ABCDE is a rectangular-based pyramid with a height of 14 cm.
13 cm
E
Submit Answer
1
0
D
Find the angle between the line DE and the plane ABCD.
Give your answer correct to 1 decimal place.
C
10 cm.

5a^3 x 2b^2 x 4a^2 x b^5 / 3a^2 x 5b^3 (rewrite)

= 20a^5 x 2b^7 / 3a^2 x 5b^3
= 40a^5 x b^7 / 15a^2 x b^3
= (8/3) x a^3 x b^5

Answer:

2'

Step-by-step explanation:

An eleven-foot long board must be cut into three pieces so that one piece is 1-foot shorter than half the length of the longest piece and the other piece is 3 feet shorter than the longest piece. How long is the shortest piece?

board 1 = 0.5L - 1

board 2 = L - 3

board 3 = L

so:

(0.5L - 1) + (L - 3) + L = 11'

0.5L - 1 + L - 3 + L = 11'

combine L on left side:

2.5L - 4 = 11

add4 from both sides:

2.5L - 4 + 4 = 11 + 4

2.5L = 15

divide both sides by 2.5:

2.5L/2.5 = 15/2.5

L = 6

Formula for boards are, substitute in L = 6:

board 1 = 0.5L - 1

= 0.5(6) - 1

= 3 - 1

= 2'

board 2 = L - 3

= 6 - 3

3'

board 3 = L

= 6

shortest board is board 1 at 2'

Answer:

y = - x - 6

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - x ← is in slope- intercept form

with slope m = - 1

• Parallel lines have equal slopes , then

y = - x + c ← is the partial equation of the parallel line

to find c substitute (- 8, 2 ) into the partial equation

2 = 8 + c ⇒ c = 2 - 8 = - 6

y = - x - 6 ← equation of parallel line

Answer: We will be needing 78.54 square meters of sheet metal to make the grain storage silo shown.

Step-by-step explanation: to calculate he total square meters of sheet metal needed to make this grain storage silo we need to calculate the total surface area of the entire structure

for the given structure,

Total surface area = Curved surface area of the cone + curved surface area of the cylinder

curved surface area of cone = [tex]\pi rl[/tex] where r= radius of the base of cone

Given, [tex]2r= 4m[/tex]

⇒[tex]r = \frac{4}{2}=2 metres[/tex]    

slant height of cone [tex]l=\sqrt{(r^{2}+h^{2} ) }[/tex]   where h=1.5 m is the vertical height of the cone

∴ [tex]l = \sqrt{(2^{2}+1.5^{2} ) }=\frac{5}{2}=2.5 m[/tex]              

∴curved surface area of cone [tex]= \pi rl= \pi *2*2.5=5\pi =15.71m^{2}[/tex]             (1)

curved surface area of cylinder(without the floor) =[tex]2\pi rh[/tex]

where r= radius of cylinder and h= height of the cylinder

Given r= 2 m and h=5 m

∴curved surface area of cone =[tex]2\pi rh[/tex]=[tex]2*\pi *2*5=20\pi =62.83m^{2}[/tex]           (2)

From results (1) and (2)

the total surface area of silo = (15.71 + 62.83)[tex]m^{2}[/tex] = 78.54[tex]m^{2}[/tex]

Thus we need 78.54 [tex]m^{2}[/tex] of sheet metal to make the grain storage silo

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!! how to solve for the x

6) to solve for x just simplify both equations and set it to 180; they are co-interior angles which is why they both add to 180.

12x-29 + 4x + 1

16x -28 = 180

16x = 208;

x = 13

8) 4x - 18 = 90;

4x = 108

x = 27

The age of Raj is 4 years.

Amaan's age is 8, more than 4 times the age of Raj.

Amaan is 24 years old.

The age of Raj can be found as follows;

Therefore, the situations will form an algebraic equation.

let

the age of Raj = x

The age of Amaan is 8 more than 4 times the age of Raj.

Hence, the age of Amaan can be represented as follows:

Amaan age = 8 + 4x

Hence,

24  = 8 + 4x

subtract 8 from both sides of the equation

24 - 8 = 8 - 8 + 4x

16 = 4x

divide both side by 4

x = 16 / 4

x = 4

Therefore,

age of Raj = 4 years

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Explanation:

Sean can make 1 paper crane in 6 minutes. His unit rate is 1/6 of a paper crane per minute.

Emily's unit rate is 1/8 of a paper crane per minute.

Their combined unit rate is 1/6 + 1/8 = 4/24 + 3/24 = 7/24 of a paper crane per minute.

Each minute, they can make 7/24 of a paper crane. Put another way, every 24 minutes, they can make 24*(7/24) = 7 cranes.

Let x be the number of minutes needed to make 112 paper cranes.

Multiply the combined unit rate with x and set it equal to 112

(combined unit rate)*(amount of time) = amount made

(7/24)x = 112

x = 112*(24/7)

x = 384

They need 384 minutes if they work together to make 112 paper cranes.

Sean can make 384/6 = 64 paper cranes while Emily can make 384/8 = 48 paper cranes. As a check, 64+48 = 112 to help confirm the answer.

The correct 4 Digit Code (no spaces) is 0164 .

In the question ,

the numbers representing the equation are given

to find

the first statement

-C.P-(-K.I)

From the figure we can see that C=2 ,P=7 ,K=5 ,I=4,

hence -C.P-(-K.I) = -2.7-(-5.4) = -14+20 = 6.0    .....(i)

the second statement

E/H + -L/T

From the figure we can see that E=3 ,H=4 ,L=5 ,T=8

hence E/H + -L/T = 3/4 + -5/8 = 3/4 - 5/8 = 1/8  ...(ii)

the third statement

B/W × -N/T

From the figure we can see that B=2 ,W=9 ,N=6 ,T=8

hence B/W × -N/T = 2/9 × -6/8 = -1/6    ...(iii)

the fourth statement

-F/J ÷ -M/V

From the figure we can see that F=3 ,J=5 ,M=6 ,V=8

hence -F/J ÷ -M/V = -3/5 ÷ -6/8 = 4/5   ....(iv)

From equation (i) , (ii) , (iii) and (iv) , we get

-C.P-(-K.I) = 6.0

E/H + -L/T = 1/8

B/W × -N/T = -1/6

-F/J ÷ -M/V = 4/5

the number from the red color lines are 0,1,6,4

hence the code is 0164 .

Therefore , the correct 4 Digit Code (no spaces) is 0164 .

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The coordinates of the images of the vertices of the rectangle are B'(x, y) = (- 4, 2), C'(x, y) = (- 4, 7), D'(x, y) = (0, 7) and E'(x, y) = (0, 2).

Rectangles are defined by the location of its four vertices set on Cartesian plane, whose images must be found by using a transformation known as translation, whose formula is defined below:

P'(x, y) = P(x, y) + T(x, y)

Where:

If we know that B(x, y) = (3, 2), C(x, y) = (3, 7), D(x, y) = (7, 7), E(x, y) = (7, 2) and T(x, y) = (- 7, 0), then the images of the vertices are:

B'(x, y) = (3, 2) + (- 7, 0)

B'(x, y) = (- 4, 2)

C'(x, y) = (3, 7) + (- 7, 0)

C'(x, y) = (- 4, 7)

D'(x, y) = (7, 7) + (- 7, 0)

D'(x, y) = (0, 7)

E'(x, y) = (7, 2) + (- 7, 0)

E'(x, y) = (0, 2)

Now we proceed to present the resulting figure.

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Despite that JSR stock price was $52.33 in October, when the stock increase and decrease are accounted for, then, the price of the stock in December equals to $51.91.

Also known as share price, it refers to the price of a single share of a number of sale-able equity shares of a company.

Given data

Stock price for JSR was $52.33 in October.

November, the stock had increased by 9%

December, the price fell by 9%.

In November, the firm's stock price will be:

= Stock price in October * (1 + 0.09)

= $52.33 * (1.09)

= $57.0397

In December, the firm's stock price will be:

= $57.0397 * (1 - 0.09)

= $57.0397 * 0.91

= $51.906

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Answer: The answer should be 3 hours

Step-by-step explanation: 8+4=12, divide the sum by 36: 36÷12=3

She had worked 3 hours.

The list that shows the numbers |-0.12|, 1/8, 1/9 in order from smallest to largest is:

1/9, |-0.12|, 1/8.

The absolute value of a number is the distance of the number to the origin, hence it is represented by the number without the signal.

In the context of this problem, the absolute value of -0.12 is:

|-0.12| = 0.12.

To convert a fraction to decimal, we divide the top term of the fraction, called numerator, by the bottom term of the fraction, called the denominator.

Hence, in the context of this problem, the decimal representation of the fractions is given as follows:

To order the three numbers, both have integer part 0, hence we look at which one has the greater decimal part, hence they are ordered as 1/9, |-0.12|, 1/8, from least to greatest.

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The inverse function of f(x) = 4x is:

f⁻¹(x) =  (1/4)*x

So the correct option is the fourth one.

For any function f(x) we define the inverse f⁻¹(x) such that:

f(f⁻¹(x))  =x

f⁻¹(f(x)) = x

In this case we have f(x) = 4*x

Then the inverse is also a linear function:

f⁻¹(x) = a*x + b

Using the rules for inverses we get:

f⁻¹(f(x)) = a*f(x) + b = a*(4x) + b = x

a*(4x) + b = x

Then we have b = 0

a*4x  = x

a*4 = x/x

a*4 = 1

a = 1/4

The inverse is:

f⁻¹(x) =  (1/4)*x

The correct option is the last one.

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The value of y when x is 2 1/2 is 350

Direct variation can be defined as mathematical or arithmetic relationship having two variables that can be expressed with an equation with one variable equivalent to the a specific constant times the size of the other variable.

From the information, we have that;

y varies directly with x.

This can be expressed as;

y α x

Add a constant;

k = y/x

Now, let's determine the constant of their variation, k' by substituting the values, we have;

k = 35/1/4

Take the inverse of the divisor and multiply

k = 35(4)/1

k = 140

To determine the value of 'y' for x = 21/2 = 5/2. we have

k = y/x

140 = y ÷ 5/2

cross multiply

y = 140 × 5/2

cross multiply

y = 350

Hence, the value is 350

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Answer:

file has been attached

Step-by-step explanation:

Answer:

x = 42°

Step-by-step explanation:

 m∠AOB = 180°     {AB is a straight line}

m∠AOE + m∠EOF + m∠FOB = ∠AOB

x + 2x + 34 + 20 = 180°

Combine like terms,

       3x + 54 = 180

subtract 54 from both sides,

            3x  = 180 - 54

            3x  = 126

Divide both sides by 3

              x = 126 ÷ 3

              x = 42°

We can conclude that Angle ∠2 is 127°.

So, in order to solve for x, you must first write an expression using the following measurements from both ∠1 and ∠2.

Then, 5x + 12 = 6x - 11

Now, solve for x as follows:

We know that x = 23.

Solve for ∠2 as follows:

Therefore, angle ∠2 is 127°.

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Answer:

The correct answer is C. On the vertex of Figure A.

Step-by-step explanation:

Before you can find the answer to the question, you must first know what the center of dilation means in math. The center of dilation is a reference point used to appropriately scale the dilation of a figure. The vertex is the the point opposite to and farthest from the base of a geometrical figure, or the common endpoint of the sides of an angle.

Hope that helps! Have an amazing rest of your day!! :)

Using the mathematical operation of division, Dan has so far collected 2,000 signatures.

The division operation is one of the basic mathematical operations for deriving numerical results.

The division operation involves sharing the dividend by the divisor to obtain the result of the mathematical operation known as the quotient.

The total number of signatures needed for the petition = 10,000

The number of times that n needs to be to reach 10,000 = 5x

The number of signatures gathered so far, n, = 2,000 (10,000/5).

Thus, based on division operation, the number of signatures that Dan has collected is 2,000.

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Using the mathematical operation of division, It is found that Dan has collected 2000 signatures.

The division is defined as one of the basic mathematical operations for deriving numerical results; Which involves sharing the dividend by the divisor to obtain the result of the mathematical operation known as the quotient.

The total number of signatures, needed for the petition is; 10,000

The number of times, that n needs to be to reach 10,000 would be;

5x

The number of signatures gathered so far, n, will be;

2,000 (10,000/5).

Hence, based on division operation, the signatures that Dan has collected is; 2,000.

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Answer:

7inches

Step-by-step explanation:

using Pythagoras a²+b²=c²

so it's rearranged to c²-b²=a² or c²-a²=b²

first we get 13²-11²

next we do  169-121

this makes 48

square root 48 is 6.90 inches

this rounds up to 7 Inches

your answer would be : 7 inches

The correct answers are point of intersection and point plotted on an object.

The equation that is represented by the graph is

y = x2 + 4x + 1

This is further explained below.

Generally, The collection of ordered pairings where f(x)=y exists constitutes the graph of a function.

These pairs are Cartesian coordinates of points in two-dimensional space and so constitute a subset of this plane in the typical situation when x and f(x) are real integers.

In conclusion, Graph the parabola using the direction, vertex, focus, and axis of symmetry.

Direction: Opens Up

Vertex: (-2,-3)

Focus:[tex]\left(-2,-\frac{11}{4}\right)[/tex]

Axis of Symmetry: x=-2

Directrix: [tex]y=-\frac{13}{4}[/tex]

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Answer:

32

Step-by-step explanation:

(4[tex]\sqrt{2}[/tex] )²

= 4[tex]\sqrt{2}[/tex] × 4[tex]\sqrt{2}[/tex]

= 4 × 4 × [tex]\sqrt{2}[/tex] × [tex]\sqrt{2}[/tex]

= 16 × 2

= 32

The angles with sides HA and HE are ∠AHE and ∠EHA.

There are some angles given from which we need to find those with sides HE and HA.

The angles given are :

A. ∠AHE B. ∠AGE C. ∠EHA D. ∠EGA E. ∠AHB

For this first we need to understand the naming of angles.

An angle is either named by a single alphabet, mostly when the angle is not divided, or it is named using three letters from which we can clearly understand the sides of the angles.

For example, ∠XYZ has sides XY and YZ with the angle at the point Y.

So we will try to find the sides of each angles given in options.

A. ∠AHE has sides HA and HE with angle at the point H.

B.  ∠AGE has sides AG and GE with angle at the point G.

C. ∠EHA has sides HE and HA with angle at the point H.

D. ∠EGA has sides EG and GA with angle at the point G.

E. ∠AHB has sides HA and HB with angle at the point H.

Hence the angles for which HA and HE are sides are ∠AHE and ∠EHA.

The question is incomplete. Find the complete question below:

Select all the angles for which HA and HE are the sides.

A. ∠AHE B. ∠AGE C. ∠EHA D. ∠EGA E. ∠AHB

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Answer:2.04x10 to the 4th

Step-by-step explanation:

multiply 20.4 x 1000

Then write the answer like this: 20,400

now make a decimal under ten countaining all #s that arent 0: 2.04

count the decimal places between the end of the 2 and the last 0 in the number 20,400

There are 4 places so thats 10 the power of 4

Now just put it all together

If the length of the room is 17 inches one the architect's plan, the actual length of the room in feet if the scale of the plan is 1.25 inches to 3 feet is

40.8 feet

The length of the room on the architect's plan = 17 inches

The scale of the plan = 1.25 inches to 3 feet

That means

The length on the plan/ The actual length = 1.25 inches / 3 feet

Substitute the value of the length on the plan in the equation

17 / The actual length = 1.25/3

The actual length of the room  = 17/0.42

= 40.8 feet

Hence, if the length of the room is 17 inches one the architect's plan, the actual length of the room in feet if the scale of the plan is 1.25 inches to 3 feet is 40.8 feet

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The entered points belong to a vertical line. There is no slope.

Equation: x = -19.

Answer:

It would go 3 to the write of x.

Step-by-step explanation:

If B is the 3 spaces to the left of x and T is three spaces to the right of x, x would be in the middle.

In the picture, you have B=2, X= 5

so T goes if X is the midpoint of BT is

X= (B+T)/2

5 x 2= 2+ T

10 = 2+T

therefore, T = 8