Solve question in image (yr 8 math, 40 pt)

While E will increase, C and D won't change.

A coordinate system is a method for determining how to position points or other geometrical objects on a manifold, such as Euclidean space, uniquely using one or more numbers, or coordinates.

Due to the fact that the circle's equation is,

Nevertheless, we are aware of the circle's equation.

                           [tex]x^{2}+y^{2}+C x+D y+E=0[/tex]

(By figuring out the circle's equation[tex](x-h)^{2}+(y-k)^{2}=r^{2}[/tex], where r is the radius and (h,k) is the center)

                         [tex]x^{2}+y^{2}+2 h x+2 k y+\left(h^{2}+k^{2}-r^{2}\right)=0[/tex]

The following equation is compared to the generic equation above.

Our results are C = 2h, D = 2k, and E [tex]=\left(h^{2}+k^{2}-r^{2}\right)[/tex]

As a result, C will be unchanged if r lowers ( because C is free from r)

D won't be effected ( because D is also free from r)

E will, however, rise if r falls.

E[tex]=\left(h^{2}+k^{2}-r^{2}\right)[/tex]

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Answer:

x = 11

Step-by-step explanation:

A segment parallel to a side of a triangle cuts off proportional segments on the sides.

48/6 = (3x + 7)/5

8 = (3x + 7)/5

3x + 7 = 40

3x = 33

x = 11

If joseph sells his home,  profit will he make = (a)  $79720

What is profit and its example?

Profit earned on the house if he sells = $79720

Amount paid by Joseph for his home = $105000

His house has increased its property value by 2.0% every year

So, Property cost after 20 years :

[tex]Cost = 105000 * (1.02)^{20}[/tex]

Cost = 105000 × 1.4859

Cost = 156020

Also, Due to renovations and improvements to the house, the property cost is increased by $28700

So, Total cost of the house after 20 years = 156020 + 28700

                                                                     = $184720

So, Profit earned on the house if he sells = 184720 - 105000

                                                                      = $79720

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Answer:a)  $79720

Step-by-step explanation:edge

Answer:

  BD = √97 cm ≈ 9.849 cm

Step-by-step explanation:

Diagonal BD of rectangle ABCD is the hypotenuse of right triangle ABD. Opposite sides of the rectangle are the same length, so we have ...

  AB = 4 cm

  AD = 9 cm

The sides are related to the diagonals by the Pythagorean theorem.

The Pythagorean theorem tells you the relation between sides and hypotenuse of a right triangle:

  AB² +AD² = BD²

  4² +9² = BD² = 16 +81 . . . . . evaluating the squares

  BD = √97 . . . . . take the square root

The length of BD is √97 cm, about 9.849 cm.

correct answer is 28.

If the mean of four numbers is 25 and three numbers are 36, 12 and 24 then fourth number is 28.

given terms are:

first number =36

second number=12

third number=24

fourth number=?

let us assume the fourth number be x.

we know the formula to find mean is:

Mean=addition of given terms / total number of terms

According to given statement, we put the values in above equation and we get,

25=(36+12+24+x) / 4

By rearranging, we get

36+12+24+x=100

72+x=100

x=100-72

x=28

so, the fourth number is 28.

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the train travels at 45 meters per each second

this question can be rewritten into the equation d = 45t, where d represents the distance traveled and t represents the time elapsed.

we are given two seperate times, so we can replace the variable t with each respective time. this leaves us with only one missing variable, so we can successfully isolate to find the other.

for i), we substitute t for 30 seconds, shown as follows

d = 45t

d = 45(30)

d = 1350m

for ii), we know that there are 60 seconds in every minute, so in multiplying 60 seconds by two we get the total amount of seconds in two minutes, which is 120.

we can now use 120 to substitute t in our equation

d = 45t

d = 45(120)

d = 5400m

hope this helps!!

Answer:

i) 1350 m

ii) 5400 m

Step-by-step explanation:

To calculate the distance traveled by the train, we can use the formula:

[tex]\large\boxed{\sf Distance=Speed \times Time}[/tex]

[tex]\hrulefill[/tex]

Given values:

Substitute the given values into the formula for distance:

[tex]\begin{aligned}\sf Distance&= \sf 45\; m/s \times 30\;s\\& = \sf 1350\:m\end{aligned}[/tex]

Therefore, the train travelled a distance of 1350 meters in 30 seconds.

[tex]\hrulefill[/tex]

Given values:

As the time is given in a different unit of time than the speed, we must first convert the time into seconds. As 1 minute = 60 seconds, then:

[tex]\sf 2\; minutes = 60 \;s \times 2 = 120 \;s[/tex]

Substitute the given values into the formula for distance:

[tex]\begin{aligned}\sf Distance&= \sf 45\; m/s \times 120\;s\\& = \sf 5400\:m\end{aligned}[/tex]

Therefore, the train travelled a distance of 5400 meters in 2 minutes.

Answer: 16.63 cm

Step-by-step explanation:

The length of the arc = [tex]\frac{360-130}{360}[/tex] * 2[tex]\pi[/tex]y = [tex]\frac{23}{18}[/tex][tex]\pi[/tex]y

The perimeter = [tex]\frac{23}{18}[/tex][tex]\pi[/tex]y + y + y = y([tex]\frac{23}{18}[/tex][tex]\pi[/tex] + 1 + 1) = 6.01y = 1 m

y = 16.63 cm

Answer:

  t = 7

Step-by-step explanation:

You can use your knowledge of powers of 2, or you can use logarithms to find the value of t.

  2^1 = 2

  2^2 = 4

  2^4 = 16

  128 = 16×4×2 = (2^4)(2^2)(2^1) = 2^(4+2+1) = 2^7

Now, the equation is ...

  f(t) = 2^t = 2^7

Equating exponents, we have ...

  t = 7

Taking the log of both sides of the equation ...

  2^t = 128

we have ...

  t×log(2) = log(128)

  t = log(128)/log(2) = 7 . . . . . divide by the coefficient of t

The value of t is 7.

__

Additional comment

The relevant rule of exponents is ...

  (a^b)(a^c) = a^(b+c)

The relevant rule of logarithms is ...

  log(a^b) = b×log(a)

The volume of the triangular prism as described is; 15 cubic foot.

A triangular pyramid simply refers to any geometric solid with a triangular base, and all three lateral faces are also triangles with a common vertex

It follows from the formula for calculating the volume of a triangular prism that;

Volume = (1/3) × base area × height.

Consequently,

volume of the prism is; = (1/3) ×9 × 5

Volume = 15 cubic foot

Therefore, volume of the triangular prism as described is; 15 cubic foot.

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Answer:

6x + 4y = 16

Step-by-step explanation:

2(3x + 2y = 8)

2(3x + 2y) = 2(8)

6x + 4y = 16

Answer:

6x+4y=16

Step-by-step explanation:

2 (3x+2y=8)

2×3x+2×2y=2×8

=6x+4y=16 ans.

Area of the base = 60 inches²

Height of the prism = 4 inches

perimeter of the base = 34 inches

Surface area of the rectangular prism =  256 inches²

The surface area of a rectangular prism can be calculated as follows;

area of the base = B = 12 × 5 = 60 inches²

Height of the prism = 4 inches

Perimeter of the base is the sum of the whole side of the base of the rectangular prism.

Therefore,

perimeter of the base = 12 + 12 + 5 + 5 = 34 inches

Surface area of the rectangular prism = 2B + ph

where

Therefore,

Surface area of the rectangular prism = 2(60) + 34(4)

Surface area of the rectangular prism = 120 + 136

Surface area of the rectangular prism =  256 inches²

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Using the midpoint formula, the coordinates of the other endpoint, V is: B. (10, -25.8).

To find the coordinates of the midpoint of a segment, the midpoint formula is used, which is expressed as: M(x2 + x1/2, y2 + y1/2).

Given one endpoint of UV as, U(21.6, -8.2), and a midpoint of M(15.8, -17), let:

U(21.6, -8.2) = (x1, y1)

V(x, y) = (x2, y2)

Plug in the values into M(x2 + x1/2, y2 + y1/2):

M(15.8, -17) = (x2 + 21.6/2, y2 + (-8.2)/2)

Solve for x2

15.8 = (x2 + 21.6)/2

Multiply both sides by 2

2(15.8)= (x2 + 21.6)/2 × 2

31.6 = x2 + 21.6

Subtract both sides by 21.6

31.6 - 21.6 = x2 + 21.6 - 21.6

10 = x2

x2 = 10

Solve for y2:

-17 = (y2 + (-8.2))/2

Multiply both sides by 2

2(-17) = (y2 + (-8.2))/2 × 2

-34 = y2 + (-8.2)

-34 = y2 - 8.2

Add 8.2 to both sides

-34 + 8.2 = y2 - 8.2 + 8.2

-25.8 = y2

y2 = -25.8

The coordinates of the other endpoint, V is: B. (10, -25.8).

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Answer: B

Step-by-step explanation: edge2023

The length of the diameter formed is in the image given is: 10 ft.

The diameter of a circle is the line segment that divides the circle into two equal halves. The diameter divides the circle into semicircles. Also, the diameter of a circle is twice the length of the radius of a circle.

If we know the length of the radius, we can determine the length of the diameter of a circle by multiplying the radius by two. On the other hand, if we know the length of the diameter, to find the length of the radius, divide the diameter by 2.

The image of the circle showing the shelf and the brace line, which is the diameter are shown below.

To find the diameter of the window, add the length of the horizontal shelf and length of the brace. Thus:

Length of the diameter of the window = 8 + 2

Length of the diameter of the window = 10 ft

Thus, the length of the diameter formed is: 10 ft.

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Answer:

10 ft

Step-by-step explanation:

Answer: x =   -1

Step-by-step explanation:

To remove the radical on the left side of the equation, square both sides of the equation.

√1−3x2=(x+3)2

Simplify each side of the equation.

1−3x=x2+6x+9

Solve for x

x=−1−8

Exclude the solutions that do not make true

√1−3x=x+3

x=−1

The equation be x/100 [tex]*[/tex] 28,600 = 33,500, then we get 17%.

Trevor's total employee benefits exists 17.1% of his gross pay.

Therefore, the correct answer is option d. 17.1.

If you would like to know Trevor's total employee advantages, you can estimate this utilizing the subsequent steps:

To find the percentage of the total employee benefits x% of $28,600 exists $33,500.

To estimate the value of x, bring the variable to the left side and bring all the remaining variables to the right side. Simplify the values to estimate the result.

x/100 [tex]*[/tex] 28,600 = 33,500

x = 33,500 [tex]*[/tex] 100 / 28,600

x = 117.13% = 117%

117% - 100% = 17%

x = 17%

The correct result would be 17%.

Trevor's total employee benefits exists 17.1% of his gross pay.

Therefore, the correct answer is option d. 17.1.

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Answer:

It is D

Step-by-step explanation:

The percentage form of given fraction is 60% and the hundredths form is 0.60

According to the statement

we have given that the a fraction and we have to find the percentage of that fraction and write in the form hundredths.

So, For this purpose,

The given fraction is 12/20.

Then the definition of the percentage is that

The Percentage, a relative value indicating hundredth parts of any quantity.

so, the percentage of given fraction is :

Percentage fraction = 12/20 * 100

After solving it, The percentage fraction will become:

Percentage fraction = 60%

and Now convert into the hundredths form then

In the hundredths form it will become

from 60% to 0.60.

So, The percentage form of given fraction is 60% and the hundredths form is 0.60

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Answer:

8 pi yd.

Step-by-step explanation:

The circumference of a circle can be calculated as follows:

c = [tex]2 \cdot \pi \cdot r[/tex]

Where r is the radius of the circumference.

So in our case:

c = [tex]2 \cdot \pi \cdot 4yd = 8\cdot \pi[/tex] yd.

The circumference of the circle, in the attached image is approximately 25.1 yards.

To find the circumference of a circle, you can use the formula:

Circumference = 2 * π * radius

where π = 3.14159.

Given the radius of the circle is 4 yards, the circumference can be calculated as follows:

Circumference = 2 * 3.14159 * 4 yards ≈ 25.13272 yards

Now, rounding to the nearest tenth, the circumference of the circle is approximately 25.1 yards.

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Answer:

28

Step-by-step explanation:

Tangent is a line that touches the circle at one point and is perpendicular to the radius. Circle A has radius AB and tangent CB, so AB is perpendicular to CB. Therefore triangle ABC is a right angle, with angle B measuring 90 degrees. Since interior angles of a triangle add up to 180 degrees, measure of angle A is 180 - 90 - 62 = 28 degrees.

Answer:7 21/100

Step-by-step explanation: We will covert 7.21 into a fraction. .21 = 21/100. Since 21 can only be divided by 3 and 7, the simplest form of 21/100 is 21/100. So, the mixed number is 7 and 21/100

Answer:

7 and 21/100

Step-by-step explanation:

Since .01 is 1/100, 7.21 will be 7 and 21/100. There is no way to further simplify this, therefore, it is our final answer. Hope this helps! :)

The exponential function represented on the graph is defined by the following rule:

[tex]y = 3 \times 2^x[/tex]

An exponential function is modeled by:

[tex]y = ab^x[/tex]

In which:

From the graph, we get that when x = 0, y = 3, hence the initial value is of a = 3. Then the temporary definition is:

[tex]y = 3b^x[/tex]

Also from the graph, when x = 1, y = 6, hence we can apply to the definition to find b.

[tex]6 = 3b^1[/tex]

3b = 6

b = 2.

Hence the function is:

[tex]y = 3 \times 2^x[/tex]

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Answer:

1) (3,1)

2) (4,1)

3) No solution

Step-by-step explanation:

The solution is point where the graphs cross.  It is a little hard to see the pictures, but I think that I have the right ordered pairs.  The ordered pairs are in the order (x,y).  The x tells you how far (in these cases), the point is right of the origin (0,0 the middle of the whole graph).  The y tells us (in these cases) how high the point is from the origin (0,0).

The last answer has no solution because the lines are parallel and they do not cross.

Answer:

D

Step-by-step explanation:

Pq=opp/hyp

(135+12)=180

There are 680 combinations of four teachers include Mrs. Vera(only)

The given parameters are

Teachers, n = 18

Selected teachers. r = 4

The selection must include Mrs. Vera.

So, the remaining parameters are:

Teachers, n = 17

Selected teachers. r = 3

The combination is then calculated as:

Ways = nCr

This gives

Ways = 17C3

Apply the combination formula

Ways = 17!/(14!3!)

Evaluate the expression

Ways = 680

Hence, there are 680 combinations of four teachers include Mrs. Vera(only)

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The area of the parallelogram is 55 square feet

From the figure, we have the following dimensions:

Height = 5 ft

Base = 11 ft

The area of the parallelogram is calculated as:

Area = Base * Height

This gives

Area = 5ft * 11ft

Evaluate the product

Area = 55 square feet

Hence, the area of the parallelogram is 55 square feet

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Answer:

( 5 , 5 )

Step-by-step explanation:

→ Add 2 the x coordinates together

- 4 + 14 = 10

→ Divide answer by 2

10 ÷ 2 = 5

→ Add the 2 y coordinates together

10 + 0 = 10

→ Divide answer by 2

10 ÷ 2 = 5

Answer:

(5, 5 )

Step-by-step explanation:

given points (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is

( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] )

here (x₁, y₁ ) = (- 4, 10 ) and (x₂, y₂ ) = (14, 0 ) , then

midpoint = ( [tex]\frac{-4+14}{2}[/tex] , [tex]\frac{10+0}{2}[/tex] ) = ( [tex]\frac{10}{2}[/tex] , [tex]\frac{10}{2}[/tex] ) = ( 5, 5 )

Considering the box-plots, the means for the data-sets are given as follows:

Each shows the number of times each measure appears.

Hence, the mean of data-set A is given as follows:

mA = (3 + 4 x 3 + 5 x 2 + 6 x 2 + 7 x 3 + 8)/(1 + 3 + 2 + 2 + 3 + 1) = 5.5.

For data-set B, the mean is:

mB = (2 x 4 + 2 x 5 + 2 x 6)/(2 + 2 + 2) = 5.

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