Callie pays for a cat toy with a $10 bill and receives $2.55 in change. The equation 10 - c = 2.55 gives the cost in dollars for the cat toy. Determine whether c=6.45, c=7.45 or c=8.45 is a solution of the equation, and tell what the solution means. The

Answer:

[tex]\displaystyle \frac{100}{81}m^8p^{12}q^{16}z^2-\frac{20}{63}m^5p^7q^8z^5+ \frac{1}{49}m^2p^2z^8=\left(\frac{10}{9}m^4p^{6}q^{8}z-\frac{1}{7}mpz^4\right)^2[/tex]

Step-by-step explanation:

Trinomio Cuadrado Perfecto

El producto notable llamado cuadrado de un binomio se expresa como:

[tex](a-b)^2=a^2-2ab+b^2[/tex]

Si se tiene un trinomio, es posible convertirlo en un cuadrado perfecto si cumple con las condiciones impuestas en la fórmula:

* El primer término es un cuadrado perfecto

* El último término es un cuadrado perfecto

* El segundo término es el doble del proudcto de los dos términos del binomio.

Tenemos la expresión:

[tex]\displaystyle \frac{100}{81}m^8p^{12}q^{16}z^2-\frac{20}{63}m^5p^7q^8z^5+ \frac{1}{49}m^2p^2z^8[/tex]

Calculamos el valor de a como la raiz cuadrada del primer término del trinomio:

[tex]\displaystyle a=\sqrt{\frac{100}{81}m^8p^{12}q^{16}z^2}[/tex]

[tex]\displaystyle a=\frac{10}{9}m^4p^{6}q^{8}z[/tex]

Calculamos el valor de a como la raiz cuadrada del primer término del trinomio:

[tex]\displaystyle b=\sqrt{\frac{1}{49}m^2p^2z^8[/tex]

[tex]\displaystyle b=\frac{1}{7}mpz^4[/tex]

Nos cercioramos de que el término central es 2ab:

[tex]\displaystyle 2ab=2\frac{10}{9}m^4p^{6}q^{8}z\frac{1}{7}mpz^4[/tex]

Operando:

[tex]\displaystyle 2ab=\frac{20}{63}m^5p^7q^8z^5[/tex]

Una vez verificado, ahora podemos decir que:

[tex]\displaystyle \frac{100}{81}m^8p^{12}q^{16}z^2-\frac{20}{63}m^5p^7q^8z^5+ \frac{1}{49}m^2p^2z^8=\left(\frac{10}{9}m^4p^{6}q^{8}z-\frac{1}{7}mpz^4\right)^2[/tex]

Answer:

A. Solid

B. Pyramid

c. Prism

Step-by-step explanation:

Hope it helps you in your learning process.

The terms that correctly describe the object are prism, pyramid, and solid.

Options A, B, and C are the correct answer.

A prism is a three-dimensional object.

There are triangular prism and rectangular prism.

We have,

A prism is a solid geometric shape that has two identical parallel bases, which are typically polygons, and the sides of the shape are parallelograms.

A pyramid is a solid geometric shape that has a polygonal base and triangular faces that meet at a common point called the apex.

A solid is a three-dimensional object that occupies space and has a definite shape and volume.

A polyhedron is a three-dimensional solid that has flat faces, straight edges, and vertices (corners) where the edges meet.

A polygon is a two-dimensional shape that has straight sides and angles and is typically closed (meaning that its sides connect to form a closed shape).

A triangle is a three-sided polygon, meaning it has three straight sides and three angles.

Thus,

The terms that correctly describe the object are prism, pyramid, and solid.

Learn more about prism here:

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Answer:

Yes

Step-by-step explanation:

This is a function because each x value is given one y value. More simply, no x value was repeated.

Answer:

In analytic geometry, using the common convention that the horizontal axis represents a variable x and the vertical axis represents a variable y, a y-intercept or vertical intercept is a point where the graph of a function or relation intersects the y-axis of the coordinate system. As such, these points satisfy x = 0.

Step-by-step explanation:

Answer:

0.375 seconds

Step-by-step explanation:

In simple terms, to find the time it took to reach the ground, we need to find t from the equation.

If we differentiate h with respect to t we will get the velocity with which the fireworks is moving at.

[tex]h(t) = - 16t^2 + 4t.\\dh/dt =-32t +4[/tex]

We can now equate this to its velocity and solve for t

10 = -32t +4

t = 0.1875 ( time cannot be negative in value, so we ignore the negative sign)

Therefore, the time it took the fireworks to reach the ground is = 2 x 0.1875= 0.375 seconds.

(We need to account for the fact that the fireworks went up and came down)

Answer:

5.5

Step-by-step explanation:

Answer:

If the sum of the digits is divisible 3 and 9

Step-by-step explanation:

Answer:

Polygon Exterior Angle Sum Theorem. If a polygon is convex, then the sum of the measures of the exterior angles, one at each vertex, is 360° .

Answer:

Let y=34 and x=3

Step-by-step explanation:

y = 8x + 10

34 = 8 (3) + 10

34 = 24 + 10

34 = 34

Hence,3 and 34 satisfies this equation.

Answer:

a.

65,000

Step-by-step explanation:

There are 65000 possibilities of 4 character-password

A password is a security code that is used for verifying identities

The password has 4 characters.

The password must begin and end with a letter.

So the selections are:

First = 26

Last = 25

The other selections are:

Second = 10 digits

Third = 10 digits

So, the number of password is:

Password = 26 * 10 * 10 * 25

Evaluate

Password = 65000

Hence, there are 65000 possibilities of 4 character-password

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Answer:

23

Step-by-step explanation:

What diagram?? I dont see any

Answer:

y = -0.6x + 24.6

Step-by-step explanation:

Answer:

40

Step-by-step explanation:

The initial value of the function is 40, which represents the amount of money she deposits each week

Answer:

The answer is 10 or 10/1

Answer:

Answers are in bold

Step-by-step explanation:

Part 1A

Use the Zero Product Property to find the x-intercepts:

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

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

0=(x+4)

-4=x

x=-4

0=(x-1)

1=x

x=1

So the x-intercepts are x=-4 and x=1 which is also (-4,0) and (1,0)

For the y-intercepts, plug in x=0:

f(x)=-(0+4)(0-1)

f(x)=(-4)(-1)

f(x)=4

So the y-intercept is y=4 which is also (0,4)

Part 1B

In general, the axis of symmetry is equal to x=h in the equation y=(x-h)^2+k

For a parabola, the axis of symmetry is equal to x=-b/2a, so we expand the given equation and then plug in the values of "a" and "b" to get the axis of symmetry:

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

f(x)=-(x^2+3x-4)

f(x)=-x^2-3x+4

So now we know a=-1 and b=-3, therefore we can plug them in:

x=-b/2a

x=-(-3)/2(-1)

x=3/-2

x=-3/2

x=-1.5

So the equation of the axis of symmetry is x=-1.5

Part 1C

We'll use the equation x=-b/2a to get the x-coordinate for the vertex (which we already know is x=-1.5), then plug in that value of x in the original equation to get the y-coordinate for the vertex:

f(x)=-(-1.5+4)(-1.5+1)

f(x)=-(2.5)(-0.5)

f(x)=-(-1.25)

f(x)=1.25 <-- y-coordinate

So the coordinates of the vertex are (-1.5,1.25)

Part 1D

See the image below

I'll let someone else do the last 4 questions as I am unable to answer them.

Answer:

i am not sure try 56

Step-by-step explanation:

Hope this helps!:)

Answer:

30 cents of a dollar is 30% tax paid and 70% not paid.

A dollar is 100 cents.

Step-by-step explanation:

Answer:

x=0 x=y=z. with these presumed variable amounts, one can conclude that the equation you asked is equivalent to 0

Answer:

Step-by-step explanation:

(x+y)(x-y)+(y+z)(y-z)+(z+x)(z-x)

=x²-y²+y²-z²+z²-x²

=0

Answer:

Step-by-step ex

its 0.2

Answer:

I believe it's 3/10.

Step-by-step explanation:

Answer:

y= 30 + 3.50

Step-by-step explanation:

lol I think you're Giselle for my school but that's what the answer it im pretty sure.

Answer:

I would say A

Step-by-step explanation:

Answer:

14.5 ft

Step-by-step explanation:

We are told that the model car is built to a scale of 1 in. : 2.5 ft.

That means 1 inches represents 2.5 ft in actual measurement.

Thus, for a 5.8 inch long model, the real life measurement is;

(5.8 inch × 2.5 ft)/1 inch = 14.5 ft

Answer:

20.62 feet

Step-by-step explanation:

The ladder propped against a building forms a right angle triangle

Height of the ladder (hypotenuse) = 21 feet

Base of the ladder from the building (adjacent) = 4 feet

Height of the building (opposite) = x feet

Hypotenuse ² = opposite ² + adjacent ²

21² = x² + 4²

21² - 4² = x²

441 - 16 = x²

425 = x²

x = √425

= 20.62 feet

Answer: 20.62 ft or rounding it to 20.6 ft

Step-by-step explanation:

Answer:

it can and cant at the same time.

Answer: 11/21

Step-by-step explanation:

Answer:

11/24 or 0.453

Step-by-step explanation:

1/3 + 1/8

1/3 × 8/8 = 8/24

1/8 × 3/3 = 3/24

8/24 + 3/24 = 11/24