Answer:
The vertex of this parabola, [tex](-2, 3)[/tex], can be found by completing the square.
Step-by-step explanation:
The goal is to express this parabola in its vertex form:
[tex]g(x) = a\, (x - h)^2 + k[/tex],
where [tex]a[/tex], [tex]h[/tex], and [tex]k[/tex] are constants. Once these three constants were found, it can be concluded that the vertex of this parabola is at [tex](h,\, k)[/tex].
The vertex form can be expanded to obtain:
[tex]\begin{aligned}g(x)&= a\, (x - h)^2 + k \\ &= a\, \left(x^2 - 2\, x\, h + h^2\right) + k = a\, x^2 - 2\, a\, h\, x + \left(a\,h^2 + k\right)\end{aligned}[/tex].
Compare that expression with the given equation of this parabola. The constant term, the coefficient for [tex]x[/tex], and the coefficient for [tex]x^2[/tex] should all match accordingly. That is:
[tex]\left\lbrace\begin{aligned}& a = 3 \\ & -2\,a\, h = 12 \\& a\, h^2 + k = 15\end{aligned}\right.[/tex].
The first equation implies that [tex]a[/tex] is equal to [tex]3[/tex]. Hence, replace the "[tex]a\![/tex]" in the second equation with [tex]3\![/tex] to eliminate [tex]\! a[/tex]:
[tex](-2\times 3)\, h = 12[/tex].
[tex]h = -2[/tex].
Similarly, replace the "[tex]a[/tex]" and the "[tex]h[/tex]" in the third equation with [tex]3[/tex] and [tex](-2)[/tex], respectively:
[tex]3 \times (-2)^2 + k = 15[/tex].
[tex]k = 3[/tex].
Therefore, [tex]g(x) = 3\, x^2 + 12\, x + 15[/tex] would be equivalent to [tex]g(x) = 3\, (x - (-2))^2 + 3[/tex]. The vertex of this parabola would thus be:
[tex]\begin{aligned}&(-2, \, 3)\\ &\phantom{(}\uparrow \phantom{,\,} \uparrow \phantom{)} \\ &\phantom{(}\; h \phantom{,\,} \;\;k\end{aligned}[/tex].
which of the following number is odd?
1, 3, 5, 7 , 9 and ect.
Solve the following equation for q. 5q=8p-28+3q
Group of answer choices
q = 4p + 14
q = 4p - 14
q = 4p + 2
q = 4p - 2
PLS HELP HELP HELP HELP HELP
Answer:
B 7.5
Step-by-step explanation:
Answer:
B 7.5 because it's a dilation of -5, meaning you divide 15/2 to get the answer.
Step-by-step explanation:
A library contains 60,000 books. 14,000 are the subject of business. 22,000 are on healthcare and and 12,000 on psychology and law . What percentage of the library books is on computing . If computing books make up two thirds of the remainder
Answer:
The percentage of computing books is 13.33%.
Step-by-step explanation:
The library consist of books on different subjects:
S = {Business, Healthcare, Computing, Psychology, Law,...}
There are a total of N = 60,000 books in the library.
Business (B) = 14,000
Healthcare (H) = 22,000
Psychology and Law (P&L) = 12,000
Remaining = N - B - H - P&L
= 60000 - 14000 - 22000 - 12000
= 12000
It is provided that computing books make up two thirds of the remainder.
Compute the number of computing books as follows:
C = 12000 × (2/3) = 8000
Compute the percentage of computing books as follows:
[tex]C\% = \frac{8000}{60000}\times 100=13.33\%[/tex]
Thus, the percentage of computing books is 13.33%.
I need to know how to Expand 2.31x10^5
Answer:
Move 5 decimal places to the right. 231,000. If it was 10^-5, you would have to move 5 decimal places to the left.
Find the surface area of this rectangular prism. Be sure to include the correct unit in your answer.
Answer: 258 [tex]yard^{2}[/tex]
Step-by-step explanation: To find the surface area you add the area of all the sides. And the unit for a surface area is unit (yards) squared.
Front: 5 • 9 = 45
Back: 5 • 9 = 45
Left: 6 • 5 = 30
Right: 6 • 5 = 30
Top: 9 • 6 = 54
Bottom: 9 • 6 = 54
45 + 45 + 30 + 30 + 54 + 54 = 258.
if you can buy six jars of sun-dried tomatoes for $26.90, then how many can you buy with $53.80?
Answer:
12
Step-by-step explanation: divide 26.9 by six and you get 4.48 which is the price for one then you divide 53.8 by 4.48 and you get 12.0 which is just 12
QUESTION 4 PATTERNS, FUNCTIONS AND ALGEBRA 1. Given 6x³-8x³+2+9x7-4x a. How many terms are there in the polynomial? State the degree of the polynomial c. Determine the value of the polynomial if x=-1 b.
Answers:
a) There are 5 termsb) Degree = 7c) The value is -1==========================================
Explanation:
a) Each term is separated by a plus or a minus.b) The degree is equal to the largest exponent. This applies to single variable polynomials only.c) Replace each x with -1. Then use the order of operations PEMDAS to simplify. You should get -1 as the answer. Use a calculator to confirm. It is a coincidence that we have the same input and output. This will not always happen with any general polynomial function.18. Analyze Information Isabel made the
following graph to show the daily share
price for Company XYZ. What was the
change in the price from Monday to
Friday?
The required change in the price is equal to 0.75 cents.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Given that, Isabel made the following graph to show the daily share
price for Company XYZ.
The price on Monday = 0.75
The price on Friday = 1.50
We need to find the change in price from Monday to Friday. It can be calculated as follows;
Change = 0.75 - 1.50
Change = 0.75 cents
therefore, the required change in the price is equal to 0.75 cents.
Learn more about the unitary method;
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HELP i know this is simple but i cant seem to find the correct equation
============================================
Work Shown:
f(x) = x^2
g(x) = a*f(x) for some constant 'a' since g(x) is a scaled version of f(x).
The value of 'a' vertically stretches f(x) upward if a > 0
If 'a' is negative, then we have a reflection going on as shown in the diagram.
We want (x,y) = (3,-6) to be on the graph of g(x). This means g(3) = -6
If we plugged x = 3 into f(x), we get
f(x) = x^2
f(3) = 3^2
f(3) = 9
So,
g(x) = a*f(x)
g(3) = a*f(3) ... replace x with 3
g(3) = a*9 ... replace f(3) with 9 since f(3) = 9
-6 = a*9 ... replace g(3) with -6 since g(-3) = -6
9a = -6
a = -6/9
a = -2/3
Therefore, this means
g(x) = a*f(x)
g(x) = (-2/3)*f(x)
g(x) = (-2/3)*x^2
Quick I need help solving !!!
Answer:
it is 240
Step-by-step explanation:
put in equation and solve
2/3t+10=170
t=240
10 points please help
Which scenario is best represented by the equation y = 8x?
Haddie spent $8 on one hairbrush.
Mike bought books that cost $8 each.
Georgia has as many pennies as Sam.
A cow weights 8 pounds more than a horse.
Answer:
The answer is A.
Step-by-step explanation:
what is a good math skill grade? in apex, like a number.
Answer:
60%
Step-by-step explanation: Apologies if incorrect
If ½ inch represents 10 miles on a map, then how many inches will represent 240 miles?
Answer:
Step-by-step explanation:
There are 24 10 miles in 240. Each 1/2 inch is 10 miles, so there are 12 inches.
Answer:
Your answer will be 12 inches.
Step-by-step explanation:
1/2 inch = 10 miles
1 inch = 20 miles
240/20= 12
How do you write six hundred and eight thousand in decimal form
Answer:
In the explanation. :)
Step-by-step explanation:
608000
prove that the sum of the squares of any two odd numbers is always even
Answer:
proof below
Step-by-step explanation:
Remember that a number is even if it is expressed so n = 2k. It is odd if it is in the form 2k + 1 (k is just an integer)
Let's say we have to odd numbers, 2a + 1, and 2b + 1. We are after the sum of their squares, so we have (2a + 1)^2 + (2b + 1)^2. Now let's expand this;
(2a + 1)^2 + (2b + 1)^2 = 4a^2 + 4a + 4b + 4b^2 + 4b + 2
= 2(2a^2 + 2a + 2b^2 + 2b + 1)
Now the sum in the parenthesis, 2a^2 + 2a + 2b^2 + 2b + 1, is just another integer, which we can pose as k. Remember that 2 times any random integer, either odd or even, is always even. Therefore the sum of the squares of any two odd numbers is always even.
с
(2x + 19)
(3х + 8)
А
Answer:
x=9
Step-by-step explanation:
step one pull out the factors
3x - 27 = 3 • (x - 9)
and step two: Equations which are never true
2.1 Solve : 3 = 0
This equation has no solution.
A a non-zero constant never equals zero.
so x-9=0 and add both sides to 9 and to equal 9
In the diagram below, the lines are parallel. m∠BCD = 52° and m∠EAB = 73°. What is the measure of ∠ABC?
Answer:
235°Step-by-step explanation:
GivenAB ║ CDm∠BCD = 52° m∠EAB = 73°To findm∠ABC = ?SolutionImagine line BF parallel to both AB and CD
Then
m∠ABC = m∠ABF + m∠CBF m∠ABC = (180° - m∠EAB) + (180° - m∠BCD)m∠ABC = (180° - 73°) + (180° - 52°) = 107° + 128° = 235°Answer:
235°Step-by-step explanation:
∠EAB = 73
∠BCD = 52
125
∠ABC = 360 - 125
= 235°
Help me please question is attached in photo below
Answer:
P = 4x - 2
Step-by-step explanation:
Perimeter is all the side lengths added together.
Step 1: Set up expression
P = 2x - 5 + 5 - x + 3x - 2
Step 2: Combine like terms
P = 4x - 2
Type the base. 1/(7 ^ 2)
Answer:
,,,,,,,,,,,,,, mmmmm mm m m m
Step-by-step explanation:
m mm m m m mm m
Ted has two boards. The length of the second board is five inches more than two times the length of the first board. The total length of the two boards is 65 inches. How many inches long is the first board?
Answer:
Twenty inches
Twenty times two is forty and forty plus five is forty five add those together and you get sixty five inches
Answer:
30 inches
Step-by-step explanation:
haven't learnt this but from the question the first board is 5 inches more then the second and the both is 65 inches so if the first is 30 the second is 35 its 65. pls correct me if wrong
Which number is a factor of 22 but not a multiple of 2???
Answer:
1 times 22
Step-by-step explanation:
Answer:
11
Step-by-step explanation:
11 x 2 = 22
So 11 is a factor of 22 since 11 multiplied by 2 is 22.
11 is not a multiple of 2 though.
multiples of 2: 2,4,6,8,10,12.....
Hope this helps :)
If $11000 yields $1100 over 5 years, what is the interest rate?
Answer:
1.92449%
Step-by-step explanation:
Simple Interest Rate Formula: A = P(1 + r)ⁿ
Step 1: Define variables
Principle amount P = 11000
Total amount A = 11000 + 1100 = 12100
Years n = 5
Step 2: Substitute and Evaluate for r
12100 = 11000(1 + r)⁵
11/10 = (1 + r)⁵
1.01924 = 1 + r
r = 0.019245
Step 3: Convert to percentage
0.019245 × 100 = 1.92449%
Given: <1 - <2
Prove: p || q.
Angles Lines Statements Reasons
21
22
23
р
Statements
Reasons
3
9
2
2
Assemble the proof by dragging tiles to
the Statements and Reasons columns.
Answer:
Step-by-step explanation:
Given that alternate exterior angles ∠1 and ∠2 are equal, line p is parallel to q.
What are alternate exterior angles?Two exterior angles that lie on two different lines cut by a transversal and are placed on the opposite sides of the transversal are called alternate exterior angles.
∠1 = ∠2 (alternate exterior angles)
This implies, p||q.
Learn more about alternate exterior angles here
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in a typical bag of skittles, the ratio of red to yellow skittles is 3 to 7. If there are 40 skittles altogether, how many red skittles are there?
Answer:
I love Skittles
what's your favorite color?
The steps to convert 18/8 to a decimal are shown below in which step is the first error
Answer:
I don't understand what your asking
Answer:
You need to add like a b c d
Step-by-step explanation:
they will not know what to reply if you don't add that
Find 3 consecutive integers with a sum of -36
Answer:
-13, -12, -11
Step-by-step explanation:
Step 1: Define
1st consecutive integer - x
2nd consecutive integer - x + 1
3rd consecutive integer - x + 2
Step 2: Set up equation
x + x + 1 + x + 2 = -36
Step 3: Solve for x
Combine like terms: 3x + 3 = -36Subtract 3 on both sides: 3x = -39Divide both sides by 3: x = -13Step 4: Find other integers
1st consecutive integer = -13
2nd consecutive integer = -13 + 1 = -12
3rd consecutive integer = -13 + 2 = -11
Sue has 45 shells in her shell collection. Jared, who just started his collection, has 5 shells. Sue's collection is how many times larger than Jared?
equation:
Answer:
The segments shown below could form a triangle. 4, 3, 6. True or false
Answer: false
Step-by-step explanation:
