Answer:
x = 6
Step-by-step explanation:
x:(x + 3) = 2:3
[tex] \frac{ \\ x}{x + 3} = \frac{2}{3} [/tex]
cross multiply
3x = 2(x + 3)
3x = 2x + 6
subtract (2x) from both sides
3x – 2x = 2x – 2x + 6
x = +6
x = 6
Which area model represents the factorization x2+3x+2=(x+2)(x+1)?
The factorization of the polynomial x² + 3x + 2 gives (x + 1)(x + 2)
What is an equation?An equation is an expression that shows how numbers and variables relate with each other.
A polynomial is an expression consisting of variables and their exponents with operations of addition and subtraction. Polynomials are classified based on degree as linear, quadratic and cubic.
The standard form of a quadratic equation is:
y = ax² + bx + c
where a, b and c are constants.
Given the polynomial:
x² + 3x + 2
Factorizing the polynomial:
x² + 2x + x + 2
= x(x + 2) + 1(x + 2)
= (x + 1)(x + 2)
The factorization gives (x + 1)(x + 2)
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Solve for x : 4x-6=x+9
4x - 6 = x + 9
4x - x = 9 + 6
3x = 15
[tex]x = \frac{15}{3} \\ [/tex]
x = 5 ...
Answer:
[tex]x =5[/tex]
Step-by-step explanation:
[tex]4x - 6=x+9[/tex]
Subtract x from both sides
[tex]4x -6-x=x+9-x[/tex]
[tex]3x-6=9[/tex]
Add 6 to both sides
[tex]3x-6+6=9+6[/tex]
[tex]3x=15[/tex]
Divide both sides by 3
[tex]\frac{3x}{3} = \frac{15}{3}[/tex]
[tex]x = 5[/tex]
Zoe i aving up to buy a new bicycle. She already ha $80 and can ave an additional $6 per week uing money from her after chool job. How much total money would Zoe have after 6 week of aving? Alo, write an expreion that repreent the amount of money Zoe would have aved in ww week
If Zoe already has $80 and can save an additional $6 per week using money from her after school job then the total amount of money that Zoe saved after 6 week of saving is $116 and
the expression that represent amount of money Zoe would have saved in w weeks is [tex]80+6w[/tex] .
The amount that Zoe already saved = $80 ;
the amount that she can additionally save is = $6 per week ,
the amount of money that can be saved after 6 weeks can be written as :
[tex]Amount = \$80+(Amount Saved Per Week)\times(Number Of Weeks)[/tex]
Amount = [tex]80+6\times6[/tex]
= [tex]80+36[/tex]
= $116
and the expression for w weeks will be = [tex]80+6\times w[/tex]
The expression is ⇒ [tex]Amount = 80+6w[/tex].
The given question is incomplete , the complete question is
Zoe is saving up to buy a new bicycle. She already has $80 and can save an additional $6 per week using money from her after school job. How much total money would Zoe have after 6 week of saving ?
Also, write an expression that represent the amount of money Zoe would have saved in w weeks ?
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Write the explicit formula for the sequence below:
The explicit formula for the sequence -28, -31, -34, -37, ..., is aₙ= -28 -3d.
What is an arithmetic sequence?A series of integers called an arithmetic progression or arithmetic sequence (AP) has a constant difference between the terms.
Given:
-28, -31, -34, -37, ...
The general formula of an arithmetic sequence:
aₙ= a₁ + (n)d,
where a₁ is the first term and d is the common difference.
First, we will find the common difference between consecutive terms.
Here,
a₁ = -28
To find the common difference:
a₂ - a₁ = -31 + 28 = -3
a₃ - a₂ = -34 + 31 = 3
a₄ - a₃ = -37 + 34 = 3
Hence, d = -3.
Substitute the values to the formula,
aₙ= a₁ + (n)d,
aₙ= -28 + (-3)d,
aₙ= -28 -3d
Therefore, aₙ= -28 -3d is the required sequence.
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Write a rule for g that represents the indicated transformations of the graph of f.
f(x)=x³-6; translation 3 units left, followed by a reflection in the y-axis.
The function obtained after transformation is given as -x³ + 9x²- 27x + 21.
How to transform a graph of the function?The graph of a function can be transformed by either shifting it in the right, left, up or down.
When the transformation is rightwards, the function becomes as f(x - a).
For left shifting it is f(x + a).
The function is given as f(x) = x³- 6.
The translation of 3 units towards left can be written as,
f(x + 3) = (x + 3)³ - 6
⇒ x³ + 9x² + 27x + 21
For reflection across y axis replace -x with x as below,
⇒ (-x)³ + 9(-x)² + 27 × -x + 21
⇒ -x³ + 9x²- 27x + 21
Hence, the required form of the transformed function is -x³ + 9x²- 27x + 21.
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Solve equations - two sides
(135a)
Solve
2x - 7=7x +5
Answer:
x=-12/5
Step-by-step explanation:
2x-7=7x+5
2x-7x=5-(-7)
-5x=5+7
x=12/-5
x=-12/5
A newsletter publisher believes that more than 47% of their readers own a personal computer. Is there sufficient evidence at the 0.05 level to substantiate the publisher's claim?
There is no sufficient evidence at the 0.05 level to substantiate the publisher's claim
How to determine the substantial claim?The parameters for the claim is more than 47% of their readers own a personal computer0.05 level of significanceNote that the significance level, also known as alpha or α, is a measure of the strength of the evidence that must be present in your sample before you will reject the null hypothesis and conclude that the effect is statistically significant
In conclusion, the advertiser failed to reject the null hypotenuse so this would mean there is not sufficient evidence at the 0.02 level of significance to say that the percentage of people who own a Rolls Royce is higher than 47%
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What are the Miller indices for the plane shown in the following cubic unit cell and Explain why? O (201) O (10 1/2) O (1 infinity 1/2) O (102)
The plane intercepts on the x,y, z axes are 1, ∞, and 1/2. Hence, the Miller indices for the plane inside the cubic unit cell is (102).
Miller indices are used to specify planes and directions. These planes and directions could be in lattices or crystals. The number of indices will correspond to the size of the lattice or crystal.
Steps to find the Miller indices:Determine intercepts of the planes with the x, y, and z axes.Use fractional coordinates to specify intercepts.Take the reciprocals of the fractional interceptsIn the given graph, the plane intercepts are:
x-intercept : 1
y-intercept : ∞ (since the planes does not intercept y-axes)
z-intercept = 1/2
Take the reciprocal:
1/1 = 1
1/∞ = 0
1/(1/2) = 2
Hence, the miller indices are (102)
The graph in your question is missing. Most likely it was like on the attached picture.
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What equation represents a linier function that is proportional
Answer:
d
Step-by-step explanation:
A bookstore owner has 15 different books to arrange on the shelves in a display case. Each shelf can display 3 books.In how many different ways can the owner arrange 3 books on the top shelf of the display case
There are 15 different books and 3 each can be arranged on a shelf i.e., there are 15/3 i.e., 5 shelves to arrange the book in the the display case.
How many different ways can you arrange3 books on a shelf?different bundles of novels, and we have to put this bundle and other 3 books onto the shelf. So the total number of ways is 3! × (3 + 1)! = 144.How many ways can you arrange 3 books on a shelf from a group of 7?= 5040 arrangements. Three books that we want together have 3!Therefore, the number of ways in which the 3 letters can be arranged, taken all a time, is 3! = 3*2*1 = 6 ways.A trilogy is a set of three distinct works that are connected and can be seen either as a single work or as three individual works. They are commonly found in literature, film, and video games.When using three shelves, place the middle shelf higher or lower than the one on either side. Five shelves can be staggered with two or three higher than the others, alternating every other shelf for a horizontal groupingTo learn more about arrange3 books on a shelf refers to:
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50 POINTS!!!! urgent!!!!!!
Mary is collecting cup cakes for the school fair. She will make 12 cupcakes to start it off. She plans to collect 24 cupcakes each
day from her surrounding neighborhood for the next 3 days. If you model this word problem for Mary as y=mx+b then match the
corrects pairs.
a. 12
b. 84
c. 3
d. 24
1. m
2. y
3. x
4. b
Since the problem is about linear equation in the form of y = mx + b, initial number represents the value of b = 12, the number of days represents the value of x = 3, the daily collection of cupcakes represent the slope m = 24, then the value of y is:
y = 24*3 + 12 = 72 + 12 = 84So the matching pairs are:
a ⇔ 4, b ⇔ 2,c ⇔ 3,d ⇔ 1 .In ΔXYZ, x = 5. 2 inches, y = 9. 8 inches and z=7. 1 inches. Find the measure of ∠Z to the nearest degree
The measure of ∠Z is 165 degrees to the nearest degree.
In a triangle, the measure of each angle is equal to the sum of the measures of the other two angles subtracted from 180 degrees. This is known as the Triangle Sum Theorem.
Given that x = 5.2 inches, y = 9.8 inches, and z = 7.1 inches in triangle XYZ, we can use the theorem to find the measure of angle Z.
∠Z = 180 - (x+y)
∠Z = 180 - (5.2+9.8)
∠Z = 180 - 15
∠Z = 165
So the measure of ∠Z is 165 degrees to the nearest degree.
Therefore, The measure of ∠Z is 165 degrees to the nearest degree.
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WASTE Suppose the waste generated by nonrecycled paper and cardboard products in tons y after x days can be approximated by the function y=1000(2)0.3x.
a. Identify key features.
y-intercept: , 1 of 8.
domain: , 2 of 8.
range: , 3 of 8.
b. Identify the relevant domain and range.
Because time , 4 of 8. , the relevant domain is , 5 of 8. .
Because the amount of recycled paper and cardboard , 6 of 8. , and the amount when x=0
is , 7 of 8.tons, the relevant range is , 8 of 8. .
a. The key features of the exponential function y = 1000(2)^(0.3x) is given as follows:
y-intercept: y = 100.Domain: all real values.Range: y ≥ 1000.b. The relevant domain and range are given as follows:
Domain: x ≥ 0.Range: y ≥ 1000.What are the features of the exponential function?The exponential function for this problem is modeled as follows:
y = 1000(2)^(0.3x).
The features are given as follows:
Initial value, when x = 0, of y = 1000, representing the y-intercept.Rate of change of 2 for each period of 0.3 units.The domain of the function is the set that composes all input values of the function, and as the exponential function does not have any restrictions such as a fraction or an even root, it is composed by all real values.
However, the relevant domain is x ≥ 0, as the number of days does not assume negative values.
The range is the set containing all output values of the exponential function. As the initial value of the exponential function is of 1000 and the function is increasing, the range is y ≥ 1000.
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What is BPT Theoram please solve
In a triangle, a line is drawn parallel to one side of the triangle. Then it ratio of the two similar triangles will be con
What is the Basic Proportionality theorem?The Basic Proportionality Theorem, often known as the Thales Theorem, was developed by the eminent Greek mathematician Thales. He asserted that the ratio of any two matching sides is constant for any two equiangular triangles. He developed the basic proportionality theorem based on this idea (BPT). Similar triangles have presented this idea. When two triangles resemble one another.
Think about the triangle ΔABC in the given illustration. A line PQ connecting the sides AB and AC of P and Q in this triangle is drawn parallel to the side BC of the triangle.
AP/PB = AQ/QC
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What coins would I need to make 77 cents fewest possible
Answer:
Step-by-step explanation: Two quarters, 50 pennies: N = 52 (N+1 = 53) One quarter, 75 pennies: N = 76 (N+1 = 77) 100 pennies, N = 100 (N+1 = 101) 6 nickels, 70 pennies: N = 76 (N+1 = 77)
Answer:
2 quarters, 2 dime's, 1 Nickel, 2 penny's
Step-by-step explanation:
Well u well need to quarters because 2 quarters are $25 cent then u well need 2 dimes because when your counting dime's that 10 20 30 40 50 so to dime's and 1 Nickel that makes $75 cents so u need 2 penny's and that makes 77
How to determine if a triangle is right acute or obtuse based on side lengths calculator?
A triangle is said to be acute if the sum of the squares of its two shorter sides is greater than the square of its longest side.
How do you know if its right obtuse or acute?Less than 90 degree angles are considered acute. Right angles have a 90 degree angle. Angles that are obtuse exceed 90 degrees.
See samples of various angles and learn about them. If and only if side lengths a, b, and c satisfy a2 + b = c2, a right triangle will be formed. These numbers are referred to as a Pythagorean triple. When the square of a triangle's longest side equals the sum of the squares of its other two sides, the triangle is said to be a right triangle. So, in the ABC equation, if c2=a2+b2, then C is a right triangle, with PQR serving as the right angle.
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factor the trinomial 2xsquared + 5x -42
Basic quadratic expression:
[tex]ax^2+bx+c[/tex]
[tex]2x^2+5x-42[/tex]
Factoring a quadratic expression when a ≠ 0
1. Multiply a and c values (ac=k)
[tex]2(-42) = -84[/tex]
2. Find a factor pair whose sum adds to b and has the product of k
[tex]-7,12[/tex]
[tex]-7(12)=-84[/tex] [tex]-7+12=+5[/tex]
3. Replace the middle term (bx) with newfound values
[tex]2x^2 +12x-7x-42[/tex]
4. Factor by grouping
[tex]2x(x+6) -7(x+6)[/tex]
if done correctly the expression in the parentheses will be the same5. Perform the last factorization
[tex](2x-7)(x+6)[/tex]
you can verify your answer by expanding the factors to get the same expression in the beginningThe data below shows the orders that were placed at a local paint shop. 1 2 3 4 Paint orders 5 6 Gallons 7 8 9 10 Solve for the MEAN of this data set. If needed, round to the nearest tenth.
To find the MEAN of Natural numbers, such as 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10, a + b + c3 is the sum of the three numbers a, b, and c. Therefore, 5.5 is the MEAN of the first 10 natural numbers.
Find the MEAN Of Data setFirstly The Given set of numbers Represents Natural numbers,
A natural number is an integer greater than 0. Natural numbers begin at 1 and increment to infinity: 1, 2, 3, 4, 5, etc.
Therefore, the first ten natural numbers are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.
And the mean of three numbers a, b, c is a + b + c3
Then the mean of 10 numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 is:-
⇒1+2+3+4+5+6+7+8+9+1010
Adding and dividing we get the value of the above term as,
⇒1+2+3+4+5+6+7+8+9+1010=5510=5.5
Hence, the mean of the first 10 natural numbers is 5.5.
Note: To solve this problem, you must understand that the integers greater than zero are natural numbers and that the mean of the three numbers a, b, and c equals a + b + c3. Knowing how to calculate the average number of elements and being familiar with natural numbers can help you arrive at the correct conclusion.
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√
18
−
√
2 simplify far as possible
Answer:
2[tex]\sqrt{2}[/tex]
Step-by-step explanation:
[tex]\sqrt{2x9}[/tex] - [tex]\sqrt{2}[/tex] = 3[tex]\sqrt{2}[/tex] - [tex]\sqrt{2}[/tex] = 2[tex]\sqrt{2}[/tex]
in is 26 miles into a 62-mile backpacking trip in the wilderness. Jin ca
ike 6 miles per day. How many more days does Jin need to finish?
Jin needs how many
more days.
Answer:6 days
Step-by-step explanation:
62-26=36
36/6=
6
Which of the following is the graph of y=-4 square root x
In the second graph, these points are located. As a result, the second graph is the function's correct graph.
what is function ?In mathematics, the term "linear function" refers to two different but related ideas. In calculus and related fields, a quadratic variable of grade 0 or 1 is a linear function if its graph is a direct line. A straight line on a reference system is a representation of a linear function. For instance, the linear function y = 3x - 2 is a straight line just on coordinate plane, hence it is a linear function. Since f(x) may be connected to y, the function can be represented by f(x) = 3x - 2.
given
The function provided is
This function is defined for any x values that are positive, including 0.
The radical expression x has a constant positive value. Given that is a function, it is always negative.
At x=0, = 0
At x=1, = -4
At x=4, = -8
This indicates that the graph of the specified function traveling through the points (0,0), (1,-4) and (4,-8).
In the second graph, these points are located. As a result, the second graph is the function's correct graph.
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Please help if you can or and know how to do this pls! Can
Answer:
m<1=50
m<2=130
m<3=50
m<4=130
m<5=40
m<6=40
m<7=90
m<8=140
Step-by-step explanation:
Karl invests $100 in a savings account, which earns interest yearly.
Select the TWO changes that would earn Karl more money from this savings account.
The two changes that would Karl earn more money are "Karl increases his initial investment" and "Karl deposits more money into the account every year" (options B and D).
What factors affect the amount of money Karl can get?In this case, the amount of money Karl can get depends on both the amount of money he invest and the interest rate. Here are some examples:
If he invest $100 and the interest rate is 10% he will get $10
If the invest $1000 and the interst rate is the same (10%) he will get $1000
Moreover, if the interste rate increases he can get more money: If the invest $100 but the interst rate is 12% he gets $12
This means he can get more profit if the investment is higher or the rate increases. Based on this, the two options that would increase his amount of money are increasing the initial investment or depositing more money (option B and D).
Note: This question is incomplete; here is the missing section:
A. The bank decreases the interest rate.
B. Karl increases his initial investment.
C. The bank adds a fee to keep the account active.
D. Karl deposits more money into the account every year.
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3x-3y=-6
3x+y=10 use subtraction please help thank you
need an ordered pair
Answer:
x=2, y=4. (2, 4).
Step-by-step explanation:
3x-3y=-6 implies 3(x-y)=3(-2), so x-y=-2.
-----------------------------
x-y=-2
3x+y=10
---------------
4x=8
x=8/4=2
2-y=-2
y=2-(-2)=2+2=4
How do you find the dilation of a function?
Finding the dilation's center point is the first step in determining the scale factor. Next, we measure the distances between the center point and various points on the preimage and the image. The scale factor is equal to the ratio of these distances.
Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is a picture with the same shape as the original. However, there is a variation in the shape's size.
A graph's form is altered by dilations, frequently leading to "movement" in the process. In the figure above, the green curve has been "transformed" into the red curve. It has been three times "dilated" (or stretched) horizontally. A dilatation is an axial stretching or contraction brought on by multiplication or division.
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Stefan sells Jin a bicycle for $146 and a helmet for $19. The total cost for Jin is 150% of what Stefan spent originally to buy the bike and helmet. How much did Stefan spend originally? How much money did he make by selling the bicycle and helmet to Jin?
Stefan spend price $110 and made price $60 by selling bicycle and helmet to Jin.
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100.
Here, given that,
Selling price of bicycle = $146
Selling price of helmet = $19
Total = 146+19= $165
Let,
x represents the original cost Stefan to buy the bike and helmet.
150% of x = $165
1.5x=$165
Dividing both sides by 1.5
we get ,
x=$110
Stefan bought bicycle and helmet for $110.
Profit made by Stefan = Selling price - buying price
Profit made by Stefan = 165-110= 55
Hence, Stefan spend price $110 and, made $55 by selling bicycle and helmet to Jin.
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A jacket normally sells for $27.50.it is on sale for 20%what is the new price
Answer:
$22
Step-by-step explanation:
27.50 20 present off so you get 5.5 substract and u get 22
Each shape is 1 whole. For numbers 13a–13e, choose Yes or No to show whether the number names the parts that are shaded
In each shape there are 4 wholes hence the answer is yes.
What are fractions?A fraction is referred to as the portion of a whole in mathematics. There are two components to a fraction: a numerator and a denominator. The numerator is the number at the top, and the denominator is the number at the bottom.
13a. There are 4 wholes, hence the answer is yes.
13b. Every whole is divided into 2 parts hence the total number of equal parts is 4 *2 = 8. Hence the answer is yes.
13c. The answer is yes.
13d. No
13e. No
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Find the explicit formula for an arithmetic sequence with a common difference of 8 and whose first term is -2.
The explicit formula of the sequence is aₙ = -10 + 8n
How to determine the explicit formula of the sequence?From the question, we have the following sequence that can be used in our computation:
The first term and the common difference
These values of the first term and the common difference are given as
First term = -2
Common difference = 8
The interpretation of the above sequence is that the 8 is added to the previous term to get the current term
Using the above as a guide,
So, we have the following representation
aₙ = aₙ₋₁ + 8
When represented explicitly, we have
aₙ = a + (n - 1) * d
Where
a = -2 and d = 8
Substitute the known values in the above equation, so, we have the following representation
aₙ = -2 + (n - 1) * 8
Evaluate the products
aₙ = -2 + 8n - 8
Evaluate the like terms
aₙ = -10 + 8n
Hence, the explicit formula is aₙ = -10 + 8n
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What is the equation of the Y axis?
Answer:
x=0
Step-by-step explanation:
The general form of the equation of y-axis is x = 0. hence, the equation of line parallel to the y-axis is given by the equation: x = k.