Answer:
18 pencils in 3 packs.
Step-by-step explanation:
Assuming that each pack will have the same amount of pencils. It is given that there are 36 pencils in all when one has 6 packs. Find the amount in each pack by dividing (total amount of pencils)/(amount of packs) = Amount of pencils per pack:
36/6 = 6
There are 6 pencils in each pack.
Now, Elsa wants to know how much pencils are in 3 packs. Multiply the amount of packs with the amount of pencils in each pack:
Total amount of pencils = amount of packs (3) x amount of pencils per pack (6)
= 3 x 6
= 18
There are 18 pencils in 3 packs.
~
Simplity the expression.
3(2y - 8) - 2y(5 - y)
Answer:
2y² - 4y - 24
General Formulas and Concepts:
Pre-Algebra
Distributive PropertyAlgebra I
Terms/CoefficientsStep-by-step explanation:
Step 1: Define
Identify
3(2y - 8) - 2y(5 - y)
Step 2: Simplify
[Distributive Property] Distribute 3 and -2y: 6y - 24 - 10y + 2y²Combine like terms: 2y² - 4y - 24Find (4/5+3/6-5/12) ÷ 2/3
Answer:
1/2 + 2/3 + 5/4 = 29/ 12 = 2 5/ 12 ≅ 2.4166667
Step-by-step explanation:
Add: 1/ 2 + 2/ 3 = 1 · 3/ 2 · 3 + 2 · 2/ 3 · 2 = 3/ 6 + 4/ 6 = 3 + 4/ 6 = 7/ 6
For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of both denominators - LCM(2, 3) = 6. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 2 × 3 = 6. In the next intermediate step, the fraction result cannot be further simplified by canceling.
In words - one half plus two thirds = seven sixths.
Add: the result of step No. 1 + 5/ 4 = 7/ 6 + 5/ 4 = 7 · 2/ 6 · 2 + 5 · 3/ 4 · 3 = 14/ 12 + 15/ 12 = 14 + 15/ 12 = 29/ 12
For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of both denominators - LCM(6, 4) = 12. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 6 × 4 = 24. In the next intermediate step, the fraction result cannot be further simplified by canceling.
In words - seven sixths plus five quarters = twenty-nine twelfths.
hope it helps...
correct me if I'm wrong...
Which equation is correct?
x – 17 = 4
x – 4 = 17
x + 4 = 17
x + 17 = 4
Answer:
1 and 2.....then 3 is a different question
What form do we place a quadratic in to find the Vertex, or "extrema” of a quadratic function?
Answer:
The vertex form of the quadratic function, f(x) = a·(x - h)² + k
Step-by-step explanation:
The general form of a quadratic function is given as follows;
f(x) = a·x² + b·x + c
The vertex form of the quadratic function is f(x) = a·(x - h)² + k
Where;
(h, k) = The coordinates of the vertex of the parabola
h = -b/2·a, k = f(h)
can someone help me state domain and range
Answer:
The domain and range is (as inequalities):
[tex]x\leq 3\text{ and } -\infty < y < \infty[/tex]
Or in interval notation:
[tex]D=(-\infty, 3]\text{ and } R=(-\infty, \infty)[/tex]
Step-by-step explanation:
Recall that the domain is simply the set of all x-values of the function.
From the graph, we can see that the function is defined for all x-values less than or equal to 3.
Therefore, the domain is:
[tex]x\leq 3[/tex]
The range is the set of all y-values of the function.
From the graph, we can see that the range will extend infinitely in both directions.
Therefore, the range is all real numbers. As an inequality:
[tex]-\infty < y < \infty[/tex]
Or in interval notation, the domain is:
[tex](-\infty, 3][/tex]
And the range is:
[tex](-\infty, \infty)[/tex]
Which point is a solution to the inequality shown in this graph
Answer: C. (0, -3)
Step-by-step explanation:
You don't even need to find the function, just mentally graph every point in the options on the graph.
If it land in the white area, it's not a solution.If it land in the blue area or on the line, it's a solution.The line is not dotted, showing that the inequality is probably either ≥ or ≤, so points on the line do count as solution.
x = 4y + 3, 2x + y = -3
System of Equations
Answer:
x = -1, y = -1
Step-by-step explanation:
x = 4y + 3
2x + y = -3
We have the value of x in terms of y, so we substitute that in 2x + y = -3:
2(4y+3)+y = -3
8y+6+y = -3
9y = -9
y = -1
Now we substitute the value of y in x = 4y + 3:
x = 4(-1)+3
x = -1
Answer:
y = -1 & x = -1
Step-by-step explanation:
x = 4y + 3 .... ( 1)
2x + y = -3 ........(2)
substitute the 4y + 3 as x in the second equation
2( 4y + 3) + y = -3
simplify and solve for y
8y + 24 + y = -3
9 y + 24 = -3
9y = -3 -24
9y = -27
y = -27 / 9
y = -1
Now, substitute the value of y -1 in first equation
x = 4y + 3
solve for x
x = 4 ( - 1 ) + 3
x = -4 + 3
x = -1
find k so that x-1 is a factor of x^3 - 3x^2 + kx - 1
Answer:
[tex]{ \bf {factor : { \tt{x - 1}}}} \\ x - 1 = 0 \\ x = 1 \\ { \tt{f(x) = {x}^{3} - {3x}^{2} + kx - 1}} \\ { \tt{f(1) : {(1)}^{3} - 3 {(1)}^{2} + k(1) - 1 = 0}} \\ { \tt{k - 3 = 0}} \\ { \tt{k = 3}}[/tex]
Answer:
k = 3
Step-by-step explanation:
If x-1 is a factor of x³ - 3x² + kx - 1 then value of x is 1.
f (x ) = x³ - 3x² + Kx - 1 , then
plug 1 as x in the expression.
f ( 1) = ( 1)³ - 3 ( 1)² + k (1) - 1 = 0expand exponents
1 - 3 + k - 1 = 0combine like terms
-3 + k = 0Add 3 to both side
k = 3Can someone help me with this math homework please!
Answer:
[tex]j = - 0.45[/tex]
Step-by-step explanation:
Combine like terms and apply the rules of algebra.
[tex]2.25 - 11j - 7.75 + 1.5j = 0.5j - 1[/tex]
[tex] - 5.5 - 9.5j = 0.5j - 1[/tex]
[tex] - 9.5j = 0.5j + 4.5[/tex]
[tex] - 10 j= 4.5[/tex]
[tex]j = - 0.45[/tex]
Answer: j = -0.45
Step-by-step explanation:
Step 1: Combine like terms
2.25 - 11j - 7.75 + 1.5j = 0.5j - 1
-5.5 - 9.5j = 0.5j - 1
Step 2: isolate your variable
-5.5 - 9.5j = 0.5j - 1
Subtract 0.5j from both sides
-5.5 - 10j = -1
Add 5.5 to both sides
-10j = 4.5
Divide both sides by -10
j = -0.45
Simplify (square root)2/^3(square root)2
A. 2^1/6
B. 2^1/3
C. 2^5/6
D. 2^3/2
Answer: Personally I would do option "B" 2 1/3 because it sounds right.
Write using exponents. Rewrite the expression below in the same sequence.
Answer:
[tex]10^2a^2b[/tex]
Step-by-step explanation:
Exponents are a way of shortening multiplication statements. The exponent represents how many times a term is being multiplied by itself. So, when two terms have the same base it can be written with exponents. For example. 10*10 can be written as [tex]10^2[/tex] because 10 is being multiplied 2 times. Therefore, if we do this with every term you get [tex]10^2a^2b[/tex].
Evaluate the expression.
32 + 6 x 22-42 - 23
Answer:
25
Step-by-step explanation:
You need to simplify
.
.
.
.
................... :)
Answer:
D
Step-by-step explanation:
9+24-16+8= 25
What is the center of the circle:What is the center of the circle: (x+1)^2+(y-12)^2=25
1. 25
2. (1, -12)
3. 5
4. (-1, 12)
Answer:
option 4
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
(x + 1)² + (y - 12)² = 25 ← is in standard form
with centre = (- 1, 12 ) and radius = [tex]\sqrt{25}[/tex] = 5
Let x=−1−5i and y=5−i. Find x+y
Answer:
[tex]4-6i[/tex]
Step-by-step explanation:
Substitute the value of the variable into the expression and simplify.
Please helped timed question. Solve for a, b, and A. Round to the nearest tenth.
Answer:
[tex]\angle A=90-72[/tex]
[tex]\angle A=18[/tex]
---------------
[tex]sin~72=\frac{b}{11}[/tex]
[tex]11\times sin~72=6[/tex]
[tex]b=10.5[/tex]
----------------
[tex]11\times cos~72=a[/tex]
[tex]a=3.4[/tex]
----------------
ANSWER:
a=3.4
b=10.5
∠A=18
-----------------------
hope it helps...
have a great day!!
What is the answer for y?
the answer is in the picture
The current population of Fun City is 21000 people. If the population of the city will double every 51 years then the population after 171 years would be
Answer:
The population of Fun City after 171 years would be 214563.
Step-by-step explanation:
The statement depicts a case of exponential growth, whose model is described below:
[tex]p(t) = p_{o}\cdot r^{\frac{t}{T} }[/tex] (1)
Where:
[tex]p_{o}[/tex] - Initial population, no unit.
[tex]p(t)[/tex] - Current population, no unit.
[tex]r[/tex] - Growth rate, no unit.
[tex]t[/tex] - Time, in years.
[tex]T[/tex] - Growth period, in years.
If we know that [tex]p_{o} = 21000[/tex], [tex]r = 2[/tex], [tex]t = 171\,yr[/tex] and [tex]T = 51\,yr[/tex], then the population of the city after 171 years is:
[tex]p(t) = 21000\cdot 2^{\frac{171}{51} }[/tex]
[tex]p(t) = 214563[/tex]
The population of Fun City after 171 years would be 214563.
Write functions for each of the following transformations using function notation. Choose a different letter to represent each function. For example, you can use R to represent rotations. Assume that a positive rotation occurs in the counterclockwise direction.
• translation of a units to the right and b units up reflection across the y-axis
• reflection across the x-axis rotation of 90 degrees counterclockwise about the origin, point o
• rotation of 180 degrees counterclockwise about the origin, point o
• rotation of 270 degrees counterclockwise about the origin, point o
Answer:
1) [tex]T_{(a, \, b)}[/tex] = f(x - a) + b
Coordinate change
(x, y) → (x + a, y + b)
2) RFy(x, y) = f(-x)
Coordinate change
(x, y) → (-x, y)
3) RFx(x, y) = -f(x)
Coordinate change
(x, y) → (-y, x)
4) RCCW90(x, y) = f⁻¹(-x)
Coordinate change
(x, y) → (-y, x)
5) RCCW180(x, y) = -(f(-x))
Coordinate change
(x, y) → (-x, -y)
6) A 270 degrees counterclockwise rotation gives;
RCCW270(x, y) = -(f⁻¹(x))
Coordinate change
(x, y) → (y, -x)
Step-by-step explanation:
1) Horizontal translation a units right = f(x - a)
The vertical translation b units up = f(x) + b
Therefore, we get; [tex]T_{(a, \, b)}[/tex] = f(x - a) + b
The coordinate change
(x, y) → (x + a, y + b)
2) A reflection across the y-axis = RFy(x, y) = f(-x)
The coordinate change
(x, y) → (-x, y)
3) A reflection across the x-axis gives RFx(x, y) → (x, -y)
Therefore, in function notation, we get;
RFx(x, y) = -f(x)
4) A 90 degrees rotation counterclockwise, we get RotCCW90(x, y) → (-y, x)
In function notation RotCCW90(x, y) = INVf(-x) = f⁻¹(-x)
5) A 180 degrees counterclockwise rotation about the origin gives;
(x, y) → (-x, -y)
Therefore, we get;
In function notation RotCCW180(x, y) = -(f(-x))
6) A 270 degrees counterclockwise rotation gives RotCCW270(x, y) → (y, -x)
In function notation RotCCW270(x, y) = -(f⁻¹(x))
What is the domain of the ordered pairs shown in the graph?
{–2, –1, 0, 1}
{–2, –1, 0, 2}
{–1, 0, 1, 2}
{–2, 0, 2, 3}
Answer:
-2 0 2 3 this is the domain of the ordered pairs shown in the graph above
What should the following equation be multiplied by in order to eliminate the fractions?
Answer:
6
Step-by-step explanation:
To figure out what needs to be multiplied, we need to find the least common denominator. By finding this, we know that what we multiply the equation with will be a multiple of each denominator, meaning that there will be no fractions left.
We can find the least common denominator by listing multiples of each fraction, and finding which one is the smallest but still in each list.
3: 3, 6, 9, 12...
2: 2, 4, 6, 8...
6: 6, 12, 18, 24...
We can notice that 6 is the lowest number in each list. Therefore, 6 is our least common denominator, and if we multiply by 6, the fractions will be removed.
Answer:
6
Step-by-step explanation:
I took the quiz and got it correct.
please help asap!!!!
Answer:
Step-by-step explanation:
Given functions are,
f(x) = [tex]\sqrt{x} +3[/tex]
g(x) = 4 - [tex]\sqrt{x}[/tex]
22). (f - g)(x) = f(x) - g(x)
= [tex]\sqrt{x}+3-(4 - \sqrt{x} )[/tex]
= [tex]\sqrt{x} +3-4+\sqrt{x}[/tex]
= [tex]2\sqrt{x}-1[/tex]
Domain of the function will be [0, ∞).
23). (f . g)(x) = f(x) × g(x)
= [tex](\sqrt{x}+3)(4-\sqrt{x} )[/tex]
= [tex]4(\sqrt{x}+3)-\sqrt{x}(\sqrt{x}+3)[/tex]
= [tex]4\sqrt{x} +12-x-3\sqrt{x}[/tex]
= [tex]-x+\sqrt{x}+12[/tex]
Domain of the function will be [0, ∞).
Let u = <-7, -2>. Find 8u.
Answer:
<-56, -16>
Step-by-step explanation:
multiply the values by 8 because that's what the question tells you to do
solve for x. Round to the nearest tenth, if necessary.
Answer:
7.1
Step-by-step explanation:
We used SOHCAHTOA because it's a right angle triangle
So because we have an angle with an adjacent of 6.3 and hypotenuse of x
We will use
Cos=adjacent /hypotenuse
Can someone help me with this math homework please!
Answer:
Step 1 & Step 4 are true statements
Step-by-step explanation:
Explanation in progress! Enjoy your answer first then come back for the explanation once you've done it (●'◡'●)
STREAM WALLS BY LOUIS TOMLINSON
Answer:
OMG I LOVE LOUIS SO MUCH HE IS SO PERFECT
Step-by-step explanation:
Every floor of a 20 storey building is 5m in high. If a lift moves 2m every second, how long will it take to move from 3rd floor to 15th floor?
Answer:
30 seconds
Step-by-step explanation:
→ Work out how many floors it's going to travel
15 - 3 = 12 floors
→ Work out how many meters 12 floors is
12 × 5 = 60 meters
→ Work out how long that will take
60 ÷ 2 = 30 seconds
Find the probability of exactly three successes in six trials of a binomial experiment in which the the probability of is 50%.
Start by doing the binomial expansion of (x+y)^6 where x represents success. This is
(x^6y^0) + 6(x^5y^1) +15(x^4y^2) +20(x^3y^3) +15(x^2y^4) +6(x^1y^5) +(x^0y^6)
We are interested in the x^3y^3 term which represents exactly 3 sucesses. Since the probalbility of sucess and failure are both .5 we should be able to figure this out just using the coefficients of the terms which is
20/64 = .3125 which is 31.25%
The probability of exactly three successes in six trials of a binomial experiment in which the the probability of is 50% is 31.25%.
What is the probability?Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.
Here,
Probability =(³₆×(50%)³×(1-50%)⁶⁻³
= 20×(1/2)³×(1/2)³
= 20× 1/64
= 20/64
= 5/16
= 0.3125
= 0.3125×100
= 31.25%
Therefore, the probability of exactly three successes in six trials of a binomial experiment in which the the probability of is 50% is 31.25%.
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PLEASE HELP WILL GIVE BRAINLIEST
Sarah uses 23 of her supply of cheese to make pizza and 19 of her supply of cheese to make lasagna. If Sarah uses 213 pounds of cheese, how many pounds of cheese were in her supply?
A.)3 pounds
B.)6 pounds
C.)8 pounds
D.)9 pounds
Answer:
C.) 8 pounds
Hope that can help
the theater sells two types of tickets: adult tickets for $6 and child tickets for 5$. last night, the theatre sold a total of 375 tickets for a total of $2153. How many adult tickets did the theatre sell
Hello,
Imagine Algebra does not exist .
Let's suppose all tickets are children's tickets
The sum should be 5$*375=1875$
Not enough, we must have $2153: 2153-1875=278 ($) must be found.
Let's replace a children ticket with an adult one,
we get one dollar more.
We must thus exchange 278 tickets
There are 278 adult tickets and 375-278=97 children tickets
Proof: 278*6+97*5=2153
What is the scale factor from abc to xyz?
Answer:
C
Step-by-step explanation:
The scale factor is the ratio of corresponding sides, image to original, so
scale factor = [tex]\frac{XY}{AB}[/tex] = [tex]\frac{9}{45}[/tex] = [tex]\frac{1}{5}[/tex] → C
The scale factor will be equal to 1 / 5. the correct option is C.
What is a scale factor?The scale factor is defined as the proportion of the new image's size to that of the previous image. Dilation is the process of increasing the size of an object while maintaining its shape. Depending on the scale factor, the object's size can be increased or decreased.
In the given image all the angles are the same and the sides are dilated so the scale factor will be calculated as below,
Scale factor = Original size / dilated size
Scale factor = XY / AB
Scale factor = 9 / 45
Scale factor = 1 / 5
Therefore, the scale factor will be equal to 1 / 5. the correct option is C.
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