You can find two equivalent fractions by multiplying or dividing the numerator and denominator by the same number.
For example, if you had 2/3 and you wanted to find an equivalent fraction, you could multiply both the numerator (top number) and denominator (bottom number) by 2.
2/3 * 2/2 = 4/6, so an equivalent fraction of 2/3 is 4/6.
Now to find two equivalent fractions for 2/12: since both the numerator and denominator can be divided evenly by 2, you can divide 2/12 by 2/2.
2/12 / 2/2 = 1/6
1/6 is an equivalent fraction to 2/12.
You can also multiply 2/12 by 2/2 for another equivalent fraction.
2/12 * 2/2 = 4/24, so two equivalent fractions for 2/12 are 1/6 and 4/24.
Two equivalent fractions for 2/12 are 4/24 and 6/36.
To find equivalent fractions for 2/12, we need to multiply both the numerator and denominator by the same non-zero number. This will give us fractions that have different numerators and denominators but represent the same value.
Let's start by finding an equivalent fraction by multiplying both the numerator and denominator by 2:
2/12 x 2/2 = 4/24
The fraction 4/24 is equivalent to 2/12 because both fractions simplify to 1/6 when reduced to their simplest form.
Next, let's find another equivalent fraction by multiplying both the numerator and denominator by 3:
2/12 x 3/3 = 6/36
The fraction 6/36 is also equivalent to 2/12 because both fractions simplify to 1/6 when reduced.
Therefore, two equivalent fractions for 2/12 are 4/24 and 6/36, both of which represent the same value as 2/12, which is 1/6 when simplified.
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Select the correct answer from each drop-down menu.
A triangular piece of rubber is stretched equally from all sides, without distorting its shape, such that each side of the enlarged triangle is twice the length of the original side.
The area of the triangle to times the original area.
The area of the stretched triangle is four times the area of the original triangle
What is a Triangle?
A triangle is a plane figure or polygon with three sides and three angles.
A Triangle has three vertices and the sum of the interior angles add up to 180°
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
The area of the triangle = ( 1/2 ) x Length x Base
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
if a² + b² = c² , it is a right triangle
if a² + b² < c² , it is an obtuse triangle
if a² + b² > c² , it is an acute triangle
Given data ,
Let's assume that the original triangle has sides of length a, b, and c, and that its area is A. Without loss of generality, we can assume that side a is the shortest side.
After the rubber is stretched, each side of the enlarged triangle will be twice the length of its original length. Thus, the lengths of the sides of the stretched triangle will be 2a, 2b, and 2c.
Since the rubber is stretched equally from all sides, we know that each angle of the original triangle will be doubled. Therefore, the stretched triangle will be similar to the original triangle.
The area of a triangle is given by the formula:
A = (1/2) x base x height
where the base and height are the lengths of any two sides of the triangle that are perpendicular to each other.
Since the stretched triangle is similar to the original triangle, we can use the ratios of corresponding sides to find the lengths of the corresponding altitudes. Specifically, we have:
(altitude of stretched triangle corresponding to side 2a) = 2 x (altitude of original triangle corresponding to side a)
(altitude of stretched triangle corresponding to side 2b) = 2 x (altitude of original triangle corresponding to side b)
(altitude of stretched triangle corresponding to side 2c) = 2 x (altitude of original triangle corresponding to side c)
Therefore, the area of the stretched triangle is given by:
A' = (1/2) x (2a) x (2b) x (2/2) + (1/2) x (2b) x (2c) x (2/2) + (1/2) x (2c) x (2a) x (2/2)
Simplifying this expression gives:
A' = 4A
Hence , the area of the stretched triangle is four times the area of the original triangle.
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I need help with this problem
Answer:
Step-by-step explanation:
Let's first find out how many workstations there would be.
(7/8) / (1/16) == (14/16) / (1/16) == 14 workstationsIt says in the problem that there are two classrooms and that they both have the same number of workstations.
14 workstations / 2 classrooms = 7 workstationsThere are seven workstations in each of the two classrooms.
Whats the density of an object with the length of 5.0 cm a height of 3.0 and width of 15.0 cm and a mass of 24 grams
Answer:
The density of the object is [tex]0.1067[/tex] grams per cubic centimeter. (Rounded off to 4th decimal)
Step-by-step explanation:
Density = [Mass/Volume]
Here we have been given the dimensions of the object.
Volume = Height * Width * Length
Volume = [tex]3.0cm*15.0cm*5.0cm[/tex]
=[tex]225cm^{3}[/tex]
Now we can substitute the Mass and the Volume to the density equation.
Density = [Mass/Volume]
=[tex]\frac{24grams}{225cm^{3} }[/tex]
=[tex]0.1067[/tex] grams per cubic centimeter. (Rounded off to 4th decimal)
find the base when the area is 2.5 and the height is 1
so lets say base = x
Then 1*x=2.5
Therefore the base equals 2.5
Hope this helps!
Write a real-world situation that can modeled by the inequality 834 + 14s > 978 - 10s
when you are buying toothbrushes and s is boxes of toothbrushes, and there are 100 tooth brushes per box, 974 > 878
6.58x - 8.36x = 3.98x - 27.33
Round your answer to the nearest hundredth
Answer:
-5.76x=-27.33
-6x=-27
Step-by-step explanation:
you would bring the 3.98 over to the other side, so it would be -3.98+6.58=2.6-8.39=-5.76
the length of a certain rectangle is 5cm more than 3 times its width. if the perimeter of the rectangle is 74 what is the length and width
The perimeter of a rectangle is the sum of all four sides of the rectangle.
(Perimeter = 2width + 2length)
Let's assume the width of the rectangle to be x.
For length, the statement says that is equals to 3 times the width (= 3x) and 5cm more meaning 5cm would be added to 3 times the width.
Width = x
Length = 3x + 5
Perimeter = 2x + 2(3x+5)
74 = 2x + (6x+10)
74 = 8x + 10
solve for x
8x = 74 - 10
x = 64/8, x=8
Width = 8
length = 3(8)+5 = 29
please help!
Cassidy wants to divide 4x^2−2x+3 by x + 2 using synthetic division.
Which answer shows the correct process?
(the answers are in the pictures below)
Refer to the image attached.
Since, we have to divide the polynomial [tex]4x^2-2x+3[/tex] by (x+2) using synthetic division.
We will divide the coefficients 4 -2 3 by -2
First term = 4 will remain same.
Second term = [tex](-2 \times 4) -2 = -8-2 = -10[/tex]
So, second term = -10
Third term = [tex](-2 \times -10)+3 = 23[/tex]
So, third term = 23
So, 4 -10 23 is the correct answer
So, Option 2 is the correct answer.
what is the remainder of (3x^4+2x^3-x^2+2x-14)/ (x+2)
-2(6-x) is the remainder.
Can someone help me out plz
Simplify : (√x + √y ) (√x − √y) (x + y)(x2 + y2)
[tex]Solution, \mathrm{Expand}\::\left(\sqrt{x}+\sqrt{y}\right)\left(\sqrt{x}-\sqrt{y}\right)\left(x+y\right)\left(x^2+y^2\right):\quad :x^4-:y^4[/tex]
[tex]Steps:[/tex]
[tex]\mathrm{Expand}\:\left(\sqrt{x}+\sqrt{y}\right)\left(\sqrt{x}-\sqrt{y}\right):\quad x-y, =\left(x-y\right)\left(x+y\right)\left(x^2+y^2\right)[/tex]
[tex]\mathrm{Expand}\:\left(x-y\right)\left(x+y\right):\quad x^2-y^2, =:\left(x^2-y^2\right)\left(x^2+y^2\right)[/tex]
[tex]\mathrm{Expand}\:\left(x^2-y^2\right)\left(x^2+y^2\right):\quad x^4-y^4, =:\left(x^4-y^4\right)[/tex]
[tex]\mathrm{Expand}\::\left(x^4-y^4\right):\quad :x^4-:y^4, =:x^4-:y^4[/tex]
The correct answer is [tex]x^4-y^4[/tex]
Hope this helps!!!
The simplification involves the use of the difference of squares identity on the first two terms, yielding (x - y). There's no further simplification possible for the remaining terms (x + y)(x^2 + y^2) under general conditions, resulting in the expression (x - y)(x + y)(x^2 + y^2).
The question involves the simplification of the given expression (
oot{x} + oot{y})(oot{x} - oot{y})(x + y)(x^2 + y^2). To simplify it, we will use the properties of square roots and algebraic identities.
Firstly, we use the difference of squares identity on the first two terms: (
oot{x} + oot{y})(oot{x} - oot{y}) = x - y.
Now, we look at the second pair of terms and realize that we can reshape the given expression using the properties of exponents: (x + y)(x^2 + y^2). Since both (x + y) and (x^2 + y^2) represent sums of powers of x and y, there is no direct simplification possible without additional constraints on x and y.
Therefore, the multiplication of these expressions gives us (x - y)(x + y)(x^2 + y^2) without further simplification under general conditions.
Which equation represents a line that passes through 5,1 and has a slope of 1/2
(5,1)
x=5
y=1
m=1/2
Use this formula
y-y1=m(x-x1)
y-1=1/2(x-5)
y-1=x/2-5/2
Isolate for y
y=x/2-3/2
Hope this helps.
Answer:x-2y=3
Step-by-step explanation:
Given
Lines passes through (5,1) and slope of 0.5
i.e. [tex] tan\theta =0.5[/tex]
where [tex]\theta [/tex]is the angle made by line with horizontal
equation of line can be given by
[tex]\frac{y-1}{x-5}=tan\theta [/tex]
2y-2=x-5
x-2y=3 is the required line
HALPPPPP SHOW WORK PLZZZZZZZZZZZZZ
1) 4/5
2) -62/13
3) 1/9
4) 527/42
I only answered these four questions.
Hope this helps. By the way they are all in the exact form.
To solve the multiplication problem and simplify the fractions, follow these steps:
Multiply 32/5 × 513/1:
(32/5) × (513/1) = (32 × 513) / (5 × 1) = 16416 / 5
Now, let's find how many novels Jeffrey owns. He owns 230 books, and of them are novels:
Number of novels = (Number of novels) / Total books
Number of novels = (3/9) × 230
Number of novels = (1/3) × 230
Number of novels = 230 / 3
Number of novels = 76⅔ (mixed number)
To simplify the mixed number 76⅔, remember that ⅔ is equivalent to 2/3.
76⅔ = 76 + ⅔ = 76 + 2/3 = (76 × 3 + 2) / 3 = 230 / 3
So, Jeffrey owns 76⅔ novels.
For the standardized test practice, we have two fractions:
Fraction of students wearing school colors = 1/4
Fraction of students wearing school colors in the 6th grade = 3/20
To find the fraction of students wearing school colors in the 6th grade, we can multiply these fractions:
Fraction = (1/4) × (3/20) = 3/80
So, the fraction of students at the school dance who wore the school colors and were in the 6th grade is 3/80.
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what is f(-3) if f(x) = 2x+1 + 5
Well we know that our function is -3, so we can plug this into the equation. \
f(x) = 2x + 1 + 5
f(-3) = 2(-3) + 1 + 5, now from here we simplify (:
-6 + 1 + 5 then finally we combine our like terms
-6 + 1 equals -5, then -5 + 5 equals 0
our final answer is zero if our function is f(-3) ((((((((((((((((((((((((((((((:
If the shape of an object changes the perimeter will always change true or false
The answer is false due to the object is changes shape not size
ali drove 268 miles using12 gallons of gas at this rate how many miles would he drive using 9 gallons of gas
Divide total miles driven by the total amount of gas used to find the number of miles per gallon.
Then multiply that by the number of gallons you want to find out:
268 miles / 12 gallons = 22.333 miles per gallon.
22.333 miles per gallon x 9 gallons = 201 total miles.
What is the result of dividing x3−7 by x + 2?
The result of the division of x³-7 by x+2 will be (x²−2x+4)−15/(x+2).
What is the arithmetic operator?Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,
Division = divide any two numbers or variables called division.
For example 4/8
Multiplication = to multiply any two or more numbers or variables called multiplication.
Division of (x³-7) ÷ (x+2)
Keep quotient x² → (x³-7) - (x³+2x²) ⇒ remainder = -7-2x²
Next quotient -2x → (x³-7) - (-2x²-4x) ⇒ remainder = -7+4x
Next quotient 4 → (x³-7) - (8+4x) ⇒ reminder = -15
Therefore,
(x³-7) ÷ (x+2) = (x²−2x+4)−15/(x+2).
Hence "The result of the division of x³-7 by x+2 will be (x²−2x+4)−15/(x+2)".
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Write the following products using exponents to express the results in a simpler form. (3 inches)(5 inches) and (5 feet)(2 feet)?
Answers:
___________________________________________________________
1) (3 inches)(5 inches) = (3 in)(5 in) = 3 * 5 * in * in = 15 * in * in = " 15 in² " .
___________________________________________________________
2) (5 feet)(2 feet) = (5 ft)(2ft) = 5 * 2 * ft * ft = 10 * ft * ft = " 10 ft² " .
___________________________________________________________
Final answer:
Exponents are used for repeated multiplication of the same number, hence, (3 inches)(5 inches) and (5 feet)(2 feet) cannot be simplified using exponents since they involve different numbers. Exponents and conversion factors are distinct mathematical tools, with the latter used for converting units of measure.
Explanation:
The question addresses using exponents to express products of the same units in a simpler form. The product of (3 inches)(5 inches) suggests multiplying these two measurements, however, when writing this product using exponents, we should consider that both are units of length, and thus their product will result in a unit of area, which is square inches (in2). We cannot simplify this expression further using exponents as they are not repeated multiplication of the same number.
On the other hand, for the product (5 feet)(2 feet), we again get an area, but this time in square feet (ft2). Still, there's no need for using exponents in this expression because we are not dealing with repeated multiplication of the same number.
It is important to note that exponents are used to represent repeated multiplication of the same number. For example, if we had (5 inches)(5 inches), we could write this as 5 inches squared (5 in)2, because it's 5 inches multiplied by itself. On the contrary, when multiplying different numbers, exponents don't apply.
When converting between different units of measure, as in converting feet to inches, we use conversion factors. For instance, 1 foot equals 12 inches, so by multiplying feet by 12, we can convert it to inches. Similarly, inches can be converted to feet by dividing by 12.
Vanessa buys a strip of 25 postage stamps. The strip of stamps is 21 7/8 inches long. How long is a strip after Vanessa uses 1 stamp?
Answer:
7/8
Step-by-step explanation:
The strip is 21 7/8 inches long. You need to make this into an improper fraction so you multiply 21x8= 168 and then add 7 to that which = 175. So the improper fraction is 175/8 (instead of 21 7/8). Now you just divide 175 by 25 which is 7. Each stamp is 7/8 inches long.
To find the new length of the strip after Vanessa uses one stamp, we first divide the initial length of the strip by the total number of stamps to find the length of one stamp. We then subtract this from the original length of the strip. The new length is 21 inches.
Explanation:This question is asking how long a strip of stamps is after Vanessa uses one of them. Given that the original strip is 21 7/8 inches long and includes 25 stamps, we can find the length of one stamp by dividing the total length of the strip by the total number of stamps. So, the length of one stamp is 21 7/8 ÷ 25.
We then subtract the length of this one stamp from the original length of the strip to find the new length:
Length of one stamp = 21 7/8 inches ÷ 25 = 0.875 inchesNew length of the strip = 21 7/8 inches - 0.875 inch = 21 inchesThe new length of the strip, after Vanessa uses one stamp, is therefore 21 inches.
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WILL MARK BRAINLIEST !! PLEASE HELP ME OUT !!!
To begin, Arnold should sort on whether or not it is a screw, nut, bolt.
This might only be # 1 and 3 but you should be able to put together a number line with the information I provided. Some of the #s may look different but that is because I used the Least Common Denominator. Hope this helps!
Screws: Least to greatest (top = least)
4 Screws 4/64” x 3” long
12 Screws 5/64” x 3” long
3 Screws 6/64” x 4” long
6 Screws 11/64” x 4” long
16 Screws 24/64” x 2” long
1 Screw 28/64” x 3” long
1 Screw 32/64” x 3” long
1 Screw 48/64” x 2” long
Hex Bolts: Least to greatest by diameter (top = least)
4 Hex bolts 1.5” x 4” long
4 Hex bolts 1.875” x 4” long
1 Hex bolt 2.25” x 2” long
6 Hex bolts 3.375” x 3” long
4 Hex bolts 3.75” x 3” long
20 POINTS If each person paid an equal amount, who would save the most money?
My Numbers $47.94, $47.94, $48.60, $45
obviously $48.60 would save more.
Answer,
48.60
Hope this helps - Laura
:-)
solve for x b=1/6π n ^2 x
Answer:
[tex]\large\boxed{x=\dfrac{6b}{\pi n^2}}[/tex]
Step-by-step explanation:
[tex]b=\dfrac{1}{6}\pi n^2x\qquad\text{multiply both sides by 6}\\\\6b=\pi n^2x\qquad\text{divide both sides by}\ \pi n^2\neq0\\\\\dfrac{6b}{\pi n^2}=b[/tex]
Taylor wants to read 2 books. One book has 232 pages and the other has 184 pages. She needs to return the books to the library in 13 days.
How many pages does Taylor need to read each day in order to get the books back to the library in time?
(enter answer here)
i think you add 232 and 184 then divide by 13.
Hope this helps!
15 points! Thank you
[tex]10x^2+27x-28=10x^2+35x-8x-28=5x(2x+7)-4(2x+7)\\\\=(2x+7)(5x-4)\\\\Answer:\ D.\ 2x+7[/tex]
The sum of two consecutive numbers is -105. What are the numbers?
Which of the following expresses 16 + 36 by using the GCF of the two numbers?
4(4 + 9)
4(4 + 32)
8(2 + 28)
8(8 + 28)
16 + 36 = 52 so the answer would be A) 4(4 + 9) because that equals 52 as well.
Graph the feasibility region represented by the given inequalities and find the maximum profit if P=4x+5y. x>or=5 y
One of these doesn't seem to be required information for a feasibility region. Are you sure that these are the correct equations?
HELP 1/7z+2=-6/7z what’s the solution set please send help I’m suffocating under homework
Isolate the z. Note the equal sign. Subtract 1/7z to both sides
1/7z (-1/7z) + 2 = -6/7z (-1/7z)
2 = -6/7z - 1/7z
Simplify. Combine like terms
2 = -7/7z
2 = -1z
Isolate the z. Divide -1 from both sides
(2)/-1 = (-1z)/-1
z = 2/-1
z = -2
-2 is your answer
hope this helps
1.588 x 10 to the negative 4th power
Given the parent function f(x)=x2, what is the new equation if the function is translated 4 units to the right and 3 units down
Is the x2 supposed to be an exponent or no?
The new equation for the translated parent function f(x) = x^2, shifted 4 units right and 3 units down, is f(x) = (x - 4)^2 - 3.
Explanation:To translate the parent function f(x) = x^2 by 4 units to the right and 3 units down, we need to make the following adjustments:
The translation to the right will be represented by replacing x with (x - 4) in the equation.The translation down will be represented by subtracting 3 from the equation.So, the new equation is f(x) = (x - 4)^2 - 3.
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