Evaluate the expression \dfrac{7^2}{x^2-2} x 2 −2 7 2 ​ start fraction, 7, squared, divided by, x, squared, minus, 2, end fraction for x=3x=3x, equals, 3

Answer:

144 cm²

Step-by-step explanation:

There are five total sides to the triangular prism. The formula for the area of a rectangle is length · width. The formula for the area of a triangle is 1/2 base · height.

10 · 4 = 40

6 · 4 = 24

8 · 4 = 32

1/2(6 · 8) = 48/2 = 24

1/2(6 · 8) = 48/2 = 24

Add the surface area for each side to get the total surface area.

40 + 24 + 32 + 24 + 24 = 144 cm²

Answer:

Using the quadratic formula

x = - b ± √b² - 4ac /2a

15x² - 11x + 2 = 0

a = 15 b = -11 c = 2

x = --11 ± √ (-11)² - 4(15)(2)/2(15)

x = 11±√121-120/30

x= 11±√1/30

x = 11 ± 1/30

x = 11 + 1/30 or x = 11 - 1/30

x = 2/5 or x = 1/3

Hope this helps.

Answer:

216 cm^2

Step-by-step explanation:

A cube has 6 congruent, square faces.

Each face has side length of 6 cm.

The total surface area is the sum of the surface areas of the 6 faces, but since all faces are congruent, the total surface area is

SA = 6s^2

where s = side length

SA = 6 * (6 cm)^2

SA = 6 * 36 cm^2

SA = 216 cm^2

Answer:

2x^2 +11

Step-by-step explanation:

f(x) = 3x^2 +2

g(x) = x^2 -9

f(x) - g(x) = 3x^2 +2 - (x^2 -9)

 Distribute the minus sign

        = 3x^2 +2 -x^2 +9

    Combine like terms

         = 2x^2 +11

Answer:

2x² + 11

Step-by-step explanation:

f(x) - g(x)

(3x² + 2) - (x² - 9)

Rearrange.

3x² - x² + 2 + 9

Add or subtract like terms.

2x² + 11

Answer:

p = ±21

Step-by-step explanation:

Given  z1 = p +2i and z2 = 1 – 2i, If |z1/z2| = 13;

|p+2i/1-21| = 13

To get p from the expression above, we need to rationalize the complex function first.

p+2i/1-21 = p+2i/1-2i * 1+2i/1+2i

= p+2pi+2i+4i²/1-4i²

Since i² = -1;

= p+2pi+2i-4/1+4

= p-4+2i(p+1)/5

= p-4/5 + 2(p+1)/5 i

Then we will take the modulus of the resulting expression and equate to the value of 13 to get p

|p+2i/1-21| = √(p-4/5)²+ (2p+2/5)² = 13

(p-4/5)²+ (2p+2/5)² = 13²

(p-4)²+(2p+2)² = 13²*5²

p²-8p+16+4p²+8p+4 = 4225

5p²+20 = 4225

5p² = 4205

p² = 841

p = ±√841

p = ±21

The possible values of p are 21 and -21

Answer:

5 times

Step-by-step explanation:

Given that the probability of a 2 is [tex]\frac{1}{6}[/tex] then number of times a 2 will be rolled is

30 × [tex]\frac{1}{6}[/tex] = 5

Answer 15c3d−7c2d2

Step-by-step explanation:

Answer:

x-int: B.

y-int: C.

Step-by-step explanation:

The x-intercepts are when the line crosses at the x-axis when y=0

The y-intercepts are when the line crosses at the y-axis when x=0

Answer:269.6 square centimeters

Step-by-step explanation:

Answer:

(2y+3)(y^2+7)

Step-by-step explanation:

2y^3  + 3y^2        + 14y +21

Factory^2 from the first group and    7 from the second group

y^2(2y+3)     + 7(2y+3)

Factor out (2y+3)

(2y+3)(y^2+7)

Answer:

x = 8

[tex] m\angle A= 30\degree[/tex]

Step-by-step explanation:

By interior angle on one side of transversal postulate.

[tex] m\angle A + m\angle B = 180\degree \\

\therefore (6x - 18)\degree + (14x + 38)\degree = 180\degree \\

\therefore (20x + 20)\degree = 180\degree \\

\therefore 20x + 20 = 180

\therefore 20x = 180 - 20\\

\therefore 20x = 160\\\\

\therefore x = \frac {160}{20}\\\\

\huge \red {\boxed {\therefore x = 8}} \\\\

\because m\angle A= (6x - 18)\degree \\

\therefore m\angle A= (6\times 8- 18)\degree \\

\therefore m\angle A= (48- 18)\degree \\

\huge \purple {\boxed {\therefore m\angle A= 30\degree}} \\[/tex]

Answer:

300

Step-by-step explanation:

Change the fractions so that they have a common denominator.

2/3 = 4/6

1/2 = 3/6

The difference between 4/6 and 3/6 is 1/6. This is the number of people who left the concert (50) as the fractions changed after they left.

Since 4/6 - 3/6 = 1/6 which also = 50, the total number of seats, 6/6 = 50 × 6 = 300

Answer:

Yes, it is a quadratic equation.

Step-by-step explanation:

Let's solve it to make it a quadratic equation:

=> [tex]\frac{x^2+1}{x^2} =5[/tex]

=> x²+1 = 5x²

=> 5x²-x²-1 = 0

=> 4x²-1 = 0

Comparing it with the standard form of quadratic equation i.e.

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

So, we get

a = 4 , b = 0 and c = -1

So, yes. It is a quadratic equation and it is a pure quadratic equation since b is equal to 0.

Answer:

[tex]L=(\frac{TG}{2\pi })^2[/tex]

Step-by-step explanation:

[tex]T=2\pi \sqrt{L}/G[/tex]

[tex]TG=2\pi \sqrt{L}[/tex]

[tex]\frac{TG}{2\pi } =\sqrt{L}[/tex]

[tex](\frac{TG}{2\pi })^2 =L[/tex]

Answer:

[tex]l = {( \frac{tg}{2\pi}) }^{2} [/tex]

hope this helps you.

brainliest appreciated

good luck! have a nice day!

Answer:

(- 2, 4 )

Step-by-step explanation:

A translation of 5 units left means subtract 5 from the original x- coordinate.

A translation of 6 units up means add 6 to the original y- coordinate.

Thus

(3, - 2 ) → (3- 5, - 2 + 6 ) → (- 2, 4 )

The coordinates of the point (3,-2), translated 5 units left and 6

units up are (-2, 4) option (D) (-2, 4) is correct.

It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.

It is given that:

The point (3,-2), translated 5 units left and 6 units up.

A 5-unit left translation entails taking 5 away from the initial x-coordinate.

A translation of six units upwards entails multiplying the initial y-coordinate by six.

After applying the translation:

(3, -2) → (3- 5, - 2 + 6) → (-2, 4)

Thus, the coordinates of the point (3,-2), translated 5 units left and 6

units up are (-2, 4) option (D) (-2, 4) is correct.

Learn more about the geometric transformation here:

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Answer:

Her final score is 13

Step-by-step explanation:

To find the total score, we would add them all:

=> 30+(-10)+(-12)+(-15)+20

=> 30-10-12-15+20

=> 20-12-15+20

=> 8-15+20

=> -7+20

=> 13

Answer:13

Step-by-step explanation:

Answer:

x > -2

Step-by-step explanation:

3(x + 2) > 0

Expand the brackets.

3x + 6 > 0.

Subtract 6 on both sides of the inequality.

3x + 6 - 6 > 0 - 6

3x > -6

Divide 3 into both sides of the inequality.

3x/3 > -6/3

x > -2

Answer: 24 square units

Step-by-step explanation:

The Area of a trapezoid is:

1/2 (a + b) h

Where ;

a = Length of base 1

b = length of base 2

h = height of trapezium

From the diagram attached :

a = Length of BC =(-1 to 3) =4units

b = length of AD =(-3 to 5) = 8 units

h = (-2 to 2) = 4 units

Plugging the values :

Area = 1/2 ((4 + 8)2)

Area = 0.5 × (12) × 4 = 12

Area = 6 × 4 = 24square units

Answer:

6\left(\dfrac{2}{3}+4\dfrac{1}{2}m\right)=6296(

3

2

​

+4

2

1

​

m)=6296, left parenthesis, start fraction, 2, divided by, 3, end fraction, plus, 4, start fraction, 1, divided by, 2, end fraction, m, right parenthesis, equals, 629 t

Step-by-step explanation:

i got this from khan

left parenthesis, start fraction, 2, divided by, 3, end fraction, plus, 4, start fraction, 1, divided by, 2, end fraction, m, right parenthesis, equals, 629 t

We have given that,

A display has 666 packs of marbles with a total mass of 629\,\text{g}629g629, start a text, g, end text. The packaging of each pack has a mass of \dfrac{2}{3}\,\text{g} 3 2 ​ start fraction, 2, divided by, 3, end fraction, start a text, g, end text, and each marble has a mass of 4\dfrac{1}{2}\,\text{g}4 2 1 ​ g4, start fraction, 1, divided by, 2, end fraction, create a text, g, end text.

Total mass means the mass of the shell, its service equipment, and structural equipment, and the heaviest load authorized to be transported.

We have to determine which equation can we use to determine mmm, the number of marbles per pack.

6\left(\dfrac{2}{3}+4\dfrac{1}{2}m\right)=6296(32+421m)=6296,

left parenthesis, start fraction, 2, divided by, 3, end fraction, plus, 4, start fraction, 1, divided by, 2, end fraction, m, right parenthesis, equals, 629 t.

To learn more about the mass visit:

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Step-by-step explanation:

A) The amount is taken during the first dose is - 500 mg

In 10 days, she will take the drugs for 240/12 = 20 times

After 12 hours, 4.5 % of drugs remain in the blood therefore

after the first dose = 500

second dose, 4.5% of  500 + 500 = 22.5 +500 = 522.5 mg

third dose, 4.5 % of 522. 5 + 500 = 523.51 mg

Forth dose, 4. 5% of 523.51 + 500 = 523.55 mg

B) Highest amount will be found on 20th dose.

= 500 x (1-0.045^20/ 1- 0.045)

= 523.55 mg

C) The highest amount in the body is near to 523.55 mg therefore after 10 days also, the amount of drug will remain near the value of 523.55 mg.

Answer:

D

Step-by-step explanation:

This can be broken up into √3 / √25, since √25 = 5 the final answer is √3/5.

Answer:

D. √3/5

hope it helps!

Step-by-step explanation:

√a/b is always written as √a/√b

So √(3/25)

= √3/√25

(√25 = 5 cuz 5*5=25)

= √3/5

So the answer is D.

Answer:

27x +6

Step-by-step explanation:

3(7x+2)+6x

Distribute

21x+6 +6x

Combine like terms

27x +6

Answer:

The answer is 21x + 6

Step-by-step explanation:

1.) Multiply 3 to 7x and 2 since these ( ) means times whatever is inside them.

2.) Now you have 21x and 6, add 21x to 6x to equal 27x.

3.) Finally, you have your answer. 27x + 6.

Answer:

-4w² - 8w

Step-by-step explanation:

All you need to do is distribute -4w. That means to multiply -4w to w and 2 separately. When you multiply -4w to w, you will get -4w² and when you multiply -4w to 2, you will get -8w.

Answer:

136°

Step-by-step explanation:

Vertically opposite angles are always equal.

The opposite angle to x is 136°.

Both angles are vertically opposite angles, so they are equal.

Answer:

x = 136 degrees

Step-by-step explanation:

=> x = 136 degrees

Why?

Because x and 136 degrees are vertically opposite angles and vertically opposite angles are congruent.

Answer:

6.59 and 3.41

Step-by-step explanation:

To evaluate, substitute n for each of the given values.

So when n= 3:

0.53n + 5 = 1.59 + 5 = 6.59

And when n = -3

0.53 n + 5 = -1.59+5=3.41

Hope this helps

Answer : The expression will be

( c - 7 ) / 3

Step-by-step explanation:

Let's say Adam has c pieces of candy

He took ten pieces for himself which means we can write this as c-7

He then divided this amount between his 3 children (c-7)/3

Answer: A and C are true.

A) [tex]f\left(x\right)=2\sqrt{x}\ \ and\ \ f\left(x\right)=\sqrt{x}[/tex] both has domain and range = [0, ∞). So A is true.

B) [tex]f\left(x\right)=-2\sqrt{x}[/tex] has range = (-∞, 0] and [tex]\ f\left(x\right)=\sqrt{x}[/tex] has range = [0, ∞). So B is false.

C) Both [tex]\ f\left(x\right)=-\sqrt{x}\ and\ \ f\left(x\right)=\sqrt{x}[/tex] has domain = [0, ∞).

Range of [tex]\ f\left(x\right)=\sqrt{x}[/tex] is =  [0, ∞).

Range of [tex]f\left(x\right)=-\sqrt{x}[/tex] is = (-∞, 0]

So range are different. C is true.

D) Both [tex]f\left(x\right)=\frac{1}{2}\sqrt{x}\ and\ \ f\left(x\right)=\sqrt{x}[/tex] has range = [0, ∞).

So D is false.

Learn more: https://brainly.com/question/20521181

Answer: A and C

Step-by-step explanation:

Answer:

Option (1).

Step-by-step explanation:

In the figure attached,

Houses of three friends Jo, Boris and Carrie are located at the vertices of a triangle.

They want to meet at a place which equidistant from these vertices.

A point in a triangle which is equidistant from the vertices is its Circumcenter.

A circumcenter of a triangle is a point of intersection of perpendicular bisectors of its sides.

Therefore, the next step to find the meeting place should be,

Option (1). They should find the midpoint of the segments which connect their houses.

Answer:

36πin

Step-by-step explanation:

Formula for the circumference of a circle=2πr

r=18

2 · 18

=36

36·π

hope this helps