Answer:
Applying the binomial theorem
[tex]{\displaystyle (x+a)^{n}=\sum _{k=0}^{n}{n \choose k}x^{n-k}a^{k}}[/tex]
Here we have x = -[tex]\sqrt{2}[/tex], n = 8,
=> 4th term (k = 3) would be:
[tex]{8 \choose 3}x^{8-3}a^{3}} = {8 \choose 3}(-\sqrt{2})^{5}a^{3}} = -224a^{3}\sqrt{2}[/tex]
Hope this helps!
:)
Answer:
A
Step-by-step explanation:
help pleaseeeeeee!!!!!
Answer:
D
Step-by-step explanation:
A curve is describe by the following parametric equations:
x=3+t, y=t^2-4
Which statement best describes the curve?
A. The curve is a parabola with a vertex at (3,-4) and is traced from left to right for increasing values of t.
B. The curve is a parabola with a vertex at (3,-4) and is traced from right to left for increasing values of t.
C. The curve is a parabola with a vertex at (-3,4) and is traced from left to right for increasing values of t.
D. The curve is a parabola with a vertex at (-3,4) and is traced from right to left for increasing values of t.
Answer:
A. The curve is a parabola with a vertex at (3,-4) and is traced from left to right for increasing values of t.
Step-by-step explanation:
x = 3 + t
y = t² − 4
Eliminating the parameter:
t = x − 3
y = (x − 3)² − 4
This is an upwards parabola with a vertex at (3, -4).
x = 3 + t, so as t increases, x increases.
So the curve is traced from left to right.
Jeffrey at times can borrow some
money from his parents. He has $16,
but spent $20. He then earned $7 and
spent $4. How much money does he
have at the moment?
Answer:
-$1 dollars
Step-by-step explanation:
16 - 20 = -4
-4 + 7 = 3
3 - 4 = -1
-$1 or -1 dollars
Answer:
-1$
Step-by-step explanation:
16 - 20 = -4
-4 + 7 = 3
3 - 4 = -1
-$1 or -1 dollars
Which equation represents a proportional relationship that has a constant of proportionality equal to –10? y = x minus 10 y = StartFraction over negative 10 EndFraction y = negative 10 x y = negative 10
Answer:
The correct answer would be C. y = -10x
Step-by-step explanation: We cam eliminate the first two by common sense, that would leave us with options C, and D. The correct answer would be C, the reason it is not D is because D isn't a proportion, y = -10 is just stating that variable y equals -10, whereas, y = -10x represents a proportion.
Answer: the other guy is correct
Step-by-step explanation: it is C i got a 100%
Please Help 6th Grade Math! Box Plots! 2 questions (Image attached)
Answer:
First answer is 14
Second answer is 25
Step-by-step explanation:
Median is the middle ( 1 2 3 4 5 the median would be 3)
You start at 2 and end at 27
List all the numbers from 2 to 27 and come from both ends until you get to the middle number(s)
In this case there are two 14 & 15
14+15=29 29÷2=14.5
Since there are no decimal answers you are left with 14
Range you take the two end numbers and subtract them (27 & 2)
27-2=25
Hopefully this helps!
Which expression represents the perimeter of triangle YXZ?
Answer:
17
Step-by-step explanation:
3(w-2)+w+5+18-4w
=3w-6+w+5+18-4w
=17
Which graph shows y= (-5x) -4?
Answer:
Graph A
Step-by-step explanation
I look at the y-intercept first, and the y-intercept is -4, so looking at each graph you can see both A and D have y-intercepts of -4, since the line intercepts, or goes through the y-axis (the vertical line of the graph) at -4.
Then, you look at the variable that's changing, which is -5x. Since it's a negative, A is the graph that is negatively decreasing, because of its position on the graph. The line is going down, starting in the negative side.
What is the side lengths of volume=343 cm and side lengths of 729 cm
Answer:
Volume = 343 - Length: 7, Width: 7, Height: 7
Volume = 729 - Length: 9, Width: 9, Height: 9
Step-by-step explanation:
Assuming that the shapes are rectangular prisms.
Mateo finds a special on apples for $0.80 per pound. Which price is a better deal? A. $0.78 per pound B. $0.85 per pound C. $0.90 per pound D. $1.25 per pound
Answer: I think the answer is A
Step-by-step explanation:
Can someone please help me with these 2 questions?
Answer:
Answer is given below with explanations.
Step-by-step explanation:
[tex]in \: second \: question \: linear \ \\ pair \: of \: angles \: is \: shown \\ linear \: pair \: of \: angles \: is \: 180 \: degrees. \\ then \: a + b = 180 \: degrees \: \: (1) \\ in \: first \: equation \: \\ subtracting \: a \: on \: bot h\: sides \\ we \: get \: b = 180 - a \\ then \: D \: and \: E \: are \: correct \: \\ options \: which \: gives \: the \: relationship \: \\ between \: the \: mesure \: of \: angle \: in \: figure[/tex]
[tex]in \: third \: question \: also \: represents \: \\ linear \: pair \: of \: angles \\ here \: 88 + b + b = 180 \: degrees \\ 88 + 2b = 180 \\ so \: option \: D \: is \: the \: only \: correct \: answer \: \\ to \: represent \: the \: relationship \ \\ : between \: angles \: in \: figure.[/tex]
HAVE A NICE DAY!
THANKS FOR GIVING ME THE OPPORTUNITY TO ANSWER YOUR QUESTION.
3(4+6)-16 what does it equal and how did you get the answer
Answer:
14
Step-by-step explanation:
you can do this two ways:
First:
[tex]3(10)-16\\=30-16\\=14[/tex]
Second:
Distribute the 3 first
[tex]\\12+18-16\\=30[/tex]
Solve for d.
5d + 2 (2 - d) = 3 (1 + d) + 1
A. D= -3
B. No solutions
C. Infinitely many solutions
D. D= 4
So the answer is no solution .
Look at the attached picture
Hope it will help you
Find the value of the power.
(1/3) to the power of 3
Answer:
1/27
Step-by-step explanation:
3 times 3 times 3 = 27
as a fraction it would be 1/27
Answer:
[tex]\frac{1}{27}[/tex]
Step-by-step explanation:
When finding the power of a fraction you need to set both the numerator and denominator to the power.
(1/3)³ = 1³/3³
3³ = 27
1³/3³ = 1/27
A triangle has vertices A(-6,3), B(1,5), and C(4,-4). this triangle is dilated with the origin at its center by a scale factor of 4. Write the ordered pair of the new vertices of the new image
Answer:
(8,-3) and (4,5)
Step-by-step explanation:
Find an
explicit formula for the geometric sequence 120, 60, 30, 15, ....
Answer:
f(n) = 120 * (1/2)^n
Step-by-step explanation:
First the first number is 120, so we get y = 120, then 60/120 = 1/2
So we no the r, or constant rate is 1/2.
After that, we can finish our equation by doing
f(n) = 120 * (1/2)^n
or
y = 120*(1/2)^x
The explicit formula for the given geometric sequence is:
[tex]a_n = 120 \times 0.5^{n-1}[/tex]
We have,
To find an explicit formula for the geometric sequence 120, 60, 30, 15, ...,
we need to determine the common ratio, denoted by 'r'.
To find the common ratio, we divide any term in the sequence by its preceding term.
Let's choose the second and first terms:
r = 60 / 120 = 0.5
Now that we have the common ratio 'r', we can express the nth term of the geometric sequence using the explicit formula:
[tex]a_n = a_1 r^{n-1}[/tex]
where '[tex]a_n[/tex]' represents the nth term of the sequence, '[tex]a_1[/tex]' is the first term, 'r' is the common ratio, and 'n' is the position of the term we want to find.
Using the given sequence, '[tex]a_1[/tex]' is 120, and 'r' is 0.5.
Plugging these values into the formula, we have:
[tex]a_n = 120 \times0.5^{n-1}[/tex]
Therefore,
The explicit formula for the given geometric sequence is:
[tex]a_n = 120 \times 0.5^{n-1}[/tex]
Learn more about geometric sequence here:
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find the value of : 2x when x =5
Please help you get loads of points.
Answer:10
Step-by-step explanation: since x=5
2×5= 10
Answer:
[tex]10[/tex]
Step-by-step explanation:
[tex]2x \\ [/tex]
[tex]x = 5[/tex]
[tex]2x \\ 2 \times 5 \\ = 10[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
Write the slope-intercept form of the line that passes through the point (-3, - 6 ) and is parallel to the line y = 5x+4.
Answer
math way u can get a answer more faster
Step-by-step explanation:
oooh
Answer:
y= 5x +9
Step-by-step explanation:
Slope- intercept form:
y= mx+c, where m is the gradient and c is the y-intercept.
Parallel lines have the same gradient. Since the gradient of the given line is 5, the gradient of the unknown line is also 5. Hence, m=5.
y= 5x+c
To find the value of c, substitute a coordinate.
When y= -6, x= -3,
-6= 5(-3) +c
-6= -15 +c
c= 15 -6 (+15 on both sides)
c= 9 (simplify)
Thus, the equation of the line is y=5x+9.
15 points plz help
2. Use the system of linear equations you wrote to solve for the variables p and q. Show all work.
Answer:
(+ 50,+ 11) are the points of the equilibrium point.
Step-by-step explanation:
demand is a negative line.
supply is a positive line.
A textbook store sold a combined total of 272 biology and math textbooks in a week. The number of biology textbooks sold was three times the number of math textbooks sold. How many textbooks of each type were sold?
Number of biology textbooks sold: ?
Number of math textbooks sold: ?
Answer:
biobooks = 204
mathbooks = 68
Step-by-step explanation:
the bio textbooks make up 3 parts
the math textbooks make up 1 part
the denominator therefore is 4
so biobooks = 272 * 3/4
and mathbooks = 272 * 1/4 (272 : 2 : 2)
note that calculating the mathbooks 1st is easier, bc you can then multiply by 3 to get the biobooks.
add both numbers up to proof that the sum is 272
(would really appreciate the brainliest)
The base is a rectangle so B=l*w. Find the volume.
Answer:
472.5
Step-by-step explanation:
which x value is excluded from domain?
Please help! You don’t have to show work
Answer:
It is Number 1 A
Step-by-step explanation:
Find the slope from the table.
The slope is the change in y over the change in x
Use the first and last set given.
Slope = (11 - 3) / (2 - -2) = 8-4 =2
The slope = 2
Derek rolls a die many times and records the number of times he rolls a three. Arrange the following situations in order from the situation that gives the largest difference between relative frequency and actual probability to the situation that gives the smallest difference.
Derek rolls the
die 10 times.
Derek rolls the
die 30 times.
Derek rolls the
die 5 times.
Derek rolls the
die 20 times.
i need an order
Answer:
5,10,20,30
Step-by-step explanation:
least to greatest
Using the data below, determine the angle for the part of the pie chart the represents the people who prefer dogs?
Answer:
48
Step-by-step explanation:
The pie chart that represents the people who prefer dogs will have an angle of 172.8 degrees. The correct option is C.
What is a pie chart?A circular statistical visual with slices illustrating numerical proportion is called a pie chart. Each slice's arc length in a pie chart corresponds to the quantity it represents.
The data for the pie chart is given below:-
Dogs 24
Cats 18
Hamsters 5
Fish 3
Total number is = 24 + 18 + 5 + 3 = 50
Angle = 360 / 50 = 7.2
The pie chart that represents the people who prefer dogs will be calculated as:-
Dogs = 7.2 x 24 = 172.8 degrees.
The pie chart is attached with the answer below.
Therefore, the pie chart that represents the people who prefer dogs will have an angle of 172.8 degrees. The correct option is C.
To know more about the pie charts follow
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what is the probability of rolling both of these dice and getting both of them to land on 1
Can someone please help me thanks.
Answer:
Step-by-step explanation:
130
So the right answer is 130 degree.
Look at the attached picture
Hope it will help you
Good luck on your assignment
Which equation represents a line that passes through (2. - 1/2) and has a slope of 3?
y-2 = 3(x + 1/2)
y-3 = 2(x + 1/2)
y + 1/2 = 3(x - 2)
y + 1/ 2 = 2(x - 3)
Answer:
y + 1/2 = 3(x - 2) This matches the 3rd answer choice.
Step-by-step explanation:
Use the point-slope formula for the equation of a straight line that passes through the point (h, k) and has a slope of m:
y - k = m(x - h) becomes:
y + 1/2 = 3(x - 2) This matches the 3rd answer choice.
The equation of the line will be y + 1/2 = 3(x – 2). Then the correct option is C.
What is the equation of line?The equation of line is given as
y = mx + c
Where m is the slope and c is the y-intercept.
The slope is 3. Then the equation of line will be
y = 3x + c
If the equation is passing through (2, -1/2). Then we have
-1/2 = 3(2) + c
c = -6 - 1/2
Then the equation will be
y = 3x – 6 – 1/2
y + 1/2 = 3(x – 2)
Then the correct option is C.
More about the equation of line link is given below.
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I need urgent help plz
Hi! Got a question!
please explain!
Calculate the volume of a cubicle house with length 18 m, width 12 m and height 10 m
p.s:thanks!!
Answer:
= 2160 cubic meters
Step-by-step explanation:
For Cuboidal House
length 18 m,
width 12 m and
height 10 m
Volume of Cuboid
= l*b*h
= 18 * 12 * 10
= 2160 cubic meters
Thus, the volume of a cuboidle house is 2160 cubic meters
Answer:
2160
Step-by-step explanation: