What is the ratio of the area of the triangle to the area of the rectangle?

the right side is 4mm and the bottom is 11 mm

The area of the adjoining trapezium is 276 [tex]cm^{2}[/tex].

Given the sides of trapezium be 16 cm, 15 cm, 30 cm, 13 cm.

We are required to find the area of adjoining trapezium.

Draw two perpendiculars on AD and the points will be E and F.

From triangles ABE and CFD.

let the length of AE=x, FD=30-16-x=14-x.

BE=[tex]\sqrt{169-x^{2} }[/tex], CF=[tex]\sqrt{225-(14-x)^{2} }[/tex]

BE=CF

[tex]\sqrt{169-x^{2} }[/tex]=[tex]\sqrt{225-(14-x)^{2} }[/tex]

Squaring both sides.

169-[tex]x^{2}[/tex]=225-196-[tex]x^{2}[/tex]+28x

140=28x

x=5 cm.

Put in BE=[tex]\sqrt{169-x^{2} }[/tex]

BE=[tex]\sqrt{169-25}[/tex]

=[tex]\sqrt{144}[/tex]

=12 cm.

Area of trapezium=1/2 (sum of parallel sides)*height

=1/2 (30+16)*12

=23*12

=276 [tex]cm^{2}[/tex]

Hence if the sides of trapezium are 16 cm, 15 cm, 30 cm, 13 cm then the area of the adjoining trapezium is 276 [tex]cm^{2}[/tex].

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Answer:

[tex]4^{6}[/tex]

Step-by-step explanation:

When you are dividing exponents, you subtract them.

[tex]4^{9-3}[/tex] which gives you [tex]4^{6}[/tex]

You can check your work by writing it all out

[tex]\frac{4*4*4*4*4*4*4*4*4}{4*4*4}[/tex]

The 3 4s in the denominator will cancel out 3 4s in the numerator.

You are left with only 6 4s in the numerator, which is [tex]4^{6}[/tex]

Answer:

y=-\frac{2}{5}x+\frac{19}{5}y=−52x+519

Further explanation:

We have to find the equation of the line first to graph the line.

The general form of slope-intercept form of equation of line is:

y=mx+by=mx+b

Given

m=-\frac{2}{5}m=−52

Putting the value of slope in the equation

y=-\frac{2}{5}x+by=−52x+b

To find the value of b, putting the point (-3,5) in equation

\begin{gathered}5=-\frac{2}{5}(-3)+b\\5=\frac{6}{5}+b\\5-\frac{6}{5}+b\\b=\frac{25-6}{5}\\b=\frac{19}{5}\end{gathered}5=−52(−3)+b5=56+b5−56+bb=525−6b=519

Putting the values of b and m

y=-\frac{2}{5}x+\frac{19}{5}y=−52x+519

Answer:

11/15 km

Step-by-step explanation:

Simply sum the areas:

2/5 + 1/3 = (6 + 5)/15 = 11/15

Answer:

16.8

Step-by-step explanation:

here is that kite on a graph. you can see there are 2 sides of length 5, and 2 sides of length 3, so closest perimeter is 16.8

See attachment for the graph of cell phone plan 1: y= 7.5x and cell phone plan 2: y= 5.5x + 10.1

Linear equations are equations that have constant average rates of change, slope or gradient

The cell phone plans are given as:

Cell phone plan 1: y= 7.5x

Cell phone plan 2: y= 5.5x + 10.1

To plot the graph of both plans, we make use of the following domain for both cell phone plans

Domain: x >= 0

Next, we set x = 0, 1, 2, 3, 4 and 5 for both plans

So, we have:

Cell phone plan 1

y= 7.5x

When x = 0, y = 7.5 * 0 = 0

When x = 1, y = 7.5 * 1 = 7.5

When x = 2, y = 7.5 * 2 = 15

When x = 3, y = 7.5 * 3 = 22.5

When x = 4, y = 7.5 * 4 = 30

When x = 5, y = 7.5 * 5 = 37.5

Cell phone plan 2

y= 5.5x + 10.1

When x = 0, y = 5.5*0 + 10.1 = 10.1

When x = 1, y = 5.5 * 1 + 10.1 = 15.6

When x = 2, y = 5.5 * 2 + 10.1 = 21.1

When x = 3, y = 5.5 * 3 + 10.1 = 26.6

When x = 4, y = 5.5 * 4 + 10.1 = 32.1

When x = 5, y = 5.5 * 5 + 10.1= 37.6

Next, we plot both graphs on the domain x >= 0

See attachment for the graph of cell phone plan 1: y= 7.5x and cell phone plan 2: y= 5.5x + 10.1

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The information given that A, B, and C are equal in length; each one is 4.47 units long illustrates that the angle is an equilateral triangle.

Secondly, when two of its sides are congruent, then the triangle is an isosceles triangle.

It should be noted that an equilateral triangle simply means the triangle tht had equal shape and angles. Here, since A, B, and C are equal in length; each one is 4.47 units long illustrates that the angle is an equilateral triangle.

Secondly, when two of its sides are congruent, then the triangle is an isosceles triangle. On such triangle, two out of the three sides are equal.

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The simplified product of (√6x² +4√8x³)(√9x-x√5x^5) is 3x√6x  + 24x^2√2 - x^4√30x - 8x^5√10

The product expression is given as:

(√6x² +4√8x³)(√9x-x√5x^5)

Evaluate the exponents

(√6x² +4√8x³)(√9x-x√5x^5) = (x√6 +8x√2x)(3√x - x^3√5x)

Expand the brackets

(√6x² +4√8x³)(√9x-x√5x^5) = x√6 * 3√x + 8x√2x * 3√x - x√6 * x^3√5x - 8x√2x * x^3√5x

This gives

(√6x² +4√8x³)(√9x-x√5x^5) = 3x√6x  + 24x^2√2 - x^4√30x - 8x^5√10

Hence, the simplified product of (√6x² +4√8x³)(√9x-x√5x^5) is 3x√6x  + 24x^2√2 - x^4√30x - 8x^5√10

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Answer:

(0, - 3 )

Step-by-step explanation:

- 5x - 3y - 9 = 0 → (1)

4x - 18y - 54 = 0 → (2)

multiplying (1) by - 6 and adding to (2) will eliminate y

30x + 18y + 54 = 0 → (3)

add (2) and (3) term by term to eliminate y

34x + 0 + 0 = 0

34x = 0 ⇒ x = 0

substitute x = 0 into either of the 2 equations and solve for y

substituting into (2)

4(0) - 18y - 54 = 0

- 18y - 54 = 0 ( add 54 to both sides )

- 18y = 54 ( divide both sides by - 18 )

y = - 3

solution is (0, - 3 )

Answer:

(0, -3)

Step-by-step explanation:

This system of equations consists of two equations. There are 3 main ways to solve a system of equations:

First, start by having the variables on one side.

[tex]-5x-3y-9=0 \Rightarrow \text{Add 9 to both sides} \Rightarrow -5x-3y=9\\4x-18y-54=0 \Rightarrow \text{Add 54 to both sides} \Rightarrow 4x-18y=54 \Rightarrow \text{Simplify} \Rightarrow 2x-9y=27[/tex]

This method is the easiest to use in this situation.

In this method, we increase equations by a certain factor in order to eliminate one variable.

We can see that 3y in the first equation can be multiplied by 6 in order to obtain the 18y in the second equation. Therefore, we can multiply the whole first equation by 6:

[tex]-30x-18y=54\\4x-18y=54[/tex]

Now, subtract the two equations to eliminate y.

[tex]-34x=0\\x=0[/tex]

Plug in 0 to x in either of the equations to solve for y:

[tex]-5(0)-3y=9\\0-3y=9\\-3y=9\\ \text{Divide both sides by -3}\\y=-3[/tex]

OR

[tex]4(0)-18y=54\\0-18y=54\\-18y=54\\\text{Divide both sides by -18}\\y=-3[/tex]

Therefore:

(x, y) = (0, -3)

[tex]\frac{6xyz}{2xy-y}.\frac{2x^{2}-7x+3 }{3xz - 9z} = 2x[/tex]

The expression can be simplified as follows:

[tex]\frac{6xyz}{2xy-y}.\frac{2x^{2}-7x+3 }{3xz - 9z}[/tex]

Hence,

[tex]\frac{6xyz}{y(2x-1)}.\frac{(x-3)(2x-1)}{3z(x-3)}[/tex]

Therefore.

[tex]\frac{6xyz}{y(2x-1)}.\frac{(2x-1)}{3z}[/tex]

Hence,

[tex]\frac{2xy}{y(2x-1)}.\frac{(2x-1)}1=2x[/tex]

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Answer:

Option 2

Step-by-step explanation:

Since theta is in the third quadrant, the sine of theta is negative.

By the Pythagorean identity,

[tex]\sin \theta=-\frac{\sqrt{105}}{13}[/tex]

So, using the double angle formula for sine, we get that

[tex]\sin 2\theta=\frac{16\sqrt{105}}{169}[/tex]

Using the arrangements formula, the number of orders is given as follows:

The number of possible arrangements of n elements is given by the factorial of n, that is:

[tex]A_n = n![/tex]

When there are no restrictions, the number of ways is:

[tex]A_{11} = 11! = 39,916,800[/tex]

When they must be lined alternatively, the 6 dogs can be arranged in 6! ways, and the 5 cats in 5! ways, hence the number of orders is:

[tex]A_6A_5 = 6! \times 5! = 86,400[/tex]

When the first and last are cats, we have that:

Hence:

20 x 9! = 7,257,600.

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The estimated standard error for the sample is 6

Given,

Sample size, n = 36

Sample variance, [tex]s^{2}[/tex] = 1296

Standard deviation, s = √1296

                                   = 36

Standard error, SE = [tex]\frac{s}{\sqrt{n} }[/tex]

                              = [tex]\frac{36}{\sqrt{36} }[/tex]

                              = [tex]\frac{36}{6}[/tex]

                              = 6

Concept

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we conclude that the linear equation in the graph is:

y = -2*x + 30

We can define the variables:

On the graph we can see two points:

(0, 30) and (15, 0).

Remember that a linear equation is of the form:

y = a*x + b

For the first point, we have:

30 = a*0 + b

30 = b

Then the line is:

y = a*x + 30

Now we can use the point (15, 0) to write:

0 = a*15 + 30

-30 = a*15

-30/15 = a = -2

Then we conclude that the linear equation in the graph is:

y = -2*x + 30

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Answer:

figure A = 3 units

figure B = 9 x 3 = 27 units

scale factor =

[tex] \frac{3}{27 } = \frac{1}{9} [/tex]

so the scale factor = 9

The equation that could represent a linear combination of the system 2/3x + 5/2y = 15 and 4x + 15y = 12 is 0 = 26

Linear equations are equations that have constant average rates of change, slope or gradient

A system of linear equations is a collection of at least two linear equations.

In this case, the system of equations is given as

2/3x + 5/2y = 15

4x + 15y = 12

Multiply the first equation by 6, to eliminate the fractions.

6 * (2/3x + 5/2y = 15)

This gives

4x + 15y = 90

Subtract the equation 4x + 15y = 90 from 4x + 15y = 12

4x - 4x + 15y - 15y = 12 - 90

Evaluate the difference

0 + 0 = -78

Evaluate the sum

0 = -78

The above equation is the same equation as option (b) 0 = 26

This is so because they both represent that the system of equations have no solution

Hence, the equation that could represent a linear combination of the system is 0 = 26

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Answer:  108 square feet

===============================================

Work Shown:

L = 4 = length

W = 3 = width

H = 6 = height

SA = surface area of the box

SA = 2*(LW + LH + WH)

SA = 2*(4*3 + 4*6 + 3*6)

SA = 108

Answer:

  (5, 1)

Step-by-step explanation:

The vertex is the turning point on the graph. Its coordinates are read from the axes labels.

The term vertex is used in several different contexts. A vertex of a polygon is a point where edges meet. A vertex of a curve is an extreme value of the curve.

When applied to an ellipse, the vertices are the ends of the major axis. The ends of the minor axis are the co-vertices.

The vertex of a parabola is the extreme value of the parabola. When it opens downward, as here, the vertex is the point where the curve is at its maximum.

As with any point on any graph, the coordinates of the vertex are read from the labels of the axes. The horizontal coordinate is customarily listed first.

The vertex is (x, y) = (5, 1).

Answer:

linear

Step-by-step explanation:

This is a line with slope  m = 8  and y-axis intercept of 10

Answer:

linear

Step-by-step explanation:

y = 8x + 10

is an equation in the form y = mx + b.

The form y = mx + b is called the slope-intersect form of the equation of a line.

Since it is the equation of a line, it is linear.

Answer:

Step-by-step explanation:

(14 - 7x)/7 =

[7(2-x)]/7 =

2-x

The average of the values from that average of 6 is 0

We have the numbers to be

0 2 4 10 14 and have an average of 6

To find their distances, we should substract each from the given average

We have;

6 - 0 =6

6 -2 = 4

6 -4 = 2

6 - 10 = -4

6 - 14 = -8

The average of this distances is

= pro

= [tex]\frac{0}{6}[/tex]

= 0

Thus, the average of the values from that average of 6 is 0

The complete question is

These values have an average of 6. What is the average distance of those values from that average of 6?

0 2 4 10 14

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75  is  the least positive integers which , when subtracted 7300 would make a result a perfect square

So normally the least positive integer of all the numbers is the number 1 but when you talk about least positive integer, often times you are talking about the special function called the ceiling function

The smallest of the numbers in the set {1, 2, 3, …} is 1.

So, the number 1 is the smallest positive integer.

7300

If we Take Square root of 7300 we have to subtract 75 from 7300 to get a perfect square.

7300-75=7225

(85)^2=7225

75 to be subtracted

√7300 ≥ 85

Perfect Square = 85² =  7225     or (7300-7225 = 75)

75  is  the least positive integers which , when subtracted 7300 would make a result a perfect square

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Answer:

[tex]tan(2\theta) = -\frac{4}{3}\\[/tex]

Step-by-step explanation:

So cos is defined as: [tex]cos(\theta) = \frac{adjacent}{hypotenuse}[/tex], meaning we can tell that the adjacent side is 1, and the hypotenuse is 5, from the fraction you gave.

Using this we can solve for the opposite side.

[tex]1^2 + b^2 = \sqrt{5}^2\\1+b^2 = 5\\b^2=4\\b=2[/tex]

Now it's important to note, that b can be a negative number, so we have to use the information that sin(x) > 0, to determine the length of this side.

The sin is defined as: [tex]sin(\theta) = \frac{opposite}{hypotenuse}[/tex], and since we we're solving for the opposite side, this means that the value +\- 2, is in the top, and since the hypotenuse is positive, this means that the opposite side is also positive.

This also tells us one more thing, since both cos(x) and sin(x) are positive, we are dealing with a angle in the first quadrant.

So we can now define sin(x), using the opposite (2) and the hypotenuse (sqrt(5))

[tex]sin(\theta) = \frac{2}{\sqrt{5}}[/tex]

And we can rationalize the denominator for both the cosine and sine, by multiplying by the square root in the denominator so that

[tex]sin(\theta) = \frac{2\sqrt{5}}{5}\\\\cos(\theta) = \frac{\sqrt{5}}{5}[/tex]

Now we can define the value of tan(2 theta) using the double angle-identities such that:

[tex]tan(2\theta) = \frac{2\ tan(\theta)}{1-tan^2{\theta}}[/tex]

And we can also define tan(theta) using the definition that:

[tex]tan(\theta) = \frac{sin(\theta)}{cos(\theta)}[/tex]

So plugging in the values sin(theta) and cos(theta) we get the following:

[tex]tan(\theta) = \frac{\frac{2\sqrt{5}}{5}}{\frac{\sqrt{5}}{5}}\\\\tan(\theta) = \frac{2\sqrt{5}}{5} * \frac{5}{\sqrt{5}}\\\\tan(\theta) = 2[/tex]

Btw in the last step, I just canceled out the 5 and sqrt(5) since they were both in the denominator and numerator

So now let's plug this value, 2 as tan(theta) into the equation

[tex]tan(2\theta) = \frac{2\ *2}{1-2^2}\\\\tan(2\theta) = \frac{4}{-3}\\tan(2\theta) = -\frac{4}{3}\\[/tex]

Answer:

Step-by-step explanation:

RM 280 = 40% of 8 months

RM 700= 100% of 8 months

RM 700/8= 8 months

RM 87.5 = 1 month

Answer = 87.5

Farid's monthly salary is approximately RM 87.5. He spends 40% of his total 8-month expenditure on house rent, which amounts to RM 280 per month.

Let's assume Farid's monthly salary is RM x.

Given that he spends 40% of his total 8 monthly expenditure on house rent, and the amount he spends on house rent is RM 280, we can set up the following equation:

0.40 × 8x = 280

Now, let's solve for x:

0.40 × 8x = 280

3.2 × x = 280

x = 280 / 3.2

x ≈ 87.5

So, Farid's monthly salary is approximately RM 87.5.

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The numbers which are a part of the domain for the graph are: 6, 1 and 2.

The domain of a graph is a set of all possible input, x-values. Consequently, since the domain of the graph given ranges over intergers, 1 to 10, it follows that numbers which are part of the domain are; 6, 2, and 1.

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The first five terms of the given arithmetic sequence are:

1/5, 2/5, 3/5, 4/5, 1 (Fourth option)

The arithmetic sequence is given as follows,

f(n) = f(n-1) + 1/5 ............ (1)

Now, for finding the first five term of this arithmetic sequence, we will substitute n as 1, 2, 3, 4, and 5 one by one. Using the above formula for the arithmetic sequence, we can deduce the first five terms.

It is already given that f(1) = 1/5 ......... (2)

f(1) is the first term of the sequence.

Now, putting n=2 in equation (1), we get,

f(2) = f(2-1) + 1/5

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

Substitute f(1) = 1/5 from equation (2)

⇒ f(2) = 1/5 + 1/5

f(2) = 2/5

To find the third term of the arithmetic sequence, put n = 3 in equation (1)

f(3) = f(3-1) + 1/5

f(3) = f(2) + 1/5

⇒ f(3) = 2/5 + 1/5

f(3) = 3/5

Similarly, we can find the fourth and fifth terms of the arithmetic sequence by substituting n = 4 and n = 5 respectively.

∴ f(4) = f(3) + 1/5

⇒ f(4) = 3/5 + 1/5

f(4) = 4/5

Likewise, f(5) = f(4) + 1/5

⇒f(5) = 4/5 + 1/5

f(5) = 1

Thus, using the recursive formula, the first five terms of the arithmetic sequence come out to be:

1/5, 2/5, 3/5, 4/5, 1

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The value of function f(x) over g(x) is [tex]2x^{2} +4x-1-\frac{9}{4x+1}[/tex]

Given functions are:

f(x)=8[tex]x^{3}[/tex]+18[tex]x^{2}[/tex]-10

g(x)=4x+1

In mathematics, a function is an expression, rule, or law that establishes the relationship between an independent variable and a dependent variable (the dependent variable). Functions exist everywhere, and they are crucial for constructing physical links in the sciences.

In mathematics, a function is represented as a rule that produces a distinct result for each input x. A function is indicated by a mapping or transformation. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.

[tex]\frac{f(x)}{g(x)}=\frac{8x^{3}+18x^{2} -10 }{4x+1}[/tex]

      = [tex]2x^{2} +4x-1-\frac{9}{4x+1}[/tex]

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Answer:

-15 would be the answer because if it's below sea level it would have a negative sign in front of 15

Step-by-step explanation:

Answer:

(A∩B)' = A'∪B'

Step-by-step explanation:

U is the universal set

A and B are two subsets of U

let A' be the complement subset of A

and  B' be the complement subset of B

U = {-10,-9,…,-1,0,1,…,9,10}

A = {-1,0,1}

B = {1,2,…,9,10}

Then

A∩B = {1}

Then

the complement of A∩B :

(A∩B)' = {-10,-9,…,-1,0,2,…,9,10}

(notice the absence of 1)

On the other hand,

A' = {-10,…,-2}∪{2,…,10}

B' = {-10,…,0}

Then

A'∪B' = {-10,-9,…,-1,0}∪{2,…,10}

         =  {-10,-9,…,-1,0,2,…,9,10}

Conclusion:

(A∩B)' = A'∪B'