Answer:
Factors for 14: 1, 2, 7, and 14
Factors for 21: 1, 3, 7, and 21
Factors for 27: 1, 3, 9, and 27
Decide whether the relation defines y as a function of x. Give the domain.y=√(x-3)Is the equation a function?1)No 2)Yes
By definition, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.
In our equation, for each x value we have exactly one corresponding y-value, therefore, the following equation
[tex]y=\sqrt{x-3}[/tex]is indeed a function of x. The domain is the set of all possible inputs. The argument of a square root can't be negative, therefore, we have the following restriction:
[tex]x-3\geq0\implies x\geq3[/tex]In interval notation, our domain is:
[tex]\lbrack3,\infty)[/tex]please answer the following questions. the first one is answered
Since we have a table for the function, every time we have a value for x, we look for it on the x column and the f(x) value will be the value in the samr row on the f(x) column.
Similarly, if we have a value of f(x), we look for it in the column f(x) and get the corresponding x.
So, if we have f(x) = 1, we see that this value is in the 7th row, and the corresponding x is 6, so x = 6.
For f⁻¹(x) we do the same but switching the columns.
So, to find f⁻¹(9), we would normally look for x = 9, but since it is f⁻¹ we look for f(x) = 9, which is in the 6th row and the corresponding x is 5, so f⁻¹(9) = 5.
For f⁻¹(x) = 6, we would look for 6 on f(x), but since it is f⁻¹ we look for x = 6, which is in the 7th row and the corresponding f(x) is 1 so x = 1.
Using the indicated slopes of lines and L1 and L2, determine whether the lines are parallel, perpendicular, or neither.Assume that the lines are not the same. M1= 4/7, M₂= -7/4 Choose the correct answer below. a)Parallel b)Perpendicular c)Neither
the lines are perpendicular (option B)
Explanation:
For L1 and L2 to be parallel, their slopes must be equal
That is: M1 = M₂
The given slope: M1= 4/7, M₂= -7/4
Hence, they are not parallel as they are not equal
For the lines to be perpendicular, one of the the slope will be the negative reciprocal of the other one:
M1 = 4/7
Reciprocal of M1 = 7/4
Reciprocal means inverse. For
Negative Reciprocal of M1 = -7/4
This is equal to M₂
Hence, the lines are perpendicular (option B)
A babysitter charges $8 per hour for each job sheworks and charges a travel allowance of $10 for eachjob. Which of the following equations gives the numberof hours worked h, the babysitter worked at a job forwhich she charged $78?a) 18h = 78b) 10h + 8 = 78c) 8h + 10 = 78d) 8(10 + h) = 78
A babysitter charges $8 per hour for each job she works, then after h hours, she charges 8h dollars
Also, she charges a travel allowance of $10 for each job, then after h hours in one job, she charges 8h + 10 dollars
If she charged $78, then the equation is:
c) 8h + 10 = 78
Y = 3 x -3+4 graphed
The graph for y = 3x + 1 is given below
What is coordinate plane ?Two number lines combine to form a two-dimensional surface known as a coordinate plane. It is created when the origin, a point where the X- and Y-axes coincide, is crossed by a horizontal line. Points are located using the numbers on a coordinate grid. You can graph points, lines, and many other things using a coordinate plane. It serves as a map and provides clear directions between two points.
Y = 3 x -3+4
y = 3x +1
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We want to fill a basin 3m wide, 5m long and 1m deep using atap with a flow rate of 2m^3 / h.1 °) How long does it take to fill the basin?2 °) Express the flow rate of the tap in L / min. We will round to the hundredth.
Part 1
First we have to find the volume of the basin. We must multiply the dimensions to do so.
V= (3)(5)(1) m^3
V= 15 m^3
If the tap has a flow of 2 m^3 per hour it means that it would take 7.5 hours to fill the basin. ( Dividing 15 m^3 by 2 m^3/h)
The answer of the first part is 7.5 hours.
Part 2
To express the flow rate in L/min we would have to multiply 2m^3 by 1000 ( Since 1000 L= 1 m^3) and then divide the result by 60 minutes ( Since 1 hour has 60 minutes). Doing so, we have:
[tex]2\frac{m^3}{h}\cdot\frac{1000\text{ L}}{1m^3}\cdot\frac{1h}{60\text{ min}}=33.33\text{ L/min}[/tex]The answer of part 2 is 33.33 L/min (Rounding to the hundredth).
What is the measure of ∠ 1 if ∠ 1 is (2x-3) and ∠is (8x)
We know that:
[tex]\angle1+\angle2=180\degree[/tex]Then we have:
[tex]\begin{gathered} (2x-3)\degree+(8x)\degree=180\degree \\ (10x)\degree-3\degree=180\degree \\ (10x)\degree=183\degree \\ x=\frac{183\degree}{10} \\ x=18.3\degree \\ \angle1=2\cdot18.3\degree-3\degree \\ \angle1=33.6\degree \end{gathered}[/tex]Solve 3x + 23 + x = 7.
The answer is x = - 4. The value refers to the worth of each digit in relation to its position in the number.
What is meant by values?We compute it by multiplying the digit's place and face values. Values are benchmarks or ideals against which we judge actions, people, things, or situations. Many people support values such as beauty, honesty, justice, peace, and generosity.
Seven has the numerical value of 7. In the place value chart, seven is in the one column. The number seven can be written as 7% or 7%. By moving the decimal point two places to the left, you can convert 7% to a decimal. 5 has a place value of 500 and is in the hundreds.
Therefore,
Solving 3x + 23 + x = 7
Combine like terms
3x + 23 + x = 7
4x + 23 = 7
Subtract 23 from both sides4x +23 = 7
4x+ 23 - 23 = 7-23
4x = -16
Divide both sides by the same factor4x = -16
4x/ 4 = -16/4
Cancel terms that are in both the numerator and denominator4x/ 4 = -16/4
x = -16/4
Divide the numbersx = -16/4
x = -4
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What is the solution of to the system of the equation
The solution to the system of equation is (3, 2)
How to solve system of equation?The system of equation can be solved as follows:
y = 4x - 10
y = 2
Therefore, using substitution method, let's substitute the value of y in equation(i)
2 = 4x - 10
add 10 to both sides of the equation
2 + 10 = 4x - 10 + 10
12 = 4x
divide both sides by 4
x = 12 / 4
x = 3
Therefore, the solution is (3, 2)
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WILL GIVE BRAINS HELP ME OUT
Answer:
First translation: Horizontal Translation
Second Translation: Reflection over horizontal line
Step-by-step explanation:
Reflection over a line creates a mirror image of the original image relative to the line
Horizontal translation shifts the image to the right or left only relative to the original position and along the x-axis only
Actually, first translation =reflection over horizontal line and second translation of horizontal translation will also result in the same.
13 over 11 equals 4 over uWhat is the proportion of u?
Heather is considering purchasing an item that costs $9. The sales tax in Heather's area is set at 5.9%. What is the total purchase price that Heather would be charged on this purchase?
The total purchase price that Heather would be charged on this purchase is $10.
Solution:
Total charge = $9 x (1 + 0.059)
Total charge = $9 x 1.059
Total charge = $9.531
Total charge ≈ $10.
To calculate sales tax multiply the purchase price by the sales tax rate. Don't forget to convert the sales tax rate from percentage to decimal. When sales tax is calculated, it will be added to the purchase price. The result is the total cost and these are paid by the customer. Most states impose sales tax on top of the cost of each item you purchase.
The total amount you actually pay for the purchase is called the gross price and the price before tax is called the net selling price. To calculate the sales tax on an item, you must first convert the pre-tax cost of the item to a decimal and then multiply it by the sales tax percentage. Once sales tax is calculated, it must be added to the pre-tax value to determine the total cost of the item.
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Name the reference angle in radians for an angle of -315 degree
The angle of -315 degree means angle of 315 degree in clockwise direction from the positive x-axis.
The angle -315 degree means that angle lies in first quadrant as,
So measure of reference angle is,
[tex]360-315=45[/tex]Reference angle in radians is,
[tex]45\cdot\frac{\pi}{180}=\frac{\pi}{4}[/tex]So reference angle of -315 degree in radians is,
[tex]\frac{\pi}{4}\text{ radians}[/tex]Could any one help me figure out the last two parts? Thanks
Given the equation of a quadratic function:
[tex]f(x)=x^2-3x-28[/tex]First, we will find the x-intercepts to find the largest x-intercept
So, substitute f = 0, then solve for x as follows:
[tex]\begin{gathered} x^2-3x-28=0 \\ (x-7)(x+4)=0 \\ x-7=0\rightarrow x=7 \\ x+4=0\rightarrow x=-4 \end{gathered}[/tex]So, The largest x-intercept = 7
Second, we will find the y-coordinate of the y-intercept
So, substitute x = 0
[tex]f(x)=(0)^2-3(0)-28=-28[/tex]So, The y-coordinate of the y-intercept = -28
please help me do this i think i’mdoing it right but i’m not sure The graph shows a parabola and its focus. Write the equation of the parabola in vertex form.
Step 1
Write the parabola in vertex form eqaution
[tex](x-h)^2=-4a(y-k)[/tex]where
[tex]\begin{gathered} h=0=x-\text{coordinate of the vertex} \\ k=1=y-\text{coordinate of the vertex} \end{gathered}[/tex]Step 2
Find the required equation
The distance between the vertex and the focus = a
Therefore,
[tex]\begin{gathered} \text{The vertex=(0,1)} \\ \text{The focus= (0,-2)} \end{gathered}[/tex]Hence with the formula for the distance between two points we have
[tex]\begin{gathered} D=\sqrt[]{(0-0)^2+(-2-1)^2}^{}_{} \\ D=\sqrt[]{0^2+(-3)^2} \\ D=\sqrt[]{0+9} \\ D=\sqrt[]{9} \\ D=3 \\ a=D=3 \end{gathered}[/tex]Step 3
Get the required equation by substitution
[tex]\begin{gathered} (x-h)^2=-4(a)(y-k) \\ (x-0)^2=-4(3)(y-1) \\ x^2=-12(y-1) \end{gathered}[/tex]Hence in vertex form, the equation of the parabola will be
[tex]y=-\frac{1}{12}x^2+1[/tex]The answer is written as;
[tex]y=-\frac{1}{12}x^2+1[/tex]Graph the solution set.-10x≤2y
To be able to determine the graph of this inequality, we'll start rearranging the inequality putting the "y" variable at the left side of the equation.
[tex]\begin{gathered} -10x\leq2y \\ \frac{-10x}{2}\leq\frac{2y}{2} \\ -5x\leq y \\ or \\ y\ge-5x \end{gathered}[/tex]Since the inequality here is greater than or equal to, this means that the shade is above the solid line.
This equation also has a slope of -5 and y-intercept of 0.
Therefore, the graph of this equation looks like this:
Just wondering how I would get the area of the middle part, I have both the triangles and one square down, I just can’t get the middle one.
The total area = Area of a right angle triangle + rectangle
The area of triangle = 1/2 x b x h
base = 11
Height = 8
Area of a triangle = 1/2 x 8 x 11
Area = 8 x 11 / 2
Area = 88/2
Area = 44 square inches
For the first rectangle
Area = Length x width
Length = 11 inches and width = 9 inches
Area = 11 x 9
Area = 99 square inches
Simplify: 21 + 14 + (-18) + (-3) +4
Answer:
Step-by-step explanation:
21 + 14 + (-18) + (-3) +4= 18
21+14=35
35+-18=17
17+-3=14
14+4=18
Hopefully this Helped! :)
Round 9.948 to the nearest whole number.
Answer: 9.900
i had this before the answer is right.You want to be able to withdraw $30,000 from your account each year for 30 years after you retire.You expect to retire in 20 years.If your account earns 6% interest, how much will you need to deposit each year until retirement to achieve your retirementgoals?$Round your answer to the nearest cent.Question Help: Video Post to forum
In this case we are making deposits each year in out account. This will be compounded at a 6% interest.
After 20 years of working and making deposits, the principal accumulated has to be able to give $30,000 per year for 30 years.
We can start with the principal. We assume that during retirement, the account yield 6% interest from the capital still in the account.
Then, we can calculate this principal as the present value of an annuity with payments PMT = $30,000, rate of interest r = 0.06 and n = 30 years.
The calculation is:
[tex]\begin{gathered} PV=PMT\cdot\frac{1-(1+r)^{-n}}{r} \\ PV=30000\cdot\frac{1-(1.06)^{-30}}{0.06} \\ PV\approx30000\cdot\frac{1-0.17411}{0.06} \\ PV\approx30000\cdot\frac{0.82589}{0.06} \\ PV\approx30000\cdot13.7648 \\ PV\approx412944.93 \end{gathered}[/tex]Now we know the amount of capital that has to be accumulated with the deposits.
This value is the future value of an annuity of n = 20 years at a rate r = 0.06.
But now, we need to calculate the yearly deposit D.
We can calculate it as:
[tex]\begin{gathered} D=\frac{FV\cdot r}{(1+r)^n-1} \\ D=\frac{412944.93\cdot0.06}{(1.06)^{20}-1} \\ D\approx\frac{24776.70}{3.207-1} \\ D\approx\frac{24776.70}{2.207} \\ D\approx11225.73 \end{gathered}[/tex]Answer: the yearly deposit has to be $11,225.73.
35•43=43•t what is the value of t
35
Step-by-step explanation:
since 35.43then43.t= 35
How do I find the inserting the missing values? at the rows? How can I Write the rule ,in terms of s and t, to show how t is related to s?
Find: the missing value in the table
Expalantion: i)
[tex]52[/tex][tex]1+\frac{3}{4}\times52[/tex][tex]40[/tex]ii)
[tex]\begin{gathered} 1+(\frac{3}{4}\times x)=55 \\ x=\frac{54\times4}{3} \\ x=72 \end{gathered}[/tex]so the answer of second part will be
[tex]72[/tex][tex]1+(\frac{3}{4}\times72)[/tex]Suppose 4.2 liters of water come out of the faucet each minute. For how many minutes was the faucet on if 52.5 liters of water came out
Answer:
12.5 minutes
Explanation:
Given that:
Number of liters of water come out of the faucet each minute = 4.2 liters
To find the time(in minutes) required for 52.5 liters of water to come out from the faucet.
Number of minutes required = Quantity of water come out from the faucet/ Number of liters of water come out per minute
[tex]\begin{gathered} =\frac{52.5}{4.2} \\ =12.5\text{ minutes} \end{gathered}[/tex]12.5 minutes required for 52.5 litres of water to come out from the faucet.
Find sin 2x, cos 2x, and tan 2x if cosx= 5/13 and x terminates in quadrant IV.
Consider the following expression:
[tex]\cos(x)=\frac{5}{13}[/tex]this expression can be represented in the following right triangle:
To find y, we can apply the Pythagoras theorem as this:
[tex]y=\sqrt{13^2\text{ - 5}^2}\text{ = 12}[/tex]but since x terminates in quadrant IV, we have that
[tex]y=\text{ - 12}[/tex]and thus
[tex]\sin(x)=\text{ -}\frac{12}{13}[/tex]and
[tex]\tan(x)=\text{ -}\frac{12}{5}[/tex]now, using this data in the following formulas:
we can conclude that the correct answer is:
Answer:[tex]\sin(2x)=\text{ -}\frac{120}{169}[/tex][tex]\cos(2x)=\text{ - }\frac{119}{169}[/tex][tex]tan(x)=\frac{120}{119}[/tex]A phone company has a monthly cellular plan where a customer pays a flat monthly fee and then a certain amount of money per minute used on the phone. If a customer uses 410 minutes, the monthly cost will be $71.50. If the customer uses 720 minutes, the monthly cost will be $118.Find a linear equation for the monthly cost of the cell plan as a function of x, the number of monthly minutes used. Type your answer in slope intercept form (y=mx+b) without any spaces between the characters. The function is C(x)=AnswerUse your equation to find the total monthly cost if 687 minutes are used. The cost will be $Answer
The cost for 410 minutes is $71.50 and cost for 720 minutes is $118.
Determine the equation for (410,71.50) and (720,118).
[tex]\begin{gathered} y-71.50=\frac{118-71.50}{720-410}(x-410) \\ y-71.50=\frac{46.5}{310}(x-410) \\ y=0.15(x-410)+71.50 \\ y=0.15x-61.5+71.50 \\ =0.15x+10 \end{gathered}[/tex]So function is C(x) = 0.15x + 10.
Substitute 687 for x in equation to determine the cost for 687 minutes.
[tex]\begin{gathered} C(687)=0.15\cdot687+10 \\ =103.05+10 \\ =113.05 \end{gathered}[/tex]So monthly cost if 687 minutes used is 113.05.
Which reason justifies step 2 of the proof?
JG is common line between both triangle so both triangle's are equal .
What is known as a triangle?
A triangle is a polygon with three vertices and three sides. The triangle's angles are formed by a point where the three sides are joined end to end. The triangle's three angles add up to 180 degrees in total.Given, ∠FJG = ∠HGJ
FG ║ JH
In ΔFJG & ΔGJH
∠FJG = ∠HGJ ( Given)
FG ║ JF ( Given)
∴ JG = JG ( Common )
∵ ΔFJG = ΔGJH
JG is common line between both triangle so both triangle's are equal .
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Margaret has a monthly clothes budget of 50 she maps the Amy of money she spends each month to the number of items of clothing she buys what constraints are there on the domain
It is said that the graph plotted is the money spent to the number of items of clothing bought.
It will look like this:
The domain by definition is the set of inputs.
The constraint on the domain here is the monthly spending cannot be greater than $50.
So the domain will be [0,50] in dollars on the x-axis.
hello please help me out with this and provide an explanation. thanks
We are given the following equation that models the height of a ball:
[tex]h(t)=15t-4.9t^2[/tex]part a) is to find the distance traveled by the ball in the interval [1,3], to do that we replace the values of t=1 and t=2 in the equation, like this
[tex]\begin{gathered} h(1)=15(1)-4.9(1)^2=11 \\ h(3)=15(3)-4.9(3)^{2^{}}=0.9 \end{gathered}[/tex]The total distance is the difference between the two points, that is:
[tex]h(1)-h(3)=11-0.9=10.1[/tex]Vector v is shown in the graph.Which are the magnitude and direction of v? Round the answers to the thousandths place.
Step 1:
First, draw and label the vertical and the horizontal units of the vector.
Step 2:
Write the column vector
[tex]v\text{ = }\begin{bmatrix}{4} & \\ {8} & {}\end{bmatrix}[/tex]Step 3:
[tex]\begin{gathered} \text{Magnitude of v = }\sqrt[]{v^2_x+v^2_y} \\ v_x\text{ = 8 } \\ v_y\text{ = }4 \\ \text{Magnitude of v = }\sqrt[]{8^2+4^2} \\ =\text{ }\sqrt[]{64\text{ + 16}} \\ =\text{ }\sqrt[]{80} \\ MagnitudeofV=\text{ 8.944} \end{gathered}[/tex]Step 4:
Find the direction using the formula below
[tex]\begin{gathered} tan\theta\text{ = }\frac{v_y}{v_x} \\ \tan \theta\text{ = }\frac{4}{8} \\ \tan \theta\text{ = 0.5} \\ \theta=tan^{-1}(0.5) \\ \theta\text{ = }26.565 \end{gathered}[/tex]Final answer
[tex]\begin{gathered} \text{Magnitude = 8.944} \\ \text{Direction = 26.565} \\ \mleft\Vert v\mleft\Vert\text{ = 8.944 , }\theta\text{ = 26.565}\mright?\mright? \end{gathered}[/tex]look at the Pentagonal figure with the dimensions shown in the diagram what is area of the figure ?.
Area of Pentagonal figure = 368 feet²
Explanation:To find the area of the Pentagonal figure, we need to divide the shape into figures we can easily find their areas.
The Pentagonal figure comprise of a triangle and a rectangle.
Area Pentagonal figure = Area of triangle + Area of rectangle
Area of triangle = 1/2 base × height
base = 5 ft, height = 12 ft
Area = 1/2 × 5 × 12 = 30
Area of triangle = 30 feet²
Area of rectangle = length × width
length = 26ft, with = 13 ft
Area of rectangle = 26 × 13
Area of rectangle = 338 feet²
Area of Pentagonal figure = 30 feet² + 338 feet²
Area of Pentagonal figure = 368 feet²
