Using translation concepts, the equation for function g is given by:
g(x) = 7x/3 + 1.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
Supposing that we have a function f(x), a horizontal compression by a factor of a is equivalent to finding f(ax).
In this problem, the function is:
f(x) = 7x + 1.
For the horizontal compression by a factor of 1/3, we have that:
g(x) = f(1/3x) = 7x/3 + 1.
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Can u guys please give me the correct answe
angle at y and w are equal
hence, 54°=w
54°+w+x =180°
x=180-(54°+54°)
x=72°
add the two equations, 0.75x+1.5y=40 and −1.5x−1.5y=−60 , to find the value of x .
The value of x in the equation is 26.7
How to solve an equation?0.75x + 1.5y = 40
−1.5x − 1.5y = −60
add both equation to eliminate y .
Therefore,
−1.5x + 0.75x = -0.75x
1.5y + (- 1.5y) = 0
40 + (-60) = -20
Hence,
-0.75x = - 20
divide both sides by -0.75
-0.75x / -0/75 = - 20 / -0.75
x = - 20 / -0.75
x = 26.6666666667
x = 26.7
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Maria had a seven square-foot piece of construction paper. She used four square feet of the paper to make a large greeting card for a friend. Which operation would help to find the amount of paper she could use for another card? O division O addition subtraction multiplication
Answer:
subtraction
Step-by-step explanation:
If she had 7 sqft and used up 4 sqft, she no longer has that 4 sqft. It's used up, gone, taken away. We remove it from her total. That is "take away" this means subtraction.
7 - 4
= 3 she has 3sqft of construction paper left.
the equation of a circle given the center (–4, 4) and raduis r = 5.
Answer:
x² + y² + 8x - 8y + 7 = 0
Step-by-step explanation:
Formula: (x - a)² + (y - b)²= r²
where,
a = -4
b = 4
Substitute a and b
( x - (-4))² + (y - 4)² = 5²
(x + 4)² + (y - 4)² = 25
Open Bracket( )
(x + 4) (x + 4) = x² + 4x + 4x + 16
(y - 4) (y - 4) = y² - 4y - 4y + 16
x² + 4x + 4x + 16 + y² - 4y - 4y + 16= 25
Collect Like Terms
x² + y² + 8x - 8y + 16 + 16 - 25 = 0
x² + y² + 8x - 8y + 7 = 0
Therefore,
x² + y² + 8x - 8y + 7 = 0
Is The Equation Of The Given Circle.
Find the perimeter of the rectangle 2A+ 4
a
The percentage of each transaction contributed to the total transactions in the same Account. Use BASE_EQUIV_AMT as the unit.
The percentage that each transaction contributed to the total transactions in the same account (Cash Account and Service Revenue) is computed as follows:
Cash Account:1. Service Revenue $900 = 8%
2. Owner's Equity, Barbara Hanson $2,200 = 19.8%
3. Accounts Receivable $750 = 6.8%
5. Note Payable $6,000 = 54.1%
6. Unearned Revenue $1,250 = 11.3%
Total cash receipts = $11,100
Service Revenue:1. Cash $900 = 70.6%
4. Accounts Receivable $375 = 29.4%
Total $1,275
How is the percentage computed?The percentage that each transaction contributed to the total transactions in the same account can be computed by taking the dollar value of the transaction over the total value of transactions in the same account and then multiplying by 100.
Percentage values show the degrees of relationship among variables.
The formula for computing percentage in this scenario is transaction value/total transactions value × 100%.
Transaction Analysis:1. Cash $900 Service Revenue $900
2. Cash $2,200 Owner's Equity, Barbara Hanson $2,200
3. Cash $750 Accounts Receivable $750
4. Accounts Receivable $375 Service Revenue $375
5. Cash $6,000 Note Payable $6,000
6. Cash $1,250 Unearned Revenue $1,250
Question Completion:The following transactions occurred during July:
1. Received $900 cash for services provided to a customer during July.
2. Received $2,200 cash investment from Barbara Hanson, the owner of the business.
3. Received $750 from a customer in partial payment of his account receivable, which arose from sales in June.
4. Provided services to a customer on credit, $375.
5. Borrowed $6,000 from the bank by signing a promissory note.
6. Received $1,250 cash from a customer for services to be rendered next year.
Use the transactions to compute the percentage of each transaction relative to the total transactions in the same account.
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Suppose the length and width of the box double. Does the surface area S double? Complete the explanation.
Help!
Find the value of x.
Answer:
x = 52
Step-by-step explanation:
Since the inscribed angle measures 64 degrees, the minor arc is 64*2 = 128 degrees. Therefore the major arc is 180-128 = 232 degrees. Angle X is the difference of major and minor arc divided by 2, so X = (232-128)/2 = 52 degrees.
Madison finished 4/5 of her homework before dinner. What percent of Maddison’s homework is left to finish?
Answer:
1/5 of it
Step-by-step explanation:
5/5 represents all of her homework
5/5-4/5= 1/5
4/5 represents the homework she did before dinner
1/5 represents the homework left to do
Determine the relationship between the angle θ of a circular sector of a circumference of radius 10 cm and the area Aθ of the sector; and calculate the area for an angle of π/4
The area is:
A = (θ/2)*R^2
The circumference is:
C = θ*R
And the area of the circle when the angle is π/4 is: 39.25 cm^2
How to find the area in terms of the angle?
For a circle of radius R, the area is:
A = pi*R^2
where pi = 3.14
And the circumference is:
C = 2*pi*R
Now, remember that a circle has an angle of 2pi radians, then if we only define an arc in the circle, defined by an angle θ, the area of said arc will be:
A = (θ/2pi)*pi*R^2 = (θ/2)*R^2
And the circumference is:
C = (θ/2pi)*2pi*R = θ*R
Now, we want to find the area when the circle has a radius R = 10cm and θ = pi/4
Replacing that in the area equation, we get:
A = (pi/4/2)*(10cm)^2 = (3.14/8)*(10cm)^2 = 39.25 cm^2
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How many values are in the range?
0 to 50
Solve for x
(please write work)
Answer:
x = -9
Step-by-step explanation:
12 + 2x + 24 = 27 + x
(12 + 24) + 2x = 27 + x
36 + 2x = 27 + x
subtract 27 from both sides
36-27 + 2x = 27-27 + x
9 + 2x = x
subtract x from both sides
9 + x = 0
subtract 9 from both sides
x = -9
(the steps could've been faster but that shows the most work)
check:
12 + 2(-9) + 24 = 27 + (-9)
36 - 18 = 18
18 = 18
True!
so -9 is correct
Answer:
Step-by-step explanation:
To solve for x, bring the variable to one side, and bring all the remaining values to the other side by applying arithmetic operations on both sides of the equation. Simplify the values to find the result.
do the quantities combine?
Answer:
D
Step-by-step explanation:
Widrawal is - 30
Deposit is +30
-30+30 = 0
Show all work to write the expression in simplified rational exponent form:
[tex](\sqrt[4]{x^{2}+4 } )^{3}[/tex]
(Fourth root of x squared plus four, cubed)
Answer:
[tex]x^{\frac{1}{2} } + 48[/tex]
Step-by-step explanation:
This is hard to explain, but basically you use exponent rules to switch it to an exponent
[tex](\sqrt[4]{x^{2} +4} )^{3}[/tex]
It's easiest if you calculate [tex]4^{3}[/tex] first
4³ = 4 x 4 x 4 = 48
Then convert the root to a fraction exponent
[tex]\sqrt[4]{x^{2}} = x^{\frac{2}{4}} = x^{\frac{1}{2} }[/tex]
Combine them using addition, since addition was in the problem
[tex]x^{\frac{1}{2} } + 48[/tex]
I hope this helps!
need heeeelp please
Answer:
7.61577310586
Step-by-step explanation:
Pythagoras Theorem 7 squared + 3 squared= 49+9=58
[tex]\sqrt{58}[/tex]
Which expression can be used to find the sum of the polynomials?
(9 - 3x2) + (-8x2 + 4x + 5)
The expression which can be used to determine the algebraic sum of the given polynomials as in the task content is; -11x² +4x +14.
Which expression can be used to find the sum of the given polynomials?It follows from the task content that the polynomials whose sum are to be determined are; (9 - 3x2) + (-8x2 + 4x + 5).
Hence, the sum can be evaluated as follows;
= 9 - 3x² + -8x² + 4x + 5
= -11x² +4x +14.
Consequently, the required expression is; -11x² +4x +14.
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Answer:
Step-by-step explanation:
is 100 for the points
3. What is the measure of angle B from the right triangle below?
Answer:
angle B = 78.46°
Step-by-step explanation:
Use the cosine ratio
[tex]cosB=\frac{2}{10} =0.2[/tex]
[tex]B=cos^{-1} (0.2)=78.46^{0}[/tex]
Hope this helps
Is -2.3456 an irrational number
Answer:
No.
Step-by-step explanation:
Negative decimal numbers are rational numbers since rational numbers include all the integers both positive and negative integers, decimal as well as a fraction because decimals can be written as fractions.
HELP ASAP WITH EXPLANATION: If f(x) + f(2 − x) = 4 for all x, find f(y − 2) + f(4 − y)
Answer:
f(y-2)+f(4-y)=4
Step-by-step explanation:
Assume (let) x=y-2
So: y=x+2
f(y-2)+f(4-y)=f(x)+f(-x+2)=f(x)+f(2-x)
The value of that expression is 4 from the given.
find cube roots of -117 + 44i
By De Moivre's formula, the cubic roots of the complex number are 3 + i 4, - 4.96 + i 0.60 and 1.96 - i 4.60.
How to find the cube root of a complex number
Herein we have a complex number in rectangular form, from which we need its magnitude (r) and direction (θ) and the De Moivre's formula as well. The root formula is introduced below:
[tex]z^{\frac{1}{n} } = r^{\frac{1}{n} }\cdot \left[\cos \left(\frac{\theta + 2\pi\cdot k}{n}\right) +i\,\sin \left(\frac{\theta + 2\pi\cdot k}{n}\right)\right][/tex], for k ∈ {0, 1, ..., n - 1} (1)
Where n is the grade of the complex root.
The magnitude and direction of the complex number are 125 and 0.886π radians, respectively. Thus, by the De Moivre's formula we obtain the following three solutions:
k = 0
z₁ = 2.997 + i 4.002
k = 1
z₂ = - 4.964 + i 0.595
k = 2
z₃ = 1.967 - i 4.597
By De Moivre's formula, the cubic roots of the complex number are 3 + i 4, - 4.96 + i 0.60 and 1.96 - i 4.60.
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Use a graphing tool to solve the equation for x. -4x − 1 = 5x + 4
Answer:
-5/9
Step-by-step explanation:
-4x - 1 = 5x +4 Add 4x to both sides
-1 = 9x + 4 Subtract 4 from both sides
-5 = 9x Divide both sides by 9
-5/9 = x
Two companies working together can clear a parcel of land in 8 hours. Working alone, it would take Company A 4 hours longer to clear the land than it would Company B. How long would it take Company B to clear the parcel of land alone?
The time taken for Company B to clear the parcel of land alone is 14.25 hours
Rate of workTime for Company B to clear the parcel of land alone = xCompany B work rate = 1/xTime for Company A to clear the parcel of land alone = x + 4Company A work rate = 1/x+4Time for both Company to clear the parcel of land alone = 8 hoursBoth Company work rate = 1/81/8 = 1/x + 1/(x + 4)
1/8 = (x+4)+ (x) / (x)(x+4)
1/8 = (x+4+x) / (x² + 4x)
1/8 = 2x+4 / (x² + 4x)
cross product
1(x² + 4x) = 8(2x + 4)
x² + 4x = 16x + 32
x² + 4x - 16x - 32 = 0
x² - 12x - 32 = 0
Using quadratic formula
x = 14.25 or -2.25
The time taken for Company B to clear the parcel of land alone can only be positive,
Therefore, it is 14.25 hours
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The difference of the square of a number and 36 is equal to 5 times that number. Find the positive solution.
Answer:
x=-4, x=9
Step-by-step explanation:
We write this into words:
difference = subtraction
square = ^2
a number = x
is equal to = =
5 times that number = 5x
x^2-36 = 5x
write in standard form
x^2-5x-36
what adds to -5 and multiplies to -36?
-9 and 4!
(x-9)(x+4)
x-9 = 0
x= 9
x+4 = 0
x=-4
Answer:
9
Step-by-step explanation:
Let the number = x.
x² - 36 = 5x
x² - 5x - 36 = 0
(x - 9)(x + 4) =0
x = 9 or x = -4
Answer: 9
121 slabs . How many slabs will she need to lay in each row to make a square
She needs to lay 11 slabs on each row to make a square
How to determine the number of slabs in each row?The total number of slabs is given as:
Total = 121 slabs
Let this represent the area of the slab.
The area of a square is calculated as:
Area = Length^2
Substitute the known values in the above equation
Length^2 = 121
Take the square root of both sides
Length = 11
Hence, she needs to lay 11 slabs on each row to make a square
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Answer the following.
(a) A certain solution has a hydrogen ion concentration of 0.00000896 moles per liter. Write this number in scientific notation.
(b) A humpback whale can weigh up to ×1.1105 pounds. Write this number in standard notation.
Answer:
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a. The decimal number 0.00000896 can be written as 8.96 × [tex]10^{-6}[/tex] in scientific notation.
b. 1.1105 pounds is written in standard notation as 1.1105 pounds.
We have,
(a) To write the number 0.00000896 moles per liter in scientific notation, we move the decimal point to the right until there is one
non-zero digit to the left of the decimal point.
The number of decimal places we moved to the decimal point will be the exponent of 10 in the scientific notation.
So,
= 0.00000896
= 896/100000000
= 896 x 100/100 x [tex]10^{-8}[/tex]
= 896/100 x [tex]10^{-8 + 2}[/tex]
= 8.96 × [tex]10^{-6}[/tex]
(b)
To write the number 1.1105 pounds in standard notation, we simply write the number as it is, without any scientific notation or exponent.
1.1105 pounds is written in standard notation as 1.1105 pounds.
Thus,
a. The decimal number 0.00000896 can be written as 8.96 × [tex]10^{-6}[/tex] in scientific notation.
b. 1.1105 pounds is written in standard notation as 1.1105 pounds.
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A 1L IV contains 60meq of kcal. The IV was discontinued after 400ml has infused. How much lvl did the patient receive
If a 1L IV contains 60meq of kcal and the IV was discontinued after 400ml has infused, then the amount of IV received by the patient is 24meq of kcal.
Calculation for the Amount of IV
It is given that,
1L IV contains 60meq of kcal
⇒ 1000 mL of IV contains 60meq of kcal
⇒ 1 mL of IV will contain 60 / 1000 meq of kcal
As per the question,
The amount of IV infused in the patient = 400 mL
⇒ The amount of IV received by the patient in meq of kcal = 400 × (60 / 1000)
= 4 × 6
= 24 meq of kcal
Hence, the patient receives 24meq of kcal amount of IV.
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can someone give the exact answer for all the blanks
Considering the given function, we have that:
f(a) = 4 - 2a + 6a²f(a + h) = 6a² + 12ah + 6h² - 2a - 2h + 4.[f(a + h) - f(a)]/h = 12a + 6h - 2.What is the function for this problem?The function is:
f(x) = 4 - 2x + 6x².
When x = a, we have that:
f(a) = 4 - 2a + 6a².
When x = a + h, we have that:
f(a + h) = 4 - 2(a + h) + 6(a + h)² = 6a² + 12ah + 6h² - 2a - 2h + 4.
For the fraction, we have that:
[f(a + h) - f(a)]/h = [6a² + 12ah + 6h² - 2a - 2h + 4 - 4 + 2a - 6a²]/h = [12ah + 6h² - 2h]/h = h(12a + 6h - 2)/h
Hence:
[f(a + h) - f(a)]/h = 12a + 6h - 2.
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PLEASE help with question ASAP ASAP
Answer:
No classification is guaranteed.
Use the method of equating coefficients to find the values of a, b, and c: (x+4)(ax2+bx+c)=−2x3−7x2+3x−4.
The values of the coefficients a, b and c in the equation is -2, 1 and -1 respectively.
What is an equation?An equation is an expression that shows the relationship between two numbers and variables.
An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.
Given the polynomial:
-2x³ - 7x² + 3x - 4
Simplifying:
= -(2x² - x + 1)(x + 4)
Hence:
-2x³ - 7x² + 3x - 4 = (-2x² + x - 1)(x + 4)
(x + 4)(ax² + bx + c) = −2x³ − 7x² + 3x − 4
The values of the coefficients a, b and c in the equation is -2, 1 and -1 respectively.
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A freighter has to go around an oil spill in the Pacific Ocean. The captain sails due east for 30 miles. Then he turns the ship and heads due north for 14 miles. What is the distance and direction of the ship from its original point of course correction? Round each number to the nearest whole number.
The distance and direction of the ship from its original point of course correction is 33 miles and 23° respectively.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Pythagoras theorem is used to show the relationship between the sides of a right angled triangle.
Let x represent the distance travelled, hence:
x² = 14² + 30²
x = 33 miles
tanФ = 14/33
Ф = 23°
The distance and direction of the ship from its original point of course correction is 33 miles and 23° respectively.
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