A stainless steel patio heater is a square pyramid. The length of one side of the base is 22.6 The slant height of the pyramid is 88.6 What is the height of the​ pyramid?

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: B

Step-by-step explanation:

Dont trust me

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 main difference between a pyramid and a prism is their base shape and the number of faces, edges, and vertices they possess.

A pyramid is a 3D shape that has a base in the form of a polygon, with triangular faces that meet at a single point known as the apex. The shape of the base can vary, with some common ones being triangles, squares, and pentagons. Pyramids have a total of five faces, including the base. The number of edges and vertices depends on the number of sides of the polygonal base. Pyramids are commonly found in ancient architecture, such as the Egyptian pyramids, and are often used to represent power and strength.

A prism, on the other hand, is a three-dimensional shape that has two identical polygonal bases that are connected by rectangular faces. The shape of the bases can vary, with some common ones being triangles, rectangles, and hexagons. Prisms have a total of six faces, including the two identical polygonal bases. The number of edges and vertices of a prism depends on the shape and number of sides of its bases. Prisms are often found in modern architecture, such as in the design of buildings and bridges.

Pyramids and prisms are two distinct three-dimensional geometric shapes that differ primarily in their base shape. A pyramid's base is a polygon, whereas a prism has two parallel polygonal bases connected by rectangular faces. Pyramids have a total of five faces, including the base, while prisms have six faces, with two identical polygonal bases. The number of edges and vertices of both shapes is determined by the shape and number of sides of their respective bases.

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The complete question is: "The difference between a pyramid and a prism."

For a large sample size (greater than 30), distribution is normal.

An insurance company claims that in the population of homeowners, the mean loss and standard deviation from fire is

μ = $250

o = $5000

The distribution of loss is strongly right skewed.

a). Since for a simple random sample of size n= 15 drawn from  the population of homeowners.

Since the given sample size is small. Therefore for small sample size less the 30 the distribution of

follow t- distribution.

Since t distribution has more variance than normal distribution.

Also t- distribution is symmetric as normal distribution at t=0.

For small sample size sampling distribution is t -distribution.

b). Now if the simple random sample of size n = 10000 drawn from the population of homeowners.

Thus for the large sample size and given mean and standard deviation sampling distribution of x follow normal distribution. Also we know that normal distribution have a bell-shaped curve which is symmetric to z=0.

For a large sample size (greater than 30), distribution is normal.

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[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{1})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1}=\stackrel{m}{ \cfrac{1}{3}}(x-\stackrel{x_1}{(-2)}) \implies y -1 = \cfrac{1}{3} ( x +2) \\\\\\ y-1=\cfrac{1}{3}x+\cfrac{2}{3}\implies y=\cfrac{1}{3}x+\cfrac{2}{3}+1\implies {\Large \begin{array}{llll} y=\cfrac{1}{3}x+\cfrac{5}{3} \end{array}}[/tex]

After 29 years of compounded interest at a rate of 5% quarterly, the retirement account would be worth approximately $455527.25.

The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest.

We can use the formula for compound interest to find the future value of the retirement account:

[tex]FV = P(1 + r/n)^{(nt)[/tex]

where FV is the future value, P is the principal, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the time in years.

In this case, P = $100509, r = 0.05 (5% expressed as a decimal), n = 4 (since interest is compounded quarterly), and t = 29. Plugging these values into the formula, we get:

[tex]FV = $100509(1 + 0.05/4)^{(4*29)[/tex]

FV ≈ $455527.25

Therefore, after 29 years of compounded interest at a rate of 5% quarterly, the retirement account would be worth approximately $455527.25.

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Answer:

  (A)  x² +8

Step-by-step explanation:

You want to select the quadratic binomial from the given list.

The term "quadratic" is used interchangeably with "degree 2" when referring to a polynomial's degree.

A "binomial" is a 2-term polynomial. The prefixes mono-, bi-, tri- are used with -nomial to describe the number of terms as being 1, 2, or 3, respectively.

The quadratic binomial in the list is ...

  x² +8

__

Additional comment

This is a vocabulary question. You are expected to be familiar with the meaning of these descriptive terms. The others on the list are ...

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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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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Answer:

The jumping dolphin is approx. 6 meters under sea level

The flying seagull is approx. 8 meters under sea level

The mobula ray is approx. 2 meters under sea level

The clownfish is approx.t 4 meters under sea level

The octopus is approx.  8 meters under sea level

The jumping dolphin: The mobula ray is 9 meters lower than the jumping dolphin.

The flying seagull: The mobula ray is 11 meters lower than the flying seagull.

The octopus: The mobula ray is 11 meters higher than the octopus.

The jumping dolphin: The albatross is 1 meter lower than the jumping dolphin.

The flying seagull: The albatross is 3 meters lower than the flying seagull.

The octopus: The albatross is 13 meters higher than the octopus.

The jumping dolphin: The clownfish is 8 meters lower than the jumping dolphin.

The flying seagull: The clownfish is 10 meters lower than the flying seagull.

The octopus: The clownfish is 6 meters higher than the octopus.

If the new dolphin is above the dolphin in the picture, then its distance from the surface of the ocean is 6 - 3 = 3 meters.

If the new dolphin is below the dolphin in the picture, then its distance from the surface of the ocean is 6 + 3 = 9 meters.

✧☆*: .｡. Hope this helps, happy learning! (✧×✧) .｡.:*☆✧

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:

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.

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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In order to fulfill the requirements, we need to draw exactly 5 quadrilaterals with appropriate markings on the grid. Here's an example design:

. . . . . 1 . . . .

. . . . / \ . . .

. . . ./. \.\ . .

. . . / . . \ \ .

. . ./. 5 . \.\ .

. . / . . . . \ \ .

. ./. . 4 . . \.\ .

. 2-----------3 .

. .\ . . . . . /. .

. . \ . . . ./. .

. . .\.\ . / /. .

. . . \.\./ / . .

. . . . \  / . .

. . . . .\/. . .

A parallelogram has two pairs of parallel sides.

A rectangle is a type of parallelogram where all angles are right angles.

A rhombus is a type of parallelogram where all sides are equal in length.

A square is a type of rectangle where all sides are equal in length.

A trapezoid has one pair of parallel sides.

A quadrilateral with no other classification is any quadrilateral that does not fit into the above categories

In this design, we have:

Parallelogram 1, marked with arrows to indicate its parallel sides.

Rectangle 2, marked with right-angle symbols to indicate its right angles.

Rhombus 3, marked with tick marks to indicate its equal sides.

Square 4, marked with tick marks and a right-angle symbol to indicate its equal sides and right angles.

Trapezoid 5, marked with a line and arrows to indicate its parallel sides and non-parallel sides.

All of the shapes in this design are quadrilaterals, and we have exactly 3 parallelograms, 2 rectangles, 1 rhombus, 1 square, 1 trapezoid, and 1 quadrilateral with no other classification.

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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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Q1 = 15.15 Q2=

Step-by-step explanation:

do 5.5×3 or 5.5 to the power of 3 or add 5.5 + 5.5 + 5.5 then each square is 11secs times 3(how many sides there is ) and that's your answer

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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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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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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Therefore, Mr. Livingston can give each of his 9 students 5 stamps, with 3 stamps left over.

the quotient is the result of dividing one quantity (dividend) by another quantity (divisor). It represents the number of times the divisor can be evenly divided into the dividend. The quotient is typically expressed as a numerical value, and it can be an integer or a fraction, depending on the nature of the division.

For example, if we divide 10 by 2, the quotient is 5, because 2 can be evenly divided into 10 five times. Similarly, if we divide 9 by 4, the quotient is 2 with a remainder of 1, because 4 can be divided into 9 two times, but there is one left over.

To find out how many stamps Mr. Livingston can give to each student, we need to divide the total number of stamps (48) by the number of students (9):

48 ÷ 9 = 5 R3

The quotient is 5, meaning each student can receive 5 stamps. However, there is a remainder of 3, meaning there will be 3 stamps left over that cannot be divided equally among the students.

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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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The surface area of a cell phone screen is 117 cm².

What is unit conversion?

Unit conversion is the process of converting a quantity expressed in one unit of measurement to an equivalent quantity expressed in another unit of measurement.

We can convert mm² to cm² by dividing the area in mm² by the square of the conversion factor, which is (10 mm / 1 cm) = 100 mm² / cm². Therefore, we have:

11700 mm² / (100 mm² / cm²) = 117 cm²

Rounding to the nearest whole number, we get 117 cm².

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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]

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

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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Answer:

Step-by-step explanation:

Answer:

12.5 km

Step-by-step explanation:

To convert m to Km, divide the distance in m by 1000.

   1000 m = 1 Km

          [tex]\sf 1 m =\dfrac{1}{1000}km\\\\\\12500 \ m = \dfrac{1}{1000}*12,500\\\\[/tex]

                        = 12.5 Km

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