Answer:
Option b 18x-8 is correct answer.
Step-by-step explanation:
We need to simplify the expression 4(3x – 2) + 6x(2 – 1) and find the result.
Solving:
= 4(3x – 2) + 6x(2 – 1)
Multiplying terms with values in the bracket.
= 12x - 8 + 12x -6x
Adding like terms
= 12x + 12x - 6x -8
= 24x -6x -8
= 18x -8
So, Option b 18x-8 is correct answer.
You simplify expressions by distributing where possible and combining like terms where possible.
4(3x - 2) + 6x(2 - 1)
12x - 8 + 12x - 6x <--- Used the distributive property for both parentheses.
18x - 8 <--- Combined like terms.
So, B. 18x - 8 is the answer.
25 PTSS EAY PLZZ ANYONE KNOW THIS I WILL GIVE 5 RATED STAR THANKS AND PROMISE BRAINLIEST ASAPExplain how to write a function rule from the table below. Then write a function rule.
x 2 4 6
y 1 0 –1
Answer:
y = -1/2x +2
Step-by-step explanation:
The linear and quadratic function rules we usually study in algebra come in several forms.
For linear function rules (equations of a line), there are more than half a dozen different forms, each with its own use. A few that often come in handy are the 2-point form, the slope-intercept form, the point-slope form, and the intercept form. Here, the 2-point form can be useful, since you have several points on the line to choose from.
The 2-point form of the equation of a line is ...
y = (y2 -y1)/(x2 -x1)·(x -x1) + y1
point (x1, y1) and point (x2, y2) can be any pair of the given points, in any order. Let's use the first two for points 1 and 2.
y = (0 -1)/(4 -2)·(x -2) +1
y = -1/2(x -2) +1 . . . . . . . . this is a suitable function rule. In this simplified form, it is in point-slope form, where -1/2 is the slope and (2, 1) is the point.
If you want to simplify this a bit, you can put it into slope-intercept form by eliminating the parentheses and combining the constant terms:
y = -1/2x +2
Answer:
notice that every time x increases by 2, y decreases by 1. So, a first guess would be
y = -1/2 x
But, -1/2 (2) = -1, and y(2) = 1, so we need to add 2 at the start. So,
y = 2 - 1/2 x
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Which equation represents: "Four times an unknown integer, multiplied by three times the unknown integer plus a different unknown integer, equals 100."
A) 12x^2 + 4xy + 100 = 0
B) 12x^2 − 4xy + 100 = 0
C) 12x^2 + 4xy − 100 = 0
D) 12x^2 − 4xy − 100 = 0
Let's call the first unknown integer x and the second one y.
"Four times an unknown integer"
We can write it as 4x"Multiplied by three times the unknown integer plus a different unknown integer"
4x is multiplied by 3x+y, so 4x(3x+y)=12x²+4xy"Equals 100."
12x²+4xy=100And so the answer is C: 12x²+4xy-100=0
12x²+4xy-100=0. The equation that represents the statement of the problem is 12x²+4xy-100=0.
The equation is represents by "Four times an unknown integer, multiplied by three times the unknown integer plus a different unknown integer, equals 100."
First, we have the statement "four times an unknown integer", this is:
4x
Then, multiplied by three times the unknown integer plus a different unknown integer, that is:
4x(3x+y)
And finally, the equation above is equals to 100.
4x(3x+y)=100
Operating
(4x)(3x)+(4x)(y)=100
12x²+4xy=100
Then, subtracting 100 on both sides of the equation.
12x²+4xy-100=100-100
Obtaining
12x²+4xy-100=0
The factory produces 4 gallons of orange juice for every 24 gallons of apple juice but is use this ratio to answer the question what unit rate describes the rate at which the factory produces juice
Answer:
1/6 (1 gallon of orange juice for every 6 gallons of apple juice)
Step-by-step explanation:
4/24=24/4x1/36
This is because you reverse the division (or fraction) into a easier to solve equation, and the 1/36 is there to balance out that change.
decide if the graphs of each pair will be parallel, perpendicular or neither.
a. y = -2x + 5 and y = 1/2x - 7
b. y = 3x + 9 and 3y - x = 6
c. 4y - x = 8 and y = 1/4x - 3
part b //
find the equation of the line that is:
a. parallel to y = 3x - 5 and passes through (-2, 1).
b. perpendicular to y = -2/5x + 7 and passes through (4, 6).
so parallel is just numbers with the same slope but different x value
and perdicular is the One with different signs and oppisite reciprocals
a) perpendicular because -2 is the oppisite sign and reciprocal of 1/2
b)neither
c) niether
and B)
a) 3x-2
b)y=5/2 +4
i think
Write each expression using a single exponent. x to the ninth over x squared
Answer:
x^7
Step-by-step explanation:
The expression is written as a single exponent in x⁷
How to simply the expressionIndex forms are forms used to represent numbers or variables that are too large or small in more convenient forms.
From the information given, we have that the expression is;
x to the ninth over x squared
This is represented as;
x⁹/x²
Since the forms are of like bases, subtract the exponents, we get;
x⁹⁻²
Subtract the exponents, we get;
x⁷
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When converting from inches to feet, the measurement in inches, m, of an object varies directly with
What the object adds up to
What’s the square root of 36?
Answer:
6
Step-by-step explanation:
the square root is basically exponents 6*6 is 6^2 which is 36.
Please help. Find the value of x
21x is 21x im glad that I can help you
Match the following items.
A jar contains a mixture of 12 black marbles, 10 red marbles, and 18 white marbles, all the same size. If two marbles are drawn from the jar without being replaced, what would the probability be:
1.
of drawing two black marbles?
2.
of drawing a white, then a black marble?
3.
of drawing two white marbles?
4.
of drawing a black, then a red marble?
Options
51/260
1/13
9/65
11/130
I have to match them up
This problem can be solved using probability, the equation of the probability of an event A is P(A)= favorable outcomes/possible outcomes. The interception of two probable events is P(A∩B)= P(A)P(B).
There are 12 black marbels, 10 red marbles, and 18 white marbels, all the same size. If two marbles are drawn from the jar without being replaced.
The total of the marbles is 40.
If two marbles are drawn from the jar without being replaced, what would the probability be:
1. of drawing two black marbles?
The probability of drawing one black marble is (12/40). Then, the probability of drawing another black marble after that is (11/39) due we drawing one marble before.
P(Black∩Black) = (12/40)(11/39) = 132/1560, simplifying the fraction:
P(Black∩Black) = 11/130
2. of drawing a white, then a black marble?
The probability of drawing one white marble is (18/40). Then, the probability of drawing then a black marble after that is (12/39) due we drawed one marble before.
P(White∩Black) = (18/40)(12/39) = 216/1560, simplifying the fraction:
P(White∩Black) = 9/65
3. of drawing two white marbles?
The probability of drawing one white marble is (18/40). Then, the probability of drawing another white marble after that is (17/39) due we drawed one marble before.
P(White∩White) = (18/40)(17/39) = 306/1560, simplifying the fraction:
P(White∩White) = 51/260
4. of drawing a black marble, then a red marble?
The probability of drawing one black marble is (12/40). Then, the probability of drawing then a red marble after that is (10/39) due we drawed one marble before.
P(Black∩Red) = (12/40)(10/39) = 120/1560, simplifying the fraction:
P(Black∩Red) = 1/13
What is the slope of the line that passes through the points (1,7),
(10, 1)?
3/2
2/3
-3/2
-2/3
Answer:
The slope of a line is the change in y divided by the change in x.
( y1 - y2 ) / ( x1 - x2 )
It does not matter which point you choose as (x1, y1) and (x2,y2)
( 7 - 1 ) / ( 1 - 10 )
( 6 ) / ( -9 ) This will simplify to -2/3.
Please help will give brainliest brainliest
Answer:
D. [tex]A\subset \mathbb{R}\times\mathbb{R}.[/tex]
Step-by-step explanation:
Consider the set
[tex]A=\left\{(2,3),\ (5,1),\ (-3,-2),\ (0,3)\right\}[/tex]
This set consists of four ordered pairs.
The first numbers in these pairs are [tex]2,\ 5,\ -3,\ 0.[/tex] These numbers are integer numbers (not natural, because -3 is negative).
The second numbers in these pairs are [tex]3,\ 1,\ -2,\ 3.[/tex] These numbers are integer numbers too (not natural, because -2 is negative).
Options contain only natural and real sets, so, the first and the second numbers are real numbers and
[tex]A\subset \mathbb{R}\times\mathbb{R}.[/tex]
Answer:
D. R X R
Step-by-step explanation:
The answer is choice D because, the set of the actual numbers of R has a 0 so A is a subset of R X R
---2+
f(x) =
x
What is the range of the function graphed above?
A.
(-0,0)
B. [0,2-)
C. (-,0]
CD. (0,0)
Answer:
The range of the function is [0 , ∞) ⇒ answer B
Step-by-step explanation:
* lets revise the meaning of the domain and the range
- The domain is the values of x
- The domain is all the values of x which make the function is defined
- If there are some values of x make the function undefined, we
exclude these values from the domain
- The range is the values of f(x) which corresponding to the value of x
* Now lets look to the figure
∵ f(x) = √x
- We can not use the negative values for x because there is no
square root for negative numbers
∴ All real negative numbers make the function undefined
- We must exclude them from the domain
∴ The domain is all real numbers greater than or equal zero
∴ x ≥ 0
- To find the range use the first value of the domain
∵ the first value of x = 0
∴ f(0) = √0 = 0
∵ x can not be negative
∵ f(x) = √x
∴ f(x) can not be negative
∴ the range is all real numbers greater than or equal zero
∴ f(x) ≥ 0
OR
f(x) = [0 , ∞)
* The range of the function is [0 , ∞)
Which statement describes the graph of f(x) = 4x2 + 20x + 25?
The graph does not intersect the x-axis.
The graph touches the x-axis at (–2.5, 0).
The graph intersects the x-axis at (–0.4, 0) and (0.4, 0).
The graph intersects the x-axis at (2, 0) and (5, 0).
Answer:
2nd statement is true
Step-by-step explanation:
Please use " ^ " to denote exponentation: f(x) = 4x^2 + 20x + 25.
Take a look at the second statement. If you'll substitute -2.5 for x, to find f(-2.5), you'll find that the result is 0; Thus, this second statement is true.
Answer:
The graph touches the x-axis at (–2.5, 0).
Step-by-step explanation:
Given : f(x) = 4x² + 20x + 25.
To find : Which statement describes the graph .
Solution : We have given
f(x) = 4x² + 20x + 25.
On factoring
4x² + 10x + 10x+ 25 = 0
On taking common 2x from first two terms and 5 from last two terms.
2x ( 2x + 5 ) +5 (2x + 5 ) = 0
On grouping
(2x +5) (2x +5) = 0
For 2x +5 = 0
On subtracting 5 both side
2x = -5
On dividing by 2
x = [tex]\frac{-5}{2}[/tex] = - 2.5
x = - 2.5 .
Points (-2.5 , 0)
Therefore, The graph touches the x-axis at (–2.5, 0).
Movies Plus charges its customers a $10 monthly service fee plus $2 for each movie the customer rents. Movies For Less charges $3 for each movie but does not have a monthly service fee. The costs of renting movies during the same month is represented in the table below.
Which statement is true if 15 movies are rented from each company?
A)Movies For Less costs $5 more.
B)Movies Plus costs $5 more.
C)Movies Plus costs $6 more.
D)Each company charges the same amount.
↓Movie Rentals↓
Answer: A) movies for less cost $5 more
Step-by-step explanation:
10 × 3 =30
15 × 2= 30+10=40 movie plus
15 × 3= 45 movies for less
Answer:
A)Movies For Less costs $5 more.
Step-by-step explanation:
Movies Plus charges its customers a $10 monthly service fee plus $2 for each movie the customer rents.
So, 15 movies from this provider will cost = [tex]10+2(15)[/tex]
=> [tex]10+30=40[/tex] dollars.
Movies For Less charges $3 for each movie but does not have a monthly service fee.
So, 15 movies from this provider will cost = [tex]15\times3=45[/tex] dollars.
Comparing both providers, we can see that Movies For Less charges $5 more than Movies Plus.
Therefore, option A is correct.
At a pizza shop, 80% of the customers order a pizza, 15% of the customers
order a salad, and 10% of the customers order both a pizza and a salad.
If a customer is chosen at random, what is the probability that he or she
orders either a pizza or a salad?
90% out of 105% which would be 0.85
Answer: 0.85
Step-by-step explanation:
Let A be the event that the customer orders a pizza and B be the event that the customer orders a salad.
Then , we have [tex]P(A)=80\%=0.80[/tex]
[tex]P(B)=15\%=0.15[/tex]
[tex]P(A\cap B)=10\%=0.10[/tex]
Now, the probability that he or she orders either a pizza or a salad is given by :-
[tex]P(A\cup B)=P(A)+P(B)-P(A\cap B)\\\\\Rightarrow\ P(A\cup B)=0.80+0.15-0.10=0.85[/tex]
Hence, the required probability = 0.85
Which statement is true about the letter H? It has line symmetry only. It has rotational symmetry only. It has both line and rotational symmetry. It has neither line nor rotational symmetry.
Answer:
it has both line and rotational symmetry
Answer:
youre answer is it has both line and rotational symmetry
Step-by-step explanation:
A printer can print 27 pages in 4.5 min. How much time does it need to print 324 pages?
Answer:
54 minutes
Step-by-step explanation:
We can write a proportion to solve this problem. Put the number of pages over the minutes
27 pages 324 pages
-------------- = ---------------
4.5 minutes x minutes
Using cross products
27 * x = 324 * 4.5
27x = 1458
Divide each side by 27
27x/27 = 1458/27
x =54
How many solutions does the equation −2y + 2y + 3 = 3 have? One Zero Infinitely many Three
Answer:
Infinitely many solutions.
Step-by-step explanation:
In the equation −2y + 2y + 3 = 3 we see only one variable, and that variable is of the first power. Ordinarily, we'd say that this equation will have 1 solution. However, if we combine like terms, we get 0 + 3 = 3, or 0 = 0, which is true for any and all y values. Infinitely many solutions.
Answer:
Infinitely
Step-by-step explanation:
we have
[tex]-2y+2y+3=3[/tex]
Group terms that contain the same variable
[tex]-2y+2y=3-3[/tex]
Combine like terms
[tex]0=0[/tex] ----> the equation is true for any value of y
therefore
The equation has infinite solutions
Which of the following expressions are equivalent to 48? Select all that apply.
4(-3 +15)
4(4 + 2 + 5)
4(7 + 2 + 3)
4(8 + 6-2)
4-2-4 + 16)
Answer:
see below
Step-by-step explanation:
4(-3 +15) = 48
4(4 + 2 + 5) = 44
4(7 + 2 + 3) = 48
4(8 + 6-2) = 48
4(-2-4 + 16) = 40
We are required to select all expressions equivalent to 48
All expressions are equivalent to 48 except 4(4 + 2 + 5) and 4(-2-4 + 16)
Check all options:
4(-3 +15)= 4(12)
= 48
4(4 + 2 + 5)= 4(11)
= 44
4(7 + 2 + 3)= 4(12)
= 48
4(8 + 6-2)= 4(12)
= 48
4(-2-4 + 16)= 4(10)
= 40
Therefore, all expressions are equivalent to 48 except 4(4 + 2 + 5) and 4(-2-4 + 16)
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The expression 37-6 can be written as____
Answer:
31
Step-by-step explanation:
Do the subtraction: 37 - 6 = 31
Hello! I’m confused and I need some help to complete this. I will mark brainliest
Answer: a) x=37,
b)no solutions
c)x=0
Step-by-step explanation:
In then the problem, you will need to isolate the x, use the inverse operation, and solve. For example, if I had the problem x-6=64, i would have to use the inverse operation of 6 to isolate the x. You would add 6 on both sides.(addition is the inverse of subtraction). THat would be x=58.
Given that K is the centroid of EFG find GE and GI
Answer:
D) GE = 10 and GI = 12
Step-by-step explanation:
Given: KI = 4 and GH = 5
K is the centroid of EFG
So
KI = 1/3 (GI)
GI = 3 (KI) = 3(4) = 12
Because K is the centroid of EFG so GH = HE = 5
GE = GH + HE
GE = 5 + 5
GE = 10
Answer
GE = 10 and GI = 12
Answer:
D. GE = 10; GI = 12
Step-by-step explanation:
Given that K is the centroid of EFG, then GH = HE = 5, so GE = GH + HE = 5 + 5 = 10
The 2/3 rule states that the centroid is 2/3 of the way from the vertex to the opposite midpoint. This means that GK is doubled than KI, then GK = 2*4 = 8, and GI = GK + KI = 8 + 4 = 12
NNEED HELP!! GEETSS BRAINLIEST**
Answer:
D. [tex]y=3\cos \left(\dfrac{4}{3}x-2\pi\right)+2[/tex]
Step-by-step explanation:
The period of the functions [tex]y=\cos x,\ y=\sin x[/tex] is [tex]2\pi.[/tex]
The period of the function [tex]y=a\cos (kx+b),\ y=a\sin(kx+b)[/tex] is ALWAYS [tex]\dfrac{2\pi}{k}[/tex]
In your case, you have function [tex]y=-3\sin \left(\dfrac{2}{3}x-2\pi \right)+2[/tex] and this function has the period
[tex]\dfrac{2\pi}{\dfrac{2}{3}}=3\pi.[/tex]
You need to find the function that will have the period that is half of [tex]3\pi,[/tex] so
[tex]\dfrac{3\pi}{2}=\dfrac{2\pi}{k}\\ \\3k=4\\ \\k=\dfrac{4}{3}.[/tex]
So, correct choice is
[tex]y=3\cos \left(\dfrac{4}{3}x-2\pi\right)+2[/tex]
Answer:
The answer is y = 3 cos(4/3 x - 2π) + 2 ⇒ last answer
Step-by-step explanation:
* Lets revise the sine function
- If we have a sine function of the form f(x) = Asin(Bx + C) + D, where
A, B , C and D are constant, then
# Amplitude is A
- The Amplitude is the height from the center line to the peak .
Or we can measure the height from highest to lowest points and
divide that by 2
# Period is 2π/B
- The period goes from one peak to the next
# phase shift is C (positive is to the left)
- The Phase Shift is how far the function is shifted horizontally
from the usual position.
# vertical shift is D
- The Vertical Shift is how far the function is shifted vertically from
the usual position.
* Now lets solve the problem
∵ y = -3sin(2/3 x - 2π) + 2
- the period is 2π ÷ 2/3 = 2π × 3/2 = 3π
∴ The period of the function is 3π
- We look for a function has one-half (3π), means 3π/2
* Lets look to the answer to find the right one
- All of them have the same value of B except the last one, lets
check it
∵ y = 3cos(4/3 x - 2π) + 2
∵ B = 4/3
∴ The period = 2π ÷ 4/3 = 2π × 3/4 = 6π/4 = 3π/2
∵ 3π/2 is half 3π
∴ The last answer is right
How many edges, vertices, and faces does the figure shown have?
A.12 edges, 6 vertices, and 8 faces
B.12 edges, 8 vertices, and 6 facesC.
8 edges, 12 vertices, and 6 faces
D.12 edges, 8 vertices, and 8 faces
Answer:
A. 12 edges. 6 vertices, and 8 faces.
Step-by-step explanation:
The edges are the places where the faces meet. They can be easily identified as the lines that form the shape. There are 12 edges.
The vertices are the places where the edges meet. They are more commonly known as the corners of the figure. There are 6 vertices.
The faces are the flat sides/surfaces of the figure. In this case, the faces are the triangles. There are 8 faces.
Hope this helps!
The given figure has 12 edges, 6 vertices, and 8 faces. This can be obtained by understanding what edges, vertices and faces are and counting them.
What are edges, vertices and faces?Edge: A line segment on the boundary and is known as side of a polygon.Vertex (plural: vertices): A point where two line segments meet forming an angle.Face: A flat surface of a solid.For example, a cube has 12 edges, 8 vertices and 6 faces.In the given figure we can count the edges, vertices and faces.
It is observed that there are 12 edges, 6 vertices, and 8 faces.
Hence the given figure has 12 edges, 6 vertices, and 8 faces. The correct answer is A.
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Q(t)=Q(0)e^pt
The above model describes the exponential decay of chemical element. t is the time in years, Q(0) is the initial amount of the chemical element, Q(t) is the amount of chemical element after t years and p is a constant. It is known that every 1600 years the amount of the chemical element drops to half ( its half-life is 1600 years). If the term e^p in the above equation can be replaced by the term x^y, where both x,y rational numbers, what is x and y?
(a) x=sqrt{frac{1}{2}}, y=frac{1}{1600}
(b) x=frac{1}{2}, y=frac{1600}{3}
The constant p is determined by the half-life of 1600 years, and since after one half-life, the amount of the element is half of its initial value, we find that x=1/2 and y=1/1600, as e^p can be expressed as (1/2)^(1/1600). Therefore, option (a) is the correct answer.
The equation Q(t) = Q(0)e^pt describes an exponential decay process, such as the decay of a chemical element over time. Given that the half-life of the chemical element is 1600 years, after this period the quantity of the element will be half of its original amount. According to the properties of exponential decay, we know that after one half-life, Q(t) = Q(0)/2.
Substituting t = 1600 into the equation and knowing that Q(1600) = Q(0)/2, we get Q(0)/2 = Q(0)e^(1600p). Simplify by dividing both sides by Q(0), resulting in 1/2 = e^(1600p). To find p, take the natural logarithm of both sides, yielding ln(1/2) = 1600p ln(e), and since ln(e) = 1, we have p = ln(1/2)/1600.
Now, to express e^p as x^y, with both x and y being rational numbers, we look for a rational base x that can represent e^ln(1/2), which simplifies to (1/2). So, x would be 1/2, and because the half-life is 1600 years, y will be proportional to the fraction of that time. Hence, y = t/1600, where t is time in years. From this, you can infer that the base x equals 1/2 and y is 1/1600 for each year surpassing the half-life. Therefore, the correct answer is (a) x = sqrt(1/2), y = 1/1600.
How do you know how long a trip will take if you have 399 mileage on one tank of gas but the maximum you can drive in one day is 600?
Answer:
Step-by-step explanation:
600 minus 399 is 201
The trip will take at least two days given the car's mileage limit per tank and the daily driving limit.
To determine how long a journey will take with the given constraints, we first need to understand the limitations. The car can run for 399 miles on one tank of gas, and the maximum you can drive in one day is fixed at 600 miles. Since the daily maximum driving distance is greater than the mileage per tank, the limiting factor is the gas tank range.
Assuming you start with a full tank, you would need to refill once you've driven 399 miles. If there is no wait time for refilling and the efficiency of the car does not change, you could potentially drive for another 399 miles after refilling. However, due to the 600 miles per day limit, you would need to stop before exhausting your second tank. To find out the total driving time, divide the total distance by the daily driving limit (if the total distance is larger than what can be covered in one day).
For example, if the total trip is 700 miles, it would take at least two days because you can cover 600 miles on the first day and the remaining 100 miles on the second day. However, this does not account for any potential stops, breaks, or other delays.
Shelley drove from New Haven, Connecticut, to New York City in 90 minutes. Which equation relates the distance she traveled to her speed?
A.
distance = speed + 90
B.
distance = speed × 90
C.
distance − speed = 90
D.
distance × 90 = speed
The correct answer is B.
Distance = speed + 90
The equation relates the distance she traveled to her speed is Speed x 90 = distance.
The speed a person travels is the total distance driven per the total time it took to travel.
Speed = total distance / total time
The time it took to drive is 90 minutes: Speed = distance / 90
In order to determine the equation that relates distance to speed, make distance the subject of the formula. In order to do this, multiply both sides of the equation by 90: Speed x 90 = distance.
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What is the rule for the reflection
Answer:
hey user!
your answer is here...
laws ( rules ) of reflection are :-
• angle of incidence is equal to angle of reflection.
• the incident ray, Normal ray and reflected ray all lie in same plane.
cheers!!
Step-by-step explanation:
-x+ 3y = 14
3x – 3y =-6
How would do in steps ?
for the first part:
Let's solve for x.
−x+3y=14
Step 1: Add -3y to both sides.
−x+3y+−3y=14+−3y
−x=−3y+14
Step 2: Divide both sides by -1.
−x/−1 = −3y+14/−1
x=3y−14
Answer:
x=3y−14
Second part:Let's solve for x.
3x−3y=−6
Step 1: Add 3y to both sides.
3x−3y+3y=−6+3y
3x=3y−6
Step 2: Divide both sides by 3.
3x/3= 3y−6/3x=y−2
Answer:
x=y−2
You roll a standard number cube once. Find P(number greater than o).
Answer:
6/6
Step-by-step explanation:
If a standard number cube has six sides and all the numbers are larger than 0 you have a 6/6 chance