A bookcase is 3 feet high and 3 feet wide. Two braces are going to be built to diagonally cross the back of the case. How long is the piece of wood that is needed to build each brace?

Therefore ,the ordered pairs which are the solutions of the system of equations shown in the graph below are (1,-4) and (4,-7).

The term "ordered pair" refers to a pair of two variable that are shown in a way that they convey a specific order.

In an order pair, the first term denotes the x- and second term, the y-coordinates. The ordered pair is written in close brackets as shown in the example below.

Here ,

Is an equation system:

A set of equations is referred to as a system of equations when a limited set of equations is available and a common solution is sought.

The intersection of two lines, for the two equations drawn on a graph, represents the system's solution.

In the given graph, one linear line and one parabola is shown. In this graph the parabola intersect with the line at point (1,-4) and (4,-7).

Therefore ,the ordered pairs which are the solutions of the system of equations shown in the graph below are (1,-4) and (4,-7).

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Answer:

(2x+10°) + (x°) +(2x-20°) = 540°

540 is the sum angle of the polygon

collect like terms

2x+x+2x+10°-20°=540°

5x-10°=540°

5x=540°+10°

5x=550°

x=550°/5

x=110°

(2(110)+10)+(110)+(2(110)-20)=540°

Answer:

2 + m

Step-by-step explanation:

A triangle having an area of 142. 74 ft^2 and a height of 18. 3 ft, has a base of 15.6 ft.

What is the area of a triangle?

In a two-dimensional plane, a triangle's area is the area that it completely encloses. A triangle is a closed shape with three sides and three vertices, as is common knowledge. The entire area occupied by a triangle's three sides is referred to as its area. Half of the product of the triangle's base and height provides the general formula for calculating the area of the triangle.

The area of the triangle is 142.74 ft^2.

The height of the triangle is 18.3 ft.

Let the base of the triangle be x.

The formula for area of a triangle is -

Area = (height × base)/2

Plugging in the values in the equation -

142.74 = (18.3 × x)/2

142.74 = 18.3x/2

18.3x = 285.48

x = 285.48/18.3

x = 15.6

Therefore, the base of the triangle measures 15.6 ft.

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Answer:

To drain the tank to the right level, you need to remove 859 - 635 = <<859-635=224>>224 gallons.

So you need to work for 224 / 56 = <<224/56=4>>4 minutes.

Step-by-step explanation:

The annual salary will be 49750

Gross salary would be the total amount of compensation that an employer or business pays an employee during their employment. The Cost of Company, as well as CTC, on the other hand, would represent the overall compensation of employees. The CTC seems to be an employee's gross pay, but their net compensation is how much they actually take home.

Now, According to the question:

Let x be the annual salary.

Then 10% of x+250 equates 0.1(x+250).

Thus, the bonus equates $5000, then we will get the equation:

0.1(250 + x) = 5000

Solving for 'x' we get:

250 + x = [tex]\frac{5000}{0.1}[/tex]

250 + x = 50000

x = 50000 - 250

x = 49750

CTC and gross salary are sometimes confused. But there is a distinction among the two. Before taxes, Employee Provident Fund (EPF) contributions, and gratuities deducted from the CTC, the amount paid to the employee would be known as their gross salary.

The complete question is this:

__"Ayesha earns a 10% bonus based on her annual salary plus the number of sales she makes. She made 250 and earned a $5,000 bonus last year. Write and solve an equation to find her salary last year__"

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Answer: To solve a division problem of the form a ÷ b = c, you need to find the value of c that makes the equation true. This means that if you multiply b by c, the result should be equal to a.

a) In the problem 3.2 ÷ 0.8 = ?, we are looking for the value of c that makes the equation true.

To solve this problem, we can multiply 0.8 by c to find the value of c that makes the equation true:

0.8 * c = 3.2

Dividing both sides of the equation by 0.8, we get:

c = 4

Therefore, the value of c that makes the equation 3.2 ÷ 0.8 = ? true is 4.

b) In the problem 7.5 ÷ 0.5 = ?, we are looking for the value of c that makes the equation true.

To solve this problem, we can multiply 0.5 by c to find the value of c that makes the equation true:

0.5 * c = 7.5

Dividing both sides of the equation by 0.5, we get:

c = 15

Therefore, the value of c that makes the equation 7.5 ÷ 0.5 = ? true is 15.

P.S. I don't need a brainliest, i am just happy that I am helping someone

Step-by-step explanation:

Therefore , the solution of the given problem of tractable problem comes out to be halting problem claims that no computer can be created that can anticipated.

an algorithm that takes a polynomial amount of time to solve a tractable issue. The upper bound is described by a polynomial. Any issue that cannot be addressed in a polynomial period of time is considered to be intractable. The lowest limit is exponential.

Here,

The halting problem claims that no computer can be created that can anticipated.

the likelihood that any other program will halt after a certain number of steps, making it an unsolved algorithmic challenge.

Software development is directly affected in practice by the stopping problem's insoluble nature.

Therefore , the solution of the given problem of tractable problem comes out to be halting problem claims that no computer can be created that can anticipated.

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Answer:

A. The ratios are both identical (three fifths and three fifths).

Step-by-step explanation:

ratio means fraction

ratio also means division

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"SOHCAHTOA"

sine equals opposite over hypotenuse cosine equals adjacent over hypotenuse tangent equals opposite over adjacent

mathworldwolframcom

sine equals opposite over hypotenuse

sine X equals 3 over 5

cosine equals adjacent over hypotenuse

cosine Y equals adjacent over hypotenuse

cosine Y equals 3 over 5

side thats 3 is adjacent for y but

side thats 3 is also opposite for x

both identical, aka C on their question is right

its the 1st option for flvs

Therefore , the solution to the given problem of time comes out to be the time to pick up by your parents is 7:32.

the idea that time was the fourth dimension and that space and time were therefore inseparably connected. According to his general theory of relativity (opens in new tab), the mass and momentum of adjacent matter influence how much space-time enlarges and compresses.

Here,

Given : The game starts at 18:30

Thus,

They play for eight minutes quarters and half time last for 30 minutes.

So,

To find the time to pick up by your parents:

=> 8*4 + 30

=> 32 + 30

=> 62

Thus time after 62 minutes is 7:32

Therefore , the solution to the given problem of time comes out to be the time to pick up by your parents is 7:32.

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The composite function is the result of first applying the function (x^2 - 1) to the input and then applying the function (5x + 2) to the result. The final result of the composite function is 5x^3 + 2x - 3.

Step 1: Apply (x^2 - 1) to the input:

(x^2 - 1) = x^2 - 1

Step 2: Apply (5x + 2) to the result:

(5x + 2)(x^2 - 1)

= 5x^3 - 5x + 2x - 2

Step 3: Simplify:

5x^3 - 5x + 2x - 2

= 5x^3 + 2x - 3

A composite function is the result of applying two or more functions in succession. The order of operations for a composite function is to first apply the first function, then apply the second function to the result of the first, and so on. In the example given, the composite function

f(x) = (5x + 2) ∘ (x^2 - 1)

is the result of first applying the function

(x^2 - 1)

to the input and then applying the function (5x + 2) to the result. The calculation can be broken down into three steps: Step 1 is to apply (x^2 - 1) to the input to get x^2 - 1, Step 2 is to apply (5x + 2) to the result to get 5x^3 - 5x + 2x - 2,

and Step 3 is to simplify the result to get the final answer of

5x^3 + 2x - 3.

To summarize, the composite function

f(x) = (5x + 2) ∘ (x^2 - 1)

is the result of first applying the function (x^2 - 1) to the input, and then applying the function (5x + 2) to the

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Two graph functions can be compared by analyzing their shape, direction, and relative position.

To compare two graph functions, one must look at the overall shape of the graphs, which can be either linear, quadratic, cubic, or some other shape. The direction of the graph, whether it's increasing or decreasing, should also be considered. The relative position of the graph, including the x and y intercepts, as well as any asymptotes, should also be considered.

Additionally, it's important to examine the domain and range of the function, which are the set of input values and output values that the function can produce, respectively. By comparing these different aspects of the graph, one can determine the similarities and differences between the two functions and draw conclusions about their behavior.

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Answer: 5 x 4/5

Step-by-step explanation:

In each column there is 4/5 shaded . There are 5 columns .

So , 5 x 4/5

Answer:

A) 5 × 4/5

Step-by-step explanation:

The shaded part each column in the model represents what fraction of a mile that Jada rode her bike each day.

There are 5 columns.

Therefore, to determine the total distance in miles that Jada rode over the days, we can multiply the distance that she rode each day by the number of days that she rode that distance (5 days):

A) [tex]5 \textrm{ days} \times \dfrac{4}{5} \textrm{ mile each day}[/tex]

Answer:

The answer is $4.50.

Step-by-step explanation:

To solve this problem, divide the result ($6.75) by the percentage (150%). This gives you the original number which was multiplied by the percentage. So,

$6.75 / 150% = $4.50.

Answer:

$4.50

Step-by-step explanation:

150% × □ = $6.75

First, we can rewrite 150% as the fraction 3/2.

[tex]\dfrac{3}{2} \times \square = \$ 6.75[/tex]

Then, we can also rewrite 6.75 as the fraction 27/4.

[tex]\dfrac{3}{2} \times \square = \$ \, \dfrac{27}{4}[/tex]

Next, we can isolate the unknown by multiplying both sides by 2/3 (the reciprocal of 3/2).

[tex]\left(\dfrac{2}{3} \right)\left(\dfrac{3}{2} \times \square \right) = \left(\$ \, \dfrac{27}{4}\right)\left(\dfrac{2}{3} \right)[/tex]

After that, simplify by multiplying out the numerators and denominators on the right side of the equation.

[tex]\square = \$ \, \dfrac{27 \times 2}{4 \times 3}[/tex]

[tex]\square = \$ \, \dfrac{54}{12}[/tex]

Finally, simplify the expression on the right side to a decimal form.

[tex]\square = \$ \, \dfrac{54 \div 2}{12 \div 2}[/tex]

[tex]\square = \$ \, \dfrac{27 \div 3}{6 \div 3}[/tex]

[tex]\square = \$ \, \dfrac{9}{2}[/tex]

[tex]\square = \$ 4.50[/tex]

Answer:

Don't join the points with lines

Make the numbers on the vertical axis larger

Label the axes

Step-by-step explanation:

Make all the points different colours → I don't think that would be useful. Unless the teacher asked you to in class, it's probably not a good answer.

Put the title on the bottom → Same. Unless the teacher asked you to in class, it's not really useful and probably not a good answer.

Don't join the points with lines → Teachers ask indeed not to do this, so I think it's a good answer. Most of the time they prefer students to use curves (hope it's the good translation).

Make the numbers on the vertical axis larger → Since both axes represent notes, it would be easier to compare with the same scale. If that's what the teacher meant, then I think it's correct.

Label the axes → This one is interesting, because right now we don't what they represent at all.

Hope it helps, good luck for your exercices :)

The numeric value for each trigonometric expression is given as follows:

3. [tex]\sin{\left(-\frac{5\pi}{6}\right)}\cos{\left(\frac{2\pi}{3}\right)} - \cos{(-\pi)} = \frac{5}{4}[/tex]

4. [tex]\frac{\sin{\left(\frac{\pi}{4}\right)}}{\cos^2{\left(\frac{\pi}{3}\right)}} = 2\sqrt{2}[/tex]

The first trigonometric expression for this problem is defined as follows:

[tex]\sin{\left(-\frac{5\pi}{6}\right)}\cos{\left(\frac{2\pi}{3}\right)} - \cos{(-\pi)}[/tex]

The numeric value of each term of the expression is given as follows, using equivalent angles on the trigonometric circle:

Hence:

[tex]\sin{\left(-\frac{5\pi}{6}\right)}\cos{\left(\frac{2\pi}{3}\right)} - \cos{(-\pi)} = \left(-\frac{1}{2}\right)^2 + 1 = \frac{1}[4} + 1 = \frac{5}{4}[/tex]

For item 4, the angles are on the first quadrant, hence:

Hence the numeric value of the expression is given as follows:

[tex]\frac{\frac{\sqrt{2}}{2}}{\left(\frac{1}{2}\right)^2} = 4 \times \frac{\sqrt{2}}{2} = 2\sqrt{2}[/tex]

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Answer:

x ≈ 70.6°

Step-by-step explanation:

using the tangent ratio in the right triangle

tan x = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{17}{6}[/tex] , then

x = [tex]tan^{-1}[/tex] ( [tex]\frac{17}{6}[/tex] ) ≈ 70.6° ( to the nearest tenth )

The value of the expression is -44 and thus does not depend on the value of x

An algebraic expression can be described as a mathematical expression made up of variables, terms, factors, coefficients and constants.

They are also made up of mathematical or arithmetic operations, which includes;

From the information given, we have that;

(x-5)(x+8)-(x+4)(x-1)

expand the bracket

x² + 8x - 5x - 40 - (x² -x + 4x - 4)

x² + 8x - 5x - 40 - x² + x - 4x + 4

collect like terms

3x - 3x - 40 - 4

add or subtract like terms

0 - 44

Hence, the expression does not depend o x

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As a professional artist and judging from the current sales ratio and commission rates, one would earn more if one apprenticed for Sara.

As evident in the task content; the current ratio of Sara's sales to Ravi's sale is 100 : 2.

Since Sara's pieces of art sell for $25, the total earnings is; 25 × 100 = $2500.

Hence, since the commission rate is 60%, it follows that the commission earned on sales of Sara's pieces is; 60% of 2500 = 0.6 × 2500 = $1500.

Also, since Ravi's pieces each cost $2000, it follows that for 2 pieces, the total earnings is; 2 × $2000 = $4,000.

Hence, since the commission rate for Ravi's pieces is 25%, the commission earned is therefore; 25% of 4000 = 0.25 × 4000 = $1000.

On this note, one would earn more if one apprenticed for Sara.

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Answer:

Step-by-step explanation:

Answer:

a) 110

b) 250

Step-by-step explanation:

Read the top row of numbers for a.  We are starting at zero and going to 110

Reflex is when two angles add up to 360

360 - 110 = 250

Answer:

17

Step-by-step explanation:

Hence option (B) is a correct choice and rest all other options are incorrect

1/b^2 ∑ (-1)^k(t^2/b^2)^k                                        
                             

Step-by-step explanation:

 Remember that the sum of infinite GP is given by the formula blow:
First term=a
Common ratio=r

S=a/1 - r                                          

Wherever the common ratio r falls within the interval (-1,1)

When the given series is compared to the infinite sum:

First term=a
Common ratio=r
S=  a/1-r = 1/b^2+t^2
Now given: |t| < |b|=0<t^2/b^2<1
S=1/B^2.1/1-(-T^2/B^2)
=A=1
R=-T^2/B^2
Writing the general form:

Hence option (B) is a correct choice.

What are real numbers simple definition?

Real numbers can be defined as the union of both rational and irrational numbers. They can be both positive or negative and are denoted by the symbol “R”. All the natural numbers, decimals and fractions come under this category.

INCOMPLETE QUESTION: if b and t are real numbers such that 0<|t|<|b|, which of the following infinite series has sum 1b2 t2
A) 1/b^2 ∑(t^2/b^2)^k.
B) 1/b^2 ∑(-1)^K(t^2/b^2)^k.
C)B^2∑(T^2/B^2)^K
D)b^2∑(-1)(t^2/b^2)^k

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Answer:

DQR

Step-by-step explanation:

DEF is complentary to DQR

Answer:

  ∆DQR

Step-by-step explanation:

You want the similarity statement if the triangles shown are similar.

Triangles will be similar if they have congruent corresponding angles, or proportional corresponding sides.

No angles are shown in the figure, but side lengths are given.

We expect that if the triangles are similar that the corresponding sides will be ...

The attached calculator display shows the ratios of these side lengths are the same: 14/3. That means ...

  ∆DEF ~ ∆DQR

<95141404393>

Answer:Slope is -2/3

Step-by-step explanation:

What you do is use the formula y2-y1/x2-x1.

y1 and y2 are at the end of the parenthesis so y1 is 5 and y2 is -1.

x1 and x2 are at the beginning of the parenthesis so x1 is -3 and x2 is 6.

Then you put it into the formula:

-1-5/6-(-3)

This then equals -2/3.

-2/3 is the answer.

No, a TV with a 60 inch diagonal would not fit in an entertainment center that is 52 inches wide and 40 inches high.

Diagonal is a line connecting two or more points that are not in a straight line. It is used to describe the shape of a polygon and also used in mathematics to refer to lines, angles, and shapes. It can also refer to a line, or direction, that is not parallel or perpendicular to something else. In geometry, diagonal lines are used to divide shapes into equal parts, and are used in the construction of polygons. In linear algebra, diagonal lines are used to calculate the determinant of a matrix.

The diagonal measurement of a TV is the length of a line drawn between the opposite corners of the TV. For a 60 inch diagonal TV, the width of the TV would be around 52 inches and the height would be around 33 inches. As the entertainment center is only 40 inches high, the TV would not fit in it.

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Answer:

it looks like a reflection or translation but my gut is saying translation

A triangle is a three-sided polygon and each of its interior angles must add up to 180°; so each angle can have at most 180°.

A triangle is a three-sided polygon with three interior angles. According to the mathematical rule known as the “sum of interior angles”, the sum of the three interior angles of any triangle must always equal 180 degrees. Therefore, if the three angles of a triangle are A, B, and C, then A + B + C = 180. Since the sum of the three angles must equal 180 degrees, it means that each angle can have at most 180 degrees; none of the angles can be greater than 180 degrees. In other words, the maximum possible value of the angles in a triangle is 180 degrees, so the triangle can have only 180 degrees in total.

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Using the Pythagoras Theorem the value of c=11.40 and the number that goes beneath the radical is 130.

What is Pythagoras Theorem?

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse. Due to its position opposite the 90° angle, the hypotenuse in this case is the longest side.

The rectangle is divided into two triangles which have exactly same sides.

So take any one triangle.

Apply the Pythagoras theorem since it is a right-angled triangle with base = 9 and perpendicular = 7.

So, according to Pythagoras theorem -

(Hypotenuse)^2=(Base)^2+(Perpendicular)^2

Plugging in the values in the equation -

c^2=(9)^2+(7)^2

c^2=81+49

c^2=130

c=[tex]\sqrt{130}[/tex]

c=11.40

Therefore, the value of c is obtained as 11.40.

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