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
prisoha [69]
3 years ago
5

Here is an inequality: 7x+6/2 < 3x +2

Mathematics
1 answer:
Archy [21]3 years ago
7 0

Answer:

x=1

Step-by-step explanation:

You might be interested in
If 't' bags of chips cost $c, what is the cost of 5 bags of chips?
allsm [11]

Answer:

$ (C/t ) × 5

= $ 5C/t

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

4 0
2 years ago
Find cos(2*ABC) 100POINTS
juin [17]

Answer:

-\dfrac{7}{25}

Step-by-step explanation:

<u>Trigonometric Identities</u>

\cos(A \pm B)=\cos A \cos B \mp \sin A \sin B

<u>Trigonometric ratios</u>

\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}

where:

  • \theta is the angle
  • O is the side opposite the angle
  • A is the side adjacent the angle
  • H is the hypotenuse (the side opposite the right angle)

Using the trig ratio formulas for cosine and sine:

  • \cos(\angle ABC)=\dfrac{3}{5}
  • \sin(\angle ABC)=\dfrac{4}{5}

Therefore, using the trig identities and ratios:

\begin{aligned}\implies \cos(2 \cdot \angle ABC) & = \cos(\angle ABC + \angle ABC)\\\\& = \cos (\angle ABC) \cos (\angle ABC) - \sin(\angle ABC) \sin (\angle ABC)\\\\& = \cos^2(\angle ABC)-\sin^2(\angle ABC)\\\\& = \left(\dfrac{3}{5}\right)^2-\left(\dfrac{4}{5}\right)^2\\\\& = \dfrac{3^2}{5^2}-\dfrac{4^2}{5^2}\\\\& = \dfrac{9}{25}-\dfrac{16}{25}\\\\& = \dfrac{9-16}{25}\\\\& = -\dfrac{7}{25} \end{aligned}

7 0
2 years ago
Read 2 more answers
How do you find perimeter
Veronika [31]
All you do is add up all your sides! So if your shape has 4+4+5+5 = 18. All you do is add them up! 
3 0
3 years ago
Evaluate the integral following ​
alina1380 [7]

Answer:

\displaystyle{4\tan x + \sin 2x - 6x + C}

Step-by-step explanation:

We are given the integral of:

\displaystyle{\int 4(\sec x - \cos x)^2 \, dx}

First, we can use a property to separate a constant out of integrand:

\displaystyle{4 \int (\sec x - \cos x)^2 \, dx}

Next, expand the expression (integrand):

\displaystyle{4 \int \sec^2 x - 2\sec x \cos x + \cos^2 x \, dx}

Since \displaystyle{\sec x = \dfrac{1}{\cos x}} then it can be simplified to:

\displaystyle{4 \int \dfrac{1}{\cos^2 x} - 2\dfrac{1}{\cos x} \cos x + \cos^2 x \, dx}\\\\\displaystyle{4 \int \dfrac{1}{\cos^2 x} - 2 + \cos^2 x \, dx}

Recall the formula:

\displaystyle{\int \dfrac{1}{\cos ^2 x} \, dx = \int \sec ^2 x \, dx = \tan x + C}\\\\\displaystyle{\int A \, dx = Ax + C \ \ \tt{(A \ and \ C \ are \ constant.)}

For \displaystyle{\cos ^2 x}, we need to convert to another identity since the integrand does not have a default or specific integration formula. We know that:

\displaystyle{2\cos^2 x -1 = \cos2x}

We can solve for \displaystyle{\cos ^2x} which is:

\displaystyle{2\cos^2 x = \cos2x+1}\\\\\displaystyle{\cos^2x = \dfrac{\cos 2x +1}{2}}

Therefore, we can write new integral as:

\displaystyle{4 \int \dfrac{1}{\cos^2 x} - 2 + \dfrac{\cos2x +1}{2} \, dx}

Evaluate each integral, applying the integration formula:

\displaystyle{\int \dfrac{1}{\cos^2x} \, dx = \boxed{\tan x + C}}\\\\\displaystyle{\int -2 \, dx = \boxed{-2x + C}}\\\\\displaystyle{\int \dfrac{\cos 2x +1}{2} \, dx = \dfrac{1}{2}\int \cos 2x +1 \, dx}\\\\\displaystyle{= \dfrac{1}{2}\left(\dfrac{1}{2}\sin 2x + x\right) + C}\\\\\displaystyle{= \boxed{\dfrac{1}{4}\sin 2x + \dfrac{1}{2}x + C}}

Then add all these boxed integrated together then we'll get:

\displaystyle{4\left(\tan x - 2x + \dfrac{1}{4}\sin 2x + \dfrac{1}{2} x\right) + C}

Expand 4 in the expression:

\displaystyle{4\tan x - 8x +\sin 2x + 2 x + C}\\\\\displaystyle{4\tan x + \sin 2x - 6x + C}

Therefore, the answer is:

\displaystyle{4\tan x + \sin 2x - 6x + C}

4 0
1 year ago
What is the area of a rectangle with vertices at ​ (−4, 0) ​, ​ (−3, 1) ​ , (0, −2) , and (−1, −3) ?
skad [1K]

Answer: 6\ units^2

Step-by-step explanation:

Plot the vertices of the rectangle on a coordinate plane (Observe the figure attached where the rectangle is identified as ABCD).

The area of a rectangle can be calculated with this formula:

A=lw

Where "l" is the lenght and "w" is the width.

In order to find the lenght and the width, you can use the formula for calculate the distance between two points:

d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

Knowing the coordinates of the vertices, you get:

w=d_{AB}=\sqrt{(-4-(-3))^2+(0-1)^2}=\sqrt{2}\ units\\\\l=d_{BC}=\sqrt{(0-(-3))^2+(-2-1)^2}=3\sqrt{2}\ units

Therefore, substituting values into the formula A=lw, you get that the area of the rectangle is:

A=(3\sqrt{2}\ units)(\sqrt{2}\ units)=6\ units^2

8 0
3 years ago
Other questions:
  • What is the probability that the code number for a new customer will begin with a 7
    15·1 answer
  • Help with #12, 13, 14, 15! I will mark u as brainliest answer
    12·1 answer
  • A train travels 75 miles in 55 minutes what is the average speed in miles per minute
    13·1 answer
  • How do I solve 1/4w-1/3=4 2/3
    7·1 answer
  • 2 Points
    5·1 answer
  • What equation is equal to 6/7. I'm very confused.Can one of you guys please help me? Thank You
    13·1 answer
  • Which correctly Applies the distributaries property to show an equivalent expression to (-2.1)(3.4)
    8·1 answer
  • Marc makes 6 1/4 pounds of granola. He wants to freeze 3/4 of the granola. Which expressions can be used to find the number of p
    11·1 answer
  • Solve 33 1/2 of 48<br><br> Plz thanks &lt;3
    12·1 answer
  • Rose went to the craft store to buy beads to make bracelets. Each bag of beads cost $4.59. Which equation can be used to find th
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!