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3 years ago

A train can be on time, early or late.

Mathematics

1 answer:

grigory [225]3 years ago

7 0

Answer:

0.31

Step-by-step explanation:

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Use the diagram below to solve for x and y.

Mrac [35]

Answer:

Option A. x=30,y=42

Step-by-step explanation:

we know that

If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

In this problem

Triangles ABC and ZYX have three congruent interior angles

therefore

Triangles are similar

step 1

Find the value of x

$\frac{ZY}{AB}=\frac{ZX}{AC}$

substitute the values

$\frac{20}{x}=\frac{12}{18}$

$x=20*18/12=30\ units$

step 2

Find the value of y

$\frac{ZY}{AB}=\frac{XY}{CB}$

substitute the values

$\frac{20}{30}=\frac{28}{y}$

$y=30*28/20=42\ units$

8 0

3 years ago

A school sells chips and candy bars for a fundraiser.

Mashcka [7]

Answer: 21

Step-by-step explanation: 21 + 21 = 21

7 0

3 years ago

Divide 16x3 – 12x2 + 20x – 3 by 4x + 5.

nalin [4]

Answer:

$4x^2 - 8x + 15 - \frac{78}{4x+5}$

Step-by-step explanation:

<em>To solve polynomial long division problems like these, it's helpful to build a long division table. Getting used to building these can make problems like this much simpler to solve.</em>

Begin by looking at the first term of the cubic polynomial.

What would we have to multiply $4x + 5$ by to get an expression containing $16x^3$ ? The answer is $4x^2$ , since $(4x + 5) \times 4x^2 = 16x^2 + 20x$ .

This is the first step of our long division, and we write out the start of our long division table like this:

${ }\qquad{ }\quad{ }\quad{ }\,\,\,\,\,4x^2\\4x + 5\quad)\!\!\overline{\,\,\,16x^3 - 12x^2 + 20x - 3}\\{ }\qquad{ }\quad{ }\quad{ }\,\,16x^3 + 20x^2\\$

On the left is the divisor. On top is $4x^2$ . In the middle is the polynomial we are dividing, and on the bottom is the result of multiplying our divisor by

The next step is to subtract the bottom expression from the middle one, like so:

${ }\qquad{ }\quad{ }\quad{ }\,\,\,\,\,4x^2\\4x + 5\quad)\!\!\overline{\,\,\,16x^3 - 12x^2 + 20x - 3}\\{ }\qquad{ }\quad{ }\quad{ }\,\,\underline{16x^3 + 20x^2}\\{ }\qquad{ }\quad{ }\quad{ }\,\,\,\,\,0x^3 - 32x^2\\$

We are left with $-32x^2$ . The next thing to do is to add the next term of the polynomial we are dividing to the bottom line, like this:

Now we return to the beginning of the instructions, and repeat the process: namely, what would we have to multiply $4x + 5$ by to get an expression containing $-32x^2$ ? The answer is $-8x$ , and we fill out our long division table like so:

${ }\qquad{ }\quad{ }\quad{ }\,\,\,\,\,4x^2 - \,\,\,\,8x\\4x + 5\quad)\!\!\overline{\,\,\,16x^3 - 12x^2 + 20x - 3}\\{ }\qquad{ }\quad{ }\quad{ }\,\,\underline{16x^3 + 20x^2}\\{ }\qquad{ }\quad{ }\quad{ }\,\,\,\,\,\,\,\,\,\,\,\,\,\, - 32x^2 + 20x\\{ }\qquad{ }\quad{ }\quad{ }\,\,\,\,\,\,\,\,\,\,\,\,\,\, - 32x^2 - 40x\\$

Once again, we subtract the bottom expression from the one above it, and include the next term of the divisor, like so:

${ }\qquad{ }\qquad{ }\quad{ }4x^2 - \,\,\,\,8x \,+ 15\\4x + 5\quad)\!\!\overline{\,\,\,16x^3 - 12x^2 + 20x - 3}\\{ }\qquad{ }\quad{ }\quad{ }\,\,\underline{16x^3 + 20x^2}\\{ }\qquad{ }\quad{ }\quad{ }\,\,\,\,\,\,\,\,\,\,\,\,\,\, - 32x^2 + 20x\\{ }\qquad{ }\quad{ }\quad{ }\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\underline{- 32x^2 - 40x}\\{ }\qquad{ }\qquad{ }\qquad{ }\qquad{ }\qquad{ }\,\,\,\,\,60x - 3\\$

And repeat. What do we multiply $4x + 5$ by to get an expression containing $60x$ ? The answer is 15. Our completed long division table looks like this: ${ }\qquad{ }\qquad{ }\quad{ }4x^2 - \,\,\,\,8x \,+15\\4x + 5\quad)\!\!\overline{\,\,\,16x^3 - 12x^2 + 20x - 3}\\{ }\qquad{ }\quad{ }\quad{ }\,\,\underline{16x^3 + 20x^2}\\{ }\qquad{ }\quad{ }\quad{ }\,\,\,\,\,\,\,\,\,\,\,\,\,\, - 32x^2 + 20x\\{ }\qquad{ }\quad{ }\quad{ }\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\underline{- 32x^2 - 40x}\\{ }\qquad{ }\qquad{ }\qquad{ }\qquad{ }\qquad{ }\,\,\,\,\,60x - 3\\{ }\qquad{ }\hspace{3cm}\,\,\underline{60x + 75}\\{ }\hspace{4.3cm}\,\,-78$

Now, the expression at the top,

$4x^2 - 8x + 20x + 15$

is our quotient, and the last number, $-78$ , is our remainder.

Hence we arrive at the solution of

$\frac{16x^3-12x^2+20x-3}{4x+5} =4x^2 - 8x + 15 - \frac{78}{4x+5}.$

6 0

3 years ago

2+?=-1 I don’t know what this is

nydimaria [60]

Answer:

x=-3

Step-by-step explanation:

lets make the "?" to a "x"

2+x=-1

do the math and its x=-3

so that means 2+-3=-1

3 0

3 years ago

Read 2 more answers

A large pizza at Palanzio’s Pizzeria costs $6.80 plus $0.90 for each topping. The cost of a large cheese pizza at Guido’s Pizza

Dafna11 [192]

Let's begin by assigning a letter to represent our unknown: x = # of toppings to be added to each pizza Now let's come up with expressions for the cost of each pizza with its toppings: Palanxio's Pizza: 6.80 + 0.90x Guido's Pizza: 7.30 + 0.65x Now let's equate the costs of both pizzas and solve for our unknown (x): 6.80 + 0.90x = 7.30 + 0.65x 0.90x - 0.65x = 7.30 - 6.80 0.25x = 0.50 x = 0.50/0.25 x = 2 toppings to be added to each pizza Finally, we can verify our answer by plugging it back into our equation and see if both costs are the same: 6.80 + 0.90x = 7.30 + 0.65x [equation] 6.80 + 0.90(2) = 7.30 + 0.65(2) [answer plug-in] 6.80 + 1.80 = 7.30 + 1.30 $8.60 = $8.60 [both costs are the same] Since both costs are the same, we are confident that our answer is correct.

8 0

3 years ago