The equation that represents the quotient of a number x, and five is half the difference of a number and four is [tex]\frac{x}{5}=\frac{1}{2}(x-4)[/tex]
Given,
The number = x
When you divide a number with another number the result is called the quotient
The quotient of a number x and five = [tex]\frac{x}{5}[/tex]
Difference of a number and four = x-4
Half the difference of a number and four = [tex]\frac{1}{2}(x-4)[/tex]
Here the quotient of a number x and five is half the difference of a number and four, the equation will be
[tex]\frac{x}{5}=\frac{1}{2}(x-4)[/tex]
Hence, the equation that represents the quotient of a number x, and five is half the difference of a number and four is [tex]\frac{x}{5}=\frac{1}{2}(x-4)[/tex]
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For each pair of functions, find f(g(x)) and g(f(x)) .
f(x)=x+3, g(x)=x-5
A composite function exists as a function that depends on another function. The value of f(g(x)) = x-8 and g(f(x)) = x-2.
What is meant by composition function?In mathematics, function composition exists as an operation ∘ that takes two functions f and g, and has a function h = g ∘ f such that h(x) = g. In this operation, the function g exists used to the result of applying the function f to x.
Function composition is a mathematical procedure where two functions, f, and g, are taken and a function, h = g ∘ f, is produced such that h(x) = g(f(x)). The function g exists used in this operation on the outcome of applying the function f to x.
Let the two functions be f(x) = x+3 and g(x) = x-5
f(g(x)) = f(x-5)
simplifying the above equation, we get
f(x-5) = x-5+3
f(g(x)) = x-8
g(f(x)) = g(x+3)
simplifying th above equation, we get
g(x+3) = x+3-5
g(x+3) = x-2
Therefore, the value of f(g(x)) = x-8 and g(f(x)) = x-2.
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Which expression is equal to √49/100
A. 7√10/10
B. √7/10
C. 7/10
D. 7/50
Answer:
A
Step-by-step explanation:
70-271=20
Answer: it's 7/10
Step-by-step explanation:
the 49 simplifies to 7, and the 100 simplifies to 10
Solve for x and write your answer in simplest form.
-1/2 -1/2(4/5x+1) = -2 -3x
The solution of the equation which is as described in the task content when expressed in its simplest form is; -5/13.
What is the solution of the equation as described in the task content?It follows from the task content that the solution to the equation is to be determined and expressed in its simplest form.
Given;
-1/2 -1/2(4/5x+1) = -2 -3x
By distributing the coefficients: we have;
-1/2 - 2/5x - 1/2 = -2 -3x
Hence, by collecting like terms; we have;
-1/2 - 1/2 + 2 = -3x + (2/5)x
1 = -13x/5
Therefore; by cross-multiplication; we have;
5 = -13x
Divide both sides by; -13.
x = -5/13.
Ultimately, the solution of the equation which is as described in the task content when expressed in its simplest form is; -5/13.
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Find the value of x.
-2x = 3x + 6
Answer:
x= -6/5
Step-by-step explanation:
-2x=3x +6
collect like terms
-6=3x+2x
-6=5x
x= -6/5
Answer: x= -6/5 make that a fraction
decimal form: x= -1.2
mixed number form: x= - 1 1/5, 1 is the whole number
Step-by-step explanation: Isolate the variable by dividing each side by factors that don't contain the variable.
2x + kx = m solve for x
Answer:
x=m/2+k , k≠-2
Step-by-step explanation:
2x+kx=m
Factor out x from the expression:
(2+k)x=m
Assume 2+k≠0 and divide both sides of the equation by 2+k:
x=m/2k , 2+k≠0
Rewrite the restriction:
x=m/2+k≠-2
Solution:
x=m/2+k , k≠-2
The value of x in the given expression is x = m / (k+2)
What is an expression?An expression is a mathematical statement containing variables, numerical, and they are related by at least one mathematical operation.
Given an expression, 2x + kx = m
We are asked to rearrange the values and find the value of x.
Therefore,
2x + kx = m
Since, two terms have same variable, therefore, taking x common from both,
x(2+k) = m
x(k+2) = m
Now, transpose (k+2) to right side, we get,
x = m / (k+2)
Hence, we get the value of x as, x = m / (k+2)
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How do I set up the equations for these two problems so I can find X?
The values of x and measures of angles are:
1. x = 12; m<PQS = 71°; m<PQT = 142°; m<TQR = 41°
2. x = 8; m<GDH = 126°; m<FDH = 200°; m<FDE = 137°
How to Find the Measures of Angles?1. Since QS bisects angle PQT, therefore:
measure of angle PQS = measure of angle SQT
Given:
m<SQT = 8x - 25
m<PQT = 9x + 34
m<SQR = 112°
Thus:
m<PQT = 2(m<SQT)
Substitute
9x + 34 = 2(8x - 25)
9x + 34 = 16x - 50
9x - 16x = -34 - 50
-7x = -84
x = 12
m<PQS = m<SQT = 8x - 25
Plug in the value of x
m<PQS = 8x - 25 = 8(12) - 25
m<PQS = 71°
m<PQT = 9x + 34 = 9(12) + 34
m<PQT = 142°
m<TQR = m<SQR - m<SQT [angle addition theorem]
m<TQR = 112 - 71
m<TQR = 41°
2. Given:
m<GDE = 8x - 1
m<EDH = 6x + 15
m<CDF = 43
m<GDE = m<EDH [reason: DE bisects GDH]
Substitute
8x - 1 = 6x + 15
8x - 6x = 1 + 15
2x = 16
2x/2 = 16/2
x = 8
m<GDH = 2(m<GDE)
m<GDH = 2(8x - 1)
m<GDH = 16x - 2 = 16(8) - 2
m<GDH = 126°
m<FDG = 180 - m<CDF - m<GDE
m<FDG = 180 - 43 - (8x - 1)
m<FDG = 180 - 43 - (8(8) - 1)
m<FDG = 180 - 43 - 63
m<FDG = 74°
m<FDH = m<FDG + m<GDH
m<FDH = 74 + 126
m<FDH = 200°
m<FDE = m<FDG + m<GDE
m<FDE = 74 + 63
m<FDE = 137°
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Simplify.
√81x6y2
Assume all variables are nonnegative.
Answer:
9x³y²
Step-by-step explanation:
To simplify, factorize 81 in powers of 2 ; x⁶ in powers of 2 and y² in powers of 2.
[tex]\sf \sqrt{81x^6y^2}=\sqrt{9^2 * x^{3*2}*y^2}[/tex]
[tex]\sf = \sqrt{9^2* (x^3)^2)* y^2}\\\\ = 9 * x^3*y^2\\\\=9x^3y^2[/tex]
According to the empirical rule, ________ will be within two standard deviations of the mean.
According to the empirical rule, 95% will be within two standard deviations of the mean.
The empirical rule, also referred to as the three-sigma rule or 68-95-99.7 rule, is a statistical rule which states that for a normal distribution, almost all observed data will fall within three standard deviations (denoted by σ) of the mean or average (denoted by µ).
Under this rule, 68% of the data falls within one standard deviation, 95% percent within two standard deviations, and 99.7% within three standard deviations from the mean. Three-sigma limits that follow the empirical rule are used to set the upper and lower control limits in statistical quality control charts and in risk analysis such as VaR.
The empirical rule is used often in statistics for forecasting final outcomes. After calculating the standard deviation and before collecting exact data, this rule can be used as a rough estimate of the outcome of the impending data to be collected and analyzed.
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25 students submitted the HW this week, which was 77% of the class. How many students are in the class?
Answer:
Step-by-step explanation:
25 divide 77 = 0.32467532 x 100 = 32 (Leave off the rest, there is no such thing as a fraction of a person in this)
Simplified: (25/77)*100 = 32
To check our answer we would do 32 x 77%(.77) = 24.64 round-up and you get 25!
If you are still confused please do tell :)
NEED ANSWER ASAP WILL GIVE 40 POINTS
-6≥ 10-8x
Answer:
x≥2
Step-by-step explanation:
-16≥ -8x
x≥2
Marianna represented several percents as portions of 100 in the pictures below.
A 10 by 10 block of 100 where 8 columns of 10 are shaded.
A 10 by 10 block of 100 where the first row, and 2 and a half squares of the second row are shaded.
A 10 by 10 block of 100 where 1 row of 10 is shaded.
A.Write the percent represented in each picture.
B.Write the portion represented in each picture as a fraction in at least two different ways.
A) The percentage represented in each picture is as follows:
A-1) 80%
A-2) 12.5%
A-3) 10%
B) The portion represented in each picture is written as a fraction as follows:
B-1) 80% = 8/10 or 4/5
B-2) 12.5% = 1.25/10 or 1/8
B-3) 10 = 1/10 or 2/20
What is a percentage?A percentage is a fraction of 100.
A percentage is also a ratio, showing how much of the whole is contained by the portion.
Percentages are written with the percentage sign (%).
Data and Calculations:A-1) 80% for A 10 by 10 block of 100 where 8 columns of 10 are shaded.
A-2) 12.5% for A 10 by 10 block of 100 where the first row, and 2 and a half squares of the second row are shaded.
A-3) 10% for A 10 by 10 block of 100 where 1 row of 10 is shaded.
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Two numbers are given below.
34,856
39,670
a) Approximate the sum of these numbers
by first rounding each number to the
nearest hundred.
b) Find the exact sum of these numbers,
then round this value to the nearest
hundred.
a) The approximate sum of the numbers by first rounding each number is 74,600
b) The exact sum of the numbers rounded to the nearest hundred is 74,500
From the question, we are determine the approximate sum of the given numbers
The given numbers are
34,856 and 39,670
a) Round 34,856 to the nearest hundred
34,856 to the nearest hundred is 34,900
Also,
Round 39,670 to the nearest hundred
39,670 to the nearest hundred is 39,700
Now,
Add the rounded numbers
34,900 + 39,700 = 74,600
b) The exact sum of the numbers is
34,856 + 39,670 = 74,526
Rounding the result to the nearest hundred
74,526 rounded to the nearest hundred is 74,500
Hence, the exact sum of the numbers rounded to the nearest hundred is 74,500
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Solve. Check for extraneous solutions. √x+7 +5=x
x = 3 and x = 6 is extraneous solution.
√(x+7) +5=x
Subtracting 5 on both sides of the equation
√(x+7) + 5 - 5 = x - 5
√(x+7) = x - 5
Squaring both sides of the equation
(√(x+7))² = (x - 5)²
x + 7 = x² + 25 - 10x
x² - 9x + 18 = 0 ...(1)
By middle term splitting equation (1) can be written as
x² - 6x - 3x + 18 = 0
x(x - 6) -3(x - 6) = 0
(x - 3)(x - 6) = 0
x - 3 = 0 and x - 6 = 0
x = 3, 6
Check extraneous solution by putting the value of x in the original equation, we get
Let x = 3
√(3+7) +5 = 3
✓10 + 5 = 3
which is a contradiction, so, x = 3 is an extraneous solution.
Let x = 6
√(6+7) +5 = 3
✓13 + 5 = 3
which is a contradiction, so, x = 6 is an extraneous solution.
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For the following problems, consider a restaurant owner who wants to sell T-shirts advertising his brand. He recalls that there is a fixed cost and variable cost, although he does not remember the values. He does know that the T-shirt printing company charges $440 for 20 shirts and $1000 for 100 shirts. 331. a. Find the equation C = f (x) that describes the total cost as a function of number of shirts and b. determine how many shirts he must sell to break even if he sells the shirts for $10 each.
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Choose the definition for the function.
(-x+ 2
a. y = x + 1
(-x+ 2
b. y = x + 1
{
x < 1
x ≥ 1
x ≤1
x> 1
S-x+ 2
x+1
c. y = {
(-x+ 2
d. y = x + 1
x > 1
x ≤ 1
x ≥ 1
x < 1
Enter
Answer:
can you add a photo of the questions? So it's easier to see
5. (01.06 MC)
Solve the following equation for x: 5x + 3y = 15.
Answer:
x = [tex]\frac{15-3y}{5}[/tex]
Step-by-step explanation:
5x + 3y = 15 ( isolate the term in x by subtracting 3y from both sides )
5x = 15 - 3y ( isolate x by dividing both sides by 5 )
x = [tex]\frac{15-3y}{5}[/tex]
Let f(x)=4 x, g(x)=1/2 x+7 , and h(x)=-2 x+4 . Perform each function operation. (g⁰ f)(x)
The answer to this question is (gof)(x)=2x+7
According to question:
Given: f(x)=4 x, g(x)=1/2 x+7,h(x)=-2 x+4
(gof)(x)=g(f(x))=g(4x)=1/2×4x+7=2x+7(fog)(x)=f(g(x))=f(x/2+7)=4×(x/2+7)=2x+28We always simplify everything in brackets first using BODMAS. Therefore, in order to compute f(g(x)), g(x) must first be calculated and then substituted within f(x). Similar to this, in order to determine g(f(x)), f(x) must first be computed and then substituted in g(x). In other words, the sequence is important when locating the composite functions. It implies that g(f(x)) and f(g(x)) may not be equal. The following procedures are used to obtain the composite function f(g(a)) for any two functions f(x) and g(x).
By changing x = a in g, find g(a) (x).
Put x = g(a) into f to find f(g(a)) (x)
∴(gof)(x)=2x+7
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Solve each equation. Check your answers.
ln 4 r²=3
After solving the equation the value of r in 4 r²=3 is [tex]\sqrt{3/4}[/tex].
We have to find r in 4 r²=3
⇒ 4 r² = 3
⇒ r² = 3/4
⇒ r = [tex]\sqrt{3/4}[/tex]
So, r is equal to [tex]\sqrt{3/4}[/tex]
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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A cube had dimensions of 2cm, 4cm, and 6cm. It also has a density of 24g/cm3. Will it Sink or Float in water?
Answer:
Step-by-step explanation:
Volume of the cube = 2*4*6 = 48 cm^3.
Its density is 24 g / cm^3
The density of water is 1g /cm^3 so it will sink in water.
Given that 2x+7=27 and 3x+1=28 does 2x+7=3x+1 explain
It is false that 2x + 7 = 3x + 1
How to determine the true statement?The equations are given as
2x + 7 = 27
3x + 1 = 28
The above equations have different values
This means that
It is false that 2x + 7 = 3x + 1
The above statement is true because 27 does not equal 28
Hence, it is false that 2x + 7 = 3x + 1
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The scale on a map is 1 : 200,000.
The length of a road on the map is 4 cm.
What is the length of the road in real life?
Give your answer in kilometres.
According to the solving the length of the road in real life will be = 8 km.
What is a map scale?The relationship (or ratio) between the distance on a map and the comparable distance on the ground is referred to as map scale. For example, on a 1:100000 scale map, 1cm on the map represents 1km on the ground.
Why is a scale used on maps?You've probably seen maps with just a scale bar representing equal sections, each marked with kilometres or miles. These divisions have been used to calculate ground distance on a map. In other words, a map scale specifies the relationship between the map and indeed the entire or a portion of the earth's surface depicted on it.
According to the given data:scale on a map is 1 : 200,000.
= 1 : (200,000/(100*1000))
= 1:2
= 2km
So,
length of a road on the map is 4 cm.
= 4*2
= 8km
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Express as trinomial
(2x-2)(2x+8)
The trinomial form of the given expression (2x-2)(2x+8) is 4x² + 12x - 16.
What is the trinomial form of the given expression?Given the expression in the question;
(2x-2)(2x+8)
Expand using FOIL Method.
Apply distributive property
(2x-2)(2x+8)
2x( 2x + 8 ) -2( 2x + 8 )
Apply distributive property
2x(2x) + 8(2x) -2(2x) + 8(-2)
Perform the operation
2x(2x) + 8(2x) -2(2x) + 8(-2)
4x² + 16x - 4x - 16
Combine like terms
4x² + 16x - 4x - 16
4x² + 12x - 16
Therefore, the trinomial form of the given expression (2x-2)(2x+8) is 4x² + 12x - 16.
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Your friend used some simple functions and found that (f⁰g)(x)=(g⁰f)(x) , and concluded that function composition is commutative. Give an example to show that your friend is mistaken.
The composition of f and g, as (fog)(x) = f(g(x)) for functions f and g. g should be applied to x. If fog(x) = x and gof (x) = x for all x values in the domain of f and g, then they are inverse functions.
What is meant by function composition?In mathematics, function composition is an operation in which two functions, f and g, generate a new function, h, in such a way that h(x) = g(f(x)). This means that function g is being applied to the function x. So, in essence, a function is applied to the output of another function.
Define fog, the composition of f and g, as (fog)(x) = f(g(x)) for functions f and g. g should be applied to x. If fog(x) = x and gof (x) = x for all x values in the domain of f and g, then they are inverse functions.
In math, the domain (the x-values) of one function becomes the range (the y-value answers) of the next function. Composition notation is as follows: (f o g)(x) = f(g(x)) and exists read “f composed with g of x” or “f of g of x”.
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How can you express 5 1/3 + -7 2/3 as the sum of its integer and fractional parts
The sum of its integer and fractional parts is 5 + (-7) + 1/3 + 2/3. Option D
What are fractions?Fractions are defined as part of a whole.
The types of fractions include:
Mixed fractionsProper fractionsImproper fractionsSimple fractionsComplex fractionsGiven the expression;
5 1/3 + -7 2/3
The integers are:
5 and -7
The fractions are;
1/3 and 2/3
The sum of the integers and fractional parts are;
5 + (-7) + 1/3 + 2/3
Thus, the sum of its integer and fractional parts is 5 + (-7) + 1/3 + 2/3. Option D
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A circle has a diameter of 9cm a square has a side length 5cm use pythagoras theorem to show the square will fit in the circle without touching the sides
The answer is 9cmsquare +5cmsquare equal to =106cm
We know 5×8=56
Which of the following statements are also true?
Choose 2 answers:
A. 8 is a factor of 56.
B. 7 is a multiple of 56.
C. 7 is a factor of 56.
Answer:
A and C
Step-by-step explanation:
Factors are numbers that can multiplied with another number to create a product. The factors of 56 are 1, 2, 4, 7, 8, 14, 28, and 56.
what is greatest common denominator of 72 and 159)
Answer:
3
Step-by-step explanation:
The greatest common divisor (GCD) of two nonzero integers a and b is the greatest positive integer d such that d is a divisor of both a and b (Wikipedia)
To find out which is the GCD of 72 and 159, keep factoring both until they cannot be factored any more
Then take the factors common to both list of factors; the greatest among them is the GCD
The factors of 72 are: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
The factors of 159 are: 1, 3, 53, 159
The common factors are 1, 3
So GCD is 3
What is the Domain, Range, and Function?
Step-by-step explanation:
domain = (0,2)
range=(4,-4)
funcion =quadratic
Solve please and thanks
Answer: (10, 8)
Step-by-step explanation:
To solve a substitution question, you have to make sure either x or y is alone on the other side of equal sign.
-x + y = -2
^^^this becomes y = -2 + x
Now, since you know what "y" is, you simply replace "y" with our new equation in the other equation.
-x - 2(-2+x) = -26
Then, you do order of operations to get the answer.
First, do distributive property.
-x + 4 - 2x = -26
Next, solve the equation.
-3x + 4 = -26
-3x = -30
x = 10
Since you found what "x" is, you substitute "x" and in one of your equations to find "y", it doesn't matter which one.
-(10) + y = -2
-10 + y = -2
y = 8
Finally, after you got "x" which is 10, and "y" which is 8, you put them in an ordered pair (x, y) which is (10, 8).
P.S. I use Sora and Deltamath too!
Anya's grandparents decide they want to invest at the bank. They have $35,000 they are willing to invest for 6 years. If they get a 4% interest rate and compound quarterly, how much can they expect to have in their account at the end of their investment time.
Round to the nearest cent (if necessary). Show all work for full credit.
The amount they will expect to have in there account at the end of the investment is 44,440.71 dollars.
How to find compound interest?He grand parents wanted to invest in a bank.
They have $35,000 they are willing to invest for 6 years.
The interest rate is 4% and compounded quarterly.
The amount they will have in there account after 6 years can be calculated as follows:
using compound interest formula,
A = p(1 + r/n)ⁿᵇ
Where
p = principalr = interest rateb = time in yearsn = compoundTherefore,
p = 35000
r = 4% = 0.04
n = 4
b = 6
Amount = 35,000(1 + 0.04 / 4)⁴ˣ⁶
Amount = 35,000(1.01)²⁴
Amount = 35,000 × 1.26973464853
Amount = 44440.7126986
Amount = 44440.71 dollars
Therefore, the amount they will expect to have in there account at the end of the investment is 44,440.71 dollars.
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