(
x
)
=
x
3
+
2
x
2
−
3
x
Explanation:
given zeros
x
=
−
3
,
x
=
0
,
x
=
1
then factors are
(
x
+
3
)
,
(
x
−
0
)
,
(
x
−
1
)
⇒
f
(
x
)
=
x
(
x
+
3
)
(
x
−
1
)
⇒
f
(
x
)
=
x
(
x
2
+
2
x
−
3
)
⇒
f
(
x
)
=
x
3
+
2
x
2
−
3
x
is a possible function
graph{x^3+2x^2-3x [-10, 10, -5, 5]}
Which statements are true? Check all that apply. The population density for Montana can be found using the ratio 1,005,141:145,552. The population density for Oregon can be found using the ratio 95,997:3,899,353. The population density for Hawaii is greater than the population density for Florida. The state with the smallest population density is Oregon. The state with the smallest population density is Montana.
Florida has the highest population while Montana has the smallest population.
The statements that are true are;
The population density for Montana can be found using the ratio of 1,005,141:145,552.The state with the smallest population density is Montana.What is the pollution of Montana?The table in the question is presented as follows;
[tex]\rm Population \ density=\dfrac{Total \ population \ of \ the \ area}{Total \ area}[/tex]
By rounding down to the next whole number, we have
Population density of Florida is; 19,317,568 ÷ 53,927 mi² ≈ 358 per mi²
The population density of Hawaii is; 1,392,313 ÷ 6,423 mi² ≈ 216 per mi²
Population density of Montana is; 1,005,141 ÷ 145,552 mi² ≈ 6 per mi²
Population density of Oregon is; 3,899,353 ÷ 95,997 ≈ 40 per mi²
Therefore;
The population density for Montana can be found using the ratio of 1,005,141:145,552.
The population density of Florida (approximately 358 per mi.²) is greater than the population density of Hawaii (approximately 216 per mi²).
Montana is the state with the smallest population density with approximately 6 persons per square mile.
The true statements are;
The population density for Montana can be found using the ratio of 1,005,141:145,552.
The state with the smallest population density is Montana.
Learn more about population density here:
brainly.com/question/620528
Answer:
its a and e
Step-by-step explanation:
edge
Write all factors of 21
Answer:
1, 3, 7, 21
Step by step explanation:
Answer:
1
3
7
21
^^Factors : )
Step-by-step explanation:
please answer this question
Answer:
(i) 226 ltr
(ii) 2 m²
(iii) 16 cm
(iv) 178 ltr
Step-by-step explanation:
(i)
volume of a cylinder = [tex]\pi r^2h[/tex] (where r is the radius and h is the height)
Given:
radius = 24 cmheight = 125cm⇒ volume = [tex]\pi[/tex] x 24² x 125 = 72000[tex]\pi[/tex] cm³
As there are 1000 cm³ in 1 liter
⇒ volume = 72000[tex]\pi[/tex] ÷ 1000 = 72[tex]\pi[/tex] ltr ≈ 226 ltr (nearest whole number)
(ii)
Surface area of cylinder open at one end = [tex]\pi r^2+2\pi rh[/tex]
Given:
radius = 24 cmheight = 125cm⇒ surface area = [tex]\pi \times24^2+2\pi \times24\times125[/tex]
⇒ surface area = [tex]6576\pi[/tex] cm²
As there are 10000 cm² in 1 m²
⇒ surface area = [tex]6576\pi[/tex] ÷ 10000 = 2.065911... ≈ 2 m²
(iii)
Volume of a rectangular prism = l x w x h
(where l is the length, w is the width and h is the height)
Given:
length = 150 cmwidth = 20 cmvolume = 48000 cm³⇒ 48000 = 150 x 20 x h
⇒ 48000 = 3000h
⇒ h = 48000 ÷ 3000 = 16 cm
(iv)
Difference in capacity is the difference in volume
Volume of cylinder in liters = 226 ltr
Volume of trough in liters = 48000 ÷ 10000 = 48 ltr
⇒ difference = 226 - 48 = 178 ltr
Can someone help me with this? I’ll give brainliest if you answer.
Answer: yes, they are congruent they are just rotated
Step-by-step explanation:
WILL GIVE BRAINLIEST The number of milligrams of a certain drug that is in a patient's bloodstream h hours after the drug is injected is given by the following function.
When the number of milligrams reaches 6 , the drug is to be injected again. How much time is needed between injections?
Round your answer to the nearest tenth, and do not round any intermediate computations.
Answer:
3.6 hours
Step-by-step explanation:
[tex]D(h) = 25 {e}^{ - 0.4h} \\ \\ \implies \: 6 = 25 {e}^{ - 0.4h} \\ \\ \implies \: \frac{6}{25} = {e}^{ - 0.4h} \\ \\ \implies \: 0.24 = {e}^{ - 0.4h} \\ Taking\: natural\: log\:both\: sides \\ In(0.24) = - 0.4h \: In\: e \\ \\ \implies \: -1.42711635564 = - 0.4h\\(\because\:In\:e=1) \\ \\ \implies \: h= \frac{-1.42711635564}{ - 0.4} \\ \\ \implies \: h = 3.5677908891 \\ \\ \implies \: h = 3.6 \: hours[/tex]
Is 21/2:3 and 16:6 equivalent
What is the product?
[tex]\qquad \qquad\huge \underline{\boxed{\sf Answer}}[/tex]
Here's the solution ~
[tex]\qquad \sf \dashrightarrow \: (3 {a}^{2} {b}^{4} )( - 8a {b}^{3} )[/tex]
[tex]\qquad \sf \dashrightarrow \: (3 \times - 8)( {a}^{2} \times a)(b {}^{4} \times {b}^{3} )[/tex]
[tex]\qquad \sf \dashrightarrow \: - 24( {a}^{3} )( {b}^{7} )[/tex]
[tex]\qquad \sf \dashrightarrow \: - 24 {a}^{3} {b}^{7} [/tex]
So, The Correct choice is D
9. Find the area of a rectangular park which is 41 m long and 18. m broad. ADVANCED 10. How many tablets of 5mg can be made from 0.5 kg of medicine? 11. Mr.Verma bought a packet of toffees for his daughter and a tin of biscuits for his son. On toffees, he spent 34 of the money spent on biscuits. The price of the tin of biscuits was Rs60.20.How much money did Mr.Verma spend?
Answer:
9. 775 square meters
10. 100,000 tablets
11. ₹105.35
Step-by-step explanation:
9. You want the area of a rectangle 41 2/3 m by 18 3/5 m.
10. You want the number of 5 mg tablets that can be made from 0.5 kg of medicine.
11. You want the total spent if ₹60.20 was spent on biscuits and 3/4 of that amount was spent on toffees.
9. AreaThe area is the product of the length and width:
A = LW
A = (41 2/3 m)(18 3/5 m) = 775 m²
The area of the park is 775 square meters.
10. TabletsIf n is the number of tablets that can be made, their total mass is ...
n(5 mg) = 0.5 kg
n = (0.5 kg)/(5 mg) = (500 g)/(0.005 g) = 100,000
100,000 tablets can be made from the medicine.
11. SpendingThe total spending is the sum of the amounts spent on each item. The amount spent on toffees is 3/4 of the amount spent on biscuits, so the total is ...
₹60.20 + 3/4 · ₹60.20 = (1 +3/4)·₹60.20 = ₹105.35
Mr. Verma spent a total of ₹105.35.
A business purchases a theatre system for $2,500. If the value of the system decreases at a
rate of 13% per year, how much is the system worth after 2 years?
Please show how to do it, because I need to know how to do it again
Answer:
the system will be worth $1892.25 after 2 years.
Explanation:
as the value decreases: [tex]\sf A = P(1 - \frac{r}{n})^{nt}[/tex] ......notice the ' - ' as its *decreases*
given:
P = 2500n = 1 per year t = 2 yearsr = 13%solve:
[tex]\sf A = 2500(1 - \frac{0.13}{1})^{1*2}[/tex]
[tex]\sf A = 1892.25[/tex]
another way of doing it easily is:
[ $2500 * (100- 13)% ] * (100- 13)% = $1892.25
Use compound interest formula
[tex]\\ \rm\hookrightarrow P(1-r/100)^t[/tex]
[tex]\\ \rm\hookrightarrow 2500(1+0.13)^2[/tex]
[tex]\\ \rm\hookrightarrow 2500(0.87)^2[/tex]
[tex]\\ \rm\hookrightarrow 2500(0.76)[/tex]
[tex]\\ \rm\hookrightarrow 1900[/tex]
PLease help me with this question ill give you points
Answer:
[tex]x = -2, x = \frac{1}{6}[/tex]
completing square method:
[tex]\rf 6x^2 + 4x = 2 -7x[/tex][tex]\rf 6x^2 + 4x + 7x -2 = 0[/tex][tex]\rf 6x^2 + 11x -2 = 0[/tex][tex]\rf 6x^2 +12x - x - 2 = 0[/tex][tex]\rf 6x ( x + 2) -1(x + 2) = 0[/tex][tex]\rm (x+2)(6x-1) = 0[/tex][tex]x = -2, x = \frac{1}{6}[/tex]Factorise :
[tex]\qquad \sf \: { \dashrightarrow {6x}^{2} + 4x= 2 - 7x}[/tex]
[tex]\qquad \sf \: { \dashrightarrow {6x}^{2} + 4x + 7x - 2 =0}[/tex]
[tex]\qquad \sf \: { \dashrightarrow {6x}^{2} + 11x - 2 =0}[/tex]
[tex]\qquad \sf \: { \dashrightarrow {6x}^{2} + 12x - x - 2 =0}[/tex]
[tex]\qquad \sf \: { \dashrightarrow {6x}^{} (x+ 2) -1( x + 2 )=0}[/tex]
[tex]\qquad \sf \: { \dashrightarrow ({6x}^{} - 1) (x+ 2) =0}[/tex]
[tex]\qquad \sf \: { \therefore 6x - 1=0} [/tex]
[tex] \qquad \sf \: \dashrightarrow6x =1 [/tex]
[tex]\qquad \sf \: { \dashrightarrow x= \dfrac{1}{6} }[/tex]
[tex]\qquad \sf \: { \therefore x + 2=0} [/tex]
[tex]\qquad \sf \: { \dashrightarrow x = - 2} \\ [/tex]
Therefore, whether the value of x = 1/6, x = –2please help will give brainliest.
Answer:
Part A the answer is 9cm
Part B the answer is going to be 9cm
Step-by-step explanation:
How many litres of fuel will a car use to travel 450 km if its fuel consumption is 6,8 km/l?
Answer:
the car will use 10.64 liters of fuel to travel 450 km
Step-by-step explanation:
Subtract 3x^2+8x from -9x^2 +3x-8
The sum of half a number, n, and 15 is 24. What is the value of the number n?
Answer:
18
Step-by-step explanation:
n/2 + 15 = 24
subtract 15 from both sides
n/2 = 9
Multiply both sides by 2
n=18
anyone? I’ll brainlist.
Answer:
v = 18.38
Step-by-step explanation:
We are going to use the Pythagorean theorem
We see that there are double slits on the right side of the triangle, indicating that 5.22 applies to the other double slits, making it 5.22.
Now we put that in the equation of [tex]b=\sqrt{c^2-a^2}[/tex]
[tex]b = \sqrt{19.11^2+5.22^2}[/tex]
[tex]b = \sqrt{365.1921-27.2484}[/tex]
[tex]b = \sqrt{337.9437}[/tex]
[tex]b = 18.3832450889[/tex]
Rounded
v = 18.38
Did I earn my crown?
Give the other guy brainliest
How many solutions can be found for the equation 4x 5 = 10? Zero One Two Infinitely Many.
Answer:
there is one answer
Step-by-step explanation:
4x⁵ = 10 →
[tex]x = \sqrt[5]{ \frac{10}{4} } = \sqrt[5]{2.5} [/tex]
Which is true about the degree of the sum and difference of the polynomials 3x5y – 2x3y4 – 7xy3 and –8x5y 2x3y4 xy3?.
The degree of the sum and difference of the polynomials are 6 and 7 respectively.
given polynomials are:
[tex]3x^5-2x^3y^4-7xy^3[/tex]
[tex]-8x^5y+2x^3y^4+xy^3[/tex]
the sum of polynomials = [tex]-5x^5y-6xy^3[/tex]
the difference of polynomials = [tex]11x^5y-4x^3y^4-8xy^3[/tex]
what is the degree of a polynomial?A polynomial's degree is the highest or the greatest power of a variable in a polynomial equation.
degree of sum = monomial with highest power = 5+1=6
degree of difference = monomial with highest power = 3+4 = 7
therefore, the degree of the sum and difference of the polynomials are 6 and 7 respectively.
to get more about polynomials refer to:
https://brainly.com/question/1600696
Write a story context for 5/6 divided by 1/12. Use a model to solve
Answer:
Ronnie is a bakery maker (i dont know what you call those, baker?). He has 5/6 feet length of cake. He the order says to cut pieces that are 1/12 long. How many pieces did Ronnie cut?
Step-by-step explanation:
a story? in that case...
i dont know if thats good. im not that good at stories for fractions hope this helps tho!
Asif wants to rewrite 28+49 using the greatest common factor and the distributive property
Answer:
Step-by-step explanation:
28 = 7 *4
49 = 7 * 7
GCF = 7
28 + 49 = (7*4) + (7*7)
= 7*(4 + 7)
The difference in length of a spring on a pogo stick from its non-compressed length wen a teenager is jumping on it after θ seconds can be described by the function f of theta equals 2 times sine theta plus radical 3 period Part A: Determine hall values where the pogo stick's spring will be equal to its non-compressed length. (5 points) Part B: If the angle was doubled, that is θ became 2θ, what are the solutions in the interval [0, 2π)? How do these compare to the original function? (5 points) Part C: A toddler is jumping on another pogo stick whose length of their spring can be represented by the function g of theta equals 1 minus cosine squared theta plus radical 3 period At what times are the springs from the original pogo stick and the toddler's pogo stick lengths equal? (5 points)
Answer:
Refer to your notes from module 6 on this.
Step-by-step explanation:
Complete this test question just like you did the practice question from the module. Remember your test is an open note test, but it is not a copy from the internet test. You can do it!!!
The values of [tex]\theta[/tex] for different conditions were calculated with the help of trigonometric functions.
What are the solutions to trigonometric functions?The solution of trigonometric functions is the values of angles where the function value becomes zero.
Given function is:
A)[tex]f(\theta ) = 2Sin\theta +\sqrt{3}[/tex]
[tex]f(\theta ) = 2Sin\theta +\sqrt{3} = 0\\2Sin\theta = -\sqrt{3} \\Sin\theta =-\frac{\sqrt{3} }{2}[/tex]
[tex]\theta =n\pi +\frac{\pi }{3}[/tex] where n=1,3,5,7......
So, at [tex]\theta =n\pi +\frac{\pi }{3}[/tex] pogo stick's spring will be equal to its non-compressed length.
B)If the angle was doubled, the function will look like this,
[tex]f(\theta ) = 2Sin2\theta +\sqrt{3}[/tex]
[tex]f(\theta ) = 2Sin2\theta +\sqrt{3} =0[/tex]
[tex]2Sin2\theta +\sqrt{3} = 0\\2Sin2\theta = -\sqrt{3} \\Sin2\theta =-\frac{\sqrt{3} }{2}[/tex]
[tex]2\theta =n\pi +\frac{\pi }{3}\\\theta = \frac{n\pi }{2} +\frac{\pi }{6}[/tex]where n=1,3,5,7....
if n=1, [tex]\theta =\frac{2\pi }{3}[/tex]
n=2, [tex]\theta =\frac{7\pi }{6}[/tex]
n=3, [tex]\theta =\frac{5\pi }{3}[/tex]
So, [tex]\theta =\frac{2\pi }{3}, \frac{7\pi }{6} ,\frac{5\pi }{3}[/tex] will be solution in [0,2π}.
C)[tex]g(\theta) =1-cos^{2} \theta +\sqrt{3}[/tex]
[tex]g(\theta) =Sin^{2} \theta + \sqrt{3}[/tex]
[tex]g(\theta) =f(\theta)[/tex]
[tex]sin^{2} \theta +\sqrt{3} = 2Sin\theta+\sqrt{3}[/tex]
[tex]Sin^2\theta = 2Sin\theta[/tex]
[tex]Sin^2\theta-2Sin\theta = 0\\Sin\theta(Sin\theta-2) =0\\Sin\theta =2(NotPOSSIBLE)\\Sin\theta =0[/tex]
[tex]\theta=n\pi[/tex] where n=1,2,3.....
So, [tex]\theta=n\pi[/tex], the lengths of springs from the original pogo stick and the toddler's pogo stick are equal.
Hence, the values of [tex]\theta[/tex] for different conditions were calculated with the help of trigonometric functions.
To get more about trigonometric functions visit:
https://brainly.com/question/2291993
What is the exact volume of the cone? 28π in³ 563π in³ 1963π in³ 196π in³.
The exact volume of the considered cone is given by: Option C: [tex]\dfrac{196}{3} \pi \: \rm in^3[/tex]
How to find volume of a right circular cone?Suppose that the radius of the base of the considered right circular cone be 'r' units.
And let its height be 'h' units.
Then, its volume is given as:
[tex]V = \dfrac{1}{3}\pi r^2 h \: \rm unit^3[/tex]
Right circular cone is the cone in which the line joining peak of the cone to the center of the base of the circle is perpendicular to the surface of its base.
The missing figure of the cone is attached below.
The height of the considered cone = 4 inchesThe radius of the base of the cone = 7 inches.Thus, the volume of the considered cone is given by:
[tex]V = \dfrac{1}{3} \times 7 ^2 \times 4 \times \pi = \dfrac{196\pi}{3} \: \rm in^3[/tex]
Thus, the exact volume of the considered cone is given by: Option C: [tex]\dfrac{196}{3} \pi \: \rm in^3[/tex]
Learn more about volume of the cone here:
https://brainly.com/question/26093363
55 visitors purchased no costume.
147 visitors purchased exactly one costume.
3 visitors purchased more than one costume,
Based on these results, express the probability that the next person will purchase no
more than one costume as a percent to the nearest whole number.
Answer:
236 visitors purchased no costume.
202 visitors purchased exactly one costume.
40 visitors purchased more than one costume.
The total number of customers is, N = 236 + 202 + 40 = 478.
Let X denote the number of costumes purchased by the next person.
Compute the probability that the next person will purchase no more than one costume as follows:
Thus, the probability that the next person will purchase no more than one costume .
Find the unit rate
10 ounce jar of peanut butter is $3.90
Answer:
$0.39 per ounce of peanut butter
Step-by-step explanation:
per ounce is divided by 10
hope that helped!
Triangle Z prime is the image of triangle Z after a series of transformations.
On a coordinate plane, triangle Z has points (0, 2), (2, 6), (4, 2). Triangle Z prime has points (negative 2, 3), (negative 1, 5), (0, 3).
Aliyah and Ivan described the sequence of transformations in different ways.
Aliyah’s Sequence
Ivan’s Sequence
1. a reflection of triangle Z across the y-axis
2. a dilation by a scale factor of One-half with the origin as the center of dilation
3. a translation 2 units up
1. a dilation of triangle Z by a scale factor of One-half with the origin as the center of dilation
2. a translation of 2 units up and 2 units to the left
Which sequence or sequences are correct and why?
Only Aliyah is correct. A dilation and translation alone could not produce triangle Z prime .
Only Ivan is correct because the dilation must be the first step in the sequence.
Both Aliyah and Ivan are correct because both chose the correct scale factor for the dilation and both describe other transformations that would produce triangle Z prime.
Neither Aliyah nor Ivan is correct because the scale factor they chose for the dilation is incorrect.
Mark this and return
Answer:
ONLY ALIYAH IS CORRECT
Step-by-step explanation:
JUST DID IT
**ILL GIVE BRAINLIEST! PLEASE HELP !! :)**
What is the answer to this with explanation please
Another name for slope is the constant rate of change or speed. Question 5 options: True False.
Answer: True
Step-by-step explanation: This is because the slope can be defined as the [tex]\frac{changein yvalues}{changeinxvalues}[/tex]. It is the ratio of vertical (y) and horizontal changes (x) between two points. Rate of change of a function compares these two changes. Speed is essentially the rate at which the position of an object changes, so they are essentially all the same.
The variables x and y vary directly. Use the values to find the constant of proportionality, k. Then write an equation that relates x and y. Write any fractions in simplest form.
y=20; x=12
Answer:
k=1.66666666667
3:5 or y+9-x=17
Step-by-step explanation:
idrk, this SHOULD be the correct answer
19 points!!!!! Tyrone wants to know how much wrapping papers is needed to cover a box with the dimensions shown
Answer:
B. 54 square inches
Step-by-step explanation:
Surface Area
= 2(lb + bh + lh)
= 2(6 x 3 + 3 x 1 + 6 x 1)
= 2(18 + 3 + 6)
= 2(27)
= 54 square inches
The correct option is (B).
Casey has a loan for $400 at a rate of 13% annually. How much interest will he pay in 3 years? A) $15. 60 B) $52. 00 C) $156. 00 D) $556. 0.
Casey will pay $156.00 in 3 years, the correct option is C.
What is the rate of interest?
The interest rate is the amount a lender charges a borrower and is a percentage of the principal—the amount loaned.
Given
Casey has a loan for $400 at a rate of 13% annually.
The interset Casey pay in three years for the loan is given by;
[tex]\rm Interest = Amount \times Rate \ of \ interest \times Time\\\\Interest = 400 \times 0.13 \times 3\\\\Interest = 156[/tex]
Hence, Casey will pay $156.00 in 3 years.
To know more about interest click the link given below.
https://brainly.com/question/26175758
