If
[tex] \alpha \beta [/tex]
are the roots of 3x²+2x-1=0 then 1/
[tex] \alpha [/tex]
+1/
[tex] \beta [/tex]
is
Answer:
2
Step-by-step explanation:
Given the quadratic equation
3x²+2x-1=0
Let tthe root be α and β
Sum of root α+β = -b/a
Product of root αβ = c/a
Given that;
a = 3, b = 2 and c = -1
α+β = -2/3
αβ = -1/3
To get 1/α + 1/β
Find the LCM
1/α + 1/β
= (α+β)/αβ
= (-2/3)/(-1/3)
= -2/3 * 3/-1
= 2
Hence the required answer is 2
A ball is tossed at a hole in a board. The ball goes into the hole 15 times and misses the hole 52 times.
Based on this experiment, what is the probability that the ball will go into the hole when tossed?
Enter your answer in the box as a percent rounded to the nearest whole number.
Probability (Ball goes into hole) = 0.22388 or 22.388%
Step-by-step explanation:
Given:
Ball goes into hole = 15 times
Ball miss the hole = 52 times
Find:
Probability (Ball goes into hole)
Computation:
Total number of tries = 15 + 52
Total number of tries = 67
Probability (Ball goes into hole) = 15 / 67
Probability (Ball goes into hole) = 0.22388 or 22.388%
For each ordered pair determine if it is a solution to 7x+5y=9
(-4,-3)
(-3,6)
(5,0)
(2,-1)
(16y ⁵/ 4y³) ¹/2 simplify expression
2y
Step-by-step explanation:
16y^5-3/4)
16y²/4)
4y²)1/2
2y
Find the area of each. Use pi = 3.14
Answer:
452.16 inches
Step-by-step explanation:
A = pi r^2
A = 3.14 * (12)^2
A = 3.14 * 144
A = 452.16 inches
I want to purchase a third of a cupcake for
myself, a third for my sister, and 4 thirds for our
cousin. Katara would be great. Please help! Quickly I’m waiting 5 mins :)
Answer:
Well it would be a total of 2 Cup Cakes
Step-by-step explanation:
1/3 + 1/3 + 4/3 =2
2/3 +4/3 = 6/3
ye
Answer:
Step-by-step explanation:
it would be 2
Which graph represents the function?
f(x)=−x2+x+6
If the sum of two numbers is 10 and the diffference is 6, find the numbers
X + y = 10
Rewrite as y = 10-x
Y - x = 6
Replace y
10-x -x = 6
Simplify:
10-2x = 6
Subtract 10 from both sides:
-2x = -4
Divide both sides by -2:
X = 2
Now replace x in the first equation:
2 + y = 10
Subtract 2 from both sides:
Y = 8
The two numbers are 8 and 2
Mr. Bernstein owns 11 paintings, but has only enough wall space in his home to display five of
them at any one time. How many ways can Mr. Bernstein display three paintings in his home?
Answer:
In algebra, we often study relationships where a change to one variable causes change in another variable. Describe a situation you’re familiar with where one quantity changes constantly in relation to another quantity. How are the two quantities in the situation related? If you represent the two quantities on a graph, what will it look like?
Step-by-step explanation:
is it true or false that all whole numbers are natural numbers
Answer:it can very
Step-by-step explanation:
It depends on which definition of 'whole numbers' you use.
Some definitions say the whole numbers are the set of positive integers including zero; or the set of all non-negative integers. In this case, the answer would be 'false', since the set of integers includes negatives.
However, if you are using a definition of whole numbers which includes positive integers, including zero, and their negatives, the answer would be 'true'. Figure out how the term 'whole numbers' is being defined, then you can get your answer.
Answer:
every natural number is a whole number, but, every whole number is not a natural number.
Step-by-step explanation:
Answer 1 and 2 for brainliest
Please someone explain how to solve this piecewise function!!!! Im super confused
Answer:
From top to bottom:
[tex]0, 1, 2, -8, -8[/tex]
Step-by-step explanation:
We are given the piecewise function:
[tex]g(x) = \left\{ \begin{array}{ll} 0.5x+1 & \text{if } x \leq 2 \\ -8 & \text{if } x > 2 \end{array} \right.[/tex]
Row 1:
We want to find g(-2).
Since -2 is less than (or equal to) 2, we will use the first equation. Thus:
[tex]g(-2)=0.5(-2)+1=-1+1=0[/tex]
Row 2:
Likewise, 0 is less than or equal to 2. We will continue to use the first equation:
[tex]g(0)=0.5(0)+1=1[/tex]
Row 3:
2 is not less than 2 but it is equal to 2. So we will continue to use the first equation:
[tex]g(2)=0.5(2)+1=1+1=2[/tex]
Row 4 and 5:
Both 4 and 6 are greater than 2. Thus, we will use the second equation. Therefore:
[tex]g(4)=-8\text{ and } g(6)=-8[/tex]
5(n+1)-15=0, what is the answer to this equation? i need step by step explanation
Answer:
5n+5-15=0
5n-10=0
5n=10
therefore n = 10/5 = 2
therefore n=2
PLEASE ANSWER THIS QUESTION
Show that 4x – 7 is equivalent to 4(x - 1) – 3 when x = 3.
Answer:
4(3) - 7 = 4(3 - 1) - 3
12 - 7 = 4(2) - 3
5 = 8 - 3
= 5
They are equivalent because when they are both simplified they have the same answer 5
(a) Mary and Cynthia were building a cone-shaped sand castle. After some time, the diameter of
the sand shaped cone was 14 in. and the height was 15 in. What is the appoximate volume of the
sand cone rounded to the nearest tenth? (Show work!!) PLEASE HELP!
Answer:
[tex]\displaystyle V\approx 769.7\text{ in}^3[/tex]
Step-by-step explanation:
We are given that the diameter of the sand-shaped cone is 14 inches, and the height is 15 inches.
The volume for a cone is given by:
[tex]\displaystyle V=\frac{1}{3}\pi r^2h[/tex]
Where r is the radius and h is the height.
Since the diameter is 14, the radius is 7.
And we are given that the height is 15.
Therefore, the volume will be:
[tex]\displaystyle V=\frac{1}{3}\pi (7)^2(15)[/tex]
Use a calculator:
[tex]\displaystyle V\approx 769.7\text{ in}^3[/tex]
The volume of the cone is approximately 769.7 cubic inches.
soooo again in meters I'm soo sorryyy
I think 710 is the answer
266+266+89+89= 710
Find the solution of the system of equations. -3x – 2y = 36 3х – 5y = 6
Answer:
y = -6
x = -8
Step-by-step explanation:
I hope you can read my handwriting.
Have a wonderful day!
Can someone help me with this please
Answer:
Step-by-step explanation:
As we know, the four angles of the rectangle are 90°.
So, we need to find ∠AEB first.
∠AEB=180-44-90 (∠s sum of Δ)
= 46°
We can then work out x.
x=180-59-46 (adj. ∠s on st. line)
x=75°
Help me please......
Answer: 46
Step-by-step explanation:
Let the 3 consecutive even numbers be x, (x-2) and (x+2) respectively.
According to the question,
x + (x - 2) + (x + 2) = 132
or, x + x - 2 + x + 2 = 132
or, 3x = 132
or, x = 132 ÷ 3
or, x = 44
So, first even number = 44
Required third number = 44 + 2
= 46
Erin loves to cook with fresh herbs. So, she decides to plant 8 different herbs and keep the
small pots on her kitchen windowsill. She starts with a 2-kilogram bag of soil and puts the
same amount of soil in each pot. If she uses all of the soil, how many grams does she add to
each pot?
This is a simple division problem, there are 1000 grams in 1 kilogram, so we do 2000/8, which is 250, so Erin put 250 grams of soil in each pot.
An angle with a measurement of 90 degrees is called?
Answer:
A right angle
Step-by-step explanation:
Answer:
Right angle. Its angle is in the corner and measured 90 degrees.
Step-by-step explanation:
graph y = 1/2x+3
identify the x intercept
step by step explanation
Step-by-step explanation:
x-intercept: where y = 0
Set y to zero to find x.
0 = ½x + 3
-3 = ½x
x = -6
(-6, 0)
Write an
equation and solve.
Ten less than five times a number is 45. the equation is
(x*5)-10=45=equation
im extra so x would be 7
In a certain town there were 348 robberies last year. This year the number of robberies has gone down 40%. How many robberies were there this year, to the nearest whole number?
Answer:
209 robberies
Step-by-step explanation:
Robberies last year =348
Robberies has reduced by 40% which means there are (100-40)% = 60% robberies this year.
Number of robberies this year= 60% of 348 = 60/100 × 348 = 208.8
To the nearest whole number = 209
There are 209 robberies this year.
I hope this help.
write an expression that mean "eight less than product of seven and X".
Answer:
7x - 8
Step-by-step explanation:
eight less than product of seven and X
seven and x = 7x
eight less than = - 8
put it all together = 7x - 8
Answer:
7x - 8
Step-by-step explanation:
product of seven and X
7 X x = 7x
8 less than it
7X - 8
This is because we're looking for something that is smaller than 7X by 8
Find the equation of the line parallel to y=6 that contains the point (-1,1). Write the equation in slope intercept form
Given:
The equation of parallel line is [tex]y=6[/tex].
The line contains the point (-1,1).
To find:
The equation of the line.
Solution:
The slope intercept form of a line is:
[tex]y=mx+b[/tex]
Where, m is the slope and b is the y-intercept.
The equation of parallel line is
[tex]y=6[/tex]
It can be written as
[tex]y=(0)x+6[/tex]
The slope of this line is 0.
The slopes of two parallel lines are always equal. So, the slope of the required line is also 0. It passes through the point (-1,1) so the equation of the line is:
[tex]y-y_1=m(x-x_1)[/tex]
[tex]y-1=0(x-(-1))[/tex]
[tex]y-1=0[/tex]
[tex]y=1[/tex]
Therefore, the equation of the required line is 1.
What's the slope of the line through (1,3) and (-2,-3)
Answer:
m = 2
The slope of the line through (1, 3) and (-2, -3) is 2!
The formula to find the slope is attached below.
Hope I was of help. Have a good new year!
A square pyramid has a base with a side length of 6 inches and lateral faces with heights of 11 inches. What is the surface area of the pyramid?
Answer:
[tex]\huge\boxed{\sf 168\ in.\²}[/tex]
Step-by-step explanation:
Surface area of the base:
= Length * Length
= 6 * 6
= 36 in.²
Surface Area of 1 Lateral Face:
= [tex]\sf \frac{1}{2} (Base * Height)[/tex]
Base = 6 inches
Height = 11 inches
= 1/2 (6*11)
= 3 * 11
= 33 in.²
Surface Area of 4 lateral faces:
= 33 * 4
= 132 in.²
Surface Area of the whole pyramid:
= 132 + 36
= 168 in.²
[tex]\rule[225]{225}{2}[/tex]
Hope this helped!
~AH1807Answer:
SA = 168 in.²
Step-by-step explanation:
The surface area is the sum of the area of the base and the areas of the 4 congruent triangular sides.
s = side of the base
h = height of each side
SA = s² + 4(sh/2)
SA = (6 in.)² + 4(6 in.)(11 in.)/2
SA = 36 in.² + 132 in.²
SA = 168 in.²
PLSSS HELP Due in 5 mins!!!
Answer:
a 15
b 42
c 12
trust me
Find the equation of the line through (-5,4) which is parallel to the line y=-x+6.
Give your answer in the form y=mx+b
Answer:
[tex]y = -x -1[/tex]
Step-by-step explanation:
Given
Passed through (-5,4)
Parallel to: y=-x + 6
Required
Determine the line equation
If it is parallel to: y=-x + 6, then it means that they have the same slope.
A linear equation y = mx + b has the slope m.
So, by comparison of y = mx + b to y = -x + 6
[tex]m = -1[/tex]
The line equation is then calculated as:
[tex]y=m(x - x_1) + y_1[/tex]
Where
[tex]m = -1[/tex]
[tex](x_1,y_1) = (-5,4)[/tex]
So:
[tex]y = -1(x - (-5)) + 4[/tex]
[tex]y = -1(x +5) + 4[/tex]
[tex]y = -x -5 + 4[/tex]
[tex]y = -x -1[/tex]