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3 years ago

Jim weighs 30 pounds less than Tom, and together they weigh 210 pounds. Let n = Tom's weight in pounds. How much does Tom weigh?

1 answer:

5 0

First, let's write an equation for the situation.

Jim's weight is 30 pounds less than Tom's, so his weight is:

n - 30

If Tom's and Jim's weights add to 210:

n + (n - 30) = 210

Solve for n:

2n - 30 = 210

2n = 240

n = 120

Tom weighs 120 pounds.

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Which equation can be used to graph the line that passes through (6, 15) and is perpendicular to the graph of y-7=1/2(x+2)

Westkost [7]

Answer:

y = -2x + 27

Step-by-step explanation:

Firstly, we shall need to reform the given line equation;

y-7 = 1/2 ( x + 2)

y - 7 = x/2 + 1

y = x/2 + 1 + 8

y = x/2 + 8

Comparing this with y = mx + c

where m is the slope, then the slope of the line is 1/2

Since the line we are looking for has a slope perpendicular to this line, it means that the product of their slopes is -1

m1 * m2 = -1

1/2 * m2 = -1

m2 = -2

So we want an equation with slope -2 passing through (6,15)

we use the point slope method here;

y-y1 = m(x-x1)

y-15 = -2(x-6)

y-15 = -2x + 12

y= -2x + 12 + 15

y = -2x + 27

6 0

3 years ago

Find all zeros x^3+2x^2+4x+21

dlinn [17]

Answer:

see explanation

Step-by-step explanation:

note when x = - 3

(- 3)³ + 2(- 3)² + 4(- 3) + 21 = - 27 + 18 - 12 + 21 = 0

hence x = - 3 is a zero and (x + 3) is a factor and dividing gives

$\frac{x^3+2x^2+4x+21}{x+3}$ = (x + 3)(x² - x + 7)

For zeros equate to zero

(x + 3)(x² - x + 7) = 0

equate each factor to zero and solve for x

x + 3 = 0 ⇒ x = - 3

x² - x + 7 = 0 ← solve using quadratic formula

x = (1 ± $\sqrt{1-28}$ ) / 2 = (1 ± 3i $\sqrt{3}$ ) / 2

x = $\frac{1}{2}$ ± $\frac{3i\sqrt{3} }{2}$

zeros are x = - 3, x = $\frac{1}{2}$ ± $\frac{3i\sqrt{3} }{2}$

5 0

3 years ago

(a) Find the Riemann sum for f(x) = 4 sin(x), 0 ≤ x ≤ 3π/2, with six terms, taking the sample points to be right endpoints. (Rou

miskamm [114]

Split up the integration interval into 6 subintervals:

$\left[0,\dfrac\pi4\right],\left[\dfrac\pi4,\dfrac\pi2\right],\ldots,\left[\dfrac{5\pi}4,\dfrac{3\pi}2\right]$

where the right endpoints are given by

$r_i=i\dfrac{\frac{3\pi}2-0}6=\dfrac{i\pi}4$

for $1\le i\le6$ . Then we approximate the integral

$\displaystyle\int_0^{3\pi/2}4\sin x\,\mathrm dx$

by the Riemann sum,

$\displaystyle\sum_{i=1}^6f(r_i)\frac{\frac{3\pi}2-0}6=\pi\sum_{i=1}^6\sin\frac{i\pi}4$

$=\pi\left(\dfrac1{\sqrt2}+1+\dfrac1{\sqrt2}+0-\dfrac1{\sqrt2}-1\right)=\dfrac\pi{\sqrt2}\approx\boxed{2.221441}$

Compare to the actual value of the integral, which is exactly 4.

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4 years ago

Can someone help? With the number 4

morpeh [17]

Answer:

whats the problem?

Step-by-step explanation:

3 0

2 years ago

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Can you find the volume for this pls.

padilas [110]

Answer:

Solution given:

base of triangle [b]=10in

height of triangle [h]=12in

length of rectangle [l]=18in

Now

Volume =area of triangle *length=½(10*12)*18

=1080in³

Volume is 1080 cubic inch.

8 0

3 years ago

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