Answer:
Non-function
Explanation:
A function is a relation from a set of inputs to give a set of outputs.
In a function a particular input can only result in one output only.
Which means one input cannot generate more than one output.
For the given question;
[tex]\mleft\{\mleft(-12,3\mright),(-5,4),(-6,3),(8,-9),(-6,2),(1,7)\mright\}[/tex]We can observe that the output at the input -6 is more than one.
[tex]\begin{gathered} (-6,3) \\ \text{and} \\ (-6,2) \end{gathered}[/tex]A single input -6 produces two outputs 3 and 2.
So, since one input produces more than one output, the data is not a function.
Therefore, It is not a function
Four friends drove from their homes in four different cities to a class reunion. Maren 60 miles 1 hourSafiya 120 miles 3 hoursTomas 84 miles 1.2 hoursCam 75 miles 1.5 hoursWho drove the fastest?
To know who drove the fastest, we need to find the unit rate for every friend.
The unit rate can be calculated as follows:
[tex]undefined[/tex]Hello! The Question is included in the picture. I’m having a hard time understanding this. Please help!
Answer:
A. The sidewalk length: 24.9'
B. The sidewalk width: 21.6'
C. The garden length: 11.7'
D. The garden width: 8.4'
E. Total garden area: 98.3 square inches
Step-by-step explanation:
We have two rectangles (R). Let's define:
R₁ = the biggest rectangle = sidewalk + garden
R₂ = the smallest rectangle = garden
The area of the rectangle R₁ (AR₁) can be calculated as follows:
AR₁ = l₁.w₁
AR₁ = (1.87x+5+x+3+x+3)(1.5x+3+x+3+x+3)
AR₁ = (3.87x + 11)(3.5x + 9)
Also,
AR₁ = area of sidewalk + area of garden
Area of the sidewalk = 64875 square inches = 450.5 square feet
AR₁ = 450.5 + (1.87x + 5)(1.5x + 3)
We can equal both equations to find the value of x:
(3.87x + 11)(3.5x + 9) = 450.5 + (1.87x + 5)(1.5x + 3)
13.5x² + 34.8x + 38.5x + 99 = 450.5 + (2.8x² + 5.6x + 7.5x + 15)
13.5x² + 73.3x + 99 = 2.8x² + 13.1x + 450.5
13.5x² -2.8 x² + 73.3x - 13.1x + 99 - 450.5 = 0
10.7x² + 60.2x - 351.5 = 0
Now, we can use the quadratic formula to the value of x.
According to the quadratic formula:
For a equation:
ax²+ bx + c = 0,
x = (-b ± √Δ)/2a
and
Δ = b² - 4ac
So, in this exercise:
Δ = 60.2² - 4(10.7)(-351.5)
Δ = 3624 + 15044.2
Δ = 18668.2
x = (-60.2 ± √18668.2)/(2*10.7)
x = (-60.2 ± 136.6)/21.4
x₁ = (-60.2 + 136.3)/21.4
x₁ = 3.6'
x₂ = (-60.2 - 136.3)/21.4
x₂ = -9.2'
Since the sides of the rectangle can not be negative, we will use the value of x₁ = 3.6'.
Now, let's calculate the sides of the garden:
lenght: 1.87x + 5
length: 1.87*3.6 + 5
length: 11.7'
width: 1.5x + 3
width: 1.5*3.6 + 3
width: 8.4'
And the area of the garden AR₂:
AR₂ = 11.7*8.4
AR₂ = 98.3 square inches
Finally, let's calculate the sides of the biggest rectangle:
lenght: 11.7 + x + 3 + x + 3
lenght: 11.7 + 3.6 + 3 + 3.6 +3
lenght: 24.9'
width: 8.4 + x + 3 x + 3
width: 8.4 + 3.6 + 3 + 3.6 +3
width: 21.6'
in the graph of the functio Y = x^2 -3, which describes the shift in the vertex of the parabola if the -3 is changed to a 6 ? A.it moves up 6 unites B. it moves up 3 unites C. it moves down 6 unitesD. it moves up 9 unites
In the function y = -x² - 3, the vertex is located at (0, -3)
If we change the -3 by a 6, we get: y = -x² + 6. In this function, the vertex is located at (0, 6). And the vertex moves up 9 units
What would the outputs be when the inputs are 0,1,2,3,4,and 5 if the functionis f(x)=-2x+5
You have the following function:
f(x) = -2x + 5
In order to determine the outputs of the previous function for inputs 0,1,2,3,4 and 5, you simply replace the variable x by 0, 1, 2, 3, 4 and 5 into f(x).
f(0) = -2(0) + 5 = 5
f(1) = -2(1) + 5 = -2 + 5 = 3
f(2) = -2(2) + 5 = -4 + 5 = 1
f(3) = -2(3) + 5 = -6 + 5 = -1
f(4) = -2(4) + 5 = -8 + 5 = -3
f(5) = -2(5) + 5 = -10 + 5 = - 5
Hence, the searched outputs are 5, 3, 1, -1, -3, -5
I need help with this geometry question can someone please help?
The first answer is SSS criteria.
The second answer is SAS criteria.
Now the first answer comes from the fact that we have two triangles which sides are congruent with each other. This means, by the side side side therorem that they have to be congruent.
The second answer comes from the fact that we have two triangle with congruent two pairs of congruent sides and that the angle between them is congruent as well; this means, by the side angle side theorem that the triangles are congruent.
Point A (-4,1) is translated to point A and then point A' is reflected across the x-axis to point A''(7,6). Describe the translation rule that mapped A to A'. Use the grid below.
Point A is at (-4,1) and is translated to point A'=(7,-6).
Next, A'=(7,-6) is reflected across the x-axis to a point A'(7,6).
We can draw these points as:
To get to the point (7,6), we need to translate point (-4,1) to (7,-6) (red point to blue point) since this last point is the reflection of (7,6) (green point) across x-axis.
This can be done by adding 11 steps to x-coordinate and -7 steps to y-coordinate.That is
[tex]\begin{gathered} (-4,1)\Rightarrow(-4+11,1-7) \\ (-4,1)\Rightarrow(7,-6) \end{gathered}[/tex]In resume, the translation rule that mapped A=(-4,1) to A'=(7,-6) is:
[tex](-4,1)\Rightarrow(-4+11,1-7)[/tex]Hello what is the answer to both parts of this question
The formula for the monthly payments is:
[tex]M=P\cdot\frac{\frac{r}{12}\cdot(1+\frac{r}{12})^n}{(1+\frac{r}{12})^n-1}\text{.}[/tex]Where:
• M = monthly payments,
,• P = principal amount = $19300,
,• r = interest rate in decimals = 6.1% = 0.061,
• n = # of years = 3.
Replacing the data of the problem in the formula above, we get:
[tex]M=19300\cdot\frac{\frac{0.061}{12}\cdot(1+\frac{0.061}{12})^3}{(1+\frac{0.061}{12})^3-1}\text{.}[/tex]Answer
[tex]M=19300\cdot\frac{\frac{0.061}{12}\cdot(1+\frac{0.061}{12})^3}{(1+\frac{0.061}{12})^3-1}\text{.}[/tex]A survey asked a random sample students if they estimated they spent more or less than an hour a day on social media.Social MediaMoreLess7th grade12148th grade2026What percent of the 8th graders estimated they spend more than an hour a day on social media? Round your answer to the nearest whole number percent.
Solution
Step 1:
Total number of 8th graders students = 20 + 26 + 12 + 14 = 72
Step 2:
Number that spends less than an hour = 20
Number that spends more than an hour = 26
Step 3:
[tex]\begin{gathered} Percentag\text{e of eight graders that spends more than an hour} \\ =\text{ }\frac{20}{72}\times\text{ 100 \% = 28\%} \end{gathered}[/tex]Final answer
28%
A law firm is going to designate associatesand partners to a big new case. The dailyrate charged to the client for each associateis $600 and the daily rate for each partner is$1200. The law firm assigned a total of 10lawyers to the case and was able to chargethe client $7200 per day for these lawyers'services. Graphically solve a system ofequations in order to determine the numberof associates assigned to the case, x, and thenumber partners assigned to the case, y.
The number of associates assigned to the case = x
The number of partners assigned to the case = y
The daily rate charged to the client for each associate = $600
The daily rate charged to the client for each partner = $1200
The total number of lawyers = 10
x + y = 10............(1)
4. What is the profit the restaurant makes from selling 100 burritos? Does the restaurant make money o lose money? Explain.
if the restauran sells 100 burritos, it obtains $550 dollars.
Then, when the restauran sells 100 burritos it makes money, because the earnings are greater than zero dollars.
Graph the inequality on a plane. (Click to shade a region below or above the line).y > -1
we have the inequality
y> -1
the solution is the shaded area above the dashed line y=-1
see the attached figure below to better understand the problem
how many cups would you need if you doubled the recipe?
We need to solve the following math problem,
[tex]1\frac{3}{4}*2[/tex]Step #1. Convert mixed numbers into improper fractions
[tex]a\frac{b}{c}=\frac{a*c+b}{c}[/tex][tex]1\frac{3}{4}=\frac{1*4+3}{4}=\frac{7}{4}[/tex]Step #2. multiply 7/4 * 2
[tex]\frac{7}{4}*2=\frac{7}{4}*\frac{2}{1}=\frac{7*2}{4*1}=\frac{14}{4}[/tex]Step #3. Simplify
[tex]\frac{7*2}{2*2}=\frac{7}{2}[/tex]Step #4. Convert back to mixed number
[tex]\frac{7}{2}=3\quad\mathrm{Remainder}\quad\:1[/tex]then,
[tex]\begin{gathered} =quotient\frac{remainder}{divisor} \\ \\ \frac{7}{2}=3\frac{1}{2} \end{gathered}[/tex]Answer: 3 1/2 or option b.
14V + 25 − 5V = 4(V + 25)
Step 1
Given; 14V + 25 − 5V = 4(V + 25)
Required; Find V
Step 2
[tex]\begin{gathered} 14V+25-5V=4(V+25) \\ \mathrm{Group\:like\:terms} \\ 14V-5V+25=4\left(V+25\right) \end{gathered}[/tex][tex]\begin{gathered} Add\:similar\:elements \\ 9V+25=4\left(V+25\right) \\ Expand\text{ the bracket} \\ 9V+25=4V=100 \end{gathered}[/tex][tex]\begin{gathered} 9V-4V=100-25 \\ 5V=75 \\ \frac{5V}{5}=\frac{75}{5} \\ V=15 \end{gathered}[/tex]Answer;
[tex]V=15[/tex]If i could just get help with part A please. i have part B right
We can rewrite the fraction inside the square root as:
[tex]\frac{5\cdot3}{3\cdot3}=\frac{15}{9}\text{.}[/tex]Therefore:
[tex]undefined[/tex]a property that states you can multiply numbers mentally by breaking apart one of the numbers and writing it as a sum or difference options:distributive property associative property commutative property
Distributive property can be used to multiply numbers mentally by breaking apart one of the numbers and writing it as a sum or difference.
For example;
[tex]undefined[/tex]Good Evening, Happy Valentine's Day Hi, can you please help with my math problem? Thanks for the help. Have a lovely day. Have a great Sunday. Please help me and Please explain the answer. Can someone please help me with problem 3?
We will solve as follows:
Statement: RS Congruent with RT // Ru bisects angle SRT.
Reason: Given.
Statement: m<1 = m<2.
Reason: Result of RU bisecting
Statement: RU = RU.
Reason: Ru is a common side for triangles SRU & triangle TRU.
Statement: triangle SRU is congruent with triangle TRU.
Reason: The triangles are congruent by SAS [SR congruent with RT, RU common side, and angle 1 congruent with angle 2; what's inside brackets should not be written]
Statement:
Reason: Corresponding angles from congruent triangles are congruent.
without graphing determine the number of solutions to the system of equations
We know that:
• If the two lines have different slopes, the system has exactly one solution.
,• If the two lines have the same slope and y-intercept, the system has infinite solutions.
,• If the two lines have the same slope and different y-intercepts, they are parallel, and the system has no solutions.
Then, we need to know the slopes of the lines.
• Line 1
We write the equation in its slope-intercept form. For this, we solve the equation for y.
[tex]\begin{gathered} y=mx+b\Rightarrow\text{ Slope}-\text{intercept form} \\ \text{ Where m is the slope and} \\ b\text{ is the y-intercept} \end{gathered}[/tex][tex]\begin{gathered} -8x+9y=-8 \\ \text{ Add 8x from both sides} \\ -8x+9y+8x=-8+8x \\ 9y=-8+8x \\ \text{ Divide by 9 from both sides} \\ \frac{9y}{9}=\frac{-8+8x}{9} \\ y=-\frac{8}{9}+\frac{8}{9}x \\ \text{ Reorder} \\ y=\frac{8}{9}x-\frac{8}{9} \end{gathered}[/tex]Then, the slope of this line is 8/9.
• Line 2
As we can see, this line is already in its slope-intercept form.
Then, the slope of this line is -6/7.
Since the lines have different slopes, the system has exactly one solution.
Give the domain of the variable in the following equation
The domain is the set of possible inputs for our expression. The restrictions on the domain are the inputs that results in an indetermination on the expression. The denominator of a fraction cannot be zero, therefore, we have the following restrictions for our equation:
[tex]\begin{gathered} 5x+9\ne0 \\ x\ne0 \\ 3x-4\ne0 \end{gathered}[/tex]Solving each one of them, we get the following restrictions:
[tex]x\ne-\frac{9}{5},\:0,\:\frac{4}{3}[/tex]The domain is:
[tex]\lbrace x|x\:is\:a\:real\:number,\quad x\ne-\frac{9}{5},0,\:\frac{4}{3}\rbrace[/tex]8 as a radical to the 10 power
The correct answer is:
[tex]\sqrt[8]{10\text{ = 1.33}35\text{ }}[/tex]In our solution, we are calculating the 8th root of 10
The equation V=19.4+2.7x gives the value (in thousands of dollars) of an investment after x months.
For this problem, we are given the expression to a linear function:
[tex]V=19.4+2.7x[/tex]That represents the value of an investment in the function of the number of months it passed. We need to interpret the Slope in this situation.
In order to solve this, we first need to identify the slope. The slope is the number multiplying "x" in this instance, we have:
[tex]m=2.7[/tex]It represents the variation the invested money undergoes when one month is passed. For instance, if in the beginning, we have 19.4 thousand dollars, then after one month we will have a value that is 2.7 thousand greater than that.
The value of this investment is increased at a rate of 2.7
hello hope all is well. Can you help me with number 4 please
4.
The virus probably originated in the midwest of the country, spreading mainly to the west and northwest of the country, the most common symptons are:
Fever and headache, to a lesser extent, some patients had stomach pain, cough and nausea.
From 22 subjects tested, 10 succumbed to the disease, and turned into zombies, this represents approximately 45% of the total. Therefore, it is a very dangerous virus, and the necessary measures must be taken to contain it. In addition to starting to develop a vaccine
Write the expression in simplest form. Assume all variables are positive.[tex]x \frac{1}{4} \times x \frac{1}{3} [/tex]
where can I get the volume of this u-shaped diagram?
Answer:
Recall that the volume of a shaped diagram is given by the following formula:
[tex]\text{Volume}=BaseArea\times length\text{.}[/tex]Now, to compute the area of the given base, we will divide the figure as follows:
Then the area of the given figure is:
[tex]A=9\operatorname{cm}\times2\operatorname{cm}+6\operatorname{cm}\times2\operatorname{cm}+6\operatorname{cm}\times2\operatorname{cm}\text{.}[/tex]Simplifying the above result we get:
[tex]\begin{gathered} A=18cm^2+12cm^2+12cm^2, \\ A=42cm^2\text{.} \end{gathered}[/tex]Therefore the volume of the given u-shaped diagram is:
[tex]V=42cm^2\cdot7\frac{1}{2}cm=42cm^2\cdot7.5\operatorname{cm}.[/tex]Simplifying the above result we get:
[tex]V=315cm^3\text{.}[/tex]The volume of the given diagram is 325 cubic centimeters.
line p contains point (6 ,- 5 and is perpendicular to line q the equation for line q is y=3x+5 the slope of line q is 3. the slope of line p is -1/3.) Use the point given for line p and the slope you found to write an equation for line p in point-slope form
We are told that the slope of line p = -1/3
line p can be written as:
y = -1/3x + c
We will substitute the point (6,-5) into the equation to find c.
-5 = -1/3(6) + c
-3 = c
Line p in point slope form is therefore:
y = -1/3x - 3
Twice the product of m and n decreased by the square of the sum of m and n.
1) Gathering the data
2) Simplifying the expression. The use of brackets and parentheses is to avoid confusion.
(a+b)² = a² +2ab +b² The square of the sum
2( m . n ) - [(m+n)²]= Setting the expression
2mn -[m² +2mn +n²] Place the minus outside since it is subtracting
2mn -m² - 2mn -n² Cancel out the opposite terms
-m² -n² Simplest form.
Or we can just let it factored.
2 mn - (m+n)²
Hello. solve for x in the equation x2 - 10x+25=35?
Move the constant on the right side to the left side by subtracting both sides by 35
[tex]\begin{gathered} x^2-10x+25=35 \\ x^2-10x+25-35=35-35 \\ x^2-10x-10=\cancel{0} \end{gathered}[/tex]Now that it is in the standard form of quadratic equation, we can use the quadratic formula to solve for x
[tex]\begin{gathered} \text{The standard form is }ax^2+bx+c=0 \\ \\ \text{In }x^2-10x-10=0, \\ a=1,b=-10,c=-10 \end{gathered}[/tex][tex]\begin{gathered} \text{Use the quadratic formula} \\ x=\frac{ -b \pm\sqrt{b^2 - 4ac}}{ 2a } \\ \\ \text{Substitute the values for }a,b\text{ and }c \\ x=\frac{ -(-10) \pm\sqrt{(-10)^2 - 4(1)(-10)}}{ 2(1) } \\ x=\frac{10\pm\sqrt[]{100-(-40)}}{2} \\ x=\frac{10\pm\sqrt[]{100+40}}{2} \\ x=\frac{ 10 \pm\sqrt{140}}{ 2 } \\ x=\frac{ 10 \pm2\sqrt{35}\, }{ 2 } \\ x=\frac{ 10 }{ 2 }\pm\frac{2\sqrt{35}\, }{ 2 } \\ x=5\pm\frac{\cancel{2}\sqrt[]{35}}{\cancel{2}} \\ x=5\pm\sqrt[]{35} \end{gathered}[/tex]Therefore the solution for the given equation is
[tex]\begin{gathered} x=5+\sqrt[]{35}\text{ or }x=10.9161 \\ \text{AND} \\ x=5-\sqrt[]{35}\text{ or }x=-0.9161 \end{gathered}[/tex]4х + 5y = 19 8х - бу = -10
Here, we want to solve the system of linear equations simultaneously
We start by multiplying the first equation by 2 and the second by 1
[tex]\begin{gathered} 8x\text{ + 10y = 38} \\ 8x-6y\text{ = -10} \end{gathered}[/tex]We can now proceed to subtract the second equation from the first
That will give;
[tex]\begin{gathered} (8x-8x)+(10y-(-6y))\text{ = 38-(-10)} \\ 16y\text{ = 48} \\ y\text{ = }\frac{48}{16} \\ y\text{ = 3} \end{gathered}[/tex]To get the value of x, we will need to substitute the calculated value of y into any of the two initial equations
Thus, we have it that;
[tex]\begin{gathered} 4x\text{ + 5(3) = 19} \\ 4x\text{ + 15 = 19} \\ 4x\text{ = 19-15} \\ 4x\text{ = 4} \\ \text{ x = }\frac{4}{4} \\ x\text{ = 1} \end{gathered}[/tex]This is algebra 2 I’m confused a little bit, I remember the format but it’s a little wonky I guess!
1)
Given:
The objective is to find the transformation of the graph which contians the equation y = √x.
Explanation:
The graph of the equation y = √x is,
1. a)
First, rotate the graph of the function around x axis by multiplying the whole function by (-1).
[tex]y=-\sqrt[]{x}[/tex]By moving 2 units to the left, the transformation will be,
[tex]y=-\sqrt[]{x+2}[/tex]Further transformation of 1 unit to the down side, the equation will be,
[tex]y=-(\sqrt[]{x+2}+1)[/tex]Hence, the required equation of transformation is obtained.
1. b)
First, rotate the graph of the function around y axis by multiplying only the x values of the function by (-1).
[tex]y=\sqrt[]{-x}[/tex]Further transformation of 3 units to the right side, the equation will be,
[tex]y=\sqrt[]{-x+3}[/tex]Hence, the required equation of transformation is obtained.
At the city museum, child admission is $6.60 and adult admission is $9.80. On Sunday, 163 tickets were sold for a total sales of $1363.80. How many adult tickets were sold that day?
ANSWER
[tex]\text{90 adults}[/tex]EXPLANATION
Let the number of children's tickets sold on Sunday be c.
Let the number of adult tickets sold on Sunday be a.
The total number of tickets sold that day is 163. This implies that:
[tex]a+c=163[/tex]The total sales that day is $1363.80. This implies that:
[tex]9.80a+6.60c=1363.80[/tex]From the first equation, make c the subject of the formula:
[tex]c=163-a[/tex]Substitute that into the second equation and solve for a:
[tex]\begin{gathered} 9.80a+6.60(163-a)=1363.80 \\ 9.80a+1075.8-6.6a=1363.80 \\ 9.80a-6.6a=1363.80-1075.8 \\ 3.2a=288 \\ \Rightarrow a=\frac{288}{3.2} \\ a=90 \end{gathered}[/tex]Therefore, there were 90 adult tickets sold that day.
Without graphing, determine whether the following equation has a graph that is symmetric with respect to the x-axis, the y-axis, the origin, or none of these.x² + y² = 16Select all that apply.A. y-axisB. originC. x-axisD. none of these
Given,
The equation of the graph is,
[tex]x^{2}+y^{2}=16[/tex]By replacing x by -x, if the equation remain the same then it is symmetric about the x axis.
[tex]\begin{gathered} (-x)^2+y^2=16 \\ x^2+y^2=16 \end{gathered}[/tex]Hence, the equation is symmetric about x axis.
By replacing y by -y, if the equation remain the same then it is symmetric about the y axis.
[tex]\begin{gathered} (x)^2+(-y)^2=16 \\ x^2+y^2=16 \end{gathered}[/tex]Hence, the equation is symmetric about y axis.
The equation is symmetric about the origin.
Hence, The equation is symmetric about x- axis, y-axis and origin.