Given polynomial:
(4x²-3x+7) - (x²+8x-5)
⇛ 4x²-3x+7-x²-8x+5
⇛ (4x²-x²) +(-3x-8x)+(7+5)
⇛ (4-1)x²+(-3-8)x+12
⇛ 3x²+(-11)x+12
⇛ 3x²-11x+12
(4x²-3x+7) - (x²+8x-5) = 3x²-11x+12Note:-
When subtracting two polynomials,change the symbols of the each term in the second polynomial which is subtracted from the first polynomial.
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Answer:
[tex]3x^2-11x+12[/tex]
Step-by-step explanation:
First, distribute the negative:
[tex]4x^2-3x+7-x^2-8x+5[/tex]
Then combine like terms:
[tex]3x^2-11x+12[/tex]
write the following numbers as the product of a natural number with a power of 10
a) 2450
b) 35000
c)4000400
d) 10101010
[tex]\\ \sf\longmapsto 2450=2\times 35\times 35\times 1^{10}[/tex]
#2
[tex]\\ \sf\longmapsto 35000=35\times 10(10)(10)\times 1^{10}[/tex]
#3
[tex]\\ \sf\longmapsto 4000400=2\times 2\times 1001\times 100\times 1^{10}[/tex]
#4
[tex]\\ \sf\longmapsto 10101010=1010101\times 10\times 1^{10}[/tex]
Step-by-step explanation:
The numbers are given in the form of N*10ⁿ, where N is a natural number
a) 2450 = 245*10 b) 35000 = 35*10³ c)4000400 = 40004*10² d) 10101010 = 1010101*10How much flour and vanilla would you need for 5 batches of cookies
Answer: 25 cups of flour & 10 teaspoons of vanilla
Step-by-step explanation: A recipe for one batch of cookies calls for 5 cups of flour and 2 teaspoons of vanilla.
5 x 5 is 25 cups of flour
2 x 5 is 10 teaspoons of vanilla
How many numbers less or equal to 300 are divisible by 3, 4, or both, but not by 9?
The numbers less or equal to 300 that are divisible by 3, 4, or both, but not by 9 are 142.
What is Equation Modelling?Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
We have a 3 - digit number as 300.
Assume that the numbers less or equal to 300 that are divisible by 3, 4, or both, but not by 9 are [x].
Sequence of numbers divisible by 3 -
3, 6, 9, 12, ...., 300
300 = 3 + (n - 1)3
297 = 3n - 3
n(3) = 100
Sequence of numbers divisible by 4 -
4, 8, 12, ..., 300
300 = 4 + (n - 1)4
296 = 4n - 4
n(4) = 75
Sequence representing numbers less than 300, divisible by 9 -
9, 18, 27, ..., 297
297 = 9 + (n - 1)9
n(9) = 33
So, the numbers less or equal to 300 that are divisible by 3, 4, or both, but not by 9 are -
[x] = n(4) + n(3) - n(9)
100 + 75 - 33
175 - 33
142
Therefore, the numbers less or equal to 300 that are divisible by 3, 4, or both, but not by 9 are 142.
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Alina thinks that the first step in solving the equation shown below could
be to use the subtraction property of equality. Olivia thinks that the multiplication
property of equality could be used first. Who is correct?
Answer:
H
Step-by-step explanation:
Both.
However, multiplication is a good deal more awkward and anytime things are awkward, there's room for errors. However the question is what to do, not which is better.
The answer is both.
The quadratic function f(x)=ax^2+4x+c has a maximum at the point (1, 9) . What are the values of a and c?
Answer: a = -2 and c = 7
Step-by-step explanation:
(this answer uses some basic calculus)
We know that [tex]f'(x) = 2ax + 4[/tex], and since [tex](1,9)[/tex] is a maximum of [tex]f[/tex], then [tex]f'(1) = 0[/tex]. That means [tex]2a + 4 = 0[/tex], so [tex]\boxed{a = -2}[/tex]. Then since [tex]f(1) = 9[/tex], we have [tex]-2(1)^2 + 4(1) + c = 9[/tex], so [tex]\boxed{c = 7}[/tex].
Answer:
a = -2
c = 7
Step-by-step explanation:
Given the quadratic function, f(x) = ax² + 4x + c, for which its vertex is the maximum point occurring at (1, 9), and b = 4.
Solve for the value of a:Since the x-coordinate of the vertex, x = 1, can be calculated using the formula, [tex]x = \frac{-b}{2a}[/tex]:
We can substitute the value of the x-coordinate and b = 4 into the formula, and solve for the value of a:
[tex]x = \frac{-b}{2a}[/tex]
[tex]1 = \frac{-4}{2a}[/tex]
Multiply both sides by 2a:
(2a) 1 = [tex]\frac{-4}{2a} (2a)[/tex]
2a = -4
Divide both sides by 2 to solve for a:
[tex]\frac{2a}{2} = \frac{-4}{2}[/tex]
a = -2
Therefore, the value of a = -2.
Solve for the value of c:Next, to solve for c, substitute the coordinate values of the vertex, (1, 9) into the given quadratic function:
f(x) = ax² + 4x + c
9 = -2(1)² + 4(1) + c
9 = -2 + 4 + c
9 = 2 + c
Subtract 2 from both sides to isolate c:
9 - 2 = 2 - 2 + c
7 = c
Double-check:In order to double-check the validity of our values for a and c, substitute a = -2, and c = 7 into the function, along with the coordinates of the vertex, (1, 9):
f(x) = -2x² + 4x + 7
9 = -2(1)² + 4(1) + 7
9 = -2 + 4 + 7
9 = 9 (True statement).
Therefore, the correct answers are: a = -2, and c = 7.
what is the value of 2
Step-by-step explanation:
???
one more than 1, one less than 3
Answer:
the value of 2 is 1+1=2
Step-by-step explanation:
gamsahamnida have a great day ahead
calculate the length AB
Check the picture below.
In 2011 online sales were $192 billion and in 2014 they were $243 billion
(a) Find a linear function S that models these data, where S is the sales in billions of dollars and is the year Write S(x) in slope-intercept form
(b) Interpret the slope of the graph of S
(c) Determine when online sales were $226 billion
(a) Write S(x) in slope-intercept form S(x)=
(b) Interpret the slope of the graph of S Choose the correct answer below
A .Sales increased on average by $17 billion/yr B .Sales increased by $17 billion in next 3 years C. Sales decreased an average by $17 billion/y D.Sales decreased by $17 billion in next 3 years
(c) Online sales were 5226 billion in the year ___
A) S(x) = 18x + -36005
B) 18
C) 2013
5 div by 4=25 div by y
[tex]\dfrac 54 = \dfrac{25} y\\\\\\\implies \dfrac 14 = \dfrac 5y\\\\\implies y = 4 \times 5 =20[/tex]
3. Mr. Morris orders a bottle of lotion that contains (15)liters. He use 2/6 of a liter of
lotion a day. How many days can he use the bottle of lotion until it is empty?
Pls help and show me how to do it
Answer:
45
Step-by-step explanation:
If he uses 2/6 of a liter thats 3 days for 1 liter.
3 x 15 is 45. so 45 days
1. What is the x-intercept for the equation -2x+5y =-10?
Answer:
2x-5y=10 in slope intercept form is y=2/5x-2. The x intercept would be 5 and the y intercept would be -2. The slope is 2/5.
Step-by-step explanation:
Think about the axis for a moment. You have the y-axis and the x-axis. The y-axis crosses the x-axis at y=0. Consequently the graph must also cross the x-axis when its equation has its y-value set to 0.
Likewise the graph will cross the y-axis when x=0
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Solving your question
To find the x-intercept set y=0 giving
[tex] - 2x + 5(0) = - 10 \\ - 2x = - 1 |?| [/tex]
Multiply both sides by ( -1) giving
[tex]2x = 10[/tex]
Divide both sides by 2 giving
[tex] \frac{2}{2} \times x = \frac{10}{2} \\ [/tex]
But [tex] \frac{2}{2} = 1 \: \\ [/tex] giving
[tex]x = \frac{10}{2} \\ [/tex]- BRAINLIEST answerer
I am good at reading not math I need help please
Step-by-step explanation:
the answer is attached
I Hope This HelpPlease help when you're able to!
number of heads: 0,1,2,3 Frequency: 16,38,34,12 Find the median
Answer:
the median of 0 1 2 3 16 38 34 12 is 9.5
Please help me ASAP this has limited time olease
Answer:
x= 67
Step-by-step explanation:
Angle CGE makes a 23 degree angle, and makes a 90 degree angle with CGB.
By subtracting 90 and 23, you get 67 degrees for the angle EGB.
Since angle EGB and angle AGF are vertical angles, they are the same. So, x would equal 67.
Answer:
x = 67°
Step-by-step explanation:
Solving for x
We know that AGC is a right angle, thus AGD has to be a right triangle as well. Angle CGE is 23°, which would mean that FGD is also 23°.
90°-23°=67°
The area of a rectangle is 4y+10.A.Represent the area of the rectangle in factored form.B.Use the factored form to give one possible set of dimensions for this rectangle.
Area of rectangle=Length×Breadth
[tex]\\ \sf\longmapsto Area=4y+10[/tex]
Take 2 common[tex]\\ \sf\longmapsto Area=2(2y+5)[/tex]
L=2y+5unitsB=2unitsdue in an hour please help!!! :(
Answer:
Step-by-step explanation:
1,7 are same side exterior
1,8 alternate exterior
2,4 none
3,5 same side int
2,6 corrosponding
4,6 same side int
4,7 is none
5,4 alternate int
8,5 vertical
8,7 alternate exterior
How do the slopes of A B ↔ and the parallel line through point C compare?
Answer:
The slopes of AB↔ and the parallel line through point C are equal.
Step-by-step explanation:
Edmentum
Answer:
The slopes of the parallel AB lines through point C are equal.
Step-by-step explanation:
Find the equation of the line given the following
Answer:
1. y = -10x + 6
2. y = -x - 6
3. y = 13x + 110
4. y = -5x + 47
5. y = 7/4 x -7
Step-by-step explanation:
2. m = - 1 and Y-intercept: -20 - (- 1)(14) = -6
3. m = 13 and Y-intercept: -7 - (13)(- 9) = 110
4. (10,-3) and (7,12)
Slope = (12 - - 3)(7- 10) = 15/-3 = -5
y- intercept = 12 - (-5)(7) = 47
5. (4,0) and (0, -7)
Slope: (-7-0)/(0-4) = -7/-4 = 7/4
y-intercept: -7 - 7/4)(0) = -7
Identify which graph below contains the coordinate points (–3, 4),(–2, 0), and (0, –8). Select all that apply.
Answer:
A, C, D
Step-by-step explanation:
All of the plot curves contain (0, -8) and (-2, 0)
B doe NOT contain (-3, 4), though the plot lines seem kind of fuzzy and other curves may miss, but not by much.
Answer:
Graph A , B, and D
Step by-step explanation:
All the points are one these three graphs.
Pleaseee hellppp (find angle)
A = 14°
Step-by-step explanation:
We can use sine law in this situation, where
[tex]\dfrac{\sin A}{a} =\dfrac{\sin B}{b}[/tex]
where a and b are the lengths of the sides opposite the corresponding angles. From the given diagram, we can see that
[tex]\dfrac{\sin A}{7\:\text{yd}} = \dfrac{\sin 75°}{28\:\text{yd}}[/tex]
or
[tex]\sin A = \dfrac{7}{28}\sin 75° = 0.241[/tex]
Solving for the angle A, we get
[tex]A = \sin^{-1}(0.241) = 14°[/tex]
Solve for r.
–
17r+6r+16r+17r–19r=12
r=
Answer: R= 4
Step-by-step explanation:
FOR step by step explanation ask me by my mail , Thanks !
1000+1000-1000
I will give you branlys answer
Answer:
1000+1000-1000= 1000
Step-by-step explanation:
First you start by adding 1000 with 1000
1000+1000= 2000
Then Subtract,
2000-1000= 1000
Hope This Helps !!
???????????????????????????????????????
Answer:
Its C (Third Multiple Choice Answer)
Step-by-step explanation:
The reason being that x + 1 / 2 (6x - 4) = 6 is the way it is instead of the first step being x + 6x / 2 - 4 / 2 = 6 is because it is using legal manipulation by multiplying the 1 / 2 out.
Math:
First
2 * (x + 1 / 2 (6x - 4) = 6 * 2 [In this case the x gets multiplied by 2 and multiplies 2 to the other side as well. The reason why it isn't a Distributive Property in the first place is because we are using multiplication only and the equation is not 1 / 2 (6x - 4).
Then
2x + 6x - 4 = 12 will then equal to 8x - 4 = 12 which is adding like terms
Thirdly
(+ 4) + 8x - 4 = 12 (+ 4) [The parenthesis is to identify that the 4 is positive]
will then turn into 8x = 16
Finally
By dividing 8 on both sides of the previous equation
8x / 8 = 16 / 8 equaling x = 2.
Compensation
10. You have a choice of receiving a wage of $34,000 per year, $2840 per month, $650 per week, or $18
per hour. Which pay choice would you take? Assume a 40-hour work week with 52 weeks per year.
Answer:
Step-by-step explanation:
Monthly rate:
So if we convert $2840 per month into year that would be: 2840 * 12 (that's how many months in a year) = 34,080
Weekly rate:
There are approximately 4.345 weeks per month since it sometimes changes. So, to find the wage per month: 650 * 4.345 = 2824.25. To find the yearly rate multiply it by 12. So, 2824.25 * 12 = 33,891
Hourly rate:
Yearly Salary : $35,100
$18 per hour
PLEASE HELP GIVING BRAINLIEST
Answer:
A.10,4
B.5,10
C.5,5
D4,4
Step-by-step explanation:
KERE ON LERNER?
Mrs. Sparks is a 9th-grade Algebra 1 teacher. She teaches three
Algebra 1 courses and all the classes recently took a chapter exam.
Below are the scores. PLZ HELP 100 POINTS
Answer:
ninth grade teacher is going skipping 30 to each class
Step-by-step explanation:
What is the minimum unit cost of C(x)=0.7^2-210x+27,464?
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
Answer:
f^-1(x) = [ln (x + 4)]/2
Step-by-step explanation:
f(x) = e^(2x) - 4
y = e^(2x) - 4
x = e^(2y) - 4
x + 4 = e^(2y)
ln (x + 4) = ln (e^(2y))
ln (x + 4) = 2y
y = [ln (x + 4)]/2
f^-1(x) = [ln (x + 4)]/2
what is the sum of 6/12 and 1/2
Answer:
1
Step-by-step explanation:
Simplify 6/12 down to 1/2
1/2 + 1/2 = 1