find the volume of the prism

Answer:

Discriminant

[tex]b^2-4ac\quad\textsf{when}\:ax^2+bx+c=0[/tex]

[tex]\textsf{when }\:b^2-4ac > 0 \implies \textsf{two real roots}[/tex]

[tex]\textsf{when }\:b^2-4ac=0 \implies \textsf{one real root}[/tex]

[tex]\textsf{when }\:b^2-4ac < 0 \implies \textsf{no real roots}[/tex]

Given equation: [tex]kx^2+2x+(1-k)=0[/tex]

[tex]\implies a=k,\:b=2,\:c=(1-k)[/tex]

[tex]\begin{aligned}\implies b^2-4ac & =(2)^2-4(k)(1-k)\\ & =4-4k(1-k)\\ & =4-4k+4k^2\\ & = 4k^2-4k+4 \end{aligned}[/tex]

Complete the square:

[tex]\begin{aligned}\implies 4k^2-4k+4 & =4(k^2-k+1)\\ & = 4\left[k^2-k+\left(\dfrac{-1}{2}\right)^2+1-\left(\dfrac{-1}{2}\right)^2\right]\\ & = 4\left[\left(k-\dfrac12\right)^2+\dfrac34\right]\\ & = 4\left(k-\dfrac12\right)^2+3\end{aligned}[/tex]

[tex]\textsf{As }\left(k-\dfrac12 \right)^2 \geq 0 \implies 4\left(k-\dfrac12 \right)^2+3\geq 3[/tex]

Therefore, the roots are always real.

best answer of this equation is 10.772

Answer: 10.772

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

exact form:

x= 10 4/3

--------- (its a fraction)

2

decimal form: 10.77217345....

after that round to the nearest thousandth.

Answer

91.67inch^3

Step-by-step explanation:

The volume of a cone can be calculated using below formula

V= 1/3 π.r^2h

Where h= height of the cone

r= radius of the cone

V= volume of the cone

Given :

height= 11 inches

radius= 5 inches

π= 3.14

Then substitute into the formula we have

V= 1/3 × 3.14× 5^2 ×11

V= 91.67inch^3

Therefore volume of the cone is 91.67inch^3

Answer:

Option C, [tex]36x^2 + 60x + 25[/tex]

Step-by-step explanation:

Step 1:  Determine the perfect square

According to online, "When an expression has the general form a²+2ab+b², then we can factor it as (a+b)². For example, x²+10x+25 can be factored as (x+5)². This method is based on the pattern (a+b)²=a²+2ab+b², which can be verified by expanding the parentheses in (a+b)(a+b)"

The only one that seems to work is Option C so lets factor it.

[tex]36x^2 + 60x + 25[/tex]

[tex](6x + 5)(6x + 5)[/tex]

[tex](6x + 5)^2[/tex]

Yup!  We can see that Option C would give us a perfect square

Answer:  Option C, [tex]36x^2 + 60x + 25[/tex]

since there are 36 inches in 1 yard, 12 yards will have 12(36) = 432 inches.

Answer:

See below.

Step-by-step explanation:

A(1, 4)

B(3, 0)

C(-3, -2)

We find the coordinates of he midpoints using the midpioint formula.

D([1 + 3]/2, [4 + 0]/2) = D(2, 2)

E([1 + (-3)]/2, [4 + (-2)]/2) = E(-1, 1)

We find the slopes using the slope formula.

slope of BC:

m_BC = (-2 - 0)/(-3 - 3) = -2/(-6) = 1/3

slope of DE:

m_DE = (1 - 2)/(-1 - 2) = -1/(-3) = 1/3

Since the slopes of BC and DE are equal, the lines are parallel.

Answer:

3x - 5 fits the equation perfectly

Step-by-step explanation:

if we put the following value in X we get,

x processing y

3. 3*3 - 5. 4

5. 3*5 - 5. 10

7. 3*7 -5. 16

9. 3*9 - 5. 22

11. 3*11 - 5. 28

Step-by-step explanation:

If we have f(x) and it's inverse, and we compose them

we will get

[tex]f {}^{ - 1} (f(x) = x[/tex]

So here we compose

[tex]( \frac{1}{ \frac{1 + x}{x} - 1} )[/tex]

[tex]( \frac{1}{ \frac{1}{x} + 1 - 1} [/tex]

[tex] \frac{1}{ \frac{1}{x} } [/tex]

[tex]x [/tex]

So the composition is x, so they are inverses.

[tex]x=\frac{1+4f-\sqrt{16f^{2}+8f+25 } }{2}[/tex]

Answer:

-a^3 -3a^2

Step-by-step explanation:

(fg) (x) = x^2 (x-3)

= x^3 - 3x^2

(fg) (-a) = (-a)^3 -3 (-a)^2

= -a^3 -3a^2

[tex]6x^2 +17x -3\\\\=6x^2 +18x-x-3\\ \\=6x(x+3)-(x+3)\\ \\=(x+3)(6x-1)\\\\\text{The length and width of the rectangle are}~ (6x-1)~ \text{and}~ (x+3)[/tex]

Answer:

[tex]\textsf{length}=6x - 1[/tex]

[tex]\textsf{width}=x+3[/tex]

Step-by-step explanation:

Area of a rectangle = length × width

Given area:  [tex]A=6x^2+17x-3[/tex]

Therefore,  [tex]6x^2+17x-3=\sf length \cdot width[/tex]

To find the length and width, we need to factorize the given expression for area.

To factor a quadratic in the form [tex]ax^2+bx+c[/tex]

[tex]6x^2+17x-3 \implies a=6, b=17, c=-3[/tex]

[tex]ac=6 \cdot -3=-18[/tex]

[tex]d+e=17[/tex]

So we are looking for a pair of numbers that multiply to -18 and sum to 17.

Factors of 18: 1, 2, 3, 6, 9, 18

Therefore, the two numbers (d and e) that multiply to -18 and sum to 17 are:

18 and -1

Rewrite [tex]17x[/tex] as [tex]+18x-x[/tex]:

[tex]\implies 6x^2+18x-x-3[/tex]

Factor first two terms and last two terms separately:

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

Factor out common term [tex](x+3)[/tex]:

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

As length > width,

[tex]\textsf{length}=6x - 1[/tex]

[tex]\textsf{width}=x+3[/tex]

Answer:

1620

Step-by-step explanation:

(-18)×(-10)×9= 1620

Answer:

3 and 4

Step-by-step explanation:

30/8=3.75

3.75 lies between 3 and 4

Hey there!

30/8

= 30 ÷ 2 / 8 ÷ 2

= 15 / 4

≈ 3 3/4

≈ 3.75

It falls in between three (3) and four (4). But, fun fact it rounds to up to four (4)

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

832.5²

Step-by-step explanation:

Base x height ÷ 2 is the formula to find a triangles area.

45 x 37= 1665 then 1665 ÷ 2 = 832.5 dont forget to add the ²

Answer:

832.5²

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

2/3 * 2/3 = 4/9

2/3 * 3/2 = 1

2/3 * 3/4 = 1/2

2/3 * 4/4 = 2/3

Answer:

1 liter

Step-by-step explanation:

100 milliliters = 0.10566882 quarts

500 milliliters = 0.52834411 quarts

1 liter = 1.05668821 quarts

10 liters = 10.5668821 quarts
______________________________

From this, we can see that 1 liter is closest to a quart.

hope this helps!

The polynomial of least possible degree having the graph as given is; f(x) = x³-8x²+x +42.

It follows from the graph that the roots of the polynomial are; -2, 3 and 7.

On this note, the factors of such polynomial are;

Hence; (x+2)(x-3)(x-7) = f(x)

Read more on polynomials;

https://brainly.com/question/2833285

To calculate hydronium concentration from pH, type on you calculator

10 to the power of negative pH value

10^-5.5 = 3•10^6 mol/L

Since there are 3 hydrogens in every hydronium molecule,

There are 9 • 10^6 hydrogens in that liter of acid.

Step-by-step explanation:

1.581 × 10² like this ? : )

Answer:

It's a function because when you simplify it becomes y=-x-3. the only reason it wouldn't be a function would be if the equation were to be x = a random number that is not a variable. The equation would not pass the vertical line test which is the requirement to see if an equation is a function.

Simply put, it's a function.

[tex]y < \frac{1}{2} x - 2 \\ [/tex]

Answer:

  a. exception: C; obtuse angle with a different measure

  b. corresponding angles are congruent; corresponding sides are proportional

  c. corresponding angles are congruent among the similar triangles; they are not congruent when the triangles are not similar

  d. corresponding sides are porportional; they are not proportional when the triangles are not similar

Step-by-step explanation:

As you know, similar triangles have congruent corresponding angles, and proportional corresponding sides. This gives them the same shape, but they may be of differenent sizes.

__

Figure C appears to have a larger smallest angle and a smaller largest angle than the rest of the figures. Its long side relative to its second-longest side appears to be shorter, consistent with a smaller largest angle.

__

The similar triangles have congruent corresponding angles and proportional corresponding sides.

__

See (b) regarding similar triangles. Non-similar triangles have different angles.

__

See (b) regarding similar triangles. Non-similar triangles have different side proportions.

Answer:

Skewed right

Step-by-step explanation:

There is a 'tail' towards the right.

Answer:

The origin is at (0,0) its where the x and y coordinate intersect.

Step-by-step explanation:

what was the question here?

Answer:

B. 100 units

Step-by-step explanation:

What I did was I couunted the lines at the bottum and since it was 10 then I counted up  and that was 10 so you would do 10x10 get 100 units.

Step-by-step explanation:

Median: 35000

Mean: 383333.33333333 (round it)

Mode: 10000, 20000, 30000, 40000, 200000, 2000000 (all the numbers)

Answer:

P(A|B) = 0.5

Step-by-step explanation:

A: set of prime numbers ={1,2,3}

B: set of divisors of 3 ={1,3}

P(A)=P(1)+P(2)+P(3)= 0.1+0.1+0.3 =0.5

P(B)=P(1)+P(3)=0.1+0.3=0.4

P(A|B) means: probability of A knowing that B

In other words we have to find the probability that a prime outcome occurs knowing that it is a divisor of 3

Its formula is given by:

P(A|B) = P(AintersectionB) /P(B)

A intersection B: outcome is prime and a divisor of 3 at the same time. (common elements between sets A and B)

A int B= {1,3}

P(AintB)= P(A)xP(B) = 0.5x0.4=0.2

Now back to the formula:

P(A|B) =P(AintB) / P(B)

=0.2/0.4=0.5

HOPE THIS HELPS :)