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Explanation:
Factor the given expression
x^2+x^3
x^2*1+x^2*x
x^2(1+x)
x^2(x+1)
We end up with something where the factor x^2 is a perfect square regardless of whatever we replace x with from the set {1,2,3,...,99,100}.
In short, we don't need to worry about the x^2 portion.
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The only thing of importance is the x+1 factor.
The x+1 must be a perfect square so that the original expression is as well.
Let's say M is some perfect square between 1 and 100. That means M belongs to the set of values
{1, 4, 9, 16, 25, 36, 49, 64, 81, 100}
If we want M+1 to be a perfect square, then we'll need to subtract 1 from each item in that set above to counteract the "plus 1" in "M+1".
Subtract 1 from each item to end up with this modified set
{0, 3, 8, 15, 24, 35, 48, 63, 80, 99}
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Every item mentioned in that second set will make x^2+x^3 to be a perfect square.
For example, let's pick x = 15
x^2(x+1) = 15^2*(15+1)
x^2(x+1) = 15^2*16
x^2(x+1) = 15^2*4^2
x^2(x+1) = (15*4)^2
x^2(x+1) = 60^2
This confirms that x^2+x^3 is a perfect square for x = 15. I'll let you check the other values.
There are 10 values in the set {1^2,2^2,...,9^2,10^2} = {1,2,...,81,100}. There are also 10 values in the set {0,3,8, ..., 80, 99} we got earlier. The cardinality hasn't changed. However, we'll kick out 0 because it's not between 1 and 100. So we end up with 9 as our final answer.
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To summarize, there are 9 values of x that make x^2+x^3 a perfect square, where x is some whole number between 1 and 100 inclusive.
Steven collected $5.40 from 3 people for a train ride. How much was the train ride per person?
A. $2
B. $1.80
what is twelve billion three hundred forty two million sixty five in numbers
Answer:
12,342,000,065
Step-by-step explanation:
yeah-ya
Find the slope and use the point to write an equation of the line in point slope form.
Answer:
y + 1 = [tex]\frac{1}{2}[/tex] (x + 2)
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b ) a point on the line
Calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 2, - 1) and (x₂, y₂ ) = (0, 0) ← 2 points on the line
m = [tex]\frac{0-(-1)}{0-(-2)}[/tex] = [tex]\frac{0+1}{0+2}[/tex] = [tex]\frac{1}{2}[/tex]
Using (a, b ) = (- 2, - 1 ) , then
y - (- 1) = [tex]\frac{1}{2}[/tex] (x - ( - 2) ) , that is
y + 1 = [tex]\frac{1}{2}[/tex] (x + 2) ← in point- slope form
The ratio of juice to water is 1:5. How much
juice is needed to make 24 liters of punch?
Answer:
5.8 liters
Step-by-step explanation:
24 divided by 5 becomes 5.8
Ariel, who is 15, is 3 years more than
twice the age of Hilary. How old is
Hilary?
Answer:
6
Step-by-step explanation:
15 - 3 = 12, divide that by 2 and your answer is 6.
Answer:6
Step-by-step explanation:
yea
15. Solve the compound inequality.
3x - 4 >5 or 1 - 2x 7
A X<-3 or x > 3
B x < -3 or x > 3
CX-3 or x <3
D x>-3 or x < 3
hope you like my answer its Letter D
Calculate the angle subtended by an arc whose length is 89.5cm and radius 12cm
Answer:
Step-by-step explanation:
angle at the center
[tex]\theta=\frac{l}{r}\\where~l=length~of~arc\\r=radius\\\theta=\frac{89.5}{12}~radians[/tex]
What do you add to 2 3/7 to make 4
&
What do you add to 5 4/9 to make 7
Hope this helps, have a nice day!!!
Our answers are
1 4/7 and 1 5/9
This I my question any body help
Answer: table 2
Step-by-step explanation:
its because the rest of the tables do not have a pattern that ‘makes sense’ unlike table 2. for table 2, for every one 1 km there’s 10$
10r = –50 solve for r
Answer:
10r=-50
r = -50/10
r = -5
.........
please help if possible does anyone know where to find the answers to this packet
Answer:
This looks teacher made so i doubt you would be able to find this anywhere
Step-by-step explanation:
Could someone please help answer this, Thanks so much, please no spam, will give brainliest (homework help)
Answer:
b<-7
Step-by-step explanation:
3b+3<-18
subtract 3 on both sides
3b<-21
divide 3 on both sides
b<-7
which angles are alternate
Answer:
POL and KLO
Step-by-step explanation:
Alternate interior angles are between the parallel lines and on opposite sides of the transversal
NOL and MLO
POL and KLO
Answer:
KLO and POL
Step-by-step explanation:
PLEASE HELP ASAPPP -K-12-
What is the equation of the line in slope-intercept form?
y =
x +
Answer:
y = (3/5)x + 3
Step-by-step explanation:
(-5,0)
(0,3)
3/5 x + 3
Can you help me please?
WILL SOMEONE HELP PLZ ANSWER THESE 3 QUESTIONS*
The number line compares the numbers –6, 3, and 5.
1. Write an inequality that compares –6 and 3. Justify your inequality using the number line.
2. Write an inequality that compares 3 and 5.
3. Write an inequality that compares –6, 3, and 5.
#1
-6-3-5
Hence inequality will be
[tex]\\ \sf\longmapsto -6\leqslant 5[/tex]
#2.
3<5
But we need inequality
[tex]\\ \sf\longmapsto 3\leqslant 5[/tex]
#3
The inequality given by
[tex]\\ \sf\longmapsto -6\leqslant 3\leqslant 5[/tex]
Answer:
1. Inequality
[tex] \hookrightarrow \: { \rm{ - 6 < 0 < 3}}[/tex]
2. Inequality
[tex] \hookrightarrow \: { \rm{3 < 0 < 5}}[/tex]
3. Inequality
[tex] \hookrightarrow \: { \rm{ - 6 < 0 < 3 < 5}}[/tex]
11. Find the value of r so that the polygons have the same per
X+4
x + 5
x + 3
X-2
X+4
(Just solve 11. Pleaaase!)
Answer: i
Step-by-step explanation: dk
Volume Of This Prism
Answer:
look at the photo i have sent
Which statement best supports the generalization that the history of Earth is stored in its rocks?(1 point) ASAP PLEASE!!!!!!!
An analysis of the area known as the Siberian Traps proved that a major volcanic eruption contributed to a mass extinction on Earth.
An analysis of the area known as the Siberian Traps proved that a major volcanic eruption contributed to a mass extinction on Earth.
A study of the metal iridium revealed that it is rarely found on Earth.
A study of the metal iridium revealed that it is rarely found on Earth.
An investigation into increased ocean temperatures indicated global warming occurred on Earth.
An investigation into increased ocean temperatures indicated global warming occurred on Earth.
A test to measure the impact of an asteroid striking Earth highlighted the large clouds of dust that would block out the sun.
Answer:
the last paragraph ʕ•ﻌ•ʔʕ•ﻌ•ʔʕ•ﻌ•ʔ
Answer:
An analysis of the area known as the Siberian Traps proved that a major volcanic eruption contributed to a mass extinction on Earth.
Step-by-step explanation:
Which line has a larger slope?
Answer:
the one on the right looks best for the slope because the slope is a lot larger than the one on the right the one on the right is smaller but a few inches few times I don't know you might want to check it before I actually answer it for you so I hope you found this kind of helpful thank you bye
Write a linear function for the data in each table.
SEE EXAMPLE 2
21.
х
-2
-1
0
1
2.
1
у
N
-1 -2 1 / 4
N
f(x) = -3/2x +3
f(x) = -3/2x-1
f(x) = 2x - 1
f(x) = 2/3x - 1
f(x) = 4x + 2
Bby
f(×) =-1-21/4yn Thanks me later
1
What is the solution to the equation
1/x = x+3/2x^2
?
O X=-3
O x= -3 and x = 0
O x = 0 and x = 3
O x=3
[tex] \frac{1}{x} = \frac{x + 3}{ {2x}^{2} } \\ = > \frac{2 {x}^{2} }{x} = x + 3 \\ = > 2x = x + 3 \\ = > 2x - x = 3 \\ = > x = 3[/tex]
Answer:The answer is option d. X = 3
Please I’ll mark brainiest and I’ll give extra points !!
Answer:
B
Step-by-step explanation:
2.75 x 0.10x
x in this case is 0
so 2.75 x 0.10x0
= 2.75
A local business rents computer time for a $5 setup charge and $0.30 per minute the computer is used
Write an equation to represent the cost of using the computer for a given amount of
Us
time in minutes. Define your variables.
How much does 30 minutes of computer time cost?
Answer:
[tex]c = 0.3m + 5[/tex]
define the variables:
c is the cost and m is minutes
It costs $14
Step-by-step explanation:
[tex]c = 0.3m + 5[/tex]
To solve for cost substitute 30 in for m
[tex]c = 0.3(30) + 5[/tex]
multiply
[tex]c = 9 + 5[/tex]
add
[tex]c = 14[/tex]
What is the slope of a line perpendicular to the line whose equation is 10x + 6у –84. Fully simplify your answer.
Answer:
The slope is 3/5.
Step-by-step explanation:
I am assuming you mean
10x + 6y = 84
6y = -10x + 84
y = -5/3 x + 14.
So the slope of this line is -5/3 and the slope of a line perpendicular to it is
-1 / -5/3 = 3/5.
X = ?
Can someone tell me
The answer to this question
Answer:
113=x
Step-by-step explanation:
seeing as how the sum of all angles in a triangle is 180 degrees, we can get an equation:
28+39+x=180
simplify to get:
67+x=180
subtract 67 from both sides to get your answer:
113=x
Answer:
[tex]x=113[/tex]
[tex]y=67[/tex]
[tex]z=49[/tex]
Step-by-step explanation:
To find x:
We can use the angle sum property of a triangle which states that, The sum of all internal angles of a triangle is always equal to 180°.
Therefore, [tex]28+39+x=180[/tex]
[tex]67+x=180[/tex]
[tex]x=180-67[/tex]
[tex]x=113[/tex]
Now that we know the value of [tex]x[/tex] we can use it to find the value of [tex]y[/tex].
We can see that angle [tex]x[/tex] and [tex]y[/tex] are supplementary which means:
[tex]x+y=180[/tex]
[tex]113+y=180[/tex]
[tex]y=180-113[/tex]
[tex]y=67[/tex]
Now that we know the value of [tex]y[/tex] we can use the angle sum property of a triangle again:
[tex]64+y+z=180[/tex]
[tex]64+67+z=180[/tex]
[tex]131+z=180[/tex]
[tex]z=180-131[/tex]
[tex]z=49[/tex]
please help me!! Will give Brainly if correct
Answer:
-1
Step-by-step explanation:
Let's take two points on the line- (0,2) and (2,0).
To find the slope:
[tex]m = \frac{y_2 - y_1}{x_2-x_1}\\m = \frac{0 - 2}{2-0}\\m = \frac{-2}{2}\\m = -1[/tex]
The slope is -1.
What kind of reward and sacrifices do you believe a doctor would have?
Answer:
As a doctor, you witniss pain and death on a daily basis (which can be tramatic). You also have peoples lives put in your hands, and if you fail them you must answer their legal caretakers and or family. Also lawyers in some cases. Law can be a con of being a doctor. It is easy to get a lawsuit against yourself in that job category. But the pros (good things) are that the pay is well, and if all goes right you get to save lives for a living. This job is also deemed a sophisticated one by most, gaining you scholarships, respect, etcetera.
Can someone help me do this
Answer:
X = 2
5y + (what is that number???) can not see it
Rewrite the quadratic function in standard form,
f(x)=3x^2-4x
Answer:
x(3x-4)
Step-by-step explanation: