Answer:
See below.
Step-by-step explanation:
Problem:
Solve y=2x;y=−x+2
Steps:
I will solve your system by substitution.
y=2x;y=−x+2
Step: Solve y=2 x for y:
Step: Substitute 2x for y in y=−x+2:
y=−x+2
2x=−x+2
2x+x=−x+2+x(Add x to both sides)
3x=2
3x/3 = 2/3 (Divide both sides by 3)
x=2/3
Step: Substitute 2/3 for x in y = 2x
y=2x
y = 2(2/3)
y = 4/3 (Simplify both sides of the equation)
Answer:
x = 2/3 and y = 4/3
Answer:
only one at x = 2/3 y = 1 1/3
Step-by-step explanation:
At the same solution point Y = Y so
2x = -x + 2
3x = 2
x = 2/3
A polynomial function is represented by the data in the table.
Choose the function represented by the data.
f(x) = −14x − 11
f(x) = −12x + 1
f(x) = 2x2 + 1
f(x) = x2 − 6x + 1
Answer:
[tex]\boxed {f(x) = x^{2} - 6x + 1}[/tex]
Step-by-step explanation:
Substituting each x value and checking it corresponds to the table :
x = -6
⇒ f(-6) = (-6)² - 6(-6) + 1
⇒ f(-6) = 36 + 36 + 1
⇒ f(-6) = 73
x = -2
⇒ f(-2) = (-2)² - 6(-2) + 1
⇒ f(-2) = 4 + 12 + 1
⇒ f(-2) = 17
x = 2
⇒ f(2) = (2)² - 6(2) + 1
⇒ f(2) = 4 - 12 + 1
⇒ f(2) = -7
x = 6
⇒ f(6) = (6)² - 6(6) + 1
⇒ f(6) = 36 - 36 + 1
⇒ f(6) = 1
x = 10
⇒ f(10) = (10)² - 6(10) + 1
⇒ f(10) = 100 - 60 + 1
⇒ f(10) = 41
ind two negative and three positive angles, expressed in radians, for which the point on the unit circle that corresponds to each angle is (√2/2,√2/2)
.
Remember that for a given angle θ, any point on the unit circle is written as:
(cos(θ), sin(θ)).
And remember that:
cos(45°) = sin(45°) = √2/2
Then the angle θ = 45° is a solution.
To find another positive solution, we just add the period of the circle, which is 360°.
θ = 45° + 360° = 405°
Adding the period again:
θ = 405° + 360° = 765°
So the 3 positive solutions can be:
{45°, 405°, 765°}
To get the negative angles we just subtract the period:
45° - 360° = -315°
We can do that again:
-315° - 360° = -675°
So the two negative angles are:
{-315°, -675°}
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Help mee with this question pls I don’t understand
Answer:
a) Cat
b) 4 (unless there is a key that says otherwise)
c) 3 more people
Step-by-step explanation:
a) It has the least number of shapes (only 5)
b) Cat has 1 small square which stands for 1 person and 4 small squares put together make a big square so a big square is 4 people. Unless a key says that a small square is more or less 1, then it should be 4.
c) If one big square is 4 people, then there are 10 people for giraffes and 7 people for dogs. 10 - 7 = 3 more people.
non homogeneous recurrence relation
2fn - 6fn-1 = (n+1)(3^n)
Answer:
Non-Homogeneous Recurrence Relation and Particular Solutions
A recurrence relation is called non-homogeneous if it is in the form. Fn=AFn−1+BFn−2+f(n) where f(n)≠0.
What is the range of the given function?
{(-2, 0), (-4,-3), (2, -9), (0, 5), (-5, 7)}
O {x|x=-5, -4, -2, 0, 2}
Oy | y=-9, -3, 0, 5, 7}
{x|x = -9, -5, -4, −3,−2, 0, 2, 5, 7}
{y | y=-9, -5, -4, -3, -2, 0, 2, 5, 7}
The range of the function will be (-9, 7). Then the correct option is D.
What are domain and range?The domain means all the possible values of x and the range means all the possible values of y.
The function is given in the form of the pair of points.
{(-2, 0), (-4,-3), (2, -9), (0, 5), (-5, 7)}
Then the range of the function will be (-9, 7).
Then the correct option is D.
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Need help with this geometry question
Answer: B
Step-by-step explanation:
In triangles ABC and CED, CE=AC and AB=ED, but CD>BC, meaning the angle E is smaller than angle A.
What is the volume of a cone with a height of 22 and a radius of 6
Answer:
3041.06
Step-by-step explanation:
The formula of a cone is [tex]\pi r^{2} \frac{h}{3}[/tex] , so plugging both the height and radius will result in the answer!
PLEASE HELP
If k and r are constants, the graph of y = (x-r)²(x - k)4 does which of the following?
A)Passes through the x-axis at k and 'bounces off' the x-axis at r
B)Bounces off' the x-axis at r and k
C)Passes through the x-axis at r and 'bounces off the x-axis at k
D)Passes through the x-axis at r and k
Answer:
D
Step-by-step explanation:
Passes through the x-axis at r and k
Sarah conducted an experiment regarding the effectiveness of two mathematics tutoring programs: Math Master and Excel. She randomly selected 20 students from her high school and assigned 10 students to the Math Master program. Sarah then assigned the remaining 10 students to the Excel program.
Finding the percent increase, it is found that the correct option is given by:
C. The Master Program and the Excel Program are both effective, but Math is more effective because of the greater percent increase.
What is the percent increase?The percent increase is given by the difference between the final and the initial score, divided by the initial score and multiplied by 100%.
Researching the problem on the internet, we have that:
In the Master program, the average score increased from 75 to 87.In the Excel program, the average score increased from 73 to 81.The percent increases are given as follows:
M = 12/75 x 100% = 16%,E = 8/73 x 100% = 10.96%.Hence the correct option is given by:
C. The Master Program and the Excel Program are both effective, but Math is more effective because of the greater percent increase.
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A car is purchased for 28,000 after each year, the resale value decreased by 25% what will be the resale value be after 3 years?
Answer:
11,812.5
Step-by-step explanation:
25% = 0.25
(YEAR ONE)
[tex]28,000*0.25 -- > 21,000[/tex]
↓ (why?)
28,000 * 0.25 = 7,000
[tex]28,000 - 7,000 = 21,000[/tex]
(YEAR TWO)
[tex]21,000 * 0.25 -- > 15,750[/tex]
↓ (why?)
[tex]21,000 * 0.25 = 5250[/tex]
[tex]21,000 - 5,250 = 15,750[/tex]
(YEAR THREE)
[tex]15,750 * 0.25 -- > 11,812.5\\[/tex]
↓ (why?)
[tex]15,750 * 0.25 = 3,937.5\\15,750 - 3,937.5 = 11,812.5[/tex]
Answer = 11, 812.5
Every row and every column of this 3 x 3 square must contain
each of the numbers 1, 2 and 3.
What is the value of N + M?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
=========================================================
Reason:
We have "1" in the upper left corner and "2" in the direct middle. This means "3" goes to the left of the "2" since each row and column cannot use repeats. Just below that "3" will go "2".
In summary so far, the first column has 1, 3, 2 in that order when moving from top to bottom. Refer to the values in green in the diagram below.
For identical reasoning, the first row has 1, 3, 2 in that order when moving from left to right. These are the values in light blue.
Once the first row is filled out, we can determine the middle entry of the bottom row, which is "1" marked in pink. This item helps us determine that M = 3 which in turn leads to N = 1.
Therefore, N+M = 1+3 = 4 is the final answer.
Side note: This square has symmetry along the northwest diagonal
Need help! The answer is D, can anyone explain in detail how?
Answer:
D
Step-by-step explanation:
0.0378÷0.21=0.18
this is 18 hundredths
but its 180 thousandths
Explanation:
Now--this is an awfully odd way to word a question.
BUT, it is solvable!
digits have "place values" in numbers, let's focus on after the decimal point:
_ . _ _ _ _ _ '
we know this can go on forever, but we don't need it to (for this problem, that is)
_ . _ _ _
_ . {tenths} {hundredths} {thousandths} ........
we want to know how many thousandths we have:
the answer to this problem (0.0378 / 0.21) is 0.18
{let's consider what we know about place values:}
"10" can be thought of as ten-ones
and "1" can be thought of as ten tenths
{the reason it's always ten __ is that we use a base-ten system, and there are only ten options for each digit [0, 1, 2, 3, 4, 5, 6, 7, 8, 9] }
so, 10 could be thought of as ten ones, which could each be thought of as ten tenths--meaning that 10 is the same thing as 100 tenths
[if you ignore the decimal point, it becomes more clear]:
10.0 [100]
likewise, 10.00 is 1000 hundredths; and 10.000 is 10,000 thousandths
--------
okay, back to our problem:
how many thousandths make up 0.18?
Let's write this out to the thousandths place:
0.180
if we use our tactic of ignoring the decimal, we are left with 0180 [of course, a "0" before a number has no value, so we can rewrite it as 180], or 180
so, 0.18 is really composed of 180 thousandths, which is how option D is the answer
hope this helps!! :)
{let me know if there's anything else you would like me to explain about this!}
Four students were asked to write an expression which has terms that have a greatest common factor of ab. The
expressions provided by the students are shown below.
Olivia
20ab-14abc
Michelle
16a+3b
Michelle
Naomi
Which student wrote the correct expression?
O Olivia
O Peyton
Naomi
18abc-13abc
Peyton
15abc+ 14ab
Answer: Peyton
Step-by-step explanation:
Michelle: Greatest common factor is 1
Naomi: Greatest common factor is abc
Olivia: Greatest common factor is 2ab
Peyton: Greatest common factor is ab
1) (b + a) = 4; use a = 1 and b = 3
2) c(b + b); use b = 1 and c = 5
3) 4+ pm; use m = 4 and p =3
4) 5+ pm; use m = 4 and p = 2
5) m(p + 2); use m = 5 and p = 2
6) h+j²; use h = 1 and j = 4
7) y-(x - 5); use x = 5 and y = 6
8) 4xy; use x = 5 and y = 2
9) n(p + 3); use n = 2 and p = 2
10) y +x+x; use x = 3 and y = 5
11) 6+ a-b; use a = 4 and b = 4
Step-by-step explanation:
1). (3+1)=4
2).5(1+11)
5(2)=103).4+3(4)
4+12=16.4).5+2(4)
5+8=135).5(2+2)
5(4)=206).1+4^2
1+16=177).6-(5-5)
6-0=68).4×5×2=40
9).2(2+3)
2(5)=1010).5+3+3=11
11)6+(4-4)
6+0=6.I hope this helps. Pls mark as brainliest like and follow me
The graph shows the function f(x).
On a coordinate plane, a cube root function goes through (8, 2), has an inflection point at (0, negative 1), and goes through (8, negative 3).
Which equation represents f(x)?
f(x) = Negative RootIndex 3 StartRoot x EndRoot
f(x) = Negative RootIndex 3 StartRoot x minus 1 EndRoot
f(x) = Negative RootIndex 3 StartRoot negative x EndRoot minus 1
f(x) = Negative RootIndex 3 StartRoot negative x EndRoot
The equation that represents the given data is [tex]\RM \\f(x) = -\sqrt[3]{-x} ,[/tex] Option D is the correct answer.
What is a Function ?It is a statement where two variables , one dependent and one independent are related.
It is given that
a cube root function goes through (8, 2), has an inflection point at (0, negative 1), and goes through (8, negative 3).
The equation given in the options are
[tex]\rm f(x) = -\sqrt[3]{x} \\f(x) = -\sqrt[3]{x-1} \\f(x ) =-\sqrt[3]{-x} -1 \\f(x) = -\sqrt[3]{-x}[/tex]
The function goes through (8,2)
Substituting the values
f(x) = -2
f(x) = [tex]\sqrt[3]{7}[/tex]
f(x) = -3
f(x) = 2
The equation that represents the given data is
[tex]\RM \\f(x) = -\sqrt[3]{-x} ,[/tex] Option D is the correct answer.
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Answer:
D
Step-by-step explanation:
what is the decimal value that represents
the total percent markdown for the following scenario, after being rounded to the nearest percent:50%, 31%,and 9%
The decimal value that express the total percent markdown for the given scenerio are 0.5,0.31,0.09.
Given the total percent markdown for the following scenario, after being rounded to the nearest percent:50%, 31%,and 9%
Percentage is a ratio of the numbers expressed as a fraction of 100.
We have to just convert the percentages into decimal number which will be done as under:
To convert percentages into decimals we need to divide the number by 100. In this way the percentages will become:
50%=50/100
=0.5
31%=31/100
=0.31
9%=9/100
=0.09
Hence the decimal value of 50% ,31 % and 9% in percentages are 0.5,0.31,0.09.
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Answer:0.69
Step-by-step explanation:
Calcular cuántos números enteros diferentes de tres dígitos se pueden formar con los dígitos 2, 3 ,4 ,5 ,6 ,7 , 8 si los dígitos no pueden repetirse
There are 210 different three-digit whole numbers that can be formed with the digits 2, 3, 4, 5, 6, 7, 8 if the digits cannot be repeated.
To calculate how many different three-digit whole numbers can be formed with the digits 2, 3, 4, 5, 6, 7, 8 if the digits cannot be repeated, we need to use the permutation formula.
The number of permutations of n objects taken r at a time, where order matters and objects cannot be repeated, is given by:
P(n,r) = n! / (n-r)!
In this case, we have 7 digits to choose from, and we want to form a three-digit number, so r = 3. Therefore, the number of different three-digit whole numbers that can be formed is:
P(7,3) = 7! / (7-3)! = 7! / 4! = 7 x 6 x 5 = 210
Each of these numbers will be unique, as we are not allowed to repeat any of the digits.
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833.30/
1-(1+0.00833)^-360
Answer:
833.25 or 877.59
Step-by-step explanation:
I solved this in two different ways because I wasn't sure on how the question was meant to be read.
Attempt 1:
(833.3/1)-(1+0.00833)^-360
(1+0.00833)^-360 = 0.0505
so:
833.3 - 0.0505 = 833.25
Attempt 2:
833.3/(1-(1+0.00833)^-360)
1- 0.0505 = 0.9495
833.3/0.9495 = 877.59
Pls help me answer these questions⬇⬇⬇
Answer:
a) [tex]\frac{450}{100}[/tex] x 45 = 202.5g of sugar is in the can
b)[tex]\frac{4}{100}[/tex] x 80 = 3.2L is left
c)[tex]\frac{2400}{100}[/tex] x 70 = 1480 acres were planted with wheat
a. 202.5g
Since 45% of the energy drink is sugar
⇒ 45% of the total 450 grams will be made up of sugar
∴ sugar = [tex]\frac{45}{100}[/tex] * 450
= 202.5g
Thus, the can contains 202.5g of sugar
b. 3.2L
Since Simon used up 20% of the paint, the paint left in the can will now be 80% of the original 4 liters
∴ paint left = [tex]\frac{80}{100}[/tex] * 4
= 3.2L
Thus, the can has 3.2 liters of paint left.
c. 1680 acres
Here, 30% of the farmer's crop is and the rest is wheat
⇒ 70% is wheat
Total acres of land planted= 2400
∴ Acres planted with wheat = [tex]\frac{70}{100}[/tex] *2400
= 1680 acres
Thus 1680 acres is planted with wheat
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Work out the bearing of D from C.
(Hint: bearings are written with three digits.)
Answer:
050°
Step-by-step explanation:
The bearing of D from C is the angle between the north pole and the line joining C and D when moving in a clockwise direction.
From the diagram, the angle is 050°
Hakim, Edmund and Paul share a bag of guppies. There are 132 guppies in the bag. The ratio of Hakim's share to Edmund's share is 2:3. The ratio of Edmund's share to Paul's share is 1:2. How many guppies does each boy get? Hakim , Edmund and Paul share a bag of guppies . There are 132 guppies in the bag . The ratio of Hakim's share to Edmund's share is 2 : 3 . The ratio of Edmund's share to Paul's share is 1 : 2 . How many guppies does each boy get ?
Answer:
Hakim's share = 2 x 12 = 24 guppies
Edmund's share = 3 x 12 = 36 guppies
Paul's share = 6 x 12 = 72 guppies
Step-by-step explanation:
We will have Hakim's share as the base unit.
Hakim : Edmund = 2:3
Edmund : Paul = 1:2
Hakim : Edmund : Paul = 2:3:3x2 = 2:3:6
Total units = 2+3+6 = 11 units
11 units = 132 guppies
1 unit = 132/11 = 12 guppies
Hakim's share = 2 x 12 = 24 guppies
Edmund's share = 3 x 12 = 36 guppies
Paul's share = 6 x 12 = 72 guppies
if you put 25ml of concentration in a glass, how much water should be added
Answer:
50 ml
Step-by-step explanation:
50 ml
What is the inverse of the function f(x) = 2x + 1?
Answer:
[tex]h(x)=\frac{1}{2}x -\frac{1}{2} .[/tex]
Step-by-step explanation:
if the initial function is f(x)=2x+1, then
x=2*h(x)+1;
2h(x)=x-1;
[tex]h(x)=\frac{x}{2} -\frac{1}{2}.[/tex]
PS. change design according the local requirements.
Answer:
[tex]y^{-1} =\frac{1}{2} x-\frac{1}{2}[/tex]
Step-by-step explanation:
To find the inverse, you want to swap the inputs with the outputs, which is why you have the swapped domain and range between a function and its range.
So, given f(x)=2x+1, its inverse would give,
x=2y+1.
Solve for y,
2y=x-1 -> y=(x-1)/2 -> y=[tex]\frac{1}{2} x-\frac{1}{2}[/tex]
Therefore, [tex]y^{-1} =\frac{1}{2} x-\frac{1}{2}[/tex]
Help me with this please!!!!
Answer:
3
Step-by-step explanation:
Cardinalities are the number of elements in a set.
(A∩B∩C) is the very middle part of the circle, and there are 3 elements there.
1/a + 1/b = 1/2 (solve for a)
Answer:
1/a+ 1/b = 1/2
Adding the fractions we get
b+a/ab=1/2
cross Multiplying the denominator we get,
b+a=ab/2
a= ab/2 -b
Answer:
a = 1/(1/2 + 1/b)
Step-by-step explanation:
1/a + 1/b = 1/2
1/a = 1/2 - 1/b
1 = a(1/2 - 1/b)
1/(1/2 + 1/b) = a
41% of adults say cashews are their favorite kind of nut. You randomly select 12 adults and ask each to name his or her favorite nut. Find the probability that the number who say cashews are their favorite nut is (a) exactly three, (b) at least four, and (c) at most two. If convenient, use technology to find the probabilities.
The probability for part (a) is 0.131, for part (b) is 0.795, for part (c) is 0.0733.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
We have:
41% of adults say cashews are their favorite kind of nut.
P = 41% = 0.41
Q = 1 - P = 1 - 0.41 = 0.59
n = 2
From the binomial distribution:
[tex]\rm P(X = r) = C(n, r) P^r(1-P)^{n-r}[/tex]
a) Exactly three
[tex]P(X=3) = C(12, 3) (0.41)^3(0.59)^9[/tex]
P(X = 3) = 0.131
b) At least four:
P(X≥4) = P(X=4)+ P(X=5)+ P(X=6)+..............+ P(X=13)
[tex]\rm P(X\geq 4)=C(12, 4) (0.41)^4(0.59)^9+C(12, 5) (0.41)^5(0.59)^8+...............+C(12, 3)(0.41)^3(0.59)^9[/tex]
P(X ≥ 4) = 0.795
c) At most two:
P(X≤2) =P(X=0)+ P(X=1)+ P(X=2)
[tex]\rm =C(12, 0) (0.41)^0(0.59)^12+C(12, 1) (0.41)^1(0.59)^1^1+C(12, 2)(0.41)^2(0.59)^1^0[/tex]
P(X ≤ 2) = 0.0733
Thus, the probability for part (a) is 0.131, for part (b) is 0.795, for part (c) is 0.0733.
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Find the equation of the tangent line to the curve:
y = ( 1 + 2x)
at the point (2, 25).
Answer:
the first answer y = 20x - 15
Step-by-step explanation:
since the correct tangent line must share the same point with the originated function, only a line function that delivers y = 25 for x = 2 can be correct.
only the first answer option provides this (20×2 - 15 = 25).
so, we know, this line goes through the given point, but does it have the correct slope for the tangent ?
the correct slope we get from the first derivative of the original function.
f(x) = (1 + 2x)² = 1 + 4x + 4x²
f'(x) = 4 + 8x
for x = 2 we get the tangent slope at that point as
4 + 8×2 = 20
and the provided line is again
y = 20x - 15
with the slope being the factor of x (20).
so, it fits, and indeed, answer 1 is correct.
I NEED HELP ASAP!!!!
Samuel entered the following key strokes on his calculator.
5 EE (-) 9 divided by 2 EE 4
What did Samuel's calculator display?
A. 2.5E - 13
B. 2.5E - 4
C. 2.5E5
D. 2.5E14
Whoever gets this CORRECT may get MARKED BRAINLIEST.
In the case above about Samuel, one can say that Samuel's calculator has display option A. 2.5 E (- 13)
What is the calculation about?The function was [tex]\frac{5E (-9) }{2E(4) }[/tex] :
We know that, E implies 10 to rise to power.
So, The equation above is Converted from scientific notation into standard form.
[tex]\frac{5 x 10^-9 }{2 x 10^ 4 }[/tex]
= 5/2 x 10 ⁻⁹⁻⁴
=2.5 x 10⁻¹³
Therefore, In the case above about Samuel, one can say that Samuel's calculator has display option A. 2.5 E (- 13)
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What is the measurement of this angle?
Please explain and i need it urgently... One fifth of marked price of a watch is given as discount. What is the discount percent?
Answer:
1/5 times 100= 20%
Step-by-step explanation:
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