The volume of a rectangular prism is given by the expression 2x^4+2x^3-4x^2-4x. Write the volume as the product its dimensions. Remember, V = lwh.

Answer:

276 cm²

Step-by-step explanation:

    Construct a line DE  parallel to AB.

DE = 13 cm

So, ABED is a parallelogram

In ΔDEC,

     DE = a = 13 cm

    EC = AB - BE

         = 30 - 16

   EC = b = 14 cm

 DC = c = 15 cm

Use Heron's formula to find the area of triangle.

[tex]\sf s = \dfrac{a+b+c}{2}\\\\=\dfrac{13+15+14}{2}\\\\=\dfrac{42}{2}\\\\s = 21[/tex]

s-a = 21 - 13 = 8

s - b = 21 - 14 = 7

s - c = 21 - 15 = 6

 [tex]\sf \boxed{\bf Area \ of \ triangle = \sqrt{s(s-a)(s-b)(s-c)} }[/tex]

                                [tex]\sf = \sqrt{21 * 8 * 7* 6}\\\\=\sqrt{3 * 7 * 2* 2 * 2 * 7 * 2 * 3}\\\\= 3 * 7 * 2 * 2\\\\= 84 \ cm^2[/tex]

Area of ΔDEC = 84 cm²

[tex]\sf \dfrac{1}{2}*base * height = 84\\\\ \dfrac{1}{2}*14*height = 84[/tex]

           [tex]\sf height =\dfrac{84*2}{14}\\\\[/tex]

                     = 6 *2

          height = 12 cm

Now we know the height of the trapezium. h = 12 cm

The length of the parallel sides are a = 30 cm & b =16 cm

[tex]\sf \boxed{Area \ of \ trapezium = \dfrac{(a +b)*h}{2}}[/tex]

                                [tex]\sf =\dfrac{(30+16)*12}{2}\\\\=\dfrac{46*12}{2}\\\\= 23 * 12\\\\= 276 \ cm^2[/tex]

The length of the rectangular book is 5.8cm

In Euclidean plane geometry, a rectangle is a quadrilateral with four right angles. It can also be defined as: an equiangular quadrilateral, since equiangular means that all of its angles are equal (360°/4 = 90°); or a parallelogram containing a right angle. A rectangle with four sides of equal length is a square. The term oblong is occasionally used to refer to a non-square rectangle.

The perimeter of a rectangle is found by adding up the length of all four sides. The formula for the perimeter of a rectangle is,

P = length + breadth + length + breadth. Or, P = 2(length + breadth)

Given:

Perimeter = 16.84 cm.

length = 18/7 cm

substituting in the formula we get

16.84 = 2( 18/7 + width)

8.42 = 18/7 + width

5.8 cm = width

Thus the length of the rectangular book is 5.8cm.

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Answer:

According to Dr. Davis' law of conversion, we are able to rewrite the equation in any order we need to so that we can solve it in multiple ways. For example, we may choose to add/subtract first, then multiply/divide. Dr. Davis discovered that when solving equations order of operations does not need to be followed.

Step-by-step explanation:

Let's suppose you're getting a new phone plan. The phone plan charges a flat fee of $5 and costs $9 a month. How can we represent this relationship?

Since $5 is a flat fee, it doesn't change based on how many months you've had the plan because it always remains $5, so this is our y-intercept.

Because the plan costs $9 a month, this represents our rate of change, or slope, showing that every month you have the plan, you multiply by $9.

So, we can show this as y=9x+5 where x is the number of months of the phone plan and y is the cost of the phone plan given x amount of months

Now, what if you wanted to know how much the phone plan would cost after 4 months?

Simple enough, we can just substitute x=4 into our equation and get y=9(4)+5=36+5=41. So, getting the phone plan for 4 months costs $41.

Let's take this the other way around. What if we wanted to figure out how many months of the phone plan are covered by $50?

We would then substitute y=50 into our equation and solve for x:

y=9x+5

50=9x+5

45=9x

5=x

This would mean $50 would cover 5 months of the phone plan.

All in all, these are real-life examples of algebra.

Answer:

y = [tex]\frac{29}{3}[/tex]

Step-by-step explanation:

88 = 10y + 30 - 4y , that is

88 = 6y + 30 ( subtract 30 from both sides )

58 = 6y ( divide both sides by 6 )

[tex]\frac{58}{6}[/tex] = y , that is

y = [tex]\frac{29}{3}[/tex]

The terms are as follows:

t₃ = -62

t₇ = -29.6

tₙ = 10.8n - 105.2

t₁₄ = 46

t₁₉ = 100

Therefore,

tₙ = a + (n - 1)d

where

Hence,

46 = a + 13d

100 = a + 18d

5d = 54

d = 10.8

46 - 13(10.8) = a

a = 46 - 140.4

a = - 94.4

t₃ = a + 3d = - 94.4 + 3(10.8) = -62

t₇ = a + 6d = - 94.4 + 6(10.8) = -29.6

tₙ = -94.4 + 10.8n - 10.8 = 10.8n - 105.2

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The value of x is  21√2/2

The correct option is (A)

Trigonometry is a branch of mathematics that studies relationships between the sides and angles of triangles.

In triangle having angle 60.

sin 60 = P/ 7√3

√3/2= P/7√3

2P= 21

P= 21/2

Now again

cos 45= 21/2/x

1/√2 = 10.5/x

x=  21√2/2

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Answer: [tex]52.6^{\circ}[/tex]

Step-by-step explanation:

Let the angle of depression be x.

[tex]\sin x=\frac{27}{34}\\\\x=\sin^{-1} \left(\frac{27}{34} \right) \approx 52.6^{\circ}[/tex]

Answer:

5

Step-by-step explanation:

substitute in 2 for x

3(2) - 1 = 5

Answer:

x = 5

Step-by-step explanation:

given B is the midpoint of AC , then

AB = BC ( substitute values )

4x - 3 = 2x + 7 ( subtract 2x from both sides )

2x - 3 = 7 ( add 3 to both sides )

2x = 10 ( divide both sides by 2 )

x = 5

We'll prove first the triangles formed by diagonal are congruent then we'll prove the angles on either side of diagonal are congruent.

The steps are:

=============================================================

Answer:

24 cm^2

Step-by-step explanation:

The three sides are equal (SSS: side, side, side) so the triangles are congruent.

Using long division, 189 divided by 7 is 27

The picture below represent how to use long division.

Firstly, we divided 1 by 7, it can't go. Therefore, it zero. we put zero at the quotient space.

Multiply zero by 7 and subtract from 189.

We use 18 to divide 7. It will give us 2 remainder 4. we put the 2 at the quotient side and multiply it by 7 to get 14.

Then we subtract 14 from 18. And so on. This is done till we get 0.

Therefore, using long division, 189 divided by 7 is 27

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Answer:

14

Step-by-step explanation:

We can find the number of five-dollar bills creating a system of equations, where F represents the number of five-dollar bills and T represents the number of ten-dollar bills.  

Thus, we have 5F + 10T = 170 and F + T = 24.

We can use substitution in the second equation first to find T then finally F.

[tex]5F + 10T = 170\\F + T = 24\\\\F = 24-T\\\\5(24-T)+10T = 170\\120-5T+10T=170\\120+5T=170\\5T=50\\T=10\\\\F+10=24\\F=14[/tex]

Answer: 180

Step-by-step explanation:

i got you!!!!!!! Hope u pass

Answer:

180

Step-by-step explanation:

<f and <g are on a straight line and they are supplementary angles which means their sum is equal to 180.

Yes it is true that commercial truck owners violate laws requiring front license plates at a higher rate than owners of passenger cars because null hypothesis is rejected.

Given among 2049 Connecticut passenger cars, 239 had only rear license plates. Among 334 Connecticut trucks, 45 had only rear license plates.

let [tex]p_{1}[/tex] be the probability that commercial cars have rear license plates and [tex]p_{2}[/tex] be the probability that connected trucks have rear license plates.

                         Cars                     Trucks                         Total

Total                  2049                    334                             2383

x                          239                      45                                284

p                        0.1166                   0.1347                          0.1191

α=0.05

Hypothesis will be  :

[tex]H_{0}:p_{1} =p_{2}[/tex]

[tex]H_{1} :p_{1} < p_{2}[/tex]

It is a left tailed test at 0.05 significance.

Standard errors of p=[tex]\sqrt{p(1-p)/n}[/tex]

=[tex]\sqrt{(0.1191*0.8809)/2383}[/tex]

=[tex]\sqrt{0.1049/2383}[/tex]        

=0.0066

Test statistic Z=p difference/standard error

=(0.1166-0.1347)/0.0066

=-0.0181/0.0061

=-2.967

p value=0.001505<5%

Since p is less than 5% we reject null hypothesis.

We cannot calculate standard deviation so  we cannot calculate confidence interval.

Hence there is statistical evidence at 5% significance level to support that commercial truck owners violate laws requiring front license plates at a higher rate than owners of passenger cars.

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Answer:

A.  [tex]\frac{21}{4} \pi\ \space\ in[/tex]

Step-by-step explanation:

The formula for arc length is:

arc length = rθ

where:

r is the radius = 7 in

θ is the central angle in radians = 135  ×  [tex]\frac{ \space\ \pi\ }{180}[/tex]  = 3/4 π

Substituting these values into the formula:
arc length = 7 in × 3/4 π

                 = [tex]\frac{21}{4} \pi\ \space\ in[/tex]

The expression that represent the area of the cut off part is 81π / 4

The area of the cut off part can be found as follows:

Area of a circle = πr²

where

Therefore, the cut off part is like 1 / 4th of a circle.

Hence,

area of the cut off region = πr² / 4

r = 9 inches

area of the cut off region =  π9² / 4

area of the cut off region = 81π / 4

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if stretched vertically by a factor of 2, the resulting function will be g(x) = 2|x| and a horizontal compression by a factor of 2, the resulting function will be 1/2|x|

Transformation is a technique used to change the position of an image on an xy-plane.

If the function f(x)is vertically stretched by "a" units, the resulting function will be f(x) = a|x|.

Hence if stretched vertically by a factor of 2, the resulting function will be g(x) = 2|x|

For a horizontal compression by a factor of 2, the resulting function will be 1/2|x|

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The correct option is 'The domain of both functions is all real numbers'.

According to statement

Here, functions are f(x) = 5x and g(x) =5x

Since the domain of f(x) is, D= { x : x belongs to all real numbers.}

Therefore, Domain of f(x) is all real numbers.

Since f(x) and g(x) have the same value,

Therefore, Domain of g(x) is also the set of real numbers.

Now, range of f(x) is , R=  { 5x : x belongs to all real numbers.}

Therefore, Range of f(x) is all real numbers.

Range of g(x) is also all real numbers.

So, we can say by the above explanation, only option (1) is correct.

DISCLAIMER: The question was incomplete. Please find the full content below.

QUESTION

Keshawn is asked to compare and contrast the domain and range for the two functions.

f(x) = 5x

g(x) = 5x

Which statements could he include in his explanation? Check all that apply.

1. The domain of both functions is all real numbers.

2. The domain of f(x) is x > 5.

3. The domain of g(x) is x > 5.

4. The range of both functions is y > 5.

5. The range of f(x) is y > 0.

6. The range of g(x) is y > 0.

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The radius or any additional information related to the circle to assist in calculating the length of the 40-degree arc.

To find the length of a 40-degree arc, to know the radius or diameter of the circle to which the arc belongs. Once you have that information, use the formula to find the arc length:

Arc Length = (θ / 360) × 2 ×π ×r

Where:

θ = Central angle in degrees (40 degrees in this case)

r = Radius of the circle

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Step-by-step explanation:

1. -5(a - 9) = -5a + 45

2. [tex]\frac{-8.3-(+2.7)}{\frac{1}{5} } = \frac{-8.3-2.7}{0.2} =\frac{-11}{0.2}=-55[/tex]

3.13p + 13 - p = (13p - p) + 13 = 12p + 13

4. -11b - 3(-4b + 1) = -11b + 12b - 3 = b - 3

5.

[tex]-2n+\frac{1}{6}-4\frac{1}{2}n = (-2n-4\frac{1}{2}n)+\frac{1}{6} = [-\frac{4}{2} n-(\frac{8}{2}+\frac{1}{2} )n]+\frac{1}{6} = -\frac{4}{2} n- \frac{9}{2} n+\frac{1}{6} =-\frac{13}{2}n\\+ \frac{1}{6}[/tex]

6. It didn't show all the information on the question.

7. [tex]-\frac{3}{5}(20r-5)-(-6r) =-12r+3+6r = (-12r+6r)+3=-6r+3[/tex]

8. [tex]-\frac{5}{6}x+\frac{4}{9}+\frac{2}{3}x+\frac{1}{3}=(-\frac{5}{6}x+\frac{2}{3}x)+(\frac{4}{9}+\frac{1}{3})=(-\frac{5}{6}x+\frac{4}{6}x)+(\frac{4}{9}+\frac{3}{9})=-\frac{1}{6}x+\frac{7}{9}[/tex]

9.It didn't show all the information on the question.

The hypotenuse of the right triangle ABC, with legs of 5 and 12 inches is 13 inches, computed using the Pythagoras Theorem. Hence, the 3rd option is the right choice.

The Pythagoras Theorem states that in a right triangle, the square of the hypotenuse is always equal to the sum of the squares of the other two legs.

If the hypotenuse is taken as a, and the two legs are taken as b and c, then by the Pythagoras Theorem, we can write that:

a² = b² + c².

In the question, we are given that the right triangle ABC, has legs of lengths 5 and 12 inches each, and we are asked to find the length of the hypotenuse.

Thus, taking b = 5 and c = 12, in the above equation, we get:

a² = 5² + 12²,

or, a² = 25 + 144,

or, a² = 169,

or, a² = 13²,

or, a = 13.

Thus, the hypotenuse of the right triangle ABC, with legs of 5 and 12 inches is 13 inches, computed using the Pythagoras Theorem. Hence, the 3rd option is the right choice.

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Let's take an mathematical example

Let's find the ratio of volume of a cone and cylinder if radius and height are same for both .

See

The ratio is 1:3

#Example 1

Ratio of gems=3:4

#Example 2

Ratio of ocean to continents=5:7

Note:-

Two examples are already provided on your another question .You may refer there

Answer:

1

Step-by-step explanation:

The probability that kids will be able to write something about both the French and Spanish classes after he is finished with the interviews is 91/100.

Given 25 kids has enrolled in atleast one foreign language class. 18 kids are in French class and 21 kids are in Spanish class.

We have to find the probability that kids will be able to write something about both the French and Spanish classes after Michael is finished with the interviews.

Let F is a set showing students knowing French,

S be a set showing students knowing Spanish ,

FS= Showing students both enrolled in one languages.

FS=F+S-(F∪S)

=18+21-25

=14

F-18-14=4

S=21-14

=7

4 outcomes lead to Michael being able to write both the languages are (F,S),(FS,S)(FS,F)(FS,FS)

Required probability is the sum of all the probabilities of (F,)(FS,S)(FS,F)(FS,FS)

P(F,S)=[tex]4C_{1}*7C_{1}/25C_{2}[/tex]

=(4*7)/300

=28/300

P(FS,S)=[tex](14C_{1}*7C_{1} )/25C_{2}[/tex]

=14*7/300

=98/300

P(FS,F)=[tex](14C_{1}*4C_{1} )/25C_{2}[/tex]

=14*4/300

=56/300

P(FS,FS)=[tex]14C_{2}/25C_{2}[/tex]

=91/300

Required probability=28/300+98/300+56/300+91/300

=(28+98+56+91)/300

=273/300

=91/100

Hence the probability that kids will be able to write both the languages is 0.91.

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Answer:

6[tex]x^{2}[/tex] - 19x + 15

Step-by-step explanation:

(2x - 3) (3x - 5)

2x(3x-5) - 3 (3x-5)

6[tex]x^{2}[/tex] - 10x - 3 (3x - 5)

6[tex]x^{2}[/tex] - 10x - 9x + 15

6[tex]x^{2}[/tex] - 19x + 15

Answer:

6x² - 19x + 15

Step-by-step explanation:

(2x - 3)(3x - 5)

each term in the second factor is multiplied by each term in the first factor, that is

2x(3x - 5) - 3(3x - 5) ← distribute parenthesis

= 6x² - 10x - 9x + 15 ← collect like terms

= 6x² - 19x + 15

By applying the rigid transformations of reflection on y-axis, vertical compression and vertical translation, we find the transformed function based on f(x) = 2ˣ is f''(x) = (1/3) · 2⁻ˣ + 2.

Rigid transformations are transformations applied on functions such that their Euclidean distance is conserved. In this problem we must use the following rigid transformations to determine an expression based on f(x) = 2ˣ.

Reflection on y-axis

f'(x) = f(-x)     (1)

f'(x) = 2⁻ˣ

Vertical compression

f''(x) = k · f'(x)     (2)

f''(x) = (1/3) · 2⁻ˣ

Vertical translation

f'''(x) = f''(x) + c     (3)

f''(x) = (1/3) · 2⁻ˣ + 2

By applying the rigid transformations of reflection on y-axis, vertical compression and vertical translation, we find the transformed function based on f(x) = 2ˣ is f''(x) = (1/3) · 2⁻ˣ + 2.

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The steps used to solve the quadratic equation are

8(x2 + 2x) = –3

8(x2 + 2x + 1) = –3 + 8

x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot

Given the equation;

8x² + 16x + 3 = 0

Collect like terms

8x² + 16x = -3

Take the common factors, we have

8(x² + 2x) = -3

Completing squares in the brackets and balancing the equation in the right side

8(x² + 2x + 1) = -3 + 8

Factoring the perfect square

[tex]8(x + 1)^2} = 5[/tex]

Make 'x' subject

[tex](x + 1)^2= \frac{5}{8}[/tex]

[tex](x + 1) =[/tex] ±[tex]\sqrt{\frac{5}{8} }[/tex]

[tex]x =[/tex] -1 ±[tex]\sqrt{\frac{5}{8} } }[/tex]

Thus, we can clearly see the steps used to solve the quadratic equation are

8(x2 + 2x) = –3

8(x2 + 2x + 1) = –3 + 8

x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot

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