Domain is the set of x values, or the inputs.
Range is the set of y values, or the outputs.
They are unique.
Looking at the table,
the number of hours is the input on which we have the cost, the output.
So,
We get domain from number of hours
We get range from total cost
1, 3.5, 5, 7.5, and 9 ---- hours (domain)
B is right.
Now,
Range would be the total costs, which are:
2, 6.5, 7, 9, 12.5
F is right.
Correct answers are B and F
Marco says that -2/3 * -45 * 9 + 9 * 2/3 * 4/5 both have a product of 4 and 4/5 explain whether or not Marco is correct
Question:
Solution:
Since 4 4/5 is a mixed number, we have that
[tex]4\text{ }\frac{4}{5}\text{ = }\frac{(4\text{ x 5 ) + 4}}{5}\text{ = }\frac{24}{5}=\text{ 4.8}[/tex]On the other hand, notice that:
[tex]-\frac{2}{3}\text{ x -}\frac{4}{5}\text{ x 9 = }\frac{24}{5}\text{ = 4.8}[/tex]thus:
[tex]-\frac{2}{3}\text{ x -}\frac{4}{5}\text{ x 9 = }\frac{24}{5}\text{ = 4 }\frac{4}{5}[/tex]Now, notice that:
[tex]9\text{ x }\frac{2}{3}\text{ x }\frac{4}{5}=\text{ }\frac{9\text{ x 2 x 4}}{3\text{ x 5}}\text{ = }\frac{72}{15}\text{ = }\frac{24}{5}\text{ = 4.8}[/tex]thus:
[tex]9\text{ x }\frac{2}{3}\text{ x }\frac{4}{5}=4\text{ }\frac{4}{5}[/tex]Then, we can conclude that both expressions have a product of 4 4/5.
An artist in Portland, Oregon, makes bronze sculptures of dogs. The ratio of the height of a sculpture to the actual height of the dog is 2:3. If the height of the sculpture is 14 inches, find the height of the dog.i need a step by step run through to understand
Given,
The ratio of the height of a sculpture to the actual height of the dog is 2:3.
The height of the sculpture is 14 inch.
let the height of the dog be h.
Thus,
[tex]\begin{gathered} \frac{14}{h}=\frac{2}{3} \\ \Rightarrow h=14\times\frac{3}{2}=21inch \end{gathered}[/tex]The actual height of the dog is 21 inch.
What is the value of 22 + x ÷ 11 when x = −176?
Answer:
6
Step-by-step explanation:
22 + -176 ÷ 11
b i division m a s
-176 ÷ 11 = -16
22 - 16 = 6
Answer:
points hehehhehehehe points hehehehehhehehehehehehe points hehehehe
Step-by-step explanation:
I need a deep explanation we are doing this in school pulled out my notes and still don't understand.
For an isosceles triangle, two sides are equal and for right triangle o angle should be of 90 degree.
Let the third point coordinate be (x,y).
The distane between given point (-2,-4) and (4,-4) is 6.
The on angle is 90 degree which means one side is perependicular to the given side.
The coordinate of third point must be equal to (4,y) or (-2,y).
As triangle is isosceles so distance between point (4,y) and (4,-4) is equal to 6.
[tex]\begin{gathered} 6=\sqrt[]{(4-4)^2+(y+4)^2} \\ 6=(y+4) \\ y=6-4 \\ =2 \end{gathered}[/tex]Thus coordinate of third point can be (4,2).
Second case if third point is (-2,y).
Distance between point (-2,y) and (-2,-4) is 6, as triangle is isosceles triangle.
[tex]\begin{gathered} 6=\sqrt[]{(-2+2)^2+(y+4)^2} \\ 6=(y+4) \\ y=2 \end{gathered}[/tex]Thus third coordinate can be (-2,2).
As from the options only (4,2) is correct.
Karl borrowed $5,700 from the bank for a year at 9% simple interest. What was the amount he paid back to the bank?
Simple interest = PRT /100
where P is the principal
R is the rate
T is the time in year
From the question
P=$5700 R=9 T=1
substitute the values into the formula;
S.I = 5700 x 9 x 1 /100
=$513
Amount pay back = $5700 + $513 = $6,213
Point P is located at (4, 8) on a coordinate plane. Point Pwill be reflected over the x − axis. What will be thecoordinates of the image of point P?
SOLUTION:
Step 1:
In this question, we are given that:
Point P is located at (4, 8) on a coordinate plane.
Point P will be reflected over the x-axis.
What will be the coordinates of the image of point P?
Step 2:
How do you reflect a point over the x-axis?
When you reflect a point across the x-axis, the x-coordinate remains the same, but the y-coordinate is taken to be the additive inverse.
The reflection of point (x, y) across the x-axis is (x, -y).
CONCLUSION:
Point P ( 4, 8 ) reflected over the x-axis is ( 4, -8 ) -- OPTION C
Line a is parallel to line b line a passes through the points (1,7) and (2,-4)Line b passes through the point (6,14)The equation of line b is y=__
Given:
Line a is parallel to line b.
Line a passes through the points (1,7) and (2,-4).
Line b passes through the point (6,14).
The objective is to find the equation of the line b in slope intercept form.
For parallel lines the slope of the two lines will be equal.
Consider the coordinates of the line a as,
[tex]\begin{gathered} (x_1,y_1)=(1,7) \\ (x_2,y_2)=(2,-4) \end{gathered}[/tex]The slope of line a can be calculated as,
[tex]\begin{gathered} m_a=\frac{y_2-y_1}{x_2-x_1} \\ =\frac{-4-7}{2-1} \\ =-11 \end{gathered}[/tex]Since both are given as parallel lines, the slop of line b will be,
[tex]m_b=-11[/tex]If the line b passes throught the point (6,14), the equation can be represented as,
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-14=-11(x-6) \\ y-14=-11x+66 \\ y=-11x+66+14 \\ y=-11x+80 \end{gathered}[/tex]Hence, the equation of line b is y = -11x+80.
Find the improper fraction with a denominator of 8 that is equivalent to 3 and 1/2
Given:
he improper fraction with a denominator of 8 that is equivalent to 3 and 1/2.
Required:
Find the improper fraction.
Explanation:
[tex]\begin{gathered} \text{ According to question} \\ \frac{x}{8}=3\frac{1}{2} \\ x=8\times3\frac{1}{2} \\ x=8\times\frac{7}{2} \\ x=28 \\ \text{ So, fraction is }\frac{28}{8}. \end{gathered}[/tex]Answer:
[tex]\text{ Improper fraction is }\frac{28}{8}.[/tex]find the sum of the first 6 terms of the following sequence. round to the nearest hundredth if necessary.35, 14, 28/5,...sum of a finite geometric series:Sn=a1-a1^r^n/1-r
58.09
ExplanationTo find the sum of a finite geometric series, use the formula,
[tex]S_n=\frac{a(1-r^n)}{(1-r)}[/tex]where
[tex]\begin{gathered} a=\text{ first term} \\ r=\text{ common ratio} \\ n=\text{ number of terms} \\ S_n=sumo\text{f the firts n terms} \end{gathered}[/tex]so
Step 1
find the common ratio :
To calculate the common ratio in a geometric sequence, divide the n^th term by the (n - 1)^th term,in other words you can just divide each number from the number preceding it in the sequence
[tex]coomin\text{ ratio =}\frac{n\text{ term }}{(n-1)\text{ term}}[/tex]so
[tex]common\text{ ratio=}\frac{\frac{28}{5}}{\frac{14}{1}}=\frac{28}{70}=0.4[/tex]so r= 0.4
Step 2
Now we can use the formula
a)
let
[tex]\begin{gathered} r=0.4 \\ n=\text{ 6} \\ a=35 \end{gathered}[/tex]b) finally, replace in the formula
[tex]\begin{gathered} S_n=\frac{a(1-r^n)}{(1-r)} \\ S_n=\frac{35(1-0.4^6)}{(1-0.4)} \\ Sn=35*1.62984 \\ Sn=58.0944\text{ } \\ rounded \\ S_n=58.09 \end{gathered}[/tex]therefore, the answer is
58.09
I hope this helps you
What would be and example of a point , a plane , and a line in a classroom setting?
Consider the quadratic function y=2x2 – 12x + 20.Rewrite the equation in vertex format.
The function:
[tex]y=2x^2-12x+20[/tex]has the form:
[tex]y=ax^2+bx+c[/tex]with a = 2, b = -12, and c = 20.
The vertex form of a quadratic function is:
[tex]y=a(x-h)^2+k[/tex]where (h,k) is the vertex.
The x-coordinate of the vertex, h, is computed as follows:
[tex]\begin{gathered} h=\frac{-b}{2a} \\ h=\frac{-(-12)}{2\cdot2} \\ h=\frac{12}{4} \\ h=3 \end{gathered}[/tex]The y-coordinate of the vertex, k, is found replacing h into the formula of the function, as follows:
[tex]\begin{gathered} k=2h^2-12h+20 \\ k=2\cdot3^2-12\cdot3+20 \\ k=18-36+20 \\ k=2 \end{gathered}[/tex]Finally, the quadratic function in vertex form is:
[tex]y=2(x-3)^2+2[/tex]Show exact steps to solve and draw the construction!Don't mind the pink writing.
Step by step:
1. Open the compass to a radius less than half the segment MN.
2. Usin point P as center draw two arcs that intersecs line MN on both sides of the point P (As you use the compass those arcs are in the same distance from point P)
3. Lavel the point of intersection of arcs with line MN (Use any other letter as A and B)
4. Use the points A and B as centers and using the compass draw two arcs (one with each point A and B) above the line that intersects each other.
5. Mark the point of intersection of arcs and link it with point P (as the line needs to go throught P corss point P and continue with the line) . That line is the perpendicular line to MN trought point P)
Metropolis Elementary recommends a ratio of 2 adults for every 24 children on every field trip.
The school has 20 adults and 350 students.
If everyone goes on a field trip, would that meet the recommendation?
If everyone goes on a field trip, then 29 adults are needed for 350 students, so the recommendation by Metropolis Elementary does not meet.
What is ratio?It is the comparison of one quantity with another. For example, if your weight is 30 kg and your father's weight is 90 kg, then the ratio of weight is 1:3.
Given:
The school has 20 adults and 350 students,
The Ratio of adults over children = 2 /24 = 1 / 12, which means for every 12 children there required one adult,
So to find the total adults needed = total students / 12
Total adults needed = 350 / 12 = 29 and 2 children come as a reminder.
Therefore, If everyone goes on a field trip then 29 adults are needed for 350 students, so the recommendation by Metropolis Elementary does not meet.
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finding percent proportions
The total number is 80, Among them 30% are under the age of 7, so the number of players under the age of 7 is,
[tex]30\times\frac{80}{100}[/tex]f(x)=x4-6x2 + 3 (b)(6 pts) Find the intervals where f is concave up and where it is concave down. Locate all inflection points. (You may write on the next page if you need more space for this question.)
The inflection points are (-√3, -6), (0, 3), and (√3, -6). The interval where the function is concave up is (-∞, -1)∪(1, ∞). The interval where the function is concave down is (-1, 1).
We are given a function f(x). The function f(x) is defined as x^4 - 6x² + 3. We need to find all the inflection points of the curve. To find the points of inflection, we need to differentiate the equation of the function with respect to the variable "x". After differentiation, the equation is f'(x) = 4x³ - 12x. We now equate this equation with zero, to get the values of "x".
4x³ - 12x = 0
4x(x² - 3) = 0
So, the values of "x" are ±√3 and 0. Put these values in the original equation to get the corresponding y-coordinates. The points of inflection are (-√3, -6), (0, 3), and (√3, -6). Now we need to find the intervals where the function is concave up and where it is concave down. For this, we need to differentiate the previous equation once again with respect to "x". After differentiation, the equation is f''(x) = 12x² - 12. We now equate this equation with zero, to get the values of "x". If the result is negative, then the function is concave downward. If the result is positive, then the function is concave up.
12x² - 12 = 12(x² - 1) = 0
The values of "x" are -1 and 1.
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Reduce to lowest terms 24/36
To reduce to the lowest terms we notice that:
[tex]\frac{24}{36}=\frac{6\cdot4}{6\cdot6}=\frac{6\cdot2\cdot2}{6\cdot2\cdot3}[/tex]now, we can eliminate the 6 and 2 that repeat in the numerator and denominator, thereforew the fraction in lowest terms is:
[tex]\frac{2}{3}[/tex]write the first three terms of sequence A(n+1)=1/2A(n) for n ≥ 1 and A(1)=4write your answer separated by commas, with no space for example 5,6,7
For n= 1
[tex]A(1+1)=\frac{1}{2}A(1)[/tex]but A(1) = 4
[tex]A(2)\text{ = }\frac{1}{2}(4)\text{ = 2}[/tex]For n= 2
[tex]A(2+1)=\frac{1}{2}A(2)[/tex][tex]A(3)=\frac{1}{2}A(2)[/tex]But A(2) = 2
[tex]A(3)\text{ =}\frac{1}{2}(2)=\text{ 1}[/tex]Hence, the first three terms are;
4, 2, 1
a low-wattage radio station can be heard only within a certain distance from the station. on the graph below, the circular region represents that part of the city where the station can be heard, and the center of the circle represents the location of the station. which equation represents the boundary for the region where the station can be heard,help I need the explanation for it
In order to find the equation that represents this boundary, let's use the equation of the circumference below:
[tex](x-h)^2+(y-k)^2=r^2[/tex]Where r is the radius and the center of the circumference is the point (h, k).
Looking at the image, we can see that the circumference is centered at (-6, -1), and its radius is equal 4 units.
So we can write the following equation, using h = -6, k = -1 and r = 4:
[tex](x+6)^2+(y+1)^2=16[/tex]Therefore the correct option is the second one.
A perfectly vertical stack of dominoes has a volume of 1.8 cubic inches. Another stack of the same number of dominoes is slanted slightly to the right. What is its volume?choice:1.8 cubic inches0.9 cubic incheswe can't tell3.6 cubic inches
If we slanted the dominoes, there is no changes in volume of a dominoes so its volume is 1.8 cubic inches.
Answer: 1.8 cubic inches
a. Use the line of random numbers to obtain and report the resulting list of heads and tails. Use H for heads and T for tails.Q0000 00.000 0.0.000 00000
Given -
An unbiased coin is tossed
To Find -
The list of heads and tails while tossing a coin
Assumption -
The coin is tossed twice
Explaination -
The following table lists some possible arrangements for the experiment
Given: F(x) = 3x^2+ 1, G(x) = 2x - 3, H(x) = xF(x) + G(x) =
Explanation
to add two functions just add like terms,Like terms" are terms whose variables and their exponents, are the same
so
Step 1
let
[tex]\begin{gathered} f(x)=3x^2+1 \\ g(x)=2x-3 \end{gathered}[/tex]hence
[tex]f(x)+g(x)=3x^2+1+2x-3[/tex]we can see the only pair of like terms ar +1 and (-3), so
[tex]\begin{gathered} f(x)+g(x)=3x^2+1+2x-3 \\ \text{add like terms} \\ f(x)+g(x)=3x^2+2x-2 \end{gathered}[/tex]I hope this helps you
calculate the difference quotient and use your results to find the slope of the tangent line
Approximate Slope of a Function
We are given the function:
[tex]H(x)=8\ln x+3[/tex]We will find the approximate value of the slope at (e,11).
It's required to use 3 possible values of the approximation differential h.
Let's use h=0.1 and evaluate the function at x = e + 0.1 = 2.8182818
Compute:
[tex]H(e+0.1)=8\ln 2.8182818+3=11.2890193[/tex]Compute the difference quotient:
[tex]H^{\prime}=\frac{11.2890193-11}{0.1}=2.890193[/tex]Now we use h=0.01:
[tex]H(e+0.01)=8\ln 2.728281828+3=11.02937635[/tex]The difference quotient is:
[tex]H^{\prime}=\frac{11.02937635-11}{0.01}=2.9376353[/tex]Finally, use h=0.001:
[tex]H(e+0.001)=8\ln 2.719281828+3=11.00294249[/tex][tex]H^{\prime}=\frac{11.00294249-11}{0.001}=2.9424943[/tex]The last result is the most accurate, thus the slope of the tangent line is 2.94
Determine whether the relation is a function. y=4x-1 with inputs x= -3, x= -2, and x= -1
Given the equation:
[tex]y=4x-1[/tex]This is a linear relation, and particularly, it is a function because each x-value has one and only one y-value given by the equation above.
We evaluate this function for x = -3, x = -2, and x = -1:
[tex]\begin{gathered} x=-3\Rightarrow y=4(-3)-1=-13 \\ \\ x=-2\operatorname{\Rightarrow}y=4(-2)-1=-9 \\ \\ x=-1\operatorname{\Rightarrow}y=4(-1)-1=-5 \end{gathered}[/tex]4/8 =Express your answer as a whole number or fraction.
Given the fraction:
[tex]\frac{4}{8}[/tex]Let's simplify the fraction.
To simplify, divide the denominator and the numerator by the Greatest Common Factor (GCF).
GCF of 4 and 8 = 4
Hence, we have:
[tex]\frac{4\div4}{8\div4}=\frac{1}{2}=0.5[/tex]Hence, the simplified fraction is:
[tex]\frac{1}{2}[/tex]As a decimal:
[tex]0.5[/tex]ANSWER:
[tex]\frac{1}{2}[/tex]Comelius conducts an experiment where he selects a letter tile from the tiles shown, records the letter, then replaces it in the bag The table shows the results after 50 trialsA 1 0E 18T 18U 4What is the relative frequency that a letter was T? Express your answer as a fraction in simplest form
Relative frequency of T = 9/25
Explanation:Total number of T's = 18
Total number of A's = 10
Total number of E's = 18
Total number of U's = 4
Total = 18 + 10 + 18 + 4 = 50
Relative frequancy = number of time the letter occurred/total letters
Relative frequency = 18/50
To the simplest form:
Relative frequency of T = 9/25
Janet, Li Na, and Katie have 68 beads altogether.Janet has 3 times as many beads as Li Na.Katie has 5 more beads than Janet.How many beads does Katie have?
EXPLANATION:
Given;
We are told that Janet, Li Na and Katie all have a total of 68 beads.
We are also told that;
(i) Janet has 3 times as many beads as Li Na
(ii) Katie has 5 more beads than Janet.
Required;
We are required to find out how many beads Katie has.
Step-by-step solution;
From the conditions given, Janet has 3 times as many beads as Li Na. That means if Li has an y number of beads, Janet's would be times 3.
Therefore, if Li Na is L and Janet is J, then it means;
[tex]\begin{gathered} Li\text{ }Na=l \\ Janet=3l \end{gathered}[/tex]Also we are told that Katie has 5 more beads than Janet. That means, if Katie is K, then;
[tex]\begin{gathered} Janet=3l \\ Katie=3l+5 \end{gathered}[/tex]Bear in mind that they all have a total of 68 beads. Hence, we add up their beads as follows;
[tex]\begin{gathered} LiNa+Janet+Katie=68 \\ l+3l+3l+5=68 \end{gathered}[/tex][tex]7l+5=68[/tex]Subtract 5 from both sides;
[tex]7l+5-5=68-5[/tex][tex]7l=63[/tex]Divide both sides by 7;
[tex]\frac{7l}{7}=\frac{63}{7}[/tex][tex]l=9[/tex]This means Li Na has 9 beads. If Katie's bead is given by the expression 3l + 5, then she will have;
[tex]\begin{gathered} Katie=3l+5 \\ Katie=3(9)+5 \\ Katie=18+5 \\ Katie=23 \end{gathered}[/tex]ANSWER:
Katie has 23 beads.
Use systems to solve :The length of a rectangle is 2 cm more than itswidth. If the perimeter is 52 cm, find the width.
ANSWER
The width is 12 cm
EXPLANATION
The length L of the rectangle is 2 cm more than its width W. With this we have one equation:
[tex]L=W+2[/tex]Then the perimeter is 52cm, which is the sum of the sides of the rectangle:
[tex]P=W+W+L+L=2W+2L[/tex]Therefore the system to solve is:
[tex]\begin{cases}L=W+2 \\ 52=2W+2L\end{cases}[/tex]Using the substitution method we can solve just for W. Replace L in the second equation by its value in terms of W from the first equation:
[tex]52=2W+2(W+2)[/tex]Use the distributive property to eliminate the parenthesis:
[tex]52=2W+2W+4[/tex]Add like terms:
[tex]52=4W+4[/tex]And solve for W:
[tex]\begin{gathered} 4W=52-4 \\ 4W=48 \\ W=\frac{48}{4} \\ W=12 \end{gathered}[/tex]Therefore, the width of the rectangle is 12cm
Given the equation of a line --3x + 4y = -12, determine the following:What is the slope of the line?I22What is the y-intercept? Enter your answer as an ordered pair in the form (x, y).terceptPls see the picture
Answer:
[tex]\begin{gathered} \text{Slope}=\text{ 3/4} \\ \text{ y-intercept= -3} \end{gathered}[/tex]Step-by-step explanation:
Linear equations are represented by the following equation:
[tex]\begin{gathered} y=mx+b \\ \text{where,} \\ m=\text{slope} \\ b=y-\text{intercept} \end{gathered}[/tex]Therefore, to determine the slope and y-intercept of the given equation. Isolate "y" using inverse operations:
[tex]\begin{gathered} -3x+4y=-12 \\ 4y=3x-12 \\ y=\frac{3}{4}x-3 \\ \text{ Hence,} \\ \text{Slope}=\text{ 3/4} \\ \text{ y-intercept= -3} \end{gathered}[/tex]Compare the numbers oS and 0.05. How many times 0.05 is 0.5? Use place value to explain how you know
We will look at the process of decimal point shifts as follows:
[tex]0\text{.05}[/tex]For the above decimal to be manipulated in such a way such that the result is:
[tex]0.5[/tex]Here we see that the digits in the given decimal and the result are exactly the same. However, the placement of decimal point ( . ) has been changed. Such changes in decimal point places are usually accompained by number multiples of ( 10 ).
Now there are two possibilities for the decimal point to move i.e to the right or to the left. If we move the decimal point to the left then we are reducing the value of the decimal ( smaller number ). In such cases we divide the given decimal by multiples of ( 10 ).
Vice versa, If we move the decimal point to the right then we are increasing the value of the decimal ( larger number ). In such cases we multiply the given decimal by multiples of ( 10 ).
The decimal number given to us is smaller than the result decimal. i.e:
[tex]0.5\text{ > 0.05}[/tex]Hence, the given decimal number must be multipled by multiples of 10.
The general rule in moving the decimal point in either multiplying or dividing the multiples of ( 10 )s. Is to count the number of " 0 s" in the this multiples. E.g if we divide:
[tex]\frac{0.2}{10}\text{ = 0.02}[/tex]In above example we divided by ( 10 ). This has ( one zero ). Hence, we will move the decimal point to the left by ( one place ). Another example:
[tex]\frac{236.58}{10000}\text{ = 0.023658}[/tex]In above example we divided by ( 10000 ). This has ( four zeros ). Hence, we will move the decimal point to the left by ( four places ).
The same case applies to multiplication of multiples of 10; however, the only difference is the direction of decimal point moving i.e right.
So with the help of above guidelines and example we see that:
[tex]0.05\cdot10^x\text{ = 0.5}[/tex]We need to determine the number of zeroes for ( 10s ) for which there is only a one place shift to the right side by the decimal point.
The value must be ( x = 1 ). That is we multiple the given ( 0.05 ) by ( 10 ). 10 has only one zero which allow the decimal point to travel to the right side by one digit place. Hence,
Answer:
[tex]\textcolor{#FF7968}{10}\text{\textcolor{#FF7968}{ times 0.05 is 0.5}}[/tex]etec dego BoildName4-1Amber is saving money to buy a bicycie. She saves $60 hergrandfather gave her, and plans to save an additional $5 eachweek. How much will Amber save after wweeks?Total sawingeUse a bar diagram to represent the amountAmber will save after w weeks.S60Amber will save 60Sw dollarsWeeklyvingsMoney from grandfatherafter w weeks.Reggie drives 10 miles from the airport to the highway. Once on the highway, he drives ata speed of SS miles per hour What is Reggie's total distance from the airport h hours afterreaching the highway?1. Complete the bar diagram.Total distance55 mites per hourDitanceHourly distance on highwayhụhwY
Valencia, this is the solution:
Distance Reggie will drive from the airport to the highway = 10 miles
Distance per hour once on the highway = 55 miles
Let h to represent the number of hours Reggie will drive on the highway
In consequence,
Reggie will drive a total distance of 10 + 55h miles from the airport