
subtract 2x
x-36=0
add 36
x=36
age=36
Step-by-step explanation:
Using algebra to solve the problem, we create the equation L - 36 = 2L, representing Linda's age. Solving for 'L', we find that Linda is 36 years old.
Explanation:This problem can be solved by using algebra, a branch of mathematics. Let's assume that Linda's age is denoted by the variable 'L'. According to the problem, if Linda's age is decreased by 36, the result is twice Linda's age. We can write this as an equation: L - 36 = 2L.
In order to solve for 'L', we'll need to get all terms involving 'L' on one side of the equation. We would then subtract 'L' from both sides, giving us -36 = L, or, re-arranged, L = 36. Therefore, Linda is 36 years old.
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The equation of a linear function in point-slope form is y – y1 = m(x – x1). Harold correctly wrote the equation y = 3(x – 7) using a point and the slope. Which point did Harold use? When Harold wrote his equation, the point he used was (7, 3). When Harold wrote his equation, the point he used was (0, 7). When Harold wrote his equation, the point he used was (7, 0). When Harold wrote his equation, the point he used was (3, 7).
Answer:
When Harold wrote his equation, the point he used was (7, 0) ⇒ the third answer
Step-by-step explanation:
* Lets look to the equation to find the correct answer
- He used the point-slope form is y – y1 = m(x – x1), where m is the
slope of the line , (x1 , y1) are the coordinates of the point which
the line passes through it and (x , y) are the coordinates of any
general point on the line
- Lets solve the problem
- Harold correctly wrote the equation y = 3(x – 7)
∵ y - y1 = m (x - x1)
∵ y = 3 (x - 7)
- By comparing between the two equations
∴ y1 = 0
∴ m = 3
∴ x1 = 7
- He used the point (x1 , y1)
∴ Harold used the point (7 , 0) to write the equation
∴ The answer is when Harold wrote his equation, the point he used
was (7, 0)
ANSWER
When Harold wrote his equation, the point he used was (7, 0).
EXPLANATION
The point-slope form is given as
[tex]y-y_1=m(x-x_1)[/tex]
The equation Harold wrote correctly is:
[tex]y = 3(x - 7)[/tex]
This is the same as:
[tex]y - 0= 3(x - 7)[/tex]
Comparing to point-slope form, we have
[tex]x_1=7 \: \: and \: \: y_1=0[/tex]
Hence the point is (7,0)
When Harold wrote his equation, the point he used was (7, 0).
I need to know how to find x
First calculate the diameter of circle.
[tex]d=8+4=12[/tex]
Now we know that diameter is equal for any two points on the arc of a circle lying opposite to each other.
[tex]12=x+4[/tex]
Now just simply solve for x.
[tex]
12=x+4 \\
12-4=x+4-4 \\
\boxed{x=8} \\
[/tex]
Hope this helps.
r3t40
Which relation is a function?
Mn
The top right one, because for every argument there is only one corresponding value.
The length of a picture is 22.75 inches shorter than twice the width. If the perimeter is 116.5 inches, find the dimensions
Answer:
Step-by-step explanation:93.75
Follow below steps;
To solve for the dimensions of the picture whose length is 22.75 inches shorter than twice the width and has a perimeter of 116.5 inches, we first need to set up equations based on the given information.
Step 1: Set up the equations
Let w represent the width of the picture. Then, the length will be 2w - 22.75 inches.
Since the perimeter of a rectangle is given by the formula P = 2l + 2w where l is the length and w is the width, we can substitute the expressions for length and width to get the perimeter equation:
116.5 = 2(2w - 22.75) + 2w
Step 2: Solve for width
Expanding the perimeter equation we get:
116.5 = 4w - 45.5 + 2w
Combining like terms:
116.5 = 6w - 45.5
Adding 45.5 to both sides:
116.5 + 45.5 = 6w
162 = 6w
Divide both sides by 6 to find w:
w = 162 / 6
w = 27 inches
Step 3: Find the length
Now we calculate the length using the width (w = 27):
Length = 2w - 22.75
Length = 2(27) - 22.75
Length = 54 - 22.75
Length = 31.25 inches
So, the dimensions of the picture are a width of 27 inches and a length of 31.25 inches.