The result of the product [tex](s^2+5s)(s^3+4s^2)[/tex] is [tex]s^5+9s^4+20s^3[/tex]
The product is given as:
[tex](s^2+5s)(s^3+4s^2)[/tex]
Rewrite as:
[tex](s^2+5s)(s^3+4s^2) = (s^2+5s) \times (s^3+4s^2)[/tex]
Expand the expression on the right-hand side
[tex](s^2+5s)(s^3+4s^2) = s^2\times (s^3+4s^2)+5s \times (s^3+4s^2)[/tex]
Distribute the expressions
[tex](s^2+5s)(s^3+4s^2) = s^5+4s^4+5s^4+20s^3[/tex]
Evaluate like terms
[tex](s^2+5s)(s^3+4s^2) = s^5+9s^4+20s^3[/tex]
Hence, the result of the product [tex](s^2+5s)(s^3+4s^2)[/tex] is [tex]s^5+9s^4+20s^3[/tex]
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What expressions are equal to1/3⁶
Answer:
assuming that it is [tex](1/3)^{6}[/tex] that would be
[tex]\frac{1}{729}[/tex]
Step-by-step explanation:
Verify that –(-x) is the same as x , for x = −4/5
Answer:
Step-by-step explanation:
-(--4,5)= -(4,5)= -4,5
You expect to have $1000 in one year. A bank is offering loans at 6% interest per year.How much can you borrow today
Answer:
$943.39622
Step-by-step explanation:
A = final amount, = 1000
Interest, r = 6% = 0.06
Time, t = 1
Principal, P = amount you can borrow today
Using the simple interest formula :
A = P(1 + rt)
1000 = P(1 + 0.06*1)
1000 = P(1 + 0.06)
1000 = P(1.06)
P = 1000 / 1.06
P = 943.39622
If ? A² + b² = 7b and b² + (2b-a) ²= 7², what is (a - b) ²?
Answer:
7^2+2ab - 4b^2
Step-by-step explanation:
A² + b² = 7b
b² + (2b-a) ²= 7²
FOIL
b^2 +4b^2-4ba+a^2= 7^2
Rewriting
a^2 -2ab + b^2 +4b^2 -2ab = 7^2
Add 2ab and subtract 4b^2 from each side
a^2 -2ab + b^2 +4b^2 - 4b^2 -2ab+2ab = 7^2+2ab - 4b^2
a^2 -2ab + b^2 = 7^2+2ab - 4b^2
(a-b)^2 = 7^2+2ab - 4b^2
Can some help please
Answer:
Step-by-step explanation:
2 * 10^7 You are to use a single digit. That's the 2 on the left. Then count what it takes to get the decimal between the 2 and the 3. It's 7
0.000136
Count the number of zeros. Add a minus 1. You want the number to be counted until you get minus 1 which is the number of powers after the 1.
1 * 10^-4
26837 becomes 2 * 10^4. 4 is the number of digits you have before you get to a number between 1 and 10.
0.0302 becomes 3 * 10^-(1 + 1) = 3 * 10^-2
Which equations are equivalent to Three-fourths + m = negative StartFraction 7 over 4 EndFraction? Select three options.
Answer:
m = negative StartFraction 10 over 4 EndFraction
m = negative five-halves
Step-by-step explanation:
Given equation :
Which equations are equivalent to Three-fourths + m = negative StartFraction 7 over 4 EndFraction
3/4 + m = - 7/4
Subtracting 3/4 from both sides
3/4 + m - 3/4 = - 7/4 - 3/4
m = - 10/4
m = - 5/2
SOMEONE PLEASE ANSWER THIS ASAP!!
The population of Arlington High School can be modeled using the equation P(t) = 3,500(1.027)^t , where t represents the number of years since 2010
Is the population of Arlington High increasing or decreasing? Explain how you can tell using the equation.
How do you interpret the statement that P(6)= 4,107
SOMEONE PLEASE ANSWER THIS
Step-by-step explanation:
Arlington is increasing because it has 1.027, if it was 0.27 it would be decreasing
If p(6)= 4107 that means after 6 years there would be a total population of 4107
Which expression is equivalent to 4x +4y
Answer:
C. 4(x + y)
Step-by-step explanation:
Use the distributive property.
4(x + y) = 4x + 4y
Answer:
C. 4(x + y)
Step-by-step explanation:
If you multiply this answer out (4 times x and 4 times y) it is the equivalent to 4x + 4y.
In right A ABC, B is a right angle and sin _ C= x.
sin A=
V1 – *2
22
Ох,
O2 - 1
+1
Answer:
Step-by-step explanation:
Please help me solve this equation quickly!
Answer:
10
Step-by-step explanation:
The altitude of a graph is displayed as the square root of the two parts of the hypotenuse multiplied together. Over here, the two values are 5 and 15. That means the altitude of the graph is the square root of 5 times 15, which means the altitude of the bigger triangle is equal to the square root of 75. Now, we can use the Pythagorean theorem on the smallest triangle to figure out the value of x. We have:
[tex]5^2+(\sqrt{75})^2=x^2[/tex]
5 squared is 25 and the square root of 75 squared is 75.
[tex]25+75=x^2[/tex]
Combining like terms:
[tex]100=x^2[/tex]
Taking the square root of both sides:
[tex]10=x[/tex]
The value of x is 10.
Two tangents drawn to a circle from a point outside it, are equal in length.prove it.
pls help quick 10 points
Answer:
6.86 to 2DP.
Step-by-step explanation:
7/12 = 4/DC
Cross multiply:
7DC = 4*12
DC = 48/7
= 6.857.
the length of a rectangle pools 15m greater than its width. what is the length if the perimeter of the pool is 96m
Answer:
31.5 m
Step-by-step explanation:
Let w represent the width of the pool.
Since the length is 15 m greater than the width, it can be represented by w + 15.
Use the perimeter formula, p = 2l + 2w. Plug in the perimeter, and w + 15 as l into the formula:
p = 2l + 2w
96 = 2(w + 15) + 2w
96 = 2w + 30 + 2w
96 = 4w + 30
66 = 4w
16.5 = w
So, the width of the pool is 16.5 m. Add 15 to this to find the length:
16.5 + 15
= 31.5
The length of the pool is 31.5 m
Let the width be w
Length = w + 15
Now
Perimeter = 2(l + w)
96 = 2(w + 15 + w)
96/2 = w + 15 + w
48 = 2w + 15
48 - 15 = 2w
33 = 2w
33/2 = w
16.5 = w
Then,
Length = w + 15
Length = 16.5 + 15
Length = 31.5 m
[tex] \\ [/tex]
Christian has 1/2 of a foot of tape. His friend gives him 3/10 of a foot of tape. How much tape does Christian have now?
Answer:
4/5 foot
Step-by-step explanation:
Add the lengths together
1/2 +3/10
Get a common denominator
1/2 *5/5 + 3/10
5/10 + 3/10
8/10
Simplify the fraction by dividing the top and bottom by 2
4/5
[tex]\rm \implies \: Total \: \: length \: \: of \: \: tape \: = \: \frac{1}{2} \: + \: \frac{3}{10} \\ [/tex]
Now , we take LCM of denominators.LCM of 2 and 10 is 10.[tex]\bf \large \rightarrow \: \: \frac{5 \: + \: 3}{10} \: = \: \frac{8}{10} \\ [/tex]
Now , simplifying the fraction in simplest form.
[tex]\bf \large \rightarrow \: \: \cancel\frac{8 \: \: ^{4} }{10 \: \: ^{5} } \: = \frac{4}{5} \\ [/tex]
Christian have 4/5 foot of tape have now.
[ANSWER ASAP PLEASE] Which point is a reflection of across the x-axis? A. point A B. point B C. point C D. point D E. point E
Answer:
Point C
Step-by-step explanation:
We want to reflect across the x axis
That means the y coordinate changes sign
Z = ( 5 1/2 , 3)
Z' = ( 5 1/2 , -3)
That is point C
The diagram shows three points P, Q and R on horizontal ground.
PQ = 50 m, PR = 100 m and angie PQR = 140°.
Calculate angle PRO.
Answer:
m<PQR = 18.7°
Step-by-step explanation:
Apply the Law of Sines,
[tex] \frac{Sin A}{a} = \frac{Sin B}{b} [/tex]
Where,
Sin A = Sin 140
a = 100 m
Sin B = Sin R (<PRQ)
b = 50 m
Substitute
[tex] \frac{Sin 140}{100} = \frac{Sin R}{50} [/tex]
Cross multiply
[tex] 100*Sin(R) = 50*Sin(140) [/tex]
Divide both sides by 100
[tex] Sin(R) = \frac{50*Sin(140)}{100} [/tex]
[tex] Sin(R) = 0.32139 [/tex]
[tex] R = Sin^{-1}(0.32139) [/tex]
R ≈ 18.7° (nearest tenth)
m<PQR = 18.7°
The angle PRO is 1.7 degrees.
Given that,
The diagram shows three points P, Q, and R on horizontal ground.
PQ = 50 m, PR = 100 m and angle PQR = 140°.
We have to determine,
The angle PRO.
According to the question,
The value of angle PRO is determined by using the sin rule-following all the steps given below.
[tex]\rm \dfrac{sina}{a} = \dfrac{sinb}{b}[/tex]
Where, Sin A = Sin 140 , a = 100 m , Sin B = Sin R (<PRQ) , b = 50 m
Substitute all the values in the formula,
[tex]\rm \dfrac{sin140}{100} = \dfrac{sinR}{50}\\\\ \dfrac{0.64}{100} = \dfrac{sinR}{50}\\\\0.0064 = \dfrac{sinR}{50}\\\\0.0064 \times 50 = sinR\\\\0.321 = sinR\\\\R = sin{-1}(0.321)\\\\R = 18.7 \ degree[/tex]
Hence, The angle PRO is 1.7 degrees.
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Write an inequality and show on a number line all numbers:
greater than (-3) but less than or equal to 3
(enter the inequality in terms of x)
Eg. x<-3; 3 7
Answer:
The inequality is:
- 3 < x ≤ 3And the graph is attached
Greater than -3
x>-3-3<xLess than or equal to 3
x≤3For number line
put a open dot at -3
put a close dot at 3
join them
1. 6/5 x 3/4
2. 2/3 x 8/5
3. 5/2 x 4/3
Answer:
hope this might help you
Dylan gety twice as much time as Nina as he has more homework. of his time is to be spent on study, the other half is free time. Natasha gets 7 of an hour more than Nina but 30 minutes less than Dylan. She must spends of her time practising her French. Nina gets i of an hour each day. Z of this is to be spent on Mathletics, the rest is free time. b How many minutes must Dylan spend on study
Answer:
Dylan must spend 45 minutes of his time on studies.
Step-by-step explanation:
Natasha gets 30 minutes less than Dylan. Total there can be 1 and half hour for studies which means there are 90 minutes for the studies. Dylan must spend half of his time on his studies.
90 minutes * 50% = 45 minutes.
What is a simplified form of 1 − sin^2 θ?
Answer:
cos^2(θ)
Step-by-step explanation:
Hernando's salary was $54,500 last year. This year his salary was cut to $52,355. Find the percent decrease. Round to the nearest tenth of a percent.
Answer:
Decrease by 3.9%
Step-by-step explanation:
54,500(1-x) = 52355
x=0.03935... = 3.935% or 3.9%
Answer:
first we subtract his new salary from the old salary to get the decrease.
Then percentage decrease ,we get the decrease over the new salary and multuply by 100. to get the percentage decrease
Can someone help me out
Answer:
82.8
Step-by-step explanation:
area of the parallelogram = base × height
= 13.8×6
= 82.8 in²
Answered by GAUTHMATH
factorize: xy-3x - 5y + 15
Answer:
Step-by-step explanation:
xy-3x-5y+15
x(y-3)-5(y-3)
(y-3)(x-5)
I converting frm base ten to base 2 what do u do?
Answer:
See explanation for example.
Step-by-step explanation:
Say we want to convert 567 to binary aka base 2.
Look for highest power of 2 that will go into 567.
2^x will get us close to 567.
You could solve 2^x=567 in take the whole part of the number.
x=log_2 (567)=approximately 9.1
Of course you don't have to use logarithms here. You could have just found 2^0,2^1,...,2^9. You could have kept increasing the power on 2 until you exceeded the number,567, you wanted and use the power of 2 just before that number, 567.
2^9=512
So what's left 567-512=55
2^6=64 so that's too much, so 2^5=32 is what we will go with next.
55-32=23
2^4=16 and now 23-16=7 is left
2^2=4 so 7-4=3 is left
2^1=2 so 3-2=1 is left
2^0=1 and there is nothing left over
So we had 1, 2^9
No 2^8,2^7,2^6
We had 1, 2^5
We had 1, 2^4
We had no 2^3
We had 1, 2^2
We had 1, 2^1
We had 1, 2^0
The binary aka base 2 representation of 567 is 1000110111.
vHelena has five different flowers. She plans to give one flower to each of her five teachers in any order. She gives the first flower to one of her teachers in the morning.
In how many different ways can she give the four remaining flowers to the rest of the teachers in the afternoon?
1 combination
4 combinations
21 combinations
24 combinations
24
i'm pretty sure of this, if those are the four possible answers.
Please help me with question 4!
Answer:
I think that there might be some complex differential equation
stuff going on here if this were in the real world, but for the sake of this problem... may I suggest that the tank is filling up at a rate of
1/8 of a tank per hour...
it is evaporating at a rate of 1/12 tank per hour
you can subtract the rates
1/8 - 1/12 = 12/96- 8/96 = 3/96 = 1/32 tank/hr
so to fill the tank it should take 32 hours...
I think the logic and math work... lets see if someone else will verify this analysis?
Step-by-step explanation:
PLEASE ANSWERRRR ULL BE SO COOL ILL MARK BRAINLEST!!!
a regular deck of cards has a total of 52 cards. (Note: Aces count as 1.) if one card is drawn at random from the deck, find the probability of the following events: it a 7, 8, or a king
What is the equation of the graph?
Answer:
In the sciences, many times it is necessary to be able to interpret graphs as well as be able to graph certain equations. Often data is available in a graphical format and you must be able to extract the necessary information. Other times, it may be helpful to plot an equation in order to fully understand a problem. However, graphing can be difficult for some students. The format in this section is a little different. The first part will be simply showing what some special equations look like in graphical form and the second part will be a series of questions to help you understand graphs better.
Step-by-step explanation:
1. Match the letter of the centre to the lines that define it.
A Orthocentre
B. Incentre
C. Centroid
D. Circumcentre
median
altitude
perpendicular bisector
angle bisector
Answer:
A. (Orthocenter) → Altitude
B. (Incenter) → Angle bisector
C. (Centroid) → Median
D. (Circumcenter) → Perpendicular bisector
Step-by-step explanation:
A. The orthocenter is the point of concurrency of the three altitudes of a triangle, therefore, the matching line with the letter A is altitude
B. The incenter is the point of concurrency of the bisectors of three interior angles of a triangle, therefore, the matching line with the letter B is angle bisector
C. The centroid is the point of concurrency of the three medians of the triangle, therefore, the matching line to the letter C is median
D. The circumcenter is the point of concurrency of the three perpendicular bisectors of the three sides of a triangle, therefore, the matching line to the letter D (which corresponds with the circumcenter) is perpendicular bisector.
