which two square roots are used to estimate 47

The values of a and b are 1/2 and 7/4 respectively. The sum of a and b is 9/4.

To find the values of a and b, we need to solve the system of equations formed by the given lines. Let's start by substituting the given coordinates (1, 2) into the equations:

x = (1/4)y + a -> 1 = (1/4)(2) + a -> 1 = 1/2 + a -> a = 1 - 1/2 = 1/2

y = (1/4)x + b -> 2 = (1/4)(1) + b -> 2 = 1/4 + b -> b = 2 - 1/4 = 7/4

Therefore, a = 1/2 and b = 7/4. To find the sum of a and b, we add them: a + b = 1/2 + 7/4 = 2/4 + 7/4 = 9/4

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Final answer:

Thomas will earn $2415 per month after a 15% raise on his current salary of $2100, which results in a raise amount of $315.

Explanation:

Thomas currently earns $2100, and with a 15% raise, we need to calculate the increase in his monthly pay. To find the amount of the raise, we calculate 15% of his current earnings. That is, we multiply his earnings by the raise percentage expressed in decimal form: $2100 × 0.15 = $315.

After finding the raise amount, we add it to his current salary to find his new monthly earnings. $2100 + $315 = $2415 per month. Therefore, after a 15% raise, Thomas will make $2415 per month.

Answer:

Step-by-step explanation:

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savageluzti

12/14/2017

Mathematics

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A bicyclist started riding at 8:00 A.M. The diagram below shows the distance the bicyclist had traveled at different times. What was the bicyclist's average rate of speed in miles per hour?

8:00 A.M. <--- 4.5 ---> 8:18 A.M. <------ 7.5 ------> 8:48 A.M.

The average rate of speed is ___ miles per hour.

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Average rate of speed is equal to total distance divided by the total time. the total distance is equal to 4.5+7.5, or 12 miles. The total time from 8:00 to 8:48 is 48/60 of one hour. 12*60/48=15 miles per hour

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Answer : The bicyclist's average rate of speed in miles per hour is 15 mile/hr.

Step-by-step explanation:

Average rate if speed : It is defined as the ratio total distance to total time.

Formula used :

As per question,

Total distance traveled by bicyclist = 4.5 mile + 7.5 mile = 12 mile

Total time taken by bicyclist = (8:48 A.M - 8:00 A.M) = 48 min = 0.8 hr

conversion used : ( 1 hour = 60 minute)

Now put all the given values in the above formula, we get the bicyclist's average rate of speed in miles per hour.

Therefore, the bicyclist's average rate of speed in miles per hour is 15 mile/hr.

Answer:

What is the answer to the question

Step-by-step explanation:

The rate in gram per cup is 4.5

A rate is a measure of the quantity or change in one variable with respect to another, often expressed as a ratio.

Commonly used to describe speed, efficiency, or frequency, rates quantify how one quantity changes in relation to another, usually over time.

The rate in this scenario is the slope of the line.

slope = ∆y/∆x

∆y = change in y

∆x = change in x

slope = 18-0)/4-0

slope = 18/4

= 4.5

Therefore, the rate is 4.5 grams per cup

Answer: The slope (m) of the line using two points where the line goes through is:

m = - 4 (negative 4).

Solution:

m=(y2-y1) / (x2-x1)

Taking two points in the graph where the line goes through:

P1=(0,2)=(x1,y1)→x1=0, y1=2

P2=(1,-2)=(x2,y2)→x2=1, y2=-2

Replacing in the formula of the slope:

m=(-2-2) / (1-0)

m=(-4) / (1)

m=-4

A yard is a unit of length. Hence, the Rebeccas have  [tex]\frac{11}{20}[/tex] a yard of ribbon.

What is the yard?

A yard is a unit of length in both US Customary and British Imperial Systems of Measurement.

Here, Rebecca had [tex]\frac{9}{10}[/tex] a yard of ribbon, and Rebecca gives [tex]\frac{7}{20}[/tex] of a yard of a friend.

Now, we have to subtract [tex]\frac{7}{20}[/tex] from the original [tex]\frac{9}{10}[/tex].

Since the denominator is the same as the rules of fractions.

Now, we multiply [tex]\frac{9}{10}[/tex] by [tex]\frac{2}{2}[/tex] so that the denominator [tex]10[/tex] and [tex]20[/tex] would be the same.

Therefore,

[tex]\frac{9}{10}[/tex]×[tex]\frac{2}{2}[/tex]=[tex]\frac{18}{20}[/tex].

Here, both the denominator are the same, we can subtract [tex]\frac{7}{20}[/tex] from the [tex]\frac{18}{20}[/tex].

[tex]\frac{18}{20}-\frac{7}{20}\\=\frac{11}{20}[/tex]

Hence, the Rebeccas have  [tex]\frac{11}{20}[/tex] a yard of ribbon.

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Final answer:

Rebecca has 11/20 of a yard of ribbon left after subtracting the 7/20 yard she gave to a friend from her initial 9/10 yard of ribbon by converting both fractions to have a common denominator.

Explanation:

Rebecca started with 9/10 of a yard of ribbon and gave away 7/20 of a yard. To find out how much ribbon she has left, we need to subtract the amount she gave away from the amount she started with. This can be done following these steps:

Ensure that both fractions have a common denominator. The least common multiple of 10 and 20 is 20, so multiply the numerator and the denominator of the first fraction (9/10) by 2 to get the equivalent fraction with a denominator of 20, which gives us 18/20.

Now subtract the second fraction (7/20) from the first fraction (18/20) since they now have a common denominator. This gives us 18/20 - 7/20 = 11/20.

Therefore, Rebecca has 11/20 of a yard of ribbon left.

the correct order from greatest to least is:

0.863, 0.6833, 0.386, 0.3

Answer:

need points ty

Step-by-step explanation:

The value of a number such that The difference between three-fifths of that number and 7 is -36 is -145/3.

Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,

Summation = addition of two or more numbers or variable

Subtraction = Minus of any two or more numbers with each other called subtraction.

Let's say that number is x.

Three-fifth of x ⇒ (3/5)x

The difference of (3/5)x and 7 will be,

(3/5)x - 7 = -36

Add 7 on both sides

(3/5)x = -29

Multiply 5/3 on both sides

x = -29(5/3)

x = -145/3

Hence "The value of a number such that The difference between three-fifths of that number and 7 is -36 is -145/3".

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Answer:jgxgiddgidx

Step-by-step explanation:Hgxhfzjgxgdjgjggjdjgjgcy

Counting forwards by tens reveals a pattern where the tens digit increases and the units digit remains zero. Our decimal system is designed around powers of ten, making multiplication and division by ten intuitive by simply moving the decimal point right for multiplication and left for division.

When you count forward by tens, you can notice a pattern where the unit digit is always zero, and the digit in the tens place increases by one each time. For example, starting from 10, the sequence is 10, 20, 30, 40, 50, and so forth. This happens because each number is equivalent to a number of ten dollar bills, for example, 2 ten dollar bills make 20, 3 ten dollar bills make 30, etc.

Our numerical system is a base-10, or decimal system, influenced by the fact that humans typically have ten fingers, making it natural for us to count in tens. Each place value in a number is ten times greater than the place to its right. Therefore, when we multiply a number by ten, we effectively shift all digits one place to the left, adding a zero at the end. This is similar to when we multiply by powers of ten; for instance, 103 (or 10·10·10) is 1,000. The number of zeros in a power of ten also tells us how many places to move the decimal point to the right when multiplying.

Conversely, when we divide by powers of ten, we move the decimal point to the left by the number of zeros in that power of ten. For example, dividing 1,000 by 102 (or 100) moves the decimal two places to the left, giving us 10. This is an excellent example of the practical use of the base-10 system in arithmetic operations.

When counting forward by tens, each number is 10 greater than the previous number.

The translated point for P(6, 0) under the translation (x - 6, y - 1) is (0, -1).

let's work through this step by step.

First, let's understand the translation given: (x - 6, y - 1). This means that for any point (x, y) in the original coordinate system, the corresponding point in the translated system will be (x - 6, y - 1).

Now, let's find the translated point for P(6, 0). Using the translation rule, we substitute x = 6 and y = 0 into the formula (x - 6, y - 1):

Translated point = (6 - 6, 0 - 1)

Translated point = (0, -1)

So, the translated point for P(6, 0) under the translation (x - 6, y - 1) is (0, -1).

To solve this problem, we first understand the translation rule given. In this case, the translation rule is (x - 6, y - 1), which means we subtract 6 from the x-coordinate and subtract 1 from the y-coordinate to find the new coordinates after translation.

Next, we substitute the coordinates of point P(6, 0) into the translation rule. For x, we have 6, and for y, we have 0. Plugging these values into the rule gives us (6 - 6, 0 - 1), which simplifies to (0, -1).

Therefore, the translated point for P(6, 0) under the translation (x - 6, y - 1) is (0, -1).

complete question

P(6,0) under the translation (x -6, y -1) ?

Taking into account the definition of a system of linear equations, the amount of adult tickets sold was 125.

A group of two or more first-degree equations, whereby two or more unknowns are connected, is known as a system of linear equations.

Finding the value of each unknown is necessary to solve a system of equations and verify that all of the equations are satisfied. That is to say,  it is necessary to find the values of the unknowns since, when substituted, they must result in the suggested solution in both equations.

In this case, a system of linear equations must be proposed taking into account that:

You know:

The system of equations to be solved is

s= 2×a

s + a=375

There are a number of ways to solve an equation system; nevertheless, it is decided to use the substitution method, which involves clearing one of the two variables from one of the equations in the system and replacing it with its value in the other equation.

In this case, substituting the first equation in the second you get:

2×a + a= 375

Solving:

3×a= 375

a= 375÷ 3

a= 125

Finally, the amount of adult tickets sold was 125.

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The expression that uses the greatest common factor and the distributive property to rewrite the sum 75 + 45 is B. 15(5 + 3)

The distributive property states that an expression of the form A(B + C) can be solved by a multiplication over addition operation that is

A(B + C) = AB + AC

This property is known by distributive law and applies to subtraction also.

Given; the distributive property to rewrite the sum 75 + 45

First find the greatest common factor.

75: 1, 3, 5, 15, 25, 75

45: 1, 3, 5, 9, 15, 45

Their GCF is 15.

To get 75, we will multiply 15 by 5.

To get 45, we will multiply 15 by 3.

Therefore, 15(5 + 3) = 75 + 45.

The expression that uses the greatest common factor and the distributive property to rewrite the sum 75 + 45 is B. 15(5 + 3)

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A linear equation or function is always a representation of a straight line in the coordinate plane. The equation of the line that passes through points (4, 5) and (−3, −1) is y = (6/7)x + 9/7.

A straight line on the coordinate plane is represented by a linear function.

The formula for a linear function is f(x) = ax + b, where a and b are real values.

The equation of a straight line is given by, y = mx + c

Where m is the slope while c is the y-intercept.

The slope of line passing by two points (x₁, y₁) and (x₂, y₂)

Slope(m) = (y₂ - y₁)/(x₂ - x₁)

The slope of the line that passes through  (4, 5) and (−3, −1) will be,

m = (-1 -5)/(-3-4)

m = -6/-7 = 6/7

So equation converts as, y = (6/7)x + c

Substitute, (4,5)

5 = (6/7)4 + c

c = 9/7

So, y = (6/7)x + 9/7 will be the equation.

Hence "The equation of the line that passes through points (4, 5) and (−3, −1) is y = (6/7)x + 9/7".

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To find the new mean after increasing each score by 2, we add 2 to the original mean of 84 to get a new mean of 86

The question concerns the calculation of the new mean when each score in a set is increased by a consistent amount. Given that the mean of 100 scores is 84, if we increase each score by 2, the new mean is also increased by 2. This is because the mean is the sum of all values divided by the number of values. Adding 2 to each score adds 200 to the total sum (since there are 100 scores), but the number of values remains the same. Thus, the new mean is 84 + 2, which equals 86