Simplify each rational expression. State any restrictions on the variable.
[tex]\frac{c^{2}-8c+12 }{c^{2}-11c+30 }=\frac{(c-2)}{(c-5)}[/tex]
How the rational expression is simplified?
[tex]\frac{c^{2}-8c+12 }{c^{2}-11c+30 }\\\\= > \frac{(c-2)(c-6)}{(c-5)(c-6)} \\= > \frac{(c-2)}{(c-5)}[/tex]
What are the restrictions on the variable ?
If c= 5 , the denominator becomes,
[tex]c^{2} -11c+30[/tex] =25-55+30=0
⇒ [tex]\frac{c^{2}-8c+12 }{c^{2}-11c+30 }=\infty[/tex]
If c= 6 ,the denominator becomes,
[tex]c^{2} -11c+30[/tex] = 36- 66+30=0
⇒ [tex]\frac{c^{2}-8c+12 }{c^{2}-11c+30 }=\infty[/tex]
So, the restrictions on the variable are: c≠ 5,6
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Use the order of operations to simplify each expression.
(8+5 × 2)/ 12
Using the order of operations BODMAS to simplify each expression
( 8+ 5 × 2 ) /12 is equal to 1.5.
As given in the question,
Given expression is ( 8+ 5 × 2 ) /12
Simplify each expression by using the order of operations BODMAS is given by
( 8+ 5 × 2 ) /12
= ( 8 +10 ) /12
= 18 /12
= 3 /2
=1.5
Therefore, using the order of operations BODMAS to simplify each expression ( 8+ 5 × 2 ) /12 is equal to 1.5.
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Suppose the midpoint of line RT is M=(3,0). If R has the coordinates (-1,-4), what are the coordinates of T?
The coordinates of the point T is a T(2,-4).
According to the statement
We have to find that the the coordinates of T.
So, For this purpose, we know that the
Coordinates are a set of values which helps to show the exact position of a point in the coordinate plane.
From the given information:
the midpoint of line RT is M=(3,0). If R has the coordinates (-1,-4),
Then
For the coordinates of the t
We know that the from the description of the given points of the line RT
T = R+M
It means the coordinates of the t is the sum of the coordinates of the r and the M.
Then
T (x,y) = R(-1,-4) + M(3,0)
T (x,y) = R+M (-1+3,-4+0)
T (x,y) = R+M (2,-4)
So, The coordinates of the point T is a T(2,-4).
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Find the distance along Broadway between 37th Street and 36th Street.
The distance between 37th St. and 36th St. is
x= 275ft
What is a similar triangle?Similar triangles are those that share at least one vertex and the angular value between the sides associated to their sides is the same, which makes them proportional in their dimensions (same type of triangle).
To solve this problem we will use the relation of similar triangles, if we raise the equation we have the following way:
x /275 = 220/220
Proportion of the sides
x/275 = 1
x = 275 ft , is the distance x between the lanes N° 37 and 36.
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Triangle ABC is mathematically similar to
triangle ADE. Work out the length of DE.
Separate into
two triangles.
D
B
В.
25 cm
E
C
.cm (2
A
30 cm
12cm
cn
Answer:
25 cm
Step-by-step explanation:
triangle abc is Mathematically similar
Need asap last question on a exam
The zoo needs to replace some of the railroad tracks that support their train ride. The total length of the track is 500 feet, and there are three sections that need to be replaced. These sections measure 62/2 83/8 and 63/4 feet. How much of the zoo railroad track does not need to be replaced?
Based on the calculations, the length of the zoo railroad track which does not need to be replaced is equal to 3543/8 or 442.875.
What is a fraction?A fraction can be defined as a numerical quantity which isn't expressed as a whole number. This ultimately implies that, a fraction is simply a part of a whole number.
The parts of a fraction.In Mathematics, a fraction comprises two (2) main parts and these include the following:
NumeratorDenominatorIn order to determine the length of the zoo railroad track which does not need to be replaced, we would add all of the length of the zoo railroad track that need to be replaced and then subtract this value from the total length of the zoo railroad track as follows:
Length of replacement = 62/2 + 83/8 + 63/4
Note: Lowest common denominator (LCM) = 8.
Length of non-replacement = (248 + 83 + 126)/8
Length of non-replacement = 457/8
Length of replacement = 500 - 457/8
Length of replacement = (4000 - 457)/8
Length of replacement = 3543/8 or 442.875.
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A work survey found that 8 out of every 10 employees went on vacation last summer. If 3 employees' names are randomly chosen, with replacement, what is the probability that all 3 employees went on vacation last summer?
These are independent events because the likelihood of the first event has no bearing on the probability of the second event. Let V represent choosing holidaymakers from the previous summer.
What is probability ?
Probabilities are mathematical explanations of the likelihood that an event will occur or that a proposition is true.
P(V)= (8/10)*(8/10)*(8/10)
P(V)= 512/1000
= 51.2%.
The likelihood of an event is represented by a number between 0 and 1, with 0 typically signifying impossibility and 1 typically signifying certainty.
Basic probability is governed by three primary rules: the addition rule, the multiplication rule, and the complement rule.
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Simplify: [tex]\sqrt[3]{135}[/tex]
Aadesh joins an science club. it is $ 85 to join for the first month and then $ 125 for each month after that. he stays in the club for 14 months. how much did aadesh pay altogether?
Answer:
$1710
Step-by-step explanation:
multiply 125 by 13 which is 1625 then add 85 which gives you a total $1710
where RS=3y+3=2y+8 and RT=31 what is the value of y
The value of y in the line segment is 4
How to find the variable in a line segment ?RT is the total line segment.
Therefore,
RS = 3y + 3
ST = 2y + 8
RT = 31
Hence,
RT = RS + ST
31 = 3y + 3 + 2y + 8
31 = 3y + 2y + 3 + 8
31 = 5y + 11
31 - 11 = 5y
20 = 5y
divide both sides by 5
20 / 5 = 5y / 5
y = 4
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Alex owns three times as many brown shoes as red shoes, twice as many
black shoes as brown shoes, and four times as many white shoes as red
shoes. What is the ratio of the number of white shoes to the number of black
shoes he owns?
The ratio of the number of white shoes to the number of black
shoes Alex owns is 2:3
Let the number of red shoes be x
Then from the given information, we know that
brown shoes = 3 times red shoes = 3x
black shoes = 2 times brown shoes = 2(3x)= 6x
white shoes = 4times red shoes = 4x
We need to find the ratio between the number of white shoes and the number of black shoes owned by Alex
So, the ratio of the number of white shoes to the number of black
shoes he owns is number of white shoes : number of black shoes
= 4x: 6x
which can be simplified as 2: 3
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The formula C= 2nr is used to calculate the circumference of a circle. Solve this formula for r.
Answer:
r = C/2n
Step-by-step explanation:
that's the solution above
Mary's coffee shop makes a blend that is a mixture of two types of coffee. type a coffee costs mary $5.35 per pound, and type b coffee costs $4.15 per pound. this month, mary made 181 pounds of the blend, for a total cost of $853.15. how many pounds of type b coffee did she use?
Mary used 96 pounds of type b coffee this month.
Using algebraic expression and equation, we can solve how much of each type of coffee did Mary used that month.
An algebraic expression is a number, variable, or the combination of both and operational symbols. On the other hand, an equation is the equality of two expressions separated by "=".
Given that that month, Mary made 181 pounds of the blend that is a mixture of two types of coffee, we can express this as:
181 = a + b
where a = pounds of type a coffee that costs $5.35 per pound
b = pounds of type b coffee that costs $4.15 per pound
Also, the total cost of the blend that month is $853.15, which is the sum of the total cost of the two types of coffee. We can express that as:
$853.15 = $5.35(a) + $4.15(b)
Using substitution method to solve the two equations,
181 = a + b ⇒ a = 181 - b
$853.15 = $5.35(181 - b) + $4.15(b)
853.15 = 968.35 - 5.35b + 4.15b
5.35b - 4.15b = 968.35 - 853.15
1.2b = 115.2
b = 96
a = 181 - b
a = 181 - 96
a = 85
Hence, Mary used 85 pounds of type a coffee and 96 pounds of type b coffee that month.
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Use your results from Exercises 1-6 to determine whether the given measures define 0 , 1,2, or infinitely many acute triangles. Justify your answers.
a=6, b=9, m
Two sides without an angle measurement, such as a = 6 m and b = 9 m, can be used to create an infinite number of acute triangles.
How many distinct acute triangles can we make, for instance, if our side lengths are 6 m and 9 m and our angle value ranges from 0 to 90 degrees?
Create a triangle with a 45-degree angle, sides that are 10 and 10 meters long, and a third side that can be stretched to the required length. You've constructed a triangle.
We can create a whole different Acute triangle that is identical to this one by altering the length and angle of the third side.
Never overlook picking the side angles and lengths. It's possible that you'll choose to proceed in a different way. There are an infinite amount of distinct triangles that can be created with the same angles.
As a result, we can make an infinite number of acute triangles using a single angle and a single side length.
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State whether the sentence is true or false. If false, replace the underlined word or number to make a true sentence.
If lines p and q are parallel, then angles 3 and 6 are congruent.
The statement "If lines p and q are parallel, then angles 3 and 6 are congruent" is false because "If lines p and q are parallel, then angles 3 and 6 are supplementary".
Given,
The statement "If lines p and q are parallel, then angles 3 and 6 are congruent"
We know,
when two parallel lines are intersect by a transversal then the interior angles on the same side of the transversal is supplementary.
Here, ∠3 and ∠6 are interior angles on the same side of the transversal, So the ∠3 and ∠6 are supplementary
So, the correct statement is "If lines p and q are parallel, then angles 3 and 6 are supplementary"
Hence, the statement "If lines p and q are parallel, then angles 3 and 6 are congruent" is false because "If lines p and q are parallel, then angles 3 and 6 are supplementary".
The complete question is:
State whether the sentence is true or false. If false, replace the underlined word or number to make a true sentence.
If lines p and q are parallel, then angles 3 and 6 are congruent.
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Which is true about the triangles’ perimeters? 2 triangles labeled Triangle A and Triangle B. Triangle A has 3 sides, each labeled 9 kilometers. Triangle B's base is labeled 15 kilometers. Its other 2 sides are each labeled 8 kilometers.
Step-by-step explanation:
lex x be the common ratio/ scale factor
the sides and 13x
sum of the sides defines perimeter
that is
5x12x13x=15
30x=15
x=15/30
x=0.5
the sides of the triangle are 0.5(5)=2.5
0.5(12(=6
0.5(12)=6.5
2.5,6 6.5 All in inches
PLEASEE HELP I WILL GIVE BRAINLIST PLEASE ITS DUE TONIGHTTTTT!! ILL GIVE EXTRA POINTS PLEASE NO LINKS
What is the correct answer to
5
.
78
×
10
5
0
.
000002
?
Multiple choice question.
cross out
A)
2
.
89
×
10
8
cross out
B)
2
.
89
×
10
9
cross out
C)
2
.
89
×
10
10
cross out
D)
2
.
89
×
10
11
pls that was all my points i had left
The option that identifies the mistake that Miguel made is that Miguel found 5.78 ÷ 2 as 2.89, but incorrectly found the power of 10.
How to calculate the values?It should be noted that the number given is illustrated as:
5.78 × 10^5× 0.000002
= 2.89 × 10^5
Therefore, the mistake that Miguel made is that Miguel found 5.78 ÷ 2 as 2.89, but incorrectly found the power of 10.
In conclusion, the correct option is D
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Recognize the Error Miguel found the quotient
5
.
78
×
10
5
0
.
000002
as 0.289. Which of the following correctly identifies his mistake
Find the slope of the line that passes through the two points. (4,5) and (1,8)
The slope between the two given points (4,5) as well as (1,8) is -1.
What exactly is the slope of a line?A line's slope is a measure of its steepness & direction.
The slope of a line is defined as a change in y coordinate in relation to a change in x coordinate.
The net change in y coordinates is Δy, while the net change in x coordinates is Δx.As a result, the y coordinate change in relation to the x coordinate change could be composed as,m = Δy/Δx
where,m is the slope
Slope is also written as tan θ = Δy/Δx. Where, tanθ is also called as the line's slope.Now, as per the stated question;
The slope of a line can be calculated using only two points on a straight line. With the coordinates of two points, we can employ the slope of line formula.
Let the coordinates of those 2 points from where the line is passing is;
P1 = (x₁, y₁)
P2 = (x₂, y₂)
The slope of the line is estimated as;
Slope = m = tan θ = (y₂ - y₁)/(x₂ - x₁)
The values of the coordinates are given as;
(x₁, y₁) = (4,5) and,
(x₂, y₂) = (1,8)
Substitute the given values of coordinates in the formula to get the slope;
m = (8 - 5)/(1 - 4)
m = 3/(-3)
m = -1
Therefore, given the coordinates of such two points, the slope of a line passing through them is found to be -1.
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Solve the equation. Find the value of x.
2(-3x) + x = 5
Answer:
x = -1
Step-by-step explanation:
1. Remove parentheses
-2 * 3x + x = 5
2. Multiply
-6x + x= 5
3. Add like terms
-5x = 5
4. Divide both sides by -5
-x = -1
Maya has c decks of cards. Each deck has 52 cards in it. Using c, write an expression for the total number of cards Maya has.
Write the equation of the line in slope-intercept form.
-7-y=-3x
The equation of the line in slope-intercept form is y = 3x + (-7) .
The equation of a line in slope-intercept form can be written as follows,
y = mx + c equation 1
m in the above equation represents slope of the line and c represents the intercept.
The given equation is -7 -y = -3x .
To get the equation of the line in slope-intercept form we need to convert the given equation in the format of equation of a straight line i.e., equation1. So, now we will rearrange the given equation as
-7 -y = -3x
⇒ y = 3x + (-7) equation 2
On equating equation 1 and equation 2, we will get
Slope of the line = m = 3
Intercept = c = -7
The equation of the line in slope-intercept form is y = 3x + (-7) .
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i need help solving this problem
Answer:
The answer is x=14
Step-by-step explanation:
(4x14 - 1)
(56 - 1)
Hope this helps ( ˊᵕˋ )♡
-1/15 + (-3/5)= answer it pls
Answer:
-2/5 or -10/15
Step-by-step explanation:
find the common denominater in this case you can multiplie 5 by 3 to get 15
no your question looks like -1/15+-9/15 just add -1 and -9 which gets you -10 so now you end up with -10/15 if you want it simplified just divide by 5 and you get -2/3
Niles and Bob sailed at the same time for the same length of time. Niles' sailboat traveled 50 miles at a speed of 10 mph, while Bob's motorboat traveled 65 miles at a speed of 13 mph. For how long were Niles and Bob traveling?
what are the multiples of 2 from 101 to 200??
The multiples of 2 from 101 to 200 will be all the even numbers starting from 102 to 200.
What are multiples?It should be noted that multiples simply mean the product that can be gotten when a number is multiplied by another number.
It should be noted that the multiples of 2 from 101 to 200 will be all the even numbers starting from 102 to 200.
In this case, the odd numbers aren't multiple of 2.
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PLEASE HELP! rewrite the equation in standard form
Answer:
16x + 10y = 21
Step-by-step explanation:
the equation of a line in standard form is
Ax + By = C ( A is a positive integer and B, C are integers )
given
[tex]\frac{4}{3}[/tex] x + [tex]\frac{5}{6}[/tex] y = [tex]\frac{7}{4}[/tex]
multiply through by 12 ( the LCM of 3, 6 and 4 ) to clear the fractions
16x + 10y = 21 ← in standard form
Which of the following can be added to the number indicated on the number line above to sum to 0?
OA 0.6
OB. 1.4
OC -1.4
OD. -0.6
Answer:
1.4 should be added..................
What is the step by step solution to: x^2 -6x +9 =0
Answer:
Step-by-step explanation:
x²-6x+9 = 0
Factor
(x-3)(x-3) = 0
x = 3
Answer:
x = 3
Step-by-step explanation:
We need to find to numbers that sum up to make -6 but their product is +9 :
-3 and -3 will do :
Now we split -6x into -3x and -3x :
x² -3x -3x + 9 = 0
Factorise the first 2 terms:
x(x-3)
Keeping the terms inside the bracket the same as the 1st one factorise the next 2 terms :
x(x-3)-3(x-3) = 0
Keep 1 bracket and make another bracket out of the terms that are outside the brackets :
(x-3)(x-3) = 0
Using the integer rule :
a × 0 = 0
We know that one of these brackets are equal to zero :
x-3= 0
Add 3 to both sides :
x = 3
The other bracket is the same so our final answer is x = 3
Hope this helped and have a good day
It would be nice of you to give brainliest
Assume that you have agreed to use a cellular plan that charges a price of p=3q+500 dollars for using q GB of data. Determine a formula for q that describes the amount of data you can use in terms of the amount of money that you are willing to spend.
The linear equation that describes the amount of data you can use in terms of the amount of money that you are willing to spend is q= (p-500)/3
P=3q + 500 is a linear equation where p is the price of the cellular plan and q is the amount of data used in the form of GB
In order to form a linear equation that describes the amount of data you can use in terms of the amount of money that you are willing to spend, we just need to shuffle the linear equation in order to get the coefficient if q as 1
First step, we need to move 500 from right hand side to left hand side which would change the sign from + to -.
=p - 500 = 3q
Second step, we need to move 3 from right hand side to left hand side which would change the sign from × to ÷.
= (p-500)/3 = q
Which can also be written as q= (p-500)/3
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What is the quotient of 19.6 divided by 0.4?
0.049
0.49
4.9
49
Answer:
49
Hope this hleps :)
Step-by-step explanation:
19.6 ÷ 0.4 = 49
Check:
49 × 0.4 = 19.6 ✓
