9) Solve
(x² + 3x)³-16(x² + 3x) - 36 = 0
for x by using substitution.
a) x = -3,1,2,6
b) x = -4,0,1,5
c) x = -5,-1,0,4
d) x = -6, -2,-1,3
e) x = -7,-3, -2,2

The length of side m is, 5.1 inches.

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

In ΔMNO,

⇒ o = 8 inches, m ∠M = 28° and m ∠O = 48°.

Now, Let the length of side m = x

So, By sine rule, we get;

[tex]\rightarrow \sf \dfrac{sin \ M}{m} = \dfrac{Sin \ O}{o}[/tex]

Substitute all the values, we get;

[tex]\sf \rightarrow \dfrac{sin \ 28^\circ}{x} = \dfrac{sin \ 48^\circ}{8}[/tex]

[tex]\sf \rightarrow \dfrac{0.47}{x} = \dfrac{0.74}{8}[/tex]

[tex]\sf \rightarrow x=\dfrac{ 0.47 \times 8}{0.74}[/tex]

[tex]\sf x = 5.08\thickapprox 5.1 \ inches[/tex]

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The rigid transformations that can take AEFD to CFEB are translation, rotation, and reflection.

To describe the rigid transformations that take polygon AEFD to CFEB, we need to identify the transformations that preserve the shape and size of the polygon. Here are some possibilities:

Translation: A translation involves moving the entire polygon without changing its orientation or shape. If we shift polygon AEFD to the right, it will align with polygon CFEB. Therefore, translation is one way to achieve this transformation.

Rotation: If we rotate polygon AEFD around a fixed point, such as the center of the polygon or a vertex, by a certain angle, it can align with polygon CFEB. A rotation preserves the shape and size of the polygon.

Reflection: A reflection involves flipping the polygon across a line, resulting in a mirror image. If we reflect polygon AEFD across a line of reflection, it can match polygon CFEB.

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Answer:

The measure of the central angle in radians is 5.6/8 = 0.7 radians.

The exponential growth model for the baseball player's earnings, in millions of dollars, t years after 2015 is[tex]y = 3 \times (1.04)^t,[/tex]  with a base of 1.04.

To model the exponential growth of the baseball player's earnings, we can use the formula:

[tex]y = a \times (1 + r)^t[/tex]

where:

y represents the earning in millions of dollars

a represents the initial earning in millions of dollars (in this case, $3 million)

r represents the growth rate per year (4%, which can be expressed as 0.04)

t represents the number of years after 2015

In this case, we want to find the earning y (in millions of dollars) t years after 2015.

Since the initial earning in 2015 is $3 million, we can substitute a = 3.

Therefore, the exponential growth model for the player's earnings is:

[tex]y = 3 \times (1 + 0.04)^t[/tex]

Simplifying the expression further, we have:

[tex]y = 3 \times 1.04^t[/tex]

The base of the model is 1.04, which is the decimal representation of the growth rate (4%).

Using this model, we can calculate the player's earnings for any year after 2015 by plugging in the value of t.

For example, if we want to find the earnings 5 years after 2015, we substitute t = 5 into the equation:

[tex]y = 3 \times 1.04^5[/tex]

This will give us the projected earnings in millions of dollars for that particular year.

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Answer:

Step-by-step explanation:

2/5 of the frogs in that portion of the South American rainforest are not poisonous.

On the off chance that 3/5 of the frogs in a rainforest in South America are poisonous, at that point, the remaining division speaks to the frogs that are not poisonous.

To discover this division, we subtract the division of poisonous frogs from 1 (which speaks to the complete):

1 - 3/5 = 5/5 - 3/5 = 2/5

Hence, 2/5 of the frogs in that portion of the rainforest are not poisonous. This fraction represents the parcel of frogs that don't have poisonous characteristics.

It is important to note that this calculation expects that all frogs within the rainforest are either poisonous or notpoisonous, and there are no other conceivable outcomes or middle states.

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$316,160.00

Interest is the amount of money earned on an initial investment.

Simple Interest

Since the question does not talk about being compounded, we can assume the company is earning simple interest. Simple interest is the amount of money earned on the principal. The principal is the initial investment. Additionally, interest is earned at a specific rate; in this case, the rate is 5.2% each year.

Interest Formula

The formula to find the amount of interest earned is I = Prt. In this formula, I is the amount of interest earned, P is the principal, r is the rate as a decimal, and t is the time in years. To find the interest earned, all we need to do is plug in the information we know.

The account will earn $316,160 of interest.

We can also determine the total of the account by using the formula A = P (1 + rt). If we solve this formula, we can figure out that the account total is $1,076,160.

We can expect 258 blocks in the bag to be green.

We have to given that,

A bag has 6 blocks in it. Jerry picks a block out of the bag 60 times. He gets the green block 43 times.

Since, We know that Jerry picked a block out of the bag 60 times, and got the green block 43 times.

So the probability of picking a green block is:

P = 43/60

P = 0.7167

This means that out of every 60 blocks picked, there are 43 green.

Now, For this probability to estimate the number of green blocks in the bag.

since, Jerry picked 60 blocks 6 times

When, we assume that the bag contains a total of 360 blocks , we can multiply this total by the probability of getting a green block:

360 x 0.7167 = 258.012

Thus, We can expect 258 blocks in the bag to be green.

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Based on the given information, we cannot determine if the triangle is acute, right, or obtuse (A, B, C). However, we can conclude that the triangle is scalene (F).

To determine the terms that apply to triangle ABC with vertices A(0, 5), B(1, -3), and C(-3, 3), we can analyze the properties of the triangle based on its side lengths and angles.

Side Lengths:

AB: Distance between points A(0, 5) and B(1, -3)

BC: Distance between points B(1, -3) and C(-3, 3)

AC: Distance between points A(0, 5) and C(-3, 3)

Using the distance formula, we can calculate the side lengths:

AB = [tex]\sqrt{ (1 - 0)^2 + (-3 - 5)^2)} = \sqrt{(1^2 + (-8)^2} = \sqrt{65}[/tex]

BC = [tex]\sqrt{((-3 - 1)^2 + (3 - (-3))^2} = \sqrt{((-4)^2 + 6^2)} = \sqrt{52}[/tex]

AC = [tex]\sqrt{((-3 - 0)^2 + (3 - 5)^2)} = \sqrt{(-3)^2 + (-2)^2)} = \sqrt{13}[/tex]

We can conclude that the triangle is not equilateral (D) since all sides have different lengths. We can also conclude that the triangle is not isosceles (E) since no two sides have the same length. Therefore, the triangle is classified as scalene (F).

In summary, based on the given information, we cannot determine if the triangle is acute, right, or obtuse (A, B, C). However, we can conclude that the triangle is scalene (F).

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Answer:

sin( 3pi/4 ) = -√2/2

So, B.

The amplitude and the period of the function f(x) = 2cos[3(θ + 45)] + 2 are 2 and 2π/3

The Phase shift is 45 and the vertical shift is 2

From the question, we have the following parameters that can be used in our computation:

f(x) = 2cos[3(θ + 45)] + 2

A sinusoidal function is represented as

f(x) = Acos(B(x + C)) + D

Where

Amplitude = A

Period = 2π/B

Phase shift = C

vertical shift = D

Using the above as a guide, we have the following:

Amplitude = 2

Period = 2π/2

Next, we have

Phase shift = 45

vertical shift = 2

Hence, the amplitude is 2 and the period is 2π/3

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Answer:

Step-by-step explanation:

15 % of x  =  3

[tex]\frac{3x}{20} = 3\\ x = 20[/tex]

Answer:

Step-by-step explanation:

3 : 15 × 100 =

0.2 × 100 =

20

3 : 15 = x : 100

x = 3 × 100 : 15

x = 20

Sorry for bad handwriting

if i was helpful Brainliests my answer ^_^

Answer:

891 cm³

Step-by-step explanation:

Since they are the same shape with only their sizes different, that means they have a proportionate ratio so:

2673 / 9 = V / 3

Now make V the formula of the subject:

V = 2673 / 9 TIMES 3 = 891.

The Area of Rhombus QRST is 78.32 in².

We know the formula of Area of Rhombus

= 1/2 x product of diagonals

We have, QS = 8.8 and RT = 17.8

So, Area of Rhombus QRST

= 1/2 x QS x RT

= 1/2 x 8.8 x 17.8

= 78.32 in²

Thus, the Area of Rhombus QRST is 78.32 in².

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A weak correlation between the two variables is depicted by the scatter plot in the supplied image.

The trend line's points are widely dispersed, which suggests that there is little correlation between the variables.

In a scatter plot, the degree of connection between the two variables can be classified as strong or weak.

A weak correlation indicates that there is a lot of scatter around the trend whereas a high relationship indicates that there is very little scatter in comparison to the trend's movement.

Thus, the given association is weak correlation.

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Step-by-step explanation:

Amount = Principal ( 1 + i) ^n     i = decimal interest per month = .08/12

                                                    n = 16 months

     amount = $ 300 ( 1+ .08/12)^16 = $  333.65

Answer: It has ans an equal chance of 50-50

Step-by-step explanation: There are 10 of each type, leaving 20 total, half of the candy is Cherry, the other half is Strawberry.

Using the formula of volume of a sphere and hemisphere, the volume of the figures are given as;

1. 2144.57 m³

2. 696.6 m³

3. 20569.1m³

4. 2637ft³

5. 56.5km³

6. 6381.79 in³

The volume of a sphere is given as 4/3πr³

Where π is a constant whose value is equal to 3.14 approximately. “r” is the radius of the hemisphere.

1. The volume of the sphere is;

v = 4/3 * 3.14 * 8³ = 2144.57m³

2. The volume of the sphere is;

v = 4/3 * 3.14 * (11/2)³ = 696.6m³

3. The volume of the sphere is;

v = 4/3 * 3.14 * 17³ = 20569.1m³

4. The volume of the hemisphere is;

v = 2/3 * 3.14 * 10.8³ = 2637ft³

5. The volume of the hemisphere is;

v = 2/3 * 3.14 * 3³ = 56.5km³

6. The volume of the hemisphere is;

v = 2/3 * 3.14 * (29/2)³ = 6381.79in³

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Answer: £16.25

Step-by-step explanation:

In order to find the answer we will use a method called unitary method, it is very simple and you must know it as it's repeatedly given in Year 7 and 8 here's the explanation

Cost of 3kg= £7.50

Cost of 1 kg = £7.50÷3

=2.5

Cost of 6.5kg = 2.5×6.5 = £16.25

a. The surface area of the cube is reduced .

b . The new surface area of the new solid is 90 in²

The area occupied by a three-dimensional object by its outer surface is called the surface area.

a. The surface area of the original cube is 96 in² and a cube of another 6 in² is removed from the old cube.

This means that the surface area of the cube is reduced.

The surface area of a cube is expressed as;

SA = 6l²

where l is the side length of the cube.

b. The surface area of the new solid = surface area of big cube - surface area of old cube = 96-6

= 90 in²

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a. The category that was chosen as approximately 1/4 will be Cat.

b. The percentage that choose other or cat will be 35%.

c. The percentage that choose dog is 16%

a. It should be noted that to determine the category chosen by approximately one-fourth of the community, we need to look for the corresponding section of the pie chart. This shows the cat.

b. The percentage that choose other or cat will be:

= 10% + 25%

= 35%.

c. The percentage that choose dog is:

= 32% / 2

= 16%

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The circle on a graph by drawing the center point and then drawing a circle around it with a radius of 6.

To graph the circle with the equation (x - 3)² + (y + 3)² = 36, we can start by finding the center and radius of the circle.

The equation of a circle in standard form is (x - h)² + (y - k)² = r² (h, k) represents the center of the circle and r represents the radius.

Comparing the given equation with the standard form, we can see that the center of the circle is (3, -3) and the radius is √36 = 6.

Using this information, we can proceed to plot the circle on a graph:

Plot the center point: (3, -3).

From the center point, move 6 units in each direction (up, down, left, and right) to determine the points on the circle.

Up: (3, -3 + 6) = (3, 3)

Down: (3, -3 - 6) = (3, -9)

Left: (3 - 6, -3) = (-3, -3)

Right: (3 + 6, -3) = (9, -3)

Connect the plotted points to form a circle.

The resulting graph should look like this:

    |            • (3, 3)

    |  

    |    •

    |                     •

__|_____________________________

    |

    |

    |

    |  

    |    • (3, -3)

The center of the circle is denoted by a solid dot (•) in the graph and the other points lie on the circumference of the circle.

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Answer:

Step-by-step explanation:

The direction that the quadratic function f(x) is to be translated is to the left and the units is 4.

Here given two functions, f(x) and g(x).

General form of the quadratic function is,

ax² + bx + c.

It is clear that, f(x) is simply the square of the x values.

f(x) = x²

Since g(x) is the translation of the function f(x) and the value of g(x) = 0, when x = -4,

g(x) = (x + 4)²

That is,

g(x) = f(x + 4).

So f(x) is shifted left by 4 units.

Hence f(x) is shifted left by 4 units.

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Bishnu selling price paid Rs 1,42,048 for the motorcycle.

To find out how much Bishnu paid for the motorcycle, we need to calculate the selling price after the 8% loss.

Let's start with the purchase price: Shiva bought the second-hand motorcycle for Rs 1,53,200.

Then, Shiva spent Rs 1,200 to repair it. So, the total cost for Shiva becomes:

Total cost = Purchase price + Repair cost

= Rs 1,53,200 + Rs 1,200

= Rs 1,54,400

Now, to calculate the selling price after an 8% loss, we need to subtract 8% of the total cost from the total cost:

Loss = 8% of Total cost

= 8/100 * Rs 1,54,400

= Rs 12,352

Selling price = Total cost - Loss

= Rs 1,54,400 - Rs 12,352

= Rs 1,42,048

Therefore, Bishnu selling price paid Rs 1,42,048 for the motorcycle.

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The distance traveled by the supplies is given as follows:

27 feet.

The three trigonometric ratios are the sine, the cosine and the tangent, and they are obtained according to the rules presented as follows:

The distance is the hypotenuse of the right triangle, while the height of 23 feet is opposite to the angle of 60º.

Applying the sine ratio, we have that:

sin(60º) = 23/x

x = 23/sine of 60 degrees

x = 27 feet.

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The context which describes a certain situation from the given is spinning a spinner divided into four equal-sized sections colored red/green/yellow/blue and landing on red or yellow or green or blue.

Certain probability or certain situation is defined as the situation where the event is sure to happen.

Rolling an even number on a standard six-sided die, numbered from 1 to 6.

The die can be rolled to odd number. Soo it is uncertain.

Spinning a spinner divided into four equal-sized sections colored red/green/yellow/blue and landing on red or yellow or green or blue.

This is a certain situation since the spinner will surely land on any of the four colors.

Winning a raffle that sold a total of 100 tickets if you bought 0 tickets.

This is not possible.

Reaching into a bag full of 5 strawberry chews and 15 cherry chews without looking and pulling out a pineapple chew.

This is also not possible.

Hence the certain situation is spinning a spinner.

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