The length of a rectangle is 5 feet more than the width. The perimeter of the rectangle is 58 feet. Find the length & width of the rectangle.

Taking into account the definition of a system of linear equations, the first number is x= -14 and the second number y= -13.

A system of linear equations is a set of linear equations (that is, a system of equations in which each equation is of the first degree) in which two or more unknowns are related.

Systems of linear equations have as a solution set all ordered pairs (x, y) that satisfy the equation, where x and y are real numbers. That is, solving a system of equations consists of finding the values of the unknowns, with which, when replaced in the equations, they must give the proposed solution.

In this case, a system of linear equations must be proposed taking into account that

You know:

The system of equations to be solved is

x-y= -1

x+y= -27

It is decided to solve the system of equations using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.

In this case, isolating the variable "x" from the first equation:

x= -1 +y

Replacing this expression in the second equation:

-1 +y +y= -27

Solving:

y +y= -27 +1

2y= -26

y= (-26)÷2

y= -13

Remembering that x=-1 +y, you get

x= -1 -13

x= -14

Finally, the numbers are -13 and -14.

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The values of the first and second numbers are - 13 and - 14 respectively.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Let us assume that the two numbers are x and y.

Given, The difference between the two numbers is -1.

∴ x - y = - 1...(i)

And, Their sum is - 27 which is,

x + y = - 27...(ii)

Now, if we add eqn (i) to eqn (ii)

    x + y = - 27

+  x - y =     -1

---------------------

  2x     = - 28

+ y and - y get canceled and we get

∴ 2x = 26.

x = - 13.

Now, substitute the value of x in any of the eqn(i). we get y = - 14.

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Area = (π*r^2*α)/360°

α =72°

r = 9 mi

Then

A = (π * 81 * 72°)/360° = 81/5π square meters

If he National Research Council recommends keeping a 1 : 3 copper to zinc ratio in a horse’s diet. If the horse is getting 420 milligrams (mg) of zinc per day, The number of  milligrams of copper that the Council recommend the horse have is : 140 milligrams.

Given data:

Copper to zinc ratio  = 1 : 3

Zinc per day = 420 milligrams

Hence,

1 /3 = x / 420

x /420 = 1 / 3

Where x is the number of milligrams of copper

so,

x = 1 /3 × 430

x = 140  milligrams of copper

Therefore the  milligrams of copper is 140 milligrams.

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An exponential function has the form

Therefore, to find an exponential function that satisfies our condition, we need to find a and b.

From f(-2) = 1, we have

and from f(7) = 63, we have

Solving for a in equation (1) gives

substituting this value of a into equation (2) gives

With the value of b in hand, we now find the value of a:

Hence, the exponential function is

Evaluating the above function at x = 1 gives

which is our answer!

Answer:

chad's other friend picked up 1 3/8 pounds of berries

Step-by-step explanation:

chad = 2 1/2 = 2 4/8

friend 1 = 1 3/8

2 4/8 + 1 3/8 = 3 7/8

5 1/4 = 5 2/8

5 2/8 - 3 7/8 = 1 3/8

30

Given the expression for the instantaneous voltage expressed as:

Given the following parameter:

θ = 30⁰

Substitute the given parameter into the formula to have:

Therefore the instantaneous voltage when θ = 30⁰ is 30.

The fraction of the poster does Dwayne use for his friends from school is 5/12.

A fraction is a non-integer that has a numerator and a denominator. The numerator is the number that is above the line and the denominator is the number below the line. An example of a fraction is 5/12.

In this question, the numerator is the number of parts he gives his friends from school. The denominator is the total number of parts he divides the poster.

Fraction = parts he gave his friend from school / total number of parts

5 / 12.

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Answer:

1/24

Step-by-step explanation:

.........................

Answer:

I'll assume that "2 (1/2)^3" means 2*(1/2)^3.

Step-by-step explanation:

(1/3)/(2*(1/2)^3)

(1/3)/(1)^3

= (1/3)

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

If "2(1/2)^3" means (2+1/2)^2:

((5/2)^2 = (25/4)

--

(1/3)/(25/4)

(1/3)*(4/25) = 4/75 or 0.05333

A grizzly bear's normal heart rate when not hibernating is 50 beats per minute.

What is a heart rate?

The number of heartbeats that occur in a specific amount of time, usually one minute. The wrist, side of the neck, back of the knees, top of the foot, groin, and other areas of the body where an artery is close to the skin can all detect the heartbeat.

Here,

We let his normal heart rate = h

and given in the question,

20% of h = 10

20/100 * h = 10

h = 10*5

= 50 beats/min

Hence, a grizzly bear's normal heart rate when not hibernating is 50 beats per minute.

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Using ratios, we can conclude that Chris gets 12 sweets.

So, a number of sweets Chris receive:

Now, 7:3 = x+20:x, solve as follows:

Therefore, using ratios, we can conclude that Chris gets 12 sweets.

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The correct question is given below:
Alex and Chris share sweets in the ratio Alex: Chris = 7 : 3. Alex receives 20 more sweets than Chris. Work out the number of sweets Chris receives.

a) (2.3 × [tex]$10^4[/tex]) × (1.5 × [tex]$10^{-2}[/tex]) in standard form

The number in standard form is 345

explanation:

The given two multiplication of the numbers is :

(2.3 × [tex]$10^4[/tex]) × (1.5 × [tex]$10^{-2}[/tex])

First we multiply the non exponential terms as shown below

2.3 × 1.5 = 3.45

Now we multiply the exponential terms as shown below

[tex]$10^4[/tex] × [tex]$10^{-2}[/tex] = 100

Now multiplying the exponential and non exponential term we get the number in standard form as shown below

(2.3 × [tex]$10^4[/tex]) × (1.5 × [tex]$10^{-2}[/tex])  in standard form 345

(3.6 × [tex]10^-5[/tex])÷(1.8 × 10²) in standard form 0.0000002

(8 ×  10^-3) ×  (2 ×  [tex]10^-4[/tex] in standard form  1.6 × [tex]10^-6[/tex]

(6 × 10²)/(3 × 10-5) in standard form 20,00,0000

5.1 × [tex]$10^-1[/tex] in ordinary number is 0.51

(1.7 × [tex]10^4[/tex]) × (8.5x ×[tex]0^-2[/tex]) in standard form  1.445 × 10³.

3.45 x  100 = 345

Therefore, the number in the standard form is 345

b) (3.6 × [tex]10^-5[/tex])÷(1.8 × 10²) in standard form

The number in standard form is 0.0000002

explanation:

By dividing 3.6 by 1.8 we get “2”, hence the above equation becomes,

(2 × [tex]10^-5[/tex]) /[tex]10^2[/tex]

We know that

[tex]\frac{x^{a} }{x^{b} } = x^{a-b}[/tex]

Therefore the above equation becomes,

2 × [tex]10^-7[/tex]

since the exponent of 10 is negative , therefore 7 zeros are written on the left hand side of the number = 0.0000002

Therefore, the number in the standard form is 0.0000002

c) (8 × [tex]10^-3[/tex]) × (2 × [tex]10^-4[/tex]) in standard form

The number in standard form is 1.6 × [tex]10^-6[/tex]

explanation:

Given the product of scientific notations:

(8 ×  [tex]10^-3[/tex]) ×  (2 ×  [tex]10^-4[/tex])

This can be expressed as:

(8 × 2) ×  ([tex]10^-3[/tex] × [tex]10^-4[/tex])

= 16 ×  [tex]10^-3[/tex]-4

= 16 × [tex]10^-7[/tex]

= 1.6 × [tex]10^1[/tex] × [tex]10^-7[/tex]

= 1.6 × [tex]10^-6[/tex]

Therefore, the number in the standard form is 1.6 × [tex]10^-6[/tex]

d) (6 × 10²)/(3 × 10-5) in standard form

The number in standard form is 20,00,0000

e)  5.1 × 10^-1 as an ordinary number

The ordinary number is 0.51

usual form of 5.1 × [tex]10^1[/tex] is

5.1 ×  1/ [tex]10^1[/tex]

= 5.1/10

= 0.51

Therefore , ordinary number is 0.51

f) (1.7 × [tex]10^4[/tex]) × (8.5 × [tex]10^-2[/tex])  in standard form.

The number in standard form is 1.445 × 10³.

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Remember that to model this kind of problems, we can use the equation of a straight line

Where:

• b, are the fixed costs

• x ,represents what varies

• m, is the cost of what varies

1. Therefore, using the data provided, we can model the cost of production with a function where:

• x ,is the numbers of CD's produced

• C, is the cost of producing those CD's

2. To model the revenue, we'll have to take into account that every CD sells at $68. Therefore, the money collected by selling the x CD's produced is:

Where:

• x ,its the number of CD's produced and sold

• R, is the total revenue

3. To get the profit, we'll have to substract the production cost to the money collected by the sale. Remember we already have two expressions, in terms of x, that describe both situations. Therefore,

Where:

• x ,its the number of CD's produced and sold

• P, is the total revenue

4. In order to break even, the revenue (R) has to be equal to the cost of production (C), Thus,

Therefore, 546 CD's would have to be produced to break even.

Answer:

10^2 + 15^2 = 20^2

100+225≠400

so no, it's not a right angled triangle

:)

Remember that

1 m3=1,000 lt

2 m3=2,000 lt

The volume of the tank is equal to

V=L*W*H

we have

V=2 m3

L=4 m

W=1.5 m

H=?

substitute given values

2=4*1.5*H

solve for H

2=6H

H=2/6

Answer:

The answer is 35

Step-by-step explanation:

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The cutoff score so that only 5% of the population has a higher score is 124.7.

If 5% of the population has a higher score, then the probability of selecting these is 0.05.

Find the z-score that corresponds to the probability in the z-table. (see attached images)

probability = 1 - 0.05 = 0.95

z-score = 1.647

Using the formula for the z-score below, determine the cutoff score.

z-score = (x – μ) / σ

where x = individual data value = cutoff score

μ = mean = 100

σ = standard deviation = 15

1.647 = (x - 100) / 15

1.647(15) = x - 100

x = 24.705 + 100

x = 124.705

cutoff score = 125

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The associated number of degrees of freedom for reading the t-value is 58.

The aim is to determine an interval for the mean of a population.

The standard deviation is unknown to us. The sample consists of 59 items. The mean of the sample is determined to be 32. We need to calculate the associated number of degrees of freedom for reading the t value.

We know that the degree of freedom is one less than the number of items in the sample space.

The associated number of degrees of freedom for reading the t-value is 59-1.

The associated number of degrees of freedom for reading the t-value is 58.

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The amount of interest earned in 10 years is $75.

So, interest earned after 2 years = $15

Therefore, the amount of interest earned in 10 years is $75.

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Answer:

18*19 BECAUSE 19 is a prime number and g has to be 1 since if g was anything else like 2 it wouldn't be the same for gh

55.557 + 121.4474 + 6.3

we have that

55.557=55.5570

121.4474

6.3=6.3000

so

55.5570

121. 4474

6. 3000

------------------

Answer: [tex]y=15-5x, z=2x-2[/tex]

Step-by-step explanation:

Subtracting the first equation from the second equation yields [tex]16x-8z=16 \implies 2x-z=2 \implies z=2x-2[/tex].

Substituting this into the first equation,

[tex]-11x-y+3(2x-2)=-21\\\\-11x-y+6x-6=-21\\\\-5x-y-6=-21\\\\-5x-y=-15\\\\5x+y=15\\ \\ y=15-5x[/tex]

We have the next information

When he left the library he read 8/8-7/8= 1/8

then he read 1/10

after dinner, he read 2/5

First, we need to sum the fraction of the book he read

we need to have the same denominator in order to sum the fractions

the book complete represent 8/8 so we need to subtract 5/8 from the fraction of the complete book

the fraction of the book does he have left to read is 3/8

Answer:

x = 8 + 4[tex]\sqrt{3}[/tex]

Step-by-step explanation:

computation just means to calculate

x(2[tex]\sqrt{3}[/tex] - 3 ) = 4[tex]\sqrt{3}[/tex] ( divide both sides by (2[tex]\sqrt{3}[/tex] - 3 ) )

x = [tex]\frac{4\sqrt{3} }{2\sqrt{3-3} }[/tex]

rationalise the denominator by multiplying the numerator/ denominator by the conjugate of the denominator.

the conjugate of 2[tex]\sqrt{3}[/tex] - 3 , is 2[tex]\sqrt{3}[/tex] + 3

= [tex]\frac{4\sqrt{3}(2\sqrt{3}+3) }{(2\sqrt{3}-3)(2\sqrt{3}+3) }[/tex] ← expand denominator using FOIL

= [tex]\frac{24+12\sqrt{3} }{12-9}[/tex]

= [tex]\frac{24+12\sqrt{3} }{3}[/tex]

= [tex]\frac{24}{3}[/tex] + [tex]\frac{12\sqrt{3} }{3}[/tex]

= 8 + 4[tex]\sqrt{3}[/tex]

The required equation of line would be 2y = 5x - 8 which is shown in the given graph.

The slope of a line is defined as the angle of the line.

According to the given figure,

We clearly see that the coordinates of the y-intercept would be (0, -4).

The value of the x-coordinate is 2 when y-coordinate is 1.

Here the line passes through the points (0, -4) and (2, 1).

Let the required line would be y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x₂ -x]

x₁ = 0, y₁ = -4

x₂ = 2, y₂ = 1

⇒ y - y₂ = (y₂ - y₁)/(x₂ -x₁ )[x -x₂]

⇒ y - 1 = (1 - (-4))/(2 - 0 )[x -2]

⇒ y - 1 = 5/2[x -2]

⇒ 2y - 2 = 5[x -2]

⇒ 2y = 5x - 10 + 2

⇒ 2y = 5x - 8

Therefore, the required equation of line would be 2y = 5x - 8 which is shown in the given graph.

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Aaron has to pay $ 115 when the usage gets over by 3 GBs and
$ (40 + 25x) when the usage gets over by x GBs.

How can one calculate the cost for a multiple of the same entity?
To calculate the cost of a multiple entities when the cost of a single one is given, we linearly multiply a fixed proportion to it to calculate the same.

Given, monthly fixed cost of the smart phone data plan = $ 40
Also, amount charged by the firm for each extra GB used = $ 25
Now, amount charged for three extra GBs = 25*3 = 75
Thus, net total that Aaron has to pay for 9 GBs = 40 + 75 = $ 115
Following similar arguments, amount charged for extra 'x' GBs = 25x
Thus, net total that Aaron has to pay for x GBs = 40 + 25x = $ (40 + 25x)
Therefore, Aaron has to pay $ 115 when the usage gets over by 3 GBs and $ (40 + 25x) when the usage gets over by x GBs.

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Answer:

f(x)= -x^2-6x+7

Step-by-step explanation:

Since the graph opens downward the function for the parabola is going to be negative. This leaves us with two answers.

Now use the remaining possible equations and solve for the vertex.

Using  x= -b/2a to solve for the x value of the vertex plug in the values to solve.

a= -1 b= -6  c=7 so, since -6 is already negative plugging it in makes it positive -(-6)/2(-1) = 6/-2 = -3. So x equals negative 3.

Then plug in -3 into the equation to get the y-value.

- (-3)^2 - 6(-3) + 7 = -9 + 18 + 7 = 16 so this confirms the vertex for this equation is (-3,16) so the answer is -x^2-6x+7.

Hope this helped! :)

Answer:

2

Step-by-step explanation:

convert 1 + the other one is 2

Answer:

2

Step-by-step explanation:

You add both numbers that have been given which are 1+1

ok

Equations : 4x + y = 2 x - y = 3

Equation 1 4x + y = 2 x - y = 3

x y x y

-2 10 -2 -5

-1 6 -1 -4

0 2 0 -3

1 -2 1 -2

2 -6 2 -1

The point where both lines cross is (1, -2) so it is the solution.

Answer: slope = [tex]\frac{y}{x}[/tex]

Step-by-step explanation:
Slope means gradient which is given by change in y
                                                                      change in x
on the graph, change in y = 100-0 = 100
                        change in x = 95-45 = 50
so, gradient is 100/50
                      = 2

Answer:

2 pizzas

Step-by-step explanation:

5 7/8 - 4 1/16=

5 14/16 - 4 1/16 ==> make the denominators equal to each other so they can be easily subtracted in the next step

5 + 14/16 - (4 + 1/16)=

5 + 14/16 - 4 - 1/16 =

5 - 4 + 14/16 - 1/16 =

1 + 13/16 = 1 13/16 which is approximately 2 pizzas