Answer:
8
Step-by-step explanation:
4x - 9 = 2x + 7
4x - 2x = 7 + 9
2x = 16
x = 16 / 2
x = 8
Here, we are given with an equation in which we are given with some constants and two same variables x. We are said that the LHS and RHS are equal to each other. We are asked to find the value of the variable x. To find the value of x, we use an other concept which helps us to find the value of x and also to verify our answer. This concept is called as the transposition method. While using this method, the sign of the appropriate number or variable changes. We use this method to shift the numbers and variables on two separate sides. We can also verify our answer at the end of our answer by verification method. So, let's solve!!
[tex]\:[/tex]
➤ Solution :-[tex]{\sf \leadsto 4x - 9 = 2x + 7}[/tex]
Shift the variable value to LHS and the constant value to RHS, changing it's sign.
[tex]{\sf \leadsto 4x - 2x = 7 + 9}[/tex]
Subtract the values on LHS and add the values on RHS.
[tex]{\sf \leadsto 2x = 16}[/tex]
Shift the number 2 from LHS to RHS.
[tex]{\sf \leadsto x = \dfrac{16}{2}}[/tex]
Simplify the fraction to find the value of x.
[tex]{\sf \leadsto x = 8}[/tex]
[tex]\:[/tex]
[tex]{\red{\underline{\boxed{\bf So, \: the \: value \: of \: x \: is \: 8.}}}}[/tex]
━━━━━━━━━━━━━━━━━━━━━━━
Verification :-[tex]{\sf \leadsto 4x - 9 = 2x + 7}[/tex]
Substitute the value of x.
[tex]{\sf \leadsto 4(8) - 9 = 2(8) + 7}[/tex]
Multiply the numbers in the bracket.
[tex]{\sf \leadsto 32 - 9 = 16 + 7}[/tex]
Subtract the values on LHS and add the values on RHS.
[tex]{\sf \leadsto 23 = 23}[/tex]
So,
[tex]{\sf \leadsto LHS = RHS}[/tex]
an arrow is horizontally projected from the top of a tower with an initial velocity of 18m/s if it reaches the ground 7s later, calculate the height of the tower (take g=10m/s²)
Answer:
x[f]=at^2/2+v[i]t+x[i]
Brackets dennote a subscript.
You're given x[f], a, t,and v[i]. You can just plug in their values into the formula and solve for x[i]. The horizontal velocity is irrelevant, the height of the tower is the initial position of the arrow, and final position is gonna be when it reaches the ground,or 0.
Ik this is not math but please help
[tex]Evaluate: \int \frac{ \sin(2x) }{1 + \sin^{2} (x) }dx \\ [/tex]
Hopping for a great answer.
Answer:
ln (1 + sin^2(x)) + C
Step-by-step explanation:
Note that sin(2x) = 2 sin(x) cos(x).
So, the integrand is rewritten as:
(2 sin(x) cos(x)) / (1 + sin^2(x) ).
Now, make the substitution u = sin(x), so that du = cos(x) dx. Thus, in terms of the variable u, the integrand is
(2 u )/(1 + u^2).
Make another substitution v = 1 + u^2, so that dv = 2 u du, and the integrand in terms of v is
1 / v
Now, we integrate, and then back substitute to write that the indefinite integral is
ln |v| + C = ln |1 + u^2| + C = ln |1 + sin^2(x)| + C + ln (1 + sin^2(x)) +C, since 1 + sin^2(x) + 1 is positive for all real x.
Step-by-step explanation:
[tex]\large\underline{\sf{Solution-}}[/tex]
We have to evaluate the given integral.
[tex] \displaystyle \rm = \int \dfrac{ \sin(2x) }{1 + \sin^{2} (x) } \: dx[/tex]
[tex] \displaystyle \rm = \int \dfrac{2 \sin(x) \cos(x) }{1 + \sin^{2} (x) } \: dx[/tex]
Now let us assume that:
[tex] \rm \longmapsto u = 1 + { \sin}^{2}(x)[/tex]
[tex] \rm \longmapsto \dfrac{du}{dx} = 2 \sin(x) \cos(x) [/tex]
[tex] \rm \longmapsto dx = \dfrac{1}{2 \sin(x) \cos(x) } \: du[/tex]
Therefore, the integral becomes:
[tex] \displaystyle \rm = \int \dfrac{1}{u} \: du[/tex]
[tex] \displaystyle \rm = \ln(u) + C[/tex]
[tex] \displaystyle \rm = \ln(1 + sin^{2}x ) + C[/tex]
Therefore:
[tex] \displaystyle \rm \longmapsto \int \dfrac{ \sin(2x) }{1 + \sin^{2} (x) } \: dx = \ln(1 + sin^{2}x ) + C[/tex]
Anyone know how to do long division I know about the DMSBD but I wanna example
Step-by-step explanation:
imjteiuddjddjjdjjdjsh
usudtdbiemsihdhhdud yeh dhejuehhee
Hope's this helps
Answer:
Example Problem
1,234 ÷ 4 = 308 r 2
Step-by-step explanation:
I wasn't able to find a long division symbol so im sorry for any confusion!
0308
4 Γ1234
−0
12
−12
03
−0
34
−32
2
A pitcher can hold 1 7/8 pints if juice. part a : how many 2/5 pint glasses can the pitcher fill. show work. and part b : how many 1/4 pint glasses can the pitcher fill . show your work
Answer:
Correct answer is 0.67
Step-by-step explanation:
factor completely 1-x^2
Answer:
(1 + x)(1 - x)
Step-by-step explanation:
Step 1: Rewrite 1 as 1^2
[tex]1 - x^2[/tex] [tex]1^2 - x^2[/tex]Step 2: Apply difference of two squares formula [tex]x^2 - y^2 = (x+y)(x-y)[/tex]
[tex](1+x)(1-x)[/tex]Therefore, the answer is (1 + x)(1 - x).
What is the volume of this cylinder?
6 ft
12ft
Simplify: 36 - [18 - {14 - (15 - 4 ÷2 ×2)}]
Answer:
36 - [18 - {14 - (15 - 4 ÷ 2 × 2)}]= 36-[18-{14-(15-4)}]= 36-[18-{14-9}]=36-[18-5]=36-13=23
Step-by-step explanation:
36 - [18 - {14 - (15 - 4 ÷2 ×2)}]
= 36 - [18 - {14 - (15 - 2 ×2)}]
= 36 - [18 - {14 - (15 - 4)}]
= 36 - [18 - {14 - 11}]
= 36 - [18 - 3]
= 36 - 15
= 21
Answer:21
find the product (n- 2xb)(4n- xb)
Step-by-step explanation:
(n-2xb)(4n-xb)
= 4n^2 - 8xbn - xbn + 2(xb)^2
= 4n^2 - 9xbn + 2(xb)^2
PLEASE HELP FAST!
what is the length of segment AB?
10
12
13
15
Answer:
13
Step-by-step explanation:
This triangle appears to be 5 units wide and 12 units tall.
Using the pythagorean theorem, a^2 + b^2 = c^2, we get 25 + 144 = 169 or 13^2.
Therefore the answer is 13.
Which one is the larger average rate, -3.142 or -0.5?
Answer:
-0.5 is the larger average rate
Step-by-step explanation:
-3.142 is less than -0.5
a car salesperson earns 4% commision for each car he sells.he sells a car for $21,250. how much commission does the saleperson earn
a line passes through the point (4, -4) and has a slope of -5 / 4
write an equation in slope-intercept form for this line
Answer:
y=-5/4x+1
Step-by-step explanation:
y- y-coordinate= slope(x- x-coordinate)
y- (-4)= -5/4 (x - 4)
y - (-4)= -5/4x +5
move (-4) to the other side of the equal sign, the sign changes to +4
y= -5/4x +5 +4
y=-5/4x+1
is 9^4 equivalent to 3^8
Answer: 9^4 is 6561 and 3^8 is 6561 so yes it is equivalent.
Brainliest if you liked answer
How do you do this ?
Answer:
you're supposed to distribute the 4 to whatever "n" is
Can anyone please help me out
Answer:
B = 3.31662479
rounded to 3.32
Step-by-step explanation:
Pythagorean theorem: [tex]a^{2} + b^{2} = c^{2}[/tex]
A & B = the base and height
C = The diagonal line.
A & B can be base or height. ( base = 2 Height = 3. It can be [tex]2^{2} + 3^{2}[/tex] or [tex]3^{2} + 2^{2}[/tex] )
Because when you add it doesn't matter where each number is put.
I like doing b for the base, because there's a b in base, to make it easier for me. But you can do whatever.
A = 5
B = ?
C = 6
[tex]5^{2} + b^{2} + 6^{2}[/tex]
From here you will solve to get b.
[tex]5*5 + b^{2} = 6 * 6[/tex]
[tex]25 + b^{2} = 36[/tex]
25 - 25 + [tex]b^{2}[/tex] = 36 - 25
[tex]b^{2}[/tex] = 11
To under the exponent you have to [tex]\sqrt[/tex] it.
[tex]\sqrt{b_{2}}[/tex] = [tex]\sqrt{11}[/tex]
[tex]5^{2} + 3.32^{2} = 6^{2}[/tex]
B = 3.31662479
rounded to 3.32
Check your work :
[tex]5^{2} + 3.32^{2} = 6^{2}[/tex]
________
[tex] \: [/tex]
a² = c² - b²
a² = 6² - 5²
a² = 36 - 25
a² = 11
a = √11
a ≈ 3.316...
What is the slope of a line with one point at (2,1) and another at (5,3)
Answer:
Slope: 2/3
Step-by-step explanation:
Take the first point (2,1) as (x1, y1), and,
the second point (5,3) as (x2, y2).
Using the slope formula to calculate the slope:
m = [tex]\frac{y2-y1}{x2-x1}[/tex]
= (3-1)/(5-2)
= 2/3
Hence, the slope is 2/3
Hope this helps and be sure to have a wonderful time ahead at Brainly! :D
You have 8/12
of a blueberry pie left over from dinner. If you sent 1/5 of the leftover
blueberry pie home with your guests, how much of the blueberry pie do you have left in the dish?
Answer:
8/12-1/5=7/15 reduce 8/12 to 2/3
Hey! Can I know how to solve this problem?
(2)/((1)/(\sqrt(3))+1)
It's been driving me insane.
Answer:
Can you ask again with a picture? it's not clear with only text
explain mathematically how you know 5y+4=10 and 5y=6 are equivalent
Answer:
see explanation
Step-by-step explanation:
Given
5y + 4 = 10 ( subtract 4 from both sides )
5y = 10 - 4 , that is
5y = 6
Thus 5y + 4 = 10 is equivalent to 5y = 6
Answer: y= 9x+6y=15
Step-by-step explanation:
Which of the following is a measure of spread?
1.Range
2.Mean
3.Median
4.Mode
5.All of the above: Mean, Median, Mode, and Range
6.Mean, Median, and Mode only
Answer:
1....... range...............
Answer:
they include Quartile ,Inter-quatile , range......................
Step-by-step explanation:
10
Sarah is making 4 batches of cupcakes for a friend's birthday. Each batch requires 4 teaspoons of vanilla for the
cupcakes and 2 teaspoons of vanilla for the frosting. Which expression can you use to help find the number of
teaspoons of vanilla Sarah will need for all 4 batches?
O 4 + 2 x4
o (4 + 2) x4
(4 x 4) + 2
Answer:
Step-by-step explanation:
the answer is (4 x 4)+2
Answer:
o (4+2) x4 is the expression that means 4 batches of 4+2 teaspoons of vanilla.
Step-by-step explanation:
1c = t(4 + 2) is created as t = tspoon but any letter cna represent and maybe the o means teaspoons so lets compare
we see the brackets on (4+2) x4 and use this. And if you must put a 0 in front then I would also convert to show without 0 and show both
As long as brackets separate the (4x 2) to the 4 batches it becomes a workable expression.
When algebra becomes understandable for multiplying we show 4(4 +2)
because in brackets its always add or subtract, but we recognise mainly as the question is worked out first for one part being 1 cupcake = 1c
so 1c = 4t+2t
then; 4c = 4t+2t
we need to multiply the set as a reverse to usual equations that try to make you find what t or c means.
so as we are not subtracting the numbers either side of the = we can just demonstrate a multiplication
4( 4+2)t = 0(4+2) x 4
equation in bold = expression given and chosen
they both mean the same so we know the first one in bold is an equation and the 2nd one as asked is an expression
1. Match the polynomial with its end behavior.
A. f(x) = -2x + 3
B. f(x) = x2 - 6x + 3
1. As x gets larger and larger in either
the positive or negative direction,
f(x) gets larger and larger in the
positive direction.
C. f(x) = 1 – x2 + 2x3
D.f(x) = 7 - x4
DE
2. As x gets larger and larger in the
positive direction, f(x) gets larger
and larger in the positive direction.
As x gets larger and larger in the
negative direction, f(x) gets larger
and larger in the negative direction.
3. As x gets larger and larger in the
positive direction, f(x) gets larger
and larger in the negative (help please)direction.
As x gets larger and larger in the
negative direction, f(x) gets larger
and larger in the positive direction.
4. As x gets larger and larger in either
the positive or negative direction,
f(x) gets larger and larger in the
negative direction.
Using infinity limits, the matching pairs are:
A - 3.B - 1.C - 2.D - 4.The end behavior of a function f(x) is given by:
[tex]\lim_{x \rightarrow \infty} f(x)[/tex]
Function A:
[tex]f(x) = -2x + 3[/tex]
[tex]\lim_{x \rightarrow -\infty} f(x) = \lim_{x \rightarrow -\infty} -2x + 3 = \lim_{x \rightarrow -\infty} -2x = -2(-\infty) = \infty[/tex]
[tex]\lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} -2x + 3 = \lim_{x \rightarrow \infty} -2x = -2(\infty) = -\infty[/tex]
Thus, matches with item 3.
Function B:
[tex]f(x) = x^2 - 6x + 3[/tex]
[tex]\lim_{x \rightarrow -\infty} f(x) = \lim_{x \rightarrow -\infty} x^2 - 6x + 3 = \lim_{x \rightarrow -\infty} x^2 = (-\infty)^2 = \infty[/tex]
[tex]\lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} x^2 - 6x + 3 = \lim_{x \rightarrow \infty} x^2 = (\infty)^2 = \infty[/tex]
Thus, matches with item 1.
Function C:
[tex]f(x) = 1 - x^2 + 2x^3[/tex]
[tex]\lim_{x \rightarrow -\infty} f(x) = \lim_{x \rightarrow -\infty} 1 - x^2 + 2x^3 = \lim_{x \rightarrow -\infty} 2x^3 = 2(-\infty)^3 = -\infty[/tex]
[tex]\lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} 1 - x^2 + 2x^3 = \lim_{x \rightarrow \infty} 2x^3 = 2(\infty)^3 = \infty[/tex]
Thus, matches with item 2.
Function D:
[tex]f(x) = 7 - x^4[/tex]
[tex]\lim_{x \rightarrow -\infty} f(x) = \lim_{x \rightarrow -\infty} 7 - x^4 = \lim_{x \rightarrow -\infty} -x^4 = -(-\infty)^4 = -\infty[/tex]
[tex]\lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} 7 - x^4 = \lim_{x \rightarrow \infty} -x^4 = -(\infty)^4 = -\infty[/tex]
Thus, matches with item 4.
A similar problem is given at https://brainly.com/question/24248193
check the image below
Answer: A
Step-by-step explanation:since the dot on -3 is solid that means it is included or equal to. since the dot on 2 is not filled in that means not equal to that number but everything up to it, including everything from -3 up to but not including 2
10. The half-life of a radioactive substance is 15
years.
Write an equation that can be used to determine
the amount, s(t), of 200 grams of this substance
that remains after t years. (2 points)
Determine algebraically, to the nearest year, how
long it will take for 1/10 of this substance to
remain. (3 points)
Answer:
s(t)=200(1/2)^t/13
Step-by-step explanation:
Here's answer:
https://www.nysedregents.org/algebratwo/619/algtwo62019-mrs.pdf
The number of years it will take for 1/10 of this substance to remain is; 50 years
What is the half life formula?The half life formula is;
N(t) = N₀(¹/₂)^(t/t_1/2)
where;
N(t) is quantity of the substance remaining
N₀ is initial amount of substance
t is time elapsed
t_1/2 is half life
Thus;
S(t) = 200(¹/₂)^(t/15)
We want to find the time it will take 1/10 of the substance to remain. Thus;
1/10 = (200/200)(¹/₂)^(t/15)
1/10 = (¹/₂)^(t/15)
t/15 = In(1/10)/In(¹/₂)
t/15 = 3.32193
t = 49.88 ≈ 50 years
Read more about Half Life at; https://brainly.com/question/26689704
Can someone help me with number 36? Tysmmm
Answer: Never(!) [assuming I understand/interpret the question properly]
Step-by-step explanation: The question wants to know how many months it will take for your neighbor's total cost be the same as yours, with three televisions. One has to interpret "total cost." I deem it to be the total accumulated costs, including installation. If you interpret it as the cost per month, then they charges are the same after the month the installation cast was paid. That's because the satellite provider charges per television, and 3*(13.32) is equal to the same 39.96/month charged by the cable provider. It the questions means total cumulative costs, the satellite customer will never exceed the cable customer's total bill, because of the installation fee ($75 for cable and free for satellite)
help help pls!!!!!!!!!!!!!
Answer:D
Step-by-step explanation:the exterior angle of a triangle is equal to the sun of the opposite interior angles
120 =11x-6+10x
21x= 126
x=6
Can you subtract 8 tenths from 1 tenth?
Answer:
Not if you want it to be a positive number. You can but it will be a negative.
Step-by-step explanation:
Two golf balls are randomly selected from a bag that contains 3 Titleist, 5 Top Flite, and 2 Pinnacle golf balls .If the first golf ball is replaced before the second golf ball is selected, determine the probability that you select a Titleist and then a Top Flite.
Answer:
type b balls
Step-by-step explanation:
Answer:
b balls
Step-by-step explanation:
your mom
How do animals get nitrogen?
by eating other organisms
from the air
by absorbing the sun
through their skin
Answer:
By eating plants or other animals that contain nitrogen