The function f(x) = (x + 5)³ when expanded is f(x) = x³ + 15x² + 75x + 125
How to expand the function?The function in the equation is given as
f(x) = (x+5)^3
Rewrite this function properly
So, we have the following representation
f(x) = (x + 5)³
Solving further, we need to expand the expression into factors
So, we have the following representation
f(x) = (x + 5)(x + 5)(x + 5)
Next, we expand the first two brackets in the equation
This gives
f(x) = (x² + 5x + 5x + 25)(x + 5)
Evaluate the like terms
This gives
f(x) = (x² + 10x + 25)(x + 5)
Solving further, we need to expand the last two brackets
So, we have the following representation
f(x) = (x³ + 5x² + 10x² + 50x + 25x + 125)
Evaluate the like terms
This gives
f(x) = (x³ + 15x² + 75x + 125)
Remove the brackets
So, we have
f(x) = x³ + 15x² + 75x + 125
Hence, the function is f(x) = x³ + 15x² + 75x + 125
Read more about functions at
https://brainly.com/question/28277110
#SPJ1
What is 27.6 / 8???????????
Answer:
seriously??
have you heard of calculators lol
the answer is 3.45
Find a coordinate on the line.
y - 5 = 8(x + 2)
Question 3 options:
(8, 2)
(2, -5)
(-2, 5)
(-5, 2)
Answer:
(-2,5)
Step-by-step explanation:
What type of angle of this?
Answer:
angle x is equal to 60º so its an acute angle
Step-by-step explanation:
Answer:
x = 60
Step-by-step explanation:
obtuse angle is 180 degres so you subtract the amount that you see and you will get x. This only works for questions like this contact me if you need more help with questions like these
180-120=60
An airplane can ascend at a rate of 50 1/2 meters in 2/3 of a second. How many meters can the airplane ascend in one second?
Answer:
78.75
Step-by-step explanation:
If a function is restricted, is there no end behavior?
Answer:
If a function is restricted, it still has an end behavior!!!
Step-by-step explanation:
Let's say we have f(x)=(x-4)^2, x≥4.
If this function is graphed, we can see that the line starts at (4,0). It only has one side to it.
This means that it is restricted on the left side. In other words, x has to be greater than or equal to 4.
However, just because this function is restricted doesn't mean it doesn't have an end behavior!
As we can see, the graph continues on into eternity. As a result, we can write the end behavior as:
x --> ∞, f(x) --> ∞
There is no end behavior for the left side because that's where the graph is restricted.
Hope this helps!
Use the Distributive Property to complete the equivalent expression. Enter your answers in the boxes.
4(y – 3) = __ - ___
SOMEONE HELP EXTREMELY QUICK PLSSS
Golf Club Distance (yards) Distance (feet)
9 iron
99
7 iron
120
5 iron
144
3 iron
162
3 wood
174
Driver
192
Answer:
7 Iron
Step-by-step explanation:
Just smort
Please answer this, thank you so much
Answer:
second one
Step-by-step explanation:
Notice that there's a y intercept of 2 and an x intercept of -4
This means that the line has a positive slope of 1/2, which leaves us with
y<(1/2)x+2
Using the formula F = 9/5 C + 32, convert 25° Celsius (C) to
degrees Fahrenheit (F).
A.) 57°
B.) 77°
C.) 257°
D.) 269.5
Answer:77°
Step-by-step explanation:
Since we are trying to convert Celsius to Fahrenheit, we just need to replace C in the equation with the value of 25°.
[tex]F=\frac{9}{5}C+32[/tex]
[tex]F=\frac{9}{5}25+32[/tex]
[tex]F=45+32[/tex]
[tex]F=77[/tex]
The answer is 77°
he .......... be eating pizza.
He will be eating pizza
S + will + be + V_ing
Pls help I’ll brainlest ASAP
Answer:
Slope: -1/4x
y-int: 2
Step-by-step explanation:
32) Out of 525 people surveyed, 210 answered yes. Estimate how many people would answer yes if 900
people were surveyed.
Answer:
360 people
Step-by-step explanation:
[tex]\frac{ 210}{525}*900[/tex][tex]=360[/tex]
Hope this helped! :)
Three segments are chosen at random from six segments having lengths of 2, 3, 5, 6, 7 and 10 units. What is the probability that the three segments chosen could form a triangle? Express your answer as a common fraction
Using the probability concept, it is found that there is a [tex]\frac{7}{20}[/tex] probability that the three segments chosen could form a triangle.
A probability is the number of desired outcomes divided by the number of total outcomes.
In this problem, the order in which the sides of the segments are chosen is not important, hence, the combination formula is used to find the number of total outcomes.Combination formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
Total outcomes:
3 segments from a set of 6 lengths, hence:
[tex]C_{6,3} = \frac{6!}{3!3!} = 20[/tex]
Desired outcomes:
Segments can make a triangle if the sum of the lengths of the smaller segments is greater than the length of the larger segment.Hence, the possible options are: (2,5,6), (3,5,6), (3,5,7), (5,6,7), (5,6,10), (5,7,10), (6,7,10).There are 7 desired outcome, hence [tex]D = 7[/tex]Then:
[tex]p = \frac{D}{T} = \frac{7}{20}[/tex]
[tex]\frac{7}{20}[/tex] probability that the three segments chosen could form a triangle.
To learn more about the probability concept, you can take a look at https://brainly.com/question/24437717
Express as a single power.
[tex]\\(a)\\2^3 \times 2^6 \div 2^9 = 2^{3+6} \times \dfrac{1}{2^9} = 2^9 \times 2^{-9} = 2^{9-9} = 2^0 = 1\\\\ \\(b)\\\\(-5)^8 \div (-5)^4 \times (-5)^3\\ \\= (-5)^8 \times \dfrac 1{(-5)^4 \times (-5)^3} \\\\= (-5)^8 \times \dfrac{1}{(-5)^{4+3}} \\\\= (-5)^8 \times \dfrac{1}{(-5)^7} \\\\= (-5)^{8 - 7} \\\\=(-5)^1 \\\\ =-5\\\\\\(c)\\\\\\\dfrac{6^3 \times 6^5}{6^2 \times 6^4}= \dfrac{6^{3+5}}{6^{2+4}}= \dfrac{6^8}{6^6}=6^{8-6}=6^2 =36[/tex]
What is the quotient ?
7 with a power of -6 over 7 with a power of 2
Answer: [tex]\frac{1}{7^8}[/tex] or [tex]\frac{1}{5764801}[/tex]
Step-by-step explanation:
First, since the two roots (7) are the same, you subtract the exponents, which gives you -6 - 2 to get -8, giving you [tex]7^{-8}[/tex]
Next, you change [tex]7^{-8}[/tex] to [tex]\frac{1}{7^8}[/tex] or [tex]\frac{1}{5764801}[/tex]
I hope that helps :)
Factorise fully each of the following:
(a)
2ab + 3cd - cb - bad
-
-
Answer:
urs 6 2ab ytdguhdd bad wuy
Step-by-step explanation:
blank
(X+2b)(x-4b) simplified
Answer:
I will ASSUME X = x
x² + 2bx - 4bx - 8b²
x² - 2bx - 8b²
Answer:
[tex]\\\\\\-8b^2-2bx+x^2[/tex]
Step-by-step explanation:
[tex](x+2b)(x-4b)\\=(x+2b)(x+(-4b)\\=(x)(x)+(x)(-4b)+(2b)(x)+(2b)(-4b)\\\\x^2-4bx+2bx-8b^2\\\\-8b^2-2bx+x^2[/tex]
graph the line indicated by the slope, m = - 3, and passing through the point (-4, 1) .
The equation of a line in point slope form is expressed according to the formula;
y-y0 = m(x-x0)
m is the slope of the line(x0, y0) is any point on the lineGiven the following parameters
m = -3
(x0, y0) = (-4, 1)
Substitute into the formula above will givee;
y - 1 = -4(x+4)
y -1 = -4x - 16
y = -4x - 15
Next is to plot the graph of the line y = -4x - 15 on the coordinate plane as shown:
Learn more graphs here: https://brainly.com/question/19011142
Nick drives 7 miles in ten minutes how many miles would nick drive if he drove at the same rate for 2 hours?
Answer 84 miles
Step-by-step explanation:
2hrs= 120min
7 miles/ 10 min = x miles/ 120 min
x = 84 miles
consider equation of circle x2-2x+y2-4y-4=0,if line 2x-y+a=0 is its diameter then find value of a
Answer:
Step-by-step explanation:
x² - 2x + y² - 4y - 4 = 0
x² - 2x + y² - 4y = 4
complete the squares
(x² - 2x + x₀) + (y² - 4y + y₀) = 4
the unknown number will be the square of half of the x¹ coefficient
(x² - 2x + 1) + (y² - 4y + 4) = 4 + 1 + 4
(x - 1)² + (y - 2)² = 9
This tells us that the circle is centered on (1, 2)
Which is also a point on the diameter
2x - y + a = 0
a = y - 2x
a = 2 - 2(1)
a = 0
Suppose Bella wanted to make a gift basket worth $25 instead the gift basket must also have more wheat loaves than muffins show one way Bella can make the gift basket
. Solve the rational equation x+6 / 3 − x+8 / 5 = 0.
Answer:
x= -3
Step-by-step explanation:
[tex] \frac{x + 6}{3} - \frac{x + 8}{5} = 0[/tex]
Multiply both sides by 15 (LCM of 3 and 5):
[tex] \frac{15(x + 6)}{3} - \frac{15(x + 8)}{5} = 0[/tex]
5(x +6) -3(x +8)= 0
Expand:
5x +30 -3x -24= 0
2x +6= 0
-6 on both sides:
2x= -6
x= -6 ÷2
x= -3
I need help asap
Please help me!!
contains ordered pairs
Answer:
which question ?
Step-by-step explanation:
please help me ill mark as brainliest and its worth 50
Answer:
C [tex] \dfrac{9a^{12}}{b^3} [/tex]
Step-by-step explanation:
54/6 = 9
a^8 / a^-4 = a^{8 - (-4)} = a^12
b^2 / b^5 = b^-3 = 1/b^3
Answer: C [tex] \dfrac{9a^{12}}{b^3} [/tex]
Answer:
Option C
Step-by-step explanation:
[tex] \sf \dfrac{54 {a}^{8} {b}^{2} }{6 {a}^{ - 4} {b}^{5} } [/tex]
We know that
[tex] \sf \: \frac{ {a}^{m} }{a {}^{n} } = a {}^{m - n} [/tex]
[tex] \sf 9 \dfrac{a {}^{8} {b}^{2} }{ {a}^{ - 4} {b}^{5} } [/tex]
[tex] \sf \: 9 \dfrac{ {a}^{8 - ( - 4)} b {}^{(2 - 5)} }{1} [/tex]
[tex] \sf \: 9 \dfrac{ {a}^{12}b {}^{ - 3} }{1} [/tex]
[tex] \sf \: \dfrac{9 {a}^{12} }{ {b}^{3} } [/tex]
What is the least common denominator of this equation
Answer:
LCD = 30
Step-by-step explanation:
[tex]\frac{5}{6}[/tex] x - [tex]\frac{1}{10}[/tex] x = [tex]\frac{2}{15}[/tex]
Multiply through by 30 ( the LCM of 6, 10, 15 ) to clear the fractions
25x - 3x = 4
22x = 4 ( divide both sides by 22 )
x = [tex]\frac{4}{22}[/tex] = [tex]\frac{2}{11}[/tex]
Answer:
5
Step-by-step explanation:
[tex] \frac{5}{6} x - \frac{1}{10} x = \frac{2}{15} \\ \frac{50x - 6x}{60} = \frac{2}{15} (criss \: cross) \\ \frac{44x}{60} = \frac{2}{15 } \\ \frac{11x}{15} = \frac{2}{15} (simplify) \\ 165x = 30(criss \: cross) \\ x = \frac{30}{165} = \frac{6}{33} = \frac{2}{11} \\ x = \frac{2}{11} [/tex]
A function is shown below.
f (x) = 83 - 11
What value of x makes f (20) = 21?
Enter your answer in the grid below.
please help!
Answer:
the answer is 4
Step-by-step explanation:
if y=21 the we substitute in the main equation
21=8x-11
8x=32
x=4
Line j has an equation of y = 1/5x + 7. Perpendicular to line j is line k, which passes through
the point (-1, -3). What is the equation of line k?
Write the equation in slope-intercept form. Write the numbers in the equation as simplified
proper fractions, improper fractions, or integers.
keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above
[tex]\begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\qquad \impliedby y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{1}{5}}x+7 \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope}{\cfrac{1}{5}}\qquad \qquad \qquad \stackrel{reciprocal}{\cfrac{5}{1}}\qquad \stackrel{negative~reciprocal}{-\cfrac{5}{1}\implies -5}}[/tex]
so then line K has a slope of -5 and pass through (-1, -3)
[tex](\stackrel{x_1}{-1}~,~\stackrel{y_1}{-3})\qquad \qquad slope=m=-5 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-3)}=\stackrel{m}{-5}[x-\stackrel{x_1}{(-1)}] \\\\\\ y+3=-5(x+1)\implies y+3=-5x-5\implies y=-5x-8[/tex]
Someone help me it’s number 12
You need to find the x value
Help help math pelsss please please
Answer:
162 the answer i think bye have fun
Step-by-step explanation:
How much money should be invested every quarter at 9% per year, compounded quarterly, in order to have $3000 in 8 years? (Round your answer to the nearest cent.)
Answer:
Step-by-step explanation:
$6,146.76.