The y-intercept of the equation 6x + 12y = 60 is 5, and the slope of the line through points (1, -1) and (-2, 8) is -3. Therefore the correct option is A.
Finding the Y-Intercept of a Linear Equation
To find the y-intercept of the linear equation 6x + 12y = 60, we need to set x to 0. If x=0, the equation simplifies to 12y = 60. Dividing both sides by 12 gives us the y-intercept: y = 5. Therefore, the correct answer is A: 5.
Calculating the Slope between Two Points
The slope of a line containing the points (1, -1) and (-2, 8) can be found by using the formula (y2 - y1) / (x2 - x1). Substituting the given points into the formula results in: (8 - (-1)) / (-2 - 1) = 9 / -3 = -3.
In 2010 the population of alaska was about 710200 what is this number written in word form
Please help quick!!!!
Meyrick and his Aunt Angie(Mrs. Goodlett, 5th grade teacher from (OES) like to pick berries. Together they picked 8 pounds of berries. They want to divide them evenly between themselves and a few family members( Meyrick, Aunt Angie, Jennilee, Grandma, Uncle Mike and Uncle Barry). How many pounds should they put in each perspn's container?
One pound of berries each. 8 divided by 8 is 1 Hope this helps!
Find the directional derivative of f(x,y,z)=z3−x2yf(x,y,z)=z3−x2y at the point (−5,5,2)(−5,5,2) in the direction of the vector v=⟨−3,2,−4⟩v=⟨−3,2,−4⟩.
The directional derivative of [tex]\(f(x, y, z) = z^3 - x^2y\) at \((-5, 5, 2)\)[/tex] in the direction of [tex]\(\mathbf{v} = \langle -3, 2, -4 \rangle\) is \(-248\).[/tex]
To find the directional derivative of [tex]\( f(x, y, z) = z^3 - x^2y \)[/tex] at the point [tex]\((x_0, y_0, z_0) = (-5, 5, 2)\)[/tex] in the direction of the vector[tex]\( \mathbf{v} = \langle -3, 2, -4 \rangle \),[/tex] we'll use the formula for the directional derivative:
[tex]\[ D_{\mathbf{v}} f = \nabla f \cdot \mathbf{v} \][/tex]
where [tex]\( \nabla f \)[/tex] is the gradient of f and [tex]\( \cdot \)[/tex] denotes the dot product.
First, let's find the gradient of f :
[tex]\[ \nabla f = \left\langle \frac{\partial f}{\partial x}, \frac{\partial f}{\partial y}, \frac{\partial f}{\partial z} \right\rangle \][/tex]
Taking partial derivatives:
[tex]\[ \frac{\partial f}{\partial x} = -2xy \][/tex]
[tex]\[ \frac{\partial f}{\partial y} = -x^2 \][/tex]
[tex]\[ \frac{\partial f}{\partial z} = 3z^2 \][/tex]
Substituting the given point [tex]\((x_0, y_0, z_0) = (-5, 5, 2)\)[/tex] into these partial derivatives:
[tex]\[ \frac{\partial f}{\partial x} = -2(-5)(5) = 50 \][/tex]
[tex]\[ \frac{\partial f}{\partial y} = -(-5)^2 = -25 \][/tex]
[tex]\[ \frac{\partial f}{\partial z} = 3(2)^2 = 12 \][/tex]
So,[tex]\( \nabla f = \langle 50, -25, 12 \rangle \).[/tex]
Now, let's find the directional derivative using the dot product:
[tex]\[ D_{\mathbf{v}} f = \langle 50, -25, 12 \rangle \cdot \langle -3, 2, -4 \rangle \][/tex]
[tex]\[ D_{\mathbf{v}} f = (50)(-3) + (-25)(2) + (12)(-4) \][/tex]
[tex]\[ D_{\mathbf{v}} f = -150 - 50 - 48 \][/tex]
[tex]\[ D_{\mathbf{v}} f = -248 \][/tex]
Therefore, the directional derivative of f at the point (-5, 5, 2) in the direction of the vector[tex]\( \mathbf{v} = \langle -3, 2, -4 \rangle \) is \( -248 \).[/tex]
The Correct question is:
Find the directional derivative of f(x,y,z)=z^3−x^2y,f(x,y,z)=z3−x2y at the point (−5,5,2),(−5,5,2) in the direction of the vector v=⟨−3,2,−4⟩,v=⟨−3,2,−4⟩.
An arc that subtends a full angle of 360 degrees is called a(n) ______.
A) angle
B) circle
C) circular arc
D) line segment
Answer:
B) Circle
Step-by-step explanation:
What we will do is to define all the term, then we will now pick the correct option
Angle : An angle can simply be define as a point where two straight line meets.
Arc : An arc is a curved line which formed a circle or part of the circumference of a circle
Circle : A circle is an arc that goes round a central points. A circle subtends a full angle of 360°
Line Segment: A line segment is the shortest distance between two points, or simply put a line that connects to points or joins two points together.
From the above definitions, we can deduct that an arc that subtends a full angle of 360 degree is called a circle.
An airline offers tickets on 3 routes from Atlanta: Chicago for $150, Boston for $160, and Dallas for $180, represented by the matrix [150 160 180] We can find the cost of four of each of the tickets by multiplying this matrix by one of the matrices below. Find it. (Please help @gmanyp)
[tex]\left[\begin{array}{ccc}150&160&180\end{array}\right]\\\\Answer:\ B)\ \left[\begin{array}{ccc}4&0&0\\0&4&0\\0&0&4\end{array}\right][/tex]
[tex]Check:\\\\\left[\begin{array}{ccc}150&160&180\end{array}\right] \cdot\left[\begin{array}{ccc}4&0&0\\0&4&0\\0&0&4\end{array}\right][/tex]
[tex]=\left[\begin{array}{ccc}(150)(4)+(160)(0)+(180)(0)&(150)(0)+(160)(4)+(180)(0)&(150)(0)+(160)(0)+(180)(4)\end{array}\right][/tex]
[tex]=\left[\begin{array}{ccc}600&640&720\end{array}\right][/tex]
Cost of four of each of the tickets:
[tex]Chicago:4\cdot\$150=\$600\\\\Boston:4\cdot\$160=\$640\\\\Dallas:4\cdot\$180=\$720[/tex]
CORRECT :)
Answer: BWhat is the greatest number that can be written with the digits two, five, eight
[tex]2^{5^{8}}[/tex]
that is a number with more than 100,000 digits
Using each of those numbers as digits of a number then it is 852
However, if we raise each number to a power then 2^(5^8) where
5^8 = 390,625 So, 2^390,625 can be estimated by
multiplying the log of 2 (0.30102999566) by 390,625 which equals
117,589.842054688 So, 117,589 is our exponent and then we need to look up the anti-log of .842054688 which equals 6.9511184318 and our number is 6.9511184318 x 10^117,589
DON'T read my comments. I can't delete them.
What is 9 x 200 in another way? Is it 18 ones, hundreds, tens, of thousands?
Answer: 18 hundreds
Step-by-step explanation:
9 x 200
= 9 x 2 x 100
= 18 x 100
= 1800
aka: 18 hundreds
6. Which is an equivalent form of the equation
2x-y=12
A) y=2x+12
B) y=12-2x
C) y=2x-12
D) y=-12-2x
To find an equivalent form of the equation 2x-y=12, isolate y by moving 2x to the other side and changing the sign of each term.
Explanation:To find an equivalent form of the equation 2x-y=12, we want to isolate y. To do this, we need to get y alone on one side of the equation. Let's start by moving the 2x term to the other side by adding 2x to both sides of the equation, giving us -y=12+2x. Next, we can multiply every term in the equation by -1 to change the sign of each term, resulting in y=-12-2x.
So the equivalent form of the equation 2x-y=12 is y=-12-2x, which is option D.
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WILL GIVE BRAINLIST. ANSWER ASAP.
Each week, Lucia earns $x working at a store and receives $20 babysitting. To find how much she will earn in total over 4 weeks, Lucia calculates: x + 20 + x + 20 + x + 20 + x + 20
What is another way Lucia can calculate how much she will earn in total over the 4 weeks?
Drag and drop the equivalent expression in the box.
1. 4x + 20
2. x + 20
3. .x + 80
4. 4(x+20)
The Answer would be 4. 4(x+20)
on the highway trip a midsize car traveled 208 miles on 4 gallons of gasoline. which direct variation equation describes the relationship between gallons of gasoline x and distance traveled in miles y
Remark
It is a direct variation.
y = k x
You can solve for k .
y = 208
x = 4
k= ??
y = k * x
208 = k * 4 Divide by 4
208 / 4 = k
k = 52
So the equation becomes
y = 52 x
Julia has 2 identical rooms in her house. If each room measures 8 feet on one side and 12 feet on another, what is the total area of the rooms?
Answer
192 ft²
Explanation
The rooms measures 12 feet by 8 feet. So it is a rectangle.
The area of a rectangle = length × width
= 12 × 8
= 96 ft²
The area of one room is 96 ft². There are 2 similar rooms.
The area of the 2 rooms = 96 × 2
= 192 ft²
. A student decides to run a simulation of rolling an even number with a single die. Use the simulat results from 20 attempts to estimate the probability, then compare your estimation with the theoretical probability.
1 5 3 2 3 6 5 6 3 3 4 4 1 3 6 5 3 2 2 6
Answer:
Probability of observed is less that probability of theoretical of getting an even number.
Step-by-step explanation:
Given : A student decides to run a simulation of rolling an even number with a single die.
Outcomes - 1 5 3 2 3 6 5 6 3 3 4 4 1 3 6 5 3 2 2 6
To find : Use the simulate results from 20 attempts to estimate the probability, then compare your estimation with the theoretical probability?
Solution :
First we make the frequency distribution table,
X Frequency
1 2
2 3
3 6
4 2
5 3
6 4
Total - 20
Now, The observed probability of getting an even number.
Favorable outcomes of number appeared even = 3+2+4=9
Total number of outcome = 20
Probability of getting even number is [tex]P=\frac{9}{20}=0.45[/tex]
Then, Theoretical probability of getting an even number.
Favorable outcome = 3
Total number of outcome = 6
Probability of getting even number is [tex]P=\frac{3}{6}=\frac{1}{2}=0.5[/tex]
As 0.45<0.5 , Observed < Theoretical
We simulate that probability of observed is less that probability of theoretical of getting an even number.
The estimated probability is 0.45 while theoretical probability is 0.5
Estimated probability :
Number of even values : (2,6,6,4,4,6,2,2,6) = 9The estimated probability can be computed thus ;
favorable outcomes/ total possible outcomesNow we have ;
Probability= 9/20 = 0.45The theoretical probability can be computed thus ;
Even numbers = (2,4,6) = 3Hence, theoretical probability= 3/6 = 0.5
Hence, the theoretical probability is greater than the estimated probability.
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Randy said that the number 0.03 has a value 10 times greater than 0.003.Is he correct ?Explain your answer.
given that (2,3) is on the graph of f(x),find the corresponding point for the function f(x) - 4
The corresponding point for the function f(x) - 4 is (2, -1)
What is a function?A function in mathematics set up a relationship between the dependent variable and independent variable. on changing the value of the independent variable the value of the dependent variable also changes.
given that (2,3) is on the graph of f(x)
So, for x = 2, f(x) = f(2) = 3
Now, define another function g(x) such that
g(x) = f(x) - 4
g(2) = f(2) - 4
g(2) = 3 - 4 = -1
Hence, corresponding point for the function f(x) - 4 is (2, -1)
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if the blue radius below is perpendicular to the green chord and the segment AB is 6.5 units long, what is the length of the chord?
A. 13 units
B. 6.5 units
C. 3.25 units
D. 26 units
if the blue radius below is perpendicular to the green chord and the segment AB is 6.5 units long what is the length of the chord? the correct answer is:
13 units
Answer:
If the radius is perpendicular to a chord, the length of the chord is 13 units (option A).
Step-by-step explanation:
AB=6.5 units
When a radius is perpendicular to a chord divides it into to equal parts, then:
AB=BC=6.5 units
Chord: AC=AB+BC
Chord: AC=6.5 units+6.5 units
Chord: AC=13 units
Solve for x: −2(x + 3) = −2(x + 1) − 4. (1 point) a 2 b 3 c All real numbers d No solution
The correct answer would be
C. All Real Numbers
what is the point slope form of the line with slope -1/4 that passes through the point (-2, 9) ?
•y - 9 = -1/4 (x + 2)
•y + 2 = -1/4 (x - 9)
•y + 9 = -1/4 (x - 2)
•y - 2 = -1/4 (x + 9)
The point-slope form of a line:
[tex]y-y_0=m(x-x_0)[/tex]
We have
[tex]m=-\dfrac{1}{4}\\\\(-2,\ 9)\to x_0=-2,\ y_0=9[/tex]
Substitute
[tex]y-9=-\dfrac{1}{4}(x-(-2))\\\\y-9=-\dfrac{1}{4}(x+2)[/tex]
What is half of 5 3/4?
What is -8+5i. NamrvComplex conjugate and compute the product
A photographer is printing a photograph for a client. The ratio of the photograph’s width to its length is 8:10. The client wants a smaller version of the photograph printed, but the ratio of the width to the length needs to stay the same.
If the length of the printed photograph is 5 inches, what should the width be?
3 inches 4 inches 6 inches 7 inches 8 inches
The ratio is 4:5
because 8 divided by 2 is 4
and 10 divided by 2 is 5
so the answer as said before is 4:5
I hope this helps :)
Answer:
Step-by-step explanation:
4 inches
jim is reading a 303 page book hes already read 87 pages if he can read 12 pages in an hour how many more hours will it take him to finish the book
Is this statement true or false? The Symmetric Property of Equality lets you exchange the expressions on each side of the equals sign.
Math worksheet lesson 10
The given problems on subtraction is solved as follows:
a. 1.8 - 0.9 = 0.9
b. 41.84 - 0.8 = 41.04
c. 341.84 - 21.92 = 319.92
d. 5.182 - 0.09 = 5.092
e. 741 - 3.91 = 737.09
The detailed explanation is as follows:
a. 1.8 - 0.9 = 0.9
Explanation: When you subtract 0.9 from 1.8, you get 0.9. This is a straightforward subtraction of two decimal numbers.
b. 41.84 - 0.8 = 41.04
Explanation: When you subtract 0.8 from 41.84, you get 41.04. Again, this is a simple subtraction of decimals.
c. 341.84 - 21.92 = 319.92
Explanation: Subtracting 21.92 from 341.84 results in 319.92. This is a standard decimal subtraction.
d. 5.182 - 0.09 = 5.092
Explanation: Subtracting 0.09 from 5.182 gives you 5.092. Decimal subtraction works the same way as whole number subtraction.
e. 741 - 3.91 = 737.09
Explanation: When you subtract 3.91 from 741, you get 737.09. This involves carrying over from the hundredth's place to the tenth's place.
In all these calculations, it's essential to align the decimal points and perform the subtraction as you would with whole numbers, taking care to carry over as needed when subtracting decimal places.
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HURRY HELP ASAP!!!!!!! Which of these measurements is more precise and explain why. Explain the difference between precision and accuracy.
Answer:
the first one (the one with more lines which is the centimeter (cm) one)
Step-by-step explanation:
Precision is when you know the exact measurement like 4.756
Accuracy is when your kind of close to the precise measurement like 4.75
Precision means exact and accuracy means close enough.
What is the constant of proportionality to. 2.5x
Luiza runs a lawn-mowing business she decides to measure the rate at which the volume of fuel she uses increases with the area of the lawn what can be an appropiate unit for luiza's purpose
Answer:
[tex]\frac{Gallons}{Feet^{2} }[/tex]
Step-by-step explanation:
We have been told that Luiza runs a lawn-mowing business she decides to measure the rate at which the volume of fuel she uses increases with the area of the lawn and we are asked to determine an appropriate unit for Luiza's purpose.
Since we can represent rate of units as [tex]\frac{Dependent Variable}{Independent Variable}[/tex]
We can see that in this case dependent variable is amount of fuel used in lawn-mowing and area of lawn is independent variable.
We know that we can represent volume of fuel as gallons and area of lawn as square feet.
Therefore, appropriate unit for Luiza's purpose is [tex]\frac{Gallons}{Feet^{2} }[/tex].
Answer:
L/KM^2
Step-by-step explanation:
Can someone help me with this Geometry Homework? Thanks
That is C. my fellow brainy hope you get an A+
Please help asap 27 pts
It's answer B since when you plug in -7 into x, the value then becomes absolute value of 2(-7) - 1, which is absolute value of -15, which becomes 15, and plugging 8 into x gives us absolute value of 2(8) - 1, which is absolute value of 15, which is just 15. That divided by 3 makes 5, so that solution is true when plugging those numbers in for x
A way to make an approximation to a given number by using fewer digits is called ____.
Answer: It is called "rounding"
Step-by-step explanation: Well you can't really explain this one.
Answer:
Rounding
Step-by-step explanation:
Rounding means to give an approximation of a decimal number. The number may be irrational. Rational numbers have a terminating decimal expansion. When rounding off a number first consider to how many decimals you want to round off the number. Then check the next decimal number if it is 5 or more than 5 then increase the preceding decimal number by 1.
Let us take and example
√2 = 1.41.........
Round to the nearest tenths
√2 = 1.4
Round 1.65 to the nearest tenths
1.7