All categories

2 years ago

Solve the equation for x, where x is a real number (5 points): -2x^2 + 6x + 4 = 5

1 answer:

6 0

Subtract 5 to both sides so that the equation becomes -2x^2 + 6x - 1 = 0.
To find the solutions to this equation, we can apply the quadratic formula. This quadratic formula solves equations of the form ax^2 + bx + c = 0
                                            x = [ -b ± √(b^2 - 4ac) ] / (2a)
                                            x = [ -6 ± √((6)^2 - 4(-2)(-1)) ] / ( 2(-2) )
                                            x = [-6 ± √(36 - (8) ) ] / ( -4 )
                                            x = [-6 ± √(28) ] / (-4)
                                            x = [-6 ± 2*sqrt(7) ] / (-4 )
                                            x =3/2 ± -sqrt(7)/ 2
The answers are 3/2 + sqrt(7)/2 and 3/2 - sqrt(7)/2.

You might be interested in

What is the volume of the cylinder?

Anna007 [38]

Answer:

B. 2010.62 ft³

Step-by-step explanation:

The formula for the volume of a cylinder is ...

V = πr²h . . . . . where r is the radius and h is the height

Filling in the numbers and doing the arithmetic, we get ...

V = π(8 ft)²(10 ft) = 640π ft³ ≈ 2010.6193 ft³ ≈ 2010.62 ft³

The volume of the cylinder is about 2010.62 ft³.

7 0

3 years ago

(08.05 LC) Which two-dimensional shape can be rotated about the y-axis to create a cone?

Illusion [34]

Any right triangle can.

4 0

2 years ago

Read 2 more answers

Write 863.141 in expanded form (THESE ARE DECIMALS)

harina [27]

800 +60 +3 + 0.1+ 0.04+ 0.001

7 0

2 years ago

emily leaves her house at exactly 8:25 am to bike to her school, which is 3.42 miles away. when she passes the post office, whic

NNADVOKAT [17]

We first calculate Emily's rate by dividing the distance from her home to the post office by the time it took her to travel that distance. From 8:25 to 8:29 (and 30 seconds), there are exactly 4.5 minutes. Thus, the rate is equal to,
r = (0.75 miles) / (4.5 minutes) = 1/6 miles/min
Then, we divide the given distance from her home to school by the calculate rate to determine the total number of minutes it will take her to travel to school.
t = (3.42 miles)/(1/6 miles/min) = 20.52 minutes
Adding this to 8:25 will give us an answer of 8:45 and 31.2 seconds. She will not be late.

6 0

2 years ago

The length of a side of a triangle is 36. A line parallel to that side divides the triangle into two parts of equal area. Find t

sp2606 [1]

Answer:

Length of DE is : 18√2 units

Step-by-step explanation:

The length of a side of a triangle is 36.

To calculate : The length of the segment DE

Now, the two parts of triangle have equal area ∴ Area(ADE) = Area(BDEC)

$\implies Area(ADE)=\frac{1}{2}\times Area(ABC) \\\\\implies \frac{Ar(ADE)}{Ar(ABC)}=\frac{1}{2}$

In ΔABE and ΔABC,

∠A = ∠A (Common angles)

∠ABE = ∠ABC (Corresponding angles are always equal)

By AA postulate of similarity of triangles, ΔABE ~ ΔABC.

Hence by area side proportionality theorem

$\frac{Ar(ADE)}{Ar(ABC)}=(\frac{DE}{BC})^2\\\\\implies \frac{1}{2}=\frac{DE^2}{36^2}\\\\\implies DE^2=\frac{36^2}{2}\\\\\bf\implies DE=18\sqrt{2}\textbf{ units}$

Hence, length of DE is 18√2 units

8 0

3 years ago