Two factors of x²-12x+36 are
(x-6) and (x-6)
Solution;
x²-12x +36
x²-6x -6x +36 ( split -12x in two parts such that if add them we will get-12x and if multiply will get 36x²)
Taking x common from first two terms and 6 from next two terms
x(x-6) -6(x -6)
taking (x-6) common
(x-6)(x-6)
Answer:
[tex]x^2 - 12x + 36 = (x-6)(x-6) = (x-6)^2[/tex]
Step-by-step explanation:
We are given the following expression:
[tex]x^2 - 12x + 36[/tex]
We need to factor the given expression.
We will do this with the help of technique of splitting the middle term.
Factorization can be done as:
[tex]x^2-12x + 36\\=x^2 - 6x-6x+36\\=x(x-6)-6(x-6)\\=(x-6)(x-6)\\=(x-6)^2[/tex]
Thus, the factored form of given expression is:
[tex]x^2 - 12x + 36 = (x-6)(x-6) = (x-6)^2[/tex]
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
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
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 -8+5i. NamrvComplex conjugate and compute the product
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
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!
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
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)
BRAINLIEST!!PLEASE HELP
Which linear inequality is shown on the graph?A)x − y ≤ −2B)x − y ≥ −2C)x − y ≤ 2D)x − y ≥ 2
Graph the inequality by finding the boundary line, then shading the appropriate area.
C.
The linear inequality shown on the graph is x − y ≤ 2. Correct option is c.
A linear inequality represents a region on the coordinate plane. The inequality may be of the form "y ≤ mx + b," "y ≥ mx + b," "y < mx + b," or "y > mx + b," where m is the slope and b is the y-intercept of the line.
To identify the correct linear inequality from the graph, look for the shaded region (if any) and the direction of the shading. The shading indicates the solution region of the inequality. If the shaded region is above the line, it represents "y > mx + b" or "y ≥ mx + b" depending on whether the line is solid or dashed, respectively. If the shaded region is below the line, it represents "y < mx + b" or "y ≤ mx + b" depending on whether the line is solid or dashed, respectively.
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A ride on the roller coaster costs 4 tickets while the boat ride only costs 3 tickets. Michael went on the two rides a total of 10 times and spent a total of 37 tickets. Which equation is true?
A. r(10 – r) = 10
B. r + (10 – r) = 4 + 3
C. 4r[3(10 – r)] = 37
D. 4r + 3(10 – r) = 37
Answer:
D. 4r + 3(10 – r) = 37
Explanation:
Let r be the roller coaster ride. Since it costs 4 tickets, this gives us the expression 4r.
We know that there were 10 rides total; this leaves Michael 10-r for the number of times he rode the boat ride.
Each boat ride costs 3 tickets; this gives us the expression
3(10-r)
Together, this gives us
4r+3(10-r) = 37
Answer:
A ride on the roller coaster costs 4 tickets while the boat ride only costs 3 tickets. Michael went on the two rides a total of 10 times and spent a total of 37 tickets.
A table titled Ride Tickets, showing Times on the Ride, Tickets per Ride, and Total Tickets. The first row shows Roller Coaster, with r, 4 and 4 r. The second row shows Boat Ride, with 10 minus r, 3, and 3 left parenthesis 10 minus r right-parenthesis. The third row shows, Total, with 10, blank, and 37.
Which equation is true?
r(10 – r) = 10
r + (10 – r) = 4 + 3
4r[3(10 – r)] = 37 this is your answer
4r + 3(10 – r) = 37
Step-by-step explanation:
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
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: B21) the admission fee at a movie theater is $5 for children and $9 for adults. If 3200 people go to the movies and $24000 is collected, how many children went to the movies?
To solve the problem, we set up a system of two equations to represent the given conditions. By solving this system, we found that 1200 children and 2000 adults went to the movies.
Explanation:
We can solve the problem using a system of linear equations. Let's denote the number of children as C and the number of adults as A. From the question, we know two things:
The total number of people is 3200, so C + A = 3200.The total amount of money received is $24,000, and as children pay $5 and adults pay $9, this gives us another equation: 5C + 9A = 24000.By solving this system, we can find the number of children and adults. Using the elimination method, multiply the first equation by 5 and subtract it from the second equation, we get 4A = 8000, so A = 2000. Substituting A = 2000 into the first equation gives us C = 1200, which means 1200 children went to the movies.
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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⟩.
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:
. 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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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
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
Jasmine has 8 packs of candle wax to make scented candels. Each pack contains 14 ounces of wax. Jasmine uses 7 ounces of wax to makecone candle how many candels can she make
In 2010 the population of alaska was about 710200 what is this number written in word form
Randy said that the number 0.03 has a value 10 times greater than 0.003.Is he correct ?Explain your answer.
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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What 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.
if you have 1,000,000 $ and you stend 9,899 what does that =
If you have 1,000,000 $ and you spend 9,899 what does that =
1,000,000 - 9,899 = 990,101
Answer: $990,101
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.
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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Please help quick!!!!
Can someone help me with this Geometry Homework? Thanks
That is C. my fellow brainy hope you get an A+
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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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.