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3 years ago

What is the maximum number of real distinct roots that a cubic equation can have?

Mathematics

2 answers:

Hoochie [10]3 years ago

5 0

3 but in most cases it is 2 real roots and one root has a multiplicity of 2

gogolik [260]3 years ago

4 0

an degree polynomial can have as many as n real roots.

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When Jimmy and Shane went fishing, Shane caught 2 more than three times the number of fish that Jimmy caught. Write an algebraic

ziro4ka [17]

For the answer to the question above,

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3 years ago

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If the volume of a full sphere is 4/3 x pi x radius cubed, what is the volume of a half sphere, also called a hemisphere?

Lady bird [3.3K]

The formula for a hemisphere is: 2/3 π r

if there was a problem to solve, i would be happy to do it.

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3 years ago

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This will be the last prob for today but thx soo much for helping

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Answer:

Step-by-step explanation:

If you simplify you get 0 = 19/3, which is false. So there is no solution.

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3 years ago

2 to the exponent of 5 x 2 to the exponent of 15

just olya [345]

Answer:

${2}^{150}$

Step-by-step explanation:

Expression is represented as:

$( {2}^{5 \times 2} )^{15}$

Solve what's inside the parentheses:

$(2^{10} )^{15}$

Include exponent outside parentheses:

$2^{150}$

This exponent represents 2 to the power of 150.

6 0

2 years ago

If triangle CAT is similar to triangle DOG, which of the following statements is incorrect?

jeyben [28]

Answer:

1. triangle TCA ~ triangle GOD

4. If TC/GD=3/2, then m<T/m<G=3/2.

Step-by-step explanation:

The statements of the question are

1. triangle TCA ~ triangle GOD

2. AT: OG= AC:OD

3. If TC/GD=3/2, then AC/OD=3/2.

4. If TC/GD=3/2, then m<T/m<G=3/2.

5. If the scale factor of triangle CAT to triangle DOG is 3 to 2, then the scale factor of triangle DOG to triangle CAT is 2 to 3.

6. If AC is twice as long as AT, then OD is twice as long as OG

Verify each statement

1) triangle TCA ~ triangle GOD

we know that

If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

In this problem

triangle CAT ~ triangle DOG -----> is given

Reorder

Corresponding sides are named using pairs of letters in the same position on either side of the congruence statement

triangle TCA ~ triangle GDO

therefore

The statement is not correct

2). AT: OG= AC:OD

we know that

If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

In this problem

triangle CAT ~ triangle DOG -----> is given

Applying proportion

$\frac{AT}{OG}=\frac{AC}{OD}=\frac{TC}{GD}$

The statement is true

3). If TC/GD=3/2, then AC/OD=3/2.

we have that

$\frac{AT}{OG}=\frac{AC}{OD}=\frac{TC}{GD}$ ---> see part 2)

$\frac{TC}{GD}=\frac{AC}{OD}$

therefore

The statement is true

4). If TC/GD=3/2, then m<T/m<G=3/2

Remember that

In two similar triangles, corresponding angles are congruent

$m\angle T=m\angle G$

$m\angle T/m\angle G=1$

therefore

The statement is false

5). If the scale factor of triangle CAT to triangle DOG is 3 to 2, then the scale factor of triangle DOG to triangle CAT is 2 to 3

we know that

If the scale factor of triangle CAT to triangle DOG is a/b. then the scale factor of triangle DOG to triangle CAT is b/a

The scale factor will be the reciprocal

therefore

The statement is true

6). If AC is twice as long as AT, then OD is twice as long as OG

we know that

$\frac{AT}{OG}=\frac{AC}{OD}$

Reorder

$\frac{AT}{AC}=\frac{OG}{OD}$

If AC is twice as long as AT ----> AC=2AT

If OD is twice as long as OG ----> OD=2OG

substitute

$\frac{AT}{2AT}=\frac{OG}{2OG}$

simplify

$\frac{1}{2}=\frac{1}{2}$ ----> is true

therefore

The statement is true

5 0

2 years ago