Answer:
6x³ - 15x² - 1
3x divided by 3x is 1
So, here we are to simplify the polynomial :
[tex] \\ \longrightarrow \sf \qquad6x^3 - 15x^2 - \frac{3x}{ 3x}\\ \\[/tex]
We can simplify it as,
[tex]\\ \longrightarrow \sf \qquad6x^3 - 15x^2 - 1 \\ \\[/tex]
Some points to know :
Factorisation is the reverse process of multiplucation.The Factorisation is the process of finding two or more expressions such that their product is the given expression9. A bacteria population, , can be represented by the equation p= 100,000 times(1/4)^d,
where d is the number of days since it was measured.
a. What was the population 3 days before it was measured? Explain how you
know.
b. What is the last day when the population was more than 1,000,000? Explain how
you know.
#1
3days back means 3Put it
[tex]\\ \rm\Rrightarrow p=100000(0.25)^{3}[/tex]
[tex]\\ \rm\Rrightarrow p=100000(0.015625)[/tex]
[tex]\\ \rm\Rrightarrow p=1562.5[/tex]
Now
#2
Let's see
[tex]\\ \rm\Rrightarrow 100000(0.25)^d=1000000[/tex]
[tex]\\ \rm\Rrightarrow 0.25^d=10[/tex]
[tex]\\ \rm\Rrightarrow ln0.25^d=ln10[/tex]
[tex]\\ \rm\Rrightarrow dln0.25=2.3[/tex]
[tex]\\ \rm\Rrightarrow d(-1.39)=2.3[/tex]
[tex]\\ \rm\Rrightarrow d=-1.654[/tex]
Find a fraction that is bigger than ⅚, but smaller than 6/7. Show how you did it!!
please help I need to finish this-
Step-by-step explanation:
Check out the attached photo.
Is the following parallelogram actually a rectangle?
True
False
Answer:
False
Step-by-step explanation:
Check if there is a right angle using the Pythagorean Theorem:
7.2^2 + 9.1^2 ≟ 12^2
134.65 ≠ 144,
so since there isn't a right angle, this is not a rectangle.
can someone please help me out with these three questions please please please!!!!
Answer: 4. A 5. C 6. D
Step-by-step explanation: that’s it!!!!!!!!!!
HELPPP please help i don’t get it
this is what would make sence for me
the frist one was confusing
Show that the sum of the first 2n natural numbers is n(2n+1)
Not really sure if there’s a typo in my book or not
Answer:
This sum is the sum of an arithmetic sequence. There is a formula for the sum of an arithmetic sequence which can be looked up or derived by a variety of means.
A nice approach for this sequence is the following. Notice that the sum of first and last number in the sequence is the same as the sum of the second and second last, and also the same as the sum of the third and third last, and so on.
There are n of these pairs. So the desired sum is n x (first number + last number). But the first number is 1 and the last on is 2n. Thus the desired sum is n(1 + 2n).
Hope this helps!!
Mark Brainleast!!!!!!!!!!!
Consider the set {1, 2, 3, 4, ..., m} where m is some natural number, i.e. a positive whole number.
Now let's say we wanted to add everything in that set.
What we can do is write out the terms
1, 2, 3, 4, ..., m
then just underneath, we write the reverse of that set
m, ..., 4, 3, 2, 1
Here's an example of what I mean. I'll use m = 7
[tex]\begin{array}{|c|c|c|c|c|c|c|} \cline{1-7}1 & 2 & 3 & 4 & 5 & 6 & 7\\\cline{1-7}7 & 6 & 5 & 4 & 3 & 2 & 1\\\cline{1-7}\end{array}[/tex]
For each column, add straight down
The third row will be nothing but 8's
[tex]\begin{array}{|c|c|c|c|c|c|c|} \cline{1-7}1 & 2 & 3 & 4 & 5 & 6 & 7\\\cline{1-7}7 & 6 & 5 & 4 & 3 & 2 & 1\\\cline{1-7}8 & 8 & 8 & 8 & 8 & 8 & 8\\\cline{1-7}\end{array}[/tex]
We can see there are seven copies of '8' being added here, so the sum of all the numbers in the set {1,2,3,4,5,6,7} is 8*7 = 56. But wait, we double-counted each item when we formed the second row. So we must divide by 2 to fix the double-counting error.
Therefore, 1+2+3+4+5+6+7 = 56/2 = 28 instead.
-----------------------------
That previous example showed that adding from 1 to 7 means we have 7 copies of (1+7). In other words, 7 copies of 8 being added.
We could write that as 7(1+7)
Then divide that by 2 to fix the double-counting error.
We have 7(1+7)/2
Now imagine that we applied all of what was mentioned to the set {1,2,3,4,5,6,7,8}. Instead of 7's, we use 8's this time to get 8(1+8)/2
Then we can extend it out to the set {1,2,3,4,..., m} and we get the formula m(1+m)/2
We have m copies of (1+m) being added; hence the m(1+m). Don't forget to divide by 2 to fix the double-counting error.
-----------------------------
The key takeaway here is that summing 1+2+3+4+...+m gets us m(1+m)/2
In this case, m = 2n because we want the first 2n natural numbers.
Therefore,
m(1+m)/2
2n(1+2n)/2
n(1+2n)
n(2n+1)
represents the sum 1+2+3+...+n+...+2n
-----------------------------
Try out a value like n = 5 to find that 2n = 2*5 = 10, and,
1+2+3+4+5+6+7+8+9+10 = 55
also
n(2n+1) = 5(2*5+1) = 5*(11) = 55
Showing that the formula works for n = 5. I'll let you try other values of n.
Complete the table for each circle. Use paper to help you with your thinking
Help please
Answer:
written out in the explanation.
Step-by-step explanation:
Area of a circle = [tex]\pi r^{2}[/tex]
Circumference of a circle = [tex]2\pi r[/tex]
The radius is the center point of a circle to the edge of a circle. The diameter is a line from one edge of a circle to the opposite edge.
So, the radius is simply half of the diameter.
For circle A, the radius is 12. Therefore, the diameter is 24.
The circumference is 2·[tex]\pi[/tex]·12 ≈ 75.39822 inches. rounded, the circumference is 75.4 inches.
The area is [tex]\pi 12^{2}[/tex] ≈ 452.38934. rounded, the area is 452.39.
For B,
you have already solved the diameter and radius correctly, good job :). The steps for finding the circumference are the same as for circle A.
the circumference is 2·[tex]\pi[/tex]·6 ≈ 37.69911. rounded, the circumference is 37.7 inches.
the area is [tex]\pi 6^{2}[/tex] ≈ 113.09734. rounded, the area is 113.1.
For C,
the circumference is 12. We can use the circumference equation to solve for the radius.
12 = [tex]2\pi r^{2}[/tex]
divide both by 2[tex]\pi[/tex]
7.63943726841 = [tex]r^{2}[/tex]
square root of 7.63943726841 = 2.76395319577
radius = 2.76395 inches. rounded, the radius is 2.8 inches.
so, radius ·2 = 5.52790639154.
meaning diameter = 5.52791. rounded, the diameter is 5.5 inches.
the area is [tex]\pi 2.76395^{2}[/tex] ≈23.99994. rounded, the area is 24.
I need help with this question for my 8th grade math test
1. Given the following coordinates, complete the listed transformations in sequence, which means you do one after the other.
X(2, 4)
Y(5,-3)
Z(-7, 1)
a) Rotate the points 90 degrees clockwise
b) Dilation by a scaling factor of 2
c) Reflect across the x-axis
d) Translation 2 Up and 5 to the Left
Transforming the points involves changing their coordinates
The image of the points are: (3, 6), (-11, 12) and (-3, -12)
How to complete the transformations?The coordinates of the points are given as:
X(2, 4)
Y(5,-3)
Z(-7, 1)
a) Rotate the points 90 degrees clockwiseThe rule of this transformation is:
(x, y) to (y, -x)
So, we have:
X' = (4, -2)
Y' = (-3, -5)
Z' = (1, 7)
b) Dilation by a scaling factor of 2The rule of this transformation is:
(x, y) to (2x, 2y)
So, we have:
X'' = (8, -4)
Y'' = (-6, -10)
Z'' = (2, 14)
c) Reflect across the x-axisThe rule of this transformation is:
(x, y) to (x, -y)
So, we have:
X''' = (8, 4)
Y''' = (-6, 10)
Z''' = (2, -14)
d) Translation 2 Up and 5 to the LeftThe rule of this transformation is:
(x, y) to (x -5, y + 2)
So, we have:
X'''' = (3, 6)
Y'''' = (-11, 12)
Z'''' = (-3, -12)
Hence, the image of the points are: (3, 6), (-11, 12) and (-3, -12)
Read more about transformation at:
https://brainly.com/question/4289712
Jose made 5 2/3 cups of juice. He served 3/4 of it at dinner. Which equation shows the amount of juice that Jose served?
Answer:
4 1/4 cups were served
Step-by-step explanation:
Just multiply 5 2/3 cups by 3/4:
17 3
---- * ---- = 4 1/4 cups were served.
3 4
An equation shows the amount of juice that Jose served is x= 3/4 × 17/3.
What is the product of two fractions?The product of two fractions is the product of the numerators and the product of the denominators.
Product of two fractions = Product of their numerators / Product of their denominators.
Given that, Jose made [tex]5\frac{2}{3}[/tex] cups of juice. He served 3/4 of it at dinner.
Here, [tex]5\frac{2}{3}[/tex] cups can be written as 17/3
Let the amount of juice that Jose served be x
Now, x= 3/4 × 17/3
x= 17/4
x= [tex]4\frac{1}{4}[/tex] cups
Therefore, an equation shows the amount of juice that Jose served is x= 3/4 × 17/3.
To learn more about the product of two fractions visit:
https://brainly.com/question/7335118.
#SPJ2
The base length of a triangle is 4 feet and the height is 2 feet. What is the area of the triangle? O2 square feet 04 square feet O 6 square feet O 8 square feet
Answer:
4 square feet
Step-by-step explanation:
hope this helps :)
Please help me with this algebra question please u need help
[tex] \huge\rightarrow\sin( θ ) = \frac{ - 2 \sqrt{5} }{5} [/tex]
To find↷cos(θ) in IV quadrantAnswer↷[tex] \huge\rightarrow\cos( θ ) = \frac{ \sqrt{5} }{5} [/tex]
Solution↷We know that,
sine is the ratio of adjacent side over the hypotenuse.
[tex] \rightarrow\sin( θ ) = \frac{ - 2 \sqrt{5} }{5} = \frac{adjacent \: side}{hypotenuse} \\ [/tex]
also,
cosine is the ratio of base over the hypotenuse.
[tex]\rightarrow\cos( θ ) = \frac{?}{5} \\ [/tex]
base = √(h²-a²)h= hypotenusea= adjacent side[tex]\rightarrow\cos( θ ) = \frac{ \sqrt{ {5}^{2} - ( - 2\sqrt{ 5} {}^{} ) {}^{2} } }{5} \\ [/tex]
[tex]\rightarrow\cos( θ ) = \frac{ \sqrt{ {5}^{2} - {(2\sqrt{ 5})}^{2} } }{5} \\ [/tex]
[tex]\rightarrow\cos( θ ) = \frac{ \sqrt{25 - 20} }{5} \\ [/tex]
[tex]\rightarrow\cos( θ ) = \frac{ \sqrt{5} }{5} \\ [/tex]
since ,cosine is always positive in the quadrant IV, option 3rd =√5/5 is correct ✓
Note:-
★theta to be used as A
[tex]\\ \rm\Rrightarrow sinA=\dfrac{-2\sqrt{5}}{5}[/tex]
Now
cosA=1-sin²A[tex]\\ \rm\Rrightarrow cosA=\sqrt{1-(dfrac{-2\sqrt{5}}{5})^2}[/tex]
[tex]\\ \rm\Rrightarrow cosA=\sqrt{1-\dfrac{20}{25}}[/tex]
[tex]\\ \rm\Rrightarrow cosA=\sqrt{\dfrac{25-20}{25}}[/tex]
[tex]\\ \rm\Rrightarrow cosA=\dfrac{\sqrt{5}}{5}[/tex]
Option C
The cake that Larry is baking requires 1 cup of sugar. Larry is adding sugar to a bowl using a measuring scoop. In the first scoop, he adds 7/8 cup of sugar. In the second scoop, he adds another 7/8 cup of sugar. Has Larry measured the sugar correctly?
PLS HELP ME WITH THIS IM GONNA CRY ITS SO HARD....
Arsenic‐74 is used to locate brain tumors. It has a half‐life of 17.5 days. 90 mg were used in a procedure. Write an equation that can be used to determine how much of the isotope is left after x number of half-lives.
Let that be x
Use the general formula used for calculating half-life
[tex]\\ \rm\Rrightarrow A=A_o(0.5)^{\frac{t}{h}}[/tex]
H is half-life,t is timetime given xput values
The equation is
[tex]\\ \rm\Rrightarrow A=90(0.5)^{x/17.5}[/tex]
I need help with this
Step-by-step explanation:
Doesn't the line show where the median is? Then it would be class 1
How many solutions does this
equation have?
3s = 8s -5s
A one solution
C no solution
B two solutions
D infinite
Answer:
D
Step-by-step explanation:
3s = 8s - 5s
8s = 8s
s = 0, 1, 2, 3.......
so infinite solutions
D)
Step-by-step explanation:Given equation:
[tex]3s = 8s - 5s[/tex]To simplify this equation, we need to isolate the variables on one side of the equation and the constants on the other side of the equation. To do this, we can simplify the R.H.S as like terms can subtract.
⇒ [tex]3s = 8s - 5s[/tex]
⇒ [tex]3s = s(8 - 5)[/tex]
⇒ [tex]3s = s(3) = 3s[/tex]
⇒ [tex]3s= 3s[/tex]
Since both sides of the equation are the same, this system of equations has infinite solutions.
Check:We can check our answer by substituting the value of "s" into the equation. As a result, you will see that many values of "s" are satisfying the equation. Thus, Option D is correct.
3,900,000 / 2 please help
Answer: 1,950,000
Step-by-step explanation: Divide by 2 beginning with the first digit which is 3 up to the last zero
Please help ASAP (30 POINTS)
NO LINKS OR BOTS IF I SEE YOU WILL GET REPORTED!
Only answer if you know for sure!
What is the overlap of Data Set 1 and Data Set 2?
a) high
b) moderate
c) low
d) none
Answer:
Low
Step-by-step explanation:
Low because it only overlaps twice.
A total of 640 people voted in an election. The circle graph shows the results.
A.) How many people voted for Gordon? Show your work
B.) How many people voted for Smith or Fishman? Show your work
Find the slope of the line that is parallel and perpendicular to the following equation.
2x-2y=-6
Answer:
Parallel lines 1
perpendicular lines -1
Step-by-step explanation:
2x-2y = -6
Solve for y to get it in slope intercept form
-2y = -2x-6
Divide by -2
y = x+3
This is slope intercept form y = mx+b where m is the slope
Parallel lines have the same slope
A parallel line would have a slope of 1
Perpendicular lines would have a slope that is a negative reciprocal
-1/1
Perpendicular lines would have a slope of -1
Let us first put it into slope-intercept form ⇒ [tex]y = mx + b[/tex]
m: slopeb: y-intercept of the functionTo put it into that format, we need to simply put y on one side of the equation and the rest on the other side
[tex]2x - 2y =-6\\-2y = -2x -6\\y = x +3[/tex]
What do we want to find first ⇒ a line parallel to the original line
a line that is parallel to the original line only has one requirement, it must have the same slope, such as the one below[tex]y = x +5[/tex]
What do we also want to find ⇒ a line perpendicular to the original line
a line that is perpendicular to the original line only has one requirement, the slope has to be the negative reciprocal of the original slope⇒ original slope is 1 ⇒ negative reciprocal is - 1/1 = -1
⇒ so an example is
[tex]y = -x + 3[/tex]
Answer:
Line that is parallel: slope is 1Line that is perpendicular: slope is -1Hope that helps!
5 < -5(3x-7) Solve the inequality.
Answer:
x<2
Step-by-step explanation:
5<-5(3x-7)
divide by 5
1<-3x+7
3x<7-1
3x<6
x<2
(7.8 x 10^3) (1.0 x 10^4) =?
Answer:
78000000
Step-by-step explanation:
(7.8 x 10^3) (1.0 x 10^4) =?
Justine has $13.50 left on her city bus card and each bus ride cost $2.25.what equation can be used to find the number of bus rides he has left
Answer:
6 rides
Step-by-step explanation:
Total balance = $13.50 = ($2.25/ride)x, where x is the remaining number of rides. Dividing both sides by $2.25/ride yields 6.
Justin has enough on his bus card for 6 more rides.
3. I am a cube that has a length,
width, and height of 1 unit.
A cube that has a height of 1 unit, will also have length and width that are both 1 unit in length.
What is a Cube?A cube is a three-dimensional shape that has equal length, width, and height.
We are given that the height of a cube is 1 unit. Since the length, width, and height of a cube are always equal, therefore:
Length of the cube =1 unit
Width of the cube = 1 unit.
In summary, a cube that has a height of 1 unit, will also have length and width that are both 1 unit in length.
Learn more about cube on:
https://brainly.com/question/1972490
Round 3.993 to the nearest hundredth
A. 3.90
B. 4
C. 3.9
D. 3.99
Answer:
Step-by-step explanation:
3.993,
3.99
Is –12,365 − –110 positive or negative?
Answer:
Negative
Step-by-step explanation:
This is the same as saying -12,365 + 110
This equals -12,265
Hope that helps!
Answer:
Same sign - Positive
Different sign - Negative
only for some maths
i dont understand any of this please help
Answer:
92%
Step-by-step explanation:
To convert a fraction to a percent, you can divide the numerator by the denominator to end up with a decimal, in this case 0.92. Then, to convert to a percent, move the decimal two places to the left. As a result, we have 92%.
hope this helps!
what is the measure of an angle that turns through 1/5 of a circe
How to solve [tex]2n =\frac{15}{2}[/tex] and [tex]\frac{1}{4} =\frac{n}{5}[/tex] ???
Answer:
[tex]2n=\dfrac{15}{2}[/tex]
Multiply both sides by 2:
[tex]\implies 2 \cdot 2n=2 \cdot \dfrac{15}{2}[/tex]
[tex]\implies 4n=15[/tex]
Divide both sides by 4:
[tex]\implies \dfrac{4n}{4}=\dfrac{15}{4}[/tex]
[tex]\implies n=\dfrac{15}{4}[/tex]
[tex]\dfrac14=\dfrac{n}{5}[/tex]
Multiply both sides by 5:
[tex]\implies 5 \cdot \dfrac14=5 \cdot \dfrac{n}{5}[/tex]
[tex]\implies \dfrac54=n[/tex]
[tex]\implies n=\dfrac54[/tex]
Answer:
Step-by-step explanation:
2n = 15/2
Divide both sides b y 2:
n = 15/2 / 2
= 15/2 * 1/2
= 15/4.
1/4 = n / 5
Multiply both sides by the LCM (20):
20/4 = 20n/5
5 = 4n
n = 5/4.
work out m and c for the line
2y+6x=-4
i will mark a brainlist if you get it right
Answer:
y = -2 -3x
x = -2/3 -y/3
y =-3x -2
Slope=-6.000/2.000=-3.000
2*y+6*x-(-4)=0
2y + 6x + 4 = 2 • (y + 3x + 2)
Step-by-step explanation:
The bold letters are the important and answer :)
hoped this helped
if the answer is wrong tell me pls