Fractions are in their simplest form when they have no common divisors other than one at their top and bottom. The top and bottom cannot be divided further and remain integers.
You may also hear the simplest form called "lowest term."
In preferred, an expression is in only form while it's far easiest to use not unusual methods to help you simplify:
Combine Like termsFactoringincreasing (the opposite of factoring)clean out fractions by multiplyingrecognizing a pattern you have seen earlier than, just like the difference of squaresInput:
32^ (-3/5)
Exact Value:
1/8
Decimal Form:
0.125
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4x + 5y = 6
6x - 7y = -20
Answer: x=-1, y=2
Step-by-step explanation:
4x + 5y = 6
6x - 7y = -20
(4x + 5y = 6)*1.5
6x + 7.5y = 9
6x - 7y = -20
7.5y-(-7y)=9-(-20)
7.5y+7y=9+20
14.5y=29
y=2
4x + 5y = 6
4x + 5(2) = 6
4x+10=6
4x=-4
x=-1
I feel du mb today and i have another test
iliana signed up for a store credit card with no annual fee to get a discount of 12.5 percent off her entire first purchase.
percents
total
100%
if she saved $7.29 on her first purchase by using this credit card, what was the total price of the items before the discount?
$0.91
$1.71
$58.32
$91.13
Answer:
58.32
Step-by-step explanation:
100÷12.5=8, 7.29×8=58.32.
The position of a submarine relative to sea level, changes by - 7 miles each hour. How many hours did it take
submarine to reach 43.75 miles below sea level?PLEASE HELP
43.75 divided by 7 is 6.25, thus your answer is 6.25 hours
Suppose you make a $5 bet on the number 0 on a roulette wheel with 38 slots labeled 00, 0, 1, 2, 3, ... , 36. If 0 is spun, you win a net gain of $175. If a 0 is not spun you lose the $5 bet. If you spin the wheel 50 times, how much money can you expect to gain or lose?
Lose $13.16
Here, we want to calculate the probability that we would win. The probability of winning is =
( No. of slots that win/ total no. of slots.)
For each individual spin, there are two possible outcomes:
- There is a 1 in 38 chance of winning $175.
- There is a 37 in 38 chance of losing $5.
The expected value for each spin is the sum of the products of each outcome by their respective probability.
expected value =E1×P1 + E2×p2
175×1/38 + (-5) × 37/38
175/38 - 185/38
-10/38
In 50 spins, the expected value is:
E(50) = 50 × (-10/38)
E(50) = - $13.16
expect to lose $13.16 if you spin the wheel 50 times.
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If f(x) = −3x + 4 and g(x) = 2, solve for the value of x for which f(x) = g(x) is true.
Answer: -3x+4=2 is the new equation x= 2/3
Step-by-step explanation: brainliest?
pls I need help in this question
Answer:
B = -1189/40
C = -13/18
Step-by-step explanation:
use your calculator to solve
and use the BODMAS method to help solve
At the beginning of a chemistry experiment, the volume of liquid in a container was
4 milliliters. During the experiment, the volume dropped to 2.6 milliliters. Find the percent of decrease.
I'm having trouble with this question.
Answer:
35%
Step-by-step explanation:
Decrease in Volume= 4ml-2.6ml
=1.4ml
Percentage Decrease= 1.4/4 x 100
=35%
a bag contains 6 blue marbles 4 red marbles and 2 yellow marbles.
what is the probability of selecting a blue marble replacing it then selecting another blue marble?
Answer:
1/4
Step-by-step explanation:
Blue/total x blue/total
6/12 x 6/12 Which is the same as
1/2 x /12 = 1/4
The number below is not correctly written in scientific notation.
145 × 105
What is the new exponent for the power of 10 after rewriting the number correctly in scientific notation?
1.45 × 10?
Write the new exponent in the blank below. PLEAZ HELP will give brainliest
The new exponent for the power of 10 after rewriting the number correctly in scientific notation would be 1.45 × 10^7
How does scientific notations work?The number is written in the form [tex]a \times 10^b[/tex]where we have [tex]1 \leq a < 10[/tex]
The number b shows the order, which is the most important figure for which scientific notation is used. It tells us how much order large or small a value is in powers of 10. We can for a time, ignore the value of 'a' for two comparable quantities and only compare their orders(this type of comparison is useful when difference is too big, like size of human to size of a star etc sort of comparisons).
The scientific notation is value in terms of power of 10 is known, which helps in easy comparison of quantities differing by a large value.
We have been given that number below is not correctly written in scientific notation.
145 × 10⁵
Therefore, new exponent would be 1.45 × 10^7
Hence, The new exponent for the power of 10 after rewriting the number correctly in scientific notation would be 1.45 × 10^7
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A cell phone plan cost thirty dollars for each line. does the situation represent a function
When the cell phone plan cost thirty dollars for each line, the function is C = 30x.
How to illustrate the information?It should be noted that a function is used to show the relationship that exists between the variables that are given.
In this situation, the cell phone plan cost thirty dollars for each line.
Let each line be represented by x.
Therefore, the cost for the number of likes will be:
C = 30 × x
C = 30x
Therefore, the function is illustrated.
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A desktop world globe has a volume of about 1386 cubic inches. The radius of Earth is approximately equal to the radius of the globe raised to the 10 th power. Find the radius of Earth. (Hint: Use the formula V=⁴/₃πr³ for the volume of a sphere.)
The radius of the Earth, approximately equal to the radius of the globe raised to the 10th power, is 250,562,113.2 inches.
First, solve for the radius of the desktop world globe using the formula for the volume of a sphere given by:
V = 4/3 π r^3
If the desktop world globe has a volume of about 1386 cubic inches, then
1386 cubic inches = 4/3 π r^3
r = 6.916582163 inches
Next, solving for the radius of the Earth if it is approximately equal to the radius of the globe raised to the 10th power.
Exponent, or power, is the small number written at the upper right of a constant or variable that tells how many times that constant or variable should be multiplied to itself.
If the radius of the Earth if it is approximately equal to the radius of the globe raised to the 10th power, then
r of Earth = r of globe ^10
r = 6.916582163^10
r = 250,562,113.2 inches
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Use De Morgan's Laws to write an equivalent statement using parentheses.
∼p∨∼q
Using the De Morgan's Law, the equivalent logical expression of the statement ∼p ∨ ∼q is ∼(p ∧ q)
How to determine the equivalent statement of the expression using parentheses?The expression is given as
∼p ∨ ∼q
The above expression is a logical expression
The De Morgan's Law of logical expression states that
∼x ∨ ∼y = ∼(x ∧ y)
Next, we replace the variables x and y with the given variables in the question
So, we have
∼p ∨ ∼q = ∼(p ∧ q)
The above implies that the equivalent logical expression of the statement ∼p ∨ ∼q is ∼(p ∧ q) using the De Morgan's Law
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can someone check if I did this question right, ?.
Answer:
Yes, you did it correctly. Note that shape B is 3 bigger than shape A, so it has much larger dimensions and properties.
Write each equation in logarithmic form.
4= (1/2)⁻²
The equation in logarithmic form is log base (1/2) of (4) = -2
Given the equation is:
4= (1/2)⁻²
The fundamental logarithmic function has the notation f(x) = log(r) y = log(x), where a > 0. The exponential function ay = x's inverse is represented by this. The common logarithm (log) or natural logarithm (ln) are examples of log functions (log).
Convert the exponential equation to a logarithmic equation using the logarithm base (10)of the right side (0.01) equals the exponent (−2).
A popular method for changing a mathematical equation from one form to another is to transform it from exponential to log form. The exponential form an x = N is translated into the logarithmic form.
Log aⁿ= x.The exponent of x, which is equal to N, has the exponential form a to it is converted to the logarithm of a number N to the base of a, which is equal to x.
log base (1/2) of (4) = -2
log₁/₂ (4) = ₋2
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the coefficients of variation for each data set are within 5 percentage points of each other. therefore, the systolic measurements vary ▼ the diastolic measurements.
The answer is 16.7 %.
What is meant by mean?The average of a group of variables is referred to as the mean in mathematics and statistics. There are several methods for calculating the mean, including the geometric mean, the harmonic mean, and the simple arithmetic mean.Why are you being so cruel, it demands to know. So, someone would ask you that if they thought you were being harsh or disrespectful.In just two easy steps, you can determine the mean, or average, of a set of data: Add up all of the values to determine the sum. By how many values there are in the data collection, divide the total.adjective Being cruel to another person, such as by denying them the opportunity to do something, is what it means to be mean.The necessary calculation is below:
observations Systolic(x) Diastolic(y) x^2 y^2
1 120 79 14400 6241
2 130 74 16900 5476
3 157 75 24649 5625
4 96 50 9216 2500
5 156 89 24336 7921
6 124 87 15376 7569
7 116 59 13456 3481
8 137 66 18769 4356
9 124 71 15376 5041
10 118 81 13924 6561
sum 1278 731 166402 54771
For Systolic (x)
mean= sum(x)/10 = 1278/10 = 127.8
stdev= s =sqrt( (sum(x^2 - 10*127.8^2)/9) = sqrt ( (166402 - 10*127.8^2)/9) =18.48
So coefficient of variation ( systolic) is = (stdev/mean )*100 = (18.48/127.8)*100 = 14.5 %
For Diastolic (x)
mean= sum(y)/10 = 731/10 = 73.1
stdev= s =sqrt( [tex](sum(x^2 - 10*73.1^2)/9) = sqrt ( (54771 - 10*73.1^2)/9)[/tex]= 12.18
so coefficient of variation ( systolic) is = (stdev/mean )*100 = (12.18/73.1)*100 = 16.7 %
Here, systolic is less varied than the diastolic.
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Simplify each expression. x²/₇ . x³/₁₄
The result of simplifying each number x²/₇ . x³/₁₄ using the exponent rules is [tex]\sqrt{}[/tex]x
To solve this exercise we have to resolve algebraic operations following the exponent rules.
(x²/₇) * (x³/₁₄)
Base= x
Using the product rule that indicates that: the exponent result will be the addition of these exponents, we have:
(x) ⁽²/₇ ⁺ ³/₁₄⁾
(x) ⁽⁴⁺³⁾/₁₄
(x) ⁽⁷/¹⁴⁾
(x) ⁽¹/²⁾
As we have a fractional exponent, you must convert the exponent to root:
[tex]\sqrt{}[/tex]x
What is an exponent?In mathematics an exponent is the number of time that a number, called (base) is multiplied by itself. It is also called, power or index.
Example: 3² = 3*3 = 9
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A and B are complementary angles. If mA = (6x + 2)° and m
B = (4x + 18)°, then find the measure of ZA.
The measurement of angle A and B is 44° and 46° respectively.
What are complementary angles ?
When the sum of two angle is 90 degree it is known as complementary angles and when a line divides the line than the sum of angles formed with the given straight line is always equals to 90 degree.
It is given that the angle A and B are complementary angles whose measurements are :
∠A = (6x + 2)°
and , ∠B = (4x + 18)°
The sum of angle A and B will be 90 degree as they are complementary angles that is :
∠A + ∠B = 90°
Now, solving by adding like terms and finding the value of x :
6x +2 + 4x + 18 = 90°
10x + 20 = 90°
10x = 90-20
10x = 70°
x = 7°
now, the measurement of angle A will be :
∠A = (6x + 2)°
∠A = (6 · 7 + 2)°
∠A = (42 + 2)°
∠A = 44° and ∠B = 46°
Therefore, the measurement of angle A and B is 44° and 46° respectively.
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Solve. Check for extraneous solutions. √4 x-23 -3=2
The solution for given equation is 196 and there are no extraneous solutions.
Extraneous solutions refer to the solution, which on being placed in the equation, does not make Left Hand Side and Right Hand Side equal.
Rewriting the equation and solving it by addition or subtraction of values on both sides as per the requirement -
✓4x - 23 - 3 = 2
Adding 3 on both sides of the equation
✓4x - 23 - 3 + 3 = 2 + 3
✓4x - 23 = 5
Adding 23 on both sides of the Equation
✓4x - 23 + 23 = 5 + 23
✓4x = 28
Taking square on both sides
(√4x)² = 28²
4x = 784
Shifting 4 to Right Hand Side
x = 784 ÷ 4
Performing division
x = 196
Keep the value of x in equation to find it it is extraneous or not -
✓(4 × 196) - 23 - 3 = 2
✓784 - 23 - 3 = 2
28 - 23 - 3 = 2
25 - 3 = 2
2 = 2
Since RHS and LHS are equal, there is no extraneous solution for the given equation.
Hence, the solution for given equation is 196 and there are no extraneous solutions.
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Help me pls!! 4 math questions
Which arrow would most likely represent the phase change that occurs when silver is poured into a mold and cools to become a solid bar? 1 3 4 5
The answer is 5.
When a liquid silver is poured into a mold and cools down to become a solid bar is a transition in which the liquid phase is converted into a solid phase which is termed solidification represented by arrow number 5.
Whereas other arrows represent:
Arrow 1 represents the vaporization process where the liquid state changes to a gaseous state.
Arrow 2 represents the Fusion process where the solid-state changes to a liquid state.
Arrow 3 represents the sublimation process where the solid-state changes to a gaseous state by escaping the liquid state.
Arrow 4 represents the condensation process where the gaseous state changes to a liquid state.
Arrow 6 represents the deposition process where the gaseous state changes to a solid state by escaping the liquid state.
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If x= -1 in the equation y = 2x + 2, then what is the value of y?
A/
Decrease the number 724,062.58 by 100,000
Answer:
624,062.58 is your answer :)
Step-by-step explanation:
Which is equivalent to the ratio 20:50
Answer:
Since the simplest form of the fraction 20/50 is 2/5, the simplest form of the ratio 20:50 is also 2:5.
y=-x-4
-7x+8y=16
solve by substitution
the equations y = - x - 4 and - 7 x + 8 y = 16 have the solution as x = - 16 / 5 and y = - 4 / 5.
We are given the two equations:
y = - x - 4
- 7 x + 8 y = 16
We need to solve these equations by substitution.
We will substitute the equation 1 in the equation 2 to get the values of x and y:
- 7 x + 8 y = 16
- 7 x + 8 (- x - 4) = 16
- 7 x - 8 x - 32 = 16
- 15 x = 16 + 32
- 15 x = 48
Divide both sides by - 15, we get that:
x = 48 / - 15
x = - 16 / 5
y = - x - 4
Put the value of x
y = 16 / 5 - 4
y = 16 - 20 / 5
Subtract to get the value:
y = - 4 / 5
Therefore, we get that, the equations y = - x - 4 and - 7 x + 8 y = 16 have the solution as x = - 16 / 5 and y = - 4 / 5.
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Given that 212basex + 122basex=1111 basex.Find x
Write out the decimal expansion of each number:
[tex]212_x \equiv 2x^2 + x + 2[/tex]
[tex]122_x \equiv x^2 + 2x + 2[/tex]
[tex]1111_x \equiv x^3 + x^2 + x + 1[/tex]
Note that [tex]x[/tex] must be greater than 2. Solve for [tex]x[/tex].
[tex]212_x + 122_x = 1111_x \iff (2x^2 + x + 2) + (x^2 + 2x + 2) = x^3 + x^2 + x + 1 \\\\ ~~~~ \implies 3x^2 + 3x + 4 = x^3 + x^2 + x + 1 \\\\ ~~~~ \implies x^3 - 2x^2 - 2x - 3 = 0 \\\\ ~~~~ \implies (x^3 - 3x^2) + (x^2 - 3x) + x - 3 = 0 \\\\ ~~~~ \implies x^2(x-3) + x(x-3) + (x-3) = 0 \\\\ ~~~~ \implies (x-3) (x^2+x+1) = 0 \\\\ ~~~~ \implies \boxed{x=3}[/tex]
Corinna paid $3 for 12 eggs. What was the cost of 1 egg?
Answer:
0.25
Step-by-step explanation:
All i did was divided 3 by 12
Find each product or quotient. √5(√5)
The product of √5(√5) is 5.
To find : the product of √5(√5).
This question can be easily solved using the concept of square root. It can be solved in a few simple steps
Step 1 : Check the power of roots for each term
Both the terms are √5
Since both the numbers have the same root power they can be combined under the same sqaure root for further operation
=> √ ( 5 x 5 )
=> √ 25
It can also be written as √ 5²
square root can also be mentioned as number raised to 1/2
If we solve the powers of 5 => 1/2 x 2 = 1
=> √ 25 = √ 5² = 5
Therefore, we get the product of √5(√5) as 5.
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If a gas has a volume of 1 l at a pressure of 200 kpa, what volume would it have when the pressure is increased to 400 kpa? assume the temperature and number of particles are constant.
With an inverse relationship, when the pressure is increased to 400 kPa, the volume will be 0.5L, assuming that the temperature and number of particles are constant.
Boyle's Law states the inverse relationship between volume and pressure. It states that a constant amount of gas at a constant temperature, decreasing the volume will increase its pressure, and increasing its volume will decrease its pressure.
V = k/P or P1V1 = P2V2
where V = volume
P = pressure
If a gas has a volume of 1 L at a pressure of 200 kPa, and assuming that the temperature and number of particles are constant, using the inverse relationship, solve for the volume of the gas at a pressure of 400 kPa.
P1V1 = P2V2
200 kPa(1L) = 400 kPa(V2)
V2 = 200/400
V2 = 0.5 L
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Which angle is vertical to 2?
Answer:
angle 5 is vertical to 2
Step-by-step explanation:
Vertical angles are pair angles formed when two lines intersect.
Answer: <5
Step-by-step explanation:
Find the real and imaginary solutions of each equation.
81 x⁴-1=0
A solution that is real in its nature is called the real solution of that equation.
X + 5 = 0
We can solve the above equation as,
X + 5 = 0
X = -5
Now, if we plug the value of X into the equation,
X + 5 = 0
-5 + 5 = 0
0 = 0
The solution is real and is true for this equation.
While the solution of an algebraic expression solution is imaginary if it is the square root of a negative number. It involves the imaginary unit iota.
The complete solution of the expression is given below in the picture.
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