Replace x, y, and z in the plane's equation with their appropriate parametric equations, then solve for t, then evaluate x, y, and z at this t to find the point P.
[tex]x+y-z=-5[/tex]
[tex](1+t)+2t-(-3t)=-5[/tex]
[tex]6t+1=-5[/tex]
[tex]6t=-6[/tex]
[tex]t=-1[/tex]
[tex]\implies x=0,y=-2,z=-3[/tex]
So the point P is (0, -2, -3).
Here, we are required to find the point, P where the lines:
x = 1 + t x = 1 + ty = 2t x = 1 + ty = 2tz = -3tintersects the plane x + y - z = -5.
The point, P where the lines intersects the plane is given by;
he point, P where the lines intersects the plane is given by;P (0, -2, 3)
Therefore, to find this point, we have to substitute for x, y and z in the equation of the plane.
Therefore, we have;
1 + t + 2t -(-3t) = -5.therefore 6t = - 6and ultimately t = -1To get the coordinates of the point P where the lines intersect the plane; we can then find x, y and z by substituting t into each of their equations.
Therefore;
x = 1 + (-1) = 0x = 1 + (-1) = 0y = 2(-1) = -2x = 1 + (-1) = 0y = 2(-1) = -2z = -3(-1) = 3Therefore, the point, P where the lines intersects the plane is given by;
P (0, -2, 3)Read more:
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write the value of the unknown number in the verbal description
5 times the sum of 2 and a number is 80
a. 1
b. 28
c. 4
d. 16
Answer:
B.28
Step-by-step explanation:
Determine if the following relations represent y as a function of x.
================================================
Explanation:
If y has an exponent of 2, 4, 6, etc (basically any even number) then it leads to having inputs with multiple outputs.
Consider something like y^2 = x. If x = 100, then y = 10 or y = -10 are possible. A function can only have exactly one y output for any valid x input. Similar issues happen for things like y^4 = x and so on. So this is why A and C are not functions.
The other equations do not have y values with such exponents, so we can solve for y and have each x input lead to exactly one y output. Therefore, they are functions.
A function assigns the values. The only function that represents y as a function of x is D.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
For any relation to represent a function in terms of x that represents the value of y, the order of y in the function should be equal to 1, therefore, the power of y should be 1, also, the y variable should be alone(Isolated) on one side of the equal sign.
A.) x = y⁴
It represents x in terms of y, therefore, No.
B.) 6x² + y = 4
It represents constant in terms of x and y, therefore, No.
C.) 6x + y² = -1
It represents constant in terms of x and y, therefore, No.
D.) [tex]y = \sqrt{1-x^2}[/tex]
The given function represents y in terms of x, therefore, it is a function that represents y as a function of x.
E.) -2xy = 1
It represents constant in terms of x and y, therefore, No.
Hence, the only function that represents y as a function of x is D.\
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The figure below is a rectangular shipping box.
Name two different planes that contain AD.
Answer:
The planes that contain the line AD are
1) Plane represented by bounded area ABCD
2) Plane represented by bounded area ADHE
Step-by-step explanation:
The line AD is located at the boundary of the planes ABCD and ADHE and as such is contained in the two planes.
A plane is defined as a flat surface in two dimensional space that has a linear vector boundary on alternate sides
A plane can be specified by a letter written in capitals, or by use of the letters at three non collinear points on the plane, such as plane P or plane ABC.
To shop a package, a company charges a one-time fee plus a fee based on the weight of the package. The table below shows the total shipping costs for four packages of different weights.
Answer:
C = $5 + $1.5(w)
Step-by-step explanation:
Given the following information :
Total shipping cost :
One time fee + fee based on package weight
Given the table :
Weight in pounds - - - - Total shipping cost($)
___4__________________11
___8__________________17
___12_________________23
___16_________________29
We can deduce from the table
For a package that weighs (w) 4 pounds
Total shipping cost = $11
Let one time fee = f
Fee based on weight = r
f + 4(r) = 11 - - - - - (1)
For a package that weighs (w) 8 pounds
Total shipping cost = $17
One time fee = f
Fee based on weight = r
f + 8r = 17 - - - - - (2)
From (1)
f = 11 - 4r - - - (3)
Substitute f = 11 - 4r in (2)
11 - 4r + 8r = 17
-4r + 8r = 17 - 11
4r = 6
r = 6/4
r = 1.5
Put r = 1.5 in (3)
f = 11 - 4(1.5)
f = 11 - 6
f = 5
Hence one time fee = $5
Charge based on weight = $1.5
Hence, Total shipping cost 'C' for a package weighing 'w' will be :
C = $5 + $1.5(w)
The length of a rectangle is 6 meters more than three times the width. The perimeter of the rectangle is 44 meters. What are the dimensions of the rectangle?
Answer:
width=4
length=18
Step-by-step explanation:
length-6=3width
length=3width+6
also:
perimeter of the rectangle=2(length+width)
44/2=width+length
22=width+length
now put the length we found in the 1st equation, in 22=width+length
=>22=width+3width+6
22-6=4width
width=4
now do the exact same thing with one of these equations:
22=width+length
length=3width+6
I'd do it with the 1st one:
22=4+length
22-4= length
length=18
Find the vertex of the parabola.
x² + y - 6x + 10 = 0
Can anybody help with these two problems for me please this for algebra finding slope
Answer:
Step-by-step explanation:
1. the slope is -7/2
2. the slope is 2/3
y = mx + b
m is the slope
Slope is the number before the x so
1. -7/2
2. 2/3
What is the runner’s average rate of change between the hours: 0.5 and 2? mph 1.5 and 2.5? mph Average Rate of Change
Answer:4mph
5mph
Slower
Step-by-step explanation:
The average rate of change for the runner is 0.667 miles per hour².
How to calculate the average rate of change?To calculate the average rate of change, we follow the following formula:
[tex]a = \frac{v_{2} - v_{1}}{t_{2} - t_{1}}[/tex],
where a is the average rate of change, v₂ is the final speed, v₁ is the initial speed, t₂ is the time for v₂, and t₁ is the time for v₁.
How to solve the given question?In the question, we are asked to find the runner's average rate of change between the hours 0.5 and 2 with speeds of 1.5 mph and 2.5 mph.
So we take, the initial speed v₁ = 1.5 mph, the final speed v₂ = 2.5 mph, the time for v₁, t₁ = 0.5 hours, and the time for v₂, t₂ = 2 hours.
Thus, we can calculate the average rate of change a, using the formula:
[tex]a = \frac{v_{2} - v_{1}}{t_{2} - t_{1}}[/tex],
or, a = (2.5 -1.5)/(2 - 0.5) = 1/1.5 = 0.667 miles per hour².
Therefore, the average rate of change for the runner is 0.667 miles per hour².
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One number is 38 less than another number. If the sum of the two numbers is 108, find the two numbers.
Answer:
The two numbers are 35 and 73.
Step-by-step explanation:
We can solve this problem by creating two simultaneous equations using the information given.
Let number 1 = x
Let number 2 = y
x = y - 38 -> ( 1 )
x + y = 108 -> ( 2 )
We can solve simultaneous equations using substitution or elimination. For this question, we will use substitution as it is the easier and shorter option.
Substitute ( 1 ) into ( 2 ):
x + y = 108 -> ( 2 )
( y - 38 ) + y = 108
2y - 38 = 108
2y = 146
y = 146 / 2
y = 73 -> ( 3 )
Substitute ( 3 ) into ( 1 ):
x = y - 38 -> ( 1 )
x = ( 73 ) - 38
x = 35
Therefore:
x = 35 , y = 73
Construct the perpendicular bisector for the segment in the following figure. What process did you use? Explain.
Answer:
Perpendicular bisector for the given segment AB is shown below.
Step-by-step explanation:
Construction steps for the perpendicular bisector for the given segment AB are:
1. Open your compass more than half of the distance between end points of the given segment, i.e., A and B.
2. Place the compass on point A and mark two arc on each side of line segment AB.
3. Place the compass on point B and mark two arc on each side of line segment AB, which intersect the previous arcs.
4. Arcs meet at two points. Mark them C and D.
5. Draw the line between C and D.
The perpendicular bisector for the given segment AB is shown below.
evaluate the 1/3 of 10.2
Answer:
3.4
Step-by-step explanation:
Simplify the expression.
5(2-j) + (2j-3)
Answer:
7-3j
Step-by-step explanation:
Answer:
7 - 3j
Step-by-step explanation:
5(2-j) + (2j-3)
Open the brackets. Take note of the signs.
10-5j + 2j-3
Rearrange.
10 - 3 -5 j + 2j
= 7 - 3j
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How far can you ride a bike if you ride for 10 min at speed of 150m/min
Answer:
250 meters/min = 15 km/hr
Step-by-step explanation:
The approximate number to divide from is 16.667. Divide the speed value by 16.667
Answer:
1500m
Step-by-step explanation:
If you ride 150 m every one min then you can ride 150 times 10 in 10 min.
150 times 10 = 1500m
Kendra is working on her financial plan and lists all of her income and expenses in the spreadsheet below. What is Kendra’s net cash flow? a. $295 b. $285 c. $275 d. $255
The spreadsheet is missing, so i have attached it.
Answer:
Option A - $295
Step-by-step explanation:
From the spreadsheet, net pay = $2300 and interest earned on savings = $20
Therefore, her total income = $2300 + $20 = $2320
Now,from the spreadsheet, total expenses = 800 + 120 + 90 + 45 + 95 + 80 + 275 + 520 = $2025
Now, net cash flow = Total income - Total expenses
Net cash flow = $2320 - $2025
Net cash flow = $295
Answer:
a. 295
Step-by-step explanation:
Equivalent expression 31/8 - 21/2
Answer:
-6 5/8 or -6.625
Step-by-step explanation:
31/8 - 84/8 = -53/8
-53/8 = -6 5/8 or -6.625
Find the measure of angle
Answer:
angle AEF is 60 degrees
Step-by-step explanation:
120 - 90 = 30
90 - 30 = 60
Find the distance from the point P to line m in the given figure. A) [tex]\sqrt{170}[/tex]B)[tex]\sqrt{85}[/tex] C) [tex]\sqrt{17}[/tex]D)[tex]\sqrt{34}[/tex]
Answer:
C. [tex]\sqrt{17}[/tex]
Step-by-step explanation:
use pythagorean
= [tex]\sqrt{1^2 + 4^2}[/tex]
= [tex]\sqrt{17}[/tex]
therefore, the answer is C. [tex]\sqrt{17}[/tex]
Answer:
C. √17
Step-by-step explanation:
point P to line m
= √(1² + 4²
= √17
the product of 9 and sum of a number x and 12
Answer:
9(x + 19)
Step-by-step explanation:
Product is a multiplication key word where you'll usually always put parenthesis when multiplying, and where the keyword sum comes you'd add x and 12 for your equation :)
Roslan had a total of $50 in 10-cent coins,20-cent coins and 50-cent coins. The value of his 10-cent coins was 30% of the total value of all his coins. The value of his 20-cent coins was 28% of the total value of all his coins.What was the value of his 50-cent coins?
Answer:
$21
Step-by-step explanation:
Provided total value = $50
$50 = 5,000 cents.
We are provided,
10 cent coins value = 30% of total value
= 0.3 [tex]\times[/tex] 5,000 cents = 1,500 cents
Value of 20 cents coin = 28% of total value
= 0.28 [tex]\times[/tex] 5,000 cents = 1,400 cents
Therefore, remaining value of cents = Total value of 50 cents coins
5,000 cents - value of 10-cent coins - value of 20-cent coins = total value of 50 cents coins
5,000 - 1,500 - 1,400 = 2,100 cents = $21
Which means number of 50 cents coin = [tex]\frac{2,100}{50} = 42\ coins[/tex]
Alternatively,
To calculate value of 50 cent coins
Total value = 100%
Value in 10-cent coins + 20-cent coins = 30% + 28% = 58%
Value in 50-cent coins = 100 - 58 = 42%
= $50 [tex]\times[/tex] 42% = $21
Think about your previous math courses. Identify one tope that you learned about which
you excelled
The answer for this question I don’t think could be answered by anyone but yourself. To help you figure this out, just simply think about all of the math courses you’ve had previous to your current course and think about which course you did best in.
If PQ = 8, QR = 7x, and PR
9x, what is PR?
Answer:
36
Step-by-step explanation:
PQ + QR = PR
substituting the values we have:
8 + 7x = 9x
8 + 7x - 7x = 9x - 7x
8 = 2x
8/2 = 2x/2
4 = x
Now, for the value of PR:
9 x 4
36
David bought a baseball card for $40. the value of the card increased by 25%. what is the new value of the card?
Answer:
65 i think
Step-by-step explanation:
Answer:
65 Im preety sure
Step-by-step explanation:
Determine if the following relations represent y as a function of x.
Answers:
A) yesB) yesC) yesD) noEach yes/no answer refers to the question "is this a function?"
==================================
Explanation:
The last equation is not a function because of the even exponent over the y term. If you apply the fourth root to both sides, you'll end up with y = |x| and y = -|x| as the two possibilities. For any nonzero x, there are multiple y outputs.
The first three equations are functions because we don't have the same issue as the last equation. All exponents for the y terms are odd. Something like y without an exponent really means y^1.
Solve the inequality 14a/11>4/3, and write the solution in interval notation
Answer:
[tex]a > \frac{22}{21}[/tex]
Step-by-step explanation:
Given the inequality function [tex]\frac{14a}{11}>\frac{4}{3}[/tex], to write the inequality in interval notation, we need to first get the solution to the inequality as shown;
[tex]\frac{14a}{11}>\frac{4}{3}\\cross\ multiply\\14a \times 3 > 11 \times 4\\42a >44\\divide \ both \ sides \ by \ 42\\\frac{42a}{42} > \frac{44}{42}\\ a>\frac{22}{21}[/tex]
Hence the expression in interval notation is [tex]a > \frac{22}{21}[/tex]
40 points!! tysmmmm <33
Answer:
54 lol not 40 its 20
Step-by-step explanation:
We've seen that natural numbers are closed under addition. Determine the closure of natural numbers under the other three operations, and give examples to support your answers.
Answer:
A
Step-by-step explanation:a
Find the slope, x and y intercepts and sketch the graph for the linear equation.
y = 2x + 1
Answer:
In bold below.
Step-by-step explanation:
The slope = coefficient of x = 2.
The y-intercept is when x = 0 and x-intercept is when y = 0.
y = 2(0) + 1 = 1 so the y -intercept is (0, 1).
2x + 1 = 0
x = -0.5 so the x-intercept is (-0.5, 0)
0.456(456 repeating) as a fraction
Answer:
Try 57/125
Step-by-step explanation:
Step 1: 0.456 = 456⁄1000
Step 2: Simplify 456⁄1000 = 57⁄125
Answer:
Step 1: 0.456 = 456⁄1000
Step 2: Simplify 456⁄1000 = 57⁄125
Hope this helps! （づ￣3￣）づ╭❤～
3421 ounces equals how many tons
Answer:
0.1069062
Step-by-step explanation:
divide the mass value by 32000
hope this helps.
Write the sentence as an inequality. 7 minus 5 times a number x is greater than 19. An inequality is