Answer:
The coefficients are;
1,28,378 and 3,276
Step-by-step explanation:
For the binomial expansion, when we talk of the coefficients, we mean the whole numbers that stands before the alphabets
For example, the coefficient of x in 2x is 2
Back to the question;
(x + y)^28
= 28C0 x^28y^0 + 28C1 X^27y^1 + 28C2 x^26y^2 + 28C3 x^25y^3 + ..........
So the coefficients we are looking for are;
28C0 = 1
28C1 = 28
28C2 = 378
28C3 = 3,276
Kindly note that 28C0 is read as 28 combination zero and so on
Please help me! Use the appropiate lines to solve the question 3x+1=10
Answer:
Step-by-step explanation:
3x + 1 = 10
3x = 10 - 1
3x = 9
x = 9/3
x = 3
hope this helps
plz mark as brainliest!!!!
Enter the correct answer in the box
A triangle has side lengths of 200 units and 300 units. Write a compound inequality for the range of the possible lengths for the third side, X
Answer:
100-500
Step-by-step explanation:
Both sides of a triangle cannot be shorter than the remaining side. Thus, the side must be less than 500 units. With the same rule, the side must be greater or equal to 100 units, as if it was less, then 200 + 99 < 300.
The compound inequality for the range of the possible lengths for the third side will be 100- 500.
What is inequality?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
The meaning of inequality is to say that two things are NOT equal. One of the things may be less than, greater than, less than or equal to, or greater than or equal to the other things.
p ≠ q means that p is not equal to qp < q means that p is less than qp > q means that p is greater than qp ≤ q means that p is less than or equal to qp ≥ q means that p is greater than or equal to qGiven:
side lengths of 200 units and 300 units.
The largest value of the third side will be
200+300=500
and, the smallest value will be
300-200=100
Hence, 100<X<500
Learn more about inequality here:
https://brainly.com/question/20383699
#SPJ5
• A research scientist measures the outside temperature, in degrees Fahrenheit, at various
times throughout a 24-hour period and records her findings in the graph below. In this
real-world function, the hours represent the input values, and the temperature represents
the output values. Use the graph to identify the range of the function. Write your answers
using set notation. Then write a sentence to explain what the range represents in
this function
Answer:
{t|60 <= t <= 85}
Step-by-step explanation:
The temperatures were measures at different times, but does not stop the values being real numbers (i.e. not discrete, or integer values).
So the range of the function is the set of all values between the minimum and maximum measured during the measuring interval (domain) of hours two and twenty-two.
The minimum value = 60F
The maximum value = 85F
So the interval of the range is [60,85], in interval notation.
In set-builder notation, it is
{t|60 <= t <= 85}
find the value of a and b for which the system of equations has infinitely many solutions : 2x + 3y = 7 ; (a-b)x + (a+b)y = 3a + b - 2
Answer:
a= 5 and b=1
Step-by-step explanation:
To solve, we will follow the steps below:
2x + 3y = 7
(a-b)x + (a+b)y = 3a + b - 2
We should note that since it has infinitely many solutions then,
[tex]\frac{a_{1} }{a_{2} } = \frac{b_{1} }{b_{2} } = \frac{c_{1} }{c_{2} }[/tex]
Hence
2/a-b = 3/a+b = 7/3a +b-2
2/a-b = 3/a+b
cross-multiply
3(a-b) = 2( a+b)
open the bracket
3a - 3b = 2a + 2b
collect like term
3a - 2a = 2b + 3b
a = 5b -------------------------------------------(1)
Similarly
3/a+b = 7/3a +b-2
cross-multiply
7(a+b) = 3(3a+b -2)
7a + 7b = 9a + 3b -6
take all the variables to the left-hand side of the equation
7a - 9a+ 7b-3b = -6
-2a + 4b = -6 ---------------------------------(2)
but a = 5b
substitute a= 5b in equation (2) and solve for b
-2(5) + 4b = -6
-10 + 4b = -6
add 10 to both-side of the equation
-10 + 10+ 4b = -6+10
4b = 4
divide both-side of the equation by 4
b = 1
substitute b= 1 in equation (1)
a = 5b
a =5(1)
a=5
Therefore, a= 5 and b=1
The graph shows the rate at which the depth of the water in a pond is changing over time. On a coordinate plane, a graph titled Depth of Pond Water has Minutes on the x-axis and Feet on the y-axis. A line goes through points (2, 4) and (4, 8). The depth of the water is increasing by feet each minute.
Answer:
Step-by-step explanation:
The key to solving this question is to find the distance bwtween the two points given
distance=y2-y1/x2-x1
(2,4)(4,8)
2=x1,4=y1
4=x2
8=y2
8-4/4-2
4/2=2
The depth of the water is increasing by 2 ft each minute
Answer:
it is incresing by two feet each minute
Step-by-step explanation:
b) The product of two positive numbers is 56. If their difference is 10, find the
numbers
Answer:
14 and 4
Step-by-step explanation:
xy = 56
x - y = 10
x = 10 + y
(10+y)y = 56
10y + y² = 56
y² + 10y - 56 = 0
(y-4)(y+14) = 0
y - 4 = 0
y = 4
y + 14 = 0
y = -14
y is a positive integer so y = 4.
x - 4 = 10
x = 14
The two numbers whose product is 56 and difference is 10 are 14 and 4
A = 14
B = 4
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the first number be = A
Let the second number be = B
The product of two numbers is = A x B
The difference of two numbers is = A - B
Now , the equation is
A x B = 56
A - B = 10
Now ,
( A - B )² = A² + B² - 2 ( A x B )
Substituting the values of A and B in the equation , we get
100 = A² + B² - 112
Adding 112 on both sides , we get
A² + B² = 212
When A = 14
B² = 212 - 196
B² = 16
So , B = 4
Therefore , the value of A is 14 and value of B is 4
Hence , The two numbers whose product is 56 and the difference is 10 are 14 and 4
To learn more about equations click :
https://brainly.com/question/10413253
#SPJ2
Find the nth term and the 50th term of the sequence. 2,10,18,26 6,11,16,21,26 3,11,19,27,35 1,4,7,10,13 21,24,27,30,33 40,33,26,19,12 33,25,17,9,1
Answer: 756
Step-by-step explanation:
The sum of 54 anid six times a number is 216. Find the number.
Answer:
x = 27
Step-by-step explanation:
Step 1: Write out equation
54 + 6x = 216
Step 2: Solve for x
6x = 162
x = 27
Answer:
x=27
Step-by-step explanation:
54+6x=216
Collect like terms:
6x=216-54
6x=162
Divide both sides by the coefficient of x
6x\6=162\6
x=27
helppp!!!! please!!!
Answer:
72
Step-by-step explanation:
Angle XYZ is an inscribed angle. An inscribed angle is equal to half of its arc.
144/2 is 72.
The value of XYZ is 72.
FIRST ANSWER BRAINLEST!!!! The two top NBA players played a basketball game against the RSM team. Together the NBA players made 85 baskets, scoring one point for free throws and two or three points for field goals. They scored a total of 184 points during the game. If they made 22 free throws, how many three-point field goals did they make.
Answer:
They made 36 three-point field goals
Step-by-step explanation:
For free throws , we have one point each.
So here, the total points they made from free throws is 22 * 1 = 22 points
So the number of points made from field goals would be 184-22 = 162 points
So the issue we have now is knowing the number of 3-point field goals that was made.
How can we get this?
Remember they made 85 baskets? so if we subtract the number of free throws, then we can have the number of field throws and that is 85-22 = 63
Now, let the number of 2 points throws be x and the number of 3 points throws be y
From our earlier analysis;
x + y = 63 ••••••••• (i)
Now the total number of three pointers would be 3 * y = 3y and the total number of two pointers would be 2 * x = 2x
Adding both gives a total of 162
Thus;
2x + 3y = 162 •••••••• (ii)
So we have two equations to solve simultaneously.
From equation 1, we can say that;
x = 63-y
Let’s substitute this into equation 2
2(63-y) + 3y = 162
126 -2y + 3y = 162
126+y = 162
y = 162-126
y = 36
This means that they made 36 three-point field goals
A rectangle has a long side of 8.5 cm. Its perimeter is 24 cm How long is one side?
Answer:
(8.5+x)×2=24
8.5+x=12
x=3.5
Answer:
Breadth = 3.5cm
Step-by-step explanation:
Perimeter = 2L + 2B
24cm = 2(8.5) + 2B
2B = 24 - 17
B = 7÷2
B = 3.5
Pls tell this answer somebody fast
Answer:
x = 2
Step-by-step explanation:
Using the rule of exponents
[tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{(m-n)}[/tex]
Note that 49 = 7² and 343 = 7³
Consider the left side, that is
[tex]\frac{7^{2x+1} }{7^2}[/tex] = [tex]7^{(2x+1-2)}[/tex] = [tex]7^{(2x-1)}[/tex] , thus
[tex]7^{(2x-1)}[/tex] = 7³
Since bases on both sides are equal, equate the exponents, that is
2x - 1 = 3 ( add 1 to both sides )
2x = 4 ( divide both sides by 2 )
x = 2
what is g(k+1)=x^2-4x
Answer:
g(k + 1) = k² - 2k - 3
Step-by-step explanation:
Step 1: Plug in (k + 1) in for x
g(k + 1) = (k + 1)² - 4(k + 1)
Step 2: FOIL
g(k + 1) = k² + 2k + 1 - 4(k + 1)
Step 3: Distribute
g(k + 1) = k² + 2k + 1 - 4k - 4
Step 4: Combine like terms
g(k + 1) = k² - 2k - 3
Find the area of a trapezoid with bases of 5 feet and a 7 feet, and a height of 3 feet a. 18 b. 36 c. 72 d. 40
Answer:
The answer is option A. 18Step-by-step explanation:
Area of a trapezoid = 1/2(a + b) × h
where
h is the height
a and b are the other sides
From the question
h = 3 feet
a = 5 feet
b = 7 feet
Area = 1/2(5+7) × 3
= 1/2 ( 12) × 3
= 6 × 3
The answer is
= 18
Hope this helps you.
A cyclist travels at an average speed of 9 mph for 5 hours. How far did she travel in miles?
Answer:
45
Step-by-step explanation:
since the car goes 9mph and you are traveling for 5 hours you just multiply 9 by 5 and you get 45.
ASAP!! Please help me. I will not accept nonsense answers, but will mark as BRAINLIEST if you answer is correctly with solutions.
Answer:
C. It has been stretched horizontally.
Step-by-step explanation:
According to the diagram, the parabola has not been reflected in any way, nor has it been translated, since the parabola is pointing up in a smile, and the vertex is still at the origin.
The parabola does appear to be stretched, since the parent function had points at (1, 1), and (2, 4), but this parabola does not contain those points.
Since the parabola appears to be flatter than the parent function, we can say that C. It has been stretched horizontally.
Hope this helps!
Answer: Option D
Step-by-step explanation
Because
Helppp!!!! please!!!
Answer:
Option B
Step-by-step explanation:
Area of kite = product of 2 diagonals, p and q / 2
here, p = 10 + 10 = 30 feet
q = 3 + 3 = 6 feet
∴ Area = 30 × 6 / 2
90 ft^2
Hope it helps
plz mark as brainliest!!!
Answer:
[tex]\boxed{Area = 90 ft^2}[/tex]
Step-by-step explanation:
Diagonal 1 = p = 3+3 = 6 ft
Diagonal 2 = q = 10+20 = 30 ft
Area = [tex]\frac{pq}{2}[/tex]
Area = [tex]\frac{(6)(30)}{2}[/tex]
Area = 3*30
Area = 90 ft^2
Selectie correct answer.
How many solutions for x does the following equation have?
2(x + 4) - 1 = 2x + 7
OA. 7
OB.
1
Ос.
infinite
OD. 0
Reset
Next
Answer:
OD.0
Step-by-step explanation:
because 2(X+4)-1 = 2x+7
or, 2x+8-1 = 2x+7
or, 2x+7= 2x+7
and it cancels out eachother so it will be 0
The equation 2(x + 4) - 1 = 2x + 7 has infinite solutions
How to determine the number of solutions?The equation is given as:
2(x + 4) - 1 = 2x + 7
Open the bracket
2x + 8 - 1 = 2x + 7
Evaluate the difference
2x + 7 = 2x + 7
Both sides of the equation are the same.
Hence, the equation has infinite solutions
Read more about equation solutions at:
https://brainly.com/question/18760518
What is the area of the rhombus shown below? AC=17 BD=15 AB=11.2 Answers: A. 255 square units B. 190.4 square units C. 16 square units D. 127.5 square units
Answer:
D. 127.5 square units
Step-by-step explanation:
AC=17
BD=15
AB=11.5
Diagonal (1&2) are given, base of the rhombus is also given.
Height is not given
Area of a rhombus given the diagonals
=1/2×d1×d2
Where,
d1=AC=17
d2=BD=15
Area of a rhombus=1/2×d1×d2
=1/2×17*15
=1/2×255
=127.5
D. 127.5 square units
Answer:
D for sure
Step-by-step explanation:
There are six equilateral triangles in a regular
O A. square
O B. polygon
O C. hexagon
O D. octagon
There are six equilateral triangles in a regular hexagon.
What is a triangle?A triangle is a 2-D figure with three sides and three angles.
The sum of the angles is 180 degrees.
We can have an obtuse triangle, an acute triangle, or a right triangle.
We have,
A regular hexagon has six equal sides and six equal angles.
It can be divided into six equilateral triangles by drawing lines connecting the center of the hexagon to each vertex.
Each of these triangles has the same side length and angle measures.
A square has four sides and four right angles, but it is not a regular polygon because it does not have equal side lengths.
A polygon is a general term for a shape with three or more straight sides, but it does not refer to any specific shape or properties.
An octagon has eight sides and eight angles, but it cannot be divided into equilateral triangles because the angle measures are not all equal.
Thus,
There are six equilateral triangles in a regular hexagon.
Learn more about triangles here:
https://brainly.com/question/25950519
#SPJ7
Graph this following function
Answer:
Please find attached the graph of the following function;
[tex]\left\{\begin{matrix}x - 1 & if & -2 \leq x < 0\\ 1 & if & x = 0 \\ 3 & if & 0 < x \leq 2\end{matrix}\right.[/tex]
Step-by-step explanation:
We note that the function is linear from x = 2 to just before x = 0
The linear relationship of the function f(x) with x changes just before x = 0
At x = 0, the value of f(x) is indicated as 1
From just after x = 0, the function is a straight horizontal line y = 3
The function also changes value immediately after x = 0 to the line y = 3
The areas where the function is defined are shown in continuous lines
fill in the blanks with two consecutive integers to complete the following inequality.-____<√56<____
Answer:
Since 7 is √49 and 8 is √64 and 49 < 56 < 64 the answer is 7 < √56 < 8.
Each of the walls in Harvey’s shed are square and have an area of 84 square feet. What is the approximate height, to the nearest foot, of the walls in Harvey’s shed? A. 8 feet B. 9 feet C. 10 feet D. 21 feet
Answer:
B. 9 feet
Step-by-step explanation:
area = side^2
side^2 = 84
side = sqrt(84)
side = 9.2 ft
Each side of a wall measures 9.2 ft.
Please explain how you got your answer also. A class has 21 girls and 12 boys. What is the probability that a boy's name is drawn at random?
12 over 21
21 over 12
12 over 33
21 over 33
The following table shows the possible meal combinations when choosing an entrée and a side dish at Marty's Diner. Side Dish Entrée burger with salad burger with fries burger with fruit tacos with salad tacos with fries tacos with fruit pizza with salad pizza with fries pizza with fruit What is the probability of selecting a combination that includes a burger or a salad? Enter your answer as a reduced fraction, like this: 3/14
Answer:
5/9
Step-by-step explanation:
There are 9 total combinations and 3 of them include a burger, 2 of them that have salad but not a burger. If you add them together it equals 5/9
The probability of selecting a combination that includes a burger or a salad is 5/9
Since the total of 6 outcomes include fries or fruit as the side dish.
There is a total of 9 possible meal combinations. A person must choose an Entree and a side dish.
The Entrees consist of burgers, tacos, and pizzas.
The side dishes consist of salad, fries, and fruit.
To find the number of combinations consisting of fries or fruit, we calculate the individual combinations.
With fries as side dish, which can choose a burger, a pizza or a taco as your Entree.
There are 3 combinations each, there are a total of 6 combinations with fruit or fries as the side dish.
There are 9 total combinations and 3 include a burger, rest 2 that have salad but not a burger.
then probability = 5/9
Learn more about probability here;
https://brainly.com/question/9326835
#SPJ2
A new pair of sunglasses is regularly priced at $130.00. What
will the price be after at 35% discount? *
Answer:
$ 84.50
Step-by-step explanation:
Regular price = $130
Discount = 35% of 130
= [tex]\frac{35}{100}*130[/tex]
= 0.35 * 130
= $ 45.50
Price of the sunglasses after discount = Regular price - discount
= 130 - 45.50
= $ 84.50
Solve for f. -3/4f = 5/4
Answer:
f = -5/3
Step-by-step explanation:
-3/4f = 5/4
Multiply each side by -4/3 to isolate f
-4/3*-3/4f = 5/4*-4/3
f = -5/3
Answer:
Hey there!
We have -3/4f=5/4
Multiply both sides by -4/3, to cancel out the -3/4.
f=-5/3
Hope this helps :)
21 POINTS!!!!!!!!!!!!!!!!! HEEEELPPPPPPP
If an image of a triangle is congruent to the pre image what is the scale factor of the dilation
Answer:
1
Step-by-step explanation:
Because the pre image and dilated image are congruent, the scale factor is 1.
Please help meeeee thanks
Answer:
A)21
B) 70
C)89
Step-by-step explanation:
Answer:
b=70°a=21°c= 89°Step-by-step explanation:
b=180° - 110° =70°
a = 21°
C= 180° - b - a= 180 - 70 - 21= 89°
[tex]good \: luck[/tex]