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Svetradugi [14.3K]
3 years ago
6

Multiply (−4)(−2)(−5). (5 points)

Mathematics
2 answers:
igor_vitrenko [27]3 years ago
8 0

Answer: -40

Step-by-step explanation:

The answer is -40 because (-4)(-2) = 8; 8(-5)= -40.

A positive times a negative equals a negative.

a negative time a negative equals a positive.

Remember Sleepy man/Dead man.

Sergeu [11.5K]3 years ago
6 0

Answer:

-40

Step-by-step explanation:

(-4)(-2) = positive 8

(8)(-5) = negative -40

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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
3 years ago
If the radius of a spherical rubber ball is 1 1/4 inches what is its volume to the nearest cubic inch
Yuri [45]
? = 4/3 π(1 1/4)
<span>Answer: 8</span>

5 0
3 years ago
What is the GCF of 24,48m
Phoenix [80]
24
It goes into 24 once and into 48 twice
3 0
3 years ago
Read 2 more answers
24 divided by 4 times d
nadya68 [22]

Answer:

i think 6 not sure tho sorry if its worng

3 0
3 years ago
Can someone pls help me with this?! I’m stumped lol
forsale [732]

Answer:

  • $3.50
  • 24

Step-by-step explanation:

The graph shows you the value stored on the card dropped by $14 when Gina rented 4 videos. Thus the cost of each one is ...

... $14/4 = $3.50

Gina now has $84 on the card, so can rent an additional ...

... $84/$3.50 = 24 . . . . videos

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Division is a way to do "repeated subtraction." That is, if we were to subtract $3.50 from $84 repeatedly, we would find we could do it 24 times.

6 0
3 years ago
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