Answer:
The equation [tex]x=4[/tex] represents in R^2 c) a line
The equation [tex]x=4[/tex] represents in R^3 a) a plane
The equation [tex]y+3x=2[/tex] represents in R^3 a) a plane
The equation [tex]z-4y=8[/tex] represents d) a plane
The pair of equations [tex]y=2,z=8[/tex] represents a) a line
Step-by-step explanation:
Let's start by studying each question :
1)
In R^2 , [tex]x=a[/tex] with [tex]a[/tex] ∈ IR is the equation of all vertical lines
In this case, the only free variable is the variable ''y''
R^2 has two dimensions (x and y) so if we set [tex]x=4[/tex] we will have only one free variable in R^2 (which is a line in R^2). Therefore, [tex]x=4[/tex] represents a line in R^2
Now, in R^3 we have three dimensions (x, y and z) so if we set [tex]x=4[/tex] we will have only two free variables (y and z) and [tex]x=4[/tex] will represent a plane (which have two dimensions) in R^3.
2) The equation [tex]y+3x=2[/tex] in R^3 has the free variable ''z'' and given that we select a value (for example for ''x'') the another value from the variable ''y'' is determined. Finally, we have the free variables ''z'' and ''x'', and the variable ''y'' restricted for our choice of the variable ''x''.
The equation [tex]y+3x=2[/tex] in R^3 (given that we have two free variables) represents a plane.
Using the same reasoning, the equation [tex]z-4y=8[/tex] represents a plane (given that it has two free variables : ''y'' and ''x'')
Finally, the pair of equations [tex]y=2,z=8[/tex] set values for ''y'' and ''z'' leading us ''x'' as the free variable. With only one free variable we will have a ''one dimensional'' geometric form. The one dimensional forms in R^3 are lines.
The final answer is a) a line.
33 points!! The line contains the point (4,-2) and is perpendicular to 4x+3y=-6 The equation of the line is:
Answer:
y = 3/4 x - 5
Step-by-step explanation:
The slopes of perpendicular lines are negative reciprocals. We find the slope of the given line. Then we can find the slope of the reciprocal.
4x + 3y = -6
Solve for y.
3y = -4x - 6
y = -4/3 x - 2
The slope of the original line is -4/3.
The slope of the perpendicular is 3/4.
Now we need to find the equation of line with slope 3/4 that contains point (4, -2).
y = mx + b
-2 = (3/4)(4) + b
-2 = 3 + b
-5 = b
b = -5
The equation is
y = 3/4 x - 5
Can you see ninths? How many lemon cookies will you eat if you eat 4/9 of the cookies?
Answer: well this really depends on how many cookies were there in the first place if there was 9 you would have eaten 4 if there was 18 you would have eaten 8.
Find and simplify each of the following for fx = 6x -3. (A) f(x+ h) (B) f(x +h) - f(x) (C) f(x + h) - f(x)/h
Answer:
A
[tex]f(x+ h) = 6x + 6h -3[/tex]
B
[tex]f(x+ h) - f(x) = 6h[/tex]
C
[tex]\frac{f(x + h) - f(x)}{h} = 6[/tex]
Step-by-step explanation:
From the question the given equation is
[tex]f(x) = 6x -3[/tex]
Considering A
[tex]f(x+ h) = 6(x + h) -3[/tex]
=> [tex]f(x+ h) = 6x + 6h -3[/tex]
Considering B
[tex]f(x+ h) - f(x) = 6x +6h -3 - (6x-3)[/tex]
[tex]f(x+ h) - f(x) = 6h[/tex]
Considering C
[tex]\frac{f(x + h) - f(x)}{h} = \frac{6h}{h}[/tex]
[tex]\frac{f(x + h) - f(x)}{h} = 6[/tex]
please help me with this
Answer:
the answer to your question is 7/4
simplify the expresion: 8(x^4 y^3)2/3
Answer:
Answer is this or not
Step-by-step explanation:
16x^4y^3/3
Mylie went by the gas station to get 2.4 gallons of gas. She paid with a $10 bill and a $5 bill and received $4.68 as change. What was the cost for one gallon of gas before taxes? $4.30 $8.20 $10.32 $24.77
We don't know what tax percentage or amount is so we have to keep this part out.
Add to find how much she paid with.
10 + 5 = $15
Subtract to find how much she paid.
15 - 4.68 = $10.32
Divide to find the unit price.
10.32 / 2.4 = $4.30 per gallon
Best of Luck!
How are integers and rational numbers the same ?
Answer:
Every integer is a rational number, since each integer n can be written in the form n/1. For example 5 = 5/1 and thus 5 is a rational number. However, numbers like 1/2, 45454737/2424242, and -3/7 are also rational, since they are fractions whose numerator and denominator are integers.
Step-by-step explanation:
Answer:
an integer is a rational number
Step-by-step explanation:
If your car travels 300 miles and uses 10.2 gallons, how many miles per gallon did you get? (Round your answer to three decimal places.)
Solve for the function X(s) in the Laplace domain by taking the Laplace transform of the following differential equations with given initial conditions. dx +9x = 161, where x(0) = 0 and (0) = 5
Answer:
X(s) = 2/[s³(s + 9)]
Step-by-step explanation:
Here is the complete question
Solve for the function X(s) in the Laplace domain by taking the Laplace transform of the following differential equations with given initial conditions.
dx/dt + 9x = 16t² x(0) = 0 and dx(0)/dt = 5
Solution
dx/dt + 9x = 16t²
Taking the Laplace transform of the differential equation, we have
L{dx/dt + 9x} = L{16t²}
L{dx/dt} + L{9x} = L{16t²}
L{dx/dt} + 9L{x} = 16L{t²}
sL{x} - x(0) + 9L{x} = 16L{t²}
L{x} = X(s)
L{t²} = 2!/s³
Substituting X(s) and L{t²} into the equation above, we have
sX(s) - x(0) + 9X(s) = 2!/s³
Substituting x(0) = 0 into the equation above, we have
sX(s) - x(0) + 9X(s) = 2!/s³
sX(s) - 0 + 9X(s) = 2!/s³
sX(s) + 9X(s) = 2!/s³
Factorizing X(s), we have
(s + 9)X(s) = 2!/s³
X(s) = 2/[s³(s + 9)]
So X(s) in the Laplace domain is
X(s) = 2/[s³(s + 9)]
what is the density of an object with 17 g and a volume of 3cm^3
Answer:
5.6666666666667 grams/cubic centimeters
Step-by-step explanation:
teps:
ρ = m / v
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
17 gram s / 3 cubic centimeter
= 5.6666666666667 grams/cubic centimeter
I believe this is correct unless you need to round it up
I hope I helped
Answer:
5.67g/cm³
Step-by-step explanation:
Density =mass ÷ volume
17÷3=5.67
The highest point in Louisiana is Driskill Mountain at 585 feet. The lowest points -8 feet in New Orleans. What is the difference in feet between the highest and lowest elevation points? PLEASE SHOW THIS ON A VERTICLE NUMBER LINE!!!!!
The answer is a 577 foot difference
You are the manager of a fast-food store. Part of your job is to report to the boss at the end of each day which special is selling best. Use your vast knowledge of descriptive statistics to write one paragraph letting the boss know what happened today. Here are the data. Do this exercise by hand. Be sure to include a copy of your work.SPECIAL NUMBER SOLD COSTHuge Burger 20 $2.95Baby Burger 18 $1.49Chicken Littles 25 $3.50Porker Burger 19 $2.95Yummy Burger 17 $1.99Coney Dog 20 $1.99Total Specials Sold 119
Answer:
A total of 119 Specials were sold today. Chicken Littles had the highest number sold, which represents about 21% (25/119 * 100) of the total sales and a cost of 24% of the total costs. This was followed by Huge Burger and Coney Dog which were sold 20 each or about 17% of the number sold. Poker Burger, Baby Burger, and Yummy trailed behind with total sales of 19, 18, and 17 respectively.
Step-by-step explanation:
a) Data and Calculations:
SPECIAL NUMBER SOLD Percentage COST Percentage
Huge Burger 20 17% $2.95 20%
Baby Burger 18 15% $1.49 10%
Chicken Littles 25 21% $3.50 24%
Porker Burger 19 16% $2.95 20%
Yummy Burger 17 14% $1.99 13%
Coney Dog 20 17% $1.99 13%
Total Specials Sold 119 100% $14.87 100%
I need help by figuring this out, this is geometry.
You have $437 in a savings account. After a deposit, the balance is $1087. What was the amount of the deposit?
Write the recurrence relation for the nth term which is defined by multiplying the prior term by 3 and subtracting 12.
Answer: Aₙ = 3*Aₙ₋₁ - 12
Step-by-step explanation:
Here our terms will be denoted as:
Aₙ
Where this is the n-th term of the sequence.
Now we have that the recurrence relation is defined by:
"by multiplying the prior term by 3 and subtracting 12."
Then we will have that:
Aₙ = 3*Aₙ₋₁ - 12
That is the equation to find all the terms in our sequence (remember that we need to know the initial term, A₀ in order to find all the other ones)
What is the slope of the line passing through the given points.
(-3,2), (6,-1)
Answer:
-1/3
Step-by-step explanation:
Since we are given two points, we can find the slope using
m = ( y2-y1)/(x2-x1)
= ( -1-2)/( 6- -3)
= ( -1-2) /( 6+3)
= -3/9
= -1/3
Answer:
Slope (m) = [tex]\frac{-1}{3}[/tex] = -0.33333333...
Step-by-step explanation:
Slope (m) = ΔY -1
ΔX 3
(m)= -1/3
Write the equation of the line that goes through the point
(7, 10) and is parallel to the line y = 2x + 5
Use point slope equation.
Since parallel, the slope is the same. Then jsut plug in the numbers to the formula (u can google this)
y - 10 = 2 (x - 7)
^^this is point slope form
for slope intercept:
y = 2x - 4
Answer:
[tex]y=2x-4[/tex]
Step-by-step explanation:
So we want to write an equation of a line that goes through the point (7,10) and is parallel the the line y=2x+5.
First, we can determine the slope of our new line. Parallel lines always have the same slope. In other words, the slope of our new line must also be 2.
Now, we can use the point-slope form to find our equation:
[tex]y-y_1=m(x-x_1)[/tex]
Let's let (7,10) be x₁ and y₁. Let's also substitute 2 for m. Thus:
[tex]y-10=2(x-7)[/tex]
Distribute:
[tex]y-10=2x-14[/tex]
Add 10 to both sides:
[tex]y=2x-4[/tex]
And we're done!
Darren drives to school in rush hour traffic and averages 30 mph. He returns home in mid-afternoon when there is less traffic and averages 40 mph. What is the distance between his home and school if the total traveling time is 1 hr 45 min?
Answer:
Distance problems are word problems that involve the distance an object will travel at a certain average rate for a given period of time.
The formula for distance problems is: distance = rate × time or d = r × t.
Things to watch out for:
Make sure that you change the units when necessary. For example, if the rate is given in miles per hour and the time is given in minutes then change the units appropriately.
It would be helpful to use a table to organize the information for distance problems. A table helps you to think about one number at a time instead being confused by the question.
Step-by-step explanation:
raji collected numerical data. which question could raji ask for categorical data?
A. what kind of pet do you have?
B. how long have you had a pet?
C. how much does your pet weigh?
D. how tall is your pet?
Marvin wages are
for moving 480 crates at a piecework rate of $1.50 per crate.
$720
O $150
None of these
$481.50
$320
Answer:
The answer to your question is 320
How many meters are in 3.5 kilometers
Answer:
Hey there!
1000 meters are in one kilometer, so 3500 meters are in 3.5 kilometers.
Hope this helps :)
Answer:
3,500 meters
Step-by-step explanation:
So this is conversation rates. So how I like to remember conversion rates in the metric system is King Henry Doesn't Usually Drink Chocolate Milk.
K=Kilo, H=Hecto, D=Deca, U=Unit (meters, liter, grams), D=Deci, C=Centi, M=Milli.
SO between meters (which is the U) and kilometers (which is the K), there's 3 letters so kilometers is 1000 times greater than meters. SO 3.5*1000=3500.
Hope this helped
4. Consider the figure below.
(5x - 14) ft
(2x) - 5x2 - 12x + 14) ft
What is the total area, in square feet, of the figure
Answer:
(10x⁴ - 52x³ + 5x² + 246x - 196) ft²
Step-by-step explanation:
The figure can be divided into two rectangles: the small rectangle and the large rectangle.
Dimensions of the small rectangle:
Length (l) = (x) ft
Width (w) = (x² - 6) - (5x - 14) = x² - 6 - 5x + 14 = (x² - 5x + 8) ft
Area of small rectangle = l*w = (x)(x² - 5x + 8)
Area = x(x²) - x(5x) + x(8) (using distributive property)
Area of small rectangle = (x³ - 5x² + 8x) ft²
Dimensions of large rectangle:
Length (l) = (2x³ - 5x² - 12x + 14) ft
Width (w) = (5x - 14) ft
Area of large rectangle = l*w = (2x³ - 5x² - 12x + 14)(5x - 14)
2x³(5x - 14) - 5x²(5x - 14) - 12x(5x - 14) + 14(5x - 14) (distributive property)
10x⁴ - 28x³ - 25x³ + 70x² - 60x² + 168x + 70x - 196
Combine like terms
Area of large rectangle = (10x⁴ - 53x³ + 10x² + 238x - 196) ft²
Area of figure = area of small rectangle + area of large rectangle
= (x³ - 5x² + 8x) + (10x⁴ - 53x³ + 10x² + 238x - 196)
Open parentheses
= x³ - 5x² + 8x + 10x⁴ - 53x³ + 10x² + 238x - 196
Combine like terms and arrange in standard form (from the greatest degree to the least)
= 10x⁴ + x³ - 53x³ - 5x² + 10x² + 8x + 238x - 196
= 10x⁴ - 52x³ + 5x² + 246x - 196
Area of the figure = (10x⁴ - 52x³ + 5x² + 246x - 196) ft²
Solve for x. x/3≤−6 A. x≥−18 B. x≤−18 C. x≥−2 D. x≤−2
Answer:
Step-by-step explanation:
x/3 ≤ -6
x ≤ -18
answer is B
Answer:
B
Step-by-step explanation:
it is simple easy..first you have to through your 3 become times with -6,then you have your answer
Helpppppppppppppppppppp pleaseeeeeeeeeeeeee
Answer:
ok
Step-by-step explanation:
what
A football field is 120 yards by 53.333 yards. What is the area of the football field in acres if 1 acre=43560 ft?? Use correct
significant figures when answering this question.
Answer:
The area of the pitch in an acre is 1.32 acreStep-by-step explanation:
This problem requires to test our understanding of unit conversion, and we are expected to present our answer in an acre
first, let us convert from the yard to feet
given that the dimension of the pitch is
120 yards by
53.333 yard
1 yard is 3 foot
120 yards will give x
cross multiply we have
x1= 120*3
x1= 360 feet
also the second dimension is
x2= 53.333*3
x2= 159.999
x2= 159.999 feet
the area of the pitch is
area= 159.999*360
area= 57599.64 ft^2
Note: an acre is a unit for land area (1 acre=43560 ft^2)
if 1 acre = 43560 ft^2
x acre = 57599.64 ft^2
cross multiply we have
x acre = 57599.64/43560
x acre = 1.32 acre
If f(x) = x+2 and g(x) = radical x-9, find g(f(x)).
Answer:
second option
Step-by-step explanation:
Substitute x = f(x) into g(x) , that is
g(f(x))
= g(x + 2)
= [tex]\sqrt{x+2-9}[/tex]
= [tex]\sqrt{x-7}[/tex]
write the sentence as an equation
z is the same as a more than 252
Answer:
it depends on what ur multipling
Which one of these is not an integer?
a 0.75
b-9
со
d 16
Check it
Answer:
A
Step-by-step explanation:
If two acute angles are added together then the result is an obtuse angle.
True
False
Find ( f - g ) (x) f (x) = 2x^2 - 2 and g (x) = 4x + 1
Answer:
( f - g ) (x) f (x) = 2x^2 - 2
g (x) = 4x + 1
answers in pics