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adell [148]
3 years ago
12

The system of inequalities graphed here is __________. A) inconsistent. B) indeterminate. C) consistent and dependent. D) consis

tent and independent.

Mathematics
1 answer:
kodGreya [7K]3 years ago
7 0
ANSWER

A) Inconsistent

EXPLANATION

If a system of equations has at least one solution, it is said to be consistent.

If the the system has a unique solution, then it is consistent and independent.

If the the system has infinitely many solutions, then it is consistent and dependent.

If the system of equations has no solution at all, then it is said to be inconsistent.

From the graph above, the two straight lines do not intersect because they are parallel and have different y-intercepts.

Since the two lines never meets, there is no solution for the system of equations they represent.

The correct choice is A.
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The volume of a cone of radius r and height h is given by V=πr²h³. If the radius and the height both increase at a constant rate
Aloiza [94]

Answer:

The volume of cone is increasing at a rate 1808.64 cubic cm per second.

Step-by-step explanation:

We are given the following in the question:

\dfrac{dr}{dt} = 12\text{ cm per sec}\\\\\dfrac{dh}{dt} = 12\text{ cm per sec}

Volume of cone =

V = \dfrac{1}{3}\pi r^2 h

where r is the radius and h is the height of the cone.

Instant height = 9 cm

Instant radius = 6 cm

Rate of change of volume =

\dfrac{dV}{dt} = \dfrac{d}{dt}(\dfrac{1}{3}\pi r^2 h)\\\\\dfrac{dV}{dt} = \dfrac{\pi}{3}(2r\dfrac{dr}{dt}h + r^2\dfrac{dh}{dt})

Putting values, we get,

\dfrac{dV}{dt} = \dfrac{\pi}{3}(2(6)(12)(9) + (6)^2(12))\\\\\dfrac{dV}{dt} =1808.64\text{ cubic cm per second}

Thus, the volume of cone is increasing at a rate 1808.64 cubic cm per second.

5 0
3 years ago
I know how many line of symmetry but i dont know how to explain how i found the lines so can someone do it for me?
11111nata11111 [884]
2 because there are 4 numbers of edges and 4 vertices
7 0
3 years ago
im offering 100 points for this. Using the GCF you found in Part B, rewrite 56 + 96 as two factors. One factor is the GCF and th
Dennis_Churaev [7]

Answer:

Step-by-step explanation: First right 56 + 96 in factor forms while one factor is the GCF and other is a sum of two numbers they do not have a common factor that all you gotta do right 56 + 96 in factor forms and follow the rest

7 0
2 years ago
Read 2 more answers
Find the value of <br><img src="https://tex.z-dn.net/?f=%20log_%7B8%7D%5E%7B512%7D%20" id="TexFormula1" title=" log_{8}^{512} "
valina [46]
Answer: 3
Explanation: logarithm base 8 of 512 is 3
8 0
2 years ago
Two corresponding sides of similar triangles are 2 cm and 5 cm. What is the area of the second triangle if the area of the first
Stella [2.4K]

Answer:

(1) Area of second triangle= 50 cm^2.

(2) Area of ΔABC=98 cm^2.

   and Area of ΔDFG=175 cm^2.

Step-by-step explanation:

<em>" For two similar triangles the ratio of sides is equal to the ratio of square of their areas".</em>

i.e. if a,b are the corresponding sides of two similar triangles and let A and B denote the area of two triangles then we have the relation as:

\dfrac{a^2}{b^2}=\dfrac{A}{B}

(1)

for the first question:

we have a=2, b=5.

A=8 cm^2.

Hence,

\dfrac{2^2}{5^2}=\dfrac{8}{B}\\\\\dfrac{4}{25}=\dfrac{8}{B}

B=50 cm^2.

Hence, the area of second triangle is 50 cm^2.

(2)

In second option we have:

a=6 and b=5.

A-B=77 cm^2.

A=77+B

\dfrac{6^2}{5^2}=\dfrac{A}{B}\\  \\\dfrac{36}{25}=\dfrac{77+B}{B}\\  \\36B=25\times77+25B\\\\36B-25B=25\times77\\\\11B=25\times77\\\\B=25\times7\\\\B=175

Hence area of second triangle i.e. ΔDFG is 175 cm^2.

and area of first triangle i.e. ΔABC=175-77=98 cm^2.




8 0
2 years ago
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