Segment Given: BA= BC and DA= EC
Proofs
Prove: BD BE
Statements
BA BC 3 DA FC. Given
BDE BE
A
Reasons

Answer: B

[tex]f(x) = 7x-2[/tex] and        [tex]g(x) = \frac{x+2}{7}[/tex]

How to solve:

check if the composite functions of f(x) and g(x) are equal to x (this means they are inverses)

f[g(x)] = x

g[f(x)] = x

Step-by-step explanation:

Checking A.

[tex]f(x) = \frac{5}{x} -2[/tex]

[tex]g(x) = \frac{x+2}{5}[/tex]

[tex]f(g(x)) = f(\frac{x+2}{5} ) = \frac{5}{\frac{x+2}{5} } -2[/tex]

This does not equal x, so we know these are not inverses

Checking B.

[tex]f(x) = 7x-2[/tex]

[tex]g(x) = \frac{x+2}{7}[/tex]

[tex]f(g(x)) = f(\frac{x+2}{7} ) = 7(\frac{x+2}{7}) - 2 = x+2-2 = x[/tex]

[tex]g(f(x)) = g(7x-2) = \frac{7x-2 + 2}{7} = \frac{7x}{7} = x[/tex]

since both f(g(x)) = x and g(f(x)) = x, we can determine that they are inverses of each other.

Answer:

make it more clear its not clear enough to understand the question

Answer:

13.5 inches

Step-by-step explanation:

3inches:10 miles

x inches: 45 miles

do cross multiply:

3*45=135

10*x=10x

so 135=10x

x=13.5 inches

Answer: 3/20

Step-by-step explanation:

Probability of drawing a blueball from Urn I is

PI=66+4=610

Probability of drawing a blue ball from Urn II is

PII=22+6=28

Probability that both balls are blue

P=PI⋅PII=610⋅28=320

Answer:

s=0.20p

Step-by-step explanation:

20% off an product means to subtract 20% of the original price from the original price.

A. Distance between A and B is: 5 units.

B. Triangle ABC is not an equilateral triangle because only two of its sides are equal.

An equilateral triangle has three sides that have the same length.

Given the vertices with their coordinate points as:

A (-3, 2)

B (-6, -2)

C (0, -2)

Use the distance formula, [tex]d =\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex], to find AB, BC, and AC:

AB = √[(−6−(−3))² + (−2−2)²]

AB = √25

AB = 5 units

BC = √[(−6−0)² + (−2−(−2))²]

BC = √36

BC = 6 units

AC = √[(−3−0)² + (2−(−2))²]

AC = 25

AC = 5 units

Only two of the sides of the triangle, AB and AC, are equal. Therefore, it is not an equilateral triangle.

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Answer:

547.40

Step-by-step explanation:

476*15%

15 percent *476

= (15/100)*476

= (15*476)/100

= 7140/100 = 71.40

71.40 + 476 = 547.40 as original price

Answer:

a, b, d, e

maybe c

Step-by-step explanation:

Answer:

no real roots

Step-by-step explanation:

Find discriminant of quadratic equation:

A

= 62 - 4aC

2 Identify a,b,c

Identify a,b,c through coefficient:

a

b

C

6

= 12

8

Substitute and calculate

Substitute the value of a,b,c and calculate

discriminant (b2 - 4ac) :

-48

Determine number of solution Determine number of solution with

discriminant:

no real roots

x = 6(√2)

Step 1:

Say, 6 is perpendicular and x is the hypotenuse.

Step 2:

As we know sine is the ratio of perpendicular and hypotenuse.

∴ [tex]sin 45 = \frac{perpendicular}{hypotenuse}=\frac{6}{x}[/tex] ......................................(1)

Step 3:

As we know, sin45 = 1/√2

∴ put the value in equation 1

⇒ [tex]\frac{1}{\sqrt{2}} = \frac{6}{x}[/tex]

By solving the above equation, we get,

x = 6(√2)

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The relationship between the number of tickets is that Hannah sold three times as many tickets as Andrea.

From the question, we have:

Andrea = h

Hannah = 3h

This means that:

Hannah = 3 * Andrea

So, the relationship is that Hannah sold three times as many tickets as Andrea.

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Answer:

Step-by-step explanation

2 * [3 * (16 + 1)] - 8 =

2 * [3 * 17] - 8 =

2 * 51 - 8

102 - 8 =

94

Answer:

24/25

Step-by-step explanation:

96%=0.96. 96/100=48/50=24/25

Answer:

term to term rule. • a rule that defines the value of each term in a sequence. if the previous terms are known, e.g. the Fibonacci sequence. xn = xn-1 + xn-1.

Step-by-step explanation:

To work out the term to term rule, give the first term and then the pattern. The first term is 17, and the pattern is to subtract 3 each time, so the term to term rule is 'start at 17 and subtract 3'. The next two terms of the sequence are 5 and 2, giving the sequence as: Question.

Answer:

= x + 5

Step-by-step explanation:

(4x+1) - (3x-4)

= (4x+1) -3x + 4

= 4x - 3x + 1 + 4

= x + 5

Answer:

8+3+7=18

probability of brown m&m is

[tex] \frac{3 }{18 } [/tex]

Answer:

7/10

Step-by-step explanation:

Answer:

Step-by-step explanation:

equation of The line L : y = -(1/2)x + 6

A(8 , b) ∈ L  then b = -(1/2)(8) +6 then b = -4 + 6 = 2

Therefore ,

A(8 , 2)

AB = 2

CD = 6

BC = 8

…………………………………………

Area of the trapezoid ABCD

= (CB÷2)×(AB + CD)

= (8÷2)×(6+2)

= 32

Based on the amount being deposited into the account each month, and the interest, the account will triple in value on 25 months..

First find the value of the account when tripled:

= 1,000 x 3

= $3,000

We can then use a spreadsheet to find the number of periods it will take to triple.

Convert the interest to a monthly figure as:

= 3.15% / 12

= 0.2625%

When you put the figures into the spreadsheet as shown, the number of months would be 25 months.

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[tex]\dfrac{2x^3+4x^2 -x+8}{x^2 +3x+2}\\\\\\=\dfrac{2x^3+6x^2+4x-2x^2-6x-4+x+12}{}\\\\=\dfrac{2x(x^2 +3x+2)-2(x^2 +3x+2)+x+12}{x^2 +3x+2}\\\\\\=\dfrac{2x(x^2+3x+2)}{x^2 +3x +2 }- \dfrac{2(x^2 +3x +2)}{x^2 +3x +2 } + \dfrac{x+12}{x^2 +3x+2}\\\\\\=2x-2 + \dfrac{x+2}{x^2 +3x +2}\\\\\\=2x-2 + \dfrac{x+12}{x^2 +2x +x +2}\\\\\\=2x-2 + \dfrac{x+12}{x(x+2) + x+2}\\\\\\=2x-2 + \dfrac{x+12}{(x+1)(x+2)}\\[/tex]

The correct answer is option E which is Cos ( 70 ) = [tex]\dfrac{LN}{8}[/tex].

The complete question is attached with the answer below:-

The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.

As we can see from the figure that ∠L = 70 and ∠M = 20 We can see that the length LN will be calculated as:-

Cos 70 = Base / Hypotenuse

So for an angle of 70, the base is LN and the hypotenuse is equal to 8 units.

Cos 70 = LN = 8

Therefore the correct answer is option E which is Cos ( 70 ) = [tex]\dfrac{LN}{8}[/tex].

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Answer:

A & E

Step-by-step explanation:

Jus took it on edge

Answer:

Step-by-step explanation:

We'll look for an equation with the form y=mx+b, where m is the slope and b is the y-intercept (the value of y when x=0.

A line parallel to y=3x+6 will have the same slope, 3.

We can write y=3x+b.  Any value of b can be used to generate a parallel line.  

If we want that line to go through a specific point, such as (0,-2), we need to find a value of b that shifts the line so that it includes (0,-2).  This can be done by using that point in the equation y=3x+b:

y=3x+b

-2=3*(0)+b  for point (0,-2)

b = -2

The equation becomes y=3x-2

See the attached plot.

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

Do that same thing for the remaining two points.  

For B:  (2,5) The equation is y=3x-1

For C:   (4,1) The equation is y=3x-11

The correct answer is option D which is No because one x-value corresponds to two different y-values.

A function in mathematics set up a relationship between the dependent variable and independent variable. on changing the value of the independent variable the value of the dependent variable also changes.

We can see from the table that the value of x at 5 is giving two different values of y that is 2 and 3. For a function, it is not possible to have two different outputs for the same input.

Therefore the correct answer is option D which is No because one x-value corresponds to two different y-values.

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Answer:

X=-46

Step-by-step explanation:

-(-46-10)

-(-56)

56 degrees

Answer:

  D.  20 m

Step-by-step explanation:

The potential energy at Point B will be the sum of the potential and kinetic energies at point A.

__

For mass M, the potential energy at h meters above a rest height is ...

  PE = Mgh

The kinetic energy of mass M with velocity v is ...

  KE = 1/2Mv²

A pendulum with mass M launched downward at v = 14 m/s will have a total energy of ...

  PE +KE = M(9.8 m/s²)(10 m) +1/2(M)(14 m/s)² = M(98 +98) = 196M J/kg

When the pendulum comes to rest at point B, its energy will all have been converted to potential energy. Then the height at point B is given by ...

  PE = Mgh

  196M J/kg = M(9.8 m/s²)h

  h = (196M)/(9.8M) m = 20 m

The height of the mass at point B will be 20 meters.

Answer:

QR = 3

Step-by-step explanation:

given that Q is on the segment PR , then

PQ + QR = PR ( substitute values )

16 + QR = 19 ( subtract 16 from both sides )

QR = 3

The calculated length of the segment QR is 3 units

From the question, we have the following parameters that can be used in our computation:

Point Q is on line segment PR

PQ = 16 and PR = 19

using the above as a guide, we have the following:

PQ + QR = PR

substitute the known values in the above equation, so, we have the following representation

16 + QR = 19

So, we have

QR = 19 - 16

Evaluate

QR = 3

Hence. the length of the segment QR is 3

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Answer:

b=204

Step-by-step explanation:

The law of sine states that: [tex]\frac{SinA}{a} =\frac{SinB}{b} =\frac{SinC}{c}[/tex]

We know that a triangle has 180° total, so we can subtract the two angle measures we know to find the third angle: [tex]180-90-41=49[/tex]°.

Using these two things, we can come up with the equality [tex]\frac{Sin90^{o} }{270} =\frac{Sin49^o}{b}[/tex], which we can use to solve for side b.

[tex]\frac{Sin90^o}{270} =\frac{1}{270}[/tex], so we know that [tex]\frac{1}{270} =\frac{Sin49^o}{b}[/tex].

Next, we would multiply both sides by b to get [tex]\frac{1}{270}b=Sin49^o[/tex].

Sin49°≈0.75471, so to find b we would multiply 0.75471×270=203.77

Since the problem asks us to round to the nearest whole number, b=204

Hope this helps! :)

All options except Option D , a² + b²  , is the square of the binomial.

A polynomial that contains only two term is called a Binomial.

The sum of square of a binomial is the sum of square of the first term , square of second term and twice of the product of the first and second term.

(a+b)² = a² +b² +2ab

(a-b)² =  a² +b²-2ab

The options have to be broken down into this form to check whether they are square of a binomial

Option A : 4m² - 6mn + 9n² = (2m -3n)²

Option B:  16x² + 24xy + 9y²=(4x+3y)²

Option C : c²- 2cd - d²=(c-d)²

Option D : a² + b² cannot be written as the square of binomial.

All options except Option D is the square of the binomial.

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Answer:

5 units

Step-by-step explanation:

Use Pythagorean Theorem

x = 4 units     y = 3 units

4^2 + 3^2 = L^2

16 + 9 = L^2

L = 5

Answer:

5 units

Step-by-step explanation:

By the Pythagorean theorem:

c² = a² + b²

c = length of the line

a = 4

b = 3

Then:

c² = 4² + 3²

c² = 16 + 9

c² = 25

√c² = √25

c = 5