A group of students and workers entering a metro station were asked whether they were riding the bus or the subway. The two-way table shows their answers.

How many people were polled?
A. 48
B. 69
C. 118
D. 166

The given equation-(3x + 5)^2 is not a perfect trinomial because it is not obtained through the multiplication of a binomial.

A perfect square trinomial is takes the algebraic expression form ax^2 +bx + c, where the square root of the first term and the third term is the equation to the second term.

Given that:

-(3x + 5)^2

Open brackets

= - (9x +30x + 55)

Multiply through by (-)

= -9x^2 - 30x - 55

Therefore, we can conclude that the given equation-(3x + 5)^2 is not a perfect trinomial because it is not obtained through the multiplication of a binomial. i.e. the multiplication of the square root of the first and the third term did not result in the 2nd term.

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The complete transformation is Rk, where k is the line with equation x = 2

The complete question is added as an attachment

From the attached graph, we can see that the triangle and its image have a common vertex at C.

This means that the triangle is reflected across a vertical line that passes through point C.

The coordinate of C is:

C = (2, -2)

The vertical line passes through the x-coordinate.

So, we have:

x = 2

Hence, the complete statement is:

The complete transformation is Rk, where k is the line with equation x = 2

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Answer:

  (c)  -3.8, 3

Step-by-step explanation:

The solutions to the equation f(x) = g(x) are the values of x where the function values are equal. These are the x-coordinates of the points where the graphs of y=f(x) and y=g(x) intersect each other.

The points where the graphs cross can be estimated to be ...

  (-3.8, 6.5) and (3, -6)

The x-coordinates of these points are the solutions to the equation:

  x = -3.8, 3

Answer:

proof given below

Step-by-step explanation:

Combine the fractions by making the denominators the same:

   [tex]\dfrac{\sin \theta}{1+ \cos \theta}+\dfrac{1+ \cos \theta}{ \sin \theta}[/tex]

[tex]=\dfrac{\sin \theta}{1+ \cos \theta} \cdot \dfrac{\sin \theta}{\sin \theta}+\dfrac{1+ \cos \theta}{ \sin \theta} \cdot \dfrac{1+ \cos \theta}{1+ \cos \theta}[/tex]

[tex]=\dfrac{\sin \theta(\sin \theta)}{\sin \theta(1+ \cos \theta)}+\dfrac{(1+ \cos \theta)(1+ \cos \theta)}{\sin \theta(1+ \cos \theta)}[/tex]

[tex]= \dfrac{\sin^2 \theta}{\sin \theta(1+ \cos \theta)} +\dfrac{1+2 \cos \theta + \cos^2 \theta}{\sin \theta(1+ \cos \theta)}[/tex]

[tex]= \dfrac{\sin^2 \theta+ \cos^2 \theta+1+2 \cos \theta }{\sin \theta(1+ \cos \theta)}[/tex]

Use the trigonometric identity [tex]\sin^2 \theta + \cos^2 \theta=1[/tex] :

[tex]= \dfrac{1+1+2 \cos \theta}{\sin \theta(1+ \cos \theta)}[/tex]

[tex]= \dfrac{2+2 \cos \theta}{\sin \theta(1+ \cos \theta)}[/tex]

Factor out 2 from the numerator:

[tex]= \dfrac{2(1+ \cos \theta)}{\sin \theta(1+ \cos \theta)}[/tex]

Cancel the common factor:

[tex]= \dfrac{2}{\sin \theta}[/tex]

[tex]\textsf{Use the identity} \quad\csc \theta=\dfrac{1}{\sin \theta}:[/tex]

[tex]=2 \csc \theta[/tex]

Hence proved.

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Step-by-step explanation:

please mark me as brainlest

A (n) Shaded background Appears behind selected text so option. 4) Is  correct.

What is shading background?

Shading background is process, When  selecting a particular  text there behind the text a shad will form which shows the number of texts selected

Thus,  shaded background appears behind selected text

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Answer:

315 chairs

Step-by-step explanation:

This question can instill your quick calculation skills which can be very useful when it comes to event planning.

1 row of chairs = 15 chairs

21 rows of chairs = 15 x 21

= 315 chairs.

Let's see

In ∆ABE and ∆CBE

So by

SAS congruence the triangles are congruent

AB=BC

Fact:-

It's already given AC is perpendicular to BD

According to general property of rhombus this parallelogram is also a rhombus.

So sides are equal hence AB =BC

Answer:

$283.07

Step-by-step explanation:

Monthly Payment Formula

[tex]\sf PMT=\dfrac{Pi(1+i)^n}{(1+i)^n-1}[/tex]

where:

Given:

Substitute the given values into the formula and solve for PMT:

[tex]\implies \sf PMT=\dfrac{15000\left(\frac{0.05}{12}\right)\left(1+\frac{0.05}{12}\right)^{60}}{\left(1+\frac{0.05}{12}\right)^{60}-1}[/tex]

[tex]\implies \sf PMT=283.0685047...[/tex]

Therefore, the monthly payments will be $283.07.

The polynomial which shoud be filled in the blank is (x+2).

Given expression ([tex]x^{2} -4)/x^{2} =x-2[/tex]  and the expression (x+2)____=[tex](x^{2} -4)[/tex]

We have to  find a polynomial which fills the blank in the given expression.

Polynomial is expression of more than two algebraic terms mainly the sum of several terms that contain different powers of the same variable.

We have been given [tex](x^{2} -4)/x+2=x-2[/tex]

first multiply both sides by (x+2)

([tex]x^{2}[/tex]-4)/(x+2) *(x+2)=(x-2)(x+2)

cancelling (x+2) from numerator and denominator we get

([tex]x^{2}[/tex]-4)=(x-2)(x+2)

If we carefully observes the expression we found that both the given expression in which blank takes place are same just on the place of blank there is (x+2).

Hence the polynomial which fills the blank is (x+2).

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Question is wrong as in this the expressions would be :

([tex]x^{2} -4)/x+2=x-2[/tex] and (x+2)____=[tex]x^{2} -4[/tex]

Answer:

475.2

Step-by-step explanation:

682 is 1.55 of the original amount so 1.55x=682

682/1.55=440

440*1.08=475.2

The Angle that would correspond to Angle N after the transformation is; Angle N'

A polygon is defined as a two-dimensional geometric figure that has a finite number of sides. The sides of a polygon are made of straight line segments connected to each other end to end. Thus, the line segments of a polygon are called sides or edges.

In the transformation of  LMNOP to create polygon L'M'N'O'P', we have that;

L corresponds to L'

M corresponds to M'

N corresponds to N'

O corresponds to O'

P corresponds to P'

Thus, we can conclude that Angle N would correspond to Angle N'

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Answer:

72 miles/day

Step-by-step explanation:

12 m/hr  *  6 hr / day  = 72 mi/day

Answer:

x^2 + 4x -4

Step-by-step explanation:

Simply combine all the like terms by adding:

x^2 + 0x - 5

0x^2 + 4x +1

_____________

x^2 + 4x - 4

An expression is defined as a set of numbers, variables, and mathematical operations. The sum of three and the square root of a number is expressed as 3 + √x.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

Let the unknown number be represented by x.

1.) The sum of three and the square root of a number.

3 + √x

2.) Nine less than a number cubed.

x³ - 9

3.) The quotient of a number and 7.

x ÷ 7

4.) Four times a quantity plus five.

4x + 5

Hence, The sum of three and the square root of a number is expressed as 3 + √x.

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Answer:

[tex]\sf \dfrac{3}{{z-3} }[/tex]

Explanation:

[tex]\Longrightarrow \sf \dfrac{1}{z} \div \dfrac{z-3}{3z}[/tex]

apply the theorem when [tex]\dfrac{a}{b} \div \dfrac{c}{d}[/tex] then [tex]\dfrac{a}{b} \times \dfrac{d}{c}[/tex]

[tex]\Longrightarrow \sf \dfrac{1}{z} \times \dfrac{3z}{z-3}[/tex]

Join the fractions

[tex]\Longrightarrow \sf \dfrac{3z}{z({z-3)} }[/tex]

Cancel out common factor z

[tex]\Longrightarrow \sf \dfrac{3}{{z-3} }[/tex]

The answer is : [tex]\boxed {\frac{3}{z-3}}[/tex]

Remember that dividing fractions is the same as multiplying the 1st fraction by the reciprocal of the other.

[tex]\mathsf {\frac{1}{z} \div \frac{z-3}{3z}}[/tex]

[tex]\mathsf {\frac{1}{z} \times \frac{3z}{z - 3}}[/tex]

[tex]\mathsf {\frac{3}{z-3}}[/tex]

The measures of GX = 13

The measures of [tex]\angle ABX=22^0[/tex]

EX = 4z + 1  and XF = 2z + 7

Take EX and XF equal time each other and then solve for z and then you will get GX because EX = XF = GX are congruent.

EX = XF

Two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.

4z + 1 = 2z + 7

2z = 6

z = 3

As,    EX = XF = GX

EX = 4(3) + 1

EX = 13

Therefore, GX = 13      ------      ( EX = XF = GX )

To find the angle ABX, divide the angle ABC by 2 you will get

[tex]\angle ABX=22^0[/tex]

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Answer:  13,  22°

Step-by-step explanation:   Trust Me!  

Answer is correct on Edge. Good Luck!  :)

GX =  13

mABX = 22 °  

The true statement about the graph from the attached image below is: The material's temperature reaches a minimum at 15 hours.

The parabolic graph is a curved U-shaped graph that is established from a quadratic equation.

The parabola of the graph can be downward creating a maximum or upward (minimum).

From the given image, the correct interpretation shows that as a result of cryogenic treatment, the material's temperature reaches a minimum at 15 hours.

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The best buy is from dealership B because dealership B has a lesser base price

For the purpose of this exercise, the add-on options to select are:

The total amount of the add-on options is:

Total = $500 + $1500

Total = $2000

The inequality

This is represented using:

Base price * (1 + Tax) + Fees + Add-on total ≤ 20000

So, we have:

(1 + 6.75%) * x + 751.56 + 2000 ≤ 20000

Solve for x

We have:

(1 + 6.75%) * x + 751.56 + 2000 ≤ 20000

Evaluate the like terms

(1 + 6.75%) * x  ≤ 17248.44

Divide both sides by (1 + 6.75%)

x  ≤ 16157.79

The solution means that the base price of the car cannot exceed $16157.78 for dealership A

The graph of the possible base price

See attachment

The total amount of the add-on options is:

Total = $750 + $1000

Total = $1750

The inequality

This is represented using:

Base price * (1 + Tax) + Fees + Add-on total ≤ 20000

So, we have:

(1 + 6.75%) * x + 1524.72 + 1750 ≤ 20000

Solve for x

We have:

(1 + 6.75%) * x + 1524.72 + 1750 ≤ 20000

Evaluate the like terms

(1 + 6.75%) * x  ≤ 16725.28

Divide both sides by (1 + 6.75%)

x  ≤ 15667.71

The solution means that the base price of the car cannot exceed $15667.71 for dealership B

The graph of the possible base price

See attachment

Buy from dealership B because dealership B has a lesser base price

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The area of the window is 8[tex]m^{2}[/tex].

An object's area is how much space it takes up in two dimensions. It is the measurement of the number of unit squares that completely cover the surface of a closed figure.

The word "area" refers to a free space. The length and width of a form are used to compute its area.

Any shape's area can be calculated by counting how many unit squares will fit inside of it.

According to the question,

Length of window=2m

Width of window=4m

Area of window=Length*Width

                          =2*4

                          =8[tex]m^{2}[/tex]

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Answer:

22

Step-by-step explanation:

The line where it says 2cm, extend that line to the top. You know have 2 triangles, call the one on the left A and the one on the right B

area of recntangle = bh

Rect A:

b = 5

h = 4 - 2

h = 2

bh = 5 x 2

bh = 10

Rect B:

b = 3

h = 4

bh = 4 X 3

bh = 12

Total = 10 + 12

Total = 22

The linear function x = -2.5 is plotted on the graph attached with an x intercept at (-2.5, 0)

An equation is an expression that shows the relationship between two or more numbers and variables.

A linear equation is in the form:

y = mx + b

Where m is the slope and b is the y intercept.

The linear function x = -2.5 is plotted on the graph attached with an x intercept at (-2.5, 0)

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Answer:

[tex]y=5^x[/tex]

Step-by-step explanation:

[tex]y=a*b^x\\(1,5)=5=a*b^1 \implies(1)\\(2,25)=25=a*b^2\implies(2)\\(2)\div(1)=\frac{25}{5} =\frac{a*b^2}{a*b^1} \\5=b[/tex]

[tex](1)=5=a*5\implies a=1 y=5^x\implies y=5^x[/tex]

The expected value of y when x is equals to 45 in the equation is 35.06

The equation is given as follows;

y = -2.61x + 152.51

where

Therefore,

when

x = 45

y = -2.61x + 152.51

y = -2.61(45) + 152.51

y = - 117.45 + 152.51

y = 35.06

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Answer:

D. 62.5

Step-by-step explanation:

2 ways

1.

7.5 ÷ 3 = 2.5

25 times 2.5 = 62.5

2.

3/7.5 = 25/x

3x = 187.5

187.5 ÷ 3 = 62.5

The actual distance for a length on a map is 62.5. so correct option is D.

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

The relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

Given The scale on a map reads 3 inches = 25 miles.

If two cities are 7.5 inches apart on the map,

Find the actual distance for a length on a map.

Let x be the actual distance

7.5 ÷ 3 = 2.5

25 times 2.5 = 62.5

Thus,

3/7.5 = 25/x

3x = 187.5

187.5 ÷ 3 = 62.5

Therefore, the actual distance for a length on a map is 62.5.

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Answer:

if boo ygdv

Step-by-step explanation:

f bi igfcnkyf f jurf

The sequence of transformations that can be performed on quadrilateral ABCD to show that it is congruent to quadrilateral is 90° counterclockwise rotation about point A followed by the reflection across y axis and a translation 20 units down.

It should be noted that a transformation simply illustrates the change in shape.

In this case, the sequence of transformations that can be performed on quadrilateral ABCD to show that it is congruent to quadrilateral is 90° counterclockwise rotation about point A.

This will then be followed by the reflection across y axis and a translation 20 units down.

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Graph (b) represents the data provided that option (b) would be the correct choice.

A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.

[tex]\rm m = \dfrac{n\sum xy-\sum x \sum y}{n\sum x^2 - (\sum x)^2}\\\\\\\rm c = \dfrac{\sum y -m \sum x}{n}[/tex]

We have the data shown in the table.

The equation of the line M = 3n represents the data provided,

After plotting all the points on the coordinate plane.

We will get a graph that represents the data.

Thus, graph (b) represents the data provided the option (b) would be the correct choice.

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Answer:

v = 130

w = 30

x = 100

y = 25

z = 30

Step-by-step explanation: