Find the distance between A(4,6) and B (9,7) . Write your answer as a radical and as a decimal rounded to the nearest tenth.

[tex] \bf\bigg( - 3 \frac{1}{4} d + \frac{3}{5} \bigg) - \bigg(2 \frac{7}{8} d + \frac{7}{10} \bigg)[/tex]

[tex] \bf \longrightarrow \boxed{ - \frac{49}{8}d - \frac{1}{10} } \: {\underline{\underline{ans}}}[/tex]

[tex] \bf \longrightarrow \bigg( - 3 \frac{1}{4} d + \frac{3}{5} \bigg) - \bigg(2 \frac{7}{8} d + \frac{7}{10} \bigg)[/tex]

[tex] \bf \longrightarrow \bigg( - \frac{4 \times 3 + 1}{4} d + \frac{3}{5} \bigg ) - \bigg(\frac{8 \times 2 + 7}{8} d + \frac{7}{10} \bigg)[/tex]

[tex] \bf \longrightarrow\bigg( \frac{ - 13}{4}d + \frac{3}{5} \bigg) - \bigg( \frac{23}{8}d + \frac{7}{10} \bigg)[/tex]

[tex] \bf \longrightarrow \frac{ - 13}{4}d + \frac{3}{5} + \frac{ - 23}{8} d + \frac{ - 7}{10} [/tex]

[tex] \bf \longrightarrow \bigg( \frac{ - 13}{4}d + \frac{ - 23}{8}d \bigg) + \bigg( \frac{3}{5} + \frac{ - 7}{10} \bigg)[/tex]

[tex] \bf \longrightarrow \bigg( \frac{(2 \times - 13) + (1 \times - 23) }{8}d \bigg) + \bigg( \frac{(2 \times 3) + (1 \times - 7)}{10} \bigg)[/tex]

[tex] \bf \longrightarrow \bigg( \frac{ (- 26) + ( - 23)}{8}d \bigg) + \bigg( \frac{(6) + ( - 7)}{10} \bigg) [/tex]

[tex] \bf \longrightarrow\bigg( \frac{ - 26 - 23}{8} d\bigg) + \bigg( \frac{6 - 7}{10} \bigg)[/tex]

[tex] \bf \longrightarrow\frac{ - 49}{8}d + \frac{ - 1}{10} [/tex]

[tex] \bf \longrightarrow \boxed{ - \frac{49}{8}d - \frac{1}{10} } \: {\underline{\underline{ans}}}[/tex]

[tex] \bf\bigg( - 2 \frac{1}{2} n + \frac{1}{4} \bigg) + \bigg(3 \frac{3}{4} n - \frac{5}{8} \bigg)[/tex]

[tex] \bf \longrightarrow \boxed{\frac{5}{4}n - \frac{3}{8} } \: {\underline{\underline{ans}}}[/tex]

[tex] \bf\frac{1}{5}(3x + 10) - \frac{11}{15}x[/tex]

[tex] \bf \longrightarrow \boxed{\frac{-2}{15}x + 2} \: {\underline{\underline{ans}}}[/tex]

[tex] \bf\longrightarrow\frac{1}{5}(3x + 10) - \frac{11}{15}x[/tex]

[tex] \bf\longrightarrow\frac{1}{5}(3x) + \frac{1}{5}(10) + \frac{-11}{15}x[/tex]

[tex] \bf\longrightarrow\frac{3}{5}x + 2 + \frac{-11}{15}x[/tex]

[tex] \bf\longrightarrow\bigg(\frac{3}{5}x + \frac{-11}{15}x\bigg) + 2[/tex]

[tex] \bf \longrightarrow \boxed{\frac{-2}{15}x + 2} \: {\underline{\underline{ans}}}[/tex]

Answer:

[tex]{ \tt{average \: \triangle = \frac{y _{2} - y _{1} }{x _{2} - x _{1} } }} \\ [/tex]

[tex]{ \tt{ = \frac{5 - ( - 3)}{3 - ( - 1)} }} \\ \\ = { \tt{ \frac{8}{4} }} \\ \\ = 2[/tex]

Answer:

28 units

Step-by-step explanation:

• the diagonals of a rectangle are congruent , then

AC = BD , that is

4x - 8 = 2x + 10 ( subtract 2x from both sides )

2x - 8 = 10 ( add 8 to both sides )

2x = 18 ( divide both sides by 2 )

x = 9

Then

BD = 2x + 10 = 2(9) + 10 = 18 + 10 = 28

the diagonals are 28 units long

Alexi’s sister saved about 18.4 meters by swimming across the river.

In this question,

Alexi walks 27 meters south and 38 meters east to get around a lake. Her sister swims directly across the lake.

The south and east directions are perpendicular.

The distance across the south, east and across the river form a right triangle, with the distance across the river as hypotenuse of right triangle.

Let x be the distance across the river.

Using Pythagoras theorem,

27² + 38² = x²

729 + 1444 = x²

2173 = x²

x = 46.6

The distance saved would be the difference between the sum of the two legs of the triangle and the hypotenuse (distance across the river).

distance saved = (27+38) - 46.6

                          = 18.4

Therefore, Alexi’s sister saved about 18.4 meters by swimming across the river.

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The slope - intercept form of the equation x-2 y+3=1 is  y = x/2 + 1 .

Simply said, the slope-intercept form is the technique to write a line's equation so that the y-intercept (where the line crosses the vertical y-axis) and slope (steepness) are instantly visible. This form is frequently known as the y = mx + b form.

The slope - intercept form is y = mx + c

The given equation is

x-2 y+3=1

Subtract 3 from both sides,

x - 2y = -2

Divide the whole equation by 2

x/2 - y = -1

Rearrange the equation -

y = x/2 + 1

So the equation in slope-intercept form is y = x/2 + 1 , where slope is 1/2 and c = 1.

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The equation -(a-b) = (-1)(a-b) has used the property of real numbers is Distributive Property.

Property of Real numbers:

A real number is a value that represents a quantity along a continuous number line. Real numbers can be ordered.

The properties of real numbers are,

Given,

The equation is

-(a-b) = (-1)(a-b)

Now we have to find the property used here.

Based on the properties of real number,

The one that exactly matches the equation is Distributive property.

Because the definition of Distributive property is explained through the following,

For three numbers m, n, and r, which are real in nature, the distributive property is represented as:

m (n + r) = mn + mr

The same will be applied in the given equation also.

Therefore, the Distributive property is used in the equation.

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Answer: Your answer would be C.

Step-by-step explanation:

4 x 3 is 12 so, if you divide the 12 by 3 you will get 4 making C your answer.

Answer:

(0,1)

Step-by-step explanation:

|x| is minimized when x=0, meaning the vertex is at (0,1).

Given the equation 6y = 2x, y varies directly with x and the constant of variation k has a value of 1/3.

There are two kinds of variations: direct and inverse.

Direct variation is a linear function defined by an equation of the form y = kx where variable y varies directly as x. On the other hand, inverse variation is a nonlinear function defined by an equation in the form y = k/x where variable y varies inversely as x.

Transforming 6y = 2x into a function of y,

y = 2/6 x

y = 1/3 x

where k = 1/3

Notice that it resembles the form y = kx which describes a direct variation between x and y.

Hence, the equation 6y = 2x shows that y varies directly with x and k = 1/3.

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Answer:

-16

Step-by-step explanation:

The y-intercept is when x=0.

[tex]y=-3(0+2)^2-4 \\ \\ =-3(4)-4 \\ \\ =-16[/tex]

The equation of the line passing through the point (4 , -3)  and has a slope of 1/2 is H. y = (1/2)x - 5.

The equation of a line can be expressed in different forms: standard form, slope-intercept form, and point-slope form

The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant. Meanwhile, slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept. On the other hand, given the slope m and a point on the line (x , y), we can express the equation in point-slope form, (y - y1) = m(x - x1).

Given the slope of 1/2 and a point (4 , -3), use the point-slope form to generate the equation of the line by plugging in the values in the equation.

(y - y1) = m(x - x1)

y - -3 = 1/2(x - 4)

y + 3 = (1/2)x - 2

Isolating the variable y in the left side,

y + 3 = (1/2)x - 2

y = (1/2)x - 2 - 3

y = (1/2)x - 5

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Answer:

Line 1 and Line 2 are parallel.

Answer: 22425

Step-by-step explanation: hope this helps!!

Answer:

22425

Step-by-step explanation:

Answer:

The table is linear because as x increases by 1, y changes by an average rate of |2|. You can also notice the tables both end in |+1|, which shows that the table has a constant rate of change between the two points at the end. Thus, the table is linear. If the table was nonlinear, there would be no constant rate of change between the 2 sets of data.

Answer:

It will take you nearly 11 weeks

Step-by-step explanation:

80+6x = 145

6x = 145-80

6x = 65

x = 65/6 (weeks)

The measure of the major arc JLK will be 206°. Then the correct option is B.

The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.

The measure of the minor arc JK will be 154°.

Then the sum of the major arc and minor arc in a circle is 360°.

Then the major arc JLK will be given as,

JLK + JK = 360°

JLK + 154° = 360°

JLK = 206°

The measure of the major arc JLK will be 206°. Then the correct option is B.

Your question was incomplete, but the complete question was attached below.

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Answer:

1/30 of a ton of the rock was left at the construction site

Hope this helps :)

Explanation below.

Step-by-step explanation:

1. Make the same denominators to add them which is 6 (LCM).

1/3 + 1/2

2/3 + 3/6 = 5/6

2. Make the same denominator to subtract them since had to take back 4/5 of a ton. 30 would be the Least Common Multiple of 6 and 5.

5/6 - 4/5

25/30 - 24/30 = 1/30

By combining the like terms, the simplified form of the expression 5+10s-8s is 2s+5

Given,

The algebraic expression = 5+10s-8s

Combine the like terms

5+10s-8s = 5+2s

Simplified form is 2s+5

Hence, by combining the like terms, the simplified form of the expression 5+10s-8s is 2s+5

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Drops of yellow pigment is 8.

A ratio is a comparison of two identical values that makes it simple to compare them. This is how a fraction with a numerator and denominator comparison is expressed. Depending on the ratio formula employed in various parts of mathematical computation, the definitions of the numerator and denominator may change.

For a certain shade of green, y = yellow and b = blue, where y/b = 2/3.

How many yellow drips are needed if there are 12 drops of blue,

y/b = 2/3 = x/12

= 2 × 12 = 3 × x

= 24 = 3x

= 24/3 = x

= x = 8

If you have 12 droplets of blue, you will need 8 drops of yellow.

y/b = 2/3

y = 2/3 × b

Substituting the value b = 12

y = 2/3 × 12

y = 24/3 = 8

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Answer:

The length is 10.

Step-by-step explanation:

[tex] \sqrt{ {(8 - 2)}^{2} + {(11 - 3)}^{2} } [/tex]

[tex] \sqrt{ {6}^{2} + {8}^{2} } = \sqrt{100} = 10[/tex]

Answer:

133.5

This is because transfer it to hours nd then divide and this is what you get

Answer:

0.07874506561 or 0.07875

Step-by-step explanation:

cubed root of 2 = 1.25992104989

or 1.260

The equation that describes the total number of pages of the book read as a function of the number of minutes of further reading is; 2.67x minutes.

The time it will take to finish the whole 396 pages is; 113.3 minutes

We are told that the book has 396 pages. Now, the student has read 3/8 of this book.

Thus, number of pages the student has read so far = 3/8 * 396 = 148.5 pages

Now, let the time spent reading these 148.5 pages be x minutes. Thus;

Number of pages read per minute = 148.5/x pages per minute

Number of pages left to finish book = 396 - 148.5 = 247.5 pages

Thus, time to finish remaining pages = 247.5/(149.8/x ) = 1.67x

Thus, time it will take to finish the whole 396 pages = 1.67x + x = 2.67x minutes

The table showing the amount of pages that can be read for specific minutes is attached.

We see that 7 pages are read in two minutes. Thus;

x = (148.5 * 2)/7 = 42.42857 minutes

Thus, time to finish whole book = 2.67 * 42.42857 ≈ 113.3 minutes

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Answer:

-27

there is a pattern of x3 every time :)

Answer:

Step-by

You have to determine how much more would $10,000 earn in 3 years compounded daily at 1.33% than compounded semiannually at 4.33%.

The first step is to calculate the final amount for both options. To do so, you have to use the following formula:

Where

A is the accrued amount

P is the principal amount

r is the interest rate expressed as a decimal value

t is the time in years

n is the number of compounding periods per year.

→ First, find the accrued amount for P=$10,000, R=1.33%, and t=3 years.

The account compounds daily,

The first fur terms of an arithmetic sequence are 4, 7, 10, 13

It is a series of numbers where the gap between succeeding phrases is always the same. for instance, 5, 7, 9, 11, 13, and 15. An arithmetic sequence's nth term is determined by the formula a = a + (n - 1)d.

Given, common difference = 3

third term = 10

formula of arithmetic sequence is an = a + (n-1)d

a3 = a + (3-1)3

10 = a + 6

a = 4

a1 = 4

a2 = a + (n-1)d

a2 =  4 + (1)3

a2 = 7

a4 = a + 3d

a4 = 4 + 3.3

a4 = 13

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The sequence is an arithmetic sequence with d = 25 and the next two terms are 125, 150.

Suppose we are given a sequence: a1, a2, a3, a4, ...

To determine whether the sequence is an arithmetic, geometric, or uncategorized one, we need to check the relation between its consecutive terms.

Arithmetic sequence.

If:

a2 - a1 = a3 - a2 = a4 - a3 = constant

then the given sequence is an arithmetic sequence. Furthermore, the constant d = a2 - a1  is usually called the common difference.

Geometric sequence.

If:

a2/a1 = a3/a2 = a4/a3 = constant

then the given sequence is a geometric sequence. Furthermore, the constant r = a2/a1  is usually called the common ratio.

The given sequence is:

25,50,75,100, ........

Let us check the difference:

50 - 25 = 75 - 50 = 100 - 75 = 25.

We can, then, conclude that the sequence is an arithmetic sequence with d = 25.

To find the next two terms, add 25 to every last terms.

100 + 25 = 125

125 + 25 = 150

Hence the next two terms are: 125, 150.

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Answer:

A car gets 25 miles per gallon of gas. It travels for.45 minutes at 65 miles per hour. How many gallons of gas does the car use during that time?

Answer:

25 miles per gallon of gas

travels 45 minutes and 65 miles per hour

Step-by-step explanation:

Answer:

63-93=-30

-4-5=-9

-156-(-45)=-111

Step-by-step explanation:

63-93=-30

-4-5=-9

-156-(-45)=-156+45=-111

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