The sum of two consecutive integers is 141. Find the integers.

Find the tangent vector T to the given line (t) = 〈 x(t), y(t), z(t) 〉, with parametric equations,

x(t) = -1 + 3t

y(t) = 6 - 3t

z(t) = 3 + 7t

by differentiating (t) component-wise:

T = '(t) = 〈 dx(t)/dt, dy(t)/dt, dz(t)/dt 〉

T = 〈3, -3, 7〉

Scale T by any real number t to get the line through the origin (when t = 0) and the point (3, -3, 7) (when t = 1), which of course runs parallel to '(t). This gives the vector tT. Translate this by any vector v = 〈a, b, c〉 to force this line to pass through the point (a, b, c) instead of the origin, while still remaining parallel. You want the new line to pass through (0, 11, -9), so take v = 〈0, 11, -9〉.

Then the vector equation of the new line is

tT + v = t 〈3, -3, 7〉 + 〈0, 11, -9〉 = 〈3t, 11 - 3t, -9 + 7t〉

with parametric equations

x(t) = 3t

y(t) = 11 - 3t

z(t) = -9 + 7t

Answer:

ANSWER IS 70!

Step-by-step explanation:

answer is 9

Step-by-step explanation:

12/4=3

1/4=3

3/4=9

Answer:

90 degrees

Step-by-step explanation:

Answer:

look at the picture

Step-by-step explanation:

the picture explains everything

Answer: F is 11m.

Step-by-step explanation: Because H,I,G are all increasing their numbers like plus 3, plus 2, and the last one has to be plus 1.

Answer:

14 pushups per min

70 pushups in 5 min

Step-by-step explanation:

Answer:

30 hens, 20 cows.

Step-by-step explanation:

Step one:

let the number of cows be x

and the number of hens be y

Each cow has 2 eyes, each hen has 2 eyes also.

the total number of eyes is

2x+2y

Each cow has 4 legs, each hen has 2 legs.

the total number of legs is

4x + 2y

Step two:

the number of legs exceeds the number of eyes by 40:  

4x+2y - (2x+2y) = 40

open bracket

4x+2y-2x-2y=40

4x-2x=40

2x=40

Divide both sides by 2

x=40/2

x=20

Step three:

we know also that x = 2/3*y, so y = 3/2*x = 3/2 * 20 = 30

30 hens, 20 cows.

Check:

60 + 40 eyes = 100, 60 + 80 legs = 140legs.

Answer:

1/2

Step-by-step explanation:

[tex]2 = {x}^{2} + 5x[/tex]

[tex]0 = {x}^{2} + 5x - 2 \\ {x}^{2} + 5x - 2 = 0[/tex]

From the standard form equation and from the given equation.

[tex]a {x}^{2} + bx + c = 0 \\ a = 1 \: \: \: b = 5 \: \: \: c = - 2[/tex]

Discriminant Formula

[tex]D = {b}^{2} - 4ac[/tex]

Substitute the value of terms in the discriminant formula.

[tex]D = {(5)}^{2} - 4(1)( - 2) \\ D = 25 - 4( - 2) \\ D = 25 + 8 \\ D = 33[/tex]

Discriminant Types

[tex]D > 0 \: \: \: \: 2 \: \: real \: \: roots \\ D = 0 \: \: \: \: 1 \: \: real \: \: root \\ D < 0 \: \: \: imaginary \: \: roots[/tex]

We can rule out the Imaginary root and double root because the discriminant is greater than 0. Therefore, the only choices are either Irrational or Rational.

However, we cannot factor the expression by using two brackets or common factor. We can say that the equation has two real irrational roots.

Answer:

reflected across the y axis, the point (1, 1) becomes (-1, 1).

Step-by-step explanation:

To reflect a point across the y-axis, all you need to do is negate the x coordinate.  That gives you (-1, 1)

Answer:

QR is 1.2 due to both triangle are similar

Answer:

the answer should be 0.96 units

Step-by-step explanation:

1.6/2.0=.8

.8x1.2= .96

Complete Question:

A closed box has a square base with side length L feet and height h feet. Given that the volume of the box is 39 cubic feet, express the surface area of the box in terms of L only.

Answer:

[tex]A = \frac{156}{L} + 2L^2[/tex]

Step-by-step explanation:

Given

[tex]Volume = 39ft^3[/tex]

Required

Express the surface area in terms of L

Because the box has a square base:

The volume is:

[tex]Volume = Base\ Area * Height[/tex]

Where

[tex]Base\ Area = L * L[/tex]

So, we have:

[tex]Volume = L * L * H[/tex]

Substitute 39 for Volume

[tex]39= L * L * H[/tex]

[tex]39= L^2 * H[/tex]

Make H the subject

[tex]H = \frac{39}{L^2}[/tex]

The surface area (A) of a box with square base is:

[tex]A = 2(LH + LH + L^2)[/tex]

[tex]A = 2(2LH + L^2)[/tex]

Open bracket

[tex]A = 4LH + 2L^2[/tex]

Substitute [tex]\frac{39}{L^2}[/tex] for H

[tex]A = 4L * \frac{39}{L^2} + 2L^2[/tex]

[tex]A = \frac{4L *39}{L^2} + 2L^2[/tex]

[tex]A = \frac{4*39}{L} + 2L^2[/tex]

[tex]A = \frac{156}{L} + 2L^2[/tex]

Answer:

Step-by-step explanation:

Each oven weights 300 pounds and there 80 ovens:

Weight left for freezers:

Number of freezers could be added:

Answer:

1

Step-by-step explanation:

281,847,583,332.9

Answer:

I think 847

Step-by-step explanation:

The order of place value is trillion, billions, millions, thousands, and ones. Billion comes third. This is why I think its 847.

I hope this helps u! :D

Answer:

v-8.4=6.62 +8.4

v=15.02

Step-by-step explanation:

prove me wrong

Answer:

4

Step-by-step explanation:

Answer:

She is determined

Step-by-step explanation:

Answer:

Determined

Step-by-step explanation:

Answer:

False

Step-by-step explanation:

a+(-a)=a-a = 0 which means irrational numbers are not closed under addition or subtraction.

False. Irrational numbers are not closed under subtraction.

Given data:

Closure under subtraction means that if you subtract two irrational numbers, the result will always be another irrational number.

However, this is not true for irrational numbers.

For example, consider the irrational numbers √2 and √2 + √2. Both of these numbers are irrational. However, when we subtract √2 from √2 + √2, we get:

(√2 + √2) - √2 = √2

The result, √2, is still an irrational number. But if we subtract two irrational numbers like √2 from √2, we get:

√2 - √2 = 0

The result, 0, is a rational number, not an irrational number.

To learn more about irrational numbers, refer:

https://brainly.com/question/4031928

#SPJ6

Answer:

5 mins.

Step-by-step explanation:

hope his helps good luck

Answer:

5 minutes

Step-by-step explanation:

Step-by-step explanation:

If you divide the distance by the elapsed time, the result will be the rate of water loss (evaporation). To convert this evaporation rate in to gallons lost over a specific time period, you will need convert the measure into a volume. WTG GLAD U GOT IT RIGHT..

Answer:

x>3 or x≤-2

Step-by-step explanation:

4x-7>5 or 5x+4≤-6

4x>5+7 or 5x≤-6-4

x>3 or x≤-2

Answer:

nice hand writing

Step-by-step explanation:

Answer:

Distributive property

Step-by-step explanation:

Answer:

126 marbles

Step-by-step explanation:

if 42 is 1/3 of the jar, times it by 3 and that's the total.

Answer:

126 marbles

Step-by-step explanation:

24 - blue

18 - green

42 are blue or green

let 't' = total number of marbles

1/3t = 42

t = 42 x 3 = 126

Answer:

 -9p3 + 6p2 + 9p - 26/ p

Step-by-step explanation:

hope this helps

Answer:

x = 121

Step-by-step explanation:

In order to solve for "x" you need to get it on one side by itself. To do that you need to add 93 to the other side. 93 + 28 is 121.

Answer:

121

Step-by-step explanation:

x-93=28

x=28+93

x=121