each side of a 4ft x 6ft rectangular flower bed was lengthened by the same amount. the area of the new flower bed is twice the area of the old one. Find the new dimensions.

Answer:

x > 6

Step-by-step explanation:

2x - 7 > 5

2x > 5 + 7

2x > 12

x > 6

Answer:

- (2x^2 - 13x + 6)

The above expression is in brackets and a negative sign is outside of the brackets. This means that when expanding the expression, we have to multiply each number with the negative sign (each number would switch their signs to the opposite one). Therefore, 2x^2 becomes -2x^2, -13x becomes 13x and 6 becomes -6.

Answer:

Step-by-step explanation:

integer and rational

Using the linear equation, T = 20x + 31, the total number of computers at the end of 2005 is: C. 191.

A linear equation is expressed as y = mx + b, where x is a function of y, m is the rate of change and b is the y-intercept or starting value.

In the scenario stated, we are given the linear equation for total number of laptop computers at the school after 1997 as, T = 20x + 31.

Rate of change = 20

y-intercept/starting value = 31

x = 2005 - 1997 = 8

To find the total number of laptop computers at Grove High School at the end of 2005 (T), substitute x = 8 into the equation, T = 20x + 31.

T = 20(8) + 31

T = 160 + 31

T = 191 computers.

Thus, total number of computers at the end of 2005 is: C. 191.

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i) The coefficients of the equation of the line are a = 20 / 3 and b = 160 / 21.

ii) The equation of the line in standard form is (20 / 3) · x + (160 / 21) · y = - 20.

iii) The x-intercept and y-intercept of the line are (- 3, 0) and (0, - 21 / 8).

iv) Two alternative solutions of the equation of the line are 20 · x + (160 / 7) · y = - 60 and 140 · x + 160 = 420.

In this problem we know that form of an equation of the line and two points, on which the line pass through. i) We determine the values of the coefficients a and b by solving the following system of linear equations:

5 · a - 7 · b = - 20

- 3 · a = - 20

Whose solution is a = 20 / 3 and b = 160 / 21.

ii) The equation of the line in standard form is (20 / 3) · x + (160 / 21) · y = - 20.

iii) Now we find the coordinates of the intercepts of the line:

x-Intercept

(20 / 3) · x = - 20

x = - 3

y-Intercept

(160 / 21) · y = - 20

y = - 21 / 8

iv) We can find two alternative solutions by using multiples:

20 · x + (160 / 7) · y = - 60

140 · x + 160 = 420

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Answer:  2.5 meters

This value is exact without any rounding.

======================================================

Explanation:

The first task is to convert the mixed number 20⅚ into an improper fraction

I'll write 20⅚ as 20 & 5/6

The rule to use is a & b/c = (a*c + b)/c

So,

a & b/c = (a*c + b)/c

20 & 5/6 = (20*6+5)/6

20 & 5/6 = 125/6

This means the volume is exactly (125/6)pi cubic meters.

Plug this into the sphere volume formula and isolate the radius r like so

V = (4/3)*pi*r^3

(125/6)pi = (4/3)*pi*r^3

125/6 = (4/3)*r^3

(4/3)*r^3 = 125/6

4r^3 = 3*(125/6)

4r^3 = 125/2

r^3 = (125/2)*(1/4)

r^3 = 125/8

r = (125/8)^(1/3)

r = 5/2

r = 2.5

The 2nd term exists 12 and 7th term exceeds the 4th by 15 exists AP : 7,12,17,....

Given : The second term exists 12th and the 7th term exceeds the 4th term by 15

The formula of the nth term :

[tex]$a_{n}=a+(n-1) d[/tex]

Where d exists a common difference

n be the number of terms

a be the first term

Substitute the value of n = 2

[tex]$a_{2}=a+(2-1) d=a+d[/tex]

Let, the second term exists 12

So, a + d = 12 ..........(1)

Substitute the value of n = 7

[tex]$a_{7}=a+(7-1) d=a+6 d[/tex]

Substitute n = 4

[tex]$a_{4}=a+(4-1) d=a+3 d[/tex]

We are given that the 7th term exceeds the 4th term by 15

So, a+6d-a-3d = 15

3d = 15

d = 5

Substitute the value of d in (1)

So, a+5 = 12

a = 12-5

a = 7

AP : a,a+d,a+2d,.... = 5, 7+5, 7+2(5),....=7,12,17,....

Therefore, AP : 7,12,17,....

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Answer:

(a)

(b) range of sample means =0.6

(c)

In order to solve a problem that begins with a negative number and is divided by a positive number, the answer must also be negative.

Divide 21 ÷ 7

we get = 3

Mark it as negative number = -3

Hope this helps :)

Answer:

1/12 mile

Step-by-step explanation:

He walks 7/12 mile in 7 minutes.

In 1 minute, he walks 1/7 of the distance.

1/7 of 7/12 mile = 1/12 mile

Debido a restricciones de extensión y la características del ejercicio, recomendamos leer la explicación de esta pregunta para mayores detalles sobre la adición de números enteros.

En este ejercicio tenemos un grupo de sumas con números enteros positivos y negativos, en las cuales se prueba la capacidad del estudiante para realizar varias operaciones en serie (adición, sustracción) y comprender las diferencias entre números positivos, negativos y neutros. Ahora procedemos a determinar el resultado de cada una de las expresiones:

20 + 50 + 30 + 7 = 107

30 + 5 + 2 = 37

- 200 - 50 - 70 - 8 = - 328

- 500 + 100 - 20 + 50 = - 370

10 - 5 = 5

20 + 50 - 25 - 10 = 35

- 100 + 20 = - 80

- 30 + 5 + 4 - 20 + 8 = - 33

- 258 + 8 = - 250

- 10 + 20 + 520 - 100 + 8 = 438

- 20 - 5 - 42 + 3 = - 64

1000 - 200 + 50 + 30 - 45 + 75 - 87 + 90 + 50 - 100 + 50 - 10 = 903

- 400 + 500 - 200 - 50 + 48 + 8 - 47 - 50 = - 191

300 + 20 - 50 + 30 - 84 + 35 - 7 + 20 - 40 + 10 - 45 + 65 + 8 - 55 = 207

800 + 50 - 69 + 8 - 35 + 85 - 54 + 40 + 85 + 74 - 32 - 8 + 65 - 27 = 982

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The correct option is B.

The enrollment capacity be 3 years from now is 2410

A series of integers in which the difference between succeeding words is always the same is referred to as an arithmetic sequence or arithmetic progression. For instance, the difference in the arithmetic series 1, 5, 9, 13, 17,... is always 4. The common difference is what we refer to as.

The formula for determining the nth term is used to locate a specific term in an arithmetic sequence. Step 1: An = a + (n - 1)d determines the nth term of an arithmetic series. Add the variables a = 2 and d = 3 to the formula in order to find the nth term.

At = a1 + (n - 1) x d is an equation that can be used to express the number of applications each year.

N equals 4 based on the information provided above. This corresponds to the term, which begins in three years.

At = 2200 + (4 - 1) x 70 = 2410

Thus, 2410 students could enroll at one time.

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Answer:

8 Hours

Step-by-step explanation:

We know she travels 220 miles in 5 hours, so lets create an equation with a ratio which finds the miles she drives in a single hour, multiply that by x, and then set it equal to 352.

[tex]\frac{220}{5}x=352[/tex]

Multiply both sides by 5

[tex]220x=1760[/tex]

Divide both sides by 220

[tex]x=8[/tex]

Therefore it would take 8 hours.

8 Hours long would it take to travel 352 miles,

The distance that an object travels in relation to the amount of time it takes to do so can be used to define speed. In other words, it is a measurement of an object's motion's speed without direction Velocities are what we get when speed and direction are combined. The SI unit system is most frequently used to express speed units. In that system, since distance is measured in metres and time is measured in seconds, speed is expressed in metres per second, or m/s. Three components make up the speed formula: distance, time, and speed.

We know she travels 220 miles in 5 hours, so lets create an equation with a ratio which finds the miles she drives in a single hour, multiply that by x, and then set it equal to 352.

Multiply both sides by 5

Divide both sides by 220

Hence, it would take 8 hours.

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Answer:

Rs 400 is the cost of an article for Ram.....

Step-by-step explanation:

X - cost of an article for Ram

120% = 1.2

1.2*X - Ram’s selling price

5% = 0.05

1.2*X*0.05 - Shyam selling price

1.2*X*0.05 = 504

X = Rs 400 is the cost of an article for Ram

Hope it Helps!!!!

The series converges to  1/(1-9x) for -1/9<x<1/9                  

Given the series is  ∑ [tex]9x^{n} x^{n}[/tex]

We have to find the values of x for which the series converges.

We know,                

∑ [tex]ar^{n-1}[/tex]    converges to  (a) / (1-r) if r < 1

Otherwise the series will diverge.

Here, ∑ [tex](9x)^{n}[/tex] is a geometric series with |r| = | 9x |

And it converges for |9x| < 1

Hence, the given series gets converge for -1/9<x<1/9

And geometric series converges to a/(1-r)

Here, a = 1 and r = 9x

Therefore, a/(1-r) = 1/(1-9x)

Hence, the given series converges to   1/1-9x  for  -1/9<x<1/9

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Answer:

Step-by-step explanation:

3x + 1 < 7...subtract 1 from both sides

3x < 7 - 1

3x < 6 ...divide both sides by 3

x < 6/3

x < 2

which means the second answer choice is correct!

Answer: Second Graph

Step-by-step explanation:

Given inequality

3x + 1 < 7

Subtract 1 on both sides

3x + 1 - 1 < 7 - 1

3x < 6

Divide 3 on both sides

3x / 3 < 6 / 3

x < 2

Apply the inequality to the graph

Since it is less than, the circle should be hollow

Since it is less than 2, the line should point to the left

Therefore, it should be the Second Graph

The direction does the parabola open is right. Option C

It is important to note that the general equation of a parabola is: y = a(x-h)² + k or x = a(y-k)² +h

where

⇒ (h , k) denotes the vertex.

Also, the standard equation of a regular parabola is y² = 4ax.

From the equation given , we have

We know that when the vertex of the parabola is (0, 0) and the directrix is x = - a, the parabola will have the form;

y² = 4ax

It is important to note that ;

From this, we can see that the parabola would open in the right direction

Thus, the direction does the parabola open is right. Option C

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Answer: D

Step-by-step explanation: The line of best fit is a straight line that passes through as many points as possible and has around the same number of points above and below it. D meets those requirements the best.

Answer:

Line D

Step-by-step explanation:

Line D is most fit because it intercepts more of the dots on the graph, if not, comes close to touching the majority of them.

The amount of water in each mug is 2 / 5 litres

The water bottle has 4/5 litres of water.

The litre of water is poured equally in 2 mugs.

Therefore, the amount of water in each mug can be calculated as follows;

amount of water in each mug = 4 / 5 ÷ 2

amount of water in each mug = 4 / 5 × 1 / 2

amount of water in each mug =  4 / 10

amount of water in each mug = 2 / 5 litres

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A polygon is a figure that has a given number of sides.

A polygon is an n - sided figure. The number of sides in a polygon is almost infinite. Let us now match the properties with the type of polygon.

a. 12.gon - An interior angle measures 150°

The polygon that has 12 sides is called the Dodecagon.

Given that the sum of the interior angles in a dodecagon is 1800, then  each interior angle is; 1,800/12

= 150°

b. 15-gon - An exterior angle measures 24°

The polygon that contains 15 sides is called pentadecagon. Given that the sum of the exterior angles of polygon is 360 degrees and each exterior angle is  24° then;

360/ 24° = 15 sides

c. 16-gon - The sum of the interior angles is 2,520°

The polygon that contains 16 sides is called the hexadecagon. The sum of its interior angles is 2,520° hence each interior angle measures; 2,520°/16 =  157.5°

d. 18-gon - An interior angle measures 160°

A polygon that contains 18 sides is called an octadecagon .

We have;

160 = (n−2) × 180° / n

160n = 180n - 360

360 = 20n

n = 18

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Missing parts;

Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.

Match the properties to the regular polygons they describe.

An interior angle measures 150".

An exterior angle measures 24.

The sum of the interior angles is 2520°.

An interior angle measures 160".

The sum of the exterior angles is 180º.

The sum of the interior angles is 2160°.

15-gon

16-gon

12.gon

18-gon

Answer:

Step-by-step explanation:

We have enough data to reject our null hypothesis if the value of our test statistics falls below critical values of z at a 1.25% level of significance (critical values are -1.645 and 1.645). This is because the test statistic value will not fall within this region.

Given that the population mean is 650, we do a two-tail hypothesis test with a level of significance of 0.025.

Let, μ = population mean

Thus, Null hypothesis, [tex]H_{0}[/tex]:μ= 650.

Alternate Hypothesis, [tex]H_{A}[/tex]:μ≠650

In this case, the population mean is equal to 650, according to the null hypothesis.

The alternative hypothesis, on the other hand, contends that the population mean is not 650.

First things first: the level of significance to be accepted for the two-tailed test is ([tex]\frac{\alpha }{2}[/tex]= [tex]\frac{0.025}{2}[/tex]) = 0.0125 or 1.25%.

Therefore, the following is the decision rule for rejecting a null hypothesis:

We have enough data to reject our null hypothesis if the value of our test statistics falls in the rejection region and is less than the critical values of z at a 1.25% level of significance (critical values are -1.645 and 1.645). This is because the test statistic value will not fall within this region.

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Answer:

5) 26

6) 18

Step-by-step explanation:

Substitute the value of the variables in the expression and evaluate.

x = 2 ; y = -3 and z = 1

Absolute value:  Absolute value of a real number is the non negative a value of x without regard its sign.

Example: I-3I = 3

               I 3I = 3

5) 24 + Ix - 4I =24 + I 2 - 4I

                      = 24 + I-2I

                      = 24 + 2

                      = 26

6) 13 + I 8 +y I = 13 + I 8 + (-3)I

                       = 13 + I 5 I

                       = 13 + 5

                       = 18

Answer:

[tex]\displaystyle{\dfrac{5x-12}{(x+3)(x-3)} }[/tex]

Step-by-step explanation:

We are given the expression:

[tex]\displaystyle{\dfrac{3}{x^2-9} + \dfrac{5}{x+3}}[/tex]

First, factor the denominator [tex]\displaystyle{x^2-9}[/tex] to [tex]\displaystyle{(x+3)(x-3)}[/tex] via difference of two squares:

[tex]\displaystyle{\dfrac{3}{(x+3)(x-3)} + \dfrac{5}{x+3}}[/tex]

Next, multiply the expression 5/(x+3) by [tex]\displaystyle{x-3}[/tex] both denominator and numerator:

[tex]\displaystyle{\dfrac{3}{(x+3)(x-3)} + \dfrac{5(x-3)}{(x+3)(x-3)}}[/tex]

Add both together since they have same denominator now:

[tex]\displaystyle{\dfrac{3+5(x-3)}{(x+3)(x-3)} }[/tex]

Simplify the numerator:

[tex]\displaystyle{\dfrac{3+5x-15}{(x+3)(x-3)} }\\\\\displaystyle{\dfrac{5x-12}{(x+3)(x-3)} }[/tex]

Therefore, the sum is:

[tex]\displaystyle{\dfrac{5x-12}{(x+3)(x-3)} }[/tex]

Answer:

4x=90

X=90÷4

X=22.5

5x-27=90

5x=90+27

5x=117

X=117÷5

X=23.4

So 23.4 is a larger angle

a) The equation represents an ellipse.

b) The equation represents a circle.

c) The equation represents a parabola.

In this problem we have general equations of the form A · x² + B · y² + C · x + D · y + E = 0, which have to be modified into standard form to infer its graphical form. This procedure can be done by algebra properties:

16 · x² + 4 · y² + 96 · x - 8 · y + 84 = 0

[(4 · x)² + 2 · 12 · (4 · x)] + [(2 · y)² - 2 · 2 · (2 · y)] = - 84

[(4 · x)² + 2 · 12 · (4 · x) + 144] + [(2 · y)² - 2 · 2 · (2 · y) + 4] = 64

(4 · x + 12)² + (2 · y + 2)² = 64

4² · (x + 3)² + 2² · (y + 2)² = 64

(x + 3)² / 4 + (y + 2)² / 16 = 1 : Ellipse

x² + y² + 8 · x - 6 · y - 15 = 0

(x² + 8 · x) + (y² - 6 · y) = 15

(x² + 2 · 4 · x + 16) + (y² - 2 · 3 · y + 9) = 40

(x + 4)² + (y - 3)² = 40 : Circle

x² + 6 · x + 4 · y + 5 = 0

x² + 6 · x + 5 = - 4 · y

y = - (1 / 4) · x² - (3 / 2) · x - (5 / 4) : Parabola

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Answer:[tex]\Large\boxed{First~choice.~y\leq \frac{1}{2}x+2 }[/tex]

Step-by-step explanation:

Given function form

Point-Slope form : y = mx + b

Given the information from the graph

Since the graph crosses (0, 2), b = 2

Find the slope

Choose any two points from the graph

(x₁, y₁) = (0, 2)

(x₂, y₂) = (2, 3)

Slope = (y₂ - y₁) / (x₂ - x₁)

Slope = (3 - 2) / (2 - 0)

Slope = 1 / 2

m = 1 / 2

Therefore, the equation form of the inequality is y = (1/2)x + 2

Since it is a solid line, the values on the line are also included. Thus, it must be either greater than or equal to, or less than or equal to.

The shaded region is below the solid line, therefore, it is ≤

Therefore, the inequality is [tex]\Large\boxed{y\leq \frac{1}{2}x+2 }[/tex]

To double-check the sign, we can substitute (0, 0) into the inequality to see whether it is true.

y ≤ (1/2) x + 2

0 ≤ (1/2) 0 + 2

0 ≤ 2              TRUE

Hope this helps!! :)

Please let me know if you have any questions

A statement which best defines an output is: B. an output is the result of a relation or the function rule, usually the y-values in a set of ordered pairs or on a table or graph.

A function can be defined as a mathematical expression that defines and represents the relationship between two or more variable, which is typically modelled as input (x-values) and output (y-values).

In Mathematics, there are different types of functions and these include the following;

In this context, we can infer and logically deduce that a statement which best defines an output is that it's the result of a relation or the function rule, which usually are the y-values in a set of ordered pairs, on a table or a graph.

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Complete Question:

Which of the following best defines an output?

A. An output is the value that determines another based on the relation or the function rule, usually the x-values in a set of ordered pairs or on a table or graph.

B. An output is the result of a relation or the function rule, usually the y-values in a set of ordered pairs or on a table or graph.

C. An output is a special type of relation for which there is a rule that pairs each input with exactly one output.

D. An output is a set of ordered pairs in which no y-value repeats.