The simplified form of the rational expression 6x^2-54/5x^2+15x is 6(x - 3)/5x. This was achieved by factoring the original expressions, cancelling out common terms, and applying the difference of squares formula.
Explanation:The subject here is the simplification of a rational expression. First, let's factor the numerator (6x^2 - 54) and the denominator (5x^2 + 15x). The common factor in the numerator is 6 and in the denominator is 5x. After factoring we get:
6x^2 - 54 = 6(x^2 - 9)
5x^2 + 15x = 5x(x + 3)
Now, we can use the property a^2 - b^2 = (a + b)(a - b) to further simplify x^2 - 9 to (x - 3)(x + 3). This gives our new numerator as 6(x - 3)(x + 3).
The denominator 5x(x + 3) remains the same. Therefore, the simplified form of the rational expression is 6(x - 3)(x + 3)/5x(x + 3). The (x + 3) terms can be cancelled out leaving us with the final simplified rational expression of:
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Write a numerical or variable expression for the quantity: the number of seconds in m minutes
To find the number of seconds in m minutes, you can multiply m by 60. The numerical expression is 60m and the variable expression is 'm * 60.'
Explanation:To write a numerical or variable expression for the quantity 'the number of seconds in m minutes,' we need to know the conversion rate between minutes and seconds. There are 60 seconds in 1 minute. So, to find the number of seconds in m minutes, we can multiply m by 60.
The numerical expression would be 60m.
The variable expression would be 'm * 60.'
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the graph of a line has a slope of -2/3 and a y intercept of (0,2). rewrite the equation in standard for (Ax+By=C) with a positive term. A,B, and C must all be intergers. what is the answer?
Answer:
2x + 3y = 6
Step-by-step explanation:
obtain the equation in slope- intercept form
y = mx + c ( m is the slope and c the y-intercept )
here m = - [tex]\frac{2}{3}[/tex] and c = 2
y = - [tex]\frac{2}{3}[/tex] x + 2 ← in slope-intercept form
multiply all terms by 3 to eliminate the fraction
3y = - 2x + 6 ( add 2x to both sides )
2x + 3y = 6 ← in standard form
which of the following have the same y-intercept as the eqaution y=2x+3
Considering it's concept, any function with f(0) = 3 was the same y-intercept as y = 2x + 3.
What is the y-intercept of a function f(x)?The y-intercept is f(0), that is, the value of y when x = 0, which is interpreted as the initial value of the function.
In this problem, the function is given by:
y = 2x + 3.
The y-intercept is given by:
y = 2(0) + 3 = 3.
Hence, any function with f(0) = 3 was the same y-intercept as y = 2x + 3.
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12 is what percent of 50
Answer:24%
Step-by-step explanation:
Step 1: We make the assumption that 50 is 100% since it is our output value.
Step 2: We next represent the value we seek with x
Step 3: From step 1, it follows that 100\%=50.
Step 4: In the same vein, x\%=12.
Step 5: This gives us a pair of simple equations:
hope this helps
If (a, -8) is a solution to the equation -a = 4b - 7 what is a?
The value of 'a' when (a, -8) is a solution to the equation -a = 4b - 7 is '39'.
If we have the point (a, -8) as a solution to the equation -a = 4b - 7, and we're given the value of b from the point, which is -8, we can substitute this value into the equation to find 'a'.
Substituting b = -8 into the equation gives us:
-a = 4(-8) - 7
-a = -32 - 7
-a = -39
Now, we can solve for 'a' by multiplying both sides by -1 to get:
a = 39
Therefore, the value of 'a' is 39.
Which values make this equation true?
(5x^7 y^2)(-4x^4 y^5)=-20x^a y^b
A.) a=11, b=7
B.) a=11, b=10
C.) a=28, b=7
D.) a=28, b=10
When multiplying terms with exponents, just add the exponents together.
You have x^7 and x^4, so 7 +4 = 11
Y^2 and Y^5 = 2+5 = 7
so it would be -20x^11 y^7
The answer is A.) a=11, b=7
An electrician has $120 to spend on interior light fixtures. the wholesale price for 13-watt low-energy lamp is $4. The price for a high-energy lamp is $5. write an expression for how much the electrician spends for A units of the low-energy lamp and B units of the high-energy lamp.
complete the table for the electrician's purchase. assume that all of the $120 is spent
To find the expression for the cost of low-energy lamps and high-energy lamps, use the expressions 4A and 5B respectively. To find the values of A and B that make the total cost equal $120, solve the equation 4A + 5B = 120.
Explanation:To write an expression for how much the electrician spends on low-energy lamps and high-energy lamps, we can use the following expressions:
Cost of low-energy lamps: 4A
Cost of high-energy lamps: 5B
To complete the table, we need to calculate the values of A and B such that the total cost equals $120. Since all of the $120 is spent, the expression for the total cost would be:
Total cost: 4A + 5B = 120
We can solve this equation to find the values of A and B.
What is the value of x?
Answer:
The value of x is 68 degrees!
Step-by-step explanation:
In this question, we have an isosceles triangle because of Base Angles Theorem. The 2 sides are congruent, which means its an isosceles and that the Base angles are congruent. So far, we know that 2 angles are equal to 112 degrees. Due to Sum Angles Theorem, we can go 180-112 to get 68 degrees!
Answer:
x=68
Step-by-step explanation:
Since this is an isosceles triangle, the bottom two angles are the same value, 56 degrees. The three angles of a triangle add to 180 degrees.
56+56+ x = 180
Combine like terms
112 +x = 180
Subtract 112 from each side
112-122 +x = 180 -112
x =68
what the answer to
-2v+8 (1+2v)=-90
Answer:
v=2-2root7, v=2+2root7
Step-by-step explanation:
-2v+8(1+2v)=-90
-2-4v^2+8+16v=-90
6-4v^2+16v=-90
-4v^2+16v=-96
v=2-2root7, v=2+2root7
Answer
-2v+8 (1+2v)=-90 then V = -7
Step-by-step explanation:
-2v + 8 x (1 + 2v) = -90
-2v + 8 + 16v = -90
14v + 8 = -90
14v = -98
V = -98/14
V= -7
Hope this helps ;)
There are some rabbits and some hutches. If eight rabbits are put in each hutch, one rabbit is left over. If eleven rabbits are put in each hutch, one hutch is left empty. How many rabbit hutches are there, and how many rabbits are there?
Answer:
there's 33 rabbits and 4 hutches
Step-by-step explanation:
8 x 4 = 32 plus the one left over
11 x 3 = 33 with and extra hutch
Answer:
33 rabbits and four hutches
Step-by-step explanation:
;)brainliest?
Which of the following is a solution to the inequality 7-1/5x>0?
[tex]7-\dfrac{1}{5}x>0\qquad\text{subtract 7 from both sides}\\\\-\dfrac{1}{5}x>-7\qquad\text{change the signs}\\\\\dfrac{1}{5}x<7\qquad\text{multiply both sides by 5}\\\\\boxed{x<35}[/tex]
which describes the angle measures of an equilateral triangle?
A) 30*,30*,30*
B) 60*,60*,60*
C) 90*,90*,90*
Answer:
B
Step-by-step explanation:
All sides have to be equal and add up to be 180 degrees therefore the answer would be 60 because 60 plus 60 plus 60 is 180.
Answer:
B
B is the only answer that adds to 180, the interior angle measures of a triangle.
x+y=10 and 2x+4y=30
What are the steps to solve this equation?
Answer:
x=5 and y=5
Step-by-step explanation:
You "plug" one equation into the other, to get a new equation that only has one variable (x or y), then you can simplify that and have your answer.
So let's plug the first into the second:
First, we convert the first equation into an x=... form. For this one, this means moving the +y to the other side:
x = 10 - y
Now we substitute 10-y for x in the second equation:
So 2x+4y=30 becomes:
2(10-y) + 4y = 30
And simplify that:
20 - 2y + 4y = 30
20 + 2y = 30
2y = 30-20
2y = 10
y = 5
This is the first answer! If we put this into the first equation, we get:
x = 10 - 5 = 5
Now we have both answers, x=5 and y=5
Write the following equation in the general form Ax + By + c = 0. 1/2 y- 1/3 x-1=0
Answer:
2x- 3y = - 6
Step-by-step explanation:
given [tex]\frac{1}{2}[/tex] y - [tex]\frac{1}{3}[/tex] x - 1 = 0
multiply all terms by 6 to eliminate the fractions
3y - 2x - 6 = 0 ( multiply all terms by - 1 )
- 3y + 2x + 6 = 0 ( subtract 6 from both sides )
2x - 3y = - 6 ← in standard form
In parallelogram ABCD , diagonals AC⎯⎯⎯⎯⎯ and BD⎯⎯⎯⎯⎯ intersect at point E, BE=x2−21 , and DE=4x .
What is BD ?
__units
Answer:
BD= 56units
Step-by-step explanation:
Since, Diagnols of a parallelogram bisect each other.
Therefore in parallelogram ABCD where AC and BD are the diagnols wich intersect at Point E, we have, BE=DE
Therefore, x^2-21=4x
x^2-21-4x=0
x^2-4x-21=0
x^2-7x-3x-21=0 [middle term splitting]
x(x-7)+3(x-7)=0
(x+3)(x-7)=0
Hence, x= -3 and x= 7
Since x cannot be negative because no side can have negative values
Therefore, we have x=7
Now, BD= BE+DE [Since E is the intersecting point of BD]
= 4x+x^2-21
= 4(7)+7^2-21
=28+49-21= 56 units
what is the approximate surface area of the cylinder 3mm 16mm (use 3.14 for π)
A. 301.44mm^2
B. 357. 96mm^2
C. 339.12mm^2
D. 370.52mm^2
The formula of a Surface Area of a cylinder:
[tex]S.A.=2\pi r^2+2\pi rH[/tex]
r - radius
H - heihgt
We have r = 3mm and H = 16mm. Substitute:
[tex]S.A.=2\pi(3)^2+2\pi(3)(16)=2\pi(9)+2\pi(48)=18\pi+96\pi=114\pi\ mm^2\\\\\pi\approx3.14\to S.A.\approx114\cdot3.14=357.96\ mm^2[/tex]
Answer: B. 357.96 mm^2The expression 50w+400 represents the amount of money Jenny has in her savings account after an unknown number of weeks. How much money does Jenny originally have in her savings account? Which part of the equation represents the amount of money she will put away each week? Explain your answers.
Answer:
400 originally, and 50 dollars a week from there!!
Step-by-step explanation:
Since the 50 is followed by the variable "w", and the w stands for week, we can believe that Jenny makes 50 dollars a week.
Because the 400 was in the her account to begin with, we know this is the amount she originally had!
Find the length of side x in simplest radical form with a rational denominator
It's the triangle 30° - 60° - 90°.
The sides are in proportion 1 : √3 : 2 (look at the picture).
Therefore we have:
[tex]x=\dfrac{\sqrt6\cdot\sqrt3}{2}=\dfrac{\sqrt{(6)(3)}}{2}=\dfrac{\sqrt{18}}{2}=\dfrac{\sqrt{(9)(2)}}{2}\\\\=\dfrac{\sqrt9\cdot\sqrt2}{2}=\boxed{\dfrac{3\sqrt2}{2}}[/tex]
Answer:
ok
Step-by-step explanation:
The coordinates of point b
Answer:
(3, -1) PLEASE GIVE BRAINLIEST
Step-by-step explanation:
this property says you can rewrite 3 x (4+5) as (3x4) +(3 x 5).
Answer:
distributive property
Step-by-step explanation:
Distributive property says that x(y + z) = (x*y) + (x *z)
The property used in the given expression is
Distributive property of multiplication over addition.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
The distributive property of multiplication over addition states that,
a(b + c) = a x b + a x c
Now,
3(4 + 5) = (3 x 4) + (3 x 5)
This is the Distributive property of multiplication over addition.
Thus,
The property of distributive multiplication over addition is used.
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what is the value of x
enter your answer in the box
Answer:
x = 19
Step-by-step explanation:
3x - 3 = 6(x - 10)
3x - 3 = 6x - 60
+3 +3
3x = 6x - 57
- 6x
- 3x = -57
= 19
Answer:
x = 19Step-by-step explanation:
[tex](3x-3)^{0} =\left[6(x-10)] ^{0}\\[/tex] (opposite angle)
[tex]3x-3=6(x-10)\\ 3x-3=6x-60\\ 60-3=6x-3x\\ 57=3x\\ \frac{57}{3} =x\\ 19=x[/tex]
What is the solution to the system of equations?
y = x – 10
2x + y = 4
(–8, 6)
(–6, 16)
(6, –8)
(16, –6)
Answer:
The solution is the point (6,-8)
Step-by-step explanation:
we have that
The first equation is [tex]y=(1/3)x-10[/tex] instead [tex]y=x-10[/tex]
[tex]y=(1/3)x-10[/tex] -----> equation A
[tex]2x+y=4[/tex] -----> equation B
Solve the system of equations by substitution
Substitute equation A in equation B and solve for x
[tex]2x+[(1/3)x-10]=4[/tex]
[tex](7/3)x=14[/tex]
[tex]x=6[/tex]
Find the value of y
[tex]y=(1/3)(6)-10=-8[/tex]
therefore
The solution is the point (6,-8)
41.073 round each number to the place of the underlined digit. The underline number is 0
Answer:
41.1
Step-by-step explanation:
The number will be cut off after the digit you are rounding off to.
Rewrite the number, but stop at the 0.
41.0
Now you need to decide if the 0 stays as 0 or if it goes up to 1.
When the next digit is from 5 to 9, the last digit you keep goes up 1. When the next digit is 0 through 4, the last digit you keep stays as it was.
Since the first digit that was dropped is a 7, the 0 goes up one unit to 1.
Answer: 41.1
Answer:
41.1
Step-by-step explanation:
If we are rounding at the 0, we have to look at the next digit, which is 7.
Since 7>=5, we will round up. Zero becomes a 1
41.073 becomes 41.1
The area of a rectangular mirror is 15 15/16 square feet. The width of the mirror is 3 3/4 feet. If there is a 5 foot tall space on the wall to hang the mirror, will it fit? Explain. _________ fit because the height is ______ feet.
Answer: The mirror will fit because the height of the mirror is 4 feet.
Step-by-step explanation:
we just divide 15 by 3 3/4 and get the answer of 4.
Yes, the mirror will fit on the wall because its height is approximately 4.25 feet, which is less than the 5-foot tall space on the wall.
Explanation:To determine whether the mirror will fit, we need to calculate its height. Since the area of a rectangle is given by the formula Area = Height × Width, we can find the height by rearranging the formula to Height = Area ÷ Width.
The given area of the mirror is 15 15/16 square feet and the given width is 3 3/4 feet.
After performing the division, we get the height of the mirror to be approximately 4.25 feet.
Since the space on the wall is 5 foot tall and the height of the mirror is less than this, the mirror will fit on the wall. So, the answer is: Yes, it will fit because the height is 4.25 feet.
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The shallowest section of an underground tunnel is -50 feet. The deepest section of the tunnel is -135 feet. How many feet below the shallowest section is the deepest section
A. -95 feet
B. - 185 feet
C. 85 feet
D. 195 feet
Answer:
The answer would be c)85 FEET
Step-by-step explanation:You start with the deepest section(-135) and add the shallowest point(50). the result is an 85 foot difference.
Answer: c 85ft
Step-by-step explanation:
makito answered 70 pecent of 30 test quedtions correctly how many questions did he answer correctly
Answer:
21
Step-by-step explanation:
Please need help on this
Answer:
A: 20 km/hr B: 10 km/hr
Step-by-step explanation:
HELP PLEASE whats the rate of change
Solve the inequality.
4d + 7 ≤ 23
Answer:
d ≤ 4
Step-by-step explanation:
4d + 7 ≤ 23
Subtract 7 from both sides:-
4d ≤ 16
d ≤ 4
[tex]Solution, 4d+7\le \:23\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:d\le \:4\:\\ \:\mathrm{Interval\:Notation:}&\:(-\infty \:,\:4]\end{bmatrix}[/tex]
[tex]Steps:[/tex]
[tex]4d+7\le \:23[/tex]
[tex]\mathrm{Subtract\:}7\mathrm{\:from\:both\:sides},\\4d+7-7\le \:23-7[/tex]
[tex]\mathrm{Simplify},\\4d\le \:16[/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}4,\\\frac{4d}{4}\le \frac{16}{4}[/tex]
[tex]\mathrm{Simplify},\\d\le \:4[/tex]
[tex]\mathrm{The\:Correct\:Answer\:is\:d\le \:4}[/tex]
[tex]\mathrm{Hope\:This\:Helps!!!}[/tex]
[tex]-Austint1414[/tex]
6(3c - 5d +6) using distributive property
Expanding, you get 6(3c) - 6(5d) + 6(6) = 18c - 30d +36
Answer:
18c - 30d +36
Step-by-step explanation:
6(3c - 5d +6)
When we use the distributive property, we distribute the 6 to all the terms inside the parentheses
6*3c - 6*5d +6*6
18c - 30d +36