find the area of the shaded region in each of the following​

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

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Answer:

He needs to make 13 deliveries

Answer:

20

Step-by-step explanation:

Given that:

Red flowers = 1/8

Purple = 1/4

(1/8 + 1/4) = (1 + 2) / 8 = 3/8

Fraction left :

1 - 3/8 =. 5/8

Pink flowers :

1/4 of fraction left ;

1/4 * 5/8 = 5/32

Number of pink flowers

Total number of flowers = 128

5/32 * 128

640 / 32

= 20

20 pink flowers

Answer:

35

Step-by-step explanation:

The numbers are 35 and 24

35 + 24 = 59

35 - 24 = 11

35 > 24

Answer:

RS = 38

Step-by-step explanation:

20x - 12 = 18x + 12

2x = 24

x =  12

3(12) + 2 = 38

The value of the side of triangle RS is equal to 38.

If two objects are having the same shape then they will be termed as similar. So in mathematics, if two figures have the same shapes, lines or angles then they are called similar.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the sides of the triangle XYZ are, XY = 5x - 3, XZ = 60 and the sides of the triangle TR = 40, RS = 3x + 2.

The value of RS will be calculated as,

( 5x - 3 ) / ( 3x + 2 ) = ( 60 / 40 )

( 5x - 3 ) / ( 3x + 2 ) = ( 6 / 4 )

20x - 12 = 18x + 12

2x = 24

x = 12

RS = 3x + 2

RS = ( 3 x 12 ) + 2

RS = 36 + 2

RS = 38

Therefore, the value of the side of triangle RS is equal to 38.

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Answer:

we need the full picture of the circle to see if 10 cm is only half or not

Answer:

700 I think...

Step-by-step explanation:

Multiply

Answer:

Step-by-step explanation:

1) 36:81

2)81 pints

3)14.625 gallons of paint

17.5 = √6² + w²

17.5² = 36 + w²

306.25 = 36 + w²

270.25 = w²

√270.25 = w

16.4392822 = W

=  w = 16.44 in

Given:

A right prism has height 7½ and triangular bases with sides of length 5, 12, and 13.

To find:

The total surface area of the prism.

Solution:

We have,

Height of prism = 7½ = 7.5

Sides of triangular base are 5, 12, 13. These sides of Pythagorean triplets because

[tex]5^2+12^2=13^2[/tex]

[tex]25+144=169[/tex]

[tex]169=169[/tex]

So, the base of the prism is a right triangle.

Area of a triangle is

[tex]Area=\dfrac{1}{2}\times base \times height[/tex]

[tex]A_1=\dfrac{1}{2}\times 5\times 12[/tex]

[tex]A_1=30[/tex]

The area of the base is equal to the area of the top, i.e., [tex]A_2=30[/tex] sq units.

Perimeter of the base is

[tex]P=5+12+13[/tex]

[tex]P=30[/tex]

The curved surface area of the prism is

[tex]CSA=\text{Perimeter of the base}\times \text{Height of the prism}[/tex]

[tex]CSA=30\times 7.5[/tex]

[tex]CSA=225[/tex]

Now, the total area of the prism is

[tex]A=A_1+A_2+CSA[/tex]

[tex]A=30+30+225[/tex]

[tex]A=285[/tex]

Therefore, the total surface area of the triangular prism is 285 square units.

Answer:

I love algebra anyways  

the ans is in the picture with the steps  

(hope it helps can i plz have brainlist :D hehe)

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

for every one day there is a distance of 50 miles, therefore you multiply the days (T) by 50 to get your distance

Answer:

AC = 3 cm

Step-by-step explanation:

sum the parts of the ratio, 2 + 1 = 3 parts, then

AC = [tex]\frac{2}{3}[/tex] × AC = [tex]\frac{2}{3}[/tex] × 4.5 = 2 × 1.5 = 3 cm

Answer:

A'B' = 7.5

Step-by-step explanation:

uhhh

AC = A'C'

4 = 6

×1.5

AB^2 = 4^2 + 3^2

AB^2 = 16 + 9

AB^2 = 25

AB = √25

AB = 5

A'B' = 5 × 1.5 = 7.5

The value of A'B' for the given congruent triangle will be 7.5.

If two figures are exactly the same in sense of their side of all things then they will be congruent.

If it is possible to superimpose one geometric figure on the other so that their entire surface coincides, that geometric figure is said to be congruent or to be in the relation of congruence.

As per the given congruent triangle,

In triangle ABC,

AB = √(3² + 4²) = 5

The ratio of the corresponding sides of the two triangles is the same.

A'B'/A'C' = AB/AC

A'B'/6 = 5/4

A'B' = 30/4 = 7.5

Hence "The value of A'B' for the given congruent triangle will be 7.5".

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Answer:

the answer is 21x+11

Step-by-step explanation: hope this helps

Step-by-step explanation:

5(3x+3) + 2(3x-2)

15x + 15 6x - 4

15x + 16x + 15 - 4

21x + 11

Answer:

A circle has a circumference of 7,805 units.

2πr= 7,805 units.

r=7805/2π1=1242.20unit is radius

Answer:

7 is C

8 is B

9 is C

Step-by-step explanation:Focus on your class please

Answer:

1. C

2. A

3. C  

Step-by-step explanation:

Answer:

80√3

Step-by-step explanation:

here's your solution

=> First number is 4√5

=> Second number is 4√15

=> we need to find product

=> 4√5*4√15

=> 4*4 = 16

=> √5*√15. = √75

=> √75 = 5√3

=> now, multiple 5√3*16 = 80√3

hope it helps

Answer:

The common denominator is 15.

2 3/5 = 13/5 = 39/15

1 1/3 = 4/3 = 20/15

Answer:

39/15 and 20/15

Step-by-step explanation:

Given function:

Rewrite 2 3/5 and 1 1/3 by a number that is equivalent to 5 and 3:

Multiply each numerator by how much times it turned into 15:

Simplfly the fraction terms:

Therefore, 39/15 and 20/15 is equivalent to 2 3/5 and 1 1/3.

Answer

$128

Step-by-step explanation:

Okay well if $80 is 100% then 60% is 48 dollars.

so 80 +48=128

Answer:

-3-6= -9

.......................

Answer:

if you mean -3-3 +2 then it is -4

if you mean -3-3(2) then it is -9

Step-by-step explanation:

Answer:

Cierto

Step-by-step explanation:

Los triángulos equiláteros son siempre iguales porque siempre tienen ángulos de 60 grados.

Si esto le ayudó, marque como más inteligente

Answer:

C 4 yards

Step-by-step explanation:

random guess sorry.

Answer:

A is the answer!

Step-by-step explanation:

134 inches is equal to 3.7 yards

134 inches is equal to 11.1667 feet.

Answer:

2 books

Step-by-step explanation:

10 + 5x = 16 + 2x

    - 2x         - 2x

10 + 3x = 16

-10          -10

3x = 6

/3    /3

x = 2