Question Write a quadratic function in standard form whose graph has the given characteristics. vertex: (1,\ 9) ; passes through (4,\ 6)
Answers
The quadratic function of graph given characteristics vertex(1,\9); passes through (4,\6) is y=1/3x2+2/3x+26/3.
A quadratic function is a polynomial function with one or more variables where the highest exponent of the variable is two. Due to the fact that the biggest degree term in a quadratic function is of second degree, it is sometimes referred to as the polynomial of degree 2. There must be a quadratic function with at least one second-degree term. It performs algebraic operations.
Assum:y=ax2+bx+c
Point (1,9)(4,6) into it:{9=a+b+c/6=16a+4b+c} (point 1and 2)
Therefore, vertex(1,9) –b/2a=1→-b=2a
Point 3 into 1 and 2={9=-a+c/b=8a+c}
a=1/3, b=2/3, c=26/3
y=1/3x2+2/3x+26/3
For: y=ax2+bx+c
The graph intersects the x axis at x1 and x2,
X1= -b+√b2-4ac/2a , X2= -b-√b2-4ac/2a
The x-coordinate of the vertex must be in the middle of x1 and x2.
Assume the x-coordinate of the vertex as x
So : x=x1+x2/2 = -b+√b2-4ac/2a + -b-√b2-4ac/2a / 2 = -b/2a
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Related Questions
Which of the following are remote interior angles of 26? Check all that apply.
A. 6
B. 5
C. 1
D. 2
E. 4
F. 3
Answers
Answer:
The answer is 6 which is A .Please Help, If you could provide a step by step on how to solve these it'd be greatly appreciated as well <3
Answers
Answer:
animals vs. gender:
male dogs: 74.4%
marginal distribution for female animals: 49.4%
weight class vs gender:
marginal distribution for female: 62.0%
males who are underweight: 71.5
overweight individuals: 21.8%
Step-by-step explanation:
animals vs. gender:
male dogs:
there are 43 dogs
and there are 32 male dogs
32 divided by 43
say it like 32.000 ÷ 43 = .744186
move the decimal two times to the right to find your percentage
74.4%
marginal distribution for female animals:
there are 39 females
and 79 animals
39 divided by 79
.49367
move the decimal two times to the right to find your percentage
49.36%
which would approximate to
49.4%
weight class vs gender:
marginal distribution for female:
there are 620 girls
and 1000 people
so, 620 divided by 100
write it like this 620.0 ÷ 1,000
.62
move the decimal two times to the right to find your percentage
62%
males who are underweight:
there are 93 underweight males
and 130 underweight people in total
93 divided by 130
.7153846
move the decimal two times to the right to find your percentage
71.5%
overweight individuals:
there are 218 overweight people and 1000 people in total
218 divided by 1000
.218
move the decimal two times to the right to find your percentage
21.8%
For each direct variation, find the constant of variation. Then find the value of y when x=-3 .
y=4 when x=3
Answers
After direct variation y = -4 when x = -3.
What exactly do we mean by "direct variation"?Direct variation equations use the same phrase, to give the reader a hint.Either "directly proportional" or "directly varies" is the phrase.The area of a square, for example, is proportional to the square of its side.If y varies directly as x and y = 6 when x = 2, the variational constant is k = 3.As a result, the direct variation equation is y = 3x.So,
The initial statement is y = kx
Then to find y when x = -3.
K constant will be y/x ⇒ 4/3That is y = kx ⇒ y = 4/3 × xWhen x = -3:
y = 4/3 × -3 ⇒ y = -4Therefore, y = -4 when x = -3.
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I'm failing Geometry right now please help
Answers
Answer:
x = 61
Step-by-step explanation:
2x + 6 + x - 9 = 180
3x - 3 = 180 add 3 to the side
3x = 183 Divide the sides by 3 And you get 61 for x
Solve the equation t − 5 = 12 for t.
17
7
−7
−17
Answers
Step-by-step explanation:
t - 5 = 12 | add 5 to both sides
t = 17
and that is it. that's all we needed to do.
Add 5 plus 12 and it equals 17 which you can sub in for y and it equals 12
2 + (8 - 4) + 32 * 3
Answers
Answer: 102
Step-by-step explanation:
solved
What is the quotient of 3 and 1 over 5 divided by 1 over 3? SHOW WORK
Answers
The quotient of 3 and 1 over 5 divided by 1 over 3 is 9.6
How to solve for the quotientWe we would start first by having the definition for the term quotient. This is defined as the value that is gotten when we divide on quantity by another quantity.
From the definition that we have gotten here, we would have to divide the values by themselves and get the final solution.
We have 3 and 1 over 5 divided by 1 over 3 to be represented as
[tex]3\frac{1}{5} / \frac{1}{3}[/tex]
This would be rewritten as
(16 /5) / (1/3)
= 16 / 5 x 3/1
= 48 / 5
= 9.6
Hence the quotient of 3 and 1 over 5 divided by 1 over 3 is 9.6
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Kayla and Shawna are selling fruit for a school fundraiser. Customers can buy small boxes of tangerines and large boxes of tangerines. Kayla sold 7 small boxes of tangerines and 4 large boxes of tangerines for a total of $166. Shawna sold 7 small boxes of tangerines and 3 large boxes of tangerines for a total of $ 149. Find the cost each of one small box of tangerines and one large box of tangerines.
Answers
The price of small box of tangerines is $14.43 approx. and price of large box of tangerines is $ 17
Let the price of small boxes be x and the price of large boxes be y
we need to form a linear equation in two variable
So, Kayla's equation is
7x + 4y = 166
and Shawna's equation is
7x+ 3y = 149
Subtracting equation 2 from equation 1
7x + 4y = 166
(-) 7x +3y = 149
we get y = 17
Now substituting the value of y in equation 1
7x + 4(17) = 169
7x +68 = 169
7x = 101
x= 14.428
Hence, The price of small box of tangerines is $14.43 approx. and price of large box of tangerines is $ 17
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What is each product or quotient in simplest form?
b. √x³ / ³√x²
Answers
Converting the given radicals into their exponential forms, √x³ / ³√x² = ⁶√x⁵
When work with radical numbers, sometimes it is easier to express them in exponential form first.
[tex]\sqrt[n]{a^{b}}=a^{\frac{b}{n}[/tex]
Recall the rules of exponent operations:
Product. [tex]a^{b}.a^{c}=a^{b+c}[/tex]Quotient. [tex]a^{b}:a^{c}=a^{b-c}[/tex]Power. [tex](a^{b})^{c}=a^{b.c}[/tex]Power of a product. [tex](a.b)^{c}=a^{c}.b^{c}[/tex]Zero power. a⁰ = 1Negative exponent. [tex]a^{-b}=\frac{1}{a^{b}}[/tex]Note that the first 3 rules use the same base. If there are more than 1 base number, then group the exponent that have the same base first.
Example:
[tex](2^{3}.3^{-2}) : (2^{-3}.3^{2})=( 2^{3}:2^{-3}).(3^{-2}:.3^{2})[/tex]
Tips: To simplify exponent numbers, sometimes it is useful to modify the base whenever possible.
Example:
8².2⁻⁵ = (2³)². 2⁻⁵ = 2⁶. 2⁻⁵ = 2⁶⁻⁵ = 2¹ = 2
The given problem:
Simplify √x³ / ³√x²
[tex]\sqrt{x^{3}}=x^{\frac{3}{2}}[/tex]
[tex]\sqrt[3]{x^{2}} =x^{\frac{2}{3}[/tex]
Using quotient rule of exponent:
[tex]x^{\frac{3}{2}}:x^{\frac{2}{3}}=x^{(\frac{3}{2}-\frac{2}{3}) }=x^{\frac{5}{6} }=\sqrt[6]{x^{5}}[/tex]
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help i need help on this question
t-r divided by 21 and t= -6 and r= 12
Answers
Answer: (t-r) / 21 = -0.857 where, t= -6 and r= 12
Step-by-step explanation:
Given data,
t-r divided by 21
where, t= -6 and r= 12
So, we can write,
= (t-r) / 21
Let us assume,
(t-r) / 21 = x
So,
x = (t-r) / 21 { t = -6 and r = 12 (eq-1)
x = (t-r) / 21
We can substitute, t = -6 and r = 12 values in this equation 1
so, we can write,
x = (t-r) / 21
x = (-6-12) / 21
x = -18/21
x = -6/7
x = -0.857
Therefore,
(t-r) / 21 = -0.857 where, t= -6 and r= 12
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Please help will give great points
Answers
The sample space is 0, 1, 2, 3, 4, 5, 6, 7.
Set A is {0, 1, 2, 3, 4}
Set B is {1, 2,3, 4, 5, 6, 7}
The probability of selecting a number less than 5 is 5 / 8.
The probability of spinning a natural numbers is 7/8
The probability of spinning natural numbers and numbers less than 5 is 1/2
A and B is {1, 2, 3, 4}
A' and B = {5, 6, 7}
The probability of spinning a number not less than 5 or a natural number is 1 3/8
What is the sample space?A Venn diagram uses circles that overlap each other to show logical relationships between two or more sets of items. The relationship that is being illustrated with this Venn diagram is the relationship between natural numbers and numbers less than 5.
A natural number includes all positive numbers from 1 to infinity. Natural numbers does not include zero (0). The sample space represents all the possible sets of outcome. In mathematics, a set can be described as a collection of objects whose elements are fixed and cannot be changed.
The probability of selecting a number less than 5 = numbers less than 5/ total numbers
5 / 8
The probability of spinning a natural numbers = all natural numbers / total numbers
7/8
The probability of spinning natural numbers and numbers less than 5 = 4/8 = 1/2
A' = 5,6,7
B = 1, 2, 3, 4, 5, 6, 7
A' and B - 5, 6, 7
The probability of spinning a number not less than 5 or a natural number= ( 4/8) + (7/8) = 11/8 = 1 3/8
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A rectangle has a length 6 meters more than six times the
width. The area of the rectangle is less than 72 meters².
Using the variable x, write an expression that represents all
possible widths of the rectangle. Write your answer as an
inequality in the form a
Answers
The required expression or inequality for possible widths of the rectangle is -4 < x < 3.
Given:
A rectangle has a length 6 meters more than six times the width.
The area of the rectangle is less than 72 meters squared.
We have to find,
The expression or inequality that represents all possible widths of the rectangle.
Let x be the width of the rectangle.
Length of the rectangle is 6 meters more than six times the width.
length = 6x + 6
Area of rectangle is:
Area = length × width
Area = (6x + 6) × x
Area = 6x² + 6x
The area of the rectangle is less than 72 meters squared.
6x² + 6x < 72
6x² + 6x -72 < 0
Divide both sides by 6.
x² + x - 12 < 0
x² + 4x - 3x - 12 < 0
x(x + 4) - 3(x + 4) < 0
(x + 4) (x - 3) < 0
It is true if one factor is negative and other is positive. So,
x - 3 < 0 ⇒ x < 3 ...(i)
x + 4 > 0 ⇒ x > -4 ...(ii)
Using (i) and (ii), we get
-4 < x < 3
Therefore, the required expression or inequality for possible widths of the rectangle is -4 < x < 3.
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Determine the solution for 0.4(3y + -18) = 1.2y + 7.2.
No solution
Infinite solutions
y = 10
y=6
Answers
Answer:
i think its B
Step-by-step explanation:
The bakery at Oaktown Grocery Store sells two types of bread, white and wheat. Last week, the store sold 4 loaves of white bread for every 5 loaves of wheat bread. If the store sold 117 loaves of bread in all last week, how many loaves of white bread did they sell?
Answers
The number of white bread sold is 65.
What is an equation?A mathematical equation that represents the relationship of two expressions on either side of the sign.
We have,
Let the White bread be M
Let the Wheat bread be N
4 loaves of white bread for every 5 loaves of wheat bread can be written as:
4M = 5N _____(1)
Total number of bread sold = 117
M + N = 117 _______(2)
The number of white bread sold:
From (1)
N = 4M / 5 Putting in (2)
M + 4M/5 = 117
(5M + 4M) / 5 = 117
9M = 117 x 5
M = 13 x 5
M = 65
Thus the number of white bread sold is 65.
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Answer:
52 i just did the test
Step-by-step explanation:
Given f (x) = 10x and g (x) = 2x – 1, find (f /g) (x).
Then evaluate the division when x = 3
Answers
Answer:
6
Step-by-step explanation:
(f / g)(x)
= [tex]\frac{f(x)}{g(x)}[/tex]
= [tex]\frac{10x}{2x-1}[/tex] ← substitute x = 3
= [tex]\frac{10(3)}{2(3)-1}[/tex]
= [tex]\frac{30}{6-1}[/tex]
= [tex]\frac{30}{5}[/tex]
= 6
Multiply. (√5+√11)(√5-√11)
Answers
The multiplication of the expression ( √5 + √11 )( √5 - √11 ) is - 6.
Multiplication in elementary algebra is the process of figuring out the outcome of multiplying a number by a number b. The product of a and b is the outcome of multiplication, and each of the integers a and b is referred to as a factor of the product ab.
Consider the expression,
y = ( √5 + √11 )( √5 - √11 )
Using the distributive property,
a( b + c ) = ab + ac
y = (√5 + √11 )( √5 - √11 )
y = √5( √5 - √11 ) + √11( √5 - √11 )
y = ( √5 )² - √5 × √11 + √11 × √5 - ( √11 )²
y = 5 - √55 - √55 - 11
y = 5 - 11
y = - 6
The value of the expression (√5 + √11 )( √5 - √11 ) when simplified is - 6.
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3/
A and B are two similar solids.
15 cm
10 cm
A
B
The volume of A is 400 cm³.
Work out the volume of B.
+
Answers
Use ratios to find x
Round to 2 dp
Remember units are cm^3
What is the estimate of 827 times 4 ?
Answers
Answer:
3,308
Step-by-step explanation:
the internet said that 3,308 was the answer.
[tex]827 \times 4 \approx820 \times 4[/tex]
[tex]820 \times 4 = 800 \times 4 + 20 \times 4 \\ 820 \times 4 = 3200 + 80 \\ 820 \times 4 = 3280[/tex]
[tex]827 \times 4 \approx3280[/tex]
In reality it's just that additional 4 sevens,so
[tex]827 \times 4 = 820 \times 4 + 4 \times 7 \\ 827 \times 4 = 3280 + 28 \\ 827 \times 4 = 3308[/tex]
What is the area of the figure? step by step please
Answers
Answer:
*A = 60 sq units
Step-by-step explanation:
Area(*A) = Length(*l)×breath (*b)
split the shape in two such that you get two rectanglesrectangle(*rec) 1 dimensions being *l=2,*b=18*rec 2 dimensions being*l=2 *b=12*A of *rec1 = 2 × 18 = 36*A of *rec2 = 2× 12 =24*A of the total shape = *A of *rec1 + *A of *rec1*A of the total shape = 36 +24*A of the total shape = 60 sq units
Answer:
Area = 60
Step-by-step explanation:
First make the rectangle 12 and 4 and a square 6 and 2.
12*4=48
6*2=12
48+12=60
0.0939 as a fraction
Answers
Answer:
0.0939 as a fraction is 939/10000
Step-by-step explanation:
939 all over 10,000
in 0.0939 the point move
trying to figure out how to put in a question so if it works say hi as an answer
Answers
Answer:
hello!!
i like ur pfp! :)
Suppose 3 < a < 4 and 4 < b < 5. find all possible values of each expression. 1/a+1/b
Answers
9/29 < 1/a + 1/b < 7/12
Here we have two expression
3 < a < 4 and 4 < b < 5
We have to find the value of the expression
1/a + 1/b
The lower bound of the expression is when we take the maximum value of both the expression a and b
a = 4 and b = 5
From this we get
= 1/ 4 + 1/5
= 5 + 4 / 20
9/ 20
In the same way, we get the higher bound of the expression taken by taking the minimum value of both the expression a and b
a = 3 and b = 4
By putting the value of a and in the expression we get:
1/ 3 + 1/4
= 4+3 / 12
= 7/12
Thus we get the possible value of the expression :
9/20 <1/a + 1/b < 7/12
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What are the slope of the two lines?
Answers
Answer:
- 3/4 for line passing through AB
- 2/3 for line passing through CD
Step-by-step explanation:
Slope = rise/run = (y2-y1)/(x2-x1) for any two points (x1, y1) and (x2, y2)
Line Passing through AB
Take points (0, 6) and (8, 0)
Slope = (0-6)/(8-0) = - 6/8 = -3/4
For line passing thru CD
take points (0, 2) and (3, 0)
Slope = (0 - 2)/(3 - 0) = -2/3
The slope of the two lines - 3/4 for line passing through AB
- 2/3 for line passing through CD
What is a meaning of a slope?
A line's steepness can be determined by looking at its slope. Slope is calculated mathematically as "rise over run" (change in y divided by change in x).The ratio of how much y grows as x grows by a certain amount is known as a line's slope. The slope of a line indicates how steep it is, or how much y rises as x rises.two points (x1, y1) and (x2, y2)
Slope [tex]m = \frac{y_{2}- y_{1} }{x_{2} - x_{1} }[/tex]
Line Passing through AB
Take points (0, 6) and (8, 0)
Slope = (0-6)/(8-0) = - 6/8 = -3/4
For line passing through CD
take points (0, 2) and (3, 0)
Slope = (0 - 2)/(3 - 0) = -2/3
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Leo knows that each time a dight moves one place to the left in a whole number, the value of the dight is 10 times as much
Describe an example you would show to Leo to
demonstrate that this is true for decimal numbers also.
Help me if you may
Answers
The example regarding the values of digits is also true for decimal numbers, as we showed with 0.52.
How do values of digits work?For the integer part of a number, the unit digit is worth 1, and for each subsequent digit, moving left, the value of the digit is multiplied by 10. For example 22, 22 = 2 x 10 + 2 x 1 = 22.For the fractional part of a number, the first decimal digit is worth 0.1, and for each subsequent digit, moving right, the values is divided by 10.For example, for the decimal 0.52.
.52 = 5 x 0.1 + 2 x 0.01 = 0.52.
Hence, moving a digit one place to the left, the value is 10 times as much, as we saw with digits 5 and 2 in the number 0.52.
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25 students are going on a field trip and each student have to pay 10$ for lunch in addition to their ticket.write an expression that could represent the total cost for the students going on the trip.
Answers
Answer:
(10+t)*25
Step-by-step explanation:
25 students so the cost for 1 student needs to be multiplied by 25 for all the students
If lunch costs $10 by itself not including the ticket, we don't know how much the ticket costs so lets say ticket cost = t
$10+t = the cost for ONE student
but there are 25 students so, ($10+t)*25 could work
Expressions don't have equal signs so the total is (10+t)*25
12. DIG DEEPER The sum of a three-digit
number and a one-digit number is 731.
The product of the numbers is 2,908,
What are the numbers?
Answers
The three digit number is 727 while the one digit number is 4
Given data
The sum of a three-digit number and a one-digit number is 731.
The product of the numbers is 2,908
How to solve for the numberslet three digit number be x, y, and z
let the one digit be w
The sum
xyz + w =731
xyz * w = 2,908
making xyz the subject of formula
xyz = 731 - w
plugging in xyz into xyz * w = 2,908
( 731 - w ) * w = 2908
731w - w^2 = 2908
w^2 - 731w + 2908 = 0
solving the quadratic equation gives
w = 727 or 4
since w is a one digit number then w = 4
plugging in w = 4 into xyz + w =731 we have
xyz + w =731
xyz + 4 =731
xyz =731 - 4
xyz = 727
Hence the three digit number is 727 while the one digit number is 4
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The measure of Angle b is 40 degrees and the measure of angle c is 66 degrees. What is the measure of angle a?
Answers
Answer:
74
Step-by-step explanation:
All the angles of a triangle add up to 180
66+40 = 106
To find the missing angle...
180-106 = 74
Answer:
ANGLE A=74
Step-by-step explanation:
LET ANGLE A BE X
ANGLE B=40°
ANGLE C=66°
SUM OF ADJACENT ANGLE IS 180°
SO, WHEN:
40+66+X=180
X=180-106
ANGLE A=74°
HAVE A NICE DAY!!
4. 1 / 3y + 9 = 12
Linear equations
Answers
Answer:
-2.886
Step-by-step explanation:
4.1/3y+9=12
41/10/3y+9=12
41/10=12(3y+9)
41/10=36y+108
41=10(36y+108)
41=360y+1080
41-1080=360y
-1039=360y
y= -1039/360
y= -2.886
Write 3.73 x 10^-2 in standard form.
Answers
Answer:
0.0373
Step-by-step explanation:
move the decimal over 2 spots to the left
when the power is negative, move left
when the power is positive, move right
a) Select all of the fractions below that are smaller than 1/9 1/8 1/3 1/10 5/9 1/90
Answers
Rearrange the Fraction in the order of least to largest:
1/8 > 1/91/3 > 1/9 1/10 < 1/95/9 > 1/91/90 < 1/9What is Fraction?A fraction is a portion of a larger total. The number is expressed in arithmetic as a quotient, which is the numerator divided by the denominator. Both are integers in a simple fraction. A complicated fraction contains a fraction in either the numerator or the denominator.
What is the significance of fraction?Fractions are significant because they indicate what percentage of a whole you require, have, or desire. In baking, fractions are used to indicate how much of an ingredient to use.
Why is it necessary to study fractions?Fractions are a vital basis for studying more advanced math's. As a student's first introduction to abstraction in mathematics, fractions give the greatest foundation for algebra.
According to the given data:Rearrange the items in the order of least to largest.: 1/8 > 1/9
Rearrange the items in the order of least to largest.: 1/3 > 1/9
Rearrange the items in the order of least to largest.: 1/10 < 1/9
Rearrange the items in the order of least to largest : 5/9 > 1/9
Rearrange the items in the order of least to largest.:1/90 < 1/9
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