Answer:
α² +β² = 3 4/9
Step-by-step explanation:
Assuming α and β are solutions to the equation, it can be factored as ...
(x -α)(x -β) = 0
Expanding this, we get ...
x² -(α +β)x +αβ = 0
Dividing the original equation by 3, we find ...
x² +(1/3)x -5/3 ≡ x² -(α+β)x +αβ ⇒ (α+β) = -1/3, αβ = -5/3
We know that the square (α+β)² can be expanded to ...
(α +β)² = α² +β² +2αβ
α² +β² = (α +β)² -2αβ . . . . . . subtract 2αβ
Substituting the values for (α+β) and αβ, we find the desired expression is ...
α² +β² = (-1/3)² -2(-5/3) = 1/9 +10/3 = 31/9
α² +β² = 3 4/9
In how many ways can a committee of three men and three women be formed from a group of eight men and seven women
==========================================================
Explanation:
Order doesn't matter when it comes to committees without rankings. Each person on the committee is of equal rank to anyone else. This means we'll use a combination instead of a permutation.
We have 8 men and 3 seats to fill for the men. Plug n = 8 and r = 3 into the nCr combination formula
n C r = (n!)/(r!(n-r)!)
8 C 3 = (8!)/(3!*(8-3)!)
8 C 3 = (8!)/(3!*5!)
8 C 3 = (8*7*6*5*4*3*2*1)/((3*2*1)*(5*4*3*2*1))
8 C 3 = (40320)/((6)*(120))
8 C 3 = (40320)/(720)
8 C 3 = 56
This means there are 56 ways to select the three men from a pool of eight.
Through similar steps, you should plug n = 7 and r = 3 into the nCr combination formula to get 7 C 3 = 35. This means there are 35 ways to pick the three women from a pool of seven.
Overall, there are 56*35 = 1960 ways to select the entire committee of 3 men and 3 women (from a pool of 8 men and 7 women).
A machine can pack a 3 ft by 2 ft by 2 ft carton with packing material in 3 seconds. How long would it take to fill a carton that measures 4 ft by 5 ft by 6 ft?
6.4 sec
24 sec
36 sec
30 sec
1) we calculate the volume of the first carton:
volume=length x width x height
volume=3 ft * 2 ft * 2 ft=12 ft³
Therefore:
A machine can fill 12 ft³ in 3 seconds.
2) we calculate the volume of the second carton.
volume=length x width x heigth
volume=4 ft * 5 ft * 6 ft=120 ft³
3) we calculate the time that the machine needs for fill the second carton with packing material by the rule of three.
12 ft³---------------------3 seconds
120 ft³-------------------- x
x=(120 ft³ * 3 seconds) / 12 ft³=30 seconds.
answer: 30 seconds.
Please mark brainliest if it helped
factor 1/3 out of 1/3p-2/3
Answer:
[tex]\frac{1}{3}(p-2)[/tex] , 1/3(p-2)
Step-by-step explanation:
[tex]\frac{1}{3} p-\frac{2}{3}[/tex]
[tex]\frac{1}{3}(p-2)[/tex]
Which matrix respresents the system of equations shown below?
4x - 2y = 12
2x - 3y = 8
Answer:
Hey, kevinlopez1225, your answer is Number one!
Astradele
Betty is having invitations printed for a holiday party. It costs $3.90 to set up the printing machine and $2.44 per invitation. In the equation below, x represents the number of invitations Betty is having printed, and y represents the cost to print the invitations.
y = $2.44x + $3.90
How much will it cost Betty to print 100 invitations?
A.
$392.44
B.
$251.80
C.
$103.90
D.
$247.90
Answer:
D) $247.90
Step-by-step explanation:
Understanding the equation:[tex] \underline{\sf{y = 2.44x + 3.90}}[/tex]
y is the dependent function whereas x is the independent function.
(What does this mean?)
The values of y depend on the values of x, I.e., any change in the value of x causes a change in the value of y, meanwhile, the opposite doesn't happen.
x represents the number of invitations y represents the cost to print the invitationsThe cost to print the invitation depends on the number of invitations, for real.
Solution to the problem:The question asks us to find the cost of printing 100 invitations.
Substituting x for 100:
y = (2.44 × 100) + 3.90
y = 244 + 3.90
y = 247.90
Answer:The value of y obtained for x = 100 is the cost of printing 100 invitations – $ 247.90
*PLEASE HELP* *ANY IRRELEVANT ANSWERS WILL BE REPORTED AS SPAM*
After 30 baseball games, Bryce Harper had 25 hits and after 100 games he had 165 hits. How many hits would he have after 106 games?(include units)
Find Slope(Rate of Change):
Then Find the Amount After 106 games.
Answer:
177 hits
Step-by-step explanation:
Let [tex]x[/tex] = number of baseball games
Let [tex]y[/tex] = number of hits
(30, 25) = [tex](x_1,y_1)[/tex]
(100, 165) = [tex](x_2,y_2)[/tex]
Slope formula: [tex]m=\frac{y_2-y_1}{x_2-x_1} =\frac{165-25}{100-30} =2[/tex]
Using the point-slope formula to create an equation:
[tex]y-y_1=m(x-x_1)\\\\\implies y-25=2(x-30)\\\\\implies y=2x-35[/tex]
Now substitute [tex]x = 106[/tex] into the equation and solve for [tex]y[/tex]:
[tex]\implies y=(2 \times 106)-35=177[/tex]
Therefore, the number of hits Bryce would have after 106 games is 177
Take 2 points
(30,25)(100,165)Slope:-
[tex]\\ \rm\hookrightarrow m=\dfrac{165-25}{100-30}[/tex]
[tex]\\ \rm\hookrightarrow m=\dfrac{140}{70}=2[/tex]
Equation in point slope form
[tex]\\ \rm\hookrightarrow y-25=2(x-30)[/tex]
[tex]\\ \rm\hookrightarrow y-25=2x-60[/tex]
[tex]\\ \rm\hookrightarrow 2x-y-35=0[/tex]
Convert to slope intercept form y=mx+b[tex]\\ \rm\hookrightarrow y=2x-35[/tex]
Put x=106[tex]\\ \rm\hookrightarrow y=2(106)-35=212-35=177[/tex]
Brianna has $2.80 in quarters, dimes and nickels in her purse. She has nine more dimes than quarters and six more nickels than quarters. How many of each coin does she have?
Answer:
She has 4 quarters, 13 dimes, and 10 nickels in her purse
Step-by-step explanation:
Let q be the amount of quarters, d be the amount of dimes, and n be the amount of nickels she has in her purse. We can use this to set up a system of equations:
25q+10d+5n=280
This is because a quarter is 25 cents, a dime is 10 cents, and a nickel is 5 cents. We also have to convert $2.80 to cents since all our other values are in cents.
d=q+9
She has 9 more dimes than quarters
n=q+6
She has 6 more nickels than quarters
We can solve this system using substitution (substitute q+9 for d and q+6 for n)
25q+10(q+9)+5(q+6)=280
25q+10(q)+10(9)+5(q)+5(6)=280
25q+10q+90+5q+30=280
40q+120=280
Subtract 120 from both sides
40q=160
Divide both sides by 40
q=4
Now we plug this back into the other equations to find the amount of nickels and dimes
d=q+9=4+9=13
n=q+6=4+6=10
She has 4 quarters, 13 dimes, and 10 nickels in her purse
2x
P
10nº
8 nº
R
S
x + 3
PQRS is a parallelogram. Find each measure.
RS-
type your answer....
angle S =
type your answer...
angle R=
type your answer...
Answer: The simplified sum is
Step-by-step explanation: we have
Can you please help
Graph any third-degree polynomial (a cubic graph) that has exactly one x-intercept, a relative/global minimum at (-2.1), and a relative/
global maximum at
(4,3)
Step-by-step explanation:
A notable ______ of the symposium was the speech by a famous entrepreneur.
Find sinx+cosx if sinx*cosx=3/8
Answer:
[tex]^+_-\frac{\sqrt{7}}{2}.[/tex]
Step-by-step explanation:
[tex]1.| \ sinx+cosx| =\sqrt{(sinx+cosx)^2}=\sqrt{sin^2x+2sinxcosx+cos^2x}=\sqrt{1+2sinxcosx};[/tex]
2) according to the item 1:
[tex]sinx+cosx=^+_-\sqrt{1+2*\frac{3}{8}} =^+_-\sqrt{\frac{7}{4}}=^+_-\frac{\sqrt{7} }{2}.[/tex]
Four standard, six-sided dice are to be rolled. If the product of their values turns out to be an even number, what is the probability their sum is odd? Express your answer as a common fraction.
Answer:
Your answer is 8/15.....
could someone please help me
Answer:
A is correct since,
x>-3 and x<1
x=(-2,-1,0)
|x+1|<2
|-2+1|<2
|-1|<2
1<2
|-1+1|<2
|0|<2
0<2
|0+1|<2
|1|<2
1<2
Therefore A is correct
please mark me brainliest
The graph of a function f is shown above. What is the value of [tex]\int\limits^7_0 {f(x)} \, dx[/tex]
==============================================
Explanation:
Split the graph into separate regions (see the diagram below)
The red trapezoid has the parallel vertical sides of b1 = 1 and b2 = 2. The height of the trapezoid is h = 2
The area of the red trapezoid is
A = h*(b1+b2)/2 = 2*(1+2)/2 = 3
--------------
The blue rectangle has a horizontal side of 2 and vertical side of 2. Its area is 2*2 = 4 square units.
--------------
The pink triangle has a base of 1 and height of 2
area = base*height/2 = 1*2/2 = 1 square unit
--------------
The green triangle has an area of base*height/2 = 2*2/2 = 2 square units
--------------
For any region above the x axis, it gets assigned a positive area. Anything below the x axis gets a negative area to counterbalance the positive areas.
The regions above the x axis add to 3+4+1 = 8 square units. Then we subtract off the area of the green triangle to get 8-2 = 6 square units.
Therefore, [tex]\displaystyle \int_{0}^{7}f(x)dx = 6[/tex]
PLEASE HELP ME
ILL GIVE BRAINLIEST
Answer:
r=8cm/2=4cm
using Pythagoras theorem.
(Slant height)²=radius²+height²
slant height²=(4cm)²+(9cm)²
s²=16cm²+81cm²
s²=97cm²
s=(97cm²)⁰'⁵
s=9.8cm
hope it was helpful.
the slant height is 9.8cm
Multiply 3.4 x 104 times 2.1 x 108 by using scientific notation. Write your
answer in scientific notation.
(Round your answer to the nearest tenth.)
Answer:
[tex]7.14\times10^{12}[/tex]
Step-by-step explanation:
Given the following question:
[tex]3.4\times10^4\times2.1\times10^8[/tex]
In order to find the answer to this question we convert both scientific notations into standard form, multiply, and then convert back into scientific notation.
[tex]3.4\times10^4\times2.1\times10^8[/tex]
[tex]3.4\times10^4[/tex]
[tex]3.4\times10^4=3.4.0.0.0.=34000[/tex]
[tex]2.1\times10^8=2.1.0.0.0.0.0.0.0.=210000000[/tex]
[tex]34000\times210000000[/tex]
[tex]34000\times210000000=7140000000000[/tex]
[tex]7140000000000=7.14\times10^{12}[/tex]
[tex]7.14\times10^{12}[/tex]
Hope this helps.
please answer with explanation
Answer: 624
Step-by-step explanation:
The area of a rhombus is the product of the diagonals divided by 2 so the area of the rhombus in this case is 12 * 16 / 2 or 96 multiply with 6.5 we get 624 so that's the answer
Solve for d.
4 + 20 = 8
d =
[tex]4 + 20 = 8d \\ \\ 8d = 24 \\ \\ d = \frac{24}{8} \\ \\ d = 3.[/tex]
The value of d is 3 .
Can someone help me with this ASAP please
Answer:
6+(2x5)=60
Step-by-step explanation
10+(2x5)=20
20+(2x5)=30
30+(2x5)=40
40+(2x5)=50
50+(2x5)=60
Please HELP IN 10 MINS!!!!!!!!!!!!!!!!!!!!Lisa, Melinda, and Rahul love the same board game. The game must
be played by at least two people. Lisa can play every two days,
Melinda can play every three days, and Rahul can play every four
days. Today, all three played 1 game together. What is the total
number of games they will play from Day 1 to Day 50 if today is
Day 1? (Exactly 1 game is played per day.)
Answer:
25 games were played
Step-by-step explanation:
I first found how many games were played in 10 days
and then multiplied it by 5 to know how many games were played in 50 days
(but I am not sure if it is correct since it said that 1 game was played everyday and with rules I am not sure if it is even possible)
feel free to correct me
Answer: 17
Step-by-step explanation:
Lisa and Melinda will play together 8 times
Lisa and Rahul will play together 12 times
Melinda and Rahul will play together 4 times
So total games are 24 -- but they all will play together 4 times.
Since, "exactly 1 game is played per day", they cannot play 2 and 3 together at any day.
So total number will be: (8-4) + (12-4) + (4-4) = 12
Now, we must consider 4 where they played all 3 together; so total number: 12 + 4 = 16
Also, they already played 1 game at 1st day; so total number: 16 + 1 = 17
What is the prob of an event that must happen.
Answer:
%100 Elon Musk going to Mars
Step-by-step explanation:
yes yes yes
i don't know if this is the answer you want
please mark brainliest i need 3 more
simplify the radical below
3√x^18
The radical is 3sqrt(x^18)
18/2=9
so, the radical is
3x^9
Help please 10 points
Answer:
1, -2, -4, -6, -6.9, -6.99, -6.999
The sum of several consecutive natural numbers is 2012. How many numbers were in that sum
Answer:
8
Step-by-step explanation:
first number = a, there are n numbers
so last number is a + n - 1
sum = [a + (a + n - 1)} * n/2 = (2a + n - 1) / 2 = 2012
n * (2a + n - 1) = 2012 * 2 = 4024
4024 is even, so n must be even, divisible by 2, 4, 8
4024 = 2 * 2012 = 4 * 1006 = 8 * 503
If n = 2, 2a + n - 1 = 2012, 2a + 2 - 1 = 2012, 2a = 2011, impossible.
If n = 4, 2a + n - 1 = 1006, 2a + 4 - 1 = 2a + 3 = 1006, 2a = 1003, impossible
If n = 8, 2a + n - 1 = 503, 2a + 8 - 1 = 2a + 7 = 503, a = 248
so n = 8, a = 248
If f(x) = -x-11 ; find the following.
4f(-2) + 5f(1)
The value for the given expression will be -96.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
The given expression will be solved as below:-
E = 4(-(-2) - 11) + 5(-1 - 11)
E = 4(-9) + 5(-12)
E = -36 + (-60)
E = -96
Therefore, the value for the given expression will be -96.
To know more about an expression follow
https://brainly.com/question/723406
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Two consecutive angles of a parallelogram are supplementary. 4. Always true C Never true 5 Sometimes true D. Sometimes false Which of the following statements are NOT TRUE about parallelograms? A Adjacent sides are congruent. e The opposite angles are congruent. C. Consecutive angies are supplementary Diagonals bisect each other. Two consecutive angles of a parallelogram have measures of (2x + 7 3x - 2)". What is the measure of the larger angle? A 103 C. 1339 B 73 D. 107 What is the measure of 22 in rhombus TRUE? 90" 80° 3/ 100 2 R Refer to the figure at rhombus TRUE in item 7. What is the measure of 21 is 100 A 80 C. 110 B 90 D 100° Which of the following group of quadrilaterals have diagonal tha perpendicular A Rectangle square C.Rhombus, rectangle Rhombus square D. Rectangle, rhombus, and s 10 Which of the following is NOT a characteristic of parallelograms? A Diagonals are angle bisector B. Diagonals bisect each other Opposite angies are congruent o Consecutive sides are congruent . We the following is NOT ar
Adjacent sides of a parallelogram are not congruent.
QuadrilateralA quadrilateral is a polygon with four sides and and four angles. A parallelogram has opposite sides parallel and equal. Two consecutive angles of a parallelogram are supplementary. Opposite angles and diagonals are congruent. The diagonals bisect each other.
(2x + 7) + (3x - 2) = 180 (consecutive angles)
x = 35°
Find out more on Quadrilateral at: https://brainly.com/question/23935806
can someone please help with my work!
Answer:
900 km i think
Step-by-step explanation:
umm so first 8*10=80%, then 4500-80%
la edad de selly. e es mayor que 15
hellllllllllllllllllllllllllllllpppppp meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
That equals to 5x5x5 which 5x5x5 = 125
But the correct answer on that quiz is 1st I think
Step-by-step explanation:
Sorry if im wrong
Challenge Last month, Stephen's neighbors paid him to take care of their dog when they went on
vacation. He spent $3 of his earnings on an afternoon snack and $16 on a new book. Afterward,
he had no less than $6 left. How can you best describe how much Stephen's neighbors paid him?
Select the correct choice below and fill in the answer box to complete your choice.
O A. They paid him exactly $
OB. They paid him no less than $
OC. They paid him no more than $
Answer:
his neighbors payed him 25 dollers
Step-by-step explanation:
3+16=19
19+6=25