All categories

3 years ago

Use the quadratic formula to si 3x2 + 8x – 4= 0

Mathematics

1 answer:

omeli [17]3 years ago

3 0

Answer:

$\large\boxed{x=\dfrac{-4-2\sqrt7}{3}\ or\ x=\dfrac{-4+2\sqrt7}{3}}$

Step-by-step explanation:

$\text{The quadratic formula for a quadratic equation}\ ax^2+bx+c=0\\\\\text{determinant:}\ \Delta=b^2-4ac\\\\\text{If}\ \Delta0,\ \text{then the equation has two different solutions}\ x=\dfrac{-b\pm\sqrt\Delta}{2a}.$

$\text{We have:}\\\\3x^2+8x-4=0\\\\a=3,\ b=8,\ c=-4\\\\\Delta=8^2-4(3)(-4)=64+48=112>0\\\sqrt\Delta=\sqrt{112}=\sqrt{(16)(7)}=\sqrt{16}\cdot\sqrt7=4\sqrt7\\\\x=\dfrac{-8\pm4\sqrt7}{2(3)}=\dfrac{-8\pm4\sqrt7}{6}=\dfrac{2(-4\pm2\sqrt7)}{6}=\dfrac{-4\pm2\sqrt7}{3}$

You might be interested in

Indicate the answer choice that best completes the statement or answers the question.

Tema [17]

Answer:

Step-by-step explanation:

m<2:

180 - 60 - 48 = 72

Vertical angle thm:

m<1 = 48

m<3:

180 - 62 - 48 = 70

6 0

3 years ago

1. an alloy contains zinc and copper in the ratio of 7:9 find weight of copper of it had 31.5 kgs of zinc.

m_a_m_a [10]

Answer:

Step-by-step explanation:

Question (1). An alloy contains zinc and copper in the ratio of 7 : 9.

If the weight of an alloy = x kgs

Then weight of copper = $\frac{9}{7+9}\times (x)$

= $\frac{9}{16}\times (x)$

And the weight of zinc = $\frac{7}{7+9}\times (x)$

= $\frac{7}{16}\times (x)$

If the weight of zinc = 31.5 kg

31.5 = $\frac{7}{16}\times (x)$

x = $\frac{16\times 31.5}{7}$

x = 72 kgs

Therefore, weight of copper = $\frac{9}{16}\times (72)$

= 40.5 kgs

2). i). 2 : 3 = $\frac{2}{3}$

4 : 5 = $\frac{4}{5}$

Now we will equalize the denominators of each fraction to compare the ratios.

$\frac{2}{3}\times \frac{5}{5}$ = $\frac{10}{15}$

$\frac{4}{5}\times \frac{3}{3}=\frac{12}{15}$

Since, $\frac{12}{15}>\frac{10}{15}$

Therefore, 4 : 5 > 2 : 3

ii). 11 : 19 = $\frac{11}{19}$

19 : 21 = $\frac{19}{21}$

By equalizing denominators of the given fractions,

$\frac{11}{19}\times \frac{21}{21}=\frac{231}{399}$

And $\frac{19}{21}\times \frac{19}{19}=\frac{361}{399}$

Since, $\frac{361}{399}>\frac{231}{399}$

Therefore, 19 : 21 > 11 : 19

iii). $\frac{1}{2}:\frac{1}{3}=\frac{1}{2}\times \frac{3}{1}$

$=\frac{3}{2}$

$\frac{1}{3}:\frac{1}{4}=\frac{1}{3}\times \frac{4}{1}$

= $\frac{4}{3}$

Now we equalize the denominators of the fractions,

$\frac{3}{2}\times \frac{3}{3}=\frac{9}{6}$

And $\frac{4}{3}\times \frac{2}{2}=\frac{8}{6}$

Since $\frac{9}{6}>\frac{8}{6}$

Therefore, $\frac{1}{2}:\frac{1}{3}>\frac{1}{3}:\frac{1}{4}$ will be the answer.

IV). $1\frac{1}{5}:1\frac{1}{3}=\frac{6}{5}:\frac{4}{3}$

$=\frac{6}{5}\times \frac{3}{4}$

$=\frac{18}{20}$

$=\frac{9}{10}$

Similarly, $\frac{2}{5}:\frac{3}{2}=\frac{2}{5}\times \frac{2}{3}$

$=\frac{4}{15}$

By equalizing the denominators,

$\frac{9}{10}\times \frac{30}{30}=\frac{270}{300}$

Similarly, $\frac{4}{15}\times \frac{20}{20}=\frac{80}{300}$

Since $\frac{270}{300}>\frac{80}{300}$

Therefore, $1\frac{1}{5}:1\frac{1}{3}>\frac{2}{5}:\frac{3}{2}$

V). If a : b = 6 : 5

$\frac{a}{b}=\frac{6}{5}$

$=\frac{6}{5}\times \frac{2}{2}$

$=\frac{12}{10}$

And b : c = 10 : 9

$\frac{b}{c}=\frac{10}{9}$

Since a : b = 12 : 10

And b : c = 10 : 9

Since b = 10 is common in both the ratios,

Therefore, combined form of the ratios will be,

a : b : c = 12 : 10 : 9

7 0

3 years ago

Add 34+(−212) using the number line. Select the location on the number line to plot the sum.

nexus9112 [7]

Answer:

-1 3/4

Step-by-step explanation:

3/4 + (-2 1/2)

3/4 - 2

-1 3/4

5 0

3 years ago

PLEASE HELP SOON! ALSO INCLUDE A SMALL EXPLANATION as well as the answer ! I am rewarding 100points if you answer quickly

alina1380 [7]

Answer:

the answer is B

f(x)=-2x+3

Step-by-step explanation:

to get the -2x I did --->

pick two points I used (0,3) and (1,1) and used the equation $\frac{y2-y1}{x2-x1}$

where y2 would be 1 and y1 would be 3

and where x2 would be 1 and x1 would be 0

so you would put the numbers in the equation which would look like $\frac{1-3}{1-0}=\frac{-2}{1}$ and equal -2 which would be -2x in the answer

And the +3 is the y-intercept

4 0

3 years ago

Read 2 more answers

Math help ( 20 pts )

Nimfa-mama [501]

A) The answer is 24 m

x - the distance from the spot on the beach to the parking lot

Triangles that are divided by x distance is similar, and therefore:
x : 18 = 32 : x
x * x = 18 * 32
x² = 576
x = √576
x = 24

Thus, the distance <span>the spot on the beach from the parking lot is 24 m.
</span>

b) The answer is 40 m.

x - the distance from the spot on the beach to the parking lot
b - distance from the parking lot to the refreshment stand.

First, find the horizontal leg (a) of the biggest right triangle. According to the Pythagorean theorem:
a² + b² = c²
a = ?
b = ?
c = 32 m + 18 m = 50 m

Find a from the right triangle which sides are a (as a hypotenuse), x, and 18 m.
x² + 18² = a²
x = 24
24² + 18² = a²
576 + 324 = a²
900 = a²
a = √900
a = 30 m

Now, find b:
a² + b² = c²
30² + b² = 50²
900 + b² = 2500
b² = 2500 - 900
b² = 1600
b = √1600
b = 40 m

Thus the distance from the parking lot to get the refreshment stand is 40 m.

6 0

3 years ago