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3 years ago

Factor this trinomial: 5x^2+17x+6

Mathematics

1 answer:

nevsk [136]3 years ago

7 0

Step-by-step explanation:

Hey there!

Given;

$= 5 {x}^{2} + 17x + 6$

Solve it through mid-term factorization.

$= 5 {x}^{2} + (15 + 2)x + 6$

Simplify it.

$= 5 {x}^{2} + 15x + 2x + 6$

$= 5x(x + 3) + 2(x + 3)$

$= (5x + 2)(x + 3)$

Therefore the factors are; (5x+2) (x+3).

Hope it helps...

You might be interested in

Write √3 x √6 in the form b√2 where b is an integer

bagirrra123 [75]

Answer:

3√2

Step-by-step explanation:

√3 x √6

= √3×6

= √18

= √9×2

= √9 × √2

= 3 × √2

= 3√2

I hope this was helpful, please rate as brainliest

7 0

3 years ago

sing the expression x + 3, write one equation that has one solution, one equation that has no solution, and one equation that ha

8090 [49]

Answer: one solution x + 3 = 5 x = 2 no other other value for x is possible

No solution: (x + 3) = 2(x +3)

Infinitely many solutions: x+3 = 3 + x

Step-by-step explanation:

why (x + 3) = 2(x +3) has no solution. Can you solve?

x+3=2x+6 -x=3 x=-3 substute -3 for x

(-3)+ 3)= 2[(-3) +3]

-3+3 = -6 +3

0 = -3 False!

x+3 = 3 + x has infinitely many solutions. Substitute any number for x, and the equation is true (5)+3=3+(5) 8=8 . 11111+3 =3+11111 11114=11114

6 0

3 years ago

A cabinet door has a perimeter of 62 inches its area is 228 in.² what are the dimensions of the door

Vlad1618 [11]

P=2(L+W)
A=LW

given
P=62
62=2(L+W)
divide 2
31=L+W
minus W
L=31-W

sub into other one
A=LW
A=(31-W)(W)
228=31W-W^2
times -1
W^2-31W=-228
add 228 both sides
W^2-31W+228=0
factor
what 2 numbers multiply to get 228 and add to get -31
-19 and -12
(W-19)(W-12)=0
set to zero

W-19=0
W=19

W-12=0
W=12

sub back

L=31-W
L=31-12
L=19
or
L=31-19
L=12

the doorway is 12in by 19in

4 0

3 years ago

Find the x- and y- intercepts of parabola y=5x^2-16x+10

____ [38]

Y-INTERCEPT

$y = 5x^2 - 16x + 10$

The y-intercept is where the equation/curve/parabola cosses the y-axis.

The y-axis is where x = 0. (The x-axis is where y = 0)

To find the y-intercept:

$\text{y-axis} \rightarrow \text{x = 0} \rightarrow y = 5(0)^2 -16(0) + 10 = 10$

The y-intercept must be at (0, 10)

X-INTERCEPT (ROOTS/SOLUTIONS)

$y = 5x^2 - 16x + 10\\\text{make it equal 0}\\y = 0\\\therefore 5x^2 - 16x + 10 = 0$

We need to use the quadratic formula

The quadratic formula helps us find what values of $x$ make the equation = 0

Quadratic formula: $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

$x=\frac{-(-16) + \sqrt{(-16)^2-4(5)(10)}}{2(5)}\\\\x = \frac{16 + \sqrt{256-200}}{10}\\x = \frac{16 + \sqrt{56}}{10}\\x = \frac{16 + 2\sqrt{14}}{10}\\x = \frac{8 + \sqrt{14}}{5}\\\\\\x=\frac{-(-16) - \sqrt{(-16)^2-4(5)(10)}}{2(5)}\\\text{doing the same thing...}\\\text{end up with...}\\x = \frac{8 - \sqrt{14}}{5}\\$

The x-intercepts are at:

$(\frac{8 + \sqrt{14}}{5}, 0)\\(\frac{8 - \sqrt{14}}{5}, 0)$

5 0

2 years ago

If Florist B increases the cost per rose to $5.20,for what number of roses is it less expensive to order from Florist A? From Fl

Alenkinab [10]

Answer:

For 38 roses at $5.15 per rose, Florist A is Less Expensive then Florist B

For 34 roses at $5.20 per rose, Florist A is Less Expensive then Florist B

Step-by-step explanation:

The Full Question Reads:

Derek wants to order some roses online. Florist A charges $4.75 per blue rose plus $40 delivery charge. Florist B charges $5.15 per red rose plus $25 delivery charge. If Florist B increases the cost per rose to $5.20, for what number of roses is it less expensive to order from Florist A? From Florist B?

To begin we need to understand our given information and what we are actually looking for.

Given Information

Florist A:

charges $4.75 per blue rose

charges $40 per delivery

Florist B:

charges $5.15 per red rose

charges $25 per delivery

Note: in this problem we ignore the colour of the rose (red or blue) as it does not affect our solution or contributes to it. Therefore we shall call our first variable representing the number of roses as $x$ .

The next step is to construct a system of equations representing our problem and our given information. Here we are looking at linear relationships so a linear function of the form:

$y=ax+b$ Eqn(1).

will suffice where

$y$ : represents the total cost from the Florists (i.e. number of roses and delivery charges). Dependent Variable

$x$ : represents the number of roses purchased from the Florists. Independent Variable

$a$ : is our relationship factor between $y$ and $x$

$b$ : is our constant which in this problem is the delivery charge value for each florist.

Since we have two Florists, we will construct two equations, one for each florist, by employing Eqn(1). and our given information as follow:

Florist A: $y=4.75x+40$ Eqn(2).

Florist B: $y=5.15x+25$ Eqn(3).

By employing both equations above and writing them as an inequality since we are looking for which value of $x$ (i.e. number of roses) will the less expensive Florist be and then solving for $x$ we have:

$4.75x+40$

$4.75x-5.15x$ Gathering all similar terms together

$-0.4x$ Simplifying

$x>\frac{-15}{-0.4}\\$ Solving for x

$x>37.5$

(note how < changes to > since any multiplication/devision process of negative sign in an Inequality will change the order of < to > and vice versa).

Since a rose has to be sold as a whole and not half we will say that $x>38$ So we can then plug in the value of $x$ in Eqn(2) and Eqn(3) and find the cost of buying more than 38 roses from each:

Eqn(2): Florist A: $y(x>38)=4.75*38+40=220.5$

Eqn(3): Florist B: $y(x>38)=5.15*38+25=220.7$

Which tells us that Florist A is less expensive than Florist B by $0.20 for a purchase of more than 38 roses.

Next the question tells us that Florist B increases the cost from $5.15 to $5.20 per rose, which in Eqn(3) denotes our $a$ value and thus Eqn(3). now becomes:

Florist B: $y=5.20x+25$ Eqn(3).

Applying the same method like before and solving for the value of $x$ we have:

$4.75x+40$

$4.75x-5.20x$ Gathering all similar terms together

$-0.45x$ Simplifying

$x>\frac{-15}{-0.45}\\$ Solving for x

$x>33.3$

Similarly as a rose has to be sold as a whole and not half we will say that $x>34$ So we can then plug in the value of $x$ in Eqn(2) and Eqn(3) and find the cost of buying more than 34 roses from each:

Eqn(2): Florist A: $y(x>34)=4.75*34+40=201.5$

Eqn(3): Florist B: $y(x>34)=5.15*34+25=201.8$

Which tells us that Florist A is again less expensive than Florist B by $0.30 for a purchase of more than 34 roses. It was also shown that as the cost of the rose increased by $0.05 the number of roses for purchase decreased.

4 0

3 years ago