1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Georgia [21]
3 years ago
14

Reduce 7y + 2y 2 - 7 by 3 - 4y.

Mathematics
1 answer:
NARA [144]3 years ago
7 0

Answer:

D. 2y^2+11y-10.

Step-by-step explanation:

Given:

We need to reduce 7y+2y^2-7 by 3-4y

Solution:

To reduce the equation means we need to subtract the one equation from other.

First we will arrange the equation n proper format we get;

2y^2+7y-7  ⇒ equation 1

Also Arranging other equation we get;

-4y+3   ⇒ equation 2

Now we will subtract equation 2 from equation 1 we get;

(2y^2+7y-7)-(-4y+3)

Now Applying distributive property for the sign we get;

2y^2+7y-7+4y-3

Now Arranging the like terms we get;

2y2+7y-+4y-7-3\\\\2y^2+11y-10

Hence the reduce form of the given equation is 2y^2+11y-10.

You might be interested in
What is the domain and range please?
Stella [2.4K]
The second graph: y = 3
Domain: all real number
Range: y = 3
7 0
3 years ago
CALCULUS - Find the values of in the interval (0,2pi) where the tangent line to the graph of y = sinxcosx is
Rufina [12.5K]

Answer:

\{\frac{\pi}{4}, \frac{3\pi}{4},\frac{5\pi}{4},\frac{7\pi}{4}\}

Step-by-step explanation:

We want to find the values between the interval (0, 2π) where the tangent line to the graph of y=sin(x)cos(x) is horizontal.

Since the tangent line is horizontal, this means that our derivative at those points are 0.

So, first, let's find the derivative of our function.

y=\sin(x)\cos(x)

Take the derivative of both sides with respect to x:

\frac{d}{dx}[y]=\frac{d}{dx}[\sin(x)\cos(x)]

We need to use the product rule:

(uv)'=u'v+uv'

So, differentiate:

y'=\frac{d}{dx}[\sin(x)]\cos(x)+\sin(x)\frac{d}{dx}[\cos(x)]

Evaluate:

y'=(\cos(x))(\cos(x))+\sin(x)(-\sin(x))

Simplify:

y'=\cos^2(x)-\sin^2(x)

Since our tangent line is horizontal, the slope is 0. So, substitute 0 for y':

0=\cos^2(x)-\sin^2(x)

Now, let's solve for x. First, we can use the difference of two squares to obtain:

0=(\cos(x)-\sin(x))(\cos(x)+\sin(x))

Zero Product Property:

0=\cos(x)-\sin(x)\text{ or } 0=\cos(x)+\sin(x)

Solve for each case.

Case 1:

0=\cos(x)-\sin(x)

Add sin(x) to both sides:

\cos(x)=\sin(x)

To solve this, we can use the unit circle.

Recall at what points cosine equals sine.

This only happens twice: at π/4 (45°) and at 5π/4 (225°).

At both of these points, both cosine and sine equals √2/2 and -√2/2.

And between the intervals 0 and 2π, these are the only two times that happens.

Case II:

We have:

0=\cos(x)+\sin(x)

Subtract sine from both sides:

\cos(x)=-\sin(x)

Again, we can use the unit circle. Recall when cosine is the opposite of sine.

Like the previous one, this also happens at the 45°. However, this times, it happens at 3π/4 and 7π/4.

At 3π/4, cosine is -√2/2, and sine is √2/2. If we divide by a negative, we will see that cos(x)=-sin(x).

At 7π/4, cosine is √2/2, and sine is -√2/2, thus making our equation true.

Therefore, our solution set is:

\{\frac{\pi}{4}, \frac{3\pi}{4},\frac{5\pi}{4},\frac{7\pi}{4}\}

And we're done!

Edit: Small Mistake :)

5 0
3 years ago
I need help with this, please. Any advice would be appreciated.
mote1985 [20]

Answer:

see explanation

Step-by-step explanation:

The sum to n terms of an arithmetic sequence is

S_{n} = \frac{n}{2} [ 2a₁ + (n - 1)d ]

where a₁ is the initial value and d the common difference

Given

S_{n} = \frac{n}{2} [ 10 + (n - 1)3 ]

Then by comparison

2a₁ = 10 ( divide both sides by 2 )

a₁ = 4 ← initial value

and d = 3 ← common difference

Thus

S_{8} = \frac{8}{2} [ 10 + (7 × 3) ]

   = 4(10 + 21)

   = 4 × 31

   = 124

8 0
4 years ago
The blue dot is at what value on the number line?
Paladinen [302]

Answer: 1

Step-by-step explanation: it goes -7 -5 -3 -1 1

8 0
3 years ago
At a certain real estate firm, realtors selling homes receive a commission of: 7% for the first $100,000 of the selling price, a
scoray [572]

Answer: The actual price of house sold at $109000.

Step-by-step explanation:

Since we have given that

Selling price = $100000

Rate of commission = 7%

So, Amount of commission would be

\dfrac{7}{100}\times 100000\\\\\=\$7000

Total commission = $7540

So, Remaining amount of commission would be

\$7540-\$7000\\\\=\$540

Rate of commission exceeding $100000 = 6%

Let the selling price of house be 'x'.

According to question,

\dfrac{6}{100}\times x=540\\\\0.06x=540\\\\x=\dfrac{540}{0.06}\\\\x=\$9000

Hence, the actual price of house sold at

$100000+$9000=$109000.

3 0
3 years ago
Other questions:
  • Complete this statement 20ax^2+25ax+15a=5a( )
    13·1 answer
  • Simplify the expression 7 × 3g
    7·1 answer
  • The length of a garden is 25 feet.
    9·1 answer
  • Slove this equation<br>28 /3​
    12·1 answer
  • Find the compound interest earned by the deposit. $16,000 @3% annually for 13 years
    11·1 answer
  • 2. Determine whether each table of values represents a linear function. If so write the function. If not, explain why.
    15·1 answer
  • ILL MARK AS BRAINLESS PLS
    15·2 answers
  • Natilie invested $200 in a savings account that earned 4% simple interest each year. She invested for
    10·1 answer
  • Solve for y.<br><br><br><br> y - 12 = -10
    13·2 answers
  • A sphere has a radius that is 9 inches long. What is the volume of the sphere?
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!