the graph shows the mass of the bucket containing liquid depends on the volume of liquid in the bucket. Use the graph to find the domain of the function.
Answers
The domain of the function for the volume of the liquid = 0 ≤ V ≤ 7.5 liters.
What is domain of a function?The domain of a function is the complete set of possible values of the independent variable.
Also a domain of a function refers to "all the values" that go into a function.
From the graph the domain of the function of the volume of the of liquid in the bucket is calculated as follows;
The minimum value of the volume of liquid in the bucket = 0
The maximum value of the volume of liquid in the bucket = 7.5 liters
The domain of the function for the volume (V) of the liquid = {0, 1, 2, 3, 4, 5, 6, 7.5 liters}
0 ≤ V ≤ 7.5 liters
Thus, the domain of the function or independent variables that satisfies the function include natural numbers between 0 to 7.5 liters. That is the domain of the function is {0, 1, 2, 3, 4, 5, 6, 7.5 liters}.
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Related Questions
Use intercepts to graph the line described by the equation.4y =5x +20
Answers
We have to graph the equation 4y=5x+20 using the intercepts.
First we are going to find the y-intercept of the line, to do this we have to remember that the line intercepts the y-axis when x=0. Plugging this value of x in the equation we have
[tex]\begin{gathered} 4y=5(0)+20 \\ 4y=20 \\ y=\frac{20}{4} \\ y=5 \end{gathered}[/tex]Hence the y-intercept is 5. This represents the point (0,5).
Now we draw this point on the graph:
Now we have to find the x-intercept of the line, this happens when y=0. Plugging this value of y in the equation we have that
[tex]\begin{gathered} 4(0)=5x+20 \\ 0=5x+20 \\ 5x=-20 \\ x=-\frac{20}{5} \\ x=-4 \end{gathered}[/tex]Then, the x-intercept is -4. This represents the point (-4,0).
Drawing this point on the graph we have.
Now we only connect the points with a straight line:
That's the graph of the line that we find with the intercepts.
f(x)=x^2-8, g(x)=17-x
(f/g)(-4)=?
Answers
The quotient between the two functions evaluated in -4 is equal to 8/21.
How to find the quotient?
Here we have the two functions:
f(x) = x^2 - 8
g(x) = 17 - x
And we want to find:
(f/g)(-4)
That can be rewritten as:
f(-4)/g(-4)
By evaluating the two functions we get:
f(-4) = (-4)^2 - 8 = 16- 8 = 8
g(-4) = 17 - (-4) = 17 + 4 = 21
replacing that in the quotient we get
f(-4)/g(-4) = 8/21
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Consider the following equation. State any restrictions on the variable, if they exist.
Answers
In equation like this one, the restriction happens when there are variables in the denominator. Since the denominator can't be equal to zero, when we have a variable in the denominator, we have to find the restrictions to the variable.
However, in this case, no denominator have variables in it.
So, in this case, there is no restriction for the values of x.
Washing his dad's car alone, Matt takes 6 hours. If his dad helps him, then it takes 2 hours. How long does it take Matt's dad to wash the car by himself?
Answers
If it takes 6 hours for Matt to wash the car, then he washes at a rate of 1/6 cars per hour:
[tex]\begin{gathered} \frac{1}{x}=6 \\ x=\frac{1}{6} \end{gathered}[/tex]Let y be the time in which Matt's dad washes the car and state an equation that describes the situation in which Matt and his dad wash the car together:
[tex]\begin{gathered} \frac{1}{6}+\frac{1}{y}=2 \\ \frac{1}{y}=2-\frac{1}{6} \\ \frac{1}{y}=\frac{11}{6} \\ y=\frac{6}{11} \end{gathered}[/tex]It means that he washes the car in 6/11 hours (approximately 0.54hours).
What is the reflection image of p (0,0) after two reflections,first across x=4 and Than across y= -3
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After two reflections, P(0, 0)'s reflection image is P (8,-6).
What do we mean by reflection of image?A reflection is the shape's mirror image. A line, called the line of reflection, will allow an image to reflect through it. Every point in a figure is said to reflect the other figure when it is equidistant from every corresponding point in the other figure.The given point is(0,0)
A point will reflect across x = 4 ,then(x,y) → (-x+8,Y)(0,0)→(-0+8,0)(0,0)→(8,0)A point will reflect across x = -3 ,then(X,Y)→(X,-Y-6)(8,0)→(8,-0-6)(8,0)→(8,-6)Therefore, P' is the reflection image of P(0, 0) following two reflections (8,-6).
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I believe the answer to be 0.15 but I just want to make sureSuppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.57 and a standard deviation of 0.44. Using the empirical rule, what percentage of the students have grade point averages that are greater than 3.89? Please do not round your answer
Answers
First, we need to find the z-score for the measure x=3.89. This is given by
[tex]z=\frac{x-\mu}{\sigma}=\frac{3.89-2.57}{0.44}[/tex]which gives
[tex]z=3[/tex]Now, from the empirical rule :
we can see that
[tex]P(x>3.89)=P(z>3)\approx0.15\text{ \%}[/tex]Then, the answer is 0.15%
What type of transformation is illustrated in the picture below? A. rotationB. translation
Answers
Rotation simply means turning around a centre . From the diagram above the vehicle rotated in a clockwise fashion.
HELPP ASPP PLS HELP Combine "like terms" in this expression:
6x - 8x - 4y - x + 5y - 2y
A. -6x - y
B. -3x + y
C. -3x -2y
D. -3x - y
Answers
Answer:-3x-y
Step-by-step explanation:
6-8-1=-3
-4+5-2=-1
-3x-y
A gift wrapping store has 8shapes of boxes, 14types of wrapping paper, and 12 different bows. How many different gift-wrapping options are available at this store?
Answers
14*12*8=1344
1344 options
Use synthetic division to determine whether the first expression is a factor of the second. If it is, indicate the factorization. (If the first expression is not a factor of the second, enter DNE.)x − 2, 9x^4 − 35x^2 − 4(x − 2)
Answers
[tex]9x^4-35x^2-4[/tex]
Lets divide this polynomial by x - 2
9x^4 0x³ -35x² 0x -4 | x - 2
-9x^4 +18x³ | 9x³
18x³ -35x² 0x -4 | x - 2
-18x³ 36x² | 9x³ + 18x²
x² 0x -4 | x - 2
-x² +2x |9x³ + 18x² + x
2x -4 |x - 2
-2x + 4 |9x³ + 18x² + x +2
0
Since there is no rest for the division, x - 2 is a factor of the given polynomial:
[tex]9x^4-35x^2-4=(x-2)\cdot(9x^3+18x^2+x+2)[/tex]Write the correct expression for the following statement:
A difference of x and six
Answers
Write a quadratic function in standard form whose graph has the given characteristics.
Answers
The quadratic function in standard form that passes through (-2, 0), (4, 18), and (10, 0) is y = (- 1/2) x² + 4x + 10.
Given that, (-2, 0), (4, 18) and (10, 0).
What is a quadratic function in standard form?The standard form of a quadratic equation is given as:
ax² + bx + c = 0 where a, b, c are real numbers and a ≠ 0.
Now, the equation passes through (- 2, 0)
y = ax² + bx + c
0 = 4a - 2b + c ----------------(1)
The equation passes through (4, 18)
y = ax² + bx + c
18 = 16a + 4b + c ----------------(2)
The equation passes through (10, 0)
y = ax² + bx + c
0 = 100a + 10b + c ----------------(3)
Using the Gauss elimination method to solve the system of equations we get,
a = -1/2, b = 4, and c = 10
The quadratic equation will be:
y = ax² + bx + c
y = (- 1/2) x² + 4x + 10
Therefore, a quadratic function in standard form with the given characteristics is y = (- 1/2) x² + 4x + 10.
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please help with this practice question asap
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The slope of the line passing through the points (4, -5), (-4, -5) is m = 0.
What do we mean by a slope?The slope of a line can be used to gauge how steep it is.Mathematically, the slope is calculated as "rise over run" (change in y divided by change in x).Every time the equation of a line is written as y = mx + b, the slope-intercept form of the equation is used.The slope of the line is shown by M.B is the value of b at the location of the y-intercept (0, b).For instance, y = 3x - 7 has a slope and y-intercept of 3 and 0, respectively.So, the slope of (4, -5) (-4, -5):
The slope formula: m = y₂ - y₁/x₂ - x₁Now, substitute the values in the formula and find the slope as follows:
m = y₂ - y₁/x₂ - x₁m = (-5) - (-5)/(-4) - 4m = -5 + 5/-4 - 4m = 0/-8m = 0Therefore, the slope of the line passing through the points (4, -5), (-4, -5) is
m = 0.
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Rewrite y = a (2)¹/3 in the form y = a(1+r) or y = a(1-r)'. Round each value to the nearest hundredth, if necessary. Then state the growth or decay rate.yoThe rate is about %.This is a rate.
Answers
we have the equation
[tex]y=a(2)^{\frac{t}{3}}[/tex]Rewrite the given equation
[tex]\begin{gathered} y=a(2^{\frac{1}{3}})^t \\ y=a(1.26)^t \\ y=a(1+0.26)^t \end{gathered}[/tex]the base of the exponential function is b=1.26
1.26 > 1
that means
is an exponential growth function
1+r=1.26
r=1.26-1
r=0.26
therefore
The rate is about 26%This is a growth rateWhat was done to the linear parent function, f(x) = x, to get the functiong(x) = ?A. Horizontally compressed by a factor of 6B. Vertically stretched by a factor of 6C. Vertically compressed by a factor of 6D. Shifted unit up
Answers
Given
Two functions
[tex]\begin{gathered} f(x)=x \\ g(x)=\frac{1}{6}x \end{gathered}[/tex]Procedure
When we multiply a function by a positive constant, we get a function whose graph is stretched or compressed vertically in relation to the graph of the original function.
I need help on this question
Answers
DA bisects EB
then
DC is congruent with AC
EC is congruent with BC
and
ED is congruent with AB
Philip purchased s pairs of shoes for the school year. He also purchased jeans and T-shirts.
The number of pairs of jeans is 3 more than the number of pairs of shoes and the number of
T-shirts is twice as many as the number of pairs of jeans. How many shoes did he purchase if he purchased a total of 17 items?
Answers
Answer:
3 pairs of shoes
Step-by-step explanation:
You can represent the amount of each item with these:
2(jeans) = t-shirts
shoes + 3 = jeans
shoes + t-shirts + jeans = 17
By plugging in 3 for s, you get:
(3) + 3 = 6
(6) × 2 = 6
3 + 6 + 6 = 17
operations of rational algebraic expression 1/4+2/4
Answers
Answer:
3/4
Step-by-step explanation:
7.) A jug of egg nog sells for $5.12One jug holds(128 ounces. What is the unit priceper ounce?
Answers
To find the unit price per ounce, we just need to divide the total price by the total amount of egg nog(in ounces). The total price is $5.12 and the amount of egg nog is 128 ounces, therefore, the unit price per ounce is
[tex]\frac{5.12}{128}=0.04[/tex]$0.04.
Determine if triangle EFG and triangle HIJ are or are not similar, and, if they are, state how you know. (Note that figures are NOT necessarily drawn to scale.)
Answers
Given the triangles EFG and HIJ, you can identify that:
[tex]EG=19\text{ }[/tex][tex]EF=18[/tex][tex]\begin{gathered} FG=16\text{ } \\ \\ \text{ }HI=90 \\ \\ IJ=80 \end{gathered}[/tex][tex]\begin{gathered} m\angle F=67\text{ \degree} \\ \\ m\angle I=67\text{ \degree} \end{gathered}[/tex]By definition, two triangles are similar if the lengths of the corresponding sides are in proportion and their corresponding angles are congruent.
In this case, you can identify that you know two pairs of corresponding sides. Then, you can find in they are in proportion. Set up that:
[tex]\frac{EF}{HI}=\frac{FG}{IJ}[/tex]Substituting values and simplifying, you get:
[tex]\begin{gathered} \frac{18}{90}=\frac{16}{80} \\ \\ \frac{1}{5}=\frac{1}{5} \end{gathered}[/tex]Notice that they are in proportion.
You can also identify that the corresponding angles F and I are congruent because they have equal measure.
Therefore, since you know that two sides are proportionate and the included angles are congruent, you can conclude that the triangles are similar, based on the Side-Angel-Side Theorem (SAS).
Hence, the answer is: Third option.
please look at screenshots
Answers
Answer:
c
Step-by-step explanation:
it not linear relationship
Identify the sample space of the probability experiment and determine the number of outcomes in the sample space.
randomly chosing a number from the even number between 10 and 20 nclusive
Answers
For the given experiment, the sample space has 6 elements which are:
{10, 12, 14, 16, 18, 20}
How to identify the sample space?
For any experiment with different outputs (each output with a defined probability).
We define the sample space as the set of all the possible outcomes of the experiment.
Now, the experiment here is:
"randomly choosing a number from the even number between 10 and 20 inclusive"
So the possible outcomes are all the even numbers on the interval [10, 20]
Then the sample space of the experiment is:
{10, 12, 14, 16, 18, 20}
It has 6 elements.
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i know the answer i just don’t know the steps.
Answers
Answer:
x = 4Step-by-step explanation:
1/2x - 2 = 0
1/2x = 2
x = 2 * 2/1
x = 4
----------------------------
check1/2(4) - 2 = 0
2 - 2 = 0
0 = 0
the answer is good
The equation of a line is x + 4y = 15.What is the y-intercept of the line? −151515/44/15
Answers
Given:
[tex]x+4y=15[/tex][tex]4y=-x+15[/tex][tex]y=-\frac{1}{4}x+\frac{15}{4}[/tex][tex]\text{The general equation is }[/tex][tex]y=mx+c[/tex]c is the y-intercept
[tex]y-\text{intercept (c)= }\frac{15}{4}[/tex]HELP! How do I solve this!!?
Answers
x ki power 3 is the answer
Step-by-step explanation:
use x is equal to root over x
What is the magnitude of -5 + 121?
Answers
Question:
Solution:
For a complex number z = x + yi, we define the magnitude, |z|, as follows:
[tex]|\text{ z |=}\sqrt[]{x^2+y^2}[/tex]thus, according to this, we can conclude that the magnitude of the given complex number is:
[tex]|\text{ z |=}\sqrt[]{(-5)^2+(12)^2}\text{ = 13}[/tex]so that, the correct answer is:
[tex]13[/tex]
which expression is equivalent to (4^2)^-2?
Answers
Answer:
[tex](4^2)^{-2}=\frac{1}{x^4}[/tex]Explanation: We need to simplify the given expression to get an equvilant expression: The given is as follows.
[tex](4^2)^{-2}[/tex]Simplification:
Using the following exponent property:
[tex](x^a)^{-b}=x^{a\times(-b)}^{}=x^{-ab}^{}=\frac{1}{x^{ab}}[/tex]The equvilant expression we get is:
[tex](4^2)^{-2}=x^{2\times-2}=x^{-4}=\frac{1}{x^4}[/tex]Need to study for finals need help on this problem on my study guide find the measure of each angle calculate the length of each side
Answers
Answer:
[tex]\begin{gathered} m\angle B\text{ = 28}\degree \\ AB\text{ = 9.75} \\ BC\text{ = 7.7} \end{gathered}[/tex]Explanation:
Here, we want to calculate the measure of each of the missing angles and sides
We have one missing angle and 2 missing sides
a) Let us get the angle at B
Mathematically, the sum of angles in a triangle is 180 degrees
Thus:
[tex]\begin{gathered} 90\text{ + 62 + B = 180} \\ B\text{ = 180-90-62} \\ B\text{ = 28}\degree \end{gathered}[/tex]b) Let us get the measure of AB
We can use the appropriate trigonometric ratio here
The side that measures 6 is an opposite to the angle B
Since AB is the hypotenuse (the side facing the right angle and the longest side of in the triangle), we use sine
Sine is the ratio of the opposite and the hypotenuse
Mathematically:
[tex]\begin{gathered} sin\text{ 38 = }\frac{6}{AB} \\ \\ AB\text{ =}\frac{6}{sin\text{ 38}} \\ \\ AB\text{ = 9.75} \end{gathered}[/tex]c) side BC
We can use tan to get this
Tan is the ratio of the opposite to the adjacent side
The opposite side here is the side AC, while the adjacent is BC
Thus, we have it that:
[tex]\begin{gathered} Tan\text{ 38 = }\frac{6}{BC} \\ \\ BC\text{ = }\frac{6}{Tan\text{ 38}} \\ \\ BC\text{ = 7.7} \end{gathered}[/tex]10s = 12 help!!!! pls
Answers
Answer:
12-10=2 which means an extra 2seconds was added therefore it's impossible for 10seconds to be equal to 12
What is the value of 7 + z ÷ 2, when z = 10?
Answers
Answer:
12
Step-by-step explanation:
7 + z ÷ 2 ,z=10(bodmas , division is the first)
7 + 10 ÷2
7 + 5
12
Answer:
12
Step-by-step explanation:
Substitute 10 for z
7+10 ÷ 2
divide first
7+5=
12