slader (a) Find parametric equations for the line through (4, 1, 8) that is perpendicular to the plane x − y + 4z = 2. (Use the parameter t.) (x(t), y(t), z(t)) = Correct: Your answer is correct. (b) "In what points does this line intersect the coordinate planes?"

Answers

Answer 1

Answer:

(x(t), y(t), z(t)) = (4 + t, 1 - t, 8 + 4t)

xy - plane    (x, y, z) = (2, -1, 0)

yz - plane    (x, y, z) = (0, 5, -8)

xz - plane     (x, y, z) = (5, 0, 12)

Step-by-step explanation:

The given point (x, y ,z) = (4, 1, 8)

The plane x -y + 4z = 2

Normal vector (n) = < 1, -1, 4 >

The equation of line through point (4, 1, 8) and the plane is:

(x(t), y(t), z(t)) = (4, 1, 8) + t(1, -1, 4)

(x(t), y(t), z(t)) = (4 + t, 1 - t, 8 + 4t)

Any point on the line P(x, y, z) = ( 4 + t, 1 - t, 8 + 4t)

xy-Pane ⇒ z = 0

8 + 4t = 0

4t = - 8

t = -8/4

t = -2

(x, y, z) = (4 - 2, 1 - 2, 8 + 4(-2))

(x, y, z) = (2, -1, 0)

yz-plane ⇒ x = 0

4 + t = 0

t = -4

(x, y, z) = (4 + (-4) , 1-(-4), 8 + 4(-4)

(x, y, z) = (0, 5, -8)

xz-plane ⇒ y = 0

1 - t = 0

-t = -1

t = 1

(x, y, z) = ( 4 + 1, 1 - 1, 8 + 4(1) )

(x, y, z) = (5, 0, 12)


Related Questions

Can someone please help me with this I really need help

Answers

Answer:

ADD ME ON FORtXVXVVXVXNIZZLE KE2DAEV12

Step-by-step explanation:

Answer:

Number 3

It's a cube

Step-by-step explanation:

A pyramid. This shape has faces. This shape has vertices. This shape has edges.

Answers

Answer:

5 faces 5 vertices 8 edges

Step-by-step explanation: i just finished it.

Answer:

This shape has  

✔ 5

faces.

This shape has  

✔ 5

vertices.

This shape has  

✔ 8

edges.

Step-by-step explanation:

Trust me on this, also can I have brainiest please?

Hope you do well! :D

I did the instruction, and I got it correct.

solve it pleeeease
will give you brainliest ​

Answers

Answer:

Step-by-step explanation:

I m sorry if i m wrong.

e no is 100% correct

Which equation is true when k = -15?

a) 4k - 11 = -34

b) -53 + 4k = 7

c) k/3 + 17 = 12

d) k/5 + 2.5 = 0.5

Answers

Answer:

c) k/3 + 17 = 12

#JUST A TEXT

convert standard form to factored form
f(x)=x^+5x+6







(LT 5.6)

Answers

Answer:

(x+3)(x+2)

Step-by-step explanation:

f(x)=x²+5x+6=x²+2x+3x+6=x(x+2)+3(x+2)=(x+3)(x+2)

[tex] {x}^{2} + 5x + 6[/tex]

[tex] {x}^{2} + 2x + 3x + 6[/tex]

[tex]x(x + 2) + 3(x + 2)[/tex]

[tex](x + 3)(x + 2)[/tex]

Jackson is building a bookshelf and has a piece of wood that is 5/8 long. He needs to cut pieces that are 1/16 foot long. How many pieces can Jackson cut?

Answers

Answer:

6 is the Answer.

Step-by-step explanation:

A fraction consists of two parts the top number and the bottom one.

Think of the top number as the count and the bottom as the size indicator. So you have:

countsize indicator −−−−−−−−−−→proper names numeratordenominator

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Consider the action example of dividing 3 into 6.

We can do this division directly because their size indicators are the same. That is, we have: 61÷31. People do not normally write it this way but it is correct.

To directly divide the counts the size indicator must be the same

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

So we need to see how many of 18 will fit into 34

We can not do this directly in one operation as the size indicators are not the same.

Lets make the size indicators (denominators) the same

Multiply by 1 and you do not change the value but

1 comes in many forms.

[34×1]÷18 → [34×22]÷18

[3×24×2]÷18 → 68÷18

Now that the size indicators (denominators) are the same we can just divide the counts (numerators)

countsize indicator→[68÷18]=6÷1=6

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

I could explain more showing the connection between this and the shortcut method but what I have shown you will do for now.

3n - (2 +n)


plz help me I need help I’m stuck

Answers

Answer:

if you are factoring the answer is 2(n-1)

if simplifying the answer is 2n-2

Step-by-step explanation:

See image below:)

Find the mean of the data set {4.5,5, 3.5, 2, 2.5}.



So what is the answer ;, I nordeste im

Answers

Answer:

Mean = 3.5

Step-by-step explanation:

The given data is :

4.5,5, 3.5, 2, 2.5

We need to find the mean of the given data.

We know that,

Mean = sum of observations/total no. of observations

Here,

Total no. of observations = 5

Sum of observations = 4.5 + 5+ 3.5+ 2+ 2.5 = 17.5

Mean,

[tex]m=\dfrac{17.5}{5}\\\\m=3.5[/tex]

Hence, the mean of the data set is equal to 3.5.

A boy throws a baseball across a field. The ball reaches its maximum height, 18 meters, after 1 second. After approximately 2.3 seconds, the ball lands on the ground. The ball’s motion can be modeled using the function f(x) = –10x2 + 20x + 8. What is the height of the ball 1.5 seconds after it is thrown?

11.7 meters
13.8 meters
15.5 meters
17.5 meters

Answers

Answer:

15.5 meters

Step-by-step explanation:

on a highway, Nick's car uses 12.5 gallons of gas to travel 240 miles. The gas tank in Nick's car holds 20 gallons of gas.

How far can Nick's car travel on a highway using a full tank of gas?

Answers

Answer:

Nick's can travel 384 miles on a highway using a full tank of gas of his car

Step-by-step explanation:

Given

Fuel used by Nick's car = 12.5 gallon

In 12.5 gallon Nick can travel up to 240 miles

The gas tank of Nick's car can hold upto 20 gallons of fuel

With a full tank Nick can travel

[tex]\frac{240}{12.5} * 20 \\384[/tex]miles

Aldo needs 46 cookies for a party.
The cookies he wants come in packs of 8.
How many packs should he buy?

Answers

Answer:

6 Packs

Step-by-step explanation:

Since he needs 46 cookies, he will have to buy 46/8 which is 5.75 packs. But since the packs are sold in whole, not fractions, he buys a ceil approximation of the packs which is 6, because if he buys 5, it will not be enough.

∠A and \angle B∠B are complementary angles. If m\angle A=(2x-4) ∘ and m\angle B=(5x+17) ∘ , then find the measure of \angle A∠A.

Answers

Answer: 18°

Step-by-step explanation:

Complementary angles are the angles that when we add them together, the value will equal 90°.

In this question, we've to add both angles and equate them to 90°. This will be:

(2x - 4) + (5x + 17) = 90

2x - 4 + 5x + 17 = 90

Collect like terms

2x + 5x = 90 + 4 - 17

7x = 77

x = 77/7

x = 11

Angle A will be:

= (2x-4)

= 2(11) - 4

= 22 - 4

= 18°

A biologist studying the relationship between tilapia and catfish in a pond finds that the ratio of tilapia to catfish is 6:20. If the pond has 30 catfish, how many tilapia are in the pond?

Answers

Answer: 9 tilapia

Step-by-step explanation:

The ratio of 6:20 for tilapia to catfish means that for every six tilapia, there are 20 catfish in the pond.

If there are 30 catfish, use direct proportion to find out the number of tilapia:

6     :      20

x     :       30

Cross multiply:

20x = 180

x = 180 / 20

x = 9 tilapia

What does difference of squares mean? How can you recognize it when looking at an expression?

Answers

It is called a difference of squares because there are two things squared being subtracted. You can recognize it when there are two terms, subtraction between the two of them, and you know the square root of both
When an expression can be viewed as the difference of two perfect squares, i.e. a²-b², then we can factor it as (a+b)(a-b). For example, x²-25 can be factored as (x+5)(x-5). This method is based on the pattern (a+b)(a-b)=a²-b², which can be verified by expanding the parentheses in (a+b)(a-b).

Please help me I will choose brainliest

Answers

Answer:

hello

Step-by-step explanation:

hil

Answer:

The Answer Is Not Simmilar

Step-by-step explanation:

This is because you are not given all the info you need, and what you have, the triangle is not similar.

Every 2 days, Marina spends a total of 5.25 hours baking cupcakes and 4.75 hours decorating the cupcakes. At this rate, what is the total number of hours that Marina will spend baking and decorating cupcakes in 7 days?

PLS HELP!!! I HAVE A TIME LIMIT

Answers

Answer:

70

Step-by-step explanation:

Ok so we first add 4.75 and 5.25. 4.75+5.25=10. So 10 hours each day so 10 x 7 = 70. 70 hours in 7 days

Answer:

i would say it is either 30 or 35

Step-by-step explanation:

7/2=3.5

so you would round it down to 3 or keep it that

and 4.75+5.25=10

3(10)=30 and 3.5(10)=35

If it's every two days.

PLSS answer
The graph below can be used to solve which equation?

Answers

Answer:

Ix + 2I - 5 = -(x - 1)*(x - 3)

Step-by-step explanation:

In the graph, we can see two functions a red one, f(x), and a blue one, g(x)

And the equation would be f(x) = g(x)

The red one is an absolute value function, we can see that the vertex is at x = -2 and at y = -5, and it has a slope equal to 1.

Remember that for an absolute value equation with a vertex (a, b) is:

f(x) = Ix - aI + b

Then in this case, the absolute value equation is:

f(x) = Ix - (-2)I - 5

f(x) = Ix + 2I - 5

The blue equation is a quadratic equation, with roots 1 and 3, and we can see that it opens down, so the leading coefficient is negative.

Remember that for a quadratic equation with roots a and b, with leading coefficient A is:

g(x) = A*(x - a)*(x - b)

Then in this case the quadratic equation is something like:

g(x) = -N*(x - 1)*(x - 3)

Then the equation will be something like:

f(x) = Ix + 2I - 5 = g(x) = -N*(x - 1)*(x - 3)

Ix + 2I - 5 = -N*(x - 1)*(x - 3)

The only option that has this shape is the first option (the top one) such that N = 1, then:

Ix + 2I - 5 = -(x - 1)*(x - 3)

is the correct option.

please help with this. I only need help with the first question I have the second one figured out,

Answers

Answer:

m∠WZX = 41°

Step-by-step explanation:

diagonals bisect angles and opposite angles are congruent

therefore, ∠WXY ≅ ∠WZY

∠WZY must equal [360 - 2(68)] ÷ 2 which equals 112°

If ∠WXZ = 71° then so does ∠XZY

Which means that ∠WZX must equal 112-71 which is 41°

Answer:  41 degrees

===================================================

Explanation:

Refer to the diagram below. I've marked up the figure with various angles to point out the angles we'll be working with.

angle XYZ = 68 in greenangle WXZ = 71 in redangle WZX = unknown, in blue

To make things a bit simpler in terms of notation, and to match up colors with variable letters, I'm going to use the following

R = red angleG = green angleB = blue angle

Notice how the two red angles I've marked up are alternate interior angles. This works because WX is parallel to ZY. Also notice that the red and blue angles combine to form the angle WZY, which is adjacent to angle XYZ in green.

For any parallelogram, the adjacent angles always add to 180.

(angle WZY) + (angle XYZ) = 180

(blueAngle+redAngle) + (greenAngle) = 180

(B+R) + (G) = 180

(B+71) + (68) = 180

B+139 = 180

B = 180-139

B = 41

The blue angle is 41 degrees, which means angle WZX is 41 degrees

Side note: Your steps and answer to problem 11 are correct. Nice work.

Find the value of x
a) 57
b) 60
c) 69
d) 63​

Answers

Answer:

b

Step-by-step explanation:

The tangent- secant angle 55° is equal to half the difference of its intercepted arcs, that is

[tex]\frac{1}{2}[/tex] (170 - x) = 55 ( multiply both sides by 2 to clear the fraction )

170 - x = 110 ( subtract 170 from both sides )

- x = - 60 ( multiply both sides by - 1 )

x = 60 → b

A farmer is monitoring the water content of the soil during a dry summer. The water content of the soil is decreasing at a rate of 2.5% per week. If a certain soil sample contains 200 grams of water on July 1st, which equation describes the relationship between y, amount of water in grams, and t, time in weeks after July 1st?

Answers

Sir or ma’am it’s easy, the answer is the 2 one

How would you simplify this? Please help

Answers

[tex]8^{\frac{4}{3}} = \sqrt[3]{8^4} = \sqrt[3]{(2^3)^4} = \sqrt[3]{2^{3*4}} = 2^4 = 16[/tex]

Answer: C (16).

[tex]2\sqrt{6} - 6\sqrt{54} = 2\sqrt{6} - 2 * 3 * \sqrt{6} * \sqrt{9} = 2\sqrt{6}(1-3\sqrt{9}) = 2\sqrt{6}(1-3*3) = 2\sqrt{6}(1-9)=2*\sqrt{6}*(-8) = -16\sqrt{6}[/tex]

1.

[tex] \sqrt[3]{8^{4} } [/tex]

2.

[tex]2 \sqrt{6} - 6 \sqrt{54} \\ 2 \sqrt{6} - 6 \sqrt{9 \times 6} \\ 2 \sqrt{6} - 18 \sqrt{6} \\ - 16 \sqrt{6} [/tex]

The measurement of angle C is _____ degrees

Answers

Answer:

23°

Step-by-step explanation:

157° = D

D + C = 180°

157 + C = 180

(group like terms)

C = 180 - 157

C= 23°

Function g can be thought of as a scaled version of f(x) = x^2
write the equation for g(x)

Answers

Answer:

g(x) = - x^2

Step-by-step explanation:

The negative sign flips the f(x) graph across the x-axis.

Answer:

The first guy is right

Step-by-step explanation:

2.1x10^6
______
7x10^3

answer in standard form
...................10^......

Answers

Given:

The expression is:

[tex]\dfrac{2.1\times 10^6}{7\times 10^3}[/tex]

To find:

The simplified form of the given expression in standard form.

Solution:

We have,

[tex]\dfrac{2.1\times 10^6}{7\times 10^3}[/tex]

It can be written as:

[tex]\dfrac{2.1\times 10^6}{7\times 10^3}=\dfrac{21\times 10^5}{7\times 10^3}[/tex]

[tex]\dfrac{2.1\times 10^6}{7\times 10^3}=\dfrac{21}{7}\times \dfrac{10^5}{10^3}[/tex]

[tex]\dfrac{2.1\times 10^6}{7\times 10^3}=3\times 10^{5-3}[/tex]        [tex][\because \dfrac{a^m}{a^n}=a^{m-n}][/tex]

[tex]\dfrac{2.1\times 10^6}{7\times 10^3}=3\times 10^2[/tex]

Therefore, the required value is [tex]3\times 10^2[/tex].

. A bridge over a river is built in the shape of a parabolic arch. The bridge has a span of 100 feet. The height of the arch is 10 feet at a point 40 feet from the center. Find the height of the arch at its center.

Answers

Answer:

The height of the arch at its center is 250/9 or about 27.78 feet.

Step-by-step explanation:

We can write an equation to model the parabolic arch.

Let the left-most point of the arch be the origin (0, 0).

Since the bridge has a span of 100 feet, the right-most point must be (0, 100).

We can use the factored form of a quadratic:

[tex]y=a(x-p)(x-q)[/tex]

Where p and q are the x-intercepts.

Our x-intercepts are x = 0 and x = 100. Hence:

[tex]y=ax(x-100)[/tex]

At a point 40 feet from the center, the height of the arch is 10 feet.

The center is x = 50. So, a point 40 feet from the center can be either x = 10 or x = 90.

So, for instance, when x = 10, y = 10. Substitute and solve for a:

[tex]10=10a(10-100)[/tex]

So:

[tex]\displaystyle a=-\frac{1}{90}[/tex]

The same value will result if we let x = 90 and y = 10.

Hence, our equation is:

[tex]\displaystyle y=-\frac{1}{90}x(x-100)[/tex]

The height of the arch at its center will be when x = 50. Hence:

[tex]y(50)=\displaystyle -\frac{1}{90}(50)((50)-100)=\frac{250}{9}\approx 27.78\text{ feet}[/tex]

Elizabeth buys to red cans of tomato juice and three blue cans of tomato juice in all how many cups of tomato juice does she by

Answers

The answer to this is 5

Math help 60!!!!!!!!!!!!!

Answers

Answer:

perimeter is 36 and area I think is 72

Step-by-step explanation:

Tickets are arranged from 1 to 25 at a ticket counter. if one of the tickets is drawn at random whag is the probability that the chosen ticket is a multiple of 5. and what is the probability that the chosen ticket is a multiple of 6? ​

Answers

Answer:

The probability of choosing a ticket thats a multiple of 5 is 5/25

The probability of choosing a ticket thats a multiple of 6 is 4/25

Step-by-step explanation:

multiples of 6 are 6, 12, 18, and 24

multiples of 5 are 5, 10, 15, 20, and 25

The probability of choosing a ticket thats a multiple of 5 is 5/25

The probability of choosing a ticket thats a multiple of 6 is 4/25

una camisa me costo $10.500, con lo que gaste el 25% de mi dinero ¿cuanto dinero tenia? debe ir desarrollo

Answers

Answer:

25%------10500

100%------x = 100 * 10500 /25 = 42000

Rta: Tenías 42000

1/3 of a cup of milk each time she makes a batch of pancakes how many batches can she make if she only has 11/12 of a cup of milk left

Answers

Answer:

She can make [tex]\frac{33}{12}[/tex] batches.

Step-by-step explanation:

This question is solved by proportions, using a rule of three.

We have that:

For each batch of pancakes, 1/3 cups of milk are needed. Now, she has 11/12 cups of milk, so how many batches can she make?

1 batch - 1/3 cups

x batches - 11/12 cups

Applying cross multiplication:

[tex]\frac{x}{3} = \frac{11}{12}[/tex]

[tex]12x = 33[/tex]

[tex]x = \frac{33}{12}[/tex]

She can make [tex]\frac{33}{12}[/tex] batches.

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