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2 years ago

If f(x) = 2x^2+3 and g(x)= 5x, evaluate the following: a. f(g(x)) b. g(g(3)) c. g(f(-2))

Mathematics

1 answer:

marissa [1.9K]2 years ago

8 0

Answer:

A = 50x^2+3

B = 75

C = 55

Step-by-step explanation:

$f(x)=2x^2+3\\g(x)=5x$

A. f(g(x))

$2(5x)^2+3\\2(25x^2)+3\\=50x^2+3$

B. g(g(3))

$5(5(3))\\5(15)\\=75$

C. g(f(-2))

$g(2(-2)^2+3)\\g(8+3)\\g(11)\\5(11)\\=55$

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Use the discriminant to determine how many real number solutions exist for the quadratic equation –4j2 + 3j – 28 = 0. A. 3 B. 2

Zepler [3.9K]

Answer:

C. 0

Step-by-step explanation:

–4j^2 + 3j – 28 = 0

The discriminant is b^2-4ac if >0 we have 2 real solutions

=0 we have 1 real solutions

<0 we have 2 imaginary solutions

a = -4, b =3 c = -28

b^2 -4ac

(3)^2 - 4(-4)*(-28)

9 - 16(28)

9 -448

This will be negative so we have two imaginary solutions.

Therefore we have 0 real solutions

5 0

3 years ago

Masteriza [31]

Answer:

3 units by 4 units

8 0

3 years ago

Photo attached A. -2 B. -1 C. 1/-2 D. 1/2

kifflom [539]

Step-by-step explanation:

(X1,Y1) = (-2,2)

(X2,Y2) = (0,1)

• Find slope.

m = (Y2 - Y1)/(X2 - X1)

m = (1 - 2)/(0 - (-2))

m = -1/2

The answer is C.

6 0

2 years ago

En la preparación de un perfume se cuenta con dos tipos de esencia base: 1600 ml de una y 1680 ml de otra. Se quiere envasarlas,

Lostsunrise [7]

Answer:

33,600 frascos

Step-by-step explanation:

Resolvemos esta pregunta utilizando el método mínimo común múltiple

Encuentre y enumere los múltiplos de 1600 y 1680 hasta encontrar el primer múltiplo común. Este es el mínimo común múltiplo.

Múltiplos de 1600:

1600, 3200, 4800, 6400, 8000, 9600, 11200, 12800, 14400, 16000, 17600, 19200, 20800, 22400, 24000, 25600, 27200, 28800, 30400, 32000, 33600, 35200, 36800

Múltiplos de 1680:

1680, 3360, 5040, 6720, 8400, 10080, 11760, 13440, 15120, 16800, 18480, 20160, 21840, 23520, 25200, 26880, 28560, 30240, 31920, 33600, 35280, 36960

Por lo tanto,

LCM (1600, 1680) = 33,600

La menor cantidad de frascos necesarios es 33,600 frascos.

4 0

3 years ago

A rectangle has a height of 5 and a width of 4x^2 – 2x – 6.

bogdanovich [222]

The area of the rectangle is $20x^{2} -10x-30$ units.

Step-by-step explanation:

Step 1:

The area of a rectangle is obtained by multiplying the length with the width of the rectangle.

Considering this a whole rectangle, the length of the rectangle is 5 units and the width is the sum of $4x^{2}$ , $-2x$ , and -6.

So the length of the rectangle = 5 units and

the width of the rectangle $= 4x^{2} -2x-6$ units.

The area of a rectangle = (length)(width).

Step 2:

By substituting the known values, we get

The area of the rectangle $= (5) (4x^{2} -2x-6) = 20x^{2} -10x-30.$

So the area of the rectangle is $20x^{2} -10x-30$ units.

3 0

3 years ago