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3 years ago

Factor completely: x2 + 7x + 10 (5 points)

Mathematics

2 answers:

Arada [10]3 years ago

8 0

Answer:

the correct answer is A.

Step-by-step explanation:

cause when u expand it u get the same as the figure in question.

jolli1 [7]3 years ago

8 0

The answer is A

You need to find factors of ten that will add or subtract to 10 and if a is on you use two parentheses (like in the answer) sorry if it doesn’t make sense

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Find the distance using the modulus of the difference between z1 = -8 + 3i and z2 = 4 - 7i. Show all work for full credit.

alexandr402 [8]

Answer:

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Step-by-step explanation:

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3 years ago

Write the equation: Five times the difference of a number and six is twenty.

xz_007 [3.2K]

Answer:

C. 5(x-6)=20

Step-by-step explanation:

we can represent the value of x decreased by 6 times 5 as 5(x-6) and then show that that is equal to 20.

4 0

3 years ago

Read 2 more answers

Write an equation for the nth term of the given geometric sequence<br> -12,-36,-108...an

julsineya [31]

Answer:

nth term of the geometric sequence

an= -12*3^(n-1)

Step-by-step explanation:

First term

a= -12

Second term

ar= -36

-12r=-36

r=-36/-12

Third term

ar^2= -108

-12(3)^2

= -12(9)

= -108

nth term of the geometric sequence

an=ar^(n-1)

= -12*3^(n-1)

7 0

3 years ago

PLEASE HELP ME!!! :) Which of the following coordinate points is a solution to the equation y = -2 x + 1?

nirvana33 [79]

Its D i did this test :)

8 0

3 years ago

Read 2 more answers

Please help!! 20 POINTS

shepuryov [24]

<h2>Hello!</h2>

The answers are:

First image:

The answer is the second option, the angles is $53\°$

Second image:

The answer is the third option:

$\frac{5}{13}$

Third image:

The length of the adjacent leg is the first option:

$8\sqrt{2}units$

Fourth image:

The answer is the fourth option, $72\°$

Fifth image:

The answer is the fourth option, DF (hypothenuse) is equal to 25 units.

To solve these problems, we need to use the following trigonometric identities and the Pythagorean Theorem, since we are working with right triangles.

$Tan(\alpha)=\frac{y}{x}\\\\(Tan(\alpha))^{-1} =(\frac{y}{x})^{-1}\\\\\alpha =Arctan(\frac{y}{x})$

$Sin(\alpha)=\frac{opposite}{hypothenuse}$

Pythagorean Theorem:

$c^{2}=a^{2} +b^{2}$

So, solving we have:

First image:

We are given a right triangle that has the following lengths:

$base=x=6units\\height=y=8units\\hypothenuse=10units$

Then, calculating we have:

$\alpha =Arctan(\frac{y}{x})\\\\\alpha =Arctan(\frac{8}{6})\\\\\alpha =Arctan(1.33)\\\\\alpha =53\°$

Hence, the answer is the second option, the angles is $53\°$

Second image:

We are given a right triangle that has the following lengths:

$base=x=12units\\height=y=5units\\hypothenuse=13units$

Then calculating the sin ratio, we have:

$Sin(\alpha)=\frac{opposite}{hypothenuse}$

$Sin(\alpha)=\frac{5}{13}$

Thence, the answer is the third option:

$\frac{5}{13}$

Third Image:

We are given the following information:

$hypothenuse=16units\\\\\alpha =45\°$

Then, calculating one of the angle legs, since both will have the same length, using the sine trigonometric identity, we have:

$Sin(\alpha)=\frac{Opposite}{Hypothenuse}\\ \\Sin(45\°)=\frac{Opposite}{16}\\\\Opposite=Sin(45\°)*16\\\\Opposite=\frac{\sqrt{2} }{2}*16=8\sqrt{2}$

Hence, the answer is the first option the length of the adjacent leg is

$Opposite=\frac{\sqrt{2} }{2}*16=8\sqrt{2}units$

Fourth image:

We are given the following information:

$base=x=9units\\height=y=3units$

To calculate the angle at the B vertex, first, we need to calculate the angle at the C vertex, and then, calculate the B vertex by the following way:

Since the sum of all the interior angles of a triangle are equal to 180°, we have that:

$180\°=Angle_{B}+Angle{C}+90\°$

$Angle_{B}=180\° -90\°-Angle_{C}$

So, calculating the angle at the C vertex, we have:

$\alpha =Arctan(\frac{y}{x})$

$\alpha =Arctan(\frac{3}{9})$

$\alpha =Arctan(0.33)=18.26\°$

Then, calculating the angle at the B vertex, we have:

$Angle_{B}=180\° -90\°-18.26\°=71.74\°=71.8\°=72\°$

Hence, the answer is the fourth option, $72\°$

Fifth image:

We are given the following information:

$base=x=24units\\height=y=7units$

Now, to calculate the distance DF (hypothenuse) we need to use the Pythagorean Theorem:

$c^{2}=a^{2} +b^{2} \\\\hypothenuse^{2}=adjacent^{2}+opposite^{2}\\\\\sqrt{hypothenuse^{2}}=\sqrt{adjacent^{2}+opposite^{2}}\\\\hypothenuse=\sqrt{adjacent^{2}+opposite^{2}}$

Then, substituting we have:

$hypothenuse=\sqrt{24^{2}+(7)^{2}}$

$hypothenuse=\sqrt{576+49}=\sqrt{625}$

$hypothenuse=\sqrt{625}$

$hypothenuse=25units$

Hence, the answer is the fourth option, DF (hypothenuse) is equal to 25 units.

Have a nice day!

4 0

3 years ago