Use the discriminant to determine the number and type of solutions for the equation 2x^2−4x+7=0

(A). The equation has 2 real solutions because the discriminant is positive.
(B). The equation has 1 real solution and 1 imaginary solution because the discriminant is negative.
(C). The equation has 2 imaginary solutions because the discriminant is negative.
(D). The equation has 1 real solution because the discriminant is 0.

Given:

The area of the cross-section is 55cm².

The volume of the prism is 330cm³.

To find:

The length of the prism.​

Solution:

We have,

Area of the cross-section = Area of base = 55 cm²

Volume of the prism = 330cm³.

Let x be the length(height) of the prism.

We know that,

[tex]\text{Volume of prism}=\text{Base area}\times height[/tex]

[tex]330=55\times x[/tex]

[tex]\dfrac{330}{55}=x[/tex]

[tex]6=x[/tex]

Therefore, the length of the prism is 6 cm.

Answer:

Home inventory lol

Step-by-step explanation:

Answer:

Step-by-step explanation:

Y=1/2y

Answer:

There is no net....can you add a picture of it please? Thank you.

Step-by-step explanation:

Answer:

A. $101/month

Step-by-step explanation:

From January to February, it changes by 195

From February to March, it changes by -72

From March to April, it changes by 180.

Now, you just find the average of these three numbers.

195 - 72 + 180 = 303

303 / 3 = 101

This means that the answer is A. $101/month

Answer:

[tex]x=42[/tex]

Step-by-step explanation:

Use this to remember the trigonometry ratios:

SOH-CAH-TOA

Because:

Sine=Opposite/Hypotenuse → SOH

Cosine=Adjacent/Hypotenuse → CAH

Tangent=Opposite/Adjacent → TOA

Use the inverse of the tangent ratio since you need to find the angle measure.

:D Tehe

Answer:

x approximately equals 42.0

Step-by-step explanation:

give other person brainliesttt

Answer:

The smallest number is 1

Step-by-step explanation:

1+2=3

2-1=1

1•3=3

Answer:

401 meters    

Step-by-step explanation:

To change the units without changing the value, we use the Multiplicative Identity (that is, 1).

The formula for the circumference of a circle is:    C=Πd

The problem gives d=85 cm, so C=85Π cm.    So, (1 revolution)=(85Π cm)  

            or 1= (85Π cm) / (1 revolution)

Billy traveled:

    150 revolutions

    (150 revolutions)*1

    (150 revolutions) * ( (85Π cm) / (1 revolution) )      [note: revolutions cancel, leaving only cm]

    (150)*(85Π) cm

    40055.27 cm * ( (1 meter)/(100 cm) )

    401 meters        (rounded to nearest meter)

(this isnt my work credits to David W.

Answer:

Summary:

Step-by-step explanation:

Given

We know opposite sides of a parallelogram are equal.

Therefore,

now subtitute AD = x-28 and BC = 3x in AD = BC

AD = BC

x-28 = 3x

switch sides

3x = x-28

subracting x from both sides

3x-x = x-28+x

2x = -28

divide both sides by 2

2x/2 = -28/2

x = -14

Therefore,

The value of x = -14

Now subtitute AB = 12 and CD = 2/3y in AB = CD

AB = CD

12 = 2/3y

switching sides

2/3y = 12

y = 3/2 × 12

y = 18

Therefore,

The value of y = 18

We also know that the opposite angles of a parallelogram are equal.

Therefore,

5w = 70°

divide both sides by 5

5w/5 = 70°/5

w = 14

Therefore,

The value of w = 14

We know that the sum of the measures of the adjacent angles of a parallelogram is 180°.

Here,

m∠B = 70°.

m∠A = (3w+2z)°

As m∠B is adjacent to m∠A.

so

m∠A + m∠B = 180°

so substituting m∠B = 70° and m∠A = (3w+2z)° in the equation

70° + (3w+2z)° =  180°

now substituting w = 14 in the equation

70° +  (3(14) + 2z)° = 180°

70° + (42+2z)° =  180°

70° + 42 + 2z = 180°

112 + 2z = 180°

2z = 180° - 112

2z = 68

divide both sides by 2

2z/z = 68/2

z = 34

Therefore,

The value of z = 14

Summary:

Answer:

[tex]27,648,000[/tex]

Step-by-step explanation:

The area of a rectangle is given by [tex]l\cdot w[/tex]. Landen's 20 feet by 80 feet front lawn therefore has an area of [tex]20\cdot 80 = \fbox{$1600\: \mathrm{ft^2}$}[/tex].

He counts there are 120 blades of grass per square inch. There are [tex]12^2=144[/tex] square inches in one square foot.

Therefore, his lawn has an area of [tex]1600\: \mathrm{ft^2}\cdot \frac{144\:\mathrm{in^2}}{1\:\mathrm{ft^2}}=230,400\:\mathrm{in^2}[/tex].

Thus, there are [tex]230,400\:\mathrm{in^2}\cdot 120=\fbox{$27,648,000$}[/tex] blades of grass in the entire lawn.

Step-by-step explanation:

what is the unit of measurement for the 1/4, 1/4, and 1/2?

6. A

7. C

8. C

9. B

-FWEW

Answer:

[tex] {(x - 2)}^{2} + {(y + 7)}^{2} = 16[/tex]

Step-by-step explanation:

[tex] {(x - 2)}^{2} + {(y + 7)}^{2} = 16[/tex]

Step-by-step answer:

0.5(x+0.8)=1.4

0.5x+0.4=1.4

0.5x+0.4-0.4=1.4-0.4

0.5x=1

0.5x/0.5=1/0.5

x=2

Plzzzzz give me Brainliest!!!!!  

Answer:

0.12 miles is it flying per second.

Step-by-step explanation:

The distance d is related to time t in seconds is given by the equation as follows :

d =0.12 t

We need to find how many miles is it flying per second.

[tex]\dfrac{d}{t}=0.12\\\\\dfrac{\text{miles}}{\text{second}}=0.12[/tex]

So, the speed of the airplane is 0.12 miles per second, Hence, 0.12 miles is it flying per second.

Answer:

Set up the composite function and evaluate.

g(−5x+5)=25x−20

Step-by-step explanation:

Answer:

56a + 40b

Step-by-step explanation:

hope this helps!

Answer: 56a + 40b

Step-by-step explanation:

43a - 12b + 13a + 52b

Bring like terms together

43a + 13a - 12b + 52b

Combine like terms

56a + 40b

Hope that helped!

1+1 = 84, explanation is quite simple. i should get brainliiest

Answer:

7-6g

Then you do the 1 step equation.

Divide both sides by 6.

1.16=g

I'm not sure if it's right.

Answer:

Is the 4

Step-by-step explanation:

Answer:

60 minutes

Step-by-step explanation:

We solve this question using Lowest Common Factor method

Find and list multiples of each number of minutes( 12 and 10 minutes) until the first common multiple is found. This is the lowest common multiple.

Multiples of 10:

10, 20, 30, 40, 50, 60, 70, 80

Multiples of 12:

12, 24, 36, 48, 60, 72, 84

Therefore,

LCM(10, 12) = 60

The number if minutes until they both drip again is 60 minutes

Answer:

x+(x+1)=471

Step-by-step explanation:

Answer:

area of the original square = 36 in²

Step-by-step explanation:

given data

one side is increased = 9 inches

other side is decreased = 2 inches

area of the resulting rectangle = 60 in²

solution

we consider here x as the length of any one side

and

longer side of the resulting rectangle = x + 9

and

the shorter side x - 2

so that area of this rectangle is (s+9) × (s-2) = 60 in²

standard form of equation is  x² + 7x - 18 = 60   .....................1

it will be

x² + 7x - 78 = 0

(s+13) (s-6) = 0

so that here x  = -13

and  x = 6

here we Discard x = -13 because the side length cannot be negative.

so x = 6

and area of the original square = 36 in²

Answer:

The equation of a line that passes through the point (-1,5) and has a slope of -7 will be:

Step-by-step explanation:

The slope-intercept form of the line equation

[tex]y = mx+b[/tex]

where

Given

substituting m = -7 and the point (-1, 5) in the slope-intercept form of the line equation

[tex]y = mx+b[/tex]

5 = -7(-1) + b

5 = 7+b

b = 5-7

b = -2

Thus, the y-intercept is: b = -2

now substituting b = -2 and m = -7 in the slope-intercept form of the line equation

y = mx+b

y = -7x+(-2)

y = -7x-2

Therefore, the equation of a line that passes through the point (-1,5) and has a slope of -7 will be: