The graph of y = In(x) was transformed by shifting 8 units left and 12 units up. Write an equation( please help!!)
Answers
The parent function and transformed function will be y = ln x and y = ln (x + 8) + 12, respectively.
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
The function is given below.
y = ln x
The function is transformed by shifting 8 units left and 12 units up. Then replace x with (x + 8) and y with (y - 12). Then we have
y - 12 = ln (x + 8)
y = ln (x + 8) + 12
The parent function and transformed function will be y = ln x and y = ln (x + 8) + 12, respectively. The graph of the function is given below.
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Related Questions
at an entertainment center, two groups of people bought batting tokens and miniature golf games. the first group bought 16 tokens and 3 golf games for $30. the second group bought 22 tokens and 5 golf games for $43. find the cost of a battling token and the cost of a miniature golf game.
Answers
An equation system's solution is a collection of values for the variable that concurrently fulfill each equation.
The system's answer is: what is it?An equation system's solution is a collection of values for the variable that concurrently fulfill each equation. Finding all of the possible sets of variable values that make up the system's solutions is necessary to solve an equation system. However, the second equation does not have a solution at (5, 4).An equation system's solution is a collection of values for the variable that concurrently fulfill each equation.There are an endless number of ordered pairs that satisfy both of the equations if both variables are removed and you are left with a true assertion. Actually, the lines of the equations are identical.To lean more about system's solution refer to:
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The cost of a battling token is $1.5 and the cost of a miniature golf game is $2.
The system's answer is: what is it?The set of values for the variable that simultaneously satisfy all of the equations in an equation system is called the solution. In order to solve an equation system, all sets of variable values that could possibly exist must be found. The second equation, however, is initially without a solution (5, 4).
The set of values for the variable that simultaneously satisfy all of the equations in an equation system is called the solution.
If both variables are eliminated and you are left with a true statement, there are an infinite number of ordered pairs that satisfy both equations. In reality, the equations' lines are the same.
Let cost token be x and golf games be y, i.e.
16x + 3y = 30
22x + 5y = 43
Lets Solve by using Elimination method both the expression in equal terms
80x + 15y = 150
- 66x + 15y = 129
14x = 21
x = 21/14
x = 1.5
Then, for y
16(1.5) + 3y = 30
y = 2
Thus, The cost of a battling token is $1.5 and the cost of a miniature golf game is $2.
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how to solve 66 divided by 7 using standard algorithm
Answers
Answer: The standard algorithm for division is also known as long division, it is a method for solving division problems that involve larger numbers. To solve 66 divided by 7 using the standard algorithm, you can follow these steps:
Step 1: Write the dividend (66) and the divisor (7) in a division problem format, like this:
66 | 7
--- |
Step 2: Divide the first digit of the dividend (6) by the divisor (7). Since 6 is less than 7, write a 0 as the first digit of the quotient.
66 | 7
--- | 0
Step 3: Multiply the divisor (7) by the first digit of the quotient (0) and write the product (0) under the first digit of the dividend (6).
66 | 7
--- | 0
0 |
Step 4: Subtract the product (0) from the first digit of the dividend (6) and write the result (6) under the subtraction.
66 | 7
--- | 0
0 | 6
Step 5: Bring down the next digit of the dividend (6) and append it to the result of the subtraction to form a new 2-digit number (66).
66 | 7
--- | 0
0 | 6
| 66
Step 6: Divide the new 2-digit number (66) by the divisor (7) and write the quotient (9) above the line.
66 | 7
--- | 09
0 | 6
| 66
Step 7: Multiply the divisor (7) by the quotient (9) and write the product (63) under the new 2-digit number (66).
66 | 7
--- | 09
0 | 6
--- | 63
Step 8: Subtract the product (63) from the new 2-digit number (66) and write the result (3) under the subtraction.
66 | 7
--- | 09
0 | 6
--- | 63
| 3
Step 9: Write the final result (9) as the quotient and the remainder (3) of the division problem.
66 | 7
--- | 09
0 | 6
--- | 63
| 3
So, 66 divided by 7 = 9 with a remainder of 3
So the answer is 9 R 3
Step-by-step explanation:
The solution is: 66 divided by 7 is 9 with a remainder of 3.
The standard algorithm for division is also known as long division, it is a method for solving division problems that involve larger numbers.
To solve 66 divided by 7 using the standard algorithm, you can follow these steps:
Step 1: Write the dividend (66) and the divisor (7) in a division problem format, like this:
66 | 7
--- |
Step 2: Divide the first digit of the dividend (6) by the divisor (7). Since 6 is less than 7, write a 0 as the first digit of the quotient.
66 | 7
--- | 0
Step 3: Multiply the divisor (7) by the first digit of the quotient (0) and write the product (0) under the first digit of the dividend (6).
66 | 7
--- | 0
0 |
Step 4: Subtract the product (0) from the first digit of the dividend (6) and write the result (6) under the subtraction.
66 | 7
--- | 0
0 | 6
Step 5: Bring down the next digit of the dividend (6) and append it to the result of the subtraction to form a new 2-digit number (66).
66 | 7
--- | 0
0 | 6
| 66
Step 6: Divide the new 2-digit number (66) by the divisor (7) and write the quotient (9) above the line.
66 | 7
--- | 09
0 | 6
| 66
Step 7: Multiply the divisor (7) by the quotient (9) and write the product (63) under the new 2-digit number (66).
66 | 7
--- | 09
0 | 6
--- | 63
Step 8: Subtract the product (63) from the new 2-digit number (66) and write the result (3) under the subtraction.
66 | 7
--- | 09
0 | 6
--- | 63
| 3
Step 9: Write the final result (9) as the quotient and the remainder (3) of the division problem.
66 | 7
--- | 09
0 | 6
--- | 63
| 3
So, 66 divided by 7 = 9 with a remainder of 3
So the answer is 9 R 3.
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Which of the following is a right triangle?
55°
70°
55
Triangle A
OA. Triangle D
OB. Triangle A
O C. Triangle C
OD. Triangle B
24°
45°
SAA
90°
45
Triangle C
30°
126
Triangle B
60°
60
60°
Triangle D
Answers
Step-by-step explanation:
A right triangle is a triangle that has one angle that measures 90 degrees. Based on the information provided, the following triangles are right triangles:
Triangle A - OA. 55° and 70° are not right angles
Triangle B - OB. 30° and 60° are not right angles
Triangle C - O C. 45° and 45° form a right angle
Triangle D - OD. 60° and 60° form a right angle.
SAA is a mnemonic for solving the triangle, not a triangle itself
24°, 45°, and 126° are not angles that form a triangle as the sum of all angles in a triangle is 180.
Alyssa draws the following model to solve a problem.
Which problem is Alyssa trying to solve?
A. 3 5/8−1 7/8
B. 3 7/8−1 3/4
C. 4 5/8−1 7/8
D. 4 1/2−1 7/8
Answers
According the diagram, Alyssa trying to solve the problem 4 5/8 - 1 7/8. So the option C is correct.
Alyssa draws the following model to solve a problem.
We can see on the diagram that there have lock of two colors red and black. Some block are cut in both colors.
The total block of red color = 3
The total block of black color = 13/8
So the total block = 3 + 13/8
The total block = (24 + 13)/8
The total block = 37/8
The total block = 4 5/8
The block cut in color red = 1
The block cut in color black = 7/8
Total cut block = 1 + 7/8
Total cut block = (8 + 7)/8
Total cut block = 15/8
Total cut block = 1 7/8
So the problem should be
= The total block - Total cut block
= 4 5/8 - 1 7/8
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The complete question is given below:
Sentence letter are ingle letter P,Q, R, etc. tranlated to Englih entence that are either true or fale.
Answers
The English sentences that are translated from single letters, such as P, Q, R, etc., can either be true or false depending on the context in which they are used.
For example, if P is translated as "the sky is blue," then this sentence is true. However, if P is translated as "the sky is orange," then this sentence is false. In order to determine the truth value of the translated sentence, we must first identify the context in which the letter is being used. Then, we can decide whether the translation is true or false by using logic and reasoning. For example, if we know that the sky is not orange, then the translation of P can be determined to be false.
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PLEASE HELP Graph the line that represents a proportional relationship between y and x where the unit rate of change of y with respect to x is 0.4. In other words, a change of 1 unit in x corresponds to a change of 0.4 units in y.
Graph the line and write the equation of the line.
Answers
A proportional relationship between y and x can be represented by a linear equation of the form:
y = kx
where k is the unit rate of change of y with respect to x. Given that the unit rate of change of y with respect to x is 0.4, we can substitute this value for k in the equation:
y = 0.4x
This equation represents the line that shows the proportional relationship between y and x.
To graph this equation, we can use the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept. We can rewrite our equation as:
y = 0.4x + b
Since the y-intercept is the point where the line crosses the y-axis, we can substitute any value of x with 0 and solve for b
y = 0.4x + b
y = 0.4*0 + b
y = b
So the y-intercept is b = 0
Therefore, the slope-intercept form of the equation is y = 0.4x + 0
To graph the line, we can take any two x values and substitute them into the equation, and then plot the corresponding y values on the graph. For example, when x = 0, y = 0.40 + 0 = 0 and when x = 1, y = 0.41 + 0 = 0.4.
We can use these points to plot the line on a graph, it will be a straight line passing through the point (0,0) with a slope of 0.4.
Note: This line is also known as the direct variation equation.
Answer:
Y=0.4X
Step-by-step explanation:
when x=1, Y =0.4
when x=2, Y=0.8
Now you have 2 points, draw a line. voila.
see attached
(x^4+10x^3+10x^2-15x-6)/(x+2) Synthetic Division
Answers
(x^4+10x^3+10x^2-15x-6)/(x+2) Synthetic Division
The synthetic division for the polynomial (x^4+10x^3+10x^2-15x-6) divided by (x+2) would be:
x^3 + 8x^2 - 19x - 12 + (R)
Where R is the remainder.
The quotient is x^3 + 8x^2 - 19x - 12
What is a synthetic division for the polynomial?A synthetic division, also known as long division of polynomials or polynomial synthetic division, is a method of dividing polynomials that is faster and simpler than the traditional polynomial long division method. It is particularly useful for dividing a polynomial by a linear factor of the form (x - a), where a is a real number.
Synthetic division allows you to divide a polynomial by a linear factor without having to perform the traditional long division algorithm, by using the polynomial's coefficients instead of the polynomial itself. Synthetic division is also useful for finding the remainder of a polynomial division. The quotient and the remainder are written in a form of simplified polynomials.
Therefore, the correct answer is as given above
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100 POINTS ANSWER QUICKLY Question 3 Part C (4 points): Based on what you learned about causation in lesson 5. 07, give a real world scenario that would represent a causal relationship
Answers
The real world scenario that would represent a causal relationship in causation:
Example 1: Shark attacks and sales of ice cream
Example 2: Box Office Income and Master's Degrees
Example 3: Nuclear Energy Production vs. Pool Drownings
Example 4: Marriage Rate versus. Measles Cases
The concept of causation states that one occurrence results in another event. Just a test with a correct engineering can demonstrate correlation. Similar groups are given various treatments in these trials, and the results of each group are examined. Only when there is a discernible difference between the groups' results can we say that a treatment had an impact.
People frequently misunderstand and misuse the concept of causality in statistics because they believe that just because data reveals a correlation, there must definitely be an underlying causal relationship.
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Create a diagram based on the given symbolic statement. Be sure enough information is provided in the diagram to validate each statement. △FUN≅△CAR
Answers
The triangle △FUN is congruent to the triangles △CAR. And the diagram is given below.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
The ratio of the matching sides will remain constant if two triangles are comparable to one another.
In triangles △FUN and △CAR, then we have
∠FUN = ∠CAR = 90°
∠UFN = ∠ACR
FN = CR
Then the triangles △FUN and △CAR are congruent triangles. And the diagram is given below.
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Which is the y-intercept of the relationship represented in the table?
x y
-8 -3
-5 0
-2 3
1 6
-3
-5
5
3
Answers
Two teammates competed in a long jump competition. Their distances on 4 jumps are
listed in the table. Which statement about the recorded data is true?
Answers
Heath had the longest jump of 6 meters in the competition.
What is Comparison Theory?Comparison theory is a psychological theory that proposes that people use social comparisons to better understand their own value and place in society. According to this hypothesis, people compare themselves to others in order to assess themselves, typically focusing on the traits that they have and the qualities that other people have. Individuals utilise the comparison to estimate their own value and how they should conduct in order to achieve approval and acceptance from their peers.
This question requires the use of the Comparison Theory.
This theory states that when presented with two or more items, we can compare them to determine which is larger, smaller, longer, shorter, etc.
In this case, we need to compare the distances of each jump for each teammate in order to determine which one had the longest jump.
Step 1: Look at the distances of each jump for Heath.
Step 2: Look at the distances of each jump for Amari.
Step 3: Compare the distances of each jump for both Heath and Amari.
Step 4: Determine which jump was the longest - Heath's 6 meter jump.
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what is y=12x-35 domain and range
Answers
The domain and the range of y = 12x - 35 are the set of all real numbers
How to determine the domain and the range?from the question, we have the following parameters that can be used in our computation:
y = 12x - 25
There is no restriction on the input values, x
So, the domain of y = 12x - 35 is all real numbers, since there is no restriction on the input (x).
The range of y = 12x - 35 is also all real numbers, since the output (y) can be any real value, depending on the input (x).
This can be seen by considering that for any real number x, the output y = 12x - 35 will also be a real number.
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4. If 2 is subtracted from three times a number, the result is equal to 5 less than three times
the number. Find the number.
Answers
The resulting equation: 3x - 2 = 3x - 5
This equation does not have any true answer, meaning either the question asked is wrong or you have typed this equation wrong.
The only answer you could write for this is No Solution.
Suppose the diameter of a circle is 8 units. What is its circumference? Use 3.14 for ππpi and enter your answer as a decimal.
Answers
The circumference of a circle with diameter 8 units is equal to 25.14 units.
How to calculate the circumference of a circle
Circumference is the perimeter of a circle, circles are featured solely by diameter. The formula for circumference is described below:
s = π · D
Where D is the diameter, in units.
If we know that D = 8 units, then the circumference of the circle is:
s = π · 8
s = 8π
s = 25.14
The circle (diameter: 8 units) has a circumference of 25.14 units.
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You sell triangular flags made from felt. How much felt do you need to make 60 60 flags?
Answers
The cost of making 60 triangular flags with base 3.5feet and height 2.5 feet with making charges of $0.40per square foot is equal to $105.
Flag is triangular in shape.
Base of the flag = 3.5 feet
Height of the flag = 2.5feet
Area of the flag = ( 1/2) base × height
= ( 1/2 )× ( 3.5 ) × ( 2.5)
= 4.375 square feet.
Cost of one square foot flag = $0.40
Cost of making one flag = $ ( 0.40 × 4.375 )
= $ 1.75
Cost of making 60 flags = $ ( 1.75 × 60 )
= $ 105.
Therefore, the cost of making 60 triangular flag is equal to $105.
The given question is incomplete, I answer the question in general according to my knowledge:
You make and sell triangular flags. Each flag has a base of 3.5 feet and a height of 2.5 feet. Fabric for the flags costs $0.40 per square foot. What is the cost to make 60 flags?
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HELP ASAP!!! GIVING 50 POINTS!!
Answers
Answer:
200,000 times
Step-by-step explanation:
80 km × (1000 m)/(1 km) × (100 cm)/(1 m) = 8,000,000 cm
8,000,000 cm / 40 cm = 200,000
Answer: 200,000 times
imagine you are painting a series of towers built from cubes. You are going to paint only the exposed faces of the cubes. If the tower you paint has 25 exposed faces, how many cubes are in the tower?
Answers
Answer:
101 Faces
Step-by-step explanation:
Hope it helps + get it right
PLEASE HELP ASAP!!!!
Answers
The inverse matrix of the given matrix is
[tex]\left[\begin{array}{ccc}3/2&-2\\-1/2&1\end{array}\right][/tex]
What is meant by inverse matrix?
If A is a non-singular square matrix, then A^-1, often known as the inverse matrix of A, must exist if it is to satisfy the following property:
AA^-1 = A^-1A = I, Where I is the Identity matrix
Now, we will first find the determinant of the given matrix, whichis as follows:
Determinant = 6-4 = 2
Since, the determinant is not zero, this means that the inverse matrix exists.
Now, let's find the inverse matrix i.e. A^-1
[tex]A^{-1} = \frac{1}{D} \left[\begin{array}{ccc}d&-b\\-c&a\end{array}\right][/tex]
[tex]A^{-1} = \frac{1}{2} \left[\begin{array}{ccc}3&-4\\-1&2\end{array}\right][/tex]
[tex]A^{-1} = \left[\begin{array}{ccc}3/2&-4/2\\-1/2&2/2\end{array}\right][/tex]
[tex]A^{-1} = \left[\begin{array}{ccc}3/2&-2\\-1/2&1\end{array}\right][/tex]
Hence, the inverse matrix of the given matrix is as under
[tex]\left[\begin{array}{ccc}3/2&-2\\-1/2&1\end{array}\right][/tex]
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The scatter plot shows a hiker's elevation above sea level during a hike from the base to the top of a mountain. The equation of a trend line for the hiker's elevation is y=9.54x+694, where x represents the number of minutes and y represents the hiker's elevation in feet. Use the equation of the trend line to estimate the hiker's elevation after 145 minutes.
Answers
By using the equation of the trend line, the hiker's elevation after 145 minutes is equal to 2,077.3 feet.
How to determine the hiker's elevation after 145 minutes?In order to determine the hiker's elevation after 145 minutes, we would have to substitute the value representing the number of minutes (x) into the linear equation that models the hiker's elevation in feet and then evaluate as follows;
y = 9.54x + 694
When the value of x = 145 minutes, the hiker's elevation (y) in feet is given by;
Hiker's elevation (y) = 9.54x + 694
Hiker's elevation (y) = 9.54(145) + 694
Hiker's elevation (y) = 1,383.3 + 694
Hiker's elevation (y) = 2,077.3 feet.
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✓3
After how many minutes will the two pools have the same
amount of water?
minutes
Check
5
Two pools are being filled with water. To start, the first pool contains 654 liters of water and the second pool is empty. Water is being added to the first pool at a
rate of 18.5 liters per minute. Water is being added to the second pool at a rate of 45.75 liters per minute.
How much water will be in each pool when they have the
same amount?
liters
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Answers
a. The amount of minutes it will take for the two pools to have thesame amount of water is 24 minutes
b. The amount of water in each pool is 1098liters
What are Simultaneous equations?Simultaneous equations are two or more algebraic equations with the same unknown variables and the same value of the variables satisfies all such equations. This implies that the simultaneous equations have a common solution. Some of the examples of simultaneous equations are: 2x - 4y = 4, 5x + 8y = 3.
Represent the number of minutes it will take the two pool to have thesame amount y be x
therefore ;
y = 654+ 18.5x equation 1
y = 0+ 45.75x equation 2
from equation 2, y = 45.75x
substitute 45.75x for y in equation 1
45.75x = 654+ 18.5x
collect like terms
654 = 45.75x - 18.5x
654 = 27.25x
x = 654/27.25
x= 24minutes
from equation 2,
y = 0 + 45.75 × 24
y = 1098 litres
therefore at 24minutes the first and second pool will have the same volume of water of 1098litres
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The water in each pool when they have the same amount will be 1098 liters.
How to calculate the equation?An equation simply has to do with the statement that illustrates the variables given.
In this case, two pools are being filled with water. To start, the first pool contains 654 liters of water and the second pool is empty. Water is being added to the first pool at arate of 18.5 liters per minute.
Water is being added to the second pool at a rate of 45.75 liters per minute.
Let the minute be represented by m. The equation will be:
653 + 18.5m = 45.75m
Collect the like terms
45.75m - 18.5 m = 654
27.25m = 654
Divide
m = 654 / 27.25
m = 24 minutes
The water in each pool when they have the same amount will be:
= 45.75 × 24
= 1098 liters
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A model of Seattle, Washington space Needle is 20 inches tall The actual Space Needle is approximately 600 feet tall a: what does the 1 inch represent in the model? what is the scale? b: what is the scale factor model ?
Answers
Answer: 30
Step-by-step explanation: 600/20=30 so each inch on the scale represents 30 feet in real life.
Does this equation have any possible values?
x+1/2=x-1/2
Answers
Answer: No solution
Step-by-step explanation:
x + 1/2 = x - 1/2
Subtract x from both sides:
1/2 = -1/2
This is not true, so there are no solutions to this equation
Answer:
Step-by-step explanation: multiply one and a half by x then thats ur answer
find the size of x
write your answer in degrees
Answers
Size of x = 102°
What is angle ?In geometry, an angle is formed when two rays are joined at their endpoints. These rays are called the sides or arms of the angle.
Given,
In triangle ABC
Sum of interior angles is 180°
∠CAB + ∠ABC + ∠BCA = 180°
87° + ∠ABC + 36° = 180°
123° + ∠ABC = 180°
∠ABC = 180° - 123°
∠ABC = 57°
In triangle DBG
Exterior angle is equal to sum of two opposite interior angles.
DGF = GDB + DBG
DGF = GDB + ABC
DGF = 45° + 57°
DGF = 102°
DGF and EFC are alternate angles made by EF and DG on BC
∴ EFC = DGF
x = 102°
Hence, 102° is size of x.
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A father Share Gtty 51, 110 among
children Atta, Abena anel Kojor Kojo has
1/2 time as much as Abena and Abeng
has 3 times
as much as Alta
Find the ratio of their shares.
Find the amount each received.
Answers
The ratio of their shares is 1:2:3 and amount is 180.5, 3564, 5371.5 respectively.
To find the amount each received:
Atta received 13.5*(51+110) = 1807.5
Abena received 27*(51+110) = 3564
Kojo received 40.5*(51+110) = 5371.5
The total amount shared is 51 + 110 = 161
The ratio of their shares is 1:2:3, meaning Atta receives 1/6 of the total amount, Abena receives 2/6 of the total amount, and Kojo receives 3/6 of the total amount.
To find the amount each received, we multiply their respective share (1/6, 2/6, and 3/6) by the total amount (161)
Kojo received 3 times as much as Atta, and Atta received 1/2 times as much as Abena.
Atta received 1/6 of the total amount, which is (51 + 110)/6 = 81/6 = 13.5
Abena received 2/6 of the total amount, which is (51 + 110)*2/6 = 162/6 = 27
Kojo received 3/6 of the total amount, which is (51 + 110)*3/6 = 243/6 = 40.5
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PLEASE HURRY TEST QUESTION LIMITED TIME!!
Question-The signals of a radio station can be received up to 80 miles away. Your house is 50 miles east and 20 miles south of the station. Can you receive the radio signals? Show all work using the equation editor to justify your answer.
Answers
Yes I can receive the radio signals.
Un empleado de una cafetería tomó 3/8 de un saco de café, lo que corresponde a 1.6875kg ¿de cuantos kilogramos era el saco de café?
Answers
Using cross multiplication method, a total of 2.7 kilograms of coffee was in the bag.
What is cross multiplication?Cross multiplying is the process of multiplying the denominator of the second fraction on the other side of the equals to symbol by the numerator of the first fraction on one side of the equals to symbol.
Comparably, the numerator of the second fraction is multiplied by the denominator of the first fraction. Cross multiply is another name for the butterfly method of multiplication. The cross-multiply method is used to find one or more variables in a fraction. Cross multiplying can also be used to compare fractions.
The fraction of 3/8 of a bag of coffee = 1.6875kg
Let, The total mass of the bag of coffee be x, i.e.
3/8 = 1.6875/x
Using Cross-multiplication
3x = 1.6875 × 8
3x = 13.5
x = 13.5/5
x = 2.7kg
Thus, Using cross multiplication method, a Total of 2.7 kilograms of coffee was in the bag.
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English Full question
An employee of a cafeteria took 3/8 of a bag of coffee, which corresponds to 1.6875kg. How many kilograms was the bag of coffee?
You are going on vacation and need to rent a car. You must chose between Hertz and Enterprise.
At Hertz you will be charged a one-time insurance fee of $80, plus $60 per day.
At Enterprise you will be charged a one-time insurance fee of $100, plus $55 per day.
Answers
Answer:
what's the question? how many days? 4 day is the breakeven mark.
Step-by-step explanation:
80+60x = 100+55x
5x =20
x=4
for a 4-day rental, it'll be the same.
if longer than 4 days, go with enterprise. shorter than 4 days go with hertz.
PLEASE HELP ASAP!!!!!!!!!
Answers
Answer:2x
Step-by-step explanation:
Answer: the correct answer would be 2x
Step-by-step explanation:
Lee made a scale drawing of a city. The scale of the drawing was 1 inch : 8 yards. The actual length of a neighborhood park is 96 yards. How long is the park in the drawing?
Answers
Answer:
12 inches
Step-by-step explanation:
Use a proportion.
1 inch is to 8 yards as x inches is to 96 yards
1/8 = x/96
Cross multiply.
8x = 96
x = 12
Answer: 12 inches
The numbers 528 and 540, written as the products
of their prime factors, are 528 = 24 x 3 × 11 and
540=22 x 3³ x 5. Hence, find
(i) the smallest non-zero whole number h for
which 528h is a multiple of 540,
(ii) the smallest whole number k for which
a factor of 540
Answers
Answer: To find the smallest non-zero whole number h for which 528h is a multiple of 540, we need to find the smallest positive whole number h such that 528h is divisible by 540.
First, we can simplify the prime factorization of 540:
540 = 22 x 3³ x 5
To make 528h a multiple of 540, we need to ensure that the prime factors of 528h are the same as the prime factors of 540.
528 = 24 x 3 x 11
So, 528h = (24 x 3 x 11)h = 24h x 3h x 11h
We can see that 24h and 11h are not factors of 540.
So, the only way to make 528h a multiple of 540 is to make 3h a factor of 3³.
3h = 3³ = 27
So, h = 27/3 = 9
So, the smallest non-zero whole number h for which 528h is a multiple of 540 is 9.
For (ii)
The smallest whole number k for which a factor of 540
540 = 22 x 3³ x 5
The smallest whole number k that is a factor of 540 is 5.
Step-by-step explanation: