We will select the third row from the pascal triangle to expand the binomial expression (22³ + 3y²)² which is equal to
(22³ + 3y²)² = 22⁶ + 63888y² + 9y⁴
We know that when we need to expand the expression (a + b)² we select the coefficients from the row of triangle beginning with 1,2 which is (1,2,1).
And when we write the expansion we note that with each new term we decrease the power of a and increase the power of b.
Thus the expansion can be written as
(a + b)² = 1a² + 2ab + 1b²
which we normally write as
(a + b)² = a² + 2ab + b² (1)
According to the question we have been the expression as
(22³ + 3y²)² which is equal to the above expression where,
a = 22³ and b = 3y²
Putting the required values in equation (1) we get
(22³ + 3y²)² = (22³)² + 2(22³)(3y²) + (3y²)²
= 22⁶ + 63888y² + 9y⁴
Hence we will select the third row from the pascal triangle to expand the binomial expression (22³ + 3y²)² which is equal to
(22³ + 3y²)² = 22⁶ + 63888y² + 9y⁴
Learn more about Pascal triangle here : https://brainly.com/question/3442415
#SPJ9
Which is the solution to the equation below? 32 = q/2
A) 16
B) 64
C) 46
D) 30
Answer:
Step-by-step explanation:
B buster
Answer:
64
Step-by-step explanation:
32*2 = q
q=64
-2x + y =0
5x + 3y = -11
Answer:
(-1, -2)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Algebra I
Solving systems of equations using substitution/eliminationSolving systems of equations by graphingStep-by-step explanation:
Step 1: Define Systems
-2x + y = 0
5x + 3y = -11
Step 2: Rewrite Systems
-2x + y = 0
Add 2x on both sides: y = 2xStep 3: Redefine Systems
y = 2x
5x + 3y = -11
Step 4: Solve for x
Substitution
Substitute in y: 5x + 3(2x) = -11Multiply: 5x + 6x = -11Combine like terms: 11x = -11Isolate x: x = -1Step 5: Solve for y
Define equation: y = 2xSubstitute in x: y = 2(-1)Multiply: y = -2Step 6: Graph Systems
Check the solution set.
There are 400 marbles in a bag. 60 of the marbles are blue. What percent of the marblesare not blue?
Answer:
80%
Step-by-step explanation:
400-60= 320
320 is 80% of 400
Michael and Landon work at a dry cleaners ironing shirts. Michael can iron 40 shirts per hour, and Landon can iron 20 shirts per hour. Michael and Landon worked a combined 14 hours and ironed 360 shirts. Graphically solve a system of equations in order to determine the number of hours Michael worked, ,x, and the number hours Landon worked, y.
I need two equations in y=mx+b form pls
Answer:
Michael worked 4 hours and Landon worked 10 hours.
Step-by-step explanation:
Michael can iron 40 shirts each hour, so in xx hours he can iron 40x40x shirts. Landon can iron 20 shirts each hour, so in yy hours he can iron 20y20y shirts. The total number of shirts ironed 40x+20y equals 360:
40x+20y=360
40x+20y=360
Since Michael and Landon worked a combined 14 hours, we know x+yx+y must equal 14.
x+y=14
Write System of Equations:
40x+20y= 360
x+y=14
Solve for y in each equation:
40x+20y = 360 x+y = 14 20y = -40x+360
[tex]\frac{-20y}{20}[/tex] =[tex]\frac{-40x+360}{20}[/tex]
y = -2x+18
Ppz help due tomorrow
Answer:
I think it’s just option 1. Tell me if I was wrong.
Step-by-step explanation:
Please help and thank you im failing at school so decided to download this app
Answer:
you could scan and take a picture in the app when u login
List the angles in order from least to Greatest.
Answer:
I think it would be B) A,B,C
Step-by-step explanation:
well A is smaller than B or C and B is smaller than C.
What is the equation of a line that has a slope of 2 and passes through point (-1, 7)?
Answer:
2x+9
Step-by-step explanation:
PLEASE HELP
Complete the proofs below using the most appropriate method, SSS or SAS.
7. Given: AM = CP, CM = GP, C is the midpoint of AG
Prove: A4CM = ACGP
G
M
Statements
Reasons
1.
1.
2.
2.
3.
3.
4.
4.
5.
5.
answer
AM= CP-given
CM=GP-given
C is the midpoint of AG-given
AC=CG- definition of midpoint
ACM=CGP- SSS
The complete proof is as follows:
[tex]\mathbf{AM = CP}[/tex] -- Given[tex]\mathbf{CM = GP}[/tex] -- GivenC is the midpoint of AG -- Given[tex]\mathbf{AC \cong CG}[/tex] --- Definition of Midpoint[tex]\mathbf{\triangle ACM \cong \triangle CGP}[/tex] ---- Congruent by SSSThe given parameters are:
[tex]\mathbf{AM = CP}[/tex] [tex]\mathbf{CM = GP}[/tex] C is the midpoint of AGThis means that, the above statements would represent the first three blanks, and their respective reason is "Given"
Because of (3), above
4. [tex]\mathbf{AC \cong CG}[/tex] --- midpoint definition
(1), (2) and (4) imply that:
The three sides of both triangles are congruent by SSS
Hence, the last statement would be:
[tex]\mathbf{\triangle ACM \cong \triangle CGP}[/tex] ---- Congruent by SSS
Read more about mathematical proofs at:
https://brainly.com/question/14361320
How much grape juice would you need to mix with 154 quarts of sparkling water?
The amount of grape juice need to mix with 15 / 4 quarts of sparkling water is , 15/8 quarts.
What is Quart measurement ?The quart is a measurement which is use to find the capacity of liquid. Or we can say Quart is a unit of liquid volume which is measured in gallon. There are different measurements into which we can convert the unit such as ounces and liters.
Mathematically, we can write :
1 quart = 32 fluid ounces
or
1 quart = 0.94 US liters = 4 cups (approx.)
According to question,
[tex]1\frac{1}{2}[/tex] quarts of water = 3/2 quarts of water = 3/4 quarts of grape
let, 15 /4 quarts of sparkling water = x
now, solving the equation
x = ( 3/4 × 15/4 ) ÷ 3/2
x= 3/4 × 15/4 ×2/3
x =15/8
Thus, The grape juice needed is , 15/8 quarts.
To know more about mixtures, visit :
brainly.com/question/16845760
#SPJ9
The complete question is :
A recipe of sparkling grape juice is made with [tex]1\frac{1}{2}[/tex] quarts of sparkling water and 3/4 quarts of grape juice? How much of grape juice would you need to mix with 15/4 quarts of sparkling water?
Stephanie's school is selling tickets to a play. On the first day of ticket sales the school sold 4 adult tickets and 10 student tickets for a total of $150. The school took in $105 on the second day by selling 1 adult ticket and 10 student tickets. What is the price each of one adult ticket and one student ticket?
Answer:
The price of
1 adult ticket = $15
1 student ticket = $9
Step-by-step explanation:
Let
The price of adult tickets be represented by a
The price of student tickets be represented by s
Therefore:
On the first day of ticket sales the school sold 4 adult tickets and 10 student tickets for a total of $150.
4a + 10s = $150.... Equation 1
The school took in $105 on the second day by selling 1 adult ticket and 10 student tickets.
a + 10s = $105.... Equation 2
a = $105 - 10s
Therefore, we substitute : $105 - 10s = a in Equation 1
4a + 10s = $150.... Equation 1
4($105 - 10s) + 10s = $150
$420 - 40s + 10s = $150
Collect like terms
- 40s + 10s = $150 - $420
-30s = -$270
Divide both sides by -30
-30s/-30 = -$270/-30
s = $9
We find a
a = $105 - 10s
a = $105 - 10($9)
a = $105 - $90
a = $15
Therefore, the price of
1 adult ticket = $15
1 student ticket = $9
write a real world problem for 5/6 divided by 1/12. Use a model to solve.
Answer:
Step-by-step explanation:
Two boxes have a volume of 5/6 and 1/12 cubic meters respectively. How many times does the petty box (1/12) fit in the big box (5/6)?
[tex]\frac{\frac{5}{6} }{\frac{1}{12} } =\frac{(5)(12)}{(6)(1)} =\frac{60}{6} =10[/tex]
ten times
Hope this helps
What is 1338384.444 x .8
Answer:
1070707.5552
Step-by-step explanation:
Answer:
10707075.552
Step-by-step explanation:
used a calculator because I'm way too tired to write this down...
What is your monthly take-home pay if your take-home pay is $1034.65 every two weeks? Round intermediate calculations and the final answer to the nearest cent; use 365 days in a year.
The monthly take-home pay is $2240.83.
What is Algebraic expression ?
Algebraic expression can be defined as combination of variables and constants.
To calculate the monthly take-home pay, we need to first find the annual take-home pay and then divide by 12 (since there are 12 months in a year).
We are given that the take-home pay is $1034.65 every two weeks, which means the total take-home pay for a year can be calculated as follows:
annual take-home pay = 1034.65 * 26 = 26889.9
Next, we divide the annual take-home pay by 12 to get the monthly take-home pay:
monthly take-home pay = 26889.9 / 12 = 2240.825
Rounding this to the nearest cent, we get:
monthly take-home pay = $2240.83
Therefore, the monthly take-home pay is $2240.83.
To learn more about Algebraic expression from given link.
brainly.com/question/28884894
#SPJ1
At what value of x does the second
function's output exceed (get bigger
than) the first function's output?
Explain your solution steps.
f(x)= x+7 and f(x)= x²)
The second function's output exceeds (get bigger than) the first function's output for x∈(-∞,[tex]\frac{1-\sqrt{29} }{2}[/tex])∪([tex]\frac{1+\sqrt{29} }{2}[/tex],∞)
Given the functions f(x)=x+7 and f(x)=[tex]x^{2}[/tex]
To know when to exceed, need to equate both functions.
⇒[tex]x^{2} =x+7[/tex]
⇒[tex]x^{2} -x-7=0[/tex]
x=[tex]\frac{-b+\sqrt{D} }{2a}[/tex] and [tex]\frac{-b-\sqrt{D} }{2a}[/tex]
⇒x=[tex]\frac{1-\sqrt{29} }{2}[/tex],[tex]\frac{1+\sqrt{29} }{2}[/tex]
f(x)=[tex]x^{2}[/tex] decreases from -∞ to 0 and increases from 0 to ∞ it cuts the graph of x+7 two times and for x∈(-∞,[tex]\frac{1-\sqrt{29} }{2}[/tex])∪([tex]\frac{1+\sqrt{29} }{2}[/tex],∞) f(x)=[tex]x^{2}[/tex] is greater than f(x)=x+7
Therefore,The second function's output exceeds (get bigger than) the first function's output for x∈(-∞,[tex]\frac{1-\sqrt{29} }{2}[/tex])∪([tex]\frac{1+\sqrt{29} }{2}[/tex],∞)
Learn more about function here:
https://brainly.com/question/12431044
#SPJ9
A lemonade recipe calls for 6 gallons of water. How many cups of water are needed for the recipe.
Answer:
96
Step-by-step explanation:
Hope this helps
what is the slope of a line passing through the points (7,5) and (3,5)
Answer:
[tex]m=0[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Step-by-step explanation:
Step 1: Define
Point (7, 5)
Point (3, 5)
Step 2: Find slope m
Substitute: [tex]m=\frac{5-5}{3-7}[/tex]Subtract: [tex]m=\frac{0}{-4}[/tex]Divide: [tex]m=0[/tex]Answer:
0/-4
Step-by-step explanation:
You would us the slope formula: [tex]\frac{y2-y1 }{x2-x1}[/tex]
so y2 is 5 and y1 is 5 so 5-5= 0
then x2 is 3 and x1 is 7 so 3-7= -4
so the slope is [tex]\frac{0}{-4}[/tex]
Which of these is equal to 5 (8 – t)?
A) 5t - 40
B) 5t + 40
C) t - 40
D) 40 - 5t
Answer:
D) Is the correct answer 40 - 5t
Step-by-step explanation:
I hope that help's
someone help asap pleasee :)
Hillary can read 560 words in 7 minutes. how many can he ready in 1 minute?
Two health clubs offer different pricing plans for their members. Both health clubs charge a one-time sign-up fee and a monthly membership fee. The graph below represents what Health Club A charges.
The table below represents what Health Club B charges.
Answer:
The answer is below
Step-by-step explanation:
The question is not complete but I would show how this charges can be represented by an equation.
For health club A:
The graph (x, y) passes through the points (2, $136) and (4, $242). Let x represent the total months and y represent the total charges. The equation is given by:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-136=\frac{242-136}{4-2}(x-2)\\\\y-136=53(x-2)\\\\y-136=53x-106\\\\y=53x+30[/tex]
For health club B:
The table (x, y) has the points (4, 173) and (6, 23y). Let x represent the total months and y represent the total costs. The equation is given by:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-173=\frac{237-173}{6-4}(x-4)\\\\y-173=32(x-4)\\\\y-173=32x-128\\\\y=32x+45[/tex]
5030000000 in scientific notation
5.03 × 10^7
(word format): 5 and 3 hundredths times 10 to the 7th power
Answer:5.03 x 10^9
Step-by-step explanation:
Write an equation of the line in slope-intercept form.
slope: 6
y-intercept: 3
Answer:
y=6x+3
Step-by-step explanation:
What is the difference between an equation and an inequality?
a - an equation includes numbers, but an inequality doesn't
b- an inequality includes numbers, but an equation doesn't
c- an equation includes an equal sign, but an inequality doesn't
d- an inequality includes an equal sign, but an equation doesn't
Answer:
The correct answer should be C. Hope I helped.
Answer:
C - an equation includes an equal sign, but an inequality doesn't
Step-by-step explanation:
Although both equations and inequalities are ways to show how expressions relate to one another, an equation is the relationship between expressions with an equals sign ( [tex]=[/tex] ) between them, however, an inequality is a way to express two or more expressions with [tex]<[/tex], [tex]\leq[/tex], [tex]>[/tex] or [tex]\geq[/tex] between them. They both include numbers, so the correct option is C.
Hope this helps :)
the density of a certain material is such that it weighs 9 kilograms for every 7 cubic feet of volume. express this density in pounds per pint.
The density in pounds per pint is 0.047 pounds per pint
Density is calculated using the formula -
Density = [tex]\frac{mass}{volume}[/tex]
To find the density in pounds per pint, we will convert mass and volume to the respective units.
Converting mass in kilograms to pounds -
1 kilogram = 2.205 pounds
9 kilograms = [tex]\frac{2.205*9}{1}[/tex]
9 kilograms = 19.84 ppounds
Converting volume in cubic feet to pints -
1 cubic foot = 59.844 pints
7 cubic foot = [tex]\frac{59.884*7}{1}[/tex]
7 cubic foot = 418.9 pints
Now, keeping the values in formula to find density
Density = [tex]\frac{19.84}{418.9}[/tex]
Performing division to find density -
Density = 0.047 pounds per pint
Hence, the density in pounds per pint is 0.047.
Learn more about density -
https://brainly.com/question/6838128
#SPJ4
a. no; the domain values are at regular intervals and the range values have a common sum 1. b. no; the domain values are not at regular intervals. c. yes; the domain values are at regular intervals and the range values have a common factor 2. d. yes; the domain values are at regular intervals and the range values have a common sum 1.
Yes; the domain values are at regular intervals and the range values have a common factor of 0.25 so option (D) will be correct.
What is the range and domain of a function?A function's range is the set of all values that the function accepts, and its domain is the set of all values for which the function is defined.
The domain is for the independent variable while the range is for the dependent variable.
Given a table of dependent(x) and independent variable (y)
Now the domain is set of the dependent variable so x {3,2,1,-1} so it is decreasing between two points so it is an interval.
Now in the independent variable (x)
If we multiply by 0.25 then the next term will come so it has a common factor of 0.25.
Hence "Yes; the domain values are at regular intervals and the range values have a common factor of 0.25".
For more details about the range and domain of the function,
brainly.com/question/28135761
#SPJ4
The given question is incomplete, the complete question with a table is given below ;
From the table below, determine whether the data shows an exponential function. Explain why or why not.
a No, the domain values are at regular intervals and the range values have a common factor of 0.25.
b. No, the domain values are not at regular intervals although the range values have a common factor.
c. Yes, the domain values are at regular intervals and the range values have a common factor 4.
d. Yes; the domain values are at regular intervals and the range values have a common factor of 0.25.
30 POINTS AND I'LL MARK YOU BRAINLIST IF YOU ANSWER!!
Troy made a scale drawing of the Statue of Liberty which has an actual height of 305 feet. He decides to use a scale in which 1 inch represents 25 feet. What is the height in inches of Troy's drawing?
Answer:
Step-by-step explanation:
The height of statue is 12.2 inches in Troy's drawing.
Step-by-step explanation:
Given,
Actual height of statue = 305 feet
Scale used by Troy;
25 feet = 1 inch
1 feet =
305 feet =
305 feet =
305 feet = 12.2 inches
The height of statue is 12.2 inches in Troy's drawing.
Answer:
12.2 inches
Step-by-step explanation:
The scale is 1 inch = 25 ft
305 ft * (1 inch)/(25 ft) = 305/25 inches = 12.2 inches
Answer: 12.2 inches
3 4/5 - 2 1/3 and if needed simplify
Answer:
1 7/15 or 22/15
Step-by-step explanation:
help ASAP Now 10 points
Answer:
A: One student has lived in 7 states.
Step-by-step explanation:
According to the graph shows, the answer should be A, which is one student has lived in 7 states.
x2+4<0 in graphical
I won't be able to graph for you because I am currently on phone but I will tell how to graph an Inequality in coordinate plane.
[tex] {x}^{2} + 4 < 0[/tex]
We don't need to solve the Inequality. The graph will do.
We draw the parabola with the vertex at (0,4) Basically plot point (0,4) then draw parabola.
Because it is < sign, thus the shade/region will be below the graph.
So the shade will be outside of the curve and not inside.