Answer:
[tex]y=\frac{1}{2} x[/tex]
Step-by-step explanation:
The equation of a line through two points can usually (except when the line is a vertical line) be written in slope intercept form, [tex]y=mx+b[/tex] , where "m" is the slope of the line, and "b" is the y-intercept of the line.
General outlineFind the slopeFind the y-interceptTo find "m", use the formula for slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\dfrac{(3)-(-2)}{(6)-(-4)}[/tex]
[tex]m=\dfrac{3+2}{6+4}[/tex]
[tex]m=\dfrac{5}{10}[/tex]
[tex]m=\dfrac{1}{2}[/tex]
So, the slope is 1/2 and we know that the equation for the line that passes through these two points should look like: [tex]y=\frac{1}{2} x+b[/tex]
Step 2. Find the y-interceptTo find "b", substitute one of the known points, and solve for "b":
[tex]y=\frac{1}{2} x+b[/tex]
[tex](3)=\frac{1}{2} (6)+b[/tex]
[tex]3=3+b[/tex]
Subtracting 3 from both sides to isolate the "b"...
[tex](3)-3=(3+b)-3[/tex]
[tex]0=b[/tex]
So, the y-intercept is 0. Substituting into our line equation, [tex]y=\frac{1}{2} x+(0)[/tex] which simplifies to [tex]y=\frac{1}{2} x[/tex]
Help
if g(x)=x+1 and h(x)=4-x, what is the value of (gh)(-3)
---------
x-2
Answer: 8/5
Step-by-step explanation:
[tex](g \circ h)(-3)[/tex] is the same as g(h(-3)).
[tex]h(-3)=4-(-3)=7\\g(h(-3))=g(7)=\frac{7+1}{7-2}=\boxed{\frac{8}{5}}[/tex]
Look at the corners of the shape below. Which of the following points is located at one of the corners?
Answer: Coordinate (1,6)
Step-by-step explanation: Because it is located on one of the corners already if you count the spaces! I hope this helped!! :D
Answer:
the person above me is right its (1,6) its the only one thats located on a corner
Step-by-step explanation:
In the 3rd quarter of year 5, what
were the approximate total sales in
the coastal region?
In the 3rd quarter of year 5, the approximate total sales in the coastal region is; $7 million
How to find total sales?
The image of the graph showing the quarterly sales has been attached. From the graph, the red lines indicates the coastal region, the blue lines indicates the northern region, and the green lines indicates the southern region.
From the graph, in the third quarter, we can trace the total sales on the y-axis to be approximately $7 million dollars.
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What is the percentage of 0,4(That is a decimal fraction)
Answer:
0.4= 4/10= 2/5
Step-by-step explanation:
The first decimal place after the point represent the place holder "tenth's"
0.4 = 4/10
This can simply to 2/5
Hope it will help:-)
2 over 5
Step-by-step explanation:
0.4=4 over 10 simplify=2over5
Compare the equations represented in the table, equation, and graph over
the interval
[-5, 3]. Which function is increasing the fastest?
Answer:
Tabled Function
Step-by-step explanation:
To determine which function is increasing the fastest over the interval [-5, 3], we need to calculate and compare each function's average rate of change over the given interval.
The average rate of change of function f(x) over the interval a ≤ x ≤ b is given by:
[tex]\dfrac{f(b)-f(a)}{b-a}[/tex]
Given interval: -5 ≤ x ≤ 3
Therefore, a = -5 and b = 3
Tabled function[tex]f(3)=7[/tex]
[tex]f(-5)=-17[/tex]
[tex]\implies \textsf{Average rate of change}=\dfrac{f(3)-f(-5)}{3-(-5)}=\dfrac{7-(-17)}{3+5}=3[/tex]
Equation: y = x² - 2[tex]f(3)=(3)^2-2=7[/tex]
[tex]f(-5)=(-5)^2-2=23[/tex]
[tex]\implies \textsf{Average rate of change}=\dfrac{f(3)-f(-5)}{3-(-5)}=\dfrac{7-23}{3-(-5)}=-2[/tex]
Graphed functionFrom inspection of the graph:
[tex]f(3)\approx8[/tex]
[tex]f(-5) \approx 0[/tex]
[tex]\implies \textsf{Average rate of change}=\dfrac{f(3)-f(-5)}{3-(-5)} \approx \dfrac{8-0}{3-(-5)}=1[/tex]
Therefore, the Tabled Function has the greatest average rate of change in the interval [-5, 3] and so it is increasing the fastest.
f(x) = 3 and g(x) = x – 2
3 = x – 2
5 = x
Answer:
The question is incomplete
Step-by-step explanation:
Because the question not tells that what is to be find .
Determine the value of Y.
Answer:
y=10°
Step-by-step explanation:
Here,
→(3x+18)°=(5x-4)°
→18°+4°=5x-3x
→22°=2x
→x=11°
Also,
3(4y+3)°+5x-4°=180°[The sum of the linear pair is 180°]
12y+9°+5x-4°=180°
12y+5°+5×11°=180°
12y+5°+55°=180°
12y=180°-60°
12y=120°
y=120°/12
y=10°
Opposite angles are equal
3x+18=5x-422=2xx=11Now
linear pairs are supplementary
3x+18+3(4y+3)=1803(11)+18+12y+9=18033+18+12y+9=18012y+60=18012y=120y=10It takes 15 people to play a 13 minute pool game. How many people would it take to play a 39 minute game?
Answer:
depends on how much beer is left
Step-by-step explanation:
45 people would it take to play a 39 minute game.
What is Ratio?Ratio is defined as a relationship between two quantities, it is expressed one divided by the other.
What is percentage?The percentage is defined as the ratio expressed as a fraction of 100.The percentage is denoted by sign of %.For example, if XYZ scored 46% marks in his test, it means that he scored 46 marks out of 100. It is written as 46/100 in the fraction form and 46:100 in terms of ratio.
Given that,
It takes 15 people to play a 13 minute pool game
So, a 23 minute pool game played by 15 people
A one minute pool game played by 15/13 people
The ratio of one minute pool game to people = 15 : 13
A 39 minute pool game played by number of people = 39(15/13)
A 39 minute pool game played by number of people = 45
Hence, 45 people would it take to play a 39 minute game.
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A spherical balloon is inflated with gas at the rate of 500 cubic centimeters per minute. How fast is the radius of the balloon increasing at the instant the radius is 70 centimeters
Using implicit differentiation, it is found that the radius is increasing at a rate of 0.0081 cm per minute.
What is the volume of a sphere?The volume of a sphere of radius r is given by:
[tex]V = \frac{4\pi r^3}{3}[/tex]
Applying implicit differentiation, the rate of change is given by:
[tex]\frac{dV}{dt} = 4\pi r^2\frac{dr}{dt}[/tex]
In this problem, we have that:
[tex]\frac{dV}{dt} = 500, r = 70[/tex]
Hence the rate of change of the radius is given as follows:
[tex]\frac{dV}{dt} = 4\pi r^2\frac{dr}{dt}[/tex]
[tex]19600\pi\frac{dr}{dt} = 500[/tex]
[tex]\frac{dr}{dt} = \frac{500}{19600\pi}[/tex]
[tex]\frac{dr}{dt} = 0.0081[/tex]
The radius is increasing at a rate of 0.0081 cm per minute.
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please help! please do not copy and paste i have seen the other ones
Given the function f(x) = 2(3)x, Section A is from x = 0 to x = 1 and Section B is from x = 2 to x = 3.
Part A: Find the average rate of change of each section.
Part B: How many times greater is the average rate of change of Section B than Section A? Explain why one rate of change is greater than the other.
Answer:
Given function:
[tex]f(x)=2(3)^x[/tex]
Part AThe average rate of change of function f(x) over the interval a ≤ x ≤ b is given by:
[tex]\dfrac{f(b)-f(a)}{b-a}[/tex]
[tex]\begin{aligned}\textsf{Average rate of change - Section A} & =\dfrac{f(1)-f(0)}{1-0}\\\\& =\dfrac{2(3)^1-2(3)^0}{1-0}\\\\& =\dfrac{6-2}{1}\\\\& =4 \end{aligned}[/tex]
[tex]\begin{aligned}\textsf{Average rate of change - Section B} & =\dfrac{f(3)-f(2)}{3-2}\\\\& =\dfrac{2(3)^3-2(3)^2}{3-2}\\\\& =\dfrac{54-18}{1}\\\\& =36 \end{aligned}[/tex]
Part B[tex]\dfrac{\textsf{Average rate of change of Section B}}{\textsf{Average rate of change of Section A}}=\dfrac{36}{4}=9[/tex]
Therefore, the average rate of change of Section B is 9 times greater than Section A.
The function is an exponential function (with 3 as the growth factor) so the rate of change increases over time.
11.3 9 9 9 7.8 surface area of triangular prism
Answer:
Total area = 187.65 cm^2
Step-by-step explanation:
AREA of a triangle = 1/2 base * height
THREE sides 3 * 1/2 *9 * 11.3 = 152.55 cm^2
Bottom 1/2 * 9 * 7.8 = 35.1 cm^2
total = 187.65 cm^2
The point-slope form of the equation of the line equation of the line that passes through (-9,-2) and (1,3) is y-3=1/2(x-1)
Answer:slope is 1/2, intercept is 2.5
Step-by-step explanation:slope is coefficient of x. Intercept is sun of constants on right side when left side is y. Add 3 to both sides
What is the sum of √-2 and √-18?
O 4√2
O 4√21
O 5√2
O 5√21
Answer:
[tex]4 \sqrt{2} \: i[/tex]
Step-by-step explanation:
[tex] \sqrt{ - 2} + \sqrt{ - 18} \\ ( \sqrt{2} \times \sqrt{ - 1} ) + ( \sqrt{18} \times \sqrt{ - 1} ) \\ ( \sqrt{2} \times \sqrt{ - 1} ) + (3 \sqrt{2} \times \sqrt{ - 1} ) \\ \sqrt{2} i + 3 \sqrt{2} i \\ = 4 \sqrt{2} i[/tex]
The sum of √-2 and √-18 is 4i√2.
What are Irrational Number?Any real number that cannot be written as the quotient of two integers, p/q, where p and q are both integers, is referred to as an irrational number.
We have √-2 and √-18.
To find the sum of √-2 and √-18 we need to perform addition as
= √-2 + √-18
= √2i + √18i
= √2i + 3i√2
= 4i√2
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what is 10 1/2 divide by 2 1/4
Answer: 4 2/3 or 14/3 if wanting a improper fraction.
Solve the equation
3(2x + 2) = 3x - 15
A. X = -7
B. X = -17/3
C. X = 3
D. X = 7
When starting a problem, almost every single problem needs to be understood by the person answering so they can see what needs to be done. In this example, we are given an expression and told to solve the equation which means that we need to solve for the unknown, in this case x.
Now that we know what we must do, we can start to solve the problem. Looking at the problem we can see that the step that we must take is to distribute 3 into the parenthesis.
Distribute
[tex]3(2x + 2) = 3x - 15[/tex][tex](3*2x) +(3* 2) = 3x - 15[/tex][tex](6x) +(6) = 3x - 15[/tex][tex]6x+6 = 3x - 15[/tex]Now that we distributed the values inside of the parenthesis we can move onto the next step which is to help isolate x. What we should do is subtract 6 from both sides which will help leave x with its coefficient alone.
Subtract 6 from both sides
[tex]6x+(6 - 6 )= 3x +(- 15 - 6)[/tex][tex]6x= 3x +(- 15 - 6)[/tex][tex]6x= 3x - 21[/tex]The next step that we should take to help solve for the unknown is to subtract 3x from both sides.
Subtract 3x from both sides
[tex](6x - 3x)= (3x - 3x) - 21[/tex][tex](6x - 3x)= - 21[/tex][tex]3x = - 21[/tex]The final step that we must take to help isolate the unknown would be to divide both sides by 3. This would remove the coefficient from x and we would get -21 divided by 3.
Divide both sides by 3
[tex]\frac{3x}{3} = \frac{- 21}{3}[/tex][tex]x = \frac{- 21}{3}[/tex][tex]x = -7[/tex]Therefore, after simplifying the expression that was given to solve for the unknown we were able to determine that the option that would best match the solution is option A, x = -7.
Answer:
a) x = -7
Step-by-step explanation:
Given: 3(2x + 2) = 3x - 15
1. Distribute:
3(2x) + 3(2) = 3x - 15
⟹ 6x + 6 = 3x - 15
2. Subtract 3x from both sides:
6x - 3x + 6 = 3x - 3x - 15
⟹ 3x + 6 = -15
3. Subtract 6 from both sides:
3x + 6 - 6 = -15 - 6
⟹ 3x = -21
4. Divide both sides by 3:
3x ÷ 3 = -21 ÷ 3
⟹ x = -7
5. Check your work:
3(2x + 2) = 3x - 15
3(2(-7) + 2) = 3(-7) - 15
3(-14 + 2) = -21 - 15
3(-12) = -21 - 15
⟹ -36 = -36 ✔
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2. Identify the missing factors:
d) 20 = (4) (?)
e) -14x = (7) (?)
f) x3 =x2 (?)
Answer:
d) 20 = (4) (5)
e)-14x = (7) (0) = undefined
f) Every Real numbers are solutions, here.
Step-by-step explanation:
2) Identify the missing factors:-
d) 20 = 4(?)
Solved:
Let us assume that *?* = x here.
20 = 4x20/4 = x5 = xx =5e)-14x = (7) (?)
Assume *?* as x
-14x = 7x−14x−7x=7x−7x−21x=0x = 0/-21 = undefinedf) x^3=x^2(?)
Assume ? as x
x³=x²(x)x³−x³=x^3−x^30=0Real numbers are solutions.Hi, I'm in 7th grade and I'm about to fail Mathematics. Please help me...
2x - 5x =
i beliebe 3×=0
ao the answer should be x/0
Answer:
-3x
Step-by-step explanation:
The order of where the terms are placed definitely matter for subtraction. 5x-2x is 3x, but because the smaller number is first, we've gone into the negatives. Think of it like this:
2x - 5x
-2x -2x
__ __
0 -3x
Because we still have the - in front of the 3, it is a negative 3.
Hope this helps!
Algebra please help!!
The airplane reaches its maximum height of 95 feet after 10 seconds
How to calculate the maximum height of an object?The maximum height of an object the point where the velocity of the object is zero.
Given the function that represents the height of the airplane is expressed as h(t) = -(t-10)² + 95
The maximum height is the point where h'(t) = 0
h'(t) = -2(t-10)
0 = -2t + 10
2t = 10
t = 5secs
Substitute t =10 into the function
h(5) = -(10-10)² + 95
h(5) = -0 + 95
h(5) = 95feet
Hence the airplane reaches its maximum height of 95 feet after 10 seconds
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oam. The pit
p is the pit?
The gymnastics center where Alexander
works has a rectangular pit filled with
foam. The pit has a volume of 70
m³, and it has a length of 7 m and a width
of 5 m. How deep is the pit?
35 m
2m
14 m
10 m
Answer:
2 m.
Step-by-step explanation:
Volume = length * width * depth
70 = 7 * 5 * d where d = depth
d = 70 / (7*5)
= 70/35
= 2 m.
What is the closest point on the line y = 2x - 5 to (4, 8)?
Answer: I think it is (6.5, 8).
Step-by-step explanation:
I don't know if you had any choices, but I graphed it on Desmos and that was the closest point. I hope this helps!! :)
please help with this math problem i will give brainliest
Write the rational number as a decimal.
−38 =
Answer:
-0.38
Step-by-step explanation:
For each of the examples below, identify
the bearing of D from C.
a)
b)
N
220°
140°
155°
D
C
205°
Not drawn accurately
Answer:
140°
205°
Step-by-step explanation:
For A
The bearing of D from C is the angle at the line joining D and C while coming from the north pole in a clockwise direction.
from the diagram, the answer is = 140°
For B
The bearing of D from C is obtained same as A
so the answer is = 205°
BRAINLIEST if correct answer
total price of made dolls:
n×£8.50
=170×£8.50
=£1445
total cost:
C= 5n+432
C = 5×170+432
C= £1282
profit=price-cost
p= £1445-£1282
= £165
What is the intermediate step in the form (x + a)2 = b as a result of completing the square for the following equation? x² + 4x = 12
The equation in the form (x + a)² = b is (x + 2)² = 16
How to determine the intermediate step?The equation is given as:
x² + 4x = 12
Take the coefficient of x
k = 4
Divide by 2
k/2 = 2
Square both sides
(k/2)² = 4
Add this result to both sides of x² + 4x = 12
x² + 4x + 4 = 12 + 4
Evaluate the sum
x² + 4x + 4 = 16
Express as a perfect square
(x + 2)² = 16
Hence, the equation in the form (x + a)² = b is (x + 2)² = 16
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What should be done so that the expression will have a value of 10?
12 - 2 + 2 2 ÷ 8
Suppose you invest $1850 at an annual interest rate of 5.2% compound annually. write a function to re[resent the total earnings e(t) as a function of time in years,t.
Answer:$1,942.50
Step-by-step explanation:
A = P(1 + rt)
Calculation:
First, converting R percent to r a decimal
r = R/100 = 2.5%/100 = 0.025 per year.
Solving our equation:
A = 1850(1 + (0.025 × 2)) = 1942.5
A = $1,942.50
The total amount accrued, principal plus interest, from simple interest on a principal of $1,850.00 at a rate of 2.5% per year for 2 years is $1,942.50.
Solve system of equation using elimination by addition.
Will give brainliest!!
Answer:
x = 6
Step-by-step explanation:
Add the system of equations together:
2x - 3y = 12
4x + 3y = 24
you get
6x = 36
divide by the coefficient
6x/6 = 1
36/6 = 6
x = 6
Not sure if you need the y, but if so, let me know!
Hope this helps!
Solve for all values of y in simplest form.
21 = |7y|
Answer: y =
Submit Answer
prove that n^2 +(n+1)^2 is always an odd number
I assume [tex]n\in\mathbb{Z}[/tex] (or at least [tex]n\in\mathbb{N}[/tex]).
[tex]n^2+(n+1)^2=n^2+n^2+2n+1=2n^2+2n+1=2(n^2+n)+1[/tex]
The above is always odd, because one of the factors of [tex]2(n^2+n)[/tex] is even, which makes the product even as well, and 1 is odd, and the sum of an even number and an odd number is an odd number.
ANYONE?? PLEASE HELP??!
Answer:
the answer is B:42.8
Step-by-step explanation:
because when u do this :24+58+30+42+87+11+ 12+55+91+18 = 428
the total numbers here is 10. so 428÷10 = 42.8
That is how u get ur final answer
u hope have helped you dear