Find the lateral area of the cone in terms of π.




15π cm2


18π cm2


21π cm2


12π cm2

The value of x and y in the both equations are -3 and 2 respectively.

An equation is an expression that shows the relationship between two or more numbers and variables using mathematical operations.

Given the equations:

y + 3x = -4     (1)

And

y = x + 4         (2)

To solve both equations simultaneously, substitute x + 4 for y in the first equation:

x + 4 + 3x = -4

4x + 4 = -4

4x = -8

x = -2

y = x + 4

y = -2 + 4

y = 2

The value of x is -3 and the value of y is 2.

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No, the sides of a triangle cannot have lengths 7, 15, and 20.

What is triangle?

A triangle is a three-sided polygon with three angles. It is a fundamental geometric shape and is often used in geometry and trigonometry. A triangle is defined by its three sides and the three angles formed by those sides. The sum of the three angles in a triangle is always 180 degrees.

No, the sides of a triangle cannot have lengths 7, 15, and 20.

This is because of the triangle inequality theorem, which states that the sum of any two sides of a triangle must be greater than the third side.

In this case, if we add the two smaller sides, 7 and 15, we get 22, which is less than the length of the longest side, 20. Therefore, it is impossible to form a triangle with these side lengths.

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The solution to the integral of e^√x with respect to x is:

∫ e^√x dx = 2√x * e^√x - 2e^√x + C.

The integral of e^√x with respect to x is:

∫ e^√x dx

This integral can be solved using substitution. Let u = √x, then du/dx = 1/(2√x), which means that dx = 2u du.

Substituting these values, the integral becomes:

∫ e^√x dx = ∫ e^u * 2u du

This integral can be solved using integration by parts.

Let u = u and dv = e^u * 2u du, then du/dx = 0 and v = e^u.

Using the integration by parts formula, we have:

∫ e^√x dx = ∫ e^u * 2u du

= u * e^u - ∫ e^u du

Simplifying this expression, we get:

∫ e^√x dx = 2√x * e^√x - 2e^√x + C

where;

Therefore, the solution to the integral of e^√x with respect to x is:

∫ e^√x dx = 2√x * e^√x - 2e^√x + C

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Answer: The most preferred way to travel is car, most non preferred way is to travel bus

Step-by-step explanation: Not sure if their was multiple choice questions but based off what i saw, that what i got.

Answer:

13/15

Step-by-step explanation:

We Know

2/3 of them are chocolate chip cookies.

1/5 of them are sugar cookies.

What fraction of the cookies are chocolate chip or sugar?

2/3 + 1/5 = 10/15 + 3/15 = 13/15

So, 13/15 of the cookies are chocolate chip or sugar.

Answer:

24x

Step-by-step explanation:

Answer: 91

Step-by-step explanation: cross multiply.

Answer: The equation of the line through the points (-3,-4) and (5,3) using point-slope form is y - (-4) = (7/8)(x - (-3)) and the equation of the line in slope-intercept form is y = (7/8)x - (11/8).

Step-by-step explanation:

If he did all three activities today , it takes 12 days do all three activities again.

What is LCM?

Least Common Multiple is a mathematical term. The smallest number that is a multiple of both of two numbers is called the least common multiple.

Here Tom hits golf balls at the driving range every 3 days practices putting every 4 days and goes golfing every 6 days.

Then we need to find LCM , then.

3 = 1*3

4 = 1*2*2

6 = 1*2*3

Then LCM = 1*3*2*2 = 12

Hence If he did all three activities today , it takes 12 days do all three activities again.

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By answering the presented question, we may conclude that As a result, fraction the animal existed around 7,142 years ago (rounded to the nearest year).

A whole can be represented by any number of equal pieces, or fractions. In standard English, fractions denote the number of units of a specific size. 8, 3/4. Fractions are included in a whole. In mathematics, numbers are stated as a ratio of the numerator to the denominator. In simple fractions, each of these is an integer. A fraction can be found in the numerator or denominator of a complex fraction. True fractions have denominators that are greater than their numerators. A fraction is a sum that represents a percentage of a total. You may assess it by splitting it down into smaller chunks. For example, 12 represents half of a whole number or object.

The first step is to use the information provided to calculate the proportion of Carbon-14 that remains (f):

f = 88.5% = 0.885

Carbon-14 decay formula is as follows:

[tex]N(t) = N0e^(-0.00012t) (-0.00012t)[/tex]

Where:

N(t) denotes the quantity of Carbon-14 that remains after t years.

N0 is the starting quantity of Carbon-14, and t is the period in years.

Carbon-14 decay constant is 0.00012.

We know that the remaining fraction is equal to:

f = N(t) / N0

We can solve for t by rearranging the formula:

t = -ln(f) / 0.00012

In place of the values we have:

t = -ln(0.885) / 0.00012

7141.83 years = t

As a result, the animal existed around 7,142 years ago (rounded to the nearest year).

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Only the following two conclusions can be made:

This conclusion can be made by calculating the volume of water in Carmen's flask at time 6 seconds and at time 8 seconds, and comparing it to the volume of water in Matt's flask at the same times.

At time 6 seconds, the volume of water in Carmen's flask is 30 + 8.5(6) = 84 milliliters. At time 8 seconds, the volume of water in Carmen's flask is 30 + 8.5(8) = 94 milliliters. At time 6 seconds, the volume of water in Matt's flask is 10(1 + 0.28)^6 = 45.57 milliliters. At time 8 seconds, the volume of water in Matt's flask is 10(1 + 0.28)^8 = 64.15 milliliters.

Therefore, the volume of water in Carmen's flask is increasing at a faster rate than the volume of water in Matt's flask over the interval [6, 8].

This conclusion can be made because Matt's flask is increasing in volume by 28% each second, while Carmen's flask is increasing in volume by a fixed amount of 8.5 milliliters per second.

As time goes on, the percentage increase in Matt's flask will result in a faster rate of increase in volume compared to Carmen's flask.

Therefore, at some point, the volume of water in Matt's flask will be greater than the volume of water in Carmen's flask.

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The value of 'Y' and Angle A = y - 5 = 60 degrees and value of 'X' = 97 and angle B = x + 3 = 100 degrees.

A quadrilateral is a geometric shape that consists of four straight sides connected end to end to form a closed figure. The term "quadrilateral" comes from the Latin words "quadri" (meaning "four") and "latus" (meaning "side").

Quadrilaterals come in a variety of shapes and sizes, including rectangles, squares, parallelograms, trapezoids, and kites. They can be classified based on their properties, such as the length and angles of their sides, the degree of symmetry, and the presence or absence of parallel sides.

In a quadrilateral, the sum of all angles is 360 degrees. Therefore, we can use this fact to find the measures of angles A and B. We have:

Angle A + Angle B + Angle C + Angle D = 360°

Substituting the given values, we get:

[tex](y - 5) + (x + 3) + 120 + 80 = 360[/tex]

Simplifying and solving for x and y, we get:

[tex]x + y -2 = 360-200\\x + y = 162[/tex]

Therefore, we have one equation in two unknowns. We need another equation to solve for x and y. To find this equation, we can use the fact that the sum of opposite angles in a quadrilateral is 180 degrees. Therefore, we have:

∠ A + ∠ C = 180

∠ B + ∠ D = 180

Substituting the given values, we get:

(y - 5) + 120 = 180

(x + 3) + 80 = 180

Simplifying and solving for x and y, we get:

y = 65

x = 97

Therefore, angle A = y - 5 = 60 degrees and angle B = x + 3 = 100 degrees.

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The volume of the shape is 490cm³

A prism is a solid shape that is bound on all its sides by plane faces. prism is named after the shape of these bases.

The base of this prism is rectangular. The volume of a prism is expressed as;

V = base area × height

base area = 7 × 10 = 70cm²

height = 7cm

the volume of the shape = 70× 7 = 490cm²

therefore the volume of the shape is 490cm³.

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The probability a student is a graduate student if they are a history major is [tex]0.157.[/tex]

What is probability ?

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is.

To calculate probability we can you these formulae:

Probability= probability of graduate and history students/ Total Number of students

p(graduate/ History) = [tex]73 / 463 = 0.157[/tex]

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Answer: B

Step-by-step explanation:

Dont trust me

Using the circles:

A circle with a radius of 8 inches has an area and circumference given by:

A = πr² = π(8²) ≈ 201.06 square inches

C = 2πr = 2π(8) ≈ 50.27 inches

Rounding to the nearest hundredth:

A ≈ 201.06 square inches

C ≈ 50.27 inches

Therefore, the area is approximately 201.06 square inches and the circumference is approximately 50.27 inches.

A circle with a diameter of 20 meters has a radius of 10 meters. The area and circumference are given by:

A = πr² = π(10²) ≈ 314.16 square meters

C = 2πr = 2π(10) ≈ 62.83 meters

Rounding to the nearest hundredth:

A ≈ 314.16 square meters

C ≈ 62.83 meters

Therefore, the area is approximately 314.16 square meters and the circumference is approximately 62.83 meters.

Using these relationships, find the measures of some of the angles:

a) mJKP = mJKN (by vertical angles) and mJKP + mPKL = 90° (by complementary angles), so mJKN + mPKL = 90°.

b) mJKN = mJKP (by vertical angles) and mJKN + mKNM = 90° (by complementary angles), so mJKP + mKNM = 90°.

c) mJLK = mMPL (by alternate interior angles) and mMPL = 63°, so mJLK = 63°.

d) mKNM = 90° - mJKN (by complementary angles). We cannot determine the measure of mJKN.

e) mJLK = mMPL (by alternate interior angles) and mJLR = mJLP (by vertical angles), so:

mJLK + mKLP + mPLJ + mJLP = 360° (by the sum of angles in a quadrilateral)

63° + 90° + mPLJ + mJLP = 360°

mPLJ + mJLP = 207°

f) mJLR = mJLP (by vertical angles) and mKPL = 90°, so:

mJLR + mJLP + mKPL = 180° (by the angles in a triangle)

mJLR + mJLP + 90° = 180°

mJLR + mJLP = 90°

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Image transcribed:

Use the circle below for questions 1-7.

1. Name a radius.

2. Name a diameter.

1.

2.

3.

R

3. Name a chord that is not a diameter.

P

4. Name a central angle.

4.

S

5. Name a minor arc.

5.

6. Name a major arc.

7.

7. Name a semicircle.

For questions 8 and 9, find the area and circumference. Round to the nearest hundredth.

8.

A =

C=

9.

A =

20 m

8 in

C=

10. If m∠MPL = 63°, find each measure.

K

a) mR= =

= m KNM d) 이이

=

b) - =

c) L

=

f) mJLR =

N

M

Gina Wilson (All Things Algebra, LLC), 201

Answer:

Step-by-step explanation:

let xbe side of A.

let x=3

then perimeter=3×3= 9 m

area=1/2×3×√(3²-(3/2)²=1/2×3×3√3/2=9√3/4≈3.879≈3.9 m²

side of triangle B=27/3=9 m

area of triangle=1/2×9×√(9²-(9/2)²=1/2×9×9√3/2=81√3/4≈35.07 ≈35.1 m²

or side of B=3×3=3×side of A

area of triangle B=3²×area of A=9×3.9=35.1 m²

Using central angle theorem,

The measure of the arc BC = 110°.

An angle with its vertex in the middle of the circle it creates with its two radii is said to be central.

Here in the question,

As per the central angle theorem:

(2x -30) ° + x° = 180°

⇒ 2x - 30 + x = 180

⇒ 3x - 30 = 180

Adding 30 on both sides:

⇒ 3x = 180 + 30

⇒ 3x = 210

Dividing both sides by 3.

⇒ x = 70°

Now BC = 2x-30

= 2 × 70 -30

= 140 - 30

= 110°

Therefore, the measure of BC = 110°.

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Step-by-step explanation:If x and y vary directly, it means that they are proportional to each other. We can write an equation that relates x and y using the proportionality constant k:

y = kx

To find k, we can use the given information that y = 56 when x = 14:

56 = k(14)

Solving for k, we get:

k = 4

Now we can use this value of k to find y when x = 5:

y = 4x

y = 4(5)

y = 20

Therefore, when x = 5, y = 20.

Answer:

Step-by-step explanation:

The measure of angle D in the given parallelogram, is 127° on the basis of the fact that the 360° is the angle sum property of any four sided quadrilateral.

what is parallelogram?

A four-sided polygon or quadrilateral with two pairs of sides  parallel is known as a parallelogram. The opposing sides must be equal and congruent. Four edges and four corners make up a parallelogram. A parallelogram is a two-dimensional shape having parallel, equal-length sides on two matching pairs of its opposite sides. The angles inside the two sides of the shape must sum up to 180°, which means that they must add up to 360° overall. It has parallel and equal sides on either side. It has equal opposite angles. Its diagonals cut each other in half.

Given that ∠A= (13x - 25)° , ∠C=(9x - 1)°

We know that in a parallelogram, the opposite angles are congruent & sum of adjacent angles are 180°

∴∠A = ∠C

(13x - 25)° = (9x - 1)°

13x - 9x = -1 + 25

        4x = 24

          x = 6

∠A= (13x - 25)°

    = 13(6) -25

    = 78 - 25

∠A = ∠C = 53°

As ∠A & ∠D are adjacent angles,

∠A + ∠D = 180°

53° + ∠D = 180°

         ∠D = 180° - 53

          ∠D = 127°

∴The measure of angle D in parallelogram ABCD=127°

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let's say A(-6 , 4) and B(-2 , -4), so let's have point C partitions it from A to B in a 3:5 ratio, so

[tex]\textit{internal division of a line segment using ratios} \\\\\\ A(-6,4)\qquad B(-2,-4)\qquad \qquad \stackrel{\textit{ratio from A to B}}{3:5} \\\\\\ \cfrac{A\underline{C}}{\underline{C} B} = \cfrac{3}{5}\implies \cfrac{A}{B} = \cfrac{3}{5}\implies 5A=3B\implies 5(-6,4)=3(-2,-4)[/tex]

[tex](\stackrel{x}{-30}~~,~~ \stackrel{y}{20})=(\stackrel{x}{-6}~~,~~ \stackrel{y}{-12}) \implies C=\underset{\textit{sum of the ratios}}{\left( \cfrac{\stackrel{\textit{sum of x's}}{-30 -6}}{3+5}~~,~~\cfrac{\stackrel{\textit{sum of y's}}{20 -12}}{3+5} \right)} \\\\\\ C=\left( \cfrac{ -36 }{ 8 }~~,~~\cfrac{ 8}{ 8 } \right)\implies C=\left(-\cfrac{9}{2}~~,~~1 \right)\implies C=\left(-4\frac{1}{2}~~,~~1 \right)[/tex]

The graph of the function y=x²- 4x + 5 is attached accordingly. See it's features below.

The features of the function y = x² - 4x + 5 if graphed are:

Opens: The coefficient of the x² term is positive, so the graph opens upwards.

Vertex: To find the vertex, we can use the formula x = -b / (2a) where a and b are the coefficients of the x² and x terms, respectively. In this case, a = 1 and b = -4, so x = -(-4) / (2*1) = 2. Substituting x = 2 into the equation gives y = 1, so the vertex is at (2, 1).

Axis of Symmetry: The axis of symmetry is a vertical line that passes through the vertex. In this case, the axis of symmetry is x = 2.

Circle Max or Min value: Since the graph opens upwards, the vertex is a minimum point. The minimum value of the function is y = 1.

Y-intercept: To find the y-intercept, we can set x = 0 in the equation. This gives y = 5, so the y-intercept is (0, 5).

Zeroes (x-intercepts): To find the x-intercepts, we can set y = 0 in the equation and solve for x. This gives x² - 4x + 5 = 0, which can be factored as (x - 2)² + 1 = 0. Since (x - 2)² is always non-negative, the equation has no real roots, and the graph does not intersect the x-axis.

Increasing interval: The function is increasing to the left of the vertex and decreasing to the right of the vertex. The increasing interval is (-∞, 2).

Decreasing interval: The decreasing interval is (2, ∞).

Average Rate of Change: The average rate of change between any two points on the graph is equal to the slope of the secant line that passes through the two points. The slope of a secant line between two points (x1, y1) and (x2, y2) is (y2 - y1) / (x2 - x1).


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the surface area of the triangular prism is 151.18 cm².by using  triangular prism surface area formula we can solve this

what is triangular prism ?

A triangular prism is a three-dimensional geometric shape that consists of two parallel congruent triangles as its bases and three rectangular faces that connect the corresponding sides of the two triangles.

In the given question,

To find the surface area of a triangular prism, we need to add up the areas of all its faces.

In this case, the triangular prism has two identical triangular bases and three rectangular faces. The dimensions of the triangular base are 5 cm, 5 cm, and 8 cm, while the height of the prism is 6 cm. The dimensions of the rectangular faces are 5 cm by 6 cm and 8 cm by 6 cm, and 4 cm by 6 cm.

The surface area can be calculated as follows:

The area of each triangular base is (1/2) * base * height, where the base is the length of one of the sides and the height is the perpendicular distance between the side and the opposite vertex. The height can be calculated using the Pythagorean theorem, since the base is an isosceles triangle. Thus, the area of one base is:

(1/2) * 5 cm * √(5² - (5/2)²) = 24.59 cm²

Therefore, the total area of both bases is 2 * 24.59 cm² = 49.18 cm².

The area of each rectangular face is the product of its length and width. Thus, the area of the rectangular face with dimensions 5 cm by 6 cm is 5 cm * 6 cm = 30 cm², the area of the rectangular face with dimensions 8 cm by 6 cm is 8 cm * 6 cm = 48 cm², and the area of the rectangular face with dimensions 4 cm by 6 cm is 4 cm * 6 cm = 24 cm²

Therefore, the total area of all three rectangular faces is 30 cm² + 48 cm² + 24 cm² = 102 cm².

Finally, we add up the area of the two triangular bases and the three rectangular faces to get the total surface area:

49.18 cm² + 102 cm² = 151.18 cm²

Therefore, the surface area of the triangular prism is 151.18 cm².

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The table that identifies the one-sided and two-sided limits of function f at x = 2 is table A.

It should be.noted that to graph this piecewise function, follow these steps:

Plot the two given points: open circle (2, 4) and closed circle (2, 1).

Draw a smooth curve that starts at the open circle (2, 4) and curves down toward the x-axis in quadrant 2. This is the curve part of the piecewise function.

Draw a straight line that starts at the closed circle (2, 1) and passes through the point (3, -2). This is the line part of the piecewise function.

The two parts of the piecewise function meet at the point (2, 0), which is where the curve intersects the x-axis. Mark this point with an open circle to indicate that it is not included in the function.

Shade in the region above the curve and to the left of the line, since those are the parts of the plane where the function is defined. The correct option is A.

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Answer:

[tex]\frac{7}{11} * \frac{1}{4}[/tex] = [tex]\frac{7}{44}[/tex].

Cannot reduce it. Then it will make the numerator a decimal

Which cannot happen.

[tex]\frac{7}{44}[/tex] is the answer then

Answer:

7/11 x 1/4 = 0.015

I hoped it helped you.

The equation that represents the relationship between the amount of green chilies used and the cups of sauce Renita can make is:

y = 2x

What is slope?

In mathematics, slope refers to the steepness or incline of a line on a graph.

Let's say that the amount of green chilies used is represented by "x" (in cups), and the amount of sauce Renita can make is represented by "y" (in cups). Then, the equation of the line that represents this relationship is:

y = mx + b

where "m" is the slope of the line (which represents the amount of sauce Renita can make per cup of green chilies used), and "b" is the y-intercept of the line (which represents the amount of sauce Renita can make when she uses 0 cups of green chilies).

To find the values of "m" and "b", we need two points on the line. Let's say that Renita can make 2 cups of sauce when she uses 1 cup of green chilies, and she can make 4 cups of sauce when she uses 2 cups of green chilies. Then, we have the following two points:

(1, 2) and (2, 4)

Using these points, we can find the slope "m" of the line:

m = (y2 - y1) / (x2 - x1)

= (4 - 2) / (2 - 1)

= 2

Now, we can use one of the points to find the y-intercept "b":

y = mx + b

2 = 2(1) + b

b = 0

Therefore, the equation that represents the relationship between the amount of green chilies used and the cups of sauce Renita can make is:

y = 2x.

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cot²θ . cos²θ is the value of x in trigonometric functions.

What do the trig ratios indicate?

Trigonometric All trigonometric functions' values that are dependent on the right-angled triangle's side ratio are referred to as ratios. The trigonometric ratios of a certain acute angle are the ratios of a right-angled triangle's sides to that angle. A reference angle's sine, cosine, tangent, cotangent, secant, and cosecant are the six trigonometric ratios.

L.H.S.

=  cot²θ - cos²θ

= Cos²θ/sin²θ - cos²θ

=  cos²θ - (cos²θ)sin²θ/sin²θ

 =  cos²θ(1 - sin²θ)/sin²θ

 =  cos²θ * cos²θ/sin²θ

  = cot²θ . cos²θ

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Answer:

Here are the probabilities for each event when a card is chosen at random from the set of cards:

Probability of choosing a yellow card:

There are 15 yellow cards out of a total of 15 + 10 + 10 = 35 cards in the set. So, the probability of choosing a yellow card is 15/35 or approximately 0.4286, which can be expressed as a fraction as 15/35.

Probability of choosing a green card:

There are 10 green cards out of a total of 15 + 10 + 10 = 35 cards in the set. So, the probability of choosing a green card is 10/35 or approximately 0.2857, which can be expressed as a fraction as 10/35.

Probability of choosing a blue card:

There are 10 blue cards out of a total of 15 + 10 + 10 = 35 cards in the set. So, the probability of choosing a blue card is 10/35 or approximately 0.2857, which can be expressed as a fraction as 10/35.

Please note that these probabilities assume that each card has an equal chance of being chosen at random, and that the total number of cards in the set remains the same throughout the process of random selection.

Step-by-step explanation: