Greenwood Middle School is having a math competition. Four students are called to the stand to answer a question. The question is:

51.32 – 11.98

answer : -40/41

steps:

soh cah toa

sin is soh

meaning opposite/hypotenuse

opposite is 9 and

hypotenuse is 41

now you can treat it like a triangle and use the pythagorean theorem

a^2 + 9^2 = 41^2

a^2 + 81 = 1681

a^2 = 1600

a = 40

in soh cah toa

cos is adjacent/hypotenuse so

cos is 40/41

its in quadrant 2 so its negative

-40/41

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Answer:

the answer is x=16

Step-by-step explanation:

trust me bro

The matrix expressions are:

The rule for matrix product states that:

If the dimensions of matrix A is m by n, and the dimension of matrix B is n by p.

Then, the dimension of the product matrix is: m by p

Using the above rule, we have:

Expression 1:

[tex]\left[\begin{array}{cc}12&7\\5&3\end{array}\right] * \left[\begin{array}{cc}a&b\\c&d\end{array}\right] = \left[\begin{array}{cc}2&-1\\3&2\end{array}\right][/tex]

Expand:

[tex]\left[\begin{array}{cc}12a + 7c&12b + 7d\\5a + 3c &5b + 3d\end{array}\right] = \left[\begin{array}{cc}2&-1\\3&2\end{array}\right][/tex]

By comparison, we have:

12a + 7c = 2

5a + 3c = 3

12b+ 7d = -1

5b + 3d = 2

Using a graphing tool, we have:

a = -15, b = -17, c = 26 and d = 29

Hence, the matrix expression is:

[tex]\left[\begin{array}{cc}12&7\\5&3\end{array}\right] * \left[\begin{array}{cc}-15&-17\\26&29\end{array}\right] = \left[\begin{array}{cc}2&-1\\3&2\end{array}\right][/tex]

Expression 2:

[tex]\left[\begin{array}{cc}6.75&3\\-9&-4\end{array}\right] * \left[\begin{array}{c}a&b\end{array}\right] = \left[\begin{array}{c}8&5\end{array}\right][/tex]

Expand:

[tex]\left[\begin{array}{c}6.75a +3b\\-9a - 4b\end{array}\right] = \left[\begin{array}{c}8&5\end{array}\right][/tex]

By comparison, we have:

6.75a + 3b = 8

-9a - 4b = 5

Using a graphing tool, the system of equation has no solution

Hence, the matrix expression cannot be solved

Expression 3:

[tex]\left[\begin{array}{cc}-2&3\\-4&5\end{array}\right] * \left[\begin{array}{c}a&b\end{array}\right] = \left[\begin{array}{c}6&8\end{array}\right][/tex]

Expand:

[tex]\left[\begin{array}{c}-2a +3b &-4a +5b\end{array}\right] = \left[\begin{array}{c}6&8\end{array}\right][/tex]

By comparison, we have:

-2a + 3b = 6

3a + 5b = 8

Using a graphing tool,

a = 3 and b = 4

Hence, the matrix expression is:

[tex]\left[\begin{array}{cc}-2&3\\-4&5\end{array}\right] * \left[\begin{array}{c}3&4\end{array}\right] = \left[\begin{array}{c}6&8\end{array}\right][/tex]

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Answer:

Step-by-step explanation:

32.8 = 164/5

= 32/4/5

as a fraction

To convert the decimal 32.8 to a fraction, just follow these steps:

Step 1: Write down the number as a fraction of one:

32.8 = 32.8/1

Step 2: Multiply both top and bottom by 10 for every number after the decimal point:

As we have 1 numbers after the decimal point, we multiply both numerator and denominator by 10. So,

32.8

1

= (32.8 × 10)

(1 × 10)

= 328/10

.

Step 3: Simplify (or reduce) the above fraction by dividing both numerator and denominator by the GCD (Greatest Common Divisor) between them. In this case, GCD(328,10) = 2. So,

(328÷2)

(10÷2)

= 164/5

when reduced to the simplest form.

As the numerator is greater than the denominator, we have an IMPROPER fraction, so we can also express it as a MIXED NUMBER, thus 328/ 10

is also equal to 32/4 /5

when expressed as a mixed number.

Answer:

The incenter....

Step-by-step explanation:

The point at which all three of the angle bisectors of a triangle meet is known as the incenter

dont confuse it with the circumcenter and the centroid.

i hope this helps!!!

The equation y = 2x + 3 is a linear equation, and the equivalent equation of y = 2x + 3 is y - 3 - 2x = 0

The equation is given as:

y = 2x + 3

Subtract 3 from both sides

y - 3 = 2x

Subtract 2x from both sides

y - 3 - 2x = 0

The above means that the equation y - 3 - 2x = 0 is equal to the equation  y = 2x + 3

Hence, the equivalent equation of y = 2x + 3 is y - 3 - 2x = 0

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Answer:

h ÷ 4.2

Step-by-step explanation:

30/7

Step-by-step explanation:

1.5kg : 350g

1kg = 1000g

So, 1.5kg = 1500g

1500g : 350g

1500/350 = 30/7

The answer is 30/7.

Answer:

$11.40

Step-by-step explanation:

Subtract the bookmark from the total amount

82.00 - 2.20 = 79.80

Divide the answer by how many books you purchased

79.80/7

= ($11.40)

Answer:

All integers are rational numbers .

Step-by-step explanation:

please mark as branliest

Answer:

C

Step-by-step explanation:

the area of a triangle is

baseline × height / 2

so, we know in our case

b(b+12) = 189 cm²

b² + 12b - 189 = 0

let's try to solve this by completing the square.

that means we try to find the expression

(b + k)² + c

that is equal to

b² + 12b - 189

(b + k)² + c = b² + 2kb + k² + c = b² + 12b - 189

so,

2k = 12

k = 6

and then

k² + c = -189

6² + c = -189

36 + c = -189

c = -225

(b + 6)² - 225 = 0

(b + 6)² = 225

b + 6 = 15

b = 9

so, the baseline b = 9 cm.

the height b+12 = 9+12 = 21 cm.

Answer:

It will become 64 times larger

Step-by-step explanation:

Answer:

Its a categorical variable

Step-by-step explanation:

I took the test on edge

Answer:

T-shirt size is a categorical variable.

Step-by-step explanation:

I used chatopenai.com

Answer:

5*4= 20

Step-by-step explanation:

The commutative property is a math rule that says that the order in which we multiply numbers does not change the product.

4*5 = 20

We can change to order and the result is still the same

5*4= 20

Answer:

so just think of it as you drawing circles with the number of shapes in each one like 4x6=24 draw 6 big circles and 4 squares in each one or in this case do it with 4x5

Step-by-step explanation:

Answer: $32

Step-by-step explanation:

Answer:

A Square, Rectangle, and a Rhombus

Step-by-step explanation:

I think that is all of them.

Answer:

2ft 2ft

Step-by-step explanation:

2ft,2ft,2ft,2ft

Answer:

28 hours for 7 days

Step-by-step explanation:

8/2 =

4

4 hours for 1 day

1 x 7 =

7

7 x 4

28

28 for 7 days

Answer:

I would say the answer is 28

Step-by-step explanation:

In two days, you would work 8 hours. To make sense, in one day you would work 4 hours.

Mulitply 4*7

or

2 days: 8 hrs

4 days: 16 hrs

6 days: 24 hrs

7 days: 28hrs

Answer:

Y = -(1/3)X

Step-by-step explanation:

Extract two points

P1(6; -2) P2(-6; 2)

Now:

Y=mX+n. n=0 (interception with Y axis) exis)

Y=mX +0. m= (y2-y1) / (x2-x1)

m= (2+2) / (-6-6)

m= -(1/3)

Y=-(1/3)X

Linear function : y = x + 4

Exponential function : y = 4.5 e^(0.144 x)

Power function : y = 4.5 x^0.415

Answer:

C' (- 25, 5 )

Step-by-step explanation:

since the dilatation is centred at the origin, then multiply each of the coordinates by the scale factor 5

C (- 5, 1 ) → C' (5 × - 5, 5 × 1 ) → C' (- 25, 5 )

Answer:

The right angles are B,D,E,and F

Answer:

x ≈ 17.5

Step-by-step explanation:

using Pythagoras' identity in the right triangle.

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides , that is

x² = 9² + 15² = 81 + 225 = 306 ( take square root of both sides )

x = [tex]\sqrt{306}[/tex] ≈ 17.5 ( to the nearest tenth )

The function is a quadratic function, and none of the given options is a factor of the graph of the function

The zeros of the function are given as:

-3 and 5

This means that:

x = -3 and x = 5

Rewrite as:

x + 3 = 0 and x - 5 = 0

Multiply both equations

(x + 3)(x -5) = 0 * 0

This gives

(x + 3)(x -5) = 0

Express as a function

f(x) = (x + 3)(x -5)

The above means that the factors of the function are (x + 3) and (x -5)

Hence, none of the given options is a factor of the graph of the function

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Answer:

1.6 to nearest tenth.

Step-by-step explanation:

This will be a line which is perpendicular to y = 3x + 5 and the line will also pass through the point (0,0).

Equation of that line:

Slope = -1/3  so we can write:

y - 0 = -1/3(x - 0)

So its y = -1/3 x,

The point where it intersects with  the given line is now found:

-1/3x = 3x + 5

10/3 x = -5

x = -5 *3/10 =  -1.5.

- and the y coordinate = 3(-1.5) + 5 = 0.5.

So the point is (-1.5, 0.5)

and the required distance = √((-1.5)^2 + 0.5^2)

=  1.58

= 1.6 to nearest tenth.