Answer:
5/6+1/8 = 23/24
Step-by-step explanation:
The lowest common denominator here is the smallest denominator that can be divided evenly by both 6 and 8. It is 24. Note that 6 = 2·3 and that 8 = 2·2². We use the factors 2³ and 3 to come up with the LCD 24.
Then 5/6 + 1/8 can be rewritten with this LCD as:
20/24 + 3/24 = 23/24
5/6+1/8 = 23/24
Solve this quadratic equation by factorisation:
2y² + 4y – 30 = 0
my answer is
(2y+6)×(y-5)
2y+6=0 or y-5=0
y=-3 or y=5
is that correct?
Answer:
Y=5 y=-3
Step-by-step explanation:
Two real solutions:
y =(2+√64)/2=1+4= 5.000
or:
y =(2-√64)/2=1-4= -3.000
3^12*(2^x)^2 = 6^12 then x equals to..?
Answer:
x=6
Step-by-step explanation:
Subtract and simplify. 12 3\8 − 9 1\8 =
Answer:
[tex]3\dfrac{1}{4} \ \ or \ \ 3,25[/tex]
Step-by-step explanation:
[tex]\displaystyle12 \frac{3}{8} -9\frac{1}{8} =12-9+\frac{3}{8} -\frac{1}{8} =3+\frac{2}{8} =3\frac{1}{4} \ \ or \ \ 3,25[/tex]
(d). Find the area of the region enclosed by the graphs of f(x)= x³ and g(x)=x²+2x. [Verify your answer by MATHEMATICA and attach the printout of the commands and output (e). Find the area of the region enclosed by the graphs of y = 3/X and y=4-X. [Verify your answer by MATHEMATICA and attach the printout of the commands and output
Answer:
d . 37/12 unit^2.
Step-by-step explanation:
d) First find the points of intersection of the the 2 graphs, by solving them simultaneously:
x^3 = x^2 + 2x
x^3 - x^2 - 2x) = 0
x(x^2 - x - 2) = 0
x(x - 2)(x + 1) = 0
So they intersect at x = -1, x = 0 and x = 2.
Take the area from x = 0 to x = 2)
2 2
Area = ∫ x^2 + 2x dx - ∫ x^3 dx
0 0
2
= [ x^3/3 + x^2 ) - x^4/4]
0
= ((8/3 + 4) - 0) - (16/4 - 0) -
= 8/3 unit^2
Now calculate the area from x = -1 to x = 0.
0
= (x^3/3 + x^2 ) - x^4/4 )
-1
= (( 0 +1/3 - 1) ) - (0 - 1/4)
= 5/12 unit^2
So the total area of the region = 8/3 + 5/12 = 37/12 unit^2.
Solve the Quadratic
2x^2–5x-8=0
Solution 1:
Solution 2:
[tex]2x^2 -5x-8 =0\\\\\implies x = \dfrac{ -(-5) \pm \sqrt{(-5)^2 - 4\cdot 2 \cdot (-8)}}{2 \cdot 2}\\\\\\\implies x = \dfrac{5 \pm \sqrt{89}}{4}\\\\\\\text{Hence}~ x = \dfrac{5 + \sqrt{89}}{4},~~ x = \dfrac{5 - \sqrt{89}}{4}[/tex]
Answer:
[tex]\sf \boxed{\sf x=\frac{5+\sqrt{89}}{4}}[/tex]
[tex]\sf \boxed{\sf x=\frac{5-\sqrt{89}}{4}}[/tex]
✰Step-by-step explanation✰ ⤵[tex]\sf 2x^2-5x-8=0[/tex]
☁ We'll solve this equation using The Quadratic Formula:
[tex]\boxed{\sf \cfrac{-b\pm \sqrt{b^2-4ac}}{2a}}[/tex]
A= 2, b= -5, c= -8
[tex]\sf x=\cfrac{-\left(-5\right)\pm \sqrt{\left(-5\right)^2-4\times \:2\left(-8\right)}}{2\times \:2}[/tex]
[tex]\mapsto \sf \sqrt{\left(-5\right)^2-4\times \:2\left(-8\right)}[/tex]
[tex]**\sf \left(-5\right)^2=5^2[/tex]
[tex]\mapsto \sf \sqrt{5^2+4\times \:2\times \:8}[/tex]
[tex]\mapsto \sf \sqrt{5^2+64}[/tex]
[tex]\mapsto \sf \sqrt{89}[/tex]
______________
[tex]\sf x=\cfrac{-\left(-5\right)\pm \sqrt{89}}{2\times \:2}[/tex]
☁ Now, we'll Separate solutions, first, we'll solve the equation when ± is plus:
[tex]\mapsto \sf \cfrac{-\left(-5\right)+\sqrt{89}}{2\times \:2}[/tex]
☁ Multiply 2*2 =4
[tex]\boxed{\sf \cfrac{5+\sqrt{89}}{4}}[/tex]
_________________
☁ Now solve the equation when ± is minus:
[tex]\mapsto \sf \cfrac{-\left(-5\right)-\sqrt{89}}{2\times \:2}[/tex]
☁ Multiply 2*2 =4
[tex]\boxed{\sf \cfrac{5-\sqrt{89}}{4}}[/tex]
[tex]\sf Solution \:1:\boxed{\sf x=\frac{5+\sqrt{89}}{4}}[/tex]
[tex]\sf Solution \:2:\boxed{\sf x=\frac{5-\sqrt{89}}{4}}[/tex]
☁❅☁❅☁☁❅☁❅☁☁❅☁❅☁❅☁
Learn more: https://brainly.com/question/22286698
BETWEEN WHAT TWO INTEGERS IS THE FIRST ZERO?
Answer:
0 and 1
Step-by-step explanation:
The scale of the graph is not marked, so we assume each grid line represents 1 unit. The leftmost crossing of the x-axis is between 0 and 1.
_____
Additional comment
The other real zero is between 2 and 3. If this is a polynomial function, it will have additional complex zeros.
7 divided by 1946
i need the anwer
A driver travels 120 miles, stops, and then travels ¼ of the distance she has already driven. After stopping again, the driver travels ⅔ of the distance she has already traveled. Now, the entire distance she has driven is 55 miles more than 1 ⅔ of the remaining trip. How many miles does the driver still have to travel?
Answer:
75 miles
Step-by-step explanation:
We know that she has driven 120 miles before the first stop.
Then she drives for 1/4 of the the distance she has already driven (120 miles). One fourth of 120 is 30.
So now, she's driven for 120 + 30 miles, or 150 miles.
She drives for another 2/3 of the distance she's traveled (150 miles). Two thirds of 150 is 100.
So now, she's driven for 150 + 100 miles, or 250 miles.
What we need to find out now is how much of the trip has she traveled.
We know that the entire distance she has driven is 55 miles more than 1 ⅔ of the remaining trip. So, in other words, the distance she has traveled minus 55 is equal to 1 2/3 of the trip.
To put this in an equation:
250 - 55 = 1 2/3t
t = the whole trip
Now, we solve for t.
250 - 55 = 195
1 2/3 = 5/3
so, 195 = 5/3t
t = 325
We subtract what she has already driven to the total to get the remaining distance.
325 - 250 = 75
The final velocity V of an object
Answer:
The final velocity, V, of an object under constant acceleration can be found using the formula V2=v2+2as , where v is the initial velocity in meters per second, a is acceleration in meters per second, and s is the distance in meters.
Today only, a table is being sold at a 33% discount. The sale price is 201.
What was the price yesterday?
I need help... pls.
Answer:
Administer 14 ml, 350mg/125mg=2.8×5ml=14ml
An expression is given.
6x (3x + 11)
Create an equivalent expression with the fewest terms possible.
HELP ASAP!!!!
Equivalent expressions are simply expressions that have the same value, irrespective of their form.
The equivalent expression of [tex]\mathbf{6x(3x + 11)}[/tex] is [tex]\mathbf{18x^2 + 66x}[/tex]
The expression is given as:
[tex]\mathbf{6x(3x + 11)}[/tex]
Start by opening the brackets; i.e. apply distributive property
[tex]\mathbf{6x(3x + 11) = 6x \times 3x + 6x \tiimes 11}[/tex]
Evaluate all products
[tex]\mathbf{6x(3x + 11) = 18x^2 + 66x}[/tex]
The expression cannot be further simplified.
Hence, the equivalent of [tex]\mathbf{6x(3x + 11)}[/tex] is [tex]\mathbf{18x^2 + 66x}[/tex]
Read more about equivalent expressions at:
https://brainly.com/question/15715866
PLEASE HELP WITH THIS ONE QUESTION
Answer:
The graph moved down 5 units
Step-by-step explanation:
Answer:
Step-by-step explanation:
The best way to get an answer to this question is to study the graph you get when you study the result from Desmos, which is a free graphing program.
Notice the way the graph is laid out. If the graph was simply y = x^2 - 6x then the y value for the minimum value would be x = 3 (just like the 2 values you do get) and y = -9
But y = x^2 - 6x + 3 has you moving up 3 units to y = - 6 and y = x^2 - 6x + 8 moves you to y = - 1. Which way are you going? The difference is 5 units and you are moving down because you start at y = x^2 - 6x + 8 and move down to x^2 - 6x + 3.
Without finding minimums (which is a cumbersome process which needs to be done twice) there's no easy way to do this except graphing.
The answer is B.
When four times a number is decreased by 9, the result is 19. What is the number?
Answer:
7
Step-by-step explanation:
Working backwards:
19 + 9 = 28
28/ 4 = 7
Checking work:
7 x 4 = 28
28 - 9 = 19
If point A is located at (-7 , 5) on a coordinate plane, and point B is located at (4 , 5), what is the distance between the two points?
Answer:
[tex]11[/tex]
Step-by-step explanation:
[tex]\sf{Use\: the\: distance\: formula\: to\: determine\: the\: distance\: between\: two\: points.[/tex]
[tex]\sf{Distance=\sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}[/tex]
[tex]\mathrm{Plug\:the\:points}[/tex]
[tex]\sqrt{\left(4-\left(-7\right)\right)^2+\left(5-5\right)^2}[/tex]
[tex](4+7)^2=11^2\\(5-5)^2=0[/tex]
[tex]\sqrt{11^2+0}[/tex]
[tex]11^2+0=11^2\\\sqrt{11^2}[/tex]
[tex]\mathrm{Apply\:radical\:rule:\:}\sqrt[n]{a^n}=a,\:\quad \mathrm{\:assuming\:}a\:\mathrm{is\ greater\ than \:or\ equal\: to \:0}[/tex]
[tex]=11[/tex]
A housepainter mixed 5 gal of blue paint with every 9 gal of yellow paint in order to make a
green paint. Which ratio of gallons of blue paint to gallons of yellow paint will make the same
shade of green paint?
I think any of these would work
10;18
15;28
20;35
Answer:
5:9
Step-by-step explanation:
To Find:
ratio of yellow paint to blue paint to make a particular shade of green.
Solution:
The ratio can be written as 5 to 9, or 5:9
We know that if we mix 5 gallons of blue paint with 9 gallons of yellow paint we get the particular shade of green that we want.
Then the ratio of gallons of blue paint to gallons of yellow paint is 5 to 9, or 5:9
Meaning that for every 5 gallons of blue paint we need 9 of yellow paint.
For the amusement of the guests, some hotels have elevators on the outside of the building. One such hotel is 400 feet high. You are standing by a window 100 feet above the ground and 150 feet away from the hotel, and the elevator descends at a constant speed of 20 ft/sec, starting at time t = 0, where t is time in seconds. Let θ be the angle between the line of your horizon and your line of sight to the elevator. 4 (a) Find a formula for h(t), the elevator's height above the ground as it descends from the top of the hotel. h(t) = (b) Using your answer to part (a), express θ as a function of time t. θ(t) = Find the rate of change of θ with respect to t. dθ dt = (c) The rate of change of θ is a measure of how fast the elevator appears to you to be moving. At what time does the elevator appear to be moving fastest? time = seconds At what height does the elevator appear to be moving fastest?
9514 1404 393
Answer:
a. h(t) = -20t +400
b. θ(t) = arctan(2 -2/15t); dθ/dt = -30/(1125 -120t +4t^2)
c. 15 seconds; 100 ft
Step-by-step explanation:
a. The initial height of the elevator is 400 ft. The rate of change of height is -20 ft/s, so the height equation can be ...
h(t) = -20t +400
__
b. The tangent of the angle above the line of sight is "opposite"/"adjacent":
tan(θ) = (h(t) -100)/(150) = -2/15t +2
θ(t) = arctan(2 -2/15t) . . . . radians
The derivative of the angle function is ...
dθ/dt = 1/(1+(2 -2/15t)^2)(-2/15)
dθ/dt = -30/(1125 -120t +4t^2)
__
c. The value of dθ/dt will have a peak where the denominator has a minimum, at t = -(-120)/2(4)) = 15. (The quadratic vertex coordinate is t=-b/(2a).)
The elevator appears to be moving fastest at t=15 seconds.
The height at that time is ...
h(15) = 400 -20(15) = 100
The elevator appears to be moving fastest when it is at eye level, 100 ft above the ground.
help me with math and ill mark brainliest
Answer:
I and II
Step-by-step explanation:
All trapezoids have a midsegment. The base angles of isosceles trapezoids are always congruent. Because the top and bottom side are parallel, the same side interior angles are supplementary not complementary.
show how to find slope of a line that passes through the points in the table
Answer:
Step-by-step explanation:
here you go m = (y2-y1)/(x2-x1)
= (11-(-9))/(3-(-1))
= 20/4
= 5
Find (a) the axis of symmetry and (b) the vertex of the graph of the function.
Ax) = 4x² - 8x
Step-by-step explanation:
I am not sure, what is the level of math for you currently.
do you do differentiation and derivatives already ?
because that is how I find "extreme points" and "turning points" of a function right away.
the vertex is the turning point for a quadratic parabola.
that means the point where the slope (= the first derivative) of the function is 0.
and that is also where the axis of symmetry is.
8x - 8 = 0
8x = 8
x = 1 (axis of symmetry).
y = 4×1² - 8×1 = 4 - 8 = -4
so, the vertex is (1, -4)
in case you don't understand derivatives yet, there is a shortcut for this for quadratic equations (fyi - in fact, the generic result of the first derivative) :
y = ax² + bx + c
the x value for the axis is then
x = -b/(2a)
in our case
a = 4
b = -8
x = - -8/8 = 8/8 = 1
and then y is calculated as above.
The graph of linear function fpasses through the point (1, -8) and has a slope of 2.
What is the zero of f?
-5
2
5
-2
Answer:
5
Step-by-step explanation:
set up point slope form
y + 8 = 2(x-1)
set y to zero
0+8=2(x-1)
8=2x-2
10= 2x
x = 5
How much is 2+10.
Please help me i dont know
Will give brainliest
Answer: 12
2 + 10
12
:)
Answer: 12
Step-by-step explanation: just add 2 to 10
dear and kind community I have a question that urges me which is the following, let's imagine that there are 73 million coins that can be fractioned to a hexadecimal value of a minimum unit of 0.00000001 and would need 0.99999998 to reach a full unit of the coin 1, my question is what would happen if instead of this minimum hexadecimal number of coin 0.00000001 was a hundred 100=1? how many coins would exist if before it was 73 million with hexadecimals (0,00000001) now with a hundred it would be equivalent to one unit (1=100) how many coin units would there be? if now each unit would only be divided in hundreds and not in hexadecimals? thanks in advance to the one who responds.
Answer:
that have no answer so sorry
Determine the greatest common factor of the numbers 24 and 56
Answer:
8
Step-by-step explanation:
yw :)
Alan will spend at most $30 on gifts. So far, he has spent $19. What are the possible additional amounts he will spend?
Answer:
$11
Step-by-step explanation:
This is because If you subtract 19 from 30 your answer will be 19.
How is solving for speed similar to solving for time
Answer: The both involve writing a rate
I hope this helps i would appreciate brainliest if possible :)
3. Rewrite the statement, "A dog is a puppy if and only if it is young," as a conditional and its converse.
O A. Conditional: A dog is a puppy. Converse: A dog is young.
O B. Conditional: A puppy is a dog. Converse: A puppy is young.
OC. Conditional: If a puppy is young, then it is a dog. Converse: If a puppy is a dog, then it is young.
O D. Conditional: If a dog is young, then it is a puppy. Converse: If a dog is a puppy, then it is young.
Answer:
I think the answer would be A
help me pls help me
Answer:
Well I’m not sure what Answers do you want
Step-by-step explanation:
Solve the following system of equations:y=x2−4x+3 y=2x−2
[tex]y = 2x -2 ~~~~.....(i) \\\\y = x^2 -4 x +3 ~~~~ .....(ii) \\\\\\x^2-4x +3 = 2x -2\\\\\implies x^2 -4x -2x +3 +2 =0\\\\\implies x^2 -6x +5 =0\\\\\implies x^2 -5x -x +5 =0\\\\\implies x(x-5) -(x-5) =0\\\\\implies(x-5)(x-1) =0\\\\\implies x = 5 ~~ \text{or}~~ x = 1 \\\\\\\text{Substitute x = 1 in equation (i):}\\\\y = 2 -2 =0\\\\ \text{Substitute x = 5 in equation (i):}\\\\\\y = 2(5) -2 = 10 -2 =8 \\\\\text{Hence,}~~ (x,y) = (1,0) ~ \text{and} ~ (x,y) = (5,8)[/tex]
Two numbers have a sum of 18. Their product is 72. Find the numbers
Answer:
Step-by-step explanation:
x + y = 18
y = 18 - x
xy = 72
x(18 - x) = 72
-x² + 18x = 72
0 = 72 - 18x + x²
x = (18 ± √(18² - 4(1)(72))) / (2(1))
x = (18 ± 6)/2
x = 12
x = 6