Answer:
The parametric equations are
x = - 2 t + 4 , y = - 5 t + 2 , z = - 3 t + 4
Step-by-step explanation:
Step(i):-
Given point P = ( 4,2,4)
Given vector is -2 i - 5 j - 3 k
The vector equation of a line through the point a⁻ and parallel to b⁻ is
r⁻ = a⁻ + t b⁻
Given r⁻ = 4 i + 2 j + 4 k
r⁻ = 4 i + 2 j + 4 k + t (-2 i - 5 j - 3 k)
Step(ii):-
The Cartesian form
[tex]\frac{x-a_{1} }{b_{1} } = \frac{y-a_{2} }{b_{2} } = \frac{z-a_{3} }{b_{3} } = t[/tex]
[tex]\frac{x-4 }{-2 } = \frac{y-2 }{-5 } = \frac{z-4 }{-3 } = t[/tex]
[tex]\frac{x-4 }{-2 } = t[/tex]
⇒ x - 4 = -2 t
⇒ x = - 2 t + 4
[tex]\frac{y-2 }{-5 } = t[/tex]
⇒ y - 2 = - 5 t
⇒ y = - 5 t + 2
[tex]\frac{z-4 }{-3 } = t[/tex]
z - 4 = -3 t
z = - 3 t + 4
Conclusion:-
The parametric equations are
x = - 2 t + 4 , y = - 5 t + 2 , z = - 3 t + 4
Margareta is selling freshly baked cookies at 50¢ a cookie, and $2.00 for a pack of 5 cookies. Nathan is selling freshly picked strawberries for $2.00 per pound, and $10.00 for 5 pounds. Who has a proportional relationship between cost and item?
Margareta
Nathan
Both Margareta and Nathan
Neither of them
Answer: Nathan has a proportional relationship between cost and item
Step-by-step explanation:
Using Margareta's statement we will say that if you buy 1 cookie you pay 50 cents and if you by 5 cookies you will pay $2
To find out how much you will pay for one cookie by using the 5 cookies $2 statement we will divide 2 by 5
2/5 = 0.4 which means you pay 40 cents for 1 cookie and that is not equivalent to paying 50 cents per cookie so Margereta method is not proportional.
Nathan sells freshly picked strawberries for $2 per pound and $10 for 5 pounds. Now we want to know how much you have to pay per pound if you were to buy 5 pounds to $10 .
Divide 10 by 5 to find out how much you will pay per pound.
10/5 = 2
So Nathan is selling his strawberries at a proportional rate which is $2 per pound.
solve for x
4 - 2(x - 3) = 24
Answer:
-7
Step-by-step explanation:
4-2x+6=24
10-2x=24
-2x=24-10
-2x=14
X=-7
The solution to the equation is x = -7.
To solve the equation 4 - 2(x - 3) = 24 for the variable x, you can follow these steps:
Step 1: Simplify the expression on the left side by applying the distributive property:
4 - 2x + 6 = 24
Simplifying further:
10 - 2x = 24
Step 2: Move the constant term to the right side by subtracting 10 from both sides:
10 - 10 - 2x = 24 - 10
-2x = 14
Step 3: Divide both sides of the equation by -2 to solve for x:
(-2x) / -2 = 14 / -2
x = -7
Therefore, the solution to the equation is x = -7.
Learn more about Equation here:
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One rule of thumb for estimating crowds is that each person occupies 2.5 square feet. Use
this rule to estimate the size of the crowd watching a concert in an area that is 150 feet long
and 240 feet wide
Answer:
The number of people that will occupy 36000 square feet= 14400 people
Step-by-step explanation:
each person occupies 2.5 square feet.
Area of concert in an area that is 150 feet long and 240 feet wide
Area=150*240
Area=36000 square feet
If one person occupies 2.5 square feet
The number of people that will occupy 36000 square feet
= 36000/2.5
= 14400 people
The number of people that will occupy 36000 square feet= 14400 people
there are twelve bottles in each box of bottled water. Write an equation representing the total number of bottles you get if you buy x boexes. use y to represent the total number of of bottles
Answer:
what does y and x represent no one can answer unless they have x and y
Step-by-step explanation:
Answer:
y=12x
Step-by-step explanation:
Since there are 12 bottles in each box, the total number is the number of boxes multiplied by 12.
For example, buying 1 box will give you 12 bottles (1x12) and buying 2 boxes would give you 24 (2x24).
Therefore the equation of the total number of bottles if you buy x boxes is:
y=12x
Hope this helped!
Is 10 greater than 10.1
Answer:
no
Step-by-step explanation: 10.1 is .1 higher
Answer:
yes
Step-by-step explanation:
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simplify the equation
4 power to 2 . 4 power to 4
Answer:
4^6
Step-by-step explanation:
Because they have the same base (4) and are being multiplied together, the powers simply add together so:
4^2 * 4^4 = 4^(2+4) =4^6
Hope this helped!
On a trip to the grocery store, Zach purchased 7 pounds of fruits and vegetables. How many
kilograms is 7 pounds? Round your answer to the nearest hundredth of a kilogram.
Answer:
3.18 kg
Step-by-step explanation:
It is given that, Zach purchased 7 pounds of fruits and vegetables.
We know that,
1 kg = 2.20462 pounds
It means that, 1 pound = 0.453592 kg
We need to find how kilograms is 7 pounds. So multiply 7 by 0.453592 to convert into kg.
So,
7 pound = 3.17515 kg
or
7 pounds = 3.18 kg
So, the weight of fruits and vegetables is 3.18 kg.
Point and line are coplanar.
Answer:
If they are in the same plane
Step-by-step explanation:
84 ÷ (17 × 3 - 23) × 4
Answer: 12
Step-by-step explanation:
15 POINTS
1.) name two planes that intersect in WX in the figure to the right
Solve this absolute value inequality
8 |u-2| -7<33
Answer:
In set-builder notation, the set of solutions is:
[tex]\left \{u|-3<u<7\right\}[/tex]
Step-by-step explanation:
Let's start by isolating the absolute value expression on one side of the inequality:
8 | u - 2 | - 7 < 33
add 7 on both sides:
8 | u - 2 | < 40
divide both sides by 8:
| u - 2 | < 5
Now, in order to remove the absolute value symbols, we need to consider two different cases:
1) what is inside the absolute value symbols is larger than or equal to zero, so in such case when we remove the absolute value we get exactly what was inside:
u - 2 < 5
u < 5 + 2
u < 7
Now the other case;
2) what is inside the absolute value is smaller than zero, then when removing the symbols we get:
2 - u < 5
2 - 5 < u
-3 < u
Then the set of solutions of this inequality are the set of u values such that u is larger than -3 (to the right of -3 on the number line, and smaller than 7 (to the left of the number 7 on the number line.
In graph form this should look like a highlighted segment on the number line that starts at -3 on the left, ends at 7 on the right, and doesn't include the endpoints -3 and 7.
in set builder notation, the set of solutions is given by:
[tex]\left \{u|-3<u<7\right\}[/tex]
which of the following decimal numbers are greater 2.1 or 2.0113
Answer:
2.1 is greater
Step-by-step explanation: 2.0113 cannot be rounded up since the last number is 3 if it was above 5 or greater it could have been rounded but would have only affected the second number.
43,678 to the nearest ten
Answer:
43,680
Step-by-step explanation:
4 in below let him go
5 and above bump him up
8>5 so we bump him up
so 7-> 8
Answer:
43,680
Step-by-step explanation
Rounding numbers to the nearest 10 means finding which 10 they are nearest to. For example, 78 rounded to the nearest 10 is 80.
The sum of two numbers is eleven. One number is thirty-eight less than six times the other. Find the numbers.
Answer:
One of the number is 4 while the other is 7
Step-by-step explanation:
The sum of two numbers is eleven
Let the numbers be x and y
X+ y = 11
One number is thirty-eight less than six times the other
X= 6y-38
X+ y = 11
6y-38 +y= 11
6y+y= 11+38
7y=49
Y= 49/7
Y= 7
X+ y = 11
X+7= 11
X= 11-7
X= 4
Yuki bought a dress on sale for $48. The sale price was for 40% off, what was the original price of the dress
HELP MEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
I think the answer is A.
How should a random heterogeneous material be sampled in order to construct a representative sample?
Answer:
Explained below.
Step-by-step explanation:
Heterogeneous denotes to a form with different components or features, give the impression as uneven or varied.
A heterogeneous population or sample is the one where each and every individual has a diverse value for the distinctive characteristic one is interested in.
To select a representative sample from the random heterogeneous material one should divide the material into segments and then use random number, either by the random number table or by the random number generator, to select random segments of the material.
If a $20,000 investment earns $1,600 over 2 years, what is the annual interest rate?
Answer:
Annual interest rate = 4%
Step-by-step explanation:
We are given;
Principal; P = $20000
Interest; I = $1600
Period; T = 2 years
Formula for simple interest is;
I = PRT
Making R, rate the subject of the formula gives;
R = I/PT
Plugging in the relevant values gives;
R = (1600)/(20000 × 2)
R = 0.04
In percentage form, R = 4%
Factor.
14y2 + 70y
14y2 + 70y=
Answer:
14y(y+5)
Hope this helps!
Answer:
the answer is 14y(y+5)
Step-by-step explanation:
Using the slope-intercept form to graph the equation y=-8/9 times + 4
so
y=-8/9x+4
Your y intercept is 4
For every 9 units you go (to the right) along the x axis, you go 8 units down on the y axis.
Write the following expression without negative exponents and without parentheses. 5x^-2
Solution:
5x^-2
5 * x^-2
5 * 1/x^2
5/x^2
Best of Luck!
The given expression without negative exponent is [tex]\frac{5}{x^2}[/tex]
Exponents and indicesGiven the indices expression
5x^-2
We are to express with the negative exponent:
According to the indices expression
[tex]x^{-n}=\frac{1}{x^n}[/tex]
Hence the given expression is [tex]\frac{5}{x^2}[/tex]
Learn more on indices here; https://brainly.com/question/10339517
The difference of the quotient of 5 and x and the product of 18 and y
Answer:
(5/x)-(18y)
Step-by-step explanation:
First write the expression (5/x) and then the second expression (18y) the write the difference, so basically a subtraction. (5/x)-(18y)
Find the least common multiple of 4, 2, and 7
Answer:
28
Step-by-step explanation:
So we know that 2 is already a multiple of 4 so we can just find the least common multiple of 4 and 7. So we can do:
4, 8, 12, 16, 20, 24, 28
7, 14, 21, 28
So the least common multiple between 4, 2, and 7 is 28
Find the product of (5/16)(-2)(-4)(-4/5)
Answer:
It's -2
(5/16)(-4/5)=(-20/80)
(-2)(-4)=(8)
(8)(-20/80)= -160/80
-160/80=-2
reggie pays 982.27 each month to rent an apartment. how much will it cost him to rent the apartment for two years
Answer:
982.27 = 1 month
12 months in one year
1 month x 12 is 12 months
982.27 x 12 = 11787.24
11787.24 x 2 = 23574.48
So, it is $23574.48
Try your best!
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15+0= 15
O Communative Property
O Associative Property
O identity Property
O Distributive Property
First of all, let's take a look on the question.
[tex]\large{15 + 0 = 15}[/tex]
Here, 0 is added to 15 and the resultant is 15 only. So, we can say that 0 when added with any number gives the same number as the resultant.
So, the property is known as Identity property because 0 is added to get the identity of the same number.
The Correct Option:
[tex] \large{ \boxed{ \red{ \bf{Option \: C}}}}[/tex]
So, let's know more...
Commutative property ➝ a + b = b + aAssociative property ➝ a + (b + c) = (a + b) + cDistributive property ➝ a(b + c) = ab + acSo this is the general form of these properties which is general observed in the rational numbers.
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What is the solution to the equation 1/4x+2=-5/8-5
Answer: [tex]x=-61/2[/tex]
Simplify both sides of the equation
[tex]1/4x+2=(-5/8+-5)[/tex] (Combine Like Terms)
[tex]1/4x+2=-45/8[/tex]
Subtract 2 from both sides
[tex]1/4x+2-2=-45/8-2\\1/4x=-61/8[/tex]
Multiply both sides by 4
[tex]4*(1/4x)=4*(-61/8)\\x=-61/2[/tex]
Scott and Greg were asked to add two whole numbers. Instead, Scott subtracted the two numbers and got 16, and Greg multiplied them and got 1305. What was the correct sum?
Answer:
One number is 29, and the other one 45
Step-by-step explanation:
Solve this problem by creating two equations that represents the statements, and solve for the unknowns using substitution:
Let's say that one of the numbers is X , and the other one Y, and assume that Y is larger than X, so when we do their difference we get the 16 units they mention in the problem:
Y - X = 16
The info on the product of the two numbers will give us our second equation:
X * Y = 1305
Now use the first equation to substitute Y with 16 + X, in the second equation:
X (16 + X) = 1305
16 X + X^2 = 1305
X^2 + 16 X - 1305 = 0
Now use the quadratic formula to solve for X, and we get two possible answers: X = -45 or X = 29
So, since we are looking for whole numbers, we discard the negative answer, and keep X = 29
Then, the value of the other number "Y" is = 29 + 16 = 45
Angie and Kenny play online video games. Angie buys 1 software and of game play. Kenny 2 buys software and 6 months of game play. Each software package costs $50. If their total cost is $295, what is the cost of one month of game play?
Answer:
The cost of one month of gameplay is $99.2
Step-by-step explanation:
295/6 + 50
49.2 + 50
99.2
(I rounded to the nearest tenth on multiple occasions)
You want to buy 4 CDs for $15.99 each. Estimate the total cost. about $64 about $57 about $60 about $68
Answer:
about $64
Step-by-step explanation:
4 x $15.99 = $63.96
round $63.96 to get $64