Find the length of each segment.

The perimeter of the canvas remains is 56 inches.

The perimeter of a square is defined as the addition of the lengths of the square.

If the area of the square canvas is 196 square inches, then each side of the square has a length of:

√(196) = 14 inches

Let the width of the border be x inches. Then the dimensions of the framed canvas will be (14 + 2x) inches by (14 + 2x) inches, and its area will be:

(14 + 2x)² square inches

The area of the framed canvas is 196 square inches plus the area of the border.

So, (14 + 2x)² = 196 + 4x(14 + 2x)

196 + 56x + 4x² = 196 + 56x + 8x²

Subtracting 196 and 56x from both sides:

4x² = 0

Dividing both sides by 4:

x² = 0

This implies that x = 0, which would mean that there is no border at all.

Therefore, the perimeter of the canvas remains 14 x 4 = 56 inches.

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Answer:

congrats you just found 118,222.36 pounds of pennies worth $134,061.9

you should buy a house or car with 59 tons of pennies

Answer:

Step-by-step explanation:

x+y-22=-16

But x =-7

then

-7+y-22=-16

y-29=-16

y=-16+29

y=13

Answer:

A A one-sample t-interval for a population mean

Step-by-step explanation:

The biologist will collect a random sample of dolphins and use the sample weights to create the estimate.

In a confidence interval, we take the data from the sample and want to estimate it for the entire population, so the interval is for a population mean.

The standard deviation will be taken from the sample, which means that the t-interval is used.

We want for one population, so it is a one sample for the population mean, and the correct answer is given by option A.

The number of dimes that we have are 3, the number of nickels are 6 and the number of quarters are 5.

Let the number of dimes be x.

So, we get that:

The number of quarters will be = x + 2

The number of nickels will be = 2 x

Now, 1 dime = $0.10.

1 nickel = $ 0.05

1 quarter =  $ 0.25

Amount of dimes = 0.10 x

Amount of nickels = 0.10 x

Amount of quarters = 0.25 x + 0.5

Total amount of coins = $ 1.85

So, we get the equation as:

0.10 x + 0.10 x + 0.25 x + 0.5 = 1.85

0.45 x = 1.35

x = 135 / 45

x = 3

Dimes = 3

Nickels = 6

Quarters = 5

Therefore, we get that, the number of dimes that we have are 3, the number of nickels are 6 and the number of quarters are 5.

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Answer:

It should be 15 pounds

Step-by-step explanation:

If you divide 5 weeks (the amount you need) by 2 weeks (the current ratio 6:2) then you get 2.5. Lastly just multiply 6 pounds to it (the other part of the ratio/ pounds per 2 weeks)

The constant of variation of the given problem is calculated as; 240 miles

A constant of variation (k) is defined as a ratio that represents the relationship between the independent variable (x) and the dependent variable (y).

Now, we are told that average speed, s, in miles per hour is inversely proportional to the time, t, the trip takes in hours. Thus;

s ∝ 1/t

Thus;

s = k(1/t)

where k is the constant of proportionality

we are told that If the train takes 2 hours, and the average speed is 120 mph. Thus;

120 = k(1/2)

Multiply both sides by 2 to get;

240 miles = k

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Answer:

e = 2

Step-by-step explanation:

7(2e - 1) - 3 = 6 + 6e

14e - 7 - 3 = 6 + 6e

14e - 10 = 6 + 6e

14e - 6e - 10 = 6

8e - 10 = 6

8e = 6 + 10

8e = 16

8e/8 = 16/8

e = 2

Recheck:

7(2e - 1) - 3 = 6 + 6e

7(2(2) - 1) - 3 = 6 + 6(2)

7(4 - 1) - 3 = 6 + 12

7(3) - 3 = 18

21 - 3 = 18

18 = 18 ✅

The solution is Option A.

The equation of line is y = ( -2/3 )x + 2 , where the slope is m = ( -2/3 ) and the y intercept is 2

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be P ( 3 , 0 )

Let the second point be Q ( 0 , 2 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

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

Slope m = - ( 2/3 )

Now , the equation of line is y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 0 = ( -2/3 ) ( x - 3 )

On simplifying the equation , we get

y = ( -2/3 )x + 2

Hence , the equation of line is y = ( -2/3 )x + 2

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Answer:

-2y + 10

Step-by-step explanation:

Substitution method:

On the second equation of the system, we have to find x as a function of y.

-x - 2y = -10

We have to find x as a function of y, so:

\(-x = -10 + 2y\)

Multiplying both sides of the equality by -1:

\(x = -2y + 10\)

So -2y + 10 is the answer to this question.

Answer:

I THINK rachel will be 12

Step-by-step explanation:

Answer:

i cant see the whole thing

Step-by-step explanation:

Answer:

\(4x^3-7x^2-23x-10\)

Step-by-step explanation:

So we have the expression:

\((4x+5)(x^2-3x-2)\)

Distribute. Multiply (4x+5) to each term:

\((x^2)(4x+5)+(-3x)(4x+5)+(-2)(4x+5)\)

Distribute:

\(=(4x^3+5x^2)+(-12x^2-15x)+(-8x-10)\)

Combine like terms:

\(=(4x^3)+(5x^2-12x^2)+(-15x-8x)+(-10)\)

Add and simplify:

\(=4x^3-7x^2-23x-10\)

And this is in descending order, so it's in standard form.

Total water bill for the month is $62.37.

It seems that you may have accidentally left out the total amount of your water bill.

The total amount by simply adding the amounts of the individual bills together:

Total water bill =\($36.34 + $26.03\)

= \($62.37\)

You have not provided enough information to determine your total water bill.

You have only given the amounts of your individual bills from Metro Water Services and Madison Suburban Utility District.

To find your total water bill, you simply need to add the two bills together.

So, the total amount you owe for water this month would be:

Total water bill = \($36.34 + $26.03\)

= \($62.37\)

It appears that you may have forgotten to include the full amount of your water bill by accident.

Simple addition of the separate bill amounts yields the following sum:

Water bill total = \($36.34 + $26.03\)

= \($62.37\)

Your total water bill cannot be calculated because not enough information has been given.

Only the amounts of your individual Metro Water Services and Madison Suburban Utility District bills have been provided.

You just need to combine the two invoices together to get your total water bill.

As a result, this month's total water bill for you would be:

Water bill total =  \($36.34 + $26.03\)

= \($62.37\)

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Answer: The solution is C. 1/7.

Step-by-step explanation: Just plug 1/7 as x. You will find that the statement is true when you plug in 1/7.

Let x be the number of hours spent typing by each student.

Since Mitchell can type at a speed of 3 pages per hour, and has already typed 9 pages, the expression that would model Mitchell's situation is:

Similarly, Roxanne can type at a speed of 2 pages per hour, and has already typed 12 pages, the expression that would model Roxanne's situation is:

Now, we know that after some time both will have the exact same page count. Let's call this number y. This way, we'll have two equations that describe a system of equations:

We'll solve it by substitution, so we'll solve the first equation for x, substitute in the second equation and then find the value of y, as following:

This way, we can conlcude that:

Since we've calculated an expression for x in terms of y , we just have to plug in this value in it to find the value of x:

Therefore, the solution to our system is:

This way, we can conclude that:

cos(tan^(-1)(-2/3)) simplifies to 3√13 / 13.

To evaluate the expression cos(tan^(-1)(-2/3)), we can use the trigonometric identity:

cos(tan^(-1)(x)) = 1 / √(1 + x^2)

In this case, x is -2/3. Substituting the value into the identity:

cos(tan^(-1)(-2/3)) = 1 / √(1 + (-2/3)^2)

Now, let's calculate the value:

cos(tan^(-1)(-2/3)) = 1 / √(1 + 4/9)

                   = 1 / √(13/9)

                   = 1 / (√13/3)

                   = 3 / √13

                   = 3√13 / 13

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The area of the rhombus, obtained from the dimensions, of the diagonals, found from the trigonometric of sines of the angle can be presented as follows;

Area = 8·√3

The area of a plane figure is the two dimensional space occupied by the figure on a plane.

The measure of the angle ABC, m∠ABC = 60°

The length of the segment AE = 2 units

The diagonals of a rhombus bisect each other at right angles, and the right angles through which they pass, therefore;

BE = ED, m∠AEB = 90°

m∠ABE = 30°

sin(30°) = AE/AB

sin(30°) = 2/AB

AB = 2/(sin(30°)) = 4

AB = 4

BE = √(4² - 2²) = √(12) = 2·√3

Therefore; AC = 2 + 2 = 4

BD = 2·√3 + 2·√3 = 4·√3

The area of a rhombus = (1/2) × The product of the length of the diagonals

Therefore;

Area of the rhombus = (1/2) × (4·√3) × 4 = 8·√3

The area of the rhombus = 8·√3

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Answer:

D

Step-by-step explanation:

Answer:

0.75 g ≤ 35

Step-by-step explanation:

if each games costs $0.75, then the answer of g will be given by 35/0.75.

he can go up to exactly $35 but not over

so, the inequality is given by 0.75 g ≤ 35

Answer:

Z

Step-by-step explanation:

The value of side TS is,

⇒ TS = 28

First, we are going to divide the figure and named new points X and Y as:

Now, we know that TS is the sum of TX and XS.

TS = TX + XS

Additionally, TX has the same length of HJ, so:

TX = HJ = 14

Now, we want to know the length of YK, and we can calculate it using the following equation:

LK = LY + YK

LY = HJ,

so, LY = 14

And, 42 = 14 + YK

42 - 14 = YK

28 = YK

Finally, since T and S are midpoints, the length of XS is the half of the length of YK. It means that XS is:

XS = YK/2

XS = 28/2

XS = 14

Therefore, TS is equal to:

TS = TX + XS

TS = 14 + 14

TS = 28

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The probability that the buyer waits more than 10 minutes is 0.0271

From the question, we have the following parameters that can be used in our computation:

Probability function:

fy(y)=0.2e^(-0.2y), y ≥ 0

The inequality expression y ≥ 0 means that

The value of y is atleast 0

The probability that the buyer waits more than 10 minutes means that

y = 10

So, we have the following representation

y = 10 in fy(y)=0.2e^(-0.2y)

Substitute the known values in the above equation, so, we have the following representation

fy(10)=0.2e^(-0.2 * 10)

Evaluate the exponents

fy(10)=0.2 * 0.13533528323

Evaluate the products

fy(10) = 0.0271

Hence, the probability is 0.0271

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Translation of the point (-8, -6) to the new origin (5, 4) is thus (-13, -10). Hence, the response is (-13, -10).

A sequence of numbers known as coordinates is used to describe the location of a point or object in space or on a plane. Coordinates in two-dimensional space typically have two values, which are typically written as (x, y), where x denotes the horizontal position and y denotes the vertical position. Coordinates in three dimensions can have three values, denoted as (x, y, z), where x, y, and z stand for the position along the x, y, and z axes, respectively. In many different fields, such as geometry, physics, and computer graphics, coordinates are used.

given

The coordinates of the new origin must be subtracted from the given point in order to translate the point (-8, -6) to the new origin (h, k) = (5, 4).

x' = -8 - 5 = -13

y' = -6 - 4 = -10

Translation of the point (-8, -6) to the new origin (5, 4) is thus (-13, -10). Hence, the response is (-13, -10).

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Answer:

the 2nd one

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

Multiply 2/5 by three, creating 6/15. subtract 15 by 6, 15-6=9

Answer:

(2,3 is dilated to 8,12 by a scale factor of 4)

Step-by-step explanation:

multiply 2,3 by numbers until it gets to 8,12, once you multiply by 4 you get 8,12 which means the answer is a scale factor of 4