The given situation can be written as a system of equations. Based on the given information you have:
x + y = 457
2x + 3y = 1161
where x is the number of student tickets and y is the number of y tickets.
In order to determine the values of x and y, proceed as follow:
- multiply the first equation by -2:
(x + y = 457)(-2)
-2x - 2y = -914
- then, add the previous equation to the second equation of the system:
-2x - 2y = -914
2x + 3y = 1161
y = 247
- next, replace the previous value of y into the first equationof the system, and solve for x:
x + y = 457
x + 247 = 457
x = 457 - 247
x = 210
Hence, the number of student tickest sold was 210, and adult tickets sold was 247
To qualify for a certain need-based scholarship, a student must get a score of at least 75 on a qualification test. In addition, the student's family must make less than $40.000 a year. Define the variables, write a system of inequalities to represent this situation, and name one possible solution.WRITE TWO INEQUALITIES AND ONE POSSIBILITY:
In this problem we have to define the variables, so we can call the score of the student as x and the amount of money of the family let's call y so the inequalitys are:
[tex]\begin{gathered} x>75 \\ y<40000 \end{gathered}[/tex]How do I match these polynomial and what are the correct matches?!
Add the polynomials:
[tex](-4x^2-3x+6)+(6x^2-2x+1)[/tex]Removing the parentheses:
[tex]-4x^2-3x+6+6x^2-2x+1[/tex]Collecting like terms:
[tex]2x^2-5x+7[/tex]Find the opposite of:
[tex]2x^2+x-7[/tex]We change the signs of all terms:
[tex]-2x^2-x+7[/tex]Subtract:
[tex](-4x^2+2x-1)-(-2x^2+3x+6)[/tex]Remove the parentheses, but the last one requires changing the signs of the second polynomial (find the opposite):
[tex]-4x^2+2x-1+2x^2-3x-6[/tex]Collecting like terms:
[tex]-2x^2-x-7[/tex]Hello there I need help with this.Ben and his friend go to buy some water.Still water and sparkling water both cost $p per bottle. Ben and his friend bought 2 bottles of sparkling water and 3 bottles of still water.They spent $6.50 altogether.What is the algebraic equation of the total price T?
ANSWER
The algebraic equation of the total price T is T = 3p + 2p or (6.50 = 3p + 2p)
STEP-BY-STEP EXPLANATION:
Given parameters
• Cost of still water per bottle = $p
,• Cost of sparkling water per bottle = $p
,• The number of sparkling water bottles purchased = 2
,• The number of still water bottles purchased = 3
,• The total amount of money spent altogether = $6.50
As you can see from the question, Ben and his friend spent $6.50 altogether to purchase 2 bottles of sparkling water and 3 bottles of still water. This implies that the total cost is $6.50
Total cost = (number of still water bottles x cost per bottle) + (number pf sparkling water bottles x cost per bottle)
Let the total cost be T
Mathematically, this can be written as
T = (3 * p) + (2 * p)
T = 3p + 2p
Recall that, T = $6.50
6.50 = 3p + 2p
Hence, the algebraic equation of the total price T is T = 3p + 2p or (6.50 = 3p + 2p)
consider the function w(x) = 2x^3 + 15x^2 -36x - 6 on interval -6 ≤ x ≤ 2
On the given interval this function has absolute:
Minimum at the point -
Maximum at the point -
The minimum absolute value of the function is at x = 1 and the maximum absolute value is at x = -6.
What is absolute value?Absolute value describes the distance from zero that a number is on the number line, without considering direction.
Given a function, f(x) = 2x³+15x²-36-6
f'(x) = 6x²+30-36
Let f'(x) = 0
6x²+30-36 = 0
On solving, we get,
x = 1 or -6
Putting x = 1,-6, 2 for maximum and minimum values
f(1) = -25
f(-6) = 318
f(2) = -2
Hence, the minimum absolute value of the function is at x = 1 and the maximum absolute value is at x = -6.
For more references on absolute value, click;
https://brainly.com/question/1301718
#SPJ1
Blake is cutting drdles out of construction paper. Each circle has a radius of 6 inches. How
much paper will he use to cut 10 circles (round your answer to the nearest tenth of a square
inch)?Use 3.14 for #.
Anyone can help like now?☹️
He is cutting circles. Each circle has 6 inches of radius. He needs 10 circles.
So, the area of one circle is A=pir²
A=3.14*6²
A=3.14*36
A=113.04
But there are 10 of them, so the total area will be 1130.4 in² of construction paper.
Simplify the expression by combining like terms [tex]16 + 8a - 3a + 6b - 9[/tex]
There are two kinds of like terms:
• Variable like terms: These are the terms that have the same variable. For example, 10x and -3x are like terms.
,• Independent like terms: are the terms that don't have any variables. For example, 7 and -30 are like terms.
The important thing about like terms is that we can combine them.
The expression we have is:
[tex]16+8a-3a+6b-9[/tex]The terms 8a and -3a are variable like terms because they have the same variable "a", so we combine them by subtracting 8a-3a which results in 5a:
[tex]16+5a+6b-9[/tex]The term 6b does not have any like term because there are no other terms that contain the variable "b", so we leave that term as is.
Now, the terms 16 and -9 are independent like terms, so we can also combine them.
To combine 16 and -9, we subtract 16-9, and the result is7, so we put 7 in the expression in the place of 16-9:
[tex]5a+6b+7[/tex]Answer:
5a+6b+7
I did something wrong here according to my teacher. Can you help?
Answer:
• Line of Symmetry: x=-0.5
,• Vertex: (-0.5, 5.5)
,• Maximum
,• y-intercept: (0, 3)
Explanation:
Given the quadratic function:
[tex]y=-10x^2-10x+3[/tex]Comparing with the form y=ax²+bx+c:
[tex]a=-10,b=-10,c=3[/tex](a)Line of Symmetry
The equation of symmetry is determined using the formula:
[tex]\begin{gathered} x=-\frac{b}{2a} \\ =\frac{-(-10)}{2(-10)} \\ =\frac{10}{-20} \\ x=-0.5 \end{gathered}[/tex](b)Next, we find the corresponding y-value.
[tex]\begin{gathered} y=-10x^{2}-10x+3 \\ y=-10(-0.5)^2-10(-0.5)+3 \\ y=5.5 \end{gathered}[/tex]The vertex of the parabola is (-0.5, 5.5).
(c)Since the value of a is negative, the vertex is a maximum.
(d)y-intercept
The y-intercept is the value of y when x=0.
[tex]\begin{gathered} y=-10x^{2}-10x+3 \\ y=-10(0)^2-10(0)+3 \\ y=3 \end{gathered}[/tex]The y-intercept is at (0, 3).
Consider the function [tex]y = x ^{3} - 3x[/tex]Find the intervals the function is increasing. Express your answer in interval notation (a,b)
The given expression is
[tex]y=x^3-3x[/tex]To know the intervals where this function is increasing, we graph it
As you can see from the graph, the increasing intervals are
[tex]I=(-\infty,-1)\cup(1,\infty)[/tex]Ella finished a bike race in 37.6 minutes. Miranda finished the race 9 1/10 minutes sooner than Ella finished it. How many minutes did it take Miranda to finish the race?A. 32.5 minutes B. 46.7 minutes C. 28.59 minutes D. not here
The time that it took Ella to finish the race is: 37.6 minutes.
Since Miranda finished the race 9 1/10 minutes sooner, to find Miranda's time we need to subtract 9 1/10 from Ella's time of 37.6 minutes.
Miranda's time:
[tex]37.6-9\frac{1}{10}[/tex]To solve the problem it is easier if we convert 9 1/10 to a decimal number. Since 1/10 is equal to .1, the equivalent value of 9 1/10 is:
[tex]9\frac{1}{10}=9.1[/tex]Updating the expression to find Miranda's time:
[tex]37.6-9.1[/tex]And the result of the subtraction is:
[tex]28.5[/tex]It took Miranda 28.5 minutes to finish the race. Since this value is not one of our options, the answer is D. not here
F(x) =2x^2+12x-6 Does this function have a minimum or maximum value? What is this minimum or maximum value?
Let's compare the given function with the model for a quadratic equation:
[tex]\begin{gathered} f(x)=ax^2+bx+b \\ a=2,b=12,c=-6 \end{gathered}[/tex]Since the value of a is positive, the parabola has its concavity upwards, and the function has a minimum value.
The minimum value can be found calculating the y-coordinate of the vertex:
[tex]\begin{gathered} x_v=-\frac{b}{2a}=-\frac{12}{4}=-3 \\ \\ y_v=2\cdot(-3)^2+12\cdot(-3)-6 \\ y_v=2\cdot9-36-6^{} \\ y_v=-24 \end{gathered}[/tex]Therefore the minimum value is -24.
Determine number of lines of symmetry for this figure
There are 4 lines of symmetry in the figure. The angle of rotation that map the figure onto itself is angle 90°.
What is a line of symmetry?
This refers to the line that cuts a shape or an object into two equal and symmetrical parts. It also is called the axis of symmetry or mirror line this is because it divides the figure symmetrically, thus dividing the parts to look like mirror reflections of each other.
Types of Symmetry
.Rotational symmetry
.Reflection symmetry
.Translation symmetry
.Glide reflection symmetry.
Learn more about lines of Symmetry on
https://brainly.com/question/4032475
#SPJ1
how would you solve d=9rt for t
d = 9rt
9 and r are multiplying on the right, then they will divide on the left
[tex]\frac{d}{9r}=t[/tex]Find an equation of the line parallel to the graph of y = -3x - 11 that passes through the point of (2,4). Write your equation in slope-intercept form.
Find an equation of the line parallel to the graph of y = -3x - 11 that passes through the point of (2,4). Write your equation in slope-intercept form.
__________________________________________________________
Line parallel to the graph of y = -3x - 11
1. The slope-intercept form.
y = mx + b
m= slope
y-intercept is (0, b)
The lines parallel has the same slope (m) = -3
_______________________________________
Using the point-slope form
(y-y1)= m (x-x1)
2. Replacing the point and the slope
(2,4) x1= 2; y1 = 4
(y- 4)= -3 (x- 2)
3. Write your equation in slope-intercept form.
y = -3x +6 +4
y = -3x + 10
___________________
Answer
y = -3x + 10
PLEASE HELP!!!
Match the number with the most specific number set to which it belongs.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
-45
100−−−√
89−−√
4.91919191.....
-2/5
0.12112111211112....
The translation rule that matches the transformation for congruent angles is given as follows:
(x,y) -> (x + 4, y - 5).
What are the translations?The translations are movements to the triangle in each of these directions:
Up.Down.Left.Right.There were two translations in this problem, listed as follows:
From triangle GHI to triangle G'H'I'.From triangle G'H'I' to triangle G''H''I''.For the first translation, the triangle was moved down five units, hence the rule is given as follows:
y -> y - 5.
For the second translation, the triangle was moved right four units, hence the rule is given as follows:
The complete translation, obtained by the combination of each translation, is given as follows:
(x,y) -> (x + 4, y - 5).
Meaning that the first option is the correct option.
More can be learned about translations at brainly.com/question/28174785
#SPJ1
Find the simple interest and the total amount after three years.Principal = 7800 rupeesAnnual rate of interest = 9.5%Total interest=rupeesTotal amount =rupees
Answer:
The value of the simple interest and the total value after three years is;
[tex]\begin{gathered} \text{Total interest = 2223 rupees} \\ \text{Total amount = 10023 rupees} \end{gathered}[/tex]Explanation:
Given the following;
[tex]\begin{gathered} \text{ Principal P= 7800 rupees} \\ \text{Annual rate of interest = 9.5\%} \end{gathered}[/tex]We want to find the simple interest and the total amount after three years.
[tex]t=3\text{ years}[/tex]The simple interest formula;
[tex]\begin{gathered} I=\frac{Prt}{100} \\ F=P+I \end{gathered}[/tex]substituting the given values;
[tex]\begin{gathered} I=\frac{7800\times9.5\times3}{100} \\ I=2223\text{ rupees} \end{gathered}[/tex][tex]\begin{gathered} F=P+I=7800+2223 \\ F=10,023\text{ rupees} \end{gathered}[/tex]Therefore, the value of the simple interest and the total value after three years is;
[tex]\begin{gathered} \text{Total interest = 2223 rupees} \\ \text{Total amount = 10023 rupees} \end{gathered}[/tex]Is there a tutor that can help me?
You have the following equation:
9x - 5y = 6
In order to find the equation of the line, you first calculate the slope of the previous line equation:
9x - 5y = 6 subtract 9x both sides
9x - 9x - 5y = 6 - 9x simplify
-5y = -9x + 6 divide by -5 both sides
-5y/(-5) = -(9/5)x + 6/5 simplify
y = -(9/5)x + 6/5
y = -1.8x + 1.2
Then, the slope of the line is m=-1.8
Now, to find the equation of the line with the point (6,-2) you use the following formula for the slope of a line:
m=(y-yo)/(x-xo)
due to the required line is parallel to the line with slope -1.8, the slope of the required line is the same, m = -1.8. xo and yo are the given coordiantes of the given point (6,-2), that is, xo = 6 and y = -2. You replace these values into the formula for the slope and solve for y:
m = (y - (-2))/(x - 6) = (y + 2)/(x - 6) multiply both sides by (x-6)
(x-6) m= y + 2
y = mx - 6m - 2 = (-1.8)x - 6(-1.2) - 2
y = -1.8x - 5.2
This last equation is the required equation
the width of a rectangular rug is 3 1/4 inches longer than twice its length. if the perimeter of the rug is 54 1/2 inches, which equation represents this situation?
The equation represents the relation of perimeter with length and width is 109/4 = 24 l + 13.
What is meant by the perimeter of the rectangle?For the given question;
Let the dimensions of the rectangle be;
Length lWidth wPerimeter PFor the condition, width of a rectangular rug is 3 1/4 inches longer than twice its length.
w = 2×l + 3 1/4
Solve the mixed fraction;
w = 2×l + 13/4
Now, the perimeter is;
P = 2(l + w)
P = l x w
Put the value of w.
P = 2 ( l + 2×l + 13/4) ....eq1
P = 54 1/2 inches = 109/4
Put in eq 1
109/4 = 3 l + 13/4
109/4 = 24 l + 13
Multiplying equation by 4.
109/4 = 24 l + 13
Thus, the equation represents the relation of perimeter with length and width is 109/4 = 24 l + 13.
To know more about the perimeter of the rectangle, here
https://brainly.com/question/27591380
#SPJ1
Let g(x) = - 7x + 4. Find g(2)
The given expression : g(x) = -7x+4
to find the value of g(2)
Substitute x = 2 in the function of g(x)
g(x) = -7x + 4
g(2) = -7 (2) +4
g(2) = -14+4
g(2) = -10
Answer : -10
Harry owns a car dealership during a sale one week he sold 8 small cars out of 11 cars he sold Harry sold a total of 33 cars doing the sale. How many cars did he sell during the sale?a. 8b. 9c. 24d. 33
Harry sold 8 smalls cars out of 11 cars.
At the end of the sale He sold 33 cars.
In order to determine how many small cars did Harry sell in the week, you take into account that the proportion of small cars for each sale is 8/11.
To find the total small cars sold in the week you multiply the proportion of small cars by the total cars sold in the week, just as follow:
(8/11)33 = 8(33/11) = 8(3) = 24
Hence, the small cars sold during the week were 24.
c. 24
Complete the two-column proof that the diagonals of a rhombus are perpendicular. Glven: JKLM Is a rhombus Prove:JL I MK J N M K L Part 1 out of 7 Statements Reasons 1.JM JK 1. Definition of rhombus 2. MN AKN 2. (select) Check Next
Corresponding parts of the congruent triangles are congruent. This implies that the corresponding part of the triangles are equal
Also, all the four angles are congruent and they are equal to 90 degrees.
The diagonals are perpendicular to each other
The table below shows Addison's novel collection on her bookshelf.
Please help me with this I need it fast (view the image)
The total number of books is 11 thus the ratio of fiction novels to all novels will be 5/11 thus, option (C) is correct.
What are the ratio and proportion?The ratio is the division of the two numbers.
For example, a/b, where a will be the numerator and b will be the denominator.
Proportion is the relation of a variable with another. It could be direct or inverse.
As per the given,
Number of nonfiction books = 2
Number of mystery books = 4
Number of fiction books = 5
Total number of books = 2 + 4 +5 = 11
Thus, the ratio of fiction books to all books,
⇒ 5/11
Hence "The total number of books is 11 thus the ratio of fiction novels to all novels will be 5/11".
For more information about ratios and proportions,
brainly.com/question/26974513
#SPJ1
lan's mom works two part time jobs, one in the morning and one in the afternoon, for a total of 35 hours each 5-daywork week. If her schedule is the same each day, and she works 4 hours each morning, how many hours does she workin the afternoon?
lan's mom work for total 35 hours in 5-days week, so each day she worked for,
[tex]\frac{35}{5}=7[/tex]So Ian's mom worked 7 hours each, in which she work 4 hours each morning.
Determine the number of hour's Ian's mom work in afternoon in one day.
[tex]7-4=3\text{ }[/tex]So each day Ian's mom work 3 hours in the afternoon.
A marketing research company desires to know the mean consumption of meat per week Among people over age 31 they believe that the meat consumption has mean of 3.1 pounds and want to construct a 85% confidence interval with the maximum error of 0.06 pounds assuming a standard deviation of 0.8 pounds what is the minimum number of people over age 31 they must include in their sample? Round your answer up to the next integer
ANSWER:
369
STEP-BY-STEP EXPLANATION:
Given:
Mean (μ) = 3.1
Standard deviation (σ) = 0.8
Margin of error (E) = 0.06
At 85% confidence level the z is:
[tex]\begin{gathered} \alpha=1-\text{ confidence level} \\ \\ \alpha=1-85\%=1-0.85=0.15 \\ \\ \alpha\text{/2}=\frac{0.15}{2}=0.075 \\ \\ \text{ The corresponding value of z according to the table is:} \\ \\ Z_{\alpha\text{/2}}=1.44 \end{gathered}[/tex]We can determine the sample size using the following formula:
[tex]\begin{gathered} n=\:\left(\frac{Z_{\alpha\text{/2}}\cdot\sigma}{E}\right)^2 \\ \\ \text{ We replacing:} \\ \\ n=\left(\frac{1.44\cdot0.8}{0.06}\right)^2 \\ \\ n=368.64\cong369 \end{gathered}[/tex]The size of the sample is 369
Zeros 4 and -3iI already asked for the last question, but I’m confused for the i
Given:
The zeros of the polynomial are 4 and 3i.
Required:
To find the polynomial of the function.
Explanation:
Here
[tex]\begin{gathered} x=4 \\ x=-3i \end{gathered}[/tex][tex]\begin{gathered} x-4=0\text{ and} \\ x+3i=0 \end{gathered}[/tex]Therefore
[tex]\begin{gathered} (x-4)(x+3i)=0 \\ \\ x^2-4x-3ix-12i=0 \\ \\ x^2-(4+3i)x-12i=0 \end{gathered}[/tex]Final Answer:
[tex]x^2-(4+3i)x-12i=0[/tex]angle1=73°angle2=34°angle3=73°Classify the triangle(by the side and by the angles)
isosceles triangle
Explanation
we have a triangle with two equal angles
[tex]\text{angle}1=\text{angle}3=73\text{ degr}ees[/tex]An isosceles triangle, therefore, has both two equal sides and two equal angles
IncorrectYour answer is incorrectA vehicle factory manufactures cars. The unit cost C (the cost in dollars to make each car) depends on the number of cars made. If x cars are made, then theunit cost is given by the function C()0.3x-66x + 13,267. What is the minimum unit cost?Do not round your answer.Unit cost: S1dxCheckSave For LaterSubmit AssignmentPrencyAceeshhy1125 PMWednesday1620212021 MMcGraw-H Education, All Riathts Resered.Torms of Use9Type here to search
Please check that the expression for the cost you typed reflects what you read in the problem.
Isn't there a "square" in one of the "x" values of the cost equation?
Great. I see now the actual equation for cost to be:
Cost = 0.3 x^2 - 66 x + 13267.
The minimum unit cost will be given by the minimum of this quadratic function (a parabola) which has a minimum at the parabola's vertex. Notice this is a parabola with branches pointing UP because the coefficient of the term in x^2 is POSITIVE.
Recall then the equation for the x position of the vertex of a pparabola with equation of the form:
y = a x^2 + b x + c
the x-position of the vertex is: x = - b / (2a)
which in our case gives:
x of the vertex = - (- 66) / (2 * 0.3) = 110
Then, since the x values represent the number of cars that are made , we now that that minimum occurs when the number of cars produced is 110.
We replace this value in the cost equation and get:
Cost = 0.3 (110)^2 - 66 (110) + 13267 = 9637
Then, the unit cost for making the 110 cars is $9637, which is in fact the minimum value we were looking for.
What is the range of the function?Type the range using interval notation example : (#,#]
The range of the function is the values of y
Then to find it, look for the smallest and the greatest value of y of the graph of the function
From the given figure
The lowest value of y is -1
The highest value of y is 3
Then the range of the function is [-1, 3]
complete the number sentence to solve enter this answer in simplest form 6 students share 8 granola bars equally how many granola bars does each student get?
4/3 of each granola bar ( 1 1/3)
1) Given that 6 students share 8 granola bars we can write the following fraction with 8 on the numerator and 6 on the denominator since it is a division:
[tex]\frac{8}{6}=\frac{4}{3}\text{ or 1.333}[/tex]2) Each student will get 4/3 of each granola bar or 1 and 1/3
Divide by multiplying by the reciprocal of the divisor 1/4 / 2/7
We want to divide 1/4 / 2/7
If we take the reciprocal of the 2/7, it means that the division sign will change to multiplication. Reciprocal of 2/7 = 7/2
Thus, the expression will be
1/4 x 7/2
= 7/8
I need help converting standard form to vertex form with quadratic equations. The equation is: y = -x^2 + 12x -4I think I am supposed to complete the square, but I am unsure how to do this. I am also unsure about what to do with the negative sign. I would love clear, step by step instructions on the process so I can know how to do it in the future.
Okay, here we have this:
Considering the provided equation in standard form, we are going to convert it to vertex form step by step, so we obtain the following:
y = -x²+ 12x -4
Considering that the model of an equation in standard form is y=ax²+bx+c. First we are going to axtract "a" from the first two terms:
y=-1(x²-12x)-4
Now, we are going to complete the square for the expressions with x, so we have:
y=-1(x²-12x+36-36)-4
y=-1((x - 6)²-36) -4
And, finally we are going to simplify:
y=-1(x - 6)²+36-4
y=-(x - 6)²+32
We obtain that the equation in vertex form is y=-(x - 6)²+32.