On combining the like terms of the expression y²/2 + y/3 + y²/3 - y/5 the simplified value is 5y²/6 +2y/15.
In an algebraic expression Like terms are defined as those terms that have same variable and that variable has the same power .
For Example : 5a,9a are like terms .
In the given question
=y²/2 +y/3 +y²/3 -y/5
On combining the like terms , one with y² and other with y.
We get;
=y²/2 +y²/3 +y/3 -y/5
Taking LCM of like terms with y² as "6"
and LCM of like terms with y as "15".
We get ;
=(3y²+2y²)/6 +(5y-3y)/15
=5y²/6 +2y/15
Therefore , On combining the like terms of the expression y²/2 + y/3 + y²/3 - y/5, the simplified value is 5y²/6 +2y/15.
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express 985 cm cube as a percentage of 1 litre
Answer:
98.5%
Step-by-step explanation:
1000 cubic centimeters = 1 litre
(3 decimal spaces to the left)
985 cubic centimeters = .985 liters (almost 1 litre)
.985 = 98.5% (2 decimal spaces to the right)
A builder makes staircases where each step is
28
cm
28cm28, start text, c, m, end text long and rises
18
cm
18cm18, start text, c, m, end text so people don't trip. Every staircase has a stringer — a diagonal support connecting all of the steps.
the length of the stringer for the staircase of 6 steps is 199.74 cm.
The sum of the squares of the two sides (a and b) equals to the square of the hypotenuse (c). In mathematics, the Pythagorean theorem, also known as Pythagoras' theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle.
According to the question,
Each step is 28 cm long that is the length of one step of the staircase. And 18 cm high which is the height of the step at 90-degree angle thus forming a right-angle triangle and the stringer acts as a hypotenuse. Therefore, we can use Pythagoras theorem to find the length of the stringer of one step.
Length=a=28 inch
Breadth=b=18 inch
Applying the Pythagoras theorem, we get
28²+18²= (length of the stringer)²
28²+18²= = 1108
Now, √1108 = 33.29
to find the length of 6 steps multiply 33.29 with 6
33.29*6 = 199.74
Therefore, the length of the stringer for the staircase of 6 steps is 199.74 cm.
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Answer:
199.7 cm
Step-by-step explanation:
In the formula V= (1/3)πr²h , which expression is equal to h ? (A) V/3πr²(B) V - - -(1/3)πr² (C) 3V/πr² (D) 3Vπ/r²
In the formula V = (1/3)πr²h , (A)V/3πr² is the expression equal to h.
How to solve an equation?To solve linear equations, utilize the steps that are provided below.
Remove parentheses from each side of the equation and combine similar terms to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The common denominator can be multiplied by each side of the equation to eliminate fractions.Lets take an example of solve z for 7z – (3z – 4) = 12
Here is no multiplication or division, so this will be easy to solve
⇒ 7z – (3z – 4) = 12
⇒ 7z – 3z + 4 = 12
⇒ 4z = 12 – 4
⇒ 4z = 8
⇒ z = 8/4
⇒ z = 2
See, that was so simple, using the mentioned methods, every linear equation can be solved easily
Here given that,
V= (1/3)πr²h
V/3πr² = (1/3)πr²h/3πr² (divided both sided with 3πr²)
V/3πr² = h or h = V/3πr²
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Alexandra and her children went into a bakery where they sell cupcakes for 3.25 each and donuts for 1.25 each. Alexandra has 25 to spend and must buy a minimum of 11 cupcakes and donuts altogether. If x represents the number of cupcakes purchased and y represents the number of donuts purchased, write and solve a system of inequalities graphically and determine one possible solution.
explanation up top:) that's the explanation I hope you understand
The number of maximum cupcakes and cookies sold is 6 and 5 respectively.
What is Inequality?Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
Given:
Alexandra sell cupcakes for 3.25 each and donuts for 1.25 each.
let x be the number of cupcakes purchased and y be the number of donuts purchased.
Now, Alexandra has 25 to spend and must buy a minimum of 11 cupcakes and donuts altogether.
So, x+ y ≥11
and, 3.25x + 1.25y ≤ 25.
Thus, x= 5.625 and y= 5.375
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Please help me with this!!!!
The scale on a map is stated as
1: 100 000
On the map, Jennifer estimates that the distance to her destination is 8 cm.
If she is correct in her estimate, how many kilometres is it to her destination?
The required estimate of the destination on the map is 800,000 kilometers.
Given that,
The scale on a map is stated as 1: 100 000 on the map, Jennifer estimates that the distance to her destination is 8 cm. If she is correct in her estimate, how many kilometers is it to her destination is to be determined.
The scale factor is defined as the ratio of modified change in length to the original length.
Here,
1 cm = 100, 000 km
Multiply both sides by 8
8cm = 800,000 kilometers.
Thus, the required estimate of the destination on the map is 800,000 kilometers.
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need help fast !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The correct location of the system of equations are;
Single solution;
y = 11 - 2•x
4•x - y = 7
x + y = 15
2•x - y = 15
No solution;
2•x + y = 7
-4•x = 2•y + 14
x = 12 - 3•y
3•x + 9•y = 24
Infinite solution;
2•x + y = 7
-6•x = 3•y - 21
What are the types of solutions to linear system of equations?The possible system of equations and their solution are presented as follows;
System of equations
y = 11 - 2•x4•x - y = 7Solution;
4•x - y = 7
Therefore;
11 - 2•x = 4•x - 7
6•x = 18
x = 3; Single solution;
System of equations
2•x + y = 7-4•x = 2•y + 14Solution;
2•x + y = 7 gives;
y = 7 -2•x
-4•x = 2•y + 14 gives;
y = -2•x - 7
7 -2•x = -2•x - 7
0 = 14, no solution
System of equations
x = 12 - 3•y3•x + 9•y = 24Solution;
x = 12 - 3•y gives;
3•x + 9•y = 24 gives;
x = (24 - 9•y) ÷ 3 = 8 - 3•y
Which gives;
12 - 3•y = 8 - 3•y
12 = 8 no solutionSystem of equations
2•x + y = 7-6•x = 3•y - 21Solution;
2•x + y = 7 gives;
y = 7 - 2•x
-6•x = 3•y - 21 gives;
3•y = 21 - 6•x
y = 7 - 2•x
7 - 2•x = 7 - 2•x Infinitely many solutions
System of equations
x + y = 152•x - y = 15Solution;
x + y = 15 gives;
y = 15 - x
2•x - y = 15 gives;
y = 2•x - 15
Which gives;
15 - x = 2•x - 15
3•x = 15 + 15 = 30
x = 30 ÷ 3 = 10 Single solution
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Each sequence has eight terms. Evaluate each related series. 1/2, 3/2, 5/2, . . . . . . , 15/2
The result of the evaluation of the series described by 1/2, 3/2, 5/2, . . . . . . . , 15/2 is:
∑ = 28
What is a series?A series is the summation of a set of numbers or sequences.
What is sigma notation?The sigma notation is a mathematical operation used to determine the final value of the sum of "n" terms consecutively, when dealing only with numbers without variables this is known as an arithmetic series.
The equation for this type of problem is:
∑ = n(a1 + an)/2
n : number of termsa1 : first terman : last termOur values are:
1/2, 3/2, 5/2, . . . . . . , 15/2
a1 =1/2an = 15/2n = 7∑ = 7(1/2 + 15/2)/2
∑ = 7(8)/2
∑ = 28
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A) x^8 • x^6 = x^p, where is p=
B) (x^8)^6 = x^r, where is r
Answer: p=14, r=48
Step-by-step explanation:
x^8 • x^6 = x^p
x^(8+6) = x^p
8+6=p
p=14
(x^8)^6 = x^r
x^(8*6)=x^r
8*6=r
r=48
For a ride on a rental scooter , ahmad paid $3 fee to start the scooter plus 11 cents per minute of the ride. The total bill for Ahmad’s ride was $20.49. For how many minutes did ahmad ride the scooter
Answer:
159 minutes
Step-by-step explanation:
y = .11x + 3
$3 initial fee to start the scooter
$0.11 per minute
y = the total bill price of the scooter ride
x = the total minutes of the ride
plug in what we know : $20.49 for the whole ride
20.49 = 0.11x + 3
SOLVE !! 20.49 - 3 = 0.11x
17.49 = 0.11x
17.49 / 0.11 = x
x = 159 minutes
check answer if you want
20.49 = 0.11 (159) + 3
20.49 = 17.49 + 3
20.49 = 20.49
Which expression best represents a simpler form of 4m+3(m+n) ?
A 7m+3n
B 4m+3mn
C 3m+4n
D 7m²+3n
The expression 7m+3n best represents a simpler form of 4m+3(m+n).
The Simplified Algebraic Expression is defined as the expression that do not have any like terms and also it cannot be simplified further.
For Example : 2x+5y+6x , the simplified form will be 8x+5y as it cannot be simplified further.
In the given question,
=4m+3(m+n)
=4m+3m+3n ...(multiplying 3 with m and n)
Now Combining the like terms ,
We get ;
=7m+3n
Therefore , the expression that best represents a simpler form of 4m+3(m+n) is 7m+3n.
The correct option is (A) 7m+3n.
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Determine whether each relation is a function. (1,1),(2,0),(3,1),(4,3),(0,2)
Range - { 1 , 0, 1 , 3 , 2 } is relation is a function.
What is domain and range ?
The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.Definitions of domain and example?
The domain is the set of x -coordinates, {0,1,2} , and the range is the set of y -coordinates, {7,8,9,10} .
function. (1,1),(2,0),(3,1),(4,3),(0,2)
Domain - { 1,2, 3 , 4 , 0 }
Range - { 1 , 0, 1 , 3 , 2 }
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can anyone help much appreciated (30 points) image below btw
The sum of the polynomial is equal to -10x^3 + 2x^2 + 7x + 8.
what are polynomials?In mathematics, polynomials refers to an algebraic equation which have more than two terms, the terms are usually same variable but the exponents tends to increase the number of terms.
An algebraic equation with the highest power as two is generally called parabolic equation/ When the power goes above two they are called polynomial.
How to add polynomialsaddition of polynomials is achieved by adding like terms together. the like terms as in the question include similar alphabet and same exponents
( -4x^3 + 10x^2 + 6 ) - ( 6x^3 + 8x^2 - 7x - 2 )
terms with x^3: -4 - 6 = -10
terms with x^2: 10 - 8 = 2
terms with x: 0 - ( - 7 ) = 0 + 7 = 7
constant terms : 6 - ( - 2 ) = 6 + 2 = 8
constant terms refers to terms that does not have x
writing the equation together with their terms gives -10x^3 + 2x^2 + 7x + 8. Hence we can conclude that addition of polynomials involves addition performed considering the terms by adding like term.
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Convert -5/8 into a decimal
Answer:
-0.625
Step-by-step explanation:
A fraction is the numerator (top) divided by the denominator (bottom). In this case it is -5 divided by 8. Put that into a calculator and you will get -0.625.
i need help solving this
Answer:
Step-by-step explanat
36=10x-4
40=10x
10x=40
x=40/10
x=4
4th term 19 and 7th term is 7 of A5
Find d a1 an a11
Answer: a₁=31 a₁₁=-9
Step-by-step explanation:
[tex]\displaystyle\\\left \{ {{a_4=19} \atop {a_7=7}} \right. \\\\a_n=a_1+(n-1)d\\\\\left \{ {{a_1+(4-1)d=19} \atop {a_1+(7-1)d=7}} \right. \\\\\left \{ {{a_1+3d=19\ \ \ \ (1)} \atop {a_1+6d=7\ \ \ \ \ (2)}} \right.[/tex]
Subtract equation (2) from equation (1):
[tex]3d=-12[/tex]
Divide both parts of the equation by 3:
[tex]d=-4[/tex]
Thus,
[tex]a_1+(3)(-4)=19\\a_1-12=19\\a_1-12+12=19+12\\a_1=31\\a_{11}=a_1+(11-1)d\\a_{11}=31+(10)(-4)\\a_{11}=31-40\\a_{11}=-9[/tex]
Answer:
a = 43
d = -6
[tex]\sf a_{11} = -17[/tex]
Step-by-step explanation:
Arithmetic sequence:
Use the formula to find the nth term:
[tex]\sf \boxed{\bf a_n= a+(n-1)d}[/tex]
Here, a is the first term, n is the number of terms and d is the common difference.
[tex]\sf a_4 = 19\\\\a+(4-1)*d = 19\\\\a + 3d = 19 -------------------(i)[/tex]
[tex]\sf a_7 = 7\\\\a + 6d = 7 ------------------(ii)\\[/tex]
Subtract equation (i) from (ii) and thus 'a' will be eliminated and we can find the value of 'd'.
(ii) a + 6d = 7
(i) a + 4d = 19
- - = -
2d = -12
d = -12/2
[tex]\sf \boxed{\bf d = -6}[/tex]
Now, plugin d = -6 in any of the two equations. We are substituting the 'd' value in equation (i)
a + 4*(-6) = 19
a - 24 = 19
a = 19 + 24
[tex]\sf \boxed{\bf a = 43}[/tex]
[tex]\sf a_{11} = a + 10d[/tex]
= 43 + 10*(-6)
= 43 - 60
[tex]\sf \boxed{\bf a_{11} = -17 }[/tex]
Determine the values of x in the equation x2 = 49.
whoever gets it right gets a crown pls help
Answer:
49/2 or 24 1/2
Step-by-step explanation:
Divide both sides by 2 to get x by itself.
Answer:
x = 7
Step-by-step explanation:
➟ x² = 49
in order to find the value of x will have to take square root of both side
➟ [tex] \sf \sqrt{x} = \sqrt{49} [/tex]
Calculate
➟ [tex] \sf \: x = 7[/tex]
Please help with problem 25, part a and b Algebra 1, In the attachment.
The equation to represent the number of people that can attend the event will be 18500 +/- 1200.
How to calculate the value?Based on the information, equation to represent the number of people that can attend the event will be 18500 +/- 1200.
The maximum number will be:
= 18500 + 1200
= 19700
The minimum number will be:
= 18500 - 1200
= 17300
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4 is subtracted from the product of 5 and a number.
Answer:
5x-4
Step-by-step explanation:
Product of a number, x , and 5 = 5x
subtract 4 5x -4
Make a conjecture about the sum of the measures of the interior angles of a triangle.
The Conjecture is : "the sum of the measures of the interior angles of a triangle is 180° ".
What are interior angles?The interior angle of any triangle is defined as the angle which is inside the triangle. In the other words if the triangle has the point within the angle it is in the interior of the angle. A triangle has three internal angles. The interior angles are always less than 180.
Triangle Angle-Sum TheoremAccording to triangle Angle Sum theorem, the measurement of the sum of all interior angles of a triangle is always equals to 180°. That means, For a given triangle say ΔABC if ∠A, ∠B and ∠C are the interior angles then their sum i.e. ∠A + ∠B + ∠C = 180°.
Thus according to this we can make the conjecture about the sum of measures of the interior angles of a triangle.
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Sonya has two rectangular gardens. The larger garden is four times as wide and five times as long as the smaller one. If the area of the smaller one is x, what is the difference in size between the two gardens?
A. 20x
B. 19x
C. 9x
D. 1x
E. None of the above
The required difference in the size between the two garden is 20x. Option A is correct.
Given that,
Sonya has two rectangular gardens. The larger garden is four times as wide and five times as long as the smaller one. If the area of the smaller one is x, what is the difference in size between the two gardens is to be determined.
The rectangle is 4 sided geometric shape whose opposites sides are equal in length and all angles are about 90°.
Here,
length and width of the small rectangular garden is l and b
Let the are of the small garden be x = lw
Now according to the question
Length of the larger garden = 5l
And the width of the larger garden = 4w
Now the area of the larger garden = 5l * 4w
= 20lw
= 20x
Thus, the required difference in the size between the two gardens is 20x. Option A is correct.
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Which of the following is a like radical to 3 √6x²?
Answer:
Answer: Option 3
Step-by-step explanation:
like radicals are radicals that have the same root number and the same 'radicand' (number or expression under the square root)
The sum of four consecutive numbers is thirty. Enter the value of the largest number.
ok so the answer is
i might be wrong but
6+7+8+9 = 30
so 9
Choose an equivalent expression for two thirds to the fourth power times two thirds raised to the third power comma all raised to the second power.
four ninths raised to the fourteenth power
four ninths raised to the twenty fourth power
two thirds raised to the fourteenth power
two thirds raised to the twenty fourth power
The equivalent expression for the given expression is [tex](\frac{2}{3} )^{14}[/tex]. Therefore, option C is the correct answer.
The given expression is [tex]((\frac{2}{3} )^{4}\times(\frac{2}{3} )^{3})^{2}[/tex].
We need to find the equivalent expression for the given expression.
What is an equivalent expression?Equivalent expressions are expressions that work the same even when they seem different. When we enter the same value for the variable, two algebraic expressions that are equivalent have the same value.
Now, [tex]((\frac{2}{3} )^{4}\times(\frac{2}{3} )^{3})^{2}[/tex] using [tex]a^{m} \times a^{n}=a^{m+n}[/tex].
We get, [tex]((\frac{2}{3} )^{4+3})^{2}=((\frac{2}{3} )^{7})^{2}[/tex]
Using the exponents rule [tex](a^{m} )^{n}=a^{m\times n}[/tex]
=[tex]=(\frac{2}{3} )^{7\times 2}=(\frac{2}{3} )^{14}[/tex]
The equivalent expression for the given expression is [tex](\frac{2}{3} )^{14}[/tex]. Therefore, option C is the correct answer.
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50 PTS - functional notation (yes or no)
Can someone explain what I have to do for this? Do I just plug them in or what also yes or no for what?? Thanks!
The solution to the functional notations would be either yes or no if the function on the left hand side and right hand side are the same. Hence we would have:
c. No: f ( x ) ≠ f ( -x )
d. Yes: ( - x ) = - f ( x )
What is function notation?Function notation is way of writing functions so that they can easily be understood in the mathematical sense. This method is applied in the question to help read the meaning in the question without much explanations.
Given data
f ( x ) = x^3
f ( -x ) = - x^3
How to solve the function notationsc. No f ( x ) ≠ f ( -x )
f ( x ) = x^3 and f ( -x ) = - x^3
f ( x ) is not equal to f ( -x )
plugging the values for the left hand side of the equation gives
x^3
and plugging the values for the right hand side of the equation gives
- x^3
since the left hand side of the equation is not equal to the right hand side of the equation it means that the both sides of the equation are not equal hence equation sated in c is not correct
f ( x ) ≠ f ( -x ) ( take note of the sign )
d. Yes ( - x ) = - f ( x )
( - x ) is equal to - f ( x )
This represents odd functions where the negative sign persists at the left hand side and the right hand side of the equation. Odd function do appear for functions which have negative signs and have odd exponents too.
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Corey wrote an equation in factored form , quadratic function . Kimberly wrote the equation y = (x + 8)(x - 2); y=x^ 2 +6x-16, to represent a and Joshua wrote the equation y = (x + 3) ^ 2 - 25 A. Reason Do all three equations represent the same function ? If not, whose is different ? Explain algebraically .
All the three equations represent the same function as they equal x² + 6x - 16.
How to illustrate the equation?It should be noted that the function that Corey wrote is:
y = (x + 8)(x - 2)
y = x² - 2x + 8x - 16
y = x² + 6x - 16
Kimberly wrote y = x² + 6x - 16
Joshua wrote (x + 3)² - 25
= (x + 3)(x + 3) - 25
= x² + 3x + 3x + 9 - 25
= x² + 6x - 16
In conclusion, the three equations represent the same function as they equal x² + 6x - 16.
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On a construction crane, the amount of force needed to move objects is directly proportional to the weight of the objects. If 4 Newtons of force is needed to move an object that is 1200 pounds, how much force would be needed to move an object that is 900 pounds?
Based on the fact that the force needed to move object is directly proportional to the weight of the objects, the force needed to move and object that is 900 pounds is 3 newtons of force.
How much force is needed?When things are directly proportional, it means that they increase by a given amount together and also decrease by the same amount.
If 4 Newtons are needed for 1,200 pounds, the newtons needed for 1 pound is:
= 4 / 1,200
= 1/300 newtons
If there are 900 pounds to be moved, the newtons needed are:
= 1/300 x 900
= 3 newtons of force
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I need this answered please
If the length of a rectangle is four less than twice its width and the perimeter is 220 inches, what is the width of the rectangle?
Step-by-step explanation:
Let's denote the length of the rectangle to be L and the width to be W.
The first sentence tells us that the length, L, is "4 less than twice the width". "4 less than" implies we subtract 4 from some quantity. What is that quantity? Well that's "twice the width." We can rewrite this sentence in terms of L and W as: L = 2W - 4.
Now we know the length of the rectangle in terms of the width.
The area of a rectangle is given by A = L x W. Using this equation, we can substitute our values for area and length:
A = L x W
96 = (2W - 4) x W
From this we can solve for W and subsequently solve for L using algebra:
96 = (2W - 4) x W
96 = 2W^2 -4W
96 = 2(W^2 - 2W)
48 = W^2 - 2W
W^2 - 2W - 48 = 0
(W - 8)(W + 6) = 0
W = 8 or W = -6
Since W is the side-length of a rectangle, we can disregard the negative solution. Therefore W = 8 ft.
If W = 8, then L = 2W - 4 = 2(8) - 4 = 12 ft.
Lastly, we know the Perimeter of a rectangle is given as P = 2L + 2W. Substituting into this equation we solve for the perimeter:
P = 2L + 2W = 2(12) + 2(8) = 40 ft.
The width of the rectangle will be 38 inches.
What is the perimeter of the rectangle?Let W be the rectangle's width and L its length. The perimeter of the rectangle will be defined as the total length of all of its sides. So the rectangle's perimeter will be
Perimeter of the rectangle = 2(L + W) units
If the length of a rectangle is four less than twice its width and the perimeter is 220 inches.
L = 2W - 4
Then the equation is given as,
P = 2(L + W)
220 = 2W - 4 + W
110 = 3W - 4
3W = 114
W = 38 inches
The width of the rectangle will be 38 inches.
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A bolt of fabric is a large rectangular strip of fabric. Starr-Lyn designs her own fabric. The design is then produced and placed on a bolt that is 81.5 meters (m) long and 1.32 m wide. Part A: Determine the area in Square meters of a bolt of fabric with Starr- Lyn's design.
The area of the rectangle according to the given length and width is 107.58m².
What do we mean by a rectangle?A rectangle is a quadrilateral with four right angles in Euclidean plane geometry. It can also be defined as an equiangular quadrilateral because all of its angles are equal, or a parallelogram with a right angle. A square is a rectangle with four equal-length sides. A rectangle is a closed two-dimensional shape with four sides, four corners, and four right angles (90°). A rectangle's opposite sides are equal and parallel. Because a rectangle is a 2-D shape, it has two dimensions: length and width.The formula of the area of a rectangle: l × w
Now, substitute the values in the formula:
l × w81.5 × 1.32107.58m²Therefore, the area of the rectangle is 107.58m².
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