The left and right page numbers of an open book are two consecutive integers whose sum is 253. Find these page numbers.

Using the given information, the equation of the circle with radius 2 and center at (-1 , -5) is (x + 1)^2 + (y + 5)^2 = 4.

The general form of the equation of  circle is given by (x - h)^2 + (y - k)^2 = r^2, where (h , k) is the location of the center and r is the radius of the circle.

Given the radius and center of the circle, substitute these values to the general form of the equation of the circle.

(x - h)^2 + (y - k)^2 = r^2

where (h , k) = (-1 , -5)

r = 2

(x - -1)^2 + (y - -5)^2 = 2^2

(x + 1)^2 + (y + 5)^2 = 4

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Answer:

Step-by-step explanation:

The equation in slope-intercept form is x – 5y = -12

Given,

y = -5x – 8

This is in slope-intercept form, y = mx + b

Where, m is slope and b is y-intercept.

Here, m = -5

Perpendicular lines have slopes that are negative reciprocals, [tex]m_{p}[/tex] = -1/m

Here we need equation of line through (-2, 2) with slope -1/-5 = 1/5

y = (1/5)x + b

where (-2, 2) is on the line.

2 = 1/5(-2) + b

2 = -2/5 + b

b = 2 + 2/5 = 12/5

therefore, equation we need is:

y = 1/5x + 12/5

that is,

1/5x – y = -12/5

Multiplying 5 in both sides, we get

5(1/5x) – 5y = (-12/5)5

That is, the equation we need is:

x – 5y = 12

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A scale drawing of a school bus has a scale of ; inch to 6 feet. If the length of the school bus is 4, inches on the scale drawing, what'is the actual length of the bus?

The temperature will be represented by the negative number -21.7 degrees.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that the quantity is a positive or negative number the record low temperature for a date is 21.7 degrees below zero.

T = 0 - 21.7

T = -21.7 degrees

Therefore, the temperature will be represented by the negative number -21.7 degrees.

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Tessellation in trapezoid is possible only if it is rotated

see the fig, attached.

But tessellation in parallelogram is possible both rotated and non rotated

see the fig, attached.

A tessellation or tiling is the seamless application of one or more geometric shapes, known as tiles, to a surface, frequently a plane. Tessellation in mathematics can be expanded to include other geometries and higher dimensions.

A tiling constructed of materials like cemented ceramic hexagons or squares is referred to as a real-world tessellation. Such tilings may be ornamental designs or serve practical purposes such providing long-lasting and water-resistant pavement, floor, or wall coverings.

Tessellations were historically employed in Islamic art, such as the Moroccan architecture and the ornamental geometric tiling of the Alhambra palace. They were also used in Ancient Rome.

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Answer: the midpoint of the segment is (6,5)

Step-by-step explanation:

(2,2)     (10,8)

[tex]\displaystyle\\ A_x=\frac{2+10}{2} \\\\A_x=\frac{12}{2} \\\\A_x=6[/tex]

[tex]\displaystyle\\A_y}=\frac{2+8}{2}\\ \\A_y=\frac{10}{2} \\\\A_y=5\\[/tex]

Thus, A(6,5)

Answer:

The factor pairs of the number 48 are: 1 x 48, 2 x 24, 3 x 16, 4 x 12, and 6 x 8. When you multiply each of these factor pairs together, you get 48.

Step-by-step explanation:

1 x 48 = 48

2 x 24 = 48

3 x 16 = 48

4 x 12 = 48

6 x 8 = 48

HOPE IT'S HELP:)

The simplification of the given each sum or difference of the expression [tex]\frac{5x}{x^{2} -x-6} + \frac{4}{x^{2} +4x+4}[/tex] is equal to [tex]\frac{5x^{2} +14x-12}{(x-3)(x+2)^{2}}[/tex] , restriction on the variables is given by x ≠ 3 , x≠ -2.

As given in the question,

Given expression : [tex]\frac{5x}{x^{2} -x-6} + \frac{4}{x^{2} +4x+4}[/tex]

Simplify the given expression by taking least common multiple,

[tex]\frac{5x}{x^{2} -x-6} + \frac{4}{x^{2} +4x+4}\\\\\\= \frac{5x}{x^{2} -3x+2x-6} + \frac{4}{(x+2)^{2}} \\\\\\= \frac{5x(x+2)+4(x-3)}{(x-3)(x+2)^{2}}\\ \\=\frac{5x^{2} + 14x-12}{(x-3))x+2)^{2}}[/tex]

Restriction on the variables is given by x ≠ 3 , x≠ -2.

Therefore, simplification of the given each sum or difference of the expression [tex]\frac{5x}{x^{2} -x-6} + \frac{4}{x^{2} +4x+4}[/tex] is equal to [tex]\frac{5x^{2} +14x-12}{(x-3)(x+2)^{2}}[/tex] , restriction on the variables is given by x ≠ 3 , x≠ -2.

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we  know she poured already 2 qts of a 62% sugar solution, hmmm how much will that be in quarts?  well, just (62/100) * 2 = 1.24 quarts.

we also know she wants to mixed say "x" quarts of a 38% sugar solution, how many quarts will that be?  well, (38/100) * x = 0.38x.

let's make a quick table from that as well as including the desired mixture.

[tex]\begin{array}{lcccl} &\stackrel{solution}{quarts}&\stackrel{\textit{\% of }}{amount}&\stackrel{\textit{qts of }}{amount}\\ \cline{2-4}&\\ \textit{62\% solution}&2&0.62&1.24\\ \textit{38\% solution}&x&0.38&0.38x\\ \cline{2-4}&\\ desired~mixture&y&0.54&0.54y \end{array}\qquad \begin{cases} ~\hfill 2+x&=y\\\\ 1.24 + 0.38x &= 0.54y \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{substituting on the 2nd equation}}{1.24 + 0.38x ~~ = ~~ 0.54(\underset{y}{2 + x})}\implies 1.24+0.38x=1.08+0.54x \\\\\\ 0.16+0.38x=0.54x\implies 0.16=0.16x\implies \cfrac{0.16}{0.16}=x\implies \stackrel{qts}{1}=x[/tex]

Answer:

-3.4

Step-by-step explanation:

"| |" are absolute value which means |-4| is actually 4. However, if there is a  negative outside of the lines, than the answer is negative.

Step-by-step explanation:

the area of a rectangle is

length × width.

so, in our case

30 × 6 = 180 cm²

be careful to use the right unit for the result. an area is measured in square units based on the units of the given lengths. hence cm² as the given lengths are in cm.

Based on the elevation that the mountaineer has to climb of 6,282 meters, supplementary oxygen is needed because this distance is above 18,000 feet.

The limit for what is considered extremely high altitude is given in feet so the mountaineer's elevation of 6,282 meters needs to be converted to feet.

1 meter in feet is 3.28084 feet.

6,282 meters in feet is therefore:

= 6,282 x 3.28084

= 20,610.24 feet

This distance is more than the 18,000 feet above sea level which makes it extremely high altitude and so supplementary oxygen is needed.

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The quotient in this Carl multiplies the both value instead of dividing so that is the mistake that made by Carl.

The quotient of 4 divided by 2 1/3 and also explain the mistake that done by Carl

The value of 4  1/3 is 14/3

And the value of 2  1/3 is 7/3

So then we divide 4 2/3 by 2 1/3 is,

[tex]\frac{14 / 3}{7 / 3}=\frac{14}{3} \frac{3}{7}[/tex]

      =2

Carl's mistake is thinking that his quotient (2) is equal to the value of the terms involved in it. In fact, 2 is just a multiplier for 7/3 and doesn't have any specific value associated with it.

Hence, this is the quotient in this Carl multiplies the both value instead of dividing so that is the mistake that made by Carl.

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By using the fact that the two angles whose measures are expressed in terms of x are vertical angles, we will see that x = 8.

Then using that we will see that the measure of angle BAC is 63 degrees.

On the given diagram, we can see that the two angles whose measures are expressed in terms of x are vertical angles, thus, these two angles have the same measure, then we can write a linear equation that helps us to find the value of x, which is:

(2x + 3) = (4x - 5)

Solving the linear equation for x we get:

2x + 3 = 4x - 5

3 + 5 = 4x - 2x

8 = 2x

8/2 = x = 4

So we can see that the value of x is 4.

Now we want to find the measure of angle BAC.

We can see that the measure of angle BAC plus the measure of the angle to its right will be a right angle, then we can write:

m∠BAC + (4x - 5)° = 90°

Replacing the value of x we get:

m∠BAC + (4*8 - 5)° = 90°

m∠BAC + 27° = 90°

m∠BAC = 90° - 27° = 63°

We conclude that the measure of angle BAC is 63 degrees.

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⊂ Hey, ausemkattom2559 ⊃

Answer:

x = 1

Step-by-step explanation:

Solve each equation.

Check your solutions.

x /2 = x + 1/4

From the given: [tex]\frac{x}{2}=\frac{x+1}{4}[/tex]

Applying fraction cross multiply: [tex]\mathrm{if\;\frac{a}{b}=\frac{c}{d}\mathrm{\:then\:}a\cdot \:d=b\cdot \:c}[/tex]

[tex]x\cdot \:4=2\left(x+1\right)[/tex]

Distribute:

[tex]x\cdot \:4=2x+2[/tex]

Subtract 2x from both sides:

[tex]x\cdot \:4-2x=2x+2-2x[/tex]

[tex]2x=2[/tex]

Divide both sides by 2:

[tex]\frac{2x}{2}=\frac{2}{2}[/tex]

x = 1

As a result, x = 1

We can substitute to check our solution:

1/2 = 1 + 1/4

1/2 = 1/2

Hence, x = 1

xcookiex12

9/12/2022

Answer:

5 points

Step-by-step explanation:

because yes

Answer: X=3, Y=6 z=-1

Step-by-step explanation:

Experiment: Rolling three dice simultaneously

No of possible outcomes: 6*6*6 = 216

The Sample space is shown below:

(1,1,1) (1,1,2) (1,1,3) (1,1,4) (1,1,5) (1,1,6)

(1,2,1) (1,2,2) (1,2,3) (1,2,4) (1,2,5) (1,2,6)

(1,3,1) (1,3,2) (1,3,3) (1,3,4) (1,3,5) (1,3,6)

(1,4,1) (1,4,2) (1,4,3) (1,4,4) (1,4,5) (1,4,6)

(1,5,1) (1,5,2) (1,5,3) (1,5,4) (1,5,5) (1,5,6)

(1,6,1) (1,6,2) (1,6,3) (1,6,4) (1,6,5) (1,6,6)

(2,1,1) (2,1,2) (2,1,3) (2,1,4) (2,1,5) (2,1,6)

(2,2,1) (2,2,2) (2,2,3) (2,2,4) (2,2,5) (2,2,6)

(2,3,1) (2,3,2) (2,3,3) (2,3,4) (2,3,5) (2,3,6)

(2,4,1) (2,4,2) (2,4,3) (2,4,4) (2,4,5) (2,4,6)

(2,5,1) (2,5,2) (2,5,3) (2,5,4) (2,5,5) (2,5,6)

(2,6,1) (2,6,2) (2,6,3) (2,6,4) (2,6,5) (2,6,6)

(3,1,1) (3,1,2) (3,1,3) (3,1,4) (3,1,5) (3,1,6)

(3,2,1) (3,2,2) (3,2,3) (3,2,4) (3,2,5) (3,2,6)

(3,3,1) (3,3,2) (3,3,3) (3,3,4) (3,3,5) (3,3,6)

(3,4,1) (3,4,2) (3,4,3) (3,4,4) (3,4,5) (3,4,6)

(3,5,1) (3,5,2) (3,5,3) (3,5,4) (3,5,5) (3,5,6)

(3,6,1) (3,6,2) (3,6,3) (3,6,4) (3,6,5) (3,6,6)

(4,1,1) (4,1,2) (4,1,3) (4,1,4) (4,1,5) (4,1,6)

(4,2,1) (4,2,2) (4,2,3) (4,2,4) (4,2,5) (4,2,6)

(4,3,1) (4,3,2) (4,3,3) (4,3,4) (4,3,5) (4,3,6)

(4,4,1) (4,4,2) (4,4,3) (4,4,4) (4,4,5) (4,4,6)

(4,5,1) (4,5,2) (4,5,3) (4,5,4) (4,5,5) (4,5,6)

(4,6,1) (4,6,2) (4,6,3) (4,6,4) (4,6,5) (4,6,6)

(5,1,1) (5,1,2) (5,1,3) (5,1,4) (5,1,5) (5,1,6)

(5,2,1) (5,2,2) (5,2,3) (5,2,4) (5,2,5) (5,2,6)

(5,3,1) (5,3,2) (5,3,3) (5,3,4) (5,3,5) (5,3,6)

(5,4,1) (5,4,2) (5,4,3) (5,4,4) (5,4,5) (5,4,6)

(5,5,1) (5,5,2) (5,5,3) (5,5,4) (5,5,5) (5,5,6)

(5,6,1) (5,6,2) (5,6,3) (5,6,4) (5,6,5) (5,6,6)

(6,1,1) (6,1,2) (6,1,3) (6,1,4) (6,1,5) (6,1,6)

(6,2,1) (6,2,2) (6,2,3) (6,2,4) (6,2,5) (6,2,6)

(6,3,1) (6,3,2) (6,3,3) (6,3,4) (6,3,5) (6,3,6)

(6,4,1) (6,4,2) (6,4,3) (6,4,4) (6,4,5) (6,4,6)

(6,5,1) (6,5,2) (6,5,3) (6,5,4) (6,5,5) (6,5,6)

(6,6,1) (6,6,2) (6,6,3) (6,6,4) (6,6,5) (6,6,6)

Favorable outcome (three similar numbers, i.e. getting an identical number in all the three dice) : 6

Probability = No of favorable outcomes/Total no of outcomes = 6/216 = 0.0278

Answer:

7th term = (-1)

rule for the nth term = an = a+(n-1)d

Step-by-step explanation:

a = 5, d = a2-a1 = 4-5 = -1, n = 7

an = a+(n-1)d

a7 = 5+(7-1)(-1)

a7 = 5-6

a7 = (-1)

Answer: A unit rate is when you need to convert between measurement systems. There is no picture for the points so this is all i can answer.

Step-by-step explanation:

Answer: t=2

Step-by-step explanation:

[tex]1=t+\sqrt{2t} -3\\1-1=t+\sqrt{2t}-3-1\\0= t+\sqrt{2t} -4\\Thus,\\t+\sqrt{2t} -4=0\\Let`s\ \sqrt{t} =x\geq 0\\\Rightarrow\ x^2+\sqrt{2} x-4=0\\x^2-\sqrt{2} x+2\sqrt{2}x-4=0\\ x(x-\sqrt{2})+2\sqrt{2} ( x-\sqrt{2})=0\\ (x-\sqrt{2})(x+2\sqrt{2})=0\\\\x-\sqrt{2} =0\\ x-\sqrt{2}+\sqrt{2}=0+\sqrt{2} \\ x=\sqrt{2}\\ \Rightarrow\ t=(\sqrt{2})^2\\ t=2\\\\x+2\sqrt{2} =0\\x+2\sqrt{2} -2\sqrt{2} =0-2\sqrt{2} \\x=-2\sqrt{2} \notin(x\geq 0)[/tex]

The given sequence is geometric, with common ratio = 0.1.

A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.

Given: 7, 0.7, 0.07, 0.007,...

Here, 0.7/7 = 0.07/0.7 = 0.007/0.07 = 0.1

That is, the given sequence follows the only necessary condition required for a sequence to be geometric.

Hence, The given sequence is geometric, with common ratio = 0.1.

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Answer:

61 miles

Step-by-step explanation:

0.90 x 61 = 54.9

Answer:

a=−2 and b=−2

Step-by-step explanation:

Let's solve your system by substitution.

7a−12b=10;−2a−4b=12

Step: Solve7a−12b=10for a:

7a−12b=10

7a−12b+12b=10+12b(Add 12b to both sides)

7a=12b+10

7a/7=12b+10/7

(Divide both sides by 7)

[tex] \sf \: a = \frac{12}{7} b + \frac{10}{7} [/tex]

Step: Substitute: 12/7b+10/7 for a in−2a−4b=12:

−2a−4b=12

−2(12/7b+10/7)−4b=12

−52/7b + −20/7=12(Simplify both sides of the equation)

−52/7b+−20/7+20/7=12+20/7

(Add 20/7 to both sides)

−52/7b=104/7

[tex] \sf \: \frac{ \frac{ - 52}{7}b }{ \frac{ - 52}{7} } = \frac{ \frac{104}{7} }{ \frac{ - 52}{7} } [/tex]

(Divide both sides by (-52)/7)

b=−2

Step: Substitute −2 for b in a =12/7b+10/7:

a=/12/7b+10/7

a=12/7(−2)+10/7

a=−2(Simplify both sides of the equation)

The total salary for the month will be $4535

From the information, Alex earns a weekly base salary of $650 as a car salesman. He also earns a 9% commission on his monthly sales after the first $10,000.

If he sold 7 cars whose average price was $4,500 each. The total amount will be:

= $4500 × 7.

= $31500

The commission will be

= 9% × ($31500 × $10000)

= 9% × $21500

= $1935

The total salary for the month will be:

= ($650 × 4) + $1935

= $4535

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Answer:710.4

Step-by-step explanation:

Answer: 3

Step-by-step explanation: