Write the prime factorization of 27. Use exponents when appropriate and order the factors from least to greatest

Answer: (-4,0), (4,0)

Step-by-step explanation:

x-intercepts are when y=0.

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 °  

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.

Answer:

v = 130

w = 30

x = 100

y = 25

z = 30

Step-by-step explanation:

Answer:

[tex]\frac{1}{2}[/tex]

Step-by-step explanation:

note that [tex]\frac{x}{2}[/tex] represents [tex]\frac{1}{2}[/tex] x

so the coefficient of the x- term is [tex]\frac{1}{2}[/tex]

The root of the polynomial equation x (x-2) (x + 3) = 18 is x = 3.

Concept: An expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s).

Given:

x (x-2) (x + 3) = 18

Divide both sides of the equation by x:

x (x-2) (x + 3) / x = 18 / x

(x-2) (x) + 3) = 18 / x

You can use the following simultaneous equations.

(1) y = (x-2) (x + 3)

(2) y = 18 / x

Using a graphing calculator, we get:

x = 3, y = 6 → point = (x, y) = (3,6)

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Answer:

perimeter = 42 units

Step-by-step explanation:

Answer:

8x+55y ≤ 184

Step-by-step explanation:

8x: The x in 8x signifies the amount of books you can buy. So let's say you want to buy 4 books then x would be 4 and 8x would be equivalent to 42.

55y: The y in 55y signifies the amount of video games you can buy. So let's say you want to buy 2 video games then y would be 2 and 55y would be equivalent to 110.

≤: We're using this sign because you can spend a maximum of 184 dollars. Meaning that the amount you spend (which is the 8x+55y) has to be less than or equal to 184 dollars.

184: The amount of money you are able to spend total.

Hope that helps! If you have any questions feel free to ask me :)

Answer:

187 Points

Step-by-step explanation:

Total ratio units = 17 + 14 = 31 units

Total they scored = 341 points

Therefore total units = 31 = 341 points

31 units = 341 points

1 unit = (341/31) points

1 unit = 11 points

Nina scored 17 units of the total points

17 units = (17 x 11) points

= 187 points

Answer:

She left a $2 tip

Step-by-step explanation:

0.2*25 = 5

The addition is one of the four fundamental mathematical operations. The total wage that Titan needs to pay is $414.63.

The addition is one of the four fundamental mathematical operations, the others being subtraction, multiplication, and division. When two whole numbers are added together, the total quantity or sum of those values is obtained.

Given Each employee is paid a minimum wage of $8/hour for an 8-hour day. They are also paid a commission of 12% on all sales they make. Therefore, the expression for the minimum wage can be written as,

Pay for an employee = (8x8) + 0.12(Sales made) = $64 + 0.12(Sales made)

Pay of the first employee = $64 + 0.12($785.96) = $158.32

Pay of the second employee = $64 + 0.12($452.87) = $118.34

Pay of the third employee = $64 + 0.12($616.42) = $137.97

The total wage that is needed to be paid for the day i,

Total = $158.32 + $118.34 + $137.97 = $414.63

Hence, The total wage that Titan needs to pay is $414.63.

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∠BDC and ∠AED are right angles, is  a piece of additional information is appropriate to prove △ CEA ~ △ CDB

Triangle AEC is shown. Line segment B, D is drawn near point C to form triangle BDC.

Similar triangles, are those triangles which have similar properties,i.e. angles and proportionality of sides.

Image is attached below,
as shown in figure
∡ACE = ∡BCD ( common angle )
∡AED = ∡BDC ( since AE and BD are perpendicular to same line EC and make right angles as E and C)
∡EAC =- ∡DBC ( corresponding angles because AE and BD are parallel lines)

Thus, △CEA ~ △CDB , because of the two perpendiculars AE and BD.

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Answer:

A

Step-by-step explanation:

Hence, the variable y can be entirely eliminated using by applying the identity property of elimination

the numerator of the rational expression in the simplest form is z

the denominator of the rational expression in the simplest form is x

expression is a combination of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.). This math operation can be addition, subtraction, multiplication, or division. The structure of an expression is: Expression is (Number/Variable, Math Operator, Number/Variable)

we have,

             [tex](\frac{xy^3}{yz^2} )(\frac{z^3}{y^2x^2} )[/tex]

on simplifying,

we get.  [tex]\frac{z}{x}[/tex]

Hence, the variable y can be entirely eliminated using by applying the identity property of elimination

the numerator of the rational expression in the simplest form is z

the denominator of the rational expression in the simplest form is x

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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

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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Answer:

60 meter

Explanation:

[tex]\begin{tabular}{|c|c|c|c|} \cline{1-2} \multicolumn{2}{|c|}{\bf {SOH CAH TOA Formula's}} \\ \cline{1-2} \cline{1-2} \rm{sine rule} & sin(\theta) \sf = opposite/hypotenuse \\ \cline{1-2} \rm{cosine rule} & cos(\theta) \sf = adjacent/hypotenuse \\\cline{1-2} \rm{tan rule} & tan(\theta) \sf = opposite/adjacent \\ \cline{1-2}\end{tabular}[/tex]

Given following:

hypotenuse: 68 meter

---

tan(θ) ratio = opposite/adjacent = 15/8

---

To find ratio of hypotenuse (use Pythagoras theorem):

(hypotenuse)² = (adjacent)² + (opposite)²

(h)² = (8)² + (15)²

h² = 289

h = √289 = 17

The height of the kite above ground is the opposite size.

[tex]\sf real \ size = ratio \ size[/tex]

[tex]\sf \dfrac{height \ above \ ground}{hypotenuse} = \dfrac{opposite}{hypotenuse}[/tex]

[tex]\sf \dfrac{height \ above \ ground}{68} = \dfrac{15}{17}[/tex]

[tex]\sf {height \ above \ ground}= \dfrac{68(15)}{17}[/tex]

[tex]\sf {height \ above \ ground}= 60 \ m[/tex]

Answer:

60 m

Step-by-step explanation:

Trigonometric ratios

[tex]\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}[/tex]

where:

The given scenario can be modeled as a right triangle (see attached diagram) where:

As we have been given the hypotenuse (thread) and the angle θ, and need to find the height (side opposite the angle), we can use the sine trigonometric ratio.

The angle θ has been given as a tan trigonometric ratio.  

[tex]\sf \textsf{Therefore, if }\tan \theta=\dfrac{15}{8} \textsf{ then } \cos \theta=\dfrac{8}{17} \textsf{ and } \sin \theta = \dfrac{15}{17}[/tex]

To calculate the height of the kite above the ground, substitute the values into the sine ratio formula and solve for height:

[tex]\implies \sin \theta=\sf \dfrac{height}{thread}[/tex]

[tex]\implies \sf \dfrac{15}{17}=\sf \dfrac{height}{68}[/tex]

[tex]\implies \sf height=\dfrac{15}{17} \cdot 68[/tex]

[tex]\implies \sf height=\dfrac{1020}{17}[/tex]

[tex]\implies \sf height = 60 \:m[/tex]

Therefore, the height of the kite above the ground is 60 m.

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Answer:

if boo ygdv

Step-by-step explanation:

f bi igfcnkyf f jurf

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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The point of concurrency of the perpendicular bisectors represents the point P with regard to the triangle. so option D is correct.

An altitude is a line that is perpendicular to a side and passes through the opposite vertex.

Point P is the center of the circle that is circumscribed around the triangle.

Triangle is inscribed within a circle. Point P is at the center of the circle.

The point P is the circumcenter of the triangle and the point is also equidistant from all the vertices of the triangle.

The one that represents the point P with regard to the triangle.

The point of concurrency of the perpendicular bisectors

Option (D) is correct.

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The point of concurrency of the perpendicular bisectors represents the point P with regard to the triangle. so option D is correct.

What is altitude?

An altitude is a line that is perpendicular to a side and passes through the opposite vertex.

Point P is the center of the circle that is circumscribed around the triangle.

Triangle is inscribed within a circle. Point P is at the center of the circle.

The point P is the circumcenter of the triangle and the point is also equidistant from all the vertices of the triangle.

The one that represents the point P with regard to the triangle.

The point of concurrency of the perpendicular bisectors

Option (D) is correct.

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Answer:

(x,y) --> (2,1)

Step-by-step explanation:

hope this helps

Answer:

2√23 cm or  9.59 cm to the nearest hundredth

Step-by-step explanation:

The 12 cm chord is 6 cm away from the centre and the other chord is 7 cm away from the centre.

If we draw 4 radii from the ends of the 2 chords to the centre  and 2 lines perpendicular from the centre to the 2 chords we have   2 pairs of congruent right triangles.

So by Pythagoras:

r^2 =  6^2 + 6^2   ( the given chord)

r^2 = 7^2 + x^2     where x is 1/2 * length of the second chord.

Therefore:

7^2 + x^2 = 6^2 + 6^2

x^2 = 36+ 36 - 49 = 23

x = √23

and length second chord = 2√23.

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]

Answer: 33

Step-by-step explanation:

Angles inscribed in the same arc are congruent, so

[tex]13+4x=-7+8x\\\\20+4x=8x\\\\20=4x\\\\x=5\\\\\implies m\angle CDE=-7+5(8)=33^{\circ}[/tex]

The value of the relative frequency distribution of the first interval, having a frequency of 14, and the total frequency given is 40, is 0.35.

In a Relative Frequency Distribution, we list how often a data value appears and scale it using the total frequency.

The sum of Relative Frequencies adds to 1.

In the question, we are informed that the first interval has a frequency of 14.

This implies that the data appears 14 times in the first interval.

Also, we are told that the total frequency is 40.

Thus, the relative frequency can be calculated as the ratio of the frequency of the interval to the total frequency.

Therefore, Relative frequency = 14/40 = 0.35.

Thus, the value of the relative frequency distribution of the first interval, having a frequency of 14, and the total frequency given is 40, is 0.35.

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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: D. -0.002

Step-by-step explanation: You always do the stuff in parenthesis first (P.E.M.D.A.S.). -1/6 is about -0.167. Next you do -0.167 to the fourth power, which is -0.0007777963. Finally, you multiply that number and 2. And BOOM: you get -0.0015555926, which rounds up to -0.002!

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:

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Answer:

===============

The sum:

We can notice that:

Since the difference between subsequence terms is same, the terms form an arithmetic progression.

Use the nth term equation to find the number of terms:

Use the given values and find n:

Now use the equation for sum of the first n terms of AP:

Substitute the values and calculate the sum: