Answers
Step 1
Given;
[tex]f(x)=(x^2+5)^3[/tex]Required; To simplify
[tex]\frac{f(x)-f(0)}{x},\text{ x}\ne0[/tex]Step 2
[tex]\frac{(x^2+5)^3-(0^2+5)^3}{x}[/tex][tex]\mleft(a+b\mright)^3=a^3+3a^2b+3ab^2+b^3---(apply\text{ p}\operatorname{erf}ect\text{ cube formula)}[/tex][tex](x^2+5)^3=(x^2)^3+3(x^2)^2(5)+3x^2(5^2)+5^3[/tex][tex](x^2+5)^3=x^6+15x^4+75x^2+125[/tex][tex]\frac{(x^6+15x^4+75x^2+125)-125}{x}[/tex][tex]\begin{gathered} \frac{x^6+15x^4+75x^2+125-125}{x} \\ \frac{x^6+15x^4+75x^2}{x} \\ \frac{f(x)-f(0)}{x}=x^5+15x^3+75x \end{gathered}[/tex]Hence if we factorize we get;
[tex]x(x^4+15x^2+75)[/tex]Therefore;
[tex]\frac{f(x)-f(0)}{x}=x(x^4+15x^2+75)[/tex]Answer:
See below
Step-by-step explanation:
f(x) = ( x^2 + 5)^3 f(0) = 5^3 = 125
(x^2+5)^3 = x^6 + 15x^4 + 75 x^2 + 125
so you have (x^6 + 15x^4 + 75x^2 + 125 - 125) /x
= x^5 + 15x^3 + 75x = x ( x^4 + 15x^2 + 75)
Related Questions
jo buys a pair of boots for £63 in a sale she saves 1/10 of the original price of the boots how much money does she save
Answers
Answer:
She saves £6.30
Step-by-step explanation:
You multiply 63 by 1/10 to get 6.30 this is how much she saves
40 students participated in track. This was 5% of the students at the school. How many students attend the school?
Answers
Answer: 800 students
If there are 40 students who participated and that's 5% of the entire school. 100% of the entire school would be 800.
In California, we need more rain to sustain the health of our natural environment, argriculture, andeconomic. A group of statistics students in Oxnard College recorded the amount of rain during2016-2017 school year, measuring the intensity by the inches of rain, and the results were:Inches of Rain123456Frequency332334The mean rain intensity, , isinches.Please show your answer to 1 decimal place.The median rain intensity isinches.The rain intensity mode isinches.Please separate your answers by','in bimodal situation. Enter DNE if there is no mode.CalculatorScratchwork Area
Answers
Given data:
1. The mean rain intensity
[tex]\bar{x}=\frac{\sum fx}{\sum f}=\frac{66}{18}=3.7\text{ inches}[/tex]2. The median rain intensity,
[tex]\begin{gathered} \text{Median = (}\frac{\text{N+1}}{2})th \\ =(\frac{18+1}{2})th=(\frac{19}{2})th=9.5th\text{ term} \\ \text{The 9.5th term from the frequency table is }4 \\ \text{The median is 4} \end{gathered}[/tex]3. The rain intensity mode (intensity with the highest frequency)
[tex]6[/tex]Therefore,
The mean : 3.7
The median : 4
The mode: 6
Write an explicit formula for a_na
nthe n^{\text{th}}n
th
term of the sequence 8, 4, 2, ...8,4,2,....
Answers
The explicit formula of the sequence is aₙ = 8(1/2)ⁿ
How to determine the explicit formula of the sequence?From the question, we have the following sequence that can be used in our computation:
8, 4, 2
In the above sequence, we can see that the previous term is divided by 2 get the current term
using the above as a guide,
so, we have the following representation
aₙ = aₙ₋₁/2
When represented explicitly, we have
aₙ = a * rⁿ
So, we have
aₙ = 8 * (1/2)ⁿ
Evaluate the products
aₙ = 8(1/2)ⁿ
Hence, the explicit formula is aₙ = 8(1/2)ⁿ
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i have three number cards. the median is 4. if the range is 3, whats the missing number?
Answers
The missing number in those three card are 5 and 2 when the median is 4 and the range is 3.
Median:
Median refers the middle value of the given set of numbers.
Given,
i have three number cards. the median is 4.
Here we need to find the missing number when the range is 3.
Let us consider x and y be the missing number.
We know that, the range is difference of smallest and largest number,
So, we can write it as,
x - y = 3
Now, we know that the median is the middle value
Then it can be written as,
y, 4, x
The smallest possible values of y is 1, 2, and 3
Similarly, the possible values of x is 5, 6, 7
But based on the value of range we have only take the values, 5 and 2.
Because that one is satisfies the condition of range.
Therefore, the missing numbers are 5 and 2.
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Find the coefficient of the term x^5 in 2x^5+5x^4-9x+5
Answers
Solution:
Given:
[tex]2x^5+5x^4-9x+5[/tex]A coefficient is a number multiplied by a variable.
Hence,
[tex]The\text{ coefficient of }x^5\text{ is 2}[/tex]Therefore, the coefficient is 2.
Please please help me it needs to be in for tomorrow :(
Answers
Answer:
[tex]2.44 \times 10^6[/tex]
Step-by-step explanation:
[tex]R=\frac{(3.8 \times 10^5)^2}{5.9 \times 10^4} \\ \\ =\frac{14.44 \times 10^{10}}{5.9 \times 10^4} \\ \\ \approx 2.44 \times 10^6[/tex]
Answer:
I hope it helps .The final answer is 2,447 × 10 to the power of 3
Find the solution to the equation by substitution
13x-5y=-8
y=3x
Answers
Answer:
x=4
y=12
Step-by-step explanation:
replace y in the first equation since we already know what y is equal to
13x-5y=-8
13x-5(3x)=-8
13x-15x=-8
-2x=-8
/-2. /-2
x=4
Now fill in X to find y
y=3(4)
y=12
Hopes this helps please mark brainliest
Which comparison is true?
A. 0.680 > 0.68
B. 0.74 = 0.740
C. 0.51 < 0.510
D. 0.990 < 0.99
Answers
Answer:
The answer is B
Ronan and Kelsey each think of a number.
2 less than Ronan's number is equal to 4
lots of Kelsey's number.
3 lots of Ronan's number added to Kelsey's
number is 97.
Using the information above, write and
solve two simultaneous equations to work
out Ronan and Kelsey's numbers.
Answers
The 2 equations which can be used to solve the given situations of the numbers are:
x - 2 = 4x3x + x = 97What are equations?A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. A mathematical statement that has an "equal to" symbol between two expressions with equal values is called an equation. As in 3x + 5 Equals 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others. The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.So, the equations that can be formed are:
Let, Ronan's number be 'x' and '4x' be Kelsey's number.
(1) x - 2 = 4xNow, solve as follows:
4x - x = -23x = -2x = -2/3Ronan's number be: -2/3
Kelsey's number be: 4 × 2/3 = -8/3
Let, let, Kelsey's number be 'x' and Ronan's number be '3x'.
(2) 3x + x = 97Now, solve as follows:
4x = 97x = 97/4x = 24.25Ronan's number be: 72.75
Kelsey's number be: 24.25
Therefore, the 2 equations which can be used to solve the given situations of the numbers are:
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Mia has 50$ on a gift card to her favorite coffee shop. Each time she visits the coffee shop sh spends $3.75 on her favorite drink. Write an equation to represent the relationship between n, the number of times she visits the coffee shop, and b, the total balance on her gift card.
Answers
Answer:
50.00-3.75n = b
Step-by-step explanation:
50.00 is the beginning balance she has on the gift card.
If she spends 3.75 every visit, and n represents the number of visits, then 3.75n will tell you how much she has spent with each visit.
1 visit: 50.00 - 3.75(1) = 46.25
2 visits: 50.00 - 3.75(2) = 42.50
3 visits: 50.00 - 3.75(3) = 38.75
Ross is saving up to buy a new car. he has been saving for 12 months and so far he has $3,200.in another 12 months, he expects to have $8,000.how much is ross saving each month during his 2nd year saving?
Answers
Answer:
$400
Step-by-step explanation:
For the first 12 months, he saved
3200/12
= $266.7 each month
In another 12 months,
= $3,200 + x = $8000
(Use x as the unknown total money)
= 8000 - 3200
= 4,800
So, in another 12 months, his total savings will be $4,800
For each month,
= 4,800/12
= $400
Directions: Solve each system of equations algebraically. Verify the solution using the graph of the system. 1. y=-x-4 y=3.x y 5
Answers
y=-x-4 (a)
y=3x (b)
Put (b) into (a) and solve for x:
3x=-x-4
3x+x = -4
4x= -4
Divide both sides by 4
4x/4 = -4/4
x= -1
Replace the value of x on any equation:
y=3x = 3(-1) = -3
Solution : (-1,-3)
Graph:
Simplify 3p²-2q+2p² +17-q?
F p²-3q+17
G 5p²-3q+17
H p²-q+17
J5p²-q+17
Answers
Answer: The answer is G 5p²-3q+17
Step-by-step explanation:
Aliyah left the airport and traveled home at an average speed of 40 km/h.
Shanice left at the same time and traveled in the opposite direction with an
average speed of 60 km/h. How long does Shanice need to travel before they are
300 km apart?
Answers
Answer:
3 hoursStep-by-step explanation:
When moving in opposite directions from the same point the speeds add up.
Total speed:
60 + 40 = 100 km/h
Distance is 300 km, find the time.
time = distance / speedt = 300/100t = 3 hoursAnswer:
Time = 3 hours
Step-by-step explanation:
The total speed is,
→ 40 km/h + 60 km/h
→ 100 km/h
Formula we use,
→ v = d/t
Then the time taken will be,
→ v = d/t
→ 100 = 300/t
→ 100 × t = 300
→ t = 300/100
→ [ t = 3 ]
Hence, answer is 3 hours.
solving inequalities in real life 5. Dennis is selling chocolate bars for a fundraiser, and if he sells over $175 worth of candy, he'll win a prize. If chocolates sell for $2.50 a bar, and Dennis has already sold $40 worth of candy, then how many more bars does he have to sell in order to win a prize? 6. The a roller-cod inches ta grows ab months w coaster?
Answers
Start by putting the inequality in the form
[tex]ax+c>d[/tex]in this case c wil be how much he has sold, and d will be how much he needs to sell, and a is the price for the bar.
it would look like this
[tex]2.5x+40>175[/tex]solve it like a regular equation
[tex]\begin{gathered} 2.5x>175-40 \\ 2.5x>135 \\ x>\frac{134}{2.5} \\ x>54 \end{gathered}[/tex]He will have to sell over 54 bars to win the prize.
true or false: the student t distribution may be used to construct a confidence interval for the mean of any population, so long as the sample size is small.
Answers
False. The student t distribution may be used to construct a confidence interval for the mean of a population that is normally distributed, so long as the sample size is small.
The student t distribution may be used to construct a confidence interval for the mean of any population, so long as the sample size is small. The student t distribution is a probability distribution that is used to estimate the population mean when the sample size is small and the population standard deviation is unknown. The student t distribution is also used to construct confidence intervals for the population mean.
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PLEASE ANSWER I NEED THIS FOR A UNIT TEST AND I DON'T WANT TO FAIL
Answers
we will have to follow given below steps if we want to plot this inequality x is less than or equal to 2.6.
What is linear inequality and examples?A linear inequality is formed by any two real numbers or any two algebraic expressions marked by the symbols "," ">," "," or "." Ones of numerical inequality include 911 and 18>17, while algebraic examples include x+7>y, y10-x, and x y > 11
How do you identify a linear inequality?One of the inequality symbols is present in a linear inequality:. It displays non-equal data in graph style. With the inequality sign in place of the equality sign, a linear inequality appears exactly like a linear equation.
The values of x that satisfy the inequality must be determined before we may graph the inequality x = 2.6 on a number line. This can be done by changing x to a variety of values and observing which ones cause the inequality to hold true. When x is less than or equal to 2.6, we know that the inequality x = 2.6 is true. This means that the inequality will be satisfied for any value of x that is lower than or equal to 2.6. This has a range of inclusive values from -infinity to 2.6. We can use a dotted line spanning from negative infinity to 2.6 to graph the inequality on a number line. We would insert a dot for each number between negative infinity and 2.6, including 2.6 itself, since the dots on the line denote the numbers in the range. The dots on the line represent the integers in the range, which spans from negative infinity to 2.6. (i.e., all numbers less than or equal to 2.6). The open circle at 3 shows that the number is outside of the range, while the solid point at 2.6 indicates that the number is within the range.
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Given: TU II XW
Prove: XW=8
Statements Reasons
TWIIXW Given
UTV=XYV alternate angles theorem
TVU= vertical angles theorem
TVU~WVX AA
? ?
XW\14=4/7substitution property of equality
7(XW)=56 cross product
XW=8 division property of equality
Which step is missing?
A.
Statement: WX/UT=UZ/VW Reason: Corresponding sides of similar triangles are proportional.
B.
Statement :XW/UT=VW/XV Reason: Corresponding sides of similar triangles are proportional.
C.
Statement: XW/UT=VW/XV Reason: Corresponding sides of similar triangles are proportional.
D.
Statement: XW/UT=UV/XV Reason: Corresponding sides of similar triangles are proportional.
Answers
The missing step is XW/UT=VW/XV because corresponding side of similar triangle are proportional.
What is similar triangle?
Similar triangles are the triangles that have corresponding sides in proportion to each other and corresponding angles equal to each other. Similar triangles look the same but the sizes can be different.
When two triangles are similar, then their corresponding angles would be congruent while their opposite sides will be proportional to each other
In the proof, it is given, Both triangle are similar, by AA similarity theorem, hence, XW/UT=VW/XV because corresponding side of similar triangle are proportional.
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(Solving quadratic equations) Hello, I need help with just 3 questions. Thanks :)
Answers
Answer:
Check the pic i attached
7. Write the equation of the parabola. Pay close attention to the scale on both axes.
Answers
We can start with the equation of the parabola in vertex form, as we know the coordinates of the vector:
[tex]y=a(x-h)^2+k[/tex]The vertex is (h,k) = (-5,2), so we get:
[tex]y=a(x-(-5))^2+2=a(x+5)^2+2[/tex]We can use another known point, as (-6,4) to calculate the parameter a:
[tex]\begin{gathered} y=a(x+5)^2+2 \\ 4=a(-6+5)^2+2 \\ 4=a\cdot(-1)^2+2 \\ 4=a+2 \\ a=4-2 \\ a=2 \end{gathered}[/tex]Now that we have no more unknown parameters, we can expland the equation to the standard form:
[tex]\begin{gathered} y=2(x+5)^2+2=2(x^2+10x+25)+2=2x^2+20x+50+2 \\ y=2x^2+20x+52 \end{gathered}[/tex]The equation is y=2x^2+20x+52.
Find the other endpoint of the line segment with the given endpoint and midpoint. Endpoint: (5,-1) Midpoint: (5,-4)
Answers
The formula for calculating the midpoint of a line segment is given below
[tex](x,y)=\frac{(x_1+x_2)}{2},\frac{(y_1+y_2)}{2}[/tex]Where the values are
[tex]\begin{gathered} x=5,y=-4 \\ x_1=5,y_1=-1 \end{gathered}[/tex]By substituting the values, we will have
[tex]\begin{gathered} (x,y)=\frac{(x_1+x_2)}{2},\frac{(y_1+y_2)}{2} \\ (5,-4)=\frac{(5_{}+x_2)}{2},\frac{(-1_{}+y_2)}{2} \end{gathered}[/tex]By comparing coefficient, we will have
[tex]\begin{gathered} \frac{(5_{}+x_2)}{2}=5 \\ \frac{(-1_{}+y_2)}{2}=-4 \end{gathered}[/tex]Cross multiply to get the values of x2
[tex]\begin{gathered} \frac{(5_{}+x_2)}{2}=5 \\ 5+x_2=10 \\ \text{substract 5 from both sides} \\ 5-5+x_2=10-5 \\ x_2=5 \end{gathered}[/tex]Cross multiply to get the values of y2
[tex]\begin{gathered} \frac{(-1_{}+y_2)}{2}=-4 \\ -1+y_2=-8 \\ \text{add 1 to both sides} \\ -1+1+y_2=-8+1_{} \\ y_2=-7 \end{gathered}[/tex]Hence,
The coordinate of the other endpoint is ( 5, -7 )
HELP ME PLEASE TYYYYY
Answers
Answer:
66
Step-by-step explanation:
The ratio of guinea pigs to the total number of animals is 5:11.
So, there are (30)(11/5)=66 animals in all.
what is this answer
6p>48
Answers
Answer: p is greater than or equal to 8
Step-by-step explanation:
To isolate the variable (p) you divide both sides of the equation by 6 to get p by itself and the answer comes out clean because 48 is a multiple of 6.
Answer:
Divide both sides by the same factor
6p > 48
6p > 48
--- ---
6 > 6
result
p > 8
The equation for line j can be written as y= 1/8 x+7. Parallel to line j is line k, which passes through the point ( – 3, – 1). What is the equation of line k?
Answers
Answer:
please help I need thos answer too
Step-by-step explanation:
I wish I knew the answer to this I have 20 mins to be dont and I've already spend 10 on this question
6 Given: TY XY, ZTVY = ZXWY Prove: ATVY = AXWY Statements Reasons 1. TY ~ XY 1. Given 2. Given 2. LTVY & LXWY 3. 3. 4. 4. 5. 5. OTVY Z OXWY Gina wison All Things Aige
Answers
Statement 3:
[tex]TV\cong XW[/tex]Reason: Law of cosines
Statement 4:
[tex]VY\cong WY[/tex]Reason: Law of cosines
Proof
We have the following situation:
Because the law of cosines,
[tex]\begin{gathered} a^2=c^2+d^2-2cd\cos (b) \\ a^2=e^2+f^2-2ef\cos (b) \end{gathered}[/tex]Therefore,
[tex]c^2+d^2-2cd\cos (b)=e^2+f^2-2ef\cos (b)[/tex]A line has a slope of
9 and includes points (9,d) and (8,3). What is the value of d?
Answers
The value of 'd' will be;
⇒ d = 12
What is Equation of line?
The equation of line in point-slope form passing through the points (x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
A line has a slope of 9 and includes points (9, d) and (8, 3).
Now,
We know that,
Slope of line (m) = (y₂ - y₁) / (x₂ - x₁)
⇒ m = (3 - d) / (8 - 9)
⇒ 9 = (3 - d) / (-1)
⇒ - 9 = 3 - d
⇒ d = 3 + 9
⇒ d = 12
Thus, The value of 'd' will be;
⇒ d = 12
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can you please help me I need 22 and 23
Answers
22. the coordinates are:
[tex]Q(-8,7),R(-7,2),S(-8,13),t(-11,-2)[/tex]So to know if the are parallel or perpendicular we have to calculate the slopes so:
For QR
[tex]m=\frac{2-7}{-7-(-8)}=-\frac{5}{1}=-5[/tex]For ST
[tex]m=\frac{-2-13}{-11-(-8)}=-\frac{15}{3}[/tex]So they are not parallel or perpendicular.
23. the coordinates are:
[tex]Q(-1,4),R(-1,-9),S(11,-2),T(11,6)[/tex]Now the slopes are
For QR
[tex]m=\frac{-9-4}{-1-(-1)}[/tex]This is undefine so is a vertival line
for ST:
[tex]m=\frac{8-(-2)}{11-11}[/tex]Is undefine so is also a vertical line, this means that they are parallel
Solve the following proportion
X/2 = 8/9
Answers
150 is 15% of what number?
Answers
If 150 is the 15%, to find which number is the 100% we use the rule of 3
[tex]\begin{gathered} x\to100 \\ 150\to15 \end{gathered}[/tex]and the rule say that:
[tex]\begin{gathered} x=\frac{100\times150}{15} \\ x=1000 \end{gathered}[/tex]