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3 years ago

Question 4) -6x + 9 + 6x -13 Your answer Question 5) 8x - 9 -11 -14x Your answer

Mathematics

1 answer:

Digiron [165]3 years ago

3 0

Answer:

4) -4

5) -6x-20

Step-by-step explanation:

Add x with x's and numbers with numbers

4) -6x + 9 + 6x -13

-6x+6x+9-13

x's cancel

9-13 = -4

5) 8x - 9 -11 -14x

8x-14x-9-11

-6x-20

hope this helps

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write an inequality for the description of: ten times a number increased by four is no more than twenty five

Xelga [282]

10x +4 </ 25 (the </ is a less than or equal to sign)

3 0

3 years ago

Prove that the roots of x2+(1-k)x+k-3=0 are real for all real values of k

masha68 [24]

Answer:

Roots are not real

Step-by-step explanation:

To prove : The roots of x^2 +(1-k)x+k-3=0x

+(1−k)x+k−3=0 are real for all real values of k ?

Solution :

The roots are real when discriminant is greater than equal to zero.

i.e. b^2-4ac\geq 0b

−4ac≥0

The quadratic equation x^2 +(1-k)x+k-3=0x

+(1−k)x+k−3=0

Here, a=1, b=1-k and c=k-3

Substitute the values,

We find the discriminant,

D=(1-k)^2-4(1)(k-3)D=(1−k)

−4(1)(k−3)

D=1+k^2-2k-4k+12D=1+k

−2k−4k+12

D=k^2-6k+13D=k

−6k+13

D=(k-(3+2i))(k+(3+2i))D=(k−(3+2i))(k+(3+2i))

For roots to be real, D ≥ 0

But the roots are imaginary therefore the roots of the given equation are not real for any value of k.

6 0

3 years ago

(9x-4)-(3x+2) I need to know how to solve this

Karolina [17]

$(9x-4)-(3x+2)=9x-4-3x-2=6x-6$

8 0

3 years ago

Which additional fact proves that ΔRST and ΔWXY are congruent if ∠T ≅ ∠Y and RT ≅ WY?

sergejj [24]

Answer:

Hence, option A is correct.

Step-by-step explanation:

We are asked to find the fact such that ΔRST and ΔWXY are congruent.

Since, we are given: ∠T ≅ ∠Y and RT ≅ WY.

we are given the following assumptions:

∠W = x + 5

∠X = 3x - 9

∠Y = 2x + 4

as we are given one angle congruent and one side congruent so in order to prove two triangles are congruent we just need to show that one more pair of angles are congruent.

so from the two triangle we could have that ∠W≅∠R

and ∠X≅∠S

Now we will go by options:

if ∠S=2x+20 then as ∠X≅∠S.

3x-9=2x+20

x=29

∠S=∠W=78°.

if ∠R = 2x + 20 then as ∠W≅∠R

⇒ x+5=2x+20

⇒ x= -15 which is not possible as it will make measure of angle W negative (x+5= -15+5= -10)

if ∠S=2x^2+5 then as ∠X≅∠S.

⇒ 3x-9=2x^2+5

⇒ 2x^2-3x+14=0

on solving this quadratic equation we will get complex zeros.

Hence, option (C) is not correct.

if ∠R = 2x

+ 5 then as ∠W≅∠R.

⇒ x+5=

+ 5

⇒ 2x^2-x=0

⇒ x(2x-1)=0

either x=0 or x=1/2 which is not possible.

because by putting this x value in all the angles we see that sum of all the angles of a triangle is not equal to 180°

Hence, option D is not possible.

Hence, option A is correct.

4 0

4 years ago

What is the length of AC?

sladkih [1.3K]

When the question says that triangle ABC ~ triangle DEF, that means the triangles are similar. This means that their proportions are the same.
In triangle ABC, side length AB is the equivalent of side length DE in triangle DEF.

Since the proportions must be the same, we can take the known side from triangle ABC, find the equivalent of it on triangle DEF, and find the proportions.
We already found that side length AB ~ side length DE.
Now we can divide the lengths to find the proportions.
28 / 8 = 3.5
This means that each side on triangle ABC will be 3.5 times greater than the equivalent side on triangle DEF.

The length of AC in triangle ABC is 3.5 times the length of DF in triangle DEF.
Side length DF is 10.
Multiply 3.5 by 10 to get the length of AC.
3.5 • 10 = 35
So the length of AC is 35 units.

Answer:
Side length AC in triangle ABC is 35 units.

Hope this helps!

7 0

4 years ago