Use the GCF to factor the expression 40x+24y-56.

Answer:

a=-1

Step-by-step explanation:

1/2a=1/4a+2

by cross multiplying,

2a=4a+2

2a-4a=2

-2a=2

a=2/-2

a=-1

hope you understood  :)

The inequality that represents p, the number of people the theater can seat is p ≤ 25

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

A movie theater can seat a maximum of 25 people

This means that

Maximum =  25 people

In other words, the movie theatre can allow 25 or less people to attend a movie

In inequality, 25 or less means less than or equal to 25

When represented as an inequality expression, we have

≤ 25

Using the variable p, we have

p ≤ 25

Hence, the inequality is p ≤ 25

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The inverse of the given matrix is:

( 0 1/2 -1/2 )

(-3 1 -3 )

( 1 -1 0 )

What is inverse ?

In linear algebra, the inverse of a square matrix A is another matrix A^{-1}, such that when A and A^{-1} are multiplied together, the result is the identity matrix I. In other words, A^{-1} is the "inverse" of A, and multiplying A by its inverse "undoes" the effect of A.

To find the inverse of a matrix A using the adjoint method, we follow these steps:

Find the determinant of A.

Find the adjugate of A.

Multiply the adjugate of A by 1/det(A) to get the inverse of A.

Let's follow these steps to find the inverse of the given matrix:

Step 1: Find the determinant of A.

We can use the cofactor expansion method to find the determinant:

det(A) = 1(0-2) - 2(3-0) + 1(6-0) = -2 - 6 + 6 = -2

So det(A) = -2.

Step 2: Find the adjugate of A.

The adjugate of A is the transpose of the matrix of cofactors of A. To find the matrix of cofactors, we need to compute the cofactor of each element of A. The cofactor of an element aij is (-1)i+j times the determinant of the submatrix obtained by deleting the row and column containing aij.

The matrix of cofactors is:

( 0 -6 2 )

( 2 2 -2 )

(-2 6 0 )

Taking the transpose of this matrix gives us the adjugate of A:

( 0 2 -2 )

(-6 2 6 )

( 2 -2 0 )

Step 3: Multiply the adjugate of A by 1/det(A).

We have det(A) = -2, so:

A^{-1} = adj(A)/det(A) = (1/-2)( 0 2 -2 ) ( 0 -1 1 )

(-6 2 6 ) = (-3 1 -3)

( 2 -2 0 ) ( 1 -1 0 )

Therefore, the inverse of the given matrix is:

( 0 1/2 -1/2 )

(-3 1 -3 )

( 1 -1 0 )

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Answer:

Step-by-step explanation:

To get the y values all you need to do is substitute the x value in the equation y=-2/3x+7.

For example:

y=-2/3(-6)=7

-2/3x6=-4

-4+7=3

(-6,3)

You can double check your work by filling the x and y coordinates in the equation and when solved if it it true you know you were correct.

To get the x value, you need to fill in the y in the equation y=-2/3x+7

for example:

5=-2/3x+7

-2=-2/3x

3=x

(3,5)

y=-2/3x+7

y=-2/3(15)+7

y=-10+7

y=-3

(15,-3)

y=-2/3x+7

15=-2/3x+7

8=-2/3x

-12=x

(-12,15)

Answer:

Here's the parallel line: y = 5x - 4

Another way to look at it is to draw the chord UW. Then ΔWZU is an isosceles triangle, and the perpendicular bisector of UW bisects ∠Z and also goes through the circle center. Then the figure is symmetrical about that diameter secant, making WT ≅ UV.

A secant of a circle is known to be a straight line that intersects the circle at two different points. Secant is derived from the Latin secare, meaning "to cut". It can also be understood beyond the circle as an extension of the chord of the circle.

If the secant intersects the circle at two points, you get chords at the two points of intersection. A chord of a circle is a segment whose endpoint lies on an arc.  

Using the secant rule:

ZW × WT = ZU × UV

Substituting for ZT and ZV, you have

ZW × (ZW + WT) = ZU × (ZU + UV)

ZW² + ZW×WT = ZU² + ZU×UV

Substituting ZW for ZU everywhere, we have

ZW² + ZW×WT = ZW² + ZW×UV

Dividing by ZW gives

ZW + WT = ZW + UV

and subtracting ZW leads us to the conclusion

WT = UV

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You need to multiply by 5 instead of 6 because each pair of opposite faces on a cuboid has the same area, so by considering one face from each pair, you ensure that you don't count any face twice.

When calculating the total surface area of a cuboid, you need to understand the concept of face pairs.

A cuboid has six faces, but each face has a pair that is identical in size and shape.

Let's break down the reasoning behind multiplying by 5 instead of 6 in the given scenario.

To find the surface area of a cuboid, you can add up the areas of all its faces.

However, each pair of opposite faces has the same area, so you avoid double-counting by only considering one face from each pair. In this case, you have five pairs of faces:

(1) top and bottom, (2) front and back, (3) left and right, (4) left and back, and (5) right and front.

By multiplying the average area of a pair of faces by 5, you account for all the distinct face pairs.

Essentially, you are considering one face from each pair and then summing their areas.

Since all the pairs have the same area, multiplying the average area by 5 gives you the total surface area.

When dividing 150 by 4 (to find the average area of a pair of faces), you are essentially finding the area of a single face.

Then, by multiplying this average area by 5, you ensure that you account for all five pairs of faces, providing the total surface area of the cuboid.

Thus, multiplying by 5 is necessary to correctly calculate the total surface area of the cuboid by accounting for the face pairs while avoiding double-counting.

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Answer:

AE = 12 units

Step-by-step explanation:

ce is the same unit as AE

Answer:

C: 12 units

Step-by-step explanation:

We substitute -1+1/6y for x in the second equation (bottom equation) in order to solve the system by the substitution method.

The given system of equations are 2x-1/3y = -2...(1)

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

We solve this system of equations by using substitution method.

Let us solve for x in equation to substitute it in equation (2).

2x=-2+1/3y

Divide both sides of equation by 2.

x=-1+1/6y

Now plug in the value of x in equation 2.

Hence, we substitute -1+1/6y for x in the second equation (bottom equation) in order to solve the system by the substitution method.

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Answer:

-0.33333333333 in other word it o.3 with line over 3

Step-by-step explanation:

Tim's last year performance = 57 + (40% of 57) = 57+(0.40x57)=57+22.8 =79.8 approximately 80 performance.

In a case whereby a boat travels with velocity vector (25, 25√3) the directional bearing of the boat is ON 30° E.

The given velocity vector are; 25 and  25√3)

horizontal  components =25

vertical components =25√3

Then the angle

Tan(θ) = {vertical component / horizontal component }

= 25√3 / 25

= √3 / 1

= √3

Tangent √3= 60 degrees, Then the directional bearing of angle 60 degrees is 30° E

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start by graphing y=7

after this we can see that the slope of the line must be 0

since it has to be parallel the other line must have the slope slope 0 too.

this is because it is a completely horizontal line

since the y point of the coordinate is -10, the equation of the line must be

y=-10

Answer:

$20

Step-by-step explanation:

First you have to find how much for the least amount of money. So divide to get 9 and $4, which is the least. Now we multiply them by 5 to get 45 cards and $20. So the answer is $20

Answer:

1

Step-by-step explanation:

1 that is to the power of 0 is 1

Galaxy distance is 118 mpc.

Given:

Suppose a distant galaxy has a recessional velocity of 8254 km/s. What is its distance given that the hubble constant is 70 km/s/mpc.

According to hubble's law:

v = \(H_0\\\) * D

where

v = velocity = 8254

\(H_0\\\) = hubble constant = 70

D = v/\(H_0\\\)

= 8254/70

= 4127/35

= 117.91

≈ 118 mpc.

Therefore Galaxy distance is 118 mpc.

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Answer:

If using the exact value of pi: 50.27 in

If using 3.14 for pi: 50.24 in

Step-by-step explanation:

I full circle around is the circumference of that wheel.

Circumference = 2πr

If you are using 3.14 for pi, it's 50.24

-Chetan K

Therefore , the solution of the given problem of expressions comes out to be it is 4 units between locations C and D.

Calculations like arbitrary division, joining, multiplication variable and removal are required. If they were merged, they would produce the following: A mathematical formula, some data, and an equation. A declaration of veracity is made up of values, elements, formulae, and mathematical operations like additions, subtractions, errors, and segments. It is possible to assess and analyse words and sentences.

Here,

We can apply the distance calculation to determine the separation between two points:

=> distance=  √((x2 - x1)² + y2 - y1)²)

where the coordinates for the two points are (x1, y1) and (x2, y2).

This formula allows us to determine the separation between points

C (6, -4) and D (6, -8) as follows:

=> distance = √[(6 - 6)^2 + (-8 - (-4))^2]

=> distance = √[0^2 + (-4)^2]

=> distance = √[16]

=> distance = 4

As a result, it is 4 units between locations C and D. Both of the available answer options are incorrect.

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Answer:

A.

Step-by-step explanation:

Give the data set: 2, 4, 6, 8, 10, 12.

Find the following:

Min, Q1, Median, Q3, and Max.

Min. = 2

Q1 = 4

Median = (6+8)/2 = 7

Q3 = 10

Max = 12

Check the box plot to see which one represents these values above.

Thus:

The correct box plot would have the whisker to your left at 2, representing the min value.

The Q1 would be at represented by the beginning box the edge of the rectangular box that starts at 4.

The median would be represented by the vertical line that divides the box which would be on 7.

The Q3 would be on the end of the box which is at 10.

The max would be represented by the other whisker that goes to our right, representing 12.

The box plot is that represents this data is the box plot given in option A.

Answer:

x=34

Step-by-step explanation:

Use pythaogrean therom to find the answer. a^2+b^2=c^2 With that in mind, the answer 16^2+30^2=1156. To get the exact answer, you'll have to square root the 1156 to get 34. If you want to check you answer, take the 34 and square it then subtract it by one of the numbers it gives you.

Answer:

It will take 20 minutes to pump out 1000 unit milk tank

Step-by-step explanation:

The pump on the milk tank pumps milk out at a rate of 50 units per minute,

1 minute = 50 units

x minutes = 1000 units

Using the  unitary method x= = 1000*1/50=  20 minutes

It will take 20 minutes to pump out 1000 unit milk tank

Answer:

76

Step-by-step explanation:

10+9= 19

19*4=76

Answer:

76

Step-by-step explanation:

1 Simplify  10+910+9  to  1919.

4\times 19

4×19

2 Simplify.

76

76

Answer:

D. similar

Step-by-step explanation:

similar but not congruent to one another.

A pyramid has cross-sectional shapes, taken parallel to its base, that are similar to one another.

Therefore, A pyramid has cross-sectional shapes, taken parallel to its base, that are similar to one another.

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Answer:

y = x + 60

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (20, 80) and (x₂, y₂ ) = (40, 100) ← 2 points on the line

m = \(\frac{100-80}{40-20}\) = \(\frac{20}{20}\) = 1

the line crosses the y- axis at (0, 60 ) ⇒ c = 60

y = x + 60 ← equation of line

Answer: \(x=0, -\frac{3}{2}\)

Step-by-step explanation:

\(4x^2 +6x=0\\\\2x(2x+3)=0\\\\2x=0, 2x+3=0\\\\x=0, -\frac{3}{2}\)

Answer:

What is wrong is that the combinations were not used. It has to be used because of the different ordering that the customers may be chosen. The correct answer is 0.333

Step-by-step explanation:

For each custoer, there are only two possible outcomes. Either they are confortable with drones delivering their purchases, or they are not. Customers are independent. So the binomial distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

And p is the probability of X happening.

38​% of consumers are comfortable having drones deliver their purchases.

This means that \(p = 0.38\)

Four consumers are randomly​ selected

This means that \(n = 4\)

Probability that exactly two of them are comfortable with the drones

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 2) = C_{4,2}.(0.38)^{2}.(0.62)^{2} = 6*(0.38)*(0.38)*(0.62)*(0.62) = 0.3330\)

What is wrong is that the combinations were not used. It has to be used because of the different ordering that the customers may be chosen.

Answer:

Below in bold.

Step-by-step explanation:

x + y = 33      where x = 10 cent coin and y = 20 cent coin

10x + 20y = 460

Multiply first equation by 10:

10x + 10y = 330

Subtract this from the second equation:

10y = 130

y = 13

So there are 13 20c coins

and 33 - 13 = 20 10c coins.

Answer:

To find the mean waiting time, you need to add up all the waiting times and divide by the number of customers. In this case, the total waiting time is 6.8 + 7.5 + 7.2 = 21.5 minutes. Since there are 3 customers, the mean waiting time is 21.5 / 3 = 7.17 minutes. Rounded to one decimal place, the mean waiting time is 7.2 minutes.

Step-by-step explanation:

The approximate surface area of the package is approximately 245.05 square inches.

The best model for the package is a cylinder.

To calculate the approximate surface area of the package, we need to find the lateral surface area of the cylinder and the area of the circular base.

The lateral surface area of a cylinder can be calculated using the formula:

Lateral Surface Area = 2πrh

where r is the radius of the base and h is the height.

The area of the circular base can be calculated using the formula:

Area of Base = \(πr^2\)

Given that the diameter of the bottom is 9 inches, the radius (r) would be half of that, which is 4.5 inches.

Using the given height of 13 inches, we can now calculate the surface area:

Lateral Surface Area = 2πrh = 2π(4.5)(13) ≈ 117.81 square inches

Area of Base = \(πr^2 = π(4.5)^2 ≈ 63.62\) square inches

To find the total surface area, we add the lateral surface area and the area of the base:

Total Surface Area = Lateral Surface Area + 2 × Area of Base = 117.81 + (2 × 63.62) ≈ 245.05 square inches

Therefore, the approximate surface area of the package is approximately 245.05 square inches.

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