Answer:
Distribution is used from steps 1-2
They eliminate 2x by subtracting it on both sides (steps 3-4)
They eliminated 6 by subtracting it from both sides (steps 5-6)
(steps 3-6 is eliminating like-terms)
Thus this leaves the answer being x=-3
Step-by-step explanation:
Equation 3(x+2) = 2x+3 solved using distributive property and simplification, final solution is x = -3.
Let's identify the reason for each step in the solution to the equation 3(x+2) = 2x+3:
Distributive Property
The first step applies the Distributive Property,
which states that multiplying a number outside the parentheses by the terms inside the parentheses.
Here, we multiply 3 by (x+2),
3(x+2)
= 3 × x + 3 ×2
= 3x + 6
Combining Like Terms
In the second step, combine like terms on both sides of the equation.
On the left side, we have 3x, and on the right side, we have 2x.
We also have constants 6 on the left side and 3 on the right side.
3x + 6 = 2x + 3
Move Variables to One Side
To solve for 'x', we want all the terms with 'x' on one side of the equation.
Here, move the term with 2x to the left side by subtracting 2x from both sides of the equation:
3x + 6 - 2x = 2x + 3 - 2x
Simplify
On the left side, the term 2x cancels out with the 2x on the right side, leaving us with:
x + 6 = 3
Move Constants to the Other Side
To isolate 'x', we need to get rid of the constant term on the left side.
Subtracting 6 from both sides of the equation:
x + 6 - 6 = 3 - 6
Simplify
On the left side, the +6 and -6 cancel out, leaving us with:
x = -3
Final Solution
After simplifying, find that the value of 'x' that satisfies the original equation is x = -3.
This means that if we replace 'x' with -3 in the equation, it will hold true:
3(-3 + 2) = 2(-3) + 3
-3 = -6 + 3
-3 = -3
And that's why the solution to the equation is x = -3.
Therefore, the reason required for solving the equation are distributive property and simplification which gives solution is x = -3
learn more about simplification here
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11. Given a polynomial P(x) = x³-4x²-5x is one of the zeroes.
a) Factorise P(x) completely
b) Sketch the graph of P(x)
C)Find the domain and range.
Answer:
thats some tuff
Step-by-step explanation:
Answer:
Step-by-step explanation:
P(x)=x³-4x²-5x=x(x²-4x-5)
=x(x²-5x+x-5)
=x[x(x-5)+1(x-5)]
=x(x-5)(x+1)
domain (-∞,∞)
range: (-∞,∞)
Which expression is equivalent to fourteen more than the product of three and nine
Answer:
Step-by-step explanation:
The product of 3 and 9 just means to multiply 3 and 9. This is written as:
3 x 9
14 more than this just means to add 14 to the above.
3 x 9 + 14
(45 points!)
Line n contains points (3, 4) and (-6, -2). What is the slope of a line perpendicular to the given line?
Answer: -3/2
Step-by-step explanation:
Answer:
y=nx−2+6n
Step-by-step explanation:
I have used the slope-intercept form to find the answer.
Hope this helps :)
why? just why. why are we here? should i off myself? should i stay?
Answer:
It can be a passing thought or a question that launches a full-on existential exploration. Having a sense of meaning and purpose in life is usually a positive motivator, at home and at work. But maybe the questioning itself is where life's true mission is found...
Step-by-step explanation:
Becky and claire went trick or treating.At the end of the night ,they combined their candy and found they each had four large candy bars.Becky ate two candy bars and clair ate one
Answer:
Well, You possibly did all the math depending on the question. But if it was subtraction that means there's one candy bar left
step-by-step explanation:
I hope this helped in any way!
What is the sum of the fractions? Use the number line to help find the answer.
3/5 plus -7/5
Answer:
-4/5
Step-by-step explanation:
Answer:
The answer is -4/5
Step-by-step explanation:
Hope this helps!:)
which figure has 6 lines of symmetry draw is needed
Answer:
C
Step-by-step explanation:
i believe it C.
no matter which point to point of line you go,
it will always be a six line symmetry.
9514 1404 393
Answer:
C
Step-by-step explanation:
Figure C has 6 lines of symmetry as shown in the attachment.
15.9687194227 rounded to the nearest tenth
Answer:
i think its 16
Step-by-step explanation:
Answer:
16.0
Step-by-step explanation:
Nearest tenth place value is the digit directly to the right of the decimal point. Locate the tenth place value. It will be underlined and bolded:
15.968194227
Look at the number directly right of the given term. Note that:
If the digit is 5 or greater, round up.
If the digit is 4 or less, round down.
Since the digit is 6, round up.
15.968194227 rounded to the nearest tenth is 16.0
~
Come One Come All!!!!!
Answer: 1. is A, 2. is C, i dont know 3. 4. is B i think. then 5. is probably option 2
Step-by-step explanation:
Can someone help me with this question for geometry.
Thanks will mark brainliest
Answer:
none of the above ,,,,,,,
The manager of an apartment building increases the monthly
rent of each apartment in the building by 3% each year. At
the beginning of year 1, the monthly rent of an apartment
was $500.
What was the monthly rent of the apartment at the
beginning of year 3?
Answer:
The answer is 513
Answer:545
Step-by-step explanation:
Karen flies her Cessna Skyhawk aircraft 360 miles with a tailwind of 10 miles per hour in the same time it could fly 300 miles with a headwind of 10 miles per hour. Find the speed of the aircraft.
Answer:
The speed of the aircraft is 126.667 miles per hour.
Step-by-step explanation:
Let suppose that aircraft travels at constant speed. From Mechanical Physics, we understand speed as travelled distance divided by time. In this case, the absolute speed of the aircraft is the sum of wind speed and speed of the aircraft relative to wind. That is:
Tailwind (Wind flows in the same direction of aircraft)
[tex]t = \frac{s_{T}}{v_{W,T}+v_{A/W,T}}[/tex] (Eq. 1)
Headwind (Wind flow in the direction opposite to aircraft)
[tex]t = \frac{s_{H}}{v_{W,H}+v_{A/W,H}}[/tex] (Eq. 2)
Where:
[tex]s_{T}[/tex], [tex]s_{H}[/tex] - Travelled distances on tailwind and headwind conditions, measured in meters.
[tex]v_{W,T}[/tex], [tex]v_{W,H}[/tex] - Tailwind and headwind speeds, measured in meters per second.
[tex]v_{A/W,T}[/tex], [tex]v_{A/W,H}[/tex] - Relative speeds of aircraft relative to tailwind and headwind, measured in meters per second.
We proceed to equalize both expressions to eliminate time:
[tex]\frac{s_{T}}{v_{W,T}+v_{A/W,T}} = \frac{s_{H}}{v_{W,H}+v_{A/W,H}}[/tex] (Eq. 3)
If we know that [tex]s_{T} = 360\,mi[/tex], [tex]s_{H} = 300\,mi[/tex], [tex]v_{W,T} = 10\,\frac{mi}{h}[/tex], [tex]v_{W,H} = -10\,\frac{mi}{h}[/tex] and [tex]v_{A/W,T} = v_{A/W,H}[/tex], then:
[tex]\frac{360}{v+10} = \frac{300}{v-10}[/tex]
The relative speed of the aircraft is now cleared:
[tex]360\cdot (v-10)=300\cdot (v+10)[/tex]
[tex]360\cdot v-3600 = 300\cdot v +3000[/tex]
[tex]60\cdot v = 7600[/tex]
[tex]v = 126.667\,\frac{mi}{h}[/tex]
The speed of the aircraft is 126.667 miles per hour.
Graph the line with slope – 7 and y-intercept 6.
Answer:
(✿◠‿◠)
I put the link in the comments!
A graph of the line with a slope of -7 and y-intercept of 6 is shown in the image below.
What is the slope-intercept form?In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;
y = mx + b
Where:
m is the slope or rate of change.x and y are the points.b is the y-intercept or initial value.Based on the information provided about this line, the y-intercept is 6 and the slope is -7.
In this context, we can logically deduce that a linear equation that models the line is given by;
y = mx + b
y = -7x + 6
Read more on slope-intercept here: brainly.com/question/7889446
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Find the value(s) of "k" that will cause the equation 4x^2 +kx + 4 to have one real solution.
Answer: k = {8, -8}
Step-by-step explanation:
In order for a quadratic equation to have exactly one solution, the discriminant must equal zero. → b² - 4ac = 0
4x² + kx + 4 = 0
↓ ↓ ↓
a=4 b=k c=4
b² - 4ac = 0
k² - 4(4)(4) = 0
k² = 64
k = √64
k = ± 8
2/7 divided by 8/9. HURRY
Answer:
9/28 in fraction , 0.3214285714 in decimal
Step-by-step explanation:
0.32142857142 in decimal form
Solve the following quadratic equation by factorising: 15x^2 + 2x - 8 = 0
BRAINLIEST WILL BE AWARDED!!!!!!!!!!!!!!!!!
Answer:
1. = 5
2. = -7
3. = -4
The stem-and-leaf plot shows the test scores of a science class. Use the plot to answer the question.
How many students scored 78?
Answer:
4 students
Step-by-step explanation:
Understanding stem-and-leaf plots
A stem and leaf plot is designed in a way to group the numbers by their values before the ones place;
i.e. 92, 100, 101, 103, 113
Charted as
9 | 2
10 | 0 1 3
11 | 3
So, with that in mind we know 78 is grouped under the 7 | # # #
stem and has the leaf of 8 which is displayed by # | # # # 8
SO,
TO SOLVE:
Count the 8's under the 7 | # # # # group
We can see that there are 4 8's under that section, and assuming that each number is representative of one students score, we can conclude that 4 students scored 78
Hope this helps,
J.M."Jamon"
Pennsylvania State University
Full-Time B.S.CE. Undergrad
Answer:
4 Students
Step-by-step explanation:
If you look at the four and cout how many 8 are across you will get 4!
To determine whether or not they have a certain desease, 304 people are to have their blood tested. However, rather than testing each individual separately, it has been decided first to group the people in groups of 19. The blood samples of the 19 people in each group will be pooled and analyzed together. If the test is negative, one test will suffice for the 19 people (we are assuming that the pooled test will be positive if and only if at least one person in the pool has the desease); whereas, if the test is positive each of the 19 people will also be individually tested and, in all, 20 tests will be made on this group. Assume the probability that a person has the desease is 0.04 for all people, independently of each other, and compute the expected number of tests necessary for the entire group of 304 people.
Answer:
The expected number of tests necessary for the entire group of 304 people is 180.0325
Step-by-step explanation:
Probability of person being positive = p = 0.04
Probability of person being negative = q = 1-0.04=0.96
Number of people in each group = 19
We will use binomial over here
Probability of no test positive :
[tex]P(x=0) = ^{19}C_0 (0.04)^0 (0.96)^{19} =0.460419201958[/tex]
P( at least one tests positive) = 1-P( no one tests positive)= 1-0.460419201958= 0.539580798042
Expected number of tests for each group = 1(0.460419201958)+20(0.539580798042) = 11.2520351628
Number of groups =[tex]\frac{\text{Total population}}{\text{no. of people in each group}}=\frac{304}{19}=16[/tex]
Expected number of tests necessary for the entire group of 304 people:
=[tex]\text{Expected number of tests for each group} \times \text{No. of groups}[/tex]
=[tex]11.2520351628 \times 16[/tex]
=180.0325
Hence The expected number of tests necessary for the entire group of 304 people is 180.0325
Rewrite the following expression: x3 + x5 =
Answer:
x + 8 = x8
Step-by-step explanation:
This is one of the many ways to rewrite this equation. The reason this is a way of rewriting it is because 3x plus 5x equals 8x and if you take away the variable from 3 and 5 and add the numbers together you get 8. So take the variable x add it to 8 and you get x8. Both equations have the same answer so therefor this is another way of writing the equation.
If James bought 5/12 of cherries and 1/3 of cranberries. How much fruit did he buy. Write your answer in simplest form.
Answer:
The correct result would be 3/4 of a pound of dried fruit.
Plz help ty very much
Answer:
A fungus breaks down the body of a dead animal or organism.
btw you cant be in college I did this years ago in fourth grade
A fungus breaks down the of a dead animal
divide 8/10 ÷ 1 5/6 and put it in its simplest form
Answer
24/55 as a fraction
The solution of the given equation is 24/55
What is Division method?
Division method is used to distributing a group of things into equal parts.
Given that;
The equation is,
8/10 ÷ 1 5/6
Now,
Solve the expression as;
= 8/10 ÷ 1 5/6
= 8/10 ÷ 11/6
= 8/10 x 6/11
= 48/110
= 24/55
So, The solution of the given equation is 24/55.
Learn more about the division visit:
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The circle graph shows how the money will be spent for the party.
Food: 30%
Drinks: 20%
Prizes and favors: 35%
Paper productions: 15%
The class has $300 for a party.
How much will be spent on party favors and prizes?
A: $35.00
B: $105.00
C: $195.00
D: $265.00
Answer:
B. $105.00
Hope this helps!
Please help me with these 2 questions :(
Answer:
1st: y=-2x-3
2nd:y=-2x-13
Step-by-step explanation:
Since the line is parallel to y = -2x-4, its slope is -2. Therefore, we have the equation y=-2x
But when we evaluate that equation at -1, we get -2(-1)=2, but we want to make it equal to -1 when evaluated at -1. Therefore, we can subtract 3, as 2-3=-1.
Therefore, the equation is y=-2x-3.
For the second question, we can use a similar concept. The slope will be -2, but if you directly evaluate it at -4, it's going to be 8, but we want it to be -5, so we subtract 13.
Therefore, the equation is y=-2x-13
Problem 1
Answer: y = -2x-3--------------
Explanation:
Parallel lines have equal slopes but different y intercepts.
Linear equations in the form y = mx+b have slope m and y intercept b.
The slope of y = -2x-4 is m = -2
So any parallel line to this will also have m = -2
Plug (x,y) = (-1,-1) along with the value of m, into y = mx+b and solve for b
y = mx+b
-1 = -2(-1)+b
-1 = 2+b
2+b = -1
b = -1-2
b = -3
The parallel line is y = -2x-3
==============================================
Problem 2
Answer: y = -2x-13--------------
Explanation:
We'll use the same ideas and steps as problem 1.
y = -2x-5 has slope m = -2
The parallel line also has slope m = -2
We want the parallel line to go through (x,y) = (-4,-5)
So,
y = mx+b
-5 = -2(-4)+b
-5 = 8+b
8+b = -5
b = -5-8
b = -13
The parallel line is y = -2x-13
MLN=QPR. What is the measure of <1 and <2?
Answer:
B. <1 = 90, <2 = 40
Step-by-step explanation:
Given that ∆MLN = ∆QPR, it follows that the measure of their corresponding angles would be of the same measure.
<P = right angle = 90°
<1 corresponds to <P, therefore, <1 = 90°
<R = 40°
<2 corresponds to <R, therefore, <2 = 40°.
The answer would be: B. <1 = 90, <2 = 40
You have wanted a car you entire life (literally since you were born)!! It is time...you found the car of you dreams AND the car is marked as 80% of!!!! What a deal!!! "What could go wrong" you ask yourself. You buy the car for $625 (and the man in the hood walks off smiling). As your parent(s) drive you home after picking you up next to your broken down vehicle 3 hours later, they ask you what the original price of the car was before the price reduction. What was the original price of your.... "dream car"?
Answer:
200,000
Step-by-step explanation:
Round 1,439 to the nearest ten
Answer:
1,440.
Step-by-step explanation:
39 is closer to 40.
1,400 is unchanged.
Dionne Washington wants to sell natural fruit flavored water at her neighborhood block party. She wrote the amount of money she spent as a function of the number of bottles sold. Which set of numbers would be an appropriate domain for Dionne's function?
Complete question is;
Dionne Washington wants to sell natural fruit flavored water at her neighborhood block party. She wrote the amount of money she spent as a function of the number of bottles sold. Which set of numbers would be an appropriate domain for Dionne’s function?
A) 0, 1, 2, 3, 4, …
B) …, −4, −3, −2, −1, 0
C) …, −3, −2, −1, 0, 1, 2, 3, …
D) …, −3.5, −2.5, −1.5, 0, 1.5, 2.5, 3.5, …
Answer:
Option A: {0,1, 2, 3, 4,....}
Step-by-step explanation:
Domain is simply a set of input while the range is a set of output values.
For example, if we have a function named f(x) = x², the domain will be all possible values of x being inputed while the range will be the value of f(x) for all possible values of x inputed.
Now, from the question, we are told that she wrote the amount of money she spent as a function of the number of bottles sold.
If the number of bottles sold is denoted by "x", it means the function is; f(x).
Now, number of bottles has to be a non-negative whole number or simply a non-negative integer. Thus, the possible values of x are all non-negative whole numbers like, 0,1, 2, 3, 4, 5....
Thus,domain is {0,1, 2, 3, 4,....}
Answer:
A. 0,1,2,3,4,.....
Step-by-step explanation:
Can someone please help?