The simplified expression of the given equation is [tex]\frac{x^{2} + 4x + 6}{3x + 12}[/tex]
There are three basic steps for addition or subtraction of two fractions
Step 1: Make sure the bottom numbers (the denominators) are the sameStep 2: Add the top numbers (the numerators), put that answer over the denominatorStep 3: Simplify the fraction (if possible)The given expression :- [tex]\frac{x+6}{x+4} +\frac{x-3}{3}[/tex]
Taking LCM or making the denominators same we get,
= {3(x+6) + (x-3)(x+4)}/3(x+4)
= {3x + 18 + x² +x -12}/3(x+4)
={x² + 4x + 6}/3x + 12
= [tex]\frac{x^{2} + 4x + 6}{3x + 12}[/tex]
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Answer:
i believe its B
Step-by-step explanation:
Which of these is NOT an arithmetic sequence?
A.3, 9, 15, 21, 27, ...
B.-3, -9, -15, -21, -27,...
C.27, 21, 15, 9, 3, ...
D.3, 9, 27, 81, 243, ...
Answer:
D
Step-by-step explanation:
Sequence A is increasing using + 6
Sequence B is decreasing using - 6
Sequence C is decreasing using - 6
Sequence D is increasing using x 3
D is the odd one out
The exchange rate in some prehistoric village was 6 jagged rocks for every 2 smooth pebbles. Also, one shiny rock could be traded for 3 smooth pebbles. If Joaquin has 30 jagged rocks, what is the maximum number of shiny rocks he could trade for?
A. 6
B. 4
C. 5
D. 3
30 Jagged rocks are the same 3 shiny rocks using the exchange rates provided(i.e. option D)
What is an exchange rate?
Exchange rate means the rate at which one item exchanges hands with another, for instance, in this case, 6 jagged rocks are equivalent to 2 smooth pebbles.
6 jagged rocks=2 smooth pebbles
divide both sides by 2
6/2 jagged rocks=2/2 smooth pebbles
3 jagged rocks=1 smooth pebble
We can rewrite as below:
1 jagged rock=1/3 smooth pebble
30jagged rocks=1/3*30 smooth pebbles
30 jagged rocks=10 smooth pebbles
Now we need to convert 10 smooth pebbles to shiny rock equivalence
3 smooth pebbles=1 shiny rock
1 smooth pebble=1/3 shiny rock
10 smooth pebbles=1/3*10 shiny rocks
10 smooth pebbles=3 shiny rocks( even though it is 3.33, but the final answer should be rounded to a whole number)
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Maths Trigonometry Question
40 Points!
Will give brainliest to whoever answers
The calculation of the trigonometry illustrates that:
sin 45° = 1/✓2
cos45/tan 45 =
cos 45 sin 45 = 1/2
How to illustrate the trigonometry?Opposite = 1
Adjacent = 1
Hypothenuse = ✓2
Tan 45 = opposite/adjacent = 1
Sin 45 = opposite/hypothenuse = 1/✓2
Cos 45 = adjacent/hypothenuse = 1/✓2
cos45/tan 45 = (1/✓2) / 1 = 1/✓2
Cos 45 sin 45 = 1/✓2 × 1/✓2 = 1/2
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a store marks up the wholesale price of a skateboard by 112%. The retail price is $35. What is the wholesale price of the skateboard?
Write the slope-intercept form of the line that has a slope of 2 and intersects the line, 2x - 3y = 6 at x = 3. Include
your work in your final answer. Type your answer in the box provided to submit your solution.
Answer:
y= 2x -6
Step-by-step explanation:
The slope-intercept form of a line is given by y= mx +c, where m is the slope and c is the y-intercept.
To find the equation of a line, two information are needed:
Slope (given/ calculated)A pair of coordinatedGiven that the slope is 2, m= 2. Substitute m= 2 into y= mx +c:
y= 2x +c
Let's find the coordinate in which the line intersects the line 2x -3y= 6. Point of intersection refers to the point at which two lines cuts through each other i.e., the point lies on the graph 2x -3y= 6 and the line of interest.
2x -3y= 6
When x= 3,
2(3) -3y= 6
6- 3y= 6
3y= 6 -6
3y= 0
Divide both sides by 3:
y= 0
Coordinate that lies on the graph is (3, 0).
Substitute the point into the equation and solve for c:
y= 2x +c
When x= 3, y= 0,
0= 2(3) +c
0= 6 +c
c= -6
Substitute the value of c back into the equation:
Thus, the equation of the line in slope-intercept form is y= 2x -6.
Additional:
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plssss help
90 + 6x = 180
-90
6x = 90
÷6
x = 15
5y + 4y + 90 + (6x15) =360
9y + 90 + 90 = 360
9y + 180 = 360
- 180
9y = 180
÷9
y = 20
Hope this helps!
Which graph represents the solutions to the inequality |2x − 6| < 4? (5 points) number line with a closed circle on 1, shading to the left and a closed circle on 5, shading to the right number line with a closed circle on 1, shading to the right and a closed circle on 5, shading to the left number line with an open circle on 1, shading to the left and an open circle on 5, shading to the right number line with an open circle on 1, shading to the right and an open circle on 5, shading to the left
The graph that represents the inequality is:
Number line with an open circle on 1, shading to the right and an open circle on 5, shading to the left.
What is the inequality?The inequality is:
|2x - 6| < 4
Which means that the distance of 2x - 6 to the origin is less than 4, hence:
-4 < 2x - 6 < 4.
The solution is:
2x - 6 > -4
2x > 2
x > 1
2x - 6 < 4
2x < 10
x < 5
The solution has open circles at x = 1 and x = 5, as they are not part of the solution, and the shading is in the middle, as the solution is 1 < x < 5, hence the correct option is:
Number line with an open circle on 1, shading to the right and an open circle on 5, shading to the left.
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Mohal bought 20 chicken wings for
$50.00. If Mohal spent $30.00, how
many chicken wings did he buy?
Answer:
If Mohal bought 20 chicken wings for $50.00 as a result of spending $30.00 he gets 12 chicken wings.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.
It is given that Mohal bought 20 chicken wings for $50.00 and spend $30.0.
We'll apply division by Splitting into equal halves or groups, the division may be used to decide how to distribute a dish of cookies evenly among a group.
The price of one chicken wing is,
= $ 50 / 20
= $ 2.50
The number of chicken wings he can buy after spending $30.00,
= $30.00 / = $ 2.50
=12
Thus, Mohal bought 20 chicken wings for $50.00 as a result of spending $30.00 he gets 12 chicken wings.
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Type the correct answer in the box.
Net of a triangular prism includes 3 same-sized rectangles that coincide along their width. Each rectangle has length labeled 10 centimeters and width labeled 15 centimeters. Isosceles triangle is placed above and below of second rectangle.
The surface area of the three-dimensional figure is
square centimeters.
The surface area of this three-dimensional figure is equal to 536.6 square centimeters.
How to determine the surface area?First of all, we would determine the total area of the three rectangles by using this formula:
Total area = 3 × Length × Width
Total area = 3 × 15 × 10
Total area = 450 cm².
Next, we would determine the total area of the two triangles by using this formula:
Total area = 2 × (1/2 × b × h)
Total area = b × h
Total area = 8.66 × 10
Total area = 86.6 cm².
Surface area = 450 + 86.6
Surface area = 536.6 cm².
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Question
If the length of the side of a square is 3x - y, what is the area of the square in terms of x and y?
3x² - 2xy + y²
3x² - 6xy + y²
09x² +6xy-y²
9x² - 6xy + y²
The area of the square is given by the quadratic expression:
[tex]A = 9x^2 - 6xy + y^2[/tex]
How to express the area of the given square?If we have a square whose side measures S, the area of said square is given by the equation:
[tex]A = S^2[/tex]
In this case, we know that the side length of our square is given by:
[tex]S = 3x - y[/tex]
Replacing that in the area equation we get:
[tex]A = (3x - y)^2[/tex]
Now we just need to expand that product, we will get:
[tex]A = (3x - y)^2 = (3x)*(3x) + (3x)*(-y) + (-y)*(3x) + (-y)*(-y) \\\\A = 9x^2 - 6xy + y^2[/tex]
Then we can see that the correct option is the last one.
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will give brainliest
ax² + bx + c = 0
discriminant = b² - 4ac
----> x² + 7x + 12
---> Discriminant of this equation = 7² - 12.1.4 = 49 - 48 = 1 (Positive discriminant)
x = (-7 + 1)/(2.1) = -6/2 = -3
or
x = (-7 - 1)/(2.1) = -8/2 = -4
Therefore, this equation has two real solutions and has a positive discriminant.
The correct answer is B
Match the information on the left with the appropriate equation on the right.
m=1, b=-3. x+y=1
m=1, (-1,2) x-y=-1
(-2,3),(-3,4) x-y=-3
x-y=3
The equation of the line passing the points (-2,3),(-3,4) is y = -x + 1 or x+y = 1
Equation of a lineA line is the shortest distance between two points. The equation of a line in slope-intercept form is expressed as;
y = mx + b
m is the slope
b is the y-intercept
Given that m=1, b=-3, the required equation will be y = x - 3 or x - y = 3
For the parameter m=1, (-1,2)
y - 2 =1(x+1)
y - 2 = x+1
y =x + 3
Hence the equation of the line for the parameters m=1, (-1,2) is y = x + 3
For the coordinates (-2,3),(-3,4)
Slope = 4-3/-3+2
Slope = -1
For the intercept;
4 =-1(-3) + b
b = 4 - 3
b = 1
Hence the equation of the line passing the points (-2,3),(-3,4) is y = -x + 1 or x+y = 1
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Given that L1 || L2, find the measures of angles a and b when 0 = 43°
Answer:
a = 43 degrees
b = 137 degrees
Step-by-step explanation:
according to the alternate interior angle theorem, angle a equals angle theta, so angle a = 43 degrees
angle b is the supplement of angle a, so angle b = 180-angle a, or 137
The sets L and J are defined as follows:
L = {d, e, g}
J = {b,c, h}
Find the intersection of L and J .
Answer:
The intersection of L and J or simply (L ∩ J)= ∅
or { }
Step-by-step explanation:
Hello!
The intersection operation is denoted by the symbol ∩. The set A ∩ B—read “A intersection B” or “the intersection of A and B”—is defined as the set composed of all elements that belong to both A and B.
Thus, at this situation there is no similar terms between the to set elements of L and J.
Find the slope-intercept form of the line that
passes through the point (-7, 3) and is
parallel to the line 2x+5y = 3.
Given the graph of g(x), describes the transformation of the parent function f(x)=2^x
Answer:
The transformation being described is from g(x)=x2 g ( x ) = x 2 to f(x)=x2 f ( x ) = x 2 . The horizontal shift depends on the value of h . The horizontal shift is described as: f(x)=f(x+h) f ( x ) = f ( x + h ) - The graph is shifted to the left h units
A music store sells music equipment at a 35%
markup. It a piece of equipment costs $150.00
what will the selling price be? I
The selling price of an equipment costing $150.00 with 35% markup is $202.50
What is an equation?An equation is an expression that shows the relationship between two numbers and variables.
An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.
Given that the mark up is 35%, hence:
Markup = [(selling price - cost price)/cost price] * 100%
Substituting:
$202.50
Selling price = $202.50
The selling price of an equipment costing $150.00 with 35% markup is $202.50
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What is the name of the green segment in the hyperbola below?
A. Minor axis
OB. Transverse axis
OC. Major axis
OD. Directrix
If $4,000 is invested in an account for 25 years. Calculate the total interest earned at the end of 25 years if the interest is: (a) 7% simple interest: $ (b) 7% compounded annually: $ (c) 7% compounded quarterly: $ (d) 7% compounded monthly: $ Round your answers to the nearest cent.
The interest is a) $7000
b) $17709.73
c) $18672.62
d) $18901.67
What is the formula for simple and compound interest?
Simple interest = (P× r× t)
Compound interest = P(1+r/n)^nt - P
We will find the interest as shown below:
P=$4,000
t=25 years
a) r=7%=0.07
Simple interest = (P× r× t)
= (4000×0.07×25)
= $7000
b) r=7%=0.07
Compound interest = P(1+r)^t - P
= 4000(1+0.07)^25-4000
= $17709.73056
rounding to nearest cents
= $17709.73
c) r=7%=0.07
n=4
Compound interest = P(1+r/n)^nt - P
= 4000(1+0.07/4)^(25*4)-4000
= $18672.62375
rounding to nearest cent
= $18672.62
d) r=7%=0.07
n=12
Compound interest = P(1+r/n)^nt - P
= 4000(1+0.07/12)^(25*12)-4000
= $18901.6728
rounding to nearest cent
= $18901.67
Hence, the interest is a) $7000
b) $17709.73
c) $18672.62
d) $18901.67
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Your local pizza store sells medium pizzas for $6.79 each, and breadsticks for $2.49 per order.
For a party, you decide to order 4 pizzas and 2 orders of breadsticks. There is a $3 delivery fee, and a 9.4% sales tax will be added to the total. What will be the total bill after tax?
The total bill after tax is $38.44.
What is the total bill?The first step is to determine the total cost of 4 pizzas and 2 orders of breadsticks: (4 x $6.79) + (2 x 2.49) = $32.14
Now, determine the total cost after delivery fee has been added : $3 + $32.14 = $35.14
Now determine the total cost after tax : (1.094) x $35.14 = $38.44
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The total bill after tax of 9.4% is $38.44.
It worthy of note that the sales tax of 9.4% is a percentage of the total purchase bills prior to tax computation, it is the tax due on purchases which is an added percentage of the sales price
total cost of 4 pizzas= $6.79 *4
total cost of 4 pizzas=$27.16
total cost of 2 orders of breadsticks=$2.49*2
total cost of 2 orders of breadsticks=$4.98
total cost of purchase prior to adding delivery cost=$27.16+$4.98
total cost of purchase prior to adding delivery cost=$32.14
total cost of purchase after delivery cost=$32.14+$3
total cost of purchase after delivery cost=$35.14
total cost inclusive of 9.4% sales tax=$35.14*(1+9.4%)
total cost inclusive of 9.4% sales tax=$35.14*1.094
total cost inclusive of 9.4% sales tax=$38.44
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Solve the following equation. Write your answer in reduced fraction form, if necessary. (7x−2)(x+6)=0
Answer:
x = 2/7
x = -6
Step-by-step explanation:
You can solve the equation by setting each set of parentheses equal to 0 and simplifying.
7x - 2 = 0 <----- First set of parentheses
7x = 2 <----- Add 2 to both sides
x = 2/7 <----- Divide both sides by 7
x + 6 = 0 <----- Second set of parentheses
x = -6 <----- Subtract 6 from both sides
A line graph titled Meals per Day has number of days on the x-axis, and number of meals prepared on the y-axis. At 5 days there are 30 meals prepared; at 10 days, 60 meals; at 15 days, 90 meals; at 20 days, 120 meals.
Use proportional reasoning to find the constant of proportionality for the relationship shown on the graph.
What is the value of y when the value of x is 1?
The constant of proportionality is 6.
How to calculate the constant?From the information given, the constant will be:
30 meals ÷ 5 days = 6
60 meals ÷ 10 days = 6
90 meals ÷ 15 days = 6
120 meals ÷ 20 days = 6
The constant of proportionality is 6. Therefore, the function will be:
y = kx
y = 6x
The value of y when x is 1 will be:
y = kx
y = 6 × 1 = 6
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Answer:
what they said
Step-by-step explanation:
What is the total repayment made, including principal and interest, on a loan of $1,100 at 3.5% interest compounded annually over four years?
The total repayment made, including principal and interest is $1262.27
Compound interestThe formula for calculating the compound interest is calculated as shown below;
A = P(1+r)^t
where
P is the principal = $1100
rate = 3.5% = 0.035
time "t" =4 years
Substitute
A. = 1100(1+0.035)^4
A = 1100(1.035)^4
A = 1100(1.14752)
A = 1262.27
Hence the total repayment made, including principal and interest is $1262.27
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Part A Your presentation should make a convincing argument that human activity is the major cause of climate change. Your presentation should answer some of these questions: What is climate? How is Earth’s climate changing? What are the natural and human factors that affect climate? How do scientists know that human activity is the major force behind climate change? What evidence do scientists have that climate is changing? Write down two additional questions you have about climate change that will help you make this argument in your presentation. 12pt
Climate is the long-term weather pattern that can be seen in an area over a period of years.
How to explain the climate?Earth’s climate changing as the Earth's atmosphere heats up, it collects, retains, and drops more water, thereby changing weather patterns and making wet areas wetter and dry areas drier.
The factors that affect climate includ deforestation, desertification, urbanization, etc.
Scientists know that recent climate change is largely caused by human activities from an understanding of basic physics by comparing observations with models, and then fingerprinting the detailed patterns of climate change caused by different human and natural influences
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Identifying the values a, b, and c is the first step in using the Quadratic Formula to find solution(s) to a quadratic equation.
What are the values a, b, and c in the following quadratic equation?
In the given quadratic equation, - 3x² - 5x + 9 = 0, we have the values, a = -3, b = -5, and c = 9. Hence, option C is the right choice.
A quadratic equation is a polynomial of degree 2, in a single variable x.
The standard form of a quadratic equation is ax² + bx + c = 0.
The quadratic formula is used to find the solution(s)/root(s) of this equation.
The quadratic formula is:
[tex]x = \frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]
Thus, identifying the values of a, b, and c, is the first step in using the quadratic formula to find a solution(s)/root(s) to a quadratic equation.
In the question, we are asked to find the values of a, b, and c, in the given quadratic equation - 3x² - 5x + 9 = 0.
To find the values of a, b, and c, we compare the given equation, to the standard form of a quadratic equation, ax² + bx + c = 0.
On comparing, we get a is the coefficient of x², that is, a = -3.
On comparing, we get b is the coefficient of x, that is, b = -5.
On comparing, we get c is the constant term, that is, c = 9.
Thus, in the given quadratic equation, - 3x² - 5x + 9 = 0, we have the values, a = -3, b = -5, and c = 9. Hence, option C is the right choice.
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The provided question is incomplete.
The complete question is:
"Identifying the values a, b, and c is the first step in using the Quadratic Formula to find solution(s) to a quadratic equation.
What are the values a, b, and c in the following quadratic equation?
- 3x² - 5x + 9 = 0
A. a = 5, b = 9, c = 0B. a = 3, b = 5, c = 9C. a = −3, b = −5, c = 9D. a = −5, b = 9, c = 0."help with this question please !
Answer:
angle 8 is congruent to angles 3, 6, and 1
Step-by-step explanation:
If n and q are parallel then corresponding and vertical angles would be congruent. So: angle 8 is congruent to angles 3, 6, and 1.
You are training to compete in a 10-kilometer race, and you know the circular running trail at
your park is one mile long. How many times will you need to run this trail in order to run 10
kilometers? (round to the nearest whole number) 1 Kilometer=0.62
.
Answer:
6.2 rounds
Step-by-step explanation:
since 1 kilometer is 0.62 miles
10 kilometers is 6.2 miles
so about 6 and 1/5 rounds
Blue Ocean Realty Co. pays weekly salaries of $33,300 for a six-day workweek (Monday through Saturday).
A road sign has the shape of an equilateral triangle with a side length of 48 inches. What is the height of the sign? The road sign is about 38.2 inches tall The road sign is about 38.2 inches tall The road sign is about 23.5 inches tall The road sign is about 23.5 inches tall The road sign is about 41.6 inches tall The road sign is about 41.6 inches tall The road sign is about 43.7 inches tall
The height of the equilateral triangle is 41. 6 inches. Option C
How to determine the height
The formula for finding the height of an equilateral triangle is given as;
h = (a√3)/2
we have a = 48 inches
Let's substitute the value
Height, h = [tex]\frac{48\sqrt{3} }{2}[/tex]
Height = [tex]\frac{48 * 1. 732}{2}[/tex]
Height = [tex]\frac{83. 14}{2}[/tex]
Height = [tex]41. 6[/tex] Inches
Thus, the height of the equilateral triangle is 41. 6 inches. Option C
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Please answer this question for me
Answer: B
Step-by-step explanation:
The vertical asymptotes are at x=-4 and x=1, so the denominator needs to have factors of (x+4) and (x-1).
This eliminates everything except for B.