Answer:
4x² - 24x + 20 = 0
Step-by-step explanation:
a(1)² + b(1) + 20 = 0
a(5)² + b(5) + 20 = 0
a + b = - 20 ⇒ b = - a - 20 ...... (1)
25a + 5b = - 20 .......... (2)
(1) -----> (2)
25a + 5( - a - 20) = - 20
20a - 100 = - 20 ⇒ a = 4
4 + b = - 20 ⇒ b = - 24
4x² - 24x + 20 = 0
Greg buys 60 garden plants at a cost price of $2.00 each to sell in his shop. He sells 25 of them at the profit of 75% and 18 of them at the profit of 35%. He sells the rest of the plants for 4/5 of the cost price calculate the profit or loss he makes from selling 60 plants stating if it is a profit or loss
Answer:
$43.30 profitStep-by-step explanation:
Total cost of plant:
60*2 = 120Greg makes total of:
25*(2 + 0.75*2) + 18*(2 + 0.35*2) + (60 - 25 - 18)*2*4/5 = 163.3Since Greg mare than cost, he has a profit and the amount is:
163.3 - 120 = 43.3-10ab(13c) what is the answer
Answer:
Answer:[tex]13c = 65 \ \ c = \frac{65}{13} \ \ c = 5[/tex] More
What is the radius of the circle: (x+1)^2+(y-12)^2=25
1. (-1, 12)
2. 5
3. 25
4. (1, -12)
Answer:
radius = 5
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
Here r² = 25 ( take the square root of both sides )
r = [tex]\sqrt{25}[/tex] = 5
(cos2a *cos 4a+ sin 2a*sin 4a)/sin4a
Answer:
Step-by-step explanation:
(cos 4a*cos 2a+sin 4a*sin 2a)/sin 4a
=[cos (4a-2a)]/sin 4a
=(cos 2a)/sin 4a
=(cos 2a) /(2 sin 2a cos 2a)
=1/(2 sin 2a)
=1/2 csc 2a
To solve the equation t? - t = 12 by factoring, you would use
t(t - 1) = 12
Ott - 1) - 12 = 0
(t - 4)(t + 3) = 0
Answer:
it is what it is
Step-by-step explanation:
The point-slope form of the equation of a line that passes through points (8, 4) and (0, 2) is y - 4 = - (x - 8). What is
the slope-intercept form of the equation for this line?
O y=1/4x - 12
O y= 1/4x-4
O y= 1/4x +2
O y=1/4x+6
A farmer in China discovers a mammal
hide that contains 71% of its original
amount of C-14.
N = Noekt
No = inital amount of C-14 (at time
t = 0)
N = amount of C-14 at time t
k = 0.0001
t = time, in years
Answer:
Step-by-step explanation:
I'm assuming you're looking for the age of the mammal hide, since there's no question here, but there's also nothing else to solve for. Remember a few things before we move on. First, if we are not told the initial amount with which we start, we have to assume that it's 100%. Second, remember that natural log and e are inverses of each other so they eliminate each other in application. Now to set up the problem. It looks like this:
[tex]71=100e^{-.0001t}[/tex] and begin by dividing both sides by 100 to get
[tex].71=e^{-.0001t}[/tex] and take the natural log of both sides. The other important thing to remember about the rules for logs and natural logs is that when you take the natural log of something, you are "allowed" to move the exponent down out front, which is why we do this. We cannot currently solve for t when it's stuck up there where it is right now. Taking the natural log allows us to bring that exponent down AND eliminate both the natural log and the e at the same time:
ln(.71) = -.0001t and we divide to solve for t:
[tex]\frac{ln(.71)}{-.0001}=t[/tex] and
[tex]\frac{-.3424903089}{-.0001}=t[/tex] so
t = 3424.9 years, or rounded, 3425 years.
Express 600g as a ratio of 1kg
please show working.
3:5
Step-by-step explanation:
change the kilogram into gram and then divide it
Answer:
3 : 5
Step-by-step explanation:
The quantities must have the same units
1 Kg = 1000 g , then
600 : 1000 ( divide both parts by 200 )
= 3 : 5 ← in simplest form
Which graphs are the graphs of even functions?
HELP ASAP
Answer:
Step-by-step explanation:
Even functions have symmetry about the y-axis, so the graphs of even functions are the bottom 2.
Hhheeelllpppppppplllllzzzz
Answer:
D.
Step-by-step explanation:
Because it's shaded above both lines, both equations need a 'y >'
pls help w explanation!!
A town with a population of 5,000 is being divided
into two voting districts: District X and District Y.
The populations of the two districts must differ by no
more than 500 people. Which of the following
systems represents all possible values for the
population x of District X and the population y of
District Y?
A) x-y ≤ 500 and x+y =5,000 B) x-y =500 and x+y ≤ 5,000 C) -500 ≤ x - y ≤ 500 and x+ y =5,000 D) -250 ≤ x - y ≤ 250 and x + y = 5,000
Answer:
A is the Answer
Step-by-step explanation:
Since the population is being split up into 2 divisions out of 5,000.
This means District X and Y must add up 5000.
[tex]x + y = 5000[/tex]
District X and Y must differ no more than 500 people.
So this means that X and Y total people difference cannot be over 500 people. So the equation for this is
[tex]x - y \leqslant 500[/tex]
A shows this so A is the answer.
Which represents f(x)=g
help it’s easy but yh still need help lol
Answer:
14 students walk
Step-by-step explanation:
40 total
22 girls
18 boys - 7 boys who cycle = 11 boys - 6 who take the bus. That leaves 5 boys who walk.
9 girls walk
5 + 9 = 14 total.
a rectangle consists of two identical squares with a common side. The perimeter of the rectangle is 27 inches. Find its area
Answer:
40.5 square inches
Step-by-step explanation:
Rectangle consists of two identical squares.
So, if the sides of square = x,
Then, Width of rectangle = x &
Length of rectangle = x +x = 2x
Perimeter of rectangle = 27 inches
2*(length + width) = 27
2*( 2x + x) = 27 {Combine like terms]
2* 3x = 27
6x= 27 {Divide both sides by 6}
x = 27/6
x = 4.5
Width = x = 4.5 inches
Length = 2x = 2*4.5 = 9 inches
Area of rectangle = length *width
= 4.5 *9
= 40.5 square inches
Answer:
40.5
Step-by-step explanation:
Ion kno this help pls?????????????
Answer:
[tex]2 {x}^{2} - x - 1 \\ 2 {x}^{2} - (2 - 1)x - 1 \\ 2 {x}^{2} + 2x - 1x - 1 \\ 2x(x + 1) - 1(x + 1) \\ (2x - 1)(x + 1)[/tex]
Ben uses a compass and a straightedige to bisect angle PQR, as shown below.
B
Wie statement beste wy Ben uses the cate with to draw Som there?
Answer:
The answer is <AQS = BQS when AS=BQ and AQ=BQ
Step-by-step explanation:
Find the average rate of change of g(x)=-2x^3-5 from x=-4 to x=1
Answer:
26
Step-by-step explanation:
We have the average rate of change on the interval [a,b] as
f(b)-f(a)/(b-a)
b = 1 and a = -4
f(b) = f(1) = -2(1)^3 -5 = -2-5 = -7
f(a) = f(-4) = -2(-4)^3 -5 = 128 -5 = 123
so we have;
(123 + 7)/(1+4) = 130/5 = 26
maths questions on coordinate geomery
Answer:
:
Example Question #1:
Step-by-step explanation:
Which of the following is the equation of a line that is parallel to the line 4x – y = 22 and passes through the origin?
Possible Answers:
4x – y = 0
(1/4)x + y = 0
4x + 8y = 0
4x = 8y
y – 4x = 22
Correct answer:
4x – y = 0
Explanation:
We start by rearranging the equation into the form y = mx + b (where m is the slope and b is the y intercept); y = 4x – 22
Now we know the slope is 4 and so the equation we are looking for must have the m = 4 because the lines are parallel. We are also told that the equation must pass through the origin; this means that b = 0.
In 4x – y = 0 we can rearrange to get y = 4x. This fulfills both requirements.
', .
i really need someone’s help on this one asap.
Answer:
(3,-19)
Step-by-step explanation:
To find the approximation where both functions equal, find where both lines intersect at. Both lines intersect in the Fourth Quadrant so The first 2 are wrong.
The y coordinate is lesser than -10 so the 4th one is wrong.
The answer is (3,-19)
Explanation:
The solution to f(x) = g(x) is where the f(x) and g(x) curves cross, aka the intersection point.
Based on the graph alone, it's a bit tricky to tell where they cross. Luckily, your teacher gave you multiple choices to pick from. We can rule out choices A and B since x < 0 here, but the x coordinate of the intersection is positive.
Choice D can be ruled out because the intersection point has a y coordinate such that -20 < y < -15. It looks like y is much closer to -20 than it is to -10. So there's no way to have y = -8 happen.
The only thing left is choice C. It appears that the intersection point could be (3,-19).
x+3=5 . Find x in the given equation
Answer:
2
Step-by-step explanation:
x + 3 = 5
x = 5 - 3
x = 2
Therefore, x=2 in the given equation
Answer:
2
Step-by-step explanation:
x+3=5
x=5-3
x=2
Hope it helps
verify that a÷(b+c)#(a÷b)+(a÷c) for each of the following values of a=6,b=5 and c=7
Answer:
[tex]a \div (b + c) = (a \div b) + (a \div c) \\ 6 \div (5 + 7) = (6 \div 5) + (6 \div 7) \\ 0.5 = 1.2 + 0.86 \\ 0.5 = 2.06[/tex]
A pair of linear equations is shown
y=-3x5
y=x+2
Which of the following statements best explains the steps to solve the pair of equations graphically?
on a graph, find the point of intersection stwo lines; the first line has y-intercept - 5 and slope - -3, and the second line has y-intercept = 2 and slope - 1.
On a graph, find the point of intersection of two lines, the first line has y-intercept -3 and slope - 5, and the second line has y-intercept - 1 and slope - 2.
On a graph, find the point of intersection of two lines, the first line has y-intercept -- and slope - 3, and the second line has y-intercept = -2 and slope --1
On a graph, find the point of intersection of two lines; the first line has y-intercept = 3 and slope -5, and the second line has y-intercept -1 and slope --2.
Answer:
y=-3×5
so'n
y=-15ans
another has no number only one number 2 alphabets
EXERCISE 81 Solve each of the following word problems: 1) A triangular shaped roof is 4 metres in all sides. What is its perimeter
Answer:
12 m/metersStep-by-step explanation:
3 sides= triangle
so.. 4m+4m+4m= 12 meters
Help!!
Marta is solving the equation S = 2πrh + 2πr2 for h. Which should be the result?
StartFraction S Over 2 pi r EndFraction equals h. – r = h
StartFraction S minus r Over 2 pi r EndFraction equals h. = h
S – S minus StartFraction r Over 2 pi EndFraction equals h. = h
S – S minus StartFraction 2 pi Over r EndFraction equals h. = h
Answer:
(S-2πr^2)/ 2πr = h
Step-by-step explanation:
S = 2πrh + 2πr^2
Subtract 2 pi r^2 from each side
S-2πr^2 = 2πrh + 2πr^2 -2πr^2
S-2πr^2 = 2πrh
Divide each side by 2 pi r
(S-2πr^2)/ 2πr = 2πrh/2πr
(S-2πr^2)/ 2πr = h
It is given that,
→ S = 2πrh + 2πr²
Now subtract 2πr² from the both sides,
→ S - 2πr² = 2πrh + 2πr² - 2πr²
→ S - 2πr² = 2πrh
Then divide both sides by 2πr,
→ (S-2πr²)/2πr = 2πrh/2πr
→ (S-2πr²)/2πr = h
Hence, (S-2πr²)/2πr = h is the result.
Write the number in standard notation. 9.07 x 10−2
Answer:
Yeah, so that is right, just put it into a formula.
[tex]9.07*10x^{-2}[/tex]
find missing side of triangle, help!
Answer:
A √202km
Step-by-step explanation:
x²=11²-9²
x²=121-81
x²=202
√x²=√202
x=√202
The temperature of a chemical solution is originally 21^\circ\text{C}21 ∘ C21, degrees, start text, C, end text. A chemist heats the solution at a constant rate, and the temperature of the solution is 75^\circ\text{C}75 ∘ C75, degrees, start text, C, end text after 121212 minutes of heating. The temperature, TTT, of the solution in ^\circ\text{C} ∘ Cdegrees, start text, C, end text is a function of xxx, the heating time in minutes. Write the function's formula. T=
Answer:
T(x) = 21 + 4.5x
Step-by-step explanation:
Given :
Original temperature = 21°C
Final temperature = 75°C
Time, x = 12 minutes
The temperature, T as a function of x, heating time in minutes :
We need to obtain the constant heating rate per minute :
Final temperature = initial temperature + (constant rate change,△t * time)
75 = 21 + 12△t
75 - 21 = 12 △t
54 = 12 △t
△t = 54 / 12
△t = 4.5°C
Hence, temperature change is 4.5°C per minute.
Hence,
T(x) = 21 + 4.5x
Answer:
T= 21+4.5x
Step-by-step explanation:
I got it right on Khan Academy
PLEASE MARK BRAINLIEST
PLZ HELP WILL GIVE BRAINLIEST
(sat prep) For the figure, which of the following is true?
I m∠1+m∠2=m∠6+m∠5 m
II∠1+m∠3=m∠6+m∠4
III m∠1+m∠3+ m∠6=m∠2+m∠4+m∠5
A I only
B I and II only
C II only
D II and III only
what is the value of x?
When a pair of parallel lines is intersected by a transversal, then
Interior opposite angles are equal.
So, (3x + 4)° = 115°
=> 3x + 4 = 115
=> 3x = 115 - 4
=> 3x = 111
=> x = 111/3
=> x = 37
Answer:
37
Step-by-step explanation:
So, if you got two parallel line, which are crossed by another line, the conterminal angles are gonna be as big as each other.
what we get outta this explanation is
3X+4=115===> 3X=111===> X=37
What is the value of this exspession when c=-4 and d=-10 1/4(c^3+d^2)
Answer:
2
Step-by-step explanation:
1/4(-4×3 + 10×2)
1/4(-12 + 20)
THERE ARE 2 WAYS YOU COULD SOLVE THIS!
1. 1/4( -12) + 1/4( 20) = -3 + 5 = 2
2. 1/4 ( -12+20) = 1/4(8) = 2
Answer:
[tex]9[/tex]
Step-by-step explanation:
Given:-
Expression: [tex]\frac{1}{4} (c^3+d^2)[/tex]
Value of c = [tex]-4[/tex]
Value of d = [tex]-10[/tex]
Solution:-
Add the given values in the expression, writing them inside the bracket:
[tex]\frac{1}{4} ((-4)^3+(-10)^2)[/tex]
[tex](\frac{1}{4}) ((-4)^3)+(\frac{1}{4} )((-10)^2)[/tex]
[tex]-16+25[/tex]
[tex]9[/tex]
