A rectangular piece of metal is 5 in longer than it is wide. Squares with sides 1 in lòng are cut from the four corners
and the flaps are folded upward to form an open box. If the volume of the box is 234 in³, what were the original
dimensions of the piece of metal?

Answer:

(2, -1)

Step-by-step explanation:

Given system of equations:

[tex]\begin{cases}y=-2x+3\\y+9=4x\end{cases}[/tex]

To solve the given system of equations, we can use the method of substitution.

Substitute the first equation into the second equation to eliminate the y term:

[tex](-2x+3)+9=4x[/tex]

Solve for x:

   [tex]-2x+3+9=4x[/tex]

       [tex]-2x+12=4x[/tex]

[tex]-2x+12+2x=4x+2x[/tex]

                  [tex]12=6x[/tex]

                 [tex]\dfrac{12}{6}=\dfrac{6x}{6}[/tex]

                   [tex]2=x[/tex]

                   [tex]x=2[/tex]

Substitute the found value of x into the first equation and solve for y:

[tex]y=-2(2)+3[/tex]

[tex]y=-4+3[/tex]

[tex]y=-1[/tex]

Therefore, the solution to the system of equations is (2, -1).

To verify the solution by graphing the system, find two points on each line by substituting two values of x into each equation. Plot the points and draw a line through them. The solution is the point of intersection.

Graphing y = -2x + 3

[tex]\begin{aligned} x=0 \implies y&=-2(0)+3\\y&=0+3\\y&=3\end{aligned}[/tex]            [tex]\begin{aligned} x=-2 \implies y&=-2(-2)+3\\y&=4+3\\y&=7\end{aligned}[/tex]

Plot points (0, 3) and (-2, 7) and draw a straight line through them.

Graphing y + 9 = 4x

[tex]\begin{aligned} x=0 \implies y+9&=4(0)\\y+9&=0\\y&=-9\end{aligned}[/tex]                 [tex]\begin{aligned} x=3 \implies y+9&=4(3)\\y+9&=12\\y&=3\end{aligned}[/tex]

Plot points (0, -9) and (3, 3) and draw a straight line through them.

The solution to the graphed system of equations is the point of intersection of the two lines: (2, 1).

The solution to the simultaneous equations is x = 3 and y = 7

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

y = 2x + 1

y = 10 - x

Subtract the equations

So, we have

3x - 9 = 0

This gives

3x = 9

So, we have

x = 3

Next, we have

y = 10 - x

y = 10 - 3

Evaluate

y = 7

Hence, the solution is x = 3 and y = 7

Read more about equations at

https://brainly.com/question/32583193

#SPJ1

Answer:

try (gauth math) could be helpful take screen shot and upload it it may be there or not hopefully it is

Based on the provided data sets, it can be observed that both Data Set K and Data Set L have identical values. Therefore, their centers and spreads are also identical.

The center of a data set can be measured using various statistical measures such as the mean, median, or mode. Since the data sets have the same values, all these measures will yield the same result for both sets.

In this case, the center of Data Set K is equal to the center of Data Set L.

Similarly, the spread of a data set refers to the measure of variability or dispersion within the data. Common measures of spread include the range, variance, and standard deviation.

However, since the data sets are exactly the same, all these measures will yield identical results for both sets. Thus, the spread of Data Set K is the same as the spread of Data Set L.

In summary, both the center and the spread of Data Set K are the same as those of Data Set L. Therefore, there is no difference between the two data sets in terms of their central tendency or variability.

For more such questions sets,click on

https://brainly.com/question/13458417

#SPJ8

Answer:

1

Step-by-step explanation:

So, 1 dozen is 12. Two dozen is 24.

She used 24 Mud Bugs in this soup.

This soup makes 20 cups.

So, 24 Mud Bugs are in 20 cups of soup.

To find the amount of Mud Bugs in each cup of soup, you divide the amount of Mud Bugs by the number of cups.

24/20

Which equals 1.2

You asked for the nearest whole number, so there is 1 Mud Bug per sup of soup.

Answer:

If you are in Acellus trust me the answer is 394

Step-by-step explanation:

SA = 2 ( 2 x 12 ) + 2 ( 2 x 10 ) + ( 8 x 6 ) + 2 ( 3 x 8 ) + ( 3 x 6 ) + ( 12 x 16 )

SA = 48 + 40 + 48 + 48 + 18 + 192

SA = 394 square cm.

Answer:

When p, the probability of success, is zero in a binomial distribution, the probability of getting exactly k successes in n trials is also zero for all values of k except when k is zero (i.e., when there are no successes).

So, in the case of (0.3)^0, the result would be 1, because any number raised to the power of 0 is equal to 1. Therefore, the probability of getting zero successes in a binomial distribution when the probability of success is 0.3 is 1.

You will need to purchase approximately 1/42 of a tube, which is less than a full tube. In practical terms, you would need to purchase at least one tube to meet your requirement of 42 ounces of capsaicin arthritis rub.

To determine the number of tubes of capsaicin arthritis rub you will need to purchase, we can divide the total required quantity by the quantity in each tube.

Given that the cost of capsaicin arthritis rub is $21 and you need to buy 42 ounces, we need to find out how many ounces are in each tube.

Let's assume that each tube contains x ounces of capsaicin arthritis rub.

Now we can set up a proportion to solve for x:

42 ounces / x tubes = 1 tube / x ounces

Cross-multiplying gives us:

42x = 1 * x

Simplifying the equation:

42x = x

Dividing both sides of the equation by x (since x cannot be zero):

42 = 1

Since this equation is not true, it means that there is an error in our assumption. We need to revise our assumption.

Let's assume that each tube contains 1 ounce of capsaicin arthritis rub.

Now we can set up a new proportion:

42 ounces / x tubes = 1 tube / 1 ounce

Cross-multiplying gives us:

42x = 1 * 1

Simplifying the equation:

42x = 1

Dividing both sides of the equation by 42:

x = 1/42

As a result, you will need to buy less than a full tube—roughly 1/42 of a tube. In order to get the 42 ounces of capsaicin arthritis rub you need, you would essentially need to buy at least one tube.

for such more question on purchase

https://brainly.com/question/28787564

#SPJ8

Answer:

B)  There are two solutions, but only one is viable.

Step-by-step explanation:

Given system of equations:

[tex]\begin{cases}A=w^2+4w\\A=4w+45\end{cases}[/tex]

To solve the system of equations, substitute the first equation into the second equation:

[tex]w^2+4w=4w+45[/tex]

Solve for w using algebraic operations:

[tex]\begin{aligned}w^2+4w&=4w+45\\w^2+4w-4w&=4w+45-4w\\w^2&=45\\\sqrt{w^2}&=\sqrt{45}\\w&=\pm \sqrt{45}\\w &\approx \pm 6.71\; \sf cm\end{aligned}[/tex]

Therefore, there are two solutions to the given system of equations.

However, as length cannot be negative, the only viable solution is w ≈ 6.71 cm.

Answer:

[tex]\dfrac{\sqrt{2}-\sqrt{6} }{4} }[/tex]

Step-by-step explanation:

Find the exact value of cos(105°).

The method I am about to show you will allow you to complete this problem without a calculator. Although, memorizing the trigonometric identities and the unit circle is required.    

We have,

[tex]\cos(105\°)[/tex]

Using the angle sum identity for cosine.

[tex]\boxed{\left\begin{array}{ccc}\text{\underline{Angle Sum Identity for Cosine}}\\\\\cos(A+B)=\cos(A)\cos(B)-\sin(A)\sin(B)\end{array}\right}[/tex]

Split the given angle, in degrees, into two angles. Preferably two angles we can recognize on the unit circle.

[tex]105\textdegree=45\textdegree+60\textdegree\\\\\\\therefore \cos(105\textdegree)=\cos(45\textdegree+60\textdegree)[/tex]

Now applying the identity.

[tex]\cos(45\textdegree+60\textdegree)\\\\\\\Longrightarrow \cos(45\textdegree+60\textdegree)=\cos(45\textdegree)\cos(60\textdegree)-\sin(45\textdegree)\sin(60\textdegree)[/tex]

Now utilizing the unit circle.

[tex]\boxed{\left\begin{array}{ccc}\text{\underline{From the Unit Circle:}}\\\\\cos(45\textdegree)=\dfrac{\sqrt{2} }{2}\\\\\cos(60\textdegree)=\dfrac{1}{2}\\\\\sin(45\textdegree)=\dfrac{\sqrt{2} }{2}\\\\\sin(60\textdegree)=\dfrac{\sqrt{3} }{2} \end{array}\right}[/tex]

[tex]\cos(45\textdegree)\cos(60\textdegree)-\sin(45\textdegree)\sin(60\textdegree)\\\\\\\Longrightarrow \Big(\dfrac{\sqrt{2} }{2}\Big)\Big(\dfrac{1 }{2}\Big)-\Big(\dfrac{\sqrt{2} }{2}\Big)(\dfrac{\sqrt{3} }{2}\Big)[/tex]

Now simplifying...

[tex]\Big(\dfrac{\sqrt{2} }{2}\Big)\Big(\dfrac{1 }{2}\Big)-\Big(\dfrac{\sqrt{2} }{2}\Big)(\dfrac{\sqrt{3} }{2}\Big)\\\\\\\Longrightarrow \Big(\dfrac{\sqrt{2} }{4} \Big)-\Big(\dfrac{\sqrt{6} }{4} \Big)\\\\\\\therefore \cos(105\textdegree)= \boxed{\boxed{\frac{\sqrt{2}-\sqrt{6} }{4} }}[/tex]

Answer:

Step-by-step explanation:

To find the number of antiviral proteins injected into the person, we can set up a proportion:

2 mL contains 2.3 × 10^3 antiviral proteins

x mL contains how many antiviral proteins?

The proportion can be written as:

2 mL / 2.3 × 10^3 = x mL / (unknown number of antiviral proteins)

We can solve this proportion by cross-multiplication:

2 mL * (unknown number of antiviral proteins) = 2.3 × 10^3 antiviral proteins * x mL

x = (2.3 × 10^3 antiviral proteins * x mL) / 2 mL

Simplifying, we get:

x = 1.15 × 10^3 * x mL

Therefore, the number of antiviral proteins injected into the person is 1.15 × 10^3.

The total number of cells in the person's body is approximately 1 × 10^14. If 8% of the person's cells are infected with the virus, we can calculate the percentage of cells that can be affected by the medication:

Percentage of cells affected = (Number of infected cells / Total number of cells) * 100

Number of infected cells = 8% of 1 × 10^14 cells

Number of infected cells = (8/100) * 1 × 10^14

Number of infected cells = 8 × 10^12

Percentage of cells affected = (8 × 10^12 / 1 × 10^14) * 100

Percentage of cells affected = 8 × 10^-2 * 100

Percentage of cells affected = 8%

Therefore, the administered medication can affect 8% of the person's cells.

To find the amount of medication needed to have 1 antiviral protein for every infected cell, we can set up a proportion:

2.3 × 10^3 antiviral proteins in 2 mL

1 antiviral protein in x mL

The proportion can be written as:

2.3 × 10^3 antiviral proteins / 2 mL = 1 antiviral protein / x mL

We can solve this proportion by cross-multiplication:

(2.3 × 10^3 antiviral proteins) * x mL = 2 mL * 1 antiviral protein

x = (2 mL * 1 antiviral protein) / (2.3 × 10^3 antiviral proteins)

Simplifying, we get:

x = 0.8696 mL

Therefore, to have 1 antiviral protein for every infected cell, approximately 0.8696 mL of medication needs to be administered. This is equivalent to 0.0008696 liters.

Answer:

Step-by-step explanation:

Let's revisit the equation and the solution using the values x = -4, 0, and 5.

The given equation is: 5 + x - 12 = x - 7

Let's go through the steps again to solve it:

5 + x - 12 = x - 7

Combine like terms:

x - 7 = x - 7

Now, subtract x from both sides:

x - x - 7 = x - x - 7

Simplify:

-7 = -7

The equation simplifies to -7 = -7, which is true.

Now, let's use the values x = -4, 0, and 5 to verify the solution.

For x = -4:

5 + (-4) - 12 = (-4) - 7

-11 = -11

The equation is satisfied for x = -4.

For x = 0:

5 + 0 - 12 = 0 - 7

-7 = -7

The equation is satisfied for x = 0.

For x = 5:

5 + 5 - 12 = 5 - 7

-2 = -2

The equation is satisfied for x = 5.

Therefore, the solution x = 0 is correct, and it satisfies the equation for the given values. My earlier statement that x = -4 and x = 5 do not satisfy the equation was incorrect. I apologize for the confusion caused.

The equation of the red graph is g(x) = f(x) - 5

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

The functions f(x) and g(x)

Where, we have

f(x) = -x

i.e.. the parent equation of the function

From the graph, we can see that

The function is shifted down by 5 units

This means that

g(x) = f(x) - 5

This means that the equation of the red graph is g(x) = f(x) - 5

Read more about transformation at

brainly.com/question/27224272

#SPJ1

The calculated length of the arc JK is 7π

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

Central angle = 140 degrees

Radius, IJ = 9 inches

Using the above as a guide, we have the following:

JK = Central angle/360 * 2 * π * Radius

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

JK = 140/360 * 2 * π * 9

Evaluate

JK = 7π

Hence, the length of the arc is 7π

Read more about arc lengths at

brainly.com/question/16552139

#SPJ1

Answer:

Area of triangle = (1/2)(12²) = (1/2)(144) = 72

Area of circle = π(12²) = 144π

P(point falls in triangle) = 72/(144π)

= 1/(2π)

= about .16

= about 15.92%

Answer: [tex](-\infty, 0) \cup (0, \infty)[/tex]

Step-by-step explanation:

The graph of [tex]\frac{\sin x}{x}[/tex] is continuous for all real [tex]x[/tex] except [tex]x=0[/tex], and multiplying this by [tex]1/3[/tex] does not change this.

Answer:

a)

[tex] \frac{1}{( - 7)^{4} } [/tex]

Answer:

[tex](-7)^-^4=\frac{1}{(-7)^4}[/tex]

Step-by-step explanation:

The user aswati already wrote the correct answer, but I wanted to help explain why their answer is correct so that you'll understand.

According to the negative exponent rule, when a base (let's call it m) is raised to a negative exponent (let's call it n), we rewrite it as a fraction where the numerator is 1 and the denominator is the base raised to the same exponent turned positive.

Thus, the negative exponent rule is given as:

[tex]b^-^n=\frac{1}{b^n}[/tex]

Thus, [tex](-7)^-^4[/tex] becomes [tex]\frac{1}{(-7)^4}[/tex]

Answer:

$4929

Step-by-step explanation:

I assume the cost is proportional to the area.

15 ft × 20 ft = 300 ft²

25 ft × 26 ft = 650 ft²

650/300 = x/$2275

300x = 650 × $2275

x = $4929

Answer: $4929

Answer: 88.94

Step-by-step explanation:

First, l found what was 8.125 out of 110 which is 8.94

then added 8.125 and 8.94 which got 118.94

But Angela gave the retailer an $30 coupon so l subtracted 30 from 118.94 which got me 88.94

Answer:

a. Y(t) = At³ + Be^t + Ct² + Dt + E

b. Y(t) = At + B + Ce^t + Dsin(t) + Ecos(t)

c. Y(t) = Aet + Bte^t + Csin(t) + Dcos(t)

d. Y(t) = At³ + Bt² + Ct + D + Ecos(2t) + Fsin(2t)

e. Y(t) = At² + Bt + C + Dsin(t) + Ecos(t) + Fsin(t) + Gcos(t)

f. Y(t) = Aet + Bte^-t + Ccos(t) + Dsin(t) + E + Ft + G

The correct answer choice is: A. The system has exactly one solution. The solution is (13, 5).

The correct answer choice is: A. all three countries had the same population of 5 thousand in the year 2013.

Based on the information provided above, the population (y) in the year (x) of the counties listed are approximated by the following system of equations:

-x + 20y = 87

-x + 10y = 37

y = 5

where:

By solving the system of equations simultaneously, we have the following solution:

-x + 20(5) = 87

x = 100 - 87

x = 13

-x + 10(5) = 37

x = 50 - 37

x = 13

Therefore, the system of equations has only one solution (13, 5).

For the year when the population are all the same for three countries, we have:

x = 2010 + (13 - 10)

x = 2013

Read more on solution and equation here: brainly.com/question/25858757

#SPJ1

Answer:The solution of the linear equations y = 4x − 19.4 and y = 0.2x − 4.2 will be (4, -3.4). Then the correct option is A.

What is the solution to the equation?

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The equations are given below.

y = 4x − 19.4      ...1

y = 0.2x−4.2      ...2

From equations 1 and 2, then we have

4x - 19.4 = 0.2x - 4.2

3.8x = 15.2

x = 4

Then the value of the variable 'y' will be calculated as,

y = 4 (4) - 19.4

y = 16 - 19.4

y = - 3.4

The solution of the linear equations y = 4x − 19.4 and y = 0.2x − 4.2 will be (4, -3.4). Then the correct option is A.

More about the solution of the equation link is given below.

brainly.com/question/545403

#SPJ1

1/3 of a full rotation: (-0.5, √3/2)

1/2 of a full rotation: (-1, 0)

2/3 of a full rotation: (0.5, -√3/2)

These are the coordinates of point P after the corresponding rotations around the unit circle's center.

To find the coordinates of point P after the unit circle rotates a certain amount counter-clockwise around its center, we can use the properties of the unit circle and the trigonometric functions.

1/3 of a full rotation:

A full rotation in the unit circle corresponds to 360 degrees or 2π radians. Therefore, 1/3 of a full rotation is equal to (1/3) * 360 degrees or (1/3) * 2π radians.

When the unit circle rotates 1/3 of a full rotation, point P will end up at an angle of (1/3) * 2π radians or 120 degrees from the positive x-axis.

In the unit circle, the x-coordinate of a point on the circle represents the cosine of the angle, and the y-coordinate represents the sine of the angle.

At an angle of 120 degrees or (1/3) * 2π radians, the cosine is -0.5 and the sine is √3/2.

Therefore, the coordinates of point P after rotating 1/3 of a full rotation are (-0.5, √3/2).

1/2 of a full rotation:

Similarly, 1/2 of a full rotation is equal to (1/2) * 360 degrees or (1/2) * 2π radians.

When the unit circle rotates 1/2 of a full rotation, point P will end up at an angle of (1/2) * 2π radians or 180 degrees from the positive x-axis.

At an angle of 180 degrees or (1/2) * 2π radians, the cosine is -1 and the sine is 0.

Therefore, the coordinates of point P after rotating 1/2 of a full rotation are (-1, 0).

2/3 of a full rotation:

Again, 2/3 of a full rotation is equal to (2/3) * 360 degrees or (2/3) * 2π radians.

When the unit circle rotates 2/3 of a full rotation, point P will end up at an angle of (2/3) * 2π radians or 240 degrees from the positive x-axis.

At an angle of 240 degrees or (2/3) * 2π radians, the cosine is 0.5 and the sine is -√3/2.

Therefore, the coordinates of point P after rotating 2/3 of a full rotation are (0.5, -√3/2).

for such more question on coordinates

https://brainly.com/question/23907194

#SPJ8

Answer:

Least to greatest:

√143

4π

√79 + √63

Step-by-step explanation:

√79 + √63 = 16.82

4π = 12.57

√143 = 11.96

The cost of a single unit is given as follows:

$1.05.

El costo de un plátano es el seguiente:

$1.05.

The cost of a single unit is obtained applying the proportions in the context of the problem.

The cost of 22 units is of $23.10, hence the cost of a single unit is obtained dividing the total cost by the number of units, as follows:

23.1/22 = $1.05.

More can be learned about proportions at https://brainly.com/question/24372153

#SPJ1

The correct answer is b. Extrapolation since 20 is within the range.

In this scenario, finding the best predicted value for x = 20 would be an example of extrapolation. Extrapolation involves estimating values outside the given range of data based on the trend or pattern observed within the existing data.

Given the data set: 4, 10, 2, 18, 15, we can see that the values provided are not in any particular order. To perform extrapolation, it is generally helpful to first examine the trend or pattern within the data. However, without additional information or context, it is difficult to determine the underlying trend in this case.

Since the given data set does not explicitly indicate any pattern or trend, any estimation made for x = 20 would be considered extrapolation. Extrapolation involves projecting or extending the existing trend or pattern beyond the known data points. In this case, the value of 20 falls outside the range of the given data set, so estimating its corresponding value would require extending the trend beyond the known data points.

Consequently, the appropriate response is b. Extrapolation since 20 is within the range.

for such more question on range

https://brainly.com/question/16444481

#SPJ8