2. How much heat in kilojoules has to be removed from 225g of water to lower its temperature from 25.0oC to 10.0oC?

Using completing the square method (x + 8)2 = +1 is the intermediary step in the equation (x + a)2 = b after the square is complete.

Get the intermediate step:

Divide the equation by 3 into both sides:

Adding 1 on both sides to complete the square:

Therefore, (x + 8)2 = +1 is the intermediary step in the equation (x + a)2 = b after the square is complete.

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The equation is c = 31 + 0.13x and total cost on driving 180 miles is $54.4.

Firstly we will form the equation using one time charge and the product of number of miles and charge per mile. Then we will keep the value in equation to find the total cost.

Forming the equation -

c = 31 + 0.13x

Keep the value of x in formula for calculation of total cost.

c = 31 + 0.13×180

Performing multiplication on Right Hand Side of the equation

c = 31 + 23.4

Performing addition on Right Hand Side of the equation

c = $54.4

Thus, the equation for calculation of total cost is c = 31 + 0.13x and total cost is $54.4.

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The coat has a total cost of  $533.644

From the question, the given parameters are:

Cost of a coat = $74.95

Sales tax in the city = 612%

Using the sales tax, the total cost for the coat is calculated using

Total cost of coat = Cost of a coat + Cost of a coat * Sales tax in the city

Substitute the known values in the above equation

So, we have the following equation

Total cost of coat = 74.95 + 74.95 * 612%

Evaluate the products

Total cost of coat = 74.95 + 458.694

Evaluate the sum

Total cost of coat = 533.644

Hence, the total cost of the coat is $533.644

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The car was driven 105 miles.

What is rent?

An agreement where a fee is paid for the temporary use of a good, service, or property owned by another is known as renting, sometimes known as hiring, or letting.

In the given example the cost function is, c = 15 + 2m

Where, c is the total cost and m is the number of miles car driven.

The total cost was $225.

So, plug c = $225 in the above equation.

225 = 15 + 2m

210 = 2m

   m = 105

Therefore, the car was driven 105 miles.

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These are the solutions of all the questions

The coordinates of the point on the directed line segment are (-4, 4).

What is partitions of the segment?

Finding a position that is an equal distance from A and b equal distance from B is necessary for partitioning a line segment, AB, into a ratio of a/b.

Trying to find the coordinates of point that splits the line between (-7, -2) to (-2, 8) at a ratio of 3:2.

Since the ratio is 3:2 we are going o find the point that is 3/5 of the distance from (-7, -2) to (-2, 8).

For the x coordinate, find the distance between x coordinates (-2-(-7)) = 5.

Take 3/5 of 5 equals to 3 and add that to the first x coordinate (-7) to get the x - coordinate of interest -4.

For the y - coordinate, find the distance between y coordinates (8-(-2)) = 10.

Take 3/5 of 10 equals to 6 and add that to to the first y coordinate (-2) to get the y coordinate of interest 4.

The coordinates of the point on the directed line segment  from (-7, -2) to (-2, 8) that partitions the segment into a ratio of 3:2 are (-4, 4).

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The measure of ∠E will be equal to 38°.

Given,

m∠BFE = 118° and m∠C = 86°

And BF bisects ∠ABD

From the Property of Linear Pair,

∠AFB + ∠BFE = 180°

=> ∠AFB + 118° = 180°

=> ∠AFB = 62°

Now, we can see that ∠AFB and ∠FBD are equal because they are alternate angles.

And ∠FBD and ∠ABF are equal because BF bisects ∠ABD.

So, In ∆ABF,

∠AFB + ∠ABF + ∠BAF = 180° (because of the angle sum property of a triangle)

=>62° + 62° + ∠BAF = 180°

=>∠BAF = 180° - 124°

=> ∠BAF = 56°

Similarly, in ∆ABE,

∠A +∠C  +∠E = 180°

=> 56° + 86° + ∠E = 180°

=> ∠E = 38°

Therefore, m∠E = 38°.

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The transformation on a line such that a line is obtained which is pependicular to previous line is possible only when it is reflected through y = x axis. This can be understood as,

When line is reflected about x-axis, the x coordinate remain same where as y-coordinate changes in opposite sign with same magnitude. So reflection of line x = 3 about x axis remain same.

Simillarly reflection of line x = 3 about x = 1 remain same as x = 3.

The reflection of line x = 3 about y-axis results n a parallel line passing through x = -3.

So answer is reflection across y = x.

Answer:

B) 50

Step-by-step explanation:

its in tens place

hope this helps you!!!

Answer:

8500/10=850

value of digit 5=50

⇒I will use the trig ratios to find the value x.

[tex]\frac{sin(x)}{11cm}=\frac{sin( 38)}{8} \\[/tex]

⇒Moving on solving I will use the cross multiplication

[tex]8sin(x)=11sin(38)\\sin(x)=\frac{11sin(38)}{8} \\x=sin^{-1} (\frac{11sin(38)}{8} )\\x=57,8[/tex]

∴ x=57,8°

Goodluck!!

From the given diagram, let's find the length of the park's boundary.

We can see the side of the park's boundary is a circular arc and the top and bottom are the bases of triangles.

To find the length of the circular sides, apply the length of arc formula:

Where:

Θ = 120 degrees

π = 3.14

radius, r = 50 yards

Hence, we have:

This means the length of one circular side of the boundary is 104.67 yards.

We have two circular sides of the boundary.

The top and bottom sides form equilateral traingles.

Hence, the length of the top and bottom sides are 50 yards each.

To find the total length of the boundary, we have:

Total length = 104.67 + 104.67 + 50 + 50 = 309.34 yards

Rounding off to the nearest yard, the length of the park's boundary is:

309 yards

ANSWER:

D. 309 yards

Answer:

18*19 BECAUSE 19 is a prime number and g has to be 1 since if g was anything else like 2 it wouldn't be the same for gh

The solution to the inequality given as 3 - x/2x + 1 ≥ 2 is (-oo, -1/2) u [1/5, oo]

The inequality expression is given as

3 - x/2x + 1 ≥ 2

Cross multiply in the above inequality

So, we have

3 - x ≥ 2(2x + 1)

Open the brackets in the inequality

So, we have

3 - x ≥ 4x + 2

Collect the like terms

4x + x ≤ 3 - 2

Evaluate the like terms

5x ≤ 1

Divide by 5

x ≤ 1/5

Because of the denominator 2x + 1, we have

x > -1/2

This means that the solution is (-oo, -1/2) u [1/5, oo]

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Answer: You could assume that X=8 and y=0

Step-by-step explanation:

Answer:

Solutions below.

Step-by-step explanation:

This Question involves the concept of intercepts of a graph.

Intercepts of a graph are namely the x-intercept and y-intercept.

x-intercept is when y = 0. Example: (3,0)

y-intercept is when x = 0. Example: (0,9)

We are given the equation: x + 4y = 8

To find x-intercept, we can substitute y = 0 into the equation to obtain the value of x.

x + 4(0) = 8

x + 0 = 8

x = 8

Coordinates: (8, 0)

To fins y-intercept, we can substitute x = 0 into the equation to obtain the value of y.

0 + 4y = 8

4y = 8

y = 8 ÷ 4

y = 2

Coordinates: (0, 2)

We were told that Ben earned 625.5 points out of 700 on an essay. Expressing his score in the essay in terms of percentage, it becomes

625.5/700 x 100 = 89.29%

Also, he scored 65 out of 70 on an assignment. Expressing his score in the assignment in terms of percentage, it becomes

65/70 x 100 = 92.86%

We would find the average between the two percentages

Average = sum of percentages/number of percentages

Average = (89.29 + 92.86)/2

Average = 91.075

Average is approximately 91%

Since in order to earn an A in the class, he needed to average a 91 on these two

assignments and he got an average of 91%, then we can conclude that he got an A

Solution:

The spinner has a total of 8 sections.

There are two green sections and 4 four vowel sections where one of the vowels is also green.

Then, the probability of landing on green or a vowel is;

Answer:

In this photo.

Put a heart and 5 mark for the answer.

Thanks ヽ(>∀<☆)ノ: o(≧▽≦)o

ヽ(・∀・)ﾉ: (´｡• ω •｡)

(o･ω･o): (＠＾◡＾)

(´• ω •: (＾▽＾)

(a) Complex zeros of a polynomial come in pairs.

If a + bi is a zero of a polynomial then its conjugate a - bi is also a zero of the polynomial.

The given complex zeros of R(x) are 1 + 3i and -2i.

1 - 3i is the conjugate of 1 + 3i.

Hence, another zero of R(x) is 1 - 3i

b)

Since the polynomial R(x) is of order 13 then R(x) must have 13 zeros.

The given complex zeros of R(x) are 1 + 3i and -2i. We also know that the conjugates of 1 + 3i and -2i are zeros of R(x). Hence, R(x) has at least 4 complex roots

Hence, the maximum number of real zeros of R(x) is (13 -4).

The maximum number of real zeros of R(x) is 9

c) Let the maximum number of nonreal zeros (complex roots) be n

Complex roots come in pairs. Therefore, n must be even.

Hence, n ≤ 13 - 1 = 12

n ≤ 10

We have been given a real zero of R(x), 3 ( With the multiplicity of 4).

12 - 4 = 8

Therefore,

n ≤ 8.

Hence the maximum number of nonreal zeros of R(x) is 8

Answer:

Concept:

Mean is just another name for average. To find the mean of a data set, add all the values together and divide by the number of values in the set. The result is your mean!

The values are given below as

The image below shows how to calculate the mean

By substituting values, we will have

Hence,

The mean = 10

To calculate the variance, we will use the formula below

Hence

The variance = 21

To calculate the standard deviation,

Hence,

The standard deviation is = 4.58

Solution:

Remember the following formula :

P(AUB) = P(A)+P(B)-P(AnB)

According to the data of the problem and applying the previous equation, we obtain the following equality:

This is equivalent to:

solving for P(A n B), we get:

so that, we can conclude that the correct answer is:

Answer:

8/15(-2/3)

we simply multiply them

-8*2/15*3

as we know that+*-=-

-16/30

so simply divided by 2 because it whole decide them 16/2and30/2

-8/15

The given identity sin(x+ y) - sin (x- y) = 2 cos x sin y  has been verified

The identity is

sin(x+ y) - sin (x- y) = 2 cos x sin y

Here we have to use the trigonometric function

Consider the right hand side of the equation

We know

sin (x+ y) = sin x cos y + cos x sin y

sin (x-y) = sin x cos y - cos x sin y

Then

sin(x+ y) - sin (x- y) = sin x cos y + cos x sin y - (sin x cos y - cos x sin y)

= sin x cos y + cos x sin y - sin x cos y + cos x sin y

Eliminate the terms

= cos x sin y + cos x sin y

= 2 cos x sin y

Hence, the given identity sin(x+ y) - sin (x- y) = 2 cos x sin y  has been verified

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The kite's height above the earth is 287 feet.

A right-angled triangle is formed by the length of the string, the height of the kite (h) above ground, and the perpendicular distance from the end of the kite string to the man.

The link between the lengths and angles of a right-angled triangle is demonstrated through trigonometry.

Using trigonometric ratios,

the height of the kite above the ground is

sin(55) = h ÷ 350

h = 287 ft

As a result, the kite's height above ground is 287 feet.

A trigonometric function is a real function in mathematics that relates the angle of a right triangle to the ratio of the lengths of the sides. They are frequently used in earth sciences such as navigation, structural mechanics, astrophysics, geography, and many other fields.

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g( x ) = 2x² + 12x + 22 is the standard form of the the function g( x ) = 2( x + 3 )² + 4.

Polynomials in standard forms are written in a way that arrange the terms in descending order.

Given the data in the question.

g( x ) = 2( x + 3 )² + 4

First, we expand; ( x + 3 )² → ( x + 3 )( x + 3 )

g( x ) = 2( ( x + 3 )( x + 3 ) ) + 4

Using FOIL Method

g( x ) = 2( x² + 3x + 3x + 9 ) + 4

g( x ) = 2( x² + 6x + 9 ) + 4

Apply distributive property

g( x ) = 2( x² + 6x + 9 ) + 4

g( x ) = ( 2x² + 12x + 18 ) + 4

Add 18 and 4

g( x ) = 2x² + 12x + 18 + 4

g( x ) = 2x² + 12x + 22

Therefore, the function in standard form is g( x ) = 2x² + 12x + 22

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Answer:

sss

Step-by-step explanation:

Answer:

[tex]x=\frac{vw}{k-y}[/tex]

Step-by-step explanation:

Answer:

2[tex]\sqrt{23}[/tex]

Step-by-step explanation:

The distance between the points (-4, -7) and (-8, -13) is 2√13 units as per the concept of distance between the two points.

To determine the distance between two points, we can use the distance formula, which is derived from the Pythagorean theorem. The formula is as follows:

[tex]Distance = \sqrt{((x2 - x1)^2 + (y2 - y1)^2)[/tex]

Given the two points (-4, -7) and (-8, -13), we can assign the coordinates as follows:

x1 = -4, y1 = -7 (coordinates of the first point)

x2 = -8, y2 = -13 (coordinates of the second point)

Now, we substitute these values into the distance formula:

[tex]Distance = \sqrt{(-8 - (-4))^2 + (-13 - (-7))^2)}\\\\= \sqrt{((-8 + 4)^2 + (-13 + 7)^2}\\= \sqrt{((-4)^2 + (-6)^2)}[/tex]

= √(16 + 36)

= √52

= 2√13

Therefore, the distance between the points (-4, -7) and (-8, -13) is 2√13 units.

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We were given that:

For P

Answer: 1 dollar per bottle

Step-by-step explanation:

       If they cost $20 and she bought 20 bottles, we can use division.

$20 / 20 bottles = 1 dollar per bottle