Solve the equation in the image (yr 8 maths, 50pts)

Answer Section 1. <3
Heyy, I'm sunny and I'm here to help you :)
(P.S: answer in explanation)

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Explanation Section:

It is false

If f(x) is a function , then for each value of x there should be  a single y values

For input 0 there is a output 0

for input 10, the output is 2

for input 15, output is 3

For input 5, we have two output 1 and 3

for single input 5, the function cannot have two outputs 1  and 3

So this f(x) is not a function

Bye! - SunnyBunny <3

The probability that the red die shows a 2 and the green die shows a 5 is 1/36

The sample space of a die is

S = {1, 2, 3, 4, 5, 6}

This means that

Red die = {1, 2, 3, 4, 5, 6}

Green die = {1, 2, 3, 4, 5, 6}

On the dice, we have

P(Red = 2) = 1/6

P(Green = 5) = 1/6

The probability that the red die shows a 2 and the green die shows a 5 is

P = P(Red = 2) * P(Green = 5)

Substitute the known values in the above equation

P = 1/6 *1/6

Evaluate the product

P = 1/36

Hence, the probability that the red die shows a 2 and the green die shows a 5 is 1/36

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Answer:

g(x) = (x + 1)² + 1

Step-by-step explanation:

the original function

f(x) = x²

for the new function g(x)

it is shifted 1 unit to the left and 1 unit up.

the shift to the left is done by adding these units to the input variable x :

g(x) = f(x+1) = (x+1)²

that way we get the function value for x+1 already at x :

1 unit "earlier" than in the original.

and the shift up is easy.

whatever the function calculates, we simply add 1 to everything.

the whole curve stays as it is, just one unit higher. g

so, the final g(x) = f(x+1) + 1 = (x + 1)² + 1

The sum of the given expression expressed as a quadratic equation is 10x^2 + 13x + 11

Expressions are equations separated by mathematical signs. This expressions are known to contains certain unknowns

Given the following expression

10x^2 +7x+6 and 6x + 5

We are to take the sum of both expression to have:

f(x) = 10x^2 +7x+6 + 6x + 5

Collect the like terms

f(x) = 10x^2 + 7x + 6x + 6 + 5

f(x) = 10x^2 + 13x + 11

Hence the sum of the given expression expressed as a quadratic equation is 10x^2 + 13x + 11

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Answer:

4/7

Step-by-step explanation:

[tex]\frac{6}{7} times \frac{2}{3}[/tex] 6x2=12

7x3=21

[tex]\frac{12}{21} = \frac{4}{7}[/tex]

The answer is B.

If the terminal point of θ is at (0, -1), then tanθ is equal to :

The tangent of the given angle is undefined, so the correct option is B.

The tangent function is one of the main six trigonometric functions and is generally written as tan x. It is the ratio of the opposite side and the adjacent side of the angle in consideration in a right-angled triangle.

Given that on a unit circle, the terminal point of θ is (0, - 1) we need to determine tan θ,

We know that the terminal point of θ is (0, -1).

Now, the tangent of an angle is equal to the quotient between the y-component and the x-component of the terminal point, then we have:

tan(θ) = =1/0

And we can't divide by zero, so it is undefined, then the correct option is B.

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The total number of students that plotted the number of books they read was 18, making the 4th option, a correct choice, using the dot plot.

Any data that may be shown as dots or tiny circles is called a dot plot. Given that the height of the bar created by the dots indicates the numerical value of each variable, it is comparable to a bar graph or a simple histogram. Small amounts of data are shown using dot plots.

In the question, we are informed that Mrs. Kelley asked her students to plot the number of books they read over the summer. a dot plot titled books read over the summer goes from 0 to 7. 0 has 1 dot, 1 has 3 dots, 2 has 6 dots, 3 has 2 dots, 4 has 3 dots, 5 has 1 dot, 6 has 2 dots, and 7 has 0 dots.

We are asked to find the total number of students that plotted the number of books they read using the dot plot.

The dot plot is attached to the solution.

The total number of students = The total number of dots = 1 + 3 + 6 + 2 + 3 + 1 + 2 + 0 = 18.

Thus, the total number of students that plotted the number of books they read was 18, making the 4th option, a correct choice, using the dot plot.

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The smaller number that we can take is x = 14, and in that case, the value of the other number is y = 34

First, we have two numbers, x and y, such that:

y = 6 + 2*x

"the first number is 6 more than 2 times another number".

Now we know that the sum of these two numbers is smaller than 50, then we can write:

x + y < 50

Replacing y by the above equation we get:

x + 6 + 2x <  50

3x + 6 < 50

Now we can solve that inequality for x:

3x < 50 - 6 = 44

x < 44/3 = 14.6

And x can only be a whole number, then:

x ≤ 14

The smaller number that we can take is x = 14, and in that case, the value of the other number is:

y = 6 + 2*14 = 34

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Answer:

angle l = 115

angle k = 115

angle j = 114

angle i = 66

Step-by-step explanation:

angle l = it is opposite to 115 so its the same

angle k = opposite opposing angles with angle l

angle j = 180-66=114 (between 2 parallel lines the sum of 2 angles is 180)

andle i = 180-114=66 (straight line = 180 degrees so subtract angle j to get i)

2r + t + r

3r + t

The correct answer is C - None of the Above.

When we combine like terms, we combine terms that have the same variables but different coefficients. We cannot add 2r and t because r and t are not the same variables.

Hope this helps!

Answer:

None of the above

Step-by-step explanation:

Because the answer is 3r + t

When we make inferences about the difference of two independent population proportions, we assume that it is a random sample, and the number of successes and failures are at least 15 in each group.

Two independent proportions tests involve comparing the proportions of two unrelated datasets.

For these two datasets to be regarded as an independent population, the following must be true or assumed to be true

Hence, the above highlights are the assumptions of two independent population proportions.

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By direct evaluation we conclude that the point (x, y) = (1, - 2) lies on the graph of the quadratic equation h(x) = - 2 · x². (Correct choice: C)

In this problem we have three ordered pairs to be checked on a given function by direct evaluation, a ordered pair lines on the curve of function if and only if the x-value of the ordered pair leads to the y-value by evaluating in the function. Now we proceed to evaluate each of the three points at the function presented in the statement:

(x, y) = (1, 4)

h(1) = - 2 · 1²

h(1) = - 2

By direct evaluation we conclude that the point (x, y) = (1, - 2) lies on the graph of the quadratic equation h(x) = - 2 · x². (Correct choice: C)

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The dimensions of the rectangular plot of land that sits on a riverbank is 32 m by 9 m or 18 m by 16 m.

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value while a dependent variable is a variable that depends on other variable.

Let x represent the length and y represent the width. Hence:

x + 2y = 50

x = 50 - 2y

Also:

xy = 288

(50 - 2y)y = 288

y = 9; and y = 16

x = 32; and x = 18

The dimensions of the rectangular plot of land that sits on a riverbank is 32 m by 9 m or 18 m by 16 m.

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Answer:

She used 9 tiles which are 3 cm long

Step-by-step explanation:

cuz 3x9=27 and yea

x + 7 = -8

(x + 7) - (7) = -8 - (7)

x = -8 - 7 = -15

The correct answer is -15

❄ Hi there,

let us first consider this: What should we do to get x all alone, on one side of the equation?

Since

we should

[tex]\ \sf{x=-8-7}[/tex]

[tex]\triangleright \ \sf{x=-15}[/tex]

That's it!

❄

The number of rectangles of different sizes can be formed from 36 identical rectangles is 5

From the question, we have proofs of;

Total number of identical squares = 36

Now, let the measurement of the side of each square be 1 unit

We have that the formula for area of a square is;

Area of a square = Side × Side square units

We have the area of the square to be;

Area of each square = 1×1 = 1 square units

This is so because the rectangles are identical both in length and width

Let's find the area of the identical squares

Area of total 36 identical squares

=  36×1 square units

=  36 square units

So Area of the rectangle = length × breadth square units

if the rectangles are formed from 36 identical squares then their areas are the same

Total area of required rectangles = 36 square units

It can be written as;

36 = length × breadth

(1,36) , (2,18),(3,12),(4,9),(6,6) are the different rectangles formed from 36 identical squares

Total rectangles = 5

Thus, the number of rectangles of different sizes can be formed from 36 identical rectangles is 5

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The work done (in foot-pounds) in stretching the spring from its natural length to 0.7 feet beyond its natural length is 1.23 foot-pound

From the question given above, the following data were obtained:

F = Ke

Divide both sides by e

K = F/ e

K = 3 / 0.6

K = 5 pound/foot

Thus, the spring constant of the spring is 5 pound/foot

Wd = ½Ke²

Wd = ½ × 5 × 0.7²

Wd = 2.5 × 0.49

Wd = 1.23 foot-pound

Therefore, the work done in stretching the spring 0.7 feet is 1.23 foot-pound

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Answer: [tex]\Large\boxed{Midpoint=(5,~-2 )}[/tex]

Step-by-step explanation:

Given information

[tex](x_1,~y_1)=(6,~-7)[/tex]

[tex](x_2,~y_2)=(4,~3)[/tex]

Given the midpoint formula

[tex]Midpoint=(\dfrac{x_1+x_2}{2} ,~\dfrac{y_1+y_2}{2} )[/tex]

Substitute values into the given formula

[tex]Midpoint=(\dfrac{(6)+(4)}{2} ,~\dfrac{(-7)+(3)}{2} )[/tex]

Simplify values on the numerator

[tex]Midpoint=(\dfrac{10}{2} ,~\dfrac{-4}{2} )[/tex]

Simplify the fractions

[tex]\Large\boxed{Midpoint=(5,~-2 )}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

Sample space:

{(H, 1), (H, 2), (H, 3), (H, 4), (H, 5), (T, 1), (T, 2), (T, 3), (T, 4), (T, 5)}

Step-by-step explanation:

Tossing a coin has two possible outcomes, heads (H) and tails (T).

Spinning the spinner has 5 possible outcomes, 1, 2, 3, 4, 5.

Table:

First spin                   H     H     H     H     H    T     T     T     T     T

Second spin              1      2      3     4      5     1     2     3     4     5

Sample space:

{(H, 1), (H, 2), (H, 3), (H, 4), (H, 5), (T, 1), (T, 2), (T, 3), (T, 4), (T, 5)}

The correct graph is in the attached image.

Answer:

  B.  A linear graph of solid line intercepts X-axis at the point (2, 0) and Y-axis at the point (0, -4)

Step-by-step explanation:

The boundary line of an inequality is graphed as though the expression were an equality. The nature of the line used will depend on the nature of the inequality.

When the inequality includes the "or equal to" case (≤ or ≥), the boundary line is part of the solution set. It is drawn as a solid line.

When the inequality excludes the "or equal to" case (< or >), the boundary line is not part of the solution set. It is drawn as a dotted or dashed line.

The given inequality

  y ≤ 2x -4

includes the "or equal to" case, so the boundary line is solid.

The equation of the boundary line is written in slope-intercept form:

  y = mx +b . . . . . . . line with slope m and y-intercept b

  y = 2x -4 . . . . . . . boundary line with slope 2 and y-intercept -4.

This tells you that the boundary line intercepts the y-axis at the point (0, -4).

The correct expressions are sinC = 12/25.5 = 24/51, <A = 62 degrees and tan A = 1.875

The given figure is a right triangle with legs 12.0 and 22.5cm and the hypotenuse 25.5cm

For sinA, <A is the reference angle, hence the opposite side will be 22.5cm

sin A = opp/hyp

sinA = 22.5/25.5

For cos C, the adjacent side will be 22.5cm, hence the measure of cos C is 22.5/25.5

cosC = 22.5/25.5

Similarly, sinC = 12/25.5 = 24/51

<A = 180-(90 +38)

<A =180 - 128
<A = 62 degrees

tan A = opp/adj

tan A = 22.5/12 = 1.875

tan C = 12/22.5

tan C = 0.533

Hence the correct expressions are sinC = 12/25.5 = 24/51, <A = 62 degrees and tan A = 1.875

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The line that is not another name for Q is RL

For a line to represent the point Q, the following must be true:

Using the above highlights,

Hence, the line that is not another name for Q is RL

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Answer:

3, 7, 14

Step-by-step explanation:

Considering the given box plots, it is found that:

a) They had the same IQR.

b) Athlete A went on the shortest training ride.

c) Athlete B went on more rides longer than 35 miles.

d) Athlete B had a greater median distance.

It is a plot that focuses the interquartile range of the population, which is the difference between the third and the first quartile, but gives a five number summary of the population, composed by these following measures.

Hence, for Athlete A, we have that:

For Athlete B, we have that:

Hence:

a) They had the same IQR.

b) Athlete A went on the shortest training ride.

c) Athlete B went on more rides longer than 35 miles(as it is less than his median).

d) Athlete B had a greater median distance.

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The value of the product expression 6 * 330 is 1980

The product expression is given as:

6 * 330

Express 330 as the product of 33 and 10

6 * 330 = 6 * 33 * 10

Express 33 as the product of 3 and 11

6 * 330 = 6 * 3 * 11 * 10

Evaluate the product of 6 and 3

6 * 330 = 18 * 11 * 10

Evaluate the product of 11 and 10

6 * 330 = 18 * 110

Evaluate the product of 18 and 110

6 * 330 = 1980

Hence, the value of the product expression 6 * 330 is 1980

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Answer: (f+g)(x)=2(x-2)(x+1).

Step-by-step explanation:

[tex]f(x)=x^2-3x-4\ \ \ \ \ g(x)=x^2+x\\(f+g)(x)=(x^2-3x-4)+(x^2+x)\\(f+g)(x)=x^2-3x-4+x^2+x\\(f+g)(x)=2x^2-2x-4\\(f+g)(x)=2*(x^2-x-2)\\(f+g)(x)=2*(x^2-2x+x-2)\\(f+g)(x)=2*(x*(x-2)+(x-2))\\(f+g)(x)=2*(x-2)*(x+1).[/tex]

Step-by-step explanation:

Because the two sides have been shown to be equivalent, the equation is an identity.

Answer:

The slope is -3.

Step-by-step explanation:

The slope is the Rise/Run between the two points.  The change in y for every change in x.  Take the two points and calculate the:

RISE = (-6 - 3) = -9

RUN = (8 - 5) = 3

Rise/Run, or slope, is = -9/3 or -3

I graphed a line with slope of -3 and then added 18 to force the line to intersect the two given points.

The factors of the given expression is (4m/n + 5m/n)(5m/n-6n/m).

The given expression is 20m²/n²- 30n²/m² +1.

We need to factorise the given expression.

To factor, a trinomial in the form x²+ bx + c, find two integers, r and s, whose product is c and whose sum is b.

Rewrite the trinomial as x²+ rx + sx + c and then use grouping and the distributive property to factor the polynomial. The resulting factors will be (x + r) and (x + s).

Now, we can rewrite 20m²/n² +1 - 30n²/m² as 20m²/n² +25mn/mn- 24mn/mn- 30n²/m².

=(20m²/n² +25mn/mn)- (24mn/mn- 30n²/m²)

=5m/n(4m/n + 5m/n)-6n/m(4m/n+5n/m)

=(4m/n + 5m/n)(5m/n-6n/m)

Therefore, the factors of the given expression is (4m/n + 5m/n)(5m/n-6n/m).

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