find the gradient and intercept of the following equation of line y= -2x - 5​

The actual area of the rectangular desk is 264 feet²

An equation is an expression composed of variables and numbers linked together by mathematical operations.

Scaling is used to increase or decrease the size of a figure by a scale factor.

The drawing is at a scale of 1 inch = 2 feet.

11 inches = 11 inches * 2 feet per 1 inch = 22 feet

6 inches = 6 inches * 2 feet per 1 inch = 12 feet

Area of the desk = length * width = 22 feet * 12 feet = 264 feet²

The actual area is 264 feet²

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Using Pascal's triangle we can find the binomial coefficient, by which we get 1m^4 + 16m^3 + 96m^2 + 128m + 256

Pascal's triangle is a triangular array of numbers in which each number is the sum of the two numbers directly above it. It is named after the French mathematician Blaise Pascal, who studied its properties in the 17th century. The rows of the triangle are numbered starting from 0, and the first number in row n is always 1. The other numbers in row n are the sum of the corresponding number in row n-1 and the number directly above it. The nth number in the kth row of Pascal's triangle is denoted by C(n,k) and it is called binomial coefficient, it is also denoted by nCk. It is used in many areas of mathematics, particularly in combinatorics and algebra, and it can be used to expand binomial expressions using the binomial theorem.

The binomial theorem states that for any non-negative integer n and any binomial expression (a+b)^n, the expansion is given by:

(a+b)^n = C(n,0)a^n*b^0 + C(n,1)a^(n-1)*b^1 + C(n,2)a^(n-2)b^2 + ... + C(n,n)a^0b^n

where C(n,k) = n!/(k!(n-k)!) is the binomial coefficient, which can be found using Pascal's triangle.

Using this theorem:

(m+4)^4 = C(4,0)m^44^0 + C(4,1)m^34^1 + C(4,2)m^24^2 + C(4,3)m^14^3 + C(4,4)m^0*4^4

Using Pascal's triangle we can find the binomial coefficient:

C(4,0)=1, C(4,1)=4, C(4,2)=6, C(4,3)=4, C(4,4)=1

So the expanded form of (m+4)^4 is:

1m^4 + 4m^34 + 6m^24^2 + 4m4^3 + 14^4

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Answer:

2

Step-by-step explanation:

The link between s, t, and u is therefore u2= t2+s2 and provides the answer to the triangle problem.

A triangle is a polygon since it has three parts and three vertices. It is a basic geometric shape. A triangle with the corners A, B, & C is referred to as a triangle ABC. A singular plane & triangle in Geometric shapes are found so when three components are not collinear. Due to its right side and three corners, triangles are considered polygons. The corners of a triangle are defined as the locations at which its three sides meet. 180 degrees is obtained by multiplying three triangle angles.

Here,

Given: Triangle STU is a right triangle in this instance.

Thus,

We learn:

parts s, t, and u

Their connection is as follows:

Given that it's a right triangle

So,

The Pythagoras Theorem states that

=>u²= t²+s²

The link between s, t, and u is therefore u2= t2+s2 and provides the answer to the triangle problem.

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The solutions to the different sides and values of square are given below. The length of the side of the square is 6.71m.

Square is a polygon which four equal sides and all angles are right- angles.

Given area of square = 45 m²

     Area = side²

     Side = √Area = √45 = 6.71 m

Therefore side of the square is 6.71m.

41) Negative numbers do not have square roots.

Therefore √-4 is undefined.

42) Option D is correct as it is not a fraction.

43) Any number multiplied by zero is zero.

Therefore (a) is the correct option.

44) When y = 15, x = 3

   For direct variation, y =kx

so k = y/x =15/3 = 5

When x=5, y = kx =5*5 = 25

Therefore (a) is correct.

45) For inverse variation

   MN = k

  Given 5*3 = k

k=15

When M = 10 , N = k/M = 15 /10 = 3/2

Therefore option a is correct.

48) Let the amount of work be W

     For 3 men,

          8 days = W

             1 day = W/8

Now work done by 1 man in one day = (W/8) /3 =W/24

In six days, work done by one man = W/24 * 6 = W/4

Therefore for the work to be completed, the number of men required is 4 (W/4 *4 = W).

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According to angle symmetry, the value of x=125°

The two parallel lines intersected by a transversal form alternate angles. Consider the following figure, where EF and GH are two parallel lines. The transversal line RS intersects EF at L and GH at M. If a transversal cuts two parallel lines, the alternate angles are equal.

Since, AK and BL are parallel lines.

Hence,

∠ADC=∠BED=72°

∠EIH=∠DHG=55°

∠DHG+∠GHK=180°

∠GHK=180°-55°

∠GHK=125°=x

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Answer:

30

Step-by-step explanation:

10 = 2 × 5

15 = 3 × 5

LCD = 2 × 3 × 5 = 30

The angle x in a right-angled triangle is 12.8°.

What is a right-angled triangle?

A triangle is said to have a right angle if one of the angles is 90 degrees. Right triangles are those with angles at 90 degrees, which are referred to as right angles.

The diagram shows a right-angled triangle with opposite = 12 units and hypotenuse as 54 units.

To find the angle x, apply the formula -

sin(x) = opposite/hypotenuse

sin(x) = 12/54

x = sin^-1(12/54)

x = sin^-1(2/9)

x = 12.84°

Rounding it to nearest tenth gives x = 12.8°.

Therefore, the value of x is 12.8°.

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On solving the provided question we can say that the given equation yield solution as x=27.4 and y= -5/8.

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

On solving simultaneously,

x=27.4

y= -5/8

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In Class 12, to find the domain and range of a function, you can use the following steps:

For example, if the function is f(x) = 1/x, the domain of the function is all real numbers except 0, because dividing by 0 is undefined. In this case, the domain of the function is (-∞,0) U (0,+∞)

For example, if the function is f(x) = √x, the domain of the function is all non-negative real numbers, because √x is only defined for non-negative values of x. In this case, the range of the function is [0,+∞)

Note that some functions may have more complex expressions, in such cases, you may have to use algebraic methods to find the domain and range.

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Answer:

[tex]\dfrac{2}{3}[/tex]

Step-by-step explanation:

To find the scale factor of the dilation of a figure, simply divide the x-value (or y-value) of a vertex of the dilated image Q'R'S'T' by the x-value (or y-value) of the corresponding vertex of the pre-image QRST.

[tex]\implies \sf Scale\;factor=\dfrac{x_{Q'}}{x_{Q}}=\dfrac{-2}{-3}=\dfrac{2}{3}[/tex]

[tex]\implies \sf Scale\;factor=\dfrac{y_{T'}}{y_{T}}=\dfrac{4}{6}=\dfrac{2}{3}[/tex]

Therefore, the scale factor is 2/3.

To find the scale factor of the dilation of a figure, first find the lengths of corresponding sides using the distance formula.

[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Distance between two points}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the two points.\\\end{minipage}}[/tex]

From inspection of the given diagram:

[tex]\implies QR=\sqrt{(x_R-x_Q)^2+(y_R-y_Q)^2}[/tex]

[tex]\implies QR=\sqrt{(3-(-3))^2+(6-9)^2}[/tex]

[tex]\implies QR=\sqrt{(6)^2+(-3)^2}[/tex]

[tex]\implies QR=\sqrt{36+9}[/tex]

[tex]\implies QR=\sqrt{45}[/tex]

[tex]\implies QR=3\sqrt{5}[/tex]

From inspection of the given diagram:

[tex]\implies Q'R'=\sqrt{(x_{R'}-x_{Q'})^2+(y_{R'}-y_{Q'})^2}[/tex]

[tex]\implies Q'R'=\sqrt{(2-(-2))^2+(4-6)^2}[/tex]

[tex]\implies Q'R'=\sqrt{(4)^2+(-2)^2}[/tex]

[tex]\implies Q'R'=\sqrt{16+4}[/tex]

[tex]\implies Q'R'=\sqrt{20}[/tex]

[tex]\implies Q'R'=2\sqrt{5}[/tex]

To find the scale factor of dilation that maps QRST onto Q'R'S'T', divide the length of Q'R' by the length of QR:

[tex]\implies \dfrac{Q'R'}{QR}=\dfrac{2\sqrt{5}}{3\sqrt{5}}=\dfrac{2}{3}[/tex]

Therefore, the scale factor is 2/3.

The value of X that satisfies both -9X + 4Y = 8 and -3X - Y = 4 given the same value of Y is X = -8/7.

An equation is a mathematical statement that shows that two mathematical algebraic expressions are equal. For example, x + 7 = 10 is an equation, in which x + 7 and 10 are two expressions separated by an 'equal to' sign.

An equation also has two sides, the let hand side and the right hand side.

Solving the two equations simultaneously we have:

-9x + 4y = 8 --- (1)

-3x - y = 4 --- (2)

Multiply 2 by 3 and subtract from (1) as shown below

-9x + 4y = 8

-9x - 3y = 12

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

0 + 7y = - 4

7y = -4

y = -4/7

Substituting the value of y in equation 2 we get the value of x.

-3x - (- 4/7) = 4

-3x + 4/7 = 4

-3x = 4 - 4/7

-3x = 24/7

x = -8/7

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a) Vertical plane not passing through the cone's topmost point - hyperbola.

b) Horizontal plane - circle.

c) Diagonal plane - ellipse or parabola

What is a cone?

A cone is a three-dimensional geometric shape that narrows smoothly from a flat base (typically circular base) to a point called the apex or vertex (which creates an axis to the center of the base).

Cross section of a cone:

A cross section is a representation of a shape's axis of symmetry intersected by a plane. When a plane cuts a solid, such as a cone, cylinder, or sphere, it creates a shape known as a cross-section. Depending on how the plane cuts the cone, the cross-section of a solid, such as a cone, can be a circle, a parabola, or a triangle.

When a cone's cross-section is split horizontally, it is circular.

When a cone is cut vertically, its cross-section is an isosceles triangle, and this plane slices through the center of the cone.

When a cone is cut vertically, the cross-section is parabolic except for the plane running through the center.

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With the help of cosine function, the amount fan rotates each minute is 1000 times.

We can use the cosine function:

Y = a cos ( b c - x ) + d

Y = equals 6 cosine (2000 pi x) + 11

Where x is time in minutes.

To find the period (p):

P = 2 pi/b

P = 2 pi/ 2000 pi

P = 1/1,000

P = 0.001

To find the rotation per minute we can use:

Rpm = 1/p

Rpm = 1/0.001

Rpm = 1,000

As the result, the amount of rotation is 1,000 times per minute

Your question is incomplete, but most probably your full question was:

A ventilation fan is installed in a vertical position. As the fan rotates, the distance, in inches, between the tip of a fan blade and the ceiling is modeled by y = Equals 6 cosine (2,000 pi x) + 11, where x is time in minutes.

How many times does the fan rotate each minute?

A 1,000

B 2,000

C 4,000

D 6,000

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From the explicit rule the first three terms of sequence is 16, 16.5, 17.

Here given,

F(n) = 16+(1/2)(n-1)

We have to find first three terms.

F(1) = 16 + (1/2)(1-1)

      = 16 + 1/2 x 0

      = 16

F(2) = 16 + (1/2) (2-1)

       = 16 + 1/2

       = 16 + 0.5

       = 16.5

F(3) = 16 + (1/2) (3-1)

      = 16 + 1/2 x 2

      = 16 + 1

      = 17

So the first three terms in the sequence is 16, 16.5, 17 with common difference of .05.

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The statement if False.

A family budget is a game plan for your family's money. Your plan identifies where and how your money comes and goes by focusing on income and expenses. Importantly, it also reflects your family's goals and values by how you spend and save.

Given statement,

You overhear a friend discuss how Americans are frivolous in their spending and waste lots of money.

The most expensive items in American spending are needs like housing, taxes, and transportation, while wants like wants are the least expensive.

In America, besides taxes three largest cost categories are households, transportation and food.

A family's transportation costs are $1,847 more than its food expenses.

Typically, needs make up 80% of expenses rather than wants.

Housing, fees, and medical expenses, continuing to be the same each month. The cost of clothing, entertainment, food, and transportation changes every month.

Hence,  we can conclude that, Americans don't necessarily waste money on wants because they have to spend on needs before wants, which results in a lot of spending on things like housing and taxes.

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For this kind of issue, you can select any option and the procedure will remain the same. Let's choose coffee as the beverage to analyse for the purposes of this response.

When a correlation coefficient's magnitude is between 0.5 and 0.7, it means that the variables are moderately correlated. Low correlation between the variables is indicated by correlation coefficients with magnitudes between 0.3 and 0.5.

In this equation, x stands for price, and y for sales.

-22.7x+130.3

The slope indicates the number of units that the sales would change by if we raised the price by one unit. Since our slope is -22.7, this indicates that a 1 unit price increase would result in a 22.7 decrease in sales.

The scatterplot's points are all intersected by the line of best fit, as can be seen. We can also calculate the Pearson correlation coefficient, which gives us -0.998, to add to the evidence. This suggests a very adverse relationship.

For this item we will just need the equation for the line of best fit and the data that has been given in the problem. For the actual sales, we will just refer to the given while we will compute for the predicted sales using the line of best fit.

PRICE            ACTUAL SALES              PREDICTED SALES

1.5                              96                                       96

1.6                              94                                       94

1.8                              91                                       89

2.0                              85                                       85

2.1                              83                                       83

2.2                              79                                       80

2.5                              73                                       74

2.7                              70                                       69

2.9                              64                                       64

3.0                              63                                       62

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In order to make the stream of water from a garden hose approximate a sine curve, the nozzle of the hose should be moved in an up-and-down motion.

The reason is because a sine curve is a smooth wave-like pattern that oscillates between positive and negative values. If the nozzle is moved up and down, it will cause the water to be released in a similar wave-like pattern, creating a stream that approximates a sine curve. This is due to the nozzle moving in a sinusoidal motion, which causes the water to be released in the same motion. This kind of motion is known as a harmonic motion, and it's the same motion that causes a wave to have a sinusoidal shape.

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Answer:

3/10(3x+1)

Step-by-step explanation:

Answer:

The principle of factorization is that every square matrix can be expressed as a product of a lower triangular matrix and upper triangular matrix. On the basis of this fact, these lower and upper triangular matrices help us in finding the unknowns.

Step-by-step explanation:

Hope it helps!

Answer: 9

Step-by-step explanation:

Given equation is

3v-12 = 15

Now let's add 12 to both sides of the equation.

You'll get

3v = 27

Divide 3 from both sides, and you get

v = 9

Let's check.

Substitute 9 for v in the equation and you get

27 - 12 = 15

Which is true.

Final Answer: v=9

The solution to the given equation 3v - 12 = 15 is x = 9.

What is the solution to the equation?

A solution to an equation is a number that can be substituted for the variable to provide a true number statement.

The equation is given in the question, as follows:

3v - 12 = 15

We have to determine the solution to the given equation.

As per the question, we have

3v - 12 = 15

Rearrange the terms in the above equation, and solve for v:

3v = 15 + 12

3v = 27

Divided by 3 into the above equation, we get

v = 27/3

v = 9

Thus, the solution to the given equation is x = 9.

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Displacement is the change in the position of an object relative to a reference point over a period of time.

It is usually represented by a vector quantity and is measured in meters (m). The formula for displacement is displacement = final position - initial position. Mathematically, displacement is denoted by s and is equal to the final position (x2) minus the initial position (x1), or s = x2 - x1. As an example, if a person walks a path of length 10 meters, starting at the origin (x1 = 0) and ending at x2 = 10, then their displacement would be s = 10 - 0 = 10 meters. To calculate displacement, we need to know the initial and final positions of the object, and the direction in which it moves.For example, if an object moves from position 5 m to position 10 m, the displacement is 5 m. This can be calculated by subtracting the initial position (5 m) from the final position (10 m). The result is 5 m, which is the displacement of the object.

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One equation that represents the total value of the coins in cents is:

0.25x + 0.10y = 995

where x is the number of quarters and y is the number of dimes.

Another equation that represents the total number of coins is:

x + y = 47

These two equations make up a system of equations that can be used to find the number of quarters and dimes that add up to $9.95 and have a total of 47 coins.

Answer:

[tex]\begin{cases}x+y=47\\0.25x+0.1y=9.95\end{cases}[/tex]

Step-by-step explanation:

To solve this problem, we can create and solve a system of equations.

Define the variables:

Values of the coins:

Given there are a total of 47 coins:

[tex]x+y=47[/tex]

Given there is a total of $9.95 in quarters and dimes:

[tex]0.25x+0.1y=9.95[/tex]

Therefore, the system of equations that represents the problem is:

[tex]\begin{cases}x+y=47\\0.25x+0.1y=9.95\end{cases}[/tex]

To solve the system of equations, rewrite the first equation to isolate y:

[tex]y=47-x[/tex]

Substitute this into the second equation to eliminate y:

[tex]0.25x+0.1(47-x)=9.95[/tex]

Solve the equation for x to find the number of quarters:

[tex]\begin{aligned}0.25x+0.1(47-x)&=9.95\\0.25x+4.7-0.1x&=9.95\\0.15x+4.7&=9.95\\0.15x&=5.25\\x&=35\end{aligned}[/tex]

Therefore, there are 35 quarters.

Substitute the found value of x into the first equation and solve for y:

[tex]\begin{aligned}35+y&=47\\y&=12\end{aligned}[/tex]

Therefore, there are 12 dimes.

Answer:

n= 84

Step-by-step explanation:

After setting each fraction to equal each other, cross multiply. Multiply 7 and 60, and multiply 5 and n.

You will get 60 x 7 = 5 x n

60 times 7 equals 420.

420=5n

Divide 5 from both sides to get n= 84.

Answer:

Step-by-step explanation: add i'll the sides togetheir

The area of the triangle would be 49 cm².

Area of a triangle = (length x breadth)/2

Area of the triangle = (14cm x 7cm)/2

Area of the triangle = (98cm)/2

Area of the triangle = 49 cm²

The area of a triangle can be calculated by using the formula (length x breadth)/2. In this scenario, the length and breadth of the triangle is 14cm and 7cm respectively. Therefore, the area of the triangle can be calculated by using the formula. The area of the triangle would be (14cm x 7cm)/2 = (98cm)/2 = 49 cm². Hence, the area of the triangle with the given length and breadth would be 49 cm².

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The expression that represents the perimeter of the triangle is 3x

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

Side length = x

Triangle type = equilateral triangle

The perimeter of an equilateral triangle can be calculated as

P = 3 * side length

substitute the known values in the above equation, so, we have the following representation

P = 3 * x

So, we have

P =3x

Hence, the perimeter expression is 3x

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Value of X is 8.

A rectangle is a closed two-dimensional figure with four sides. The opposite sides of a rectangle are equal and parallel to each other and all the angles of a rectangle are equal to 90°.

Given,

Figure OUTD is a rectangle.

Each angle in a rectangle measures 90 degrees.

Therefore,

(7X + 2) + 4X = 90

7X + 2 + 4X = 90

11X + 2 = 90

Subtract 2 from both sides of the equation

11X = 88

Divide both sides of the equation by 11

X = 8.

Hence, 8 is the value of x.

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Both expressions are equivalent

What is the expression in mathematics?

In mathematics, an expression is a combination of numbers, variables, and mathematical operations that can be evaluated to a specific value or result. Expressions can be simple or complex, and they can be used to represent mathematical relationships or to perform calculations.

Let c represent the number of ceramic pottery pieces in each box, and let p represent the number of handpainted plates in each box.

To find the total number of ceramic pottery pieces that Solana bought, we can use the following expression:

c* (50 + 58) = c*108

This expression shows that the total number of ceramic pottery pieces is equal to the number of ceramic pottery pieces in each box multiplied by the total number of boxes of ceramic pottery that Solana bought.

Alternatively, we can use the following expression:

c50 + c58 = 108*c

This expression shows that the total number of ceramic pottery pieces is equal to the product of the number of ceramic pottery pieces in each box and the number of boxes Solana bought on Monday plus the product of the number of ceramic pottery pieces in each box and the number of boxes Solana bought on Thursday.

Similarly, to find the total number of handpainted plates that Solana bought, we can use the following expression:

p* (40 + 46) = p*86

This expression shows that the total number of handpainted plates is equal to the number of handpainted plates in each box multiplied by the total number of boxes of handpainted plates that Solana bought.

Alternatively, we can use the following expression:

p40 + p46 = 86*p

This expression shows that the total number of handpainted plates is equal to the product of the number of handpainted plates in each box and the number of boxes Solana bought on Monday plus the product of the number of handpainted plates in each box and the number of boxes Solana bought on Thursday.

Both expressions are equivalent, as they provide the same value for the total number of ceramic pottery pieces and handpainted plates that Solana bought.

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1. The sequence is 2, 8, 16, 32.

2. The sequence is 4, 16, 64, 256.

A grouping of numbers in a specific order is known as a sequence. On the other hand, a series is described as the accumulation of a sequence's constituent parts.

For example, 3, 7, 11, 15, ... is a sequence as there is a pattern where each term is obtained by adding 4 to its previous term.

Given:

The first term of a sequence is 4.

1. let the common ratio 2.

Then, second term= 4 x 2= 8

third term = 8 x2 =16

fourth term = 16 x 2= 32

So, the sequence is 2, 8, 16, 32..

2. let the common ratio 4.

Then, second term= 4 x 4 = 16

third term = 16 x 4 = 64

fourth term = 64 x 4 = 256

So, the sequence is 4, 16, 64, 256.

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