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quester [9]
2 years ago
13

Given: f(x)= x² + 3x-4 and g(x) = x-4​

Mathematics
1 answer:
kifflom [539]2 years ago
3 0

Answer:

x-intercept of f(x)=x²+3x-4 is (1,0) &(-4,0)

x-intercept of g(x)=x-4 is (4,0)

y-intercept of f(x)=x²+3x-4 is (0,-4)

y-intercept of g(x)=x-4 is (0,-4)

Step-by-step explanation:

f(x) = x {}^{2}  + 3x - 4 \\ to \: find \: x \: intercept \: subistitute \: f(x) = 0 \\ 0 = x {}^{2}  - 3x - 10 \\ x { }^{2}  - 3x - 1 = 0 \\ x {}^{2}  + 2x - 5x - 10 = 0 \\ x(x + 2) - 5x - 10 = 0 \\ x(x + 2) - 5(x + 2) = 0 \\ (x + 2).(x - 5) = 0 \\ x + 2 = 0 \\ x - 5 = 0 \\ x =  - 2 \\ x = 5 \\ the \:equation \: x \: intercept \: are \:  - 2and \: 5 \\ f(0) = 0 {}^{2}  + 3(0) - 4 \\  - 4 \: is \: y \: intercept \: of \: f(x) = x {}^{2}  + 3x - 4 \\ where \: as \: for \: g(x) = x - 4 \\ to \: find \: x \: intercept \: f(x) = 0 \\ 0 = x - 4 \\  - x =  - 4 \\ x = 4 \\ 4is \: the \: x \: intercept \: and \: for \: the \: y \: intercept \\ g(0) = 0 - 4 \\ y =  - 4is \: the \: y \: intercept.

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The second angle of a triangle is double the first angle. The third angle is 40 less than the first angle. Find the three angles
ArbitrLikvidat [17]

Answer:

Angle 1: 55

Angle 2: 110

Angle 3: 15

Step-by-step explanation:

Angle 1: x

Angle 2: 2x

Angle 3: x-40

The total degrees for all the angles in a triangle add up to 180, so we now have the equation x+2x+x-40=180. From here we solve to get 55 degrees for x, so angle 1 is 40 degrees, angle 2 is 110 (2 times 40) and the third angle is 15 (55-40).  

6 0
4 years ago
Solve sin 0 + 1 = cos20 on the interval 0 ≤ 0 < 2pi. Show work please!
yan [13]

Answer:

\theta=\frac{\pi}{2},\frac{3\pi}{2}\frac{2\pi}{3}\frac{4\pi}{3}

Step-by-step explanation:

You need 2 things in order to solve this equation:  a trig identity sheet and a unit circle.

You will find when you look on your trig identity sheet that

cos(2\theta)=1-2sin^2(\theta)

so we will make that replacement, getting everything in terms of sin:

sin(\theta)+1=1-2sin^2(\theta)

Now we will get everything on one side of the equals sign, set it equal to 0, and solve it:

2sin^2(\theta)+sin(\theta)=0

We can factor out the sin(theta), since it's common in both terms:

sin(\theta)(2sin(\theta)+1)=0

Because of the Zero Product Property, either

sin(\theta)=0 or

2sin(\theta)+1=0

Look at the unit circle and find which values of theta have a sin ratio of 0 in the interval from 0 to 2pi.  They are:

\theta=\frac{\pi}{2},\frac{3\pi}{2}

The next equation needs to first be solved for sin(theta):

2sin(\theta)+1=0 so

2sin(\theta)=-1 and

sin(\theta)=-\frac{1}{2}

Go back to your unit circle and find the values of theta where the sin is -1/2 in the interval.  They are:

\theta=\frac{2\pi}{3},\frac{4\pi}{3}

7 0
3 years ago
What is the equation to solve for p
allochka39001 [22]
I don't what that says
8 0
3 years ago
HELP ASAP!!!!!
Sergeu [11.5K]
Answer: Y= - 1/2x - 8
If you move y to one side by itself that’s what you’ll get and you can check this answer by multiplying each side by 2 and moving the x ti the left side and you’ll get your beginning equation

If it not right feel free to comment and tell me
6 0
3 years ago
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valkas [14]

Step-by-step explanation:

it is negative 20 I'm pre sure

6 0
3 years ago
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