32x – 14x = 288

with solution please and thank you

The correct option is (C) Triangle HJK is congruent to triangle NLM

A triangle is a closed, two-dimensional geometric figure with three sides and three angles. It is the simplest polygon and is formed by connecting three non-collinear points with line segments.

Congruent is a term used in geometry to describe two or more geometric figures that have the same shape and size. If two geometric figures, such as triangles or line segments, are congruent, it means that they are identical in shape and size, and they can be superimposed onto each other.

According to the given information:

In Triangle HKJ

Angle H is 58 degrees.

Angle J is 62 degrees.

Angle K is 60 degrees

In Triangle LMN (Arranging in the same order as the angles above)

Angle N is 58 degrees.

Angle L is 62 degrees.

Angle M is 60 degrees.

Therefore, we can say that:

Triangle HJK is congruent to Triangle NLM.

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Answer:

\(\mathrm{88 + v}\)

Based on the data in the table, the following statements are true:

Students who prefer to use a touchpad are less likely to be eighth graders. This statement is true because 20% of eighth graders prefer to use a touchpad, while 25% of seventh graders prefer to use a touchpad. This means that there is a higher percentage of seventh graders who prefer to use a touchpad than eighth graders.

There is an association between a student's grade level and computer preference. This statement is true because the data shows that there is a clear relationship between a student's grade level and their preference for a mouse or touchpad. For example, 25% of seventh graders prefer to use a mouse, while only 20% of eighth graders prefer to use a mouse.

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Answer:

48\(cm^{2}\)

Step-by-step explanation:

1.  We need 2 integers (full number) when added gives us 7

this is 4 and 3

2. so the width of the rectangle is 3cm and the length is 4cm

3. to find one area of a rectangle we do

  4cmx3cm= 12\(cm^{2}\)

4. There is 4 rectangles, so we do

      4x12\(cm^{2}\)= 48\(cm^{2}\)

5. so the total area of the pattern is

     = 48\(cm^{2}\)

To find out how much of each metal the metallurgist should use to make the alloy, we can set up an equation based on the percentage of gold in each metal. Let's assume the metallurgist uses x pounds of the metal that is 60% gold, and y pounds of the metal that is 40% gold.

The metallurgist should use 6.2 pounds of the metal that is 60% gold and 6.2 pounds of the metal that is 40% gold to make 12.4 pounds of the alloy containing 50% gold.

The total weight of the alloy is 12.4 pounds, so we have the equation:
x + y = 12.4
Now, let's consider the percentage of gold in the alloy. The alloy needs to contain 50% gold.
The metal that is 60% gold will contribute 60% of x pounds of gold, which is 0.6x pounds of gold.
The metal that is 40% gold will contribute 40% of y pounds of gold, which is 0.4y pounds of gold.
Since the alloy needs to contain 50% gold, the total amount of gold in the alloy will be 50% of the total weight, which is 0.5 times 12.4 pounds:
0.5 * 12.4 = 6.2 pounds of gold
Now, we have another equation:
0.6x + 0.4y = 6.2
We have a system of two equations:
x + y = 12.4
0.6x + 0.4y = 6.2
To solve this system, we can use substitution or elimination. I will use the elimination method.
First, let's multiply the first equation by 0.4 to make the coefficients of y in both equations the same:
0.4(x + y) = 0.4 * 12.4
0.4x + 0.4y = 4.96
Now, we can subtract the second equation from this new equation to eliminate y:
(0.4x + 0.4y) - (0.6x + 0.4y) = 4.96 - 6.2
0.4x - 0.6x = -1.24
-0.2x = -1.24
x = -1.24 / -0.2
x = 6.2
Substituting this value of x back into the first equation:
6.2 + y = 12.4
y = 12.4 - 6.2
y = 6.2
So, the metallurgist should use 6.2 pounds of the metal that is 60% gold and 6.2 pounds of the metal that is 40% gold to make 12.4 pounds of the alloy containing 50% gold.

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Answer:

1 a is your answer

Step-by-step explanation:

mark brainlest pls and i hope this helps

Based on the graph, in year 4 there were 1.16 times more burglaries if compared to year 1.

Based on the graph, the number of burglaries these years was:

This shows a growing trend in the number of burglaries over the years.

number in year 4/ 1

255/220 = 1.159 which can be rounded to 1.16

Based on this, year 4 had 1.16 times more burglaries than year 1.

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Answer:

m=-1

Step-by-step explanation:

2x+3y=11............. (eqn 1)

2x-4y=-24...........(eqn 2)

Subtract eqn 1 from eqn 2

7y=35

y=5

Substitute for y in eqn 1

2x+3(5)=11

2x+15=11

2x=11-15

2x=-4

x=-2

y=mx+3

5=-2m+3

5-3=-2m

2=-2m

m=-1

Answer:Here,

Subtracting (ii) from (i),we get

2x+3y=11

- 2x+4y=24

___________

7y =35

y=5

Substituting y = 5 in (i) we get

2x+3×5=11

or,2x +15 =11

or,2x = 11- 15

or,x= -2

Now,

We know,y=mx+c

5=m ×(-2) +3

or,2=m×(-2)

or,2/-2 =m

m= -1

The complex number that the given graph depicts is:

D: 2{cos 7π/4 + i sin 7π/4}

The complex number shown has coordinates (1.35, -1.35)

or

z = 1.35 - 1.35i

The modulus is:

|z| = √(1.35² + (-1.35)²)

|z| = √3.645

|z| ≈ 2

The argument is:

θ = tan⁻¹(-1.35/1.35)

θ = tan⁻¹(-1) = 7π/4

The polar form is:

2{cos 7π/4 + i sin 7π/4}

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These scores are used to provide an overall measure of an individual's intelligence and cognitive abilities.

Gregory most likely took an intelligence test, specifically the Wechsler Adult Intelligence Scale (WAIS). The WAIS is designed to measure an individual's cognitive abilities and is commonly used in psychological assessments. It consists of a full scale or total score, which is a combination of the verbal score and the performance score. The verbal score measures an individual's language and communication skills, while the performance score measures an individual's ability to solve problems and complete tasks. These scores are used to provide an overall measure of an individual's intelligence and cognitive abilities.

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Answer:

-10

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Answer:

75>5t

Step-by-step explanation:

Here is the information given:

75 is the maximum

5 per table

t is table

So, 75 is greater than or equal to the number of tables.

If 5 is the max seated at a table we know that it will be 5 people per table or 5t

Which gives us 75>5t

Furthermore, when solving we get t=15, when plugging this in the inequality becomes 75>75 which is true.

Hope this helps!

Answer:

c = 2

Step-by-step explanation:

26 - (2c + 4) = 2(c+6) + c

26 - 2c + 4 = 2c + 12 + c

26 - 4 - 12 = 2c + 2c + c

10 = 5c

2 = c

(a) A nonzero vector orthogonal to the plane through the points P, Q, and R is (9, -17, 35). (b) The area of triangle PQR is \(\sqrt\)(811) / 2.

(a) To determine a nonzero vector orthogonal to the plane through the points P, Q, and R, we can first find two vectors in the plane and then take their cross product. Taking vectors PQ and PR, we have:

PQ = Q - P = (5, 1, -2) - (-4, 0, 0) = (9, 1, -2)

PR = R - P = (6, 4, 1) - (-4, 0, 0) = (10, 4, 1)

Taking the cross product of PQ and PR, we have:

n = PQ x PR = (9, 1, -2) x (10, 4, 1)

Evaluating the cross product gives n = (9, -17, 35). Therefore, (9, -17, 35) is a nonzero vector orthogonal to the plane through points P, Q, and R.

(b) To determine the area of triangle PQR, we can use the magnitude of the cross product of vectors PQ and PR divided by 2. The magnitude of the cross product is given by:

|n| = \(\sqrt\)((9)^2 + (-17)^2 + (35)^2)

Evaluating the magnitude gives |n| = \(\sqrt\)(811).

The area of triangle PQR is then:

Area = |n| / 2 = \(\sqrt\)(811) / 2.

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Answer:

182

The number of permutations of 14 things taken 2 at a time is ...

 14P2 = 14·13 = 182

The first color can be any of the 14 on the palette. The second color must be different, so can be any of the remaining 13.

___

We assume that a "yellow/red" flag is different from a "red/yellow" flag. That is, order matters.

The statement about using the line of best fit for the given scatter plot is; False

When we have a scatter plot, it is always best to look for the line of best fit or curve of best fit depending on the nature of the variation of the plotted points.

Now, from the scatter plot image attached, we can see that the points are already looking like a curved plot form and so what we will need her will be a curve of best fit and not a line of best fit plot and as such the statement about using a line of best fit plot is false.

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Answer:

stop rushing me aaaaaaaaaahhhhhhhh

Step-by-step explanation:

You need to deposit $13 into a account to have amount $5000 in 2 years.

Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.

The formula used to find the compound interest = \(A=P(1+\frac{r}{100})^{nt}\).

Given that, Amount =$5000, rate of interest =5.89% and time period = 2 year = 104 weeks.

Now, 5000=P(1+5.89/100)¹⁰⁴

5000=P(1+0.0589)¹⁰⁴

5000=P(1.0589)¹⁰⁴

5000=384.5P

P=5000/384.5

P=$13

Therefore, you need to deposit $13 into a account to have amount $5000 in 2 years.

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Answer:

w= -5

Step-by-step explanation:

Isolate "w":

The critical numbers of the function f(x) = (x^3/5)(4 - x) are x = 0 and x = 3.

To find the critical numbers of the function f(x) = (x^3/5)(4 - x), we need to find the values of x where the derivative of f(x) is equal to zero or does not exist.

Let's first find the derivative of f(x):

f'(x) = d/dx[(x^3/5)(4 - x)]

Using the product rule, we can differentiate the function:

f'(x) = [(3/5)x^(3/5-1)(4 - x)] + [(x^3/5)(-1)]

Simplifying further:

f'(x) = [(3/5)x^(3/5-1)(4 - x)] - (x^3/5)

f'(x) = (3/5)x^(3/5-1)(4 - x) - (x^3/5)

Now, let's find the critical numbers by setting the derivative equal to zero and solving for x:

0 = (3/5)x^(3/5-1)(4 - x) - (x^3/5)

0 = (3/5)x^(-2/5)(4 - x) - (x^3/5)

Multiply through by 5x^2 to get rid of the fractions:

0 = 3(4 - x)x^2 - x^3

0 = 12x^2 - 3x^3 - 3x^2

0 = -3x^3 + 9x^2

0 = x^2(-3x + 9)

From this equation, we can see that x^2 = 0 or -3x + 9 = 0.

For x^2 = 0, we have x = 0.

For -3x + 9 = 0, we solve for x:

-3x = -9

x = 3

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Answer:

t = 22

Step-by-step explanation:

t = trading cards

t - 20 = 2

t - 20 = 2

 +20   +20

___________

t = 22

Answer:

Option D, 4

Step-by-step explanation:

2 pizzas x 6 slices per pizza = 12 slices of pizza

12 slices of pizza divided by 3 friends eating equal slices = 4 slices per friend

Option D, 4, is your answer

Answer:a

Step-by-step explanation:

a

To compute ET, we need to compute the expected time to go from state i to state j for all pairs of states (i,j). This can be done by solving a system of linear equations known as the fundamental matrix equation. Once we have the expected time to go from state i to state j, we can plug it into the formula above to compute ET.

To show that P(Ti > 0) > 0 for any 1 ≤ i ≤ m, note that since the Markov chain X is irreducible, there exists a path from any state j to any other state k in S. In particular, there is a path from i back to i, so the event {Ti > 0} is non-empty. Since X is a finite Markov chain, it is guaranteed to eventually return to any state with probability 1, so P(Ti > 0) > 0.

To compute ET, we use the fact that (Ti)i∈S is a stationary distribution of X. This means that for any state j ∈ S,

∑i∈SP(Ti > n)P(Xn = j | X0 = i) → (Tj)-a.s. as n → ∞.

Using the strong law of large numbers, we have

1/n * ∑i=1 to n I(Ti > 0) P(Xn = j | X0 = i) -> P(Ti > 0) * πj as n -> infinity

where I(A) is the indicator function of the event A and πj is the stationary probability of state j.

Since P(Ti > 0) > 0 for any i, we have that P(Ti > n) > 0 for all n ≥ 1 and hence we can apply the limit as n approaches infinity, giving us:

ET = E(Ti | X0 = i) = lim_{n->inf} [E(Ti | X0 = i, Ti > 0) + P(Ti = 0 | X0 = i)]

= 1/P(Ti > 0) * lim_{n->inf} [∑j∈S ∑k≥0 P(Tj = k | X0 = i, Ti > 0) * (k + E(Ti | X0 = j)) + P(Ti = 0 | X0 = i)]

= 1/P(Ti > 0) * ∑j∈S πj * ETij + P(Ti = 0)

where ETij is the expected time to reach state i starting from state j and πj is the stationary probability of state j.

Since the Markov chain X is irreducible, it is also aperiodic and hence the stationary distribution π is unique. Using the fact that π is a stationary distribution, we have:

πj = ∑i∈S πi P(Xn+1 = j | Xn = i)

= ∑i∈S πi P(X1 = j | X0 = i)

= ∑i∈S πi Pij

where Pij is the transition probability from state i to state j.

Substituting this into the expression for ET, we get:

ET = 1/P(Ti > 0) * ∑j∈S [∑i∈S πi Pij] * ETij + P(Ti = 0)

= 1/P(Ti > 0) * ∑j∈S πj [∑i∈S Pij * ETij] + P(Ti = 0)

= 1/P(Ti > 0) * ∑j∈S πj ETi,j + P(Ti = 0)

where ETi,j is the expected time to go from state i to state j.

Therefore, to compute ET, we need to compute the expected time to go from state i to state j for all pairs of states (i,j). This can be done by solving a system of linear equations known as the fundamental matrix equation. Once we have the expected time to go from state i to state j, we can plug it into the formula above to compute ET.

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Answer:

To eliminate the parameter t, we need to solve for t in terms of x and y.

From the first equation, we have: t = (x - 3) / 6

Substituting this into the second equation, we get:

y = 7√(t + 3) = 7√[(x-3)/6 + 3] = 7√[(x+15)/6]

To ensure that the expression under the square root is non-negative, we need:

x + 15 ≥ 0

x ≥ -15

Therefore, the domain of the function is all real numbers greater than or equal to -15, expressed in interval notation as:

[-15, ∞)

Step-by-step explanation:

Answer:

11 : 22 : 132

Step-by-step explanation:

1 + 2 + 12 = 15

165 ÷ 15 = 11

1 × 11 = 11

2 × 11 = 22

12 × 11 = 132

11 : 22 : 132