The function of the given data would be F(x) = y = 4x.
What is a function?The function is a type of relation, or rule, that maps one input to specific single output.
Given;
X(input) Y ( output)
0 0
1 4
2 8
3 12
We can see that
When the input is zero the output is also zero.
And when the input is some real number the output gives the multiple of 4.
Thus, The function could be
f(x) = 4x
The given function is represented by x as the independent variable.
Therefore, The function of the given data would be F(x) = y = 4x.
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What is 2b - a? If b=12 and a=5
Answer:
24-5=19
Step-by-step explanation:
1. (2b)= 2(12)
2. a=5
3. 24-5
4.9
e) If the cheetah made a round-trip and took half the amount of time on the return trip as on the front end of the trip, what would be the relationship between the average rates on each leg of the trip? Using a complete sentence, explain how you arrived at this conclusion.
The relationship between the average rates is that ; The average rate of return trip is twice the average rate of front trip.
How to determine algebra relationship?From the complete question seen online, we can say that;
Time taken on front trip = t
Time taken on return trip = 1/2 × t = t/2
Relationship between speed(Rate) and time is;
Rate ∝ 1/time
This means that Rate is inversely proportional to time.
Thus, for the front trip, the rate is; r = 1/t
For return trip, the rate is; R = 1/(t÷2)
R = 1 × 2/t
R = 2/t
Rate of front trip = 1/t
Rate of return trip = 2/t
Thus, we can say that the average rate of return trip is twice the average rate of front trip.
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A triangle has the dimensions shown. The perimeter of the triangle would be represented by which type of expression?
linear expression
quadratic expression
exponential expression
rational expression
The third side is a linear expression , Option A is the right answer.
The missing diagram is attached with the figure.
What is a Triangle ?A triangle is a polygon with three sides , three vertices , three angles .
It is given that the side of the triangle as 3x+1 , 5x-2 , y
Perimeter is given as 10x-1
Perimeter = 3x+1 +5x-2 + y = 10x-1
8x -1 +y = 10x -1
y = 2x
which is a linear expression.
Therefore the third side is a linear expression , Option A is the right answer.
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What is the equation of the line that is parallel to the
given line and passes through the point (-3, 2)?
3x - 4y = -17
3x - 4y = -20
4x + 3y = -2
4x + 3y =-6
Step-by-step explanation:
Let, the given point of the equation of the line are (3,-1) and (0,3) i.e
(x1,y1)=(3,-1) and (x2,y2) = (0,3)
Now,
The slope of the line (m1) = y2-y1 ÷ x2-x1
= 3-(-1) ÷ 0-3
= 3+1 ÷ -3
= 4/-3
since, the lines are parallel i.e.
m1 = m2
or, m2 = -4/3
Again,
The required equation of the line passing through the point (-3,2)=(x1,y2) is
y-y1 = m2(x-x1)
or, y-2 = -4/3 ( x +3)
or, 3(y-2) = -4(x+3)
or, 3y-6 = -4x - 12
or, 4x+3y = -12+6
Therefore, 4x+3y = -6 is the right answer.
How do you write an effective explanation to explain this problem?
The error happens in the last line.
The relevant log rule is ln(A) - ln(B) = ln(A/B)
The issue is that the 0 isn't ln(0), so that 0 cannot be thrown into the natural log like that.
What we can do is this set of steps
ln(3x) - 0
ln(3x) - ln(1)
ln(3x/1) ... applying the log rule mentioned
ln(3x)
But these steps are a needlessly overcomplicating things. We can simply go from ln(3x)-0 to ln(3x) in one step. Subtracting off zero doesn't change ln(3x) at all.
--------------------------
Let's continue the steps to solve for x.
ln(x^2) = ln(3x)
x^2 = 3x
x^2-3x = 0
x(x-3) = 0
x = 0 or x-3 = 0
x = 0 or x = 3
Those are the two possible solutions.
However, x = 0 isn't valid because it's not in the domain of ln(x^2). In other words, ln(0) isn't defined. The domain of y = ln(x) is x > 0
This means that x = 3 is the only solution.
N
2. a carpenter wants to cut a wood board that is feet long
into pieces that are feet long. how many whole pieces
can be cut from the board? how much wood is left over
5
16
i
Step-by-step explanation:
i
Use the properties of exponents to rewrite this expression. Then evaluate the rewritten expression for the given values to
complete the statement.
(11j³k²) (³4)
When j = -8and k = 7
The value of the expression for the given values is 1294139
Evaluating an expression
From the question, we are to rewrite the expression
(11j⁻³k²) (j³k⁴)
This can be rewritten as
11 × j⁻³ × k² × j³ × k⁴
11 × j⁻³ × j³ × k² × k⁴
11 × j⁻³⁺³ × k²⁺⁴
11 × j⁰× k⁶
= 11 × 1 × k⁶
= 11k⁶
Now we are to evaluate the expression for when j = -8 and k = 7
The expression is
= 11 × k⁶
= 11 × 7⁶
= 1294139
Hence, the value of the expression for the given values is 1294139
Here is the complete question:
Use the properties of exponents to rewrite this expression. Then evaluate the rewritten expression for the given values to
complete the statement.
(11j⁻³k²) (j³k⁴)
When j = -8 and k = 7
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Answer:
539
Step-by-step explanation:
A(-5, 2)
-10-8-6-4-2
10
↑リ
8
64
2
2
4.
6
-8
-10
B(1,6)
2
4
6 8 10
D(3,-10)
C(9,-6)
What is the area of rectangle ABCD?
O 43 units²
52 units²
O104 units²
O208 units²
The area of ABCD is 104 units²
What is area of rectangle?The area of rectangle is the product of its length to its breadth.
i.e., Area of rectangle= length * breadth
As, ABCD is in the shape of rectangle.
Using distance formula,
AB = √(1-(-5)² + (6-2)²
AB = √36+16
AB = √52
AB= 2√13
BC= √(9-1)² + (-6-6)²
BC= √64+144
BC =√208
BC= 4√13
Now, area of rectangle
=length * breadth
= 2√13 * 4√13
= 8*13
=104 units²
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2.8 + 32x + 1 =16.6
Answer:
x = 0.4Step-by-step explanation:
Assuming you are looking for x
2.8 + 32x + 1 = 16.6
32x = 16.6 - 2.8 - 1
32x = 12.8
x = 12.8 : 32
x = 0.4
-----------------------
check
2.8 + 32 * 0.4 + 1 = 16.6
2.8 + 12.8 + 1 = 16.6
16.6 = 16.6
the answer is good
2) You translate an object point 3 units to the right and 2 units down. Explain (with the aid of an equation) how you would find the coordinates of the image point. (4 marks)
Answer: By adding 2 to y and subtracting x by 3.
Step-by-step explanation: Let’s use the equation y = x since it’s simple. In order to translate an equation anywhere to the right, you have to subtract x by a unit. Since it’s 3 units, the equation is now y = x - 3. To translate an equation down, you have to add a unit to y. Since the questions asks for two units, add 2 to y. The equation should now be y + 2 = x - 3.
Which inequality is equivalent to |x-4| less than 9? –9 > x – 4 < 9 –9 < x – 4 < 9 x – 4 < –9 or x – 4 < 9 x – 4 > –9 or x – 4 < 9
[tex]f(x) = \sqrt{9 - {x}^{2} } [/tex]
I have a doubt. I know that the domain will be [-3, 3] because this is a real function. But what will be the range. Everywhere it is given as [0, 3]. But shouldn't it be [-3, 3].
For example let x = 0, then f(x) = √9, and it can be either -3 or 3. Why are we considering just the positive value?
Please explain.
Answer:
range of f is [0,3]
Step-by-step explanation:
The "square root" symbol, [tex]\sqrt{\text{ \quad }}[/tex], is a function. As a result, it only has a single output because functions must only have a single output for each input.
Thinking about it graphically, if the square root function did give both a positive and a negative result, the function "f" would not pass the vertical line test and it would not be a function.
When solving an equation like [tex]x^2=25[/tex], to solve, we must apply the square root property. The square root property says that to find both solutions, one must look at both the positive and the negative of the square root. So, to solve:
[tex]x^2=25[/tex]
Apply square root property...
[tex]\sqrt{x^2} = \pm \sqrt{25}[/tex]
[tex]x=\sqrt{25}[/tex] or [tex]x=-\sqrt{25}[/tex]
[tex]x=5[/tex] or [tex]x=-5[/tex]
In this case, because the square root function itself only outputs non-negative results (so, including zero, as you already identified), the range will only be [0,3].
BRANILIST PLS HELP
The triangles below are similar.
Triangle S R P. Angle S is 54 degrees, R is 41 degrees, P is 85 degrees. Triangle X Y Z. Angle X is 54 degrees, Z is 41 degrees, and Y is 85 degrees.
Which similarity statements describe the relationship between the two triangles? Check all that apply.
Triangle P R S is similar to triangle X Y Z
Triangle R S P is similar to triangle Z X Y
Triangle S R P is similar to triangle X Z Y
Triangle P S R is similar to Triangle Z Y X
Triangle R P S is similar to triangle Z Y X
Answer:
RSP, ZXY
SRP, XZY
RPS, ZYX
Step-by-step explanation:
Obviously, the numbers match each other.
ex. R = 41, Z = 41
Those two have the ability to pair in the same order
Assume that the number of patients visiting a medical facility in a day is distributed as a poisson variable. the mean number of patients visiting is 16 per day.
what is the probability that the number of patients visiting is 15 in a day.
find the mean number of days in a month (30 days) with 15 patients visiting.
Using the Poisson distribution, it is found that:
The probability of 15 patients in a day is of 0.0992.In a month, the mean number of days with 15 patients is of 2.976.What is the Poisson distribution?In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
The parameters are:
x is the number of successese = 2.71828 is the Euler number[tex]\mu[/tex] is the mean in the given interval.In this problem, the mean is of [tex]\mu = 16[/tex], hence the probability of 15 patients in a day is given by:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
[tex]P(X = 15) = \frac{e^{-16}16^{15}}{(15)!} = 0.0992[/tex]
Hence the mean number of days in a month (30 days) with 15 patients visiting is given by:
M = 30 x 0.0992 = 2.976.
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The first number in a pattern is 186. The pattern follows the rule subtract 17. What are the next three numbers?
Answer:
169, 152, 135
Step-by-step explanation:
186-17=169
169-17=152
152-17=135
What is the equation of the line?
y=13x
y=−13x
y = 3x
y=−3x
Hi!
I am not completely sure what you mean but if you are looking for the slope of a line here is the best way to find it.
Y=Mx+b
it look difficult but really it's quite easy and once you get it it's super memorable. Y will always be Y that doesn't change. The M is the slope of the line (don't let equations confuse you with different letters! the M might be different but it is always the letter next to x) and b is the y intercept (where the line crosses y). All you need to find the slope of a line is 3 points. I see here you have a graph. So what you do is count how much it's moving up each block on the graph. I would say your slope is about 1/3. Y is really easy! just find the point it crosses the y axis(horizontal axis or the one going up and down) for yours it's 0. So your answer is y=1/3x+0
Identify the constant of proportionality from the table.
xy
3 6
4 8
7 14
9 18
the sum of m and n is 32, and the value of m is three times the value of n. what is the value of m and n?
A. m+n=32
n= 3m
B. m+3n=32
m=3n
C. m+n=32
m=3n
D. m+n=3
32m=n
Answer:
The correct set of equations is C.
Step-by-step explanation:
m + n = 32
m = 3n
We have 4n = 32, so n = 8 and m = 24.
The coefficient of 8 · 2N is
Answer:
The coefficient is 2
Which list of numbers is shown on the number line below?
A number line going from negative 3 to positive 2. There are 4 equal spaces between each number. A point is halfway between negative 3 and negative 2. A point is between the second and third mark between negative 2 and negative 1. A point is on the mark 1 space to the right of 0. A point is halfway between 1 and 2.
Negative 2.5, 1 and three-fourths, 50 percent, 1.5
Negative 2.5, negative 1 and one-third, 50 percent, 1.5
Negative 2.5, negative 1 and three-fourths, 25 percent, 1.5
Negative 2.5, negative 1 and one-third, 25 percent, 1.5
Answer:
is A
Step-by-step explanation:
Negative 2.5, 1 and three-fourths, 50 percent, 1.5
Pls Mark Brainliest
Answer:
The first choice on edge / A
Step-by-step explanation:
don't come at me if its wrong
The dimensions of a cylindrical can of pet food are shown below.
What is the volume of the can, in terms of π?
A
2.25π cubic inches
B
4.5π cubic inches
C
9π cubic inches
D
18π cubic inches
Answer:
4.5 pie cubic inches
Answer:
B. 4.5π cubic inches
Step-by-step explanation:
The volume of a cylinder is given by the formula below, where r is the radius of the base and h is the height.
[tex]\boxed{\text{Volume of cylinder}=πr^2h}[/tex]
Given: diameter= 3 in, height= 2 in.
Diameter= 2(radius)
r= 3 ÷2
r= 1.5
Substitute the value of r and h into the formula:
Volume of cylinder
= π(1.5²)(2)
= 4.5π in³
Thus, B is the correct option.
Additional:
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https://brainly.com/question/6204273CD is the perpendicular bisector of both XY and ST, and CY = 16. Find TY.
The value of TY is 14
Given that CD is the perpendicular bisector of XY and ST and CY = 16
We need to find the value of TY
Here M is the midpoint of ST and D is the midpoint of XY
As shown in the diagram we can say that
CT = CS =12
We can also say that ST║XY
So , ∠CST = ∠CSY
∠CTS = ∠CYX
ΔSCT = ΔXCY
SX = CS - CX
= CY - CX
We can say that MT = SM = 5
DY = DX = 7
TY = SX = 4
CY = CX = 16
ST = SM + MT
ST= 5+5
∴ ST= 10
XY = XD +DY
XY = 7+7
∴ XY = 14
Hence the value of XY is 14
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Yo! Solving linear equations with integers! These are just some practice exercises I need help with! So they should probably be simple, I need these done asap, I’d appreciate work shown C:
1) - 4 + 3x = 4 x - 8
2) -5x - 8 = 2
3) 12 r - 14 = 5 ( 2 - r )
4) 3 x - 8 = - ( 17 + 2x)
Ty!
Answer:
Step-by-step explanation:
Solving linear equation with one variable:1) -4 + 3x = 4x - 8
Add 4 to both sides
-4 + 3x + 4 = 4x - 8 + 4
3x = 4x - 4
Subtract 4x from both sides,
3x - 4x = -4x + 4x - 4
-x = -4
[tex]\sf \boxed{\bf x = 4}[/tex]
2) -5x - 8 = 2
Add 8 to both sides
-5x - 8 + 8 = 2 + 8
-5x = 10
Divide both sides by (-5)
[tex]\sf \dfrac{-5}{-5}x =\dfrac{10}{-5}[/tex]
[tex]\sf \boxed{\bf x = -2}[/tex]
3) 12r - 14 = 5(2-r)
12r - 14 = 5*2 - 5*r
12r - 14 = 10 - 5r
Add 14 to both sides
12r - 14 + 14 = 10 - 5r + 14
12r = 24 - 5r
Add 5r to both sides
12r + 5r = 24
17r = 24
Divide both sides by 17
r = 24/17
4) 3x - 8 = -(17 + 2x)
3x - 8 = -17 - 2x
Add 8 to both sides
3x - 8 + 8 = -17 - 2x + 8
3x = -9 - 2x
Add 2x to both sides
3x + 2x = -9
5x = -9
Divide both sides by 5
[tex]\sf \dfrac{5}{5}x=\dfrac{-9}{5}\\\\\boxed{x = \dfrac{-9}{5}}[/tex]
Answer:
1) x = 4
2) x = -2
3) [tex]r= \frac{24}{7}[/tex] [tex](1\frac{7}{17})[/tex]
4) [tex]x=-\frac{9}{5}[/tex] [tex](-1\frac{4}{5})[/tex]
Step-by-step explanation:
hope this helps!!
(work shown in photo :) )
If the independent variable is in the rows of a cross-tabulation and the dependent variable is in the columns, which percents do we use for comparisons?
We make use of the row percentage for comparisons
How to determine the percentage of comparison?From the question, we have:
Row ⇒ Independent variableColumn ⇒ Dependent variableThe data represented by the independent variable is always used to make comparison
Since this variable is on the rows, then the row percentage would be used for comparisons
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if the ratio to cats to dogs at the city pound is 92 to 144. which statement describes this relationship?
Answer:
For every 92 cats in the city pound, there are 144 dogs.
OR
For every 144 dogs in the city pound, there are 92 cats
Step-by-step explanation:
You didn't provide the options, so that was my best shot at it.
Write the fraction as a decimal.
six tenths
0.6
0.06
6.0
1.6
Answer:
[tex]\huge\boxed{\dfrac{6}{10}=0.6}[/tex]
Step-by-step explanation:
[tex]0.6=\dfrac{6}{10}[/tex]
one digit after the decimal point - one zero in the denominator
[tex]0.06=\dfrac{6}{100}[/tex]
two digits after the decimal point - two zeros in the denominator
[tex]6.0=6[/tex]
[tex]1.6=1\dfrac{6}{10}\ \text{or}\ 1.6=\dfrac{16}{10}[/tex]
write equation of the log base of 3
Answer:
see below
Step-by-step explanation:
The graph is shifted to the RIGHT so it will be a ' x-1'
and it is shifted UP 3 units so:
Looks like log3 (x-1) + 3
at x = 4 the value of the graph is 4
log3 (4-1) + 3 = 4 CHECK !
What is the sum of (4x² + 2x - 3) and (3x² + 6)?
A 7x² + 2x + 3
B. 7x² + 3
C. c. 7x² + 2x - 3
D. 7x² - 2x + 3
Answer:
A
Step-by-step explanation:
(4x² + 2x - 3) + (3x² + 6)
= 4x² + 3x² + 2x - 3 + 6
= 7x² + 2x + 3
A scale model of a statue has a height of 20 cm. The real statue has a height of 2 m. The model and statue are both made of the same stone which has a density of 1.8 g/cm3. The mass of the real statue is 104.4 kg. Find the volume of the model in cm3
The volume of the model in cm³ is 52.2 if the scale model of a statue has a height of 20 cm. The real statue has a height of 2 m
What is density?It is defined as the mass-to-volume ratio. The density indicates the object's density and is represented by the symbol. The density is measured in kilograms per cubic meter.
A scale model of a statue has a height of 20 cm.
The formula for density:
D = mass/volume
Volume = base area×hieght
104.4 kg = 104400 grams
2 m = 200 cm
Volume = Mass/D
Volume(real statue) = 104400/200 = 522 cubic cm
Scale factor = 20/200 = 1/10
Volume of model statue = 522(1/10) = 52.2 cubic cm
Thus, the volume of the model in cm³ is 52.2 if the scale model of a statue has a height of 20 cm. The real statue has a height of 2 m
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Which table of ordered pairs represents a proportional relationship?
Answer:
The second table
Step-by-step explanation:
A proportional relationship is a relationship in which the ratio of two variables is equivalent.
2:10, 4:20, and 6:30 are all equivalent ratios that can all be simplified and written as 1:5, thus the second table is the correct answer
