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find the length of side x in simplest radical form with a rational denominator

The sum of 3/4 and a number is equal to 1/4 subtracted from six times the number. The number is \(\frac{1}{5}\).

Given The sum of \(\frac{3}{4}\)and a number is equal to \(\frac{1}{4}\) subtracted from six times the number.

Let us take the number as 'n'.

So, we can write

The sum of \(\frac{3}{4}\) and a number as \(\frac{3}{4} +n\).

To sum, one must add two or more numbers or values to produce a new number.

To subtract is to take away from another value in order to obtain the desired value.

\(\frac{1}{4}\) subtracted from six times the number as \(6n-\frac{1}{4}\)

\(\frac{3}{4} +n=6n-\frac{1}{4}\\n-6n=-\frac{1}{4}-\frac{3}{4}\\-5n=-\frac{4}{4}\\5n=1\\n=\frac{1}{5}\)

Therefore, the number is \(\frac{1}{5}\).

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The total area of the composite figure which has triangle and rectangle is  24.41 square inches

The given composite figure has two triangles and one rectangle

Area of rectangle =length × width

=4.6×3.15

=14.49 square inches

Area of left side triangle, it has base of 3.3 in and height 3.15 inches

Area of triangle = 1/2×3.3×3.15

=5.1975 square inches

Area of triangle on right side

Base = 3 in

Height = 6.3-3.15=3.15 in

Area of triangle = 1/2×3×3.15

=4.725 square inches

Total area = 14.49 + 5.1975  + 4.725

=24.41 square inches

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Answer:

B. x = 0

Step-by-step explanation:

we notice that a point and it’s image have the same y-coordinate and opposite x-coordinates

Example :

A(-2 , 2) is a point and A(2 , 2) it’s image by the reflection

\(y_{A}=2=y_{A^{\prime }}\)

\(x_{A}=-2=-x_{A^{\prime }}\)

Then the reflection is across the y-axis

Or The equation of the y-axis is  x = 0

The value of y for this ordered pair is 7.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of line AC;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (-2 + 8)/(-4 + 8)

Slope (m) = 6/4

Slope (m) = 3/2

At data point (-4, -2) and a slope of 3/2, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y + 2 = 3/2(x + 4)  

y = 3x/2 + 4

When x = 2, the y-value is given by;

y = 3(2)/2 + 4

y = 7.

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A rational number is a number that is the form p/q where p and q are integers, and q is not equal to 0.

So, in this case, we have:

We can rewrite this number as the division of two integers like this:

We can rewrite this number as the division of two integers like this:

We can rewrite this number as the division of two integers like this:

We can rewrite this number as the division of two integers like this:

We can rewrite this number as the division of two integers like this:

Therefore, all given numbers are rational because they can be expressed in the form p/q where p and q are integers, and q is different from zero.

Answer:

130 degrees

Step-by-step explanation:

DE+DA=130

Step-by-step explanation:

Actually, it tells you exactly what to do.

First, translate, i.e., move over, the coordinates up by 3:

\((1, 4)\rightarrow (1+3, 4+3) = (4, 7)\)

Then reflect this point about the x-axis and to do this,

\((x, y) \rightarrow (x, -y)\)

\((4, 7) \rightarrow (4, -7)\)

Answer:

Step-by-step explanation:

To calculate the probability of winning any amount of money, we need to sum up the probabilities of winning each individual prize.

Given the probabilities stated on the game card:

Probability of winning $10 prize = 0.2

Probability of winning $5 prize = 0.1

Probability of winning $0 prize = 0.7

To find the probability of winning any amount of money, we add these probabilities together:

0.2 + 0.1 + 0.7 = 1

The sum of the probabilities is 1, which indicates that the total probability of winning any amount of money is 1 or 100%.

Therefore, the probability of winning any amount of money in this game is 100%.

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The volume of the given cylinder in terms of pi as required to be determined in the task content is; 5000 pi.

It follows from the task content that the volume of the cylinder which is as represented is to be determined.

Since the volume of a cylinder is;

V = 2πr²h

where r = 10 and h = 25.

V = 2π × 10² × 25.

V = 5000π.

Ultimately, the volume of the given cylinder as required to be determined is; V = 5000 pi.

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Answer:

let's see what to do buddy...

Step-by-step explanation:

\( \frac{zinc}{copper} = \frac{3}{17} \\ \\ \frac{zinc}{799} = \frac{3}{17} \)

Multiply the sides of the equation by 799

\(zinc = \frac{3}{17} \times 799 \\ \\ zinc = \frac{3}{17} \times 17 \times 47 \\ \\ zinc = 3 \times 47 = 141 \)

So A jar of the chemical contains 141 grams of zinc.

And we're done.

Thanks for watching buddy good luck.

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The given statement "a divide of the collection of integers is the positive integer set and the negative integer set" is FALSE.

Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers.

The inverse additives of the equivalent positive numbers are the negative numbers.

The Z symbol is a common way for mathematicians to refer to an integer set.

The set of integers is not divided into the set of positive integers and the set of negative integers.

The lowest group and ring of the natural numbers are formed by the integers.

To distinguish them from the more generic algebraic integers, the integers in algebraic number theory are occasionally designated as rational integers.

In actuality, (rational) integers are rational numbers that are also algebraic integers.

Therefore, the given statement "a divide of the collection of integers is the positive integer set and the negative integer set" is FALSE.

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Answer:

A = 9

B = 4 (If not included the minus)

Step-by-step explanation:

We are given the expression:

\( \displaystyle \large{4 \tan (x) \sin (x) + 5 \sec(x) }\)

We are going to rewrite the expression as Asec(x)-Bcos(x).

Let's recall the Identity of Trigonometric Function:

\( \displaystyle \large{ \tan(x) = \frac{ \sin(x) }{ \cos(x) } } \\ \displaystyle \large{ \sec(x) = \frac{1}{ \cos(x) } } \\ \displaystyle \large{ { \sin}^{2} x = 1 - { \cos}^{2} x}\)

We are going to use these identities to rewrite the expression. First, let's convert tan(x) to sin(x)/cos(x) and sec(x) to 1/cos(x).

\( \displaystyle \large{4 ( \frac{ \sin(x) }{ \cos(x) } )\sin (x) + 5( \frac{1}{ \cos(x) }) }\)

Simplify the expression — multiply sin(x) to sin(x)/cos(x).

\( \displaystyle \large{4 ( \frac{ { \sin}^{2} x}{ \cos(x) } )+ 5( \frac{1}{ \cos(x) }) }\)

Rewrite sin^2 of x as 1-cos^2(x).

\( \displaystyle \large{4 ( \frac{ 1 - { \cos}^{2} x}{ \cos(x) } )+ 5( \frac{1}{ \cos(x) }) }\)

Separate the fraction:

\( \displaystyle \large{4 ( \frac{1}{ \cos(x) } - \frac{ { \cos }^{2} x}{ \cos(x) } )+ 5( \frac{1}{ \cos(x) }) }\)

Rewrite 1/cos(x) as sec(x) again as we need it for rewrite.

\( \displaystyle \large{4 ( \sec(x) - \frac{ { \cos }^{2} x}{ \cos(x) } )+ 5\sec(x) }\)

Simplify cos^2 of x and cos(x).

\( \displaystyle \large{4 ( \sec(x) - \frac{ \cos(x) }{ 1} )+ 5\sec(x) } \\ \displaystyle \large{4 ( \sec(x) - \cos(x) )+ 5\sec(x) }\)

Expand 4 in sec(x)-cos(x).

\( \displaystyle \large{4 \sec(x) - 4 \cos(x) + 5\sec(x) }\)

Add 4sec(x) and 5sec(x).

\( \displaystyle \large{9 \sec(x) - 4 \cos(x) }\)

Hence, rewritten in form of Asec(x)-Bcos(x)

The value of A is 9 and B is 4 (If not included the sign).

The difference in the proportions of both surveys goes from a maximum of 12.57% to a minimum of 4.76%.

Given that a survey found that in a sample of 75 families, 26 owned dogs, while a survey done 15 years ago found that in a sample of 60 families, 26 owned dogs, to find the 95% confidence intervals of the true difference in the proportions, the following calculation must be performed:

Therefore, the difference in the proportions of both surveys goes from a maximum of 12.57% to a minimum of 4.76%.

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Answer:

A polyhedron is a 3-dimensional solid made by joining together polygons. The word 'polyhedron' comes from two Greek words, poly meaning many, and hedron referring to surface. The polyhedrons are defined by the number of faces it has.

Step-by-step explanation:

Answer:

x- intercept = - 8 , y- intercept = 4

Step-by-step explanation:

to find the x- intercept let y = 0 in the equation and solve for x

x - 2(0) = - 8

x - 0 = - 8

x = - 8 ← y- intercept

to find the y- intercept let x = 0 in the equation and solve for y

0 - 2y = - 8

- 2y = - 8 ( divide both sides by - 2 )

y = 4 ← y- intercept

7 is added to=7+

8 times a certain number=8x

is 3 less than twice a number=2x-3

8x+7=2x-3

The two given angles are opposite interior angles, using that we will find that y = 23.

Here we have the diagram of a quadrilateral and we know that:

STU = 112°

UVS = (5y - 3)°

These are opposite interior angles on the quadrilateral, then these have the same measure, so we can write:

112 =  (5y - 3)

112 = 5y - 3

112 + 3 = 5y

115/5 = y

23 = y

That is the value of y.

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Answer:

Step-by-step explanation:

a) To find how much farther Jill's best friend jumped, we need to subtract Jill's distance from her best friend's distance. First, we need to convert both distances to the same unit, in this case inches. 6 7/8 feet is equal to 6 7/8 * 12 inches/foot = 82 7/8 inches. 6 15/16 feet is equal to 6 15/16 * 12 inches/foot = 83 16/16 inches. Now that both distances are in inches, we can subtract them: 83 16/16 inches - 82 7/8 inches = 1 9/16 inches. Therefore, Jill's best friend jumped 1 9/16 inches farther.

b) To determine if Jill's best friend beat the school record, we need to compare her distance to the record distance. The record distance for seventh graders is 6 feet 1 3/5 inches, which is equal to 6 1/5 * 12 inches/foot = 74 inches. Jill's best friend jumped 83 16/16 inches, which is greater than 74 inches. Therefore, Jill's best friend beat the school record and the seventh graders should be awarded 50 points.

c) To find the total distance thrown by Claire and Grace, we need to add their individual distances. First, we need to convert both distances to the same unit, in this case inches. 42 5/8 feet is equal to 42 5/8 * 12 inches/foot = 510 5/8 inches. 39 3/5 feet is equal to 39 3/5 * 12 inches/foot = 472 3/5 inches. Now that both distances are in inches, we can add them: 510 5/8 inches + 472 3/5 inches = 983 8/5 inches. Therefore, the total distance thrown by Claire and Grace is 983 8/5 inches.

d) To determine if the total distance thrown by Claire and Grace is greater than 83.7 feet, we need to compare their distance to the record distance. The record distance for seventh graders is 83.7 feet, which is equal to 83.7 * 12 inches/foot = 1004.4 inches. The total distance thrown by Claire and Grace is 983 8/5 inches, which is less than 1004.4 inches. Therefore, the total distance thrown by Claire and Grace is not greater than the record distance and the eighth graders should be awarded 50 points.

Answer:

The ratios are not equal, so this is not a dilation.

Step-by-step explanation:

4/3 is the first ratio

3/4 is the second ratio

Since these ratios are not equal there is not a dilation.

Ston:A

ep-by-step explnswer:

anati

We can complete the blanks with the following ratios:

(7.5 mi/1) * (1 mi/ 5280 ft) * (400ft/1 yd) * (3 ft/1 ft) =33 flags

Since we do not need a flag at the starting line, then 32 flags will be required in total.

To solve the problem, we would first convert 400 yds to feet and miles.

To convert to feet, we multiply by 3. This gives us: 400 yd * 3 = 1200 feet.

To convert to miles, we would have 0.227 miles.

Now, we divide the entire race distance by the number of miles divisions.

This gives us:

7.5 mi /0.227 mi

= 33 flags

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Answer and Step-by-step explanation:

\(\frac{13}{20}\), or 0.65 miles.

Convert both to common denominator, then add together.

They have a common denominator of 20.

\(\frac{1}{4}\) × \(\frac{5}{5} = \frac{5}{20}\)

\(\frac{2}{5}\) × \(\frac{4}{4} = \frac{8}{20}\)

\(\frac{5}{20} + \frac{8}{20} = \frac{13}{20}\)

Answer:

I would walk \(\frac{13}{20}\) or 0.65 miles.

Step-by-step explanation:

\(\frac{1}{4}\) + \(\frac{2}{5}\) = \(\frac{5}{20}\) + \(\frac{8}{20}\) = \(\frac{13}{20}\) or 0.65

Answer:

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Step-by-step explanation:

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Answer:

1\( \frac{19}{23} \)

Step-by-step explanation:

\( \frac{3}{2} \div ( \frac{1}{4} + \frac{4}{7} )\)

\( \frac{3}{2} \div ( \frac{7 + 16}{28} )\)

\( \frac{3}{2} \div \frac{23}{28} \)

Cross Multiply

\( \frac{3}{2} \times \frac{23}{28} = \frac{84}{46} \)

Reduce

\( \frac{84}{46} \div \frac{2}{2} = \frac{42}{23} \)

Divide, set the answer as the whole number and the remainder as the numerator.

1\( \frac{19}{23} \)

Answer:

1 \(\frac{19}{23}\)

Step-by-step explanation:

\(\frac{3}{2}\) ÷ (\(\frac{1}{4}\) + \(\frac{4}{7}\))  Add the fractions together first.

Rewrite them with the common denominator of 28.

\(\frac{1}{4}\) + \(\frac{4}{7}\)    4x7 = 28, so multiply the top of the first fraction by 7 to get the equivalent fraction.   7x4 = 28, so multiply the top of the second fraction  by 4 to the second equivalent fraction

\(\frac{7}{28}\) + \(\frac{16}{28}\) = \(\frac{23}{28}\)

\(\frac{3}{2}\) ÷ \(\frac{23}{28}\)  Which is the same as

\(\frac{3}{2}\) x \(\frac{28}{23}\) = \(\frac{84}{46}\)  Divide the top and bottom by 2

\(\frac{42}{23}\)      23 goes in 42 1 time with 19 left over

1 \(\frac{19}{23}\)