How do you do number 1?
Whenever I tried to answer it, I always get fraction. help me.​

Answer:

B if m=2

(Just to make sure that isn't m=-2, right?)

Step-by-step explanation:

7.8 + 2(0.75m + 0.4) = -6.4m + 4(0.5m - 0.8)  

Let's plug in 2 for m.

7.8+2(0.75*2+0.4)  = -6.4*2+4(0.5*2-0.8)

If 2 is a solution, then both sides will be the same.

If 2 is not a solution, then both sides will be different.

If both sides are the same, it is a true equation.

If both sides are different, it is a false equation.

Let's simplify 7.8+2(0.75*2+0.4)

According to PEMDAS, we must perform the operations in the parenthesis.

We have multiplication and addition in ( ).  We will do the multiplication because the MD comes before the AS.

0.75*2=1.5

So now our expression 7.8+2(0.75*2+0.4) becomes 7.8+2(1.5+0.4)

Now to do the addition in the ( ).

1.5+0.4=1.9.

So now our expression 7.8+2(0.75*2+0.4) becomes 7.8+2(1.9).

We have multiplication to be perform now because again MD becomes before AS.

7.8+2(0.75*2+0.4) becomes 7.8+3.8

Last step perform the addition (the only operation left here on the left hand side)

7.8+2(0.75*2+0.4) becomes 11.6 .

Let's focus on the right now.

-6.4*2+4(0.5*2-0.8)

-6.4*2+4(1       -0.8)  I did the multiplication in the ( ) first.

-6.4*2+4(.2)              I did the subtracting in the ( ).

-12.8+.8                    I did the multiplication by -6.4*2 and 4*.2 simultaneously

-12

I'm going to put all of this together because I think it might be easier to read:

7.8 + 2(0.75m + 0.4) = -6.4m + 4(0.5m - 0.8)  

Plug in 2 for m

7.8 + 2(0.75*2  + 0.4)=-6.4*2 + 4(0.5*2 - 0.8)

7.8 + 2(1.5        + 0.4)= -6.4*2 + 4(1       -0.8)

7.8 + 2(1.9)                = -6.4*2 + 4(.2)

7.8 +  3.8                 =   -12.8  +.8

11.6                          =-12

This is false because 11.6 is not the same as -12.

m=2 leads to a false equation

B.

The value of m for the expression 7.8 + 2(0.75m + 0.4) = -6.4m + 4(0.5m - 0.8) is -2. Hence, Mia's statement is false.

Simplification in mathematical terms is a process to convert a long mathematical expression in simple and easy form.

The given equation is,

7.8 + 2(0.75m + 0.4) = -6.4m + 4(0.5m - 0.8)

Also, Mia solved the equation and determine that the value of m is 2.

To find the value of m, simplify the expression,

7.8 + 1.5m + 0.8 = -6.4m + 2m - 3.2

1.5m + 8.6 = -4.4m - 3.2

1.5m + 4.4m = -3.2 - 8.6

5.9m = -11.8

m = -2

Mia is incorrect because the value of m is -2,  

Therefore the statement is false.

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Answer:

A = 44.2cm²

Step-by-step explanation:

The surface area of a square pyramid that has the sides of the base of 4 cm and a height of 10 cm is 44.2cm².

Formula: A=AB(4h2+AB)+AB

A=AB(4h2+AB)+AB=4·(4·102+4)+4≈44.1995cm²

Answer:

C. 3 times

Step-by-step explanation:

If cube a has an edge length of 2 and cube b has an edge length of 6,the volume of cube b than cube a is 3 times greater.

For this case we have that by definition, the volume of a cube is given by:

[tex]V = l ^ 3[/tex]

Where:

l: It's the side of the cube

Cube A:

[tex]l = 2\\V = 2 ^ 3 = 8 \ units ^ 3[/tex]

Cube B:

[tex]l = 6\\V = 6 ^ 3 = 216 \ units ^ 3[/tex]

We divide:

[tex]\frac {216} {8} = 27[/tex]

Thus, the volume of cube B is 27 times larger than that of cube A.

Answer:

Option A

Answer:

Step-by-step explanation:

[tex]\text{Because}\\\\125x^3=5^3x^3=(5x)^3\qquad\bold{it's\ a\ cube}\\\\169=13^2\qquad\bold{it's \ a \ square}\\\\125x^3+169=(5x)^3+13^2[/tex]

[tex]13-\text{it's a prime number}[/tex]

Answer:

y=x-4

Step-by-step explanation:

What you are looking for is also known as the slant asymptote.  The slant asymptote occurs when the degree of the numerator is one degree more than the denominator which is what you have.

So to find the slant asymptote we can use polynomial division.

We have a choice to use synthetic division here because the denominator is linear.

-1 goes on the outside because we are dividing by (x+1).

-1  |    1     -3      -4

   |           -1        4

   |----------------------

        1      -4        0

The asymptote is the quotient part which is y=x-4.

So answer is y=x-4.

Option D is correct, y=x-4​ is the equation of the oblique asymptote h(x)= x²-3x-4/x+1

Two or more expressions with an Equal sign is called as Equation.

To find the equation of the oblique asymptote, we need to perform polynomial division of the numerator (x² - 3x - 4) by the denominator (x + 1):

       x - 4

    ------------

x + 1 | x² - 3x - 4

        x² + x

      -------

          -4x - 4

          -4x - 4

             -------

               0

The quotient is x - 4, which represents the equation of the slant asymptote.

Hence, y=x-4​ is the equation of the oblique asymptote h(x)= x²-3x-4/x+1

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The correct solution is,

⇒ 2 / (1 - tan²x)

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ tan (2x) / tan x

Now, We know that;

tan 2x = (2 tanx / 1 - tan²x)

Hence, We can simplify as;

⇒ tan (2x) / tan x

⇒ (2tan (x) /1 - tan²x) / tan x

⇒ 2 / (1 - tan²x)

Thus, The correct solution is,

⇒ 2 / (1 - tan²x)

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The expression tan(2x)/tan(x) simplifies using the double-angle identity for tangent to 2/(1 - tan^2(x)), which corresponds to Option A.

To simplify the trigonometric expression tan(2x)/tan(x) using double-angle identities, we can use the double-angle identity for tangent:

tan(2x) = 2tan(x)/(1 - tan2(x)).

Now, if we divide tan(2x) by tan(x), we get:

tan(2x)/tan(x) = (2tan(x)/(1 - tan2(x)/tan(x).

With tan(x) in the numerator and denominator, it cancels out, leaving:

2/(1 - tan2(x)).

Therefore, the correct answer is Option A: 2/(1 - tan2(x)).

Answer:

Hi there!

The answer to this question is: D

Step-by-step explanation:

The pattern is; up (red), down (blue), up (red)

so therefore the next pattern is down (blue) which is D

To find the next figure in the geometric pattern, analyze the given information and identify the pattern in the dot placements. Based on the description, each figure is obtained by adding dots in specific positions. The next figure can be determined by continuing this pattern.

The next figure in the geometric pattern can be determined by analyzing the given information. Based on the description, we can infer that each figure is obtained by adding dots in a specific pattern. The third dot is located one and two-thirds perpendicular hash marks to the right of the center top perpendicular hash mark, while the fourth dot is in the same position as the Car X figure (one perpendicular hash mark above the center right perpendicular hash mark). To find the next figure, we need to continue this pattern by adding dots in the specified positions.

[tex]x^2-x[/tex] is nothing interesting you can just factor out x and result with [tex]x(x-1)[/tex].

However the difference of squares is defined as,

[tex]a^2-b^2=(a+b)(a-b)[/tex]

Hope this helps.

r3t40

Answer:

(1/7)(-9n + 7)

Step-by-step explanation:

1/7-3(3/7n-2/7)  can be factored:  factor out 1/7.

We get:  (1/7)[1 - 3(3n - 2)], or

              (1/7)[1 - 9n + 6], or

              (1/7)(-9n + 7)

Answer:

Option B AC≅XZ

Step-by-step explanation:

we know that

ASA (angle, side, angle) means that we have two congruent triangles where we know two angles and the included side are equal

In this problem we have

∠X≅∠A

∠Z≅∠C

In the triangle ABC the included side between the angles ∠A and ∠C is the side AC

and

In the triangle XYZ the included side between the angles ∠X and ∠Z is the side XZ

therefore

AC≅XZ

Answer:

This is a right triangle

Step-by-step explanation:

Pythagoras theorem is used to determine if a triangle is right, acute or obtuse

If the sum of squares of two shorter lengths is greater than the square of third side then the triangle is an acute triangle.

If the sum of squares of two shorter lengths is less than the square of third side then the triangle is an obtuse triangle.

If the sum of squares of two shorter lengths is equal the square of third side then the triangle is a right triangle.

so,

[tex](17)^2 = (15)^2+(8)^2\\289 = 225+64\\289=289[/tex]

Therefore, the given triangle is a right triangle ..

Answer:

56.4 miles

Step-by-step explanation:

4228/75 = 56.37333333

Answer:

1st and 2nd quadrants

Step-by-step explanation:

You have sine is positive since it is 4/5.

Sine is the y-coordinate.

On the coordinate plane y is positive in the 1st and 2nd quadrants.

The values of θ that could terminate when sin θ = 4/5 are in the first and second quadrants. In the first quadrant, both the sine and cosine values are positive, while in the second quadrant, only the sine value is positive.

To find the quadrants where θ could terminate when sin θ = 4/5, we need to examine the values of sin θ in each quadrant. The sine function is positive in the first and second quadrants so that θ could terminate in either of these quadrants. In the first quadrant, the sine and cosine values are positive, while in the second quadrant, only the sine value is positive.

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Answer:

First we need to set a proportion

Currently the negative measures 15 inches by 2 inches. And the longer dimension of the printed version is 4 inches. Therefore:

[tex]\frac{2}{y} = \frac{15}{4}[/tex]

[tex]15y = 8[/tex]

[tex]y = 0.5333[/tex]

Therefore, the dimension of the shorter dimension is 0.5333.

None of the options matches this response, so maybe you forgot to add some information?

[tex]\bf \qquad \qquad \textit{sum of a finite geometric sequence} \\\\ \displaystyle S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad \begin{cases} n=\textit{last term's}\\ \qquad position\\ a_1=\textit{first term}\\ r=\textit{common ratio}\\ \cline{1-1} n=4\\ a_1=2\\ r=\frac{1}{3} \end{cases}[/tex]

[tex]\bf S_4=2\left( \cfrac{1-\left( \frac{1}{3} \right)^4}{1-\frac{1}{3}} \right)\implies S_4 = 2\left( \cfrac{1-\frac{1}{81}}{\frac{2}{3}} \right)\implies S_4 = 2\left( \cfrac{\frac{80}{81}}{~~\frac{2}{3}~~} \right) \\\\\\ S_4=2\left( \cfrac{40}{27} \right)\implies S_4=\cfrac{80}{27}\implies S_4=2\frac{26}{27}[/tex]

Answer:

80/27.

Step-by-step explanation:

Sum of n terms = a1 * (1 - r^n) / (1 - r)

Sum of 4 terms = 2 * (1 -(1/3)^4) / ( 1 - 1/3)

= 2 * 80/81 / 2/3

= 160 / 81  *  3/2

= 480/ 162

= 80/27  (answer

The value of the product (3 - 21) * (3 + 21) is -432, obtained by applying the distributive property.

To find the value of the product (3 - 21) * (3 + 21), we can use the distributive property or the difference of squares identity. Here's how it works:

(3 - 21) * (3 + 21) = (3 - 21) * [(3) + (21)]  (Apply the distributive property)

Now, let's calculate each part:

1. (3 - 21) = -18

2. (3 + 21) = 24

Now, we multiply these results together:

-18 * 24 = -432

So, the value of the product (3 - 21) * (3 + 21) is -432.

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Final answer:

The product of (3-21) and (3 + 21) is -324.

Explanation:

The value of the product (3-21) (3 + 21) is -324.

To find the product, first calculate the values within the parentheses:

3 - 21 = -18

3 + 21 = 24

Multiply these two values: -18 * 24 = -324.

Answer:

[tex]\large\boxed{x=-1\pm\sqrt5}[/tex]

Step-by-step explanation:

[tex]x^2+2x-4=0\qquad\text{add 4 to both sides}\\\\x^2+2x=4\\\\x^2+2(x)(1)=4\qquad\text{add}\ 1^2=1\ \text{to both sides}\\\\\underbrace{x^2+2(x)(1)+1^2}=4+1^2\qquad\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\(x+1)^2=5\to x+1=\pm\sqrt5\qquad\text{subtract 1 from both sides}\\\\x=-1\pm\sqrt5[/tex]

The two values of x for the given equation are ( -1  + √5 ) and ( - 1 - √5 ).

The polynomial having a degree of two or the maximum power of the variable in a polynomial will be 2 is defined as the quadratic equation and it will cut two intercepts on the graph at the x-axis.

The solution of the given equation is:-

=  x²  + 2x - 4

x²  +  2x  =  4

x²  +  2x ( 1 )  +  1²  =  4  +  1²

(  x  +  1  )²  =  5

x  +  1   =  ± √5

x  =  -1  ± √5

Therefore the two values of x for the given equation are ( -1  + √5 ) and ( - 1 - √5 ).

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Answer:

Option B, C and D are correct choices.

Step-by-step explanation:

We have been given an equation [tex]3.5+1.2(6.3-7x)=9.38[/tex]. We are asked to choose the steps that are involved in solving the equation.

Let us solve the equation.

Using distributive property [tex]a(b+c)=ab+ac[/tex], we will distribute 1.2 to 6.3 and [tex]-7x[/tex].

[tex]3.5+1.2*6.3-1.2*7x=9.38[/tex]

[tex]3.5+7.56-8.4x=9.38[/tex]

Therefore, option B is the correct choice.

Now, we will combine like terms.

[tex]11.06-8.4x=9.38[/tex]

Therefore, option C is the correct choice.

Now, we will subtract 11.06 from both sides of our equation.

[tex]11.06-11.06-8.4x=9.38-11.06[/tex]

[tex]-8.4x=-1.68[/tex]

Therefore, option D is the correct choice.

Now, to solve for x, we need to divide both sides of our equation by [tex]-8.4[/tex]

[tex]\frac{-8.4x}{-8.4}=\frac{-1.68}{-8.4}[/tex]

[tex]x=0.2[/tex]

Answer:

Distribute 1.2 to 6.3 and –7x;

Combine 3.5 and 7.56.

Subtract 11.06 from both sides.

Step-by-step explanation:

To answer this expression. Let's follow P.E.M.D.A. order, the acronym for  PArenthesis, Exponents, Multiplication, Division and Addends.  So distributing the factor 1.2 to the parenthesis content:

[tex]3.5+1.2(6.3-7x)=9.38 \\3.5+7.56-8.4x=9.38[/tex]

Then adding the 3.5 to 7.56 to simplify it:

[tex]3.5+7.56-8.4x=9.38\\\11.06-8.4x=9.38[/tex]

The next step in order to isolate is to subtract 11.06 from both sides

[tex]11.06-8.4x-11.06=9.38-11.06[/tex]

Then it goes on

[tex]-8.4x=-1.68\:\:*(-1)\\8.4x=1.68\Rightarrow x=\frac{1.68}{8.4}\Rightarrow x=\frac{1}{5}\\S=\{ {\frac{1}{5}\}[/tex]

Answer:

2.95

Step-by-step explanation:

The radius of a circle is half of the diameter.

r = (1/2)d

r = (1/2)(5.9)

r = 2.95

Answer:

radius = 2.95

Step-by-step explanation:

The radius is the distance from the centre O to the circumference and is one half the diameter,

radius = 0.5 × 5.9 = 2.95

Answer:

First case The coefficient of the squared term is 4

Second case The coefficient of the squared term is 1/16

Step-by-step explanation:

I will analyze two cases

First case (vertical parabola open upward)

we know that

The equation of a vertical parabola in vertex form is equal to

[tex]y=a(x-h)^{2}+k[/tex]

where

a is the coefficient of the squared term

(h,k) is the vertex

we have

(h,k)=(-5,-2)

substitute

[tex]y=a(x+5)^{2}-2[/tex]

Find the value of a

Remember that

when the x-value is -4, the y-value is 2.

substitute

For x=-4, y=2

[tex]2=a(-4+5)^{2}-2[/tex]

[tex]2=a(1)-2[/tex]

[tex]a=2+2=4[/tex]

the equation is equal to

[tex]y=4(x+5)^{2}-2[/tex]

therefore

The coefficient of the squared term is 4

Second case (horizontal parabola open to the right)

we know that

The equation of a horizontal parabola in vertex form is equal to

[tex]x=a(y-k)^{2}+h[/tex]

where

a is the coefficient of the squared term

(h,k) is the vertex

we have

(h,k)=(-5,-2)

substitute

[tex]x=a(y+2)^{2}-5[/tex]

Find the value of a

Remember that

when the x-value is -4, the y-value is 2.

substitute

For x=-4, y=2

[tex]-4=a(2+2)^{2}-5[/tex]

[tex]-4=a(4)^{2}-5[/tex]

[tex]-4+5=a(16)[/tex]

[tex]a=1/16[/tex]

the equation is equal to

[tex]x=(1/16)(y+2)^{2}-5[/tex]

therefore

The coefficient of the squared term is 1/16

to better understand the problem see the attached figure

The boy bought 9 pencils and 9 pens, with a total cost of 90 soles. This calculation is based on the cost of 3 soles per pencil and 7 soles per pen, resulting in a total expenditure that aligns with the given information.

1: Define the costs.

We know the cost of each pencil and pen:

Pencils: 3 soles each

Pens: 7 soles each

2: Let x be the number of items.

Since the boy buys the same number of pencils and pens, let x represent the number of each item he buys.

3: Set up the total cost equation.

The total cost he spends is 90 soles. We can express this as an equation:

Total cost = Pencils cost + Pens cost

90 soles = (x pencils * 3 soles/pencil) + (x pens * 7 soles/pen)

4: Simplify and solve for x.

Combine like terms:

90 soles = 3x soles + 7x soles

90 soles = 10x soles

x = 90 soles / 10 soles/item

x = 9 items

5: Find the number of pencils and pens.

Since x represents both the number of pencils and pens, he bought 9 pencils and 9 pens.

Therefore, the boy bought 9 pencils and 9 pens.

Complete question:

A boy buys the same number of pencils as pencils for 90 soles. Each pencil costs 3 soles and each pencil 7 soles. How many pencils and pens has he bought?

Answer:

See below in bold,.

Step-by-step explanation:

There are 30-17 = 13 boys in the class.

a.  Prob(First is a boy ) = 13/30 and Prob( second is a boy = 12/29).

As these 2 events are independent:

Prob( 2 boys being picked) = 13/30 * 12/29 =  26/145 or 0.179 to the nearest thousandth.

b. By a similar method to a:

Prob ( 2 girls being picked) =  17/30 * 16/29 = 136/435 = 0.313 to the nearest thousandth.

c.  Prob (First student is a boy and second is a girl) =  13/30 * 17/29 = 221/870.

Prob ( first student is a girl and second is a boy)  = 17/30 * 13/29 = 221/870

These 2 events are not independent so they are added:

Prob( one of the students is a boy)  = 2 (221/870 =  221/435 = 0.508 to the nearest thousandth.

Answer:

[tex]\frac{x-1}{x+3}[/tex]

Step-by-step explanation:

Let's factor the numerator and denominator first.

x^2+5x-6 is a quadratic in the form of x^2+bx+c.

If you have a quadratic in the form of x^2+bx+c, all you have to do to factor is think of two numbers that multiply to be c and add to be b.

In this case multiplies to be -6 and adds to be 5.

Those numbers are 6 and -1 since -1(6)=-6 and -1+6=5.

So the factored form of x^2+5x-6 is (x-1)(x+6).

x^2+9x+18 is a quadratic in the form of x^2+bx+c as well.

So we need to find two numbers that multiply to be 18 and add to be 9.

These numbers are 6 and 3 since 6(3)=18 and 6+3=9.

So the factored form of x^2+9x+18 is (x+3)(x+6).

So we have that:

[tex]\frac{x^2+5x+-6}{x^2+9x+18}=\frac{(x-1)(x+6)}{(x+3)(x+6)}[/tex]

We can simplify this as long as x is not -6 as

[tex]\frac{x-1}{x+3}[/tex]

I obtained the last line there by canceling out the common factor on top and bottom.

Answer:

We can simplify this as long as x is not -6 as

\frac{x-1}{x+3}

Step-by-step explanation:

Answer:

[tex]\large\boxed{x=-2\ or\ x=-\dfrac{1}{3}}[/tex]

Step-by-step explanation:

The quadratic formula of a quadratic equation

[tex]ax^2+bx+c=0\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

We have the equation:

[tex]3p^2+7p+2=0\to a=3,\ b=7,\ c=2[/tex]

Substitute:

[tex]b^2-4ac=7^2-4(3)(2)=49-24=25\\\\\sqrt{b^2-4ac}=\sqrt{25}=5\\\\x_1=\dfrac{-7-5}{2(3)}=\dfrac{-12}{6}=-2\\\\x_2=\dfrac{-7+5}{2(3)}=\dfrac{-2}{6}=-\dfrac{1}{3}[/tex]

Answer:

-1/3,-2

Step-by-step explanation:

The quadratic formula is [-b±√(b^2-4ac)]/2a.  In this equations 3p^2 is a, 7p is b, and 2 is c.

Then just plug in the numbers.

[-7±√((-7^2)-4(3)(2)]/2(3)

[-7±√(25)]/6

(-7+5)/6  and  (-7-5)/6

-1/3 and -2 are the answers, if you plug these numbers into the original equation, you find that they equal 0 which means that they work.

Answer:

Ok

Step-by-step explanation: what is this???????

Answer:

The slope of XZ is 3/4 , the slope of XY is -4/3 , and XZ = XY = 5 ⇒ 3rd answer

Step-by-step explanation:

* Lets look to the attached figure to solve the problem

- To prove that the Δ XYZ is an isosceles right triangle, you must

  find two sides the product of their slopes is -1 and they are equal

  in lengths

- From the figure the vertices of the triangle are;

  X = (1 , 3) , Y = (4 , -1) , Z = (5 , 6)

- The slope of the line whose endpoints are (x1 , y1) and (x2 , y2)

  is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

∵ The slope of [tex]XY=\frac{-1-3}{4-1}=\frac{-4}{3}[/tex]

∵ The slope of [tex]XZ=\frac{6-3}{5-1}=\frac{3}{4}[/tex]

∴ The slope of XY = -4/3 , the slope of XZ = 3/4

∵ -4/3 × 3/4 = -1

∴ XY ⊥ XZ

∴ ∠ X is a right angle

∴ Δ XYZ is a right triangle

- The distance between the two points (x1 , y1) and (x2 , y2) is

  [tex]d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]

∵ [tex]XY=\sqrt{(4-1)^{2}+(-1-3)^{2}}=\sqrt{9+16}=\sqrt{25}=5[/tex]

∵ [tex]XZ=\sqrt{(5-1)^{2}+(6-3)^{2}}=\sqrt{16+9}=\sqrt{25}=5[/tex]

∴ XY = XZ = 5

∴ Δ XYZ is an isosceles right triangle

* The statement which prove that is:

 The slope of XZ is 3/4 , the slope of XY is -4/3 , and XZ = XY = 5  

Answer:

its C

Step-by-step explanation:

yw :)

Answer:

Step-by-step explanation:

It's a right triangle.

Use the Pythagorean theorem:

[tex]leg^2+leg^2=hypoyenuse^2[/tex]

We have:

[tex]leg=13.5\ cm,\ leg=x\ cm,\ hypotenuse=(x+8.45)\ cm[/tex]

Substitute:

[tex]13.5^2+x^2=(x+8.45)^2\qquad\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\182.25+x^2=x^2+2(x)(8.45)+8.45^2\qquad\text{subtract}\ x^2\ \text{from both sides}\\\\182.25=16.9x+71.4025\qquad\text{subtract 71.4025 from both sides}\\\\110.8475=16.9x\qquad\text{divide both sides by 16.9}\\\\\dfrac{110.8475}{16.9}=x\to x\approx6.6\ cm[/tex]

Answer:

62.8

Step-by-step explanation:

The volume of the cylinder is = base * height

base=Pi*radius*radius, where

base=3.1416*2*2 , height=5

Volume=3.1416*2*2*5

Volume =62.8 cubic units.

Answer:

Option B.

Step-by-step explanation:

It is given that right cylinder has a radius of 2 units and a height of 5 units. It means

r = 2

h = 5

The volume of a right cylinder is

[tex]V=\pi r^2h[/tex]

where, r is radius and h is height of the cylinder.

Substitute r=2 and h=5 in the above formula.

[tex]V=\pi (2)^2(5)[/tex]

[tex]V=\pi (4)(5)[/tex]

[tex]V=20\pi[/tex]

On further simplification we get

[tex]V=62.831853[/tex]

[tex]V\approx 62.8[/tex]

The volume of right cylinder is 62.8 cubic units.

Therefore, the correct option is B.

let's recall Cavalieri's Principle, solids with equal altitudes and cross-sectional areas at each height have the same volume, so even though this cylinder is slanted with a height = x and a radius = 8, the cross-sectional areas from the bottom to top are the same thickness and thus the same area, so its volume will be the same as a cylinder with the same height and radius that is not slanted.

[tex]\bf \textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\ \cline{1-1} r=8\\ h=x\\ V=768\pi \end{cases}\implies 768\pi =\pi (8)^2(x)\implies 768\pi =64\pi x \\\\\\ \cfrac{768\pi }{64\pi }=x\implies 12=x[/tex]

Answer:

x = [tex]\frac{7 - r}{a}[/tex]

Step-by-step explanation:

ax+r=7

ax = 7 - r

x = [tex]\frac{7 - r}{a}[/tex]