An Atlas moth has a wingspan of 11 inches. What is the wingspan of 26 Atlas moths?

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:

Step-by-step explanation:

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:

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

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:

Lucey reads 10 pages fewer than Carey.

3c - 7

3 times c = 3c

7 less than is subtraction

Answer:

3c - 7

Step-by-step explanation:

less than = flip the equation

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

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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:

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.

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:

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:

[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]

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:

I am not agree with him. Because -2 is the leading coefficient of this  polynomial.

Step-by-step explanation:

Pat multiplied the polynomials for a math assignment.

Then he found the product is [tex]-4x+8x^2-2x^3+5[/tex]

Now Pat wants to find the leading coefficient to this polynomial.

Pat's answer was -4.

But I am not agree with him.

Because for a given polynomial we can calculate the leading coefficient when comparing with degrees of the polynomial.

Leading coefficient means that the coefficient whose degree is the highest.

When compared with the given polynomial we have [tex]x^3[/tex] is the highest degree, so that -2 is the leading coefficient to this polynomial.

Answer:

9

Step-by-step explanation:

1+8=9

Answer:

9

Step-by-step explanation:

1+8=9

Step-by-step explanation:

There are certain methods for solving a system of equations. Some of which are:

Substitution Method

Substitution method to solve a system of equations is suitable if a variable of a any equation seems isolated or could comfortably be isolated without any ration/fraction resulting.

For example, for the following system of equations

x - 2y = 11....[A]

x = 5 - y....[B]

substituting the value of x = 5 - y from equation [B] into equation [A], so that

(5 - y) - 2y = 11

5 - y - 2y = 11

3y = -6

y = -2

Elimination Method

Elimination method to solve a system of equations is suitable if both equation are in standard form, and just adding or subtracting the equations to determine an equation in one variable.

For example, for the following system of equations

2x + 7y = -5....[C]

5x - 7y = 12....[D]

Adding Equation [C] and Equation [D].

7x + 0 = 7

x = 1

Graphing Method

Sometimes graphing method may be used to solve the system of the equation and visualize the solution.

For example,

y = -2....[E]

y = 3x + 1....[F]

The solution for this system of equation is the point of intersection of both the lines, which is shown in attached figure. The point of intersection is (-1, -2).

Hence, the solution of this system of equations is (-1, -2), as shown in attached figure.

Keywords: system of equations, elimination method, substitution method, graphing method

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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:

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:

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:

122

Step-by-step explanation:

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

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: 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.

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:

They have 18 vegetable plants.

Step-by-step explanation:

Given:

Emily's family loves to work together  in the garden.

They have a. preference for flowers as 80% of  their plants are flowers and the rest  are vegetables.

They have 90 plants  in the garden.

Now, to find the number of vegetable plants.

Total plants in the garden = 90.

80% of the plants are flowers.

So, number of plants which are flowers = 80% of 90.

[tex]=\frac{80}{100} \times 90[/tex]

[tex]=\frac{7200}{100}[/tex]

[tex]=72\ plants.[/tex]

The number of flower plants = 72.

Total plants = 90 (given)

So, to get the number of vegetable plants we subtract:

[tex]90-72=18\ plants.[/tex]

Thus, vegetable plants = 18.

Therefore, they have 18 vegetable plants.

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:

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:

Monthly sales = $15000

Step-by-step explanation:

Let x be the monthly sale.

Given:

The monthly salary of a show room attendant is the sum of a fixed  salary of $600 plus 8% of all monthly sales.

8% of monthly sale = [tex]\frac{8}{100}\times mothly\ sale[/tex]

8% of monthly sale = [tex]\frac{8}{100}\times x[/tex]

So, the monthly salary of attendant is.

[tex]Monthly\ salary = 600+8\ percent \ of\ monthly\ sales[/tex]

[tex]Monthly\ salary = 600+\frac{8}{100}\times x[/tex]

Monthly salary is given.

[tex]1800 = 600+\frac{8}{100}\times x[/tex]

[tex]1800 - 600 = \frac{8}{100}\times x[/tex]

[tex]1200 = \frac{8}{100}\times x[/tex]

[tex]x=\frac{1200\times 100}{8}[/tex]

[tex]x=\frac{120000}{8}[/tex]

[tex]x=15000[/tex]

Therefore, the monthly sale is $15000

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:

Median

Step-by-step explanation:

Median, in geometry, is a line segment that is drawn from the vertex or the corner of the shape that extends to the middle or the midpoint of the side opposite of that corner.

When you say opposite the corner, that means it is the one across it. Look at the attached picture for emphasis.

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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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