100 Points!!!
Polynomial Identities
Part 1. Pick a two-digit number greater than 25. Rewrite your two-digit number as a difference of two numbers. Show how to use the identity (x − y)2 = x2 − 2xy + y2 to square your number without using a calculator.
Part 2. Choose two values, a and b, each between 8 and 15. Show how to use the identity a3 + b3 = (a + b)(a2 − ab + b2) to calculate the sum of the cubes of your numbers without using a calculator.
Let's see
#a
Take 28
(28)²(30-2)²30²-2(30)(2)+2²900-120+4780+4784#2
Take 9,10
9³+10³(9+10)(9²-9×10+10²)(19)(81-90+100)19(181-90)19(91)1729Answer:
Two-digit number greater than 25: 32
Rewrite 32 as the difference of 2 numbers: 40 - 8
Therefore, x = 40 and y = 8
[tex]\begin{aligned}\implies (40-8)^2 & =40^2-2(40)(8)+8^2\\ & = (4 \cdot 10)^2-(80)(8)+64\\ & = 4^2 \cdot 10^2-640+64\\ & = 16 \cdot 100-640+64\\ & = 1600-640+64\\ & = 960+64\\ & = 1024\end{aligned}[/tex]
Let a = 10
Let b = 11
[tex]\begin{aligned}\implies 10^3+11^3 & =(10+11)(10^2-10 \cdot 11+11^2)\\& = 21(100-110+121)\\ & = 21(-10+121)\\ & = 21(111)\\& = 21 (100 + 10 + 1)\\ & = (21 \cdot 100)+(21 \cdot 10)+(21 \cdot 1)\\ & = 2100 +210+21\\ & = 2310 + 21\\ & = 2331\end{aligned}[/tex]
Scientific models can be used for a variety of different purposes. Which of the following statements about scientific models is not true?
a.
Scientific models can save money and lives.
b.
Scientific models allow scientists to test their predictions.
c.
Scientific models allow scientists to study systems that no longer exist.
d.
Scientific models are used rarely.
Answer:
D
Step-by-step explanation:
Characteristics of scientific models
They can save money and livesThey allow scientists to test their predictionsThey allow scientists to study systems that no longer existThey are widely usedOut of the given options, only D is an incorrect statement.
Answer:
D
Step-by-step explanation:
Just took the test
Find the perimeter and area of the parallelogram. 14 cm 18 cm 6 cm
Answer:
b
Step-by-step explanation:
A part of linear function g is graphed on the grid.
Which inequality best describes the domain and range of the part shown?
By looking at the graph, we can see that:
Domain: -7 ≤ x ≤ 6Range: -4 ≤ y ≤ 5.How to find the domain and range of a function?For a function:
y = f(x)
We define the domain as the set of the possible inputs x, and the range as the set of the possible outputs y.
Here, to find the domain, we need to see the range of "horizontal values" that the graph takes. We can see that it goes from -7 to 6, then the domain is:
-7 ≤ x ≤ 6
The range goes from -4 to 5, so the range is: -4 ≤ y ≤ 5.
Then the correct option is the first one.
If you want to learn more about domain and range, you can read:
https://brainly.com/question/1770447
(Will give brainliest answer)
NEED HELP ASAP! SHOW SOLUTION AND EXPLANATION PLEASE!!
1. Find the volume of the solid that results when the region enclosed by the given curves = ^(−2), = 0, = 0, and = 1 is revolved about the x-axis.
2. Find the volume of the solid that results when the region enclosed by the given curves = ^(−2), = 0, = 0, and = 1 is revolved about the y-axis.
The volume of the solid that results when the region enclosed by the given curves y = e⁻²ˣ, y = 0, x = 0, and x = 1 is revolved around the x-axis and the y-axis is 0.77 and 0.7135.
What is the revolution of the curve?Revolving the region bordered by y = f(x) and the x-axis on the interval [a, b] around the x-axis generates the volume (V) of a solid.
The volume is given as
[tex]\rm Volume = \int _a^b \pi y^2 \ dx[/tex]
The volume of the solid that results when the region enclosed by the given curves y = e⁻²ˣ, y = 0, x = 0, and x = 1 is revolved around the x-axis.
[tex]\rm Volume = \int _0^1 \pi (e^{-2x})^2 \ dx\\\\\\Volume = \int _0^1 \pi (e^{-4x}) dx\\\\\\Volume = \pi [\dfrac{e^{-4x}}{-4}]_0^1\\\\\\Volume = - \dfrac{\pi}{4} [e^{-4} - e^0]\\\\\\Volume = -\dfrac{\pi}{4} [-0.98168]\\\\\\Volume = 0.77[/tex]
The volume of the solid that results when the region enclosed by the given curves y = e⁻²ˣ, y = 0, x = 0, and x = 1 is revolved around the y-axis.
[tex]\rm Volume = \pi \left [\int_{0}^{0.135} dy + \int_{0.135}^{1}\left ( \dfrac{\ln x}{-2} \right )^{2}dy \right ]\\\\Volume =0.71375[/tex]
More about the revolution of the curve link is given below.
https://brainly.com/question/14640419
#SPJ1
Write the expression in exponential form.
Answer:
In exponential form given function is equal to [tex]N = b^{r}[/tex]
Step-by-step explanation:
We are given with function,
[tex]log_{b} ^[/tex] [tex]^{N} = r[/tex]
We have to express it in exponential form.
Consider,
[tex]log_{b}^[/tex] [tex]^ {N} = r[/tex]
exponential both side to the power of b as base of given log function is b.
we get
[tex]b ^{logb}[/tex] [tex]^ {N} = b^{r}[/tex]
[tex]N = b^{r}[/tex]
Therefore In exponential form given function is equal to [tex]N = b^ {r}[/tex]
Math and experimental probability for this irrady stuff………
Answer:
so whats the question now?
Step-by-step explanation:
Darnell collected data from two different sales teams in his department, each with four employees the results of the study, based on each workers age and sales, are listed in the tables below. Which of the following is a true statement
The correct statement states that the sales range for team 2 is greater than the sales range for team 1.
What is the range?The range is defined as the difference between the maximum value to the minimum value.
Team 1
Worker's Age Sales
25 30,000
27 29,000
28 32,000
33 35,500
Team 2
Worker's Age Sales
25 35,000
28 37,000
29 38,000
31 65,000
Range Team 1 = 38000 - 30000 = 8000
Range Team 2 = 65000 - 29000 = 36000
Thus, The sales range for team 2 is greater than the sales range for team 1.
Learn more about the range:
brainly.com/question/2264373
#SPJ1
Find the third fourth and eleventh terms of the sequence described by the rule A(n)=-2+(n-1)(5)
Answer:
8,13,48
Step-by-step explanation:
Third = A(3) = -2 + (3-1)(5) = -2 + 10 = 8
Fourth = A(4) = -2 +(4-1)(5) = -2 + 15 = 13
Eleventh = A(11) = -2 + (11-1)(5) = -2 + 50 = 48
Which equation correctly uses the law of cosines to solve for the missing side length of trianglepqr? 62 = p2 82 – 2(p)(8)cos(39°) p2 = 62 82 – 2(6)(8)cos(39°) 82 = 62 p2 – 2(6)(p)cos(39°) p2 = 62 62 – 2(6)(6)cos(39°)
The equation that correctly uses the law of cosines to solve for the missing side length of trianglepqr is 8^2 = 7^2 +11^2 - 2(7)(11) cos <P
The cosine rule formulaFor us to use the cosine formula, an angle must be situated between two sides of the triangle.
According to the rule;
c^2 = a^2 + b^2 - 2ab cos C
From the given diagram, if cos<P is the reference angle, then;
a = 11
b = 7
c = 8
Substiute
8^2 = 7^2 +11^2 - 2(7)(11) cos <P
Hence the equation that correctly uses the law of cosines to solve for the missing side length of trianglepqr is 8^2 = 7^2 +11^2 - 2(7)(11) cos <P
Learn more on law of cosine here: https://brainly.com/question/8288607
Adrian is planning to drive from City X to City Y. The scale drawing below shows the distance between the two cities with a scale of ¼ inch = 18 miles.
City X to City Y is 3 1/2 in.
If Adrian drives at an average speed of 30 miles per hour during the entire trip, how much time, in hours and minutes, will it take him to drive from City X to City Y?
Answer:
takes him 8.4 hrs
Step-by-step explanation:
if 1/4=18inch then 3 1/2=7/2 so 7/2 divide by 1/4=14 then 18 x 14=252
so distance is 252 miles
speed is 30mph so 252/30=8.4h
the answer might need the 0.4 in hrs too
Doing math please help, thanks
Answer:
the x-coordinate of the vertex is the equation of the axis of symmetry of the parabola.
The vertex of the parabola is (-2,3)
So, the axis of symmetry is the line x = -2
Step-by-step explanation:
2+9 is 13 is this the write answer
No this is not the right answer. 2+9 equals 11.
calculate the total perimeter and area of the shaded ring
Answer:
be specific
Step-by-step explanation:
which shaded eing
PLSSS HELP IF YOU TURLY KNOW THISS
Answer:
1 1/2
Step-by-step explanation:
Answer:
1 1/2
Step-by-step explanation:
3 x 1/2 = 1.5 or 1 1/2
y
4
Triangle ABC shown at right is rotated 360
degrees about the y-axis.
А
3
طربيه
This rotation forms a
2
[ Select
with a
1
B
С
20
volume of [ Select]
-1
0
2
3
cubic units.
-1
The rotation of the triangle ABC 360 degrees about the y-axis forms a cone
How to determine the shape after rotation?From the question, we understand that the triangle ABC is a right triangle
The vertical cross-section of a cone is a right triangle.
This means that a right triangle can be rotated 360 degrees on one of its legs (opposite or adjacent) to form a cone
Hence, the rotation of the triangle ABC forms a cone
Read more about rotation at:
https://brainly.com/question/13147596
True or false? pls help me get this right
Find the volume of the sphere shown. Give each answer round to the nearest cubic unit. 15 CM
Answer:
a
Step-by-step explanation:
the volume (V) of a sphere is calculated as
V = [tex]\frac{4}{3}[/tex]πr³ ( r is the radius )
here the diameter = 15, then r = 15 ÷ 2 = 7.5 , then
V = [tex]\frac{4}{3}[/tex]π × 7.5³
= [tex]\frac{4}{3}[/tex]π × 421.875
= [tex]\frac{4\pi (421.875)}{3}[/tex]
≈ 1767 cm³ ( to the nearest cubic cm )
Determine the solutions of the equation. what solution makes sense for the situation? x = what are the dimensions of the rectangle? width = inches length = inches
Answer:
Determine the solutions of the equation. What solution makes sense for the situation?
x = 8
width = 8inches
length = 13
Need ASAP!
What is the exact value of TanA
Answer:
See below
Step-by-step explanation:
Ina right traingle tan (angle) = (opposite side) / (adjacent side)
So tan A = sqrt (161)/8 exactly
a
A circle has a center of (-6,0) and passes
through the point (-1,3). What is its radius?
Answer: 10
Step-by-step explanation:
Given that a circle has the center at
(6.0) and the circle passes through the point (2,−3).So the distance between these two points will give us the measure of the radius.So(x1,y1)=(6
So by using the distance formula the radius of the given circle is-r=√(x2−x1)2+(y2−y1)2r=√(2−6)2+(−3−0)2r=√16+9r=√25=5 unitsSo the diameter of the given circle is=2rd==2(5)d=10units
Let's see
Find distance between these points and radius
√(x_1-x_2)²+(y_1-y_2)²√(-6+1)²+(0-3)²√(-5)²+(-3)²√25+9√34 unitsWhat's the circumference of a circle with a diameter of 25 inches
When rotating the figure you turn it around at a point this can be any coordinate point like the origin which is at?
Answer:
Yes, if you know the coordinates of a point PP in your original figure as (x,y)(x,y), you can figure out the coordinates of PP following rotation and given by (x′,y′)(x′,y′) as
x′=−yx′=−y
y′=xy′=x
HELPPPPPPPPPPPPPPPPP
Answer:
x=6
Step-by-step explanation:
24÷4=6
so 6×4=24 because of distributive proterty meaning that x=6 :))
HELP PLEASE ILL GIVE BRAINLEST IF U HELP QUICK
[tex]\qquad\qquad\displaystyle \huge Answer[/tex]
Let's check if (3 , 6) is the point of intersection of the given lines ~
[tex] \qquad \displaystyle \: y = 4x - 2[/tex]
and
[tex] \qquad \displaystyle \: y = \frac{1}{2} x + 5[/tex]
If the point is the point of intersection of these two lines, then it should satisfy both the equations ~
let's try each of them, using x coordinate of point.
[tex] \qquad \displaystyle \: y = 4(3) - 2[/tex]
[tex] \qquad \displaystyle \: y = 12 - 2[/tex]
[tex] \qquad \displaystyle \: y = 10[/tex]
So, the point didn't actually satisfy one of the equation. hence we can infer that the given statement is wrong.
What is the value of p?
what is 5x-y=10 and 7x - 2y =11
Step-by-step explanation:
they are both linear functions. A function is linear when the degree on X is equal to 1
Cylinder candle has a volume of 125.6 cu in. The height is 10in. What is the radius
Answer:
1.123
Step-by-step explanation:
first find the area of the circle which is 125.6/10 or 12.56. Then divide take the square root which is around 3.54 and divide by pi which you get 1.1.23
Answer:
12.56 inches 10 × 12.56 = 125.6
The answer is 125.6 , If it is wrong i'm srry.
Step-by-step explanation:
Henry has x blue pens. Rachel has $5$ blue pens and $y$ black pens. Jake has $3$ times the total number of pens Henry and Rachel have. Write a simplified expression for the number of pens Jake has.
pen(s)
Answer:
Step-by-step explanation:
Henry X blue
Rachel 5 blue and Y black
Jack 3 times the total of pens ( blue & black)
So
X + 5 + Y for Henry and Rachel
Jack : 3( X + 5 + Y)
Jack has 3X + 15 + 3Y.
Pens of jack 3X + 15 Blue & 3Y black.
Simplify. 3x - 2x + 3 - 2?
Answer:
x+1
Step-by-step explanation:
Answer:
x + 1
Step-by-step explanation:
If we take away 2x from 3x, the remaining is 1x which is simply written as x. If we take away 2 from 3, the remaining is 1. (3 - 2 = 1)