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2 years ago

The straight line ℓ is perpendicular to the line y + 2x = 9 and passes through the point p(4, 3). find the x-intercept of ℓ.

1 answer:

8 0

The slope of the line l is the opposite reciprocal of y+2x=9. Rearranged the equation to y=9-2x and we get a slope of -2. The opposite reciprocal of -2 is 1/2.

y-y=m(x-x)
y-3=.5(x-4)
y=.5x+1

At the x-intercept, y=0, so
0=.5x+1
-1=.5x
x=-2

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18 cajas de manzanas y peras fueron llevadas a la escuela. Las peras trajeron 210 kg en 6 cajas. ¿Cuántos kilos de manzanas fuer

Katyanochek1 [597]

Answer:

504 kilos de manzanas fueron llevados a la escuela.

Step-by-step explanation:

Sean $x$ , $y$ la cantidad de cajas de manzanas y peras, respectivamente. De acuerdo con el enunciado, tenemos el siguiente sistema de ecuaciones:

Total de cajas

$x+y = 18$ (1)

Masa de cada caja de peras

$y\cdot m_{P} = 210$ (2)

$y = 6$ (3)

Masa de caja de manzanas

$m_{M} = m_{P}+7$ (4)

De (2) en (3), tenemos que la masa de cada caja de peras es:

$m_{P} = 35\,kg$

Por (4), encontramos que la masa de cada caja de manzanas es:

$m_{M} = 35\,kg+7\,kg$

$m_{M} = 42\,kg$

Finalmente, de (1) tenemos la cantidad de cajas de manzana:

$x = 18-y$

$x = 12$

La cantidad de kilos de manzanas llevada a la escuela se obtiene al multiplicar la cantidad de cajas de manzana por la masa de cada caja:

$M = (12)\cdot (42\,kg)$

$M = 504\,kg$

504 kilos de manzanas fueron llevados a la escuela.

7 0

2 years ago

Please help if your awake lol ugh it’s a question check the picture :)

ladessa [460]

I really hope that helps cause I went all out and best of wishes!!

8 0

2 years ago

Add the equations.<br>2x-3y = -1<br>+ 3x + 3y= 26<br><br>

hichkok12 [17]

Answer:

The answer in the procedure

Step-by-step explanation:

we have

2x-3y=-1 ----> equation A

3x+3y=26 --> equation B

Solve the system by elimination

Adds equation A and equation B

2x-3y=-1

3x+3y=26

----------------

2x+3x=-1+26

5x=25

x=25/5

x=5

Find the value of y

substitute the value of x in equation A or equation B and solve for y

2(5)-3y=-1

10-3y=-1

3y=10+1

y=11/3

8 0

2 years ago

Match the answer with the question

vlada-n [284]

Answer:

18219

Step-by-step explanation:

7 0

2 years ago

HELP ME PLEASE

solmaris [256]

Answer:

The initial mass of the sample was 16 mg.

The mass after 5 weeks will be about 0.0372 mg.

Step-by-step explanation:

We can write an exponential function to model the situation.

Let the initial amount be A. The standard exponential function is given by:

$P(t)=A(r)^t$

Where r is the rate of growth/decay.

Since the half-life of Palladium-100 is four days, r = 1/2. We will also substitute t/4 for t to to represent one cycle every four days. Therefore:

$\displaystyle P(t)=A\Big(\frac{1}{2}\Big)^{t/4}$

After 12 days, a sample of Palladium-100 has been reduced to a mass of two milligrams.

Therefore, when x = 12, P(x) = 2. By substitution:

$\displaystyle 2=A\Big(\frac{1}{2}\Big)^{12/4}$

Solve for A. Simplify:

$\displaystyle 2=A\Big(\frac{1}{2}\Big)^3$

Simplify:

$\displaystyle 2=A\Big(\frac{1}{8}\Big)$

Thus, the initial mass of the sample was:

$A=16\text{ mg}$

5 weeks is equivalent to 35 days. Therefore, we can find P(35):

$\displaystyle P(35)=16\Big(\frac{1}{2}\Big)^{35/4}\approx0.0372\text{ mg}$

About 0.0372 mg will be left of the original 16 mg sample after 5 weeks.

5 0

2 years ago