which of the following is equivalent to log9w

the speed at which the ball has a force of 0.5 N on it is [tex]\( 2.5 \)[/tex] meters per second.

To find the speed at which the drag force F on the steel ball is 0.5 N, we need to solve the equation:

[tex]\[ F = 0.5 + 0.004(x + 50)(x - 2.5) \][/tex]

Given that [tex]\( F = 0.5 \)[/tex], we can substitute this value into the equation and solve for x:

[tex]\[ 0.5 = 0.5 + 0.004(x + 50)(x - 2.5) \][/tex]

Subtracting \( 0.5 \) from both sides, we get:

[tex]\[ 0 = 0.004(x + 50)(x - 2.5) \][/tex]

Now, since the product of two factors is equal to zero, at least one of the factors must be zero. So we have:

[tex]\[ x + 50 = 0 \][/tex] or [tex]\[ x - 2.5 = 0 \][/tex]

Solving these equations:

1. [tex]\( x + 50 = 0 \)[/tex]

[tex]\[ x = -50 \][/tex]

2. [tex]\( x - 2.5 = 0 \)[/tex]

[tex]\[ x = 2.5 \][/tex]

Since the speed cannot be negative, the only valid solution is [tex]\( x = 2.5 \)[/tex] meters per second.

Therefore, the speed at which the ball has a force of 0.5 N on it is [tex]\( 2.5 \)[/tex] meters per second.

The complete Question is given below:

A steel ball is traveling through water with a speed of x meters per second, where x is positive. The drag force, F , in newtons (N) is: F=0.5+0.004(x+50)(x-2.5) At what speed in meters per second does the ball have a force of 0.5N on it?

Answer: It has no exact solution

Answer:

1.[tex]x^\circ= 7^\circ[/tex]

2.(a)Therefore , Side LJ =side CA

(b) BC = KL

Step-by-step explanation:

1.

we know that, vertically opposite angles are congruent .

[tex]\therefore (x+16)^\circ= (4x-5)^\circ[/tex]

[tex]\Leftrightarrow 4x^\circ-x^\circ= 5^\circ+16^\circ[/tex]

[tex]\Leftrightarrow 3x^\circ= 21^\circ[/tex]

[tex]\Leftrightarrow x^\circ= 7^\circ[/tex]

2.

(a)SAS = side,angle , side

Given ,side AB = side KJ

and ∠CAB= ∠LJK

All Pythagorean Triples are unique.

Since side AB = side KJ

Therefore , Side LJ =side CA

It satisfies SAS postulate ThereforeΔABC≅ΔKJL

(b)

HL Theorem: If hypotenuse and one leg of of a right triangle are congruent to the hypotenuse and one leg of of other right triangle , then the triangle congruent.

Since,

All Pythagorean Triples are unique.

Then hypotenuse of ΔABC=ΔLKJ ⇔BC = KL

Answer:

1

Step-by-step explanation:

13  15  17  x  20  21

Cross out all outer numbers

We are left with 17 and x

With double medians, you add those two together and then divide them by two.

With the median (total) being 18, we will first add 17+x then divide Y/2 = 18

The value of x is 1

Question:

Which summation formula represents the series below? 1 + 2 + 6 + 24

(a) [tex]\sum_{n=2}^{5}(n-1) ![/tex]

(b) [tex]\sum_{n=0}^{3} n ![/tex]

(c) [tex]\sum_{n=1}^{4}(n+1) ![/tex]

(d) [tex]\sum_{n=2}^{5} n ![/tex]

Answer:

Option a: [tex]\sum_{n=2}^{5}(n-1) ![/tex] is the correct answer.

Explanation:

Option a: [tex]\sum_{n=2}^{5}(n-1) ![/tex]

By substituting the values of n and expanding the summation, we have,

[tex](2-1) !+(3-1) !+(4-1) !+(5-1) ![/tex]

Subtracting, we have,

[tex]1 !+2!+3 !+4 ![/tex]

Expanding the factorial,

[tex]1+(2*1)+(3*2*1)+(4*3*2*1)[/tex]

Simplifying, we get,

[tex]1+2+6+24[/tex]

Thus, the summation [tex]\sum_{n=2}^{5}(n-1) ![/tex] represents the series [tex]1+2+6+24[/tex]

Hence, Option a is the correct answer.

Option b: [tex]\sum_{n=0}^{3} n ![/tex]

By substituting the values of n and expanding the summation, we have,

[tex]0!+1!+2!+3![/tex]

Expanding the factorial,

[tex]0+1+(2*1)+(3*2*1)[/tex]

Simplifying, we get,

[tex]0+1+2+6[/tex]

Thus, the summation [tex]\sum_{n=0}^{3} n ![/tex] does not represents the series [tex]1+2+6+24[/tex]

Hence, Option b is not the correct answer.

Option c: [tex]\sum_{n=1}^{4}(n+1) ![/tex]

By substituting the values of n and expanding the summation, we have,

[tex](1+1) !+(2+1) !+(3+1) !+(4+1) ![/tex]

Adding, we have,

[tex]2!+3!+4!+5![/tex]

Expanding the factorial,

[tex](2*1)+(3*2*1)+(4*3*2*1)+(5*4*3*2*1)[/tex]

Simplifying, we get,

[tex]2+6+24+120[/tex]

Thus, the summation [tex]\sum_{n=1}^{4}(n+1) ![/tex] does not represents the series [tex]1+2+6+24[/tex]

Hence, Option c is not the correct answer.

Option d: [tex]\sum_{n=2}^{5} n ![/tex]

By substituting the values of n and expanding the summation, we have,

[tex]2!+3!+4!+5![/tex]

Expanding the factorial,

[tex](2*1)+(3*2*1)+(4*3*2*1)+(5*4*3*2*1)[/tex]

Simplifying, we get,

[tex]2+6+24+120[/tex]

Thus, the summation [tex]\sum_{n=2}^{5} n ![/tex] does not represents the series [tex]1+2+6+24[/tex]

Hence, Option d is not the correct answer.

Hence, the correct answer is Option a: [tex]\sum_{n=2}^{5}(n-1) ![/tex]

Answer: A

Step-by-step explanation:

To create a 30-lb batch of sweets that is 22% nuts and dried fruit, you should mix 12 lbs of sweet item A and 18 lbs of sweet item B.

To find the solution, we can set up a system of equations based on the percentages of nuts and dried fruit in each brand of granola and the desired final percentage.

Let x represent the amount of sweet item A (in pounds) and y represent the amount of sweet item B (in pounds) to be mixed.

The total weight of the mixture is x + y = 30 lbs.

The percentage of nuts and dried fruit in brand A is 25%, so the amount of nuts and dried fruit from A is 0.25x lbs.

The percentage of nuts and dried fruit in brand B is 10%, so the amount of nuts and dried fruit from B is 0.10y lbs.

The desired final percentage in the mixture is 22%, so we have the equation: (0.25x + 0.10y) / 30 = 0.22.

Now, we can solve this system of equations to find x and y.

First, we'll multiply the last equation by 30 to get 0.25x + 0.10y = 6.6.

Then, we can use substitution or elimination to solve for x and y.

In this case, it's simpler to use elimination, and we find that x = 12 lbs and y = 18 lbs.

Therefore, you should mix 12 lbs of sweet item A and 18 lbs of sweet item B to create the desired 30-lb batch with 22% nuts and dried fruit.

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Option C

Container with the dimensions 3 by 5 by 10 inches has a volume of 150 cubic inches, which is large enough to hold a volume of 130 cubic inches

Solution:

Anusha needs to find a rectangular container large enough to hold a volume of 130 cubic inches

The volume of rectangular container is:

[tex]volume = length \times width \times height[/tex]

Option A

Container with the dimensions 2 by 5 by 10 inches

Therefore, volume is given as:

[tex]Volume = 2 \times 5 \times 10 = 100[/tex]

Thus volume is 100 cubic inches

Option B

Container with the dimensions 3 by 4 by 10 inches

Therefore, volume is given as:

[tex]Volume = 3 \times 4 \times 10 = 120[/tex]

Thus volume is 120 cubic inches

Option C

Container with the dimensions 3 by 5 by 10 inches

Therefore, volume is given as:

[tex]Volume = 3 \times 5 \times 10 = 150[/tex]

Thus volume is 150 cubic inches

Option D

Container with the dimensions 4 by 2 by 10 inches

Therefore, volume is given as:

[tex]Volume= 4 \times 2 \times 10 = 80[/tex]

Thus volume is 80 cubic inches

Thus Container with the dimensions 3 by 5 by 10 inches has a volume of 150 cubic inches, which is large enough to hold a volume of 130 cubic inches

Answer:C. a container with the dimensions by 5 by 10 inches

Answer:   [tex]Perimeter= 71.75[/tex]

The parameter of a 2-D figure is the total length of its boundaries.

Step-by-step explanation:

In the given figure a hexagon is given with the length of its sides given in mixed fraction.

A mixed fraction can be solved by    [tex]p\frac{x}{y} =\frac{(p*y)+x}{y}[/tex]

So adding the given sides in the figure:

[tex]Perimeter=14\frac{3}{4}+ 4\frac{1}{2}+ 8\frac{1}{2}+10 \frac{2}{5}+10 \frac{2}{5}+12 \frac{4}{5}[/tex]

[tex]=\frac{(14*4)+3}{4} +\frac{(4*2)+1}{2} +\frac{(8*2)+1}{2} +\frac{(10*5)+2}{5}+ \frac{(10*5)+2}{5} +\frac{(12*5)+4}{5}[/tex]

[tex]=\frac{59}{4}+ \frac{9}{2}+ \frac{17}{2}+ \frac{52}{5}+ \frac{52}{5}+ \frac{64}{5}[/tex]

[tex]=14.75+4.5+8.5+10.4+10.4+12.8[/tex]

[tex]Perimeter= 71.75[/tex]

The perimeter of the given figure is 71.75

Answer:

22.5 weeks

Step-by-step explanation:

y = 1.12x + 28.78 represents the height of the puppy.  Here that height is 54 cm:

Then 54 = y = 1.12x + 28.78

Combining the constants, we get 1.12x = 25.22.  Dividing both sides by 1.12, x turns out to be 22.5 weeks.

Answer:

D:  y = 5x

Step-by-step explanation:

According to Google, a proportional relationship is one in which two quantities vary directly with each other. We say the variable y varies directly as x if: y=kx. for some constant k , called the constant of proportionality.  So the only one in that form would be the y = kx.  

The constant k = 5

Answer:

Step-by-step explanation:

Answer:

0.032 Amperes

Step-by-step explanation:

in this question We are given;

We are required to determine the current, I

We need to know that power, P is given by the product of current and voltage.

That is;

Power = VI

But; 1 mW = 0.001 Watts

Thus, 500 mW = 0.5 watts

Rearranging the formula;

I = Power ÷ V

 = 0.5 watts ÷ 15.81 V

 = 0.0316 Amperes

 = 0.032 A

Thus, the current, I is 0.032 Amperes

Answer:

The length of the radius of the sphere is 11.0 units

Step-by-step explanation:

we know that

To calculate the radius of the sphere, we can use the distance formula

[tex]d=\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2}+(z_2-z_1)^{2}}[/tex]

where

d is the length of the radius

(x_1,y_1,z_1) is the center of the sphere

and

(x_2,y_2,z_2) is one point on the surface of the sphere

we have

[tex](x_1,y_1,z_1)=(0,0,0)[/tex]

[tex](x_2,y_2,z_2)=(4,9,-5)[/tex]

substitute in the formula

[tex]d=\sqrt{(4-0)^{2}+(9-0)^{2}+(-5-0)^{2}}[/tex]

[tex]d=\sqrt{(4)^{2}+(9)^{2}+(-5)^{2}}[/tex]

[tex]d=\sqrt{122}[/tex]

[tex]d=11.0\ units[/tex]

therefore

The length of the radius of the sphere is 11.0 units

Answer: 14x^5y^8

Step-by-step explanation:

(-7x^2y^4)(-2x^3y^4)

-7x^2y^4*-2x^3y^4, next take out the constants

−(7×−2)x^2x^3y^4y^4, -(7*-2)=14, so now you just need to add the variables.

(x^2+x^3)+(y^4+y^4)=x^5y^8

14x^5y^8

Hope this helps, HAVE A BLESSED AND WONDERFUL DAY! I also hope you had a great Superbowl Weekend! :-)

- Cutiepatutie ☺❀❤

Step-by-step explanation:

(1/2x)+7 is a equation

Answer:

on edgenuit it's c

Step-by-step explanation:

-15x-53/x^2+8x+15

Answer: s > 5

Step-by-step explanation:

-s² + 25s - 100 > 0

Coefficient of s² is -1, multiply the equation through by -1.

-1 × (-s² + 25s - 100)

s² — 25s + 100

ax² + bx + c

Then you get the factors x and y that gives x + y = b and xy = c

b = -25 and c = 100, x = -20 and y = -5

-20 × -5 = 100 and -20 + -5 = -25

Then

s² — 20s — 5s + 100 > 0

Factorising,

s (s — 20) — 5(s — 20) > 0

(s — 5)(s — 20) > 0

(s — 5) > 0 and (s — 20) > 0

s>5 and s>20

s > 5

Hope this Helps?

Answer:

0.039

Step-by-step explanation:

Answer:

[tex]\theta=38.7\degree[/tex]

Step-by-step explanation:

We want to solve [tex]\tan \theta=\frac{4}{5}[/tex] given that [tex]\theta[/tex] is acute.

We take tangent inverse of both sides to get:

[tex]\theta=\tan^{-1}(\frac{4}{5})[/tex]

Now set your calculator to degree mode and evaluate [tex]\tan^{-1}(\frac{4}{5})[/tex] to obtain:

[tex]\theta=38.6598\degree[/tex]

To one decimal place, we have;

[tex]\theta=38.7\degree[/tex]

To solve the equation 'tangent theta equals four fifths', we use the inverse tangent function, or arctan(4/5). Using a calculator in degree mode, the result is approximately 38.7 degrees.

To solve the equation tangent theta equals four fifths, we need to find the angle whose tangent is 4/5. We can find this using the inverse tangent function (also known as arctan)

So, theta = arctan(4/5)

Use a calculator to find out the value of arctan(4/5). Make sure your calculator is in degree mode because the answer needs to be in degrees. The answer is approximately 38.7 degrees, rounded to one decimal place.

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Answer:

78 witch is 15%

Step-by-step explanation:

Answer:

The length of the base the pyramid is 116 feet.

Step-by-step explanation:

See the diagram attached to this answer.

Let Δ OAB is the side triangle of the square pyramid, and A'B' is the mid segment parallel to the ground with length of 58 feet.

Now, Δ OAB and Δ OA'B' are similar triangle and the length of sides of the triangle Δ OA'B' are in the same ratio with the corresponding sides of Δ OAB.

Hence, [tex]\frac{OA'}{OA} = \frac{OB'}{OB} = \frac{A'B'}{AB} = \frac{1}{2}[/tex]

⇒ AB = 2 × 58 = 116 feet.

The length of the base the pyramid is 116 feet. (Answer)  

Final answer:

The length of the base of the pyramid in question, referenced as the Great Pyramid of Cheops, is historically known to be 230 meters on each side.

Explanation:

The student's question relates to finding the length of the base of a pyramid with a known mid-segment length in one of the triangular faces.

Based on the information provided, which references the Great Pyramid of Cheops (or the Great Pyramid of Giza), the original square base length of the pyramid was 230 meters on each side.

This measurement is crucial for answering questions related to the geometry and scale of pyramids in mathematical problems.

Answer:

Nothing

Step-by-step explanation:

You can't divide by zero

Answer:

ANYTHING DIVIDED BY 0 IS ALWAYS ZERO

Step-by-step explanation:

PLEASE MARK BRAINLIEST

Answer:

14.04

Step-by-step explanation:

you mupltiy

Answer:

b

Step-by-step explanation:

2.34 x 6 = 14.04

so it would total up to 14.12

127 children and 264 adults swam at the public pool that​ day

Solution:

Let "c" be the number of children swam

Let "a" be the number of adult swam

Cost for each children = $ 1.25

Cost for each adult = $ 2.25

391 people used the public swimming pool

Therefore,

c + a = 391

a = 391 - c ------- eqn 1

The receipts for admission totaled $752.75

Therefore, we frame a equation as:

number of children swam x Cost for each children + number of adult swam x Cost for each adult = 752.75

[tex]c \times 1.25 + a \times 2.25 = 752.75[/tex]

1.25c + 2.25a = 752.75 ---------- eqn 2

Let us solve eqn 1 and eqn 2

Substitute eqn 1 in eqn 2

1.25c + 2.25(391 - c) = 752.75

1.25c + 879.75 - 2.25c = 752.75

c = 879.75 - 752.75

c = 127

Substitute c = 127 in eqn 1

a = 391 - 127

a = 264

Thus 127 children and 264 adults swam at the public pool that​ day

I apologize if you are offended by the "bad words" in the answer below. Brainly's censor got offended.

Answer:

-1

Step-by-step explanation:

Slope = (y2 - y1)/(x2 - x1)

= (7 - (-3))/(-2 - 8)

= (7+3)/(-10)

= 10/(-10) = -1

Answer:

19 1/4

Step-by-step explanation:

5 1/2 of 2 1/3

Change mixed fraction to improper fraction

11/2 of 7/2

Of means multiplication

11/2 x 7/2

77/4

19 1/4

The mixture contains 61.5% of water.

Step-by-step explanation:

Total parts = 4+ 2.5 = 6.5

Parts of water =4

parts of drink = 2.5

Percent of water in the mixture = 4 × 100/ 6.5

                                                     = 400/6.5

                                                      = 61.53%

It is rounded to the nearest tenth as 61.5%.

To find the percentage of water in the mix, we calculate the proportion of water (4 parts) to the total mixture (6.5 parts) and multiply by 100%, resulting in approximately 61.5%.

To determine what percent of the mixture is water when a drink is made with 4 parts water and 2.5 parts drink mix, we add together the parts of water and drink mix to find the total parts of the mixture. Then, we calculate the fraction of the mixture that is water and convert that to a percentage.

First, we find the total parts of the mixture:

Water: 4 parts

Drink mix: 2.5 parts

Total parts: 4 + 2.5 = 6.5 parts

Next, we calculate the percentage of the mixture that is water:

(Parts of water / Total parts) × 100%

(4 parts / 6.5 parts) × 100% \approximately 61.5%

Rounding to the nearest tenth, we get:

61.5

Answer:

1.21052631579 is the exact answer or 1.2 is if you round it

Step-by-step explanation:

This is the answer I got from dividing 690 by 570. Hope this helped

Answer:

1.21 to the nearest hundredth.

Step-by-step explanation:

570 * x = 690

x = 690/570

x = 1.210526316.

Answer:

D would be the best choice.

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Did the test

Answer:

-2

Step-by-step explanation:

x-3=-5

x=-5+3

x=-2