According to the question, the given rational expression can be simplified and as shown below:
Rational expression = [tex]\frac{x^{2} -7x+10}{x^{2} -8x+15}/\frac{4-x^{2} }{x^{2} +3x-18}[/tex]
To simplify the given rational expression, calculate the factors of the numerator as well as denominator. And later divide it from each other. These expressions are also called as polynomial expressions.
Rational expression = [tex]\frac{(x-5)(x-2)}{(x-3)(x-5)}/\frac{(2-x)(2+x)}{(x+6)(x-3)}=\frac{-(x+2)}{(x+6)}[/tex]
The final expression of the given equation is [tex]\frac{-(x+2)}{(x+6)}[/tex] .
What is polynomial expression?
Polynomial expression are those equation whose highest degree is two. It is also called as quadratic equation. And it is simplified by performing the factors on the given expressions.
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whats the gcf of 11 and 19?
Answer:
1
Step-by-step explanation:
which is a true statement? y=6x+3 the slope is 6 and the point passes through (-2,-9)__x+3=12 the slope is 1/3 the point passes through (-3,5)___ 4x-5y=35 the slope is 4/5 the point passes through (-3,5)__y=-2x-4 the slope is -2 the point passes through (-1,-6)
Answer:
y=6x+3
Step-by-step explanation:
Draw it on a graph, then use rise over run, 6/1 and you get 6.
Translate the following expression the product of a number and 3 decreased by 5
F (x ) = 3x-5
Solution :
Expression: An expression is a number, a variable, or a combination of numbers and variables and operation symbols
Education: An equation is made up of two expressions connected by an equal sign.
Product of a number by 3 and decreased by 5
let the number be x
product a number by 3 =3x
number is decreased by 5 = -5
Then,
F (x ) = 3x-5
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what is the answer to -5 - (-9) =
Answer: 4
Step-by-step explanation:
= Multiply -1 by -9 to change 9 to a positive number
= Add -5 to 9 (-5 + 9 = 4)
= 4
Simplify each expression. (16)³/₄
The simplified expression is 8
To find the simplified form of the mentioned expression, we will first simplify the value in bracket. Then, multiply the powers to solve it.
As per the known fact, 4² and 2⁴ result to give the number 16.
Expression = (2⁴)³/₄
Now, again as per the known fact, the exponents can be multiplied.
Exponents = 4×(3/4)
Cancelling 4 as it is common in both numerator and denominator
Exponents = 3
Putting the resultant exponent back to the expression -
Expression = 2³
Taking cube -
Expression = 2×2×2
Performing multiplication
Expression = 8
Hence, the simplified form of expression is 8
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Which expression is equivalent to
√81/100
A. √9/10
B. 9/10
C. 9/50
D. 9√10/10
===================================================
Work Shown:
[tex]\sqrt{\frac{81}{100}}\\\\\\\frac{\sqrt{81}}{\sqrt{100}}\\\\\\\frac{\sqrt{9^2}}{\sqrt{10^2}}\\\\\\\frac{9}{10}\\\\\\[/tex]
Therefore, [tex]\sqrt{\frac{81}{100}}=\frac{9}{10}\\\\\\[/tex]
--------------------
Explanation:
I broke up the single square root to make a fraction of square roots. Then I rewrote 81 as 9^2, and 100 as 10^2. This is so the square roots cancel out with the squares.
The general rule is that [tex]\sqrt{\text{x}^2} = \text{x} \ \text{ , where x} \ge 0[/tex]
Carolyn and Gershon are competing to see who can raise the most money for cancer research. Carolyn’s parents gave her $100, and she raised $15 a day. Gershon’s parents gave him $50, and he raised $15 a day. If they continued at the same rate, who won the contest?
Carolyn will win the contest as the money raised by her is more than the money raised by Gershon.
We are given that:
For Carolyn:
Money given by parents = $ 100
Money she raises every day = $ 15
For Gershon:
Money given by parents = $ 50
Money he raises every day = $ 15
Let the number of days a contest lasts be x.
So, the equations for both will be:
For Carolyn:
100 + 15 x
For Gershon:
50 + 15 x
By comparing, we get that:
Money raised by Carolyn > Money raised by Gershon.
Therefore, we get that, Carolyn will win the contest as the money raised by her is more than the money raised by Gershon.
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Solve each equation. If necessary, round to the nearest ten-thousandth. log x²=2
The solution of the given equation by rounding off it to the nearest ten-thousandth is 2.7182.
What is a round-off of the digit?
In mathematics, a round-off is defined as an approximation of the given number to a fewer number of significant digits by taking into consideration some rules.
For eg: 13.58 ~ 13.6
Solving the given equation: log x² = 2
We are given a logarithmic expression: log x² = 2 —- 1
We know that log x² = 2 log x and log (ab) = log a + log b
Using in equation 1, we have,
2 log x = 2
log x = 1
Using exponential on both sides, we have
e^(log x) = e^1
x = e
x = 2.7182
Hence, the solution of the given equation rounded off to the nearest ten-thousandth is 2.7182.
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Rio has 3/4 liters of milk. He uses 1/3 of the milk to make tea. How much milk does Rio use for the tea?
Answer:
5/12
I'm assuming this means how much milk is left because it tells how much milk was used in the question
Step-by-step explanation:
Convert to common denominator and you get 9/12 of milk - 4/12 of milk and you get 5/12
5. The sequence of numbers below is missing the
fourth value. Which of the following is the form
of the missing value in its lowest terms?
3/11, 6/16,9/21,__, 15/31, 18/36
a. 12/25
b. 4/13
c 6/13
d. 1/2
E.7/26
Answer: A i think
Step-by-step explanation:
Solve each equation. Round to the nearest ten-thousandth. Check your answers.
5-3x=-40
After solving the equation, x = 15 is the value of x in 5-3x = -40 .
⇒ 5 - 3x = -40
⇒ - 3x = -40-5
⇒ - 3x = -45
⇒ 3x = 45
⇒ x = 45/3
⇒ x = 15
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.
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pls help with this question attached
The value of equation P (x) = [tex]2[/tex] + [tex]\frac{x}{2}[/tex] + [tex]x^{2}[/tex] - [tex]\frac{x^{2} }{3}[/tex] when x = (-1) is P(-1) = [tex]\frac{13}{6}[/tex]
P (x) = [tex]2[/tex] + [tex]\frac{x}{2}[/tex] + [tex]x^{2}[/tex] - [tex]\frac{x^{2} }{3}[/tex]
If the value of x = -1
P (-1) = 2 + [tex]\frac{-1}{2}[/tex] + [tex](-1)^{2}[/tex] - [tex]\frac{(-1)^{2} }{3}[/tex]
P (-1) = 2 - [tex]\frac{1}{2}[/tex] + 1 - [tex]\frac{1}{3}[/tex]
The above equation consist of fractional numbers as well as the whole numbers to therefore it is not possible to apply the operations in this particular conditions.
Equation is statement which equates two algebraic expressions.On taking LCM for the denominators of the fractional numbers (2 , 3), we get 6 as the Least Common Multiple.
To apply the sum and difference operation, we need to make the denominators of all the terms same.
[tex]2 * \frac{6}{6} = \frac{12}{6}[/tex][tex]\frac{1}{2} * \frac{3}{3} = \frac{3}{6}[/tex][tex]1 * \frac{6}{6} = \frac{6}{6}[/tex][tex]\frac{1}{3} * \frac{2}{2} = \frac{2}{6}[/tex]P (-1) = [tex]\frac{12}{6} - \frac{3}{6} + \frac{6}{6} - \frac{2}{6}[/tex]
P (-1) = [tex]\frac{12-3+6-2}{6}[/tex]
P (-1) = [tex]\frac{13}{6}[/tex]
Value of the equation P when 'x' is replaced by (-1) will be [tex]\frac{13}{6}[/tex]
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Question 3 of 10
Will the answer to the subtraction problem below be odd or even?
9297-9178 = ?
OA. Odd
OB. Even
SUBMIT
Answer:
Odd
Step-by-step explanation:
9281-9178=119
119 is a Odd number
Do y’all need any help
Answer:
Yes
Step-by-step explanation:
Math, due tomorrow and i can't find the rate of enlargement of my dilation in transformation....
Given a∥b , and c is not parallel to a or b, which statements must be true? Select each correct answer. Responses m∠1=m∠5 the measure of angle 1 equals the measure of angle 5 m∠5=m∠12 the measure of angle 5 equals the measure of angle 12 m∠4=m∠5 the measure of angle 4 equals the measure of angle 5 m∠7=m∠11
The correct answers of the statement are as follows;
m∠1=m∠5 the measure of angle 1 equals the measure of angle 5m∠4=m∠5 the measure of angle 4 equals the measure of angle 5How to find angles in parallel lines?Line a and b area parallel lines.
c is not parallel to a or b.
When parallel lines are cut by a transversal, angle relationships are formed. The angle relationship includes corresponding angles, alternate angles, vertically opposite angles etc.
Therefore, let's select the correct answer in the options.
m∠1 = m∠5
Therefore, the measure of angle 1 is equals to the measure of angle 5 because they are corresponding angles.
m∠4 = m∠5
Therefore, the measure of angle 4 is equals to the measure of angle 5 because they are alternate angles.
Hence, the correct answers of the statement are as follows;
m∠1=m∠5 the measure of angle 1 equals the measure of angle 5m∠4=m∠5 the measure of angle 4 equals the measure of angle 5learn more on parallel lines and angles here: https://brainly.com/question/11546031
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Part A
Write - 1/33 as a decimal.
Answer:
0.030303...
Step-by-step explanation:
i put the dots because this is a repeating decimal
Answer:
0.03030303030303.
I need help with this don’t bs please
Answer: download the app photo math and rewrite your equation and replace your variables with your numbers so the app can understand it. then just take a pic with it on the app and it will give you the answer. its a super useful app!
Step-by-step explanation:
Round to the nearest ten, then estimate the product. 46 x 63 =_ O 2,400 O2,800 O 3,000 0-3,500
The product of 46 and 63 to the nearest ten is 3000
What is the product?Product is the result of the multiplication process. Multiplication is the mathematical operation where a number a number is added to another number repeatedly. The sign that represents multiplication is x.
In order to round to the nearest ten, if the unit digit is greater than 5 or equal to 5, 1 is the added to the tens digit and the unit digit becomes zero. If the unit digit is less than 5, there is no change in the tens digit and the unit digit becomes zero.
46 to the nearest ten becomes 50
63 to the nearest ten becomes 60
50 x 60 = 3000
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The product of 46 x 63 when it is been rounded off into the nearest ten can be written as 3,000.
What is Rounding Off?Rounding off can be described as the mathematical term of making a particular number to become simpler even though the value of that number is still intact .
From the question, product of ( 46 x 63 ) will give us 3,818. however this number can be rounded off, to tens which will now give us 3,000 because it is tens the first two number from the right has been rounded off.
Therefore, option C is correct.
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10 pts + brainliest
help pleasee
(science)
The mass number of the atom is 4.
How to find the mass number of an atom?The mass number, also called atomic mass number or nucleon number, is the total number of protons and neutrons (together known as nucleons) in an atomic nucleus.
Therefore, the sum of protons and neutron in the nucleus of an atom is mass number of that atom.
Therefore, the atoms in the diagram has 2 electrons, 2 protons and 2 neutrons.
Notice the electrons revolving around the nucleus of an atom.
Therefore,
mass number = mass of neutron + mass of proton
mass number = 2 + 2
mass number = 4
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The sales tax on a purchased item in a given state is a function of the selling price
The statement that the sales tax on a good that has been purchased is a function of the selling price in a given state, is TRUE.
How does sales tax relate to the selling price?The sales tax on an item that is purchased is calculated on the selling price of the item and then added to the item so that the person purchasing the item can pay for the sales tax as well.
Because the sales tax is based on the selling price, it is therefore a function of the selling price with the given state being the percentage of the sales tax.
For instance, a 4% sales tax on a good that is $10 is:
= 4% x 10
= $0.40
This sales tax is based on the selling price and so is a function of it.
Options for the question are:
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Graph the function y equals 12 times the quantity 1 over 3 end quantity to the x power. Does the function represent growth or decay? What is the equation of the asymptote?
Exponential equation are inverse of of the logarithmic equation. Since b = 1/3 which is less than 1, hence it is a decay.
Exponential equationExponential equation are inverse of of the logarithmic equation. The standard exponential equation is y= ab^x
Exponential equation can either be growth or decay depending on the rate constant value.
If the value of b < 1, it is a decay while if the value of b > 1, then it is growth. Given the exponential equation below;
y = 12(1/3)^x
Since b = 1/3 which is less than 1, hence it is a decay. Find the graph attached.
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Answer:
D. Decay; y = 0Step-by-step explanation:
anyone know the answer?
Please answer this question.
Answer:
I have attached as an image. Kindly check.
Step-by-step explanation:
2x−y+2z=−6−3y+z=−22x−3z=4
Enter your answer, in the form (x,y,z), in the boxes in simplest terms.
Answer:
1/2
Step-by-step explanation:
Point Form:
(
3
4
,
−
2
,
1
2
)
Equation Form:
x
=
3
4
,
y
=
−
2
,
z
=
1
2
Since the cookie sheets can hold exactly 1 dozen cookies, bbcc will produce and sell cookies by the dozen. How much time will it take to fill an order of 2, 3, or 4 dozen cookies?
Time taken to fill an order of 2, 3, 4 dozen cookies are 45 minutes, 64 minutes and 89 minutes respectively.
To calculate time taken to fill the orders, we will add time used in different processes separately.
time taken to spoon =2 min for each dozen
time taken to bake = 10 min for each dozen
time taken to cool = 5 min for each dozen
time taken to pack = 2 min for each dozen
time taken to receive payment = 1 min for each dozen
time for cookies = mins to mix + mins to spoon + total baking mins + mins to cool + mins to pack + min to receive payment
putting the values in the above formula, we get
Cycle time for 2 dozen cookies = 6 mins to mix + 4 mins to spoon + 20 total baking mins + 10 mins to cool + 4 mins to pack + 1 min to receive payment = 45 mins
Cycle time for 3 dozen cookies = 6 mins to mix + 6 mins to spoon + 30 total baking mins + 15 mins to cool + 6 mins to pack + 1 min to receive payment = 64 mins
Cycle time for 4 dozen cookies = 12 mins to mix + 8 mins to spoon + 40 total baking mins + 20 mins to cool + 8 mins to pack + 1 min to receive payment = 89 mins
Therefore, Time taken to fill an order of 2, 3, 4 dozen cookies are 45 minutes, 64 minutes and 89 minutes respectively.
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Frankie bought 212 appetizers and he invited 12 people to his party. use compatible numbers to estimate the number of appetizers each guest can have? no links
The estimate of the number of appetizers per guest is 20
How to estimate the number of appetizers?The given parameters from the question are:
Number of appetizers = 212
Number of people invited = 12
From the question, we are to make use of compatible numbers
This means that we have the following approximation
Number of appetizers = 200
Number of people invited = 10
Next, we estimate the number of appetizers using
Number of appetizers = Total umber of appetizers/Number of people invited
Substitute the known values in the above equation, so, we have the following representation
Number of appetizers = 200/10
Evaluate
Number of appetizers = 20
Hence, the number of appetizers is 20
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PLS HELP WHY NOBODY ANSWERING ME ?
Answer:
10×5.6=56 5.6×10=56
Step-by-step explanation:
apple trees 10× 5.6 acres of land = 56 apple trees
2=2 how to get the answer for this
Answer:
16 if 8/2(2+2)
Step-by-step explanation:
First take 8 and divide it by 2, and then multiply by 4. This gets to the correct answer of 16.
Absolute value what is greater |-4.3| or |-7.2|
Answer:
The absolute value of -7.2 is greater.
Step-by-step explanation:
Absolute value means the distance from zero. Distance is always measured with a positive number. Which number is farther from 0, -7.2 or -4.3? -7.2
if the diameter of a circle is 18 feet, which is closest to the circumference
If the diameter of the circle is 18 feet, the circumference of the circle is 56.55 feet.
The circumference of a circle or ellipse in geometry is its perimeter. That is, if the circle were opened up and straightened out to a line segment, the circumference would be the length of the arc.
The diameter of a circle is 18 feet.
D = 18 feet
Now, the radius of the circle is half the diameter of the circle.
Therefore,
Diameter = 2 × Radius
Radius = Diameter / 2
D = 2r
r = D / 2
r = 18 feet / 2
r = 9 feet
Now, the circumference of a circle is given as:
Circumference = π × diameter
Circumference = π × 2r
Circumference = 2πr
Circumference = 2 × π × 9 feet
Circumference = 2 × 3.14159 × 9
Circumference = 56.55 feet
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