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3 years ago

Are these two figures congruent? Why or why not?

Mathematics

1 answer:

AnnZ [28]3 years ago

7 0

Yes they are congruent because they have just been translated in a rotation. But they still hold the same area and perimeter.

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Cedric purchased a new refrigerator and stove at Home Depot for $3,729 on a deferred payment plan with no down

lesya [120]

Answer:

correct option is d. $242.81

Step-by-step explanation:

given data

APR = 25.5% = $\frac{25.5}{12}$ = 2.125

paid = $3,729

solution

we get here finance charge on the 1st month by multiplying 3,729 and now adding it to existing balance

so we get finance charge for the second and third months similarly as

APR ÷ 100 = $\frac{2.125 }{100}$ = 0.02125

so 1st

= $3,729 × 0.02125

= 79.25

and

$3,729 + $79.25 = $3808.24

so for next

= $3808.24 × 0.02125

= 80.93

and

$3808.24 + $80.93 = $3889.17

so for next

= $3889.17 × 0.02125

= 82.64

and

$3889.17 + $ 82.64 = $3971.81

finance charge = 3971.81 - 3729

finance charge = 242.81

so correct option is d. $242.81

8 0

3 years ago

If 5x+6-19=5 what is x

Troyanec [42]

Answer:

x equals 3.6.

Step-by-step explanation:

A way to solve this equation is to preform the inverse operations on both sides.

1. Add 19 to -19 and 5: 5x + 6 - 19 + 19 = 5 + 19 ---> 5x + 6 = 24

2. Subtract 6 from 6 and 5: 5x + 6 - 6 = 24 - 6 ---> 5x = 18

3. Divide 5x and 18 by 5: 5x / 5 = 18 / 5 ---> x = 3.6

4. 3.6 is the answer.

To prove it, substitute x with 3.6 in the equation: 5 · 3.6 + 6 - 19 = 5

I hope this made sense and helped you a lot! :)

5 0

3 years ago

Read 2 more answers

kayla took $36.75 to the state fair. each ticket in the fair cost x dollars. kayla bought 3 tickets. write an expression that re

Gennadij [26K]

F(x)=y=the amount of money, in dollars , that Kad had after she bought the tickets.
x=price of one ticket

f(x)=-3x+36.75 or y=-3x+36.75

7 0

2 years ago

For each of the following vector fields F , decide whether it is conservative or not by computing curl F . Type in a potential f

Phantasy [73]

The key idea is that, if a vector field is conservative, then it has curl 0. Equivalently, if the curl is not 0, then the field is not conservative. But if we find that the curl is 0, that on its own doesn't mean the field is conservative.

$\mathrm{curl}\vec F=\dfrac{\partial(5x+10y)}{\partial x}-\dfrac{\partial(-6x+5y)}{\partial y}=5-5=0$

We want to find $f$ such that $\nabla f=\vec F$ . This means

$\dfrac{\partial f}{\partial x}=-6x+5y\implies f(x,y)=-3x^2+5xy+g(y)$

$\dfrac{\partial f}{\partial y}=5x+10y=5x+\dfrac{\mathrm dg}{\mathrm dy}\implies\dfrac{\mathrm dg}{\mathrm dy}=10y\implies g(y)=5y^2+C$

$\implies\boxed{f(x,y)=-3x^2+5xy+5y^2+C}$

so $\vec F$ is conservative.

$\mathrm{curl}\vec F=\left(\dfrac{\partial(-2y)}{\partial z}-\dfrac{\partial(1)}{\partial y}\right)\vec\imath+\left(\dfrac{\partial(-3x)}{\partial z}-\dfrac{\partial(1)}{\partial z}\right)\vec\jmath+\left(\dfrac{\partial(-2y)}{\partial x}-\dfrac{\partial(-3x)}{\partial y}\right)\vec k=\vec0$

Then

$\dfrac{\partial f}{\partial x}=-3x\implies f(x,y,z)=-\dfrac32x^2+g(y,z)$

$\dfrac{\partial f}{\partial y}=-2y=\dfrac{\partial g}{\partial y}\implies g(y,z)=-y^2+h(y)$

$\dfrac{\partial f}{\partial z}=1=\dfrac{\mathrm dh}{\mathrm dz}\implies h(z)=z+C$

$\implies\boxed{f(x,y,z)=-\dfrac32x^2-y^2+z+C}$

so $\vec F$ is conservative.

$\mathrm{curl}\vec F=\dfrac{\partial(10y-3x\cos y)}{\partial x}-\dfrac{\partial(-\sin y)}{\partial y}=-3\cos y+\cos y=-2\cos y\neq0$

so $\vec F$ is not conservative.

$\mathrm{curl}\vec F=\left(\dfrac{\partial(5y^2)}{\partial z}-\dfrac{\partial(5z^2)}{\partial y}\right)\vec\imath+\left(\dfrac{\partial(-3x^2)}{\partial z}-\dfrac{\partial(5z^2)}{\partial x}\right)\vec\jmath+\left(\dfrac{\partial(5y^2)}{\partial x}-\dfrac{\partial(-3x^2)}{\partial y}\right)\vec k=\vec0$