The area of the circular base of a cone is 16π cm², and the slant height of the cone is 4 times the radius of the cone.

What is the approximate lateral area of the cone?

The triangle mid-segments will be the two opposite or adjacent sides of a triangle.

What is the triangle?

The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle.

The sum of all angle of triangle = 180

A line connecting the midpoints of two of a triangle's sides is known as the midsegment. There are always three midsegments in a triangle. The midsegment between any two sides of a triangle is parallel to and half the length of the third side, according to the Triangle Midsegment Theorem, often known as the midsegment theorem.

A midsegment of a triangle is a line segment that joins the midpoints or center of two opposite or adjacent sides of a triangle.

Hence The triangle mid-segments will be the two opposite or adjacent sides of a triangle.

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Complete question:

Define the triangle mid segments.

The size of the angle between EM and the base of the prism is equal to 28.5°.

First of all, we would determine side length MA based on the ratio between side lengths DM and MA as follows;

DM : MA = 3 : 4

Total side parts = 14 cm

(3 + 4) parts = 14 cm

7 parts = 14 cm

1 part = 2 cm

Therefore, side length MA = 2 × 4 = 8 cm.

By applying Pythagorean's theorem to right triangle MAB, we have the following:

c² = a² + b²

Where:

a, b, and c represents the side lengths of a right triangle.

c² = 8² + 14²

c² = 260

c = √260

c = 16.1245 cm.

By applying tan trigonometry to right triangle AEB, we have:

tanθ = opposite/adjacent

opposite = tan32° × 14

opposite = 8.7482 cm.

By applying tan trigonometry to right triangle EMB, we have:

tanθ = opposite/adjacent

θ = tan⁻¹(opposite/adjacent)

θ = tan⁻¹(8.7482/16.1245)

θ = tan⁻¹(0.5425)

θ = 28.5°.

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Answer:

Step-by-step explanation:

i do 6th grade aleks too!

Answer:

Option B) A and C

Step-by-step explanation:

The greatest number of boxes is 4

From the question, we have the following parameters that can be used in our computation:

88 books and 76 DVDs

To do this, we simply calculate the GCF

So, we have the following representation

88 = 2^2 * 11

76 = 2^2 * 19

This gives

GCF = 2^2

GCF = 4

The greatest number of boxes he could have used is 4 boxes.

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The  two different subtraction that each have a different of 1 are 1/2 and 1/2

A fraction is a way to describe a part of a whole. such as the fraction 1/4 can be described as 0.25.

To solve the problem we must know about fractions.

The number should be odd, therefore, the number should be 1, 3, 5, 7, etc.

1          9/8 - 5/8 = 4/8 = 1/2

2          7/8 -5/4 = 2/4 = 1/2

These for the two different subtraction that each have a different of 1

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If two figures can be mapped onto one another or if all pairings of angles and side lengths are congruent, the figures are said to be congruent.

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.

If two triangles are the same size and shape, they are said to be congruent. To establish that two triangles are congruent, not all six matching elements of either triangle must be located. There are five requirements for two triangles to be congruent, according to studies and trials. The congruence properties are SSS, SAS, ASA, AAS, and RHS.

here, we have,

Both triangles are said to be congruent if the three angles and three sides of one triangle match the corresponding angles and sides of the other triangle.

In Δ PQR and ΔXYZ, as shown in figure,

we can identify that PQ = XY, PR = XZ,

and QR = YZ

and ∠P = ∠X,

∠Q = ∠Y and ∠R = ∠Z.

Then we can say that Δ PQR ≅ ΔXYZ.

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The number of degrees moved by the minute hand of a clock in 2/3hours is 240°

Angles around a point describes the sum of angles that can be arranged together so that they form a full turn. Angles around a point add to 360 °.

The hand of minute will move 360° to complete an hour.

If a full round will make angle at a point. Which is 360°

Therefore 2/3 of an hour will give an angle of 2/3 of 360°

= 2/3 × 360

= 240°

therefore the number of degrees moved by the minute hand in 2/3 hour is 240°

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Answer: 48$

Step-by-step explanation: well 20% of 40$ is 8$ so the total cost is 48$ that he payed

Answer:

$48.00

Step-by-step explanation:

Answer: -42

Step-by-step explanation:

Answer:

2418

Step-by-step explanation:

Step 1: Setup

Set up your multiplication problem like this:

             9 3

     x       2 6

Step 2: Multiply

3 x 6 = 18. Put 8 below the line and 1 as a reminder on top:

             1  

             9 3

     x       2 6

               8

Step 3: Multiply

6 x 9 = 54. Take 54 and add 1 from the previous step to get 55. Enter 55 at the bottom:

             9 3

     x       2 6

           5 5 8

Step 4: Add 0

Enter a 0 at the bottom right as a place holder, because you now move over one digit:

             9 3

     x       2 6

           5 5 8

     +         0

Step 5: Multiply

2 x 3 = 6. Put 6 below the line and 0 as a reminder on top:

             0  

             9 3

     x       2 6

           5 5 8

     +       6 0

Step 6: Multiply

2 x 9 = 18. Take 18 and add 0 from the previous step to get 18. Enter 18 at the bottom:

             9 3

     x       2 6

           5 5 8

     +   1 8 6 0

Step 7: Add to get an answer

Add up the bottom two numbers (558 + 1860 = 2418) to get the answer:

             9 3

     x       2 6

           5 5 8

     +   1 8 6 0

     =   2 4 1 8

The bottom line is the answer. Therefore, 93 times 26 equals:

2418

Answer:

25 min

Step-by-step explanation:

60-50=10

10+15=25

Step-by-step explanation:

The cost of a phone has lowered by 19% to $319.14 from its original $394 pricing.

In arithmetic, a percentile is a number or statistic that is given as a fraction of 100. Occasionally, the acronyms "pct.," "pct," nor "pc" are also used. But it is broadly classified into the following by the cent sign, "%." The % amount has no characteristics. Percentages are essentially integers when the denominator is 100. Use the percent sign (%) to indicate that a number is a percentage by placing it close to it. For instance, you score a 75% if you properly answer 75 so out 25 pages on a test (75/100). Divide the money by the whole and multiply the results by 100 you compute percentages. The formula for calculating the percentage is (value/total) x 100%.

given

Put this together using the conditions given: 319.14 / (1- 19%)

Determine the total or difference: 319.14 / 0.81

Diminish the fraction: 394

Response: 394

The cost of a phone has lowered by 19% to $319.14 from its original $394 pricing.

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Answer:

MN = 7x + 3

Step-by-step explanation:

Because MN connects the midpoints M and N  of AD and BC respectively

MN is the midsegment of trapezoid ABCD , then

MN = [tex]\frac{AB+DC}{2}[/tex]

AB + DC = 6x + 7 + 8x - 1 = 14x + 6

MN = [tex]\frac{14x+6}{2}[/tex] = [tex]\frac{14x}{2}[/tex] + [tex]\frac{6}{2}[/tex] = 7x + 3

Step-by-step explanation:

It is explained in the figure above.

The length of side p of the triangle rounded to the nearest tenth is 7.5.

The cosine rule relates the lengths of the sides of a triangle to the cosine of one of its angles.

It is expressed as;

p = √( n² + m² - ( 2nm × cosθ ) )

Given the figure in the diagram;

Plug the values into the above formula and simplify.

p = √( n² + m² - ( 2nm × cosθ ) )

p = √( (11)² + (13)² - ( 2 × 11 × 13 × cos( 35 ) ) )

p = √( 121 + 169 - ( 286 × cos( 35 ) ) )

p = √( 290 - ( 286 × cos( 35 ) ) )

p = √( 290 - 234.27748  )

p = √( 290 - 234.27748  )

p = √55.72252

p = 7.5

Therefore, the value of p is 7.5.

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The negation of the given statement

In Mathematics, the negation of a statement is the opposite of the given mathematical statement.

Given:

Statement: None of the members of the club can vote.

We have to focus on the word  "None" and the negation of word None is Some or at least.

So, Every member of the club can vote is not negation of the statement.

and, At least one member of the club cannot vote is not negation of the statement.

and, Some members of the club can vote is negation of the statement.

and, At least one member of the club can vote is negation of the statement.

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To evaluate [tex]f(g(3))[/tex], we need to first evaluate g(3), then evaluate f(g(3)).

[tex]$$g(3)=7 \cdot 3^2+6 \cdot 3+2=65$$[/tex]

A relationship between a number of inputs, each of which has an output, is known as a function. A function is, to put it simply, a relationship between inputs that are individually connected to exactly one output. There are two domains or scopes for each function. f is typically used to represent functions (x). The input is x. Y = f is a common way to represent the function (x).

To evaluate [tex]f(g(3))[/tex], we need to first evaluate g(3), then evaluate f(g(3)).

[tex]$$g(3)=7 \cdot 3^2+6 \cdot 3+2=65$$[/tex]

So

[tex]f(g(3))=f(65)=\frac{1}{2} \cdot 65-4=\frac{1}{2} \cdot 65-4=28[/tex]

To evaluate [tex]g(f(8))[/tex], we need to first evaluate [tex]f(8)[/tex], then evaluate [tex]f(8)[/tex].

[tex]f(8)=\frac{1}{2} \cdot 8-4=2\\\\g(f(8))=g(2)=7 \cdot 2^2+6 \cdot 2+2=46\\g(f(8))=46[/tex]

[tex]g\left(\frac{1}{8}\right)=7\left(\frac{1}{8}\right)^2+6 \cdot \frac{1}{8}+2=\frac{121}{8}+\frac{3}{2}+2=\frac{135}{8}[/tex]

[tex]f\left(g\left(\frac{1}{8}\right)\right)=f\left(\frac{135}{8}\right)=\frac{1}{2} \cdot \frac{135}{8}-4=\frac{135}{16}-4=\frac{135-64}{16}=\frac{71}{16}\\f\left(\frac{1}{2}\right)=\frac{1}{2} \cdot \frac{1}{2}-4=-4[/tex]

So,

[tex]$$f\left(f\left(\frac{1}{2}\right)\right)=f(-4)=\frac{1}{2} \cdot-4-4=-8-4=-12$$[/tex]

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The density of the block of wood is 1.04g/cm³

Density is the ratio of the mass of an object to its volume. It is a scalar quantity and it is measured in g/cm³ or kg/m³.

Density = mass/volume

Mass = 0.280kg = 0.280 × 1000 = 280g

volume = 270cm³

Density = mass/volume

Density = 280/270

= 1.04g/cm³

Because the density of the object is just slightly higher than the density of water which is 1g/cm³

, therefore the object will float in water.

For an object to float in water, it must be equal to the weight or density of the water

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The given function is continuous at  x = 3,  RHL = LHL = F(3)

In mathematics, The function is called as continuous at the particular value of x,  if right hand limit, left hand limit and the value of function at x all are equal.

RHL   = LHL  = F(x)

Limit exist and continuous

Given that,

F(x)  =  x²  + 5(x - 2)⁷

To check whether it is continuous at x = 3

First taking LHL,

[tex]\lim_{h \to \00 } F(x)[/tex]  

[tex]\lim_{h \to \00 }[/tex]   (3-h)²  + 5(3 - h - 2)⁷

⇒  9 + 5

⇒   14

Now, taking RHL

[tex]\lim_{h \to \00 }[/tex]   (3+ h)²  + 5(3 + h - 2)⁷

⇒  9 + 5

⇒   14

The value at x = 3

F(3)  =  3²  + 5(3 - 2)⁷

       =  14

Hence Proved,   RHL = LHL = F(3)

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To solve the equation, you can use the following steps:

Start by isolating the absolute value expression on one side of the equation:

-5|x+3| = 18

Now, since the absolute value is positive, it has two solutions:

x + 3 = -18 or x + 3 = 18

Solving for x in each case:

x = -21 (if x + 3 = -18) or x = 15 (if x + 3 = 18)

So the two solutions to the equation are x = -21 and x = 15.

Answer:

y=3x+5

Step-by-step explanation:

tjrjrkrlrorlp3ñ34mrmrr

Answer:

y=mx+c

Step-by-step explanation:

-5/y=3x meaning that y=mx+c, hope this helps :)

Answer:

The function f(x) to model U. S. cell phone usage over the time period of 2010 to 2016 can be expressed as f(x) = 43 * (1.23^x), where x is the number of years since 2010. Part b: The estimated cell phone usage in 2013 can be calculated by substituting x = 3 into the function f(x) = 43 * (1.23^x). This yields an estimated cell phone usage of 68.4 million in 2013, which can be rounded to the nearest ten thousand to 68 million.

Step-by-step explanation:

Answer:

0 + 11i

Step-by-step explanation:

A complex number is a number in the form a + bi, where a is the real part and b is the imaginary part. In this case, the real part is given as 0 and the imaginary part is given as 11. Therefore, the complex number is:

0 + 11i

where 0 is the real part and 11i is the imaginary part.

The correct answer is Tasha, because she has the highest ratio since 0.625 > 0.7.

Receive is a comparison between two or more quantities expressed as a fraction or a set of relative quantities it is used to compare the size of one number to another or the compare changes overtime ratio can be expressed in word as fraction or decimal receiver in important concept in mathematics used to analyse data and solve problem.

Tasha has hit the ball 10 times out of 16 attempts, which means her batting average is 0.625. Jana has hit the ball 7 times out of 10 attempts, which gives her a batting average of 0.7. Therefore, Tasha has the better batting average.

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The rate of change of the volume is 871.2 ft³/sec

Rate of change of volume is the change in volume with time.

The rate of change of radius is 6 feet per second.

rate of change in volume = dv/dt

rate of change in radius = dr/dt

to find radius of the sphere;

V = 4/3 πr³

163 = 4/3 x3.14r³

r³ = 163× 3)/4×3.14

r³ = 488/12.56

r³ = 38.85

r = 3.4 feet

therefore

dr/dt = 1/4πr² × dv/dt

= 6 = 1/4×3.14× 3.4² × dv/dt

dv/dt = 6×4× 3.14× 3.4²

dv/dt = 871.2 feet³ per second

therefore the rate of change of the volume is 871.2 feet³ per second

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Answer:

231

Step-by-step explanation:

From the pie chart we see that the story artists constitute 20% of the total employee strength of 1540 employees and the interns constitute only 5% of that number

In actual values

Number of story artists = 1540 x 20% = 1540 x 20/100 = 308

Number of interns = 1540 x 5% = 1540 x 5/100 = 77

Difference = 308 - 77 = 231