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The dimensions of the rectangle are 70.5 by 72.5 units.

What is a dimension?

A length measurement that only goes one way. Dimensions include things like width, depth, and height. One dimension is that of a line, two dimensions are found in a square, three dimensions are found in a cube, and one dimension is that of something's height, length, or width. For instance, the room is 26 feet by 15 feet in size.

Solution Explained:
Given,

Area = 143 unit^2

A/Q,

Let length be x and width be x + 2.

So, Area = l X w

      143 = x + x + 2

      143 = 2x + 2

      x = (143 - 2)/2

      x = 70.5

So width = x + 2 = 70.5 + 2 = 72.5

So, the dimensions are 70.5 by 72.5

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Answer:

9

Step-by-step explanation:

5,6,7,8,9

Answer:

18.475?

Step-by-step explanation:

The equation of the given function is y = -1/3 x. By using the points through which the line passing through, we can find its equation. Option A is correct.

The equation of the line passing through two points such as (x1, y1) and (x2, y2) is

y - y1 = [(y2 - y1)/(x2 - x1)] × (x - x1)

From the given graph, the line is passing through the points (0, 0), (-3, 1), and (3, -1).

The equation of the line passing through (-3, 1) and (3, -1) is

y - y1 = [(y2 - y1)/(x2 - x1)] × (x - x1)

⇒ y - 1 = (-1 - 1)/(3 + 3) × (x + 3)

⇒ y - 1 = -2/6 (x + 3)

⇒ y - 1 = -1/3 (x + 3)

⇒ 3y - 3 = -x - 3

⇒ 3y = -x

⇒ y = -1/3 x

So, option A is correct.

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The probability of choosing red ribbon on both Monday and Tuesday is 1/4.

What is the probability?

The Probability in mathematics is possibility of an event in time. In simple words how many times that incident is happening in any given time interval.

Given that each morning Tess chooses either red ribbon or blue ribbon at random to wear in her hair.

That means probability of choosing between blue or red is 1/2 in one morning.

Now the probability of choosing red ribbon on both Monday and Tuesday,

1/2 × 1/2

= 1/4

Therefore, the probability of choosing red ribbon on both Monday and Tuesday is 1/4.

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The zeroes of the expression f(x) = 2x³ + 4x² - 8x - 16 are (x-2), (x+2) and (x+2). And multiplicity of x = -2 is 2.

What is Cubic equation?

Cubic equations are polynomials of degree3. That means the maximum degree of polynomial is three.

And the standard form of cubic equation is;

f(x) = ax³ + bx² +cx +d, where a, b, c and d are constant coefficients a ≠ 0.

Given that the expression

f(x) = 2x³ + 4x² - 8x - 16

Now we find the roots or zeroes of equation;

for that we will try hit and trial method,

let x = 2

f(x) = 2 (8) - 4 (4) - 8(2) -16

f(x) = 0

That means (x-2) is one of roots of cubic equation.

Now to find other roots of the cubic equation, we will simplify the cubic expression

f(x) = 2x² (x-2) + 8x (x-2) + 8 (x-2)

f(x) = (x-2)  (2x²+ 8x + 8)

Now we will find the roots of quadratic equation (2x²+ 8x + 8).

let g(x) = (2x²+ 8x + 8).

factors of quadratic equation is (x+2) and (x+2).

Therefore the zeroes of the expression f(x) = 2x³ + 4x² - 8x - 16 are (x-2), (x+2) and (x+2). And multiplicity of x = -2 is 2.

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Answer:

Below

Step-by-step explanation:

a + c = 240      re-arrange to   c = 240-a

revenue from child tix = 8.50 ( 240-a)

revenue from adult tix = 12.50 a              summed, the revenues = 2400

8.5(240-a)     +      12.5 a       = 2400

2040   - 8.5 a   + 12.5 a   = 2400

                     4.5 a  = 360

                          a = 80 tix        then c = 240 - a = 160 tix

Answer:

y = 5/2x + 11.5

Step-by-step explanation:

(-3, 4) (-5, -1)

m = -1-4/ -5+3

m = -5 / -2

m = 5/2

y = 5/2x + b

-1 = 5/2(-5) + b

-1 = -12.5 + b

b = 11.5

y = 5/2x + 11.5

Answer:

y-y1=y2-y1/x2-x1(x-x1)

y-4= (-1-4/-5+3) (x+3)

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

y=5/2x+15/2+4

y=5/2x+15+8/2

y=5/2x+23/2

Answer:

$253.20

Step-by-step explanation:

The minimum number of dogs 24kg is 6 and the maximum number of dogs is 18    

The highest amount or value or number that may be obtained or reached or can be counted is the Maximum value                              

The least amount or value or number that may be admitted or reached or can be counted is the Minimum value            

Here we have a table  

Which represents the masses of various dogs

Mass (x) kg          frequency  

0 ≤ x < 10                    2

10 ≤ x < 20                  7

20 ≤ x < 30                12

30 ≤ x < 40                 6      

Here the mass of dogs is represented in class intervals

a) The minimum number of dogs with a mass of more than 24kg.

From the given table,

24 kg will lie in class intervals 20 ≤ x < 30, and 30 ≤ x < 40                      

In class interval 20 ≤ x < 30, there is a possibility that the mass of dag will be less than 24 kg since it started from 20 kg and is up to 30 kg  

In class interval 30 ≤ x < 40, there is no possibility that the mass will be less than 24 kg since it started from 30 kg and is up to 40 kg

So The minimum number of dogs that have a mass of more than 24kg the frequency of class interval 30 ≤ x < 40

Therefore,

The minimum number of dogs with a mass of more than 24kg is 6

b) The maximum number of dogs that have a mass of more than 24kg.

To get the maximum number of dogs we need to take the class interval of 20 ≤ x < 30 as in this the mass could be more than 24 kg.

And in class 30 ≤ x < 40 the mass will be more than 24 kg.

Thus, the Maximum number of dogs with more than 24 kg = 12 + 6 = 18

Therefore,

The maximum number of dogs with a mass of than 24kg is 18    

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Answer:

A Square

B Square

C Circle

D Triangle

The least possible height of AB is 3.650 m.

What is a word problem?

A word problem is described as a few phrases outlining a "real-life" situation where a problem needs to be solved using mathematics.

For everything from counting pennies to calculating a tip, we can employ the three primary sorts of word problems: part-part whole, separate and join, and multiply and divide.

Given, CD=2.6 m,  BD=12 m

From the figure,

or, tan x = [tex]\frac{AB - 2.6}{12}[/tex]

or, tan 5  [tex]\leq \frac{AB - 2.6}{12}[/tex]

When AB be least, then

[tex]\frac{AB - 2.6}{12}[/tex] = tan 5

or, AB = (12*tan 5) + 2.6

or, AB = 3.650 m

Hence, the least possible height of the  AB is 3.650 m.

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The probability is the first and the second case will be 0.625 and 0.3683, respectively.

Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.

Then the probability is given as,

P = (Favorable event) / (Total event)

A pack contains five white balls and three torpedoes. You want to draw two white balls.

Total events = 5 + 3

Total events = 8

You all the while drawing two balls aimlessly. Then the probability that they are both white is given as,

P = 5 / 8

P = 0.625

You all the while drawing two balls aimlessly. Whenever you have drawn two balls, you set back any debases, and redraw with the goal that you again have two drawn balls. Then the probability is given as,

P = [(3/8) x (5/8)] + [(3/8) x (5/8) x (4/7)]

P = (15 / 64) + (60 / 448)

P = 0.3683

The probability is the first and the second case will be 0.625 and 0.3683, respectively.

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Answer:

Below

Step-by-step explanation:

6m + 8+4+3m    <==== 6 and 3 are coefficients    8 and 4 are constants

9m + 12    <===== 9 is a coefficient   12 is a constant

Answer:

The coefficients are 6 and 3

The constants are 8 and 4

Step-by-step explanation:

coefficients are the numbers before the letters.

Constants do not have letters.

The required time will be 12.9 years.

What is compound interest?

The interest charged on a loan or deposit is referred to as compound interest. It is the idea that we employ the most frequently on a daily basis. Compound interest is calculated for an amount based on both the principal and cumulative interest.

Given, P = $1700

I = $500

A = P + I = 1700 + 500 = $2200

r = 2% = 0.02

compounded quarterly, n = 4

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

or, 2200 = 1700(1+ (0.02/4))^(4t)

or, 1.294 = 1.005^4t

or, t = 12.9 years

Hence, the required time will be 12.9 years.

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The inequality that shows when the unicorn gets ahead of the chinchilla is 30s > 100 + 5.75s.

Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.

Let the number of seconds be represented by s.

The chinchilla is one hundred feet a head of the unicorn and running at a rate of 5.75 feet per second. This will be 100 + 5.75s.

The unicorn is running at a rate of 30 feet

per second. This will be 30s

The inequality will be 30s > 100 + 5.75s.

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A) The inverse of f(x) is f⁻¹(x) = (x² + 9)/3 and B) f is not an inverse of g.

First to be an inverse function that function needs to one to one function, meaning every different preimage must correspond to a different image.

We can obtain the inverse of a function by switching the variables x and y with their respective positions and solving for y in terms of x.

Given, f(x) = [tex]\sqrt{3x - 9}[/tex].

y = [tex]\sqrt{3x - 9}[/tex].

y² = 3x - 9.

3x = y² + 9.

x = (y² + 9)/3.

y = (x² + 9)/3.

f⁻¹(x) = (x² + 9)/3 and g(x) = 3x² - 9, so f is not an inverse of g.

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Answer: the answer is 4

Step-by-step explanation:

Step-by-step explanation:

i just answered this question. how often did you post it ?

Answer:

See below

Step-by-step explanation:

320 x .1 = 32

320 + 32 = 352

352 x .5 = 176

352 + 176 = 528

320 x .65 = 208

320 + 208 = 528

Hello,

I hope you and your family are doing well!

To write an expression that is equivalent to 2/3 (4x + 9), you can simply distribute the 2/3 over the parentheses:

2/3 (4x + 9) = (2/3 * 4x) + (2/3 * 9)

This simplifies to:

2/3 (4x + 9) = (8/3)x + (18/3)

Therefore, an expression that is equivalent to 2/3 (4x + 9) is (8/3)x + (18/3).

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Answer: 2 2/3x + 6

Step-by-step explanation: 1 of 3 ways to find how to make the equivalent is to use the distributive property. So, that means we need to multiply or distribute 2/3 to both 4x and 9. So, 2/3 x 4 is roughly 2 2/3. Also, 2/3 x 9 = 6. So, I combined the like terms to get 2 2/3x + 6 as my equivalent expression. I hope this helps.

Answer:

If you are having trouble understanding the graph, it may be helpful to break it down into smaller pieces. Start by looking at each axis and what it represents. Then, look at each data point and see how it relates to the axes. Finally, look at the overall shape of the graph and what it is trying to tell you. If you are still having trouble understanding the graph, you may want to reach out to someone who is knowledgeable about graphs or data analysis for assistance.

Step-by-step explanation:

Yes; the triangles are congruent by SAS.

What is triangle ?

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.

A triangle is a 3-sided polygon that is occasionally (though not frequently) referred to as the trigon. There are three sides and three angles in every triangle, some of which may be the same.

AC and BD bisects one another

AE = CE --- Side

and

BE = DE --- Side

When both lines bisect one another, they form a pair of vertical angles  and

When we apply the theorem of vertical angles to this, we have that:

∠AEB = ∠CED   --- Angle

At this point, we have established:

Two sides of ABE and CDE are congruent and One angle in each of ABE and CDE are also congruent

Hence, the triangles are congruent by SAS.

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Answer:

12

Step-by-step explanation:

(3x2) + 6

6 + 6 = 12

Answer:

12

Step-by-step explanation:

3 × 2 is 6

6 + 6 is 12

thus answer is 12

2=3/4,13=1/4,2-3/4=0,13-1/4=0,2-3/4=0*13,13-1/4=0*2

Answer:

fraction 23/10 that's 2 ³/10

decimal 2.3

Apply the fraction rule model can be used to find 4/5 divided by 1/10.

What is  fraction rule?

For fractions to be added or subtracted, their denominators must match (the bottom value). the same denominators are used for addition and subtraction. It only requires adding or subtracting the numerators if the denominators are already equal.

[tex]$\frac{\frac{4}{5}}{\frac{1}{10}}$[/tex]

Apply the fraction rule: [tex]$\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a \cdot d}{b \cdot c}$[/tex]

[tex]$=\frac{4 \cdot 10}{5 \cdot 1}$[/tex]

Cancel [tex]$\frac{4 \cdot 10}{5 \cdot 1}: 8$[/tex]

=8

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