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2 years ago

What is the value of x in the triangle? х 30 7V3 60°

Mathematics

1 answer:

Hatshy [7]2 years ago

3 0

Answer:

A. 21

Step-by-step explanation:

Use the trigonometric function for the tangent of an angle because the adjacent side of the right-angled triangle is provided in the question, whilst the opposite side is x.

tan = opposite / adjacent

tan 60° = x / 7 * sqrt(3)

Now make x the subject of the equation.

x = tan 60° * 7 * sqrt(3)

x = 21

When multiplying, take into consideration all the digits on your calculator display.

Hope this helped!

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3 to the power 2x+3 is subtracted by 9 which is equal to 2 times 9 to the power x+1 and is subtrcted by 6

hichkok12 [17]

Answer:

x = -0.5

Step-by-step explanation:

Here we have the sentence:

"3 to the power 2x+3 is subtracted by 9 which is equal to 2 times 9 to the power x+1 and is subtracted by 6"

The first part:

"3 to the power 2x+3 is subtracted by 9..."

This can be written as:

$3^{2x + 3} - 9$

"... is equal to 2 times 9 to the power x+1 and is subtracted by 6"

$3^{2x + 3} - 9 = 2*9^{x + 1} - 6$

Let's solve this for x.

First, we can add 9 in both sides:

$3^{2x + 3} = 2*9^{x + 1} - 6 + 9 = 2*9^{x + 1} + 3$

We also know the relations:

$a^n*a^b = a^{n + b}$

and

$(a^n)^m = a^{n*m}$

We can write the left part as:

$3^{2x + 3} = 3^{2x}*3^3 = (3^2)^x*3^3 = 9^x*27$

And the right side as:

$2*9^{x + 1} + 3 = 2*9^x*9 + 3 = 18*9^x + 3$

Then the equation becomes:

$27*9^x = 18*9^x + 3$

Now let's move both terms with 9^x to the left side:

$27*9^x - 18*9^x = 3\\$

$(27 - 18)*9^x = 3$

$9*9^x = 3$

$9^x = 3/9 = 1/3$

Now remember that:

Ln(a^b) = b*Ln(a)

Then if we apply the Ln( ) function to both sides, we get:

$Ln(9^x) = Ln(1/3)$

$x*Ln(9) = Ln(1/3)$

$x = \frac{Ln(1/3)}{Ln(9)} = -0.5$

5 0

3 years ago

Estion 3/10

Rus_ich [418]

Answer:

I believe its c but I'm not clearly sure

4 0

3 years ago

Read 2 more answers

What happens to the value of the expression <img src="https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7Bx%7D%20%2B5" id="TexFormula1" tit

Paraphin [41]

Answer:

A) increases

Step-by-step explanation:

5/x + 5

suppose x = 5; then 5/5 + 5 = 1 + 5 = 6

x = 2; then 5/2 + 5 = 2.5 + 5 = 7.5

x = 1 ;then 5/1 + 5 = 5 + 5 = 10

So when x value decreases from a large positive number to a small positive number, 5/x + 5 increases

3 0

3 years ago

When an automobile is stopped with a roving safety patrol,each tire is checked for tire wear, and each headlight is checkedto se

ryzh [129]

Answer:

a) Joint ptobability distribution

$\begin{pmatrix} &Y=0&Y=1&Y=2&Y=3&Y=4\\X=0&0.3&0.05&0.025&0.025&0.1\\ X=1&0.18&0.03&0.015&0.015&0.06 \\ X=2&0.12&0.02&0.01&0.01&0.04\end{pmatrix}$

b) P(X<= 1 and Y <= 1) = P(X<= 1) * P(Y<=1) = 0.56

c) P(X + Y = 0)=0.3

d) P(X + Y <= 1)=0.53

Step-by-step explanation:

We have to construct the joint probability table with the marginal probabilities of X and Y.

X can take values from 0 to 2, and Y can take values from 0 to 4.

We can calculate each point of the joint probability as:

$P(x,y)=P_x(x)*P_y(y)$

Then, the joint probabilities are:

X=0 Y=0 Px=0.5 Px=0.6 P(0,0)=0.3

X=0 Y=1 Px=0.5 Px=0.1 P(0,1)=0.05

X=0 Y=2 Px=0.5 Px=0.05 P(0,2)=0.025

X=0 Y=3 Px=0.5 Px=0.05 P(0,3)=0.025

X=0 Y=4 Px=0.5 Px=0.2 P(0,4)=0.1

X=1 Y=0 Px=0.3 Px=0.6 P(1,0)=0.18

X=1 Y=1 Px=0.3 Px=0.1 P(1,1)=0.03

X=1 Y=2 Px=0.3 Px=0.05 P(1,2)=0.015

X=1 Y=3 Px=0.3 Px=0.05 P(1,3)=0.015

X=1 Y=4 Px=0.3 Px=0.2 P(1,4)=0.06

X=2 Y=0 Px=0.2 Px=0.6 P(2,0)=0.12

X=2 Y=1 Px=0.2 Px=0.1 P(2,1)=0.02

X=2 Y=2 Px=0.2 Px=0.05 P(2,2)=0.01

X=2 Y=3 Px=0.2 Px=0.05 P(2,3)=0.01

X=2 Y=4 Px=0.2 Px=0.2 P(2,4)=0.04

We can write it in the form of a matrix:

$\begin{pmatrix} &Y=0&Y=1&Y=2&Y=3&Y=4\\X=0&0.3&0.05&0.025&0.025&0.1\\ X=1&0.18&0.03&0.015&0.015&0.06 \\ X=2&0.12&0.02&0.01&0.01&0.04\end{pmatrix}$

b) From the joint probability P(X<= 1 and Y <= 1) is equal to

$P(X\leq 1 \& Y \leq 1)=P(0,0)+P(0,1)+P(1,0)+P(1,1)\\\\P(X\leq 1 \& Y \leq 1)=0.3+0.05+0.18+0.03=0.56$

We can calculate P(X<= 1) * P(Y<=1)

$P_x(X\leq 1)=P_x(0)+P_x(1)=0.5+0.3=0.8\\\\P_y(Y\leq1)=P_y(0)+P_y(1)=0.6+0.1=0.7\\\\P_x(X\leq1)*P_y(Y\leq1)=0.8*0.7=0.56$

Both calculations give the same result.

c) Probability of no violations

$P(X+Y=0)=P(0,0)=0.3$

d) P(X + Y <= 1)

$P(X+Y \leq 1)=P(0,0)+P(0,1)+P(1,0)\\\\P(X+Y \leq 1)=0.3+0.05+0.18=0.53$

5 0

3 years ago

Please answer correctly !!!!!!!!! Will mark brainliest !!!!!!!!!!!!!!!

Ugo [173]

Answer:

Step 3 they took the square root incorrectly

Step-by-step explanation:

5 ( x-2)^2 +6 = 86

Subtract 6 from each side

5 ( x-2)^2 +6 -6= 86-6

5 ( x-2)^2 = 80

Divide each side by 5

5 ( x-2)^2 /5 = 80/5

(x-2)^2 = 16

Take the square root of each side

sqrt((x-2)^2) = ±sqrt(16)

x-2 = ±4

4 0

2 years ago