=========================================================
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.
--------------------
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}
--------------------
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.
--------------------
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.
Help help help please help
[tex] \frac{ {8}^{4} }{8 {}^{2} } \times 8 {}^{3} [/tex]
Cancel the fraction to simplify it.[tex]8 {}^{2} \times 8 {}^{3} [/tex]
Calculate the product[tex]8 {}^{5} [/tex]
Hope it helps...Rise over run pleaseee???
Rise = -4
Run = 3
Rise/run = -4/3
Answer:
-4/3
Step-by-step explanation:
Rise: 4
Run:3
And, this is negative because any line slanted downward right (pointing to the left) indicates it is negative.
what is the behavior?
Answer:
as x -> -∞, y-> ∞ and as x-> ∞, y -> -∞ - Second option
Step-by-step explanation:
If you look carefully to the left, when x becomes negative the y value becomes positive. On the right, x becomes positive and y becomes negative.
I don't understand this question can someone help me with this please, please explain!! and thank you for the help!! If u dont know try your best :D
Answer:
A. 5y = 45.00; y = 9.00
Step-by-step explanation:
Step 1:
There are 5 friends in total and since we don't know how much money each of them contributed to the total amount ($45.00), we will substitute it with the variable y.
So, the amount of money the friends contributed is 5y.
The total amount of all the friends' money put together is given; $45.00.
So 5y = 45.00
______________
Step 2:
Divide 45.00 by 5 to find out how much each of the five friends contributed individually;
45.00 ÷ 5 = 9.00
So the amount of money the each friend contributes individually/ have to spend to buy a present for her individually is $9.00.
y = 9.00
______________
Model it:
5y = 45.00; y = 9.00
______________
Hope this helps! :)
10x+5 is greater than or equal to 2x-3
Answer:
x ≥ - 1
Step-by-step explanation:
10x + 5 ≥ 2x - 3 ( subtract 2x from both sides )
8x + 5 ≥ - 3 ( subtract 5 from both sides )
8x ≥ - 8 ( divide both sides by 8 )
x ≥ - 1
the jenkins family drinks 3/4 of a gallon of orange juice every 3 days. how much orange juice do they drink per day?
Answer:
1/4 gallon per day
Step-by-step explanation:
Find the 'unit rate:' the measure of juice drunken daily. To do this, divide '3/4 gallon' by '3 days:"
3/4 gallon
------------------- = 1/4 gallon per day
3 days
w + 2x + 1 = x – 2w +26
Describe the transformation of y=-2/x
Answer:
This transformation is known as a vertical stretch. This is the graph of a transformation of \begin{align*}y=x^2\end{align*}. The points are plotted from the vertex as right and left one and down one-half, right and left 2 and down two, right and left three and down four and one-half
find the width of radius r if the width w of the shaded region is 2cm and its area is 176cm^2, use 22/7 for pi (its a full circle)
The area of a shape is the amount of space it can occupy.
The value of r is 13
From the question (see attachment), we have:
[tex]\mathbf{A =176}[/tex] --- area of the shaded region
[tex]\mathbf{w = 2}[/tex] --- the width of the shaded region
The area of the complete circle would be:
[tex]\mathbf{A_1 =\pi (r + w)^2}[/tex]
The area of the small circle is:
[tex]\mathbf{A_2 =\pi r^2}[/tex]
So, the area of the shaded region is:
[tex]\mathbf{A = A_1 - A_2}[/tex]
Substitute known values
[tex]\mathbf{176 =\pi (r + w)^2 - \pi r^2 }[/tex]
Substitute 2 for w
[tex]\mathbf{176 =\pi (r + 2)^2 - \pi r^2 }[/tex]
Expand
[tex]\mathbf{176 =\pi (r^2 + 4r + 4) - \pi r^2 }[/tex]
Open brackets
[tex]\mathbf{176 =\pi r^2 + 4\pi r + 4\pi - \pi r^2 }[/tex]
Cancel out line terms
[tex]\mathbf{176 =4\pi r + 4\pi }[/tex]
Divide through by 4
[tex]\mathbf{44 =\pi r + \pi }[/tex]
Factor out pi
[tex]\mathbf{44 =\pi(r+ 1) }[/tex]
Divide through by pi
[tex]\mathbf{r + 1= \frac{44}{ \pi} }[/tex]
Substitute 22/7 for pi
[tex]\mathbf{r + 1= \frac{44}{ 22/7} }[/tex]
Using a calculator, we have
[tex]\mathbf{r + 1= 14}[/tex]
Solve for r
[tex]\mathbf{r= 14 -1}[/tex]
[tex]\mathbf{r= 13}[/tex]
Hence, the value of r is 13
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If 4 basketball game tickets and 5 football game tickets were purchased for $61.50, and if 5 basketball game tickets and 3 football game tickets were purchased for $55.75, what are the costs of basketball game tickets and football game tickets?
Answer:
basketball game tickets: $7.25;
football game tickets: $6.50
Step-by-step explanation:
Let B represent the cost of a basketball ticket and F represent the cost of a football ticket.
Amount for basketball ticket plus amount for football tickets equal the total cost.
4B + 5F = 61.50
5B + 3F = 55.75
Choose one equation in the system to solve for a variable.
Solve the first equation for F.
4B + 5F = 61.50
5F = −4B + 61.50 Subtract 4B from both sides.
F = −0.8B + 12.30 Divide both sides by 5.
Substitute the expression −0.8B + 12.30 for F in the other equation.
5B + 3F = 55.75
5B + 3(−0.8B + 12.30) = 55.75 Substitute.
5B − 2.4B + 36.90 = 55.75 Distribute.
2.6B + 36.90 = 55.75 Combine like terms.
2.6B = 18.85 Subtract 36.90 from both sides.
B = 7.25 Divide both sides by 2.6.
Substitute the B-value into one of the original equations to solve for F.
4B + 5F = 61.50
4(7.25) + 5F = 61.50 Substitute.
29 + 5F = 61.50 Multiply.
5F = 32.50 Subtract 29 from both sides.
F = 6.50 Divide both sides by 5.
The cost of a basketball ticket is $7.25, and the cost of a football ticket is $6.50.
The cost of basketball game tickets is $7.15 and football game ticket is $6.5
Let the cost of a basketball game ticket be x
Let the cost of football game ticket be y
If 4 basketball game tickets and 5 football game tickets were purchased for $61.50, hence;
4x + 5y = 61.50 ..................1
If 5 basketball game tickets and 3 football game tickets were purchased for $55.75, hence;
5x + 3y = 55.75 ...........................2
Solving 1 and 2 simultaneously
4x + 5y = 61.50 ..................1 * 3
5x + 3y = 55.75 ...........................2 * 5
_________________________________
12x + 15y = 184.5
25x + 15y = 278.75
Subtract
12x - 25x = 184.5 - 278.75
-13x = -94.25
x = 7.25
Substitute x = 7.25 into equation 1:
From 1:
4x + 5y = 61.50
4(7.25) + 5y = 61.50
29 + 5y = 61.50
5y = 61.50 -29
5y = 32.5
y = 32,5/5
y = 6.5
Hence the cost of basketball game tickets is $7.15 and football game ticket is $6.5
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https://brainly.com/question/15165519
Which of the following equations represents a line that passes through the points (-10, -9)(−10,−9) and (10,-1)(10,−1)?
I. y+1=-\frac{2}{5}(x-10)y+1=−
5
2
(x−10)
II. 2x-5y=252x−5y=25
Answer:
y = 2/5x - 5
Step-by-step explanation:
(-10,-9) and (10,-1)
Slope: (-1 - - 9) / ( 10 - - 10)
Slope = 8/20 = 2/5
b = -9 - (2/5(10)
b = -5
The equation of the line that passes through the point (−10,−9) and (10,-1) is; y = 2/5x - 5
What is the Point-slope form?The equation of the straight line has its slope and given point.
If we have a non-vertical line that passes through any point(x1, y1) and has a gradient m. then general point (x, y) must satisfy the equation
y-y₁ = m(x-x₁)
Where x₁ - x coordinate, y₁ - y coordinate, m - slope
Slope: (-1 - - 9) / ( 10 - - 10)
m = Slope = 8/20 = 2/5
Now intercept;
b = -9 - (2/5(10)
b = -5
Now Write the equation as
y = 2/5x - 5
Hence, the equation of the line that passes through the point (−10,−9) and (10,-1) is; y = 2/5x - 5
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please answer quick !!! The intersection of parallel lines b and c and transversal line d form several special angle relationships, as shown in the image below. If ∠1 measures 135°, what is the measure of ∠6? 90° 135° 45° 65°
Answer:
45
Step-by-step explanation:
please show work tyvm 4+3x6x(4-3³)²
Answer:
9526
Step-by-step explanation:
simplify 3^3+27
4+3*6(4-27)^2
simplify: 4-27+ -23
4+3*6(-23)^2
since the power of 2 is even it will be a positive
4+3*6*23^2
simplify: 23^2 to 529
4+3*6*529
simplify 3*6 to 18
4+18*529
then simplify 18*529 to 4+9522
and 4+9522= 9526
please help me........
What is the value of the 3 in this number?
5,400,387,214
is the value of this number.
Answer:
The value of 3 is in the three-hundred thousands place
300,000
A car rental agency charges $75 per day, which includes 100 miles. For each mile over 100 miles, there is an additional cost of $0.35 per mile. Write an equation relating
m, the number of miles driven, if the total cost for a one-day rental was $131.
Part A. Write an equation relating m , the number of miles driven, if the total cost for a one-day rental was $131.
Part B. Find the solution to the equation you created in the previous question and explain what the solution means in this situation.
The number of miles, m driven if the total cost for a one-day rental was $131 is; m = 160
According to the question;
The agency charges $75 per day, which includes 100 miles.Additionally, the agency charges $0.35 per mile for each additional mile;a) The equation relating m , the number of miles driven, if the total cost for a one-day rental was $131 is therefore;
$0.35m + $75 = $131.b) To find the solution to the equation;
$0.35m = $131 - $75$0.35m = $56m = $56/$0.35m = 160.
The number of miles, m driven if the total cost for a one-day rental was $131 is; m = 160.
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A collection of 40 dimes and nickels
is worth $2.90. How many nickels are
there? (Hint: In your equation, use
290¢ instead of $2.90.)
9514 1404 393
Answer:
22 nickels18 dimesStep-by-step explanation:
Let d represent the number of dimes (the higher-value coin). Then the number of nickels is 40-d, and the total value in cents is ...
5(40 -d) +10(d) = 290
200 +5d = 290
5d = 90
d = 18
40 -d = 22
There are 22 nickels (and 18 dimes).
_____
Additional comment
If you write the equation in terms of the number of nickels (n), you end up with the equation -5n = -110. The formulation used above avoids negative numbers, which can be confusing for some people.
PLEASE HELP
Given f(x) = x^2 – 5x + k, and the remainder when f(x) is
divided by x - 7 is 34, then what is the value of k?
Step-by-step explanation:
f(7) = 34
7² -5(7) +k = 34
49-35+k =34
14+k = 34
k = 34-14
k = 20
__________
[tex] \: [/tex]
f(x) = x² - 5x + k
f(7) = 34
Soo :
f(7) = 34
(7)² - 5(7) + k = 34
49 - 35 + k = 34
14 + k = 34
k = 34 - 14
k = 20✔
HELP ASAP
Briefly describe the relationship between the construction of a robotic arm and the stability of the robot.
Answer:
If the same tech in the robotic arm is used throughout the body then depending on whether the arm tech is good the stability of the body will be good or bad.
can someone help me with this? PROBABILITY QUESTION
A psychologist plans an experiment in which subjects draw an object based on a verbal description. For each trial, one person draws, one reads the description, and one records how long it takes to get a successful drawing.
From a group of 8 people, in how many ways can the psychologist select a person to draw, a person to read, and a person to record time?
Answer:
336
Step-by-step explanation:
just took the test
The correct answer is 336.
How many ways can the psychologist select a person to draw, a person to read, and a person to record time?
By using the arrangement calculation formula:
⇒ [tex]A^{3}[/tex][tex]^{8}[/tex]
⇒ 8 × 7 × 6
⇒ 336
The correct answer is 336.
How do you calculate an arrangement?Remember that combinations are a way to calculate the total outcomes of an event where the order of the outcomes does not matter. To calculate combinations, we will use the formula NCR = n! / r! * (n - r)!, where n represents the number of items, and r represents the number of items being chosen at a time.
Learn more about arrangement calculation formula here: brainly.com/question/251701
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the legs of an isosceles triangle have lengths 3x-1 and 2x+4. The base has length 3x+5. Whatis the length of the base?
Answer:
3x+5
Step-by-step explanation:
The base has length 3x+5. You answered your own question darling
simplify (3a^4b^3)^3
Answer:
Step-by-step explanation:
(3a^4b^3)^3
=3^3a^4*3b^3*3
=27a^12b^9
Answer:
27(a^12)(b^9)
Step-by-step explanation:
Can be reorganized to (3^3)((a^4)^3)((b^3)^3)
27(a^12)(b^9)
If l || m, find the value of each missing variable(s).
Use the distributive property to write an expression equivalent to 6(53)
Answer:
here the answer it's 16.
given m || n, calculate the value of x
Answer: x = 41
Step-by-step explanation:
4x - 68 = 2x + 14 [since alternate interior angles are equal]
4x - 2x = 14 + 68
2x = 82
x = 41
Answer:
x=41
Step-by-step explanation:
this problem can be solved using the alternate interior angles converse theorem, which states that if two coplanar lines are cut by a transversal so that a pair of alternate inerior angles are congruent, then the two lines are parallel.
4x-68=2x+14
2x-68=14 <- subtract 2x from both sides
2x=82 <- add 68 to both sides
x=41 <- divide both sides by 2
check:
4(41)-68=96
2(41)+14=96
Express this number in standard form.
5.301 \times 10^{7} = {?}5.301×10
7
=
Answer:
53010000
Step-by-step explanation:
At 100 Fahrenheit a certian insect Chirps at a rate of 94 times per minute and at 103 Fahrenheit they trip at 112 times per minute write an equation in slope intercept form that represents the situation
Answer:
y=6x-506
Step-by-step explanation:
Start by finding the slope.
Let your x-axis be temperature and you y-axis be chirps per minute.
This leaves you with your two points to find slope.
The first point would be (100,94) and your second point would be (103,112).
From here we can do the standard slope equation [tex]\frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex].
[tex]\frac{112-94}{103-100}[/tex]=[tex]\frac{18}{3}[/tex]
[tex]\frac{18}{3}[/tex] Is your slope for the line which can be simplified to 6.
Next find your y-intercept. This can be found by moving around your
y=mx+b equation.
y-mx=b
Pick a point to substitute into the equation. Ill use (103, 112).
[tex]112-6(103)=b[/tex]
[tex]112-618=b[/tex]
[tex]-506=b[/tex]
[tex]b=-506[/tex]
Knowing slope and the y-intercept we can write the slope intercept equation
y=6x-506
In 2010, the population of a city was 168,000. From 2010 to 2015, the population grew by 7%. From 2015 to 2020, it fell by 6%. How much did the population decrease from 2015 to 2020, to the nearest 100 people?
Answer:
169,000 people
Step-by-step explanation:
increase from 2010-2015:
168000/100 = 1680 = 1%
1680 x 7 = 11,760 people
population at 2015 = 168000+11760 = 179,760
decrease from 2015-2020:
179760/100 = 1797.6 = 1%
1797.6 x 6 = 10,785.6 people
population at 2020 = 179760-10787.6 = 168,974.4 people
rounded to the nearest 100 = 169,000 people
please someone help me. Giving branliest!
Answer:
K would be 8
Step-by-step explanation:
8-2 = 6
6/3 = 2
If the domain of a function is [1,10), select a point that could be included within the function.
(0,5)
(1,4)
(10,3)
(12,0)
Answer:
1,4
Step-by-step explanation:
trust me.........................well I am a stranger but trust I guess
