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
yawa3891 [41]
2 years ago
8

For Problem 10, simplify the expressions using properties of operations. 10. (t - 1) – (-7t+2)​

Mathematics
1 answer:
zvonat [6]2 years ago
4 0

Answer:

8t-3

Step-by-step explanation:

(t-1)-(-7t+2)

t-1+7t-2

t+7t-1-2

8t-1-2

8t-3

You might be interested in
Work out the area of abcd.<br><br> please ensure you give workings out too.
ipn [44]

Answer:

\displaystyle A_{\text{Total}}\approx45.0861\approx45.1

Step-by-step explanation:

We can use the trigonometric formula for the area of a triangle:

\displaystyle A=\frac{1}{2}ab\sin(C)

Where a and b are the side lengths, and C is the angle <em>between</em> the two side lengths.

As demonstrated by the line, ABCD is the sum of the areas of two triangles: a right triangle ABD and a scalene triangle CDB.

We will determine the area of each triangle individually and then sum their values.

Right Triangle ABD:

We can use the above area formula if we know the angle between two sides.

Looking at our triangle, we know that ∠ADB is 55 DB is 10.

So, if we can find AD, we can apply the formula.

Notice that AD is the adjacent side to ∠ADB. Also, DB is the hypotenuse.

Since this is a right triangle, we can utilize the trig ratios.

In this case, we will use cosine. Remember that cosine is the ratio of the adjacent side to the hypotenuse.

Therefore:

\displaystyle \cos(55)=\frac{AD}{10}

Solve for AD:

AD=10\cos(55)

Now, we can use the formula. We have:

\displaystyle A=\frac{1}{2}ab\sin(C)

Substituting AD for a, 10 for b, and 55 for C, we get:

\displaystyle A=\frac{1}{2}(10\cos(55))(10)\sin(55)

Simplify. Therefore, the area of the right triangle is:

A=50\cos(55)\sin(55)

We will not evaluate this, as we do not want inaccuracies in our final answer.

Scalene Triangle CDB:

We will use the same tactic as above.

We see that if we can determine CD, we can use our area formula.

First, we can determine ∠C. Since the interior angles sum to 180 in a triangle, this means that:

\begin{aligned}m \angle C+44+38&=180 \\m\angle C+82&=180 \\ m\angle C&=98\end{aligned}

Notice that we know the angle opposite to CD.

And, ∠C is opposite to BD, which measures 10.

Therefore, we can use the Law of Sines to determine CD:

\displaystyle \frac{\sin(A)}{a}=\frac{\sin(B)}{b}

Where A and B are the angles opposite to its respective sides.

So, we can substitute 98 for A, 10 for a, 38 for B, and CD for b. Therefore:

\displaystyle \frac{\sin(98)}{10}=\frac{\sin(38)}{CD}

Solve for CD. Cross-multiply:

CD\sin(98)=10\sin(38)

Divide both sides by sin(98). Hence:

\displaystyle CD=\frac{10\sin(38)}{\sin(98)}

Therefore, we can now use our area formula:

\displaystyle A=\frac{1}{2}ab\sin(C)

We will substitute 10 for a, CD for b, and 44 for C. Hence:

\displaystyle A=\frac{1}{2}(10)(\frac{10\sin(38)}{\sin(98)})\sin(44)

Simplify. So, the area of the scalene triangle is:

\displaystyle A=\frac{50\sin(38)\sin(44)}{\sin(98)}

Therefore, our total area will be given by:

\displaystyle A_{\text{Total}}=50\cos(55)\sin(55)+\frac{50\sin(38)\sin(44)}{\sin(98)}

Approximate. Use a calculator. Thus:

\displaystyle A_{\text{Total}}\approx45.0861\approx45.1

8 0
2 years ago
In a popular tale of wizards and witches, a group of them finds themselves in a room with unmarked doors which change position,
SSSSS [86.1K]

Answer:

Expected number of hours before the the group exits the building = E[Number of hours] = 3.2 hours

Step-by-step explanation:

Expected value, E(X) is given as

E(X) = Σ xᵢpᵢ

xᵢ = each variable

pᵢ = probability of each variable

Let X represent the number of hours before exiting the building taking each door. Note that D = Door

D | X | P(X)

1 | 3.0 | 0.2

2 | 3.5 | 0.1

3 | 5.0 | 0.2

4 | 2.5 | 0.5

E(X) = (3×0.2) + (3.5×0.1) + (5×0.2) + (2.5×0.5) = 3.2 hours

Hope this Helps!!!

7 0
2 years ago
Tessa had $90 in her checking account. She paid her cable/internet bill for $60. She deposited $50 from her part-time job before
Lady bird [3.3K]

90-60+50-65=15


$15 in her account

4 0
3 years ago
Read 2 more answers
PLEASE HELP !!! WILL MARK BRAINLIEST TO WHOEVER GETS IT RIGHT !!
erica [24]

Answer:

5th option

52° bc its alternating interior with 2.

added together they would equal 180°

7 0
3 years ago
Do<br>main of ln(2x+3/×-1)
lozanna [386]
<span>so your equation  would be  2x-3=-1  then your answer would be -1

</span>
7 0
3 years ago
Other questions:
  • How do I graph 3x-7y=14
    5·1 answer
  • Use Euler's Formula to find the missing number. vertices:14 Edges:36 Faces:?
    11·2 answers
  • Find the number of distinguishable permutations of the letters in the word vaccination
    15·1 answer
  • Reduce 12/30 to lowest term
    14·2 answers
  • the management of a hotel found that they will sell all 800 tickets at 4 dollars per per person for a hour concert for one night
    7·1 answer
  • Prove that A is idempotent if and only if AT is idempotent. Getting Started: The phrase "if and only if" means that you have to
    5·1 answer
  • What is the quotient? a-3/7 - 3-9/21
    10·2 answers
  • Why do vertices connected by a diagonal of a polygon have to be nonconsecutive?
    12·2 answers
  • HELPS NOWWWWWW:
    12·1 answer
  • A concession stand charges $2.50 for a bag of popcorn. The stand has already sold 30 bags of popcorn. How many more bags x of po
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!