The cube of a number divided by two

Answer:

Diameter = 8

Step-by-step explanation:

Area of a circle: pi r^2

16 pi = r^2 pi

r^2 = 16

r = 4

And since the diameter is equal to 2r, the diameter is

2(4) = 8

This ODE is separable:

[tex]\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{4y}{x^2}\implies\dfrac{\mathrm dy}y=\dfrac4{x^2}\,\mathrm dx[/tex]

Integrating both sides gives

[tex]\ln|y|=-\dfrac4x+C[/tex]

Given the initial condition [tex]y(-4)=1[/tex] we find

[tex]\ln|1|=-\dfrac4{-4}+C\implies C=-1[/tex]

so that the particular solution is

[tex]\ln|y|=-\dfrac4x-1[/tex]

[tex]\implies y=e^{-(1+4/x)})[/tex]

so the answer is D.

Answer:

The correct answer is 10:20 and 10:30 on E2020

Hope this helps you!

(p.s please mark me as brainlyest)

Step-by-step explanation:

I just took the test on E2020 and got 100% but if you want the work just ask and I'll explain it to you.

Answer:

[tex]F=201.2\°[/tex]

Step-by-step explanation:

we know that

[tex]\°C=\frac{5}{9}[\°F-32][/tex]

For [tex]C=94\°[/tex]

substitute in the formula and solve for F

[tex]94=\frac{5}{9}[F-32][/tex]

[tex](\frac{9}{5})*94=[F-32][/tex]

[tex]F=(\frac{9}{5})*94+32[/tex]

[tex]F=201.2\°[/tex]

Final answer:

To combine the expression 4 log x - 6 log (x+2) into a single logarithm, we use the exponentiation and division rules for logarithms to obtain log((x^4)/(x+2)^6).

Explanation:

To write the expression 4 log x - 6 log (x+2) as a single logarithm, we can apply log rules.

The logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number: log(x^n) = n log x.

The logarithm of a product of two numbers is the sum of the logarithms of the two numbers: log xy = log x + log y.

The logarithm of the number resulting from the division of two numbers is the difference between the logarithms of the two numbers: log(x/y) = log x - log y.

Using these rules, we can

rewrite the given expression:

4 log x - 6 log (x+2) can be rewritten as log(x^4) - log((x+2)^6), which simplifies to log((x^4)/(x+2)^6) according to the division rule for logarithms.

The expression [tex]4 log x - 6 log (x+2)[/tex] can be simplified as a single logarithm by using the logarithm properties of exponents and division, resulting in [tex]log(x^4 / (x+2)^6).[/tex]

The student is asking to write the expression [tex]4 log x - 6 log (x+2)[/tex] as a single logarithm. To do this, we recall two important properties of logarithms:

Using these properties, we can rewrite the expression:

Therefore, the expression [tex]4 log x - 6 log (x+2)[/tex] written as a single logarithm is[tex]log(x^4 / (x+2)^6).[/tex]

Answer:

The function describing the relationship of V and t is V = 3t²

Step-by-step explanation:

* Lets explain the meaning of direct variation

- The direct variation is a mathematical relationship between two

  variables that can be expressed by an equation in which one

  variable is equal to a constant times the other

- If Y is in direct variation with x (y ∝ x), then y = kx, where k is the

 constant of variation

* Now lets solve the problem

# V is varies directly with the square  of t

- Change the statement above to a mathematical relation

∴ V ∝ t²

- Chang the relation to a function by using a constant k

∴ V = kt²

- To find the value of the constant of variation k substitute V and t

 by the given values

∵ t = 6 when V = 108

∵ V = kt²

∴ 108 = k(6)² ⇒ simplify the power 2

∴ 108 = 36k ⇒ divide both sides by 36 to find the value of k

∴ 3 = k

- The value of the constant of variation is 3

∴ The function describing the relationship of V and t is V = 3t²

Answer:

120?

Step-by-step explanation:

-5 times -2 equals 10 (since a negative times negative equals positive)

10 times -3 equals -30

-30 times -4 equals 120

Hope this helps.

Note: this may be incorrect

Answer:

120

Step-by-step explanation:

Answer:

Hmm... None of these choices seem to be correct.

Step-by-step explanation:

The exact dimensions of the TV are approximately 14 inches by [tex]14\sqrt{3}[/tex] inches, which simplifies to 14 inches by 142 inches

The correct answer is:

 B. 14 inches by 142 inches.

To find the exact length and width of the TV, we can use the properties of a 30-60-90 right triangle. In such a triangle, the side lengths are related as follows: the length of the side opposite the 30-degree angle is [tex]\( \frac{1}{2} \)[/tex] times the length of the hypotenuse, and the length of the side opposite the 60-degree angle is [tex]\( \frac{\sqrt{3}}{2} \)[/tex] times the length of the hypotenuse.

Given that the diagonal of the TV forms the hypotenuse of two 30-60-90 right triangles, let's denote the length and width of the TV as [tex]\( L \)[/tex] and [tex]\( W \)[/tex] respectively, and the length of the diagonal as [tex]\( D \).[/tex]

We have the following equations:

[tex]\[ L = \frac{1}{2}D \][/tex]

[tex]\[ W = \frac{\sqrt{3}}{2}D \][/tex]

Given that the diagonal [tex]\( D = 28 \)[/tex] inches, we can substitute this value into the equations to find the exact length and width:

[tex]\[ L = \frac{1}{2} \times 28 = 14 \text{ inches} \][/tex]

[tex]\[ W = \frac{\sqrt{3}}{2} \times 28 \approx 14\sqrt{3} \text{ inches} \][/tex]

Now, we need to rationalize the denominator for the width:

[tex]\[ W = 14\sqrt{3} \times \frac{\sqrt{3}}{\sqrt{3}} = \frac{42}{\sqrt{3}} \][/tex]

To rationalize the denominator, multiply both numerator and denominator by[tex]\( \sqrt{3} \):[/tex]

[tex]\[ W = \frac{42\sqrt{3}}{3} = 14\sqrt{3} \text{ inches} \][/tex]

So, the exact dimensions of the TV are approximately 14 inches by [tex]14\sqrt{3}[/tex] inches, which simplifies to 14 inches by 142 inches. Therefore, the correct answer is B.

Complete question:

The diagonal of a TV is 28 inches long. Assuming that the diagonal form a pair of 30-60-90 right triangles, what are the exact length and width of the TV?

A. 55 inches by 568 inches

B. 14 inches by 142 inches

C. 56 inches by 56.5 inches

D. 14 inches by 14.5 inches

Answer:

y = 9.75

Step-by-step explanation:

(4y - 3)2 = 72

Opening the brackets;

8y - 6 = 72

8y = 72 + 6 = 78

y = 78 ÷ 8 = 9.75

Answer:

[tex]y = \frac{3+6\sqrt{2}}{4}\text{ and } y = \frac{3-6\sqrt{2}}{4}[/tex]

Step-by-step explanation:

Given quadratic equation,

[tex](4y-3)^2=72[/tex]

[tex]\implies 4y - 3 = \pm \sqrt{72}[/tex]   ( Taking root on both sides )

[tex]4y=3 \pm 6\sqrt{2}[/tex]     ( Additive property of equality ),

[tex]y = \frac{3 \pm 6\sqrt{2}}{4}[/tex]   ( Division property of equality )

[tex]\implies y = \frac{3+6\sqrt{2}}{4}\text{ or }y =\frac{3-6\sqrt{2}}{4}[/tex]

Hence, the solution of the given equation is,

[tex]\implies y = \frac{3+6\sqrt{2}}{4}\text{ and }y =\frac{3-6\sqrt{2}}{4}[/tex]

Answer:

1. D ∠4 and ∠5

2. C 37°

3. A 50°

Step-by-step explanation:

1. Complementary angles are those that add up to 90°.

From the diagram you can see that angles 4 and 5 together form right angle, so angles 4 and 5 are complementary.

2. Angles 1 and 4 are vertical angles. Vertical angles have the same measure, so

∠4=∠1=37°

3. From 1,

∠4+∠5=90°

From 2

∠1=∠4

Since ∠1=40°, then ∠4=40°

So,

∠5=90°-40°=50°

Answer:

1. Sine (sin) 2. Cosine (cos) 3. Tangent (tan) 4. Secant (sec) 5. Cosecant (csc) 6. Cotangent (cot) These functions are used to relate the angles of a triangle with the sides of that triangle.

Step-by-step explanation:

Sine and cosine functions are examples of trigonometric functions that generate periodic waves. These waves can be represented in equations like y = A sin(wt + p) and x(t) = A cos(wt + p), where A is the amplitude, w is the angular frequency, t is the time, and p is the phase shift.

Trigonometric functions like the sine, cosine, and tangent functions are often used to generate periodic waves in mathematics and physics. For instance, simple harmonic motion, which is related to alternating cycles in physics, can be represented by sine and cosine functions.

Let's consider the example of a bouncing object on a spring. The object's position over time can be represented by a sine function, resulting in a wave-like pattern on a graph. A sine function generating a periodic wave would look like this: y = A sin(wt + p), where A is the amplitude, w is the angular frequency, t is the time, and p is the phase shift.

Another example is a cosine function that might represent a phase-shifted wave, like this: x(t) = A cos(wt + p). Again, A is the amplitude, w is the angular frequency, t is the time, and p is the phase shift. This function is effectively identical to the sine function but is shifted to the right on the x-axis.

https://brainly.com/question/12502943

#SPJ3

Answer: $8.2

Step-by-step explanation:

Answer:

8.2 dollars an hour is the answer

Step-by-step explanation:

50.43 divided by 6.15 is 8.2

Step-by-step explanation:

(picture explains)

Hope this helps!

Answer:

The vertical asymptote is [tex]x=3[/tex]

Step-by-step explanation:

we know that

The vertical asymptote is the value of x that makes the denominator equal to zero:

In this problem we have

[tex]f(x)=\frac{6}{x-3}[/tex]

[tex]x-3=0[/tex]

Solve for x:

[tex]x-3+3=0+3[/tex]

[tex]x=3[/tex]

The vertical asymptote is [tex]x=3[/tex]

see the attached figure to better understand the problem

Answer:

a. 2,2,3,3

b. 1.7 2.2 pi= 3.14 3.4= 2,2,3,3

Step-by-step explanation:

Tessellation is when a shape is repeated without any gaps/ spaces and without overlapping.

The semi circle shape shown cannot be uses because there would be gaps on the inner part of the circle.

Answer:

The answer would be B. The highest price and the lowest price of the game differ by less than $14. Hope this helps!

B. The highest price and the lowest price of the game differ by less than $14.

Given is that the the price of Song Hero showed greater variability. This means their prices are more varied in range.

If Song Hero was priced between $35 and $49 during the 10-month period, This means the variability of Star chasers is less than [tex]49-35=$14[/tex]

Since, $14 is Song Hero’s range, the range for Star chasers should be less.

Therefore, option B is correct.

Answer:

20

Step-by-step explanation:

Two tangent segments drawn to a circle from the same point outside the circle are congruent. The two tangents at A measure 2. The two tangents at B measure 5. The two tangents at C measure 3.

perimeter = 2 + 2 + 5 + 5 + 3 + 3

perimeter = 20

ANSWER

[tex]32 \sqrt{3} {ft}^{2} [/tex]

EXPLANATION

The area of a tra-pezoid is half times sum of the bases times the vertical height.

From the diagram ( see attachment) we use the Pythagoras Theorem to obtain,

[tex] {x}^{2} + {(4 \sqrt{3}) }^{2} = {8}^{2} [/tex]

[tex] {x}^{2} + 48 = 64[/tex]

[tex]{x}^{2} = 64 - 48[/tex]

[tex]{x}^{2}=16[/tex]

[tex]x = \sqrt{16} = 4ft[/tex]

This implies that , y=10-4=6ft

The area of tra-pezoid

[tex] = \frac{1}{2} (10 + 6) \times 4 \sqrt{3} [/tex]

[tex] = \frac{1}{2} (16) \times 4 \sqrt{3} [/tex]

[tex] = 8\times 4 \sqrt{3} [/tex]

[tex] = 32 \sqrt{3} {ft}^{2} [/tex]

Answer:

y = 30 and y = 40

Step-by-step explanation:

All you have to do is add 10 and 12, and see if its is greater than 34. Add the rest of the listed numbers to 12.

Answer:

Option b. y = 0

Step-by-step explanation:

we know that

The slope of the line that coincides with the y-axis is equal to zero (horizontal line) and the equation is equal to

y=0

Answer:

The value of x is 10, and the value of y is 6

Step-by-step explanation:

ABC and GEF are congruent

so

x - 8 = 2

x = 10

x - y = 4

10 - y = 4

y = 10 - 4

y = 6

Answer

x = 10, y = 6

Answer:

x = 10 and y = 6

Step-by-step explanation:

In the given figure ΔABC and ΔGEF are congruent which means all the corresponding sides of the given triangles should be congruent.

So measure of AC = mfg

x - 8 = 2

x = 2 + 8

x = 10

Similarly mBC = mEF

x - y = 4

10 - y = 4

y = 10 - 4 = 6

Therefore, answer are x = 10 and y = 6

Answer is 1)

3V= pi•h•r^2 divide both sides by (pi•h) ; 3V/pi•h = r^2; sqrt (3V/pi•h) =r

Answer:

34.48

Step-by-step explanation:

Use PEMDAS

12.98-(7.6÷19)+22

12.98-0.4+22

12.48+22

34.48

Answer:

34.480000000000000000000000

Step-by-step explanation:

Answer:

145

Step-by-step explanation:

The volume of the rectangular prism bin is area of base * height.

Base/top is a square, so area would be 150 * 150 = 22,500

Thus, volume of bin = 22,500 * 210 = 4,725,000

Using volume of sphere formula and given radius of each ball is 16cm, we can say that

Volume of 1 Ball = [tex]\frac{4}{3}\pi r^3 = \frac{4}{3}\pi (16)^3=17,157.28[/tex]

Since, 190% is including the packing, we can take volume of 1 ball (inclusive of packaging) to be  1.9 * 17,157.28 = 32,598.83

How many of this will fit in the bin, we divide bin volume by this:

Number of Balls = [tex]\frac{4,725,000}{32,598.83}=144.94[/tex]

Rounding, we can say that we can fit 145 balls, 2nd answer choice is right.

Step-by-step explanation:

3 quarts of soda + 2½ quarts of fruit juice = 5½ quarts of punch

Writing a proportion:

3 / 5½ = x / 100

5½ x = 300

x = 54 ⁶/₁₁

x ≈ 54.55

Answer:

1.4 inches

Step-by-step explanation:

The picture is a rectangle 8 cm by 6 cm. The area of a rectangle is length * width. The area of the picture is 8 cm * 6 cm = 48 cm^2

After the mat is applied, the area doubles, so the new area will be 2 * 48 cm^2 = 96 cm^2.

Let the width of the mat be x. The mat has the same width all around the rectangular picture, so it adds x on each side of the length and x on each side of the width.

old length: 8

new length: 2x + 8

old width: 6

new width: 2x + 6

Area of the new rectangle with mat = new length * new width

area = (2x + 8)(2x + 6)

The new area is 96, so that give us an equation.

(2x + 8)(2x + 6) = 96

Use FOIL on the left side:

4x^2 + 12x + 16x + 48 = 96

Combine like terms, and subtract 96 from both sides:

4x^2 + 28x - 48 = 0

Divide both sides by 4:

x^2 + 7x - 12 = 0

To factor the trinomial, we need two numbers that add to 7 and multiply to -12. There are no such numbers, so we need to use the quadratic formula.

x = [-b +/- sqrt(b^2 - 4ac)]/(2a)

x = [-7 +/- sqrt(7^2 - 4(1)(-12)]/[2(1)]

x = [-7 +/- sqrt(49 + 48)]/2

x = [-7 +/- sqrt(97)]/2

x = 1.4 or x = -8.4

Since the mat cannot have a negative width, the negative solution is discarded.

Answer: The width of the mat is 1.4 inches.

Answer:

D

Step-by-step explanation:

half of the miles he drove yesterday is (42/2) and +5 because he said five more than half.

hope this helps and is correct!

Answer:

○ D. (42 ÷ 2) + 5

Step-by-step explanation:

Five more than half tells it all. He 42 miles on Monday, then drove 5 more than half:

(42 ÷ 2) + 5

Half means you either multiply by ½, or divide by 2.

I am joyous to assist you anytime.

Answer:

3/2

-3

Step-by-step explanation:

here

Answer:

[tex]x = \frac32, x = -3[/tex]

Step-by-step explanation:

Hello!

We have to solve for x by using the quadratic formula.

Standard form of a quadratic: [tex]ax^2 + bx + c = 0[/tex]

Quadratic Formula: [tex]x = \frac{-b\pm\sqrt{b^2 - 4ac}}{2a}[/tex]

First, convert it into standard form:

Given our equtaion: [tex]2x^2+3x - 9 = 0[/tex]

Plug it into the formula and solve.

The roots are 1.5 and -3.

Answer:

Maggie bought 77 pencil sharpeners

$46.20 divided by .60 = 77

Step-by-step explanation:

46.20÷0.60= 77

Maggie can buy 77 pencil sharpeners is she would like

Please, please, pppllleeeeaassssee

Mark Brainlyest