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3 years ago

Plsss helppppp I need it right now plss :(

Mathematics

2 answers:

In-s [12.5K]3 years ago

7 0

Answer:

a) IJ is median

IJ = 1/2(HG + EF)
IJ = 1/2(8 + 12) = 10 cm

b) I is midpoint of HE, therefore, HI = IE

<u>Substitute values and solve for x:</u>

10 = x - 4
x = 10 + 4
x = 14 cm

Tamiku [17]3 years ago

6 0

Answer:

a) IJ is median

IJ = 1/2(HG + EF)

IJ = 1/2(8 + 12) = 10 cm

b) I is midpoint of HE, therefore, HI = IE

Substitute values and solve for x:

10 = x - 4

x = 10 + 4

x = 14 cm

Step-by-step explanation:

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Reptile [31]

Answer:

D I think

Step-by-step explanation:

5 0

3 years ago

A cafeteria made 28.5 liters of lemonade. How many gallons of lemonade did the cafeteria make? (1 gallon is approximately 3.8 li

sergejj [24]

Answer:

7.5 gallons

Step-by-step explanation:

We know that 1 gal = 3.8 L, and we have 28.5 L. So, set up a proportion:

1 gal / 3.8 L = x gal / 28.5 L , where x is the number of gallons the cafeteria made

Cross-multiply:

1 * 28.5 = 3.8 * x

28.5 = 3.8x

Divide by 3.8:

x = 28.5 / 3.8 = 7.5 gallons

<em>~ an aesthetics lover</em>

6 0

3 years ago

Two events, X and Y, are independent of each other. P(Y)= and P(X and Y)=. What is P(X) written as a decimal? Round to the neare

kirill [66]

Answer:

0.4

Step-by-step explanation:

For independent events,

P(X ∩ Y) = P(X)* P(Y)

1/3 = P(X)*(5/6)

solve for P(X) =>

P(X) = (1/3)*(6/5) = 2/5 = 0.4

6 0

4 years ago

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

Which relation is a function?

kirill115 [55]

Answer:

Step-by-step explanation:

The graph certainly is, if you ignore the fact that you don't know what the equation for the graph is.

Each x has only 1 y associated with it. That's the definition of a function. This one presumably follows that definition, but I caughten you, without the equation, you can't be sure.

7 0

2 years ago