PLEASE BE FAST :')
Determine whether the ordered pair is a solution to the given system of equations.
1) (1,5); -5m + 6n = 25 -7m +8n=33
2) (-2, 0); 8x-3y=-16 50= -9x - 2y​

The total number of cupcakes needed will be 3 cupcakes.

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 situation, in a simple fraction, the numerator as well as the denominator are both integers.

Since you 5 halves of a cupcake for my family plus some extra for my 2 friends, the total number of cupcakes needed will be:

= 5 ( 1 /2) + 2 ( 1 / 4)

= 2 1/2 + 1/2

= 3

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Complete question

Id like to order 5 halves of a cupcake for my family plus some extra for my 2 friends. They'll each like a quarter of a cupcake. What is the total cupcakes needed?

Answer:

[tex] \frac{p}{5} \times 8 = \frac{8p}{5} [/tex]

Answer:

Solution to the question of figure : c

Step-by-step explanation:

The speed of a car is 0.61 kilometer per hour.

The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.

From the figure, time =1.68 minutes and distance =17 meter

Now, in kilometer per hour is

Here, speed = Distance/Time

= 17 meter/1.68 minute

= 0.017 km/0.028 hours

= 0.017/0.028

= 0.61 kilometer per hour

Therefore, the speed is 0.61 kilometer per hour.

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We can find a matrix P such that PTAP orthogonally diagonalizes A, and the diagonal entries of PTAP are the eigenvalues of A, verifying that the diagonal form of A is correct.

We can orthogonally diagonalize a matrix A by finding a matrix P such that PTAP is orthogonal. An orthogonal matrix is a matrix whose columns are orthogonal unit vectors. This means that the dot product of any two columns is 0.

Let's calculate the matrix P to orthogonally diagonalize A. We will use the Gram-Schmidt process to calculate the orthonormal vectors for the columns of P.

Let v1 = (7,1) be the first column vector of A. We will use this vector to calculate the first column of P. We normalize v1 and get an orthonormal vector u1 = (7/sqrt(50), 1/sqrt(50)). We set the first column of P to be u1.

For the second column, we take the second column vector of A and subtract its projection on u1. This gives us a new vector v2 = (7, -6). We normalize v2 and get an orthonormal vector u2 = (7/sqrt(73), -6/sqrt(73)). We set the second column of P to be u2.

Now, we have the matrix P = [[7/sqrt(50), 7/sqrt(73)], [1/sqrt(50), -6/sqrt(73)]]. We can verify that the dot product of the columns of P is 0, which shows that P is an orthogonal matrix.

We can now calculate the product PTAP. We get PTAP = [[7^2/50+7^2/73, 7*7/50-6*7/73], [7*7/50-6*7/73, 7^2/50+6^2/73]]. We can see from this matrix that the diagonal entries are equal to the eigenvalues of A, which were 7 and 1. This shows that PTAP is a diagonal matrix which orthogonally diagonalizes A.

We can find a matrix P such that PTAP orthogonally diagonalizes A, and the diagonal entries of PTAP are the eigenvalues of A, verifying that the diagonal form of A is correct.

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An expression that shows the total pounds of apples Garrett bought in all include the following: D. 4 + g.

In order to write an equation that model this situation, we would assign a variable to the total pounds of green apples and the total pounds of red apples respectively, and then translate the word problem into algebraic equation as follows:

Since Garrett bought 4 pounds of red apples and g pounds of green apples, an equation that models the total pounds of apples that he bought is given by:

Total pounds of apples = r + g

Total pounds of apples = 4 + g

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BBI's bonds after the increase given the rise in basis points, would be 6. 54 %

Basis points (bps) are a unit of measurement used to express the change in the value of a financial instrument, such as a bond or stock, or the difference in interest rates or yields. One basis point is equal to 0.01% (1/100th of 1%) and is used to express small changes in the value of a financial instrument.

A rise by 52 basis points would lead to BBI's bond YTM being:

= 6. 02 + 0.52

= 6. 54 %

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Answer:

84

Step-by-step explanation:

540 is the sum of angle of a pentagon.

we get the equation,

X + 110 +131 +108 + 107 = 540

X = 540 - 456

X = 84

The solution results in Jay spending all his money to buy 4 items is (3, 1)

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

Signed baseballs = x

Signed miniature bats = y

Using the above as a guide, we have the following:

2x + 6y <= 12

x + y <= 4

Next, we graph the system (see attachment)

The solution results in Jay spending all his money to buy 4 items is (3, 1)

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The first box is satisfied by  3 1/4

The second box is satisfied by 3 1/3

A fraction is a mathematical expression that represents a part of a whole or a ratio of two numbers. It consists of two parts: the numerator and the denominator.

The numerator represents the number of parts being considered, and the denominator represents the total number of parts in the whole. If we work on the boxes that we can see in the question then we end up with the values as shown above.

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Answer:

Since there are 54 cards in a standard deck, and only 1 ace of hearts:

You would have 1/54 of a chance of drawing the ace of hearts.

You would also have 1.85% of a chance drawing the ace of hearts.

Step-by-step explanation:

Hope it helps! =D

Answer:

5

Step-by-step explanation:

subtract: 34-4=30.

divide: 30/6=5

Based on the given values,  the unknown number is 5.

Let's use algebra to solve the problem.

Let's call the unknown number "x".

We know that when this number is multiplied by 6 and 4 is added, the result is 34:

6x + 4 = 34

Solve for x by isolating it on one side of the equation.

First,  simplify the left side of the equation by subtracting 4 from both sides:

6x = 30

Then, solve for x by dividing both sides by 6:

x = 5

Therefore, the unknown number is 5.

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Using Pythagoras theorem, The missing side of the right triangle is 4,9 mm long.

Pythagoras' Theorem states that the square of the hypotenuse side in a right-angled triangle is equal to the sum of the squares of the other two sides. The Perpendicular, Base, and Hypotenuse are the names of the three sides of this triangle. The hypotenuse in this example is the longest side because it is located across from the 90° angle. A right triangle's positive integer sides (let's say sides a, b, and c) are squared to produce a Pythagorean triple equation.

Right triangles are what the provided triangle is.

The Pythagorean Theorem is used:

[tex]a^{2} + b^{2} = c^{2}[/tex]

[tex](5)^{2} + (7)^{2} = c^{2}[/tex]

25 + 49 =[tex]c^{2}[/tex]

c = 4.9

Hence, the missing side of the right triangle is 4,9 mm long.

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The banner should be 56 feet long to fit the garage door.

The perimeter of a rectangle is the total length of all the sides of the rectangle.

P = 2 (L + B)

P = perimeter of rectangle, L = Length of rectangle, B = Breadth of rectangle

Given length of garage door = 12 feet

Given breadth of garage door = 16 feet

P = 2 (L + B)

P = 2 ( 12 + 16)

P = 2 (28)

P = 56 feet

Hence, The total length of the banner should be 56 feet to cover the entire door.

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After much testing, John comes up with a "law" that states that the light wavelengths absorbed as hydrogen gas follow a pattern that can be expressed mathematically.

When hydrogen gas is placed in the discharge tube as well as the light released on the passing electrical discharges at low pressure is inspected using a spectroscope.

Thus, John comes up with a "law" that states that the light wavelengths absorbed as hydrogen gas follow a pattern that can be expressed mathematically.

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The correct question is-

after much experimentation, john discovers a _____ which says that the wavelengths of light absorbed by hydrogen gas fit into a pattern which he is able to express in a mathematical formula.

Multiply a number by 2 and then find the product of the number obtained with 3 is the statement required

An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.). Expressions are made up of terms.

Given here: The equation 3(2x)=6x

Clearly here the associative property of multiplication is used above

First, a number x is multiplied by 2

Then the number obtained above i.e 2x is multiplied again by 3

Thus the word problem can be of the form

Multiply a number by 2 and then find the product of the number obtained with 3

Hence, Multiply a number by 2 and then find the product of the number obtained with 3 is the statement required

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Answer:

Step-by-step explanation:

Answer:

8 2/3

Step-by-step explanation:

Since she has 1/3 already, we need more. So here, we SUBRACT.

Subtract 9 with 1/3.

You'll get 8 2/3

The measures of the two complementary angles are 44° and 132°.

Given that the difference between the measures of two complementary angles of any given triangle is 88°, it means that one angle is 88° smaller than the other. To find the measures of the two angles, divide the sum of the difference by 2. That is given as, (88°/2) = 44°. One angle is given as  44°, and the other angle is equal to the sum of the two angles in a triangle, which is 180°, minus the first angle, which is 44°, which is equal to 136°.

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The graph of the given equation are attached below.

A graph contains data of which input maps to which output.

Analysis of this leads to the relations which were used to make it.

For example, if the graph of a function is rising upwards after a certain value of x, then the function must be having increasingly output for inputs greater than that value of x.

If we know that the function crosses x axis at some point, then for polynomial functions, we have those as roots of the polynomial.

We are given the equation as;

3x - 4y = 8

3=y

From 3x – 4y = 8  

⇒ -4y  = -3x + 8

y =  (3/4x) + -2

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Answer:f(0) = sin (0), g(0) = cos (0). Find the exact value of the function g(0) if 0 = 45°.

f(0) = sin (0), g(0) = cos (0). Find the exact value of the function g(0) if 0 = 45°.

Step-by-step explanation:f(0) = sin (0), g(0) = cos (0). Find the exact value of the function g(0) if 0 = 45°.

f(0) = sin (0), g(0) = cos (0). Find the exact value of the function g(0) if 0 = 45°.f(0) = sin (0), g(0) = cos (0). Find the exact value of the function g(0) if 0 = 45°.f(0) = sin (0), g(0) = cos (0). Find the exact value of the function g(0) if 0 = 45°.f(0) = sin (0), g(0) = cos (0). Find the exact value of the function g(0) if 0 = 45°.f(0) = sin (0), g(0) = cos (0). Find the exact value of the function g(0) if 0 = 45°.f(0) = sin (0), g(0) = cos (0). Find the exact value of the function g(0) if 0 = 45°.f(0) = sin (0), g(0) = cos (0). Find the exact value of the function g(0) if 0 = 45°.f(0) = sin (0), g(0) = cos (0). Find the exact value of the function g(0) if 0 = 45°.

The total weight exerted on the floor of the silo is 138,973,475 lbs

The volume of the cylindrical silo is given by the formula:

V = πr^2h

where r is the radius, h is the height and π (Pi) is approximately 3.14.

First, find the radius:

r = D/2 = 90ft / 2 = 45ft

Next, find the volume:

V = π * 45^2 * 275 = 31,875 * 3.14 * 275 = 2836275 cubic feet

Finally, calculate the weight of the grain:

W = V * w_grain/ft^3 = 2836275 * 49lbs/ft^3 = 138,973,475 lbs

This is the total weight exerted on the floor of the silo.

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The exact surface area of the cone is 113.097 units².

The area of a three dimensional object on it's outer surface is called the surface area of the object.

Base of a cone is circle.

Base area = π r²

                 = π (4)² = 16π

Lateral surface area = π r √(h² + r²)

                                  = 4π √(3² + 4²)

                                  = 4π √25

                                  = 4π × 5

                                  = 20π

Total surface area = 16π + 20π

                              = 36π

                              = 113.097 units²

Hence the total surface area of the given cone is 113.097 units².

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The capacity of the two containers can be measured with a jar with a maximum capacity of 20 litres.

In this problem we find the case of two containers with different capacity, one with a capacity of 40 litres and other with a capacity of 60 litres, we can measure each of them based on the number of adds needed to fill each container. The number of adds (n) is equal to the container capacity (C), in litres, divided by the jar capacity (c), in litres:

n = C / c

If we assume that the number of adds is a natural numbers, then we determine the greatest common factor of both container capacities. First, decompose each number related to each container:

40 = 2³ × 5

60 = 2² × 3 × 5

Second, find the common factors and create the resulting product:

G.C.F. = 2² × 5

G.C.F. = 20

A jar with a maximum capacity of 20 litres can be used to measure the capacity of both containers.

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The equivalent form of the given polynomials are A) (x+1) (x-12) B) (x+2) (x-6) C)(x+4) (x-3) D) ( x+2) (x+4)

A quadratic equation can be written in the standard form as ax2 + bx + c = 0, where a, b, c are constants and x is the variable. The values of x that satisfy the equation are called solutions of the equation, and a quadratic equation has at most two solutions.

Given here:  The quadratic equations as

1)

[tex]x^2-11x-12\\x^2-12x+x-12\\x(x-12)+(x-12)\\(x+1)(x-12)[/tex]                  

2)

[tex]x^2-4x-12\\x^2-6x+2x-12\\x(x-6)+2(x-6)\\(x+2) (x-6)[/tex]

3)

[tex]x^2+x-12\\x^2+4x-3x-12\\x(x+4)-3(x+4)\\(x+4) (x-3)[/tex]

4)

[tex]x^2-x-12\\x^2-4x+3x-12\\x(x-4)+2(x-4)\\(x+2) (x+4)[/tex]

Thus the factorization of the polynomials given are given above.

Hence, The factorization of the given polynomials yields the following results.

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Answer:

f(x) =(x+2) (x-6) B

f(x) =(x-4) (x+3) D

f(x) =(x-12) (x+1) A

f(x) =(x-3) (x+4) C

Step-by-step explanation:

edge 2023

Here we have a relation to perform changes of units, we will see that:

1 pound = 0.455 kilograms

We know that one kilogram is 2.2 pounds, and we want find what is the "kilogram per pound".

We can write the relation:

1 kilogram = 2.2 pounds

To get the "kilogram per pound" we need to have a "1" on the right side, so we can divide both sides by 2.2, then we will get:

(1 kg)/2.2 = (2.2 lb)/2.2

0.455 kg = 1lb

This means that one pound is equalto 0.455 kilograms.

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Answer:

13 ft

-----------------------------

Area of the cross-section of the first story is:

Area of the cross-section of the second story is the sum of rectangular and triangular sections:

Since both story's have same cross-section area, we have equation:

The height of the second story is 13 inches.

Area is the amount of space occupied by a two-dimensional figure. In other words, it is the quantity that measures the number of unit squares that cover the surface of a closed figure. The standard unit of area is square units which is generally represented as square inches, square feet, etc.

Given that, the first story has length=30 inches and width=8 inches.

Now, area of the cross-section of the first story is

A = Length×Width

A = 30×8

A = 240 square inches

Area of the cross-section of the second story is the sum of rectangular and triangular sections:

A = Length×Width + 1/2×Base×Height

A = 30×3 + 1/2×30×(h - 3)

A = 90 + 15(h - 3)

A = 90 + 15h - 45

A = 15h + 45

Since both story's have same cross-section area, we have equation:

15h + 45 = 240

15h = 195

h = 195/15

h = 13 inches

Therefore, the height of the second story is 13 inches.

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The 3.13%  interest rate will cause his money to double in approximately 23 years.

The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest. Compound interest is commonly abbreviated C.I. in mathematics.

Given that Arnulfo deposited $55 into a savings account for which interest is compounded semiannually.

According to the rule of 72, we should divide 72 by the interest rate to determine how many years it will take to double our money at a specific interest rate (r).

time is taken to double the money = 72/r,

where r represents the interest rate and time is in years.

As we have been given that it will take approximately 23 years to double Arnulfo's money, so we can set an equation as:

23 = 72/r

r = 72/23

r = 3.13

Hence the interest rate is 3.13%.

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The complete question is,

Arnulfo deposited $55 into a savings account for which interest is compounded semiannually. according to the rule of 72, what interest rate will cause his money to double in approximately 23 years?