-3×2d=12
-6d=12
d=12÷(-6)
then d= -2Hope this helps.
3
There are 900 students in a school.
47% of the 900 students are girls.
Work out the number of girls in the school.
Is (x + 5) a factor of f(x) = x3 − 4x2 + 3x + 7? Use either the remainder theorem or the factor theorem to explain your reasoning. This is worth 100 points. Will mark brainliest. Whatever you want. Please answer this.
Answer:
(x + 5) is not a factor of, [tex] f(x) = x^ 3 − 4x^2 + 3x + 7 [/tex]
Step-by-step explanation:
[tex] f(x) = x^ 3 − 4x^2 + 3x + 7 \\ \\ let \: x + 5 = 0 \\ \implies \: x = - 5 \\ \\ plug \: x = - 5 \: in \: f(x) \\ \\ f( - 5) = ( - 5)^ 3 − 4( - 5)^2 + 3( - 5) + 7 \\ \\ f( - 5) = - 125 − 4(25) - 3( 5) + 7 \\ \\ f( - 5) = - 125 − 100 - 15 + 7 \\ \\ f( - 5) =7 - 240 \\ \\ f( - 5) = - 233 \\ \\ \because \: f( - 5) \neq 0 \\ \implies \: remainder\: is\: not\: zero\\ \therefore \: (x + 5) \: is \: not \: a \: factor \: of \: \\ f(x) = x^ 3 − 4x^2 + 3x + 7 \\ [/tex]
According to the table, how many students in the seventh grade bike to school?
Answer:
The anwser is B.) 49
Step-by-step explanation:
If you subtract 79 (the amount of 7th graders riding the bus) from 128 (the total number of 7th graders) you will get 49. Therefore 49 is the answer.
Hope this helps!!
Answer:
yeh its b
Step-by-step explanation:
because the first persons answer was right and well i want the points.
1) 15 = 2W - 5
2) 24 = 2x - 9
9514 1404 393
Answer:
1) W = 10
2) x = 33/2
Step-by-step explanation:
These are 2-step linear equations. Step 1: Add the opposite of the constant on the right. Step 2: Divide by the coefficient of the variable.
__
1) 15 = 2W -5
20 = 2W . . . . . add +5
10 = W . . . . . . . divide by 2
__
2) 24 = 2x -9
33 = 2x . . . . . add +9
33/2 = x . . . . divide by 2
_____
As always, whatever you do to one side of the equation must also be done to the other side. That is, the same number is added to both sides; both sides are divided by the same number.
You spend 3 hours every day practicing the piano. What fraction of the day do you spend practicing the piano? Give your answer in simplest form.
Answer:
1/8th
Step-by-step explanation:
since there are 24 hours in a day
Answer: 1/8
Step-by-step explanation:
a day is 24 hours long. If you spend 3 hours out of 24 hours a day to practice piano it would be 3/24. Then to get it in simpilest form, you divide 3 by 3 and 24 by 3 which would get you the answer 1/8.
Hope i helped have a good rest of your day!!
Which expression is equivalent to (8x – 20) + (-4x + 12)?
A. 12x + 8
B. 4x – 8
C. – 4x – 8
D. – 4x
Answer:
B. 4x-8
Step-by-step explanation:
ASAP PLEASE HELP ME
Answer:
6 would be opposite
Step-by-step explanation:
PLS ANSWER IM DLING MIDTERM RN
Given that triangle GHI is congruent to triangle NOP which of the following statements is FALSE?
GI = NP
Angle G = angle N
O=H
GH = PO
GH=po
That is answer
Yay
4x4 - 6x3 +6x-7
-2x2 + 3
what is the quotient
Answer:
12x
Step-by-step explanation:
Not a quotient because its not division.
math!
POINTS
TODAY
POINTS
THIS WEEK
Hwk #28: DistRateTime
GAME
CREDITS
V. Whitehea
$
$
$
First try was incorrect
Rosa travels 20 miles per hour. How long does it take her to travel 2
miles? Your answer should be in hours, rounded to the nearest tenth.
label required
Х
x² f(x) qx x
✓
(x) x < > TI"
Answer:
it takes her 1/10 of an hour
Step-by-step explanation:
math
I need help
Write a linear inequality to represent the graph
Answer:
y < 1/2x -5
Step-by-step explanation:
1/2 is the slope
-5 is the y intercept
A constant volume of pizza dough is formed into a cylinder with a relatively small height and large radius. The dough is spun and tossed into the air in such a way that the height of the dough decreases as the radius increases, but it retains its cylindrical shape. At time t=k, the height of the dough is 13 inch, the radius of the dough is 12 inches, and the radius of the dough is increasing at a rate of 2 inches per minute.
(a) At time t=k, at what rate is the area of the circular surface of the dough increasing with respect to time? Show the computations that lead to your answer. Indicate units of measure.
(b) At time t=k, at what rate is the height of the dough decreasing with respect to time? Show the computations that lead to your answer. Indicate units of measure. (The volume V of a cylinder with radius r and height h is given by V=πr2h.)
(c) Write an expression for the rate of change of the height of the dough with respect to the radius of the dough in terms of height h and radius r.
Answer:
a) [tex]\frac{dA}{dt} = 48 \pi\frac{in^{2}}{min}[/tex]
b) [tex] \frac{dh}{dt} = - \frac{13}{3} \frac{in}{min}[/tex]
c) [tex]\frac{dh}{dt} = - 2\frac{h}{r} \frac {dr}{dt}[/tex]
Step-by-step explanation:
In order to solve this problem, we must first picture a cylinder of height h and radius r (see attached picture).
a) So, in order to find the rate at which the area of the circular surface of the dough is increasing with respect to time, we need to start by using the are formula for a circle:
[tex]A=\pi r^{2}[/tex]
So, to find the rate of change of the area, we can now take the derivative of this formula with respect to the radius r:
[tex]dA = \pi(2) r dr[/tex]
and divide both sides into dt so we get:
[tex]\frac{dA}{dr} = 2\pi r \frac{dr}{dt}[/tex]
and now we can substitute:
[tex]\frac{dA}{dr} = 2\pi(12in)(2\frac{in}{min})[/tex]
[tex]\frac{dA}{dt} = 48\pi\frac{in^{2}}{min}[/tex]
b) In order to solve part b, we can start with the formula for the volume:
[tex]V=\pi r^{2} h[/tex]
and solve the equation for h, so we get:
[tex]h=\frac{V}{\pi r^{2}}[/tex]
So now we can rewrite the equation so we get:
[tex]h=\frac{V}{\pi}r^{-2}[/tex]
and now we can take its derivative so we get:
[tex]dh=\frac{V}{\pi} (-2) r^{-3} dr[/tex]
we can rewrite the derivative so we get:
[tex]\frac{dh}{dt}=-2\frac{V}{\pi r^{3}}\frac{dr}{dt}[/tex]
we can take the original volume formula and substitute it into our current derivative, so we get:
[tex]\frac{dh}{dt}= -2\frac{\pi r^{2} h}{\pi r^{3}} \frac{dr}{dt}[/tex]
and simplify:
[tex]\frac{dh}{dt} =-2\frac{h}{r} \frac{dr}{dt}[/tex]
so now we can go ahead and substitute the values provided by the problem:
[tex]\frac{dh}{dt} =-2\frac{13in}{12in} (2\frac{in}{min})[/tex]
Which simplifies to:
[tex] \frac{dh}{dt} = - \frac{13}{3} \frac{in}{min}[/tex]
c)
Part c was explained as part of part b where we got the expression for the rate of change of the height of the dough with respect to the radius of the dough in terms of the height h and the radius r:
[tex]\frac{dh}{dt} =-2\frac{h}{r} \frac{dr}{dt}[/tex]
The rate of change of the height of the pizza with respect to (w.r.t.) time
can be found given that the volume of the pizza is constant.
(a) The rate of increase of the surface area with time is 4·π in.²/min(b) The rate at which the height of the dough is decreasing is [tex]\underline{4.\overline 3 \ in./min}[/tex](c) Rate of change the height of the dough with respect to the radius [tex]\dfrac{dh}{dr}[/tex], is [tex]\underline{-2 \cdot \dfrac{h}{r}}[/tex]Reasons:
The height of the dough when t = k is 13 inches
Radius of the dough = 12 inches
Rate at which the radius of the dough is increasing, [tex]\dfrac{dr}{dt}[/tex] = 2 in.²/min
(a) Required: The rate of increase of the surface area with time
Solution:
The circular surface area, A = π·r²
By chain rule of differentiation, we have;
[tex]\dfrac{dA}{dt} = \mathbf{\dfrac{dA}{dr} \times \dfrac{dr}{dt}}[/tex]
[tex]\dfrac{dA}{dt} = \dfrac{d ( \pi \cdot r^2)}{dr} \times \dfrac{dr}{dt} = 2 \cdot \pi \times 2 = 4 \cdot \pi[/tex]
The rate of increase of the surface area with time, [tex]\mathbf{\dfrac{dA}{dt}}[/tex] = 4·π in.²/min.
(b) Required: The rate of decrease of the height with respect to time
The volume of the pizza is constant, given by; V = π·r² ·h
Therefore;
[tex]h = \mathbf{ \dfrac{V}{\pi \cdot r^2}}[/tex]
[tex]\dfrac{dh}{dt} = \dfrac{d \left( \dfrac{V}{\pi \cdot r^2} \right)}{dr} \times \dfrac{dr}{dt} = \dfrac{-2 \cdot V}{\pi \cdot r^3} = \dfrac{-2 \cdot \pi \cdot r^2 \cdot h}{\pi \cdot r^3} \times \dfrac{dr}{dt} = \mathbf{-2 \cdot \dfrac{h}{r} \times \dfrac{dr}{dt}}[/tex]
[tex]\dfrac{dh}{dt} = -2 \cdot \dfrac{h}{r} \times \dfrac{dr}{dt} = -2 \times \dfrac{13}{12} \times 2 = \dfrac{13}{3} = 4. \overline 3[/tex]
The rate at which the height of the dough is decreasing, [tex]\mathbf{\dfrac{dh}{dt}}[/tex]= [tex]\underline{4.\overline 3 \ in./min}[/tex]
(c) Required:]The expression for the rate of change the height of the dough with respect to the radius of the cone.
Solution:
[tex]\dfrac{dh}{dr} = \dfrac{d \left( \dfrac{V}{\pi \cdot r^2} \right)}{dr} = \dfrac{-2 \cdot V}{\pi \cdot r^3} = \dfrac{-2 \cdot \pi \cdot r^2 \cdot h}{\pi \cdot r^3} = -2 \cdot \dfrac{h}{r}[/tex]
[tex]\dfrac{dh}{dr} = \mathbf{ -2 \cdot \dfrac{h}{r}}[/tex]
The rate of change the height of the dough w.r.t. the radius is [tex]\underline{\dfrac{dh}{dr} = -2 \cdot \dfrac{h}{r}}[/tex]
Learn more here:
https://brainly.com/question/20489729
I need help with this
Answer:
24.3470022334
Step-by-step explanation:
Every day after dinner, a child is to put his plate in the sink. Which formula calculates percent of occurrences?
Answer:
Percent of occurrences= (Numbers of behavior/Numbers of opportunities)*100
Step-by-step explanation:
Based on the information given if a child is to put his/her plate in the sink everyday after having dinner the formula that will be use to calculates percent of occurrences is :
Percent of occurrences=( Numbers of behavior/Numbers of opportunities)*100
Where:
Numbers of behavior represent the Numbers of times the plate was put in the sink by child everday
Numbers of opportunities represent the Numbers of dinners the child had everyday
A line is perpendicular to the line given by the equation - 8 = 2y + 3x. What is the slope of the perpendicular line? 3
Answer:
2/3 is the slope of the perpendicular line
Step-by-step explanation:
1) put into slope-intercept form (y=mx+b)
-8=2y+3x
-2y=3x+8
y=-3/2x-4
2) the line is perpendicular so the slope will be opposite and the reciprical of the original slope.
so, because the original was -3/2, the new one is 2/3
on his shelves trenton has 15 biogrophies,15 science fiction books,7 refrence books,and 11 mystery books. find the ratio of biographies to the total number of books
IF YOU ACTUALLY HELP I WILL GIVE BRAINLY!!
Answer:
B: (2, -1)
Step-by-step explanation:
HELP PLEASE 100 points IM BEING TIMED ILL EVEN GIVE A CROWN THING
Which rule describes the composition of transformations that maps ΔABC to ΔA"B"C"?
A.) 90 degree rotation about point 0 composition reflection across the x-axis
B.) Reflection across the x-axis composition 90 degree rotation about point 0
C.) 180 degree rotation about point 0 composition reflection across the x-axis
D.) Reflection across the x-axis composition 180 degree rotation about point 0
Answer: A
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
The guy above me was correct. I got a 99% on my test.
an elevator began at an elevation of 85.5 feet and ascended at a rate of 2.75 feet per second. what was the elevation of the elevator after 8 seconds?
Answer:
107.5
Step-by-step explanation:
8 × 2.75ft = 22ft
22ft + 85.5ft = 107.5ft
Answer:
107.1
Step-by-step explanation:
the elevator is at 85.5 feet.
if the ascending (going up) rate is 2.75 and you want to know how far in 8 seconds, it's an easy process.
1. find the direction your going (up or down)
2. how far? (what rate for this one)
3. multiply said problem (2.75 x 8)
4. get your answer (21.6 ft per 8 seconds)
5. add or subtract to the height you are at now (85.5 ft)
6. you now have your answer! (107.1 ft in the air)
The length of each side of an equilateral triangle is increased by 20%, resulting in triangle ABC. If the length of each side of the original equilateral is decreased by 20%, resulting in triangle DEF, how much greater is the area of triangle ABC than the area of triangle DEF?
Answer: Area of ΔABC is 2.25x the area of ΔDEF.
Step-by-step explanation: Because equilateral triangle has 3 equal sides, area is calculated as
[tex]A=\frac{\sqrt{3} }{4} a^{2}[/tex]
with a as side of the triangle.
Triangle ABC is 20% bigger than the original, which means its side (a₁) measures, compared to the original:
a₁ = 1.2a
Then, its area is
[tex]A_{1}=\frac{\sqrt{3} }{4}(1.2a)^{2}[/tex]
[tex]A_{1}=\frac{\sqrt{3} }{4}1.44a^{2}[/tex]
Triangle DEF is 20% smaller than the original, which means its side is:
a₂ = 0.8a
So, area is
[tex]A_{2}=\frac{\sqrt{3} }{4} (0.8a)^{2}[/tex]
[tex]A_{2}=\frac{\sqrt{3} }{4} 0.64a^{2}[/tex]
Now, comparing areas:
[tex]\frac{A_{1}}{A_{2}}= (\frac{\sqrt{3}.1.44a^{2} }{4})(\frac{4}{\sqrt{3}.0.64a^{2} } )[/tex]
[tex]\frac{A_{1}}{A_{2}} =[/tex] 2.25
The area of ΔABC is 2.25x greater than the area of ΔDEF.
PLEASE HELP!!!
Karl filled up the tank of his truck with 400 liters of fuel and set out to deliver a shipment of bananas to Alaska. The truck consumed 0.8 liters of fuel for each kilometer driven.
Graph the relationship between the amount of fuel remaining in the truck's tank (in liters) and distance driven (in kilometers).
Answer:
you have it almost good. all you have to do is move the dot from (500,80) to (500,0) because by 500 kilometres all 400 liters of fuel has been used.
500*.8=400
Answer:
Step-by-step explanation:
This is the right answer
I screenshot the picture and it shows i got it right
this is it help pls.
Answer:
1/5
Step-by-step explanation:
Hope this helps!
Use the point-slope equation to identify the slope and the coordinates of a point
on the line y - 4 = {(x - 1).
The slope of the line is
A point on the line il
Answer:
A point on the line is m=1/2
A point on the line is (1,4)
Step-by-step explanation:
HELP PLEASE ITS SO HARD IM CRYING PLS HELP
Answer:
I think it might be d
Step-by-step explanation:
Im not completely sure, BUT YOU GOT THIS
Help Please! Solve For Y.
Answer:
i think 7
Step-by-step explanation:
Need help please thank you
Answer:
3
Step-by-step explanation:
RS + ST will equal RT.
So, 2 + 3x must equal 5x.
2+3x = 5x
2 = 2x
x = 1
ST = 3x
ST = 3*(1)
ST = 3
Sarah is making shortbread biscuits. She has: 600g of butter 300g of caster sugar 1kg of plain Klour 500g of cornKlour She has found this list of ingredients for making 8 shortbread biscuits Sarah wants to make as many shortbread biscuits as possible. Work out how many shortbread biscuits Sarah can make.
Answer and explanation:
We are told that Sarah has 600g of butter, 300g of caster sugar, 1kg of plain flour, and 500g of cornflour
We are also told that she found this list of ingredients for making 8 shortbread biscuits. The question isn't clear on whether the ingredients listed above are for the 8 shortbreads, or ingredients for 8 shortbreads were omitted.
We are told Sarah wishes to make as many shortbreads as possible.
To work out how many shortbreads Sarah can make, we need to know the ingredients required for one shortbread(or a number of shortbreads) and ingredients Sarah currently has. The question lists Sarah's ingredients and the number of shortbreads(8) that can be made with them, but doesn't go further than this. Therefore we can conclude that Sarah can only make 8 shortbreads given the amount of ingredients in her possession.
Can someone please explain to me how to do this
Step-by-step explanation:
u should:
7t = t + 48 » 7t - t = 48 » 6t = 48 » t = 8
and another one is:
2u + t + 13 = 10t + u - 44» 2u + 8 + 13 = 80 + u - 44»
» 2u + 21 = u + 36 » 2u - u = 36 - 21 » u = 15
Simplify 7 + (−3). (1 point)
Question 5 options:
Answer:
4
Step-by-step explanation:
7+ (-3)= 4 lol not sure if thats what you wanted but thats what i understood from your question
PLEASE HELP ME WITH THIS!!