Which exponent goes in the triangle to
complete the prime factorization of 24
2A X 3 = 24

The coordinates of point K can be given by (-1/4, 5/8).

What are cartesian coordinates?

Cartesian coordinates are the values on a graph that can be used to show the location of a point on the graph.

The coordinates of point K can be found as follows:

There are 4 lines between 0 and -1 on the x-axis which divide it into 4 equal parts.

Point K lies on the first line. This means that the x-coordinate of the point is -1/4.

There are 8 lines between 0 and 1 on the y-axis which divide it into 8 equal parts.

Point K lies on the fifth line. This means that the y-coordinate of the point is 5/8.

From this, we can understand that the coordinates of the point K on the graph can be given by (-1/4, 5/8).

Therefore, the coordinates of point K can be given by (-1/4, 5/8).

Answer:

114 in²

Step-by-step explanation:

Area Triangles:

Area left rectangle:

Area square:

Area right rectangle:

Area Total :

The area is  \(\boxed{\text{114 square inches}}\)

-Chetan K

Answer:

7.02

Step-by-step explanation:

the answer is 7.02 because 0.78×9=7.02

Answer:

7.02

Step-by-step explanation:

cost of 1 bag = 0.78

cost of 9 bags = 9 × 0.78 = 7.02

The value of X and y when substitution method is used to solve the given quadratic equation would be = 8 and 2 respectively.

The equations that are given is listed below:

X - 3y = 2 ---> equation 1

2x - 6y = 6 ----> equation 2

In equation 1, make X the subject of formula;

X = 2 + 3y

Substitute X = 2 + 3y into equation 2,

2( 2 + 3y) - 6y = 6

4 + 6y - 6y = 6

y = 6-4

y = 2

Substitute y = 2 into equation 1;

x - 3(2) = 2

X = 2 + 6

X= 8

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The amount he will pay with the friend  if 20% is deducted before adding tax is $56.55

We should know that we have to deduct the tip for excellent driving g before adding up the tax to the total first.

The given parameters are

Bill =$65

Tax rate= 7%

Tip for excellent driving =20%

First deduct 0.2*65

=13

Balance = $(65-13)

Balance= $52.00

Tax = 0.07*65

Tax = 4.55

Then $(52.00+4.55)

= $56.55

In conclusion, the amount he will pay with the friend  if 20% is deducted before adding tax is $56.55

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The value of the fraction for 4 multiplied by 3/4 will be 4.

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split.

In this case, 4 x 3/4 can be solved using multiplication and division as follows:

Multiply the whole number 4 by the numerator of the fraction 3/4:

4 x 3 = 12

Write the product 12 over the original denominator of the fraction 4:

12/4

Simplify the fraction by dividing both the numerator and denominator by their greatest common factor (GCF), which in this case is 4:

12/4 = 3

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To find directional derivative of the function g(x, y, z), at point P(3, 9, 0) in the direction of the vector PO, where O is the origin (0, 0, 0), we haveto find derivative , The directional derivative of the function g(x, y, z) = \(xye^(3z)\) at point P(3, 9, 0) in the direction of the vector PO is 3√10.

To calculate the gradient of the function: \(∇g = (∂g/∂x, ∂g/∂y, ∂g/∂z) = (ye^(3z), xe^(3z), 3xze^(3z)\)) the gradient at point \(P:∇g(P) = (9e^(3*0), 3e^(3*0), 3*3*0e^(3*0)) = (9, 3, 0).\)

The unit vector in the direction of PO: OP = P - O = (3, 9, 0) Magnitude of OP = |OP| = \(√(3² + 9² + 0²) = √90\), Unit vector, \(u = OP / |OP| = (1/√90)(3, 9, 0) = (1/3√10, 3/√10, 0)\)

Compute the directional derivative of g at P in the direction of \(u: D_ug(P) = ∇g(P) · u = (9, 3, 0) · (1/3√10, 3/√10, 0) = (9(1/3√10)) + (3(3/√10)) + (0*0) = 3√10\)

The gradient of a function is a vector that points in the direction of the steepest increase in the function and its magnitude represents the rate of change of the function at that point.

The directional derivative of the function g(x, y, z) = \(xye^(3z)\) in the direction of the vector PO is 3√10.

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Answer:

Smaller #: 19

Larger #: 70

Step-by-step explanation:

Step 1:

We can set the smaller number as x. We can find the larger number by adding 51, hence represented as 51+x.

Step 2:

We can write an equation with the given information. Four times the smaller number is equal to six more than the larger:

\(4x=51+x+6\\3x=57\\x=19\)

If the smaller number represented as x is \(\fbox{19}\) , then the larger number represented as 51+x would be \(\fbox{70}\) .

I hope this helps! Let me know if you have any questions :)

The integral of du/sqrt(a^2 - u^2) is arcsin(u/a) + C, where a is a constant and C is the constant of integration.

To evaluate the integral of du/sqrt(a^2 - u^2), we can use a trigonometric substitution. Let's substitute u = asin(theta), where theta is a new variable. Differentiating u with respect to theta gives du = acos(theta)*d(theta).

Now, let's substitute these expressions back into the integral:

∫(du/sqrt(a^2 - u^2)) = ∫((acos(theta)d(theta))/sqrt(a^2 - a^2sin^2(theta)))

Simplifying the expression under the square root:

= ∫((acos(theta)d(theta))/sqrt(a^2(1 - sin^2(theta))))

= ∫((a*cos(theta)d(theta))/(acos(theta)))

= ∫d(theta)

= theta + C

Since we made the substitution u = asin(theta), we need to express the result in terms of u. Using the relationship u = asin(theta), we can find theta = arcsin(u/a). Therefore, the integral becomes:

∫(du/sqrt(a^2 - u^2)) = theta + C = arcsin(u/a) + C

Hence, the integral of du/sqrt(a^2 - u^2) is arcsin(u/a) + C, where a is a constant and C is the constant of integration.

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Answer:

Divide by 39 on both sides

Step-by-step explanation:

y = 6

Answer:

Divide by 39 on both sides y=6

3 exponent 2 × 5 exponent 1 × 7 exponent 1

Answer:

is 3 units away from c

Step-by-step explanation:

Given statement solution is :-Time cannot be negative in this context, we discard the solution t = -1,  the book will hit the ground after approximately 2.5 seconds.

To find the time when the book hits the ground, we need to determine when the height (h) becomes zero. We can set up the equation and solve for t.

The equation given is:

h = -\(16t^2 + 24t + 40\)

Setting h = 0, we have:

0 = \(-16t^2 + 24t + 40\)

Now we can solve this quadratic equation. There are a few methods to solve quadratic equations, such as factoring, completing the square, or using the quadratic formula. In this case, we'll use the quadratic formula:

t = \((-b ± √(b^2 - 4ac)) / (2a)\)

For our equation, a = -16, b = 24, and c = 40. Plugging these values into the quadratic formula, we get:

t = \((-24 ± √(24^2 - 4*(-16)40)) / (2(-16))\)

t = \((-24 ± √(576 + 2560)) / (-32)\)

t = (-24 ± √3136) / (-32)

t = (-24 ± 56) / (-32)

Now we have two possible solutions:

t = (-24 + 56) / (-32) = 32 / (-32) = -1

t = (-24 - 56) / (-32) = -80 / (-32) = 2.5

Since time cannot be negative in this context, we discard the solution t = -1. Therefore, the book will hit the ground after approximately 2.5 seconds.

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Answer:

5x + 10 = 5(11 - 2x)

5x + 10 = 55 - 10x

5x + 10x = 55 - 10

15x = 45

15x ÷ 15 = 45 ÷ 15

x = 3

so the answer is 3

Answer:

where is full question ?

So, the last three digits of m*n is 001.

Let p be the probability that Alfred wins given that he goes first. Then, the probability that Bonnie wins given that she goes first is 1-p. Therefore, the probability that Alfred wins the second game given that Bonnie went first in the first game is 1-p. Similarly, the probability that Alfred wins the third game given that he went first in the second game is p, and so on.

Therefore, the probability that Alfred wins the sixth game given that he went first in the first game is:

p(1-p)(1-p)(p)(p)(p) = p^4 (1-p)^2

Since m and n are relatively prime, the last three digits of m*n are the last three digits of p^4 * (1-p)^2, which is the last three digits of p^4 and the last three digits of (1-p)^2. Since p is the probability of winning given that you go first, it is a number between 0 and 1. Therefore, the last three digits of p^4 and (1-p)^2 are 001, resulting in the last three digits of the final answer being 001.

Therefore, the last three digits of m*n is 001.

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The weight of the eggs in grams 95.38 grams.

Let X the random variable that represent the weights of a population, and for this case we know the distribution for X is given by:

X ~ N(58,21)

where µ = 58 and σ = 21

The z score for this case is given by this formula:

z = x -  µ/σ

We know that the value of z = 1.78 and we want to estimate the value of X. If we solve for X from the z formula we got:

X =  µ+1.78σ

= 58 + 1.78×21

= 95.38

So, the corresponding weight for a z score of 1.78 is 95.38 grams.

Hence we get the required answer.

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Because it diverges using a comparison test, the correct answer is an option (E).

The comparison test, also known as the direct comparison test to distinguish it from other closely related tests, offers a method for determining whether an infinite series or an improper integral will converge or diverge.

The test is effective in both situations by contrasting the given series or integral with one whose convergence characteristics are known.

So, refer to the image attached below.

According to the image which has the reason for convergence and divergence, we know that the correct answer would be option (E).

The reason is the comparison test.

Therefore, because it diverges using a comparison test, the correct answer is an option (E).

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Two positive angles that have a sum of π/2 radians are complementary angles, whereas two positive angles that have a sum of π radians are supplementary angles.

Complementary angles are two angles whose measures add up to a right angle, which is equal to π/2 radians or 90 degrees. In other words, if α and β are complementary angles, then α + β = π/2.

Supplementary angles, on the other hand, are two angles whose measures add up to a straight angle, which is equal to π radians or 180 degrees. If α and β are supplementary angles, then α + β = π.

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Answer:

∠RSU is equal to 39

Step-by-step explanation:

∠RST = 90.

So, 90 - 51 = 39

So ∠RSU = 39

Hope this helps!!

Answer:

39°

Step-by-step explanation:

I hope this helps!

Answer:

2) x/ 2y^2

Explanation:

1) reduce the fraction:

27x^3 -----> x^3

216y^6----> 8y^6

2) evaluate the cube root

x

------

2y^2

Answer:

x/2y²

Step-by-step explanation:

What is the cube root of 27?

3. because 3x3x3 = 27.

What is the cube root of 216?

6. because 6x6x6 = 216.

For the 3 on the right side, since it's a power or an exponent, we just divide by 3. Same thing for the 6 in the right.

Now, we have 3x/6y².

We need to simplify.

The GCF of 3 and 6 is 3, because 3 is the highest number that can be divided by both 3 and 6 while the results are whole numbers.

3/3 = 1

6/3 = 2

x/2y² is the answer.

The number of fish in the lake follows an arithmetic sequence

The number of fish in the lake the second year is 7800, and it is represented by f(2)  

The model of the number of fish is given as:

\(\mathbf{f(n + 1) = f(n) - 400}\)

Such that:

\(\mathbf{f(1) = 8200}\)

Set n = 1, to calculate f(2)

Substitute 1 for n in the given model \(\mathbf{f(n + 1) = f(n) - 400}\)

So, we have:

\(\mathbf{f(n + 1) = f(n) - 400}\)

\(\mathbf{f(1 + 1) = f(1) - 400}\)

Simplify, by adding 1 and 1

\(\mathbf{f(2) = f(1) - 400}\)

Substitute 8200 for f(1)

\(\mathbf{f(2) = 8200 - 400}\)

Subtract 400 from 8200

\(\mathbf{f(2) = 7800}\)

Hence, the value of f(2) is 7800

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Answer:

y=90x+2,000

y=mx+b

Answer: 12

Step-by-step explanation:

a² = b² + c²

15² = b² + 9²

b² = 15 ² - 9²

b² = 144

b =

b= 12mm

I HOPE IT WILL HELP YOU A LOT.

I hope your day goes great.

In x axis y become minus .

In y axis x become minus .

Your answer i s

A' (1 ,-2 )

B' (3,-5)

C' (2,-1 )

Answer:

SAS

Step-by-step explanation:

In triangle ABC and triangle EFD

1. BC = CD (S) Given

2. < BCD = < EFD (A) being vertically opposite. angles.

3. AC = CE (S) Given

Hence

By SAS postulate Triangle ABC and triangle EFD are congruent.

HOPE IT HELPS :)❤

The conditional probability formula is

which gives

Then, for the first question, we get

which gives

Now, for the second question, we know that, for independent events

then, we have

which gives

Now, for question 3, we know that, when the events are dependent and mutually non-exclusive

By substituting the given values, we have

Finally, for the 4th question, we have

which gives

In summary, the solutions are:

Question 1:

Question 2:

Question 3:

Question 4:

Answer:

156

its 156 owo

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