Answer:
Part A)
[tex]\displaystyle z_6 = 9609600000x^{10}[/tex]
Part B)
[tex]z_4 = 10500 x^9[/tex]
Step-by-step explanation:
Recall the binomial expansion theorem:
[tex]\displaystyle (x+y)^n = \sum_{k=0}^{n}{n \choose k} x^{n-k} y^k[/tex]
Part A)
Our expression is equivalent to:
[tex]\displaystyle (2x+5)^{15} = \sum_{k = 0}^{15} {15 \choose k} (2x)^{15-k}\cdot 5^k[/tex]
To find the sixth term, let k = 5. Therefore, the sixth term is:
[tex]\displaystyle \begin{aligned} z_6 &= {15\choose 5} (2x)^{15-5}\cdot 5^5 \\ \\ & = {15\choose 5}x^{10} \cdot (2)^{10}\cdot 5^5 \\ \\ &= 9609600000x^{10}\end{aligned}[/tex]
Part B)
Likewise:
[tex]\displaystyle \begin{aligned} \left(x^2 + \frac{5}{x}\right)^9 = \sum_{k=0}^9 {9\choose k}(x^2)^{9-k}\left(\frac{5}{x}\right)^{k}\end{aligned}[/tex]
To find the fourth term, let k = 3. Therefore, the fourth term is:
[tex]\displaystyle \begin{aligned} z_4 & = {9\choose 3}\left(x^2\right)^{9-3} \left(\frac{5}{x}\right)^{3} \\ \\ & = {9\choose 3}x^{12} \cdot \frac{5^3}{x^3} \\ \\ & = 10500x^9\end{aligned}[/tex]
Find the area of the triangle ?
Answer:
16 cm²/m²
Step-by-step explanation:
The formula to find the area of a triangle is:
Area of the triangle = [tex]\frac{1}{2}[/tex] × base × height
Where base = 8 and height = 4
So, the area of the triangle = [tex]\frac{1}{2}[/tex] × 8 × 4 = 16 cm²/m²
what is the average rate of change for this quadratic function for the interval fr x=2 to x=4?
Answer:
0-4
derivate first
function is missing
substitute the value of X
PROVE :
sin^2(-300°).cos^2 (120)+ cos^2(-240 ).sin^2(390)=1/4
Step-by-step explanation:
[tex] \sin {}^{2} ( - 300) \cos {}^{2} (120) + \cos {}^{2} ( - 240) \sin {}^{2} (390) = \frac{1}{4} [/tex]
[tex] \sin {}^{2} (60) \cos {}^{2} ( {}^{} 120) + \cos {}^{2} (120) \sin {}^{2} (30) [/tex]
[tex] \frac{3}{4} \frac{1}{4} + \frac{1}{4} \frac{1}{4} [/tex]
[tex] \frac{3}{16} + \frac{1}{16} = \frac{4}{16} = \frac{1}{4} [/tex]
I get the part A of the question its just the part B that i would really appreciate for someone to explain
Step-by-step explanation:
650065 = (a² + 1)(c² + 1)
and
650065 = (ac - 1)² + (a + c)² = the sum of 2 squared numbers (ac - 1)² and (a + c)².
we see that 5 and 13 and therefore 5×13=65 are all factor of 650065. and then 650065/65 = 10001.
and we know that 65 = (64 + 1) = (8² + 1)
and 10001 = (10000 + 1) = (100² + 1)
so, a = 8, c = 100
that means the 2 squared numbers summing up to 650065 are
(ac - 1)² = (8×100 - 1)² = 799² = 638,401
(a + c)² = (8 + 100)² = 108² = 11,664
650,065 = 638,401 + 11,664 = 799² + 108²
Which of the following equations describes the graph?
y=-x^2+1
An equation that describes the graph is [tex]y=-x^{2} +1[/tex]
What is an equation?"It is a mathematical statement which consists of equal symbol between two algebraic expressions."
What is parabola?"It is a curve, such that a point on the curve is equidistant from a fixed point, and a fixed line. "
For given question,
The graph describes the parabola.
The parabola opens downward, so the equation of the parabola would be,
[tex]y=-x^{2}[/tex]
We know that, for a function f(x) is transformed to f(x) + c if c > 0 then the graph of the function moves up by c units.
if c < 0 then the graph of the function moves down by c units.
As the graph of the parabola moves down by 1 unit, the equation of the parabola would be,
[tex]y=-x^2+1[/tex]
Therefore, the equation that describes the graph is [tex]y=-x^{2} +1[/tex]
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what are the key features of the graph of a trigonometric function? How do you find them from a graph or an equation?
Answer:
The basic sine and cosine functions have a period of 2π. The function sin x is odd, so its graph is symmetric about the origin. The function cos x is even, so its graph is symmetric about the y-axis. The graph of a sinusoidal function has the same general shape as a sine or cosine function.
They are the three x-intercepts, the maximum point, and the minimum point. All of these are on your unit circle. The values of sin x correspond to the y-values, so those key points are (angle, y-value) or (0,0), (π/2, 1), (π, 0), (3π/2, -1), (2π, 0).
Find the equation of the straight line passing through the point (0, 2) which is perpendicular to the line y=1/4x+5
Answer:
Step-by-step explanation:
perp. -4
y - 2 = -4(x - 0)
y - 2 = -4x + 0
y = -4x + 2
Which of the following can be used to find the sum of the interior angles for
any regular polygon?
A. Multiply the number of sides by 180
B. Add 1 to the number of sides and multiply the sum by 180
OC. Divide the number of sides by 180
OD. Subtract 2 from the number of sides and multiply the difference by
180
The table represents quadratic function g. Which statement is true about the function?
I
-5
-4 -3
-2 -1 0
-1
0
-1
-4 -9 -16
O A. The minimum occurs at the function's x-intercept.
O B.
The maximum occurs at the function's x-intercept.
O C.
The maximum occurs at the function's y-intercept.
The minimum occurs at the function's y-intercept.
O D.
Answer:
B. The maximum occurs at the function's x-intercept.
Step-by-step explanation:
Given table:
[tex]\large\begin{array}{| c | c | c | c | c | c | c |}\cline{1-7} x & -5 & -4 & -3 & -2 & -1 & 0\\\cline{1-7} g(x) & -1 & 0 & -1 & -4 & -9 & -16\\\cline{1-7}\end{array}[/tex]
From inspection of the table, we can see that:
[tex]g(-5) = -1[/tex] and[tex]g(-3) = -1[/tex]This indicates symmetry.
The line of symmetry is the mid-point between the two x-values.
Therefore, the line of symmetry is x = -4
The vertex (minima/maxima) is on the line of symmetry, therefore the vertex is at (-4, 0). As the function decreases as x → 0, the vertex is a maximum.
As the y-value of the vertex is 0, the maximum occurs at the function's x-intercept.
Answer:
B
Step-by-step explanation:
Finding the line of symmetry :
⇒ Two x-values have the same y-coordinate → (-5) and (-3)
⇒ This means the symmetry is exhibited and it lies between these 2 x-values
⇒ Line of symmetry : x = -4
=============================================================
Now, on plotting these points on a graph we see that this graph has a negative coefficient.
⇒ This means this graph will have a maximum point as the vertex
⇒ The vertex lies on the line of symmetry, hence the vertex (according to the graph and table) is (-4, 0)
Hence, we can say that the maximum occurs at the function's x-intercept.
A set of equations is given below: Equation C: y = 6x + 9 Equation D: y = 6x + 2 How many solutions are there to the given set of equations? (1 point) a One solution b No solution c Two solutions d Infinitely many solutions
Since the values on both sides are different, hence the set of equations has no solution
System of equationsSystem of equation are made of two equations with unknown variables. Given the following equations
y = 6x + 9
y = 6x + 2
Equate
6x + 9 = 6x + 2
Collect the like terms
6x - 6x = 2 - 9
0x = -7
Since the values on both sides are different, hence the set of equations has no solution
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9+2×42+6-2
Please show the work
Answer:
The answer is 97
Step-by-step explanation:
According to PEMDAS, we will solve the multiplication first. 2 × 42 is 84. Next, we will add or subtract from left to right. 9 + 84 + 6 – 2 is 97, the answer to our problem.
9 + 2 × 42 + 6 - 2
Multiply 2 and 42 to get 84.
9 + 84 + 6 - 2
Add 9 and 84 to get 93.
93 + 6 - 2
Add 93 and 6 to get 99.
99 - 2
Subtract 2 from 99 to get 97.
97 ===> Answer
[tex]\red{\boxed{\green{\boxed{\boldsymbol{\sf{\purple{Pisces04}}}}}}}[/tex]
Write the equation of the following line in slope-intercept form. X
Answer:
[tex]y=-\frac{1}{2}x+2[/tex]
Step-by-step explanation:
The equation for slope-intercept form is [tex]y=mx+b[/tex].
First, we find b by looking at where the line passes through where [tex]x=0[/tex]. We can see that it is 2, so in our equation for slope-intercept form [tex]b=2[/tex].
Next, we find the slope or m. Find the slope by taking two points and plugging them into this expression [tex]\frac{x_{1}-x_{2}}{y_{1}-y_{2}}[/tex]. To demonstrate, I will choose points (0,2) and (2,1), however, any pair of points will give you the same answer. When we plug in these points, we should get the expression [tex]\frac{0-2}{2-1}[/tex]. By solving this, we get -1/2. Therefore, in our equation for slope-intercept form, [tex]m=-\frac{1}{2}[/tex].
By putting the information we have about m and b together, we get the equation [tex]y=-\frac{1}{2}x+2[/tex].
Find the value of x.
Answer:
x=36
Step-by-step explanation:
2x+2x+70+78+68=360
4x+216=360
4x=360-216
4x=144
x=144/4=36
There are 20 students in a class.
12 of the students are girls.
Find the ratio of the number of girls to the number of boys.
Give your ratio in the form n : 1.
Answer:
1.5:1
Step-by-step explanation:
the original answer is 12:8, so you have to simplify it down. you can get it down to 3:2 with whole numbers, but to get it down to a ratio with one, you'll have to divide each number by 2 because the bottom number is 2, so the final answer would be 1.5:1
Solve three fourths times two thirds
Answer:
1/4
Step-by-step explanation:
3/4 x 2/4 = 6/24
6/24 simplified is 1/4
Please mark Brainliest!!
Answer:
6/12 or 1/2
Step-by-step explanation:
Start by multiplying the numerators
3 x 2 = 6
Then multiply the denominators
4 x 3 = 12
Then you get your answer of 6/12
But if you want it simplified then divide both the denominator and numerator by 6 and you will get your final answer of
1/2
Hope this helped
Please mark me the Brainliest
(x-1)(x+1)= выполнить умножение
Answer:
x^2-1^2
Step-by-step explanation:
formula:
(a-b)(a+b)=a^2-b^2
What are the approximate solutions to the equation? A. X=1.2 and x=3 B. X= 1.7 and x= 6 C. X= 2.6 and X = -3 D. X=1 and x=4.2
The solutions are where the red and blue lines cross each other.
Answer would be D. X ≅ 1 and x ≅ 4.2
20 POINTS!!! WILL GIVE BRAINLIEST!!!
Answer:
equivalent. not equivalent. not equivalent
Step-by-step explanation:
Lines m and n are parallel on a coordinate plane. Lines m and n are transformed by the same rotation, resulting in image lines s and t. Which statement describes the relationship between lines s and t?
The statement that best describes the relationship between lines s and t is: Lines s and t are parallel.
What are parallel lines?Parallel lines can be defined as those lines that are equal to one another but does not intersect one another.
For Lines s and t to be parallel lines this means that lines s ant t are cut by transversal. Hence, transversal intersect lines s and t to make it parallels lines.
Therefore Lines s and t are parallel.
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A 7th grade teacher at a local middle school wants to know which
of two candidates for class president is more popular among the
7th grade students in the school. Which group of people should
make up a sample that will best answer her question?
OA) other 7th grade teachers in her
school
OB) parents of 7th graders in her school
OC) 7th graders in her school
OD) 7th graders in her homeroom
The answer is Option C) 7th graders in her school.
In order to ascertain the suitability of a candidate for any popular position, his popularity can be assessed by taking a survey of the concerned sample.
Answer:
She should ask the 7th graders in the school
Step-by-step explanation:
Because their opinion is important in electing the president.
how would i solve this the shaded region is the whole inside circle.
Answer:
34.48cm²
Step-by-step explanation:
Assuming the shaded area doesn't contain the triangle:
area of triangle = bh/2
area of triangle = 4(2)/2
area = 4
area of circle = πr²
area = π3.5²
area = 38.48
area of shaded = 38.48 - 4
area = 34.48cm²
how do i divide 431.25 by 61
Answer:
7.070 to the nearest thousandth
Step-by-step explanation:
You could use a calculator or do it manually using long division:
61)431 .2500(7.0695 <---------Quotient
427
425
367
580
549
310
305
what the 2 soultion answer to
y = 6x − 4
y = 5x − 3
[tex]y= 6x -4~~~~~~...(i)\\\\y = 5x -3~~~~~~...(ii)\\\\\text{From (i) and (ii):}\\\\~~~~~6x -4 = 5x -3\\\\\implies 6x -5x = -3 + 4\\\\\implies x = 1\\\\\text{Substitute x = 1 in equation (i):}\\\\y = 6(1) -4 = 2\\\\\text{Hence,}~ (x,y) = (1,2)[/tex]
What is the area of the kite?
A. 1,500 ft^2
B. 640 ft^2
C. 320 ft^2
D. 160 ft^2
thank you ! :)
You design a bean bag toss board using a coordinate plate. You plot vertices of the board at C (3,2) D (3,6) E (5,2) F (5,6). What is the perimeter of the bean bag toss board?
The perimeter of the bean bag toss board is 12 units
What is the perimeter of the bean bag toss board?The points are given as:
C (3,2) D (3,6) E (5,2) F (5,6)
Calculate the distance between adjacent points using:
[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
So, we have:
[tex]CD = \sqrt{(3 - 3)^2 + (2 - 6)^2} = 4[/tex]
[tex]DF = \sqrt{(3 - 5)^2 + (6 - 6)^2} = 2[/tex]
[tex]FE = \sqrt{(5 - 5)^2 + (2 - 6)^2} = 4[/tex]
[tex]CE = \sqrt{(3 - 5)^2 + (2 - 2)^2} = 2[/tex]
The perimeter is then calculated as:
P = CD + DF + FE + CE
This gives
P = 4 + 2 + 4 + 2
Evaluate
P =12
Hence, the perimeter of the bean bag toss board is 12 units
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What is the end behavior of the graph of
?
Question 9 options:
as x increases, f(x) increases
as x decreases, f(x) decreases
as x increases, f(x) increases;
as x decreases, f(x) increases
as x increases, f(x) decreases;
as x decreases, f(x) increases
as x increases, f(x) decreases;
as x decreases, f(x) decreases
The end behavior of the graph of f(x) = -0.25x2 - 2x + 1 is that A) As x increases, f(x) increases. As x decreases, f(x) decreases.
What is the end behavior about?The end behavior of a function f tells us that the way that the graph function behaves at the "ends" of the x-axis.
Note that the end behavior of a function tells the trend of the graph and in this graph, f(x) -----> +∞ as x----> -∞ (as the value of x decreases the value of f(x) increases) and f(x) -----> -∞ as x----> +∞ (as the value of x increases the value of f(x) decreases).
Therefore, The end behavior of the graph of f(x) = -0.25x2 - 2x + 1 is that A) As x increases, f(x) increases. As x decreases, f(x) decreases.
See full question below
What is the end behavior of the graph of f(x) = -0.25x2 - 2x + 1?
A) As x increases, f(x) increases. As x decreases, f(x) decreases.
B) As x increases, f(x) decreases. As x decreases, f(x) decreases.
C) As x increases, f(x) increases. As x decreases, f(x) increases.
D) As x increases, f(x) decreases. As x decreases, f(x) increases
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(07.04A)
Which of the tables represents a function?
Table A
Input Output
8 −9
8 −8
10 −8
Table B
Input Output
4 11
7 12
7 13
Table C
Input Output
−4 0
−3 3
−2 5
Table D
Input Output
10 0
10 4
3 7
Table A
Table B
Table C
Table D
Answer:
Table C
Step-by-step explanation:
The input value in Table C gives a different value in the output.
which is the value of the expression 4 / 1/8
Answer: Your answer is going to be 32
Step-by-step explanation:
Answer:
32
Step-by-step explanation:
1/8 is nothing but 0.125
4/.125 = 32
.125 goes into four 32 times.
HELP ASAP
stats and probs
Answer:
Step-by-step explanation:
Anyone know how to do this?
To solve this, we need to use our trignometric functions;
⇒ look at the diagram attached
Let's examine what the problem wants:
hypotenuse (longest side) of the triangleLet's examine what the problem gives us:
side adjacent to the 45-degree angleangle that has measure of 45-degreesLet's solve:
[tex]sin(45)=\frac{5}{x} \\5=x*sin(45)\\x = \frac{5}{sin(45)} \\x=7.07[/tex]
Answer: 7.1 (rounded to nearest tenth)
Hope that helps!
Answer:
[tex]5\sqrt2[/tex]
Step-by-step explanation:
This is a 45-45-90 triangle so we can find all the side lengths easily.
The ratio between the base and the hypotenuse of a 45-45-90 triangle is [tex]1:\sqrt2[/tex], which means for this triangle it would be [tex]5:5\sqrt2[/tex]. This means the length of the hypotenuse is [tex]5\sqrt2\\[/tex], which is [tex]x[/tex], which is the answer.