Put the trinomial x^2+8x+14 into (x+a)^2+b form where a and b can be positive or negative. Thanks!

Step-by-step explanation:

the solutions for a quadratic equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

a = 1

b = -4

c = k

x = (4 ± sqrt(16 - 4k))/2 = 2 ± sqrt(4 - k)

x1 = 2 + sqrt(4 - k)

x2 = 2 - sqrt (4 - k)

x1 = 2 + x2

2 + sqrt(4 - k) = 2 + 2 - sqrt(4 - k)

2×sqrt(4 - k) = 2

sqrt(4 - k) = 1

4 - k = 1

k = 4 - 1 = 3

x1 = 3

x2 = 1

Answer:

The roots are 1 and 3.

k = 3.

Step- by-step explanation:

We use the facts that if α and β are the roots of ax^2 + bx + c = o then α+ β = -b/a and  α β = c/a.

The roots are written as  α and α+2, then:

α + α + 2 = -(-4)

2α + 2 = 4

α + 1 = 2

α = 1

also

α (α + 2) = k

Substituting for α:

1(1 + 2) = k

k = 3.

The roots are 1 and 1 + 2 = 3.

Answer: i took the test its number 555555

Step-by-step explanation:

Answer:

A(0,3)

Step-by-step explanation:

the line crosses y-axis so its x-coordinates must be zero,

so we subistitute by x=0 in the equation of the line, from this we get y=3

then the coordinates of point A will be (0,3)

Answer:

b)252 is the answer

Step-by-step explanation:

x\42=6

x=6*42

x=252

Answer:

1/5 so the first option

Step-by-step explanation:

slope

(y2-y1)/(x2-x1)

Step-by-step explanation:

1.Find the sample size, n, and the sample proportion. The sample proportion ρ is the number in the sample with the characteristic of interest, divided by n.

2. Multiply the sample proportion by 1 - ρ.

3. Divide the result by n.

4. Take the square root of the calculated value.  You now have the standard error

[tex] \frac{4}{6} \times \frac{2}{5} \\ = \frac{4 \times 2}{6 \times 5} \\ = \frac{8}{30} \\ = \frac{4}{15} [/tex]

Hope you could get an idea from here.

Doubt clarification - use comment section.

Answer:

second pack

Step-by-step explanation:

1.25÷4= 0.31 so for the first pack 1 pencil cost $0.31

2.50×20%= 0.5 so its ¢50 off. 2.50-0.50= 2. 2÷8= 0.25. so for the second pack 1 pencil costs $0.25 which is lower than the 1st pack.

I hope it wasn't too confusing

Answer:

y=3x+5

Step-by-step explanation:

y-y1=m(x-x1)

y-5=3(x-0)

y-5=3(x)

y-5=3x

y=3x+5

Note that the slope intercept form is y=mx+b where m=slope and b=y-intercept.

If you're satisfied with the answer, then please mark me as Brainliest. Thank you.

Answer:

f(x) - 3 : the ones that move the graph down

f(x -3)  : the ones that move the graph to the RIGHT

Step-by-step explanation:

graph transformations:

f (x-3):

if the number is inside the "()" sign with the x -> you will have to move the graph sideways (left or right), but it has a little twist: if the number is negative (i.e: f(x)-3), you will move the graph to the right, and if it is positive, you will move it to the left.

f (x) -3:

if the number is outside the "()" -> you will have to move the graph up or down. there is no twist here: if its negative, it goes down, if its positive, it goes up.

hope i could help:)

Answer:

  (4, -2)

Step-by-step explanation:

Use the expression for y given by the first equation to substitute for y in the second equation.

  2(2x -10) = x -8 . . . substitute for y

  4x -20 = x -8 . . . . . eliminate parentheses

  3x = 12 . . . . . . . . add 20-x

  x = 4 . . . . . . . . .divide by 3

  y = 2(4) -10 = -2 . . . substitute for x in the first equation

The solution is (x, y) = (4, -2).

[tex]\huge\bf\underline{\underline{\pink{A}\orange{N}\blue{S}\green{W}\red{E}\purple{R:-}}}[/tex]

We've been given to find out the values of x & y from the two given linear equations by substitution method.

Here we have,

As we have given the value of y i.e (y = 2x - 10) placing this value of y in the second equation we get,

[tex]:\implies\tt{2(2x - 10) = x - 8}[/tex]

[tex]:\implies\tt{4x - 20 = x - 8}[/tex]

[tex]:\implies\tt{4x - x = - 8 + 20}[/tex]

[tex]:\implies\tt{3x = 12}[/tex]

[tex]:\implies\tt{x = \frac{12}{3} }[/tex]

[tex]:\implies\tt{x = 4}[/tex]

Placing x = 4 in equation (1) we get,

[tex]:\implies\tt{y = 2x - 10}[/tex]

[tex]:\implies\tt{y = 2 \times 4 - 10}[/tex]

[tex]:\implies\tt{y = 8 - 10}[/tex]

[tex]:\implies\tt{y = - 2}[/tex]

Answer:

12x - 18

Step-by-step explanation:

3 x 4x = 12x

3 x -6 = -18 (Negative and positive make a negative.)

12x - 18

Answer:

14

Step-by-step explanation:

x=4 y=1

Substitute them into the equation 3x-4yy+6

3(4)-4(1)+6

12-4+6

Answer:

mass=300kg

acceleration=5m/S2

force=?

Now,

force= m×A

=300kg×5

=1500 Newton answers

Step-by-step explanation:

hop this may help you

Answer:

area = PI x r^2

area = 3.14 x 13^2

area = 3.14 x 169

area = 530.66

Step-by-step explanation:

Plz Mark as brainliest hope this helps

10% off means the jeans will sell for 90% of the original price ( 100% - 10% = 90%)

Multiply the original price by 90%

65.00 x 0.90 = 58.50

He will pay $58.50

Answer:

C

Step-by-step explanation:

If the line goes from 6 to 0 then that means it is decending and that T is LESS than 6

the answer to your question is B.) 12x

Answer:

(C)

Step-by-step explanation:

If can't have a meaning as something can't decrease more than 100% of itself.

The statement that is meaningless is

There was a 120% decrease in the amount of water in a dam.

Option C is the correct answer.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

A percentage increase can be of any number.

A percentage decrease can not be below 100%.

Now,

A.

There was a 3% decrease in the price of sugar.

This is possible.

B.

There was a 200% increase in the population of the town.

This is possible.

C.

There was a 120% decrease in the amount of water in a dam.

This is not possible.

The highest percentage decrease can be up to 100%.

D.

There was a 0% change in the temperature in the room after 1 hour.

This is possible.

Thus,

There was a 120% decrease in the amount of water in a dam is meaningless.

Learn more about percentages here:

https://brainly.com/question/11403063

#SPJ2

Answer:

x=-9, y=-6. (-9, -6).

Step-by-step explanation:

4x-5y=-6

-6x+7y=12

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

6(4x-5y)=6(-6)

4(-6x+7y)=4(12)

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

24x-30y=-36

-24x+28y=48

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

-2y=12

y=12/-2

y=-6

4x-5(-6)=-6

4x+30=-6

4x=-6-30

4x=-36

x=-36/4

x=-9

Step-by-step explanation:

Pythagoras :

c² = a² + b²

c is the Hypotenuse (side opposite of the right angle), which is in our case the distance of the 2 cars.

after 2 hours the east car was driving x miles. and the south car was driving x + 2×25 = x + 50 miles.

x² + (x + 50)² = 250²

x² + x² + 100x + 2,500 = 62,500

2x² + 100x = 60,000

x² + 50x = 30,000

x² + 50x - 30,000 = 0

the solution for a quadratic equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

a = 1

b = 50

c = -30,000

x = (-50 ± sqrt(2500 - 4×1×-30000))/(2×1) =

= (-50 ± sqrt(2500 + 120000)/2 =

= (-50 ± sqrt(122500))/2 = (-50 ± 350)/2 =

= -25 ± 175

x1 = -25 + 175 = 150 miles

x2 = -25 - 175 = -200 miles.

negative distances don't make any sense here in our scenario, so the solution is x = 150 miles.

therefore, the east car was going 75 mph (traveled in 2 hours 150 miles).

and the south car was going 75 + 25 = 100 mph (traveled in 2 hours 200 miles).

Answer:

X = 10*9/5

= 2*9

= 18

Answer = 18

Answer:

[tex]x=18[/tex]

Step-by-step explanation:

First way (equivalent fractions):

[tex]\frac{x}{10}=\frac{9}{5}[/tex]

[tex]\frac{x}{10}=\frac{18}{10}[/tex]

[tex]x=18[/tex]

Second way (cross multiplication):

[tex]\frac{x}{10}=\frac{9}{5}[/tex]

[tex]5x=90[/tex]

[tex]x=18[/tex]

Answer:

n+3n=$850  n is one person and 3n is the other represented by n

Step-by-step explanation:

answer is probably just 4

4/1 rise over run

Answer:

Linear functions are equations where the greatest power of the variable (typically x) is 1;

They are graphed as straight lines;

So, any function that has the following format:

f(x) = ax + b;

Nonlinear functions would be any equation that has a variable to a power greater than 1;

This could be a quadratic equation or an exponential equation

Step-by-step explanation:

honestly kinda stumped so ima give you the best copy and pasted answer ever

A:

Isolate the variable by dividing each side by factors that don't contain the variable. y = x/3 − 4/3

and also x=7 y=1

HOPE I HELPED, SORRY IF I GOT IT WRONG <3

Answer:

Step-by-step explanation:

The 22 degree angle is opposite to the 10 m side of the right triangle.

We need to find the length x of the hypotenuse.

Use trigonometry:

Answer:

PLEASE HELP!!!!! 100 points!!!

The angle of elevation from an anchor to the top of a flag pole is 22 If the pole is

10 meters high, how long does the wire connecting the anchor to the pole must be?

(Round answer to the 1st decimal place.)

Answer:

  cos(52°) = 18/x

  x = 18·sec(52°)

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you that ...

  Cos = Adjacent/Hypotenuse

In this geometry, that means ...

  cos(52°) = 18/x

You can use the relation sec(x) = 1/cos(x) to rewrite this as ...

  x = 18·sec(52°)

_____

You can also use the complementary angle and the complementary trig function.

  sin(90° -52°) = 18/x

Answer:

3x²

im lazy to solve right now

hope it helps

Answer:

Step-by-step explanation:

half of the circle is 180 degrees

so x + 3x = 180

4x = 180

x = 45