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2 years ago

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1.) The grade 6 class harvested 3 44 kg of tomatoes, 53 kg of eggplants and 2 42 kg of green pepper from their "Gulayan sa Paara

lan”. How many kilograms of vegetables did they harvest in all? a. What is asked in the problem? b. What are the given facts? c. What operation will be used? d. What is the number sentence? e. What is the answer?

1 answer:

Zinaida [17]2 years ago

5 0

Answer:

649 kg of vegetables

Step-by-step explanation:

What is asked?

The total number of vegetables planted

The given facts?

$Tomatoes= 344kg$

$Eggplants =53kg$

$Green\ pepper =242kg$

The operation to be used?

The addition operation

The number sentence?

$344 + 53 + 242$

The answer?

$344 + 53 + 242 =639$

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Reading and Writing Decimal Numbers through Ten Thousandths

Vladimir [108]

Answer:

1. Sixteen thousandths 2.Twenty-four Ten-thousandths 3.Eighty-four Ten-thousandths 4. Twenty-six And Thirty-seven Ten-thousandths 5.Nine And Three hundred Sixty-eight Thousandths

8 0

3 years ago

Need help for number 4 please

Marina CMI [18]

Answer:

Step-by-step explanation:

4) ΔSTW ≅ ΔBFN . So, corresponding parts of congruent triangles are congruent.

a) BN = SW d) m∠W = m∠N

BN = 9 cm m∠W = 82°

b) TW = FN e) m∠B = m∠S

TW = 14 cm m∠B = 67°

c) BF = ST f) m∠B + m∠N + m∠F = 180°

BF = 17 cm 67 + 82 + m∠F = 180

149 + m∠F = 180

m∠F = 180 - 149

m∠F = 31°

5) ΔUVW ≅ ΔTSR

UV = TS

12x - 7 = 53

12x = 53+7

12x = 60

x = 60/12

x = 5

UW =TR

3z +14 = 50

3z = 50 - 14

3z = 36

z = 36/3

z = 12

SR =VW

5y - 33 = 57

5y = 57 + 33

5y = 90

y = 90/5

y = 18

7) ΔPHS ≅ ΔCNF

∠C = ∠P

4z - 32 = 36

4z = 36 + 32

4z = 68

z = 68/4

z = 17

∠H = ∠N

6x - 29 = 115

6x = 115 + 29

6x = 144

x = 144/6

x = 24

∠P + ∠H + ∠S = 180 {Angle sum property of triangle}

36 +115 + ∠S = 180

151 + ∠S = 180

∠S = 180 - 151

∠S = 29°

∠F = ∠S

3y - 1 = 29

3y = 29 + 1

3y = 30

y = 30/3

y = 10

8) ΔDEF ≅ ΔJKL

DE = 18 ; EF = 23

DF = 9x - 23

JL= 7x- 11

DF = JL {Corresponding parts of congruent triangles}

9x - 23 = 7x - 11

9x - 7x - 23 = -11

2x - 23 = -11

2x = -11 + 23

2x = 12

x = 12/2

x = 6

JK = DE {Corresponding parts of congruent triangles}

3y - 21 = 18

3y = 18 + 21

3y = 39

y = 39/3

y = 13

4 0

3 years ago

A tank with a capacity of 500 gal originally contains 200 gal of water with 100 lb of salt in the solution. Water containing1 lb

devlian [24]

Answer:

(a) The amount of salt in the tank at any time prior to the instant when the solution begins to overflow is $\left(1-\frac{4000000}{\left(200+t\right)^3}\right)\left(200+t\right)$ .

(b) The concentration (in lbs per gallon) when it is at the point of overflowing is $\frac{121}{125}\:\frac{lb}{gal}$ .

(c) The theoretical limiting concentration if the tank has infinite capacity is $1\:\frac{lb}{gal}$ .

Step-by-step explanation:

This is a mixing problem. In these problems we will start with a substance that is dissolved in a liquid. Liquid will be entering and leaving a holding tank. The liquid entering the tank may or may not contain more of the substance dissolved in it. Liquid leaving the tank will of course contain the substance dissolved in it. If <em>Q(t)</em> gives the amount of the substance dissolved in the liquid in the tank at any time t we want to develop a differential equation that, when solved, will give us an expression for <em>Q(t)</em>.

The main equation that we’ll be using to model this situation is:

Rate of change of <em>Q(t)</em> = Rate at which <em>Q(t)</em> enters the tank – Rate at which <em>Q(t)</em> exits the tank

where,

Rate at which <em>Q(t)</em> enters the tank = (flow rate of liquid entering) x (concentration of substance in liquid entering)

Rate at which <em>Q(t)</em> exits the tank = (flow rate of liquid exiting) x (concentration of substance in liquid exiting)

Let $C$ be the concentration of salt water solution in the tank (in $\frac{lb}{gal}$ ) and $t$ the time (in minutes).

Since the solution being pumped in has concentration $1 \:\frac{lb}{gal}$ and it is being pumped in at a rate of $3 \:\frac{gal}{min}$ , this tells us that the rate of the salt entering the tank is

$1 \:\frac{lb}{gal} \cdot 3 \:\frac{gal}{min}=3\:\frac{lb}{min}$

But this describes the amount of salt entering the system. We need the concentration. To get this, we need to divide the amount of salt entering the tank by the volume of water already in the tank.

$V(t)$ is the volume of brine in the tank at time t. To find it we know that at t = 0 there were 200 gallons, 3 gallons are added and 2 are drained, and the net increase is 1 gallons per second. So,

$V(t)=200+t$

Therefore,

The rate at which $C(t)$ enters the tank is

$\frac{3}{200+t}$

The rate of the amount of salt leaving the tank is

$C\:\frac{lb}{gal} \cdot 2 \:\frac{gal}{min}+C\:\frac{lb}{gal} \cdot 1\:\frac{gal}{min}=3C\:\frac{lb}{min}$

and the rate at which $C(t)$ exits the tank is

$\frac{3C}{200+t}$

Plugging this information in the main equation, our differential equation model is:

$\frac{dC}{dt} =\frac{3}{200+t}-\frac{3C}{200+t}$

Since we are told that the tank starts out with 200 gal of solution, containing 100 lb of salt, the initial concentration is

$\frac{100 \:lb}{200 \:gal} =0.5\frac{\:lb}{\:gal}$

Next, we solve the initial value problem

$\frac{dC}{dt} =\frac{3-3C}{200+t}, \quad C(0)=\frac{1}{2}$

$\frac{dC}{dt} =\frac{3-3C}{200+t}\\\\\frac{dC}{3-3C} =\frac{dt}{200+t} \\\\\int \frac{dC}{3-3C} =\int\frac{dt}{200+t} \\\\-\frac{1}{3}\ln \left|3-3C\right|=\ln \left|200+t\right|+D\\\\$

We solve for C(t)

$C(t)=1+D(200+t)^{-3}$

D is the constant of integration, to find it we use the initial condition $C(0)=\frac{1}{2}$

$C(0)=1+D(200+0)^{-3}\\\frac{1}{2} =1+D(200+0)^{-3}\\D=-4000000$

So the concentration of the solution in the tank at any time t (before the tank overflows) is

$C(t)=1-4000000(200+t)^{-3}$

(a) The amount of salt in the tank at any time prior to the instant when the solution begins to overflow is just the concentration of the solution times its volume

$(1-4000000(200+t)^{-3})(200+t)\\\left(1-\frac{4000000}{\left(200+t\right)^3}\right)\left(200+t\right)$

(b) Since the tank can hold 500 gallons, it will begin to overflow when the volume is exactly 500 gal. We noticed before that the volume of the solution at time t is $V(t)=200+t$ . Solving the equation

$200+t=500\\t=300$

tells us that the tank will begin to overflow at 300 minutes. Thus the concentration at that time is

$C(300)=1-4000000(200+300)^{-3}\\\\C(300)= \frac{121}{125}\:\frac{lb}{gal}$

(c) If the tank had infinite capacity the concentration would then converge to,

$\lim_{t \to \infty} C(t)= \lim_{t \to \infty} 1-4000000\left(200+t\right)^{-3}\\\\\lim _{t\to \infty \:}\left(1\right)-\lim _{t\to \infty \:}\left(4000000\left(200+t\right)^{-3}\right)\\\\1-0\\\\1$

The theoretical limiting concentration if the tank has infinite capacity is $1\:\frac{lb}{gal}$

4 0

3 years ago

Solving systems of equations using substitution p=q+2<br> 4p+3q= -27

GREYUIT [131]

Ok, so you are given the value of P=q+2

The substitution method tells us that we must insert the value we know, into the second equation, 4P+3q= -27

Doing so will give us 4(q+2)+3q= -27

For right now, lets just focus on the first part, 4(q+2)

We can simplify this by distributing(multiplying) the 4 to whats inside the variables.

This will give us 4q+8

now lets add this back to the rest of the equation >>> 4q+8+3q = -27

We can further simplify by adding like terms >>> 7q+8 = -27

subtract the 8 from both sides >>> 7q = -35

now divide both sides by 7 >>> q = -35/7

Therefor q = -5

EDIT*

now that we know q = -5 we can put q into the equation for P !

we know that p=q+2

so lets put q in now >>> p=(-5)+2

and simplify>>> p = -3

I hope this helps:)

6 0

3 years ago

Which of the following statements are not true?

lubasha [3.4K]

That one correct so yes um cause the app said answer must be above 20 characters

6 0

3 years ago