If AD=5x+8 and BD=3x-10, what is the length of AB?
A)28
B)148
C)74
D)222

Coach's errors are;

Wrong conversion when converting hour to seconds

There is wrong conclusion since Eliza was running fast enough at a speed of 34ft/s compared to 8.8ft/s

The speed required by eliza is 8.8 ft/s

Converting 5.8miles to feet per second

Taking the coach conversion

This shows that 5.8mi/hr is equivalent to 34.0ft/s in accordance with coach conversion rate.

The coach made the first error by taking 60s as 1hr instead of 3600s as 1hr

The mistake that Eliza is not running fast enough to exceed her fastest time. Eliza is running at pace as her speed at 34ft/s exceed 8.8ft/s.

Hence the second error was the wrong conclusion made by the coach.

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The value of a is 2.5

As FG is the line and M is the midpoint of the line

  F   ______________·_________________G

                                    M

So by this, we have that

    FG = FM + MG

Where FM = MG as M is the midpoint of the line.

Therefore FG = 2FM

As it is given that FM = 8a + 1 and FG = 42

Now putting the values we have

42 = 2( 8a + 1)

21 = 8a + 1

20 = 8a

a = 2.5

Therefore the value of a is 2.5.

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The volume of the cylinder as a function of its radius is V = 2πr^3

The given parameters are

Diameter = Height

This can be represented as

d = h

The radius of a cylinder is calculated as

r = d/2

This means that

d = 2r

Substitute d = 2r in d = h

h = 2r

The volume of a cylinder is

V = πr^2h

Substitute h = 2r in V = πr^2h

V = πr^2(2r)

Evaluate

V = 2πr^3

Hence, the volume of the cylinder as a function of its radius is V = 2πr^3

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The interval to find the true average tip is  (14.62,13.78).

Average is a number that is calculated by adding quantities together and dividing the total by the number of quantities.

The Standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean of the set, while a high standard deviation indicates that the values are spread out over a wider range

Given:

We know that the confidence interval = sample mean ± standard deviation substitute the values in it then confidence interval = 14.2  ±2.5/(35)^1/2

confidence interval = 14.2 ± 2.5/5.91

confidence interval = 14.2 ± 0.42

confidence interval = 14.2 + 0.42 ,

confidence interval = 14.2 - 0.42

confidence interval = (14.62,13.78)

So, an interval to estimate the true average tip is  (14.62,13.78).

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The possible number of flowers you sell is 3 to 25

The given parameters are:

Selling price = $5

Total cost of trip = $75

Bus ride = $15

If you earn enough to cover the total cost of the trip, the maximum numbers (Max) of flowers you sell is

Max = Total cost of trip/Selling price

This gives

Max = 75/5

Max = 25

If you earn enough to cover the bus ride, the minimum numbers (Min) of flowers you sell is

Min = Bus ride/Selling price

This gives

Min = 15/5

Min = 3

Hence, the possible number of flowers you sell is 3 to 25

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Solving a quadratic equation, it is found that the largest possible value of a is of a = 5.

A quadratic equation is modeled by the following rule:

y = ax^2 + bx + c

The solutions of the equations are the values of x for which y = 0.

For this problem, the equation is:

a² - 6a - 9 = b.

b = -9 - a, hence we replace in the equation as follows;

a² - 6a - 9 = -9 - a

a² - 5a = 0.

Traditionally, the solutions are given using Bhaskara's formula, however, since the coefficient c is zero, we can solve the equation by elimination as follows:

a² - 5a = 0.

a(a - 5) = 0.

Then the solutions are:

5 > 0, hence the largest possible value of a is of a = 5.

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Answer:

y = x + 5

Step-by-step explanation:

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

m = (16 - 5)/(9 - 0) = 9/9 = 1

Using m = 1, y = 5, x = 0

then y = mx + b

5 = 1(0) + b

b = 5

so y = x + 5

Answer:

a. Price needs to decrease by 6 Bozats.

[tex]\sf b. \ \ \sf x =-\dfrac{1}{6} p+\dfrac{100}{3}[/tex]

Explanation:

Equation: p = 200 - 6x

where:

a.

To sell an additional kilogram of snig that is (x + 1) kilogram of snig.

current price = 200 - 6(x + 1) = 200 - 6x - 6

b.

[tex]\rightarrow p = 200 - 6x[/tex]

[tex]\rightarrow - 6x = p-200[/tex]

[tex]\rightarrow x =\dfrac{ p-200 }{-6}[/tex]

[tex]\rightarrow x =-\dfrac{1}{6} p+\dfrac{100}{3}[/tex]

Answer:

FH = 24

Step-by-step explanation:

HG = 13

FH = 37 - 13

= 24

Answer:

The value of FH is 24.

Step-by-step explanation:

The equation will be,

→ FHG = FH + HG

Then the value of FH will be,

→ 37 = FH + 13

→ FH = 37 - 13

→ [ FH = 24 ]

Hence, the value of FH is 24.

The expression 2×2×2×5 shows the prime factorization of 40.

Prime factorization:

The number 40 is equal to

2 x 2 x 2 x 5, or   = 40

23 x 5. = 40

In mental arithmetic, fractions, finding square roots, and computing the HCF and LCM of two smaller numbers, prime factorization is a highly helpful tool when working with whole numbers. A whole number higher than 1 whose only elements are 1 and itself is referred to as a prime number. A whole number that may be split evenly into another number is referred to as a factor.

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Answer:

2 × 2 × 2 × 5

Step-by-step explanation:

2 × 2 × 2 × 5 = 4 × 2 × 5 = 8 × 5 = 40

The expression is simplified to 6w

Algebraic expressions are expressions made up of terms, variables, factors, coefficients and constants.

They also consist of arithmetic operations such as addition, subtraction, multiplication, division, etc

Given the expression;

-2w+w+7w

Using the BODMAS rule, we have to add

-2w + 8w

6w

Thus, the expression is simplified to 6w

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Answer:

(0, 1 )

Step-by-step explanation:

2x + 5y = 5 → (1)

- 3x + 7y = 7 → (2)

to eliminate y multiply (1) by 7 and (2) by - 5 , then add the result

14x + 35y = 35 → (3)

15x - 35y = - 35 → (4)

add (3) and (4) term by term to eliminate y

29x + 0 = 0

29x = 0 ⇒ x = 0

substitute x = 0 into (1) and solve for y

2(0) + 5y = 5y

0 + 5y = 5

5y = 5 ( divide both sides by 5 )

y = 1

solution is (0, 1 )

Pattern uses 6233.76 inches² fabric.

Firstly we will convert units in required form. Therefore, converting equivalent of yard² in inches². As per the given information, 1 yard = 3 feet and 1 foot = 12 inches.

As 1 foot = 12 inches, so, 3 feet = 36 inches, which is further equal to 1 yard.

Now, 1 yard² = (36 inches)²

1 yard² = 1296 inches²

Coming back to the problem, we will now calculate inches² from fabric measurement in yard². So, relating the units for conversion.

1 yard² = 1296 inches²

4.81 yard² = 1296 × 4.81

Performing multiplication

Measurement of 4.81 yard² in inches² = 6233.76

Hence, the pattern uses 6233.76 inches² fabric.

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x+12+4x-16= 6x-13

5x-4=6x-13

-4=x-13

x=9

9+12+4(9)-16

21+36-16

57-16= 41

JL=41 units

Answer:

131°

Step-by-step explanation:

Sum of all angles of a quadrilateral = 360°

We can find the unknown angle ∠B, by subtracting the sum of the angles ∠A, ∠C, ∠D from 360°.

∠A + ∠B + ∠C + ∠D = 360

105 + ∠B + 34 + 90  = 360

           ∠B +  229      = 360

                     ∠B       = 360 - 229

                           ∠B = 131°

Answer:

The measure of m<GHE is 49°, the correct option is B.

What is a Quadrilateral?

A quadrilateral is a polygon with four sides.

It is of various types,

Trapezoid, which have one pair of parallel sides,

Parallelogram, it has two pairs of parallel sides,

Rhombus, it has all sides equal,

Rectangle, opposite sides are parallel and equal, and,

Square, all sides are equal and opposite sides are parallel, and all angles have measure of 90 degree.

The quadrilateral ABCD is ≅ quadrilateral EFGH

When two figures are congruent then by CPCTC, corresponding parts of congruent figures are congruent.

The measure of the angle

B = m<BCD = 90°

m<BAD = 131°

As the quadrilaterals are congruent,

By CPCTC

∠F = ∠FGH = 90°

m ∠FEH =  131°

The measure of m<GHE has to be determined.

The sum of the measures of all angle so of a quadrilateral is 360 degree.

The ∠F + ∠FGH + ∠FEH + ∠GHE = 360

90 +90+ 131 +∠GHE = 360

∠GHE = 49°

Step-by-step explanation:

The measure of ∠EBF is 56°.

Here, we are given that-

m ∠EBC = 3 r + 10 °

and m ∠ABE = 2 r − 20 °

Also we can observe that ∠EBC and ∠ABE are angles on a straight line and hence will be supplementary.

⇒ ∠EBC + ∠ABE = 180

⇒ 3r + 10 + 2r - 20 = 180

5r - 10 = 180

5r = 180 + 10

5r = 190

r = 190/5

r = 38

Thus, ∠ABE = 2(38) - 20

= 76 - 20

= 56

Now, from the figure, m ∠EBF = m ∠ABE

⇒ m ∠EBF = 56°

Thus, the measure of ∠EBF is 56°.

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Your question was incomplete. Check for the missing figure below.

fraction of the volume of the atom taken by nucleus = 1.07*10^-13

Space occupied by the sphere is the volume of sphere.

A straight line passing from side to side through the center of the body especially a circle or sphere is known as diameter.

Volume of sphere = 4/3πr³

Diameter of an Atom = 2.00Â

Diameter of an nucleus = 9.50×10⁻⁵Â

Radius of an Atom = 1.00Â

[tex]\frac{4}{3}\pi r^3=\frac{4}{3}\pi (4.75*10^(-5))^3\\[/tex]

Volume of an Atom = [tex]\frac{4}{3}\pi r^3= \frac{4}{3}\pi 1^3=\frac{4}{3}\pi[/tex]

Volume of nucleus = [tex]\frac{4}{3} \pi r^3=\frac{4}{3} \pi (4.75*10^-5)^3\\=\frac{4}{3} \pi 107.1718*10^-15[/tex]

fraction of the volume of the atom taken by nucleus =

4/3π 107.17*10^-15/ 4/3π =107.17*10^-15 = 1.07 *10^-13

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The solution to the system of equation is x = 6, y = 4, z = 5

The equation is

1.5x + y - z = 8

x + 3y = 18

2y + z = 13

From this we have,

y = 8 - 1.5x + z

x + 3y = 18

2y + z = 13

x + 3(8 - 1.5x + z) = 18

2(8 - 1.5x + z) + z = 13

Apply the Distributive Property

x + 24 - 4.5x + 3z = 18

16 - 3x + 2z + z = 13

Combine like terms

-3.5x + 24 +3z = 18

16 - 3x + 3z = 13

Rearrange variables to the left side of the equation

-3.5x + 3z = 18 - 24

-3x + 3z = 13 - 16

Subtract the two equation

-3.5x + 3z - (-3x + 3z ) = 18-24 - ( 13-16)

-3.5x + 3z + 3x -3z = 18 - 24 - 13 + 16

-3.5x + 3x = 18 - 24 - 13 + 16

x = 6

Substitute the value of x in one of the equation

-3×6 + 3z = 13 - 16

-18 + 3z = -3

3z = 15

z = 5

Now put the value of x and z

y = 8 - 1.5x + z

y = 8 - 1.5×6 + 5

  = 8 -9 + 5

  = 4

Therefore the solution to the system of equation is x= 6, y = 4 and z = 5

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The number after rounding off to the nearest tenth will be 9.4

In this question, we have been given that Miguel made up an equation in which three times of square of a particular number equals 265. We have to set up the equation according to this.

Taking the number as 'x'. We get the equation according to the condition :

               => 3x² = 265

By solving this equation we get :

               =>  3x² = 265    =>  x² = 88.3

               => x = 9.39

We get x = 9.39. By rounding off x to the nearest tens, we get x = 9.4

Hence, the number to the nearest tenth will be 9.4

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The investigator can test the presence of simple sugars in the sample by using Benedict's solution.

Simple carbs are tested for using Benedict's Test. With free ketone or aldehyde functional groups, reducing sugars (monosaccharides and some disaccharides) are recognized by the Benedict's test.

Benedict's solution turns orange or brick red when heated in the presence of simple carbohydrates. The reducing characteristic of simple carbs is what triggers this response. The Benedict's solution changes color as a result of the reduction of copper (II) ions to copper (I) ions.

The produced red copper(I) oxide precipitates out of solution because it cannot be dissolved in water. This explains how the precipitate was created. The closer the final hue is approaching brick-red and the more precipitate is generated as the reducing sugar concentration rises. Copper oxide, a brick-red solid, can occasionally precipitate out of a solution and gather at the test tube's bottom.

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The measure of angle BOD is 65°

From the question, we are to determine the measure of angle BOD (m ∠ BOD)

The measure of angle BOD can be determine from the given protractor.

To determine the measure of angle BOD, we will read from line BO, in the counterclockwise direction, to line DO.

Reading in the counterclockwise direction, line BO is on 0°, and line DO is on midpoint of 60° and 70°.

The midpoint of 60° and 70° is 65°

Hence, the measure of angle BOD is 65°.

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Answer:

answer for this question is alternative A (80, 60) & (95,85)

Order from greatest to least

0.7

0.07

0.072

7.2

7

0.27

Answer:

(largest) 7.2 , 7 , 0.7 , 0.27 , 0.072 , 0.07 (smallest)

Answer:

he has $6 left.

Step-by-step explanation:

Answer:

$18.99 for each student

Step-by-step explanation:

First we need to find out how much he spent on each student for the calculators.

We can do that by dividing 84.14, the total, by the number of students, 14:

84.14/14 = 6.01

He spent 6.01 on each student and has 25 for each student, so we can subtract that:

25 - 6.01 = 18.99

The length of the diagonal across the field is 212.132 feet.

A rectangle whose all sides are equal is called a square.

A square is always a rectangle, parallelogram, and a quadrilateral but its reverse statement may or may not be true.(ie it is not always necessary that a rectangle is a square or a parallelogram is a square).

Given that a square field has an area of 22,500 square feet. Now, the length of the side of the square field can be written as,

Area of the square field = (Length of square field)²

22,500 square feet = (Length of square field)²

Length of square field = √(22,500 sq. feet)

Length of square field = 150 feet

Now, the length of the diagonal of the field can be written as,

(Length of the diagonal)² = 2(Length of the side of square field)²

(Length of the diagonal)² = 2(150²)

(Length of the diagonal)² = 45,000 sq. feet

(Length of the diagonal) = 212.132 feet

Hence, the length of the diagonal across the field is 212.132 feet.

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Answer:

267/5 ( or ) 53.2

Step-by-step explanation:

Note : -

□ means 90°

2x - 42 + 3x + 45 + 90 = 360

2x + 3x + 45 - 42 + 90 = 360

5x + 3 + 90 = 360

5x + 93 = 360

5x = 360 - 93

5x = 267

x = 267/5 ( in fraction )

    ( or )

x = 53.2° ( in decimal )