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3 years ago

Mon wants to make 5 lbs of the sugar syrup. How much water and how much sugar does he need to make 50% syrup?

Mathematics

1 answer:

zalisa [80]3 years ago

6 0

He needs 2.5 lbs of sugar and 2.5 lbs of water

since 2.5 if 50% of 5 then thats how much sugar he needs.

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An extremely large sink hole has opened up in a field just outside of the city limits. It is difficult to measure across the sin

abruzzese [7]

Triangle ABC and triangle DCE are congruent, so line DE = line AB

Use the cosine rule to find angle ACB
$52.2^{2}= 50^{2}+ 70^{2}-(2*50*70*cos(ACB))$
$2724.84=7400-(7000cos(ACB))$
$2724.84-7400=-7000cos(ACB)$
$-4675.16=-7000cos(ACB)$
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$Angle ACB= cos^{-1} ( \frac{4675.16}{7000})$
Angle ACB = 48.1°

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3 years ago

A rectangle has a height of 5x and a width of x + 2. Express the area of the entire rectangle.

o-na [289]

Rectangle Area = length • width

5x • (x + 2) = area

(5x^2 + 10x) is the area, with no further ways to simplify.

8 0

3 years ago

Find the equation of the form y=ax²+bx+c whose graph passes through the points (1,6), (3, 20), and (−2,15).

Korolek [52]

Answer:

$c = \dfrac{25}{4}$

$b = \dfrac{-13}{8}$

$a = \dfrac{11}{8}$

Step-by-step explanation:

given ,

equation y=ax²+bx+c

passing through points (1,6), (3, 20), and (−2,15).

then these points will satisfy the equation

at (1,6)

y = a x²+b x+c

6 = a(1)² + b (1) + c

a + b + c = 6------(1)

at (3 , 20)

y = a x²+b x+c

20 = a(3)² + b (3) + c

9 a + 3 b + c = 20------(2)

at (−2,15)

y = a x²+b x+c

15 = a(-2)² + b (-2) + c

4 a -2 b + c = 15------(3)

solving equation (1),(2) and (3)

a = 6 - b - c

9 (6 - b - c)+ 3 b + c = 20

6 b + 7 c = 34-------(4)

4 (6 - b - c) -2 b + c = 15

2 b + c = 3----------(5)

on solving equation (4) and (5)

$c = \dfrac{25}{4}$

$b = \dfrac{-13}{8}$

$a = \dfrac{11}{8}$

6 0

3 years ago

Which of the following is a quadratic function?

sp2606 [1]

A is the answer, because the highest exponent is 2.

<u>quadratic</u>

A's expression foiled would be 2x^2 + x - 6

B's expression foiled would be 3x - 12, where the exponent on x is only 1.

D's expression foiled would be x^3 - x^2 - 12x, where the exponent on x is 3.

6 0

3 years ago

Determine what type of model best fits the given situation:

kondaur [170]

Answer:

Ok, i will suppose the situation that:

The rocket has a constant speed S (So the acceleration of the rocket is equal in magnitude, but opposite in direction, to the gravitational acceleration)

Here we can remember that:

Velocity = distance/time.

Then if the distance is the height of the rocket, we can write this as:

H = velocity*time

h = S*t

This is a linear model that represents the height of the rocket as a function of time.

Case 2:

The rocket is fired with an initial velocity v0, but no acceleration:

In this case the only acceleration acting on the rocket is the gravitatonal acceleration pulling the rocket down, so the acceleration is:

a = -g

To get the velocity as a function of time, we should integrate:

a = -g*t + v0

To get the height as a function of time, we integrate again:

h(t) = (-g/2)*t^2 + v0*t + p0

Where p0 is the initial position of te rocket, but the rocket starts at the ground, so p0 = 0m.

The height as a function of time is:

h(t) = (-g/2)*t^2 + v0*t

This is a quadratic equation.

8 0

3 years ago