the width of a box is one third of its length. the height of the box is one third of its width. if the length of the box is 27cm, what is the volume of the box?
a. 81cm³
b. 162cm³
c. 243cm³
d. 729cm³

Answer:

No solution.

Step-by-step explanation:

4x + 16y = -19

-2x – 8y = 10         Multiply this equation by 2:

-4x - 16y = 20      Add this equation to the first equation:

0  +    0   = 1

0 = 1

This is absurd so there are no solutions.

Answer:

2x + y - 6 = 0

OR 2x + y = 6

Step-by-step explanation:

First write the equation given in the problem:

y = -2x + 6        This is in slope-intercept form (y = mx + b).

Standard form is written Ax + By + C = 0. When C is a negative number, you might also see it as Ax + By = -C.

The main difference between the two forms in that slope-intercept form isolates the 'y' whereas standard form equates to 0. Don't confuse the 'b' in standard from with the 'B' in slope-intercept form.

To convert from slope-intercept form to standard form, move everything over to the side with 'y'. When you move something, you do its reverse operation to the whole equation. (The reverse of addition is subtraction, the reverse of multiplication is division.)

y = -2x + 6         Do the reverse operations for -2x and +6

y + 2x - 6 = -2x + 2x + 6 - 6      Add 2x and subtract 6 on both sides

y + 2x - 6 = 0            Right side cancels out to be '0'.

2x + y - 6 = 0       Rewrite with the 'x' in front of the 'y'

Here you can see the new equation and what each variable in Ax + By + C = 0 is.

A = 2

B = 1              When a number is not written with the variable, it is 1.

C = -6

Some teachers ask it to be rewritten as Ax + By = -C when 'C' is a negative number.

2x + y = 6

Solving [tex]2\frac{1}{4}(4x-1)=1\frac{3}{5}(1+4x)[/tex] we get [tex]x=\frac{77}{52}[/tex]

Step-by-step explanation:

We need to solve the problem: [tex]2\frac{1}{4}(4x-1)=1\frac{3}{5}(1+4x)[/tex]

Solving:

[tex]2\frac{1}{4}(4x-1)=1\frac{3}{5}(1+4x)\\\frac{9}{4}(4x-1)=\frac{8}{5}(1+4x)\\9x-\frac{9}{4}=\frac{8}{5}+\frac{32x}{5}[/tex]

Add 9/4 on both sides:

[tex]9x-\frac{9}{4}+\frac{9}{4}=\frac{8}{5}+\frac{32x}{5}+\frac{9}{4}[/tex]

[tex]9x=\frac{8}{5}+\frac{9}{4}+\frac{32x}{5}\\9x-\frac{32x}{5}=\frac{8}{5}+\frac{9}{4}\\\frac{9x*5-32x}{5}=\frac{8*4+9*5}{20}\\\frac{45x-32x}{5}=\frac{32+45}{20}\\\frac{13x}{5}=\frac{77}{20}\\x=\frac{77}{20}\times \frac{5}{13}\\x=\frac{77}{4*13}\\x=\frac{77}{52}[/tex]

So, Solving [tex]2\frac{1}{4}(4x-1)=1\frac{3}{5}(1+4x)[/tex] we get [tex]x=\frac{77}{52}[/tex]

Keywords: Solving Fractions

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Answer:

C

Step-by-step explanation:

f(x) = 3x + 5

Let y = 3x + 5

3x = y - 5

x = y/3 -5/3

The inverse of the function is

g(x) = x/3 - 5/3

Answer:

therefore for direct variation that will include the point (4, 16) is  y = 4x

Step-by-step explanation:

i) for direct variation we can say that y = k [tex]\times[/tex] x

ii) substituting the given values of x and y into the equation in i) we get

16 = k [tex]\times[/tex] 4

Therefore  k  = [tex]\frac{16}{4}[/tex] = 4

iii) therefore for direct variation that will include the point (4, 16) is  y = 4x

Answer:

It means that it divides into two equal parts

Answer:

Step-by-step explanation:

The total surface area is 125 square yards.

The base area is 37.5 square yards.

Hence, the area of the curved surface is 125 - 37.5 = 87.5 square yards.

According, to the formula, the area of the curved surface is [tex]\frac{5}{2} \times bs[/tex], where b is the base length and s = slant height.

Here, it is given that b = 5 yards.

Thus, [tex]\frac{5\times5\times s}{2} = 87.5\\s = 7[/tex].

Answer:

Sample Response: First, draw and label a net of the pyramid. The triangular faces have a base of 5 yards and a height of 12 yards. Find the area of each of the faces. The square base has an area of 25 yd2. Each of the triangular faces has an area of 30 yd2. Add the areas together to find the surface area: 25 + 30 + 30 + 30 + 30 = 145 yd2.

Step-by-step explanation:

(❁´◡`❁):-P(✿◡‿◡)

Answer:

Two

Step-by-step explanation:

If you have one and added one you have two

Answer:

4 Because that’s what you get when you add them together

Answer:x•0.70=y

Step-by-step explanation:

Answer:

0.30x

Step-by-step explanation:

Answer:

(x - 3)² = - (y - 14)

The maxima of the function is (3,14).

Step-by-step explanation:

The formula of a quadratic function is given by y = - x² + 6x + 5

We have to write this in the vertex form.

Now, y = - x² + 6x + 5

⇒ y = - (x² - 6x + 9) + 9 + 5

⇒ y - 14 = - (x - 3)²

⇒ (x - 3)² = - (y - 14)  

This is the equation of the parabola in vertex form.

This parabola has the vertex at (3,14) and the axis of the parabola is parallel to the negative y-axis.

Therefore, the maxima of the function is at (3,14). (Answer)

Answer:

2130 feet per hour

Step-by-step explanation:

462*60; because your trying to find out how many feet per hour so you have to multiply 462 inches by 60 minutes because 60 minutes= 1 hour.

462*60= 27720

27720/12; because you want to find out how many feet and not inches, so you have to divide 27720 by 12 because there is 12 inches in one foot.

27720/12= 2130

so your answer is 2130 feet per hour. Hope this helps :D

Answer: y - 4x + 11 = 0

Step-by-step explanation:

Formula

             y₂ - y₁

y -  y₁ =  ---------     ₓ  ( x - x₁ )

             x₂ - x₁

y - y₁ = 4( x - x₁ )

substitute for the coordinate of x and y

y - (-3) = 4( x - 2 )

y + 3 = 4x - 8

      y = 4x - 8 - 3

     y = 4x - 11

The equation now becomes

   y - 4x + 11 = 0

Answer:

the gradient of the line is 4

Answer:

[tex]\displaystyle \frac{5x}{8y^{4}}\sqrt{x}[/tex]

Step-by-step explanation:

Simplfy in Algebra

We have the following expression

[tex]\displaystyle E=\sqrt{\frac{25x^9y^3}{64x^6y^{11}}}[/tex]

Simplifying like factors in the denominator and numerator

[tex]\displaystyle E=\sqrt{\frac{25x^3}{64y^{8}}}[/tex]

All the factors are perfect squares except [tex]x^3[/tex], thus we rewrite:

[tex]\displaystyle E=\sqrt{\frac{25xx^2}{64y^{8}}}[/tex]

Taking the square root of all the perfect square factors:

[tex]\boxed{\displaystyle E=\frac{5x}{8y^{4}}\sqrt{x}}[/tex]

Answer:

D On edge.

Step-by-step explanation:

Its Very Simple i Took it just now :D

Answer:103/6

Step-by-step explanation:

All numerators above least common denominators 6

108-3-2/6

Calculate difference

103/6

Answer:

x=6

Step-by-step explanation:

The equation is 2/3x=4. So to get x alone we divide 2/3x by 2/3 and we divide 4/(2/3) because we have to do the same to both sides. So we end out with x=6. To check our work, we can do 2/3 * 6 and we get 4

Answer:

0

Step-by-step explanation:

In mathematics, the additive inverse of a number a is the number that, when added to a, yields zero. This number is also known as the opposite, sign change, and negation.

Hence, -96 + 96 = 0

Answer:

1. 6x + 2y = 25.92

4x + 3y = 33.93

2 the site charges $0.99 for a song and $9.99 for an album.

Step-by-step explanation:please see attachment for explanation

Answer:

25 boys.

Step-by-step explanation:

To solve this problem, first add the two parts of the ratio. 9 + 5 = 14. Then divide 70 by 14 to get 5. Since the total is 5 times the ratio total, multiply both sides of the ratio by 5. The result is 45 : 25. If you add them together, you get a total of 70. Therefore, there are 25 boys in the class.

Answer:

There are 25 boys in the class.

Step-by-step explanation:

9-5

9-5=18-10

9-5=27-15

9-5=36-20

9-5=45-25

45+25=70

Answer:

Around 8 pounds: A,NewBorn Baby    (I was 7.8 pounds)

Most likely used in inches: C,length of your nose      

Complete the statement. 8 c = C,4pt

7 3/5 ft = C

Little Explanation:

Around 8 pounds is a newborn because I was about 8 pounds, a large dog would weigh WAYYY more than that!

We might measure nose length with inches.  Centimeter might be used occasionally, but inches is more common.  (proccess of elimination)

2 Cups = 1 pint.   8 divided by 2 is 4.

1 yard is 3 feet, therefore you can only think it's 2 8/15

Contact for questions!!!

Final answer:

A newborn baby typically weighs 8 pounds. Inches are ideal for measuring the length of your nose. 8 cups convert to 4 pints and 7 3/5 feet is equivalent to 2 8/15 yards.

Explanation:

Understanding Weights and Measurements

Out of the given options, a newborn baby is likely to weigh about 8 pounds. This rules out the mother whale, large dog, and professional football player, as they all typically weigh significantly more than 8 pounds.

When it comes to measuring in inches, the length of your nose is the most appropriate of the given options. Width of a road, the length of a hallway, and the distance to the moon are all too large and would be better measured in feet, meters, or miles respectively.

For the conversion of cups to pints, we know that there are 2 cups in a pint. Therefore, 8 cups is equal to 4 pints because 8 divided by 2 equals 4.

Lastly, converting feet to yards for 7 3/5 feet to yards, we use the fact that 1 yard is equal to 3 feet. So, we divide 7 3/5 by 3, which gives us 2 8/15 yards.

Answer:

Let j =1

Step-by-step explanation:

9j+21+3j= 3(3j+j+7)

9j+21+3j=9j+3j+21

Since j=1,

9+21+3=9+3+21

Therefore both equations are equivalent

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Answer:

Step-by-step explanation:

[tex]-17(y-2)=-17y+64\qquad\text{use the distributive property}\\\\(-17)(y)+(-17)(-2)=-17y+64\\\\-17y+34=-17y+64\qquad\text{add}\ 17y\ \text{to both sides}\\\\-17y+17y+34=-17y+17y+64\\\\34=64\qquad\bold{FALSE}\\\\\bold{CONCLUSION:}\ \large\boxed{\text{no solution}}[/tex]

The equation -17(y-2)=-17y+64 have no solution.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

-17(y-2)=-17y+64

Now solving for y

-17y + 34= -17y + 64

0 = 30

As, there no variable left for which we have to find the value.

Hence, the equation have no solution.

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Answer:

28 degrees

Step-by-step explanation:

step 1

Find the measure of angle 1

[tex]m\angle 1+65^o=180^o[/tex] ----> by supplementary angles

[tex]m\angle 1=180^o-65^o=115^o[/tex]

step 2

Find the value of x

[tex](10x+5)^o=m\angle 1[/tex] ----> by corresponding angles

substitute

[tex](10x+5)^o=115^o[/tex]

[tex]10x=110\\x=11[/tex]

step 3

Find the measure of angle 2

Remember that the sum of the interior angles in any triangle must be equal to 180 degrees

[tex]m\angle 1+m\angle 2+(4x-7)^o=180^o[/tex]

substitute

[tex]115^o+m\angle 2+(4(11)-7)^o=180^o[/tex]

[tex]m\angle 2=180^o-152^o=28^o[/tex]

Answer:

see explanation

Step-by-step explanation:

Using the sine ratio in right Δ ACD and the exact value

sin30° = [tex]\frac{1}{2}[/tex]

sin30° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{AD}{AC}[/tex] = [tex]\frac{y}{150}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )

2y = 150 ( divide both sides by 2 )

y = 75

----------------------------------------------------------------------

Using the tangent ration in right Δ ABD and the exact value

tan60° = [tex]\sqrt{3}[/tex]

tan60° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{AD}{BD}[/tex] = [tex]\frac{y}{z}[/tex] = [tex]\frac{75}{z}[/tex] = [tex]\sqrt{3}[/tex] ( cross- multiply )

[tex]\sqrt{3}[/tex] z = 75 ( divide both sides by [tex]\sqrt{3}[/tex] )

z = [tex]\frac{75}{\sqrt{3} }[/tex] × [tex]\frac{\sqrt{3} }{\sqrt{3} }[/tex] = [tex]\frac{75\sqrt{3} }{3}[/tex] = 25[tex]\sqrt{3}[/tex]

Answer:

5

Step-by-step explanation:

a^2 + b^2 = c^2

4^2 + 3^2 = 25

Then you square root 25 and that is 5

To solve the system of equations using the elimination method, we want to eliminate one variable by multiplying the equations by different numbers so that we can add or subtract them to cancel out one variable. In this case, we can multiply the first equation by 5 and the second equation by 2 to cancel out the y variable.

To solve the system of equations using the elimination method, we want to eliminate one variable by multiplying the equations by different numbers so that we can add or subtract them to cancel out one variable. In this case, we can multiply the first equation by 5 and the second equation by 2 to cancel out the y variable. After multiplying, we get:

10x + 15y = 60
10x - 2y = 26

Now we can subtract the equations to eliminate the y variable:

(10x + 15y) - (10x - 2y) = 60 - 26
17y = 34
y = 2

Substituting the value of y back into one of the original equations, we can solve for x:

2x + 3(2) = 12
2x + 6 = 12
2x = 6 - 6
2x = 6
x = 3

Therefore, the solution to the system of equations is x = 3 and y = 2.

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Final answer:

The elimination method in solving linear equations involves manipulating the equations to remove one variable, making it possible to solve for the other. It's a widely-used technique and usually applies to equations that are amenable to multiplication or subtraction for simplifying purposes.

Explanation:

The student seems to be asking about solving systems of linear equations using the elimination method. In this method, you manipulate the equations to eliminate one variable, allowing you to solve for the other. Elimination is particularly useful when equations are in a form that allows for straightforward manipulation, like when coefficients of variables are opposites or can be made so through multiplication.

For example, if we have the equations 7x - 2y = 24 and 3x + 9y = 30, we can multiply the first equation by 3 and the second by 7 and then subtract one from the other to eliminate the variable y:
21x - 6y = 72
21x + 63y = 210
Subtracting these two equations gives us:
-69y = -138
Which simplifies to y = 2. Once y is found, substitute it back into one of the original equations to solve for x.

[tex]\[21x - 6(2) = 72\]\[21x - 12 = 72\]Now, let's solve for \( x \):\[21x = 72 + 12 = 84\]\[x = \frac{84}{21} = 4\][/tex]

So, the solution to the system of equations is [tex]\( x = 4 \) and \( y = 2 \).[/tex]

Answer:

The first picture corresponds the correct dilation by a scale of factor of 1/3 as the image rectangle is reduced and has the coordinates (-2, 0), (0, 2), (2, 0), and  (0, -2) after a rectangle is dilated by a scale of factor of 1/3.

Step-by-step explanation:

A dilation is said to be a transformation which generates an image that is the same shape as the original object, but has a different size.

If the scale factor is greater than 1, then the image will be enlarged. In other words,

If the scale factor is greater than 0 but less than 1, then the image will be reduced. In other words,

Considering the quadrilateral with the vertices (-6, 0), (0, 6), (6, 0) and (0, -6).

According to dilation rule, when a figure is dilated by a scale of factor of 1/3, the the coordinates of that point are multiplied by 1/3. So,

(x, y) → (1/3x, 1/3y)

So, lets apply this on the quadrilateral with the vertices  (-6, 0), (0, 6), (6, 0) and (0, -6).

For (-6, 0)

(x, y) → (1/3x, 1/3y) = (-6, 0) → (-2, 0)

For (0, 6)

(x, y) → (1/3x, 1/3y) = (0, 6) → (0, 2)

For (6, 0)

(x, y) → (1/3x, 1/3y) = (6, 0) → (2, 0)

For (0, -6)

(x, y) → (1/3x, 1/3y) = (0, -6) → (0, -2)

So, the image rectangle will have the coordinates (-2, 0), (0, 2), (2, 0), and  (0, -2) after a rectangle is dilated by a scale of factor of 1/3.

Therefore, the first picture corresponds the correct dilation by a scale of factor of 1/3 as the image rectangle is reduced and has the coordinates (-2, 0), (0, 2), (2, 0), and  (0, -2) after a rectangle is dilated by a scale of factor of 1/3.

So, correct picture is also attached below.

Keywords: dilation, transformation, quadrilateral

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Answer:

The value of x, y and z are:

[tex]x=91^{0}, y = 89^{0}, z=31^{0}[/tex]

Step-by-step explanation:

Label the image as given below.

Consider the triangle ABC.

Use the property: Sum of angles of a triangle is [tex]180^{0}[/tex], to determine the value of x as follows:

[tex]51^{0} +38^{0}+x =180^{0}\\x=91^{0}[/tex]

Use the property: Sum of angles on a straight line is [tex]180^{0}[/tex], to determine the value of y as follows:

[tex]x+y=180^{0}\\91^{0} + y = 180^{0}\\y=89^{0}[/tex]

Consider the triangle ADC.

Use the property: Sum of angles of a triangle is [tex]180^{0}[/tex], to determine the value of z as follows:

[tex]60^{0} + 89^{0} + z = 180^{0}\\z = 31^{0}[/tex]

Answer:

∠x = 91°

∠y = 89°

∠z = 31°

Step-by-step explanation:

x = 180 - (51 + 38) = 91

∠x = 91°

then to find the value of y = 180 - x

y = 180 - 91 = 89

∠y = 89°

z = 180 - (60 + 89) = 31

∠z = 31°

[tex](6^{2})^{4}[/tex] is the same as [tex]6^{8}[/tex]

[tex]6^{8}[/tex] = 1,679,616‬