Make A the subject of the formula

When a multiple of a row is added to another row, then the determinant does not change.

When we consider two matrices P and Q,

Suppose that a multiple of a row in A is added with another row which results in the matrix B.

Let the determinant of A = x.

Then the determinant of B will also be not changing.

It will also be equal to x.

So the determinant remains unchanged.

Hence when a multiple of a row is added to another row, then the determinant does not change.

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We have to indicate the steps to follow in order to evaluate:

(12.9-3.1) x 6.2-2 + 43

So FIRST: we solve for the operation indicated inside the parenthesis

12.9 - 3.1 = 9.8 (we subtract 3.1 from 12.9)

This is the answer you need to select.

The GPA of a student who studies for 15 hours a week is 2.935.

What is a GPA?

Grade point average, or GPA, is a conventional method of evaluating academic performance in the United States on a scale of 0 to 4.

How to calculate GPA?

To calculate your GPA, divide the total number of grade points earned by the total number of letter-graded units undertaken.

Here,

We have an equation y = 0.164x + 0.475

put x= 15

we get,

y = 0.164* 15 + 0.475

y = 2.935

Hence, The GPA of a student who studies for 15 hours a week is 2.935

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Answer:

it's 25, just did it

Step-by-step explanation:

1 /2  o f  ( − 10 ) =  − 5 ,  ( − 5 )^ 2  =  25

Answer:

C. 25

Step-by-step explanation:

The general solution to the differential equation is: y(t) = y_h(t) + y_p(t) = c1e^(2t) + c2e^(-t) - (1/6) e^(2t) + (1/2)e^(-t) + (1/3)cosh(2t).

To find the general solution of the given differential equation, we first find the homogeneous solution by solving the characteristic equation:

r^2 - r - 2 = 0

This factors as (r-2)(r+1) = 0, so the roots are r=2 and r=-1. Therefore, the homogeneous solution is of the form:

y_h(t) = c1e^(2t) + c2e^(-t)

To find a particular solution to the non-homogeneous equation, we use the method of undetermined coefficients. Since cosh(2t) = (e^(2t) + e^(-2t))/2, we guess a particular solution of the form:

y_p(t) = Ae^(2t) + Be^(-t) + C*cosh(2t)

where A, B, and C are constants to be determined. We then take the first and second derivatives of y_p(t) and substitute them, along with y_p(t), into the original differential equation. Solving for A, B, and C, we find:

A = -1/6, B = 1/2, C = 1/3

Therefore, the general solution to the differential equation is:

y(t) = y_h(t) + y_p(t) = c1e^(2t) + c2e^(-t) - (1/6)e^(2t) + (1/2)e^(-t) + (1/3)cosh(2t)

where c1 and c2 are constants determined by the initial or boundary conditions.

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It takes approximately 86.67 hours for Alex, Bethany, and Carol to collectively finish a total of 26 miles. This is determined by calculating the harmonic mean of their individual running speeds.

To determine how many hours it takes for Alex, Bethany, and Carol to collectively run a total of 26 miles, we need to consider their individual running speeds. Alex runs at a rate of 26 miles in 6 hours, Bethany runs at a rate of 26 miles in 5 hours, and Carol runs at a rate of 26 miles in 4 hours.

To find the total time it takes for them to finish 26 miles together, we can calculate the harmonic mean of their individual running speeds. The harmonic mean is used because it accounts for the different rates at which they run.

The formula for the harmonic mean is given by:

Harmonic Mean = Total Distance / (1 / Speed1 + 1 / Speed2 + 1 / Speed3)

Substituting the values, we have:

Harmonic Mean = 26 / (1 / 6 + 1 / 5 + 1 / 4)

To simplify the equation, we find the common denominator:

Harmonic Mean = 26 / ((5 + 6 + 7) / 60)

Harmonic Mean = 26 / (18 / 60)

Harmonic Mean = 26 / (3 / 10)

Harmonic Mean = 26 * (10 / 3)

Harmonic Mean ≈ 86.67

Therefore, it takes approximately 86.67 hours for Alex, Bethany, and Carol to collectively finish a total of 26 miles.

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The probability that a basketball player with a 71% free throw shooting accuracy does not make his next free throw shot is 29%.

The probability that a basketball player with a 71% free throw shooting accuracy does not make his next free throw shot.
To calculate the probability of missing a free throw shot, we need to subtract the shooting accuracy percentage from 100%.

In this case, the probability of making a free throw is 71%, which means the probability of missing the free throw is 29%.

Therefore, the probability that the basketball player does not make his next free throw shot is 29%.
It is important to note that free throw shooting accuracy can vary depending on the player's physical and mental condition, as well as external factors such as the audience's noise, the game's pressure, and the distance from the basket.

Thus, it is crucial for basketball players to train and practice regularly to improve their shooting skills and increase their chances of making free throw shots.
To answer this, we need to consider the complement of the success probability.

Since the player has a 71% chance of making the free throw, it means there is a 29% chance that he will not make it (100% - 71% = 29%).

The probability can also be expressed as a decimal, which is 0.29 (29/100 = 0.29).

Therefore, the probability that your favorite basketball player does not make his next free throw shot is 29% or 0.29.
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Answer:

the equal side are vu and st which equal 4 units and vs equal 5.5 units im pretty sure by looking at it

Step-by-step explanation:

if its wrong im sorry

Answer:

ST: 4

TU: 5.1

VU: 4

SV: 5.1

Explanation:

You can use the Pythagorean theorem to determine the length of the slanted sides, and you only need to find the length of two since it is symmetrical,

Answer:

Step-by-step explanation:

4(x-3)^2 = 80

4x-12^2= 80              --- (distribute)

4x+144= 80          --- ( why a positive 144 because a (-) * a (-) = a (+)

4x =  (80-144)      --- ( subtract -144 from +144(do it on both sides)

4x = -64    --- (divide both sides by 4)

x= -16

Answer:

2√5 +3

Step-by-step explanation:

Isolate x:

4(x-3)^2 = 80

Divide both sides by 4.

(x-3)^2 = 20

Then take the square root of each side.

(x-3) = √20

Add 3 to each side.

x = √20 + 3

√20 can be rewritten as 2√5.

x = 2√5 + 3

Answer:

To solve the given system of equations using the substitution method, we need to solve one equation for one variable and then substitute that expression into the other equation for that same variable. Let's solve the second equation for y.

-x + y = 4

y = x + 4

Now we can substitute this expression for y into the first equation and solve for x.

-2x + 2(x + 4) = 7

-2x + 2x + 8 = 7

8 = 7

The equation 8 = 7 is not true, which means the system of equations has no solution. We can see this visually by graphing the two lines. They are parallel and will never intersect, which means there is no point that satisfies both equations.

Therefore, the solution to the system of equations is "No solution."

Note: Please be sure to double-check your work to avoid mistakes.

Step-by-step explanation:

Hope this helps you!! Have a wonderful day/night!!

Answer:

I have graphed and attached it in the explanation.

Step-by-step explanation:

y–2=4(x+8)

y - 2 = 4x + 32

y = 4x + 34

Answer:

1 is FALSE

2 is TRUE

3 is FALSE

4 is FALSE

Step-by-step explanation:

1 is false because the blue marble is 2 only

2 is true because green marble has a 100% you get this.

3 is false because we din't have yellow marble

4 is false because red is has 10 marble so you get this red marbke is has 82% because red marble is 2nd most at the number of color

The area of the domain enclosed by the curve with parametric equations x = tsin t, y = cost, t ∈ [0, 2π] is 2π + 2.

The parametric equations given are:

x = t sin t
y = cos t

To find the area of the domain enclosed by the curve, we can use the formula for the area of a region bounded by a curve given in parametric form:

A = ∫[a,b] y dx

where a and b are the limits of the parameter t that describe the domain of the curve.

In this case, we have:

a = 0
b = 2π

So, we need to compute:

A = ∫[0,2π] cos(t) (t sin(t)) dt

Using integration by parts with u = t and dv = sin(t) dt, we get:

A = [t cos(t)]|[0,2π] - ∫[0,2π] cos(t) dt + ∫[0,2π] sin(t) dt

The first integral evaluates to:

[t cos(t)]|[0,2π] = 2π

The second integral evaluates to:

∫[0,2π] cos(t) dt = [sin(t)]|[0,2π] = 0

The third integral evaluates to:

∫[0,2π] sin(t) dt = [-cos(t)]|[0,2π] = 2

Therefore, the area of the domain enclosed by the curve is:

A = 2π - 0 + 2 = 2π + 2

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Answer: D. as a total number of family member increases the amount of money that the family spends on food increases

Step-by-step explanation:

i.e. independent variable acts like a cause to effect the dependent variable.

This can be seen only in Option D. as it is very obvious that increase in family member will increase the cost of food.

Hence, there is direct effect of number of people on food's cost.

Rest of options represents correlation but not causation .

Hence, the correction option is D.

The sum in terms of p of four consecutive even integers with p been the smallest is 4(p + 3)

Even numbers are numbers that can be divided into two equal groups and they can be easily divisible by 2 without any remainder.

p is the smallest of the four consecutive even integers. This means p come first and it is the first term of the numbers.

Therefore, the 4 consecutive even integers is represented as follows;

p, p + 2, p + 4, p + 6

So the sum is equal to:

sum = p + p + 2 + p + 4 + p + 6

sum = 4p + 12

sum = 4(p + 3)

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Answer:

We can evaluate the function f(2) to find its value:

f(2) = -3(2)^2 - 2 = -12

Therefore, the point (2, -12) is on the graph of the function.

To determine which graph represents the function, we need to look for a graph that contains the point (2, -12).

Out of the provided graphs, only graph (B) contains the point (2, -12). Therefore, graph (B) represents the function f(2) = -3(2)^2 - 2.

Answer:

When two parallel lines are cut by a transversal, Alternate interior angles are supplementary.

Step-by-step explanation:

a. The required equation that gives the answer to the question is

b. Train B passed train A at t = -4 hours.

Let

Since at 10:00 train A left the station and an hour later train B left the same station on a parallel track, we have that

t' = t + 1

Let

If train A travelled at a constant speed of 60 kilometres per hour and train B at 80 kilometres per hour, then

For each train to cover the same distance, we have that

vt = v'(t + 1)

60t = 80(t + 1

So, the equation that can be used to give the answer to the question is

So, solving the equation, we have

60t = 80(t + 1)

60t = 80t + 80

60t - 80t = 80

-20t = 80

t = 80/-20

t = -4

So, train B passed train A at t = -4 hours.

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Answer:

The answer is B) 40 yards for $45.00

Step-by-step explanation:

Options:

A) 20 yards per $30.00

B) 40 yards per $45.00

C) 50 yards per $70.00

C) 65 yards per $85.00

Think if buying something at the lowest cost which gives more.

1 yard per $1.00, sounds like a good deal.

20 yards per $30.00 which mean $10.00 more.

40 yeards per $45.00 which mean $5.00 more.

50 yards per $70.00 which mean $20.00 more.

65 yeards per $85.00 which mean $25.00 more.

Answer:

51°

Step-by-step explanation:

Plain reasoning:

the arc of CD is 180°

78° is alrdy cut out for AB

the rest (102°) has to be equally decided between AC and BD

pls brainliest (although a second answer is needed to give the crown)

we can say that Y is directly proportional to X with a constant of proportionality 2.5. This can be expressed using the equation: Y = 2.5X.

what is the proportional relationship?

In mathematics, a proportional relationship is a relationship between two variables where their ratio remains constant. In other words, if we increase one variable by a certain factor, the other variable also increases by the same factor.

To determine whether the values in the table show a proportional relationship, we need to check whether the ratio between any two corresponding values of X and Y is constant.

Let's calculate the ratios for each pair of corresponding values in the table:

Ratio of Y to X for (1, 2.5): 2.5/1 = 2.5

Ratio of Y to X for (2, 5): 5/2 = 2.5

Ratio of Y to X for (3, 7.5): 7.5/3 = 2.5

Ratio of Y to X for (4, 10): 10/4 = 2.5

We can see that the ratio of Y to X is constant at 2.5 for all pairs of corresponding values. This means that the values in the table do show a proportional relationship.

Therefore, we can say that Y is directly proportional to X with a constant of proportionality 2.5. This can be expressed using the equation:

Y = 2.5X

So, if we double X, Y will also double, and if we triple X, Y will triple, and so on.

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Answer:

Given AD = 7 and DB = 12, to find AB you need to add them

AB = 12+7

AB = 19

The measure of the line segment AB is 19 units.

Suppose we've two endpoints of a line segment as:

A(p,q), and B(m,n)

Then let the midpoint be M(x,y) on that line segment. Then, its coordinates are:

\(x = \dfrac{p+m}{2}andy = \dfrac{q+n}{2}\)

We are given that;

AD = 7, and DB = 12

Now,

To find the measure of the line segment AB, we need to use the segment addition postulate. The segment addition postulate states that if a point is between two other points on a line segment, then the sum of the lengths of the two smaller segments is equal to the length of the larger segment.

In this problem, D is between A and B, so we can apply the segment addition postulate and write:

AD + DB = AB

Substituting the given values of AD and DB, we get:

7 + 12 = AB

Simplifying, we get:

19 = AB

Therefore, by the given point the answer will be 19 units.

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The probability of choosing a fair coin and observing 2 heads when flipping it twice can be calculated as follows:

P(fair coin and 2 heads) = P(fair coin) * P(2 heads | fair coin) = (2/6) * (0.5)^2 = 0.0833.

To calculate the probability of choosing a fair coin and observing 2 heads when flipping it twice, we need to consider the individual probabilities of these events. We are given that we have a total of 6 coins, with 2 fair coins and 4 unfair coins. The fair coins have a 50% chance of flipping heads, while the unfair coins have varying probabilities: 0.5, 0.8, 0.2, 0.1, and 0.3.

To begin, we compute the probability of selecting a fair coin from the total pool of coins. Since there are 2 fair coins out of 6, the probability of choosing a fair coin is 2/6, or 1/3. Next, we calculate the probability of observing 2 heads when flipping a fair coin twice. Each individual coin flip is an independent event, so the probability of getting heads twice in a row is the product of the probabilities for each flip. Therefore, the probability of getting 2 heads when flipping a fair coin is (0.5)^2, which equals 0.25.

Now, we can calculate the overall probability by multiplying the probability of choosing a fair coin (1/3) with the probability of getting 2 heads when flipping a fair coin (0.25). Thus, P(fair coin and 2 heads) = (1/3) * 0.25 = 0.0833, or approximately 8.33%.

In conclusion, the probability of selecting a fair coin and observing 2 heads when flipping it twice is 0.0833, or approximately 8.33%.

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Answer:

x = 22°

3x + 2 = 64°

Step-by-step explanation:

All angles in a triangle must add up to 180°

90 + x + 3x + 2 = 180

Rearrange and collect like terms and place them on either side

4x = 88

x = 22°

3x + 2

3(22) + 2

= 64°

Answer:

f multiplied by 3 divided by 625

Step-by-step explanation:

cant really explain