Answer:
The answer would be 14
Step-by-step explanation:
you just divide 28,00 by 200 and that gives you 14
A bag contains 5 red cubes and 7 white cubes. Celinda will select one cube, put it in her pocket, and then select a second cube. Which expression gives the probability that she will select two red cubes?
Answer:
The expression which gives the probability that she will select two red cubes = 5/12 * 4/11 ....
Step-by-step explanation:
According to the statement there are 4 red cubes and 7 white cubes.
The total number of cubes are = 7+5 = 12
If she picks up one red cube then the number of ways of picking up red cubes out of 12 is = 5/12
If she picks up 2nd red cube then the number of ways of picking up 2nd red cube = 4/11
Therefore the expression which gives the probability that she will select two red cubes = 5/12 * 4/11 ....
Using the given zero, find one other zero of f(x). Explain the process you used to find your solution.
2 - 3i is a zero of f(x) = x4 - 4x3 + 14x2 - 4x + 13.
*Can someone show the work I have the answers
Answer:
One other zero is 2+3i
Step-by-step explanation:
If 2-3i is a zero and all the coefficients of the polynomial function is real, then the conjugate of 2-3i is also a zero.
The conjugate of (a+b) is (a-b).
The conjugate of (a-b) is (a+b).
The conjugate of (2-3i) is (2+3i) so 2+3i is also a zero.
Ok so we have two zeros 2-3i and 2+3i.
This means that (x-(2-3i)) and (x-(2+3i)) are factors of the given polynomial.
I'm going to find the product of these factors (x-(2-3i)) and (x-(2+3i)).
(x-(2-3i))(x-(2+3i))
Foil!
First: x(x)=x^2
Outer: x*-(2+3i)=-x(2+3i)
Inner: -(2-3i)(x)=-x(2-3i)
Last: (2-3i)(2+3i)=4-9i^2 (You can just do first and last when multiplying conjugates)
---------------------------------Add together:
x^2 + -x(2+3i) + -x(2-3i) + (4-9i^2)
Simplifying:
x^2-2x-3ix-2x+3ix+4+9 (since i^2=-1)
x^2-4x+13 (since -3ix+3ix=0)
So x^2-4x+13 is a factor of the given polynomial.
I'm going to do long division to find another factor.
Hopefully we get a remainder of 0 because we are saying it is a factor of the given polynomial.
x^2+1
---------------------------------------
x^2-4x+13| x^4-4x^3+14x^2-4x+13
-( x^4-4x^3+ 13x^2)
------------------------------------------
x^2-4x+13
-(x^2-4x+13)
-----------------
0
So the other factor is x^2+1.
To find the zeros of x^2+1, you set x^2+1 to 0 and solve for x.
[tex]x^2+1=0[/tex]
[tex]x^2=-1[/tex]
[tex]x=\pm \sqrt{-1}[/tex]
[tex]x=\pm i[/tex]
So the zeros are i, -i , 2-3i , 2+3i
The zeros of a function are the points where the function cross the x-axis.
One other zero of [tex]\mathbf{f(x) = x^4 - 4x^3 + 14x^2 - 4x + 13}[/tex] is 2 + 3i.
The zero of [tex]\mathbf{f(x) = x^4 - 4x^3 + 14x^2 - 4x + 13}[/tex] is given as:
[tex]\mathbf{Zero = 2 - 3i}[/tex]
The above number is a complex number.
If a complex number a + bi is the zero of a function f(x), then the conjugate a - bi is also the zero of f(x).
This means that, one other zero of [tex]\mathbf{f(x) = x^4 - 4x^3 + 14x^2 - 4x + 13}[/tex] is 2 + 3i.
Read more about zeros of functions at:
https://brainly.com/question/22101211
Two sat math questions. Percentage and a graph
Answer:
15) 300%
Step-by-step explanation:
15)
Let the item originally cost n dollars.
The new incorrect price is (n-.6n).
So we want to find k such that (n-.6n)+k(n-.6n)=n+.6n
since we actually wanted it to be (n+.6n).
So we have (n-.6n)+k(n-.6n)=n+.6n
Distribute:
n-.6n+kn-.6nk=n+.6n
Subtract n on both sides
-.6n+kn-.6nk=.6n
We are trying to solve for k. So add .6n on both sides:
kn-.6nk=1.2n
Divide both sides by n:
k-.6k=1.2
.4k=1.2
Divide both sides by .4
k=1.2/.4
k=3
So 3=300%.
The incorrect price must be increased by 300% to get to the proper new price.
Here is an example:
Something cost $600.
It was reduce by 60% which means it cost 600-.6(600)=600-360=240
This was the wrong price.
We needed it to be increased by 60% which would have been 600+360=960.
So we need to figure out what to increase I wrong price 240 to to get to our right price of 960.
240+k(240)=960
1+k=960/240
1+k=4
k=3
So 240*300%+240 would give me my 960.
16) Speed=distance/time
In the first half hour, she traveled 5 miles (8:30 to 9).
In 1/3 hour she traveled (5-2)=3 miles (9 to 9:20).
We are told not to do anything where she stayed still.
In the last half hour, she traveled (2-0)=2 miles (9:30 to 10).
The average speed=[tex]\frac{5+3+2}{\frac{1}{2}+\frac{1}{3}+\frac{1}{2}}=\frac{10}{\frac{4}{3}}=\frac{10(3)}{4}=\frac{30}{4}=\frac{15}{2}=7\frac{1}{2}[/tex].
Which is equivalent to (9y^2-4x)(9y^2+4x), and what type of special product is it?
A: 81y^4-16x^2, a perfect square trinomial
B: 81y^4-16x^2, the difference of squares
C: 81y^4-72xy^2-16x^2, a perfect square trinomial
D: 81y^4-72xy^2-16x^2, the difference of squares
Answer:
Option B: 81y^4-16x^2, the difference of squares
Step-by-step explanation:
we know that
The Difference of Squares is two terms that are squared and separated by a subtraction sign
so
[tex](a+b)(a-b)=(a^{2}-b^{2})[/tex]
In this problem we have
[tex](9y^{2}-4x)(9y^{2}+4x)[/tex]
Let
[tex]a=9y^{2}[/tex]
[tex]b=4x[/tex]
so
[tex]a^{2}=(9y^{2})^{2}=81y^{4}[/tex]
[tex]b^{2}=(4x)^{2}=16x^{2}[/tex]
substitute
[tex](9y^{2}-4x)(9y^{2}+4x)=81y^{4}-16x^{2}[/tex]
Answer: b
Step-by-step explanation: edge 2022
What properties does a square have in common with a quadrilateral?
Check all that are true.
Both shapes always have opposite sides that are parallel.
Both shapes are closed plane figures.
Both figures always have four sides.
Both figures always have right angles.
All sides are the same length in both figures.
A square and quadrilateral share the properties of having parallel opposite sides, being closed plane figures and having four sides. Not all quadrilaterals have right angles and equal side lengths like squares.
Explanation:A square and a quadrilateral share several properties due to the fact that a square is a specific type of quadrilateral. The following statements are true: Both shapes always have opposite sides that are parallel, Both shapes are closed plane figures, and Both figures always have four sides. Not all quadrilaterals have right angles or equal length sides, so those properties are unique to squares and not shared with all quadrilaterals.
Learn more about Geometry here:https://brainly.com/question/31408211
#SPJ6
What is the length of AC? Round to the nearest tenth.
The equation sin(40°) = can be used to determine the
length of line segment AC.
11.8
12.9 cm
14.9 cm
15.3 cm
Answer:
12.9
Step-by-step explanation:
!!!!
The length of AC is approximately 12.9cm
Triangle identityGiven the following identity
Opposite = ACHypotenuse = 20cmUsing the SOH CAH TOA identity
sin 40 = AC/20
AC = 20sin40
AC = 20(0.6428)
AC = 12.9cm
Hence the length of AC is approximately 12.9cm
Learn more on SOH CAH TOA here;
https://brainly.com/question/20734777
to solve the equation below by completing the square, what is your first step?
3x^2+18x=21
Answer:
Multiply both sides of the equation by 1/3
Step-by-step explanation:
3x^2+18x=21
The first step is to get the x term with a coefficient of 1, so divide by 3 on both sides of the equation
This is the same as multiplying by 1/3
1/3 * (3x^2+18x)=21*1/3
x^2 +6x = 7
6⁄10 _______ 9⁄12 A. > B. ≤ C. = D.
For this case we must indicate the sign corresponding to:
[tex]\frac {6} {10}[/tex]and [tex]\frac {9} {12}[/tex]
We have to:
[tex]\frac {6} {10} = 0.6\\\frac {9} {12} = 0.75[/tex]
It is observed that[tex]0.75> 0.6[/tex]
So we have to:
[tex]\frac {6} {10} <\frac {9} {12}[/tex]
Answer:
[tex]\frac {6} {10} <\frac {9} {12}[/tex]
Find the area of the shaded region if the dimensions of the unshaded region are 18ft x 22ft. Use 3.14 for π as necessary.
A. 1,419.84 ft²
B. 1,111.84 ft²
C. 709.92 ft²
D. 957.84 ft²
See the attached picture:
Answer:
Answer is option B. 1,111.84 ft²
Step-by-step explanation:
The given dimensions of the un shaded region or rectangle are 18 feet x 22 feet.
Now we have additional 7 feet at both ends to form the diameter of the semicircle, making it [tex]14+18=32[/tex] feet
Radius = [tex]\frac{32}{2}=16[/tex] feet
We have 2 semicircles, one at each end. If we combine it it forms a circle.
Area of the circle (2 semicircles) = [tex]\pi r^{2}[/tex]
= [tex]3.14\times(16)^{2}[/tex] = 803.84 square feet
Now we will find the area of the shaded rectangles above and below the non shaded one. The length is 22 feet and width is 7 feet.
So, area = [tex]22\times7=154[/tex] square feet
We have 2 similar rectangles. So, area of both = [tex]2\times154=308[/tex] square feet
So, total area of shaded region = [tex]803.84+308=1111.84[/tex] square feet.
What do I do for this question?
a chord intersected by a radius segment at a right-angle, gets bisected into two equal pieces, namely MO = NO and PZ = QZ.
[tex]\bf MO=NO\implies \stackrel{MO}{18}=NO\qquad \qquad NO=6x\implies \stackrel{NO}{18}=6x \\\\\\ \cfrac{18}{6}=x \implies 3=x \\\\[-0.35em] ~\dotfill\\\\ PZ=x+2\implies PZ=3+2\implies PZ=5=QZ \\\\[-0.35em] ~\dotfill\\\\ PQ=PZ+QZ\implies PQ=5+5\implies PQ=10[/tex]
There are 5 students in a small class. To make a team, the names of 2 of them will be drawn from a hat. How many different teams of 2 students are possible?
Answer:
10 possible teams.
Step-by-step explanation:
5C2
=5!/(5-2)!2!
=5!/3!2!
=5*4*3*2*1/3*2*1*2*1
=5*4/2*1
=20/2
=10
Therefore answer is 10 possible teams....
what is 12/6 multiple 2/3
Answer:
[tex]\frac{4}{3}[/tex]
Step-by-step explanation:
Simplify your first fraction.
[tex]\frac{12}{6} =2[/tex]
Solve by multiplying your numerators against each other and your denominators against each other.
[tex]\frac{2}{1} *\frac{2}{3} =\frac{4}{3}[/tex]
Answer: 4/3
Step-by-step explanation: You can start off by simplifying 12/6 to 2/1. Then, you can multiply.
2/1 x 2/3 = 4/3
Multiply the numerators. 2x2=4.
Multiply the denominators. 1x3=3
LOOK AT PICTURE. VOLUME OF CAN PROBLEM
Answer:
The correct answer is third option. 994
Step-by-step explanation:
Points to remember
Volume of cylinder = πr²h
Where 'r' is the radius and 'h' is the height of cylinder
From the given question we get the cylinder height and radius
The height h = 3 times the diameter of one ball
= 3 * 7.5 = 22.5 cm
Radius = half of the diameter of a ball
= 7.5/2 = 3.75 cm
To find the volume of cylinder
Volume of cylinder = πr²h
= 3.14 * 3.75² * 22.5
= 993.515 ≈ 994
The correct answer is third option. 994
Which relation is a function?
A. {(2, 3), (1, 5), (2, 7)}
B. {(-1,5), (-2, 6), (-3, 7)}
OC. {(11, 9), (11, 5), (9,3)}
D. {(3, 8), (0, 3), (3,-2)}
Answer:
B is a function.
Step-by-step explanation:
A relation that is a set of points is a function if all the x's are different. Each ordered pair in the set (excluding the duplicates if any) all have to have a distinct x.
For example if someone ask you if this is a function they are trying to trick you:
{(4,5),(1,3),(4,5)}.
They are trying to trick you because they listed the element (4,5) twice.
The set is really {(4,5),(1,3)}.
This would be a function because all the x's are distinct, ex 4 is different than 1.
Let's look at your choices:
A This is not a function because you have two pairs with the same x-coordinate.
B This is a function. There are no repeats of any x,
C This is not a function because you have 11 as x twice.
D This is not a function because x=3 happens twice.
If the same x happens more than once than it isn't a function.
Answer:
b
Step-by-step explanation:
took test
15 points!!
What do you think? And why?
The seats at a local baseball stadium are arranged so that each row has five more seats than the row below it. If there are four seats in the first row, how many total seats are in the first 24 rows?
Answer:
Thus the last row has 119 seats.
The total number of seats in 24 rows = 1476
Step-by-step explanation:
The number of seats in each row make an arithmetic series. We will use arithmetic equation to find the number of seats in last row:
An = a1+ (n-1)d
An = 4+(24-1)5
An = 4 + (23)(5)
An = 4 + 115
An = 119
Thus the last row has 119 seats.
Now to find the sum of seats we will apply the formula:
Sn = n(a1 + an)/2
Sn = 24(4+119)/2
Sn = 24(123) /2
Sn = 1476 .....
The total number of seats in 24 rows = 1476....
Answer:
1476 seats
Step-by-step explanation:
We are given that each row in a baseball stadium has five more seats than the row below it. Given that there are four seats in the first row, we are to find the total number of seats in the first 24 rows.
For this, we can use arithmetic sequence:
[tex]a_n = a_1+ (n-1)d[/tex]
[tex]a_n = 4+(24-1)5[/tex]
[tex]a_n=119[/tex]
Now that we know the number of seats in the last row, we will plug the value to find total seats in first 24 rows:
[tex]S_n=\frac{24(4+119)}{2}[/tex]
[tex]S_n=1476[/tex]
Therefore, there are 1476 seats in the first 24 rows.
Look at the long division problem shown on the
right Complete the division to determine what the
remainder will be.
What is the remainder?
Answer:
c=2
The remainder is 7.
Step-by-step explanation:
They want you to subtract those last two lines:
[tex]0x^4+0x^3-5x^2-18x[/tex]
[tex]-(0x^4+0x^3-5x^2-20x)[/tex]
----------------------------------------------------
[tex]0x^4+0x^3+0x^2+2x[/tex].
2x comes from doing -18-(-20) or -18+20.
Then you bring down the +15 so you have 2x+15 below that last bar in the picture.
Anyways, you then need to find how many times x goes into 2x or what times x gives you 2x?
Hopefully you say 2 here and put that as c.
Now anything you put above the bar has to be multiplied to your divisor so 2(x+4)=2x+8.
We want to see what's left over from subtract (2x+15) and (2x+8). That gives you a remainder of 15-8=7.
Here are my steps for this division:
4x^3+2x^2-5x+2
-------------------------------------
x+4| 4x^4+18x^3+3x^2-18x+15
-(4x^4+16x^3)
--------------------------------------
2x^3+3x^2-18x+15
-(2x^3+8x^2)
----------------------------
-5x^2-18x+15
-( -5x^2-20x)
----------------------------
2x+15
-( 2x+8)
------------
7
c=2
The remainder is 7.
Answer:
Step-by-step explanation:
The radius of the sphere is 10 units. What is the approximate volume of the sphere? Use and round to the nearest whole cubic unit. 42 cubic units 126 cubic units 4187 cubic units 73,385 cubic units
Answer:
The approximate volume of the sphere= 4187 cubic units
Step-by-step explanation:
Points to remember
Volume of sphere = (4/3)πr³
Where 'r' radius of sphere
To find the volume of sphere
It is given that the radius of the sphere is 10 units. ,
Here radius r = 10 units
Volume = (4/3)πr³
= (4/3) * 3.14 * 10³
= (4/3) * 3140
= 4186.666 ≈ 4187 cubic units
Answer:
Option C.
Step-by-step explanation:
Radius of the sphere is given as 10 units.
We have to calculate the volume of this sphere.
Since formula to measure the volume of sphere is V = [tex]\frac{4}{3}\pi r^{3}[/tex]
V = [tex]\frac{4}{3}\pi 10^{3}[/tex]
= [tex]\frac{4}{3}(3.14)(10^{3})[/tex]
= 4186.67
≈ 4187 cubic units.
Option C. is the answer.
Consider the example of finding the probability of selecting a black card or a 6 from a deck of 52 cards.
Answer:
The probability of selecting a black card or a 6 = 7/13
Step-by-step explanation:
In this question we have given two events. When two events can not occur at the same time,it is known as mutually exclusive event.
According to the question we need to find out the probability of black card or 6. So we can write it as:
P(black card or 6):
The probability of selecting a black card = 26/52
The probability of selecting a 6 = 4/52
And the probability of selecting both = 2/52.
So we will apply the formula of compound probability:
P(black card or 6)=P(black card)+P(6)-P(black card and 6)
Now substitute the values:
P(black card or 6)= 26/52+4/52-2/52
P(black card or 6)=26+4-2/52
P(black card or 6)=30-2/52
P(black card or 6)=28/52
P(black card or 6)=7/13.
Hence the probability of selecting a black card or a 6 = 7/13 ....
There is a tall tree in Iva’s backyard. She thinks it might hit her house if it fell over. She measures that the base of the tree is 50 feet from her house. When Iva stands at the edge of her house, the angle of elevation from her feet to the top of the tree is 50°. Iva’s house is safe if the tree’s height is less than the tree’s distance from the house. Complete the statement based on this information.
The height of the tree is_____50 feet, so Iva’s house is ______.
Answer choices:
1. Greater than, less than, equal to
2. Safe, not safe
Answer:
The height of the tree is Greater than 50 feet, so Iva’s house is not safe
Step-by-step explanation:
step 1
Find the height of the tree
Let
h ----> the height of the tree
we know that
The tangent of angle of 50 degrees is equal to divide the opposite side to the angle of 50 degrees (height of the tree) by the adjacent side to the angle of 50 degrees (tree’s distance from the house)
so
tan(50°)=h/50
h=(50)tan(50°)=59.6 ft
therefore
The height of the tree is Greater than 50 feet, so Iva’s house is not safe
Answer:
greater than and not safe
Step-by-step explanation:
Simplify (4x − 6) + (5x + 1).
Answer:
[tex]\displaystyle =9x-5[/tex]
Step-by-step explanation:
[tex]\displaystyle 4x-6+5x+1[/tex]
Group like terms.
[tex]\displaystyle 4x-6+5x+1[/tex]
Add the numbers from left to right.
[tex]4+5=9[/tex]
[tex]9x-6+1[/tex]
Add and subtract numbers from left to right to find the answer.
[tex]6-1=5[/tex]
It change to postive to negative sign.
[tex]\displaystyle=9x-5[/tex], which is our answer.
Answer:
The simplified form is 9x - 5
Step-by-step explanation:
It is given an expression in variable x
(4x − 6) + (5x + 1).
To find the simplified form
(4x − 6) + (5x + 1). = 4x − 6 + 5x + 1
= 4x + 5x - 6 + 1
= 9x -5
Therefore simplified form of given expression (4x − 6) + (5x + 1) is,
9x - 5
Which of the binomials below is a factor of this trinomial?
22-5x-14
Answer:
The factors are the binomials (x - 7)(x + 2)
Step-by-step explanation:
* Lets explain how to factor a trinomial
- The trinomial ax² ± bx ± c has two factors (x ± h)(x ± k), where
# h + k = -b/a
# h × k = c/a
- The signs of the brackets depends on the sign of c at first then
the sign of b
# If c is positive, then the two brackets have the same sign
# If b is positive , then the signs of the brackets are (+)
# If b is negative then the sign of the brackets are (-)
# If c is negative , then the brackets have different signs
* Lets solve the problem
∵ The trinomial is x² - 5x - 14
∴ a = 1 , b = -5 and c = -14
∵ c is negative
∴ The brackets have different signs
∴ (x - h) (x + k) are the factors of the trinomial
∵ h + k = -5/1
∴ h + k = -5 ⇒ (1)
∵ h × k = -14/1
∴ h × k = -14 ⇒ (2)
- From (1) , (2) we search about two numbers their product is 14 and
their difference is 5 , they will be 7 and 2
∵ 7 × 2 = 14
∵ 7 - 2 = 5
- The sign of b is negative then we will put the greatest number in the
bracket of (-)
∴ h = 7 and k = 2
∴ The brackets are (x - 7)(x + 2)
* The factors are the binomials (x - 7)(x + 2)
What are the solutions of the equation 6x2 +5x+1 = 0 ?
Answer:
Step-by-step explanation:
6x^2+5x+1=0
Descr= b^2-4ac
Descr= 25-24=1
X1= (-b+√descr)/2a = (-5+1)/12= -1/3
X2= (-b-√descr)/2a = (-5-1)/12= -1/2
Answer:
see explanation
Step-by-step explanation:
Given
6x² + 5x + 1 = 0
To factorise the quadratic
Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term
The factors are + 3 and + 2
Use these factors to split the x- term
6x² + 3x + 2x + 1 = 0 ← ( factor the first/second and third/fourth terms )
3x(2x + 1) + 1 (2x + 1) = 0 ← factor out (2x + 1) from each term
(2x 1)(3x + 1) = 0
Equate each factor to zero and solve for x
2x + 1 = 0 ⇒ 2x = - 1 ⇒ x = - [tex]\frac{1}{2}[/tex]
3x + 1 = 0 ⇒ 3x = - 1 ⇒ x = - [tex]\frac{1}{3}[/tex]
How do I solve multiplication property of inequality
Answer:
Yes, C is correct.
Step-by-step explanation:
circle O has a circumference of 36tt cm. what is length of the radius r
Answer:
5.73cm
Step-by-step explanation:
Given parameters:
Circumference of the circle = 36cm
Unknown
Length of the radius = ?
Lets represent the radius by r
Solution
The circumference of a circle is the defined as the perimeter of a circle. The formula is given as:
Circumference of a circle = 2πr
Since the unknown is r, we make it the subject of the formula:
r = [tex]\frac{circumference of the circle}{2π}[/tex]
r = [tex]\frac{36}{2 x 3.142}[/tex] = [tex]\frac{36}{6.284}[/tex] = 5.73cm
Answer:
The radius = 18 cm.
Step-by-step explanation:
I am assuming that is 36π.
If so, then circumference = 2 π r and:
2 π r = 36 π
r = 36π / 2π
r = 18.
Solve for x
3(x – 3) = 5x – 4 +3(7 – x)
Answer:
ok seems easy *ahem*
x=26
Step-by-step explanation:
*MLG intensufys*
What is the equation of the new function???
Answer:
The correct answer option is C. [tex] g ( x ) = | x - 4 | + 6 [/tex].
Step-by-step explanation:
We know that the transformation which shifts a function along the horizontal x axis is given by [tex]f(x+a)[/tex], while its [tex]f(x-a)[/tex] which shifts the function to the right side.
Here we are to shift the function 4 units to the right and 6 units up.
Therefore, the function will be:
[tex] g ( x ) = | x - 4 | + 6 [/tex]
Answer: Option C
[tex]g (x) = | x-4 | +6[/tex]
Step-by-step explanation:
If we have a main function and perform a transformation of the form
[tex]g (x) = f (x + h)[/tex]
So:
If [tex]h> 0[/tex] the graph of the function g(x) will be equal to the graph of f(x) displaced h units to the left
If [tex]h <0[/tex] the graph of the function g(x) will be equal to the graph of f(x) displaced h units to the right
Also if the transformation is done
[tex]g (x) = f(x) + k[/tex]
So
If [tex]k> 0[/tex] the graph of the function g(x) will be equal to the graph of f(x) displaced k units up
If [tex]k <0[/tex] the graph of the function g(x) will be equal to the graph of f(x) displaced k units downwards.
In this case the main function is [tex]f(x) = | x |[/tex] and moves 4 units to the right and 6 units to the top, then the transformation is:
[tex]g (x) = f (x-4) +6[/tex]
[tex]g (x) = | x-4 | +6[/tex]
Can someone explain how to do this? So I can stop askin for help... plzzzzzz!
Answer:
y = 5x
Step-by-step explanation:
The equation to do this is y = mx + b.
b is y intercept which is 0
m is the slope, which is 5
y = 5x + 0 or y = 5x
Answer:
y=5x
Step-by-step explanation:
So we have the points (0,0) and (2,10) that are on the line.
The slope can be calculate the slope by finding the rise and the run, and then putting the rise/run.
If you want to use the graph to count the rise, you can. If you start at 0 and need to get to 10, then you need to rise 10 units.
If you want to use the graph to count the run, you can. If you start at 0 and need to get to 2, then you need to run 2 units.
So the slope is 10/2=5.
Or, if you didn't want to count, you could use the slope formula for a line given two points on that line.
That is the formula is [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex].
There is another format for that formula that might be easier to remember. Just line the points up and subtract vertically. Then put 2nd difference over 1st difference.
So let's do that also:
( 2 , 10)
-( 0 , 0)
----------------
2 10
So the slope is 10/2=5.
Now you can get the same answer if you had done it the other way:
( 0 , 0)
- ( 2 , 10)
----------------
-2 -10
So the slope is -10/-2=5.
You get the same number either way.
So the slope-intercept form of a line is y=mx+b.
m is the slope and b is the y-intercept.
We found m which is 5.
If you look at the graph, you see the line goes through the y-axis at y=0 so the y-intercept, b, is 0.
The equation of the line here is y=5x+0 or just simply y=5x.
A non-food crop is infected by pests on the 1st of a month. The pests infect the crop in such a way that the area infected doubles after each month. If the pests continue to infect the crop in this way, the non-food crop will be entirely infected after the sixth month.
After which month will one-eighth of the non-food crop be infected?
Answer:
After month 3.
Step-by-step explanation:
If you know that the crop will be completely infected after 6 months and the area infected doubles each month, you can work backwards. So picture the 6th month as 100%. Then, basically divide that percentage by 2 until you reach 1/8, or .125, or 12.5. So 100% (month 6) > 50% (month 5) > 25% (month 4) > 12.5% (month 3). So 12.5% is equal to 1/8 or .125, which is what you are trying to look for.
Hope this helps!
The non-food crop will be infected by one-eighth of the crop after 3 months.
What is the sum of n terms in a geometric sequence?The sum of n terms of a geometric sequence is given by the formula,
Sn = [a(1 - r^n)]/(1 - r)
Where r - a common ratio
a - first term
n - nth term
Sn - the sum of n terms
Calculation:Given that,
The crop is infected by pests.
The area infected doubles after each month. So, it forms a geometric progression or sequence.
The entire crop is infected after six months.
So, n = 6, r = 2(double) and consider a = x
Then the area of the infected crop after 6 months is,
S(6) = [x(1 - 2^6)]/(1 - 2)
= x(1 - 64)/(-1)
= -x(-63)
= 63x
So, after six months the area of the infected crop is about 63x
So, the one-eighth of the crop = 63x/8 = 7.875x
For one month the infected area = x (< one-eighth)
For two months it will be x + 2x = 3x (< one-eighth)
For three months it will be x + 2x + 4x = 7x ( < one-eighth)
For four months it will be x + 2x + 4x + 8x = 15x (> one-eighth)
So, the one-eighth of the crop will be infected after 3 months.
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Write a general formula to describe the variation: x varies jointly with the inverse of r and the inverse of the square of the sum of y and z
[tex]\bf \qquad \qquad \textit{combined proportional variation} \\\\ \begin{array}{llll} \textit{\underline{y} varies directly with \underline{x}}\\ \textit{and inversely with \underline{z}} \end{array}\implies y=\cfrac{kx}{z}\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]\bf \stackrel{\textit{"x" varies with}}{x}~~=~~k\stackrel{\textit{inverse of "r"}}{\cfrac{1}{r}}\cdot \stackrel{\stackrel{\textit{inverse of}~\hfill }{\textit{square of a sum}}}{\cfrac{1}{(y+z)^2}}~\hfill x=\cfrac{k}{r(y+z)^2}[/tex]
The variation: x varies jointly with the inverse of r and the inverse of the square of the sum of y and z is, [tex]x = \frac{1}{r + y^{2} + z^{2} }[/tex]
What is an Equation ?An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.
For example, 3x+2y=0.
Types of equation
1. Linear Equation
2. Quadratic Equation
3. Cubic Equation
Given that,
the variation,
x varies jointly with the inverse of r
And the inverse of the square of the sum of y and z
[tex]x = \frac{1}{r + y^{2} + z^{2} }[/tex]
Therefore, the general formula [tex]x = \frac{1}{r + y^{2} + z^{2} }[/tex]
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