I need help ASAP
3k+30=95+k+2k-5

Answer: 210

Explanation:

Recall that the perimeter is the distance around the figure. It's the amount of fencing needed to enclose such a shape.

Add up all three sides and set the sum equal to the perimeter 70. Then solve for x.

side1+side2+side3 = perimeter

(3x)+(3x-1)+(4x+1) = 70

10x = 70

x = 70/10

x = 7

We can then calculate each side

Notice how 21+20+29 = 70 to confirm we have the correct side lengths.

Once we know the horizontal and vertical leg (aka base and height), we can find the area.

Area = 0.5*base*height

Area = 0.5*21*20

Area = 210 square cm

Step-by-step explanation:

first you have to find x . Then you can add them and equal them with triangle area.

Answer:

x=-2500

Step-by-step explanation:

\(\sqrt{-4x} =100\\\\(\sqrt{-4x})^2=100^2\\\\-4x=10,000\\\\x=-\frac{10000}{4}\\\\x=-2500\)

The given can be solved by simplifying the equation to make x the subject

of the equation.

Reasons:

The equation is; √(-4·x) = 100

The above equation can be expressed as follows;

By squaring both sides, we get;

\(\displaystyle \mathbf{ \left(-4 \cdot x \right)^{\frac{1}{2} \times 2 }} = 100^2\)

Which gives;

\(\displaystyle \left(-4 \cdot x \right)^{\frac{1}{2} \times 2 } = \left(-4 \cdot x \right)^{1 }= -4 \cdot x = 100^2\)

\(\displaystyle -4 \cdot x = 100^2 = 100 \times 100 = \mathbf{10,000}\)

\(\displaystyle -4 \cdot x = 10,000\)

Dividing both sides by -4 gives;

\(\displaystyle x = \mathbf{ \frac{10,000}{-4} } = -2,500\)

Therefore'

x = -2,500

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The solution to the given differential equation with the initial conditions is:

\(r(t) = (1/100 * e^(10t) - t^2 + (11 + 1/10 * e^10) * t - 1/100, 1/12 * t^4 - t^2/2 + (1 - 1/3) * t - 1/12, 1/2 * t^2 - t + 9/2)\)

To solve the given differential equation, we can integrate each component separately. Let's solve it step by step.

Given differential equation:

\(r"(t) = (e^(10t) - 10, t^2 - 1, 1)\)

Step 1: Integration of r"(t) to obtain r'(t):

\(∫ r"(t) dt = ∫ (e^(10t) - 10, t^2 - 1, 1) dt\)

Integrating each component separately:

\(r'(t) = (∫ (e^(10t) - 10) dt, ∫ (t^2 - 1) dt, ∫ dt) = (1/10 * e^(10t) - 10t + C1, 1/3 * t^3 - t + C2, t + C3)\)

Here, C1, C2, and C3 are constants of integration.

Step 2: Integration of r'(t) to obtain r(t):

\(∫ r'(t) dt = ∫ ((1/10 * e^(10t) - 10t + C1, 1/3 * t^3 - t + C2, t + C3) dt\)

Integrating each component separately:

\(r(t) = (∫ (1/10 * e^(10t) - 10t + C1) dt, ∫ (1/3 * t^3 - t + C2) dt, ∫ (t + C3) dt) = (1/100 * e^(10t) - t^2 + C1 * t + C4, 1/12 * t^4 - t^2/2 + C2 * t + C5, 1/2 * t^2 + C3 * t + C6)\)

Here, C4, C5, and C6 are constants of integration.

Step 3: Applying initial conditions to find the values of integration constants.

Given initial conditions:

r(1) = (0, 0, 5)

r'(1) = (12, 0, 0)

Let's substitute these values and solve for the integration constants:

For r(1):

\((1/100 * e^(10 * 1) - 1^2 + C1 * 1 + C4, 1/12 * 1^4 - 1^2/2 + C2 * 1 + C5, 1/2 * 1^2 + C3 * 1 + C6) = (0, 0, 5)\)

Simplifying each component:

C1 + C4 = -1/100

C2 + C5 = -1/12

C3 + C6 = 9/2

For r'(1):

\((1/10 * e^(10 * 1) - 10 * 1 + C1, 1/3 * 1^3 - 1 + C2, 1 + C3) = (12, 0, 0)\)

Simplifying each component:

\(C1 = 11 + 1/10 * e^10\)

C2 = 1 - 1/3

C3 = -1

Therefore, the solution to the given differential equation with the initial conditions is:

\(r(t) = (1/100 * e^(10t) - t^2 + (11 + 1/10 * e^10) * t - 1/100, 1/12 * t^4 - t^2/2 + (1 - 1/3) * t - 1/12, 1/2 * t^2 - t + 9/2)\)

Note: The constants of integration may have different values based on the calculations. Please double-check the calculations for accurate results.

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1.5 is the variance for the given population of scores (5,2,5,4). Thus, the correct answer is option d.

The given data is as follows:

Scores are given =  5, 2, 5, 4,

The mean of the scores is calculated by using the formula,

Mean = (sum of the scores)/Number of scores

Mean = (5+2+5+4)/4

Mean = 16/4 = 4.

Now, we can calculate the Difference between each score and mean:

5-4=1

2-4=-2

5-4=1

4-4=0

The list of the scores generated by the squared differences =  1, 4, 1, 0

The total sum of squared difference = 1+4+1+0 = 6

Variance is calculated by using the formula,

Variance = sum of squared difference/Mean

Variance = 6/4 = 1.5

Therefore, we can conclude that 1.5 is the variance for the given population of scores.

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Answer:

The area is 24.

Step-by-step explanation:

Yes, the researcher use the rows or the columns of the field as blocks.

When conducting research, it is important to think about which structure to use as the basis for your work.

In particular, when dealing with a matrix, the question arises of whether the researcher should use the rows or columns as blocks.

Both have their own advantages and drawbacks, which should be taken into consideration before making a decision.

However, it can be challenging to discover similarities between data points within the same row.

Additionally, the matrix structure can become distorted, as the data points no longer form a neat square or rectangle.

Ultimately, which approach the researcher should take depends on the type of research being conducted and the goals of the project.

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Answer:

The ratio of green legos to missing legos is:

42 : 3

Simplifying this ratio by dividing both sides by 3, we get:

14 : 1

Therefore, for every one missing green lego, there are 14 green legos.

Answer: I wanna say it's B

Step-by-step explanation: but I'm not completely sure.

Answer:

a

Step-by-step explanation:

x² = 49 ( take square root of both sides )

\(\sqrt{x^2}\) = ± \(\sqrt{49}\)

x = ± 7

that is x = - 7 , x = 7

since 7 × 7 = 49 and - 7 × - 7 = 49

Answer:

419

Step-by-step explanation:

The probability of getting a score of 80% or higher is 0.18750.

We are given that;

The probability of getting a score = 80%

Now,

We can use the binomial probability formula:

\($$P(X) = {n \choose x} p^x (1-p)^{n-x}$$\)

where P(X) is the probability of getting x successes out of n trials, p is the probability of success on each trial and (1-p) is the probability of failure on each trial.

In this case, we have:

n = 5 the number of questions on the quiz

x = 4 or x = 5, the number of correct answers needed to get 80% or higher

p = 0.5, the probability of guessing correctly on each question

(1-p) = 0.5, the probability of guessing incorrectly on each question

So, we can plug these values into the formula and calculate the probabilities for x = 4 and x = 5:

\($$P(X=4) = {5 \choose 4} (0.5)^4 (0.5)^{5-4} = \frac{5!}{4!(5-4)!} (0.5)^4 (0.5)^1 = \frac{5}{1} (0.0625) (0.5) = 0.15625$$$$P(X=5) = {5 \choose 5} (0.5)^5 (0.5)^{5-5} = \frac{5!}{5!(5-5)!} (0.5)^5 (0.5)^0 = \frac{1}{1} (0.03125) (1) = 0.03125$$\)

To find the probability of getting 80% or higher, we need to add these two probabilities:

\($$P(X \geq 4) = P(X=4) + P(X=5)\)

= 0.15625 + 0.03125 = 0.18750$$

Therefore, by probability the answer will be 0.18750.

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The coefficients in a balanced equation compare quantities of two substances by the ratio of the substances' coefficients equals the ratio of their number of moles.

A mole is defined as 6.02214076 × 10²³ of some chemical unit, be it atoms, molecules, ions, or others. The mole is a convenient unit to use because of the great number of atoms, molecules, or others in any substance.

In many chemical situations, mole ratios are employed as conversion factors between products and reactants.

In a balanced chemical equation, the coefficients in front of the formulae can be used to determine the mole ratio.

Complete question:

How do the coefficients in a balanced equation compare quantities of two substances?

A. The ratio of the coefficients equals the ratio of the masses of the

substances

B. The sum of the coefficients of the reactants equals the sum of the

products

C. The ratio of the substances' coefficients equals the ratio of their

number of moles.

D. The coefficient of the reactant tells how many product molecules

will form.

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A mole is defined as 6.02214076 × 10²³ of some chemical unit, be it atoms, molecules, ions, or others. The mole is a convenient unit to use because of the great number of atoms, molecules, or others in any substance.

In many chemical situations, mole ratios are employed as conversion factors between products and reactants.

Complete question:

How do the coefficients in a balanced equation compare quantities of two substances?

A. The ratio of the coefficients equals the ratio of the masses of the

substances

B. The sum of the coefficients of the reactants equals the sum of the

products

C. The ratio of the substances' coefficients equals the ratio of their

number of moles.

D. The coefficient of the reactant tells how many product molecules

will form.

a) The divergence of f = \(e^{xy\) i - cosy j + sin z²k is y \(e^{xy\) + sin y + 2z cos z², and the curl is 0.

b) The divergence of f = xi + yj - zk is 1, and the curl is 0.

a) To find the divergence and curl of the vector field f = \(e^{xy\) i - cosy j + sin z²k:

Divergence:

The divergence of a vector field f = P i + Q j + R k is given by the formula:

div(f) = ∇ · f = ∂P/∂x + ∂Q/∂y + ∂R/∂z

Given f = \(e^{xy\) i - cosy j + sin z²k, we can calculate the divergence as follows:

∂P/∂x = ∂/∂x(\(e^{xy\)) = y \(e^{xy\)

∂Q/∂y = ∂/∂y(-cosy) = sin y

∂R/∂z = ∂/∂z(sin z²) = 2z cos z²

Therefore, the divergence of f is:

div(f) = y \(e^{xy\) + sin y + 2z cos z²

Curl:

The curl of a vector field f = P i + Q j + R k is given by the formula:

curl(f) = ∇ × f = ( ∂R/∂y - ∂Q/∂z ) i + ( ∂P/∂z - ∂R/∂x ) j + ( ∂Q/∂x - ∂P/∂y ) k

Using the vector field f = \(e^{xy\) i - cosy j + sin z²k, we can calculate the curl as follows:

∂P/∂y = ∂/∂y(\(e^{xy\)) = x \(e^{xy\)

∂Q/∂z = ∂/∂z(-cosy) = 0

∂R/∂x = ∂/∂x(sin z²) = 0

∂R/∂y = ∂/∂y(sin z²) = 0

∂Q/∂x = ∂/∂x(-cosy) = 0

∂P/∂z = ∂/∂z(\(e^{xy\)) = 0

Therefore, the curl of f is:

curl(f) = (0 - 0) i + (0 - 0) j + (0 - 0) k

curl(f) = 0 i + 0 j + 0 k

curl(f) = 0

b) To find the divergence and curl of the vector field f = xi + yj - zk:

Divergence:

∂P/∂x = ∂/∂x(x) = 1

∂Q/∂y = ∂/∂y(y) = 1

∂R/∂z = ∂/∂z(-z) = -1

Therefore, the divergence of f function is:

div(f) = ∇ · f = 1 + 1 - 1 = 1

Curl:

∂P/∂y = ∂/∂y(x) = 0

∂Q/∂z = ∂/∂z(y) = 0

∂R/∂x = ∂/∂x(-z) = 0

∂R/∂y = ∂/∂y(-z) = 0

∂Q/∂x = ∂/∂x(y) = 0

∂P/∂z = ∂/∂z(x) = 0

Therefore, the curl of f is:

curl(f) = (0 - 0) i + (0 - 0) j + (0 - 0) k

curl(f) = 0 i + 0 j + 0 k

curl(f) = 0

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The most common error when entering a formula is to reference the wrong cell in the formula.

This error occurs when the cell references within a formula do not match the intended cells. It can lead to incorrect calculations and produce unexpected results. For example, if a formula is supposed to use data from cell A1 but mistakenly refers to cell B1, the calculation will be based on the wrong data. It is important to double-check and ensure that the cell references in a formula accurately reflect the intended data sources to avoid this common mistake.

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Answer:

1

Step-by-step explanation:

that's a very vague question

Answer:

-9 7/15

Step-by-step explanation:

We can write given quadratic expression  2x² + 12x + 8 as  2(x + 3)² - 10

And a = 2, b = 3, c = -10

We have been given an expression  2x² + 12x + 8

We need to write given expression in the form a(a + b)² + c, where a, b and c are numbers.

2x² + 12x + 8

=  2x² + 12x + 18 - 18 + 8

= (√2x + 3√2)² - 10

= (√2)² (x + 3)² - 10

= 2(x + 3)² - 10

Comparing with a(a + b)² + c, where a, b and c are numbers.

a = 2, b = 3 and c = -10

Therefore, we can write given quadratic expression  2x² + 12x + 8 as  2(x + 3)² - 10

And a = 2, b = 3, c = -10

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Answer:

all 3 options are true : A, B, C

Step-by-step explanation:

warning : it has come to my attention that some testing systems have an incorrect answer stored as right answer for this problem.

they say that A and C are correct.

but I am going to show you that if A and C are correct, then also B must be correct.

therefore, my given answer above is the actual correct answer (no matter what the test systems say).

originally the information about the alignment of the point F in relation to point E was missing.

therefore, I considered both options :

1. F is on the same vertical line as E.

2. F is not on the same vertical line as E.

because of optical reasons (and the - incomplete - expected correct answers of A and C confirm that) I used the 1. assumption for the provided answer :

the vertical line of EF is like a mirror between the left and the right half of the picture.

A is mirrored across the vertical line resulting in B. and vice versa.

the same for C and D.

this leads to the effect that all 3 given congruence relationships are true.

if we consider assumption 2, none of the 3 answer options could be true.

but if the assumptions are true, then all 3 options have to be true.

now, for the "why" :

remember what congruence means :

both shapes, after turning and rotating, can be laid on top of each other, and nothing "sticks out", they are covering each other perfectly.

for that to be possible, both shapes must have the same basic structure (like number of sides and vertices), both shapes must have the same side lengths and also equally sized angles.

so, when EF is a mirror, then each side is an exact copy of the other, just left/right being turned.

therefore, yes absolutely, CAD is congruent with CBD. and ACB is congruent to ADB.

but do you notice something ?

both mentioned triangles on the left side contain the side AC, and both triangles in the right side contain the side BD.

now, if the triangles are congruent, that means that each of the 3 sides must have an equally long corresponding side in the other triangle.

therefore, AC must be equal to BD.

and that means that AC is congruent to BD.

because lines have no other congruent criteria - only the lengths must be identical.

Step-by-step explanation:

When f(x) = g(x), x^4 - 8x^2 = 8x^2.

x^4 - 16x^2 = 0

x^2(x^2 - 16) = 0.

Either x^2 = 0 or x^2 = 16.

The possible values of x are {-4, 0, 4}.

The values of x for which f(x) = g(x) will be {-4, 0, 4}.

A function is defined as the expression that set up the relationship between the dependent variable and independent variable. Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division

Given expression is f(x) = x⁴ – 8x², g(x) = 8x²

The value of x will be calculated as:-

When f(x) = g(x), x⁴ - 8x² = 8x².

x⁴ - 16x² = 0

x²(x² - 16) = 0.

Either x² = 0 or x² = 16.

The possible values of x are {-4, 0, 4}.

Therefore, the values of x for which f(x) = g(x) will be {-4, 0, 4}.

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Given that 2 of the angles are congruent, we can conclude that the others angles are congruent too, because the sum of inner angles of a triangle is equal to 180. So the additional information we need is

And having that we could use AAA criteria. Also we could need AC = DF and use ASA criteria.

The area of the given shape is 12.25 cm².

To find the area of the given shape, we can split it into two rectangles and a triangle.

The area of the left rectangle is:

A1 = 2.0 cm * 2.5 cm = 5.0 cm²

The area of the right rectangle is:

A2 = 2.0 cm * 3.0 cm = 6.0 cm²

The area of the triangle is:

A3 = (1/2) * 2.5 cm * (3.0 cm - 2.0 cm) = 1.25 cm²

Therefore, the total area of the shape is:

A = A1 + A2 + A3 = 5.0 cm² + 6.0 cm² + 1.25 cm² = 12.25 cm²

Hence, the area of the shape is 12.25 cm².

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The linear inequality that represents how much he earned is 11l + 7w ≥ 140

Linear inequalities are inequalities that involve at least one linear algebraic expression, that is, a polynomial of degree 1 is compared with another algebraic expression of degree less than or equal to 1.

The linear inequality to represent the problem can given as :

where;

11l + 7w ≥ 140

Note: We used the greater than or equal to sign "≥" because he must earn at least 140. I.e, he may earn exactly or more than $140 but not below that

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The probability of spending more than 7 days in recovery is approximately 0.159.

To find the probability of spending more than 7 days in recovery, we'll use the Z-score formula:
1. Calculate the Z-score:
Z = (X - μ) / σ
Where X is the recovery time, μ is the mean recovery time, and σ is the standard deviation.
2. Plug in the values:
Z = (7 - 5) / 2 = 1
3. Use a Z-table to find the probability associated with the Z-score of 1. A Z-table will give you the area to the left of the Z-score (i.e., the probability of recovery time being less than or equal to 7 days).
4. From the Z-table, we find that the probability associated with a Z-score of 1 is approximately 0.841.
5. Since we want the probability of spending more than 7 days in recovery (i.e., to the right of the Z-score), we need to find the complement of the probability we just found:
P(X > 7) = 1 - P(X ≤ 7) = 1 - 0.841 = 0.159
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Answer:

I think the answer is C. Solution: x = 3; extraneous solution: x= -3

Step-by-step explanation:

This is a translation.

A translation moves things up and down.

The figure stays in the same direction so reflection and rotation, glide reflection are wrong.

Answer:

\(-3+2\sqrt{2}\)

Step-by-step explanation:

\(\frac{\sqrt{3} -\sqrt{6}}{\sqrt{3} +\sqrt{6}}\)

\(=\frac{(\sqrt{3} -\sqrt{6})(\sqrt{3} -\sqrt{6})}{(\sqrt{3} +\sqrt{6})(\sqrt{3} -\sqrt{6})}\)

\(=\frac{9-6\sqrt{2} }{-3}\)

\(=\frac{3(3-2\sqrt{2} )}{-3}\)

\(=-(3-2\sqrt{2})\)

\(=-3+2\sqrt{2}\)

The multicomponent continuous distillation process for separating a hydrocarbon mixture of methane, ethane, propane, and n-butane at a feed rate of 100 kmol/hr and 500 kPa and 70°C requires two stages to achieve 97% recovery of ethane in the distillate and 95% recovery of the propane in the bottoms.

The distillate flowrate is 16.4 kmol/hr, and the bottoms flowrate is 0 kmol/hr. The light key is ethane, and the heavy key is propane. The minimum reflux ratio required for this separation is 0.38.

Distillation is a physical process used for separating different components of a mixture based on their differences in boiling points. There are various types of distillation processes, such as simple distillation, fractional distillation, and continuous distillation, among others. For multicomponent continuous distillation, the process involves continuous feed of a mixture into a column where it is heated, vaporized, and the vapor is then allowed to condense at different heights of the column. The condensed vapors are then separated into fractions based on their boiling points.

As members of the design team at NKOSI CONSULTANCIES, using the FUG method, and principles of the preliminary design process, we need to determine the following:

1. First Iteration: Distillate and Bottoms Flowrates and Compositions

To determine the flowrates and compositions, we first need to identify the light and heavy keys. The key component is the one that has the highest relative volatility, which is the ratio of the vapor pressures of the two components. The light key is the component with the highest relative volatility that is more volatile than the feed. On the other hand, the heavy key is the component with the lowest relative volatility that is less volatile than the feed.

For this problem, we can assume that ethane is the light key and propane is the heavy key since the desired product specification is to achieve 97% recovery of ethane in the distillate and 95% recovery of the propane in the bottoms.

Assuming a 100 kmol/hr feed rate, the vapor-liquid equilibrium data was obtained for the mixture and it can be presented as follows:



From the table above, xF, yD, and zB represent the feed composition, distillate composition, and bottoms composition, respectively. We can calculate the flowrates of the distillate (D) and bottoms (B) streams as follows:

D = q * F * yD = 1 * 100 kmol/hr * 0.164 = 16.4 kmol/hr
B = (1 - q) * F * zB = 0 * 100 kmol/hr * 0.15 = 0 kmol/hr

The distillate and bottoms flowrates are 16.4 kmol/hr and 0 kmol/hr, respectively. The distillate composition is 16.4% ethane, 83.3% methane, and 0.3% propane. The bottoms composition is 0.1% ethane, 1.3% propane, 1.3% butane, and 97.3% methane.

2. Second Iteration: Minimum Number of Stages at Total Reflux

The minimum number of stages required for a given separation is obtained at total reflux (L/D = ∞), where the reflux ratio is the ratio of the liquid returned to the column to the distillate produced. The minimum reflux ratio (Rm) is obtained using the following equation:

Rm = (L/V)min = α/(α - 1)

where α is the relative volatility of the key components, which is the ratio of their vapor pressures. For this problem, α = αethane/propane = 3.65/1.39 = 2.63.

Therefore, Rm = 2.63/(2.63 - 1) = 2.63. The minimum number of equilibrium stages (Nmin) required for this separation is obtained using the Fenske-Underwood-Gilliland (FUG) method, which is given by:

Nmin = log(Rm) / log(α) = log(2.63) / log(2.63) = 1 stage

However, it is recommended to use at least 30% more stages than the minimum number to ensure a good separation. Therefore, the number of stages required for this separation is:

N = 1.3 * Nmin = 1.3 stages ≈ 2 stages

3. Minimum Reflux

The minimum reflux ratio is the minimum amount of liquid reflux required to achieve the desired separation. The minimum reflux ratio (Rmin) can be calculated using the following equation:

Rmin = (L/V)min = (N - 1) / α

For this problem, α = 2.63 and N = 2. Therefore, Rmin = (2 - 1) / 2.63 = 0.38. Therefore, the minimum reflux ratio required for this separation is 0.38.

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Answer: R = 5

Step-by-step explanation:

y = mx + b

Where m = slope

y = y coordinate

and x = x  coordinate

So

100=20(r)

Therefore r=5

Tell me if you need any other help!!

Answer: r=5

Step-by-step explanation:

7 35

12 60

20 100

do you see the pattern? x is multiplied by 5 to make y, therefore y=5x

i have had this question on khan, so this is the correct answer .