Find the missing side lengths of the triangle below

The roots of x^2 + (1 - k).x+k-3 = 0 are real for all real values of k

The equation is given as:

x^2 + (1 - k).x+k-3 = 0

For an equation to have real root, then the following must be true:

[tex]b^2 \ge 4ac[/tex]

In x^2 + (1 - k).x+k-3 = 0, we have:

a = 1

b = 1 - k

c = k - 3

So, we have:

[tex](1 - k)^2 \ge 4 * 1 * (k - 3)[/tex]

Evaluate

[tex]1 - 2k + k^2 \ge 4k - 12[/tex]

Collect like terms

[tex]k^2 - 2k - 4k + 1 + 12 \ge 0[/tex]

[tex]k^2 - 6k + 13 \ge 0[/tex]

Using a graphing calculator, the value of k is all real numbers

Hence, the roots of x^2 + (1 - k).x+k-3 = 0 are real for all real values of k

Read more about real values at:

https://brainly.com/question/6499629

Answer:

your answer is five

Step-by-step explanation:

and stay safe and happy

Answer:

$1.53 for tax

Step-by-step explanation:

18 times .085 = 1.53

Answer:

it's 0

Step-by-step explanation:

jdjdjdjsjnsjdbsjsjkakwpamjdjdkdjs

The simplification of the expression is 48√2

The procedure in mathematics to utilize and analyze the function or expression to make the function or expression uncomplicated or more coherent is called simplifying and the process is called simplification.

We are given the expression as;

2√98-8√32+3√72

​

Now we have to simplify

2√98-8√32+3√72

​

2√(49×2)  - 8√(4×2) + 3 √(36×2)

Now taking common;

2 x 7√2 + 8 x 2√2 + 3 x 6√2

14√2 + 16√2 + 18√2

48√2

Learn more about simplification;

https://brainly.com/question/17579585

#SPJ2

Answer:

your question is not complete...

Answer: 2/3

Step-by-step explanation:

Answer:

k = 2

Step-by-step explanation:

3(-1) + k(5) = 7

-3 + 5k = 7

5k = 10

k = 2

The value of K in the equation 3x + Ky =7 is 2.

Two algebraic expressions having same value and symbol '=' in between are called as an equation.

Given:

Equation 3x + Ky =7.

And we have also given that (-1, 5) satisfies the equation.

That means,

(-1, 5) is a solution of the equation.

To find the value of K;

Substitute the value of x = -1 and y = 5

So,

3x + Ky =7,

3(-1) + K(5) =7

-3 + 5K = 7

5K = 10

K = 2

Therefore, the value of K is 2.

To learn more about the equation;

https://brainly.com/question/12788590

#SPJ2

Answer:

1. Ratio 9-342 Unit Rate 38

2. Ratio 38-152 Unit Rate 4

3. Ratio 2-40 Unit Rate 20

4. Ratio 84-6 Unit Rate 14

5. Ratio 5-30 Unit Rate 6

6. Ratio  5-50 Unit Rate 10

Step-by-step explanation:

Ap ex

Answer:

2657/25

Step-by-step explanation:

Answer:

89.7 is the percent

Step-by-step explanation:

38.41/43.7=0.879 (87.9%).

Answer:

The answer for the question is 3/10

Answer:

470 x 1.1 = 517

Step-by-step explanation:

Answer:

I think the answer would be y<4

Answer:

It is A: 75

Step-by-step explanation:

No need

Answer:

Step-by-step explanation:

6m is the answer

Answer:

Correct

Step-by-step explanation:

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

0 and 31

a whole number, also known as a counting number, is a number that is neither a negative or a fraction

? + 31° + 94° = 180°

? + 125° = 180°

? = 180° - 125°

? = 55°

Answer: 52°

Step-by-step explanation:

Angles in a triangle always add up to 180°.

So to work out what the missing angle is, you would have to add 34 and 94 together.

34+94=128

Then you would have to take 128 away from 180.

180-128=52°

Hope this helps :)

Answer:

here you go its in the image the answer

Step-by-step explanation:

pogchamp kiddies

Answer:

x = 52°

Step-by-step explanation:

I have attached an image to depict the given angles.

From the attached image, we can see that the unknown angle is x°.

Thus, since that corner is 90°, then;

x + 38 = 90

Subtract 38 from both sides to get;

x = 90 - 38

x = 52°

Answer:

Simplified - 2x(-x+4), Solution - -2x(-x+4)

9514 1404 393

Explanation:

Use the identities ...

  csc(x) = 1/sin(x)

  cot(x) = cos(x)/sin(x)

__

  [tex]\csc(x)(\sin(x)+\cos(x))=1+\cot(x)\\\\\dfrac{1}{\sin(x)}(\sin(x)+\cos(x))=1+\cot(x)\\\\\dfrac{\sin(x)}{\sin(x)}+\dfrac{\cos(x)}{\sin(x)}=1+\cot(x)\\\\1+\cot(x)=1+\cot(x)[/tex]

Answer:

Step-by-step explanation:

Use SOH CAH TOA to recall how the trig functions fit on a triangle

SOH: Sin(Ф)= Opp / Hyp

CAH: Cos(Ф)= Adj / Hyp

TOA: Tan(Ф) = Opp / Adj

5)

Adj = 14

Hyp = 26

∠X

so use

CAH

Cos(X) = 14/26

X = arcCos(14/26)

X = 57.421°

X = 57.4 ° ( rounded to nearest 10th )

6)

∠X

Hyp = 46

Opp = 12

use SOH

Sin(x) = 12/46

X = arcSin(12/46)

X = 15.121°

X = 15.1 ° ( rounded to nearest 10th )

7)

∠X

Adj = 29

Opp = 24

use TOA

Tan(x) = 29 / 24

X = arcTan( 29 /24)

X = 50.389

X = 50.4 °  ( rounded to nearest 10th )

8)

∠X

Adj = 22

Opp = 6

use TOA agian

Tan(x) = 6 / 22

X = arcTan(6/22)

X = 5.194

X = 5.2 °  ( rounded to the nearest 10th )

:)

Answer:

y = - ( x + 2 )² + 14

Step-by-step explanation:

f(x) = ax² + bx + c

f(x) = a(x - h)² + k (where (h, k) are coordinates of the vertex.

h = - [tex]\frac{b}{2a}[/tex]

~~~~~~~~~~~~

f(x) = - x² - 4x + 10

a = - 1, b = - 4, c = 10

h = - [tex]\frac{-4}{2(-1)}[/tex] = - 2

k = - ( - 2)² - 4( - 2) + 10 = 14

(h, k) = ( - 2, 14 )

y = - ( x + 2 )² + 14

Answer:

$ 20.00 - $14.17 = $5.83

Step-by-step explanation:

you have to take the amount of money given and subtract the total of the purchase , with the total including tax that makes it easier because you dont have to calculate it . so payment - total = change

Answer:

-8+14x

Step-by-step explanation:

By distribution, -2(4-7x) = -8+14x

Answer:

Step-by-step explanation:

[tex]y=ar^t\\ \\ y=16000(1.03^x)[/tex]

9514 1404 393

Answer:

  224 cubes

Step-by-step explanation:

In terms of 1/4 cm cubes, the dimensions of the prism are ...

  (2 cm)/(1/4 cm/cube) = 8 cubes long

  (7/4 cm)/(1/4 cm/cube) = 7 cubes wide

  (1 cm)/(1/4 cm/cube) = 4 cubes high

The volume in 1/4-cm cubes is ...

  V = LWH = (8)(7)(4) = 224 . . . cubes

224 cubes are required to fill the volume.