The general form of the quadratic function is x² - 2 · x - y + 5 = 0.
How to find the general form of the quadratic function
In this question we must derive the equation of the parabola in vertex form, whose description is shown below:
4 · p · (y - k) = (x - h)² (1)
Where:
(h, k) - Coordinates of the vertex.(x, y) - Coordinates of a point of the parabola.p - Distance from vertex to focus.If we know that (h, k) = (1, 4) and (x, y) = (- 3, 20), then the distance from vertex to focus is:
p = (x - h) / [4 · (y - k)]
p = (- 3 - 1)² / [4 · (20 - 4)]
p = (- 4)² / 64
p = 16 / 64
p = 1 / 4
Then, the equation of the parabola in vertex form is y - 4 = (x - 1)². And now we find the general form of the quadratic formula, that is:
A · x² + B · x + C · y + D = 0 (2)
Then, we proceed to obtain the general form:
y - 4 = (x - 1)²
y - 4 = x² - 2 · x + 1
x² - 2 · x - y + 5 = 0
The general form of the quadratic function is x² - 2 · x - y + 5 = 0.
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The Miller family is taking a road trip. They will drive a total of 1,372 miles. So far they have driven 648 miles. How many miles do they have left to drive?
Answer:
724 miles
Step-by-step explanation:
subtract the values(1372-648)
Which of the following groups of words are listed in alphabetical order?
A) tank, target, tap, tangerine
B) peak, pearl, peanut, peasant
C) light, lock, locust, lottery
The groups of words that are listed in alphabetical order will be B. peak, pearl, peanut, peasant.
What is alphabetical order?It should be noted that alphabetical order simply had to do with the arrangement based on the alphabet.
In this case, the groups of words that are listed in alphabetical order will be peak, pearl, peanut, peasant.
Therefore, the correct option is B.
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M(- 4, 8) is the midpoint of DE. D has coordinates ( 6, 1 ). Find the coordinates of E.
I need help pls
Answer: 16, -1
Step-by-step explanation:
since the x is +10 more than d and the y is -7 less than d, you just add another +10 and -7 to get your next point
4. What value is needed to complete the square? Show all steps.
x²-2x+_
The value of the square in the mathematical identity is 1.
According to the statement, We have to find that the value of the square.
So, For this purpose, we know that the
An Mathematical identity is an equality relating one mathematical expression A to a different mathematical expression B, such A and B produce the identical value for all values of the variables within a specific range of validity.
From the given information:
The statement is the [tex]x^{2} -2x+.....[/tex]
Then
According to the squaring identity,
[tex](A-B)^2 = A^2 + B^2 -2AB[/tex]
compare it with the statement
[tex](x-1)^{2} = x^{2} -2x+1[/tex]
The value of the square is a 1.
So, The value of the square in the mathematical identity is 1.
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find the number of stamps measured 3cm × 4cm needed to fill the square card with a side of 12cm
Answer:
Breadth of stamp=3 cm
Length of stamp=4 cm
Area of stamp = Area of rectangle = l*b = 3*4 = 12 cm^2
Side of square card = 12 cm
Area of card = Area of square = side^2 = 12^2 = 144 cm^2
No. of stamps that can be filled in card
= Area of card / Area of stamp
= 144/12
= 12
:. 12 stamps can be filled in a card of side 12 cm.
URGENT but please only answer if you are xHaleyx OR beinggreat78
this means if you are not one of the two, do NOT answer because I simply don't trust the rest of you to answer correctly since you answer for the points most of the time
Answer:
0.0314
Step-by-step explanation:
[tex]a^{-b}=\frac{1}{a^b}\\3.14\cdot \frac{1}{10^2}\\a\cdot \frac{b}{c}=\frac{a\:\cdot \:b}{c}\\\frac{1\cdot \:3.14}{10^2}\\1\cdot \:3.14=3.14\\\frac{3.14}{10^2}\\10^2=100\\\frac{3.14}{100}\\\frac{3.14}{100}\\= 0.0314[/tex]
All work and answer is provided in the attached screenshot! :)
what best describes the mutually exclusive in statistics?
The best description of mutually exclusive in statistics is a. At least one and only one event occurs.
What does mutually exclusive mean?When two or more events are said to be mutually exclusive, it means that they cannot happen at the same time. If one event happens, then the other event/s cannot happen.
Another way to say this therefore is that at least one event will happen in a mutually exclusive condition, and only that one event will happen.
Options for this question include:
a. At least one and only one event occurs b. Only one event occurs c. More than one event occurs d. At least one event occursFind out more on mutually exclusive events at https://brainly.com/question/12961938
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What is (3.3 x 107) (5.2 x 108) in scientific notation?
OA 17. 16x 1015
A.
OB. 1.716x 1016
OC. 17.16x 1056
OD. 1.716x 1057
Step-by-step explanation: I hope this helps.
Answer: The answer is B.
I think this is the last one I’ll need help on :)
Answer:
The first one and the third one. 1/9 and 3^(-6) x 3^(4)
Step-by-step explanation:
3^3 x 3^(-2) is 3^ 3-2, or 3^1. 3^1 is just 3, and so 3^-2 is the answer. The choices that are equal to 3^-2 are 1/9 and 3^-6 x 3^4
A water hose cost 3.60 per meter. Sam buys a 4.5 m long hose. how much does sam pay?
Step-by-step explanation:
for 1m=3.60
for 4.5m
4.5(3.60)=16.30
16.40 is the cost!!!!
Find the five number summary for Q3
Ana has 4 pots and 7 seeds. How many fewer pots does ana have?
Ana has 3 fewer pots than she has the number of flowers.
What are some alternative names for arithmetic operations?Additions have an alternative name which is sum. Multiplication can also be called as the product, Subtraction can be called the difference and division can be called as the ratio.
To Obtain the number of fewer pots Ana has for flowers is the same as the difference between number of seeds and pots.
Number of seeds she has is 7 and the number of pots she has is 4.
∴ The number of fewer pots Ana has is ,
= (7-4) pots.
= 3 pots.
So, Ana has 3 fewer pots or Ana has 3 more seeds than the number of pots she has.
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The frequency distribution shown is constructed incorrectly.
Class
27-30
31-34
35-38
39-42
43-45
Frequency
5
3
4
8
6
Select all applicable mistakes in the frequency distribution.
The required mistake in the frequency distribution is the class interval 43 - 45 is of 2 it should be of 43 - 48.
Given that,
To determine the mistakes in the frequency distribution.
Statistic is the study of mathematics that deals with relations between comprehensive data.
Table =>
Class Frequency
27-30 5
31-34 3
35-38 4
39-42 8
43-45 6
Here,
Since the class interval is of 3
But in the last class, the interval is of 2
Thus, the required mistake in the frequency distribution is the class interval 43 - 45 is of 2 it should be of 43 - 48.
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one number is 4 times a first number. a third number is 100 more thann the first number. if the sum of the three numbers is 562, find the numbers
The numbers are 77 , 177 and 308 .
Numbers are the building blocks in mathematics. It is an arithmetic value that is used to represent a quantity. Real numbers , integers , natural numbers, whole numbers , irrational numbers are are various types of numbers.
Let us consider the first number to be x . Then the second number is 4x+100 , and the third number is 100 more than the first number. Therefore the the sum of the three numbers will be:
x+4x+(x+100)=6x+100
Now the sum of all the numbers is 562.
Therefore we can write a linear equation in x to find the values of x.
∴ 6x+100=562
or, 6x = 562 - 100
or, 6x = 462
or, x = 462 ÷ 6
or, x = 77
Therefore the second number is 4x = 4 × 77 = 308 and the third number is x + 100 = 77 + 100 = 177 .
So the numbers are 77 , 177 and 308 .
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Please solve quick i need this done and i need both parts for the first box and the second
The equation of the linear function in slope intercept form is f(x) = -2x + 1
How to represent function in slope intercept form?The table can be used to write linear equation in slope intercept form.
Therefore, the equation of the linear function in slope intercept form is as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore,
m = 3 - 5 / -1 + 2
m = - 2 / 1
m = -2
Therefore, the y-intercept can be solved as follows;
using (0, 1)
y = -2x + b
1 = -2x + b
1 = -2(0) + b
b = 1
Hence, the the equation of the linear function in slope intercept form is f(x) = -2x + 1
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newaye is making a salt solution. the instructions ask for 0.07 kilograms of salt to be added to every liter of water. how much salt should he use if he wants to make a solution with 0.5 liter of water
Answer:
0.035 kg
Step-by-step explanation:
(0.07 kg / 1 litre) x (0.5 litre)
= 0.035 kg
Notice how the units of litres cancel and all you are left with is units of kg which is what we want. Another way of solving this problem is via logic. If 1 litre of water is needed for 0.07 kg salt, then half a litre of water (0.5) would need half of the amount needed by 1 litre water so (0.07/2) = 0.035 kg
PLEASE HELP MEEEE ILL MARK AS BRAINLIEST
For which table would 70 be the missing value, x?
Answer:
Table 3 → 5 (5× 14=70)
Ann and Ben translate documents from German into English.
A set of documents that would take Ann 10 days would take Ben 12 days
Ann starts to translate the documents.
After 2 days Ann and Ben both work on translating the documents.
How many more days will it take to complete the work?
they will approximately require 4.4 days to complete the remaining work together.
Ann alone take = 10 days to translate a document.
Work done in 1 day by Ann = 1 / 10
In 2 days = 2 / 10
Work left = 8 / 10
Now, Ben alone take = 12 days to translate a document.
Work done in 1 day by Ben = 1 / 12
We will now use addition.
Combined work of both Ann and Ben in 1 day = 1 / 10 + 1 / 12 = 11 / 60
Time taken to complete the rest of the work = 8 / 10 ÷ 11 / 60
= 48 / 11 = 4.4 days.
Therefore, they will approximately require 4.4 days to complete the remaining work together.
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*Note, my question had Ann as 8 days and Ben as 12, so adjust accordingly*
Answer:
3 3/5
Step-by-step explanation:
After 2 days, 1/4 are done so 3/4 are left
1/8 + 1/12 = 10/48
3/4 ÷ 10/48
3/4 × 48/10 = 144/40 = 3 24/40 = 3 6/10 = 3 3/5
Given the quadratic function g(x)=
ax^2 - 7x - 15, and given that one root of the quadratic is 5,
which of the following could be a factor of g (x)? More than one can apply.
a. (2x-1) b. (x+3) c. (x-3) d. (2x+3)
we get that option (d) 2 x + 3 is a factor of the quadratic function g (x)= a x² - 7 x - 15.
We are given a quadratic function:
g (x)= a x² - 7 x - 15
We also know that 5 is a root for it.
So, we get that:
a (5)² - 7 (5) - 15 = 0
25 a - 35 - 15 = 0
25 a - 50 = 0
25 a = 50
a = 50 / 25
a = 2
So, the function becomes:
g (x)= 2 x² - 7 x - 15
Now factorizing the function:
2 x² - 7 x - 15
2 x² - 10 x + 3 x - 15
2 x ( x - 5 ) + 3 ( x - 5 )
( 2 x + 3 ) ( x - 5 )
Therefore, we get that option (d) 2 x + 3 is a factor of the quadratic function g (x)= a x² - 7 x - 15.
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Beau lifts weights at his local gym on a regular basis. When he started working out, he weighed 127 pounds. Beau kept track of his weight and found that he gained 2 pounds every month. If Beau’s goal is to weigh at least 155 pounds after working out for m months in a row, which inequality best represents this situation?
Answer: it would take 19 months to get to 155
Step-by-step explanation:
If Beau weighed two more each month and wanted to get to 155 then you count by two's and see that it would take 19 months to weight 155
If that was the question, I hope this helps
if that was not the question, I am sorry and will try to help more.
1) Six decreased by five times a number is thirty-one.
2) The product of five and a number increased by seven is twenty-seven.
Answer:
[tex]6 - (5 \times x) = 31[/tex][tex]5 \times x + 7 = 27[/tex]What is the slope of the line y=x+4?
O A.
1112
OB.
OC. 4
OD. -4
angle POR and angle ROQ from linear pair . If a-b=
[tex] {80}^{0} [/tex]
find the value a and b .
Answer:
a = 130
b = 50
Explanation:
Analyze that the angles a and b lies on a straight line summing up to 180°.
Equation's:
a + b = 180 ____eq 1a - b = 80 ____eq 2make 'a' subject in eq 1
a + b = 180
a = 180 - b
substitute this into eq 2
a - b = 80
(180 - b) - b = 80
180 - 2b = 80
-2b = 80 - 180
-2b = -100
b = 50
Find value of 'a':
a = 180 - b
a = 180 - 50
a = 130
Answer:
a = 130°, b = 50°
Step-by-step explanation:
The given equation is,
→ a - b = 80°
→ a + b = 180°
The equation we form is,
→ (a + b) + (a - b) = 180 + 80
Now the required value of a will be,
→ (a + b) + (a - b) = 180 + 80
→ (a + a) + (b - b) = 260
→ 2a = 260
→ a = 260/2
→ [ a = 130° ]
Hence, the value of a is 130°.
Then the required value of b will be,
→ a + b = 180
→ 130 + b = 180
→ b = 180 - 130
→ [ b = 50° ]
Hence, the value of b is 50°.
525 less than c gives 699. translate to algebraic equation and Solve the translated sentence.
Use the slope formula to solve for the slope
Answer:
1/6 pretty sure
Step-by-step explanation:
rise - 1
run - 6
going from (-5, -4) to (1, -3)
Gillian earns $7.50 an hour babysitting on the weekends. Last week she babysat for 2.2 hours on Saturday and 3.5 hours on Sunday. How much did Gillian earn?
Group of answer choices
Gillian earned $42.75 last week.
Arithmetic operators are used to perform mathematical operations like addition, subtraction, multiplication and division.
...
There are 7 arithmetic operators in Python :
Addition.
Subtraction.
Multiplication.
Division.
Modulus.
Exponentiation.
Floor division.
Gillian work
2.2 hours+3.5 hours= 5.7 hours
5.7 hours× $7.50 = $42.75
Therefore Gillian earned $42.75
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select all numbers in which the place value of the digit 6 is equal to 1/10 of the place value of the digit 6 in the number 760.000
The place value of the digit "6" in the given number 760,000 is Ten thousand's i.e., sixty thousand.
Definition of place value
The numerical value of the digit in the given number is based on its position in the number.
The place values are:
Hundred thousands(Hth) - 100,000
Ten thousands(Tth) - 10,000
Thousands(Th) - 1,000
Hundreds(H) - 100
Tens(T) - 10
Ones(O) - 1
Given number is 760,000
The place values for the given number are:
Hth Tth Th H T O
7 6 0 0 0 0
So, the digit '6' is in the ten thousand's place. So, its place value is "ten thousand" i.e., "sixty thousand".
In math, every digit in more than a few has an area cost. place value can be described as the value represented by a digit in quite a number on the premise of its position within the number.
for instance, the region value of seven in 3,743 is 7 loads or seven-hundred. but, the place value of seven in 7,432 is 7 thousands or 7,000. here, we will see that despite the fact that the digits are identical in both the numbers, it’s region cost adjustments with the exchange in it’s position.
area value Chart is a completely beneficial table format that helps us in finding the place value of each digit primarily based on it’s function in various.
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17 POINTS HELP I GIVE BRAINLIEST A line is defined by the equation y = negative x + 3. Which shows the graph of this line?
On a coordinate plane, a line goes through points (0, 3) and (3, 0).
On a coordinate plane, a line goes through points (0, negative 3) and (0, 3).
On a coordinate plane, a line goes through points (0, 0) and (2, 6).
On a coordinate plane, a line goes through points (negative 2, 6) and (0, 0).
Answer:
The first answer is correct.
Step-by-step explanation:
X-y/m= x
Solve for y
Answer:
y = mX - mx
Step-by-step explanation:
X - (y/m) = x
Multiply everything by m
(m)X - (y/m)(m) = x(m)
mX - y = mx
-mX -mX
-y = mx - mX
Divide both sides by -1
-y = mx - mX
÷ -1 ÷ -1
y = -mx + mX
or
y = mX - mx
I hope this helps!
Using the Pythagorean Theorem, find the side lengths of the triangle above. Choose all that apply.
Answer:
4 units
5 units
6.4 units
Step-by-step explanation:
we have two catheti, one measures 4 units and one measures 5 units, with Pythagoras we find the hypotenuse
hypotenuse = √(4²+5²)
hypotenuse = √(16 + 25)
hypotenuse = √41
hypotenuse = 6.4 units