Use the diagram and given information to answer the questions and prove the statement.

Re-draw the diagram of the overlapping triangles so that the two triangles are separated.
What additional information would be necessary to prove that the two triangles, XBY and ZAY, are congruent? What congruency theorem would be applied?
Prove AZ ≅ BX using a flow chart proof.

ANSWER

C. (0,4)

EXPLANATION

The given graph has equation:

[tex]y = 4( {3}^{x} )[/tex]

The y-intercept is where the graph touches the y-axis.

At this point the value of x is zero.

We substitute x=0 into the equation to obtain:

[tex]y = 4( {3}^{0} )[/tex]

Recall that any non-zero number exponent zero is 1.

This implies that,

[tex]y = 4( 1 ) = 4[/tex]

Hence the y-intercept is (0,4)

The correct answer is C.

Answer:

C. h(2) = 16

True statement

Step-by-step explanation:

The function has

Domain

-3 ≤ x ≤ 11

Range

1 ≤ h(x) ≤ 25

h(8) = 19

h(-2) = 2

Lets analyze each statement

A. h(13) = 18

False, x = 13 is not part of the domain

B. h(-3) = -1

False, -1 is not part of the range

C. h(2) = 16

True statement

D. h(8) = 21

False, the problem tells us that h(8) = 19

Answer:

see explanation

Step-by-step explanation:

Given

2x² + 9x + 10 = 0

To factor the quadratic

Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 2 × 10 = 20 and sum = + 9

The factors are + 4 and + 5

Use these factors to split the x- term

2x² + 4x + 5x + 10 = 0 ( factor the first/second and third/fourth terms )

2x(x + 2) + 5(x + 2) = 0 ← factor out (x + 2) from each term

(x + 2)(2x + 5) = 0

Equate each factor to zero and solve for x

x + 2 = 0 ⇒ x = - 2

2x + 5 = 0 ⇒ 2x = - 5 ⇒ x = - [tex]\frac{5}{2}[/tex]

Answer:

1. x = 2

2. x = - 5/2

Step-by-step explanation:  First put parenthesis around the equation

( 2x^2 + 4x ) + ( 5x + 10) = 0

2x ( x+ 2) 5 (x + 2),

when you have the same answer inside the parenthesis you know your right.

2x + 5 = 0

x + 2 = 0

Next preform basic algebra

2x = -5  

Answer:

2,-1

Step-by-step explanation:

2x^2 -2x -4 =0

Factor out a 2

2(x^2 -x-2) =0

What 2 number multiply to -2 and add to -1

-2*1 = -2

-2 +1 = -1

2(x-2) (x+1) =0

Using the zero product property

x-2 = 0               x+1 = 0

x-2+2=0+2       x+1-1=0-1

x=2                   x=-1

Answer: B.)      18x^2y^2 3squareroot 3xy^2

Step-by-step explanation:

Answer:

B. [tex]18x^{2} y^{2} \sqrt[3]{3xy^{2} }[/tex]

Step-by-step explanation:

To simplify this expression, use the fact that the root of a number (in this case is the cube root)  can be expressed like a fractional exponent (1/3). Using this, the expression changes to:

[tex]3x(648x^{4}y^{8})^{(1/3)}[/tex]

Next step is to put the exponent inside the parenthesis:

[tex]3x(648^{1/3}x^{4/3}y^{8/3})[/tex]

Find the prime factorization  of 648:

648 =3⋅3⋅3⋅3⋅2⋅2⋅2

648=3⁴∗2³

[tex]3x(3^{(4/3)}2^{(3/3)}x^{4/3}y^{8/3})[/tex]

Change all improper fractions in exponent to mixed fractions

[tex]3x(3^{1(1/3)}2^{1}x^{1(1/3)}y^{2(2/3)})[/tex]

Separate integers exponents from fractional:

[tex]3x(3\cdot3^{(1/3)}\cdot 2 \cdot x\cdot x^{1/3}\cdot y^{2}\cdot y^{2/3})[/tex]

Re-arrange (all numbers with fractional exponents must be together):

[tex]3x(3 \cdot 2\cdot x\cdot y^{2}\cdot 3^{(1/3)}x^{1/3}y^{2/3})[/tex]

Multiply the 3x with the numbers that have an integer exponent:

[tex]18x^{2}y^{2}(3^{(1/3)}x^{1/3}y^{2/3})[/tex]

Take out  the exponent 1/3 from the parenthesis:

[tex]18x^{2}y^{2}(3xy^{2})^{1/3}[/tex]

And change the representation of the root to use a radical symbol

[tex]18x^{2} y^{2} \sqrt[3]{3xy^{2} }[/tex]

Answer:

Never.

Step-by-step explanation:

Answer

πr^2 h/3

Step-by-step explanation:

pi radius squared multiplied by h/3

Answer:

The direction of 5c + 4d is approximately 19.0° clockwise with

the positive part of x-axis

Step-by-step explanation:

* Lets talk about the direction of a vector

- If the vector is (x , y), then  

# Its magnitude is √(x² + y²)

# Its direction is tan^-1 (y/x)

- The direction is the angle between the positive part of x-axis and  

  the vector

* Lets solve the problem

∵ c = (2.4 , 0.45) and d = (7 , -4)

- To find 5c + 4d , multiply the two coordinates of c by 5 and the two

  coordinates of d by 4

# Multiply c by 5

∴ 5c = [5(2.4) , 5(0.45)]

∴ 5c = (12 , 2.25)

# Multiply d by 4

∴ 4d = [4(7) , 4(-4)]

∴ 4d = (28 , -16)

- Lets add 5c and 4d

∴ 5c + 4d = (12 , 2.25) + (28 , -16)  

∴ 5c + 4d = [(12 + 28) , (2.25 + -16)]

∴ 5c + 4d = (40 , -13.75)

- The vector is in the 4th quadrant because the x-coordinate is

 positive and the y-coordinate is negative

* Find the direction of 5c + 4d

∵ The direction is tan^-1 (y/x)

∴ The direction is tan^-1 (-13.75/40) = -18.97°

* The direction of 5c + 4d is approximately 19.0° clockwise with

 the positive part of x-axis

Answer:

Probability

Step-by-step explanation:

Probability is the likelihood or chance of an event occurring. For example, the probability of flipping a coin and it being heads is ½, because there is 1 way of getting a head and the total number of possible outcomes is 2 (a head or tail). We write P(heads) = ½ .

[tex]\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ (4vy^{-9})\cdot (2x^{-6}x^6y^6)\cdot (3v^4)\implies 4vy^{-9}2x^{-6}x^6 y^6 3v^4 \\\\\\ 4\cdot 3\cdot 2vv^4y^{-9}y^6x^{-6}x^6 \implies 24v^{1+4}y^{-9+6}x^{-6+6}\implies 24v^5y^{-3}x^0 \\\\\\ 24v^5\cdot \cfrac{1}{y^3}\cdot 1\implies \cfrac{24v^5}{y^3}[/tex]

Answer:

D

Step-by-step explanation:

We need to understand the meaning of slope. The slope means the rate of change of y with every unit change of x.

In our case, it will be rate of change of sales increase (%) with respect to unit change of discount(%).

The formula for slope is the change in y divided by change in x.

From the 2 points given, we can say that slope is:

[tex]\frac{62-32}{20-10}=\frac{30}{10}=\frac{3}{1}[/tex]

This means "as discount increases 1%, sales increase by 3%". Option D is right.

Answer:

D

Step-by-step explanation:

Answer:

If x varies directly as y, then x=ky. y=5 and x=2.5 are substituted into x=ky to find k.

2.5=5k

k=2.5/5

k=5.

K =5 is substituted in x=ky to find y where x is 10.

x=5y

10=5y

y=10/2

y=2

Answer:  The required value of y is 20.

Step-by-step explanation:  Given that y is 5 when x is 2.5 and y varies directly with x.

We are to find the value of y when x is 10.

According to the given information, we can write

[tex]y\propto x\\\\\Rightarrow y=kx~~~~~~~~~~[\textup{where k is the constant of proportionality}][/tex]

When y = 5 and x = 2.5, then we have

[tex]5=k\times2.5\\\\\Rightarrow k=\dfrac{5}{2.5}\\\\\Rightarrow k=2.[/tex]

So, we get

[tex]y=2x.[/tex]

Therefore, when x = 10, then the value of y is

[tex]y=2\times10=20.[/tex]

Thus, the required value of y is 20.

Answer:

I don't understand the question can you add more information or maybe show the page where you got this question?

Step-by-step explanation:

Answer:

the answer is zero

Step-by-step explanation:

sin(θ) < 0 is another way to say sin(θ) is negative.

tan(θ) < 0 is another way to say tan(θ) is negative.

let's recall that, on the III Quadrant sine and cosine are both negative, and thus the tangent is positive, recall tan(θ)=sin(θ)/cos(θ).

on the IV Quadrant however, sine is negative and cosine is positive, thus tangent is negative.

Answer:

40 Miles Per Hour is 211,200 Feet per Hour, 3520 Feet Per Minute, and 58.67 Feet Per Second.

Answer:

Hi there!

Since you asked for a simplified fraction, the answer to this question is: 1/6

Step-by-step explanation:

Look at the fraction 14/84, there is a definite similar factor between 14 and 84, 2. So all you do is divide the two numbers by two to reduce the fraction into 7/42

then you divide both 7 and 42 by 7 to get 1/6

Answer:

1/6

Step-by-step explanation:

14 to 84

First lets make it a fraction

14/84

Divide the top and bottom by 14

1/6

Answer:

B.)7√5

Step-by-step explanation:

2√5+ 5√5 = 7√5

we simply let √5  = x

therefore;

2√5+ 5√5 = 2x + 5x

2x + 5x = 7x

but x = √5

2√5+ 5√5 = 7√5

Step-by-step explanation:

The ratio is the same each time (2/3), so this can be modeled as a geometric sequence.

an = a₁ (r)^(n-1)

where an is the nth term, a₁ is the first term, and r is the common ratio.

On the first rebound, the ball rises to 2/3 × 2 = 4/3, so a₁ = 4/3.

an = 4/3 (2/3)^(n-1)

On the sixth rebound, the ball rises to:

a₆ = 4/3 (2/3)^(6-1)

a₆ = 4/3 (32/243)

a₆ = 128/729

a₆ ≈ 0.176

Answer:

what is the question i dont get it

Step-by-step explanation:

An easy way to solve this problem is divide $23.25 by 3 or $54.25 by 7. Either way, you get $7.75. This number represents the amount of money he makes for 1 hour. So with that in mind, the correct equation is:

$7.75x = y

I hope this helped! :)))

Answer: The 9th term is 6561

Step-by-step explanation:

The geometric sequences have the following formula

[tex]a_n = a_1(r)^{n-1}[/tex]

Where [tex]a_1[/tex] is the first term of the sequence and r is the common ratio between the consecutive terms of the sequence

In this case the sequence is   1 -3 9 -27

So [tex]a_1 = 1[/tex]

Observe that the common ratio  r is:

[tex]r=\frac{-3}{1}=\frac{9}{3}=\frac{-27}{9}=-3[/tex]

So the formula is:

[tex]a_n = (-3)^{n-1}[/tex]

We want to find [tex]a_9[/tex]

[tex]a_9 = (-3)^{9-1}[/tex]

[tex]a_9 = (-3)^{8}=6561[/tex]

Answer: Undefined

Step-by-step explanation: Since there is no change in x, and it is a horizontal line, that means that the denominator is zero. Dividing anything with the denominator being 0 will always be undefined (Not to be confused with the numerator, which is just dividing by 0, thus giving you 0.) That means that our answer will be undefined.

Answer:

x = 4

Step-by-step explanation:

Using the 90-60-30 theorem, the hypotenuse is equal to 2a, so a = 4 sqrt(2). The shortest leg is therefore 4 sqrt(2). Using this, to find x, plug it into the smaller triangle. The hypotenuse of the smaller triangle is therefore 4 sqrt(2). Using the 45-45-90 theorem, 4 sqrt(2) = x sqrt(2), so x = 4. This is because there are two sqrt(2)'s', so taking that out of the equation leaves x = 4.

Hope this helps!

Answer:

For the first answer (A)

The area of the base is the area of the 8 by 4 rectangle, minus the missing 2 by 2 square in the top-right.  This is 8*4-2*2=32-4=28 square centimeters.

For the second answer (B)

The volume of the prism is the base area multiplied by the height, or 28*10=280 cubic centimeters.

Answer:

Area = 28 cm² and Volume = 280 cm³

Step-by-step explanation:

A. Area of the base of the prism = Area of rectangle with dimensions 4 × 8 cm. minus area of a rectangle with dimensions 2×2 cm.

Area = 4 × 8 - 2 × 2

       = 32 - 4 = 28 cm²

B. Volume of the given prism = Volume of full prism with dimensions 10 × 4 × 8 cm. minus volume of small prism (missing) having dimensions 2×2×10 cm.

Volume = 10 × 4 × 8 - 2 × 2 × 10

             = 320 - 40

            = 280 cm³

Area = 28 cm² and Volume = 280 cm³

Answer:

12x

Step-by-step explanation:

We require the lowest common multiple of 4x, 3 and 2x

the lowest common multiple of 4, 3 and 2 is 12

the lowest common multiple of x and x is x

Combining the two gives lowest common multiple of 12x

Multiplying through by 12x gives

72x - 9 + 4x = 6 + 60x ← no fractions

Answer:

Step-by-step explanation:

It's 32, just follow the row when g=13.

Answer: We want to know f( g (13) ), here g(13) is just a number, so you are evaluating f in a number, first we need to know the value of g(13). Looking in the diagram you can see that g(13) = 16.

So f(g(13)) = f(16)

Also, looking in the diagram you can see that f(16) = 32

So, f ( g (32) ) = 32

Answer:

5x(2 - 3x³)

Step-by-step explanation:

10x-15x^4

The GCF( Greatest Common Factor) of 10x-15x^4 is 5x

Solve:

10x/5x = 2

-15^4/5x = -3x³

Final answer is

5x(2 - 3x³)

                         Check

5x(2 - 3x³)

distribute

5x(2) + 5x(-3x³)

10x - 15x^4

Answer:

5x(2 - 3x^3)

Step-by-step explanation:

The GCF is 5x 10x/5x=2 15x^4/5x=3x^3

Answer:

$324.19

Step-by-step explanation:

First, find the price when marked down. Multiply 475 with 0.35:

475 x 0.35 = 166.25

Subtract 166.25 from the total cost:

475 - 166.25 = 308.75

Now, solve for the tax. Tax is 5% (0.05). Multiply 0.05 with the new cost:

308.75 x 0.05 = ~$15.44

Add 15.44 to the sales price:

308.75 + 15.44 = $324.19

$324.19 is your answer.

~

Answer:

D

Step-by-step explanation:

By definition for a right triangle with sides a, b, c, where c is the hypotenuse,

the following must be true:

a² + b² = c²

By using this formula on all the choices, we find that only D satisfies this formula

i.e.

for

a = √35 --------> a² = 35

b = √14 --------->b² = 14

c = 7 ------> c² = 49

a² + b² = 35 + 14 = 49 which is equal to the value of c² above

The correct answer is √35 , √14 , 7

Pythagoras' theorem that the square of a right triangle's hypotenuse is equal to the sum of the squares of the other two sides.

p^2 + b^2 = h^2 ( In a right angled triangle)

p = perpendicular of the triangle

b = base of the triangle

h = hypotenuse of the triangle

According to the Pythagoras theorem:

p^2 + b^2 = h^2 (In a right angled triangle)

In Option D

(√35)^2 + (√14)^2 = 7^2

49 = 49

Pythagoras theorem is followed in this triangle, hence it is a right angled triangle.

Learn more about Pythagoras theorem on:

https://brainly.com/question/343682

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