y=2x²-4x-16 will be the required equation of parabola as the x-intercepts of parabola is (-2, 0) and (4, 0) and a = 2.
What is parabola?A parabola is an approximately U-shaped, mirror-symmetrical plane curve in mathematics. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves. A parabola can be described using a point and a line. Drawing a parabola for the quadratic function f(x) = ax² + bx + c results in a U-shaped curve. When an is less than zero, the parabola's graph is downward (or opens downward). Three different parabolas exist. Vertex form, standard form, and intercept form are the three forms. You can access a unique key feature for the graph on each form.
Here,
y = a(x − p)(x − q)
p=-2
q=4
a=2
y=2(x--2)(x-4)
y=2(x+2)(x-4)
y=2(x²-4x+2x-8)
y=2x²-4x-16
The necessary parabola equation will be y=2x²-4x-16 since its x-intercepts are (-2, 0) and (4, 0) and its value of a is 2.
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What is the equation of a polynomial function, R, with rational coefficients that
have a zero of 4 + √5 and 3i?
The equation of a polynomial function, R, with rational coefficients will be;
P (x) = x² - (3i + √5 + 4)x + (12 + 3√5) i
What is Quadratic equation?
An algebraic equation with the second degree of the variable is called an Quadratic equation.
Given that;
The zeroes of the polynomial function are;
⇒ 4 + √5 and 3i
Now,
Since, The zeroes of the polynomial function are;
⇒ 4 + √5 and 3i
So, The factor of the polynomial function are;
(x - (4 + √5)) and (x - 3i)
Hence, We can formulate the polynomial function as;
P (x) = (x - (4 + √5)) (x - 3i)
= (x - 4 - √5) (x - 3i)
= x² - 3ix - 4x + 12i - √5x + 3√5i
= x² - (3i + √5 + 4)x + (12 + 3√5) i
Thus, The equation of a polynomial function, R, with rational coefficients will be;
P (x) = x² - (3i + √5 + 4)x + (12 + 3√5) i
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Mai is going to rent a truck for one day. There are two companies she can choose from, and they have the following prices.Company A charges $97 and allows unlimited mileage.Company B has an initial fee of $55 and charges an additional $0.70 for every mile driven.For what mileages will Company A charge less than Company B?Use m for the number of miles driven, and solve your inequality for m.
Answer:
m>60
Explanation:
Let the number of miles driven = m
Company A charges $97 and allows unlimited mileage.
[tex]\text{ Total Charge for Company A}=\$97[/tex]Company B has an initial fee of $55 and charges an additional $0.70 for every mile driven.
[tex]\text{ Total Charge for Company B}=55+0.70m[/tex]When the charge for Company A is less than that of Company B:
[tex]97<55+0.70m[/tex]We then solve the inequality for m:
[tex]\begin{gathered} 97\lt55+0.70m \\ \text{ Subtract 55 from both sides} \\ 97-55\lt55-55+0.70m \\ 42\lt0.70m \\ \text{ Divide both sides by 0.7} \\ \frac{42}{0.70}<\frac{0.70m}{0.70} \\ 6060 \end{gathered}[/tex]Company A will charge less than Company B when the number of miles driven, m is greater than 60.
Please assist me with this too if you don't mind.
The equation when solved for k is of:
k = y - a(x - h)².
The domain for the relation is:
x ≥ 0.
How to solve the equation for k?The equation is defined as follows:
y = a(x - h)² + k
To solve for k, we have to isolate the variable k, moving the term a(x - h)², which doesn't have the variable k, to the other side with inverted signal, hence the solution for k is obtained as follows:
y - a(x - h)² = k.
k = y - a(x - h)².
What is the domain for a relation?The domain of a relation is the set containing all the values assumed by the input in the relation.
For the table, the input is the number of miles driven, which assumes values of zero and greater, hence the domain of the relation is defined as follows:
x ≥ 0.
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Write an equation in point slope form for the line that passes through (-3,5) with a slope of -3
The equation of line in point slope form is y = -3x -4
Given,
The points which the line passes through;
(x, y) = (-3,5)
Slope, m = -3
We have to find the equation in point slope form;
Point slope form;
The equation of a straight line that passes through a particular point and is inclined at a specific angle to the x-axis can be found using the point slope form.
Here,
Point slope form;
y - y₁ = m(x - x₁)
Then,
y - 5 = -3(x - -3)
y - 5 = -3x -9
y = -3x - 9 + 5
y = -3x - 4
That is,
The equation of line in point slope form is y = -3x -4
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The diagram shows a tile in the shape of a trapezium.
12 cm
10 cm
Work out the area of the tile.
26 cm
The area of the trapezium would be 190 square centimeters.
What is the area of a trapezium?The area of trapezium is given by -
A = (1/2) x (height) x (sum of parallel sides)
We have a trapezium as shown in the image.
We have -
Sum of parallel sides = [a + b] = 26 + 12 = 38 cm
Height = [h] = 10 cm
Therefore, the area would be -
A = (1/2) x (height) x (sum of parallel sides)
A = 0.5 x 10 x 38
A = 10 x 19
A = 190 square centimeters
Therefore, the area of the trapezium would be 190 square centimeters.
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The graph of a function fis shown below.
Use the graph of the function to find its average rate of change from x=-9 tox=-1.
Simplify your answer as much as possible.
The average rate of change from x = -9 to x = -1 of the graph of the given function is 0.
We know that the rate of change of a function is nothing but the slope of the line.
The slope of the line is given by;
Slope = Change in y-coordinate / change in x-coordinate
We are given the graph of a function.
We need to find the average rate of change from x = -9 to x = -1.
Let us find the value of y or f(x) for the given value of x.
For x = -9, y = 2
For x = -1, y = 2.
Put the values of x and y in the slope formula, we will get;
Slope = (2 - 2) / (- 1 - (-9)) = 0
So, the rate of change of function is 0.
Thus, the average rate of change from x = -9 to x = -1 of the graph of the given function is 0.
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How many student tickets were sold if 150 general admission tickets were sold?
After simplification, 250 tickets sold to students if 150 general admission tickets were sold.
In the given question we have to find the how many student tickets were sold if 150 general admission tickets were sold.
The cost of concert ticket for general admission is $15.
The cost of concert ticket for student is $9.
Total sales of ticket is $4500.
The total 150 ticket sold to general admission.
So the total cost of ticket that received from the general admission is
=150*15 = 2250
Let x number of ticket sold to student.
Then total cost of students ticket is 9x.
Now the expression should be
9x+2250 =4500
Subtract 2250 on both side, we get
9x = 2250
Divide by 9 on both side we get
x = 250
Hence, 250 tickets sold to students if 150 general admission tickets were sold.
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The right question is
Concert ticket cost $15 for general admission, but only $9 with student ID. Ticket ales total $4500. How many student tickets were sold if 150 general admission tickets were sold?
if i have figure A (R=5ft) and figure B is (R=2ft) and the volume =(88 cu ft) what is the answer
we get that
[tex]h_b=\frac{88}{4\cdot\pi}\approx7[/tex]as the figure are congruent we get
[tex]h_a=\frac{5}{2}\cdot7=17.5[/tex]so the volume is
[tex]V_a=\pi\cdot5^2\cdot17.5=1375ft^3[/tex]Graph the polygon with the given vertices and its image after a reflection in the given line.
J(2, 1), K(3, 5), L(6, 5), M(5, 1); x = 1
I need help on the question in the picture attached. i tried posting it but no one is answering it and this was due last week. please help fast
Answer:
Yes
Explanation:
To find our whether Marrissa's budget will be enough for the party, we need to find the linear equation relating the cost and the number of guests. The linear equation is the form
[tex]y=mx+b[/tex]where y is the cost in dollars. m is the cost per guest, and b can be interpreted as additional charges for the party facility.
The cost per guest is given by the slope of cost vs. guest graph.
Let us pick two values (100, 1325) and (50, 725) and compute the slope:
[tex]\frac{\$1325-\$750}{100-50}=\frac{\$12}{\text{guest}}[/tex]With the value of slope m in hand, we now find b by using the values x = 100, y = 1325 (the choice of these values is arbitrary)
[tex]\begin{gathered} 1325=12(100)+b \\ 1325=1200+b \\ \therefore b=125 \end{gathered}[/tex]Hence, the equation relating the cost and the number of guests is
[tex]y=12x+125[/tex]Now, for 75 guests the cost will be
[tex]\begin{gathered} y=12(75)+125 \\ y=\$1025.\text{ } \end{gathered}[/tex]Therefore, Marrissa's budget, which is $1200, is greater than the cost of the party, meaning it will be enough.
Find all points on the y-axis that are 5 units from the point (4, 6). (smaller y-value)(x, y) = (larger y-value)
Step 1:
Write the parent coordinates
(4 , 6)
Step 2
The point can bo on the positive y-axis or on the negative y-axis.
New coordinates
( 4 + 5, 6 + 5)
= (9 , 11)
Or
( 4 - 5, 6 - 5)
= (-1 , 1)
Final answer
Smaller y-value = 1
Larger y-value = 11
Solve for x.
−4.5(x+3.21)=−33.21
Responses
x = 4.17
x, = 4.17
x = 6.67
x, = 6.67
x = 8.09
x, = 8.09
x = 10.59
Answer:
b
Step-by-step explanation:
Answer:
x = 4.17
Step-by-step explanation:
you just solve it using BIDMAS. I'm 100% sure I'm right
Sarah's truck can carry a maximum of 1351.5 pounds. She puts a 100-pound bag of cement mix in the truck. Which inequality can be used to find b, the number of 4.5-pound bricks that can also be put in the truck?
Sarah's truck can carry a maximum of 1351.5 pounds. She puts a 100 - pound bag of cement mix in the truck. Which inequality can be used to find b, the number of 4.5-pound bricks that can also be put in the truck?
___________________________________________
Maximum of 1351.5 pounds
Total ≤ 1351.5 pounds
The number on bricks = b
b*4.5 = bricks weight
100 + 4.5*b ≤ 1351.5
__________________
Can you see the updates?
___________________
Answer
100 + 4.5*b ≤ 1351.5
1351.5 ≥ 100 + 4.5*b
Solve the inequality. Graph the solution.
3x≤−5/4
The solution is
The resultant answer to the given inequality is x ≤ -5/12 and the graph of the answer is shown.
What is inequality?An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made.Use the following steps to solve an inequality: Step 1 Eliminate fractions by multiplying all terms by the fractions' lowest common denominator. Step 2 Combine like terms on both sides of the inequality to simplify. Step 3 Obtain the unknown on one side and the integers on the other by adding or subtracting quantities.So, solve the inequality as:
3x ≤ −5/4x ≤ −5/4-3x ≤ -5/4 × 1/3x ≤ -5/12Now, plot x ≤ -5/12 on the graph as follows:
(Refer to the graph attached below)Therefore, the resultant answer to the given inequality is x ≤ -5/12 and the graph of the answer is shown.
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use two unit multipliers to convert 500 feet to centimeters
Answer:
15240.00 cm
Step-by-step explanation:
15240.00 cm
500 feet * 30.48x(cm)
x = centimeters per foot
Question 15 only, I inserted a picture. Please show your work. graph the solution to the in equality
You have the following inequality:
√x > 2
Consider that only positive values of x result in real solutions. Moreover, if you squared both sides of the inequality, you obtain:
x > 4
The graph of the inequality is shown below:
Write an equation in standard form of the line that passes through the given point and has the given slope.
(-6, -10); m =
6
Answer:
Below
Step-by-step explanation:
First , write it in point (-6, -10) slope ( 6 ) form then manipulate it to standard form:
(y- -10) = 6 ( x - -6)
y+10 = 6x + 36
6x - y = -26
I need helpBarbara works at a law office as an entry level lawyer. She spends 2/5 of her time at the law office doing paper work. How many hours does she have to work to spend 10 hours doing paper work.
GIVEN:
We are told that Barbara works 2/5 of her time doing paper work and this fraction represents 10 hours of her total working time.
Required;
To determine how many hours she will have to work in order to have 10 hours doing paper work.
Step-by-step solution.
Take note that her entire working hours is represented by 1 whole since, a fraction of it has already been identified as two-fifths.
This means
[tex]\frac{2}{5}\times h=10[/tex]Take note that the fraction is taken as two-fifths of the total hours h and, if multiplied by the total hours, we would get 10 hours.
Hence, if we simplify the above equation, we would get the value of h as follows;
[tex]\begin{gathered} \frac{2}{5}\times h=10 \\ \\ Cross\text{ }multiply: \\ \\ h=\frac{10\times5}{2} \\ \\ h=25 \end{gathered}[/tex]Therefore,
ANSWER:
Barbara has to work for 25 hours in order to spend 10 hours on paper work.
Jan and Jo live 1,170 miles apart. At the same time, they start driving toward each other on the same road. Jo’s constant rate is 60 mph. Jan’s is 70 mph. How long will it take them to meet?
Answer:
Step-by-step explanation:
to get the time taken for Jan and Jo to meet we proceed as follows;
Jan's speed=70 mph
Jo's speed =60 mph
distance between =1170
relative speed=70+60=130
time taken for them to meet will be:
time=(distance)/(relative speed)
=1170/130
=9 hours
the answer is 9 hours
Answer:
Option (B) is correct, 9 hours.
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The two-way frequency table contains data about how students access courses.
Traditional Online Row totals
Computer: |28| |62| |90|
Mobile device: |46| |64| |110|
Column totals: |74| |126| |200|
What is the joint relative frequency of students who use a mobile device in an online class?
Answer: 32%
Step-by-step explanation:
The reason on why this answer is 32% is because in order to calculate joint relative frequency, you must have two values.
The first value is the one the question is asking you about. For this, it's mobile device in online classes, which is 64 on the table. Simply divide this number by the total of the table, which is normally on the bottom right. In this case, it's 200.
Now all that needs to be done is this:
[tex]\frac{64}{200}[/tex] = 0.32, which is 32%.
The answer is 32%, C.
The joint relative frequency of students who use a mobile device in an online class will be 32% as the "Student who use a mobile device in online class=64 and total students=200".
What is joint relative frequency?The ratio of a frequency that is not in the total row or column to the total number of values or observations is known as joint relative frequency. In a two-way frequency table, the marginal frequency is the entry in the "total" for the column and the "total" for the row. These are the frequencies in a given category divided by the total number of data values. The term "joint frequency" refers to the joining of one variable from the row and one variable from the column. The ratio of the frequency in a specific category to the total number of data values is known as joint relative frequency.
Here,
Title Traditional Online Row totals
Computer: |28| |62| |90|
Mobile device: |46| |64| |110|
Column totals: |74| |126| |200|
The joint relative frequency of students who use a mobile device in an online class,
Student who use a mobile device in online class=64
Total students=200
64/200=0.32
0.32*100=32%
As "Students who use a mobile device in an online class=64 and total students=200," the joint relative frequency of students who use a mobile device in an online class will be 32%.
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A fire drill occurred in the middle of a math test that Ms Ramirez was giving. She decided to add 5 points to everyone's original score. Which of the following statistical measures would adding these 5 points alter when compared to the original scores? 1. the mean score 2. the interquartile range 3. the range 4. the standard deviation
Concept
Given the data below as the original score of the student
[tex]5,10,\text{15,20}[/tex]The mean score is given as
[tex]\frac{5+10+15+20}{4}=12.5[/tex]Adding 5marks to the score we will be having the score below
[tex]10,15,20,25[/tex]Then the new mean score becomes
[tex]\frac{10+15+20+25}{4}=17.5[/tex]Hence the mean will be altered by adding
Other statistical measures will not be altered
The centre of a circle is the point with coordinates (-1, 3)
The point A with coordinates (6, 8) lies on the circle.
Find an equation of the tangent to the circle at A.
Give your answer in the form ax+by+c=0 where a, b and c are integers.
Answer:
[tex]7x-5y-2=0[/tex]
Step-by-step explanation:
The gradient of the line from the centre to [tex]A[/tex] is [tex]\frac{8-3}{6-(-1)}=\frac{5}{7}[/tex].
Perpendicular lines have gradients that multiply to -1, so the tangent at the point A has gradient 7/5.
So, the equation is:
[tex]y-8=\frac{7}{5}(x-6) \\ \\ 5(y-8)=7(x-6) \\ \\ 5y-40=7x-42 \\ \\ 7x-5y-2=0[/tex]
On Sunday, Steve, Jo, Lucy, Max, and Alex decide to throw aparty. On Monday, they each invite 3 friends. On Tuesday, thefriends that were invited on Monday each invite 3 more people.On Wednesday, the people who were invited on Tuesday eachinvite 3 more people.If this continues, how many people will be invited on Saturday toattend the party?
Step 1. The party will be thrown by Steve, Jo, Lucy, Max, and Alex --> 5 people.
On Monday, each invites 3 friends. So for, the number of people invited is:
[tex]5\times3=15[/tex]Step 2. On Tuesday, the friends that were invited (15) invited 3 more people each. The number of people invited now is:
[tex]15\times3=45[/tex]Step 3. On Wednesday, the 45 people invited on Tuesday, each invite 3 more people. The number of people invited again multiplies by 3:
[tex]45\times3=135[/tex]Step 4. The trend continues so for Thursday, the number of people invited on the previous day multiplies by 3:
[tex]135\times3=405[/tex]Step 5. On Friday the number of people invited is:
[tex]405\times3=1,215[/tex]Step 6. Finally, on Saturday, the day of the party, the number of people invited is multiplied one last time by 3:
[tex]1,215\times3=3,645[/tex]Answer:
3,645
The equation of the parallel line in slope-intercept form is y=
numbers: (-2,-4) 4x+7y=11
(Pls help I have a F in math rn)
The equation of the line parallel to 4x+7y=11 and passes through (-2,-4) is y = - 4 / 7x - 36 / 7
How to write equation of a line in slope intercept form?The equation of a line in slope intercept form can be represented as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore, the equation of the line is parallel to 4x+7y=11.
Parallel lines have the same slope.
Hence,
4x+7y=11
7y = - 4x + 11
y = - 4 / 7 x + 11
Therefore, the slope of the line is - 4 / 7 x. Let's find the y-intercept using (-2, -4)
-4 = - 4 / 7(-2) + b
-4 - 8 / 7 = b
b = - 36 / 7
Therefore, the equation of the line is y = - 4 / 7x - 36 / 7
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Last year at a certain high school, there were 140 boys on the honor roll and 68 girls on the honor roll. This year, the number of boys on the honor roll increased by 5% and the number of girls on the honor roll increased by 25%. By what percentage did the total number of students on the honor roll increase? Round your answer to the nearest tenth (if necessary).
Answer:
11.5%
Step-by-step explanation:
Last year:
Boys: 140
Girls: 68
Total: 208
This year:
Boys: 105% of 140 = 1.05 × 140 = 147
Girls: 125% of 68 = 1.25 × 68 = 85
Total: 232
percent change = (new - old)/new × 100%
percent change = (232 - 208)/208 × 100%
percent change = 11.5%
Which step in solving this equation is justified by the Associative Property of Addition? Consider the sequence of steps to solve the equation: 6v + 3(y – 5) = 4y -- (2v + 1) Given + 3(-5) = 4y - (2v + 1) Step 16v + 3y - 15 = 4y - (2y + 1) Step 2 6y + 3y - 15 = 4y - 2 - 1 Step 3 9y - 15 = 4y – 2v-1 Step 4 9y - 15=-2y + 4y - 1 Step 5 9v - 15 = 2y - 1 Step 6 7y - 15 =-1 Step 77y=14 Step 8y=2 a. Step 7 b. Step 3 c. Step 5 d. Step 4 2. MGSE9-12.A.REI.1 Which step in solving this equation is justified by the
First consider what the associative property of addition is:
Due to such a property, the sum of three or more numbers remains the same regardless of how the numbers are grouped.
Then, from the different steps given in the question, you can notice that in the step 3, regardless the simplifcation of like terms right side or left side, the result is the same.
China produces about 196 million metric tons of rice per year. the Philippines produces about 16 million metric tons of rice per year. how many times did Philippine yearly rice production does China produce?
For the information given in the statement let:
*C the million metric tons of rice that China produces per year
*P the million metric tons of rice that Philippines produces per year
So, you have
[tex]\begin{gathered} C=kP \\ \text{ Where k is the number of times the annual rice production of the Philippines} \\ 196=k\cdot16 \\ \text{ Divide by 16 into both sides of the equation} \\ \frac{196}{16}=\frac{k\cdot16}{16} \\ 12.25=k \end{gathered}[/tex]Therefore, annually China produces 12.25 times the amount of rice that the Philippines produces.
Answer:
12.25 times
Step-by-step explanation:
196/16 = 12.25
what line is perpendicular to the line y=2x+4 ? what line is parallel to line y + 2x+4 ? *options are for both answers*
Given the line : y = 2x + 4
the general equation of the line is y = mx + b
where m is the slope , b is the y intercept
By comparing the given line with the general form
so, the slope of the given line is :
m = 2
the slope of the perpendicular line will be = -1/m
so, the slope of the perpendicular line = -1/2
The slope of the parallel line = the slope of the given line
So, the slope of the parallel line = 2
so, the answer is:
the perpendicular line is : y = (-1/2) x + 10
The parallel line is : y = 2x + 1
what's the
measure of
LX?
HELPO PLEASEEE
Answer:
x = 40
Step-by-step explanation:
180 - 120 is 60
180 - 100 is 80
60 + 80 is 140
40 is the unknown angle
vertical angle means x is 40
Point A is at (6,1) and point C is at (2,-7)
Find the coordiantes of ppint b on line segamnt AC such that AB= 1/3BC
Answer:
A (6. 1) C (2. -7)
6-2 = 4 1- (-7) = 8
as AB= 1/3 BC = AB= 1/4 AC
so x=6-4/4 =5
y= 1-8/4 =-1
so B(5, 1)
Answer:
B(5, - 1)----------------------------------
GivenPoints A(6, 1) and C(2,- 7),Point B that partitions AC as AB : BC = 1 : 3.Find point BUse the section formula
[tex]P=(\dfrac{mx_2+nx_1}{m+n} ,\dfrac{my_2+ny_1}{m+n} )[/tex], where P- point to be found, m : n is the ratio and the (x,y) are coordinates of endpointsSubstitute and find the point B:
[tex]B=(\dfrac{1*2+3*6}{1+3} ,\dfrac{1*(-7)+3*1}{1+3} )=(20/4,-4/4)=(5,-1)[/tex]