Answers
Answer:
The fourth coefficient is 4.
Step-by-step explanation:
Pascal's Triangle in this case has 5 rows of coefficients because the highest power in (y + w)^4 is 4. 4 plus 1 is 5.
Here's the appropriate Pascal's Triangle:
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1 Use this row when expanding the 4th power of (v + w).
Notice that in the given expansion, the coefficients are
1, 4, 6, 4 1
This corresponds to the last (5th) row of Pascal's Triangle (above).
So the correct coefficient to be placed in the box is 4.
Related Questions
Simplify the expression. x^5/x^9
Answers
Answer:
1/x^4
Step-by-step explanation:
Solve for w.
69=5w – 16
Simplify your answer as much as possible.
Answers
69 + 16 = 5w
85 = 5w
Divide both sides by 5.
W = 17
A store marks up a $550 widescreen television by 30%. During a sale it is discounted by 20%. What is the percentage change in the original price of the television?
Answers
Answer:
4%Step-by-step explanation:
Marked Price = 130% of cp
= 1.3 x 550
= 715
Selling price = 80% of mp
= 0.8 x 715
= 572
% change in price =
[tex] \frac{572 - 550}{550} \times 100 = 4[/tex]
4%
Which of the following could be the measure of the angle below?
Answers
Answer:
There is nothing below.
Step-by-step explanation:
HELP PLEASE !!!!!!!!!!!
Answers
Answer:
option B
Step-by-step explanation:
[tex]\lim_{x\to \infty} f(x) = \lim_{x \to \infty} (log(x+2)-3 )[/tex]
[tex]= \lim_{x \to \infty} ( log(x+2)) - \lim_{x \to \infty} 3\\\\=\infty - 3\\\\= \infty[/tex]
[tex]\lim_{x \to 2} f(x) = \lim_{x \to 2} ( log(x+2)) - \lim_{x \to2} 3\\\\[/tex]
[tex]= log( 2 + 2 ) - 3\\\\= log 4 - 3\\\\=log(2^2) -3\\\\=2 log 2 -3[/tex]
[tex]\lim_{x \to -2} f(x) = \lim_{x \to -2} ( log(x+2)) - \lim_{x \to -2} 3\\\\[/tex] [tex]\lim_{x \to -2}_+ f(x) = \lim_{x \to -2_+} ( log(x+2)) - \lim_{x \to -2_+} 3 = -\infty\\\\\lim_{x \to -2_-} f(x) = \lim_{x \to -2}_- ( log(x+2)) - \lim_{x \to -2}_- 3 = -\infty\\\\\\\lim_{x \to -2} f(x) = - \infty[/tex]
Can someone please help me create an equation for this circle?
Answers
Answer:
[tex](x-1)^2 + (y-1)^2 = 10[/tex]
Step-by-step explanation:
From the graph ,
Centre of the circle is (1, 1)
To find radius we find a point through which the circle passes and find the distance between the Centre and the point.
Let that point be (4, 0)
[tex]radius = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2} = \sqrt{(1-4)^2 + (1-0)^2} = \sqrt{10}[/tex]
Equation of the circle :
[tex](x - a)^2 + (y-b)^2 = r^2 \ , \ where \ (a,b)\ is\ the\ centre\ of\ the\ circle\ and\ r\ is\ the\ radius\\\\(x-1)^2 + (y-1)^2 = 10[/tex]
Can anyone help me with this please? I need help along with an explanation.
Answers
if a^2 - b^2 = 21,
5^2 = 25, 2^2 = 4,
25 - 4 = 21
if a - b = 3,
5 - 2 = 3
5/2 = 2.5
hope this helps! :)
Answer:
a + b = 7
Step-by-step explanation:
a^2 - b^2 = 21
Factor the left side. It is the difference of two squares which factors into the product of a sum and a difference.
(a + b)(a - b) = 21
We are told a - b = 3, so substitute 3 for the factor a - b.
(a + b)(3) = 21
Divide both sides by 3.
a + b = 7
Middle School teaches 6th, 7th, and 8th grade classes. The sixth grade has 318 students, the 7th has 286 students, and the 8th has 306 students. If the sixth grade takes a field trip and each student needs $3.50, how much total money is needed by the students? $910 c. $1113 b. $3185 d. $1071
Answers
Answer:
$3185
Step-by-step explanation:
Multiply the number of grade 6 students by the money needed ($3.50) and you get 318x3.50=1113
Multiply the number of grade 7 students by the money needed ($3.50) and you get 286x3.50=1001
Multiply the number of grade 8 students by the money needed ($3.50) and you get 306x3.50=1071
Add all the total amounts together and you get $3185
Julie is solving the equation x2 + 5x+6= 0 and notices that the discriminant b2- 4ac has a value of 1. This tells her that the equation
has
A) no real roots
B) exactly one real root.
C) exactly two real roots.
D) exactly three real roots.
Answers
Answer: C
Step-by-step explanation:
If you use the quadratic equation you will find that there are two possible answers to this problem
The explanation shows that the equation has exactly two real roots. so the correct option is C.
What is a quadratic equation?
A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
Given that Julie is solving the equation x² + 5x+6= 0 and notices that the discriminant b²- 4ac has a value of 1.
x² + 5x+6= 0
The discriminant = b²- 4ac = 1
It will be Real and distinct because the discriminant is positive.
There are two roots of a quadratic equations always if the discriminant is positive. We say that the quadratic equation has 2 solution if roots are distinct, and have 1 solutions when both roots are same.
Hence, This tells her that the equation has exactly two real roots. so the correct option is C.
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please help soon, i can't seem to figure this one out!!
Consider the following equation. -2x + 6 = -(2/3)^x + 5. Approximate the solution to the equation above using three iterations of successive approximation. Use the graph below as a starting point.
A. x = 3/4
B. x = 13/16
C. x = 7/8
D. x = 15/16
Answers
The required solution after three successive iterations is near x = 7/8. Option c is correct.
Equation is -2x + 6 = -(2/3)^x + 5. Approximate the solution to the equation above using three iterations of successive approximation.
The equation is the values of two expressions that are equal.
Here,
[tex]-2x + 6 = -(2/3)^x + 5[/tex]
Arranging the equation
[tex]-2x + 6 +(2/3)^x - 5 = 0\\(2/3)^x-2x+1=0[/tex]
Since the solution of the equation is when f(x) = 0 at near to x = 0.8
[tex]f(x) = (2/3)^x-2x+1\\[/tex]
First iteration at x =0.8
[tex]f(0.8) = (2/3)^x-2x+1\\ = (2/3)^{0.8}-2*0.8+1\\ = 0.123[/tex]
It will go up more to get exact zero, so
Second iteration at x = 0.9
[tex]f(0.9) = (2/3)^{0.9}-2*0.9+1\\f(0.9) = -0.106[/tex]
It seems that zero is near 0.9 so will go down
The third iteration at x = 0.87
[tex]f(0.87) = (2/3)^{0.87}-2*0.87+1\\f(0.87) = -0.037[/tex]
Here , solution is much near to x = 0.87 or x =7/8.
Thus, the required solution after three successive iterations is near x = 7/8.
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Why is it easy to hammer a sharp pin than a blunt pin ? *
Answers
Answer:
It is easier to hammer a sharp nail than a blunt one
Step-by-step explanation:
This is because blunt nail occupies more area than sharped nail. As sharp will exert more pressure as it occupies less area.
Bertie won the lottery! He spends 4/5 of his money on a large house. He spends 3/4 of his REMAINING money on a luxury yacht. He spends 2/3 of his remaning money on a trip to space. He gives the remaning $50,000 to a charity. How much did he win?
Answers
Answer:
Step-by-step explanation:
Step 1
Find the fraction of the money he gave the charity
Let the total amount he had = 1
Bertie won the lottery! He spends 4/5 of his money on a large house. He spends 3/4 of his REMAINING money on a luxury yacht. He spends 2/3 of his remaning money on a trip to space.
Fraction of money he gave to charity =
1 - (4/5 + 3/4 + 2/3)
He gives the remaning $50,000 to a charity. How much did he win?
Which quotient is greater than 3? 28 divided by 10, 35 divided by 11, 38 divided by 13 or 40 divided by 14
Answers
The quotient 35 divided by 11 is the only one among the options that is greater than 3.
To determine which quotient is greater than 3, we can calculate the value of each quotient:
28 divided by 10 = 2.8
35 divided by 11 ≈ 3.182
38 divided by 13 ≈ 2.923
40 divided by 14 ≈ 2.857
Comparing these values, we can see that only the quotient 35 divided by 11, which is approximately 3.182, is greater than 3.
Therefore, the quotient 35 divided by 11 is the only one among the options that is greater than 3.
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[tex] {( \frac{5}{3} )}^{2n + 1} {( \frac{5}{3} )}^{5} = ({ \frac{5}{3} )}^{n + 2} [/tex]
Pls include steps...
Answers
Answer:
n = -4
Step-by-step explanation:
[tex](\frac{5}{3} )^2^n^+^1 * (\frac{5}{3} )^5 = (\frac{5}{3})^n^+^2[/tex]
in multiplication if the base are same u can add there exponent.
[tex](\frac{5}{3})^2^n^+^1^+^5 = (\frac{5}{3})^n^+^2[/tex]
base of both sides are equal so their exponent will be equal
2n + 1 + 5 = n + 2
2n + 6 = n + 2
2n - n = 2 - 6
n = -4
can someone help i dont understand exponential functions
Answers
Answer:
1,3,4,6
Step-by-step explanation:
The Grade 5W students at the Eber Prep School wanted to create a mural on one
side of the walls in their classroom. the area of the wall is 36 square meters or 36
meters square.
Answers
Answer:
the answer is 36 square meters since this is the proper way to phrase this answer but if you do say it the other way people will now what u are talking about
can you find function asap please
Answers
Answer:
i think the function is 7
Step-by-step explanation:
11. Square ABCD shown has sides of length 10 centimeters. The unshaded
portions are both semicircles. Calculate the area of the shaded portion to
the nearest tenth of a square centimeter. *
Answers
Answer:
21cm^2
Step-by-step explanation:
Area of Square-Area of semi circles (makes one full circle)
Squares Area = 100
LxW or (10x10)=100
Circle Area = 25/pi
/pi (radius)^2 or /pi(5)^2 = 25/pi
100cm^2-25cm^2 = 21.4601…cm^2 rounded to 21.5 cm^2
The area of the shaded region is 21.5 cm²
What is a semi-circle?
'In geometry, a semicircle is a plane figure that is formed by dividing a circle into exactly two parts.'
According to the given problem,
Side length of the square = 10
Area of the square = ( 10 × 10 )
= 100 cm²
Now, for the semi-circle,
Diameter = 10 cm
Radius = [tex](\frac{10}{2}[/tex][tex])[/tex] cm
= 5 cm
Area of the semicircle = [tex]\frac{\pi r^{2} }{2}[/tex]
= [tex]\frac{\pi * 5^{2} }{2}[/tex]
Since, there are two semicircles in the square, we multiply the area with 2,
⇒ [tex]\frac{\pi *5^{2} }{2}*2[/tex]
= 25[tex]\pi[/tex]
Area of the shaded region = ( 100 - 25π )
= ( 100 - 78.53 )
= 21.46
≈ 21.5 cm²
Hence, we can conclude, the area of the shaded region is 21.5 cm².
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If j=h and k=m then which expression represents the value of g
Answers
Answer:
Step-by-step explanation:
as given j=h and k=m then which expression for g is
as from attached image , we can see that its look like two right angle triangle
so from lower triangle we apply the pythagorean theorem .
which state that sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.
so small triangle ΔEBD
h² +k²= g² ---------------(1)
now from big triangle ΔABC
(j + h)² +(m + h)² =f²---------(2)
given j=h and k=m so from equation-2 we can find ,
(h + h)² +(k+ k)² =f²
(2h)² +(2k)²=f²
4h²+ 4k²= f²
4(h²+k²)= f² ----------(3)
now from equation 1 and 3 we can obtained .
4×g² =f²
take square root both side we get,
2×g=f
so g=f/2----- Answer
Find the sale price of an $18 item after a 50% discount.
Answers
Rewrite 50% as a decimal : 0.50
Multiply the price by 0.50:
18 x 0.50 = 9
The sale price is $9
Answer:
$9
Step-by-step explanation:
price of an item=$18
discount=50%
sale price =? (be x)
sale price= original price -discount% of original price
x=$18 -50/100 * $18
x=$1800-$900/100
=$900/100
=$9
therefore sale price of an item is $9.
Berto has $12 to put gas in his car. If gas costs $3.75 per gallon, which ordered pair relating number of gallons of gas, x, to the total cost of the gas, y, includes the greatest amount of gas Berto can buy?
(__,__ )
Answers
Answer:
If gas costs $3.75 per gallon and Berto has $12, then he can purchase 12/3.75 gallons. This is approximately 3.2 gallons. So the coordinate on this line would be (3.2, 12).
Actually... It's from web
the slope of the line that passes through the points in the table is:
Answers
Answer:
-2/7
Step-by-step explanation:
We have two points so we can use the slope formula
m = (y2-y1)/(x2-x1)
m = (8-0)/(-14-14)
= 8/-28
= -2/7
13 14 14 17 18 20 20 what's the mode?
Answers
Answer:
mode is 14,20
if you dont know mode is the frequency of the numbers
Step-by-step explanation:
Answer:
14 & 20
Step-by-step explanation:
the number that appears the most
(3a+b)³ please help me
Answers
Answer:
[tex]27a^{3} +27a^{2}b+9ab+b^{3}[/tex]
Step-by-step explanation:
[tex](3a+b)(3a+b) = 9a^{2}+6ab+b^{2}\\(9a^{2}+6ab+b^{2})(3a+b) = 27a^{3} + 27a^{2}b +9ab^{2} +b^{3}[/tex]
Answer:
Step-by-step explanation:
9a^3+18a^2b+9ab^2+b^2
7.
A ball is thrown into the air with an upward velocity of 36 ft/s. Its height h in feet after t seconds is given by the function h=-16t^2+36t+9. In how many seconds does the ball reach its maximum height? Round to the nearest hundredth if necessary. What is the ball’s maximum height?
A. 1.13 s; 69.75 ft
B. 1.13 s; 29.25 ft
C. 2.25 s; 9 ft
D. 1.13 s; 31.5 ft
Answers
Answer:
The answer is 1.13;29.25
Step-by-step explanation:
Answer: The ball reaches its maximum height in 1.13 seconds. b) The ball's maximum height is 30.25 feet.
This sort of problem is solved easily by a graphing calculator.
a) The ball reaches its maximum height in 1.13 seconds.
b) The ball's maximum height is 30.25 feet.
_____
Since you want to know when and where the peak value of the function occurs, it is convenient to put it into vertex form.
h = -16(t² -(9/4)t) + 10
h = -16(t² -(9/4)t +(9/8)²) +10 +16(9/8)²
h = -16(t -9/8)² + 10 + 81/4
h = -16(t -9/8)² + 30 1/4
The vertex of the function is (9/8, 30 1/4) ≈ (1.13, 30.25).
h = -16t^2 + 36t + 9
At maximum height h' = 0,
h' = -32t + 36 = 0
32t = 36
t = 36/32 = 1.13 s.
Maximum height = -16(1.125)^2 + 36(1.125) + 9 = 29.25 ft
Answer is option d (1.13 s, 29.25 ft)
The answer is 1.13;29.25
700=132.69x-25.96
solve please
Answers
Answer:
x = 5.5 (rounded)
Step-by-step explanation:
Equation: 700 = 132.69x - 25.96
Add 25.96 to both sides: 700+25.96 = 132.69x -25.96 + 25.96
Simplify: 725.96 = 132.69x
Isolate x
Divided both sides by 132.69: [tex]\frac{725.96}{132.69} = \frac{132.69x}{132.69}[/tex]
Simplify: x = 5.5 (rounded)
Someone help me with this……
Answers
Answer:
its the second won
Step-by-step explanation:
What is 300+3x40-25x4=?
Answers
Answer:
320
Step-by-step explanation:
300+3x40=120-25x4
300+120-25x4=100
320
Answer:
300+3x40-25x4 = 320
Step-by-step explanation:
300+3x40-25x4
= 300+ 120 - 100
= 420-100
= 320
Answer pls…………………………..
Answers
Answer:
Option 3
Step-by-step explanation:
Brainliest please~
What is the following product?
3/24 • 3/45
Answers
Answer:
6(³√5)
Step-by-step explanation:
³√24×45=6(³√5)