The figure to the right shows a square floor plan with a smaller square area that will accommodate a combination fountain and pool. The floor with the​ fountain-pool area removed has an area of 432 square meters and a perimeter of 90 meters. Find the dimensions of the floor and the dimensions of the square that will accommodate the fountain and pool

INFORMATION:

We have the next rhombus

And we must find the measure of

Knowing that DB = 10, BC = 13, and m∠WAD = 25°

STEP BY STEP EXPLANATION:

To find all measures, we need to use properties or the rhombus:

- DA: To find DA we need to know that all sides of the rhombus are equal. So, if BC measures 13, then DA measures 13 too.

- BW: To find BW we need to know that in a rhombus, diagonals bisect each other at right angles. That means, diagonals intersect in the middle. So, if DB = 10, then BW will be half of BD. BW = 10/2 = 5.

- WC: We can find it as one of the legs of the right triangle formed by BW, BC and WC. Where, BC is the hypotenuse.

So, WC = 12.

- Angle BAC: To find this angle, we need to use that the interior triangles formed in the interior of the rhombus are congruent. So, angle BAC is congruent with the angle DAC. Then, BAC = 25°.

ANSWER:

DA = 13

BW = 5

WC = 12

BAC = 25 degrees

Answer:

26 + 5x = y

Step-by-step explanation:

hope this helped

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Answer: y=2x-5

Step-by-step explanation:

6x-3y=15

6x-6x-3y=-6x+15

-3y=-6x+15

-(3y=6x-15)

3y=6x-15

3y/3=(6x-15)/3

y=6x/3-15/3

y=2x-5

Answer: x^2 + y^2 - 4x + 18y = 76 = 0

The center of the circle given is (2, 9)

radius = r

The equation of a circle for a given point is

(x - h)^2 + (y - k)^2 = r^2

Where h = 2, and y = 9

(x - 2)^2 + (y - 9)^2 = 3^2

Expand the parentheses

(x - 2) (x - 2) + (y - 9) (y - 9) = 9

(x - 2) (x - 2 ) = x* x - 2*x - 2*x + 2* 2

= x^2 - 4x + 4

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

(y - 9) (y - 9) = y*y - y*9 - 9*y + 9*9

= y^2 - 18y + 81

(y - 9) (y - 9)= y^2 - 18y + 81

Therefore, the equation becomes

x^2 - 4x + 4 + y^2 - 18y + 81 = 9

Re-arrange the equation

x^2 + y^2 - 4x - 18y + 4 + 81 = 9

x^2 + y^2 - 4x - 18y = 9 - 81 - 4

x^2 + y^2 - 4x - 18y = -76

x^2 + y^2 - 4x - 18y + 76 = 0

The equation of a circle given the center (2, 9) and radius 3 is x^2 + y^2 - 4x + 18y = 76 = 0

Answer:

The equation of a circle given the center (2, 9) and radius 3 is x^2 + y^2 - 4x + 18y = 76 = 0

Step-by-step explanation:

The volume of the given triangular prism to the nearest tenth is; 171.5 in³

The volume of a triangular prism of the kind given to us is expressed as;

Volume of a triangular prism = area of base triangle × length of the prism

Now, the formula for area of base triangle is;

Area = 1/2 * base * height

From the question, we have;

base = 9.8 in

height = 14 in

Now, the length of prism is 2.5 inches. Thus;

Volume of prism =  (1/2 * 9.8 * 14) * 2.5

Volume of prism = 171.5 in³

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The allocation for product defined and product not defined are

PD(product defined)

PND

This is further explained below.

Generally, the rule for matrix multiplication

no. of columns for the first matrix should be equal to no. of rows in the second matrix" that is if

1st matrix has =m * n

2nd has =k *l

Therefore

m=l

L=2*2,  M=4*2,

The matrix is defined as the row and the column tally

M=4*2 and L=2*2

The matrix is not defined as a row and the column do not tally

In conclusion, Q=2*1, and P=2*2 equal so the product is defined.

P=2 *2,M=4 *2,  equal so product is defined.

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By applying probability method in a Poisson distribution, we find out that the probability that in a given year that area will be hit by fewer than 4 hurricanes is 0.1512 and the probability that in a given year that area will be hit by anywhere from 6 to 8 hurricanes is 0.4015.

It is given that -

On an average, Eastern United States is hit by 6 hurricanes in a year.

We have to find out -

(a) Probability that in a given year that area will be hit by fewer than 4 hurricanes

(b) Probability that in a given year that area will be hit by anywhere from 6 to 8 hurricanes

This is a case of probability which relates to Poisson distribution that provides probability of any random event that occurs within a specific time interval.

Let us assume the number of hurricanes is represented by [tex]X[/tex]. The Poisson distribution can be represented as -

[tex]P(X) = \frac{(lambda)^{X}*e^{-lambda}}{X!}[/tex] -------(1)

​Here, [tex]X\\[/tex] = 1,2,3,...

lambda = Average = 6 (in this question)

[tex]e[/tex] = 2.718

(a) Probability that in a given year that area will be hit by fewer than 4 hurricanes

[tex]P(X < 4) = P(X=0) +P(X=1)+P(X=2)+P(X=3)\\= \frac{6^{0}*e^{-6}}{0!}+\frac{6^{1}*e^{-6}}{1!}+\frac{6^{2}*e^{-6}}{2!}+\frac{6^{3}*e^{-6}}{3!}\\=0.0025+0.0149+0.0446+0.0892\\=0.1512[/tex]

Thus, the probability that in a given year that area will be hit by fewer than 4 hurricanes is 0.1512.

(b) Probability that in a given year that area will be hit by anywhere from 6 to 8 hurricanes

[tex]P(6\leq X\leq 8)=P(X=6)+P(X=7)+P(X=8)\\=\frac{6^{6}*e^{-6} }{6!}+\frac{6^{7}*e^{-6} }{7!}+\frac{6^{8}*e^{-6} }{8!}\\=0.1606+0.1376+0.1033\\=0.4015[/tex]

Thus, the probability that in a given year that area will be hit by anywhere from 6 to 8 hurricanes is 0.4015.

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The area of the square will be 100 square meters. Then the dimensions of the pen of the rectangle will be 10 by 10 which is a square.

What is the area of the square?

Let a be the side length of the square.

Then the area of the square will be

Area of the square = a² square units

Cathy has 40 meters of fencing to build a rectangular pen for her pets.

For the maximum area of the rectangle, the length and width should be congruent.

40 = 4a

a = 10

Then the area of the square will be

A = 10²

A = 100 square meters

The dimensions of the pen of the rectangle will be 10 by 10 which is a square.

Answer:

6,12,24,48,96

Step-by-step explanation:

The value of x is -0.004624

[tex]log_{3} (x)+log_{x} (3)=2.5[/tex]

[tex]log_{3} (x)+\frac{log_{3} (3)}{log_{3} (x)} =2.5[/tex]

Let z= [tex]log_{3} (x)[/tex]

[tex]z+\frac{1}{z} = 2.5[/tex]

[tex]3z^{2} + z-2.5z=0[/tex]

z= -0.166

[tex]log_{3} (x)=-0.166[/tex]

x = -0.004624

What is a log?

The logarithm is exponentiation's opposite function in mathematics. This indicates that the exponent to which a set number, base b, must be increased in order to create a specific number x, is represented by the logarithm of that number. The logarithm, in its most basic form, counts the number of times the same factor appears when multiplied repeatedly; for instance, since 1000 = 10 x 10 x 10 = 103, its "logarithm base 10" is 3, or log10 (1000) = 3. When there is no possibility of a mistake or when the base is irrelevant, as, in big O notation, the logarithm of x to base b is written as loga (x), logb x, or even without the explicit base, log x.

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Answer: 35N

Step-by-step explanation:

Cross multiply and divide to find the missing value

Answer: 35N :)))))))))))))))))))))))))))))

The equation of the line that passes through the point (2,-3) and is parallel to the line 2x + 5y = 10 is y = - 2 / 5 x - 11 / 5

The equation of a line can be represented in various form such as point slope form, slope intercept form and standard form.

Therefore, let's find the equation of the line that passes through the point (2, -3) and is parallel to the line 2x + 5y = 10.

Hence, parallel lines have the same slope.

5y = -2x + 10

y = - 2 / 5 x + 2

Therefore, the slope of the line is - 2 / 5.

Let's find the y-intercept using the slope intercept equation.

y = mx + b

where

Hence, (2, -3)

-3 = - 2 / 5(2) + b

-3 = - 4 / 5 + b

b = - 3 + 4  /5

b = - 11 /  5

Therefore, the equation of the line is y = - 2 / 5 x - 11 / 5

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The required equation of the line y = - (2/5)x - 11/5 passes through the point (2,-3) and is parallel to the line 2x + 5y = 10.

We have to determine the line that passes through the point (2,-3) and is parallel to the line 2x+5y=10

Parallel lines are known to have the same slope.

Firstly, we have to find its slope by the given line

⇒ 5y = -2x + 10

⇒ y = - (2/5)x + 2

Thus, the slope of the line is - 2/5.

Let the required equation of the line is y - y₁ = m(x -x₁ )

Here x₁ = 3, y₁ = 1 and m = -2/5

y - 1 = (-2/5)(x - 3)

y - 1 = (-2/5)x + 3(-2/5)

y = - (2/5)x - 6/5 +1

y = - (2/5)x - 11/5

Therefore, the required equation of the line is y = - (2/5)x - 11/5.

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The set R^2  with x ≤ 0 and y ≤ 0 is not a vector space.

The 10th axiom  cv∈ V does not hold

Let u, v and w be vectors in the vector space V, and let c and d be scalars. A set S is defined as a vector space if it satisfies the following conditions:

1. u+ v ∈V

2. v + w = w + v

3. (u + v) + w = u + (v + w)

4. v + 0 = v = 0 + v

5. v + (−v) = 0

6. 1v = v

7. c(dv) = (cd)v

8. c(v + w) = cv + cw

9. (c + d)v = cv + dv

10. c v ∈V

Given the set of all vectors x, y in R^2  with x ≤ 0 and y ≤ 0

If the scalar c is such that  c<0 then c v ∉R^2as cv>0

Therefore, the 10th axiom is not satisfied and thus the set  R^2 with x ≤ 0 and y ≤ 0 is not a vector space.

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Answer:

2. y = x + 13

Step-by-step explanation:

Your points are: (-4, 9) and (2, 15)

To write an equation of a line from two ordered pairs, you first find the slope (m)

To find the slope, you do y2 - y1 / x2 - x1

(-4 is x1, 9 is y1) (2 is x2, 15 is y2)

Plug in the numbers:

15 - 9 / 2 - (-4) ----------------------> 6/6 ----------> 1, m = 1

The next equation we'll use is y - y1 = m(x - x1)

and slope intercept form is y = mx + b

Pick either ordered pair to plug in the coordinates, but this time I'll use

(2, 15) -----> 2 is x1, 15 is y1

y - 15 = m(x - 2)

Since we already know the slope, m, we can simplify the equation.

y - 15 = 1(x - 2)

Distributive property

y - 15 = x - 2

Add 15 on both sides,

y = x + 13

Answer:

x = 7 degrees

Step-by-step explanation:

Angle CDB = 49 degrees (corresponding angles triangle ABD congruent to triangle CBD)

Angle CDB = 49 degrees = 7x

7x = 49 degrees

x = 7 degrees

Answer:

I don't see any answer options, and the equation doesn't look correct.

I'll assume the equation is meant to be:

Step-by-step explanation:

(2x/5 - 9) = 9

2x/5  = 18

2x  = 90

x = 45

if the modified equation is correct.

An expression, in terms of n, for the nth term of this arithmetic sequence is aₙ = 23 - 4n.

An arithmetic sequence can be defined as a series of real and natural numbers in which each term differs from the preceding term by a constant numerical quantity.

Mathematically, the nth term of an arithmetic sequence can be calculated by using this expression:

aₙ = a₁ + (n - 1)d

Where:

For the second term, we have:

a₂ = a₃ - d

a₂ = 11 - (-4)

a₂ = 11 + 4

a₂ = 15.

For the first term, we have:

a₁ = 4 + second term

a₁ = 4 + 15

a₁ = 19

Substituting the given parameters into the formula, we have;

aₙ = a₁ + (n - 1)d

aₙ = 19 + (n - 1)(-4)

aₙ = 19 - 4n + 4

aₙ = 23 - 4n

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The angle postulate that best defined angles CAB and CAD is; Supplementary Angles

We know that there are different angle postulates such as Corresponding angles, complementary angles, supplementary angles and others.

Now, in this case we want to find the angle theorem that best describes angles CAB and CAD. Now, from the given image, it is clear that both angles form a straight line and we know that the sum of angles on a straight line equals 180 degrees.

Since both angles sum up to 180 degrees and we know that these angles are defined as supplementary angles which are linear pairs.

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Answer: y = 1/6x + 1

Step-by-step explanation:

12y - 2x= 12

    +2x  +2x

12y =  12 + 2x

DIVIDE BOTH SIDES BY 12

y = 1 + 1/6x

THEN PUT IN SLOPE INTERCEPT FORM

y = 1/6x + 1

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \: [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: 12y - 2x = 12[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: 12y = 2x + 12[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: y = \frac{2}{12} x + \frac{12}{12} [/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: y = \frac{1}{6} x + 1[/tex]

Slope = 1/6, y - intercept = 1

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Answer:

Find value of n first to find out what the angle measures are.

Linear angles have a sum of 180°.

Angle EFG + Angle GFH = 180

4n + 15 + 2n + 39 = 180

6n + 54 = 180

6n = 126

n = 21

Substitute n into the angles.

Angle EFG = 4(21) + 15 = 99°

Angle GFH = 2(21) + 39 = 81°

858 combinations are there to choose 10 players to take the field.

Pick 10 people from 13,

[tex]C^{13} _{10}[/tex] = [tex](^{13} _{2} )[/tex]

Splitting the combination,

[tex]C^{13} _{10}[/tex] = (13 × 12 × 11) ÷ 2

[tex]C^{13} _{10}[/tex] = 1716 ÷ 2

[tex]C^{13} _{10}[/tex] = 858 ways to pick the 10 to play.

There are 858 different methods to select 10 players to take the pitch.

The permutations of a set are the vaguely defined community of its members in arrangement or linear order, or the permutation of its components if the set is already collected. The act or procedure of adjusting the linear ordering of a sorted set is often named "permutation".

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Equation of the line is y = -(1/3)x+5

The figure shows a straight line of which two points and thereby the slope can be found out.

Equation of a line is in the slope-intercept form is,

y = mx +c,

where m is the slope of the line and c is the y-intercept of the line.

From the figure, two points on the line are, (0,5) and (3,4).

Then slope = (4-5)/(3-0)

                  = -1/3

Now y-intercept, c is the y-co-ordinate when x = 0.

From the figure, when x = 0, y = 5

So y-intercept, c = 5.

Thus the equation of the line is, y = -(1/3)x+5

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By translating trapezoid S′T′U′V 7 using the same translation rule, the location of T′ in the image trapezoid S′T′U′V′ is: D. (13, -1)

Generally, there are four (4) main types of transformation and these include the following:

In Geometry, a translation can be defined as a type of transformation which moves every point of a geometric figure or object in the same direction, as well as for the same distance.

By critically observing the graph (see attachment), we can logically deduce that rectangle JKLM was transformed to rectangle J'K'L'M' by translating it 7 units to the right and 5 units up.

Next, we would apply the same translation rule to T' which is located at point (6, -6) as follows:

(x, y)                →        (x + 7, y + 5)

Point T (6, -6)     →       Point T' = (6 + 7, -6 + 5) = (13, -1)

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Complete Question:

Rectangle J'K'L'M' shown on the grid is the image of rectangle JKLM after transformation. The same transformation will be applied on trapezoid STUV.

What will be the location of T′ in the image trapezoid S′T′U′V′? (10, −1) (10, 1) (13, 1) (13, −1)

Answer:

The slope is -1/3.

Step-by-step explanation:

When you count the rise/run, which is how much it goes up/down and left/right, you get -4/12. Simplify -4/12 and you'll get -1/3.

Inequality which  is equivalent to 7x - 2y > 8  x>[tex]\frac{2y}{7}[/tex] + [tex]\frac{8}{7}[/tex] and y <[tex]\frac{7x}{2} -4[/tex]

Equations don't always need to have a "equal to" symbol on both sides to be balanced. Sometimes it can be about a "not equal to" relationship, meaning that something is superior to or inferior to another. In mathematics, an inequality is a relationship between two numbers or other mathematical expressions that results in an unequal comparison. Inequalities are the name given to certain algebraic mathematical expressions.

7x - 2y>8

-2y > 8 -7x

=y <[tex]\frac{7x}{2} -4[/tex]

or

7x >2y + 8

=x>[tex]\frac{2y}{7}[/tex] + [tex]\frac{8}{7}[/tex]

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Answer: I am going to assume that 1/4 is 1 over 4 ( a fraction ) and that it is the same for 1/64

A) 0.00390625

B)     0.015625^4  <------( Here is the equation. when i put it in a calculator it was too long. here is the answer that gave me: 5.96046448 e-8 )

I can buy 75 latex balloons and 50 mylar balloons.

This is a problem from an algebraic equation. We can solve this problem by following a few steps.

We need 125 balloons. Let's assume we have to purchase x latex balloons.

So, mylar balloons are ( 125 - x ).

Our total budget is $32.50.

The cost of x latex balloons is ($.10 × x) = $.10x , as the latex balloons cost $.10 each.

The cost of ( 125- x)  mylar balloons is $[( 125- x) × 0.50] , as the mylar balloons cost $.50 each.

So the total cost is,

$[( 125- x) × 0.50] + $.10x  = 32.50

Now, we have to solve this equation, Let's simplify it.

62.50 - 0.50x + .10x = 32.50

Or, 62.50 - 0.40x = 32.50

Or, -0.40x =  32.50 - 62.50       [ deduce 62.50 from both side ]

Or, -0.40x =  -30                 [ we should devide both sides 0.40 ]

Or, x = 30/0.40 = 75

So, the number of latex balloons is 75. Therefore, the number of remaining mylar balloons is ( 125 - 75) = 50

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[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: y = - 6x+ 6[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

The given equation is :

[tex]\qquad\displaystyle \tt \rightarrow \: 24x + 4y = 24[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: 4y =24 - 24x [/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: y = \frac{ 24}{4} - \frac{24x}{4} [/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: y = - 6x + 6[/tex]

And this the equation of same line in its slope intercept form, where slope (m) = -6 and y - intercept = +6

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