Geometry: The rectangle shown has a perimeter of 34cm and the given area. Its length is 5 more than twice it's width. Write and solve a system of equations to find the dimension of the rectangle

The rational number equivalent to -20/4 is -5.

A rational number equivalent to -20/4 is -5. This can be found by dividing the numerator (which is -20) by the denominator (which is 4). The result of this division is -5. Hence, -5 is the rational number equivalent to -20/4.

recall that to get the inverse of any expression, we start off by doing a quick switcheroo on the variables, and then solve for "y".

[tex]\bf \stackrel{f(x)}{y}=2x\implies \stackrel{\textit{switcheroo}}{x=2y}\implies \cfrac{x}{2}=y\implies \cfrac{1}{2}x=\stackrel{f^{-1}(x)}{y}[/tex]

Answer with Step-by-step explanation:

Let x and y be two numbers.

One number is 3 less than twice another.

⇒ y=2x-3

Their sum is 39.

⇒ x+y=39

Hence, system of equations are:

y = 2x - 3 and x + y = 39

Putting y=2x-3 in x+y=39

x+2x-3=39

⇒ 3x-3=39

⇒ x-1=13 (dividing both sides by 3)

⇒ x=14

y=2x-3

⇒ y=2×14-3

⇒ y=28-3

⇒ y=25

Hence, Two numbers are:

14 and 25

Answer:

The numbers are 11 and 7

Step-by-step explanation:

To find these, use the statements to create equations in standard form.

3x + y = 40

x - y = 4

Now that we have these two, we can add them together and get the y's to cancel out.

3x + y = 40

x - y = 4

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

4x = 44

x = 11

Now that we have the first number as 11, we can solve for y using either equation.

x - y = 4

11 - y = 4

-y = -7

y = 7

If a, b and c are the lengths of a right triangle and c is the longest side, then:

[tex]a^2+b^2=c^2[/tex]

We have a = 18cm, b = 24cm and c = 30cm. Substitute and check:

[tex]L_s=18^2+24^2=324+576=900\\\\R_s=30^2=900\\\\L_s=R_s[/tex]

Answer:

$1.25

Sorry that i dont have an explanation i just didnt wanna confuse you lol

Answer:

x + 4 = 7 + 4 = 11 feet

Step-by-step explanation:

Do you ever have a nice "fist", meaning you have very neat handwriting.

You are told that A to MSG = B to MSG

So

Equation

3x - 10 = x + 4

Solution

Subtract x from both sides

3x - x - 10 = x - x + 4             Simplify

2x - 10 = 4                             Add 10 to both sides

2x - 10 + 10 = 4 + 10              Simplify

2x = 14                                   Divide by 2

2x/2 = 14/2

x = 7

x + 4 = 7 + 4 = 11 feet from A to Madison Square Garden

Answer:

answer is x=2

The solution set for the equation 6x - 2 = 10 using the replacement set {1, 2, 3, 4} is {2}, as 2 is the only number in the set that, when substituted into the equation, satisfies it.

The solution set for the open sentence 6x - 2 = 10 using the given replacement set {1, 2, 3, 4} can be found by solving the equation for x and then checking which numbers in the replacement set satisfy the equation.

Therefore, the solution set is {2}.

Answer:

A. $100

B. 29%

Step-by-step explanation:

A. To find total price of the items Sammy bought we will add the price of shoes and jacket after discount.

Let us find price of shoes after 25% discount.

[tex]\text{Price of shoes after discount}=40-(\frac{25}{100}*40)[/tex]

[tex]\text{Price of shoes after discount}=40-(\frac{1}{4}*40)[/tex]

[tex]\text{Price of shoes after discount}=40-10=30[/tex]

Therefore, price of shoes after discount is $30.

Now let us find price of jacket after 30% discount.

[tex]\text{Price of jacket after discount}=100-(\frac{30}{100}*100)[/tex]

[tex]\text{Price of jacket after discount}=100-30[/tex]

[tex]\text{Price of jacket after discount}=70[/tex]

Therefore, price of jacket after discount is $70.

Now let us add both prices to find the total price of the items.

[tex]\text{Total price of items}=30+70[/tex]

[tex]\text{Total price of items}=100[/tex]

Therefore, the total price of the items bought by Sammy is $100.

B. To find the percent discount which Sammy got on his total purchases, we will use percent change formula.

[tex]\text{Percent change}=\frac{\text{Difference}}{\text{Original value}}\times 100[/tex]  

Total price without discount= 100+40=140

[tex]\text{Discount percent}=\frac{140-100}{140}\times 100[/tex]

[tex]\text{Discount percent}=\frac{40}{140}\times 100[/tex]

[tex]\text{Discount percent}=0.2857142857142857\times 100[/tex]

[tex]\text{Discount percent}=28.57142857142857\approx 29[/tex]

Therefore, Sammy got approximately 29% discount on his total purchases.

Answer:

Sammy bought a car and got a discount of 2/5 off the original price of $30,000. How much did Sammy pay for the car after the discount?  

Step-by-step explanation:

Answer:

A Experimental Probability

Step-by-step explanation:

The 59 percent is based on the data from the actual data.  The theoretical probability is 50 percent for male and 50% and female.

First check the difference between terms:

[tex]\{1-(-3),5-1,9-5,\ldots\}=\{4,4,4,\ldots\}[/tex]

So every term differs by 4. The first term in the sequence is [tex]a_1=-3[/tex]. Recursively, the sequence is given by

[tex]\begin{cases}a_1=-3\\a_n=a_{n-1}+4&\text{for }n>1\end{cases}[/tex]

Then

[tex]a_2=a_1+4[/tex]

[tex]a_3=a_2+4=a_1+4(2)[/tex]

[tex]a_4=a_3+4=a_1+4(3)[/tex]

and so on, with the general rule

[tex]a_n=a_1+4(n-1)\implies a_n=4n-7[/tex]

Then the 250th term of the sequence would be

[tex]a_{250}=4(250)-7=993[/tex]

To calculate a new salary after a pay increase, multiply the current salary by the percentage increase and add it to the original salary. In this case, a 6% increase on a $62,900 salary results in a new annual salary of $66,674.

The subject of this question is determining the new salary after a pay increase, which is a common problem in mathematics related to percentages. To calculate the new salary after a 6% pay increase to a current salary of $62,900, you multiply the current salary by the percentage increase in decimal form, which is 0.06.

Step-by-Step Calculation

Determine the increase amount by multiplying the current salary by the percentage increase: $62,900 × 0.06 = $3,774.

Add the increase to the current salary to get the new salary: $62,900 + $3,774 = $66,674.

The new annual salary after a 6% increase will therefore be $66,674.

To generalize, the formula to calculate the percentage change or growth rate is given by:

Percentage change = (Change in quantity / Original Quantity) × 100

For example, a $2 per hour raise on a $10 per hour job represents

Percentage change = ($2 / $10) × 100 = 20%

Answer:

The number of plain bagels are 18 and it is 75% of the total bagels .

The amount of salt in a plain bagel to that in a sesame bagel is 81.5% .

Step-by-step explanation:

Formula

[tex]Percentage = \frac{Part\ value\times 100}{Total\ value}[/tex]

As given

Jen buys sesame bagels and plain bagels. If the ratio of sesame to plain is 1:3 and Jen bought 2 dozen bagels .

As one dozens contains 12 items .

Thus

Total number of bagels bought by Jen = 2 × 12

                                                                 = 24

Let us assume that the x be the scalar multiple of sesame bagels and plain bagels .

Number of sesame bagels = 1x

Number of plain bagels = 3x

Than the equation becomes

x + 3x = 24

4x = 24

[tex]x = \frac{24}{4}[/tex]

x = 6

Thus

Number of plain bagels = 3 × 6

                                        = 18

Part value = 18

Total value = 24

Putting all the values in the formula

[tex]Percentage = \frac{18\times 100}{24}[/tex]

[tex]Percentage = \frac{1800}{24}[/tex]

Percentage = 75 %

Therefore the number of plain bagels are 18 and it is 75% of the total bagels  .

As given

Suppose each plain bagel has 0.53 gram of salt, and each sesame bagel has 0.65 gram.

Part value = 0.53 grams

Total value = 0.65 grams

Putting all the values in the formula

[tex]Percentage = \frac{0.53\times 100}{0.65}[/tex]

[tex]Percentage = \frac{5300}{65}[/tex]

Percentage = 81.5 %

Therefore the amount of salt in a plain bagel to that in a sesame bagel is 81.5% .

Answer:

To find the perimeter, just add up the lengths of the each side.

AB = 13 units

BC = 12 units

CA = 5 units

P = 13 + 12 + 5 = 30 units

45+0.15·45=45+6.75=51.75$

Answer:

78 books

Step-by-step explanation:

Use proportion: If 52 is 2/3 of the books then  number of books shipped = 52 * the inverse of 2/3  which is 52 * 3/2:-

 52 * 3/2

= 156/2

= 78 books

Answer:

4

Step-by-step explanation:

As each x value increases by 1, the output values increase by a factor of 4. This means that each y value can be multiplied by 4 to get the next y value.

1/2(4)=2

2(4)=8

8(4)=32

4 is the factor.

Answer:

all the lines are correct but for x<= 2 there need to be a closed circle, and vica versa for all the others.

Step-by-step explanation:

The lines are correct but for x<= 2

Answer:

if that is all it says you can do simple cross multiplication

Step-by-step explanation:

18*3/2=x

x will give you the nre number. If you dont know how to do that math go to desmos and type it in. the answer should be 27 if i did it correctly in my head but please check my work.

A student helping a student

The new pentagon has a perimeter of 27 centimeters.

To find the perimeter of a regular pentagon, we multiply the length of one side by the number of sides. In this case, the perimeter is 18 centimeters, so each side of the pentagon is 18/5 = 3.6 centimeters long.

When this pentagon is dilated by a scale factor of 3/2, each side of the new pentagon will be 3/2 x 3.6 = 5.4 centimeters long.

Therefore, the new pentagon has a perimeter of 5.4 x 5 = 27 centimeters.

https://brainly.com/question/15387363

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Answer:

10200

Step-by-step explanation:

The population in 1999 was 10200.

Given is that the population of at a town has grown 2% each year. In 1998, the population of the town was about 10,000 people.

Let the population be in 1999 be {x}. Then, we can write -

{x} = 10000 + {2% of 10000}

{x} = 10000 + {2/100 x 10000}

{x} = 10000 + 200

{x} = 10200

Therefore, the population in 1999 was 10200.

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Answer:

4

Step-by-step explanation:

The equation is

x^2 - (2x + 8) = 0   where x is the number to be found.

removing the parentheses by distributing the negative:-

x^2 - 2x - 8 = 0

(x - 4)(x +2) = 0

x =  4, -2.

The value of x  must be 4 because it is positive.

Answer:

x=66.667

Step-by-step explanation:

Basically, if y varies directly with a value x, you get an equation of the form y=kx, where k is a constant. To answer the question, first substitute 9 into y, and 24 into x.

                                                   9=24k

                                                   k=0.375

k is 0.375, so to get x, substitute 0.375 into k and 25 into y

                                                   25=0.375x

                                                     x=66.667

And we got it!

Final answer:

To find x when y = 25 in a direct variation where y = 9 when x = 24, first find the constant of proportionality (k = 3/8), then use this constant to solve the equation 25 = (3/8)x which yields x ≈ 66.67.

Explanation:

The student's question concerns direct variation, which is a concept where one variable changes in proportion to another variable. In this particular problem, the measure y varies directly with x. Given that y = 9 when x = 24, we can use this information to establish the constant of proportionality k where y = kx.

First, we solve for k using the initial condition:

9 = k * 24

k = 9/24

k = 3/8

Now that we have the constant of proportionality, we can find x when y = 25 by setting up the equation:

25 = (3/8)x

x = 25 * (8/3)

x = 200/3

x ≈ 66.67

Therefore, when y = 25, the value of x is approximately 66.67.

Answer:

The second answer: y= 3/4x + 2

Step-by-step explanation:

Subtract 4x to the other side

Divide by 3 to get y by itself

Make the coefficient of the x term the negative reciprocal, for that is the perpendicular slope of the line

Answer:

16.3 hours.

Step-by-step explanation:

"Decays exponentially at a rate of 11% per hour" translates into

(1 - 0.11)^h, where h is the number of hours during which the drug decays.

The negative sign comes from "decay."

The complete formula applicable here is

d(h) = (100 mg)(1 - 0.11)^h, where h is the number of hours.  

We want to know how many hours it will be until all but 15 mg remain.  The appropriate formula for this is

15 mg = (100 mg)()^h.  Dividing both sides by 100 mg, we get:

 15 mg

------------- = 0.89^h, or 0.15 = 1.11^h

100 mg

Apply properties of logs to solve this.  Take the natural log of both sides of the above equation.  We get:

ln 0.15 = h(ln 0.89).  Dividing both sides by ln 0.89, we get:

h = 16.3

The original 100 mg dosage would decay to 15 mg after 16.3 hours.

Answer:

~5 feet.

Step-by-step explanation:

assuming that it is a right triangle. if a=5 and c=7 then b the other leg is equal to the square root of c squared minus a squared. which equals about 4.9

Answer:

The amount of Rita's pocket money left is Rs. 36.

Step-by-step explanation:

Pocket money that Rita had before = 144

Money spent for magazines = 52% of 144

= [tex]\frac{52}{100} (144)[/tex]

= 0.52(144)

= 74.88

Money spent for movies = 23% of 144

= [tex]\frac{23}{100} (144)[/tex]

= 0.23(144)

= 33.12

Money left with Rita = 144 - (74.88 + 33.12)

= 144 - 108

= 36

Hence, Rita left with Rs. 36.

Aliter:

Total money spent = (52 + 23)% = 75%

So, money left with Rita = 100 - 75 = 25%

25% of 144 = 0.25(144) = 36.

Answer:

Sammy, after picking out her clothes, bringing them to the counter and ringing them up. owes in total: $49.78

Step-by-step explanation:

Final answer:

This answer explains how to calculate the total amount of money Sammy spent on T-shirts and jeans including sales tax.

Explanation:

To find out how much Sammy spent in total:

Calculate the total cost of the 3 T-shirts: $15.75 x 3 = $47.25

Calculate the total cost of the pairs of jeans: $28.79 x 2 = $57.58

Add the total costs of the T-shirts and jeans: $47.25 + $57.58 = $104.83

Add the sales tax to get the final amount: $104.83 + $5.24 = $110.07

Therefore, Sammy spent $110.07 in all.

Answer:

142.2 meters.  

Step-by-step explanation:

We have been given that a box measures 70 cm X 36 cm X 12 cm is to be covered by a canvas.      

Let us find total surface area of box using surface area formula of cuboid.

[tex]\text{Total surface area of cuboid}=2(lb+bh+hl)[/tex], where,

[tex]l[/tex] = Length of cuboid,

[tex]b[/tex] = Breadth of cuboid,

[tex]w[/tex] = Width of cuboid.

[tex]\text{Total surface area of box}=2(70\cdot36+36\cdot 12+12\cdot 70)[/tex]

[tex]\text{Total surface area of box}=2(2520+432+840)[/tex]

[tex]\text{Total surface area of box}=2(3792)[/tex]

[tex]\text{Total surface area of box}=7584[/tex]

Therefore, the total surface area of box will be 7584 square cm.  

To find the length of canvas that will cover 150 boxes, we will divide total surface area of 150 such boxes by width of canvass as total surface area of canvas will also be the same.

[tex]\text{Width of canvas* Length of canvass}=\text{Total surface area of 150 boxes}[/tex]

[tex]80\text{ cm}\times\text{ Length of canvass}=150\times 7584\text{cm}^2[/tex]

[tex]\text{ Length of canvass}=\frac{150\times 7584\text{ cm}^2}{80\text{ cm}}[/tex]

[tex]\text{ Length of canvass}=\frac{1137600\text{ cm}^2}{80\text{ cm}}[/tex]

[tex]\text{ Length of canvass}=14220\text{ cm}[/tex]

Let us convert the length of canvas into meters by dividing 14220 by 100 as 1 meter equals to 100 cm.

[tex]\text{ Length of canvass}=\frac{14220\text{ cm}}{100\frac{cm}{m}}[/tex]

[tex]\text{ Length of canvass}=\frac{14220\text{ cm}}{100\frac{cm}{m}}[/tex]

[tex]\text{ Length of canvass}=\frac{14220\text{ cm}}{100}\times\frac{m}{cm}[/tex]

[tex]\text{ Length of canvass}=142.20\text{ m}[/tex]

Therefore, 142.2 meters of canvas of width 80 cm required to cover 150 such boxes.

Answer: 4 and 9

Step-by-step explanation:

9 x 4 = 36

The square root of 9 is 3, so 9 is a perfect square.

The square root of 4 is 2, so 4 is a perfect square.

Answer:

9 x 4 = 36

Step-by-step explanation:

you should be able to mark him brainliest now =) =) =)