Answers
The quadratic equation [tex]2 - 2x + x^2 = -3[/tex] in standard form is: [tex]x^2 - 2x + 5 = 0[/tex]
To write the quadratic equation[tex]2 - 2x + x^2 = -3[/tex] in standard form, we need to rearrange the terms such that the polynomial appears in the form:
ax^2 + bx + c = 0
where a, b, and c are constants.
First, we can simplify the left-hand side by rearranging the terms:
x^2 - 2x + 2 = -3
Next, we can add 3 to both sides of the equation to isolate the quadratic terms on the left-hand side:
x^2 - 2x + 5 = 0
Now we have the quadratic equation in standard form, where:
a = 1 (the coefficient of x^2)
b = -2 (the coefficient of x)
c = 5
This form makes it easier to analyze the properties and behaviour of the quadratic function and to solve for its roots or solutions using various methods like factoring, completing the square or quadratic formula.
For such more questions on standard
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Related Questions
14 5 18 24 15 28 34 __ what number would complete this pattern?
Answers
Answer:
the missing number is 25.
Step-by-step explanation:
the pattern is to subtract 9 and then add 13
Find the endpoint of the segment with the endpoint of (-4, 5) and midpoint of (7, -9)
Answers
Answer -4+X/2=7
-4+X=14
X=18
5+Y/2=-9
5+Y=-18
Y=-23
18,-23
Step-by-step explanation:
Answer:
x=18 , y. = -13
Step-by-step explanation:
[tex]\frac{-4 + x}{2} \\[/tex] =7 => x = 18
[tex]\frac{-5 + y}{2\\} \\[/tex] = -9 => y= -13
Please help with this question.
Answers
Answer:
3m+20>35
Explanation
m stands for months 3 every m
+ the 20 he starts with will be grater than >35
Simplify the expression 4+2(6+1)+5(5-2)
Answers
Answer:
33
Step-by-step explanation:
Use PEMDAS, so the first thing you solve is what's in the parenthesis.
(6 + 1) = 7
(5 -2) = 3
So now your equation looks like 4 + 2 x 7 + 5 x 3
Now multiply the numbers needed
2 x 7 = 14
5 x 3 = 15
So now it looks like 4 + 14 + 15
Simplify
4 + 14 = 18 + 15 = 33
Answer:
33
Step-by-step explanation:
This is the answer because:
You can use PEMDAS or GEMS
PEMDAS: Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction
GEMS: Grouping (Parenthesis), Exponents, Multiplication and Division (whichever one comes first from left to right.), Addition and Subtraction (whichever one comes first from left to right.)
1) First, we have to do grouping (parenthesis)
(6+1) = 7
(5 - 2) = 3
New equation: 4 + 2 x 7 + 5 x 3
2) Next, we have to do multiplication
7 x 2 = 14
5 x 3 = 15
New equation: 4 + 14 + 15
3) Finally, add everything up.
4 + 14 + 15 = 33
Hope this helps! :D
Explain how you know these two figures are similar
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true or false ?
- a line always contains a ray
- a line segment always contains a line
- a line segment always contains a ray
- a ray always contains a line
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Answer:
-True
-False
-False
-False
please its timed!!!!
Which equation can be used to solve the problem?
495 is 55 percent of what number?
StartFraction 55 times 1 Over 495 times 1 EndFraction = StartFraction 55 Over 495 EndFraction
StartFraction 100 times 45 Over 55 times 45 EndFraction = StartFraction 4500 Over 2475 EndFraction
StartFraction 45 times 9 Over 100 times 9 EndFraction = StartFraction 405 Over 900 EndFraction
StartFraction 55 times 9 Over 100 times 9 EndFraction = StartFraction 495 Over 900 EndFraction
Answers
Answer:
a
Step-by-step explanation:
Answer:
For me it is D
Step-by-step explanation:
I am doing the quiz/test right now and as someone said in the comments of the previous answer, I believe that it is A for the assignment and D for the test.
Part A
A scientist needs 10 liters of a 20% acid solution for an experiment, but she has only a 5% solution and a 40% solution. To the nearest tenth of
a liter, about how many liters of the 5% and the 40% solutions should she mix to get the solution she needs?
Choose the equation to match the situation
O A. (0.20) (10) = 0.05x + 0.40x
B. (0.20)(10) = 0.05x +0.40(10 – X)
OC. (0.20) (10) = 0.05(10) + 0.40(10 - x)
O D. (0.20)(10) = 0.05(10 - x) + 0.40(10 - x)
Part B
Solution
liters of 5% and
liters of 40%
Answers
Answer:
Part A Option BPart B 5.71 l and 4.29 lStep-by-step explanation:
Part ALet x be the volume of 5% solution
Then the volume of 40% solution is
10 - xAmount of acid is 10*0.20 for resultant solution, x*0.05 for 5% solution and (10- x)*0.40 is for 40% solution:
10*0.20 = x*0.05 + (10 - x)*0.40Correct equation is B.
Part BSolving
2 = 0.05x + 4 - 0.4x0.35x = 2x = 2/0.35x = 5.71 l of 5% solutionand
10 - x = 10 - 5.71 = 4.29 l of 40% solutionYou collect 30 pieces of Halloween candy and you give x pieces to
friends. Your neighbor collects 45 pieces of candy and gives away
twice as many as you. If you end up with the same number of
pieces, how many did you give away?
Answers
Answer:
You gave away 15 pieces of candy.
Step-by-step explanation:
Let x represent the number of pieces you give to friends.
Your equation:
30 - x
Your neighbor's equation:
45 - 2x
Set them equal to each other.
30 - x = 45 - 2x
Evaluate.
30 - x = 45 - 2x
-15 = -x
15 = x
hope this helps :)
Which is true about x, the quotient of the division problem shown below?
х
81 918
O The quotient contains a repeating decimal.
O The quotient contains a terminating decimal.
O The quotient is a whole number less than 11.
O The quotient is a whole number greater than 11.
Answers
Answer:
I think its the first answer
Step-by-step explanation:
The answer is choice 2 and 3, that is "The quotient has a final decimal and the whole number is less than 11".
Step-by-step explanation:
The product of a ratio: amount (r) over other(s) (variance from 0) becomes mandatory to note this quotient and in the following case Thus q is = 0.0882352941.
It wasn't a repeating decimal, however a final decimal, so it's got an end.
Its quotient may be less than 11 in total.
Numbers of W = {0,1,2, ...} and 0 < 11 are provided for this entire series of data therefore It's real .
hope this helps.
pls help me. this is inverse trigonometric function
Answers
I'll do the first problem to get you started.
In place of [tex]\sin^{-1}[/tex] I'll use arcsine
So [tex]\sin^{-1}(x) = \arcsin(x)[/tex]
-------------------------------------------------
Using that hint given, we can get the following
cos(arcsin(3x) - pi)
cos(arcsin(3x))*cos(pi) + sin(arcsin(3x))*sin(pi)
cos(arcsin(3x))*(-1) + sin(arcsin(3x))*(0)
-cos(arcsin(3x)) + 0
-cos(arcsin(3x))
Now the question is how to evaluate the cosine of an inverse trig function, especially when it's not inverse cosine.
The trick (often with many trig and geometry problems) is to draw out a triangle. Specifically we'll need a right triangle.
Check out the diagram below. I've drawn out a right triangle with reference angle theta, opposite leg of length 3x, and hypotenuse 1.
Note how sin(theta) = opposite/hypotenuse = 3x/1 = 3x
We can then go from sin(theta) = 3x to theta = arcsin(3x)
This ultimately means
cos(arcsin(3x)) = cos(theta)
cos(arcsin(3x)) = adjacent/hypotenuse
cos(arcsin(3x)) = sqrt(1-9x^2)/1
cos(arcsin(3x)) = sqrt(1-9x^2)
The sqrt(1-9x^2) is the result of using the pythagorean theorem.
---------------------------
So that means the final answer is [tex]-\sqrt{1-9x^2}[/tex]
Given the parent function f(x)=x^2 give the best description of the graph of y=x^3+3. a. expanded vertically by a factor of 5 c. expanded horizontally by a factor of 5 b. expanded vertically by a factor of 10 d. expanded horizontally by a factor of 10
Answers
Answer: We have the following function:
f (x) = x ^ 2
We have the following transformation:
Expansions and horizontal compressions
The graph of y = f (bx):
If 0 <b <1, the graph of y = f (x) expands horizontally by the factor of 1 / b.
Applying the transformation:
y = (0.2x) ^ 2
The factor is:
1 / b = 1 / 0.2 = 5
Answer:
b. expanded horizontally by a factor of 5
Step-by-step explanation:
A train can travel 1136 miles in 4 hours. What is the unit rate that this train is traveling per hour?
miles per hour. (15 points)
Answers
Answer:
284 miles per hour
Step-by-step explanation:
1136/4 = 284 when you divide these you are dividing how many miles the train went and how long it took for the train to go that far making the train go 284 miles per hour
hope this helps and make me brainliest please
Can y’all help me please...ASAP
Answers
Where would the following line cross the y-axis?
f(x) = 2x - 4
O (0, 2)
O (2,0)
O (0, -4)
O (-4, 0)
Answers
Answer:
[tex]\huge\boxed{\red{\boxed{c)(0,-4)}}}[/tex]
Step-by-step explanation:
to understand thisyou need to know about:functionPEMDASlet's solve:to find y-axis of the function we have to take 0 x and calculate it
according to the question:
f(0)=2.0-4f(0)=-4another way to think about it
the function is a linear function i.e f(x)=mx+b where m is the slope (rate of change) and b is the y-intercept (where a line would cross y-axis)
our given function is f(x)=2x-4
using a little algebra we get
f(x)=2x+(-4)where -4 is y-intercept
hence,
the line of the function would cross y-axis at (0,-4) coordinate
For the function f(x)= ab^x, what are the possible values for b if the function is an exponential decay function? (There are two)
a) 2^-1
b) 2-0.9999
c) square root of e
d) square root of 0.9
e) 1.5
Answers
Answer:
c
Step-by-step explanation:
Plz help if possible can you show how you got the answer :)
Answers
Answer:
4t(t+3), 5k²(2k-3), 4x²(2x-5), t=0 and t=1/3, y=0 and y=-2, n=0 and n=-7/4
Step-by-step explanation:
To factor these, we can factor out a constant and/or variable. For number 12, these terms have 4t in common (you can divide any term in the expression by 4t and have no remainder), so we can pull that out. This makes 4t(t+3) because if you distributed, you would end up with the same answer. The answer for 12 is 4t(t+3).
For 13, we do the same thing, except with 5k². When we pull this out of the equation, we end up with 5k²(2k-3), which is the factored expression.
For 14, we can take out 4x². This becomes 4x²(2x-5), the factored expression.
For 15, we actually have to solve, so we can take out a t. This is t(3t-1)=0. We can set both terms (one outside the parentheses and the other one inside the parentheses) equal to zero to solve. t=0, 3t-1=0. To solve the second equation for t, you use inverse operations and end up with t=1/3. The answers are 0 and 1/3.
For 16, we have to solve as well, so take out a 5y. 5y(y+2)=0. Solve for y again. 5y=0, y+2=0. y=0, y=-2 are the answers.
For 17, take out a 3n. 3n(7+4n)=0. Solve for n. 3n=0, 7+4n=0. n=0, n=-7/4 are the answers.
A bookstore had 90 copies of a magazine. Yesterday, it sold 1/6 of them. Today, it sold 1/5 of what remained. How many copies does the bookstore have left
Answers
Answer:
60 copies
Step-by-step explanation:
first you take 1/6th of the original 90 copies which is 15 and subtract that from the 90, you are left with 75 copies which is how many they had left at the end of yesterday. then you take 1/5th of the 75 copies that are left which is also 15 and you subtract that from 75 and you get 60. that's why at the end of today there are 60 copies left.
900,000-400,000 esitmate
Answers
Answer:
500,000
Step-by-step explanation:
9-4=5 just add the zeros
Answer:
aahhhh
Step-by-step explanation:
Solve for x:
2x + 8 = 22
Answers
Answer:
x=7
Step-by-step explanation:
Step 1: Subtract 8 from both sides.
2x+8−8=22−8
2x=14
Step 2: Divide both sides by 2.
2x/2=14/2
x=7
Answer:
[tex]x[/tex] = 7
1. 2[tex]x[/tex] + 8 - 8 = 22 - 8
2[tex]x[/tex] = 14
2. [tex]\frac{2x}{2}[/tex] = [tex]\frac{14}{2}[/tex]
[tex]x[/tex] = 7
Classify the four angles of the quadrilateral.
Answers
Answer:
<A= right
<B= acute
<C= obtuse
<D= acute
Step-by-step explanation:
Solve the following equations:
(2x + 7)(x - 5) = 0
Answers
Answer:
x = -7/2
x = 5
Step-by-step explanation:
Answer:
(2x+7)(x-5)=0
2x+7=x-5
2x-x=5-7
X=-2
The sum of nine times a number, and 2, is equal to eight times the number.
Answers
Answer:
x = -2
Step-by-step explanation:
let the unknown number be x
[tex]9 \times x + 2 = 8 \times x \\ 9x + 2 = 8x[/tex]
Collect like terms and simplify
[tex]9x - 8x = - 2 \\ x = - 2[/tex]
The unknown number would be x = -2.
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
We have given a statement as "The sum of nine times a number, and 2, is equal to eight times the number."
Let the unknown number be x
9x + 2 = 8x
Collect like terms and simplify;
9x - 8x = -2
x = -2
Thus, the variable would be x = -2.
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What is the scale factor of this dilation?
1/2
3/5
1 2/3
2
Answers
Answer:
3/5
Step-by-step explanation:
The scale factor is the ratio of image segment lengths to pre-image segment lengths:
PB'/PB = 3/5
The scale factor is 3/5.
Answer: 3/5
Step-by-step explanation:
if 9+x/6=11 then what’s the value of 1+3x??
Answers
Answer:
Step-by-step explanation:
It's hard to tell what you really intend. I'll do it both ways.
Way One
9 + x/6 = 11 Subtract 9 from both sides.
x/6 = 11 - 9
x/6 = 2 Multiply both sides by 6
x = 2 * 6
x = 12
1 + 3x = 1 + 3*12 = 1 + 36 = 37
Way Two
(9 + x)/6 = 11 Multiply both sides by 6
9 + x = 11 * 6 Simplify the right side
9 + x = 66 Subtract 9
x = 57
1 + 3*57 = 1 + 171 = 172
find the sum of
a)-b-4a,7b-6b
b)6d-4c,7c+6d
Answers
Answer: −3a−b;b
−4c+6d;7c+6d
Step-by-step explanation:
What is the prime factorization of 72?
0.2² x 32
O 22 x 33
O 23 x 32
O 23 x 33
Answers
Answer:
[tex]2^3\times 3^2[/tex]
Step-by-step explanation:
[tex]72\\\\72\:\mathrm{divides\:by}\:2\quad \:72=36\times\:2\\\\=2\times\:36\\\\36\:\mathrm{divides\:by}\:2\quad \:36=18\times\:2\\\\=2\times\:2\times\:18\\\\18\:\mathrm{divides\:by}\:2\quad \:18=9\times\:2\\\\=2\times\:2\times\:2\times\:9\\\\9\:\mathrm{divides\:by}\:3\quad \:9=3\times\:3\\\\=2\times\:2\times\:2\times\:3\times\:3\\\\2,\:3\mathrm{\:are\:all\:prime\:numbers,\:therefore\:no\:further\:factorization\:is\:possible}\\\\=2\times\:2\times\:2\times\:3\times\:3\\\\=2^3\times 3^2[/tex]
Answer:
So, the prime factorisation of 72 are 2 × 2 × 2 × 3 × 3 or 23 × 32, where 2 and 3 are the prime numbers.
Step-by-step explanation:
Helps please does that look right to y’all ?
Answers
===============================================
Work Shown:
i = P*r*t .... simple interest formula
i = simple interest
i = 2075-1000 = 1075
P = 1000 = amount borrowed (principal)
r = unknown interest rate
t = 5 = time in years
So,
i = P*r*t
1075 = 1000*r*5
1075 = 5000r
5000r = 1075
r = 1075/5000
r = 0.215
r = 21.5%
y + 7 = y -3 how many solutions
Answers
NOT ARITHMETIC SEQUENCE
Answers
Answer:
its ok
Step-by-step explanation:
