What is the volume of the prism? (Easy ig)

Answer:

-2

Step-by-step explanation:

As per the provided information in the given question, we have a linear equation. We have to find the value of x.

Basically, transposition method is used to solve a linear equation in one variable containing constants and variables. We just transpose the values from RHS to LHS by changing its arithmetic operators. In this way, we solve for the unknown value. During transposing the values, ( + ) changes to ( – ) and vice-versa ; ( × ) changes to ( ÷ ) and vice-versa.

Now, coming back to the question. We have,

\(\longmapsto \rm { 3x = \dfrac{x}{2}- 5} \\ \)

Taking the LCM in RHS and performing subtraction.

\(\longmapsto \rm { 3x = \dfrac{x - 10}{2}} \\ \)

Transposing 2 from RHS to LHS. Its arithmetic operator will get changed.

\(\longmapsto \rm { 3x \times 2 = x - 10} \\ \)

Performing multiplication in LHS.

\(\longmapsto \rm { 6x = x - 10} \\ \)

Transposing x from RHS to LHS. Its arithmetic operator will get changed.

\(\longmapsto \rm { 6x - x = - 10} \\ \)

Performing subtraction of the terms in LHS.

\(\longmapsto \rm { 5x = - 10} \\ \)

Transposing 5 from LHS to RHS. Its arithmetic operator will get changed.

\(\longmapsto \rm { x = \cancel{\dfrac{- 10}{5}}} \\ \)

Dividing –10 by 5.

\(\longmapsto \underline{\boxed{\bf { x = - 2}}} \; \bigstar \\ \)

Therefore, the value of x is –2.

Answer:

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Answer:

Step-by-step explanation:

idrk

Answer: m^3

Step-by-step explanation:

Taking the square root of something is the same as raising it to the half power the square root of 4 is equal to 4^(1/2). This hold true with any root, not just square root. M^(3b) to the b root is equal to m^(3b x (1/b)). Ignore the base (m) for a second and the exponents make 3b x (1/b) which equals (3b/b). The b on the top and bottom cancel and you’re left with a 3. The answer is m^3

Step-by-step explanation:

a parallel line has the same slope. that is the actual meaning of "parallel".

so we need to find the slope of line t to get our answer.

remember, the slope is the ratio " y coordinate change / x coordinate change" when going from one point on the line to another.

so, here we have 2 points (9, 10) and (3, 3).

going from the first to the second we see

x changes by -6 (from 9 to 3).

y changes by -7 (from 10 to 3).

the slope is then -7/-6 = 7/6.

and therefore, the slope of u is also 7/6.

The absolute value function for this problem is given as follows:

g(x) = |x - 1| - 2.

An absolute value function of vertex (h,k) is defined as follows:

y = a|x - h| + k.

In which a is the leading coefficient.

The coordinates of the vertex for this problem are given as follows:

(1, -2).

As the slope of the line is of 1, the leading coefficient is given as follows:

a = 1.

Hence the absolute value function for this problem is given as follows:

g(x) = |x - 1| - 2.

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Answer:

Sierra would have 16 points

Step-by-step explanation:

5×4=20

8×\(\frac{1}{2}\)=4

20-4=16

We want to show that equation (1) takes the Sturm-Liouville form given by (2) above.

So we will begin by multiplying the given equation by x.

This gives, x²y" + xy' + (a²x - n²)x = 0

Now let’s consider the case when the second term dominates over the first and third terms. Thus, we have

xy' ≫ x²y".

This means we can write xy' ≈ (xy)', which we can substitute into the above equation as follows;

(xy)' + (a²x - n²)x = 0

Now we need to take the derivative with respect to x on both sides, giving us;

x'y + y + a²x - n² = 0

xy" + y' + 2ax' = 0

=> x'y + y' + 2ax' - (n² - a²x)y/x = 0.

(4)We can then rewrite (4) in the Sturm-Liouville form as follows;

(²x - ²)y-0,

where ²x = -(x/x')(2ax') and

² = n² - a²x.

We have thus shown that the parametric Bessel equation (1) takes the Sturm-Liouville form given by (2).1.2.

By multiplying equation (2) by 2xy and integrating the subsequent equation from 0 to c, we are required to show that for n = 0;

∫₀ᶜ (x¹/(a²x¹)²)dx = (1/₂(ac)¹² + 1/₃(ac)¹³)

We can start by multiplying equation (2) by 2xy, which gives;

2xy(²x - ²)y = 0

Now, let’s expand the left side of the above equation;

2xy(²x - ²)y = 2xy(-(x/x')(2ax'))y - 2xy(n² - a²x)y/xy

= -2ax(x/y')y² - 2(n²x - a²x²)y²dx

We can simplify this further by substituting ² for n² - a²x, which gives;

-2ax(x/y')y² - 2(²x)y²dx = -2ax(x/y')y² + 2(²x)y²dx (5)

Now, we integrate the above equation from 0 to c, such that;

∫₀ᶜ [-2ax(x/y')y² + 2(²x)y²]dx = 0

For the first term on the left-hand side of the above equation, we can make a substitution using

y(x) = xnJn(x).

This gives us;

x/y' = x/{nJn(x) + xnJn-1(x)} = 1/n + xJn-1(x)/Jn(x)

Thus, we can rewrite the first term as follows;

2a∫₀ᶜ xJn-1(x)y³/n dx = 2a/n ∫₀ᶜ xJn-1(x)xnJn(x)³ dx

= 2a/n ∫₀ᶜ x¹Jn-1(x)nJn(x)³ dx

Now, we can apply integration by parts such that;

U = x¹Jn-1(x), dv

= nJn(x)³ dx;

dU/dx = Jn-1(x) + xJn-2(x) and

v = Jn+1(x)³/n³

Therefore, ∫₀ᶜ x¹Jn-1(x)nJn(x)³ dx = (Jn+1(x)³xJn-1(x))/n³ ∫₀ᶜ Jn-1(x)dx - 3/n³ ∫₀ᶜ Jn+1(x)²Jn-1(x)dx

Now, we can substitute n = 0 into the above equation, giving us;

2a/n ∫₀ᶜ x¹Jn-1(x)nJn(x)³ dx = 0 + 3/16a

Now, we need to evaluate the second term of the equation given by (5) above. This can be done as follows;

∫₀ᶜ 2(²x)y²dx = 2∫₀ᶜ (a²x²)Jn²(x)dx

= 2(a²/n) ∫₀ᶜ xJn(x)Jn-1(x)dx

We can apply integration by parts again as follows;

U = xJn(x),

dv = Jn-1(x) dx;

dU/dx = Jn(x) + xJn-1(x) and

v = -Jn(x)

Thus, we have;

∫₀ᶜ 2(²x)y²dx = -2(a²/n) ∫₀ᶜ Jn(x)²dx + 2(a²/n) ∫₀ᶜ xJn-1(x)Jn(x)dx

Now, we can substitute n = 0 into the above equation, giving us;

∫₀ᶜ 2(²x)y²dx = -2a²/16 + 2a²/24

= a²/12

Substituting the above into the initial equation gives us;

a²/6n ∫₀ᶜ x¹Jn-1(x)nJn(x)³ dx = a²/12, for n = 0.

=> ∫₀ᶜ (x¹/(a²x¹)²)dx = (1/₂(ac)¹² + 1/₃(ac)¹³)

Therefore, we have shown that ∫₀ᶜ (x¹/(a²x¹)²)dx = (1/₂(ac)¹² + 1/₃(ac)¹³) for n = 0.

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According to the given data, Ryan walked 12 small dogs.

Let x be the number of small dogs that Ryan walked.

The number of large dogs that Ryan walked would then be y = 4 - x.

Using the information given, we can set up the following equation:

x * 2 + (4 - x) * 5 = 40

Expanding and solving for x, we get:

2x + 4 - 5x = 40

-3x = 36

x = 12

So, Ryan walked 12 small dogs.

In this problem, we used a system of equations to solve for the unknown variable, x, which represents the number of small dogs that Ryan walked. By substituting this value back into the equation for the number of large dogs, we were able to confirm that Ryan walked 4 - x = 4 - 12 = 4 large dogs.

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Answer:

the answer is w/2+3

Step-by-step explanation:

combine 1/2 and w

Answer:  31.4 meters

Work Shown:

\(C = 2\pi r\\\\C \approx 2*3.14*5\\\\C \approx 31.4\\\\\)

Answer:

$17.50

Step-by-step explanation:

A principal amount of P 200,000 was deposited for a period of 4 years and 6 months, and it earned an interest of P 85,649.25. To find the rate of interest compounded monthly, we can use the formula for compound interest and solve for the interest rate.

The formula for compound interest is given by A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years.

In this case, we are given the principal amount P as P 200,000, the final amount A as P 285,649.25 (P 200,000 + P 85,649.25), the time t as 4 years and 6 months (or 4.5 years), and we need to find the interest rate r compounded monthly (n = 12).

Using the given values in the compound interest formula and solving for r, we can find the rate of interest. By rearranging the formula and substituting the known values, we can isolate the interest rate r and calculate its value.

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Answer:

y = 2x + 8

Step-by-step explanation:

We want an equation of the form y = mx + b (slope-intercept).

Look what happens to x as we go from (0, 8) to (1, 10):  x increases by 1.  This is the 'run' as we calculate the slope.

At the same time, y increases by 2 from 8 to 10.

The slope is defined as m = rise / run, and here is m = 2/1, or m = 2.

Write out y = mx + b and substitute 2 for m:  y = 2x + b.

To find the y-intercept, substitute 0 (from (0, 8) ) for x and 8 for y:

8 = 2(0) = b, so b = 8, and the desired equation is

y = 2x + 8

The constant of proportionality is 5 and the equation is c = 5g

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

The table of values

Using the point (5, 25), we have the constant of proportionality to be

r = 25/5

Evaluate

r = 5

So, the equation is

c = rg

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

c = 5g

So, the equation is c = 5g

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Answer:

X= 59/4

Step-by-step explanation:

Let's solve your equation step-by-step.

2=−4x+61

Step 1: Flip the equation.

−4x+61=2

Step 2: Subtract 61 from both sides.

−4x+61−61=2−61

−4x=−59

Step 3: Divide both sides by -4.

−4x/

−4

=

−59

/-4

x=

59

/4

To solve the expression -25 x (84/21) + (-3) x (-6), follow these steps:

Step 1: Perform the division inside the parentheses.
(84/21) = 4

Step 2: Replace the terms and rewrite the expression.
-25 x (4) + (-3) x (-6)

Step 3: Perform the multiplications.
-25 x 4 = -100
-3 x -6 = 18

Step 4: Rewrite the expression and perform the addition.
-100 + 18

Step 5: Calculate the final result.
-100 + 18 = -82

Your answer is -82.

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Answer:

d. 4x − 5y = 27x + 6y = 10

I hope my answer helps you.

the surface area should be 544 (whatever the unit is)

Step-by-step explanation:

You start by taking the rectangles on the side and finding their area.

1. (10×14)×2 ←Because there are two rectanglular sides.

2. find the area of the triangles on the side. 1/2bh = area of triangle.

(.5×8×6)×4 ← in order to find the area for all of the triangles.

3.  lastly take the base of the prism and find the area then add the previously found values together.

(12×14)+(.5×8×6)×4+ (10×14)×2 = 544

Answer:

16.3

Step-by-step explanation:

The height of the building to the nearest tenth is 16. 3 ft

The situation forms a right triangle.

The length of the ladder is the hypotenuse of the triangle formed.

The distance from the foot of the ladder to the bottom of the building is the adjacent sides.

Therefore,

c² = a² + b²

where

c = hypotenuse

a and b are the other two legs.

b² = 29² - 24²

b² = 841 - 576

b = √265

b = 16.2788205961

b = 16.3 ft

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The amount of money that terry receives is $600 .

Given :  larry is assigned to clean two-thirds of the classrooms in the school for $1,200

Also ,  terry joins him to complete the job

Since , each working at the same pace. They both will receive equal amount of money

Total amount of money to clean two-thirds of the classrooms in the school is $1,200

Amount of the $1,200 should terry receive

= Amount of the $1,200 should larry receive

= Total amount / 2 [Since , each working at the same pace. ]

= 1200 / 2 = $600

Hence , the amount of money that terry receives is $600 .

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The answer is x = -5/6

And in decimal form it would be, -0.8333333

Answer:

y=3/4x

Step-by-step explanation:

3 is the rising number 4 is the run

meaning it goes up 3 and 4 to the side.

Answer:

p=60

or,2(l+b)=60

or,2(25+b)=60

or,2b=60-50

or,b=5

Answer:

Convert to decimals:

1.5 and 0.75

Then, set up a proportion

1.5/0.75=x/1

proportion x/y=x/y

since the 3/4 and 1 are the same topic ( the room) we put them together.

Solve: 1.5/0.75=x

x=2

So 2 gallons

Hope this helps plz hit the crown :D

The odds of selecting a red 9 is 1/26.

Probability of an event E is represented by P(E)  can be defined as (the number of favorable outcomes) / (Total number of outcomes).

Given the total number of cards in a standard deck = 52

there can be  only two red9 as one 9 from heart and one red from diamond.

So the number of outcome for red 9 =2

the probability of odds of selecting red 9 is \(\frac{2}{52}\) which can be further simplified into \(\frac{1}{26}\).

Therefore , The odds of selecting a red 9 is 1/26.

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Answer:

-7 1/7

Step-by-step explanation:

Hope that helps!

Answer:

a = 6

Step-by-step explanation:

(3.14 * 18) * 17.5 = 3.14 * (3a * 17.5)

3.14(3x * 17.5) = (3.14 * 18) * 17.5

3.14(3a * 17.5) = 3.14 * 18 * 17.5

3.14(3a * 17.5) = 989.1

3.14 * 3a * 17.5 * 100 = 989.1 * 100

16485a = 98910

a = 98910/16485

a = 6

Solving the equation,  (3.14 × 18) × 17.5 = 3.14 × (3a × 17.5), the value of a is determined as: 6.2.

Given equation: (3.14 × 18) × 17.5 = 3.14 × (3a × 17.5)

Step 1: Simplify the left side:

3.14 × 18 × 17.5 = 55.89 × 17.5

= 976.575

Step 2: Simplify the right side:

3.14 × (3a × 17.5) = 52.5 × 3a

= 157.5a

Step 3: Equate the left and right sides:

976.575 = 157.5a

Step 4: Solve for the value of a by dividing both sides by 157.5:

976.575 / 157.5 = a

6.2 = a

a = 6.2

Therefore, the value of a is 6.2.

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