Mathematics High School

3x+2y+4z=12
X+y+2z=6
(X=0,y=4,z=1)
Determine if the given 2 lines intersect at the given point. Explain your reasoning.
-2x-4y+z=8
4x+2y=-5
(x=-2,y=0,z=3) same as up above

Answers

Answer 1
Substitute the given points into each equation and if the answer is as intended for both equation, then it means the given points are the intersection point

Given points x = 0, y = 4, and z = 1
Equation 1:
3x + 2y + 4z = 3(0) + 2(4) + 4(1) = 0 + 8 + 4 = 12
Equation 2: 
x + y + 2z = 0 + 4 + 2(1) = 6

Both equation 1 and equation 2 give the intended answer; 12 and 6 respectively, hence the given point is the intersection point
---------------------------------------------------------------------------------------------------------------

Given point : x = -2, y = 0, and z = 3

Equation 1:
-2x - 4y + z = -2(-2) - 4(0) + 3 = 4 - 0 + 3 = 7
Equation 2:
4x + 2y = 4(-2) + 2(0) = -8

The answers are not as intended, hence the given point is not the intersection point

Related Questions

Aiko stands 5 m from a tree. At that distance, the angle of elevation from the ground to the top of the tree is 80°. Approximately how tall is the tree?

Answers

This is the concept of trigonometry, the height of the tree will be given by:
tan theta=[opposite]/[adjacent]
theta=80
height=h
adjacent=5 m
hence;
tan80=h/5
hence;
h=5tan80
h=28.36 m

20 POINTS PLUS BRAINLIEST!!!

Which function is represented in the table of values?

x 0 -1 -2 -3
y 2 4 8 16

A.
y=2^x
B.
y=2(1/2)
C.
y=-2^x
D.
y=(1/2)^x

Answers

The correct answer is D.
y = (1/2)^x

y = (1/2)^-1 = 2
y = (1/2)^-2 = 4
y = (1/2)^-3 = 8

Hope it helped!

A "Local" train leaves a station and runs at an average rate of 35 mph. An hour and a half later an "Express" train leaves the station and travels at an average rate of 56 mph on a parallel track. How many hours after the Express train starts will the it overtake the Local?

Answers

recall your d = rt, distance = rate * time.

so...Local say "L" is going at a speed of 35mph...ok... and Express or "X" is going at 56mph.

by the time the two trains meet, and X is ready to overtake L, the distance that both have travelled, since is a parallel road, is the same, say "d".  So if L has travelled "d" miles, then X had travelled "d" miles too, over the same road, maybe different lane.

now, because X left 1 1/2 hour later, by the time they meet, say X has been running for "t" hours, but because it left 1 1/2 hour later, L has been running for " t + 1 1/2 " hours, or " t + 3/2 " hours.

[tex]\bf \begin{array}{lccclll} &distance&rate&time\\ &-----&-----&-----\\ Local&d&35&t+\frac{3}{2}\\ Express&d&56&t \end{array} \\\\\\ \begin{cases} \boxed{d}=35\left( t+\frac{3}{2} \right)\\ d=56t\\ ----------\\ \boxed{35\left( t+\frac{3}{2} \right)}=56t \end{cases} \\\\\\ 35t+\cfrac{105}{2}=56t\implies \cfrac{105}{2}=21t\implies \cfrac{105}{42}=t \\\\\\ \cfrac{5}{2}=t\implies 2\frac{1}{2}=t[/tex]

so, they met 2 and a half hours later after X left, and a milllisecond later X overtook L.

Answer:

2.5 hrs.

Hope this helps <3

Derive the equation of the parabola with a focus at (−5, 5) and a directrix of y = −1.

Answers

check the picture below.

so, the left-part of the picture is the focus point and the directrix... .so.. notice, the focus is above the directrix, meaning is a vertical parabola and is opening upwards.

now, looking at the right-part of the picture, bear in mind that, the vertex is "p" units away from the directrix and the focus, so, the vertex is half-way between those fellows, notice in the picture what "p" is, keep in mind that, because the parabola is opening upwards, "p" is a positive unit, thus is 3.

[tex]\bf \textit{parabola vertex form with focus point distance}\\\\ \begin{array}{llll} (y-{{ k}})^2=4{{ p}}(x-{{ h}}) \\\\ \boxed{(x-{{ h}})^2=4{{ p}}(y-{{ k}}) }\\ \end{array} \qquad \begin{array}{llll} vertex\ ({{ h}},{{ k}})\\\\ {{ p}}=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix} \end{array}\\\\ -------------------------------\\\\[/tex]

[tex]\bf \begin{cases} h=-5\\ k=2\\ p=3 \end{cases}\implies [x-(-5)]^2=4(3)(y-2) \\\\\\ (x+5)^2=12(y-2)\implies \cfrac{(x+5)^2}{12}=y-2\implies \cfrac{(x+5)^2}{12}+2=y \\\\\\ \cfrac{1}{12}(x+5)^2+2=y[/tex]

Answer:  D

Step-by-step explanation: took the test

Rewrite the rational exponent as a radical.

5 to the 3 over 4 power, to the 2 over 3 power

A.the cube root of 5 squared
B. the twelfth root of 5
C. the square root of 5
D.the cube root of 5 the fourth power

Answers

[tex]\left( 5^{ \frac{3}{4} } \right)^{ \frac{2}{3} }=5^{ \frac{3}{4} *\frac{2}{3} }=5^{ \frac{1}{2} }= \sqrt{5} [/tex]

C. the square root of 5

Someone please help me out!

Answers

try it with a couple different numbers

 try 4:  1^2 +2^2 +3^2 +4^2 = 1 +4 +9 +16 =30

 formula: 4(4+1)(2*4+1)/6 = 4*5*9 = 180/6=30

 this one works

now try 5

1^2 + 2^2+3^2+4^2+5^2 = 55

formula: 5(5+1)(2*5+1)/6 = 5*6*11 = 330/6=55

I tried a larger number ( 14) as well and it worked

so you can say that this is true


Factor the following.

Answers

This trinomial is also a perfect square trinomial so it can be solved using perfect squares.

(x-10)^2

Answer: B

Hope this helps :)
Please give brainliest
x² - 20x + 100

Once again, I'll just go through all of the answer choices :)

a)  (x - 5)(x - 4)

Simplify.

x² - 4x - 5x + 20

Add like terms.

x² - 9x + 20

So, A is incorrect.

b)  (x - 10)(x - 10)

Simplify.

x² - 10x - 10x + 100

Add like terms.

x² - 20x + 100

So, B is correct.

c) (x + 10)²

(x + 10)(x + 10)

Simplify.

x² + 10x + 10x + 100

Add like terms.

x² + 20x + 100

So, C is incorrect.

d)  (x + 10)(x - 10)

Simplify.

x² - 10x + 10x - 100

Add like terms.

x² - 100

So, D is incorrect.

Therefore, B is correct.

~Hope I helped!~

If the perimeter of the adult pinball machine is 172 inches, what is the length, in inches of ? Type the numeric answer only in the box below.

Answers

If you have ever seen a pinball machine, you would know that it is shaped like a rectangular box. Since a rectangle has two sets of equal parallel lines, then you would have to know the length and the width. Its perimeter is equal to the total length of all sides. Thus, the equation is 2L + 2W = 172 inches. However, since there is no other data other than the perimeter, I can't give a definite numerical answer. The only answer I could give is in variables. Thus, the length of the pinball machine is

2L = 172 - 2W
L = 86 - W

how to solve 46.2 x 10 with a negative 2 exponent

Answers

The answer is 0.462 because you have to move the decimal point 2 spaces to the left
hope this helps:)
46.2 x 10^-2  = 46.2 / 10^2  =  46.2 / 100 = 0.462

PLEASE HELP ME!!!!

Part A: Amir rented a scooter at $43 for 3 hours. If he rents the same scooter for 8 hours, he has to pay a total rent of $113.

Write an equation in the standard form to represent the total rent (y) that Amir has to pay for renting the scooter for x hours.

Part B: Write the equation obtained in Part A using function notation.

Part C: Describe the steps to graph the equation obtained above on the coordinate axes. Mention the labels on the axes and the intervals.

Answers

Part A:

The equation in standard form is given Ax+By+C = 0
where x is the gradient of a straight line (or the rate of change)

The rate of change = (113-43) / (8-3) = 70/5 = 14
This value means there's an increase of $14 for every hour rented.

We also need to work out the value of C, which is the fixed value (happen at x=0)

We know that Amir paid $43 for 3 hours. 
Amir would have paid $29 for 2 hours
Amir would have paid $15 for 1 hour
Since the hourly rate is $14, the fixed fee is 15 - 14 = $1

The equation that represents the total cost of renting a scooter is

y = 14x + 1

Rearranging this equation to get the standard form
14x - y + 1 = 0

Part B:

Writing the equation as function ⇒ f(x) = 14x + 1

Part C:

To graph the equation, we can start by choosing the x-intervals, say we have the value of x between 0 and 10

x   0   1     2    3    4    5    6     7    8     9     10
y   1   15  29  43  57  71   85   99  113  127  141

Each pair of x-value and y-value is then plotted on a graph then each plot is joined to draw a straight line.


Answer:

Step-by-step explanation:

Part A: The two points that represent this situation are (3,43) and (8,113). To put this in standard form, I will first find the slope-intercept form. I did this in the image below.

Now, to find the standard form I will rearrange, 14x -y +1 = 0.

Part B: To put this in function notation I simply take my slope-intercept equation of y=14x+1, and replace y with f(x) so,   f(x)=14x+1

​

Part C: To graph this, put the y, intercept at 1, and give the line a slope of 14/1. Label the x-axis with hours, from 0 -  8, and the y-axis with dollars, from 0-150.

The lengths of three sides of a quadrilateral are shown below: Side 1: 1y2 + 3y − 6 Side 2: 4y − 7 + 2y2 Side 3: 3y2 − 8 + 5y The perimeter of the quadrilateral is 8y3 − 2y2 + 4y − 26. Part A: What is the total length of sides 1, 2, and 3 of the quadrilateral? (4 points) Part B: What is the length of the fourth side of the quadrilateral? (4 points) Part C: Do the answers for Part A and Part B show that the polynomials are closed under addition and subtraction? Justify your answer.

Answers

A. y^2 + 3y - 6 + 4y - 7 + 2y^2 + 3y^2 - 8 + 5y = 6y^2 + 12y - 21 <==

B. 8y^3 - 2y^2 + 4y - 26 - (6y^2 + 12y - 21) = 
    8y^3 - 2y^2 + 4y - 26 - 6y^2 - 12y + 21 = 
    8y^3 - 8y^2 - 8y + - 5 <==

C. (part A) this is closed under addition
     (part B) this is closed under subtraction
     Polynomials will be closed under an operation if the operation produces      another polynomial

Answer:

Part A: 12y^2+9y-21

Part B: 4y^2+6y^2+7y-5

Part C:  A set of numbers is closed, or has closure, under a given operation if the result of the operation on any two numbers in the set is also in the set. For example, the set of real numbers is closed under addition, because adding any two real numbers results in another real number. Likewise, the real numbers are closed under subtraction, multiplication and division (by a nonzero real number), because performing these operations on two real numbers always yields another real number. Polynomials are closed under the same operations as integers.

Step-by-step explanation:

Hope this helps!!

How to subtract a negative fraction from a positive fraction?

Answers

Let's take an example to illustrate this case:

positive fraction = 2/7

negative fraction = - 3/5

Now we need to subtract  - 3/5 from 2/7

Right?

2/7 - (-3/5) = 2/7 + 3/5

here we need to unify the denominators as follows:

the lowest common factor between 7 and 5 is 35
2/7 = 10/35
3/5 = 21/35

Now back to 2/7 + 3/5:

2/7 + 3/5 = 10/35 + 21/35 = (10+21)/35 = 31/35

That's it




Hope that helps you

A ball is thrown from an initial height of 1 meter with an initial upward velocity of 13 m/s. The ball's height h (in meters) after t seconds is given by the following.

h=1+13t-5t^2

Find all values of t for which the ball's height is 8 meters.

Round your answer(s) to the nearest hundredth.
(If there is more than one answer, use the "or" button.)

Answers

Here the answer is: 0.76 and 1.84

I hope I don't have to explain it again.






For t=1.84 and t=0.76 the ball's height is 8 meters in equation h=1+13t-[tex]5t^{2}[/tex].

What is equation?

An equation is a relationship between two or more variables expressed in equal to form. Equation of two variables look like ax+ by=c. It is solved in order to find the values of variables.

How to solve equation?

We have been given an equation h=1+13t-[tex]5t^{2}[/tex] and we have to find the values of t for which h=8.

So,

1+13t-[tex]5t^{2}[/tex]=8

[tex]-5t^{2}[/tex]+13t+1-8=0

[tex]-5t^{2}[/tex]+13t-7=0

Removing negative signs.

[tex]5t^{2}[/tex]-13t+7=0

We cannot solve through factorization so e use the following formula:

x=-b+-[tex]\sqrt{b^{2} -4ac}/2a[/tex]

t=(13+-[tex]\sqrt{-13^{2} -4*5*7}[/tex])/2*5

t=(13+-[tex]\sqrt{169-140}[/tex])/10

t=(13+5.38)/10, (13-5.38)/10

t=1.838, 0.762

By rounding off to nearest hundred t=1.84, 0.76.

Hence value of t for which h=8 meters are 1.84 and 0.76.

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Please help !
(cos Θ − cos Θ)^2 + (cos Θ + cos Θ)^2

Answers

The answer is:  " 4 cos² Θ " .
_____________________________________________
Explanation:
_____________________________________________
(cos Θ − cos Θ)²  + (cos Θ + cos Θ)²  

   =   0² + (cos Θ + cos Θ)²  ;

   =  0 + (2 cos Θ)² = (2 cos Θ)(2 cos Θ)  ;

   =  4 (cos Θ)² = 4 cos² Θ .
_____________________________

Answer:  The required simplified form is [tex]4\cos^2\theta.[/tex]

Step-by-step explanation:  We are given to simplify the following trigonometric expression :

[tex]T=(\cos \theta-\cos\theta)^2+(\cos \theta+\cos \theta)^2.[/tex]

To simplify, first we need to evaluate the terms within the brackets.

The simplification is as follows :

[tex]T\\\\=(\cos \theta-\cos\theta)^2+(\cos \theta+\cos \theta)^2\\\\=0^2+(2\cos\theta)^2\\\\=0+4\cos^2\theta\\\\=4\cos^2\theta.[/tex]

Thus, the required simplified form is [tex]4\cos^2\theta.[/tex]

If 3a2 – 5ab – 2b2 is factored, one of the factors might be:

Answers

We want to factor 3a² - 5ab - 2b².

Note that 
(3a)*(-2b) + a*b = -6ab + ab = -5ab
(3a)*a = 3a²
b*(-2b) = -2b²

Therefore
3a² - 5ab - 2b² = (3a + b)(a - 2b)

The factors are (3a + b) and (a - 2b).

Answer:
One of the factors is (3a + b).
Another factor is (a - 2b).

Celia is staring at the clock waiting for school to end so that she can go to track practice. She notices that the 4-inch-long minute hand is rotating around the clock and marking off time like degrees on a unit circle. Part 1: How many radians does the minute hand move from 1:25 to 1:50? (Hint: Find the number of degrees per minute first.) Part 2: How far does the tip of the minute hand travel during that time?

Answers

there are 60 minutes marks on a clock

 360/60 = 6

 6 degree between every minute

 From 1:25 to 1:50 there are 25 minutes

25 x 6 = for a total of 150 degrees

150*pi/180 = 5pi/6 radians. ( 2.61799 radians)

 

Total distance the tip of minute hand has traveled in this time = 2pi*(4 in) * (5pi/6)/(2pi) = 10pi/3 inches (10.47 inches)


I don't know the answer can someone pls help me

Answers

line QP =


11.5*(11.5 +24) = 11.5 * 35.5 = 408.25

SqRT(408.25) = 20.205

round answer to 20 units

The formula for your situation is this:
[tex] n^{2} =PN(PN+MN)[/tex]
where your PQ is [tex] n^{2} [/tex]
So our formula, filled in and solving for PQ is this:
[tex] n^{2}=11.5(11.5+24) [/tex]
and [tex] n^{2} =11.5(35.5)[/tex]
and n = 20.2 or 20 rounded.  That's the last choice above

Determine whether the sequence converges or diverges. If it converges, give the limit.

11, 44, 176, 704, ...

Answers

The term to term rule is multiplying by 4 and if we continue doing this, we will move towards very large positive numbers.

This sequence, therefore, diverges to infinity

if <6 = <10 and <5 = <7, which describes all the lines that must be parallel?

Answers

second: Only lines t and u must be parallel

determine the value of x in the diagram where lines a and b are parallel

25°
15°
75°
55°

Answers

If lines a and b are parallel, the two angles given would be the same.
2x - 5 = x + 20
x = 25

Tobius is going to climb a ladder to reach and fix a piece of siding located 30 feet above the ground on the building. If he places the ladder at a 60° angle with the ground, about how long is the ladder?

Answers

Check the picture.

Let BC represent the wall, AC the ladder and AB the distance of the feet of the ladder to the wall.

ABC form a right triangle, with m(B)=90°, m(A)=60° and m(C)=30°.

AB is the side opposite the angle 30°, so the length of AB is half of the length of the hypotenuse AC.

Thus, let |AC|=2x, and |AB|=x.

By the Pythagorean theorem:

[tex] (2x)^{2}= x^{2} +30^{2} [/tex]

[tex] 4x^{2}= x^{2} +30^{2} [/tex]

[tex] 3x^{2}=30^{2}=900 [/tex]

[tex] x^{2}=300 [/tex]


thus [tex]x= 10\sqrt{3} [/tex]

the length of the ladder is [tex]2x= 20\sqrt{3}=34.64 [/tex] feet


Answer: [tex]20\sqrt{3}=34.64 [/tex] feet

The height of the ladder will be;

⇒ 20√3 feet

What is mean by Triangle?

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

Tobius is going to climb a ladder to reach and fix a piece of siding located 30 feet above the ground on the building.

And, He places the ladder at a 60° angle with the ground.

Now,

Let the height of the ladder = h

So, We can formulate;

⇒ sin 60° = 30/h

⇒ √3/2 = 30/h

⇒ h = 30 × 2/√3

⇒ h = 20√3

Thus, The height of the ladder = 20√3 feet

Learn more about the triangle visit:

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The question is "Find the number of elements in the following sets"
I sort of get it but it docks me points every time I get it wrong so I don't want to risk it

Answers

I hope this helps you


U=66+17+53+82=218


A' = 53+82=135


A'∩B=53


(A∩B)'=66+53+82=201


(A∪B)'=82


A' ∩ B' = 82

D: y> -1/3 x+1 helpppp

Answers

The answer is A. It is less than or equal to because the line is solid instead of dashed. It is less than because the shaded portion is below the line.

what is the least common multiple of X and Y? X=2*2*2*2 Y=2*2*2*3

Answers

[tex]\text{lcm}(x,y)=2^4\cdot3=48[/tex]
The least common multiple is the product of the highest occurring primes of the numbers prime factorizations, in this case:

2*2*2*2*3=48

PLZ HEEEEEEEELPPPPPPPP!!!!!!!!!

Answers

y= ∛(-x) - 3
for x = -8 → y = ∛-(-8) - 3 ↔ y = 2-3 ↔y = -1
for x= 8 → y= ∛(-8) - 3 ↔ y = -2 -3 ↔ y = -5
Then  - 5≤ y≤ - 1
hence the range of y is {y|-5≤y≤-1}

P(A)=25,P(B|A)=920,P(A∩B)=?

Answers

Final answer:

We use the product rule in probability to find P(A∩B) = P(B|A) * P(A). Substituting given values, P(A∩B) = (9/20) * 25, which equals 11.25.

Explanation:

The subject area of this question is probability, a topic within mathematics. Here, we are asked to find the intersection of Events A and B given the probabilities of A and the conditional probability of B given A. The rule of product in probability states that P(A∩B) = P(B|A) * P(A).

Let's calculate: P(B|A) is given as 9/20 while P(A) is 25. Thus,

P(A∩B) = P(B|A) * P(A) = (9/20) * 25 = 11.25

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Help!!!!! Identify KPN

Answers

m<KPN = 1/2(90+50) = 140/2=70

answer D. 70 (last choice)

Answer:

it is 70

Step-by-step explanation:

I guessed and got it right, lol

The scale of a map is 1 1/4 inches = 100 miles. On that map, 2 cities are 4 1/8 inches short. What is the actual distance between the cities?

Answers

need to divide 4 1/8 by 1 1/4

4 1/8 = 33/8

1 1/4 = 5/4

33/8 / 5/4 = 33/8 * 4/5 =  132/40 reduces to 33/10 = 3 3/10

100* 3 3/10 = 330 miles

Final answer:

Using the map scale of 1 1/4 inches equals 100 miles, and the measured map distance of 4 1/8 inches, the actual distance between the two cities is calculated to be 330 miles.

Explanation:

To find the actual distance between two cities on a map, we can set up a proportion based on the scale of the map. In this case, the scale is 1 1/4 inches = 100 miles. The measured distance on the map between the two cities is 4 1/8 inches.

We'll convert these measurements to an easier-to-calculate form by changing the mixed numbers to improper fractions.

First, we convert 1 1/4 inches to an improper fraction: 1 1/4 = 5/4 inches. Likewise, we convert 4 1/8 inches to an improper fraction: 4 1/8 = 33/8 inches. Now we set up the proportion using the scale.

(5/4 inches) / (100 miles) = (33/8 inches) / (x miles)

To solve for x, cross-multiply and divide:

(5/4) * x = (33/8) * 100
x = (33/8 * 100) / (5/4)
x = (33 * 100 * 4) / (8 * 5)
x = (33 * 4) / (2)
x = 66 miles

Therefore, the actual distance between the two cities is 330 miles.

Find two consecutive positive integers such that thw sqaure of the first decreased by 25 equa;s three times the second

Answers

consecutive integers are 1 apart

so

square of the first decreased by 25 equals 3 time the 2nd
the 2 integers are x and x+1

x²-25=3(x+1)
distribute
x²-25=3x+3
minus (3x+3) from both sides
x²-3x-28=0
factor
what 2 numbers muliply to get -28 and add to get -3
-7 and 4
(x-7)(x+4)=0

set to zero

x-7=0
x=7

x+4=0
x=-4
false, we want positive integers

x=7
x+1=8

the inegers are 7 and 8

for which of the following numbers does 5 appear in the tens place ?
*check all that applies*
a. 125.634
b. 56.89
c. 1250
d. 3.5
e. 92.57



Answers

5 appear in the tens place

answer:
b. 56.89 
c. 1250
The answers are b and c. It's talking about the "tens" place, not the "tenths" place, so neither d or e are correct. 

Other Questions
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