Answer:
<h2>x = -2 (verified by algebra) ✅</h2>
Step-by-step explanation:
Since we are given the value of y, we can replace it with 5x + 7.
We now have: 3x + 5x + 7 = -9
We can now simplify by adding 3x and 5x to get 8x.
8x + 7 = -9
We can subtract 7
8x = -16
And now, we divide by 8
x = -2
We can check to make sure we are correct
3(-2) + 5 (-2) + 7 = -9
-6 + -10 + 7 = -9
-9 = -9 ✅
Answer:
Sin of x does not change
Step-by-step explanation:
Whenever a triangle is dilated, the angle remains the same as well as the ratio for sides of triangle. For smshapes with dimensions, when shapes are dilated the dimensions has increment with common factor.
From trigonometry,
Sin(x)=opposite/hypotenose
Where x=4/5
Sin(4/5)= opposite/hypotenose
But we were given the scale factor of 2 which means the dilation is to two times big.
Then we have
Sin(x)=(2×opposite)/(2×hypotenose)
Then,if we divide by 2 the numerator and denominator we still have
Sin(x)=opposite/hypotenose
Which means the two in numerator and denominator is cancelled out.
Then we still have the same sin of x. as sin(4/5)
Hence,Sin of x does not change
OK. These problems are easy if you know the quadratic formula,
and they're impossible if you don't.
Here's the quadratic formula:
When the equation is in the form of Ax² + Bx + C = 0
then x = [ -B plus or minus √(B²-4AC) ] / 2A
I'm sure that formula is in your text or your study notes,
right before these questions. You should cut it out or
copy it, and tape it inside the cover of your notebook.
Then, you'll always have it when you need it, until
you have it memorized and can rattle it off.
The first question says 3x² + 5x + 2 = 0
Is this in the form of Ax² + Bx + C = 0 ?
Yes ! A=3 B=5 C=2
so you can use the quadratic formula to solve it.
x = [ -B plus or minus √(B²-4AC) ] / 2A
= [ -5 plus or minus √(5² - 4·3·2) ] / 2·3
= [ -5 plus or minus √(25 - 24) ] / 6
= [ -5 plus or minus √1 ] / 6
x = -4 / 6 = -2/3
and
x = -6 / 6 = -1 .
_______________________________________
The second question says
4x² + 5x - 1 = 0
Is this in the form of Ax² + Bx + C = 0 ?
Yes it is ! A=4 B=5 C= -1
so you can use the quadratic formula to solve it.
x = [ -B plus or minus √(B²-4AC) ] / 2A
Now, you take it from here.
The simplest form is 1/4 or 0.25
Answer:
6 ft < L₃ < 30 ft
Step-by-step explanation:
To obtain the answer to the question given above, we must bear in mind that:
The sum of the length of two sides of any triangle is always greater than the 3rd length i.e
L₁ + L₂ > L₃
With the above information in mind, we can obtain the answer to the question given above as follow:
Length 1 (L₁) = 12 feet
Length 2 (L₂) = 18 feet
Length 3 (L₃) =..?
Case 1:
L₁ + L₂ > L₃
12 + 18 > L₃
30 > L₃
L₃ < 30 feet
Case 2:
L₁ + L₃ > L₂
12 + L₃ > 18
Collect like terms
L₃ > 18 – 12
L₃ > 6 feet
Thus,
6 feet < L₃
Combining case 1 and 2,we obtained:
6 ft < L₃ < 30 ft
Therefore, the possible Lenght of the 3rd side is : 6 ft < L₃ < 30 ft
