What is the coefficients of x4 in the expansion of (1+x)4(1+2x)3.
By the binomial theorem,
(1 + x)⁴ = 1 + 4x + 6x² + 4x³ + x⁴
(1 + 2x)³ = 1 + 6x + 12x² + 8x³
In the expansion of (1 + x)⁴ (1 + 2x)³, we get an x⁴ when multiplying
• x⁴ and 1 to get x⁴;
• 4x³ and 6x to get 24x⁴;
• 6x² and 12x² to get 72x⁴; and
• 4x and 8x³ to get 32x⁴.
Add these up:
x⁴ + 24x⁴ + 72x⁴ + 32x⁴ = 129x⁴
Please help pass my final :(
Answer:
if ∠1 = 70°, then ∠5= 70°
Hence, option (A) is correct.
Step-by-step explanation:
Given
∠1 = 70°
To determine
We need to determine angle ∠5
From the diagram, it is clear that a transversal line crosses the two parallel lines, the angles in the matching corner would be corresponding angles.
We know that when two lines are parallel, their corresponding angles are equal.As angle ∠5 is the corresponding angle of angle ∠1 = 70°.
Also, the corresponding angles are equal here.Therefore,
if ∠1 = 70°, then ∠5= 70°
Hence, option (A) is correct.
Holly has $225 to spend at the shopping mall. She decides to buy sweaaters and pants with her money. Sweaters cost $45 each and pants cost $25 each. The equation 45s + 25p = 225 represents this situation.
If Holly buys 3 sweaters, what is the greatest number of pants she can buy?
Answer:
3 pairs of pants
Step-by-step explanation:
Plug 3 in for s. Your equation should now be 45(3) +25p=225
Then distribute 135+25p=225
Subtract 25p=90
Divide p=3.6
Since you cannot buy half of a pair of pants you need to round down to three
What is the answer? 2c-5 C=4
Answer:
2(4)-5=3
we know that C is going to be multiplied by 2 and the value of C=4
so 2*4 = 2(4)
2(4)-5
2*4=8
8-5=3
So, the answer is 3
if the original quanity is 10 and the new quanity is 12, what is the percent increase
Answer:
+20%
Step-by-step explanation:
None
Answer:
Step-by-step explanation:
20%
The price of mangoes in a grocery store is 3 for $5. How much will 5
mangoes cost? Round the answer to the nearest hundredth.
Answer:
8 and one thirds
Step-by-step explanation:
5 times 5 is equal to 25 and 25 divided by 3 is 8.3333
Answer:
$8.33
Step-by-step explanation:
So, to figure out how much one mango costs, I did $5 divided by 3, which gave me 1.66.
I then multiplied that by 5 to see how much 5 mangos cost, and I got $8.33
Find the difference.
60°
30°
40"
50"
40
Drag and drop the constant of proportionality into the box to match the table. If the table is not proportional, drag and drop "not proportional" into the box.
x 0 1 2 3
y 0 2 3 4
A.2/3
B.1/2
C.0
D.not proportional
Answer:
Hello! The Answer is not proportional. Hope this helps!
Step-by-step explanation:
Please help me please
Answer:
I think this AB would equal 12! Let me know if its right or wrong :3
Step-by-step explanation:
. The ratio of boys to girls in Ms. Cunningham's class is 2 to 3. There are 21 girls in the class. What is the total number of students in Ms. Cunningham's class?
Answer:
14
Step-by-step explanation:
21 times 2 = 42
42 divided by 3 = 14
What is the y-intercept when a line has a slope of 1/2 and passes
through the point (2, -1)?
Answer:
2
Step-by-step explanation:
You called this question to the right person. To find the y-intercept, you must do the formula of Point Slope (y-y1 = m (x-x1)) Since 2, is x1 and the -1 is y1, we must lay the equation out like this: y - -1 = m (x-2). Next, we must distribute the slope to the x and the 2, which would allow the x, to fit in with the slope, and the 2 to become 1 since 1/2 x 2 is 1. Now what we need to do is get rid of the -1, so what we do here is add 1. And algebra golden rule, whatever you do to one side, you must do to the other side. This would leave y = 1/2x + 2 And therefore 2 is your y-intercept, since it's at the last part of the equation.
Determine the value of −14.1 × (-7.33)
Answer:
Multiply -14.1 by -7.33.103.353 ?
Step-by-step explanation:
Sorry I'm not very good at math hope this helps..
Solve:
−7/3a+4=47/3
What is A
I will give extra points to who gets this right also will give brainliest
Answer:
a= -5
Step-by-step explanation
PEMDAS
Which of the following represent an exponential growth function?
Answer:
[tex]y=3^x[/tex]
Step-by-step explanation:
Exponential Growth Function
The exponential function is often used to model natural growing or decaying processes, where the change is proportional to the actual quantity.
An exponential growth function is expressed as:
[tex]C(t)=C_o\cdot(1+r)^t[/tex]
Where:
C(t) is the actual value of the function at time t
Co is the initial value of C at t=0
r is the (positive) growth rate, expressed in decimal
Since r is positive, 1+r is greater than 1.
From the available options, only the last two of them correspond to exponential functions according to the definition above.
Note the third option has a base of 1/3 which is not greater than 1. In fact, it corresponds to an exponential decay function.
The last option has a base 3 and corresponds to a value of r=2 which correctly fits with the definition presented above, thus the correct choice is
[tex]\mathbf{y=3^x}[/tex]
5/9 x 9=?
simplify if possible and show the work
An employee earns a gross pay of $1,200.00 per week. The employee's net pay is $850.00. The employee's voluntary 401(k) contribution is $50.00 per month.
Answer:
$300 was deducted from tax. The tax rate is 26.1%
Step-by-step explanation:
An employee earns a gross pay of $1,200.00 per week. The employee’s net pay is $850.00. The employee’s voluntary 401(k) contribution is $50.00 per month.
There was blank deducted for taxes. The tax rate is blank
Solution:
Contributions that are made for retirement such as 401(k) contribution plans are made on a pretax basis. This means that they are removed from your taxable income, thereby reducing the tax.
Gross pay = $1200
Taxable income = Gross pay - 401(k) contribution
Taxable income = $1200 - $50 = $1150
Net pay = $850
Tax = Taxable income - Net pay
Tax = $1150 - $850
Tax = $300
Tax rate = (Tax / taxable income) * 100%
Tax rate = ($300 / $1150) * 100% = 26.1%
PLEASE HURRY!!!
Use the graph of the function to answer the question.
A line that passes through points (negative 4, 5), (negative 3, 3) and (negative 2, 1).
What is the output of the function when the input is −3?
Please Help............
Answer: number 1
Step-by-step explanation:
Find a formula for the function f(x) such that f′(x)=sin(x) and f(2)=5.
Answer: f(x) = -cos(x) + 4.584
Step-by-step explanation:
we know that f'(x) = sin(x)
if we integrate that, we get:
f(x) = -cos(x) + C
Where C is a constant of integration.
And we also want that:
f(2) = 5
with that relationship we can find the value of C.
f(2) = 5 = -cos(2) + C
(The calculation is done in radians)
5 = -(-0.416) + C
5 - 0.416 = C = 4.584
Then the function is:
f(x) = -cos(x) + 4.584
Solve 7x + 2 =4x+11 please i have 100 points to offer
Answer:
x=3
Step-by-step explanation:
7x+2=4x+11 ---> subtract 2 to the other side and subtract 4x to the other side
7x-4x=11-2 ---> combine like terms
3x=9 ---> divide by 3
x=3
Answer:
x = 3
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Step-by-step explanation:
Step 1: Define Equation
7x + 2 = 4x + 11
Step 2: Solve for x
Subtract 4x on both sides: 3x + 2 = 11Subtract 2 on both sides: 3x = 9Divide 3 on both sides: x = 3Step 3: Check
Plug in x into the original equation to verify it's a solution.
Substitute in x: 7(3) + 2 = 4(3) + 11Multiply: 21 + 2 = 12 + 11Add: 23 = 23Here we see that 23 does indeed equal 23.
∴ x = 3 is the solution to the equation.
I am doing a percent equation problem and I need help please here’s the question 20% of blank =10
Answer:
[tex]50[/tex]
Step-by-step explanation:
Let [tex]x =[/tex] blank (for convenience)
[tex]20\%x=10[/tex]
[tex]0.2x=10[/tex] (change [tex]20\%[/tex] into its decimal form)
[tex]x = 10\div 0.2[/tex] (divide [tex]0.2[/tex] on both sides)
[tex]x=50[/tex]
∴ Blank = 50
Hope this helps :)
The coordinate grid below shows triangle ABC and its image after translation, triangle A'B'C': BY C' 7 B 6 2 A 3= + 2 -7-6-5-4-3-2-1 Which of the following completes the rule for this translation, (x, y) = (x - 8, points) ? (4 O y-6 Oy-3 O y + 6 O'y+3
need help asap please
Answer: y+3
Step-by-step explanation: I'm taking the test rn
Answer:
y + 3
Step-by-step explanation:
I took the test and got it right.
what is 32z-48 factored with gcf
Answer:
We found the factors and prime factorization of 32 and 48. The biggest common factor number is the GCF number. So the greatest common factor 32 and 48 is 16.
Step-by-step explanation:
What is the GCF of 32and 48?
16
Greatest common factor (GCF) of 32 and 48 is 16.
Need Help with this!
Answer: it's about 46.6% for the first card the second card depends on the first card if the first card is even the likelihood of the second being even is 40%, if the first card is odd then the likelihood of the second card being odd too be about 46,6%
Kendra washes windows in an office building. She washes 25 2 5 of the windows on Monday. She washes 13 1 3 of the windows on Tuesday. What fraction of the windows remain for Kendra to wash?
I think you mean 2/5 and not 25 for Monday and 1/3 and not 13 on Tuesday. So i will solve with the fraction.
Answer: The fraction of the windows remaining for Kendra to wash=4/15
Step-by-step explanation:
Step 1
The fraction of windows washed on Monday = 2/5
The fraction of windows washed on Tuesday= 1/3
Fraction remaining to be washed = Total windows - Fraction already washed
Step 255
Fraction already washed=2/5 + 1/3 =6+ 5/15 = 11/15
The total numbers of windows in the office will be represented as 1 whole number since we are dealing with fractions such that the
Fraction remaining to be washed = 1- Fraction already washed
= 1- 11/15 = 15/15-11/15= 4/15
Answer:
Step-by-step explanation:
PLEASE ANSWER‼️‼️‼️‼️‼️‼️‼️‼️‼️‼️‼️‼️‼️‼️
Answer:
x-intercept = 9 y-intercept = 5
Step-by-step explanation:
The vertices of are F(2,1), G(4,1), and H(4,-1). The vertices of the image of the triangle after a dilation centered at (0,0) are F'(4,2), G'(8,2), and H'(8,-2). What is the scale factor of the dilation?
Answer:
The scale factor of the dilation is 2
Step-by-step explanation:
The given vertices the ΔFGH are;
F(2, 1), G(4, 1), and H(4, -1)
The lengths of the sides of the triangle ΔFGH are;
The length of segment FG = √((4 - 2)² + (1 - 1)²) = 2
The length of segment FH = √((4 - 2)² + ((-1) - 1)²) = 2·√2
The length of segment GH = √((4 - 4)² + ((-1) - 1)²) = 2
After a dilation with the center of dilation = (0, 0), to give the ΔF'G'H', we have;
The given vertices the ΔF'G'H' are F'(4, 2), G'(8, 2), H'(8, -2)
The length of segment F'G' = √((8 - 4)² + (2 - 2)²) = 4
The length of segment F'H' = √((8 - 4)² + ((-2) - 2)²) = 4·√2
The length of segment G'H' = √((8 - 8)² + ((-2) - 2)²) = 4
The length of the sides of ΔFGH = 1/2 × The length of the sides of ΔF'G'H' or the length of the sides of ΔF'G'H' = 2 × The length of the sides of ΔFGH
Therefore, the scale factor of the dilation is 2.
Help please thank you
Calcium-41 is being used in studies testing the effectiveness of drugs for preventing osteoporosis. The half-life of calcium-41 is 100,000 years. If 20 grams of calcium-41 are present initially, how long would it take until only 2 grams
remains?
Answer:
332,193 years
Step-by-step explanation:
From the question above, we are to calculate the time in an half life question, hence, the formula is given as
t = In(Nt/No) ÷ -(In2/t½)
Where
t = time is takes for an substance to decay or reduce
Nt = Amount of sample after time = 2g
No = Initial amount of sample = 20g
t½ = Half life = 100,000 years
Hence,
t = In(2/20) ÷ (In 2/ 100,000)
t = 332192.80948874 years
Approximately = 332,193 years
IMPORTANT!!!
Combine Like Terms. 2 + 3
a. 8x
b. 16x
c. 5x
5. Combine Like Terms. 9 + 4 + 4
a. 13x+4
b. 93x+2
c. 12x+4
