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Anni [7]
3 years ago
12

Which statements are true of the graph of h(x) = ^3 square root of x-4 ? Check all that apply.

Mathematics
2 answers:
kolezko [41]3 years ago
4 0

Answer:

A,B,E

Step-by-step explanation:


Zarrin [17]3 years ago
3 0

Answer: The true statements are,

The domain of h(x) is the set of all real numbers.

The range of h(x) is the set of all real numbers.

The graph of h(x) intercepts the x-axis at (4, 0).

Step-by-step explanation:

Here, the given function is,

h(x) =\sqrt[3]{x-4} -----(1)

Which is cubic root function,

Since, a cubic function can be written as ∛p(x), where p(x) is a polynomial,

We know that,

The all possible value of x in the polynomial p(x) = Set of all real numbers

⇒ The domain of a polynomial = Set of real all numbers

⇒ The domain of a cubic function = Set of real all numbers

Hence, the domain of given function h(x) = Set of all real numbers,

Similarly, the range of a polynomial is also the set of real numbers,

⇒ The range of given function h(x) = Set of all real numbers,

Now, for x-intercept, y = 0 or h(x) = 0,

From equation (1),

0 =\sqrt[3]{x-4}

\implies x-4=0\implies x = 4

Thus, the x-intercept of h(x) is (4,0).

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Is −4[3(x−7)] and 6(14−2x) equiviant
Paraphin [41]

Answer:

Yes.

Step-by-step explanation:

Set the equations equal to each other to determine their equality.

-4[3(x - 7)] = 6(14 - 2x)

Distribute the 3 and the 6 into their respective parenthesis.

-4[3x - 21] = 84 - 12x

Distribute the -4 into the brackets.

-12x + 84

Rearrange the equations.

84 - 12x = 84 - 12x

Since the equations come out to be the same thing on both sides so that any value satisfies it, the equations are equivalent.

4 0
3 years ago
Mike had 119 dollars to spend on 6 books. after buying them he had 11 dollars. how much did each book cost ?
deff fn [24]
18 $ Hope I helped
This is how I came to the result..
119-11= 108
108 : 6 = 18 $
8 0
3 years ago
Find the tangent of ∠I.
Nady [450]

Answer:

tanI = \frac{\sqrt{70} }{5}

Step-by-step explanation:

We require to calculate GH using Pythagoras' identity in the right triangle.

GH² + GI² = HI²

GH² + 5² = (\sqrt{95} )²

GH² + 25 = 95 ( subtract 25 from both sides )

GH² = 70 ( take square root of both sides )

GH = \sqrt{70}

Then

tanI = \frac{opposite}{adjacent} = \frac{GH}{GI} = \frac{\sqrt{70} }{5}

4 0
2 years ago
What is the standard deviation of the following data set rounded to the nearest tenth? 56 ,78 ,123 , 34, 67, 91, 20
quester [9]

Answer:

The standard deviation of the following data set is 32.2

Step-by-step explanation:

step 1

Find the mean

we have

[56,78,123,34,67,9,20]

Sum the data and divided by the number of elements

[56+78+123+34+67+91+20]/7=469/7=67

step 2

For each number: subtract the Mean and square the result

[(56-67)^{2},(78-67)^{2},(123-67)^{2},(34-67)^{2},(67-67)^{2},(91-67)^{2},(20-67)^{2}]

[121,121,3,136,1,089,0,576,2,209]

step 3

Work out the mean of those squared differences

[121+121+3,136+1,089+0+576+2,209]/7=1,036

This value is called the "Variance"    

step 4

Take the square root of the variance

standard\ deviation=\sqrt{1,036}=32.2

6 0
3 years ago
A colony of bacteria is grown under ideal conditions in a laboratory so that the population increases exponentially with time. A
Naddik [55]

Answer:

Initial bacterias = 6006000

Altought I believe is safe to assume that the values were 192,000 and 384,000 instead of 192,192,000 and 384,384,000, in that case the initial bacterias is 6000

Step-by-step explanation:

A exponential growth follows this formula:

Bacterias  = C*rⁿ

C the initial amount

r the growth rate

n the number of time intervals

Bacterias (55 hours) = 192,192,000

Bacterias (66 hours) = 384,384,000

Bacterias(55hours)=C*r^{{\frac{55-t}{t}}} \\Bacterias (66hours) = C*r^{\frac{66-t}{t}}}

If you divide both you can get the growth rate:

\frac{Bacterias (66hours)}{Bacterias(55hours)}=\frac{C*r^{\frac{66-t}{t}}}{C*r^{{\frac{55-t}{t}}}} \\\frac{384,384,000}{192,192,000} =r^{\frac{66-t}{t} -\frac{55-t}{t} } \\2 =r^{\frac{11}{t}}

So with that r = 2 and each time interval correspond to 11 years

Then replacing in one you can get the initial amount of C

Bacterias (55hours)=C*2^{\frac{55-11}{11} } 192,192,000 = C*32\\C= 6006000

7 0
3 years ago
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