Answer:
A) 17,000 = 1.7x10^4
B) 26,000,000 = 2.6x10^7
C) 740,000 = 7.4x10^5
Step-by-step explanation:
Answer:
1.7x10
Step-by-step explanation:
What are the solution(s) to the quadratic equation 40 – x2 = 0?
O x= +2/10
O x = +4/10
O x = +2/5
O x = +4,5
Help please it’s timed :)
Answer:
The answer is 2 root 10.
hope it helps..
Answer:
x = ±2[tex]\sqrt{10}[/tex].
Step-by-step explanation:
40 - x^2 = 0
Subtract 40 from both sides
-x^2 = -40
Divide both sides by -1
x^2 = 40
Find the square root of both sides
x = ±[tex]\sqrt{40}[/tex]
x = ±[tex]\sqrt{2 * 2 * 2 * 5}[/tex]
x = ±[tex]\sqrt{2^2 * 2 * 5}[/tex]
x = ±2[tex]\sqrt{2 * 5}[/tex]
x = ±2[tex]\sqrt{10}[/tex]
Hope this helps!
Un agricultor tiene 140 metros de malla para instalar una cerca en su huerta de hortalizas y esa tiene forma de rectangulo a) encuentra una función que modele el área de la huerta que pueda cercar b)¿Para que valor de la longitud del largo, el area es Maxima?
Tenemos que sean x e y los lados de la huerta entonces el perímetro sería:
P = 2*x + 2*y
Sabemos que el perimetro es 140, reemplazando:
140 = 2*x + 2*y
x + y = 70
despejamos y, nos queda:
y = 70 - x
Ahora tenemos que el área sería:
A = x*y
reemplazamos y:
A = x*(70 - x)
A = 70*x - x^2
Esta sería la ecuación que modela el área de la huerta.
Derivamos e igualamos a 0:
0 = 70 - 2*x
x = 70/2
x = 35
ahora calculamos y:
y = 70 - 35
y = 35
El área máxima sería:
A = 35*35
A = 1225 m^2
Which of the following polynomials has a remainder of -7 when divided by x – 2?
A. 4x3 + 2x2 + 5
B. x3 - 2x2 - 4x + 1
c. 3x² + 6x - 2
D.-2x3 + 4x2 + 3x - 2
Answer:
[tex]B.\ x^3 - 2x^2 - 4x + 1[/tex]
Step-by-step explanation:
Given
Polynomials A to D
Divisor: x - 2
Required
Which of polynomial A - D has a remainder of -7
We start by equating the divisor to 0
[tex]x - 2 = 0[/tex]
Make x the subject of formula
[tex]x = 2[/tex]
Next is to substitute 2 for x in the polynomials to get the remainder;
[tex]A.\ 4x^3 + 2x^2 + 5[/tex]
[tex]4(2)^3 + 2(2)^2 + 5[/tex]
Open Brackets
[tex]4 * 8 + 2 * 4 + 5[/tex]
[tex]32 + 8 + 5[/tex]
[tex]Remainder = 45[/tex]
[tex]B.\ x^3 - 2x^2 - 4x + 1[/tex]
[tex](2)^3 - 2(2)^2 - 4(2) + 1[/tex]
Open Brackets
[tex]8 - 2 * 4 - 4 * 2 + 1[/tex]
[tex]8 - 8 - 8 + 1[/tex]
[tex]Remainder = -7[/tex]
[tex]C.\ 3x^2 + 6x - 2[/tex]
[tex]3(2)^2 + 6(2) - 2[/tex]
Open Brackets
[tex]3 * 4 + 6 * 2 - 2[/tex]
[tex]12 + 12 - 2[/tex]
[tex]Remainder = -2[/tex]
[tex]D.\ -2x^3 + 4x^2 + 3x - 2[/tex]
[tex]-2(2)^3 + 4(2)^2 + 3(2) - 2[/tex]
Open Brackets
[tex]-2 * 8 + 4 * 4 + 3 * 2 - 2[/tex]
[tex]-16 + 16 + 6 - 2[/tex]
[tex]Remainder = 4[/tex]
From the calculations above, the polynomial with a remainder of -7 when divided by [tex]x - 2[/tex] is [tex]B.\ x^3 - 2x^2 - 4x + 1[/tex]
The value of the polynomial [tex]x^3-2x^2-4x+1[/tex] is -7 at x = 2. So, option B is correct.
Important information:
Remainder is -7.Divisor is [tex]x-2[/tex].Remainder Theorem:According to the Remainder Theorem, if a polynomial is p(x) is divided by (x-c), then the remainder is p(c).
If polynomials have a remainder of -7 when divided by x – 2. So, the value of the polynomial must be -7 at x = 2.
Substitute x = 2 in the first polynomial.
[tex]4(2)^3+2(2)^2+5=45\neq -7[/tex]
Substitute x = 2 in the second polynomial.
[tex](2)^3-2(2)^2-4(2)+1=-7[/tex]
Substitute x = 2 in the third polynomial.
[tex]3(2)^2+6(2)-2=22\neq -7[/tex]
Substitute x = 2 in the fourth polynomial.
[tex]-2(2)^3+4(2)^2+3(2)-2=4\neq -7[/tex]
Only the value of the second polynomial is -7 at x = 2. Therefore, the correct option is B.
Find out more about 'Remainder Theorem' here:
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Pls help? This is confusing
Answer:
8.1 metresStep-by-step explanation:
[tex]sin \: 54 = \frac{opposite \: side}{hypotenuse} [/tex]
[tex]sin \: 54 = \frac{h}{10} [/tex]
[tex]0.8090 = \frac{h}{10} [/tex]
[tex]h = 10 \times 0.8090[/tex]
[tex]h = 8.09[/tex]
[tex]h = 8.1[/tex]
Hope this helps...
Good luck on your assignment..
Answer:
h = 8.1 m
Step-by-step explanation:
Sin 54 = [tex]\frac{opposite }{hypotenuse}[/tex]
Where opposite = h, hypotenuse = 10 m
0.809 * 10 = h
=> h = 8.1 m
Determine the domain and range for the function.
f (x) = x + 7
Answer:
Domain: (−∞,∞)
Range: (−∞,∞)
Step-by-step explanation:
trust me
What is the circumference of a circular swimming pool with a diameter of 6 ½ feet? ______________ ft. (use for pi) A. 6 3/7 B. 71 1/2 C. 9 9/14 D. 20 3/7
Answer:
The answer is option D
Step-by-step explanation:
Circumference of a circle is πd
where d is the diameter
From the question
d = 6½ feet = 13/2 feet
Circumference is
π × 13/2
= 22/7 × 13/2
= 143/7
[tex] = 20 \frac{3}{7} [/tex]
Hope this helps you
Answer:
d
Step-by-step explanation:
/its wat he sed
Can someone help me please
Answer:
[tex]a_{n} = 12 -3(n-1)[/tex]
Step-by-step explanation:
[tex]a_{1} = 12\\a_{n} = a_{n-1} - 3[/tex]
we have to find formula for nth term of series for this problem
[tex]a_{1} = 12\\a_{2} = a_{2-1} - 3 = a_{1} -3 = 12 -3 = 9\\a_{3} = a_{3-1} - 3 = a_{2} -3 = 9 -3 = 6[/tex]
Thus, we see series is 12, 9 ,6
Thus, we can see that series is decreasing by unit of 3.
and we know that when there is in increase or decrease in series by a a constant number then series is arithmetic progression series.
Hence, this is a decreasing AP series
In AP
nth term is given
nth term = a+(n-1)d
where a is the first term
d is the common difference
common difference is given by = nth term - (n-)th term
lets take 2nd and 1st term to get common difference.
d = 9-12 = -3
(note: this was obvious by looking at series itself that d is -3 as series was decreasing by 3 unit)
a = 12
thus, nth term = a +(n-1)d
nth term = 12 +(n-1)(-3)
nth term = 12 -3(n-1)
writing this in form of [tex]a_{n}[/tex]
[tex]a_{n} = 12 -3(n-1)[/tex] Answer
What is the area of the triangle shown below?
Answer:
given,
base= 10
height= 8
now, area of triangle =
[tex] \frac{1}{2} \times b \times h[/tex]
or, area =
[tex] \frac{1}{2} \times 10 \times 8[/tex]
therefore the area of a triangle is 40 sq units.
hope its helpful..
Answer:
A, 40 sq.units
Step-by-step explanation:
Area of Triangle: 1/2·b·h
Substitute: h= 8, b= 10
A = 1/2 (10)(8)
Simplify: A = 1/2(80) = 40
Area= 40 sq. units
the meeting room needed 4 times the amount of chairs to seat the 60 students. How many chairs did the meeting room have ?
Answer:
15
Step-by-step explanation:
4x=60
60 divided by 4 = 15
In the exam paper there are 12 questions. You will be rewarded 5 marks for each correct answer and will be deducted 2 marks if answered wrongly. Now Thurka scored 32 marks in the exam. So how many questions she did wrongly?
Answer:
Thurka got 8 questions right and 4 wrong.
Step-by-step explanation:
Thurka got "x" questions right and "y" questions wrong, therefore the sum of these questions must be equal to the total number of questions in that exam, which would be 12, therefore:
[tex]x + y = 12[/tex]
Since for each right question Thurka got 5 marks and for each wrong one 2 marks, then the total score can be written as:
[tex]5*x - 2*y = 32[/tex]
Solving the system of equations would give us the number of right and wrong questions.
[tex]\left \{ {{x + y=12} \atop {5*x-2*y=32}} \right.[/tex]
[tex]\left \{ {{2*x + 2*y=24} \atop {5*x - 2*y=32}} \right.[/tex]
[tex]7*x = 56\\x = \frac{56}{7} = 8[/tex]
[tex]y = 12 - x = 12 - 8 = 4[/tex]
Thurka got 8 questions right and 4 wrong.
Write a two-column proof. Given: Triangle ACD is isosceles; <1 is congruent to <3 Prove: Segment AB || Segment CD
Answer:
AB ║ CD, reason If two lines (AB and CD) and a transversal AD, form alternate interior angles, (∠1 and ∠4) that are congruent, then the two lines are parallel
Step-by-step explanation:
Statement, Reason
Triangle ACD is isosceles, Given
∠1 ≅ ∠3, Given
∠3 ≅ ∠4, Base angles of isosceles triangle
∠1 ≅ ∠4, Substitution
∠1 and ∠4, are alt int. ∠s, Definition
AB ║ CD, Have congruent alternate interior angles
If two lines (AB and CD) and a transversal AD, form alternate interior angles, (∠1 and ∠4) that are congruent, then the two lines are parallel
The two-column proof that shows that Segment AB║Segment CD is shown in the image attached below (See attachment).
Given the image showing an isosceles triangle, ΔACD.
The two-column proof that shows segment AB || Segment CD has been provided in the table shown in the image attached below.
We know already that:
ΔACD is isosceles
∠1 ≅ ∠3
∠3 and ∠4 base angles of the isosceles triangle, therefore, ∠3 ≅ ∠4.
By substitution, ∠1 ≅ ∠4
∠1 and ∠4 are alternate interior angles, therefore, based on the Converse of Alternate Interior Angles Theorem: AB║CD
The complete two-column proof is in the image attached below.
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At a certain time of day, a 30-foot building casts a 10 foot shadow. How tall is a person who casts a 2 foot shadow? A. 4 feet B. 5 feet C. 6 feet D. 7 feet
Answer:
6 ft
Step-by-step explanation:
We can use ratios to solve
30 ft tall x ft tall
------------------ = ------------------
10 ft shadow 2 ft shadow
Using cross products
30 * 2 = 10x
60 = 10x
Divide by 10
60/10 = 10x/10
6 =x
I need help with this question!
Answer:
A = 0 -7 b= 0 -7
3 2d 3 2d
Let's calculate A and B:
A= 0*2d- 3*(-7) = -3*(-7) = 21B= 0.2d- 3*(-7) = -3*(-7) = 21Calculte (AB)^(-1):
(AB)^(-1) = (21*21)^(-1) = (21²)^(-1) = 21^(-2)Calculte B^(-1) and A^(-1):
B^(-1) * A^(-1) = 21^(-1) * 21^(-1)= 21^(-1-1) = 21^(-2)so:
(AB)^(-1) = B^(-1) * A^(-1)
Gear A makes 2 revolutions for every 5 revolutions gear B makes. If gear A makes 36 revolutions in 1 minute, then how many revolutions does gear B make in 1 minute?
Sheila either walks or cycles to school
The probability thats she walks to school is 0.65
If she walks the probability she is late is 0.4
If she cycles, the probability she is late is 0.1
Work out the probability that on any day Sheila will not be late to school
Answer: 0.705
Hello!
________________________
Sheila either walks or cycles to school the probability that she walks to school is 0.705
Step-by-step explanation:
Probability she walks and is not late = 0.65 * 0.60 = 0.39.
Probability she cycles and is not late = 0.35*0.9 = 0.315
Therefore P(not late) = 0.39 + 0.315 = 0.705
Hope this helped you!
the amount $3:80 is 4% of what price?
Please in need the answer asap
$7.80
$15.20
$95.00
$97.20
Answer: C) $95
Step-by-step explanation:
4% is 4/100. Thus, simply divide 3.80 by 4/100 to get $95.00.
Hope it helps <3
An ordinary 6-sided die has a number on each face from 1 to 6 (each number appears on one face). How many ways can I paint two faces of a die blue, so that the product of the numbers on the painted faces isn't equal to 6?
Answer:
13
Step-by-step explanation:
There are 6 ways to choose the first number and 5 ways to choose the second number to paint so the total number of ways is 6 * 5 = 30 but we are over counting by a factor of 2 since 1 and 6 is the same as 6 and 1 so it's 30/2 = 15, not 30. The only choices that have a product of 6 are 2 and 3 or 1 and 6 so the answer is 15 - 2 = 13.
Answer:
13 ways
Step-by-step explanation:
Total number of distinct ways to pair two faces
= C(6,2) = 6! / (2!4!) = 15
Total number of ways to pair two faces so that the product equals six
=cardinality {1*6, 2*3} = 2
Therefore
number of ways to paint two faces such that the product is not six
= 15 - 2
=13
What is the solution of 3+ x-2/x-3<_4
Answer:
x≤2−√6 or 0<x≤2+√6
The altitude at which we boil an egg affects how long it takes for the egg to achieve perfect hardness. It takes 198198198 seconds to boil a perfect egg at the lowest place possible, the edge of the Dead Sea, which has an altitude of -418−418minus, 418 meters. The highest place possible is the summit of Mount Everest which has an altitude of 884888488848 meters. It takes 209209209 seconds to boil a perfect egg there. T(a)T(a)T, left parenthesis, a, right parenthesis models the time (in seconds) it takes to boil a perfect egg at an altitude of aaa meters. Which number type is more appropriate for the domain of TTT?
Answer:
The domain is -418 < a < 8848 where a is an integer.
Step-by-step explanation:
We see from the data given that the domain of T(a) takes both positive and negative integer values ( 8848 meters and -418 meters); T(a) never gets decimal values (and in real life thy won't be of much use because we are not looking for that much accuracy).
So the appropriate number type for the domain of T(a) would be integers. And if you are interested, the domain is -418 < a < 8848.
very easy trig with pic
Answer:
1st Option
Step-by-step explanation:
Pythagorean Theorem: a² + b² = c²
Step 1: Find the missing leg
2² + b² = 6²
b² = 36 - 4
b = √32
Step 2: Find cosA
cosA = √32/6
cosA = 4√2/6
cosA = 2√2/3
Ishah spins a fair 5-sided spinner. She then throws a fair coin List all the possible outcomes she could get Ishah spins the spinner and tosses the coin. Work out the probability that she will get a 2 and a head PLZ HELP ITS URGENT WHO EVER WILL GIVE GOOD ANSWER WII GET 50 POINTS AND WOULD BE MARKED AS BRAINLIST
Answer:
The answer is 2/10 :P
Step-by-step explanation:
We have To list all the possibilities first ! : 1 head, 2 head, 3 head, 4 head, 5 head, 1 tail, 2 tails, 3 tails, 4 tails and 5 tails ! ;)
We have in total 10 possibilities !
So if we want to work out the probability that she will get a 2 and a head, the answer has to be 2/10 because we have 10 possibilities !
I hope I helped you ! :P
the domain of y=x^3 is
Answer:
This is a basic cubic function- thus the domain is all real numbers. You could think about domain as the possible x values for a graph. Since this cubic function extends from x=negative infinity to x=positive infinity, the range is all real numbers, or (-infinite, infinite) if you are told to write in interval notation.
Hope this helps!
The domain of [tex]y= x^{3}[/tex] are all real numbers, or R due to the fact that [tex]x^{3}[/tex] is a polynomial, which means its domain is R too.
Solution:
The domain of a particular expression is all real numbers except in the place where expression is undefined. The domain of any graph includes all the x-values that are solutions.
Interval Notation:
(-
Set-Builder Notation:
{x|x ∈R}
Determine the domain from the graph:
Thus, the domain of is:
(−∞,∞), {x|x∈R}
Learn more about the domain of polynomial:
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A basketball team practices their shooting. The function f(x) represents the number of baskets made during practice, where x is the number of players at the practice. Does a possible solution of (12, 36) make sense for this function? Explain your answer.
A.Yes. The input and output are both possible.
B.No. The input is not possible.
C.No. The output is not possible.
D.No. Neither the input nor output is possible.
Answer:
B.No. The input is not possible.
Step-by-step explanation:
According to the given scenario, as we know that f(x) indicates that the baskets number and x the number of players at the practice.
Therefore, if we are having the point (12, 36) we can conclude that during practice there were 36 baskets and 12 players.
Hence, it does not make any sense which results that input is not possible
Find x.
help please !!!
Answer: D.) Cultural knowledge
Step-by-step explanation:
Answer:
x=27solution,
Sum of exterior angles=360°
[tex]3x + 2x + 40 + 4x + x + 50 = 360 \\ or \: 3x + 2x + 4x + x + 40 + 50 = 360 \\ or \: 10x + 90 = 360 \\ or \: 10x = 360 - 90 \\ or \: 10x = 270 \\ or \: x = \frac{270}{10} \\ x = 27[/tex]
Hope this helps..
Good luck on your assignment...
Which point is a solution to the system;
2x + 2y = 18
-2x - 2y=-6
a
(3,5)
None of these
b
С
d
(1, 2)
(0,3)
(9,0)
e
Answer:
None of the listed
Step-by-step explanation:
[tex]Solve-for ;x -in\\ 2x+2y =18\\x = 9-y\\Substitute , 9-y -for ,x- in -2x-2y=-6\\-2(9-y)-2y =-6\\18+2y-2y=-6\\18 = -6\\The -statement- is -false \\Answer ; No -Solution[/tex]
To eliminate the terms and solve for y in the fewest steps, by which constants should the equations be multiplied by before adding the equations together? First equation: 9x + 3y = -18 Second equation: 8x + 7y = 10
Answer:
y = 6
Step-by-step explanation:
You should always multiply by the easiest choice(which I see is multiplying the 7 and the 3 to get 21
7(9x + 3y = -18)
-3(8x + 7y = 10)
63x + 21y = -126
-24x -21y = -30
39x = -156
and solve to get x = -4
then plug -4 into x any of the equations to get y = 6
( 8(-4) + 7y = 10
-32 + 7y = 10
7y = 42
y = 6)
Answer:
The first equation should be multiplied by - 7 and the second equation by 3 .
Step-by-step explanation:
answer on edge
Which of the following represents the translation of M (8,-2) along vector<-5, 1 > and its reflection
across the y-axis?
Step-by-step explanation:
M(8.-2), M'(x,y) , [tex]$$\overrightarrow{v}[/tex] =(-5,1)
[tex]$$\overrightarrow{MM'} = $$\overrightarrow{v}[/tex]
--> x - 8 = -5 --> x= 3
---> y+2 = 1 --> y =-1
so M'(3,-1) and its reflection y-axis is (-3,-1)
The correct representation of given transformations is [tex]\bold{M(8,-2)\rightarrow M'(3,-1)\rightarrow M''(-3,-1)}[/tex]
What is translation?"A translation is a geometric transformation where a geometrical figure is moved from one location to another location without changing its size, shape or orientation."
What is vector?"A vector is a quantity or phenomenon that has magnitude and direction."
To find the vector from point P(a ,b) and Q(m, n)
[tex]\overrightarrow{PQ}= < m-a,n-b >[/tex]
We have been given that, the translation of M (8,-2) along vector<-5, 1 >
Let (x, y) represents the translated point along <-5, 1>
This means, <-5, 1> = <x-8, y-(-2)>
⇒ x - 8 = -5
⇒ x = -5 + 8
⇒ x = 3
Also, y + 2 = 1
⇒ y = 1 - 2
⇒ y = -1
So, the translated point is (3, -1)
The reflection of (3, -1) along y-axis is (-3, -1) .
Hence the correct representation of transformations is[tex]\bold{M(8,-2)\rightarrow M'(3,-1)\rightarrow M''(-3,-1)}[/tex] that is, option (C)
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II NEED THIS ASAP WILL GIVE BRAINLIEST Which number line correctly shows –3 – 1.5? A number line going from negative 4.5 to positive 4.5. An arrow goes from 0 to negative 3 and from negative 3 to negative 4.5. A number line going from negative 4.5 to positive 4.5. An arrow goes from 0 to 3 and from 3 to 4.5. A number line going from negative 4.5 to positive 4.5. An arrow goes from negative 3 to negative 1.5 and from 0 to negative 3. A number line going from negative 4.5 to positive 4.5. An arrow goes from negative 1.5 to 1.5 and from 0 to negative 1.5.
Answer:
An arrow that goes from 0 to negative 3 and from negative three to 4.5
Give me brainliest,5stars,and thanks plz!
Answer:
arrow goes from negative 3 to negative 1.5 and from 0 to negative 3
Step-by-step explanation:
Solve the triangle. Round your answers to the nearest tenth.
Answer:
<B = 47°
<C = 28°
b = AC = 28.0
Step-by-step explanation:
Given:
∆ABC
AB = c = 18
BC = a = 37
<A = 105°
Required:
Length of AC = b
measure of angle B and angle C
SOLUTION:
==>Use the sine rule, sin A/a = sinC/c to find the angle of C:
SinA = sin(105) = 0.9659
a = 37
sinC = ?
c = 18
0.9659/37 = sinC/18
Cross multiply
0.9659*18 = 37*sinC
17.3862 = 37*sinC
Divide both sides by 37
17.3862/37 = sinC
0.4699 = sinC
sinC = 0.4699
C = Sin-¹(0.4699)
C = 28.0° (nearest tenth)
==>Find angle B using sum of angles in a triangle:
Angle B = 180 - (105+28)
Angle B = 180 - 133
Angle B = 47°
==>Find length of b using sine rule, b/sinB = c/sinC:
SinC = sin(28) = 0.4695
SinB = sin(47) = 0.7314
c = 18
b = ?
b/0.7314 = 18/0.4695
Cross multiply
b*0.4695 = 18*0.7314
b*0.4695 = 13.1652
Divide both sides by 0.4695
b = 13.1652/0.4695
b = 28.0 (nearest tenth)
PLEASE HELP MEEEEEEEEEEEEEEEEE
Answer:
A- 5 banners
B- 2 banners
C- 2 banners
D- Shade banner 2