You have been hired as an efficiency expert for Math Nerds Inc. The company wants to cut costs and increase profits by increasing the number of math problems their employees can solve in a day. Your job is to help the Math Nerds employees solve math problems more quickly. Show the Math Nerds employees how to rework each problem below using a polynomial identity. (x2+y2)2=(x2-y2)2+(2xy)2
Show the Math Nerds employees how much time you save on each problem by using the polynomial identity to simplify.
1) ( x+2 ) 2 (x+2) 2 = (x+y) 2 =x 2 +2xy+ y 2
2) ( x−3 ) 3 (x−3) 3 = (x−y) 3 =x 3 −3 x 2 y+3x y 2 − y 3
What are the x-intercept and y-intercept of the graph of
y=1/3 x−6
x:
Y:
What is the length of a picture frame whose width is 3 inches and whose proportions are the same as a 9-inch wide by 15-inch long picture frame?
Which equation shows y=−1/2x+4 in standard form?
A. 2x+y=8
B. x+2y=8
C. x+2y=-8
D. 2x-y=8
Answer: B. x+2y=8
Explanation:
The original equation is:
[tex]y=-\frac{1}{2}x+4[/tex]
The problem asks us to convert the equation in the standard form, so in the form
[tex]ax+by=c[/tex]
with a,b and c being integers.
In order to do that, first of all let's bring on the same side both x and y:
[tex]y+\frac{1}{2}x=4[/tex]
Now we want the coefficient in front of x to be an integer, so let's multiply each term by 2, and we get
[tex]2y+x=8[/tex]
and this corresponds to option B.
The equation that represents y = -1/2x + 4 in standard form is 2x + y = 8.
The equation that shows y = -1/2x + 4 in standard form is 2x + y = 8.
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The sum of nine times a number and fifteen is less than or equal to the sum of twenty-four and ten times the number
The scale factor of the blueprint of a gymnasium to the actual gymnasium is 1in/15ft. The area of the flow on the blueprint is 114in2.
What is the area of the actual gymnasium?
B) 25, 650 ft^2
If the ratio is 1:15, then the measurements of each side of the actual gym are 15 times greater than the scale's. So the areas would have a ratio of 1:225. 114 times 225 is equal to 25, 650
Which of these terms does not describe polygon A'B'C'D ?
A) rotation
B) image
C) preimage
D) transformation
Answer:
Hence, Option: C is correct.
The term that does not describe polygon A'B'C'D' is:
Pre-image.
Step-by-step explanation:
Clearly we could observe that the polygon A'B'C'D' is the image that is obtained by the applying some transformation to the polygon ABCD.
The transformation that is applied to ABCD to obtain A'B'C'D' is:
Rotating the figure anticlockwise 90° and then translating it 7 units to the left and 1 unit downward.
Hence, Polygon A'B'C'D' is not a pre-image.
Since it is an image which is formed or obtained by applying required transformation to the pre-image ABCD.
The correct option is C) preimage. Polygon [tex]\(A'B'C'D'\)[/tex] is the image of the transformation, not the preimage.
To determine which term does not describe polygon [tex]\(A'B'C'D'\)[/tex], we need to understand the definitions of each term in the context of transformations in geometry:
Rotation : This is a type of transformation that turns a figure around a fixed point at a certain angle. Polygon [tex]\(A'B'C'D'\)[/tex] could be a result of rotating polygon [tex]\(ABCD\)[/tex]
Image : The image is the result of applying a transformation to a figure. [tex]A'B'C'D'\)[/tex] is the image of [tex]\(ABCD\)[/tex] after some transformation.
Preimage : The preimage is the original figure before a transformation is applied. In this context, [tex]\(ABCD\)[/tex] is the preimage, not [tex]\(A'B'C'D'\)[/tex]
Transformation : This is a general term that refers to any operation that moves or changes a figure in some way to produce a new figure. The process that produced [tex]\(A'B'C'D'\)[/tex] from [tex]\(ABCD\)[/tex] is a transformation.
From these definitions, the term that does not describe polygon [tex]\(A'B'C'D'\)[/tex] is preimage.
Solve the equation for the letter L: A=LW
Answer:
[tex]L=A/W[/tex]
Step-by-step explanation:
we have
[tex]A=LW[/tex]
Solve for L means -------> isolate the variable L
so
Divide by [tex]W[/tex] both sides
[tex]A/W=LW/W[/tex]
Simplify
[tex]L=A/W[/tex]
What is 7.5 as a fraction ?
What is 1.2 divided by 9?
minimize Q=x^2+2y^2, where x+y=3
To minimize the function Q=x^2+2y^2, substitute x=3-y and expand the expression. Use the vertex formula to find the minimum value of Q. The minimum value is 13.5 when x=1.5 and y=1.5.
Explanation:To minimize the function Q=x^2+2y^2, where x+y=3, we can substitute x=3-y into the function to get Q=(3-y)^2+2y^2. Expanding this expression gives Q=9-6y+y^2+2y^2. Combining like terms, we have Q=3y^2-6y+9.
To find the minimum value of Q, we can use the vertex formula. The x-coordinate of the vertex of the parabola represented by Q=a(x-h)^2+k is x=-h. In our case, h=-(-3)/2=1.5. Substituting this value of x into the equation Q=3y^2-6y+9 gives Q=3(1.5)^2-6(1.5)+9=13.5-9+9=13.5.
Therefore, the minimum value of Q is 13.5 when x=1.5 and y=1.5.
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Hey guys I have 2 short Q! Ill mark as brainliest whoevr helps me ^~^ ThankU x3 (IMAGE is Below for both Qs!)
What is the length of leg y of the right triangle?
A right triangle with hypotenuse 37 and legs 35 and y
A) 2
B) 8
C) 12
D) 35
#2: Which of the following shows the length of the third side, in inches, of the triangle below?
A right triangle is shown. One side of the triangle is labeled as 25 inches. The height of the triangle is labeled as 15 inches.
A) 20 inches
B) Square root of 850 inches
C) Square root of 10 inches
D) 40 inches
How many feet are in 30 yards?
__ ft
Suppose that we have a system consisting of two interconnected tanks, each containing a brine solution. Tank A contains
x(t) pounds of salt in 200 gallons of brine, and tank B contains
y(t) pounds of salt in 300 gallons of brine. The mixture in each tank is kept uniform by constant stirring. When t = 0, brine is pumped from tank A to tank B at 20 gallons/minute and from tank B to tank A at 20 gallons/minute. Find the amount of salt in each tank at time t if x(0) = 10 and y(0) = 40.
q plus 12 minus 2=????
whats the inverse function of f(x)=3x-1
The distance between two cities is one hundred miles, and a woman drives from one city to the other at a rate of fifty mph. At what rate must she return if the total travel time is three hours and forty minutes?
well in her first travel (when she goes to the anther city)
v1= 50mph
d1=100 m
t1=?
t=d/v=100/50=2h
that's meat that she will take 2hours during the first travel
and total travel time = 3h
she wants to take only 1 h in her second travel
v2=?
d2=100 m
t2= 1h
v2= d2 *t2 =100mph
total travel time is 3 hours and 40 minutes so i belive the correct answer is 60mph
Jake earns $7.50 per hour working at a local car wash. The function, ƒ(x) = 7.50x, relates the amount Jake earns to the number of hours he works. Write the inverse of this relation
For this case we have the following function:
[tex] f(x) = 7.50x
[/tex]
An equivalent way to write this function is:
[tex] y = 7.50x
[/tex]
From here, we clear the value of x.
We have then:
[tex] x = \frac{y}{7.50}
[/tex]
Returning the variables we have that the inverse of the function is:
[tex] f (x) ^ - 1 =\frac{x}{7.50}
[/tex]
Answer:
the inverse of this relation is:
[tex] f (x) ^ - 1 =\frac{x}{7.50}
[/tex]
Find the missing coefficient in the equation of the line that passes through the given point. ...?
Use trigonometric substitution to write the algebraic expression as a trigonometric function of θ, where 0 < θ <π/2.
√(100) - 4x^(2), x = 5cos(θ)
Each month, the census bureau mails survey forms to 250,000 U.S. households asking questions about the people living in the household and about things such as motor vehicles and housing costs. Telephone calls are made to households that don't return the form. In one month, responses were obtained from 240,000 of the households contacted. The population of interest is A.the 240,000 households contacted. B.the 250,000 households contacted. C.only U.S. households with phones. D.all U.S. households.
At the bank, brent exchanges $50 in bills for 50 one-dollar coins. the total mass of the coins is 405 grams. estimate the mass of 1 one- dollar coins
What is the period of y = 5 cos x?
What is the period of y= cos 5x
Which best explains whether a triangle with side lengths 2 in., 5 in., and 4 in. is an acute triangle? The triangle is acute because 22 + 52 > 42. The triangle is acute because 2 + 4 > 5. The triangle is not acute because 22 + 42 < 52. The triangle is not acute because 22 < 42 + 52.
Let
[tex]a=2\ in\\b=4\ in\\c=5\ in[/tex]
we know that
If [tex]c^{2} =a^{2}+b^{2}[/tex] -----> is a right triangle
If [tex]c^{2} > a^{2}+b^{2}[/tex] -----> is an obtuse triangle
If [tex]c^{2} < a^{2}+b^{2}[/tex] -----> is an acute triangle
so
substitute the values
[tex]5^{2} > 2^{2}+4^{2}[/tex] ------> is an obtuse triangle
therefore
the answer is
The triangle is not acute because [tex] 2^{2}+4^{2}< 5^{2}[/tex]
Answer: The correct option is
(C) The triangle is not acute because 2² + 4² < 5².
Step-by-step explanation: We are to select the statement that best explains the type of the triangle having lengths of three sides as 2 inch, 5 inch and 4 inch.
We know that a triangle with side lengths a, b and c (c > a, b)is
(i) an acute-angled if a² + b² > c², and
(ii) an obtuse-angled if a² + b² < c².
For the given triangle,
a = 2 inch, b = 4 inch and c = 5 inch.
So, we have
[tex]a^2+b^2=2^2+4^2=4+16=20,\\\\c^2=5^2=25.[/tex]
Since,
[tex]20<25\\\\\Rightarrow a^2+b^2<c^2,[/tex]
so the given triangle is not acute, but obtuse.
Thus, the triangle is not acute because 2² + 4² < 5².
Option (C) is correct.
____ two points are collinear.
A. Any
B. Sometimes
C. No
PLEASE HELP!
The initial amount of people that are sick with the flu is 36 and growing at a rate of 8% every day.
How many people will be sick with the flu in 11 days?
Round to the nearest whole number.
Answer: 84
Step-by-step explanation:
36 Counts as day 0
Day 1 : 36 x 1.08 = 38.88
Day 2 : 38.88 x 1.08 = 41.9904
Day 3 : 41.9904 x 1.08 = 45.349632
Day 4 : 45.349632 x 1.08 = 48.97760256
Day 5 : 48.97760256 x 1.08 = 52.8958107648
Day 6 : 52.8958107648 x 1.08 = 57.127475625984
Day 7 : 57.127475625984 x 1.08 = 61.69767367606272
Day 8 : 61.69767367606272 x 1.08 = 66.6334875701477376
Day 9 : 66.6334875701477376 x 1.08 = 71.964166575759556608
Day 10 : 71.964166575759556608 x 1.08 = 77.72129990182032113664
Day 11: 77.72129990182032113664 x 1.08 = 83.9390038939659468275712
83.9390038939659468275712 rounded to the nearest whole number is 84.
Based on the number of people who were initially sick and the rate of increase, the number who will be sick in 11 days is 84 people.
To find the number who will be sick in 11 days use the future value formula:
= Initial people x ( 1 +rate) ^ number of days
Solving will give:
= 36 x ( 1 + 8%) ¹¹
= 83.9
= 84 people
In conclusion, 84 people will be sick.
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5 1/3 * (-3 9/18) Simplify and Show your work
Write the point-slope form of the equation of the line that passes through the point (1, 3) and has a slope of 2. Include your work in your final answer
Patrick hit his neighbor's car while backing his vehicle out and caused $700 worth of damage. The insurance company paid for $300 of the damage while Patrick had to pay the remaining $400. The amount Patrick paid was his _____.
What is the gratest common factor of 84 and 108?