Last month Tara worked 16.5 hours the first week, 19 hours the second week, 23 hours the third week and 15.75 hours the fourth week. She plans to work more hours this month then last month

The Null spaces in matrix b is [tex]\left[\begin{array}{ccc}-2\\1\\0\\0\end{array}\right][/tex] , [tex]\left[\begin{array}{ccc}3\\0\\1\\0\end{array}\right][/tex]

The Null spaces for matrix C is [tex]\left[\begin{array}{ccc}0\\0\\0\end{array}\right][/tex]

For Null spaces we form an augmented matrix by appending a column of zeros to the right, and then put this matrix in reduced row-echelon form.

We convert the matrix equation back to an equivalent system. Add an equation for each free variable. Solve for each variable in terms of the free variables.

Then we collect terms into vectors and after that factor out variables on the right side. Thus, a basis for the null space is calculated. Detailed solution in the image.

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Answer:

sinΘ = [tex]\frac{4}{5}[/tex]

Step-by-step explanation:

given the point (3, 4 )

the x- coordinate indicates the horizontal length of the triangle, that is 3

the y- coordinate indicates the vertical length of the triangle, that is 4

the triangle is right and is a 3- 4- 5  , hypotenuse is 5

then

sinΘ = [tex]\frac{vertical}{hypotenuse}[/tex] = [tex]\frac{4}{5}[/tex]

Answer:

Option B

Step-by-step explanation:

Remember these facts about the following options:

An acute angle is less than 90 degrees.
A right angle is exactly 90 degrees.
A straight angle is more or less a straight line.
An obtuse angle is an angle greater than 90 degrees.

One of the most notable factors of a right angle is the fact that it takes the shape of an L, speaking of how the photo given takes the shape of an L we can immediately exclude options A, B, and D and say option B or
"right" is our answer.

Hope this helps.

Answer:

-40.6

Step-by-step explanation:

The area of the triangle is equal to 36 square units.

In this question we find a triangle whose base (b), in units, is parallel to x-axis and whose height (h), in units, is parallel to y-axis. The area formula for the triangle is shown below:

A = 0.5 · b · h

Where A is the area of th triangle, in square units.

If we know that b = 9 and h = 8, then the area of the triangle shown in the image is:

A = 0.5 · 9 · 8

A = 36

The triangle has an area of 36 square units. (Correct choice: B)

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Answer:

A

Step-by-step explanation:

what is even going on at A

The length of segment BD on the triangle is given as follows:

BD = 12.5 units.

The theorem used to solve this problem is given as follows:

A line parallel to one side of a triangle divides the other two proportionately.

The parallel lines in this problem are given as follows:

BC and DE.

Then the proportional segments are given as follows:

AB and AC.

Thus the proportional relationship that relates these side lengths is given as follows:

(x - 2)/3 = (x + 3)/5.

Applying cross multiplication, the value of x is obtained as follows:

3x + 9 = 5x - 10

2x = 19

x = 19/2

x = 9.5.

Then the length of BD is obtained as follows:

BD = x + 3 = 9.5 + 3 = 12.5.

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Answer:

It could take up less space and be more convenient.

Answer:

none

Step-by-step explanation:

the advantage depends

The area of the rectangle is [tex]60x^{7y^{9} }[/tex] whoe ide are 12x to the power of 6 y quared and 5xy to the power of 7.

What is rectangle ?

A rectangle is a type of quadrilateral that has its parallel sides equal to each other and all the four vertices are equal to 90 degrees. Hence, it is also called an equiangular quadrilateral. Since, the opposite sides are equal and parallel, in rectangle, therefore, it can also be termed as a parallelogram.

The area of a rectangle is found by multiplying its length by its width. In this case, the length is given as [tex]12x^{6y^{2} }[/tex]and the width is given as [tex]5xy^{7}[/tex]. To find the area, we simply multiply these two values together:

Area = ([tex]12x^{6y^{2} }[/tex]) * ([tex]5xy^{7}[/tex]) = [tex]60x^{7y^{9} }[/tex]

So the area of the rectangle is [tex]60x^{7y^{9} }[/tex]  whoe ide are 12x to the power of 6 y quared and 5xy to the power of 7.

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In this function, y = x + 6, the points at x = -2 will be solid and in this function y = 1, there will be a circle at x = - 2. And the correct graph is given below.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The function is given below.

y = x + 6,  x ≤ -2

y = 1, x > - 2

In this function, y = x + 6, the points at x = -2 will be solid and in this function y = 1, there will be a circle at x = - 2.

And the correct graph is given below.

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Answer:

use y=mx+b. ... ...... ...

The first four terms of the sequence are:

a1 = 2

a2 = 2 - 3 = -1

a3 = -1 - 3 = -4

a4 = -4 - 3 = -7

The sequence defined by the rule an = 2, if n = 1; an-1-3, if n > 1, starts with the first term being 2. For all subsequent terms, the value of the previous term is subtracted by 3. Therefore, the second term of the sequence is -1 (2-3), the third term is -4 (-1-3) and fourth term is -7 (-4-3). This pattern of subtracting 3 from the previous term will continue for all subsequent terms in the sequence. The sequence can be represented by the function an = 2 - 3(n-1) for any natural number n.

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Explanation:

The sequence appears to be geometric. Let's test that claim out.

Divide each term by the previous term.

Each time we get the result 0.2, which is the common ratio r. It tells us this sequence is indeed geometric.

To get the next term in a geometric sequence, we multiply the last term 2500 by this common ratio.

Follow similar steps for terms 6 through 8.

Terms 5 through 8 are 500, 100, 20, and 4 in that order.

Ratnam will have to pay Rs. (x+50y) to the agency for a journey of 50 kilometers.

A word problem is a few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.

Given that, Ratnam hired a car from a car renting agency which charges a flat amount of Rs. x for travelling up to 40 kilometers and Rs. y per km for every kilometer travelled thereafter.

We need to find how much should Ratnam pay the agency for a journey of 50 kilometers,

The amount for travelling a km is Rs. y

Therefore, for 50 km it will cost = 50y

Since, they are charging Rs. x as a flat amount,

Therefore, the total cost of travelling 50 km is = x+50y

Hence, Ratnam will have to pay Rs. (x+50y) to the agency for a journey of 50 kilometers.

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X should be subtracted from the product of X and 2 to obtain X, this can be represented as 2X - X = X, This operation is the inverse of addition, therefore it undoes the addition of X to 2X, resulting in the original number X.

To obtain the equation X from the product of X and 2, you would need to subtract X from the product. In other words, you would need to subtract the factor X from the product.

X × 2 - X = X

This can be simplified as

2X - X = X

So, X should be subtracted from the product of X and 2 to get X.

It is important to note that this is only true when X is not equal to zero, because if X is zero, any number multiplied by zero will give zero, and subtracting zero from zero will not give zero.

It can be seen that the operation of subtraction is the inverse of addition, therefore if you subtract X from 2X, you are essentially undoing the addition of X to 2X, which gives the original number X.

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Answer:

$1500

$3000

Step-by-step explanation:

let x = # of hours

$500 + ($50/hr)(20 hr) = $1500

$500 + ($50/hr)($50 hr) = $3000

Carthik weighs 225 grams, and the mean weight of the mice is 238g.

An equation is a expression that shows the relationship between numbers and variables.

Given that Dorothy weighs 152 g. Let x represent the weight of Amin, y represent that of Brenda and z represent Carthik.

Amin weighs twice as much as Carthik, hence:

x = 2z

x - 2z = 0    (1)

Brenda weighs 100g less than Carthik, hence:

y = z - 100

y - z = -100    (2)

The mean weight of the mice is 238g. hence:

(x + y + z + 152)/4 = 238

x + y + z = 800    (3)

Solving the 3 equations by elimination gives:

x = 450, y = 125 and z = 225

Carthik weighs 225 grams

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The image of the point (-9, -6) after a rotation of 90 degrees counterclockwise about the origin is (6, -9).

A point in a 2D plane can be represented by its coordinates (x, y).

A rotation of 90 degrees counterclockwise about the origin can be represented by the transformation matrix:

[cos(90) -sin(90)]

[sin(90) cos(90)]

When we apply this transformation matrix to the point (-9, -6), we get the following:

[cos(90) -sin(90)][-9] = [0 * -9 + (-1) * -6] = 6

[sin(90) cos(90)][-6] = [1 * -9 + 0 * -6] = -9

Therefore, the image of the point (-9, -6) after a rotation of 90 degrees counterclockwise about the origin is (6, -9).

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The equation  (√x^2+81 = x+10 ) is equivalent to D: ( x^2 + 81 = x^2 + 20x + 100).

To prove that ( √x^2+81 = x+10  )is equivalent to ( x^2 + 81 = x^2 + 20x + 100 ), we will show that one equation is a consequence of the other.

First, we begin by squaring both sides of the equation ( √x^2+81 = x+10 ). This gives us ( x^2+81 = x^2+20x+100 ).

We can see that if ( √x^2+81 = x+10 ) is true, then  (x^2 + 81 = x^2 + 20x + 100)  must also be true because the left side of the equation is the square of the right side.

The other way around, if ( x^2 + 81 = x^2 + 20x + 100 ) is true, then we can take the square root of both sides and get  (√x^2+81 = x+10 ).

So, the equation ( √x^2+81 = x+10 ) is equivalent to ( x^2 + 81 = x^2 + 20x + 100).

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Charlotte and her sister enjoyed a special dinner in a restaurant, and the bill was $53.86. 11.99%  tip did she leave.

Percent tip she give:

[tex]\frac{6.46}{53.86}[/tex] × 100

= 11.99 %

A percentage, or percent, is a number smaller than or equal to 100. The term "per 100" refers to a percentage of a total amount. 45 percent, for instance, is 45 out of 100. Finding the share of a whole in terms of 100 is what percentage means. You can use online calculators or manually calculate it.

Percentages are utilized extensively and in numerous contexts. Discounts in stores, interest rates at banks, inflation rates, and numerous media statistics are all expressed as percentages. Understanding the financial aspects of everyday life requires knowledge of percentages.

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The name of the triangle whose all sides are of different measures is Scalene triangle

A scalene triangle is a triangle with three different side lengths and three different angle measurements. The total of all internal angles, however, is always equal to 180 degrees.

One of the three kinds of triangles that are categorized according to their sides is the scalene triangle. The isosceles triangle and the equilateral triangle are the other triangles depending on their sides. A triangle with scalene sides is one with distinct lengths on each side.

The following are a few of the scalene triangle's key characteristics:

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The name of the triangle whose all sides are of different measures is Scalene triangle

A scalene triangle is a triangle with three different side lengths and three different angle measurements. The total of all internal angles, however, is always equal to 180 degrees.

One of the three kinds of triangles that are categorized according to their sides is the scalene triangle. The isosceles triangle and the equilateral triangle are the other triangles depending on their sides. A triangle with scalene sides is one with distinct lengths on each side.

The following are a few of the scalene triangle's key characteristics:

Obtuse, acute, or right triangles are all examples of scalene triangles.

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What will be order of steps in solution?

let x = the possible number of wood pieces

24x ≤ 72

24x/24 ≤ 72/24

x ≤ 3 wood pieces

Answer:

4.  x ≤ 3 wood pieces

[tex]\textsf{3.} \quad \dfrac{24x}{24}=\dfrac{72}{24}[/tex]

2.  24x ≤ 72

1.  Let x = the possible number of wood pieces

Step-by-step explanation:

Step 1

Define the variable:

Step 2

Given that the wood the Carpenter bought is 72 inches long and he needs to cut it into pieces that are 24 inches long:

Step 3

To find the possible number of pieces the Carpenter can cut, divide both sides of the equation by 24:

Step 4

Simplify both sides of the equation:

Using Pythagorean theorem, The height of the tree is approximately 47.98 feet.

According to Pythagoras' Theorem, the square of a right-angled triangle's hypotenuse side is equal to the sum of the squares of its other two sides. The three sides of this triangle are known as the Perpendicular, Base, and Hypotenuse.

tan(angle) = opposite side / adjacent side

The opposite side is the height of the tree and the adjacent side is the distance from Jerome to the base of the tree (90 feet).

tan(33) = height / 90

height = tan(33) * 90

The height of the tree is approximately 47.98 feet.

Keep in mind this is an approximation as the angle in question is not a right angle and also the unit is not given so the final result is not accurate.

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When the incident rays appear from a given object, then it is known as a real object. farther, the light rays emanating from the real object after reflection from the mirror, meet at a definite point, then the optically formed duplication of an object is known as an image.

There are two types of images are formed they are real image and virtual image. The real image indicates the representation of an actual object, produced when the light rays arising from a single source intersect at a particular (real) point.

On the opposite, the virtual image can be understood as the image produced due to the apparent separation of rays of light from a definite point.

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Answer:

To solve for x, you can start by moving the constant 2 to the other side of the equation by adding x to both sides:

x^2 - x = 2

x^2 - x + (1/4) = 2 + (1/4)

(x - 1/2)^2 = 9/4

x - 1/2 = +- (3/2)

x = -1/2 or x = 2

So the solutions for x are -1/2 and 2.

A sequence of the form a, a + d, a + 2d, a + 3d, a + 4d, etc. is an arithmetic sequence. The common difference of the sequence is d, and the number an is the first term. An arithmetic sequence's nth term is determined by the formula a = a + (n - 1)d.

Bracket, Of, Division, Multiplication, Addition, and Subtraction is referred to as BODMAS. A mathematical expression's order of operation is explained using the BODMAS. The acronym PEDMAS, which stands for Parentheses, Exponents, Division, Multiplication, Addition, and Subtraction, is sometimes used to refer to the BODMAS.

A geometric sequence is a set of numbers that follows a pattern in which the following term is determined by multiplying the previous one by a factor known as the common ratio, or r.

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Answer: i dont kow

Step-by-step explanation:

Latitudes and longitudes help in locating a point by providing a reference system for navigation.

They are used to pinpoint a specific location on the earth’s surface by providing coordinates. These coordinates are measured in degrees and minutes and are written in the form of a pair of numbers. Latitudes are measured in degrees north or south of the equator and are referred to as the lines of latitude. Longitudes are measured in degrees east or west of the prime meridian and are referred to as the lines of longitude. By using the coordinates of a point, the location can be accurately determined. This is especially useful for navigation, as it enables people to determine their position and travel to a specific destination.

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The permutation and combination C(n ,r) of

C(7,5) = 21.

Permutation

Permutation is the arrangement of objects, some or all of which are acquired at the same time, in a particular order. Consider ten numbers: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. The number of different 4-digit PINs that can be formed from these 10 digits is 5040. P(10, 4) = 5040. This is a simple example of permutation. The permutation of 4 numbers out of 10 is equal to the factorial of 10 divided by the factorial of the difference between 10 and 4.

Combinations

Combinations are about grouping. Combinations can be used to calculate how many different groups can be formed from existing ones. Let's try to understand this with a simple example. Five students (William, James, Noah, Logan and Oliver) form teams of two.

According to the question:

C (n, r) = C( 7,5)

⇒ 7!/ 5! × 2!

⇒ 7 × 6 ×5!/ 5! × 2 ×1

⇒ 21.

Therefore, C(n ,r) = 21

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