How would you describe the red paths pictured below? ( The picture above)


A. Perpendicular

B. None are correct

C. Parallel

D. Intersecting

​

The equation that could John solve to find w, the greatest width in centimeters he can use for the mosaic is option B: w(w + 2) = 48.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

The mosaic to be formed is rectangular in shape.

Area of a rectangle = length x width

The length is longer than the width by 2,

So, length = w+2

Area of a rectangle = (w+2) x w

The correct equation is B: w(w + 2) = 48

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Answer: B

Step-by-step explanation:

The intersecting secant theorem states the relationship between the two intersecting secants of the same circle. The given problems can be solved using the intersecting secant theorem.

When two line secants of a circle intersect each other outside the circle, the circle divides the secants into two segments such that the product of the outside segment and the length of the secant are equal to the product of the outside segment other secant and its length.

a(a+b)=c(c+d)

1.)

6(x+6) = 5(5+x+3)

6x + 36 = 25 + 5x + 15

x = 4

2.)

4(2x+4)=5(5+x)

8x + 16 = 25 + 5x

3x = 9

x = 3

3.)

8x(6x+8x) = 7(9+7)

8x(14x) = 112

112x² = 112

x = 1

4.)

(x+3)² = 16(x-3)

x² + 9 + 6x = 16x - 48

x² - 10x - 57 = 0

x = 14.0554

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Answer:

339

Step-by-step explanation:

Exponential Function

General form of an exponential function: [tex]y=ab^x[/tex]

where:

If b > 1 then it is an increasing function

If 0 < b < 1 then it is a decreasing function

Given information:

Therefore:  [tex]y=240b^x[/tex]

To find an expression for the population after 1 hour, substitute x = 1 into the found equation:

[tex]\implies y=240b^1[/tex]

[tex]\implies y=240b[/tex]

We are told that the population after 9 hours is double the population after 1 hour.  Therefore, make y equal to twice the found expression for the population after 1 hour, let x = 9, then solve for b:

[tex]\implies 2(240b)=240b^9[/tex]

[tex]\implies 480b=240b^9[/tex]

[tex]\implies 480=240b^8[/tex]

[tex]\implies 2=b^8[/tex]

[tex]\implies b=\sqrt[8]{2}[/tex]

[tex]\implies b=2^{\frac{1}{8}}[/tex]

Therefore, the final exponential equation modelling the given scenario is:

[tex]\implies y=240(2^{\frac{1}{8}})^x[/tex]

[tex]\implies y=240(2)^{\frac{1}{8}x}[/tex]

To find how many bacteria there will be after 4 hours, substitute x = 4 into the found equation:

[tex]\implies y=240(2)^{\frac{1}{8}(4)}[/tex]

[tex]\implies y=240(2)^{\frac{1}{2}}[/tex]

[tex]\implies y=339 \:\: \sf (nearest\:whole\:number)[/tex]

Therefore, there will be 339 bacteria (rounded to the nearest whole number) after 4 hours.

The y-intercept of the line is (0 -6). The given function has no vertical and horizontal asymptotes

A linear equation is an equation that has a leading degree of 1. Given the equation

g(x) = 4x - 6

The y-intercept occurs at a point where x = 0

g(0) = 4(0) - 6

g(0) = -6

Hence the y-intercept of the line is (0 -6)

The given function has no vertical and horizontal asymptotes

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Step-by-step explanation:

[-5, 4] because it is an empty circle, meaning less than

Answer:

2, 7.5

Step-by-step explanation:

2(2x - 1) + 7 < 13

4x - 2 + 7 < 1

4x + 5 < 13

4x < 8

x < 2

-2x + 5 ≤ -10

-2x ≤ -10 - 5

-2x ≤ -15

x ≤ -15 / -2

x ≤ 7.5

The correct option regarding the inverse function is given by:

B.They are reflections of each other.

The inverse function is the reflection of the original function over the line y = x, that is, they are reflections of each other, hence option B is correct.

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Answer:

D

Step-by-step explanation:

using the rule of logarithms

log x - log y ⇔ log ( [tex]\frac{x}{y}[/tex] )

then

[tex]log_{b}[/tex] ( [tex]\frac{a}{d}[/tex] ) = [tex]log_{b}[/tex] a - [tex]log_{b}[/tex] d

The solution of the equation 4x = 20, x – 11 = 9, 5x + 6x = 22, and 5(x – 2) = 30 will be 5, 20, 2, and 8.

The solution of the equation means the value of the unknown or variable.

The equations are given below.

4x = 20

 x = 5

x – 11 = 9

      x = 20

5x + 6x = 22

       11x = 22

         x = 2

5(x – 2) = 30

   x – 2 = 6

         x = 8

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The correct answer is option C which is Gas station A is selling gasoline at a lower rate its price is $3.05 per gallon.

Expression in maths is defined as the collection of numbers, variables, and functions using signs like addition, subtraction, multiplication and division.

Here we have two pieces of information

Gas station A:-

3 gallons for $9.15

1 gallons for  $9.15 / 3 = $ 3.05

Gas station B:-

P = 3.08g

It means that station B is selling the gasoline at a higher price.

Therefore the correct answer is option C which is Gas station A is selling gasoline at a lower rate its price is $3.05 per gallon.

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Answer:

x < 9

Step-by-step explanation:

Our original inequality:

[tex]9(4x-8) < 4(6x+9)[/tex]

Firstly, let's expand the brackets on both sides:

[tex]36x - 72 < 24x + 36[/tex]

Now, we add the 72 over to isolate the [tex]x[/tex]:

[tex]36x < 24x + 108[/tex]

Next, we take away the [tex]24x[/tex] to isolate the [tex]x[/tex]:

[tex]12x < 108[/tex]

Finally, we divide both sides by 12 to convert the [tex]12x[/tex] to [tex]x[/tex]:

[tex]x < 9[/tex]

This means our final answer is [tex]x < 9[/tex].

Answer:

x= 6 , y = 3

Step-by-step explanation:

x + 5y = 21

i am using trail and error method and i got the answer easily

the logic behind this is simple

the first equation is x + 5y = 21 so we can say that y  will be 5 x 1 , 5 x 2 , 5 x  3 , 5 x 4

first i did 5 x 4 = 20

x + 5 x 4 = 21

x= 1 but the equation x + y = 1 + 4 = 5  which is not equal to 9

second i tried with 5 x 3 =15

and the equation will be

x + 5 x 3 = 21

6 + 15 = 21

this time the second equation became true

x + y = 9

6 + 3 = 9

the no of pounds of salsa = 6

no of pounds of tomato = 3

Answer:

the height: h=2,25

Step-by-step explanation:

volume of rectangular box = wide*long*the height

----> the height = volume of rectangular box / ( wide*long) = 2,25

give me 5 stars and hearts^^

Answer:

a=75

b=70

c=110

d=105

e=110

f=105

Step-by-step explanation:

Using proportions, it is found that the value of the total sum that was shared was of $45.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

Considering the rates, Anne's and Kerisha's proportions, out of the total value N, are given by:

The difference is of $15, hence:

[tex]A - K = 15[/tex]

[tex]\frac{7N}{12} - \frac{3N}{12} = 15[/tex]

[tex]\frac{4N}{12} = 15[/tex]

[tex]\frac{N}{3} = 15[/tex]

N = 15 x 3 = 45

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[tex] - 5(b + 1) = 8 \\ - 5b - 5 = 8 \\ - 5b = 8 + 5 \\ - 5b = 13 \\ b = \frac{ - 13}{5} [/tex]

PLEASE GIVE BRAINLIEST

\\\///\\\///\\\///\\\///\\\///\\\///\\///\\\///\\\///\\\///\\\///\\\//\\//\\//\\//\\\///\\//\\\///\\\///\\\///\

[tex]\Rsh[/tex]Let's solve this! We can do this! [tex]\Lsh[/tex]

>>> First, let's multiply -5 by b and 1. Then we obtain

[tex]\pmb{-5b-5=8}[/tex].

>>> Now we add 5 to both sides.

[tex]\pmb{-5b=13}[/tex]

>>> And then, divide both sides by -5.

[tex]\pmb{b=-\dfrac{13}{5}}[/tex]

>>> That is the value of b.

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Hope the answer - and explanation - assisted you!

Happy studies! :)

The point on the graph f(x) = 3.4ˣ is (0, 1)

None of the given options is correct.

A function is a relationship between a number of inputs and outputs. A function is an association of inputs where each input is coupled with exactly one output. There is a range, co-domain, and domain for every function.

To determine which point is on the graph of f(x) = 3.4ˣ, we need to substitute the given x-coordinate into the function and see if we get the given y-coordinate.

Let's try each option:

A. (1, 12): f(1) = 3.4¹ = 3.4, so this point is not on the graph of f(x) = 3.4ˣ.

B. (0, 12): f(0) = 3.4⁰ = 1, so this point is not on the graph of f(x) = 3.4ˣ.

C. (12, 1): f(12) = 3.4¹² ≈ 108089.7, so this point is not on the graph of f(x) = 3.4ˣ.

D. (0, 1): f(0) = 3.4^0 = 1, so this point is on the graph of f(x) = 3.4ˣ.

Therefore, the point (0, 1) is on the graph of f(x) = 3.4ˣ. The answer is option D.

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#A

New side

Area

#2

Now it has turned rectangle

Sides

x+12 and x-7

Area

Answer:

A)  (x + 8)² cm² = (x² + 16x + 64)  cm²

B)  (x + 12)(x + 7) cm² = (x² + 19x + 84) cm²

Step-by-step explanation:

Formula

Area of a square = s²  (where s is the side length)

Given side length of square field:

⇒ Area of field = x² cm²

Part A

If the side length of the square field is increased by 8 cm then:

⇒ new side length = (x + 8) cm

Substitute the new side length into the formula for the area of a square:

⇒ Area of field = (x + 8)² cm²

Expand and simplify:

⇒ Area = (x + 8)²

⇒ Area = (x + 8)(x + 8)

⇒ Area = x(x + 8) + 8(x + 8)

⇒ Area = x² + 8x + 8x + 64

⇒ Area = (x² + 16x + 64)  cm²

Part B

If the side length of the square field is increased by 12 cm and the width is decreased by 7 cm then:

⇒ new side length a = (x + 12) cm

⇒ new side length b = (x - 7) cm

Substitute the side lengths into the formula for area of a square:

⇒ Area of a square = s × s

⇒ Area of a square = a × b

⇒ Area of the field = (x + 12)(x + 7) cm²

Expand and simplify:

⇒ Area = (x + 12)(x + 7)

⇒ Area = x(x + 7) + 12(x + 7)

⇒ Area = x² + 7x + 12x + 84

⇒ Area = (x² + 19x + 84) cm²

The decimal: 0.4545...

Can be written in fraction form as 45/99.

Here we have the number:

N = 0.4545...

Notice that the repeating digits are two, 4 and 5.

Then we can multiply our number by 100 (same number of zeros as repeating digits) so we get:

100*0.4545... = 45.4545...

Now if we subtract the original number, we get:

45.4545... - 0.4545... = 45

This means that:

(100 - 1)*0.4545... = 99*0.4545... = 45

Then we can multiply and divide our number by 99, so we get:

[tex]0.4545... = 0.4545...\frac{99}{99} = \frac{45}{99}[/tex]

So the fraction is 45/99

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The slope of CD, which is parallel to AB must be: A. -5.

If two line segments are parallel to each other, their slope value (m) would be equal to each other.

Side AB and CD in the parallelogram are parallel segments, therefore, their slope (m) would be the same.

Slope (m) of AB = -5, therefore, the slope of CD must be: A. -5.

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Answer:

[tex]\boxed {Vertex = (-7, 2)}\\\boxed {Focus = (0, \frac{49}{8})}[/tex]

Step-by-step explanation:

Completing the square :

x² + 14x - 8y + 65 = 0

x² + 14x + 49 - 49 - 8y + 65 = 0

(x + 7)² - 8y + 16

(x + 7)² = 8y - 16

⇒ x = -7, y = 2 (Vertex)

Finding a :

⇒ x² = 4ay

⇒ (-7)² = 4(2)a

⇒ a = 49/8

Finding the focus :

⇒ (0, a)

⇒ (0, 49/8) (Focus)

The measure of the largest angle of the triangular patch of grass is 81 degrees

In order to determine the measure of the largest angle, we will use the expression below;

[tex]\frac{60}{sin26^0} =\frac{135}{sinx^0}[/tex]

Cross multiply

135sin26 = 60sinx

sinx = 135sin26/60

sinx = 59.18/60
sinx = 0.986

x = 80.5 degrees

Hence the measure of the largest angle of the triangular patch of grass is 81 degrees

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The equation of the line that passes through the points (8,-1) and (2,-5) is 2x - 3y = 19.

The given coordinate are (8, -1) and (2, -5).

In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line.

The slope of the equation is [tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex].

The standard form of an equation is Ax + By = C.

The given the point-slope form is [tex]y+1=\frac{2}{3} (x-8)[/tex].

Multiply each term by 3 of the equation.

[tex](y+1) \times3=\frac{2}{3} (x-8) \times3[/tex]

⇒3y + 3 = 2x - 16

Subtract 2x from both sides of a equation.

That is, -2x + 3y + 3 = - 16

Subtract 3 from both sides of a equation.

That is, -2x + 3y = - 19

Multiply each term by - 1 from both sides of an equation.

That is, 2x - 3y = 19

Therefore, the equation of the line that passes through the points (8,-1) and (2,-5) is 2x - 3y = 19.

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The amount of zippy's gross profit (otherwise know as gross margin) is: $25,337.

Sales revenue $43,189.84

(7,796 units × $5.54)

Less Cost of goods sold $17,852.84

[($22,900/10,000)×7,796]

Gross profit $25,337

( $43,189.84-$17,852.84)

Therefore the amount of zippy's gross profit (otherwise know as gross margin) is: $25,337.

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The average speed of the Australian team's laser boat in the San Francisco final was 68.81 km/h.

The laser boat is a type of boat that uses the wind to move on the water. This type of boat is used in the SailGP Championship.

In the phase of San Francisco, the United States the winner was the team of Australia that had an average speed of 68.81 km/h and a maximum of more than 90 km/h.

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Answer:

[tex](0, -\frac{15}{2} )[/tex]

Step-by-step explanation:

When a straight line crosses the y-axis, the point that touches it is called the y-intercept. We can find the y-intercept by plugging in zero as the value for 'x', as any x value on the y-axis is zero. So plugging in x = 0 into the equation '3x - 2y = 15', we get -2y = 15, so y = -15/2. The point would be [tex](0, -\frac{15}{2} )[/tex], as x = 0 when y = -15/2.

Answer:

Step-by-step explanation:

Did you mean.

[tex] = \cot( \theta) . \sin(2 \theta) [/tex]

[tex] = \frac{ \cos( \theta) }{ \sin( \theta) } .(2 \sin( \theta) \cos( \theta) )[/tex]

[tex] = \frac{2 \sin( \theta) \cos {}^{2} ( \theta) }{ \sin( \theta) } [/tex]

[tex] = 2 \cos {}^{2} ( \theta) [/tex]

[tex] = 2.(1 - \sin {}^{2} ( \theta) )[/tex]

[tex] = 2 - 2 \sin {}^{2} ( \theta) [/tex]

No option Solution.