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AleksandrR [38]

3 years ago

13

Write the first five terms of the arithmetic sequence. First term: -8 and common difference: -2

1 answer:

Hunter-Best [27]3 years ago

7 0

Answer:

-8,-10,-12,-14,-16

Step-by-step explanation:

Just take -8 and add -2 to find each term

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The sun of 3 less than 5 times a number and the number increased by 9 is 24. What is the number?

hoa [83]

Answer:

the answer is 3

Step-by-step explanation:

5 x - 3 + x + 9 =24

6X + 6 = 24

6X =18

×=3

3 0

2 years ago

49 POINTS!!!!!!!!

belka [17]

The answer is II and III, which is the last choice from above. This is because the symbol "less than (or equal to)" indicated a conjunction, which means we have to take into account that the absolute value can be less than or equal to 15, and greater than or equal to -15. This solution set falls in between the two values, hence, the conjunction.

3 0

3 years ago

Given: ABC is a right triangle with right angle C. AC=15 centimeters and m∠A=40∘ . What is BC ? Enter your answer, rounded to th

konstantin123 [22]

In order to answer this question, the figure in the first picture will be helpful to understand what a right triangle is. Here, a right angle refers to $90\°$ .

However, if we want to solve the problem we have to know certain things before:

In the second figure is shown a general right triangle with its three sides and another given angle, we will name it $\alpha$ :

The side <u>opposite to the right angle</u> is called The Hypotenuse (h)

The side <u>opposite to the angle $\alpha$ </u> is called the Opposite (O)

The side <u>next to the angle $\alpha$ </u> is called the Adjacent (A)

So, going back to the triangle of our question (first figure):

The Hypotenuse is AB

The Opposite is BC

The Adjacent is AC

Now, if we want to find the length of each side of a right triangle, we have to use the <u>Pythagorean Theorem</u> and T<u>rigonometric Functions:</u>

Pythagorean Theorem

$h^{2}=A^{2} +O^{2}$ (1)

Trigonometric Functions (here are shown three of them):

Sine: $sin(\alpha)=\frac{O}{h}$ (2)

Cosine: $cos(\alpha)=\frac{A}{h}$ (3)

Tangent: $tan(\alpha)=\frac{O}{A}$ (4)

In this case the function that works for this problem is cosine (3), let’s apply it here:

$cos(40\°)=\frac{AC}{h}$

$cos(40\°)=\frac{15}{h}$ (5)

And we will use the Pythagorean Theorem to find the hypotenuse, as well:

$h^{2}=AC^{2}+BC^{2}$

$h^{2}=15^{2}+BC^{2}$ (6)

$h=\sqrt{225+BC^2}$ (7)

Substitute (7) in (5):

$cos(40\°)=\frac{15}{\sqrt{225+BC^2}}$

Then clear BC, which is the side we want:

${\sqrt{225+BC^2}}=\frac{15}{cos(40\°)}$

${{\sqrt{225+BC^2}}^2={(\frac{15}{cos(40\°)})}^2$

$225+BC^{2}=\frac{225}{{(cos(40\°))}^2}$

$BC^2=\frac{225}{{(cos(40\°))}^2}-225$

$BC=\sqrt{158,41}$

$BC=12.58$

Finally $BC$ is approximately 13 cm

7 0

4 years ago

Read 2 more answers

To use the Pythagorean theorem, we need

Ad libitum [116K]

Answer:

sfygyisfislsiyitiyjhjs hjgks6skyk

Step-by-step explanation:

jzsisfyisyistoisisooots

5 0

3 years ago

Read 2 more answers

You and your guest have eaten in a restaurant which had excellent service. Your bill comes to $23.00. If you leave exactly a 15%

dem82 [27]

Answer:

23*0.15=$3.45

Step-by-step explanation:

23*0.15=$3.45

3 0

3 years ago