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2 years ago

Solve. 9 m 3 − 27 m 2 − 252 m = 0

Mathematics

1 answer:

Brrunno [24]2 years ago

4 0

Answer:

m = 0

m = 7

m = -4

Step-by-step explanation:

$\sf 9m^3-27m^2-252m=0$

Divide by 9:

$\sf \implies m^3-3m^2-28m=0$

Factor out common term m:

$\sf \implies m(m^2-3m-28)=0$

Factor expression in parentheses:

$\sf \implies m(m-7)(m+4)=0$

Therefore,

$\sf \implies m=0$

$\sf \implies m-7=0 \implies m=7$

$\sf \implies m+4=0 \implies m=-4$

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How do you solve -b -2 >8 step by step?

AURORKA [14]

-b-2>8

add 2 to both sides

-b>10

multiply both sides by -1

b>-10

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3 years ago

Could you please help with this question for domain, range, and end behavior? I started it, but I think I'm doing it wrong.

Tanzania [10]

It looks like you have the domain confused for the range! You can think of the domain as the set of all "inputs" for a function (all of the x values which are allowed). In the given function, we have no explicit restrictions on the domain, and no situations like division by 0 or taking the square root of a negative number that would otherwise put limits on it, so our domain would simply be the set of all real numbers, R. Inequality notation doesn't really use ∞, so you could just put an R to represent the set. In set notation, we'd write

$\{x\in\re\mathbb{R}\}$

and in interval notation,

$(-\infty,\infty)$

The range, on the other hand, is the set of all possible outputs of a function - here, it's the set of all values f(x) can be. In the case of quadratic equations (equations with an x² term), there will always be some minimum or maximum value limiting the range. Here, we see on the graph that the maximum value for f(x) is 3. The range of the function then includes all values less than or equal to 3. As in inequality, we can say that

$f(x)\leq3$ ,

in set notation:

$\{f(x)\in\mathbb{R}\ |\ f(x)\leq3\}$

(this just means "f(x) is a real number less than or equal to 3")

and in interval notation:

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3 years ago

The table shows data from a survey about the number of times families eat at restaurants during a week. The families are either

Anna11 [10]

Solution:

1. Rome

Minimum=0

Maximum=16

$Q_{1}=3, Q_{3}=13, {\text{IQR}=Q_{3}-Q_{1}=13-3=10,$

Median , $Q_{2}=8.5$

Mean = 8

Standard Deviation(σ)=5.4

As, difference between , Maximum -Mean =Mean - Minimum=8

So, Mean will Worthy description to find the center of Data set, given about Rome.

2. New York

Minimum=1

Maximum=20

$Q_{1}=4.5, Q_{3}=6, {\text{IQR}=Q_{3}-Q_{1}=6-4.5=1.5,$

Median , $Q_{2}=5.5$

Mean = 7.25

Standard Deviation(σ)=6.1

As, for New york , Mean is not the mid value, that is difference between Mean and Minimum is not same as Maximum and Mean.

As, you can see , the three Quartiles , $Q_{1},Q_{2},Q_{3}$ are very close to each other, it means , other data values are quite apart from each other. So, Mean will not appropriately describe the given data.So, in this case Median will suitable to find the center.

Option (B): The Rome data center is best described by the mean. The New York data center is best described by the median.

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3 years ago

What is the surface area of a box that is 20.1 m long, 6.8 m wide and 7.4 m high?

blsea [12.9K]

Answer:

Surface area of the box is $=671.48m^2$

Step-by-step explanation:

The box is in the shape of a cuboid:

Surface area of the cuboid = 2(L*W+W*H+H*L)

Length(L)=20.1 m

Width(W)=6.8 m

Height(H)=7.4 m

Surface area:

$2((20.1*6.8)+(6.8*7.4)+(7.4*20.1))\\\\=2(136.68+50.32+148.74)\\\\=2(335.74)\\\\\=671.48m^2\\\\$

The surface area of the box is $=671.48m^2$

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4 years ago

The function f(x) = x2 + 10x - 3 written in vertex form is f(x) = (x + 5)2 – 28. What are the coordinates of the vertex?

alina1380 [7]

Answer:

Step-by-step explanation:

The vertex form of a quadratic function f(x) = ax² + bx + c:

f(x) = a(x - h)² + k

(h, k) - coordinates of a vertex

We have f(x) = x² + 10x - 3 in the vertex form f(x) = (x + 5)² - 28.

f(x) = (x - (-5))² + (-28) → h = -5, k = -28

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3 years ago