State the domain of the function.{-2,0, 1, 2, 3, 4){-4,0, 1, 2, 6){0, 1,2,3)(-2,4)
Answers
D= {-2,0,1, 2,3,4}
1) Considering that the Domain is the set of entries of a function, on the x-axis, and examining that graph we can state
- The lowest value for that is given by x=-2
- The highest value for that is x= 4
- The points (-2,-4) (0,0), (1,1), (2,2), (3,1) and (4,6)
2) So, we can write the set, the Domain, after examining the options as:
D= {-2,0,1, 2,3,4}
Notice that we're considering the x-coordinates
3) So the answer is D= {-2,0,1, 2,3,4}
Related Questions
Is ⅓ greater that 3/9?
Answers
1/3 and 3/9
Simplify 3/9 by 3
(3/3) / (9/3 ) = 1 /3
So, both fractions are equal
1/3 is not greater than 3/9
#11 When you were born, your grandparents deposited $10,000 in a CD. for your college education. If theaccount earns 5% interest, compounded monthly, how much will be in the account for your collegeeducation?
Answers
Replacing with the values we already know, we have:
PV = 10,000
i = 5% or 0.05 but it is compounded monthly, then it is 0.05/12
n = 18 years or 216 months
10,000 = FV * 0.4073
FV = 10,000/0.4073
FV = $ 24,551.93
It is very close to option D, where the term "about" is included.
x – a is the factor of a polynomial P(x) if P(a) is equal to
Answers
we know that
If (x-a) is a factor of P(x)
then
For x=a
the value of P(a)=0
therefore
the answer is option DBilly is making a curtain for his kitchen window. He bought 2 1/2
yards of fabric. His total cost was $15. What was the cost per yard?
Answers
The fabric has a cost per yard of $6 per yard
How to determine the cost per yard of the fabric?From the question, the given parameters are:
Yards of fabric = 2 1/2 yards
Cost of the fabric = $15
The cost per yard of the fabric is then calculated as
Cost per yard = Cost of the fabric/Yards of fabric
Substitute the known values in the above equation
So, we have
Cost per yard = 15/(2 1/2)
Evaluate the quotient
So, we have
Cost per yard = 6
Hence, the cost per yard is $6 per yard
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Triangle ABC is shown with exterior ∠z.
Determine m∠z.
49°
97°
131°
146°
Answers
Answer:
(c) 131°
Step-by-step explanation:
Given exterior angle z of a triangle with remote interior angles 97° and 34°, you want the measure of angle z.
Remote interior anglesAn exterior angle is equal to the sum of the remote interior angles.
Applicationz = 97° +34°
z = 131°
If f(x)=2x+1, what is f(2)?
Answers
f(2) means that we must substitute the value 2 in the place of x, that is
[tex]f(2)=2\cdot2+1[/tex]which gives f(2)=5.
-27\sqrt(3)+3\sqrt(27), reduce the expression
Answers
Explanation
[tex]-27\sqrt[]{3}+3\sqrt[]{27}[/tex]Step 1
Let's remember one propertie of the roots
[tex]\sqrt[]{a\cdot b}=\sqrt[]{a}\cdot\sqrt[]{b}[/tex]hence
[tex]\sqrt[]{27}=\sqrt[]{9\cdot3}=\sqrt[]{9}\cdot\sqrt[]{3}=3\sqrt[]{3}[/tex]replacing in the expression
[tex]\begin{gathered} -27\sqrt[]{3}+3\sqrt[]{27} \\ -27\sqrt[]{3}+3(3\sqrt[]{3}) \\ -27\sqrt[]{3}+9\sqrt[]{3} \\ (-27+9)\sqrt[]{3} \\ -18\sqrt[]{3} \end{gathered}[/tex]therefore, the answer is
[tex]-18\sqrt[]{3}[/tex]I hope this helps you
PLEASEEEE HELPPPPAdd. 3+(-7)=
Answers
The problem is asking as to perform an addition of signed numbers.
The firs one to add is 3 and the other one is -7.
We can understand the meaning of this type of addition by using the number line forst, and then have a very simple "short cut" every time we fce problems like this.
The number line approach:
locate yourself at the mark "3" on the number line, and then add the number "-7" whichmeans go to the left (as the negative indicates) 7 units. You will see that you move through zero, and then land on the number "-4".
a line intersects the points (2,2) and (-1, 20).What is the slope of the line in simplest form?m = _
Answers
Given: The points a line intersects as shown below
[tex]\begin{gathered} Point1:(2,2) \\ Point2:(-1,20) \end{gathered}[/tex]To Determine: The slope of the line in its simplest form
Solution
The formula for finding the slope of two points is as shown below
[tex]\begin{gathered} Point1:(x_1,y_1) \\ Point2:(x_2,y_2) \\ slope=\frac{y_2-y_1}{x_2-x_1} \end{gathered}[/tex]Let us apply the formula to the given points
[tex]\begin{gathered} Points1(x_1,y_1)=(2,2) \\ Point2(x_2,y_2)=(-1,20) \\ slope=\frac{20-2}{-1-2} \\ slope=\frac{18}{-3} \\ slope=-6 \end{gathered}[/tex]Hence, the slope of the line in simplest form is -6
A __ is a polynomial with one term.
Answers
ANSWER
Monomial
EXPLANATION
A polynomial is a expression that contains variables, coefficients and sometimes constants.
These terms relate with one another by the use of mathematical signs like addition, subtraction, multiplication, etc
A polynomial with just one term is called monomial.
An example of a polynomial is:
[tex]x^2\text{ + x + 1}[/tex]An example of a monomial is:
[tex]\begin{gathered} x^2 \\ or\text{ } \\ \frac{x}{2} \end{gathered}[/tex]Answer:
monomial
Step-by-step explanation:
What is the range of the following numbers? 12, 20, 18, 25.6 OA. 5 O B. 167/ O C. 18 O D. 19 E. 25
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
12, 20, 18, 25 , 6
range = ?
We must order the data.
Step 02:
6 , 12 , 18 , 20 , 25
Range = 25 - 6 = 19
The answer is:
The range is 19
how long is the hypotenuse of this right triangle?28 519023
Answers
To calculate the hypotenuse of a right angled triangle as shown in the diagram, we can apply the Pythagoras theorem which states as follows;
AC^2 = AB^2 + BC^2
Where AC is the hypotenuse (the longest side) 28 units, AB is one of the other two sides, 23 units and BC is the third side.
We can now re-write the formula as follows;
28^2 = 23^2 + BC^2
784 = 529 = BC^2
Subtract 529 from both sides of the equation
255 = BC^2
Add the square root sign to both sides of the equation and you have
BC = 15.9687
BC is approximately 16 units
The following circle passes through the origin. Find the equation.
Answers
Answer
(x - 2)² + (y - 2)² = 8
Step-by-step explanation
The equation of the circle centered at (h, k) with radius r is:
[tex](x-h)^2+(y-k)^2=r^2[/tex]In this case, the center of the circle is the point (2, 2), then h = 2 and k = 2, that is,
[tex](x-2)^2+(y-2)^2=r^2[/tex]Given that the circle passes through the center, then the point (0, 0) satisfies the above equation. Substituting x = 0 and y = 0 into the equation and solving for r²:
[tex]\begin{gathered} (0-2)^2+(0-2)^2=r^2 \\ 4+4=r^2 \\ 8=r^2 \end{gathered}[/tex]Substituting r² = 8 into the equations, we get:
[tex](x-2)^2+(y-2)^2=8[/tex]A small toy rocket is launched from a 32-foot pad. The height ( h, in feet) of the rocket t seconds after taking off is given by the formula h=−2t2+0t+32 . How long will it take the rocket to hit the ground?t=______(Separate answers by a comma. Write answers as integers or reduced fractions.)
Answers
Given: A small toy rocket is launched from a 32-foot pad. The height (h, in feet) of the rocket t seconds after taking off is given by the formula
[tex]h=-2t^2+0t+32[/tex]Required: To find out how long will it take the rocket to hit the ground.
Explanation: When the rocket touches the ground its height will be zero i.e.,
[tex]\begin{gathered} -2t^2+0t+32=0 \\ 2t^2=32 \\ t^2=16 \end{gathered}[/tex]Which gives
[tex]t=\pm4[/tex]Neglecting the negative value of t since time cannot be negative. We have
[tex]t=4\text{ seconds}[/tex]Final Answer: Time, t=4 seconds.
Find the length of the missing side of the triangle using the Pythagorean theorem. (Type an integer or decimal rounded to the nearest tenth as needed.)
Answers
Pythagorean theorem
[tex]\begin{gathered} a^2=b^2+c^2,\text{ where a is the hypotenuse} \\ a^2=(6.5)^2+(4.9)^2 \\ a^2=42.25+24.01 \\ a^2=66.26 \\ a=\sqrt[]{66.26}=8.1^{\prime} \end{gathered}[/tex](Type an integer or decimal rounded to the nearest tenth as needed.)
Integer = 8'
decimal rounded to the nearest tenth as needed = 8.1'
Find the slope and y intercept of the line 5x - 3y =12
Answers
Answer:
slope = 5/3
y-intercept = -4
Step-by-step explanation:
First, move the x to the other side of the equation:
-3y=-5x+12
Then, divide BOTH sides by -3, so that there is no coefficient next to y:
y=5/3x-4
Then, just look at the constant and coefficient next to x (m). The slope is 5/3 and the y-intercept is -4.
Hope this helps!
Answer:
[tex]y = \frac{5}{3}x - 4[/tex]
Step-by-step explanation:
move the 5x to a -5x
-3y= -5x+12
-3/-3= -5x÷ -3 12÷ -3
the endpoints of line segment DEF are D(1,4) and and F(16,14). Determine and state the coordinates of E, if DE:EF = 2:3.
Answers
The coordinates can be obtained using section formula
[tex]\begin{gathered} \text{Let the coordinates of D be (x}_{1_,}y_1)andFbe(x_2,y_2) \\ \text{The point E divides the line in m:n ratio.} \\ U\sin g\text{ section formula, coordinates of E is} \\ \frac{mx_2+nx_1}{m+n},\text{ }\frac{my_2+ny_1}{m+n} \\ \end{gathered}[/tex][tex]\begin{gathered} (x_1,y_1)=(1,4),(x_2,y_2)=(16,14),\text{ m:n=2:3} \\ \text{Substitute the values in section formula} \\ \frac{2\ast16+3\ast1}{2+3},\text{ }\frac{2\ast14+3\ast4}{2+3} \\ \frac{32+3}{5},\text{ }\frac{28+12}{5} \\ \frac{35}{5},\text{ }\frac{40}{5} \\ 7,\text{ 8} \end{gathered}[/tex]The x coordinate of E is 7 and y coordinate is 8.
What is the meaning of estimate
Answers
The meaning of estimate is approximately calculating an answer to check its accuracy.
Approximate calculation:
Approximate value means the value that is close to this number, less than it, as close as possible, and with a requested level of precision.
For example, the approximate value of π is 3.14
Given,
Here we have the word estimate.
Now, we have to find the meaning of it.
Estimate value means to find a value that is close enough to the right answer, usually with some thought or calculation involved.
For example, let us consider Alex estimated there were 10,000 sunflowers in the field by counting one row then multiplying by the number of rows. Here we doesn't have the exact value instead of that we take the approximate value to identify the number. This process is called estimation.
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Choose Yes or No to tell whether the expressions are equivalent. 4(5c + 3) and 9c + 7 10f – 10 and 2(8f - 5) 12g + 21 and 3(4g + 7)6(4j – 6) and 24 - 36j
Answers
Answer:
Explanation:
Part 1:4(5c + 3) and 9c + 7
[tex]4\mleft(5c+3\mright)=20c+12\neq9c+7[/tex]The answer is NO.
Part 2: 10f – 10 and 2(8f - 5)
[tex]2\mleft(8f-5\mright)=16f-10\neq10f-10[/tex]The answer is NO.
Part 3: 12g + 21 and 3(4g + 7)
Part 4: 6(4) – 6) and 24 - 36
Jason is making bookmarks to sell to raise money for the local youth center. He has 29 yards of ribbon, and he plans to make 200 bookmarks.Approximately how long is each bookmark, in centimeters?
Answers
The Solution:
The correct answer is 13.26 centimeters.
Explanation:
Given that Jason has 29 yards of ribbon, and he plans to make 200 bookmarks.
We are asked to find the approximate length (in centimeters) of each bookmark.
Step 1:
Convert 29 yards to centimeters.
[tex]\begin{gathered} \text{ Recall:} \\ \text{ 1 yard = 91.44 centimeters} \end{gathered}[/tex]So,
[tex]29\text{ yards = 29}\times91.44=2651.76\text{ centimeters}[/tex]Step 2:
To get the length of each bookmark, we shall divide 2651.76 by 200.
[tex]\text{ Length each bookmark = }\frac{2651.76}{200}=13.2588\approx13.26\text{ centimeters}[/tex]Therefore, the correct answer is 13.26 centimeters.
45. For customers generating their own solar power, ZG&E charges them $3 per month per kilowatt (kWh) for excess electricity they export to the grid. Ready Edison charges customers a flat rate of $20 per month and credits them $0.06 per kWh for excess electricity they export to the grid. Determine the monthly bills for customers of both companies for each of the following:(A) Customer owns a 3-kW system and exports 120 kWh monthly to the grid.(B) Customer owns a 5-kW system and export 300 kWh monthly to the grid.
Answers
(A) The customer that owns a 3-kW system exports 120 kWh monthly to the grid will have the following bills for both companies:
For ZG&E that collects $3 per kWh on a monthly basis, the monthly bill will be
[tex]120kWh\times\frac{\$3}{1kWh}=\$360[/tex]For Ready Edison that collects $0.06 per kWh exported energy monthly, the computation of bill will be
[tex]\$20+(120kWh\times\frac{\$0.06}{1kWh})=\$27.2[/tex](B) The customer that owns a 5-kW system exports 300 kWh monthly to the grid will have the following bills for both companies:
For ZG&E that collects $3 per kWh on a monthly basis, the monthly bill will be
[tex]300kWh\times\frac{\$3}{1kWh}=\$900[/tex]For Ready Edison that collects $0.06 per kWh exported energy monthly, the computation of bill will be
[tex]\$20+(300kWh\times\frac{\$0.06}{1kWh})=\$38[/tex]NEED TO FINISH BEFORE 9!!! PLEASE HELP!!!
Answers
A rational value that is less than zero is -√4.
An irrational value greater than five is 5 1/9.
A rational value between 10 and 20 is √225.
What are rational numbers and irrational numbers?A rational number is a number that can be expressed as a fraction of two integers. A rational number can either be a positive number, negative number, whole number, decimal or fraction. Examples of rational numbers are 100, -0.5.
A irrational number is a number that cannot be expressed as a fraction of two integers. An irrational number can either be a positive number, negative number, whole number, decimal or fraction. Examples of irrational numbers are 22/7, 1-/9.
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Triangle ABC lies on the coordinate plane with vertices located at A(7,6), B(-3,5), and C(-4,9). The triangle is transformed using the rule (x,y) -> (2x,y-3) to create triangle A'B'C'. Select all possible answers for the vertices of triangle A'B'C'. Question 1 options: (14,3) (9,3) (-6,10) (-8,6) (-6,2)
Answers
All of the possible answers for the vertices of triangle A'B'C' after using this translation rule (x, y) → (2x, y - 3) include the following:
A. (14, 3)
D. (-8, 6)
What is a translation?In Geometry, a translation can be defined as a type of transformation which moves every point of a geometric figure or object in the same direction, as well as for the same distance.
Next, we would transform triangle ABC by using this translation rule (x, y) → (2x, y - 3) to create the vertices of triangle A'B'C' as follows:
(x, y) → (2x, y - 3)
Coordinate A = (7, 6) → Coordinate A' (2(7), 6 - 3) = (14, 3)
Coordinate B = (-3, 5) → Coordinate B' = (2(-2), 5 - 3) = (-4, 2)
Coordinate C = (-4, 9) → Coordinate C' = (2(-4), 9 - 3) = (-8, 6)
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Harper just lit a new candle and then let it burn all the way down to nothing. The length of the candle remaining unburned, in inches, can be modeled by the equation L=15-1.5t,L=15−1.5t, where tt represents the number of hours since the candle was lit. What is the slope of the equation and what is its interpretation in the context of the problem?
Answers
From the information given, the slope (m) of the equation is -1.5. This means that there is an inverse relationship between the Lenght of the Candle and the number of hours. Where, the longer the number of hours, the smaller the length of the candle. See further explanation below.
What is a slope?The slope of a line is its steepness as it goes from LEFT to RIGHT. The slope is the proportion of a line's rise, or vertical change, to its run, or horizontal change. The slope of a line is always fixed (it never changes) regardless of whatever two locations on the line are chosen.
When dealing with a linear relationship, the question is usually represented in this format:
y = mx + b; where
m = slope and
b= y-intercept (or constant)
From the case above, the equation shows the relationship between time (t) the candle spends burning and the length of the candle (l).
Logically, we can infer that there will be a negative relationship between the two but first lets us determine the slope.
Restating the equation in intercept format, we have:
L = 15 - 1.5t................................1; in intercept format the slope we have
L = -1.5t + 15 ...........................2.
Where L [tex]\sim[/tex] y; m [tex]\sim[/tex] -1.5 and t [tex]\sim[/tex] x; and b [tex]\sim[/tex] 15
Hence we can state that the m (slope) = -1.5 and that if plotted on a graph, the line crosses the y-axis at y = 15 where x = 0.
Also, if L (that is y) is set to zero, then the total time taken for ALL the candles to burn is 10 hours.
See attached graph as proof.
The logical interpretation above is hence confirmed that there is an inverse relationship between x and y. This means that the longer the time, the shorter the length of the candle.
This also means that the length of the candle cannot be or is not longer than 15.
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The slope of the equation is -3/2 describing the rate at which the length of the candle is decreasing.
What are lines and their slopes?We know lines have various types of equations, the general type is
Ax + By + c = 0.
We know slope is the rate of change of the y-axis with respect to the x-axis
also, rise over run which is (y₂ - y₁)/(x₂ - x₁).
The burning equation of the candle is represented by L = 15 - 1.5t.
Where L = length of the candle and any point of time and t = time in hours.
Now, we'll need two points from this equation to obtain the slope.
At, t = 2, L = 12. and at t = 4, L = 9.
So, the two points are (2, 12) and (4, 9).
∴ Slope(m) = (9 - 12)/(4 - 2).
Slope(m) = -3/2.
The slope of this equation describes the rate at which the height of the candle is changing.
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25 men volunteered to lay 1450 pieces of sod around a new church building if each man was given an equal number of pieces how many pieces would each man get
Answers
The number of pieces of sod to lay around the church is 1450 and 25 men volunteered to lay it.
If sod is equally distributed among the men, then each man get sod is equal to number of sod divided by number of men. So,
[tex]\frac{1450}{25}=58[/tex]So each man get 58 number of sod.
Answer: 58
Match the following reasons to the statements given.Given:ABEF isEBDCProve:ACDF is
Answers
Solution
For this case we can do the following:
2. Part of lines FE and AB
4. Transitive
1. Given
5. Definition of parallelogram
3. Opposite sides of a parallelogram are II
Josslyn placed $4,400 in a savings account which earns 3.2% interest, compounded annually. How much will she have in the account after 12 years?Round your answer to the nearest dollar.
Answers
The equation for the total amount after compounded interest is as follows:
[tex]A=P(1+\frac{r}{n})^{nt}^{}[/tex]Where A is the final amount, P is the initial amount, r is the annual interest, n is how many times per year the interest is compounded and t is the time in years.
Since the interest is compounded annually, it is compounded only once per year, so
[tex]n=1[/tex]The other values are:
[tex]\begin{gathered} P=4400 \\ r=3.2\%=0.032 \\ t=12 \end{gathered}[/tex]So, substituteing these into the equation, we have:
[tex]\begin{gathered} A=4400(1+\frac{0.032}{1})^{1\cdot12} \\ A=4400(1+0.032)^{12} \\ A=4400(1.032)^{12} \\ A=4400\cdot1.4593\ldots \\ A=6421.0942\ldots\approx6421 \end{gathered}[/tex]So, she will have approximately $6421.
If a line passes thru the points (5,5) and (9,3) the slope of this line is
Answers
The initial point is (5,5)
the final point is (9, 3)
The formula for determining slope is expressed as
slope = (y2 - y1)/(x2 - x1)
y2 and y1 are the final and initial y values
x2 and x1 are the final and initial x values
From the information given,
x1 = 5, y1 = 5
x2 = 9, y2 = 3
Slope = (3 - 5)/(9 - 5) = - 2/4
Slope = - 1/2
what are the lenghths of the legs in the triangle?give your answer in simplest radical form or rounded to the nearest hundredth.
Answers
Here, we are given a 45°-45°-90° triangle.
Let's find the length of the legs.
A 45°-45°-90° triangle is an isosceles triangle, and the two legs of an isosceles triangle are of equal lengths.
To find the length of each leg apply the formula:
[tex]c=a\sqrt[]{2}[/tex]Where;
c = 12
Thus, we have:
[tex]12=a\sqrt[]{2}[/tex]Solve for a:
Divide both sides by √2
[tex]\begin{gathered} \frac{12}{\sqrt[]{2}}=\frac{a\sqrt[]{2}}{\sqrt[]{2}} \\ \\ \frac{12}{\sqrt[]{2}}=a \\ \\ a=\frac{12}{\sqrt[]{2}} \\ \\ \text{Simplify the denominator:} \\ a=\frac{12}{\sqrt[]{2}}\ast\frac{\sqrt[]{2}}{\sqrt[]{2}} \\ \\ a=\frac{12\sqrt[]{2}}{2} \\ \\ a=6\sqrt[]{2} \end{gathered}[/tex]Therefore, the length of each leg in radical form is 6√2
ANSWER:
[tex]6\text{ }\sqrt[]{2}[/tex]WW Solve the system by substitution. -10x + 4y = -18 and x= y Submit Answer
Answers
Substitute second expression (x=y) in the first expression.
[tex]\begin{gathered} -10x+4y=-18 \\ -10\times y+4y=-18 \\ -6y=-18 \\ y=\frac{-18}{-6} \\ y=3 \end{gathered}[/tex]Substitute the above value of y in the expression number 2.
[tex]\begin{gathered} x=y \\ x=3 \end{gathered}[/tex]Thus, the value of x=3 and the value of y=3.
