Solve each equation using the quadratic formula x = =
a. x2 + 3x + 2 = 0
c. 2x2 + 5x = 1
b. 4x2 + 8x - 24 = 0
d. x2 + 14x + 33 = 0​

Answer:

[tex]y\leq -\frac{1}{3}x+1[/tex]

Step-by-step explanation:

Given:

From the graph, the x and y intercepts are at the points (3, 0) and (0, 1) respectively.

Now, for a line with two points [tex](x_1,y_1)\ and\ (x_2,y_2)[/tex], the slope is given as:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Here, [tex](x_1,y_1)=(3,0)\ and\ (x_2,y_2)=(0,1)[/tex]. Therefore,

[tex]m=\frac{1-0}{0-3}=-\frac{1}{3}[/tex]

Now, y-intercept is [tex]b=1[/tex]

Therefore, the standard form of a line is of the form: [tex]y=mx+b[/tex]. So, the equation of the line on the graph is:

[tex]y=-\frac{1}{3}x+1[/tex]

Now, from the graph, the region is below the line including all the points on the line. Therefore, the inequality used is less than or equal to. This gives,

[tex]y\leq -\frac{1}{3}x+1[/tex]

Answer:

Explanation:

1. Name the angle of inclination of the line joining p to the origin α.

2. Find the relation between the coordinates of the point (x,y)

When you draw a line from the origin to the parabola, the intersection point, p(x,y) will have coordinates (x,y).

As per the definition of the tangent trigonometric ratio you have:

From which you can clear y:

Which is the expression of the coordinates of p as a function of the angle of inclination of the line joining p to the origin.

Answer:

The two numbers are -365 and -1825.

Step-by-step explanation:

5x=y

x-y=1460

--------------

x-5x=1460

-4x=1460

x=1460/-4

x=-365

-365-y=1460

y=-365-1460=-1825

Answer:

51

Step-by-step explanation:

add them altogether then times by 3

Good evening ,

Step-by-step explanation:

we know that, x-1 = (-1)×(1-x) and 1-x=(-1)×(x-1)

then each of 1-x and x-1 is a multiple of the other one,

if x>1 then x-1>0 and 1-x<0 then x-1>1-x

therefore in this case the least common multiple of x-1 and 1-x is x-1.

if x<1 then x-1<0 and 1-x>0 Then 1-x>x-1

therefore in this case the least common multiple of x-1 and 1-x is 1-x.

:)

Answer:

36792.2133

Step-by-step explanation:

36792+0.2+0.0133=36792.2133

Ms. Brown has been reading for 18 weeks so far.

To find out how many weeks Ms. Brown has been reading so far, we can set up a proportion based on the rate at which she reads books.

Ms. Brown reads 2 books every 3 weeks, so we can write this as the ratio:

[tex]\[ \frac{2 \text{ books}}{3 \text{ weeks}} \][/tex]

Now, we can set up a proportion to find out how many weeks she has been reading to reach a total of 12 books.

Let ( x) represent the number of weeks she has been reading so far. So, we set up the proportion:

[tex]\[ \frac{2 \text{ books}}{3 \text{ weeks}} = \frac{12 \text{ books}}{x \text{ weeks}} \][/tex]

Now, we can solve for ( x ) by cross-multiplying:

[tex]\[ 2 \times x = 3 \times 12 \][/tex]

[tex]\[ 2x = 36 \][/tex]

Divide both sides by 2 to solve for ( x ):

[tex]\[ x = \frac{36}{2} \][/tex]

[tex]\[ x = 18 \][/tex]

So, Ms. Brown has been reading for 18 weeks so far.

complete question given below:

Ms. Brown is reading 2 books every 3 weeks. She has read 12 books so tar. How many weeks has she been reading so far?

Answer:

y=3x

Step-by-step explanation:

The slope of this graph is 3.

The closed linear form of sequence 3, 4, 5, 6, 7, .. is a = 3 + n

Option C

Solution:

Given Sequence is 3, 4, 5, 6, 7, ...

Let us the check the each option which can form the above sequence

a) a= 2n

[tex]\begin{array}{l}{\text {For } n=0, a=2 \times(0)=0} \\\\ {\text {For } n=1, a=2 \times(1)=2} \\\\ {\text {For } n=2, a=2 \times(2)=4}\end{array}[/tex]

We get a sequence 0, 2, 4 which does not satisfy the given sequence

b) a= 2-n

[tex]\begin{array}{l}{\text {For } n=0, a=2-0=2} \\\\ {\text {For } n=1, a=2-1=1} \\\\ {\text {For } n=2, a=2-2=0}\end{array}[/tex]

We get a sequence 2, 1, 0 which does not satisfy the given sequence

c) a= 3+n

For n = 0, a = 3 + 0  = 3

For n = 1, a = 3 + 1  = 4

For n = 2, a = 3 + 2 = 5

For n = 3 , a = 3 + 3 = 6

For n = 4, a = 3 + 4 = 7

Which satisfy the given sequence

Hence, c) is the correct option

The closed linear form of the sequence 3, 4, 5, 6, 7, ... is a = 3 + n, which matches option C. The pattern in the sequence indicates that the nth term can be expressed as 3 + (n - 1). Therefore, the answer is option A: a = 2 + n.

To find the closed linear form, we identify the pattern in the sequence. The sequence starts at 3 and increments by 1 for each subsequent term. Hence, the nth term (an) can be expressed as:

an = 3 + (n - 1)

an = 2 + n

Therefore, the closed linear form of the given sequence is option A: a = 2 + n.

Answer:

Yes (6,3) is a solution

Step-by-step explanation:

It because both of the lines that are shaded intercepted so it works for both

Answer:

-8/15

Step-by-step explanation:

8*-3/15*5

=-24/75

= -8/15

The percent decrease in the mass of Finley's pumpkin after carving is approximately 40.55%.

To calculate the percent decrease in the mass of Finley's pumpkin after carving, use the following formula:

Percent Decrease = ((Original Mass - New Mass) / Original Mass) 100%

First, let's find the decrease in mass.

Decrease in Mass = Original Mass - New Mass = 6.56 kg - 3.9 kg = 2.66 kg

Then, calculate the percent decrease:

Percent Decrease = (2.66 kg / 6.56 kg) 100% = 40.55%

The percent decrease in the mass of the pumpkin after carving is approximately 40.55%.

Answer:

[tex]\displaystyle [3\frac{1}{3}, -2][/tex]

Step-by-step explanation:

{2x + 3y = ⅔

{3x - 4y = 18

¾[3x - 4y = 18]

{2x + 3y = ⅔

{2¼x - 3y = 13½

____________

[tex]\displaystyle \frac{4\frac{1}{4}x}{4\frac{1}{4}} = \frac{14\frac{1}{6}}{4\frac{1}{4}} \\ \\[/tex]

[tex]\displaystyle x = 3\frac{1}{3}[/tex][Plug this back into both equations above to get the y-coordinate of −2]; [tex]-2 = y[/tex]

I am joyous to assist you anytime.

The system of equations is solved using the elimination method. By multiplying the equations to align the coefficients and adding them to eliminate y, x is found to be 3.3333. Plugging x back into one of the original equations then gives y as -2.0000.

To solve the system of equations:

we can use the method of substitution or elimination. Let's use elimination in this case:

First, we multiply the first equation by 4 and the second equation by 3 so that the coefficients of y have the same magnitude but opposite signs:

Next, we add the two equations together to eliminate y:

8x + 12y + 9x - 12y = 8/3 + 54

17x = 54 + 8/3

17x = 54 + 2.6667

17x = 56.6667

Now we divide both sides by 17 to solve for x:

x = 56.6667 / 17

x = 3.3333

With x found, we can now substitute it back into one of the original equations to find y. We'll use the first equation for this example:

2x + 3y = 2/3

Substitute x:

2(3.3333) + 3y = 2/3

6.6666 + 3y = 2/3

3y = 2/3 - 6.6666

3y = -6.0000

Now divide both sides by 3 to solve for y:

y = -6.0000 / 3

y = -2.0000

The solution to the system is x = 3.3333 and y = -2.0000.

The following equation has infinite many solutions

3(2x+1)=2(1+3x)+1

Step-by-step explanation:

An equation has infinite solutions if there is same constant on both sides of the equation.

We will check each equation one by one to find the equation with infinite solutions.

So,

3(2x+1)=2(1+3x)+1

[tex]3(2x+1)=2(1+3x)+1\\6x+3 = 2+6x+1\\6x +3 = 6x +3\\6x-6x+3 = 3\\3 = 3[/tex]

3(2x+1)=2(1+3x)-1

[tex]3(2x+1)=2(1+3x)-1\\6x+3 = 2+6x-1\\6x+3=1+6x\\6x-6x+3 = 1\\3 = 1[/tex]

3(2x-1)=2(1+3x)-1

[tex]3(2x-1)=2(1+3x)-1\\6x-3 = 2+6x-1\\6x-3 = 1+6x\\6x-6x-3 = 1\\-3 = 1[/tex]

3(2x+1)=2(3+2x)-3​

[tex]3(2x+1)=2(3+2x)-3​\\6x+3 = 6+4x-3\\6x+3 = 3+4x\\6x-4x+3 = 3\\2x+3 = 3[/tex]

The following equation has infinite many solutions

3(2x+1)=2(1+3x)+1

Keywords: Solution of equation, Linear equation

Learn more about linear equation at:

#LearnwithBrainly

Answer:

1. For x is x=5y+30 and for y is y=1/5x−6

2. For x is x=5y−45 and for y is y=1/5x+9

Step-by-step explanation:

Answer: Option A, Option B, Option D.

Step-by-step explanation:

Let's check each option.

A. Substitute [tex]x=-7[/tex] into the equation and evaluate in order to find the value of "y". This is:

[tex]y=\frac{1}{4}x + 9\\\\y=\frac{1}{4}(-7) + 9\\\\y=7.25[/tex]

B. Substitute [tex]x=-8[/tex] into the equation and evaluate in order to find the value of "y". Then:

[tex]y=\frac{1}{4}x + 9\\\\y=\frac{1}{4}(-8) + 9\\\\y=7[/tex]

C. Substitute [tex]x=-4[/tex] into the equation and evaluate to find the value of "y":

[tex]y=\frac{1}{4}x + 9\\\\y=\frac{1}{4}(-4) + 9\\\\y=8[/tex]

D. Substitute [tex]x=5[/tex] into the equation and then evaluate in order to find the value of "y". You get that this is:

[tex]y=\frac{1}{4}x + 9\\\\y=\frac{1}{4}(5) + 9\\\\y=10.25[/tex]

Then, the correct options are: Option A, Option B, Option D.

Answer:

It will be answer choice D.

Step-by-step explanation:

It'll take the half the usual time because she is taking a road that get's her there 2 times faster, but also add 10 because she was 10 minutes late.

The linear equation in terms of x to represent the number of minutes after 5:00 pm she arrives home from work if she leaves late is (y = 0.5x + 10).

Given :

According to the given, data x represent the number of minutes her normal commute takes when she leaves on time.

Let y be the total time taken by Jade after 5:00 pm to reach home. So, the linear equation that represents the given situation is:

[tex]\rm y = \dfrac{1}{2}x+10[/tex]

Therefore, the correct option is D).

For more information, refer to the link given below:

https://brainly.com/question/11897796

Answer:

y-1=-x+2

Step-by-step explanation:

m=-1

y-1=-1(x-2)

y-1=-x+2

Answer:  monday

Step-by-step explanation:

Answer:

Step-by-step explanation:

It’s 35 because 9*5 is 45 and 80-45 is 35

The expression will be  y =8*2 or y = (48/6)*2

Step-by-step explanation:

The direct proportion is given if y varied directly as x

y∝x

When the proprtionality symbol is removed, a proportionality constant is introduced.

y = kx

as we know y = 48 when x = 6

[tex]48 = k * 6\\k = \frac{48}{6}\\k = 8[/tex]

The equation will be:

y = 8x

So when x=2

y = 8*2

y = 16

Hence,

The expression will be  y =8*2 or y = (48/6)*2

Keywords: Proportion, Direct proportion

Learn more about proportion at:

#LearnwithBrainly

To find the value of y when x is 2 in a direct variation, use the constant of variation k found from the given values (y = 48 when x = 6), which is 8 in this case, and multiply it by 2 to get y = 16.

If y varies directly as x, this means that y can be expressed as y = kx, where k is the constant of variation. Given that y = 48 when x = 6, we can find the value of k by substituting these values into the direct variation equation:

k = y/x = 48/6 = 8

Now that we have k, we can find the value of y when x is 2:

y = kx = 8 x 2 = 16

Therefore, the expression to find the value of y when x is 2 is y = 8 x 2.

Answer:

m∠NQP=74°

Step-by-step explanation:

we know that

The measure of the interior angles in a triangle must be equal to 180 degrees

In this problem

In the triangle NPQ

m∠N+m∠P+m∠Q=180°

we have

m∠N=(2x)°

m∠P=(34)°

m∠Q=(2x+2)°

substitute the values

[tex](2x)\°+(34)\°+(2x+2)\°=180\°[/tex]

solve for x

[tex](4x+36)\°=180\°[/tex]

[tex]4x=180-36[/tex]

[tex]4x=144[/tex]

[tex]x=36[/tex]

Find the measure of angle NQP

we know that

m∠NQP=m∠Q=(2x+2)°

substitute the value of x

m∠NQP=(2(36)+2)=74°

Answer:

Damien will receive a change of [tex]\$4.69[/tex]

Step-by-step explanation:

Given:

Pair of jeans = $33

Sales tax = 7%

Money paid as Sales tax = 7% of sale done on pair of jeans  = [tex]\frac{7}{100}\times \$33 = \$2.31[/tex]

Total amount paid = 40

We need to find the amount he will receive back

Amount receive back can be calculated by Total amount paid minus Amount for pair of jeans minus money paid as Sales Tax

Change amount received = Total amount paid - Amount for pair of jeans - money paid as Sales Tax = [tex]\$40 - \$33-\$2.31 = \$ 4.69[/tex]

Hence Damien will receive a change of [tex]\$4.69[/tex]

Answer:

$3.60

Step-by-step explanation:

25+20=45 (because you need the tax of both)

0.8(45)=3.60 (finding the tax amount)

The answer is $11200.

Answer:

$11,200 or its D

Step-by-step explanation:

got it right on edge