The quadratic function has an equation of f(x) = 2x²+ x - 4
How to determine the equation of the functionFrom the question, the ordered pairs are given as
(-1, -3), (0, -4), (2, 6)
A quadratic function is represented as
f(x) = ax²+ bx + c
Using the point (0, -4), we have
a(0)²+ b(0) + c = -4
So, we have
c = -4
This gives
f(x) = ax²+ bx - 4
Using the point (-1, -3), we have
a(-1)²+ b(-1) - 4 = -3
So, we have
a - b = 1
Using the point (2, 6), we have
a(2)²+ b(2) - 4 = 6
So, we have
4a+ 2b = 10
So, we have
a - b = 1
This gives
a = b + 1
Substitute a= b + 1 in 4a+ 2b = 10
4(b + 1) + 2b = 10
This gives
4b + 4 + 2b = 10
Evaluate
6b = 6
Divide
b = 1
So, we have
a = 1 + 1
a = 2
So, we have
f(x) = 2x²+ x - 4
Hence, the equation is f(x) = 2x²+ x - 4
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Why is the denominator of each fraction 12?
Pls help me
Answer: because it is out of 12
Step-by-step explanation:
can someone tell me how many cds in both columns combined be?
Answer:
2021= 700cds 2020=750cds
Step-by-step explanation:
Puedes ver como indica en el lado izquierdo que la barra de cds de el 2021 esta en la mitad de 800 y 600 que es igual a 700 cds en 2021
Y en la parte del 2020 se ve que este en la mitad de 800 y 700 considerando el calculo anterior por lo que daría 750 cds en 2020
The cookie jar contains three types of coolcies: chocolate chip, sugar and oatmeal. There are 3 times as many chocolate chip as sugar cookies, and 12 more oatmeal than chocolate chip. If there are 54 cookies in the jar, how many oatmeal cookies are there?
By solving equations, we can conclude that there are 30 oatmeals in the jar.
What are equations?A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.So, a number of oatmeals are in the jar.
Let, sugar cookies be 'x'.Chocolate chips are '3x'.Oatmeals be '3x + 12'The total number of cookies is 54.
From the equation:
x + 3x + 3x + 12 = 54Now, solve for 'x' as follows:
x + 3x + 3x + 12 = 547x + 12 = 547x = 54 - 127x = 42x = 42/7x = 6Number of oatmeals when "x = 6':
3x + 123(6) + 1218 + 1230Therefore, by solving equations, we can conclude that there are 30 oatmeals in the jar.
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3. For items 3a-3d, choose Yes or No to
tell if the digit in the hundreds place
is to the value of the digit in the
thousands place.
3a. 8,556
3b. 6,855
3c. 5,568
3d. 5,656
Yes
Yes
Yes
Yes
No
No
No
O No
The Yes or No to for digit in the hundreds place is to the value of the digit in the thousands place are-
3a. 8,556 ; No , 3b. 6,855 ; No , 3c. 5,568 ; Yes , 3d. 5,656 ; No
What is termed as the place value system?Our a whole number system is built around place value. This is a system where the value of a number is determined by the position of its digits. The numbers 42,316 and 61,432 differ so because digits are in various positions.As per the place value system,
Thousand Hundred Tens Ones
3a. 8,556
Thousand value of number = 8000
Hundred value of number = 500
1/10 × 8000
800 ≠ 500
No, the digit at hundreds place is not 1/10 of the digit at thousand place.
3b. 6,855
Thousand value of number = 6000
Hundred value of number = 800
1/10 × 6000
600 ≠ 800
No, the digit at hundreds place is not 1/10 of the digit at thousand place.
3c. 5,568
Thousand value of number = 5000
Hundred value of number = 500
1/10 × 5000
500 = 500
Yes, the digit at hundreds place is 1/10 of the digit at thousand place.
3d. 5,656
Thousand value of number = 5000
Hundred value of number = 600
1/10 × 5000
500 ≠ 600
No, the digit at hundreds place is not 1/10 of the digit at thousand place.
Thus, the condition of yes and no for the given number are obtained.
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The complete question is-
3. For items 3a-3d,
Choose yes or no to tell if the digit in the hundreds place is 1/10 the value of the digit in the thousand place.
thousands place.
3a. 8,556
3b. 6,855
3c. 5,568
3d. 5,656
(2 x 47) / (6 + 9) =
(6 +17) / 3 = =
(42 - 3)/7 =
(6 +22) / (47 - 21) =
(932) / (827) =
Bloque 2
Bloque2
Redondea a 2 decimales
Find the general form of an equation of the line through the point A that satisfies the given condition.
A( -4, 2)
a) parallel to the x-axis.
b) perpendicular to the x-axis.
The general form of equation a) y = 2, b) x = -4.
Here the point A = (-4,2)
a) we have to find the equation parallel to the x-axis
As a line should be parallel to x axis so it must pass from y-axis. As the coordinate of A is (-4, 2) so by this we get y = 2 and x = -4.
But we have to put the value of x as 0 and y = 2 then only we get an equation of a line parallel to x-axis.
So y = 2
which is parallel to x-axis
b) equation of a line perpendicular to the x-axis.
As a line should be perpendicular to x-axis, so line should pass form the x-axis and not with the y-axis. As point A is (-4. 2), so we have to take the value of x = -4 and y = 0. So we get an equation.
x = -4 is the general equation.
Therefore the general equation a) y =2 and b) x =-4.
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Regarding the search-and-replace features provided by the find and replace dialog box, what is not true?.
You cannot replace a type of formatting inside a cell with a different type of formatting.
Your search string is treated as a pattern by the dialog box, which then returns all records that do. Consider the case where you have a datasheet (a table or a query result) with details on clients, vendors, goods, and order dates. The find operation returns all occurrences of "mar" when you perform a search, along with any additional entries that meet the pattern you supplied.
The dialog box doesn't scan the full database; it simply searches one table at a time. You can search the table that supports a form if the dialog box is opened from within one.
For some features provided by the Find and Replace dialog box the search and replace feature can't accept the following condition.
That a user cannot replace a type of formatting inside a cell with a different type of formatting.
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Find the area of ABCD with vertices A(-5,2), B(-3,2), C(-2,-5),
D(-4,-5).
Answer:
14 units²=============================
Given Vertices A(-5,2), B(-3,2), C(-2,-5), D(-4,-5)To find The area of ABCDSolutionWe can observe that:
1. AB and CD are horizontal segments, since both endpoints have same y-coordinates:
A and B have y = 2, C and D have y = - 52. AB and CD are of same length:
AB = - 3 - (-5) = 2,CD = - 2 - (-4) = 2.It means the ABCD is a parallelogram, since two opposite sides are parallel and of same length.
The area of parallelogram is:
A = bh, where b- base length, h - heightWe know the length of the base, it is found above, 2 units.
The height is the difference of y- coordinates:
h = 2 - (-5) = 7The area is:
A = 2*7 = 14 units²WILL GIVE BRAINLIST IF ANSWERED CORRECTLY!!
Answer: 9 units to the right and 5 units down
Step-by-step explanation:
1) Measure the length.
You can find that you can match point C with point W. Next find how much it goes to the right and left.
Right from (C->W): 9 squares
Down from (C->W): 5
2) Fill in the blank
9 units to the right and 5 units down
Answer:
ΔABC ≅ ΔNKW because when ΔABC is translated 9 units right and 5 units down, it results in the other triangle.
Step-by-step explanation:
The triangles are congruent as the measures of their corresponding sides and angles are the same.
To determine the translation of ΔABC to ΔNKW, find the change in the x and y values from one of the points of ΔABC to its corresponding point of ΔNKW.
Point C = (0, 0)Point W = (9, -5)Therefore:
ΔABC ≅ ΔNKW because when ΔABC is translated 9 units right and 5 units down, it results in the other triangle.
4. If 24 cans of soup will feed 72 people, how many cans are
needed to serve 39 people?
Answer:
24 cans=72 people
1 people = 24÷72 cans
39 people = 24÷72×39 cans
=13 cans
An item is regularly priced at $45. It is on sale for 60% off the regular price. How much (in dollars) is discounted from the regular price?
Answer:
$27.00 is discounted from the price.
Step-by-step explanation:
60% means per hundred
60/100 when you divide by 100 you move the decimal 2 places to the left
.6 x 45 = 27
Given a rectangle with the following dimensions: Area = 50 units Length = x + 10 units Width = x units Find the value of x.
Step-by-step explanation:
the area of a triangle is
length × width
in our case
(x + 10) × x = 50
x² + 10x = 50
x² + 10x - 50 = 0
the general solution to such a quadratic equation
ax² + bx + c = 0
is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case that is
x = (-10 ± sqrt(10² - 4×1×-50))/(2×1) =
= (-10 ± sqrt(100 + 200))/2 =
= (-10 ± sqrt(300))/2 = (-10 ± sqrt(100×3))/2 =
= -5 ± sqrt(100×3/4) = -5 ± sqrt(25×3) =
= -5 ± 5×sqrt(3)
x1 = -5 + 5×sqrt(3) = 3.660254038...
x2 = -5 - 5×sqrt(3) = -13.66025404...
x2 gives us negative values for length and width. that does not make any sense for actual lengths of objects.
so,
x = 3.660254038...
how many squares whose sides are parallel to the axes and whose vertices have coordinates that are integers lie entirely within the region bounded by the line y
The factored equation y=(x−1)(x−5)(x+7) has zeros (or x-intercepts).
The zeros of the factored form of the equation is x = 1, 5, and -7.
What is Factorization ?
Factorization is the method of breaking a number into smaller numbers that multiplied together will give that original form. Factorization is expressing a mathematical quantity in terms of multiples of smaller units of similar quantities.
We have been given the factored equation as; y=(x−1)(x−5)(x+7) that has zeros (or x-intercepts).
y=(x−1)(x−5)(x+7)
then the roots of the equation;
For (x−1)
x - 1 = 0
x = 1
For (x−5)
x - 5 = 0
x = 5
For (x+ 7)
x + 7 = 0
x = -7
Hence, The zeros of the factored form of the equation is x = 1, 5, and -7.
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Need help with this problem √-5
26
Write the time.
11 12
10
87
Brian is making bags of trail mix for hiking club. He will use 21 ounces of walnuts, 10.2 ounces of almonds, and 14.3 ounces of cashews. This amount makes 25 bags of trail mix. How many ounces are in each bag?
Answer:
See explanation
Step-by-step explanation:
First add all the weights, 21+10.2+14.3=45.5oz
Then you divide 45.5 by 25 which equals 1.82oz
Given m n, find the value of x and y
Answer:
x=24
y=58
Step-by-step explanation:
5x+20=6x-4
5x-6x=-20-4
-x=-24 /:(-1)
x=24
5×24+20+y-18=180
122+y=180
y=180-122
y=58
The Jones family is having lasagna for dinner. Before dinner, 15/15 of the lasagna was in the pan. The family ate 10/15 of the lasagna.
What fraction of the lasagna was left in the pan after dinner? (PROVIDE SCREENSHOT TO SHOW HOW TO DO IT)
Answer:
5/15 of 1/3
Step-by-step explanation:
15/15-10/15=5/15
1-2p=-4p-9 solve equation
Answer: p= -5
Step-by-step explanation:
Answer:
-5
Step-by-step explanation:
carry the one over to the right side and subtract it to get an amount of -10.
then carry the -4p to the left and add it with -2p. which comes out to be 2p
now the equation reads as 2p=-10
continue to divide 2 to get p alone and divide -10 by 2 as well.
now p=-5 because a negative divided by a postive is a negative.
No Spamming or will report! Will give Brainliest. Must have explanation
Find four consecutive even integers such that the least plus twice the greatest equals 264
The four consecutive integers in the question are; 51, 52, 53, 54
What is the Sum of the Integers?Let the four consecutive integers in the question be;
x, x + 1, x + 2 and 2(x + 4)
Now, we are told that the sum of these four consecutive integers is 264. Thus;
x + x + 1 + x + 2 + 2(x + 3) = 264
Expanding the bracket gives;
3x + 3 + 2x + 6 = 264
5x + 9 = 264
5x = 264 - 9
5x = 255
x = 255/5
x = 51
Thus;
Second integer = 51 + 1 = 52
Third integer = 51 + 2 = 53
Fourth Integer = 51 + 3 = 54
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Solve for x
x+5=15
D
B
A
The value of x in the given figure is 10.
What is Pythagoras' Theorem?The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a fundamental relationship between a right triangle's three sides in Euclidean geometry.According to this statement, the areas of the squares on the other two sides add to the area of the square whose side is the hypotenuse.In the given triangle,
∠ADC = ∠BDC = 90°
Hence the triangles ΔACD and ΔBCD are right-angle triangles. Thus we can apply Pythagoras' theorem in both triangles.
So in ΔACD,
CB² = BD² + DC²
And in ΔBCD,
CA² = AD²+ DC²
But, CA = 15 and CB = x + 5
So, (x + 5)² = BD² + DC²
15² = AD² + DC²
⇒225 = AD² + DC²
Here, BD = AD as given in the figure
Replacing BD with AD in the first equation we get,
(x + 5)² = AD² + DC²
Now, equate the values of AD² + DC² to obtain the value of x,
(x + 5)² = 225
⇒ x² + 25 + 10x = 225
⇒ x² + 10x - 200 = 0
⇒ x² + 20x - 10x - 200 = 0
⇒x(x + 20) - 10(x + 20) = 0
⇒(x + 20)(x - 10) = 0
Thus x = -20, 10
Hence the value of x is 10.
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4. What does the ordered pair (0, 0) represent in this situation?
40 points!!! Please answer asap!!!
Answer:
There is a linear relationship between costumes and fabric. The rate of change is 3 1/2 yards per costume.
Step-by-step explanation:
The second possible answer is correct,
3 and 1/2
brailiest would be appreciated :]
Answer: The correct answer is B. There is a linear relationship between the number of costumes and fabric. The rate of change is 3.5 yards per costume.
Step-by-step explanation:
Divide the Fabric yards by the number of costumes:
7 / 2 = 3.5
14 / 4 = 3.5
21 / 6 = 3.5
28 / 8 = 3.5
Since they are all 3.5 yards per costume, the relationship is LINEAR
Tina's taco truck sold 3 times as many veggie tacos in August than in September. She sold twice as many in September than in October. She sold 927 veggie taco during the three months
The number of tacos sold in August, September and October is 103, 206, 618 respectively.
Let the number of veggie tacos sold by Tina in October be x
Then, number of veggie tacos sold in September is twice that of veggie tacos sold in october = 2x
Number of veggie tacos sold in August is thrice that of veggie tacos sold in September = 3 x 2x = 6x
Total veggie taco during the three months by Tina = 927
6x + 2x + x = 927
9x = 927
x = 927/9
x = 103
Tacos sold in August = 6x = 618
Tacos sold in September = 2x = 206
Tacos sold in October = x =103
Therefore, the number of tacos sold in August, September and October is 103, 206, 618 respectively.
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Copyright © McGraw-Hill Edi
7. The table shows the options Zoe's mother
has for buying tickets to an adventure day
camp for Zoe and 5 of her friends. Which
option has the lesser cost per student
ticket? (Example 2)
Adventure Camp Tickets
Option
6-pack of Student Tickets
Individual Student Ticket
Cost ($)
126.00
21.50
8.
The option for 6-pack of student tickets will be of lesser cost than that of individual cost.
What is multiplication of two numbers?
Multiplication is a way of finding the product of two or more numbers. It is one of the basic mathematical operations, that we use in our day to day life.
Given, total number of students= 6
Cost of individual student ticket= $21.50
Therefore, total cost of buying tickets to an adventure day= $(6×21.5)= $129.00
Now, cost of 6-pack of student tickets= $126.00
Thus by comparing the two costs, we can see that the lesser option between the two is the 6-pack of student tickets by $(129-126)= $3
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Please helppp immediately
A function is a relationship between inputs where each input is related to exactly one output.
The outputs are called the range
The range of the function:
R = {-1, 0, 3}
Option C is the correct answer.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
A function has an input and an output.
Example:
f(x) = x + 1
f(1) = 1 + 1 = 2
Input = domain = 1
Output = range = 2
We have,
Function:
y = x² - 1
The domain of a function = {-2, -1, 0, 1, 2 }
Let y = f(x)
x = -2, -1, 0, 1, 2.
f(-2) = 4 - 1 = 3
f(-1) = 1 - 1 = 0
f(0) = 0 - 1 = -1
f(1) = 1 - 1 = 0
f(2) = 4 - 1 = 3
Thus,
The range of the function:
R = {-1, 0, 3}
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Question 7 , 8 Geometry
Answer:
i believe the answer is the distributive property
State the line of reflection
Based on the given figures, the line of reflection will be c. Reflection across x-axis.
How to find the line of reflection?If it looks like the line of reflection is a horizontal line as is the case here, the way to find the line of reflection is by finding the midway point between corresponding points on the graph.
For instance, use the coordinates of D and D' and C and C'.
The coordinates of D and D' are:
D = (-1, 1)
D' = (- 1, -1)
The Midpoint can be found to be:
= ( (x₁ + x₂) / 2, (y₁ + y₂) / 2)
= ( (-1 + (-1)) / 2), ( (1 + (-1)) / 2
= (-1, 0)
The coordinates of C and C' are:
C = (4, 1)
C' = (4, -1)
The Midpoint can be found to be:
= ( (x₁ + x₂) / 2, (y₁ + y₂) / 2)
= ( (4 + 4) / 2), ( (1 - (-1)) / 2
= (4, 0)
The line of reflection is therefore the x-axis because the value of y is 0 and the x = axis is the line that crosses y at 0.
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a rectangular tennis court has an area of 528 m^2. If the length is decreased by 1 m and the width is increased by 1 m, the area of the tennis court is increased by 16 m^2. Find the perimeter in metres. thanks
The perimeter of the rectangular tennis court is 96.7 m
How to solve an equationAn equation shows the relationship between two or more numbers and variables.
Let x represent the length and y represent the width. A rectangular tennis court has an area of 528 m², hence:
Area = length * width
528 = xy
y = 528/x
If the length is decreased by 1 m and the width is increased by 1 m, the area of the tennis court is increased by 16 m². Hence:
new area = new length * new width
528 + 16 = (x - 1)(y + 1)
xy + x - y + 1 = 544
x(528/x) + x - 528/x + 1 = 544
528 + x - 528/x + 1 = 544
multiplying through by x:
528x + x² - 528 + x = 544x
x² -15x - 528 = 0
x = 31.67, hence y = 528/31.67 = 16.67
Perimeter = 2(x + y) = 2(31.67 + 16.67)
Perimeter = 96.7 m
The perimeter is 96.7 m
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