please help me with this question !!! I’m timed .(

Given:

[tex]x^2+kx-98=0[/tex]

One of the two roots of the given equation is double  the additive inverse of the other.

To find:

The value of k.

Solution:

Let two roots of the given equation are [tex]\alpha[/tex] and [tex]\beta[/tex].

According to the question,

[tex]\beta=2(-\alpha)[/tex]        (Additive inverse of [tex]\alpha[/tex] is [tex]-\alpha[/tex])

[tex]\beta=-2\alpha[/tex]

If [tex]\alpha[/tex] and [tex]\beta[/tex] are roots of the quadratic equation [tex]ax^2+bx+c=0,[/tex] then

[tex]\alpha+\beta=-\dfrac{b}{a}[/tex]

[tex]\alpha\beta=\dfrac{c}{a}[/tex]

We have,

[tex]x^2+kx-98=0[/tex]

Here, a =1, b=k and c=-98.

[tex]\alpha+\beta=-\dfrac{k}{1}[/tex]

[tex]\alpha-2\alpha=-k[/tex]           [tex][\because \beta=-2\alpha][/tex]

[tex]-\alpha=-k[/tex]

[tex]\alpha=k[/tex]           ...(i)

Now,

[tex]\alpha\beta=\dfrac{c}{a}[/tex]

[tex]\alpha(-2\alpha)=\dfrac{-98}{1}[/tex]          [tex][\because \beta=-2\alpha][/tex]

[tex]-2\alpha^2=-98[/tex]

Divide both sides by -2.

[tex]\alpha^2=49[/tex]

Taking square root on both sides.

[tex]\alpha=\pm \sqrt{49}[/tex]

[tex]\alpha=\pm 7[/tex]

Using (i), we get

[tex]k=\pm 7[/tex]

Therefore, the value of k is either -1 or 1.

Answer:

Step-by-step explanation:

Asymptotes 3

g(x) = [tex]\frac{3x}{x^2-3x-10}[/tex]

Factors of denominator will be,

x² - 3x - 10 = x² - 5x + 2x - 10

                 = x(x - 5) + 2(x - 5)

                 = (x + 2)(x - 5)

Therefore, factored form of g(x) will be,

g(x) = [tex]\frac{3x}{(x + 2)(x - 5)}[/tex]

Asymptotes 4

h(x) = [tex]\frac{(x-5)}{x^{2} + 14x + 40}[/tex]

      = [tex]\frac{x-5}{x^{2}+10x+4x+40}[/tex]

      = [tex]\frac{x-5}{x(x+10)+4(x+10)}[/tex]

      = [tex]\frac{x-5}{(x+10)(x+4)}[/tex]

Answer:

5 Cubic Feet

Hope this helps.

Answer:

For every 2 boys in class, there is 1 girl in class

Step-by-step explanation:

Answer:

76.8%

Step-by-step explanation:

All you have to do is multiply the decimal by 100.

Answer:

76.8%

Step-by-step explanation:

I just did a thing and got the answer -v-

its B 15 divide by 3 is 5 because 2 - 5 is -3 - 15 is 5

Reduce by cancelling the common factors.

(13)x−1=27 Convert the exponential equation to a logarithmic equation using the logarithm base (13) of the right side (27)  equals the exponent (x−1)log13(27)=x−1

Answer:

y = -2x +3

Step-by-step explanation:

Parallel lines always have the same slope

To insert the point, use the slope intercept formula: y =mx+b

insert y (9)

insert x (-3)

insert the slope -2

9 = (-2)(-3) + b

9 = 6+b

subtract 6 from both sides

3 = b

Answer:

252 cm²

Step-by-step explanation:

Find AB:

AB² = 41² - 40²

AB² = 81

AB = √81

AB = 9 cm

Area of the trapezium = ½(a + b) × h

Where,

a = 16 cm

b = 40 cm

h = 9 cm

Area = ½(16 + 40) × 9

Area = ½(56)×9

Area = 252 cm²

Answer:

2+7

Step-by-step explanation:

Answer:

the answer is e i think.

Step-by-step explanation:

Answer:

The answer is A. y =32x + 15

Step-by-step explanation:

The reason behind this is the rate. The amount of money each month is the slope (m). The additional fee would be the b.

Result, Rachel can be certain that the temperature is suitable for her cake.

Rachel cannot be certain that the temperature displayed on the oven is suitable for cooking her cake.

The manufacturer's claim of a 5% error on the displayed temperature means that the actual oven temperature can be off by 5% in either direction. To calculate the range of possible actual temperatures, we need to find 5% of 310°C. 5% of 310 = (5/100) * 310 = 15.5°C This means that the oven temperature could be 15.5°C higher or 15.5°C lower than the displayed temperature.

To find the maximum possible temperature, we add the error to the displayed temperature: 310°C + 15.5°C = 325.5°C Since the maximum possible temperature is slightly above 325°C, Rachel cannot be certain that the temperature is suitable for cooking her cake, as it needs to be cooked at a temperature below 325°C. It's important for Rachel to consider using an alternative thermometer or verifying the actual temperature with the oven manufacturer to ensure the cake is cooked at the desired temperature.

To know more about thermometer  visit:

https://brainly.com/question/16840415

#SPJ2

Answer:

The first choice

Step-by-step explanation:

It says that its decreasing so the slope is negative.

It also starts of with 565 so that's the y intercept

Answer:

f(6)=-7

Step-by-step explanation:

Just plug in n=6 into the function:

f(n)=5-2n

f(6)=5-2(6)

f(6)=5-12

f(6)=-7

Therefore, the correct answer is f(6)=-7

Answer:

the answer is g=−12+ 30/n

​

Step-by-step explanation:

Answer:

ill assume you're asking the answer for 1 hour

Step-by-step explanation:

multiply each side by 4. then, 12/4(3)=1

so 3 square feet and hour

Answer:

A

Step-by-step explanation:

Answer:

y = 2

Step-by-step explanation:

Given

7y - (9 + 4y) = - 3 ← distribute parenthesis by - 1

7y - 9 - 4y = - 3 , that is

3y - 9 = - 3 ( add 9 to both sides )

3y = 6 ( divide both sides by 3 )

y = 2

Answer:

you are not a brainly bot

Step-by-step explanation:

Slope intercept form - y = m(x) + b. m represents slope, b represents the y-intercept. You should be able to plug in any value for y and x into the equation, and it should result in a true statement.

The y-intercept is easy to find. It is the point where X is equal to zero and the graph line crosses through the y axis. In this case, y intersects at -2. Since we insert the y intercept at b, we can go ahead and plug it in there.

y = m(x) + b > y = m(x) - 2  

Since there is only one option with the y intercept equalling -2, you can go ahead and pick D) y = -x - 2 as your answer, since no other options have the correct y-intercept.

Answer:

Again...

Step-by-step explanation:

Answer:

A. & B.

Step-by-step explanation:

General form is ax2 + bx + c = 0.

Must contain an x2 term

Must NOT contain terms with degrees higher than x2 eg. x3, x4 etc

Answer:

a and b, that's what the first guy said but i dont know I think hes right

Answer:

16 months

Step-by-step explanation:

40k-16.5k=23.5k. 23.5k/1450= A little bit more than 16 months.

Two triangles, ABC and DEF, similar. <ABC = 101° and <BCA = 39°. Find the angle of FDE!

40°

The sum of all triangle angle is 180°

101 + 39 = 140°

180 - 140 = 40°

So, the angle of FDE is 40°

Subject : Math

Class : 7th Grade (Junior High School)

Chapter : -

Categorization Code : -

Keywords : Angle of a triangle

Answer:

The answer is (3-,5) watch is C cause if you do that but in math form it's the same

Answer:

.10

x

2

+

11

x

y

−

6

y

2

Step-by-step explanation:

The Expression

=

(

2

x

+

3

y

)

(

5

x

−

2

y

)

=

2

x

(

5

x

−

2

y

)

+

3

y

(

5

x

−

2

y

)

=

10

x

2

−

4

x

y

+

15

x

y

−

6

y

2

=

10

x

2

+

11

x

y

−

6

y

2

.

Answer:

3 inches

Step-by-step explanation:

If the dog chews off 4 inches every day, you first have to multiply the inches by the number of days, which in this case is 3 x 4, which equals 12. In 3 days, he chewed off 12 of the original 15 inches, leaving only 3 inches left.

Answer:

Hope this helps!!! :)

Step-by-step explanation:

#1: if there is buy 1 get 1 free, then buy 6 get 3 free. so 2.8 times 3 = $8.4

#2: 4 for $3. break it up to 1 for $0.75. now 0.75 times 6 = $4.5

#3: the second one. $4.5 < $8.4

#4: 45 times 12 = $54

Answer:

x=72/11

Step-by-step explanation:

Answer:20

Step-by-step explanation:

y=1/2x+10

1/2x=y-10

x=2y-20

y=2x-20