A company set up a food booth and a game booth at a county fair the fee for the food booth is $100 +5 dollars per day the fee for the game booth is $50 +7 dollars per day write an expression for how both booths will cost for the same number of days.

Answer:

y=3/2 x + 5

Step-by-step explanation:

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

Firstly, find m (gradient).

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

m= 8-(-1)/ 2-(-4)

m= 9/ 6

m= 3/2

Please leave gradient in improper fraction if its value is not a whole number.

Now substitute m into the equation:

y= 3/2 x + c

Then substitute a coordinate to find c:

When y= 8, x= 2,

8= 3/2 (2) + c

8= 3 + c

c= 8 - 3 = 5

Thus, the equation of the line is y= 3/2 x + 5.

Answer:

6.2 miles per hour

Step-by-step explanation:

Given: Philip ran 200 feet.

           Time taken is 22 seconds.

First lets find out speed of Philip.

Speed= [tex]\frac{distance}{time}[/tex]

∴ Speed= [tex]\frac{200}{22} \ ft/sec[/tex]

Speed= 9.09 ft/sec.

Now, converting speed feet per second to miles per hours.

Remember, 1 miles= 5280 ft and 1 hours= 3600 seconds.

∴ Speed in miles per hour= [tex]9.09\times \frac{\frac{1}{5280} }{\frac{1}{3600} }[/tex]

⇒ Speed in miles per hour= [tex]9.09\times \frac{3600}{5280}[/tex]

⇒Speed in miles per hour= [tex]9.09\times 0.68= 6.19 \frac{mi}{h}[/tex]

∴ Philip ran at a speed of 6.2 miles per hour(nearest tenth decimal).

Answer:

122

Step-by-step explanation:

6x+3y-4=6(20)+3(2)-4=120+6-4=126-4=122

Answer:

x= [tex]-2\pm \sqrt{11}[/tex]

Step-by-step explanation:

Here is the correct question: Using the quadratic formula to solve

x²+4x - 7. what are the values of x.

Solving by using quadratic formula.

Formula: [tex]\frac{-b\pm \sqrt{b^{2}-4(ac) } }{2a}[/tex]

∴  In the expression [tex]x^{2} +4x-7[/tex], we have a= 1, b= 4 and c= -7.

Now, subtituting the value in the formula.

=[tex]\frac{-4\pm \sqrt{4^{2}-4(1\times -7) } }{2\times 1}[/tex]

= [tex]\frac{-4\pm \sqrt{4^{2}-4(-7) } }{2}[/tex]

Opening parenthesis.

= [tex]\frac{-4\pm \sqrt{16+28 } }{2\times 1}[/tex]

= [tex]\frac{-4\pm \sqrt{44}}{2}[/tex]

We know 2²=4

= [tex]\frac{-4\pm \sqrt{2^{2}\times 11 }}{2}[/tex]              

we know √a²=a

= [tex]\frac{-4\pm 2 \sqrt{11 }}{2}[/tex]

Taking 2 as common in the expression.

= [tex]\frac{2(-2\pm \sqrt{11}) }{2}[/tex]

Cancelling 2

= [tex]-2\pm \sqrt{11}[/tex]

Hence we get, [tex]x=-2\pm\sqrt{11}[/tex]

Answer:

Writing 6(3x + 8) + 32 + 12x in 3 different ways:

∵ 6(3x + 8) = 18x +48 as distribute law suggests that  a(b + c) = ab + ac

Step-by-step explanation:

As the expression is 6(3x + 8) + 32 + 12x, and we have to write it in three different ways. Using the properties of operations we can write it in three different ways,

Let way one be denoted as w₁

Let way two be denoted as w₂

Let way three be denoted as w₃

So, lets write 6(3x + 8) + 32 + 12x in 3 different ways:

∵ 6(3x + 8) = 18x +48 as distribute law suggests that  a(b + c) = ab + ac

Keywords: operation properties, distributive law

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Answer:

m∠C = 115°

Step-by-step explanation:

DE≈DF

ΔDEF is an isosceles triangle ∴ m∠DEF = m∠DFE = 1/2 (180-50) = 65

∴ m∠DFB = 180 -65 = 115

∵ DCBF is a parallelogram m∠DFB = m∠DCB = 115°

Answer:

D.) 7:3

Step-by-step explanation:

First, find the LCM of the numbers, which is 8.

Then divide each number by 8

56÷8=7 24÷8= 3

Then, put them in a ratio

7:3

Answer:

A

Step-by-step explanation:

Right now, our ratio of male to female is 24:56. We need to reduce this, kind of like how you would reduce a fraction. 24÷8=3 and 56÷8=7, so our new ratio is 3:7.

Answer:

about 11 years

Step-by-step explanation:

we know that

The simple interest formula is equal to

[tex]A=P(1+rt)[/tex]

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest  

t is Number of Time Periods

in this problem we have

[tex]t=?\ years\\ P=\$4,000\\ A=\$8,000\\r=9\%=9/100=0.09[/tex]

substitute in the formula above

[tex]8,000=4,000(1+0.09t)[/tex]

solve for r

[tex]2=(1+0.09t)[/tex]

[tex]0.09t=2-1[/tex]

[tex]0.09t=1[/tex]

[tex]t=11.1\ years[/tex]

The third angle will be: 30°

Step-by-step explanation:

Amy is cutting a triangle so we know that the sum of interior angles of a triangle is 180 degrees

She has already cut two angles of 75 degrees, which means she has cut a total of 150 degrees

So,

Let x be the third angle then the sum of all angles will be: 150+x

So,

[tex]150+x = 180\\x = 180-150\\x = 30[/tex]

Hence,

The third angle will be: 30°

Keywords: Angles, triangle

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Answer:

30*

Step-by-step explanation:

Answer:

A = 2πr2 + 2πrh is the final answer

Step-by-step explanation:

Answer:

h = (x-2πr²)/2πr

Step-by-step explanation:

Given the surfaces area of a cylinder by the formula

SA = 2πr²+2πrh

To solve for h means making h the subject of the formula from the equation.

Let x be the surface area of the cylinder. The formula can be rewritten as;

x = 2πr²+2πrh

Subtracting 2πr² from both sides of the equation will give;

x-2πr² = 2πr²+2πrh-2πr²

x-2πr²= 2πrh

Dividing both sides by 2πr wikk results into;

(x-2πr²)/2πr = 2πrh/2πr

h = (x-2πr²)/2πr where x is the surface area of the cylinder.

Answer: 0.236 Liters.

Step-by-step explanation:

First you multiply 1.3 and 0.8 you get 1.064.

You subtract 1.3 and 1.064 and you get your answer 0.236 Liters.

Answer:

see explaination

Step-by-step explanation:

the diagram shows two equal parts being the divided by two in the equations. The parts are worth 8 meaning if you divide 16 by 8 it is 2 because there are two parts.

Answer:

8x2 = 16

Step-by-step explanation:

8x2 = 16

16/2 = 8

Answer:

[tex]\$833.97[/tex]  

Step-by-step explanation:

we know that    

The compound interest formula is equal to  

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

[tex]t=10\ years\\ P=\$650\\ r=2.5\%=2.5/100=0.025\\n=4[/tex]  

substitute in the formula above

[tex]A=650(1+\frac{0.025}{4})^{4*10}[/tex]  

[tex]A=650(1.00625)^{40}[/tex]  

[tex]A=\$833.97[/tex]  

Answer:

Lucey reads 10 pages fewer than Carey.

The Academy Awards, also known as Oscars, are prestigious awards recognizing achievements in the film industry. The OscarsSoWhite controversy raised concerns about diversity and representation in Hollywood.

Academy Awards, commonly known as Oscars, are prestigious awards in the film industry recognizing outstanding achievements in various categories. The controversy surrounding the OscarsSoWhite highlighted issues about diversity and representation in Hollywood.

Answer:

Cotton Gin

Explanation:

A cotton gin – meaning "cotton engine" – is a machine that quickly and easily separates cotton fibers from their seeds, enabling much greater productivity than manual cotton separation.[1] The fibers are then processed into various cotton goods such as linens, while any undamaged cotton is used largely for textiles like clothing. The separated seeds may be used to grow more cotton or to produce cottonseed oil.

Handheld roller gins had been used in the Indian subcontinent since at earliest AD 500 and then in other regions.[2] The Indian worm-gear roller gin, invented sometime around the 16th century,[3] has, according to Lakwete, remained virtually unchanged up to the present time. A modern mechanical cotton gin was created by American inventor Eli Whitney in 1793 and patented in 1794. Whitney's gin used a combination of a wire screen and small wire hooks to pull the cotton through, while brushes continuously removed the loose cotton lint to prevent jams. It revolutionized the cotton industry in the United States, but also led to the growth of slavery in the American South as the demand for cotton workers rapidly increased. The invention has thus been identified as an inadvertent contributing factor to the outbreak of the American Civil War.[4] Modern automated cotton gins use multiple powered cleaning cylinders and saws, and offer far higher productivity than their hand-powered precursors.[5]

Eli Whitney invented his cotton gin in 1793. He began to work on this project after moving to Georgia in search of work. Given that farmers were desperately searching for a way to make cotton farming profitable, a woman named Catharine Greene provided Whitney with funding to create the first cotton gin. Whitney created two cotton gins: a small one that could be hand-cranked and a large one that could be driven by a horse or water power.

The invention from the late 1700s is Cotton Gin. It was invented by Eli Whitney in 1793.

A cotton gin means “cotton engine”. It is a machine that quickly and easily sorts cotton fibers from their seeds, enabling much larger productivity than manual cotton separation.

Eli Whitney began to work on this project after moving to Georgia in search of work. At that time, farmers were desperately searching for a way to make cotton farming profitable.

The fibers of cotton are then processed into various cotton goods such as linens, while undamaged cotton is used largely for textiles like clothing. The separated seeds may be used to grow more cotton or to produce cottonseed oil.

Therefore, Cotton Gin is an invention from the late 1700s.

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Answer:

1 1/18 kilograms

Step-by-step explanation:

First add 3/8 + 11/8, which equals to 11/8. Then add 5/8, which equals to 19/8. Change the improper fraction to a mixed number, and the sum is 1 1/18.

ans is 19/8 kilogram.......

Answer:

[tex]\large\boxed{if\ x\neq-3\ \wedge\ y\neq0\ \wedge\ x\neq y\ \wedge\ x\neq -y}[/tex]

second

[tex]\large\boxed{y\neq0\ \wedge\ x\neq-y\ (y\neq-x)}[/tex]

Step-by-step explanation:

We know that dividing by 0 is impossible.

Therefore, the denominator of the expression must be different from 0.

[tex]\text{For}\\\\\dfrac{(x-y)^2}{2xy+6y}\times\dfrac{4x+12}{x^2-y^2}\\\\\\2xy+6y\neq0\qquad(1)\\\\x^2-y^2\neq0\qquad(2)[/tex]

[tex](1)\\2xy+6y\neq0\qquad\text{distribute}\\\\2y(x+3)\neq0\iff2y\neq0\ \wedge\ x+3\neq0\\\\2y\neq0\qquad\text{divide both sides by 2}\\\boxed{y\neq0}\\\\x+3\neq0\qquad\text{subtract 3 from both sides}\\\boxed{x\neq-3}\\==========================\\(2)\\x^2-y^2\neq0\qquad\text{use}\ a^2-b^2=(a-b)(a+b)\\(x-y)(x+y)\neq0\iff x-y\neq0\ \wedge\ x+y\neq0\\\boxed{x\neq y}\ \wedge\ \boxed{x\neq-y}[/tex]

[tex]\text{For}\\\\\dfrac{2(x-y)}{y(x+y)}\\\\y(x+y)\neq0\iff y\neq0 \wedge\ x+y\neq0\\\\ \boxed{y\neq0}\ \wedge\ \boxed{x\neq-y}[/tex]

Answer:

Step-by-step explanation:

Answer:

[tex] - {x}^{2} + x + 24[/tex]

Step-by-step explanation:

Subtract the functions:

[tex]f - g = (36 - {x}^{2} ) - (8 - x)[/tex]

Simplify:

[tex](36 - {x}^{2} ) - (8 - x) \\ 36 - {x}^{2} - 8 + x \\ - {x}^{2} + x + 24[/tex]

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Equations are generally in the form of:

y = mx + c

where m is the gradient and c is the y intercept

As you can see, in this equation, the y intercept is 5

Thus, your answer is C. 5

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Answer: Sin45 = x/4

x = 4Sin45

x = 2.83miles

Step-by-step explanation:

Final answer:

The horizontal distance of the ship from the bottom of the lighthouse is equal to the direct distance from the lighthouse to the ship, which is 4.00 miles, because the angle of depression is 45 degrees forming an isosceles right-angled triangle.

Explanation:

The student is asking how to calculate the horizontal distance of a ship from the bottom of a lighthouse when the angle of depression from the top of the lighthouse to the ship is 45° and the direct distance from the lighthouse to the ship is 4 miles. This is a trigonometry problem involving right-angle triangles.

Since the angle of depression is 45°, we can establish that the lighthouse height and the horizontal distance will be equal due to the properties of an isosceles right-angled triangle. Thus, the horizontal distance from the bottom of the lighthouse to the ship is the same as the distance from the top of the lighthouse directly to the ship, which is given as 4 miles. Therefore, the horizontal distance is 4.00 miles.

3c - 7

3 times c = 3c

7 less than is subtraction

Answer:

3c - 7

Step-by-step explanation:

less than = flip the equation

Answer:

[tex]Hypotenuse=10[/tex]

Step-by-step explanation:

For this exercise you can use the following Trigonometric Identity:

[tex]sin\alpha=\frac{opposite}{hypotenuse}[/tex]

Let be "x" the hypotenuse of this right triangle.

You can identify from the figure that, in this case:

[tex]\alpha=60\°\\\\opposite=5\sqrt{3}[/tex]

Then, knowing these values you can substitute them into [tex]sin\alpha=\frac{opposite}{hypotenuse}[/tex]:

[tex]sin(60\°)=\frac{5\sqrt{3}}{x}[/tex]

Finally, you need to solve for "x" in order to find the lenght of the hypotenuse.

This is:

[tex]x*sin(60\°)=5\sqrt{3}\\\\x=\frac{5\sqrt{3}}{sin(60\°)}\\\\x=10[/tex]

Answer: 6

Step-by-step explanation: First rewrite 10 as 10/1 and 1 and 2/3 as 5/3.

Mixed numbers can be changed to improper fractions by multiplying the denominator by the whole number and then adding the numerator. We then put out numerator over our old denominator.

So we have 10/1 ÷ 5/3 or 10/1 × 3/5.

It's important to understand that dividing by a fraction is the same as multiplying by its reciprocal. In other words, we can change the division to multiplication and flip the second fraction.

Now multiplying across the numerators and across the denominators, we have 30/5. Notice however that 30/5 is not in lowest terms so we divide the numerator and the denominator by the greatest common factor of 30 and 5 which is 6 and we end up with 6.

Therefore, 10 ÷ 1 and 2/3 = 6.

Final answer:

To find 10 divided by 1 2/3, convert the mixed number to an improper fraction (5/3), multiply by the reciprocal (3/5), and simplify the result to get 6.

Explanation:

To divide 10 by 1 2/3, first, we need to convert the mixed number 1 2/3 into an improper fraction. The mixed number 1 2/3 can be written as 5/3 because 1 (which is 3/3) plus 2/3 equals 5/3.

Next, we apply the rule for dividing fractions: we multiply by the reciprocal of the divisor. So, we take 10 (which is the same as 10/1) and multiply it by the reciprocal of 5/3, which is 3/5.

The multiplication looks like this: 10/1 × 3/5 = 30/5.

The result of 30/5 can be simplified to 6, which is the answer in simplest form. Therefore, 10 divided by 1 2/3 equals 6.

Answer:

c

Step-by-step explanation: first part of the equations.

[tex]-8x+3\geq 27\\-8x\geq 24\\x\leq -3[/tex]

so first you will subtract 3 from both side of the inequality. The divide by -8 on both side which will flip the inequality sign.

second equation

[tex]-13x+5\geq 57\\-13x\geq 52\\x\leq -4[/tex]

So you subtract 5 from both side then divide by -13 on both side and you need to flip the inequality sign because you divide by a negative.

now you will write the expression for it.

[tex]-4\leq x\leq -3[/tex]

we put x in the middle because it an and statement so that is why you would put x in the middle.

Answer:

Step-by-step explanation:

4x = 38

x= 38/ 4

x = 9 1/2

x=y+3 and 30x+80y=640 is the system of equations for given statement where x represents the number of commercials and y represent the number of movies on which Anna's songs were played.

Step-by-step explanation:

Given,

Earning for song played in commercial one time= $30

Earning for song played in movie one time = $80

Let,

x represent the number of  commercials Anna's song played.

y represent the number of movies Anna's song played.

According to given statement;

Anna's songs were played on 3 more commercials than movies

x=y+3    

her total earnings on the royalties from all commercials and movies was $640.

30x+80y=640

x=y+3 and 30x+80y=640 is the system of equations for given statement where x represents the number of commercials and y represent the number of movies on which Anna's songs were played.

Keywords: linear equation, substitution method

Learn more about linear equations at:

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Final answer:

To solve the question, two variables are defined: c for commercials and m for movies. The system of equations is $30c + $80m = $640 and c = m + 3, representing Anna's royalties from commercials and movies.

Explanation:

The student's question involves creating a system of equations to determine the number of commercials and movies on which Anna, a songwriter who collects royalties, had her songs played. We are given that Anna earns $30 from each commercial and $80 from each movie her songs are played in. It is also known that her songs were played in 3 more commercials than movies, and she earned a total of $640. To formulate the system of equations, we introduce two variables: let c represent the number of commercials and m represent the number of movies.

The first equation represents the total earnings based on the number of plays:
$30c + $80m = $640.

The second equation represents the relationship between the number of commercials and movies:
c = m + 3.

Combining these two equations gives us a system that can be solved to find the values of c and m.

By substituting the second equation into the first equation, we can create a system of equations:

30(M + 3) + 80M = 640

30M + 90 + 80M = 640

110M + 90 = 640

110M = 550

M = 5

Now that we have found the number of movies (M = 5), we can substitute this value back into the equation C = M + 3 to find the number of commercials:

C = 5 + 3

C = 8

Answer:

x = - 6z

Step-by-step explanation:

The equation of quantities in direct variation is

y = kx ← k is the constant of variation

Here k = - 6, thus

x = - 6z ← equation of variation

Answer:

to find how much taller Chiquita’s completed snowman is than Rhonda's completed Snowman  

We divide the Height of the Chiquita’s snowman by the height of Rhonda’s Snowman

 i.e. 7.456/8.532 = 0.87

Step-by-step explanation:

Let Vr1 be the volume of Rhonda’s first ball, and Vc1 be the volume of Chiquita’s first ball. Since the balls are spheres the formula for obtaining their Volume value is given as   V= (4/3) x ∏ r3  

Since from the question we were told that the first snowball for Rhonda and Chiquita’s Snowman are the same.

Let’s assume that the Vr1 =Vc1=10m²  

So to find the radius we make r the subject of formula so r =∛(3V/4∏)  where V is equal to 10 for the first spheres and ∏  is a constant with value 3.142 so  

r1 = ∛(3×10/4)×3.142   = 1.337m

For the Second Snow ball of Rhonda’s Snowman  

Given from the question that first Snow ball is 20% less than the Second Snow Ball

Let Vr2 Denote the volume of the second Rhonda’s Snowball  

Vr2 = 20% of Vr1 + Vr1

       = 20% of 10 + 10

       = (20/100) x 10 + 10

       = 12m²

So to find the radius of the second ball for Rhonda’s Snowman

Let r2 denote the radius of the second ball  

 r2 = ∛(3×12/4)×3.142   = 1.420m

For the Third Snow ball of Rhonda’s Snowman  

Given from the question that Second Snow ball is 20% less than the Third Snow Ball

Let Vr3 denote the volume of the third Rhonda’s Snowball

Vr3 = 20% of Vr2 +Vr2  

             = (20/100) x 12 +12

             = 14.4m²

  So to find radius of the Third ball for Rhonda’s Snowman

Let r3 denote the radius of the second ball  

  r3 =  ∛(3×14.4/4)×3.142   = 1.509m

For the Second Snow ball of Chiquita’s Snowman  

Given from the question that first Snow ball is 20% greater than the Second Snow Ball

Let Vc2 denote the volume of the second Chiquita’s Snowball

For   Vc2 = Vc1 - 20% of Vc1

               = 10 – (20/100) x 10

So to find the radius of the second ball for Chiquita  

Let c2 denote the radius of the second ball  

c2 =    ∛(3×8/4)×3.142   =1.240m

For the Third Snow ball of Chiquita’s Snowman  

Given from the question that Second Snow ball is 20% greater than the third Snow Ball

Let Vc3 denote the volume of the third Chiquita’s Snowball

For Vc3 = Vc2 - 20% of Vc2

             = 8 – (20/100) x 8

             = 6.4m²

So to find the radius of the second ball for Chiquita  

Let c3 denote the radius of the second ball  

  c3 =∛((3×6.4/4)×3.142)   = 1.151m

Therefore Height of Rhonda’s Snowman = Dr1 + Dr2 + Dr3  

          = 2×r1 +2×r2 +2×r3

          = (2×1.337) + (2×1.420) + (2×1.509)

         = 8.532m

Therefore the Height of Chiquita’s Snowman = Dc1 + Dc2 +Dc3

       = 2×c1 +2×c2 +2×c3

       = (2×1.337) + (2×1.240) + (2×1.151)

      = 7.456m

No to find how much taller Chiquita’s completed snowman is than Rhonda's completed Snowman  

We divide the Height of the Chiquita’s snowman by the height of Rhonda’s Snowman

 i.e. 7.456/8.532 = 0.87

Note: if we assume another value for Vr1 = Vc1 we will still get the same ratio.