Match each description with the expression containing terms that model it

Mathematics

1 answer:

Paul [167]3 years ago

8 0

Answer:

Step-by-step explanation:

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The difference of two numbers is 19. The larger number is three more than twice the smaller. Find the numbers.

iren [92.7K]

Let x=the larger number
y=the smaller number
If the difference of two numbers is 19,then
$x - y = 19$
If the larger number is 3 more than twice the smaller,
$x = 2y + 3$
subsituting
$x = 2y + 3 \: to \: x - y = 19$
$2y + 3 - y = 19 \\ 2y - y + 3 = 19 \\ y + 3 = 19 \\ y + 3 - 3 = 19 - 3 \\ y + 0 = 16$
$y = 16$
but ×=2y+3 so,
$x = 2 (16) + 3 \\ x = 32 + 3 \\ x = 35$
Therefore, the two numbers are 16 and 35.

4 0

3 years ago

darnell's car used 8 gallons of gasoline to travel 340 miles. after a mechanic work on teh car, it used 7 gallons of gasoline to

Radda [10]

<span> What we are going to do for this case is find the cost for each case:
Cost to run the car before the mechanic worked on it:
</span> $(4) * (8) = 32 dollars

(32) * (1/340) = 0.09 dollars / mile$
<span> Cost to run the car after the mechanic worked on it:
</span> $(4) * (7) = 28 dollars 

(28) * (1/350) = 0.08 dollars / mile$ <span>
The difference between both cases is:
</span> $0.09 - 0.08 = 0.01 dollars / mile
$
<span> Answer:
It cost to run the car after the mechanic worked on it 0.01 $ / mile less than before the mechanic worked on it.</span>

5 0

4 years ago

The diagram represents 6x2 – 7x 2 with a factor of 2x – 1. A 2-column table with 2 rows. First column is labeled 2 x with entrie

a_sh-v [17]

Factors of a polynomial can divide it without leaving remainder. The other factor of $6x^2 - 7x + 2$ is given by Option D : $3x + 2$

<h3>How to factorize a polynomial?</h3>

Let the polynomial A(x) has one factor f(x).

Then, it means, we have:

$\dfrac{A(x)}{f(x)} = g(x)$

Thus, A(x) can be written as $A(x) = f(x) \times g(x)$

Thus, the other factor of that polynomial is

$g(x) = \dfrac{A(x)}{f(x)}$

For given case, the polynomial $A(x)$ is

$A(x) = 6x^2 - 7x + 2$

Its one factor f(x) is given $f(x) = 2x - 1$

Thus, its second factor is obtained as:

$g(x) = \dfrac{A(x)}{f(x)} = \dfrac{6x^2 - 7x + 2}{(2x - 1)} = \dfrac{6x^2 -4x -3x - 2}{2x - 1}\\\\g(x) = \dfrac{2x(3x + 2) - 1(3x + 2)}{2x - 1} = \dfrac{(2x - 1)(3x + 2)}{2x - 1}\\\\g(x) = (3x + 2)$