13. a) Write 2 solutions of the equation 2x - 3y = 6
b) Write the equations two lines passing through the point (-3, 2)​

The number of incorrect answers made by Radhika is 8;  the number of incorrect answers made by Mohini = 13

We are given;

Marks obtained for 1 right answer = +3

Marks obtained for 1 wrong answer = −2

(i) Marks scored by Radhika = 20

Marks obtained for 12 correct answers = 12 × 3 = 36

Marks obtained for incorrect answers = Total score − Marks obtained for 12 correct answers = 20 − 36 = −16

Marks obtained for 1 wrong answer = −2

Thus, number of incorrect answers = (−16) ÷(−2) = 8

Therefore, the number of incorrect answers made by Radhika = 8

(ii) Marks scored by Mohini = −5

Marks obtained for 7 correct answers = 7 × 3 = 21

Marks obtained for incorrect answers = Total score − Marks obtained for 12 correct answers = − 5 − 21 = −26

Marks obtained for 1 wrong answer = −2

Thus, number of incorrect answers = (−26) ÷ (−2) = 13

So, the number of incorrect answers made by Mohini = 13

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Answer:

27

Step-by-step explanation:

Supplementary angles add up to 180 degrees

So to find the measure of an angle supplementary to a given angle, we simply subtract the given angle from 180

The given angle here has a measure of 153 degrees

So the angle's supplement has a measure of 180 - 153 = 27 degrees.

Answer:

8

Step-by-step explanation:

The correct answer is option D. which is the angle x will be 38 degrees.

The measure of the angle created when two chords collide inside a circle is one-half the sum of the arcs intercepted by the angle and its vertical angle.

Here we have a measure of arc AB = 58 and the measure of arc CD = 18, So what is the value of x?

The value of x will be calculated by using the angle of arc theorem.

x  =  Sum of the arcs / 2

x  = ( 58 + 18 ) / 2

x  = ( 38 degrees )

Therefore the correct answer is option D. which is the angle x will be 38 degrees.

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The distance between the two points. (-1, 6). (2.8) is 3.61 units

The points are given as: (-1,6) and (2,8)

The distance is calculated using:

[tex]d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2}[/tex]

This gives

[tex]d = \sqrt{(-1 -2)^2 + (6 -8)^2}[/tex]

Evaluate the sum of squares

[tex]d = \sqrt{13}[/tex]

Evaluate the exponent

d = 3.61

Hence, the distance between the two points. (-1, 6). (2.8) is 3.61 units

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Answer: -3x^4-4

Step-by-step explanation: -3x^4+4-8 > =-3x^4-4

Answer: 31

Step-by-step explanation:

Assuming this is a rhombus, then the diagonals are perpendicular, meaning angle MQN measures 90 degrees.

Now, if we consider triangle MNQ, we know that angles in a triangle add to 180 degrees, meaning NMQ measures 31 degrees.

Answer:

1/4

Step-by-step explanation:

1 hour 15 minutes = 75 minutes

25 mins + 75mins = 100 minutes

25/100 minutes x 100 = 25%

25% = 1/4 of the time was spent reading.

The formula for calculating the amount predicted at t years is expressed as:

A = P(1+r)^t. The  predicted value after 2 years is £253.62

The formula for calculating the amount predicted at t years is expressed as:

A = P(1+r)^t

where

Substitute the given parameters

A = 240(1+0.028)^2
A =240 (1.028)^2

A = £253.62

Hence the  predicted value after 2 years is £253.62

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Answer:

Step-by-step explanation:

After completing a fraction division problem, Clarice used multiplication to check her answer. Division: 7 and one-half divided by 1 and one-half = 5. Check: 5 times 1 and one-half = 5 and one-half. Could Clarice verify her answer? Explain.After completing a fraction division problem, Clarice used multiplication to check her answer. Division: 7 and one-half divided by 1 and one-half = 5. Check: 5 times 1 and one-half = 5 and one-half. Could Clarice verify her answer? Explain.Why can you use fraction multiplication to check the answer to a fraction division problem? How do you use multiplication to check a division problem?

Step-by-step explanation:

they are independent systems, so in case of an emergency both systems will activate.

this is like rolling 2 dice and asking for the probability that both will show 1.

the probability that both will fail is the product of the individual probabilities for failure :

0.01 × 0.03 = 0.0003

so, the third answer option is correct.

FYI - the probability for 2 dice to both roll 1 is

1/6 × 1/6 = 1/36

Answer:

Its is already an impoper fraction.

If Leigh uses the strategy, the statement that describes the figure is A. 3 full squares and 12 partial squares.

From the information, Leigh plans to estimate the area of the figure on the grid by identifying the full and partial squares that make up the figure.

It was stated that on a coordinate plane, a figure contains 3 full squares and 12 partial squares.

Therefore, the correct option is A.

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Answer

100

Step-by-step explanation:

bxh is the formula for area of the triangle (base_

so 5x4=20

20x5 (height) = 100

Answer:

80 cm

Step-by-step explanation:

formula

b x h x .5

b= the area of the base

Answer:

9³

Step-by-step explanation:

We know that,

[tex]a^b[/tex] ÷ [tex]a^c[/tex] = [tex]a^b^-^c[/tex]

By following the above, let us solve the given question.

Let us solve now.

⇒ 9⁵ ÷ 9²

⇒ 9⁵⁻²

⇒ 9³

Answer:

45.43

Step-by-step explanation:

Polynomial is an expression that consists of indeterminates(variable) and coefficients. The power function of the energy is e=mc².

Polynomial is an expression that consists of indeterminates(variable) and coefficient, it involves mathematical operations such as addition, subtraction, multiplication, etc, and non-negative integer exponentials.

The power function is a polynomial. Given the energy, e, produced in a nuclear reaction is proportional to the mass, m. Therefore, we can write,

e ∝ m

To remove proportionality we need to add a constant of variation which is c², the square of the speed of light

e = m c²

Hence, the power function of the energy is e=mc².

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Answer: 3360 ft squared

Step-by-step explanation:

Short side : 30 x 14 = 420

Long side 30 x 3 x 14 = 1260

420 + 420 + 1260 + 1260 =  3360

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Area of shorter side

Area of longer sides

Total Lateral surface area

Renark:-

The general LSA formula of cuboid can also be used to solve

Step-by-step explanation:

Equation=>x+x+1=59

2x=58

x=29

the numbers are 29 and 30

In the given image, [tex]a_{23}[/tex] is 5. The correct option is the first option 5

From the question, we are to determine which entry in the given matrix represents [tex]a_{23}[/tex]

NOTE: For any entry denoted as [tex]a_{mn}[/tex], it represents the entry in the m-th row and n-th column.

Thus,  

 [tex]a_{23}[/tex] represents the entry in the 2nd row and 3rd column.

In the given image, the entry in the 2nd row and 3rd column is 5.

Hence, in the given image, [tex]a_{23}[/tex] is 5. The correct option is the first option 5

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Answer:

5

Step-by-step explanation:

The value of f(g(2)) is 2.

An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

The given table is

x       f(x)

–6      1

–3       2

2       5

5       3

8       0

If the coordinates of a function f(x) is defined as (x,y)

then, the coordinates of inverse of f(x) is defined as (y,x).

f(g(y))= f(x)    [ g(x)= (y,x)]

f(g(y))= y

So, If g(x) is the inverse of f(x), the f(g(y)) = y.

Also, we know g(x) is the inverse of f(x), then f(g(2)) = 2.

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Answer:

[tex]\begin{aligned}6(n+6)-(2n+3) & = 6n+36-2n-3\\& = 4n+33\\& = 4n + 32 + 1\\& = 2(2n+16) + 1\end{aligned}[/tex]

Any number multiplied by 2 is even, therefore 2(2n + 16) is even.

If 2(2n + 16) is even, then adding 1 to this makes it odd.

Thus proving that the given expression is an odd number for all [tex]n \in \mathbb{N}[/tex]

     For both of these, we will divide the wanted outcome by the number of possible outcomes. We will end up with a decimal. A decimal multiplied by 100 becomes a percent.

[a] 50%

[tex]\displaystyle \frac{\text{wanted outcomes}}{\text{possible outcomes}} =\frac{\text{student failed}}{\text{Period 2's class}} =\frac{12}{24} =0.5,\:0.5*100=50\%[/tex]

[b] 52%

[tex]\displaystyle \frac{\text{wanted outcomes}}{\text{possible outcomes}} =\frac{\text{student failed from Period 3}}{\text{fails from both classes}} =\frac{13}{25} =0.52,[/tex]

    [tex]\displaystyle 0.52*100=52\%[/tex]

Using the percentage concept, it is found that of those students who are majoring in business, the percentage plans to go to graduate school is given by:

c. 28.8.

The percentage of an amount a over a total amount b is given by a multiplied by 100% and divided by b, that is:

[tex]P = \frac{a}{b} \times 100\%[/tex]

In this problem, there are 252 students majoring is business, and of those, 70 plan to go to graduate school, hence the percentage is given by:

[tex]P = \frac{70}{252} \times 100\% = 28.8\%[/tex]

Hence option C is correct.

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Harry Potter decides it’s too cold for him to stay in Hogwarts and wants to fly straight south, the heading he should have and the velocity of the broom with respect to the ground are mathematically given as

VR = 20, 699 m/s South

Divide horizontal and vertical components of Vs and Vw vectors

For Vs

Vs = Vs cos∅ [s] + Vs Sin∅ [w]

Vs = 18 Co58 [s] + 18 sin∅ [w]

For Vw

Vw = Vw Cos 55' [s] + Vw Sin 55 [E]

5.8333 x Cos 55 (s) + 5-8333 Sin 55 [E]

Vw = 3.3458 [s] + 4.7783 [E]

Resultant velocity VR = Vs + Vw

VR= 18 Coso (s) + 18 sine [w] +3.3458 (5) +42783 (E)

VR = (186030 +3.3458) [5] + (18sing - 4.7183)6]

(Harry Potter) flies south

18sin∅ - 4.7783 18=0

Hence

Sin∅ = 4.7783 18/18

∅ =sin{-1}(4.7783 18/18)

∅  = 15.3943

Harry Potter flies in the direction south to ∅ = $15.3943w]

Hence  velocity

VR = (18 cos∅   + 35452) s + 0

VR = (17.3541 +3-3458) s

VR = 20, 69999 m/s South

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