Hong had 8/9
of a spool of yarn. He used 2/5
of his yarn for a project. What fraction of the spool was used for the project?

Answer:23 203 feet

Step-by-step explanation:

Answer:

8.857142857

Step-by-step explanation:

Answer: 16-x

Step-by-step explanation:

Collect like terms.

-x + (6 + 10)

Simplify.

16 - x

From my calculations using  the Cymath calculator, 16 - x would be the answer, Hope I could help.

Answer:

m = -4

Step-by-step explanation:

7m + 29 = 2m + 9

-2m          -2m

--------------------------

5m + 29 = 9

      -29     -29

-----------------------

5m = -20

÷5     ÷5

--------------------

m = -4

I hope this helps!

Answer:

Step-by-step explanation:

Given that,

m∠L = 40°, m∠M = 90°

Since ΔLMN ≅ ΔPQR

(17x - y)° = 40°

(2x + 4y)° = 50°

Since, the sum of three angles of a triangle is 180 degrees.  

Then, m∠R = 1800 – 400 – 900 = 500

Remove degree from both side

17x – y = 40

2x + 4y = 50

Solving these two equations then,

x = 3, y = 11

The value of x and y would be x = 3 and y = 11.

What are congruent triangles?

Congruent triangles are triangles that have the same size and shape. In other words, congruent triangles are identical in all respects.

Given Data:

ΔLMN ≅ ΔPQR, m∠L = 40°, m∠M = 90°, m∠P = (17x - y)°, m∠R = (2x + 4y)°

as m∠L = m∠P

   17x - y = 40 ----------(I)

we know that,

m∠L + m∠M + m∠N = 180

  40 +  90 + m∠N = 180

m∠N = 50

As m∠N = m∠R

   2x + 4y = 50 -------(II)

Solving (I) and (II), we get

x=3, y=11

Hence, the value of x and y would be x = 3 and y = 11.

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Answer:

0

Step-by-step explanation:

ik my math

The value of k in the solution [tex]x=\frac{5\pm i\sqrt{k}}{8}[/tex] of the quadratic equation 4x² - 5x = -6, is 71.

Given a quadratic equation:

4x² - 5x = -6

It is required to find the solution of the quadratic equation first.

It is known that the solution of the quadratic equation of the form ax²+bx+c can be written as [tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex].

Here, the equation can be written as:

4x² - 5x + 6 = 0

Here, a = 4, b = -5 and c = 6.

Substitute.

[tex]x=\frac{-(-5)\pm \sqrt{(-5)^2-4(4)(6)}}{2(4)}[/tex]

[tex]x=\frac{5\pm \sqrt{25-96}}{8}[/tex]

[tex]x=\frac{5\pm \sqrt{-71}}{8}[/tex]

Now, [tex]\sqrt{-71} =\sqrt{-1} \sqrt{71}[/tex].

But, [tex]\sqrt{-1} =i[/tex]

So, the solution is:

[tex]x=\frac{5\pm i\sqrt{71}}{8}[/tex]

Hence, the value of k is 71.

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Answer: t=-34/3 or -11 1/3

Step-by-step explanation:

isolate t

t+19/3=-5

subtract both sides with 19/3

t=-34/3 or -11 1/3

Answer:

-34/3

Step-by-step explanation:

-5=t+6 1/3

6 1/3= 19/3

-5=t+19/3

-t. -t

-5-t=19/3

+5. +5

-t=34/3

/-1. /-1

t= - 34/3

Answer:

[tex]\frac{33\sqrt{31}}{200}[/tex]

Step-by-step explanation:

[tex]\cos x=\frac{11}{20} \implies \sin x=\sqrt{1-(11/20)^2}=\frac{3\sqrt{31}}{20} \\ \\ \sin 2x=2\sin x \cos x =2 \cdot \frac{3\sqrt{31}}{20} \cdot \frac{11}{20} =\frac{33\sqrt{31}}{200}[/tex]

Answer:  " y = x + 4 ".

Step-by-step explanation:

We shall write the equation of a line written in slope-intercept format;
 that is, " y = mx + b " ;

in which y is isolated as a single variable on the 'left-hand' side of the question, and with no "coefficient"—
   {except for the implied coefficient of 1 }; and:
m refers to the slope of the line—and is the coeffcient of x ;
and b refers to the y-intercept—or more specifically, the value of the y-coordinate when "x = 0" [i.e. the value of the y-coordinate where the line crosses the x-axis].
  So:  We can plug the given values: m = 1 ; and b = 4 ; into the equation:
  " y = mx + b " ; as follows:

   → y = 1x + 4 ;  Note: By convention,  we often omit the 1 as the coefficient of x —since the 'stand-alone' variable, x ; has an implied coefficent of x ;  and we can write the equation:                
         → y = x + 4  ;  which is our answer.|
______
 Hope this is helpful to you!  Best wishes!
______

The inequality that represents the possible depths d  reached by the vehicle is d < -725.

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

Depth record = less than -715 feet.

This means,

The depth must be -716 or less.

The vehicle breaks the depth record by more than 10 feet.

This means,

-715 - 10 = -725

The depth record must be less than -725

Thus,

The possible depths d reached by the vehicle is d < -725.

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The number of zeros of f(x) that are guaranteed to exist by the Intermediate Value Theorem is given as follows:

0.

The intermediate value theorem defines that if a continuous function passes in two points, it will pass through all the points between these two values.

The zeros of a function are all the values of x for which the function assumes a value of zero.

Hence, if for a value of x = a the function is positive, and then for a value of x = b > a the function is negative, or vice versa, a zero is guaranteed to exist in the interval between a and b.

In this problem, the function does not assume any negative values, hence a zero is not guaranteed to exist in the function, and the number is of zero.

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The total money spent on a pass and lunch for each student is $850.14.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division.

here,

As mentioned in the question, Passes for 28 pupils and 4 teachers cost the school $778.88 and the school also spends $241.64 on lunch for kids only.

Total number of person  = 28 + 4
                                     = 32
Cost per pass = 778.88 / 32
                     = $24.34
Total passes of students = 25 × 24.34 = 608.5
Total spend on lunch of student = 241.64
Total spend on lunch = 241.64 + 608.5 = $850.14

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Gavin has 6 9/20 minutes to solve the 3rd problem.

Add the time for the first two problems:

9 3/4 + 3 4/5

To add fractions rewrite them so they have a common denominator:

3/4 = 15/20

4/5 = 16/20

Now you have:

9 15/20 + 3 16/20 =  12 31/20 = 13 11/20 minutes.

Now subtract that from the time allowed:

20 - 13 11/20 = 6 9/20 minutes.

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Answer:

To find the ratio m/k, we need to combine the proportions m/n and n/k. One way to do this is to multiply the fractions to get the product m/k. This can be done by multiplying the numerators to get m, then multiplying the denominators to get k.

For example, if we let m=1, n=2, and k=5, then we have the following:

m/n = 1/2

n/k = 2/5

If we multiply the numerators and denominators to get the product m/k, we get:

(1 * 2) / (2 * 5) = 2/10 = 1/5

Therefore, the ratio m/k is 1/5.

Another way to find the ratio m/k is to use the fact that proportions are equivalent to equations. We can set up an equation using the given proportions, then solve for m/k.

For example, using the same values as before, we have:

m/n = 1/2

n/k = 2/5

We can set up an equation by setting the two proportions equal to each other:

m/n = (1/2) = n/k = (2/5)

Then we can cross-multiply to solve for m/k:

m/n * n/k = (1/2) * (2/5)

(m * 2) / (n * 5) = 1/5

m/k = (2/5) = 1/5

Therefore, in this case, the ratio m/k is also 1/5.

In general, to find the ratio m/k given the proportions m/n and n/k, we can either multiply the fractions or set up and solve an equation using the given proportions.

Answer: C; 5.32

Step-by-step explanation: If you are short $5.32, then that is represented as -5.32. The opposite of -5.32 is +5.32 or just 5.32. I hoped this helped!

Answer:

C

Step-by-step explanation:

Answer:

product is the answer good luck on your test

Answer:

x < 2 11/15

Step-by-step explanation:

Hope this helps!

a) 16 or 2/5 ratio of blue marbles not chosen

b) 86 total no. of marbles was there before the game

c) 24 blue marbles were picked

Explanation:

a) total no of blue marbles = 40

ratio of chosen blue marbles = 3/5

blue marbles picked = 40 × 3/5 = 24

blue marbles not picked = 40-24 = 16

b) total no of blue marbles + total no of red marbles = 40+ 46

total no. of marbles was there before the game = 86

c) explained in a)

What is a Ratio?

A ratio in mathematics is a comparison of two or more numbers that shows how big one is in comparison to the other. The dividend or number being divided is referred to as the antecedent, and the divisor or number that is dividing is referred to as the consequent. A ratio compares two numbers by division.

A survey of 20 respondents revealed that 13 of them preferred cake to ice cream and 7 preferred ice cream to cake. This data set can be represented as the ratio 13:7, where 13 is the antecedent and 7 is the consequent.

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Answer:

180 - (54 + 35) = 91

The answer is 'D'

Answer:2.4

Step-by-step explanation:20 - 8.99 = 2.4

Answer:

4 Inches.

Step-by-step explanation:

To find the width of Frank's scale model, we need to first determine the scale of the model. This can be done by dividing the height of the real Eiffel Tower by the height of Frank's model. Since the real Eiffel Tower is 984 feet tall and Frank's model is 12 inches tall, the scale of the model is 984 / 12 = 82 feet per inch.

Next, we can use this scale to determine the width of the model. Since the real Eiffel Tower is 328 feet wide at its base, and the scale of the model is 82 feet per inch, the width of the model must be 328 / 82 = 4 inches.

Therefore, the width of Frank's scale model of the Eiffel Tower must be 4 inches.

Answer:

1) 9x

2) 3b

3) 3m

4) 5a

5) 7x

6) 3a + 5b

7) 9x - 4

8) 2b + m

9) 13a + b + 6c

10) 9b + 1

11) 7p

12) 2a + b -10

Step-by-step explanation:

The variance in the sample data is 220

We are given the following data of 5 salespeople (expressed in thousands of dollars); 40, 60, 65, 70, 80

Suppose that the considered data set is

Then, its standard deviation is the positive square root of the variance of this data set. Variance of data set is the sum of squared differences of the data values from its mean to the total count of data values.

Thus, we get:

[tex]\sigma = \sqrt{\dfrac{1}{n} \sum_{i=1}^{n} (x_i-\overline{x})^2[/tex]

In the formula above, x represents the mean of the data points, x is the value of an individual data point, and N is the total number of data points.

x = (40+60+65+70+80)/5

x=63

So, the mean of the sample data is 63

Variance =

[tex]\sigma^2 = \dfrac{\sum_{\forall x_i} (x_i - \overline{x})^2}{n}[/tex]

Therefore, the variance is 220

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Answer:

0.15

Step-by-step explanation:

10/x=67.50

10=x*67.5

10/67.5 = x

x=0.14814814814

Part A:

We can set up a system of equations to represent the number of rocks in each person's collection. Let "S" be the number of rocks in Samuel's collection and "L" be the number of rocks in Lewis's collection. We can represent the situation as follows:

Equation 1: S = 18 + 4t

Equation 2: L = 30 + 3t

Here, "t" represents the number of weeks that have passed.

Part B:

To find out how many weeks it will take for Samuel and Lewis to have the same number of rocks in their collections, we need to set Equation 1 equal to Equation 2 and solve for "t". This gives us the following:

S = L

18 + 4t = 30 + 3t

1t = 12

t = 12 weeks

It will take 12 weeks for Samuel and Lewis to have the same number of rocks in their collections.

Part C:

To find out how many rocks Samuel and Lewis will have when the amount of rocks in their collection is equal, we can substitute the value of "t" that we found in Part B into either Equation 1 or Equation 2. For example, substituting "t = 12" into Equation 1 gives us the following:

S = 18 + 4(12)

S = 18 + 48

S = 66 rocks

Therefore, when the amount of rocks in their collection is equal, Samuel and Lewis will have 66 rocks each.

The value of the given Fraction expression is -6.93.

What is Fraction?

A fraction is a mathematical expression that represents the division of a whole number or quantity into parts. It is written as two separate numbers, a numerator and a denominator, separated by a slash. The numerator represents the number of parts being considered, and the denominator represents the total number of parts. Additionally, fractions can also represent parts of a whole number. For example, the fraction 1/2 represents one part of a whole number that has been divided into two equal parts. Fractions can also be combined to create a sum of parts.

So, we have

-15 - 3.7 + 9.15/5 * 3^2 - 4.7

Evaluate the quotient and the exponent

So, we have

-15 - 3.7 + 1.83 * 9 - 4.7

Evaluate the product

-15 - 3.7 + 16.47 - 4.7

Evaluate the sum and the difference

-6.93

Hence, the value of the given fraction expression is -6.93 (none of the options is correct)

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Algebraic representation:

[tex]\frac{4}{5}[/tex]

Answer:

2.8

Step-by-step explanation:

Answer:

2.8

Step-by-step explanation:

4/5ths is just .8 in fraction form. Add it on to your 2 and you've got your answer.

The equation of the line is y = -x/3 + 6.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction

We have the line y = 3x + 2

The slopes of perpendicular lines are negative reciprocals of each other.

The slope of the given line is m=3 the slope of the perpendicular line is -1/3.

Then the equation of the line;

y = -x/3 + b

And b is the y-intercept of the perpendicular lines passes through the point

(3,5).

Substituting the (3, 5) to the required line;

5 = -3/3 + b

b = 6

Now the line is y=-x/3 + 6

Therefore, the equation of the line is y = -x/3 + 6.

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