Consider APQR in the figure below.
The perpendicular bisectors of its sides are SV, TV, and UV. They meet at a single point V.
(In other words, V is the circumcenter of APQR.)
Suppose UV=30, PS= 64, and RV=78.
Find PU, PR, and QV.
Note that the figure is not drawn to scale.

The burgundy fabric:1.135 square yards

The yellow fabric: 0.307 square yards

The total yards of fabric will she have to buy 1.442 square yards.

The same attribute is expressed using a unit conversion, but in a different unit of measurement.

For instance, time can be expressed in minutes rather than hours, and distance can be expressed in kilometres, feet, or any other measurement unit instead of miles.

Given:

Chelsea needs 1472 square inches of burgundy fabric and 399 square inches of yellow.

As, 1 yards= 36 inches

and, 1 square yards= 1296 inches

Then, 1472 square inches of burgundy fabric

= 1472/ 1296

= 1.135 square yards

and, 399 square inches of yellow.

= 399/ 1296

= 0.307 square yards

Thus, the total yards of fabric will she have to buy

= 1.135 + 0.307

= 1.442 square yards

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Answer:

62

Step-by-step explanation:

you have to work out the surface area of a cuboid by:

3×2=6

5×3=15

5×2=10

sum of all the areas is 31

then times it by 2 which is 62

you don t really have to pay attention to the net, apart from the 2cm because you don t want to use it twice in the calculation.

The value of cos B in the fraction is 12/37.

A triangle is said to be right-angled if one of its inner angles is 90 degrees, or if any one of its angles is a right angle.

Given:

A right-angled triangle.

The trigonometric identity:

Cos B = Adjacent leg of the triangle/ Hypotenuse of the triangle

Cos B = 12/37

Therefore, Cos B = 12/37.

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It would take the two boys working together 2.38 hours to clean the pool.

The formula for working out the time it would take two people to complete a job when working together is:

T(combined) = 1 / (1/T1 + 1/T2)

Where T1 is the time it takes one person to complete the job and T2 is the time it takes the other person to complete the job.

In this case, T1 is 4 hours for Kevin and T2 is 6 hours for Jerome.

To solve the equation:

T(combined) = 1 / (1/4 + 1/6)

T(combined) = 1 / (0.25 + 0.17)

T(combined) = 1 / 0.42

T(combined) = 2.38 hours

Therefore, it would take the two boys working together 2.38 hours to clean the pool.

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Answer:

AOC=360-130 = 230

ABC= 230/2=115

Answer:

∠ABC = 115∘

Step-by-step explanation:

∠ABC = 1/2 ∠AOC

(Angle subtended by a chord on major area is half of that subtended on center)

∴ ∠ABC = 1/2 x 130 = 65

ABCD is  a cyclic quadrilateral

Sum of opposite angles = 180∘

∴ ∠ABC + ∠AOC = 180∘

 ∠ABC + 65 = 180∘

 ∠ABC = 115∘

Original Rectangle Length (cm) | Length After 21% Increase (cm)

120 | 144

50 | 61

150 | 180

Each new rectangle is 21% longer than the original, so to calculate the length after a 21% increase, we need to multiply the original length by 1 + 21%.

For the first rectangle (120 cm):

1.21 * 120 cm = 144.4 cm (rounded to 144 cm)

For the second rectangle (50 cm):

1.21 * 50 cm = 60.5 cm (rounded to 61 cm)

For the third rectangle (150 cm):

1.21 * 150 cm = 180.15 cm (rounded to 180 cm)

So the table with the length of each new rectangle would be:

Original Rectangle Length (cm) | Length After 21% Increase (cm)

120 | 144

50 | 61

150 | 180

The rounded values were used in this table.

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If a map f:X→Y between connected CW complexes induces isomorphisms f∗:πn(X)→πn(Y) for all n, then f is a homotopy equivalence. In case f

is the inclusion of a subcomplex X↪Y , the conclusion is stronger: X is a deformation retract of Y.

A fairly generic notion called isomorphism can be found in many branches of mathematics. The word is derived from the Greek words morphosis, which means "to form" or "to shape," and iso, which means "equal." An isomorphism is a bijective morphism in formal terms. An isomorphism, as used informally, is a map that maintains sets and relationships between elements.

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The given expression is polynomial and degree of the polynomial  is 2.

What is polynomials?

Using variables and coefficients, polynomials are algebraic expressions. The term "indeterminates" is sometimes used to describe variables. The terms Poly and Nominal, which together signify "many" and "terms," make up the word polynomial. When exponents, constants, and variables are combined using mathematical operations like addition, subtraction, multiplication, and division, the result is a polynomial (No division operation by a variable). The expression is categorized as a monomial, binomial, or trinomial based on the number of terms it contains.

the expression -10c° – c + 3c²

So the given expression is a polynomial,

The highest degree of the  polynomial will be 2

Hence The given expression is polynomial and degree of the polynomial  is 2.

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Answer:

591.2 kilometers

Step-by-step explanation:

times 295.6 × 2 and you will get 591.2

Answer: The force on an object is directly proportional to its acceleration, which means that if the force is increased, the acceleration will also increase, and if the force is decreased, the acceleration will decrease. This can be expressed mathematically as:

F = k * a

where F is the force, a is the acceleration, and k is a constant of proportionality.

We can use the given information to find the value of k:

30 N = k * 10 m/s^2

k = 3 N*s^2/m

Now we can use this value of k to find the acceleration when the force is 9 N:

9 N = 3 Ns^2/m * a

a = 3 Ns^2/m / 9 N

a = 1/3 m/s^2

Therefore, the acceleration of the object when the force is 9 N is 1/3 m/s^2.

The number of boys chosen Spanish are 59.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

let Girls are G, Boys are B, Spanish choose S, French chosen F and German Chosen Ge.

Total = 200

Girls = 200 - 90 = 110

P(S) = 70 (B+ G)

P(F) = 60 (B)

P(B) + P(G) = 70

S + F = 92

So, 70- G + 44 - G = 92

114 - 2G = 92

-2G = -22

G = 11

So, number of Boys choose Spanish

= 70- 11

= 59

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Answer:that is correct it is 2/9

Step-by-step explanation:

Step-by-step explanation:

5 × -8a = -40a

5 × -9 = -45

-40a - 45 = 5(-8a - 9)

5 × -8a = -40a

5 × -9 = -45

-40a - 45 = 5(-8a - 9)

Answer: To put the equation y - 4x = 17 in slope-intercept form, we need to isolate the y variable on one side of the equation and have the coefficient of x be the slope of the line and the constant term be the y-intercept.

Slope-intercept form is written as y = mx + b, where m is the slope and b is the y-intercept.

Starting with the equation y - 4x = 17, we can isolate y by adding 4x to both sides:

y - 4x + 4x = 17 + 4x

y = 4x + 17

So, the equation in slope-intercept form is y = 4x + 17, where the slope (m) is 4 and the y-intercept (b) is 17.

Step-by-step explanation:

y-4x = 17

slope intercept= y= 4x + 17

The percent of change from 5/4 to 3/8 is a 70% decrease.

To find the percent of change, we need to determine the difference between the original amount and the new amount, and then divide that difference by the original amount and multiply by 100 to express the answer as a percentage.

Let's first convert both fractions to decimals:

5/4 = 1.25

3/8 = 0.375

Next, let's find the difference between the original amount (1.25) and the new amount (0.375):

1.25 - 0.375 = 0.875

Finally, let's divide the difference by the original amount and multiply by 100 to express the answer as a percentage:

(0.875 / 1.25) * 100 = 70

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The minimum number of (whole) dictionaries that you need to measure together is s ≤ 7.0 x 10⁻⁷

Measurement is the process of determining the size, amount, or degree of something, usually using an instrument or a tool.

To determine the thickness of one page in a dictionary, you can measure a number of dictionaries together and average the results.

To achieve an uncertainty of only 7.0 x 10-7 inches in your measurement of one page, you need to determine the minimum number of dictionaries that you need to measure together.

Let's assume that you have N dictionaries and the thickness of the i-th dictionary is xi. Then, the average thickness of one page is given by:

(x1 + x2 + x3 + ... + xN) / N = x

The uncertainty in the average thickness of one page is given by:

s = √(∑((xi - x_bar)²)/(N-1)) / √(N) = √(∑((xi - x_bar)²)/N²(N-1))

We want to find the minimum value of N such that the uncertainty in the average thickness, s, is less than or equal to 7.0 x 10⁻⁷ inches.

So, we have:

s <= 7.0 x 10⁻⁷

Complete Question:

1. You have a set of calipers that can measure the thicknesses of a few inches with an uncertainty of + 0.0050 inches. You measure the thickness of one Oxford American Dictionary (2096 pages) and get 2.51 in.

You can improve this result by measuring dictionaries together. If you want to know the thickness of 1 page with an uncertainty of only 7.0 x 10⁻⁷ in., what is the minimum number of (whole) dictionaries that you need to measure together?

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The graph of the system has been attached below. The solution has been obtained by using linear inequality.

What is linear inequality?

If the equals relation were used in its place, a linear inequality would produce a linear equation.

We are given two inequalities as x+y < 1 and 5x + y > 4

For plotting the points, we need to find x and y

1. x+y < 1

So, let y be 0, then

⇒x < 1

This gives us the point as (1,0).

Now, let x=0, then

⇒y < 1

This gives us the point as (0,1).

From these two points, the graph for the inequality is drawn and represented by red line.

2. 5x + y > 4

So, let y be -1, then

⇒5x > 5

⇒x > 1

This gives us the point as (1,-1).

Now, let x=0, then

⇒y > 4

This gives us the point as (0,4).

From these two points, the graph for the inequality is drawn and represented by green line.

Hence, the graph of the system of linear inequalities is obtained.

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Answer: 4 is correct

Step-by-step explanation:

A(x) + B(x) = (4x - 1) + (8x - 3)

= 12x - 4

The total coins in Lauren's coin collection = 75

Let us assume that there are 'n' total coins in Lauren's coin collection.

She keeps 3 of the coins in her box, which is 4% of the collection.

This means that 4 percent of 'n' is equal to 3.

Using the percentage formula,

4 % of m = 3

m × (4/100) = 3

We solve above equation for m.

⇒ m × 4 = 3 × 100        ..........(multiply both the sides by 100)  

⇒ m × 4 = 300

⇒ m = 300/4              ..........(divide both the sides by 4)

⇒ m = 75

Therefore, she has 75 coins in her collection.

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To find f(2) using synthetic division, we set up the synthetic division table with the coefficients of the polynomial:

2 │ 5  -13  4  -2

 │    10 -6 -2

 └───────────

   5  -3 -2  0

The last entry in the bottom row of the table gives the remainder of the division, which is f(2). Therefore, we have:

f(2) = 5(2)³ - 13(2)² + 4(2) - 2 = 40 - 52 + 8 - 2 = -6

So, the value of the function f(x) = 5x³-13x² + 4x-2 at x = 2 is f(2) = -6.

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Answer:

[tex] {4x}^{2} - 2x - 12[/tex]

Step-by-step explanation:

To complete this problem, use FOIL. First, Outer, Inner, Last.

(2x + 3)(2x - 4)

First, multiply 2x by 2x.

[tex] {4x}^{2} [/tex]

Now, multiply the outer numbers, 2x and -4.

[tex] - 8x[/tex]

Third, multiply the inner numbers, 3 and 2x.

[tex]6x[/tex]

Lastly, multiply the last numbers, 3 and -4.

[tex] - 12[/tex]

Now, put it all together.

[tex] {4x}^{2} - 8x + 6x - 12[/tex]

The final step is to combine like, or similar terms.

The only ones that can be combined are -8x and 6x.

[tex] {4x}^{2} - 2x - 12[/tex]

The solution of the inequalities is (0.67, 3.33)

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

y >= 2

x + y <= 4

y <= 2x + 2

Next, we plot the graph of the inequalities

Using the above as a guide, we have the following:

The solution is (0.67, 3.33)

This is so because the lines intersect at (0.67, 3.33) for y >= 2

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Answer:

See the picture

Step-by-step explanation:

The 1 tells us where to start.  This is our y-intercept.  We start when x =0 and y =1.  The y intercept is 1 (0,1).  You see it in green.

From that point (0,1) you go up 1 and 2 to the right.  This is the slope. You see it in pink.

Once you have the begin part in pink.  You join it to the pink points and draw your line.

Answer:

u have to put lenght ×weight =volume

The equation Ax = 0 has no free variables, so A has n pivot columns. Since A is square, the pivots must be on the main diagonal, so A is row equivalent to the n x n identity matrix Iₙ.

In order for the equation Ax = 0 to have only the trivial solution, there must be no free variables. This means that the matrix A must have n pivot columns. Since A is square, the n pivot positions must be in different rows, which means that the pivots must be on the main diagonal. This means that A is row equivalent to the n x n identity matrix Iₙ. To make it row equivalent, we can perform elementary row operations, such as adding or subtracting rows, or multiplying or dividing a row by a non-zero constant. Once we have done this, the matrix will be in echelon form and the main diagonal will be composed of all 1s. This means that A is row equivalent to Iₙ.

The  complete question: Suppose A is nˣn and the equation Ax=0 has only the trivial solution. Explain why A has n pivot columns and A is row equivalent to Iₙ

Choose the correct answer below.

A. Suppose A is nˣn and the equation Ax = 0 has only the trivial solution. Then there are no free variables in this equation, thus A has n pivot columns. Since A is square and the n pivot positions must be in different rows, the pivots in an echelon form of A must be on the main diagonal. Hence A is row equivalent to the nˣn identity matrix,  Iₙ.

B. Suppose A is nˣn and the equation Ax = 0 has only the trivial solution. Then there are no free variables in this equation, thus A has n pivot columns. Since A is square and the n pivot positions must be in different rows, the pivots in A must be on the main diagonal. Hence A is the nˣn identity matrix,  Iₙ.

C. Suppose A is nˣn and the equation Ax=0 has only the trivial solution. Then there are n free variables in this equation, thus A has n pivot columns. Since A is square and then pivot positions must be in different rows, the pivots in an echelon form of A must be on the main diagonal. Hence A is row equivalent to the nˣn identity matrix,  Iₙ

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Answer:

Step-by-step explanation:

a) Just work backwards!

Instead of adding 4, subtract by 4

Instead of multiplying by 3, divide by 3

22 - 4 / 3 = x

b)

22 - 4 = 18

18 / 3 = 6

Therefore, x = 6

The correct statement is : The volume of the sphere is approximately equal to the volume of the cube, but the sphere has a greater surface area.

Surface Area of a Sphere. A = 4 π r². The volume of a Sphere. V = (4 ⁄ 3) π r³. Where r is the radius of the circle.

Given here: A sphere with 5 in. radius and a cube with side measuring 8.06 in.

Volume of the sphere is

V=4/3πr³

=4/3·π·5³≈523.59878 in³

Surface area of the sphere is

A=4πr²

=4·π·5²≈314.15927 in²

Now volume of the cube

a³=8.06³

≈523.60662 in³

Surface area of the cube

A=6a²

=6×8.06²

≈389.7816 in²

Thus The volume of the sphere is approximately equal to the volume of the cube, but the sphere has a greater surface area.

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