Use the grouping method to factor the polynomial below completely.
x^3 + 2x^2 + 5x + 10

Answer:

Another point is (3,1) and the vertex is (0,0)

Step-by-step explanation:

The vertex is still (0,0) since the parabola has only been stretched some way and not shifted from the parent function f(x)=x^2.

Enter in any x you like like 3 (I chose 3 because I see I'm going to multiply by 1/3). Anyways

g(3)=(1/3*3)^2=(1)^2=1  so another point on the parabola is (3,1)... Now just use the fact that all parabolas are symmetrical to graph it.

Answer:

159

Step-by-step explanation:

Please see attachment

Answer:

y = $6

Step-by-step explanation:

In the image below, the table of your question is attached

Based on the information presented in the table.

1 ounce of oregano costs $4

Because there are 4 ounces, this means that

x = 4*($4) = $16

1 ounce of garlic powder $3

Because there are 2 ounces, this means that

y = 2*($3) = $6

Total cost of the ingredients  =  x+y = 22 $

Answer:

In the middle of 2 and 3.

Step-by-step explanation:

2 < 2.49 < 3.

Therefore, 2.49 would be located in the middle of 2 and 3, assuming that the scale is 1.

Hope this helps!

It exists located to the right of the 0 on the line, and as you can see, the numbers stand increasing proceeding from left to right. 2.49 exists located 2.49 from 0.

In math, a number line can be described as a straight line with numbers positioned at equivalent intervals or parts along its length. A number line can be expanded infinitely in any direction and exists usually expressed horizontally.

It exists located to the right of the 0 on the line, and as you can see, the numbers stand increasing proceeding from left to right. 2.49 exists located 2.49 from 0.

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Answer:

9.179999999999999e+103

Answer:

C) 7,900

Step-by-step explanation:

Answer:

can't understand the question.

What do you need? The mean? Mode? Median?

Answer:

5/96.

Step by Step explanation:

The volume = width * length * height

= 1/3 * 5/8 * 1/4

= 1*5*1 / 3*8*4

= 5 / 96.

=

I'll use arithmetic series to find it.

First two-digit number divisible by 3 is 12, last such number is 99. Every 3rd number is divisible by 3.

So,

[tex]a_1=12\\a_n=99\\d=3\\n=?\\\\a_n=a_1+(n-1)\cdot d\\99=12+(n-1)\cdot 3\\3n-3=87\\3n=90\\n=30[/tex]

There are 30 such numbers.

Answer:  [tex]y=\frac{1}{30}x+1[/tex]

Step-by-step explanation:

The equation of the line in Slope-Intercept form is:

[tex]y=mx+b[/tex]

Where "m" is the slope and "b" is the y-intercept.

The slope of the line can be calculated with this formula:

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

Pick to  points of the given line. You can choose the point (60,3) and the point (30,2).

Then, substituting into the formula, you get:

 [tex]m=\frac{2-3}{30-60}=\frac{1}{30}[/tex]

You can observe in the graph that the line intercepts the y-axis at the point (0,1), therefore "b" is:

[tex]b=1[/tex]

Substituting the slope and the y-intercept found into  [tex]y=mx+b[/tex], you get the equation of this line:

 [tex]y=\frac{1}{30}x+1[/tex]

Where "y" represents the Height (1,000 ft) and "x" represents the Time in seconds.

Answer:

The equation of the given line is :y = 0.04x + 0.6.

Step-by-step explanation:

From the given data , we can select two coordinates to determine the equation of the given line:

Let the point be [tex](10,1),(60,3)[/tex]

The equation of the line will be determined by the help of point slope form:

Slope of the line = [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex](y-y_1)=m(x-x_1)[/tex]

The equation of the line is :

[tex]m=\frac{3-1}{60-10}=\frac{2}{50}=0.04[/tex]

[tex](y-1)=0.04(x-10)[/tex]

[tex]y-1=0.04x-0.4[/tex]

[tex]y=0.04x+0.6[/tex]

The equation of the given line is :y = 0.04x + 0.6.

Answer:

Step-by-step explanation:

we know that

The Domain of the function are all the values of x that can take the function

in this problem the domain is

The Range of the function are all the values of y that can take the function

in this problem the range is

therefore

{y | y = –7, –1, 0, 9}  baaaam

know my brain hurts i hope this helped because i really tried haha sorry if it doesnt

Answer:

Step-by-step explanation:

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

The formula of a slope:

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

First table:

(-4, 26), (0, 10) → b = 10

[tex]m=\dfrac{10-26}{0-(-4)}=\dfrac{-16}{4}=-4[/tex]

[tex]\boxed{y=-4x+10}[/tex]

Second table:

(-4, 14), (0, 2) → b = 2

[tex]m=\dfrac{2-14}{0-(-4)}=\dfrac{-12}{4}=-3[/tex]

[tex]\boxed{y=-3x+2}[/tex]

We have the system of equations:

[tex]\left\{\begin{array}{ccc}y=-4x+10&(1)\\y=-3x+2&(2)\end{array}\right\\\\\text{Put (1) to (2):}\\\\-4x+10=-3x+2\qquad\text{subtract 10 from both sides}\\-4x=-3x-8\qquad\text{add 3x to both sides}\\-x=-8\qquad\text{change the signs}\\x=8\\\\\text{Put the value of x to (2):}\\\\y=-3(8)+2\\y=-24+2\\y=-22[/tex]

The solution to the given system of equations is (8, -22). Therefore, option C is the correct answer.

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

From the table 1.

Slope (m) = (18-26)/(-2-(-4))

= -8/2

m=-4

Substitute m=-4 and (x, y)=(-2, 18) in y=mx+c, we get

18=-4(-2)+c

18=8+c

c=10

So, the equation is y=-4x+10 -----(i)

From table 2:

Slope (m)=(8-14)(-2-(-4))

m=-3

Substitute m=-3 and (x, y)=(-2, 8) in y=mx+c, we get

8=-3(-2)+c

c=2

So, the equation is y=-3x+2 --------(ii)

From equation (i) and (ii), we get

-4x+10 =-3x+2

x=8

Substitute x=8 in equation (i), we get

y=-4(8)+10

y=-22

So, the solution is (8, -22)

Therefore, option C is the correct answer.

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Answer:

2/5x - 2y≥  2

Step-by-step explanation:

see attachment

paul and mary

peter and mary

peter and paul

Answer:

Peter and Neil

Step-by-step explanation:

Given rates of work:

Peter = 5 hours / room

Paul = 6 hours / room

Neil = 7.5 hours / room

Mary = 3.75 hours / room

Recall the formula for combined rate for two individuals A & B is given as

Combined rate = (A's rate x B's rate) / (A's rate + B's rate)

In our case , the combined rate is given to be 3 hours, so we must find a combination of rate A and rate B that will give us 3 hours.

If you try all the combinations in the above formula, we will find that if we substitute Peter's and Neil's rates into the formula, we will get exactly 3 hours.

Combined rate for Peter and Neil

= (Peter's rate x Neil's rate) / (Peter's rate + Neil's rate)

= (5 x 7.5) / (5+7.5) = 3 hours to complete 1 room

No other combination gives exactly 3 hours.

Answer:

y=-2/5 x -1 (It says check all that apply... I hope this equation hasn't been written in a different form in your choices-let me know)

Step-by-step explanation:

Rearrange 2x+5y=10 into slope-intercept form.

First step: Subtract 2x on both sides:  5y=-2x+10

Second step: Divide both sides by 5 giving: y=-2/5 x+2

The slope is -2/5.

Parallel lines have the same slope.

So we know the equation of our new line is in the form y=-2/5 x+b.

We need to find the y-intercept of our line... let's just use the point they have our line going through to find it. Plug in and solve for b.

1=-2/5 (-5)+b

1=2+b

-1=b

So the equation is y=-2/5 x -1

Answer:

see explanation

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Rearrange 2x + 5y = 10 into this form

Subtract 2x from both sides

5y = - 2x + 10 ( divide all terms by 5 )

y = - [tex]\frac{2}{5}[/tex] x + 2 ← in slope- intercept form

with slope m = - [tex]\frac{2}{5}[/tex]

• Parallel lines have equal slopes, so

y = - [tex]\frac{2}{5}[/tex] x + c ← is the partial equation of the parallel line

To find c substitute (- 5, 1) into the partial equation

1 = 2 + c ⇒ c = 1 - 2 = - 1

y = - [tex]\frac{2}{5}[/tex] x - 1 ← in slope- intercept form

Multiply through by 5

5y = - 2x - 5 ( add 2x to both sides )

2x + 5y = - 5 ← in standard form

Answer:

I get 9.2 but if the answer is rounded then 9 should be correct

Step-by-step explanation:

Plug in the 5 and solve.

Hope this helps a bit,

Flips

Answer:

Step-by-step explanation:

Start with y=(2/3)x+1 . The slope of any line perpendicular to this is the negative reciprocal of 2/3:  -3/2.

Then we have y = mx + b, which, using the given data (12, -6), becomes

-6 = (-3/2)(12) + b, or

-6 = -18 + b, so b = 12 and y = (3/2)x + 12.

We must put this into standard form.  Mult. all three terms by 2:

2y = 3x + 24      

Answer:

y = 14x -30

Step-by-step explanation:

The slope intercept form is:

y = mx + b,

Slope intercept form is useful for finding the slope and y intercept of a line, hence why it is called "slope intercept" because it is easy to see the slope and the y intercept of a line in this form. Since the slope denoted by m, and y intercept denoted by b are clearly given.

y + 2 = 7(2x - 4)

Distribute 7 across the parentheses by multiplying x and 2x and 4 by 7.

y+2 = 14x - 28

subtract 2 from both sides. This cancels the 2 on the left and moves it to the right, while keeping the equation balanced.

y+2 -2 = 14x - 28 -2

y  = 14x - 30

y = 14x -30

As you can see our y = 14x -30 now looks like the point slope equation we had above. m = 14, and  b = -30. This means the line goes up 14 for every single unit you move to the right, and intersects the y axis at  (0, -30).

Please mark me brainliest.

Answer:

  option 3

Step-by-step explanation:

Dilation by a scale factor of 3/2 multiplies each of the coordinate values by 3/2. For example, P' = (3/2)P = (3/2)(4, 4) = (6, 6).

The only choice with coordinates matching these is option 3.

Answer:

f(x) = 10² + 3 = 100 + 3 = 103

Final answer:

Without a specific definition of ƒ(x), we can't provide a precise evaluation at x = 10. However, if ƒ(x) is a constant function such as ƒ(x) = 20 for the range of 0 to 20, then ƒ(10) would be 20.

Explanation:

To evaluate the function ƒ(x) when x = 10, we need to know the specific form of the function. However, based on the information provided, which seems fragmented and from different contexts, I can assume that ƒ(x) is defined for certain ranges. There’s reference to a horizontal line graph representation of a function, which suggests that ƒ(x) could potentially be a constant function within a certain range. If the function ƒ(x) is indeed a constant function, such as ƒ(x) = 20 for 0 ≤ x ≤ 20, then evaluating it at x = 10 would simply give the constant value, which is 20.

From the other contexts provided, it's implied that there could be scenarios where ƒ(x) represents different mathematical or physics concepts, such as force, probability distribution, or equations of motion. Without a direct specification of ƒ(x) for the x value in question, the remaining information cannot be used to definitively evaluate ƒ(x) at x = 10.

Answer:

b) 2x + y = -4

Step-by-step explanation:

To go from the Point-Slope Formula [y - y₁ = m(x - x)₁] to the Slope-Intercept Formula [y = mx + b], move -1 to the RIGHT side of the equivalence symbol to get this: y = -2x - 4. Although this is a correct answer choice, this is NOT what the question is looking for because you have to go an extra step further, Standard Formula. To go from the Slope-Intercept Formula to the Standard Formula [Ax + By = C], move 2x to the LEFT side of the equivalence symbol, and you will end up with this: 2x + y = -4. So, your answer is b).

Answer:

b) [tex]2x+y=-4[/tex]

Step-by-step explanation:

We have been given an equation [tex]y+1=-2x-3[/tex]. We are asked to write our given equation in standard form.

We know that standard form of an equation is [tex]Ax+By=C[/tex].

Let us convert our given equation in standard form as:

[tex]y+1-1=-2x-3-1[/tex]

[tex]y=-2x-4[/tex]

[tex]y+2x=-2x+2x-4[/tex]

[tex]2x+y=-4[/tex]

Therefore, the standard form of our given equation would be [tex]2x+y=-4[/tex].

Answer:

(x-5)2

Step-by-step explanation:

you must solve the expression (x-5)2 as the form (a-b)2 = a2 -2ab + b2

So it becomes x2-10x+25

Answer: (x-5)(x-5) or (x-5)²

Step-by-step explanation:

(a-b)(a-b)= a² - 2ab + b²

→ x² - 10x - 25

→ √25 = 5

so a= x, b= 5

this gives us (x-5)(x-5)

For this case we have the following quadratic equation:

[tex]2x ^ 2-4x + 9 = 0[/tex]

The solutions are given by:

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

We have to:

[tex]a = 2\\b = -4\\c = 9[/tex]

Substituting:

[tex]x = \frac {- (- 4) \pm \sqrt {(- 4) ^ 2-4 (2) (9)}} {2 (2)}\\x = \frac {4 \pm \sqrt {16-72}} {4}\\x = \frac {4 \pm \sqrt {-56}} {4}\\x = \frac {4 \pm \sqrt {-1 * 56}} {4}\\x = \frac {4 \pmi \sqrt {2 ^ 2 * 14}} {4}\\x = \frac {4 \pm2i \sqrt {14}} {4}\\x = \frac {2 \pm i\sqrt {14}} {2}[/tex]

Answer:

[tex]x_ {1} = \frac {2 + i \sqrt {14}} {2}\\x_ {2} = \frac {2-i \sqrt {14}} {2}[/tex]

Answer:

OPTION E: [tex]\frac{2+\sqrt{14}i}{2}[/tex]

Step-by-step explanation:

Given the Quadratic equation [tex]2x^2-4x+9=0[/tex], you can find the roots by applying the Quadratic formula. This is:

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

In this case you can identify that:

[tex]a=2\\b=-4\\c=9[/tex]

Then you can substitute values into the Quadratic formula:

[tex]x=\frac{-(-4)\±\sqrt{(-4)^2-4(2)(9)} }{2(2)}[/tex]

[tex]x=\frac{4\±\sqrt{(56} }{4}[/tex]

Remember that [tex]\sqrt{-1}=i[/tex], then:

[tex]x=\frac{4\±2\sqrt{14}i}{4}[/tex]

Simplifying, you get:

[tex]x=\frac{2(2\±i\sqrt{14}i)}{4}\\\\x=\frac{2\±\sqrt{14}i}{2}\\\\\\x_1=\frac{2+\sqrt{14}i}{2}\\\\x_2=\frac{2-\sqrt{14}i}{2}[/tex]

Answer:

x = 2

Step-by-step explanation:

Note that the coordinates (2, 3) and (2, 5) both have the same x- coordinate.

This indicates that the points lie on a vertical line parallel to the y- axis.

The equation of a vertical line is

x = c

where c is the value of the x- coordinates the line passes through.

In this case the x- coordinate is 2, hence the equation of the line is

x = 2

Answer:

See explanation. (Also you can write an equation several different ways so without the choices I cannot tell you which)

Step-by-step explanation:

Slope-intercept form is y=mx+b

So one way to write the equation is y=-3/4 x +3/2

There are more ways to write it.

Every line about to write is a way to write it.

Multiply both sides by 4:                 4y=-3x+6

Add 3x on both sides:               3x+4y=6

Subtract 6 on both sides:         3x+4y-6=0

There are a lot of ways to write an equation like this.

To better assist you I would need to see options.

Graph Function

  A         f(x) = x

  B        f(x) = x^2

  C         f(x) = x^3

  D         f(x) = √(x - 1)

  E          f(x) = 1/x

To match each graph with the function it represents, we need to consider the shape of the graph and the equation of the function.

Graph A: This graph is a straight line that passes through the origin and has a slope of 1.

This indicates that the function is linear and has the following equation:

f(x) = x

Graph B: This graph is a parabola that opens upwards and has its vertex at the origin.

This indicates that the function is quadratic and has the following equation:

f(x) = x^2

Graph C: This graph is a cubic function that opens upwards and has a point of inflection at the origin.

This indicates that the function has the following equation:

f(x) = x^3

Graph D: This graph is a square root function. It has a vertical asymptote at x = 1 and a horizontal asymptote at y = 1.

This indicates that the function has the following equation:

f(x) = √(x - 1)

Graph E: This graph is a reciprocal function. It has a vertical asymptote at x = 0 and a horizontal asymptote at y = 0.

This indicates that the function has the following equation:

f(x) = 1/x

Answer:

m∠1 = 142

Step-by-step explanation:

38 + m∠1 = 180

m∠1 = 142

Answer:

None of these apply

Step-by-step explanation:

Step 1: Bring the equation into the form of y=mx+c

5x-2y = -6

-2y = -6-5x

y = 6+5x

       2

y = 5/2x + 3

Step 2: Identify the slope (m)

Slope is the number with x (5/2)

Step 3: Find slope of the perpendicular line.

Slope of line 2 (perpendicular line) = -1/slope of line 1

m2 = -1/m1

m2 = -1/5/2

m2 = -2/5

Step 4: Find the y-intercept of the perpendicular line,

slope = -2/5

x and y coordinates = (5, -4)

y = mx + c

-4 = -2/5 (5) +c

-4 + 2 = c

c = 2

Step 5: Form equation of perpendicular line

y = mx + c

y = -2/5x + 2

Step 6: Check all equations and match with y = -2/5x + 2

a) y = x - 2 (It does not apply because this equation does not have a slope and y-intercept is not the same).

b) 2x + 5y = -10

   5y = -10 -2x

   y = -2/5x - 2 (This does not apply because the y-intercept does not match-it should be +2))

c) 2x - 5y = -10

   -5y = -10 - 2x

     y = 2/5x + 2 (This does not apply because the slope does not match-it should be -2/5)

d) y + 4 = (x - 5)

  y = x-5-4

  y = x-9 (This does not apply as the slope and y - intercept do not match)

e) y - 4 = (x + 5)

  y = x + 9 (This does not apply as the slope and y - intercept do not match)

!!

Answer:

3789.00 loss

Step-by-step explanation: Well She sold the stock but for every stock she sold she had to pay commission which was 39 Dollars for every stock sold. She only Made 2.5% of the Stocks sold, Which is an L, So the answer would be 3789.00, Loss.

Answer:

O = 2 π n - π/2 for n element Z

Step-by-step explanation:

Solve for O:

sin(O) = -1

Hint: | Eliminate the sine from the left hand side.

Take the inverse sine of both sides:

Answer:  O = 2 π n - π/2 for n element Z

assuming you meant sin(θ) = -1, Check the picture below.