Finding Angle Measures When Parallel Lines Are Cut By a Transversal

The function which is representative of the transformation of the parent function f(x) = log4x by reflecting it over the x-axis, stretching it vertically by a factor of two, and shifting it up five units is g(x) = -2log4(x) + 5. Option C is correct.

The reflection over the x-axis is given by the transformation:

f₁(x) = - f(x)

Therefore, the first step we get is:

f₁(x) = - log(4x)

Stretching by a factor n along the y-axis is given by the transformation:

f₂(x) = n · f₁(x)

Therefore, we will get:

f₂(x) = -2 · log(4x)

Shifting a function up of a quantity n is given by:

f₃(x) = f₂(x) + n

Therefore, we will get:

f₃(x) = -2 · log(4x) + 5

So,

g(x) = -2 log4(x) + 5

Thus, the function which is representative of the transformation of the parent function f(x) = log4x by reflecting it over the x-axis, stretching it vertically by a factor of two, and shifting it up five units is g(x) = -2log4(x) + 5. Option C is correct.

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The solution to a system of linear equations is the ordered pair (or pairs) that satisfies all equations in the system.

What ordered pair is a solution to the system of linear equations?

An equation is said to linear when it is in ax+ by = c form where a , b and c are real numbers . System of linear equation consist of a set of two or more equation with same variables. such as ,

a₁ x + b₁ y = c₁

a₂ x + b₂ y = c₂

A solution to a linear system is an ordered pair (x ,y) that solves both the equations .

To check that an ordered pair is a solution ,we have to substitute the corresponding values of our variables (x ,y) into our equations and see if they satisfy both the equations.

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The probability of first tile is less than 15, is 70% and the second tile is even or greater than 25, is 60%.

In the given question we have to find the probability of first tile is less than 15 and the second tile is even or greater than 25.

Tiles numbered 1 through 20 are placed in a box.

Tiles numbered 11 through 30 are placed in a second box.

One tile is randomly drawn from each box.

Now finding the probability of first tile is less than 15.

Since in first box tile is numbered as 1 to 20.

So the outcomes of less than 15 = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14

So favourable outcome = 14

Total number of tile = 20

So the probability = 14/20 = 70%

Now finding the probability of second tile is even or greater than 25.

Since in second box tile is numbered as 11 to 30.

So the outcomes of even or greater than 25 = 12, 14, 16, 18, 20, 22, 24, 26, 27, 28, 29, 30

So favourable outcome = 12

Total number of tile = 20

So the probability = 12/20 = 60%

Hence, the probability of first tile is less than 15, is 70% and the second tile is even or greater than 25, is 60%.

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The right question

"Tiles numbered 1 through 20 are placed in a box. Tiles numbered 11 through 30 are placed in a second box. One tile is randomly drawn from each box. Find each probability. The first tile is less than 15 and the second tile is even or greater than 25."

The distance Manatee will swim in 5 hours is 25 miles.

Distance can be defined as the length between two points.

To calculate the distance manatee can swim in 16 hours, we use the equation below

Make y₂ the subject of the equation

Where:

Substitute these values into equation 2

Hence, manatee can swim a distance of 25 miles.

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Complete question: A manatee can swim an average of 10 miles every 2 hours how far can it swim in 5 hours. Assume the distance y in miles is proportional to the number of hours x the manatee swam.

The slope between points (17,8) and (17,24) is (B) undefined.

We know that the slope of a line passing through two points (a,b) and (c,d) is given by,

m = (d-b)/(c-a)

So here given points are (17,8) and (17,24)

Then, a=17, b=8, c=17, d=24

Now the slope between these two points is given by,

m = (24-8)/(17-17) = 16/0

So the slope value does not exist or infinity.

Hence the slope between the points (17,8) and (17,24) is Infinity or undefined.

Thus, the correct option is (B).

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Answer:

in the picture

Step-by-step explanation:

hope it helped

SSS should be used to show that the triangles are congruent.

What is the congruent triangle?

Congruent triangles are two triangles that are the same size and shape. Two congruent triangles remain congruent even if we flip, turn, or rotate one of them. Two triangles must have the same angles and, as a result, must be congruent if their sides are the same.

From the given images of the triangles, it is clear that the the legs of the triangles are equal to each other.

If two legs of two triangles are equal, then the bases are equal to each other.

Thus to prove that the triangles are congruent to each other, apply SSS  postulate.

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The possible heights of the parallelogram are 2/3 and 3

So, the correct option is A and C

The given expression:

area of a parallelogram, A = 12 square unit

a side of the parallelogram,  = 18 units

another side of the parallelogram = 6 units

let,

the height of the parallelogram, h

The area of a parallelogram is given as;

Area = base (b) x height (h)

height (h) = Area/base(b)

From the given sides, the possible heights of the parallelogram are calculated as follows;

if the base, b = 18 units

height(h) =  12/18

              = 2/3

Also, if the base, b = 6 units

height(h) =  12/6

              = 2

Therefore, the possible heights of the parallelogram are 2/3 and 2

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Step-by-step explanation:

you take the specific number (males prefer cycling = 0.22) and the fitting total.

note there are 2 possibilities for that total :

all males

all people preferring cycling

the way it was phrased I would say the reference is all males.

the conditional relative frequency is then

0.22 / 0.54 = 0.407407407... ≈ 0.41

but if the meaning would be rather about how many of all people preferring cycling are male, then we would have

0.22 / 0.37 = 0.594594595... ≈ 0.59

both results are in your answer options.

I think the intended result is 0.41, because I understand the problem that way :

find the conditional relative frequency that a student athlete surveyed prefers cycling, given that the student is male.

the other should be phrased like

find the conditional relative frequency that a student athlete surveyed is male, given that the student prefers cycling.

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$6629\\ r=rate\to 10\%\to \frac{10}{100}\dotfill &0.1\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &4 \end{cases}[/tex]

[tex]A=6629\left(1+\frac{0.1}{1}\right)^{1\cdot 4} \implies A \approx 9705.52~\hfill \underset{earned~interest}{\stackrel{9705.52~~ - ~~6629}{\approx\text{\LARGE 3076.52 }}}[/tex]

The sine and cosine functions with the ordered pairs A(1,4) and B(0,-4) are given as follows:

Both the sine and the cosine functions have similar definitions, given as follows:

The meaning of the coefficients of the functions are presented as follows:

The functions vary between -4 and 4, hence the amplitude is given as follows:

a = 4.

This is the standard oscillation for a trigonometric function with amplitude 4, between -4 and 4, hence the vertical shift is of:

d = 0.

The difference between the x-coordinates of the maximum and the minimum value is half the period, hence the period is of 2 x 1 = 2, and the coefficient b is:

2π/b = 2

b = π.

The cosine function has no phase shift, it just is inverted, as it should assume a value of 4 at x = 0, hence the definition is:

g(x) = -4cos(πx).

The sine function has a phase shift, as it should assume a value of -4 at -π/2, not π/2, hence it is shifted shift π/2 units, hence the definition is:

f(x) = 4sin(π(x + π/2)).

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Answer:

D or C

Step-by-step explanation:

After differentiation of function with respect to y, the value of y'(1) is 0.225.

In the given question we have to find the value of derivative of y at 1.

The given function is [tex]\frac{x^2}{36}+\frac{y^2}{64}=1[/tex]

To find the derivative of y at 1 we have to firstly derivate the given function with respect to y.

Now writing the given function in the y form

[tex]\frac{x^2}{36}+\frac{y^2}{64}=1[/tex]

Subtract x^2/36 on both side, we get

[tex]\frac{y^2}{64}=1-\frac{x^2}{36}[/tex]

Multiply by 64 on both side, we get

[tex]y^2=64-64\times\frac{x^2}{36}[/tex]

[tex]y^2=64-\frac{16x^2}{9}[/tex]

Differentiating with respect to y on both side

[tex]2y\frac{dy}{dx}=0-\frac{16\times2x}{9}[/tex]

[tex]2y\frac{dy}{dx}=\frac{32x}{9}[/tex]

Simplifying

dy/dx = 16x/9y

We can write dy/dx as y' so

y' = 16x/9y

We have to find the value of y'(1).

Since the y is the function of x so we put x=1 and we know y(1)=7.89, so

y'(1) = 16*1/9*7.89

y'(1) = 16/71.01

y'(1) = 0.225

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Answer:

m∠X=75.75

Step-by-step explanation:

A triangle's angles combine to 180 degrees. Subtract 62.45+41.8 from 180.

The measure of the exterior angle of the triangle is given by ∠A = 104.25°

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

Given data ,

Let the triangle be represented as ΔXYZ

Let the measure of the exterior angle be m∠A

Now , the measures of the angles of the triangle are

The measure of angle ∠Y = 62.45°

The measure of angle ∠Z = 41.8°

The measure of angle ∠X = m∠X

Now , for a triangle , the sum of the interior angles = 180°

So ,

m∠X + m∠Y + m∠Z = 180°

Substituting the values in the equation , we get

m∠X + 62.45° + 41.8° = 180°

Subtracting 104.25 on both sides of the equation , we get

m∠X = 75.75°

Now , the measure of angle exterior to m∠X be ∠A = 180° - m∠X

The measure of m∠A = 180° - 75.75°

The measure of m∠A = 104.25°

Therefore , the measure of ∠A = 104.25°

Hence , the exterior angle of the triangle is ∠A = 104.25°

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Answer:

1 and 3

Step-by-step explanation:

where the dots on the graph are, you can read that in 5 minutes, 3 pages are edited. in 10 minutes, 6 pages.
so statement 1 is correct.
when every 10 minutes 6 pages are edited, divide both by 10 to get what is edited per minute. -> 6/10 pages are edited per minute.

[tex]\textit{area of a triangle}\\\\ A=\cfrac{1}{2}bh ~~ \begin{cases} b=\stackrel{width}{base}\\ h=height\\[-0.5em] \hrulefill\\ A=247\\ b=19 \end{cases}\implies 247=\cfrac{1}{2}(19)h \\\\\\ 494=19h\implies \cfrac{494}{19}=h\implies 26=h[/tex]

Answer:

Step-by-step explanation:

Between 9 and 10.

Why?

Because sq of 9 is 81 and sq of 10 is 100 which gives us the gesture that sq.rt of 84 is between 9&10.  

Hence, Two integers are 9 and 10.

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the length of each rope would be 4.9 inches.

One of the four fundamental operations in mathematics is division; the other three are addition, subtraction, and multiplication. Simply put, division is the process of dividing a large group into smaller ones so that each group has the same number of items. In mathematics, it is a procedure for equal sharing and grouping.

Callies has a rope of length = 14.7 inches,

she cut the rope into pieces = 3

let 'x' be the length of each rope,

if each piece is of the same length, the length of the original rope would be 3x.

this implies, 3x = 14.7 inches,

x = 4.9 inches.

therefore, the length of each rope would be 4.9 inches.

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(complete question)

Callie has a rope that is 14.7 inches long. She cut the rope into 3 pieces. If each piece is the same length, how long is each piece of rope?

Coordinate of circumcenter of the given triangle = (3, 2)

What is circumcenter of a triangle?

Circumcenter of a triangle is the point of intersection of the perpendicular bisectors of every sides of the triangle.

Let the coordinate of circumcenter be (x , y)

Distance of Circumcenter from (4,2) =

[tex]\sqrt{(x - 4)^2 + (y-2)^2[/tex]

Distance of Circumcenter from (3, 3) =

[tex]\sqrt{(x - 3)^2 + (y-3)^2[/tex]

Distance of Circumcenter from (2,2) =

[tex]\sqrt{(x - 2)^2 + (y-2)^2[/tex]

By the problem,

[tex]\sqrt{(x - 2)^2 + (y-2)^2} = \sqrt{(x - 3)^2 + (y-3)^2}\\(x - 2)^2 + (y-2)^2} = (x - 3)^2 + (y-3)^2}\\x^2 - 4x + 4 + y^2 -4y + 4 = x^2 -6x + 9 + y^2-6y + 9\\6x - 4x +6y -4y = 18-8\\2x +2y = 10\\x+ y = 5\\[/tex]..... (1)

Again,

[tex]\sqrt{(x - 4)^2 + (y-2)^2} = \sqrt{(x - 3)^2 + (y-3)^2}\\(x - 4)^2 + (y-2)^2} = (x - 3)^2 + (y-3)^2}\\x^2 - 8x + 16 + y^2 -4y + 4 = x^2 -6x + 9 + y^2-6y + 9\\8x - 6x +4y -6y = 20-18\\2x -2y = 2\\x- y = 1\\[/tex]...... (2)

Adding (1) and (2)

[tex]2x = 6\\x = \frac{6}{2}\\x = 3[/tex]

Putting the value of x in (1),

3 + y = 5

y = 5 - 3

y  = 2

Coordinate of circumcenter = (3, 2)

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An equation that models the relationship between the amount of time taken by Rick's bus ride and Matt's bus ride is M = t/3 + 3, which is shown in the graph attached below.

In order to write this equation, we would assign variables to the amount of time taken by Matt's bus ride and Rick's bus ride to school respectively, and then translate the word problem into algebraic equation as follows:

Next, we would translate the word problem into an algebraic equation as follows;

Matt's bus ride Time = 3 minutes more than 1/4 the time of Rick's bus ride

M = (1/4 × t) + 3

M = t/3 + 3

Based on the graph shown in the image attached below that models the relationship between the amount of time taken by Rick's bus ride and Matt's bus ride, we can reasonably and logically deduce that the y-intercept is equal to 3 and the slope of the graph is equal to 1/4.

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The distance between the two cities, Ottawa and Toronto, as determined by Greg and Max is 280.37 miles.

What is a Speedometer?

What is Distance?

How is Distance Calculated?

The distance between two locations can be calculated using the formula,
d = s x t,------ (1)

where [tex]d[/tex] is the distance travelled, [tex]s[/tex] is the average speed, and [tex]t[/tex] is the total time.

In the given question, it is given that Greg and Max travel from Ottawa to Toronto with an average speed of 40 mph and 30 mph for the return trip.

So, [tex]s_{1}=40 mph[/tex] and [tex]s_{2}=35mph[/tex].

The total travelling time for the round trip, T = 15h  ------(2)

Let the distance from Ottawa to Toronto be x.

From (1), we get that, the formula for the time taken is,

[tex]t=\frac{d}{s}[/tex]

So, the time taken to travel from Ottawa to Toronto,

[tex]t_{1} =\frac{d}{s_{1} } \\\implies t_{1} =\frac{x}{40}[/tex]      ------- (3)

And, the time taken for the return trip (back from Toronto to Ottawa),

[tex]t_{2} =\frac{d}{s_{2} } \\\implies t_{2} =\frac{x}{35}[/tex]      --------(4)

Here, the total time travelled from the round trip is equal to the sum of the time taken to travel from Ottawa to Toronto and back from Toronto to Ottawa.

T = t_1 + t_2------(5)

Substituting the values of (2), (3), and (4) in (5), we get

15 = x/40 + x/35
--> 15 = 0.0535x

Simplifying,

x = 15/0.0535
--> x = 280.37 miles

Therefore, the distance between the two cities as determined by Greg and Max is equal to 280.37 miles.

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the area of the original square garden is 80 square meters.

Let the side of the original square be a. We are given that the area of the new garden was (a - x)(a + x) = a² - x² = 64.

We want to find the area of the original square, so the value of a².

(1) The area of the new garden was 80 percent of the area of the original square garden --> 64 = 0.8a² --> a² = 80. Sufficient.

(2) x = 4 --> a² - 4² = 64 --> a² = 80. Sufficient.

the area is the quantity that expresses the quantity of a location on the aircraft or on a curved surface. The place of an aircraft region or plane vicinity refers back to the location of a form or planar lamina, at the same time as floor area refers to the place of an open surface or the boundary of a 3-dimensional object. location may be understood as the quantity of fabric with a given thickness that might be vital to style a model of the form, or the amount of paint necessary to cowl the surface with an unmarried coat. it's by far the two-dimensional analog of the duration of a curve (a one-dimensional idea) or the volume of a strong (a three-dimensional concept).

place plays a vital position in current mathematics. further to its apparent importance in geometry and calculus, the place is associated with the definition of determinants in linear algebra and is a simple asset of surfaces in differential geometry. In analysis, the vicinity of a subset of the plane has defined the use of the Lebesgue measure, though no longer every subset is measurable. In the trendy, region in better mathematics is visible as a unique case of quantity for two-dimensional regions.

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Three Expression equivalent to 12x + 8 are,

                  4 ( 3x+2 ) ,  12 (x + 2/3) ,    8 (2x/3 + 1)      

Equivalent expressions:

                                        Equivalent expressions are expressions that work the same even though they look different.

                                                                                    If two or more algebraic expressions are equivalent, then all expressions will give the same value if we put different value of variable.

Here,

         given expression is "  12x + 8 "

               we have to write three equivalent expression to 12x + 8

a.

       If we take 4 common we will get,

                      12x + 8 = 4 ( 3x+2 )

    so,

       one of the expression equivalent to 12x + 8  is 4 ( 3x+2 )

b.

     If we take 12 common then,

                   12x + 8 = 12 (x + 8/12)

                                = 12 (x + 2/3)

      one of the expression equivalent to 12x + 8  is 12 (x + 2/3)

c.

  If we take 8 common then,

                   12x + 8 = 8 ( 12x/8 + 1)

                                = 8 (2x/3 + 1)

    one of the expression equivalent to 12x + 8  is 8 (2x/3 + 1)

Hence,

           Three Expression equivalent to 12x + 8 are,

                   4 ( 3x+2 ) ,  12 (x + 2/3) ,    8 (2x/3 + 1)    

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Step-by-step explanation:

55/12

hope this helps:)

Answer:

[tex]x=\frac{(y-h)^{2} }{g^{2} }[/tex]

Step-by-step explanation:

       [tex]y=g\sqrt{x} +h\\\\[/tex]

[tex]-g\sqrt{x} =h-y[/tex]

    [tex]\sqrt{x} = -\frac{h-y}{g}[/tex]

    [tex]\sqrt{x} =\frac{y-h}{g}[/tex]

   ∴ [tex]x=\frac{(y-h)^{2} }{g^{2} }[/tex]

Makayla spend $29.87 if he was in the river for 4(1/2) hours.

Given, Makayla rents a kayak.

She pays a rental fee of $12.99 plus $3.75 for each hour that he spends in the water.

Now, we have to find that how much did she pay if she was in the river for 4(1/2) hours.

Let the no. of hours in the water be, x

So, Rental fee = 12.99 + 3.75x

As, she was in the water for 4(1/2) hours i.e. 9/2 hours

the rent will be = 12.99 + 3.75(9/2)

Rent = 12.99 + 1.875(9)

Rent = $29.865

Hence, Makayla spend $29.87 if he was in the river for 4(1/2) hours.

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The measure of the exterior angle x of the polygon is x = 105°  .

In the question ,

it is given that ,

in the figure, the measure of external angles are 75° , 90° , 90° and x .

we know that By Polygon Exterior Angle Sum Theorem states that the sum of measure of all exterior angle of a polygon is 360° ,

So , 75° + 90° + 90° + x = 360°

75° + 180° + x = 360°

255° + x = 360°

Subtracting 255 from both the sides , we get

x = 360° - 255°

x = 105°

Therefore , The measure of the exterior angle x of the polygon is x = 105°  .

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The like terms in the expression are -8x^2,-10x,14 and -6. The like terms are 14 and -6

A term can be a number, a variable, product of two or more variables or product of a number and a variable. An algebraic expression is formed by a single term or by a group of terms. For example, in the expression 5x + y, the two terms are 5x and y.

In the expression 14-8x^2-6-10x, there are 4 terms in it: 14, -8x^2, - 6, - 10x.

out of the four terms only two are alike because of they are both constant. This like terms are -6 and 14.

10x and -8x^2 are unlike terms because x^2 is a different term from 10x.

Therefore the like terms are -6 and 14

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Answer:

SAS, ASA, SSS, ASA, Yes

Step-by-step explanation: