Work out 5/8 of 10 litres

Answers

Answer 1

Answer: 5/8 of 10 litres is 6.25 litre
because 5/8=0,625
0,625 * 10 = 6,25 :))

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True or false the image of the point (-8,-5) under a reflection across the y-axis is (8,-5)

Answers

False. A reflection over the y-axis would result in: (-8,5)

The sum of x and 4 is greater than the difference of 2x and 3. Find x

Answers

Answer:

3 i think

Step-by-step explanation:

add 3 and 4 =7

multiply 2 and 3= 6 and subtract 3 = 3

How do you evaluate expressions?

Answers

To evaluate an algebraic expression, you have to substitute a number for each variable and perform the arithmetic operations. In the example above, the variable x is equal to 6 since 6 + 6 = 12. If we know the value of our variables, we can replace the variables with their values and then evaluate the expression.

A scientist needs 10 litera of a 20% acid solution for an experiment but she has only 5% solution and a 40% solution. To the nearest tenth of a liter, how many liters of the 5% and the 40% solutions should she mix to get the solution she needs?

Answers

x = liters of 5% solution

y = liters of 40% solution

The scientist wants 10 L total of a 20% solution, so

x + y = 10

0.05 x + 0.40 y = 0.20 (x + y) = 2

From the first equation,

y = 10 - x

Substitute this into the second equation and solve for x :

0.05 x + 0.40 (10 - x) = 2

0.05 x + 4 - 0.40 x = 2

2 = 0.35 x

x ≈ 5.714 L

Solve for y :

y = 10 - x

y ≈ 4.286 L

the length of a rectangle is 3 meters less than twice the width if the area is 104 square meters find the length

Answers

x-width
2x-3-length

A=lxw
104=(2x-3)(x)
104=2x^2-3x
52=x^2-3/2(x)
52+9/16=x^2-3/2(x)+9/16
841/16=(x-3/4)^2
29/4=x-3/4
x=32/4 or 8

length is 2(8)-3 which is 13 and width is 8

Answer:

l = 13 m

Step-by-step explanation:

Let's call the width of the rectangle x. Then we can form an expression for the length of the rectangle: 2x - 3

Now we need to form an equation for the area of the rectangle and solve it:

x(2x - 3) = 104

2x² - 3x = 104

2x² - 3x - 104 = 0 - now we need to factorize the equation

(2x + 13)(x - 8) = 0

Now we can say that x = 8 or x = -6.

Because we cannot have a negative length, x = 8 m.

Now we can workout the length using the expression that we formed at the beginning:

2x - 3 = l

2(8) - 3 = l

l = 16 - 3

l = 13 m

Find the x-intercept of the parabola with vertex (1,-13) and y-intercept (0,-11).

Answers

Standard form of equation for a parabola: y=A(x-h)^2+k, (h,k)=(x,y) coordinates of vertex
using given coordinates of vertex:
y=A(x-1)^2-13
using given coordinates of y-intercept:
-11=A(0-1)^2-13
A=2
Equation of parabola: y=2(x-1)^2-13
x-intercepts

set y=0
0=2(x-1)^2-13
2(x-1)^2=13
(x-1)^2=13/2
x-1=±√(13/2)
x=1±√(13

1. find equation

general solutions are:
$y = a x^(2) +bx +c \n \n (dy)/(dx) = 2ax +b$

for P(0,-11)

$-11 = 0a + 0b +c$ ⇒ $c = -11$

for p(1,-13)
$-13 = 1a + 1b -11 \n a+b = -2$

and

$0 = 2a + b \n b = -2a$

solve for a and b:
$a - 2a = -2 \n a = 2 \n b = -4$

the total equation is now:

$y = 2 x^(2) -4x -11$

To find the x-intercept set y=0 and solve for x

$0 = 2 x^(2) -4x-11$

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