Find the missing sides and leave answers as radicals in simplest form!! I need help

Answer:

c) k = - 2

Step-by-step explanation:

Equação de Segundo Grau:

Uma equação de segundo grau tem o seguinte formato:

[tex]ax^2 + bx + c = 0[/tex]

Em que [tex]a \neq 0[/tex]

Caso tenham potências de x maiores que dois, o termo que multiplica essas potências deve ser 0.

Neste exercício:

Tem-se a seguinte equação:

[tex](k^2 - 4)x^3 + (k-2)x^2 + 7x - 8 = 0[/tex]

Para ser do segundo grau, necessita-se que:

[tex]k^2 - 4 = 0[/tex]

[tex]k^2 = 4[/tex]

[tex]k = \pm \sqrt{4}[/tex]

[tex]k = \pm 2[/tex]

E também

[tex]k - 2 \neq 0[/tex]

[tex]k \neq 2[/tex]

A intersecção entre [tex]k = \pm 2[/tex] e [tex]k \neq 2[/tex] é [tex]k = -2[/tex], e portanto a resposta é dada pela alternativa c.

O valor de k que torna a equação uma equação de segundo grau para a equação considerada é dado por: Opção C: k = -2

For a single variable equation, degree of an equation is the highest power the variable possess, such that its coefficient is non-zero.

A second degree equation is that equation where the maximum power involved in that equation is 2 (such that its coefficient is non-zero).

For this case, the considered equation is:

(k² – 4) x³ + ( k – 2 )x² + 7x - 8 = 0

For making it second degree, we would have to vanish the coefficient of x³, and by vanish, we mean we would like to make it 0, but simultaneously, we'd have to take care that coefficient of x² doesn't become 0 as we need it to be non-zero.

So we get two mathematical statements:

or

[tex](k^2 - 4) = 0\\k - 2 \neq 0[/tex]

Taking first equation, we get:

[tex]k^2 -4 = 0\\k^2 = 4\\k = \pm \sqrt{4} = \pm 2[/tex]
Thus, k = 2 or k = -2

From second statement, we get:

[tex]k -2 \neq 0\\\text{adding 2 on both the sides}\\k \neq 2[/tex]

Thus, from both the results, we conclude that k = -2 is correct choice.

Thus, the value of k that makes the equation a second degree equation for the considered equation is given by: Option C: k = -2

Learn more about second degree equation here:
https://brainly.com/question/17167165

Answer:

y = 4x - 3

Step-by-step explanation:

(-2, -11) & (3, 9)

First you want to find the slope of the line that passes through these points. To find the slope of the line, we use the slope formula: (y₂ - y₁) / (x₂ - x₁)

Plug in these values:

(9 - (-11)) / (3 - (-2))

Simplify the parentheses.

= (20) / (5)

Simplify the fraction.

20/5

= 4

This is your slope. Plug this value into the standard slope-intercept equation of y = mx + b.

y = 4x + b

To find b, we want to plug in a value that we know is on this line: in this case, I will use the second point (3, 9). Plug in the x and y values into the x and y of the standard equation.

9 = 4(3) + b

To find b, multiply the slope and the input of x(3)

9 = 12 + b

Now, subtract 12 from both sides to isolate b.

-3 = b

Plug this into your standard equation.

y = 4x - 3

This is your equation.

Check this by plugging in the other point you have not checked yet (-2, -11).

y = 4x - 3

-11 = 4(-2) -3

-11 = -8 - 3

-11 = -11

Your equation is correct.

Hope this helps!

Answer: 2 g/cm^3

Step-by-step explanation:

Remember the relation:

density = mass/volume.

Now, we know that:

Density of metal A = 2.4 g/cm^3

Density of metal B = 1.8 g/cm^3

We know that their masses are combined in the ratio 2:3

Then out of the total mass of metal C, 2 parts are from metal A and 3 parts are from metal B.

Mass of metal C = 60g

mass of metal A = (2/5)*60g =24g

mass of metal B = (3/5)*60g = 36g

Now that we know the mass of each metal, we can find their volumes by:

volume = mass/density

Volume of metal A = (24g)/(2.4g/cm^3) = 10cm^3

Volume of metal B = (36g)/(1.8g/cm^3) = 20cm^3

The total volume of metal C will be equal to the sum of the volumes of metal A and B, then:

Volume of metal C = 10cm^3 + 20cm^3 = 30cm^3

Then we know the volume and weight of metal C, then the density of metal C is:

Density of metal C = (60g)/(30cm^3)= 2 g/cm^3

Answer:

9 & 12

Step-by-step explanation:

For the first box you multiply 2x3 which would give you 6 and then you would add 3 and that would give you 9.

For the second box you would multiply 2x4 which would give you 8 and then you would add 4 and that would give you the final pruduct of 12.

Answer:

C. Disagree

Explanation:

Because when you're adding mixed fractions, you don't just make them/find there denominator's equivalent/LCM and them, you have to first convert them to improper fractions.

Hope this helps