Find the surface area of the prism.

Step 1:

Write the two equations

x - y = 2 Equation 1

x + 4y = -3 Equation 2

Step 2:

From equation 1 , make x subject of the formula and substitute in equation 2.

Step 3:

Substitute x = 2 + y in equation 2

Step 4

Substitute y = -1 in x = 2 + y to find x

x = 2 - 1

x = 1

Final answer

x = 1 , y = -1

Equation: x - y = 2x + 4y = -3 x - y = -3 Equations 1st and 2 (x - y = -3) 2 equations 1 2x - 2y = -6 equation 1 -(2x + 4y = -3) equation 2 are obtained.

In the second equation, 2x - 2y = -6, 2x -4y = 3, 6y = 3, and 6y = -3/-6 = 1/2.

2x + 4y = -3 , 2x + 4×1/2 = -3

2x +2 = -3 , 2x = -3 -2 , 2x = -5 ,x = -5/2

The last solution is y = 1/2 and x = -5/2.

What you want altered should go here. After that, click the button below. It's that simple!

Taking the statement provided into consideration, if t is a linear transformation of R² into itself and the effect of t is known, then the effect of t on any vector can be computed. Therefore, the statement is true.

Consider the case where t is a parallelogram to line segment linear transformation of R² into R². If "t is a linear transformation of R² into itself and I know what t transformed" then I can calculate the impact of t on any vector, then the statement is true.

What is a linear transformation? The following characteristics must be met for a linear transformation, which is a transformation between two vector spaces:

The sum of v1 and v2 for each vector v1 and v2 in the vector space is equivalent to the transformation of the sum of v1 and v2.

The transformation of kv is equal to k times the transformation of v, in the vector space for every scalar k and vector v.

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The 90% confidence interval for the difference in the population means is -2.51 to 0.31

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

xˉ₁ = −17.1

s₁² = 8.4

n₁ = 22

​xˉ₂ = −16.0

s₂² = 8.7

n₂ = 24

Calculate the pooled variance using

P = (df₁ * s₁² + df₂ * s₂²)/df

Where

df₁ = 22 - 1 = 21

df₂ = 24 - 1 = 23

df = 22 + 24 - 2 = 44

So, we have

P = (21 * 8.4 + 23 * 8.7)/44

P = 8.56

Also, we have the standard error to be

SE = √(P/n₁ + P/n₂)

So, we have

SE = √(8.56/22 + 8.56/24)

SE = 0.86

The z score at 90% CI is 1.645, and the CI is calculated as

CI =  (x₁ - x₂) ± z * SE

So, we have

CI = (-17.1 + 16.0) ± 1.645 * 0.86

This gives

CI = -1.1 ± 1.41

Expand and evaluate

CI = (-2.51, 0.31)

Hence, the confidence interval is -2.51 to 0.31

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Answer: yards best for measuring distances

Step-by-step explanation:

The required dimensions of a rectangular rancher with perimeter for fencing, 3000 feet are equal the 500 feet and 375 feet at maximum area of 3,75,000 ft².

We have a rancher which to construct adjacent, equally sized rectangular pens with the fencing of 3000 feet. Suppose that the rancher need to be fenced in the way shown in the attached figure. Then, the perimeter is 4x + 3y = 3000

=> x \( =\frac{3000 - 3y}{4} \).

The area of rectangle is represented by A=L × W --(1) , where L and W are dimensions of rectangles. The total area will be A = 2× x × y --(2)

=> A = 2× (\(\frac{3000 - 3y}{4}\))× y

= ( \( 1500 - \frac{3y}{2} \))y

= \( 1500y - \frac{3y²}{2} \)

Now, differentiate above area function, with respect to y, and equate to 0, for determining the critical points on the graph, \(\frac{dA}{dy} \) = A'(y) =\( 1500 - \frac{6y}{2} \) = 0

=> y = \(\frac{1500}{3} = 500 \)

Also, x \( =\frac{3000 - 3× 500}{4} \).

\( =\frac{1500}{4} = 375 \).

Maximum area = 375 × 500 × 2 = 375000 ft². Hence, the dimensions that will give the maximum area are 500 feet and 375 feet.

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Complete question : attached figure complete the question.

9514 1404 393

Answer:

Step-by-step explanation:

A unit rate is a ratio. When dollars are involved, we usually want dollars in the numerator. When time is involved, we usually want time in the denominator.

__

rice: $9/(1.5 kg) = (9/1.5) $/kg = $6/kg

__

growth: (350 people)/(7 years) = (350/7) people/year = 50 people/year

Answer:

You subtracted 25 from both sides.

Step-by-step explanation:

To move one part of the equation to the other side, you need to do the opposite. 25 is already negative(or being subtracted) so you need to add it to both sides to cancel it out on the left.

10x=-75+25

10x=-50

then divide both sides by 10

x=-5

Answer:

32 gallons

Step-by-step explanation:

A standard showerhead in Marty's house dispenses 7 gallons of water per minute. If he showers for 8 minutes, he uses:

1 minute = 7 gallons

8 minutes = x

x = 7 × 8 minutes = 56 gallons of water

We are told that:

Marty changed this showerhead to an energy-saving one. The equation shows the amount of water dispensed, y, as a function of the number of minutes, x, for the new showerhead. y = 3x

The equation for the energy saving shower:

y = 3x

Where x is the number of minutes spent in the shower

For 8 minutes

y = 3 × 8

y = 24 gallons

The gallons of water Marty saved each day with the change in showerheads if he uses the shower for 8 minutes each day is calculated as:

56 gallons - 24 gallons

= 32 gallons

Answer:

She should walk at a rate of 16 km/hr

Step-by-step explanation:

At a rate of 12 km/hr, she would have traveled 4 km in 20 minutes. This can be calculated by finding the ratio of 20 minutes to 1 hour which is 1/3. We then multiply this ratio by the rate to find the distance Shalu needs to walk to school.

We then need to find the necessary km/hr in order for Shalu to travel 4 km in 15 minutes. 15 minutes is a quarter of 1 hr. Therefore a rate of 4 km/15 minutes is equal to a rate of 16 km/hr. This means that the average speed Shalu would have to walk is 16 km/hr.

Answer:

\(\displaystyle \int\limits^{\frac{2 \pi}{3}}_{\frac{- \pi}{3}} {\frac{sinx}{1 + cosx}} \, dx = ln3\)

General Formulas and Concepts:

Pre-Calculus

Calculus

Derivatives

Derivative Notation

Trig Derivatives

Integrals

Integration Constant C

Integration Rule [Fundamental Theorem of Calculus 1]:                                        \(\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)\)

Integration Property [Multiplied Constant]:                                                             \(\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx\)

Trig Integration

Logarithmic Integration

U-Substitution

Step-by-step explanation:

Step 1: Define

Identify

\(\displaystyle \int\limits^{\frac{2 \pi}{3}}_{\frac{- \pi}{3}} {\frac{sinx}{1 + cosx}} \, dx\)

Step 2: Integrate Pt. 1

Identify variables for u-substitution.

Step 3: Integrate Pt. 2

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

Book: College Calculus 10e

The result for  8/5 divided by 3 equals 8/15. We can solve a fraction with a greater numerator by multiplying both numerators and denominators.

Given fraction = 8/3

Divisor = 3

When there is no denominator for the divisor, we can assume it is One.

3 = 3/1

We can multiply the two fractions to get into one single fraction

(8/5) ÷ (3/1) = (8/5) x (1/3)

Multiply both the numerators and denominators.

(8/5) x (1/3) = (8 x 1) / (5 x 3) = 8/15

Therefore, we can conclude that 8/5 divided by 3 equals 8/15.

To solve a question with a fraction with a greater numerator,

Write the denominator as 1 and flip the fraction.

(15/8) ÷ (3/1) = (15/8) x (1/3)

Multiply the numerators and denominators together:

(15/8) x (1/3) = (15 x 1) / (8 x 3) = 5/8

Therefore, we can conclude that 15/8 divided by 3 equals 5/8.

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Answer:

n=9

Step-by-step explanation:

Subtract 4n and 2n ( 2n =18 )

Divide 2 on both sides ( 18/2 )

Once you divide, you get the answer of 9

Hope this helped, Have an amazing day!!

Answer: 31.4 or 10pi

Step-by-step explanation:

Formula: C = pi * diameter

C = 10pi

C = 10 * 3.14

C = 31.4

Answer:

31.4

Step-by-step explanation:

C=Pid

The amount accumulated after investing a principal P for t years at an interest rate compounded annually is  $46,057.58.

Compound interest is the interest you earn on interest. Compound interest is the interest calculated on the principal and the interest accumulated over the previous period.

Therefore, let's find the amount accumulated after investing a principal P for t years at an interest rate compounded annually.

\(A = p(1 + \frac{r}{n} )^{nt}\)

where

p = 15,500

r = 9.5%

t = 12

n = 1

\(A = 15500(1 + \frac{0.095}{1} )^{1(12)}\)

A = 15,500.00(1 + 0.095)¹²

A = $46,057.58

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$46,057.58, answer for acellus

Given the points:

We need to reflect the points over the line y = x

The rule of reflection is as follows:

So, the points after reflection will be:

c ccccccccccccccccccccccccccccc

Answer:

56.2

Explanation:

There is a way to remember the ways to solve for right triangles, SOH CAH TOA which stands for each of the ways to solve for angles or sides:

Sine: Opposite over Hypotenuse

Cosine: Adjacent over Hypotenuse

Tangent: Opposite over Adjacent

In this case, with the information we have, we would use tangent since we have both the opposite side, b, and the adjacent side, a.

It would be the inverse of tangent (tan⁻¹) since you are solving for the angle and not a side.

You would use a calculator to solve this, by dividing b by a.

tan⁻¹(b/a)

tan⁻¹(46.7/31.3) = 56.1686012868

Round to the nearest tenth = 56.2

*Make sure your calculator is in degrees mode or it will give you an incorrect result.

The equation is 18 * (12 + g) = 297 and the solution is g = 4.5

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

In 2021 = 297 milion

In 2021 = 18 times 12 million + g

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

In 2021 = 18 * (12  + g)

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

18 * (12 + g) = 297

So, we have

12 + g = 16.5

Subtract 12 from both sides

g = 4.5

Hence, the equation is 18 * (12 + g) = 297 and the solution is g = 4.5

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Answer:

-x² + 3x + 7

Step-by-step explanation:

• f(x) = 3x + 1

• g(x) = x² - 6

Then,

According to th' question :-

(f - g)(x) = f(x) - g(x)

= 3x + 1 - (x² - 6)

= 3x + 1 - x² + 6

= -x² + 3x + 7

To find the equation of the sphere tangent to the plane 2x + 3y - 6z = 5 with center C(-2, 3, 7), we need to find the radius of the sphere. The equation of the sphere is (x + 2)^2 + (y - 3)^2 + (z - 7)^2 = 36.

The distance from the center of the sphere to the plane is equal to the radius. We can use the formula for the distance between a point (x, y, z) and a plane Ax + By + Cz + D = 0:

Distance = |Ax + By + Cz + D| / sqrt(A^2 + B^2 + C^2)

In this case, the plane equation is 2x + 3y - 6z - 5 = 0. Plugging in the coordinates of the center C(-2, 3, 7) into the formula, we have:

Distance = |2(-2) + 3(3) - 6(7) - 5| / sqrt(2^2 + 3^2 + (-6)^2)

= |-4 + 9 - 42 - 5| / sqrt(4 + 9 + 36)

= |-42| / sqrt(49)

= 42 / 7

= 6

So, the radius of the sphere is 6.

The equation of a sphere with center C(-2, 3, 7) and radius 6 is:

(x + 2)^2 + (y - 3)^2 + (z - 7)^2 = 6^2

Simplifying further, we have:

(x + 2)^2 + (y - 3)^2 + (z - 7)^2 = 36

Therefore, the equation of the sphere is (x + 2)^2 + (y - 3)^2 + (z - 7)^2 = 36.

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Answer:

Yes

Step-by-step explanation:

Answer:

3,256bulbs

Step-by-step explanation:

The expression that represents the width of the rectangle is: 2x - 3.

Area of rectangle = length × width

Given:

Area = (10x² + 3x - 27) sq. yards

Length = (5x + 9) yards

Therefore:

Width = Area of rectangle/length

Width = (10x² + 3x - 27)/(5x + 9)

Factorize the numerator

Width = (5x + 9)(2x - 3)/(5x + 9)

Width = 2x - 3

Therefore, the expression that represents the width of the rectangle is: 2x - 3.

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Raw data can be calculated by using mathematical operations such as addition, subtraction, multiplication, and division.

This can be done manually or by using a calculator or a computer program .Additionally, statistical methods such as mean, median, mode, and standard deviation can be used to calculate raw data.Raw data can also be manipulated in various ways. For example, data can be sorted, filtered, and organized into categories or hierarchies. Data can also be visualized in graphs, charts, and diagrams to make patterns and trends easier to identify. Statistical methods such as correlation and regression can also be used to analyze and interpret raw data. Additionally, data can be combined with other data sets to create new insights and relationships. Finally, machine learning and predictive analytics can be used to make predictions about future outcomes based on existing data.

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Answer:

\( \frac{2}{3} x + 7 = 2x + 15\)

\(2x + 21 = 6x + 45\)

\(4x = - 24\)

\(x = - 6\)

\( \frac{2}{3} ( - 6) + 7 = - 4 + 7 = 3\)

\(2( - 6) + 15 = - 12 + 15 = 3\)

Answer:

x=-4 y=-1

Step-by-step explanation:

Let's solve your system by substitution.

−3x−8y=20;y=5x+19

Rewrite equations:

y=5x+19;−3x−8y=20

Step: Solve y=5x+19for y:

y=5x+19

Step: Substitute5x+19foryin−3x−8y=20:

−3x−8y=20

−3x−8(5x+19)=20

−43x−152=20(Simplify both sides of the equation)

−43x−152+152=20+152(Add 152 to both sides)

−43x=172

−43x

−43

=

172

−43

(Divide both sides by -43)

x=−4

Step: Substitute−4forxiny=5x+19:

y=5x+19

y=(5)(−4)+19

y=−1(Simplify both sides of the equation)

Answer:

x=−4 and y=−1

The probability of rolling at least one 6 in 10 rolls of a die is approximately 0.8385, or 83.85%.

The probability of rolling at least one 6 in 10 rolls of a die can be calculated using the complement rule, which states that the probability of an event happening is equal to 1 minus the probability of the event not happening.

First, we can calculate the probability of not rolling a 6 in one roll of a die, which is 5/6. Since each roll is independent, the probability of not rolling a 6 in 10 rolls is (5/6)^10, or approximately 0.1615.

Therefore, the probability of rolling at least one 6 in 10 rolls of a die is:

1 - (5/6)^10

= 1 - 0.1615

= 0.8385 (rounded to 3 decimal places)

This means that in most cases, you can expect to roll at least one 6 in a series of 10 rolls of a die.

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The average Jeremy can create 24 different outfits for school by combining 1 pair of pants, 1 shirt, 1 tie, and 1 jacket.

Jeremy can mix and match his items to create different outfits for school. Since he owns 4 pairs of pants, 3 shirts, 3 ties, and 2 jackets, he can create 24 different outfit combinations. For each outfit, he must wear 1 pair of pants, 1 shirt, 1 tie, and 1 jacket. He can mix and match any of the items he owns to create a variety of looks. For example, he could wear a blue shirt, grey pants, and a striped tie with a black jacket. Or, he could wear a white shirt, black pants, a polka-dotted tie, and a brown jacket. By combining his items in different ways, he can create 24 different outfits for school.

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The quadratic equation does not have solutions where both x and y are integers.

Here we have the following quadratic equation:

2x^2 + 5y^2 = 14

We want to check that we can't solve this equation with x and y integers, to see that, we can start by isolating one of the variables:

2x^2 + 5y^2 = 14

5y^2 = 14 - 2x^2

y^2 = (14 - 2x^2)/5

y = ±√((14 - 2x^2)/5)

Now, trivially:

(14 - 2x^2)/5

Is not an integer for any integer value of x, and this happens because 5 is not a factor of 14, thus, for any integer value of x the value of y that we get is non integer, then there aren't two integers that solve the quadratic equation.

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