Answer:
See attachedStep-by-step explanation:
The proof is attached
The first line is according to the identity:
(a + b)² = a² + 2ab + b², where a = x² and b = y²The second line is simplification where y⁴ cancels and 2x²y² doubles.
The third line is about taking the common factor of x² and factorizing.
Viết khai triển theo công thức nhị thức Niu-tơn (x + 1) ^ 5
Answer:
x^5+5x^4+10x³+10x²+5x+1
Step-by-step explanation:
A ball is dropped from a height of 9 feet and allowed to bounce. Each time the ball bounces, it reaches a height that is23the height of the previous bounce. How many times will the ball be exactly 3 feet above the ground?
I'm assuming you meant to say "it reaches a height that is 2/3 the height of the previous bounce".
We have a geometric sequence with a = 9 as the first term and r = 2/3 as the common ratio.
The nth term is a*(r)^(n-1) = 9*(2/3)^(n-1)
Set this equal to 3 and solve for n. You'll need logs to isolate the exponent.
9*(2/3)^(n-1) = 3
(2/3)^(n-1) = 3/9
(2/3)^(n-1) = 1/3
log[ (2/3)^(n-1) ] = log(1/3)
(n-1)*log(2/3) = log(1/3)
(n-1)*(-0.17609) = -0.47712
n-1 = (-0.47712)/(-0.17609)
n-1 = 2.7095235
n = 2.7095235+1
n = 3.7095235
Unfortunately we don't get a whole number. We can see that the terms of the sequence are:
9, 6, 4, 2.667
Each term is found by multiplying 2/3 by the previous term.
We don't land exactly on "3". The closest we get is 2.667 approximately.
So to answer the question, there is no way to get to exactly 3 feet above the ground based on a whole number of bounces.
One circle has a circumference of 12 pie Another circle has a circumference of 32 pie What is the ratio of the radius of the smaller circle to the radius of the larger circle?
Answer:
3 : 8
Step-by-step explanation:
The ratio of the radii is equal to the ratio of the circumference, then ratio is
12π : 32π ( divide both parts by 4π )
= 3 : 8
solve for x. round to the nearest tenth of a degree, if necessary.
x=30°
Answer:
Cos x°=adjacent/hypotenuse
Cos x°=45/52
x°=Cos-¹(45/52)
x°=30°
Combine and simplify the following radical expression.
Answer:
[tex]24 \sqrt{5} [/tex]Step-by-step explanation:
[tex]2 \sqrt{20} + 8 \sqrt{45} - \sqrt{80} [/tex]
[tex] = 2 \sqrt{2 \times 2 \times 5} + 8 \sqrt{3 \times 3 \times 5} - \sqrt{2 \times 2 \times 2 \times 2 \times 5} [/tex]
[tex] = 2(2 \sqrt{5} ) + 8(3 \sqrt{5} ) - (4 \sqrt{5} )[/tex]
[tex] = 4 \sqrt{5} + 24 \sqrt{5} - 4 \sqrt{5} [/tex]
[tex] = 24 \sqrt{5} (ans)[/tex]
Answer:
[tex]\huge\boxed{24\sqrt5}[/tex]
Step-by-step explanation:
[tex]2\sqrt{20}+8\sqrt{45}-\sqrt{80}\\\\=2\sqrt{4\cdot5}+8\sqrt{9\cdot5}-\sqrt{16\cdot5}\\\\\text{use}\ \sqrt{a\cdot b}=\sqrt{a}\cdot\sqrt{b}\\\\=2\sqrt4\cdot\sqrt5+8\sqrt9\cdot\sqrt5-\sqrt{16}\cdot\sqrt5\\\\\text{we know}\ a\sqrt{b}=a\cdot\sqrt{b},\ \text{and}\ \sqrt{a}=b\iff b^2=a\\\\\text{Therefore}\\ 2\sqrt{4}=2\cdot\sqrt4=2\cdot2=4\\8\sqrt9=8\cdot\sqrt9=8\cdot3=24\\\sqrt{16}\cdot\sqrt5=4\cdot\sqrt5=4\sqrt5\\\\\text{Therefore}[/tex]
[tex]=2\sqrt4\cdot\sqrt5+8\sqrt9\cdot\sqrt5-\sqrt{16}\cdot\sqrt5=4\sqrt5+24\sqrt5-4\sqrt5\\\\=(4+24-4)\sqrt5=24\sqrt5[/tex]
Find the slope of (3,-24)(19,-48)
Answer:
-3/2
Step-by-step explanation:
To find the slope, we use the slope formula
m = (y2-y1)/(x2-x1)
= (-48- -24)/(19 -3)
= (-48+24)/(19-3)
= -24/16
= -3/2
Answer:
[tex]-\frac{3}{2}[/tex]
Step-by-step explanation:
The slope of a line that passes through two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is given by:
[tex]m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}[/tex]
Let:
[tex](x_1, y_1)=(3, -24)\\(x_2, y_2)=(19, -48)[/tex]
Substitute into slope formula:
[tex]m=\frac{-48-(-24)}{19-3}=\frac{-24}{16}=\boxed{-\frac{3}{2}}[/tex]
help me with this math question
Step-by-step explanation:
Option D
As time increases, the temprature of soup decreases..
hope it helps
Helpppppp plssssss ! Click the image
Anyone know this question?
Identify the slope (m) and the y-intercept (b) of each line a) y= x+7 slope = y intercept = b) y = -3x slope = y intercept =
Answer:
a) y= x+7
The slope is 1 and the y intercept is 7
b) y = -3x
The slope is -3 and the y intercept is 0
Step-by-step explanation:
The slope intercept form of the equation of a line is
y = mx+b where m is the slope and b is the y intercept
a) y= x+7
The slope is 1 and the y intercept is 7
b) y = -3x
The slope is -3 and the y intercept is 0
There are 5 seats in a bus. In how many different ways if there are 5 children. How many different ways are there if there are 4 children, and how many different ways are there if there are 3 children.
Answer:
5=1
4=5
i don't really know for the third one sorry but it's more than 11
Step-by-step explanation:
Mr. Lynch bought some oranges and pears.
After giving away 10 oranges, he had twice
as many pears as oranges left. If he had 24
pears in the end, what was the ratio of
oranges to pears in the beginning?
Answer:
11: 12
Step-by-step explanation:
Let the number of oranges and pears Mr Lynch have initially be x and p respectively.
x -10= ½p
2(x -10)= p
p= 2x -20 -----(1)
Since Mr Lynch did not give any pears away, the number of pears at the end is the initial number of pears.
p= 24
Substitute p= 24 into (1):
2x -20= 24
2x= 24 +20 (+20 on both sides)
2x= 44
x= 44 ÷2
x= 22
[tex] \frac{x}{p} = \frac{22}{24} [/tex]
[tex] \frac{x}{p} = \frac{11}{12} [/tex]
Thus the ratio of orange to pears in the beginning is 11: 12.
Can somebody help me Answer to this ??
X=7
c is the answer:
[tex]3x + 50 = 10x + 1 \\ 10x - 3x = 50 - 1 \\ 7x = 49 \\ x = \frac{49}{7} \\ x = 7[/tex]
find the length of side x to the nearest tenth
Answer:
x = 2 sqrt(3)/3
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
sin theta = opp / hyp
sin 60 = 1 /x
x sin 60 =1
x = 1 /sin 60
x = 1 / sqrt(3)/2
x = 2 sqrt(3)/3
Se preguntó a 44 estudiantes por el tiempo, medido en minutos, que tardan en
llegar a su sitio de estudio. Las respuestas obtenidas fueron: 15,20,17,24,45,40,35,39,46,44,50,47,42,40,38,30,35,45,35,45,35,37,47,48,58,55,38,37,40,43,40,39,45,48,50,35,20,57,55,56,47,43,37,34,50,60
a) Clasifique la variable y construya la
TDF correspondiente al histograma.
b) Realice 4 interpretaciones de los
datos condensados en la TDF del punto a).
c) Realice el histograma, el polígono de
frecuencias y la ojiva de esta variable.
Answer:
sdfghjkl
Step-by-step explanation:
Please anyone help me
If die is rolled two times, find the probably of getting "1'twice.
Math Answer[tex] {1}\{36} [/tex]
Feel fre e too ask me
Please understand it
#BrainliestBunch
Which is a pair of vertical angles?
∠VRU and ∠SRT
∠TRS and ∠VRW
∠TRV and ∠WRU
∠WRV and ∠SRW
Answer: ∠TRS and ∠VRW (Choice B)
========================================================
Explanation:
Ignore ray RU. I would redraw the entire thing without ray RU as part of the picture. See below.
Notice how lines TW and SV intersect to form an X shape.
The angles TRS and VRW shown in red are opposite one another, so we consider them to be vertical angles. Vertical angles are always congruent.
Answer:
B ∠TRS and ∠VRW
Step-by-step explanation:
There is currently a linear bike path that goes through the points (4, 0) and (7, 4). The park commission is planning to build a new bike path that is parallel to the old one that passes through the point (2, 5).
Answer:
y = 3/4x +7/2
Step-by-step explanation:
slope of line = difference of 2nd x value - 1st x value/ 2nd y value - 1st y value
x difference /y difference = 3/4 = slope
y = 3/4x
to find y-intercept, add a variable
y = 3/4x + B
then add the first x and y value point numbers into equation
0 = 3/4(4) + B
-3 = B
put back B into equation.
y = 3/4x - 3 which is the linear path the biker is going
now you can use another variable to find the new bike path
y = 3/4x + A
plug in the x value 2 and y value 5 from (2,5)
5 = 3/2 + A
A = 7/2
there-fore the new line which is parallel to the old line is:
y = 3/4x +7/2
Which division is shown by the model?
Step-by-step explanation:
where the model step by step explanation
Please help me solve this question
Answer:
A = 16 units²
Step-by-step explanation:
The area (A) of a parallelogram is calculated as
A = bh ( b is the base and h the perpendicular height )
The right triangle on the left is a 3- 4- 5 ( Pythagorean triple )
Then b = 4 and h = 4 , so
A = 4 × 4 = 16 units²
find the missing length indicated.
Answer:
Step-by-step explanation:
x is the geometric mean because it is a part of both the small triangle on the left (with base 81) and the whole triangle (with base 225). Setting up the geometric means formula:
[tex]\frac{81}{x}=\frac{x}{225}[/tex] and cross multiply to get
[tex]x^2 =18225[/tex] so
x = [tex]\sqrt{18225}[/tex] and
x = 135
A high school coach wants to buy new athletic shorts for the 15 members of the basketball team. The coach must spend less than $200 on the shorts. Which inequality represents the maximum cost of each pair, s, the coach can buy?
Answer:
A. 15s < 200
Step-by-step explanation:
Which inequality represents how many pairs of shorts, s, the coach can buy?
A. 15s < 200
B.15s > 200
C. 15s <(with line under)200
D 15s >(with line under)200
Let
s = cost of eat short
Number of students (Short) = 15
Less than (<)
The inequality:
Number of short * cost of each short < $200
15 * s < 200
15s < 200
s < 200/15
s < $13.333333333333
Answer:A. 15s < 200
Step-by-step explanation:A. 15s < 200
When the length of each side of a square is increased by 5 cm, its area is increased by 895 cm2. Find the length of a side before the increase.
The length of a side before the increase is...
Answer:
Step-by-step explanation:
Increasing the side length by 5 is represented as s + 5. To get the area of a square we multiply side times side: [tex](s+5)^2=s^2+10s+25[/tex]
The area of a square is s². If we are increasing this area s² by 895, then to represent this we have s² + 895.
Put that together into an equation:
[tex]s^2+10s+25=s^2+895[/tex] and simplify to
10s = 870 so
s = 87
Let's check that. The area before the addition to the side is 87*87 = 7569; the area after the addition of 5 cm is 92*92 = 8464. The difference is
8464 - 7569 = 895 so we did good!
In a 100 metre race, the time of the winner was 10. 57 seconds and the time of the athel athlete who came third was 10. 64 seconds Write down a possible time for the athlete who came Second
Answer:
10.61
Step-by-step explanation:
Find y.
PLEASE HELP ASAPPPP
Answer:
y = 4
Step-by-step explanation:
[tex]\frac{sin(90)}{4\sqrt{2} } = \frac{sin(45)}{y}[/tex]
Answer:
y = 4
Step-by-step explanation:
Using the cosine ratio in the right triangle and the exact value
cos45° = [tex]\frac{1}{\sqrt{2} }[/tex] , then
cos45° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{y}{4\sqrt{2} }[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex] ( cross- multiply )
y × [tex]\sqrt{2}[/tex] = 4[tex]\sqrt{2}[/tex] ( divide both sides by [tex]\sqrt{2}[/tex] )
y = 4
The number of days (d) is equal
to the dividing of the number of hours (h) and 24.
A. d = h - 24
B. h = 24 d
C. h = 24-h
D. h = 24 + h
Answer:
B
Step-by-step explanation:
[tex]d \: = \frac{h}{24} [/tex]
[tex]h \: = 24d[/tex]
find the sum or difference of the polynomials. Write your answer in descending
order.(-3x2 + 2x + 1) + (-8x2 + 3x + 2)
i think by x2 you meant x²
(-3x² + 2x + 1) + (-8x² + 3x + 2)
-11x² + 5x + 3
the sum of two positive consecutive integers is x. in terms of x, what is the value of the smaller of these two integers?
Answer:
In terms of x, the smaller integer is (x - 1)/2
Step-by-step explanation:
Two consecutive positive integers can be written as:
n and (n + 1)
Where n is an integer and:
n > 0.
notice that the smaller of the two integers is n.
We know that the sum of these two integers is equal to x, then:
n + (n + 1) = x
we can rewrite this as:
2n + 1 = x
solving this for n (the smaller of the two integers) we get:
2n = x - 1
n = (x - 1)/2
In terms of x, the smaller integer is (x - 1)/2
Find the area of the parallelogram. 7 in. 12 in. [ ] Area = [?] in.
Answer:
Area= Base x height
Area= 7 x 12 inch
Area= [tex]84inch^{2}[/tex]
Brainliest please
Please help me!!!!! You have to match the slope of each line
Answer:
it would be line to zero slope that's all I can do for u pal maybe..
