A line with a slope of -8/3
passes through the point (0, 10). What is its equation in
slope-intercept form?
Write your answer using integers, proper fractions, and improper fractions in simplest form
Answer:
y = - [tex]\frac{8}{3}[/tex] x + 10
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mc + c ( m is the slope and c the y- intercept )
Here m = - [tex]\frac{8}{3}[/tex] and crosses the y- axis at (0, 10 ) ⇒ c = 10
y = - [tex]\frac{8}{3}[/tex] x + 10 ← equation of line
mark has a board that is 12 feet long he cuts the board into 8 peices that are the same lenght. how long is each peice
Answer: So, all you have to do is divide in this situation. He starts with a board that is 12 feet long, keep that in mind. If he cuts that into 8 pieces it's like he is dividing. So 12 divided by eight or 12/8 would be 1.5. Your answer is that each piece would be 1.5ft long.
integrate (1-x³)² with respect to x
Answer:
Start off by expanding the square:
x^6 -2x³ + 1.
Now, we can integrate it in dx:
∫x^6 - 2x^3 + 1 dx = ∫x^6 dx - 2∫x^3 dx + ∫1 dx = (x^7)/7 - 2((x^4)/4) + x = (x^7)/7 - (x^4)/2 + x.
That's the result!
[tex]\\ \sf\longmapsto {\displaystyle{\int}}(1-x^3)^2dx[/tex]
[tex]\\ \sf\longmapsto {\displaystyle{\int}}(1-x^6+2x^3)dx[/tex]
[tex]\\ \sf\longmapsto x-\dfrac{x^{6+1}}{6+1}+2\dfrac{x^{3+1}}{3+1}[/tex]
[tex]\\ \sf\longmapsto x-\dfrac{x^7}{7}+2\dfrac{x^4}{4}[/tex]
[tex]\\ \sf\longmapsto x-\dfrac{x^7}{7}+\dfrac{x^4}{2}[/tex]
Eyjafjallajokull is a volcano in Iceland. In a recent eruption, a projectile is ejected with an initial velocity of 304 feet per second. The height, H, in feet is given by the equation: H=-16t^2+304t Where t is the time in seconds. We will use the equation that traces the path of the projective to determine the following information: 1) The time it takes the projective to reach its highest point. (t=?) 2) The maximum height? (H=?) 3) The time it takes the projectile to return to the ground? (t=?)
Answer:
A volcano ejected with an initial velocity of 304 feet per second.
The height in feet is given by the equation H=-16t^2+ 304t where t is the time in seconds.
We will use the equation that traces the path of the projectile to determine the following information:
1) The time it takes the projectile to reach its maximum height (using the vertex formula: t=-b/2a)
The equation; H = -16t^2 + 304t, a=-16; b=304
t = -304/2°(-16)
t = 9.5 sec to reach max height
2) The maximum height of the projectile (use the result from part 1 to find the maximum height of the projectile)
t = 9.5
H = -16(9.5^2) + 304(9.5)
h = = -1444 + 2888
h = 1444 ft is the max height
3) Find the time it takes the projectile to return to the ground. Assume that the projectile starts at height H=0.
-16t^2 + 304t = 0
factor out -16t
-16t(t - 19) = 0
t = 19 sec to reach the ground
Step-by-step explanation:
50 POINTS
What is the slope-intercept form of the linear equation 2x + 3y = 6? Drag and drop the appropriate number, symbol, or variable to each box.
A geologist examining a road cut at this location would recognize that Layer A is
than Layer B. This conclusion is made through the principle of
This conclusion is made through the Principle of Lateral Continuity.
The statement made is that "A geologist examining a road cut at this location would recognize that Layer A is older than Layer B."
The principle that guides this observation is that of lateral continuity which states that layers of sediment extend laterally in all directions.
This means that the new layer B is simply an extension of the older layer A.
Learn more about the Principle of Lateral Continuity here:
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Answer:
Younger, superposition
Step-by-step explanation:
The first answer is younger, because for one, it's on the top of the ground sequence, and two because the second question options all prove that answer and not the "older" one.
The second answer is superposition, which states that it goes oldest to youngest from base up.
-Lexi
A rectangle that measures 2 inches by 4 inches.
What is the area of the rectangle?
Answer:
8 in
Step-by-step explanation:
because 4 x 2 = 8 inches squared
Answer:
8 inches²
Step-by-step explanation:
formula for the area of a rectangle is l x w
2 inches x 4 inches = 8 inches.
Area is written in (unit)²
so, the area of the rectangle is 8 inches²
Use the shell method to find the volume of the solid obtained by rotating the region bounded by the curves y=4x-2 and y=x^2+1 about the y-axis. Simplify your solution.
The volume of the solid of revolution is [tex]\frac{16\pi}{3}[/tex] cubic units.
First, we determine the limits between the two curves. ([tex]f(x) = 4\cdot x -2[/tex], [tex]g(x) = x^{2}+1[/tex])
[tex]f(x) = g(x)[/tex] (1)
[tex]4\cdot x - 2 = x^{2}+1[/tex]
[tex]x^{2}-4\cdot x +3 = 0[/tex]
[tex](x-1)\cdot (x-3) = 0[/tex]
The lower and upper bounds are 1 and 3, respectively. It is to notice that [tex]f(x) > g(x)[/tex] for [tex]x \in (1, 3)[/tex]. Thus, we determine the volume of the solid of revolution by shell method, that is to say:
[tex]V = 2\pi \int\limits^a_b {x\cdot |f(x) - g(x) |} \, dx[/tex] (2)
If we know that [tex]a = 3[/tex], [tex]b = 1[/tex], [tex]f(x) = 4\cdot x - 2[/tex] and [tex]g(x) = x^{2}+1[/tex], then the volume of the solid of revolution is:
[tex]V = 2\pi \int\limits^3_1 {|4\cdot x^{2}-2\cdot x -x^{3}-x|} \, dx[/tex]
[tex]V = 2\pi\int\limits^3_1 {(4\cdot x^{2}-x^{3}-3\cdot x)} \, dx[/tex]
[tex]V = 8\pi \int\limits^3_1 {x^{2}} \, dx - 2\pi \int\limits^3_1 {x^{3}} \, dx -6\pi \int\limits^3_1 {x} \, dx[/tex]
[tex]V = 8\pi\cdot \left(\frac{3^{3}}{3}-\frac{1^{3}}{3} \right)-2\pi \cdot \left(\frac{3^{4}}{4}-\frac{1^{4}}{4} \right) - 6\pi\cdot \left(\frac{3^{2}}{2}-\frac{1^{2}}{2} \right)[/tex]
[tex]V = \frac{208\pi}{3} - 40\pi -24\pi[/tex]
[tex]V = \frac{16\pi}{3}[/tex]
The volume of the solid of revolution is [tex]\frac{16\pi}{3}[/tex] cubic units.
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Please help me solve
Answer:
i think t = 24
Step-by-step explanation:
68°+(5t-8)° = 180°
5t-8 = 180-68
5t-8 = 112
5t = 120
t = 120/5
t = 24
Triangles ABC and EDC are similar.
ACE and BCD are straight lines.
Angle BAC = angle DEC
Angle CBA= angle CDE
AB = = 6 cm, BC = 2.5 cm, CD = 7.5 cm and CE = 10.5 cm.
Answer:
18cm
Step-by-step explanation:
The ratio is given by: 7.5/2.5=3
DE = 6 × 3 = 18 cm
or
DC/CB = x/AB
7.5/2.5 = x/6
3=x/6
x=6×3=18 cm
I'm giving out a lot of points for this one!
Answer:
Step-by-step explanation:
AVERAGE rate of change looks only at the endpoints
m = Δy/Δx
m = (1.2 x 10⁶ - 0.35 x 10⁶) / (2640 - 1955)
m = 0.35 x 10⁶/ 685
m = 1241 beings / year
what’s is the surface area of the tent if the length is 2 meters, the width is 2 meters, and the height is 3 meters?
Answer:
45 is the right answer
Step-by-step explanation:
(2 pts.) 9.) Find two equivalent expressions to tan 20° using the cotangent function in degrees.
tan (u) = a/b = cot (90° – u)
Let u = 20°
Take it from here.
The equivalent value of the expression is tan20 is a cot(70).
What are trigonometric identities?Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions. There are numerous distinctive trigonometric identities that relate to a triangle's side length and angle.
The area of mathematics is concerned with how triangles' sides and angles relate to one another as well as with the pertinent uses of any angle.
Given that the trigonometric expression is tan30. The equivalent expression will be written as,
tan (u) = a/b = cot (90° – u)
tan (20) = cot ( 90 - 20 )
tan 20 = cot 70
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Amanda went to the Farmer’s market with her family. She had $5.00 to spend and decided she wanted to spend it on peaches. Each peach cost 68 cents. How many peaches could she buy ?
A family buys a studio apartment for 240,000. They pay for a down payment of 72,000.
A: their down payment is what percent of the purchase price?
B.what percent of the purchase price would a 108,000 down payment be ?
Answer:
A. 30% B. 45%
Step-by-step explanation:
A. 72,000/240,000 = x/100
(72,000)(100) = (240,000)x
7,200,000 = 240,000x
30 = x
B. 108,000/240,000 = x/100
10,800,000 = 240,000x
45 = x
PLS HELP ILL MARK BRAINLIEST
TechWiz Electronics makes a profit of $35 or each MP3 player sold and $18 for each DVD player sold. Last week, TechWiz sold
combined total of 143 MP3 and
DVD players.
Let x be the number of MP3 players TechWiz sold last week. Write an expression
TechWiz made from MP3 and DVD players last week.
for the combined total profit (in dollars)
Answer:
Total profit=$35x+$18(130-x)
Total profit=$35x+$2340-$18x
Total profit=$17x+$2340
Step-by-step explanation:
The cubic curve y = x'3 + ax'2 + bx + c passes through the point (1,3) and has tangent line y = x - 2 at the point (0,-2). What are the values of a, b, and c?
Answer:
answer to your question is: a = 3, b = 1, c = -2
100 POINTS PLS ANSWER
There are 7 friends who went to the bowling alley. Three of the friends each 1 point
bought a game of bowling for $x and a snack pack for $5. The other four
friends only bought a game of bowling. Choose ALL equivalent expressions
that represent the total cost for all 7 friends.
3x+15+4x
8 + 3 + 4x
7x+15
3(x+5)+4x
8 + 15 + 4x
Answer:
8+15+4x and 3x+15+3x
Step-by-step explanation:
Un multiplu de două cifre, diferit de 24, al numărului 24 este........................
VA ROG REPEDE DAU COROANA
Answer:
Un multiplu de două cifre, diferit de 24, al numărului 24 este 48
How do you multiply fractions? Please explain step by step to get marked
Answer: 10/3
Step-by-step explanation
2/3x5
2/3x5/1
Now goahead and multiply the top and bottom numbers
Solve the following compound inequality: 4 less-than-or-equal-to x + 4 less-than-or-equal-to 12. a. 0 less-than-or-equal-to x less-than-or-equal-to 8 c. 8 less-than-or-equal-to x less-than-or-equal-to 16 b. x less-than-or-equal-to 8 d. no solution Please select the best answer from the choices provided A B C D
Answer:
A. 0 <= x <= 8
Step-by-step explanation:
4 <= x + 4 <= 12
Remove 4 from all sides
4 - 4 <= x + 4 -4 <= 12 - 4
0 <= x <= 8
f(x)=3x-1 and g(x)=-2x+5
Answer:
Step-by-step explanation:
HELP! I don't understand
Answer:
Step-by-step explanation:
Jose and Gavin are reading the same book. At the beginning of the month, Jose was
on page 10 and Gavin was on page 37. Jose will read 17 pages per day and Gavin will
read 14 pages per day. Let J represent the page of the book that Jose is on at the end
oft days into the month, and let G represent the page of the book that Gavin is on at
the end oft days into the month. Write an equation for each situation, in terms of t,
and determine what page Jose and Gavin will be on on the day they are both on the
same page.
Using linear functions, it is found that:
Jose's equation is: [tex]J = 17x + 10[/tex].Gavin's equation is: [tex]G = 14x + 37[/tex].They will be on the same page on the 9th day.Linear function:A linear function is modeled by:
[tex]y = mx + b[/tex]
In which:
m is the slope, which is the rate of change.b is the y-intercept, which is the value of y when x = 0.Jose:
Initially, he was on page 10, hence [tex]b = 10[/tex].He reads 17 pages per day, hence [tex]m = 17[/tex].Hence, Jose's equation is: [tex]J = 17x + 10[/tex].Gavin:
Initially, he was on page 37, hence [tex]b = 37[/tex].He reads 14 pages per day, hence [tex]m = 14[/tex].Hence, Gavin's equation is: [tex]G = 14x + 37[/tex].The day they will both be on the same page is x for which:
[tex]J = G[/tex]
Hence:
[tex]17x + 10 = 14x + 37[/tex]
[tex]3x = 27[/tex]
[tex]x = \frac{27}{3}[/tex]
[tex]x = 9[/tex]
They will be on the same page on the 9th day.
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Ok ok ok ok ok ok ok
Answer:
ok ok ok ok ok
Step-by-step explanation:
Answer:
ok?
Step-by-step explanation:
Help help help math math math
18
Step-by-step explanation:
X-3=15
Make X the subject of the formular by transferring the number with co-efficients in one side if the equation.
X=15+3
X=18
Answer:
18
Step-by-step explanation:
A car travels a total distance of 380 miles in a total of 5 hours. The rate the car was traveling during
that time was
Plz answer and explain. And no link please! It is appreciated.
Answer:
I think option a k.9
is correct
Evaluate f(-2) = -3x² - 2x
Answer:
-2F=7x
Step-by-step explanation:
F*-2= -2F 3x*3x=9x
-2F=9x-2x
-2F=7x
Mohal leans a 20-foot ladder against a wall so that it forms an angle of 72° with the
ground. How high up the wall does the ladder reach? Round your answer to the
nearest tenth of a foot if necessary.
Answer:
sin(72°)=x÷20ft.
sin(72°)×20ft.= 19ft 252 inches
the ladder reach 19ft 252 inches tall on the building.
Step-by-step explanation: