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3 years ago

Factor : 2b^2 + 13b - 7Please help !!! :)

Mathematics

1 answer:

julsineya [31]3 years ago

4 0

2b² + 13b - 7

First you multiply the first and last number together, which is 2 and 7.

2 · 7 = 14

Now that you got 14, you try to find all the factors of 14 and see if any of them add up to or subtract to 13.

14:

1 · 14 = 14

2 · 7 = 14

Your factors are 1, 2, 7, and 14. 14 and 1 subtract to 13, so you can replace 13b with this:

2b² + 14b - 1b - 7 (it is not -14b + 1b because 13b is positive)

Next you factor the equation separately.

2b(b + 7) - 1b - 7

2b(b + 7) - 1(b + 7)

(2b - 1)(b + 7)

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1500 soldiers arrive at a training camp. A few soldiers desert the camp. The drill sergeants divide the remaining soldiers into

iren [92.7K]

Answer:

The number of deserters is 34.

Step-by-step explanation:

We have to calculate the number of desertors in a group of 1500 soldiers.

The sergeant divides in groups of different numbers and count the lefts over.

If he divide in groups of 5, he has on left over. The amount of soldiers grouped has to end in 5 or 0, so the total amount of soldiers has to end in 1 or 6.

If he divide in groups of 7, there are three left over. If we take 3, the number of soldiers gruoped in 7 has to end in 8 or 3. The only numbers bigger than 1400 that end in 8 or 3 and have 7 as common divider are 1428 and 1463.

If we add the 3 soldiers left over, we have 1431 and 1466 as the only possible amount of soldiers applying to the two conditions stated until now.

If he divide in groups of 11, there are three left over. We can test with the 2 numbers we stay:

$(1431-3)/11=1428/11=129.82\\\\(1466-3)/11=1463/11=133$

As only 1466 gives a possible result (no decimals), this is the amount of soldiers left.

The deserters are 34:

$D=1500-1466=34$

6 0

3 years ago

<img src="https://tex.z-dn.net/?f=f%28x%29%20-%20%5Cfrac%7Bx%5E%7B2%7D-4%20%7D%7Bx%5E%7B4%7D%20%2Bx%5E%7B3%7D%20-4x%5E%7B2%7D-4%

Llana [10]

a) The given function is

$f(x)=\frac{x^2-4}{x^4+x^3-4x^2-4}$

The domain refers to all values of x for which the function is defined.

The function is defined for

$x^4+x^3-4x^2-4\ne0$

This implies that;

$x\ne -2.69,x\ne 1.83$

b) The vertical asymptotes are x-values that makes the function undefined.

To find the vertical asymptote, equate the denominator to zero and solve for x.

$x^4+x^3-4x^2-4=0$

This implies that;

$x= -2.69,x=1.83$

c) The roots are the x-intercepts of the graph.

To find the roots, we equate the function to zero and solve for x.

$\frac{x^2-4}{x^4+x^3-4x^2-4}=0$

$\Rightarrow x^2-4=0$

$x^2=4$

$x=\pm \sqrt{4}$

$x=\pm2$

The roots are $x=-2,x=2$

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

To find the y-inter, we substitute;

$x=0$ into the function

$f(0)=\frac{0^2-4}{0^4+0^3-4(0)^2-4}$

$f(0)=\frac{-4}{-4}=1$

e) to find the horizontal asypmtote, we take limit to infinity

$lim_{x\to \infty}\frac{x^2-4}{x^4+x^3-4x^2-4}=0$

The horizontal asymtote is $y=0$

f) The greatest common divisor of both the numerator and the denominator is 1.

There is no common factor of the numerator and the denominator which is at least a linear factor.

Therefore the function has no holes.

g) The given function is a proper rational function.

There is no oblique asymptote.

See attachment for graph.

6 0

3 years ago

I need help With this plz

s2008m [1.1K]

Answer:

The discount is the same.

Step-by-step explanation:

We need to find the ratios of both discounts.

41/50 = 61.5/75

If the question is True, this means that the ratios should be the same. So we have to cross multiply to find the answer.

75*41 = 50*61.5 = 3075

These two multiplication problems both equal 3075. Since the ratios are equal, the discounts are also equal.

4 0

3 years ago

Apex please help a.)graph d b.) graph b c.) graph a d.) graph c

Arte-miy333 [17]

Answer:

GRAPH D

Step-by-step explanation:

BECASUE IT IS THE WRIGHT ANSWER

4 0

3 years ago

pickupchik [31]

Answer:

2.4cm

Step-by-step explanation:

the area of a triangle is

baseline × height / 2

that means two lengths of the triangle have to be multiplied.

and to have 2 similar triangles means that all lengths inside one triangle are the corresponding lengths inside the other triangle multiplied by the scaling factor f.

multiplying 2 if these lengths with each other means also including the square of the scaling factor (multiplying with the scaling factor twice).

so, if the area of triangle 1 is

"baseline 1" × "height 1" / 2 = 45 cm²

then the area of triangle 2 is

"baseline 2" × "height 2" / 2 =

= "baseline 1"×f × "height 1"×f /2 =

= "baseline 1" × "height 1" × f² / 2 =

= ("baseline 1" × "height 1" / 2) × f² =

= 45 × f² = 20 cm²

f² = 20/45 = 4/9

f = 2/3

so, for a side of ABC being 3.6cm long, that means the corresponding side in DEF is

3.6 × f = 3.6 × 2/3 = 7.2/3 = 2.4cm

4 0

3 years ago