Im stuck on this problem, can someone please help​

Answer:

y = 1/2 x

Step-by-step explanation:

We have the slope of 1/2 and a point of (4,2)

We can use point slope form

y-y1 = m(x-x1)

y-2 = 1/2(x-4)

Distribute

y-2 = 1/2x -2

Add 2 to each side

y-2+2 = 1/2 x -2+2

y = 1/2 x

This is in slope intercept form

Answer:

The first two graphs are the exact same but it is the first two.

Step-by-step explanation:

Answer:

In the beginning ,number of inventory in the warehouse =6,000

 Increment in each month in inventory in the warehouse=3000

So, writing the above situation in terms of linear equation

 if,y is the number of inventory after x months

 y=6000 +3000x

Correct graph is attached below

⇒Items in Inventory(Thousands) ----X axis

⇒Number of Months since Opening----Y axis

Answer:

B. assumption of conclusions without prior experimentation or observation.

Step-by-step explanation:

In scientific investigation is quite important to demonstrate with facts, with observations, with numbers.  All discoveries, new insights, new knowledge found in scientific investigation is based on a very careful finding of facts in a very systematic way of doing that to establish conclusions about the question to be answered and constantly looking for objective evidence.

For instance, one hundred years ago, some physicists found a crucial fact that support one of the predictions that Einstein posted regarding a phenomena described as curved space because of the effect that a massive object exerts around its surrounding space. In fact, that year of 1919, those physicists observed that light traveled around a massive start not in straight line but curving around start's space (a fact), of course, using telescopes, writing observations and quantifying them (a systematic way).

Einstein's theory (in this case, the famous General Relativity Theory) must be supported, at least in part, with the discovery of an important fact, and not because he assumed that it was 'true' without prior experimentation or observation but because some others experimental physicists took a 'secret' from Nature (objective evidence) and gave a crucial fact about what Einstein had predicted some years before.

But it is not a definitive fact, a definitive list, there will be some more facts to look for in order to support that theory (constantly looking) and, why not, some other scientist or scientists could find another one, make a new experiment, test another hypothesis or model that contradicts the whole theory or some part of it.

Answer:

P (sum of two numbers is < 5) =2/9

Step-by-step explanation:

There are two numbers that can be picked such that the first number odd and less than 5:  1 and 3.

Then, the numbers that can be drawn with these numbers should be from: 1, 2, 3, 4, 5, 6, 7, 8 or 9.

The number of total possibilities = 18

Out of these, the following are the four possible options to have a sum which is less than 5 and 1:

1 and 1

1  and 2

1 and 3

3 and 1

So P (sum of two numbers is < 5) = [tex]\frac{4}{18}[/tex] = 2/9

Answer:

Step-by-step explanation:

2/9 is right because i just took it and got a 5/5

Answer:

A.

Step-by-step explanation:

you add all prices together and then mulitplied by the 15%. that gives you 20.0655 so you subtract that from the total price so 133.77-20.0655 and get 113.7045 or 113.70 which is the final price you pay

Answer:

[tex]y=-6.6[/tex] and [tex]y=10.6[/tex]

Step-by-step explanation:

The given ellipse has equation:

[tex]\frac{(y-2)^2}{64}+\frac{x^2}{9}=1[/tex].

The center of this ellipse is (h,k)=(0,2)

We use the equation: [tex]a^2-b^2=c^2[/tex] to determine the foci.

[tex]\implies 64-9=c^2[/tex]

[tex]\implies 55=c^2[/tex]

[tex]\implies c=\pm \sqrt{55}[/tex]

The directrices are given by [tex]y=k\pm\frac{a^2}{c}[/tex]

[tex]y=2\pm\frac{64}{\sqrt{55}}[/tex]

[tex]y=2\pm8.6[/tex]

[tex]y=2-8.6[/tex] and [tex]y=2+8.6[/tex]

The equation of the directrices are:

[tex]y=-6.6[/tex] and [tex]y=10.6[/tex]

The correct answer is D

Answer:

C.(x-5)²+(x+5)=9

D (x-9)²+(y+9)²=16

Step-by-step explanation:

Use a graph tool to visualize the circle.See attached

You can also see that  in the options

C. circle has center (5,-5) and radius 3 which will form in 4th quadrant

D. Circle has center (9,-9) and radius 4 which will still form in 4th quadrant

Answer:

  21,550

Step-by-step explanation:

An increase of 5% means the population is multiplied by 100% +5% = 1.05. This occurs each year for 12 years, so the multiplier is ...

  1.05¹² ≈ 1.7958563

When the initial population is multiplied by this factor, it becomes ...

  12,000×1.7958563 ≈ 21,550

Answer: 21550

Step-by-step explanation:

Answer:

A student finds a​ 95% confidence interval of​ (16.34,18.69) for the mean number of species counted. This is a valid interval because the mean number of species or any population mean does not necessarily have to be a whole number, as stated by the student.

This given confidence interval of (16.34,18.69) helps us to simply estimate the mean species counted.

Answer:

There are 40 band members including the band director that were notified of the new starting point

Step-by-step explanation:

The diagram below shows the band director at the top, then the three band members he called, then the next band members, and so forth.

Answer: i got 19

Step-by-step explanation:

Answer:

y < 2/3 x - 1 is the linear inequality which represented by the graph ⇒ 4th answer

Step-by-step explanation:

* Lets explain how to solve the problem

- At first lets find the equation of the line

∵ The line passes through points (3 , 1) and (-3 , -3)

∵ The form of the equation is y = mx + c, where m is the slope of the

  line and c is the y-intercept

- The rule of the slope of any line passes through points (x1 , y1) and

  (x2 , y2) is m = (y2 - y1)/(x2 - x1)

- The y-intercept means the intersection between the line and the

  y-axis at point (0 , c)

∵ (3 , 1) and (-3 , -3) are two points on the line

- Let (x1 , y1) is (3 , 1) and (x2 , y2) is (-3 , -3)

∴ The slope of the line m = (-3 - 1)/(-3 - 3) = -4/-6 = 2/3

∵ The line intersects the y-axis at point (0 , -1)

∴ c = -1

∵ The equation of the line is y = mx + c

∴ The equation of the line is y = 2/3 x + -1

∴ The equation of the line is y = 2/3 x - 1

- If the shaded part is over the line then the sign of inequality is ≥ or >

- If the shaded part is under the line then the sign of inequality is ≤ or <

- If the line represented by solid line (not dashed), then the sign of

 inequality is ≥ or ≤

- If the line represented by dashed line (not solid), then the sign of

 inequality is > or <

∵ The shading part is under the line

∵ The line is dashed

∴ The sign of the inequality is <

∴ y < 2/3 x - 1

* y < 2/3 x - 1 is the linear inequality which represented by the graph

The linear inequality represented by the graph is y < (2/3) * x - 1

To solve the problem, we can follow these steps:

Find the equation of the line that passes through the points (3, 1) and (-3, -3). The equation of a line is in the form y = mx + c, where "m" is the slope and "c" is the y-intercept.

Use the slope formula to calculate the slope (m) of the line. The slope formula is given by m = (y2 - y1) / (x2 - x1), where (x1, y1) is (3, 1) and (x2, y2) is (-3, -3).

Calculate the slope (m):

m = (-3 - 1) / (-3 - 3) = -4 / -6 = 2/3

Determine the y-intercept (c), which is the point where the line intersects the y-axis. In this case, it's at point (0, c).

Since the line passes through (3, 1), we can use this point to find the y-intercept:

1 = (2/3) * 3 + c

1 = 2 + c

c = -1

Now that we have the slope (m) and the y-intercept (c), we can write the equation of the line:

y = (2/3) * x - 1

Determine the direction of the shading in the inequality. If the shaded region is under the line, the sign of the inequality is "<."

Determine the style of the line on the graph. If the line is dashed, the sign of the inequality is also "<."

Combine the information to form the linear inequality:

y < (2/3) * x - 1

So, the linear inequality represented by the graph is:

y < (2/3) * x - 1

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Answer:

Step-by-step explanation:

1.6 pounds

Answer:

  $858

Step-by-step explanation:

You pay for 11 of the 12 months, so the average monthly payment is ...

  (11/12)×$936 = $858

Answer:

  B. {(1, 7), (2, 8), (4, 5), (0, 0), (3, 5)}

Step-by-step explanation:

You are right, it is easy. Any relation with a repeated first value is not a function.

A has (-3, -1) and (-3, -3), so the value -3 is a repeated first value.

C has (2, 5) and (2, 3), so the value 2 is a repeated first value.

D has (5, 8), (5, 9), and (5, -3), so the value 5 is a repeated first value.

None of A, C, or D is a relation that is a function. The correct choice is B, which has first values 0, 1, 2, 3, 4 -- none of which is repeated.

_____

If you plot points with repeated first values, you find they lie on the same vertical line. If a vertical line passes through 2 or more points in the relation, that relation is not a function. We say, "it doesn't pass the vertical line test."

A relation must pass the vertical line test in order to be a function. This is true of graphs of any kind, not just graphs of discrete points.

Answer:

The correct answer option is B. {(1, 7), (2, 8), (4, 5), (0, 0), (3, 5)}.

Step-by-step explanation:

We are to determine whether which of the given relations in the possible answer options is a function.

We know that the x values of a function cannot be repeated. It means that for each output, there must be exactly one input.

Therefore, we will look for the relation where no x value is repeated.

Function ---> {(1, 7), (2, 8), (4, 5), (0, 0), (3, 5)}

Answer:

  see the attachment

Step-by-step explanation:

f(x) is increasing for x > 0.

g(x) is increasing for x < 4.

Both functions are increasing on the open interval (0, 4). It will be graphed with a solid line between 0 and 4, and with open circles at 0 and 4. See the black line on the x-axis of the attachment for an example of such a graph.

Answer:

See below.

Step-by-step explanation:

52 inches - 41 inches = 11 inches

She needs to be at least 11 inches taller to be at least 52 inches tall.

Statements that describe how much taller she must be:

(The correct answers are in bold and checked with the square root symbol, √.)

at least 11 inches √

no more than 11 inches

a maximum of 11 inches

a minimum of 11 inches √

fewer than 11 inches

at most 11 inches

Answer:

Step-by-step explanation:

at least 11 inches

a minimum of 11 inches

Answer:

B

Step-by-step explanation:

Answer:

Simplifying

0x =-2, 1

0 * x =-2.1

Apply rule () *a = 0

0=-2.1

Step-by-step explanation:

Therefore, the zeroes of the function [tex]\( f(x) = x^2 - x - 2 \)[/tex] are [tex]\( x = 2 \)[/tex] and [tex]\( x = -1 \).[/tex]

To find the zeroes of the quadratic function [tex]\( f(x) = x^2 - x - 2 \),[/tex] we need to solve for [tex]\( x \)[/tex] when [tex]\( f(x) = 0 \)[/tex]. This means we need to find the values of [tex]\( x \)[/tex]that make the function equal to zero.

We can solve this quadratic equation by factoring or using the quadratic formula. Let's use the quadratic formula:

For a quadratic equation in the form [tex]\( ax^2 + bx + c = 0 \)[/tex], the solutions [tex]\( x \)[/tex] are given by:

[tex]\[ x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}} \][/tex]

For our equation [tex]\( f(x) = x^2 - x - 2 \)[/tex], we have [tex]\( a = 1 \), \( b = -1 \)[/tex], and [tex]\( c = -2 \)[/tex]. Substituting these values into the quadratic formula:

[tex]\[ x = \frac{{-(-1) \pm \sqrt{{(-1)^2 - 4(1)(-2)}}}}{{2(1)}} \][/tex]

[tex]\[ x = \frac{{1 \pm \sqrt{{1 + 8}}}}{2} \][/tex]

[tex]\[ x = \frac{{1 \pm \sqrt{9}}}{2} \][/tex]

[tex]\[ x = \frac{{1 \pm 3}}{2} \][/tex]

So, the solutions are:

[tex]\[ x_1 = \frac{{1 + 3}}{2} = 2 \][/tex]

[tex]\[ x_2 = \frac{{1 - 3}}{2} = -1 \][/tex]

Answer:

Step 1: Finding r using the formula ln 2/h

[tex]1.\ r=\frac{ln\ 2}{h}\\ r=\frac{ln\ 2}{140}\\r=0.00495[/tex]

Step 2: Substitute the values in given formula

[tex]2.\ m_t=m_0e^{-rt}\\200=300e^{-0.00495t}[/tex]

Step 3: Divide both sides by 300

[tex]\frac{2}{3} =e^{-0.00495t}[/tex]

Step 4:  Take the natural logarithm on both sides

[tex]ln\ \frac{2}{3} =ln\ e^{0.00495t}[/tex]

Step 5: Simplify

[tex]-0.405 = -0.00495t[/tex]

Step 6: Divide both sides by 0.00495

[tex]\frac{-0.405}{-0.00495} =t[/tex]

Step 7: Simplify

[tex]t=81.8\ days[/tex]

Answer:

B

Step-by-step explanation:

This was originally a third degree polynomial:

[tex]2x^3+4x^2-4x+6[/tex], to be exact.

When you divide by -3, you are basically trying to determine if x + 3 is a zero of that third degree polynomial.  The quotient is always one degree lesser than the polynomial you started with, and if there is no remainder, then x + 3 is a zero of the polynomial and you could go on to factor the second degree polynoial completely to get all 3 solutions.  To perform the synthetic division, you always first bring down the number in the first position, in our case a 2.  Then multiply that 2 by -3 to get -6.

-3|  2   4   -4   6

          -6

    2    -2

So far this is what we have done.  Now we multiply the -3 by the -2 and put that up under the -4 and add:

-3|  2   4   -4   6

          -6   6

    2    -2   2

Now we multiply the -3 by the 2 to get -6 and put that up under the 6 and add:

-3|   2   4   -4   6

           -6    6  -6

      2    -2   2   0

That last row gives us the depressed polynomial, which as stated earlier here, is one degree less than what you started with:

[tex]2x^2-2x+2[/tex]

Answer: OPTION B

Step-by-step explanation:

You need to follow these steps:

- Carry the number 2 down and multiply it by the the number -3.

- Place the product obtained above the horizontal line, below the number 4 and add them.

- Put the sum below the horizontal line.

- Multiply this sum by the number -3.

- Place the product obtained above the horizontal line, below the number -4 and add them.

- Put the sum below the horizontal line.

- Multiply this sum by the number -3.

- Place the product obtained above the horizontal line, below the number 6 and add them.

Then:

[tex]-3\ |\ 2\ \ \ \ \ 4\ \ -4\ \ \ \ \ \ 6\\\.\ \ \ \ \ |\ \ \ \ -6\ \ \ \ \ 6\ \ \ -6[/tex]

[tex]-----------------[/tex]

[tex].\ \ \ \ \ \ 2\ \ \ -2\ \ \ \ 2\ \ \ \ \ 0[/tex]

 Therefore, the quotient in polynomial form is:

[tex]2x^2-2x+2[/tex]

Answer:

  see below

Step-by-step explanation:

Attached is the output of a computer program that picked two different numbers at random from the set 1-52, then converted those numbers to a suit and value.

Such a program could be written in a spreadsheet or any of a variety of computer languages.

Answer:

(S+7)/4 = T

Step-by-step explanation:

S=4T-7

We want to solve to T

Add 7 to each side

S+7=4T-7+7

S+7 = 4T

Divide each side by 4

(S+7)/4 = 4T/4

(S+7)/4 = T

Answer:

8 + i

Step-by-step explanation:

What you need to simplify this is the following "definitions" of i to different powers.

[tex]i^1=i[/tex]

[tex]i^2=-1[/tex]

[tex]i^3=i^2*i=-1*i=-i[/tex]

[tex]i^4=1[/tex]

Now we can sub these in for the various powers of i in our expression:

[tex]6(1)+6(-i)-2(-1)+\sqrt{-1*49}[/tex]

Simplifying a bit:

[tex]6-6i+2+\sqrt{i^2*49}[/tex]

Since we know that the square root of i-squared is i, and that the square root of 49 is 7, we can get rid of the radial sign as follows:

6 - 6i + 2 + 7i

And the final answer, in a + bi form, is

8 + i

Answer:

The correct answer would be option D, Events in which neither event is dependent upon the other.

Step-by-step explanation:

Mutually exclusive events are the events which cannot occur at the same time. If there are two events, then in mutually exclusive situation, both events can not happen at the same time. One event will happen at a time. Mutually exclusive events are also called disjoint. Both events are not dependent upon one another. The occurrence of one event would not change the occurrence of the other event. The most appropriate and suitable example of mutually exclusive events is the tossing of a coin. Either tails will come or heads. Both events can't happen at the same time, and also not both events are dependent upon each other.

Answer:

Events in which neither event is dependent upon the other

Step-by-step explanation:

Events that are independent and cannot happen at the same time.

Answer:

[tex](\frac{-\sqrt{2}}{2},\frac{\sqrt{2}}{2})[/tex]

Step-by-step explanation:

Unit circle has a radius of 1.

So x=cos(3pi/4)=-sqrt(2)/2 and y=sin(3pi/4)=sqrt(2)/2

So the ordered pair is (-sqrt(2)/2  , sqrt(2)/2)

The terminal point for the unit circle that is determine by the [tex]$\frac{3 \pi}{4} $[/tex]   radians is

[tex]$\left( -\frac{1}{\sqrt 2}, \frac{1}{\sqrt 2} \right) . $[/tex]

We know the coordinates of the terminal point will be :

[tex]$x= \cos \left( \frac{3 \pi}{4} \right)$[/tex]    and   [tex]$y= \sin \left( \frac{3 \pi}{4} \right)$[/tex]

Therefore,

[tex]$x= \cos \left( \pi - \frac{ \pi}{4} \right)$[/tex]

[tex]$x= - \cos \frac{\pi}{4}$[/tex]

   [tex]$=-\frac{1}{\sqrt 2}$[/tex]

And

[tex]$y= \sin \left( \frac{3 \pi}{4} \right)$[/tex]

[tex]$y = \sin \left( \frac{\pi}{2} + \frac{\pi}{4} \right)$[/tex]

   [tex]$=\cos \frac{\pi}{4}$[/tex]

   [tex]$=\frac{1}{\sqrt 2}$[/tex]

Therefore the terminal points are : (x, y) = [tex]$\left( -\frac{1}{\sqrt 2}, \frac{1}{\sqrt 2} \right) . $[/tex]

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Answer:

[tex]x=\frac{10\sqrt{6}}{7}\ in[/tex]

Step-by-step explanation:

step 1

In the right triangle DOC

Find the measure of side DO

Applying the Pythagoras Theorem

[tex]DC^{2}=DO^{2}+OC^{2}[/tex]

substitute the given values

[tex]7^{2}=DO^{2}+5^{2}[/tex]

[tex]DO^{2}=7^{2}-5^{2}[/tex]

[tex]DO^{2}=49-25[/tex]

[tex]DO^{2}=24[/tex]

[tex]DO=2\sqrt{6}\ in[/tex]

step 2

In the right triangle DOC

Find the sine of angle ∠ODC

sin(∠ODC)=OC/DC

substitute

[tex]sin(ODC)=5/7[/tex] -----> equation A

step 3

In the right triangle DOP

Find the sine of angle ∠ODP

sin(∠ODP)=OP/DO

substitute

[tex]sin(ODP)=x/2\sqrt{6}[/tex] -----> equation B

step 4

Find the value of x

In this problem

∠ODC=∠ODP

so

equate equation A and equation B

[tex]5/7=x/2\sqrt{6}[/tex]

[tex]x=\frac{10\sqrt{6}}{7}\ in[/tex]

Answer:

If you want to round to the nearest hundredths, the answer is 1.73 seconds.

Step-by-step explanation:

So we want to solve h(t)=5 for t because this will give us the time,t, that the diver was 5 m above the water.

[tex]-4.9t^2+1.5t+17=5[/tex]

My goal here in solving this equation is to get it into [tex]at^2+bt+c=0[/tex] so I can use the quadratic formula to solve it.

The quadratic formula is [tex]t=\frac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex].

So let's begin that process here:

[tex]-4.9t^2+1.5t+17=5[/tex]

Subtract 5 on both sides:

[tex]-4.9t^2+1.5t+12=0[/tex]

So let's compare the following equations:

[tex]-4.9t^2+1.5t+12=0[/tex]

[tex]at^2+bt+c=0[/tex].

[tex]a=-4.9[/tex]

[tex]b=1.5[/tex]

[tex]c=12[/tex]

Now we are ready to insert in the quadratic formula:

[tex]t=\frac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex]

[tex]t=\frac{-1.5 \pm \sqrt{(1.5)^2-4(-4.9)(12)}}{2(-4.9)}[/tex]

I know this can look daunting when putting into a calculator.

But this is the process I used on those little calculators back in the day:

Put the thing inside the square root into your calculator first.  I'm talking about the [tex](1.5)^2-4(-4.9)(12)[/tex].

This gives you:  237.45

Let's show what we have so far now:

[tex]t=\frac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex]

[tex]t=\frac{-1.5 \pm \sqrt{(1.5)^2-4(-4.9)(12)}}{2(-4.9)}[/tex]

[tex]t=\frac{-1.5 \pm \sqrt{237.45}}{2(-4.9)}[/tex]

I'm going to put the denominator, 2(-4.9), into my calculator now.

[tex]t=\frac{-1.5 \pm \sqrt{237.45}}{-9.8}[/tex]

So this gives us two numbers to compute:

[tex]t=\frac{-1.5 - \sqrt{237.45}}{-9.8} \text{ and } t=\frac{-1.5+\sqrt{237.45}}{-9.8}[/tex]

I'm actually going to type in -1.5-sqrt(237.45) into my calculator, as well as, -1.5+sqrt(237.45).

[tex]t=\frac{-16.90941271}{-9.8} \text{ and } t=\frac{13.90941271}{-9.8}[/tex]

We are going to use the positive number only for our solution.

So we have the answer is whatever that first fraction is approximately:

[tex]t=\frac{-16.90941271}{-9.8}=1.725450277[/tex].

The answer is approximately 1.73 seconds.

Final answer:

To determine when the diver was 5 m above the water, we need to solve the equation h(t) = 5. Using the given equation h(t) = -4.9t² + 1.5t + 17, we substitute 5 for h(t) and solve the resulting quadratic equation. The solution is t ≈ 1.82 seconds.

Explanation:

To determine when the diver was 5 m above the water, we need to solve the equation h(t) = 5. We can substitute 5 for h(t) in the given equation and solve for t:

5 = -4.9t² + 1.5t + 17

-4.9t² + 1.5t + 12 = 0

Now, we can solve this quadratic equation using factoring, completing the square, or the quadratic formula. Let's use the quadratic formula:

t = (-b ± √(b^2 - 4ac))/2a

Plugging in the values a = -4.9, b = 1.5, and c = 12, we get:

t = (-1.5 ± √(1.5^2 - 4(-4.9)(12)))/(2(-4.9))

Simplifying further, we find two solutions: t ≈ 1.82 seconds and t ≈ -0.44 seconds. Since time cannot be negative in this context, the diver was 5 m above the water at approximately 1.82 seconds.

Answer:

(3 x + 2) (4 x + 3)

Step-by-step explanation:

Factor the following:

12 x^2 + 17 x + 6

Factor the quadratic 12 x^2 + 17 x + 6. The coefficient of x^2 is 12 and the constant term is 6. The product of 12 and 6 is 72. The factors of 72 which sum to 17 are 8 and 9. So 12 x^2 + 17 x + 6 = 12 x^2 + 9 x + 8 x + 6 = 3 (3 x + 2) + 4 x (3 x + 2):

3 (3 x + 2) + 4 x (3 x + 2)

Factor 3 x + 2 from 3 (3 x + 2) + 4 x (3 x + 2):

Answer:  (3 x + 2) (4 x + 3)

The quadratic expression 12x^2 + 17x + 6 can be factored completely as (4x +3) * (3x +2).

To factor the quadratic expression 12x^2 + 17x + 6 completely, we need to find two binomial factors that multiply together to give the original quadratic expression.

The factored form will have the following structure: (ax + b)(cx + d), where a, b, c, and d are constants.

To factor 12x^2 + 17x + 6, we can look for two numbers whose product is equal to the product of the leading coefficient (12) and the constant term (6), which is

12 * 6 = 72.

we can split 72 into 8 * 9= 72

Next, we need to find two numbers whose sum is equal to the coefficient of the linear term (17x). In this case, we need two numbers that add up to 17.

so

8+9=17

Now we can write the expression:

12x^2 + 17x + 6

12x^2 + 8x + 9x + 6

Now take common:

4x (3x + 2 ) + 3 (3x +2)

Taking 3x + 2 common we get:

(4x +3) * (3x +2)

Therefore, the quadratic expression 12x^2 + 17x + 6 can be factored completely as (4x +3) * (3x +2).

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Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}3x=-31+2y&\text{subtract}\ 2y\ \text{from both sides}\\5x+6y=23\end{array}\right\\\\\left\{\begin{array}{ccc}3x-2y=-31&\text{multiply both sides by 3}\\5x+6y=23\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}9x-6y=-93\\5x+6y=23\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad14x=-70\qquad\text{divide both sides by 14}\\.\qquad x=-5\\\\\text{Put it to the second equation:}\\\\5(-5)+6y=23\\-25+6y=23\qquad\text{add 25 to both sides}\\6y=48\qquad\text{divide both sides by 6}\\y=8[/tex]