What is the value of x in 5^x+2=5^9

9 ten thousanths in scientific notation

lutik1710 [3]

90,000. Hope this helps

6 0

3 years ago

A. In two or more complete sentences, explain how to find the exact value of sec 13pi/6 including quadrant location

Sergio039 [100]

Answer:

A. The exact value of sec(13π/6) = 2√3/3

B. The exact value of cot(7π/4) = -1

Step-by-step explanation:

* Lets study the four quadrants

# First quadrant the measure of all angles is between 0 and π/2

the measure of any angle is α

∴ All the angles are acute

∴ All the trigonometry functions of α are positive

# Second quadrant the measure of all angles is between π/2 and π

the measure of any angle is π - α

∴ All the angles are obtuse

∴ The value of sin(π - α) only is positive

sin(π - α) = sin(α) ⇒ csc(π - α) = cscα

cos(π - α) = -cos(α) ⇒ sec(π - α) = -sec(α)

tan(π - α) = -tan(α) ⇒ cot(π - α) = -cot(α)

# Third quadrant the measure of all angles is between π and 3π/2

the measure of any angle is π + α

∴ All the angles are reflex

∴ The value of tan(π + α) only is positive

sin(π + α) = -sin(α) ⇒ csc(π + α) = -cscα

cos(π + α) = -cos(α) ⇒ sec(π + α) = -sec(α)

tan(π + α) = tan(α) ⇒ cot(π + α) = cot(α)

# Fourth quadrant the measure of all angles is between 3π/2 and 2π

the measure of any angle is 2π - α

∴ All the angles are reflex

∴ The value of cos(2π - α) only is positive

sin(2π - α) = -sin(α) ⇒ csc(2π - α) = -cscα

cos(2π - α) = cos(α) ⇒ sec(2π - α) = sec(α)

tan(2π - α) = -tan(α) ⇒ cot(2π - α) = -cot(α)

* Now lets solve the problem

A. The measure of the angle 13π/6 = π/6 + 2π

- The means the terminal of the angle made a complete turn (2π) + π/6

∴ The angle of measure 13π/6 lies in the first quadrant

∴ sec(13π/6) = sec(π/6)

∵ sec(x) = 1/cos(x)

∵ cos(π/6) = √3/2

∴ sec(π/6) = 2/√3 ⇒ multiply up and down by √3

∴ sec(π/6) = 2/√3 × √3/√3 = 2√3/3

* The exact value of sec(13π/6) = 2√3/3

B. The measure of the angle 7π/4 = 2π - π/4

- The means the terminal of the angle lies in the fourth quadrant

∴ The angle of measure 7π/4 lies in the fourth quadrant

- In the fourth quadrant cos only is positive

∴ cot(2π - α) = -cot(α)

∴ cot(7π/4) = -cot(π/4)

∵ cot(x) = 1/tan(x)

∵ tan(π/4) = 1

∴ cot(π/4) = 1

∴ cot(7π/4) = -1

* The exact value of cot(7π/4) = -1

5 0

3 years ago

What is the value of X?

zmey [24]

Answer:50°

Step-by-step explanation:

2(x+10)=3x-30

2x+20=3x-30

50°=x

5 0

3 years ago

Mary used Delicious (d) and Golden Delicious (g) apples to make homemade applesauce. Delicious apples are $0.75 each and Golden

alina1380 [7]

Answer:

Mary bought 9 Golden Delicious apples

Step-by-step explanation:

This can be solved by setting up a system of equations. Based on the information given, the equations would be set up as follows.

$.75d+1.25g=21.00\\d+g=22$

I prefer to solve using substitution, but elimination can be used as well

$.75d+1.25g=21.00\\g=22-d$

We can now plug in this g value to the first equation

$.75d + 1.25 (22-d)=21.00\\.75d + 27.5-1.25d=21\\27.5-0.5d=21\\-.5d=-6.5\\d=13$

This means mary bought 13 delicious apples. She bought 22 apples in total, so the total number minus the amount of delicious apples will give us the amount of golden delicious apples.

22 - 13 = g

9 = g

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~`

Let me know if you have any questions! Spread the love.

3 0

2 years ago

Solve the following using Substitution method 2x – 5y = -13 3x + 4y = 15

Digiron [165]

$\huge \boxed{\mathfrak{Question} \downarrow}$

Solve the following using Substitution method

2x – 5y = -13

3x + 4y = 15

$\large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}$

$\left. \begin{array} { l } { 2 x - 5 y = - 13 } \\ { 3 x + 4 y = 15 } \end{array} \right.$

To solve a pair of equations using substitution, first solve one of the equations for one of the variables. Then substitute the result for that variable in the other equation.

$2x-5y=-13, \: 3x+4y=15$

Choose one of the equations and solve it for x by isolating x on the left-hand side of the equal sign. I'm choosing the 1st equation for now.

$2x-5y=-13$

Add 5y to both sides of the equation.

$2x=5y-13$

Divide both sides by 2.

$x=\frac{1}{2}\left(5y-13\right) \\$

Multiply $\frac{1}{2}\\$ times 5y - 13.

$x=\frac{5}{2}y-\frac{13}{2} \\$

Substitute $\frac{5y-13}{2}\\$ for x in the other equation, 3x + 4y = 15.

$3\left(\frac{5}{2}y-\frac{13}{2}\right)+4y=15 \\$

Multiply 3 times $\frac{5y-13}{2}\\$ .

$\frac{15}{2}y-\frac{39}{2}+4y=15 \\$

Add $\frac{15y}{2} \\$ to 4y.

$\frac{23}{2}y-\frac{39}{2}=15 \\$

Add $\frac{39}{2}\\$ to both sides of the equation.

$\frac{23}{2}y=\frac{69}{2} \\$

Divide both sides of the equation by 23/2, which is the same as multiplying both sides by the reciprocal of the fraction.

$\large \underline{ \underline{ \sf \: y=3 }}$

Substitute 3 for y in $x=\frac{5}{2}y-\frac{13}{2}\\$ . Because the resulting equation contains only one variable, you can solve for x directly.

$x=\frac{5}{2}\times 3-\frac{13}{2} \\$

Multiply 5/2 times 3.

$x=\frac{15-13}{2} \\$

Add $-\frac{13}{2}\\$ to $\frac{15}{2}\\$ by finding a common denominator and adding the numerators. Then reduce the fraction to its lowest terms if possible.

$\large\underline{ \underline{ \sf \: x=1 }}$

The system is now solved. The value of x & y will be 1 & 3 respectively.

$\huge\boxed{ \boxed{\bf \: x=1, \: y=3 }}$

8 0

2 years ago