Find the approximate side length of a square game board with an area of 136in^2

Answer: 3F+2F+4F+F=750

science fiction=225

mystery=150

biographies=300

fiction=75

Step-by-step explanation: To find the equation, read through the question and write down any important information, such as there are 2 twice as many mystery book as fiction books (2*fiction books=mystery books). Once you have all the information written down place it in an equation set equal to the total (750).

After you have found the equation, solve for the fiction books (F) by isolating the variable.  3F+2F+4F+F=750, 10F=750, F=750/10, F=75.

After that you plug 75 into the equation. Which would get you 3*75= 225 science fiction books 2*75= 150 mystery books and 4*75=300 biographies

To solve the problem, fantasy books (F) are used as the variable. The equation F + 3F + 2F + 4F = 750 is solved to find F = 75, leading to 75 fantasy books, 225 science fiction books, 150 mystery books, and 300 biographies.

The student is tasked with determining the number of books in each genre in a library, given certain ratios between the numbers of books in different genres. Let's use fantasy books (F) as our variable since all other genres are described in relation to fantasy books. According to the problem, there are three times as many science fiction books as fantasy books, twice as many mystery books as fantasy books, and four times as many biographies as fantasy books. The total number of books is 750.

The equation that represents the number of each type of book can be defined as:

F + 3F + 2F + 4F = 750

Combining like terms, we get:

10F = 750

Dividing both sides by 10, we find:

F = 75

Now that we have the number of fantasy books, we can calculate the numbers for other genres:

Science fiction books: 3 × 75 = 225

Mystery books: 2 × 75 = 150

Biographies: 4 × 75 = 300

Answer:

Angle ACB = 67

Step-by-step explanation:

Angle DAB and BAC are supplementary angles. This means they add up to 180 degrees. So subtract 127 from 180 to find angle BAC which is 53. We know that a triangle's degrees add up to 180. So take 180 and subtract (60+ 53) to find angle ACB.

The angles around point A should add up to 360° ∠ACB is 173°.

In the given diagram where ∠ABC is 60° and ∠DAB is 127°, you can find ∠ACB by using the fact that the angles around point A should add up to 360°.

∠DAB + ∠CAB + ∠CBA = 360°

Given that ∠DAB = 127° and ∠CAB is 60°, you can solve for ∠CBA:

127° + 60° + ∠CBA = 360°

Combine the known angles on the left side:

187° + ∠CBA = 360°

Now, isolate ∠CBA:

∠CBA = 360° - 187°

∠CBA = 173°

so, ∠ACB is 173°.

for such more question on angles

https://brainly.com/question/25716982

#SPJ3

Answer:

61 degrees

Step-by-step explanation:

We need to take the inverse cosine of both sides as follows:

cos^-1(sin(29))=cos^-1(cos(x))

61=x

Answer:

Option C, 0

Step-by-step explanation:

Step 1:  Create improper fractions

-6 4/5 = -6*5/5 - 4/5 = -30/5 - 4/5 = -34/5

6 4/5 = 6 * 5/5 + 4/5 = 30/5 + 4/5 = 34/5

Step 2:  Add

-34/5 + 34/5

0

Answer: Option C, 0

Answer:

Answer is C: 0

Step-by-step explanation:

Answer:

x=-4.37 or 1.37

Step-by-step explanation:

The equation whose solution is to be found is;

[tex]1 + \frac{3}{x}= \frac{6}{ {x}^{2} } [/tex]

we now multiply through by

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

This implies that;

[tex]( {x}^{2})1 +({x}^{2} \times \frac{3}{x})= {x}^{2} \times \frac{6}{ {x}^{2} }[/tex]

[tex] \implies{x}^{2}+3x=6[/tex]

Subtracting - 6 from both side we obtain;

[tex] {x}^{2} + 3x - 6 = 6 - 6[/tex]

[tex] \implies{x}^{2} + 3x - 6 =0[/tex]We now obtain a quadratic equation.So, let us use quadratic formula to find the solutions.

Comparing the equation ,

[tex]{x}^{2} + 3x - 6 = 0[/tex]

to the general quadratic formula,

[tex]a {x}^{2} + bx + c = 0[/tex]

we can say that,

a=1,b=3 and c=-6

putting this in to the quadratic formula,

[tex] \implies x = \frac{ -b\pm \sqrt{{b}^{2} - 4ac} }{2a} [/tex], we obtain

[tex]x = \frac{-3\pm \sqrt{ {3}^{2} - 4(1)(-6)} }{2(1)} [/tex]

Simplifying we obtain,

[tex] x = \frac{ -3\pm \sqrt{9+24}}{2} [/tex]

[tex] \implies x = \frac{-3-\sqrt{33} }{2}or \frac{-3+\sqrt{33}}{2} [/tex]

x=-4.37 or 1.37

Answer:

25x^2 + 30e^5x + 9 e^10

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

Using the definition

n[tex]C_{r}[/tex] = [tex]\frac{n!}{r!(n-r)!}[/tex]

where n! = n(n - 1)(n - 2) × 3 × 2 × 1, note that 0! = 1

Given

9[tex]C_{9}[/tex] = [tex]\frac{9!}{9!(9-9)!}[/tex] = [tex]\frac{9!}{9!(0!)}[/tex] = [tex]\frac{9!}{9!}[/tex] = 1

The value of 9C9 or C(9, 9) using Combination is 1.

In combinatorial notation, "9C9" represents the number of combinations of selecting 9 items from a set of 9 items without regard to their order. This can be calculated using the formula:

nCr = n! / (r!(n-r)!)

Here, n = 9 and r = 9.

So, 9C9 = 9! / (9!(9-9)!)

     = 9! / (9! × 0!)

Any number divided by 0 is undefined, so the denominator becomes 0!. However, 0! is defined as 1.

Therefore:

9C9 = 9! / (9! × 1)

     = 9! / 9!

     = 1

Hence, the value of 9C9 is 1.

Learn more about Combination here:

https://brainly.com/question/29595163

#SPJ6

Answer:

y=-2x+9

Step-by-step explanation:

slope formula

y= mx+ b

so 2x+y=9 can be rewritten by moving 2x to the other side of the equation:

1.

y=9-2x

2. (reorder)

Y= -2x+9

there you go

Answer: [tex]d=16.4[/tex]

Step-by-step explanation:

Step 1) Add 4 to both sides: [tex]d-4+4=12.4+4[/tex]

[tex]d=16.4[/tex]

Answer: D=16 please give brainliest

Step-by-step explanation:

D-4=12

first add +4 to both sides to reverse it

D=16 and to make sure its right

lets substutie for D

16-4=12

12=12

correct

Answer:

  6.3

Step-by-step explanation:

The rocket hits the ground at the same speed it left, only the velocity is downward, rather than upward. That is, the change in velocity is from +100 ft/s to -100 ft/s, a total change of 200 ft/s. The change in velocity is brought about by the acceleration due to gravity, 32 ft/s/s. The time required for the observed change in velocity is ...

  (200 ft/s)/(32 ft/s²) = 6.25 s

Rounded to tenths, it takes the rocket 6.3 seconds to hit the ground.

_____

The equation for the ballistic motion of the rocket is ...

  h(t) = -1/2·gt² +v0·t

where g is 32 ft/s² and v0 is 100 ft/s. A graph of this equation shows the rocket hits the ground at 6.25 seconds, as above.

Answer:

5572

Step-by-step explanation:

The shape of the ball is the same as a sphere, applying the formula for find the volume of sphere we found the answer as

Volume = 5576cm^3

Given Data

Radius r = 11cm

Applying the expression for the volume of a sphere we have

Volume of sphere = 4/3*π*r^3

Substitute our given Data into the expression we have

Volume of sphere = 4/3*3.142*11^3

Volume of sphere = 4/3*3.142*1331

Volume of sphere = 16728.008/3

Volume of sphere = 5576.00

Hence the volume of the ball is 5576cm^3

Learn more about volume of sphere:

https://brainly.com/question/22807400

[tex]-38d-57>-19d+76\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:d<-7\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:-7\right)\end{bmatrix}[/tex]

Solution:

Given inequality is:

[tex]-38d - 57 > -19d + 76[/tex]

We have to solve the inequality for "d"

From given,

[tex]-38d-57>-19d+76\\\\\mathrm{Add\:}57\mathrm{\:to\:both\:sides}\\\\-38d-57+57>-19d+76+57\\\\\mathrm{Simplify}\\\\-38d>-19d+133\\\\\mathrm{Add\:}19d\mathrm{\:to\:both\:sides}\\\\-38d+19d>-19d+133+19d\\\\[/tex]

[tex]\mathrm{Simplify}\\\\-19d>133\\\\Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)\\\\[/tex]

When we multiply or divide both sides of inequality by negative number, then we must flip the inequality sign

[tex]\left(-19d\right)\left(-1\right)<133\left(-1\right)\\\\\mathrm{Simplify}\\\\19d<-133\\\\\mathrm{Divide\:both\:sides\:by\:}19\\\\\frac{19d}{19}<\frac{-133}{19}\\\\\mathrm{Simplify}\\\\d<-7[/tex]

The solution set is given as:

[tex]-38d-57>-19d+76\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:d<-7\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:-7\right)\end{bmatrix}[/tex]

Slope of the line is -7

Step-by-step explanation:

⇒ m = (113 - -41)/(-15 - 7)

       = 154/-22 = -7

The Main Answer is the best estimation of the fraction of the batch that was left is [tex]59/168[/tex].

To find the fraction of the batch that was left, we first need to calculate how much was given away to the neighbors and how much Mr. Gallegos ate himself, then subtract those amounts from the total batch.

1. Given that Mr. Gallegos gave [tex]11/21[/tex] of the batch to his neighbors, and ate 1/8 of the batch himself.

2. We need to find the total amount given away and eaten: [tex]Total given away = 11/21[/tex] [tex]Total eaten by Mr. Gallegos = 1/8[/tex]

3. To find the fraction left, subtract the total given away and eaten from the total batch (1): [tex]Fraction left = 1 - (11/21 + 1/8)[/tex]

Now, let's calculate:

To subtract fractions, they must have the same denominator. The least common multiple (LCM) of [tex]21[/tex] and [tex]8[/tex] is [tex]168[/tex]. We'll rewrite the fractions with a common denominator of [tex]168[/tex]:

[tex]11/21 = (11/21) * (8/8) = 88/168 \\1/8 = (1/8) * (21/21) = 21/168[/tex]

So, the expression becomes:

[tex]Fraction left = 1 - (88/168 + 21/168) \\= 1 - (109/168)[/tex]

To subtract [tex]109/168[/tex] from [tex]168/168[/tex] (which equals 1), we'll subtract the numerators:

[tex]Fraction left = (168/168) - (109/168) \\= 59/168[/tex]

Therefore, the best estimation of the fraction of the batch that was left is [tex]59/168[/tex].

COMPLETE QUESTION:

Mr. Gallegos made a batch of muffins. He gave [tex]11/21[/tex] of the batch to his neighbors and ate [tex]1/8[/tex] of the batch himself. Which is the best estimation of the fraction of the batch that was left?

Answer:

12 bags of popcorn and 4 sodas

Step-by-step explanation:

Quantity: Popcorn =3x       Sodas=x

Value: Sodas - $4.50, Popcorn - $1.50

Total Value: $36

3x(1.5)+4.5x=36

4.5x+4.5x=36

9x=36

x=4

Therefore, 12 bags of popcorn and 4 sodas

The number of sodas and popcorn Kirk bought is 4 and 12 respectively.

let

(4.50×x) + (1.50×3x) = 36

4.50x + 4.50x = 36

9x = 36

x = 36/9

x = 4

Therefore, the number of sodas bought,x is 4 and the number of popcorn bought, 3x = 3 × 4 = 12

Learn more about equation:

https://brainly.com/question/2972832

Answer:

I've never done this before, but if it is balls per square foot, then i can figure it out. It is 2 balls per square foot

Step-by-step explanation:

If the gym is 100 ft by 60 ft, it will be 6,000 square ft. Since there are 12,000 balls, you divide it by 6,000 (12,000/6,000), which is 2, so it would be 2 balls per square foot

The population density of the balls in the gym is calculated by dividing the total number of balls (12,000) by the gym's area (6,000 square feet), resulting in 2 balls per square foot.

The question asks for the population density of the balls in a gym that measures 100 feet in length and 60 feet in width, with a total of 12,000 balls available. First, we must calculate the total area of the gym to determine how many balls there are per square foot. The formula for the area is length × width, so the area of the gym is 100 feet × 60 feet = 6,000 square feet.

Next, to find the population density of the balls, we divide the total number of balls by the total area of the gym. Therefore, the population density is 12,000 balls ÷ 6,000 square feet = 2 balls per square foot. This calculation offers a simple way to visualize how densely the balls are distributed throughout the gym's space.

MARK BRAINLIEST PLZZZ :))))))

Answer:

1. x=4

2. a=5

3. c=6

4. a=4

Step-by-step explanation:

#1. 2x+8+16

subtract 8 from both sides

Divide both numbers by 2

x=4

#2. 3a+2=17

subtract 2 from both sides

Divide both numbers by 3

a=5

#3. 3c-4=14

add both numbers by 4

Divide both numbers by 3

c=6

#4. 3a-5=7

add both numbers by 5

divide both numbers by 3

a=4

Answer:

Step-by-step explanation:

Answer:

y = -2x - 8

Step-by-step explanation:

Use the point slope form:  (y - y1) = m(x - x1)

(y - (-4)) = -2(x - (-2))

y + 4 = -2(x + 2)

y + 4 - 4 = -2x - 4 - 4

y = -2x - 8

Answer:  y = -2x - 8

Answer:

Step-by-step explanation:

y-y1=m(x-x1)

y+4=-2(x+2)

y+4=-2x-4

2x+y+8=0

or 2x+y=-8

Answer:

7 : 30

Step-by-step explanation:

this can be simplified by looking for a number that is common

we can first divide by 10 as this is common

1260/10 = 126

5400/10 = 540

we now have 126 : 540

we can divide by 2 as it is also common

126/2 = 63

540/ 2 = 270

we can also divide by 9 as its also common

63/9 = 7

270/9 = 30

the simplified answer is :

Answer:

72feet/min

Step-by-step explanation:

The following were obtained from the question:

Distance = 54 yards

But: 1yard = 3feets

Therefore, 54 yards = 54 x 3 = 162feets

Time = 135secs

Recall: 60secs = 1mins

Therefore, 135secs = 135/60 = 2.25mins

The rate of the Zebra = Distance /time

The rate of the Zebra = 162/2.25 = 72feet/min

Answer:

x = 25 degrees

Step-by-step explanation:

So we know that the 4x, 2x + 10°, and x - 5° and the measures of the three interior angles of the triangle. The sum of the interior angles of a triangle is 180°.

Using this, we can conclude that the sum of 4x, 2x + 10°, and x - 5° is equal to 180°.

We can write this information as the equation:

4x + (2x + 10) + (x - 5) = 180

We can use this equation to find the value of x. To find the value of x by using the equation, we need to solve for x (put the equation into the form x = _).

Solve for x:

4x + (2x + 10) + (x - 5) = 180

4x + 2x + 10 + x - 5 = 180

Combine like terms.

7x + 5 = 180

Subtract 5 from both sides to get rid of the +5 on the left side.

7x = 180 - 5

Simplify.

7x = 175

Divide both sides by 7 to get rid of the coefficient of 7 on the left side.

x = 175 ÷ 7

Simplify.

x = 25.

x would be equal to 25°.

x = 25 degrees

I hope you find this helpful. :)

Answer:

Problem #1:  x = 2.5

Problem #2:  x = 10/7

Step-by-step explanation:

Step 1:  Find the value of x in (8x - 20)

8x - 20 = 0

Add 20 to both sides

8x - 20 + 20 = 0 + 20

8x = 20

Divide both sides by 8

8x / 8 = 20 / 8

x = 2.5

Answer:  x = 2.5

Step 2:  Find the value of x in (14x - 20)

14x - 20 = 0

Add 20 to both sides

14x - 20 + 20 = 0 + 20

14x = 20

Divide both sides by 14

14x / 14 = 20 / 14

x = 10/7

Answer:  x = 10/7

Answer: 4/7

Step-by-step explanation:

Answer: 3 13/24

Step-by-step explanation:

Turn 7 1/6 into an Improper Fraction:

43/6 - 3 5/8

Turn 3 5/8 into an Improper Fraction:

43/6 - 29/8

Subtract:

43/6 - 29/8= 85/24

Turn 85/24 into a Mixed Number (Final Step):

85/24 = 3 13/24

Answer:

3 13/24

Hope this Helps!

To find the difference between 7 1/6 and 3 5/8, convert each mixed number to an improper fraction with a common denominator of 24, subtract the numerators to find 85/24, which simplified to a mixed number results in 3 13/24.

The difference between 7 1/6 and 3 5/8 can be found by converting each mixed number to an improper fraction with a common denominator and then subtracting the two. First, convert the mixed numbers to improper fractions. So, we have 7 1/6 as 43/6 and 3 5/8 as 29/8. To find a common denominator, we can use the least common multiple (LCM) of 6 and 8, which is 24. Then we convert the fractions as follows:

Now we can subtract the numerators and keep the common denominator:

172/24 - 87/24 = 85/24

To present the answer as a mixed number, we divide 85 by 24, which gives us:

3 13/24

Therefore, the difference between 7 1/6 and 3 5/8 is 3 13/24.

Answer:

(-2x^2-3)(4x+1)

Step-by-step explanation:

factor out -2x^2 from the first two terms, and -3 from last two terms

-2x^2(4x+1)-3(4x+1)

now factor out (4x+1)

(-2x^2-3)(4x+1)

Answer:Answer:

(-2x^2-3)(4x+1)

Step-by-step explanation:

factor out -2x^2 from the first two terms, and -3 from last two terms

-2x^2(4x+1)-3(4x+1)

now factor out (4x+1)

(-2x^2-3)(4x+1)

Step-by-step explanation:

Answer: 202.60

Step-by-step explanation:

324.16/8 = 40.52

40.52*5 = 202.60

Answer:

504

Step-by-step explanation:

just an estimate, 860/30 is roughly 28 so 28x18=504

Option C: 99° is the measure of angle 6

Explanation:

It is given that the measure of ∠5 is (10x-9)°

The measure of ∠7 is (9x)°

We need to determine the measure of ∠6

Since, from the diagram it is obvious that the angles 5 and 7 are vertical angles.

And, we know that the vertical angles are always equal.

Thus, we have,

              [tex]\angle 5 = \angle 7[/tex]

       [tex]10x-9=9x[/tex]

[tex]10x-9x-9=0[/tex]

           [tex]x-9=0[/tex]

                 [tex]x=9\\[/tex]

Thus, the value of x is 9.

Substituting [tex]x=9\\[/tex] in ∠5 and ∠7, we have,

[tex]\angle 5= (10x-9)^{\circ}[/tex]

    [tex]= (10(9)-9)^{\circ}[/tex]

    [tex]= (90-9)^{\circ}[/tex]

    [tex]= 81^{\circ}[/tex]

[tex]\angle 7=(9x)^{\circ}[/tex]

    [tex]=(9(9))^{\circ}[/tex]

    [tex]=81^{\circ}[/tex]

The measure of [tex]\angle 5 = 81^{\circ}[/tex] and [tex]\angle 7= 81^{\circ}[/tex]

Since, from the diagram we can see that the angles 6 and 7 are in a straight line.

And the angles in the straight line add up to 180°

Thus, we have,

[tex]\angle 6+\angle 7=180^{\circ}[/tex]

[tex]\angle 6+81^{\circ}=180^{\circ}[/tex]

         [tex]\angle 6=180^{\circ}-81^{\circ}[/tex]

         [tex]\angle 6 =99^{\circ}[/tex]

Thus, the measure of angle 6 is 99°

Therefore, Option C is the correct answer.

Answer:

C:99

Step-by-step explanation:

t is given that the measure of ∠5 is (10x-9)°

The measure of ∠7 is (9x)°

We need to determine the measure of ∠6

Since, from the diagram it is obvious that the angles 5 and 7 are vertical angles.

And, we know that the vertical angles are always equal.

Thus, we have,

\angle 5 = \angle 7∠5=∠7

10x-9=9x10x−9=9x

10x-9x-9=010x−9x−9=0

x-9=0x−9=0

\begin{lgathered}x=9\\\end{lgathered}

x=9

Thus, the value of x is 9.

Substituting \begin{lgathered}x=9\\\end{lgathered}

x=9

in ∠5 and ∠7, we have,

\angle 5= (10x-9)^{\circ}∠5=(10x−9)

∘

= (10(9)-9)^{\circ}=(10(9)−9)

∘

= (90-9)^{\circ}=(90−9)

∘

= 81^{\circ}=81

∘

\angle 7=(9x)^{\circ}∠7=(9x)

∘

=(9(9))^{\circ}=(9(9))

∘

=81^{\circ}=81

∘

The measure of \angle 5 = 81^{\circ}∠5=81

∘

and \angle 7= 81^{\circ}∠7=81

∘

Since, from the diagram we can see that the angles 6 and 7 are in a straight line.

And the angles in the straight line add up to 180°

Thus, we have,

\angle 6+\angle 7=180^{\circ}∠6+∠7=180

∘

\angle 6+81^{\circ}=180^{\circ}∠6+81

∘

=180

∘

\angle 6=180^{\circ}-81^{\circ}∠6=180

∘

−81

∘

\angle 6 =99^{\circ}∠6=99

∘

Thus, the measure of angle 6 is 99°

Therefore, Option C is the correct answer.