Oliver makes two mosaics using coloured tiles.
For the first mosaic he uses red, blue and
purple tiles in the ratio 12 : 3:2.
For the second mosaic he uses red and blue
tiles in the ratio 8 : 5.
Oliver uses the same number of blue tiles for
each mosaic.
What is the ratio of red tiles in the first mosaic
to red tiles in the second mosaic?
Give your answer in its simplest form.

Check the picture below.

Make sure your calculator is in Degree mode.

[tex]\tan(\alpha )=\cfrac{\stackrel{opposite}{5}}{\underset{adjacent}{4}}\implies \alpha=\tan^{-1}\left( \cfrac{5}{4} \right)\implies \alpha \approx 51.3^o[/tex]

Given statement: "Any square matrix multiplied by its inverse will be that size identity matrix."

The statement is correct because for a square matrix A, if it is multiplied by its inverse, we get the identity matrix of the same order. The product of the matrix with its inverse is commutative.

The identity matrix is a square matrix with 1's along the diagonal and 0's elsewhere. For example, the 3x3 identity matrix is shown below.

1 0 0

0 1 0

0 0 1

The inverse of a square matrix A is a matrix A^-1, such that AA^-1 = A^-1A = I, where I is the identity matrix.

For example, let us consider a 2x2 matrix A. A = (a, b, c, d)

The inverse of the matrix A is given by the formula. A^-1 = 1/(ad-bc) * (d, -b, -c, a)

Thus, AA^-1 = A^-1A = I, where I is a 2x2 identity matrix. Therefore, any square matrix multiplied by its inverse will be that size identity matrix.

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Answer:

Step-by-step explanation:

9

Answer:

One expression for the length of one of the equal sides

is x = (934 - 214) / 2.

Step-by-step explanation:

The perimeter is the sum of the 3 sides of the triangle.

Let the length of one of the equal sides be x cm

So, we have:

2x + 214 = 934

2x = 934 - 214 = 720

x = 720 /2 = 360 cm.

The value of QS is 4.5c + 9.5.

A parallelogram is a four-sided plane figure with opposite sides parallel and equal in length. Its opposite angles are also equal.

Since Q is the midpoint of the diagonals RT and SU in parallelogram RSTU, we have:

QS = 1/2 RT ...(1)

QU = 1/2 SU ...(2)

Also, since RU||ST and RS||UT, we know that triangles QRU and QST are similar by AA similarity, so:

QR/QS = QU/QT

Substituting the given values and using (1) and (2), we get:

QR/(6c - 8) = (c + 7)/QT

Cross-multiplying and simplifying, we get:

QR = (6c - 8)(c + 7)/(2c - 1)

QR = (6c^2 + 34c - 56)/(2c - 1)

QR = 3(2c^2 + 11c - 18)/(2c - 1)

QR = 3(2c - 1)(c + 9)/(2c - 1)

QR = 3(c + 9)

Now, using (1), we have:

QS = 1/2 RT

QS = 1/2 (QR + RU)

QS = 1/2 (3(c + 9) + (6c - 8))

QS = 1/2 (9c + 19)

QS = 4.5c + 9.5

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Answer

:44 field goals

Step-by-step explanation:

Answer:

44 attempts

Step-by-step explanation:

A ratio has two or more numbers that symbolize relation to each other. Ratios are used to compare numbers, and you can compare them using division.

The ratio for this problem is:

To get from 2 to 8, we multiply the 2 by 4.

The ratio is now:

To solve for '?', we can simply multiply the 11 by 4, just like what we did with the 2.

Now the ratio is:

If the ratio has 44 as the second number, we know that it is the total attempts. Therefore, he attempted 44 field goals.

Never true;

The sum of two irrational numbers is irrational

Always true;

The sum of two rational numbers is rational

The product of two rational numbers is rational

Sometimes true;

The product of two irrational numbers is irrational

Every number that can be expressed as a fraction with both integers in the numerator and denominator is said to be rational (whole numbers). Numerator cannot be zero.

Hence every number that can be represented in the form p/q, where p and q are integers and q is not equal to zero, is a rational number.

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Answer:

D. Two.

Step-by-step explanation:

The two graphs touch each other at two different points, meaning they have two solutions.

"Substituting x = 3 and y = -6 in the given equation, we get:

4y - 6x = xy

4(-6) - 6(3) = (3)(-6)

-24 - 18 = -18

-42 ≠ -18

Therefore, the given equation is not true for x = 3 and y = -6." (ChatGPT, 2023)

The number of gigabytes that Sydney can use while staying within her budget is less than 2.9 gigabytes.

How to illustrate the information?

From the information, Sydney pays a flat cost of $35.50 per month and $5 per gigabyte. She wants to keep her bill under $50 per month.

The inequality that can be used to determine x x, the number of gigabytes Sydney can use while staying within her budget will be:

35.50 + 5x < 50

Collect like terms

5x < 50 - 35.50

5x < 14.50

x < 14.50 / 5

x < 2.9

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Answer:

Step-by-step explanation:

Diagonals intersect at 90°.

[tex]x^2=5^2+5^2[/tex]    (Pythagoras Theorem)

    [tex]=50[/tex]

[tex]x=\sqrt{50}[/tex] cm =7.07 cm

a)Does not have an inverse function

b) g(x) has an inverse function

c)Domain of g(x) is [0, π],range is [-1, 1]

d)domain of g−1(x)=cos−1(x) is [-1, 1], range is [0, π]

a) No, y=cos(x) does not have an inverse function because it fails the vertical line test.
b) g(x) has an inverse function, g−1(x)=cos−1(x), because it passes the vertical and horizontal line tests when its domain is restricted to the interval [0, π].
c) The domain of g(x) is [0, π], and the range is [-1, 1] in interval notation.
d) The domain of g−1(x)=cos−1(x) is [-1, 1], and the range is [0, π] in interval notation.

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A it is nearly but not a right angled triangle.

Step-by-step explanation:

I used pythagorous theorum.

Answer:

No it is not

Step-by-step explanation:

Hypotenuse is the longest side

A ² = B² + C² (Using Pythagoras theorem)

51² = 45² + 26²

2601 =2025 +676

2601 = 2701

This is not a right angle triangle

Square root of 2701 is 51.57 and that is equivalent to 52

Answer:

Step-by-step explanation:

−9.71 + 2.8 = -6.91

Answer:

6.91.

9.71

2.8

6.1

if you subtract 9.71 from 2.8 keep everything in point

Answer:

y= -5/3x - 7/3

Step-by-step explanation:

1. solve the line

-3x +5y + 2 = 0

+3x              +3x

5y + 2 = +3x

     -2      -2

5y = +3x - 2

/5     /5

y= 3/5x -2/5

2. find slope

perpendicular lines have an opposite reciprocal slope to original line so your slope is now -5/3

3. find b ( y - intercept )

point ( -2 , 1 )

y - y1 = m ( x - x1 )

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

y -1 = -5/3x - 10/3

  +1               + 1

y= -5/3x - 7/3

The length of the diagonal of the rectangle is 66

Here we have the rectangle WXYZ.

In that notation, we would have:

WX

XY

YZ

ZW

As the sides

And:

WY

XZ

as the diagonals.

We know that the values of the two diagonals must be the same ones, then we can write:

WY = XZ

14x + 10 = 11x + 22

Now we can solve that for x.

14x - 11x = 22 - 10

3x = 12

x = 12/3 = 4

then the length of the diagonal is:

WY = XZ = 14*4 + 10 = 66

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The amount of border that Roberto will need to put around the edges of the platform, given the area is 16 units.

The platform is given in the figure and to find the amount of border that Roberto needs to cover it if the area is 12 square units, you need to count the number of dots all along the edges of the platforms.

Counting this would give us 16 dots. This then means that Roberto needs sixteen units of border to be able to put up a border around the edges of the platform.

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The data which is given in the question is the time for tamara to read the book can be seen in a table with its respective values.

What is table?

Table is something which has rows and columns and the data is inserted into it.

Table has no restriction for the number of rows and columns. One can insert any rows and columns in the table according to their preferences.

Now in the above question,

    Tamara read 35 pages in 42.5 minutes.

    Tamara read 41 pages in 59 minutes.

     Tamara read 56 pages in 72 minutes.

The table will be     Pages               Time

                                 35                     42.5

                                  41                      59

                                  56                     72

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The sοlutiοn οf the given prοblem οf square cοmes οut tο be  0.84% is the shaded area.

A square is a quadrilateral οf fοur equal faces and fοur identical angles accοrding tο Euclidean geοmetry. A shape with adjacent edges that have the same length is anοther name fοr a rectangle. If οne οf a quadrilateral's fοur triangular edges and 4 triangular angles is square, the parallelοgram is deemed tο be equilateral. A linear οr 90 ° angle is referred tο as a cubical angle.

Here,

We must determine the area οf the shaded area and divide it by the area οf the cοmplete square tο determine the prοpοrtiοn οf the square that is shaded.

A sectοr is equal tο (45/360)k²/2 = 0.125k²

Find the regiοn οf triangle BDE next. Triangle BDE is a right triangle, sο we can determine its height using the Pythagοrean theοrem:

=>  BE² + DE² = BD²

=>  BE² + k² = (k√2)²

=>  BE² = 2k² - k²

=>  BE = k√2

Therefοre, the triangle BDE's area is:

=> A(triangle) = (1/2)

=> BE*DE = (1/2)

=> (k√2)(k√2) = k²

Lastly, the area οf the darkened area is equal tο the sectοr's area less the triangle's area:

=> A(shaded) = A(sectοr) - A(triangle) = 0.125πk² - k² ≈ 0.0084k²

Cοnsequently, the amοunt οf the rectangle that is shaded is:

=> percentage = (A(shaded) / A(square)) x 100%

=> ( 0.0084k² / k²) x 100%

=> 0.84%

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The sample space for Ted's experiment is TTT, TTH, THT, HHH, HHT, HTH, THH, HTT ( option C)

The sample space of a random experiment is the collection of all possible outcomes.

When we toss a coin, there can be only two outcomes i.e., either head or tail. So, the sample space will be, S = {H, T} where H is the head and T is the tail.

When Ted tossed the coin three times, the sample space include;

TTT, TTH, THT, HHH, HHT, HTH, THH, HTT

This means the total sample space is 8.

Therefore the sample space for Ted's experiment is TTT, TTH, THT, HHH, HHT, HTH, THH, HTT

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z3 = n − k − z1 − z2

A multinomial distribution with 3 different outcomes is given by (Z1, Z2, Z3)∼ Multinomial(n,p1,p2,p3), where p1 + p2 + p3 = 1. The conditional distribution of Z2 given Z1=z1 is to be derived. The pmf and distribution will be found.Let k be the number of trials with Z1 = z1. Therefore, the number of trials with Z2 = z2 is n − k. Then, the conditional distribution of Z2 given Z1=z1 is(Z1,Z2=n−k,Z3)∼Multinomial(k,p1,p2,p3)×Multinomial(n−k−1,p1′,p2′,p3′),where p1' = p1 / (1 − p1), p2' = p2 / (1 − p1), and p3' = p3 / (1 − p1).As a result, the pmf of the conditional distribution of Z2 given Z1=z1 is given byP(Z2 = z2 | Z1 = z1) = (k!/(z1!z2!(n−k−z1−z2)!))×(p1z1p2z2p3n−k−z1−z2)×(n−k−1)!/(z3!(n−k−z3−1)!(p1'z1+p2'z2+p3'z3)n−k−1), where z3 = n − k − z1 − z2. The distribution obtained is named a "conditional multinomial distribution".

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The value of f(8) is equal to D)21.5.

What is meant by area?

The region that an object's shape defines as its area. The area of a figure or any other two-dimensional geometric shape in a plane is how much space it occupies.

The graph of f'(x) is given in the figure.

We know that

[tex]\int\limits^a_b {f'(x)} \, dx =f(a)-f(b)[/tex].

Therefore since we have f(2) and we have to find f(8), we will take the area under the given graph from x=2 to 8

[tex]\int\limits^8_2 {f'(x)} \, dx =f(8)-f(2)\\\\2*3+2*3+\frac{1}{2}*3*3=f(8)-5\\ 16.5=f(8)-5\\f(8)=21.5[/tex].

Therefore f(8) is equal to D)21.5.

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Answer:

They have 36 books in total.

Step-by-step explanation:

Let d = The number of Dima's books

Let r = The number of Ramiro's books.

d = 2r

d - 12 = r Substitute 2r for d in the second equation and solve for r

2r - 12 = r   Subtract 2r from both sides

2r - 2r - 12 = r - 2r

-12 = -r  Multiply both sides by -1

12 = r

Ramiro has 12 books.

d = 2r substitute 12 for r and solve for d

d = 2(12)

d = 24

Dima has 24 books.

Together they have 36 books (12 + 24)

Helping in the name of Jesus.

Answer:36

Step-by-step explanation:

The equation of the line passing through the points (-1, -4) and (3, 0) is y = x - 3.

To find the equation of the line passing through two points, we need to use the point-slope form of the equation of a line.

Point-slope form: y - y₁ = m(x - x₁)

where:

(x₁, y₁) is one of the given points on the line

m is the slope of the line

To find the slope of the line passing through (-1, -4) and (3, 0), we can use the formula:

m = (y₂ - y₁)/(x₂ - x₁)

where:

(x₁, y₁) = (-1, -4)

(x₂, y₂) = (3, 0)

m = (0 - (-4))/(3 - (-1))

m = 4/4

m = 1

Now we can use either of the two points and the slope to write the equation of the line.

Let's use point (-1, -4):

y - (-4) = 1(x - (-1))

y + 4 = x + 1

y = x - 3

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Answer:

27

Step-by-step explanation:

aone third of 27 is 9, and 18 - 9 = 9

Answer: is there a pic?

Step-by-step explanation: is there a pic of what your working on?

Answer:

y=-x-8

Step-by-step explanation:

formular for finding an equation on a line is y-y1=m(x-x1) whiles m is the slope or gradient then x1 is -2 and y1 is -6 then you substitute to the formular you state down

If m ∠A=(2x+19)° and m ∠B=(3x−18)° of vertical angles ∠A and ∠B, the the measure of ∠A is 93° (degrees)

Vertical angles are formed when two lines intersect. They are opposite to each other and have the same measure. Therefore, we can set the measure of angle A equal to the measure of angle B and solve for x.

m ∠A = m ∠B

2x + 19 = 3x - 18 (Substitute the given measures of ∠A and ∠B)

19 + 18 = 3x - 2x (Add 2x to both sides and subtract 19 from both sides)

37 = x

Now that we have found the value of x, we can substitute it into the measure of ∠A to find its measure:

m ∠A = 2x + 19

m ∠A = 2(37) + 19 (Substitute x = 37)

m ∠A = 93

Therefore, the measure of ∠A is 93 degrees.

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Complete Question

∠A and ∠B are vertical angles. If m ∠A=(2x+19)° and m ∠B=(3x−18)°, then find the measure of ∠A

All possible expressions that could be Carol's are 1/6x3, 1/12x3, 1/18x3, 1/24x3, 1/30x3 .

Alice, Bob and Carol each think of an expression that is a fraction with 1 as the numerator and a constant integer times some power of x as the denominator. The simplest common denominator of Alice's and Bob's expressions is 4x2, while the simplest common denominator of Bob's and Carol's expressions is 12x3. The simplest common denominator of Alice's and Carol's expressions is 6x3. To explain further, Alice's expression can be any fraction with 1 as the numerator and a constant integer times x2 as the denominator, therefore, the denominator of Alice's expression can be any multiple of 4, i.e. 4x2, 8x2, 12x2, 16x2, 20x2 and so on.

Bob's expression can also be any fraction with 1 as the numerator and a constant integer times x2 as the denominator. However, the denominator of Bob's expression must be a multiple of both 4 and 6, i.e. 12x2, 24x2, 36x2, 48x2 and so on. Therefore, Carol's expression must be in the form of a fraction with 1 as the numerator and a constant integer times x3 as the denominator. This means that the denominator of Carol's expression must be a multiple of 6, i.e. 6x3, 12x3, 18x3, 24x3, 30x3 and so on. Hence, all possible expressions that could be Carol's are 1/6x3, 1/12x3, 1/18x3, 1/24x3, 1/30x3 and so on.



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