What is the range of the fraction f(x) = -2(6^x)+3?

In ΔABC, the lengths of a, b, and c are 22.5 centimeters, 18 centimeters, and 13.6 centimeters, respectively.

Irina-Kira [14]

Given the values of the three sides of the triangle, we can apply the Cosine Law to find the angles of the triangle. Recall that for we can express the value of c through the equation below.

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

Rearranging this equation, we can find the value ∠C as shown below.

$\cos C = \frac{a^{2}+b^{2}-c^{2}}{2ab}$
$C = cos^{-1} (\frac{a^{2}+b^{2}-c^{2}}{2ab})$

We can apply the same reasoning for finding the value of ∠B as shown.

$B = cos^{-1} (\frac{a^{2}+c^{2}-b^{2}}{2ac})$

Plugging in the values of the sides (see image attached) from the given. It will now be straightforward to compute for ∠B and ∠C.

$C = cos^{-1} (\frac{22.5^{2}+18^{2}-13.6^{2}}{2(22.5)(18)})$
$C \approx 37.19$

$B = cos^{-1} (\frac{22.5^{2}+13.6^{2}-18^{2}}{2(22.5)(13.6)})$
$B \approx 53.13$

Answer: ∠C = 37.19° and ∠B = 53.13°

7 0

3 years ago

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22. Find the perimeter and area.

zmey [24]

Answer:

Part 22) The area is $A=15a^3b^6\ units^2($ and the perimeter is $P=10a^2b^4+6ab^2\ unit$

Part 24) The area is $A=16m^3n\ units^2$ and the perimeter is $P=24mn\ units$

Part 26) The area is equal to $A=9\pi x^6y^{2}\ units^2$

Step-by-step explanation:

Part 22) Find the perimeter and area

step 1

The area of a rectangle is equal to

$A=LW$

we have

$L=5(a^2)(b^4)\ units$

$W=3(a)(b^2)\ units$

Remember that

When multiply exponents with the same base, adds the exponents and maintain the base

substitute in the formula

$A=(5(a^2)(b^4))(3(a)(b^2))$

$A=15a^3b^6\ units^2$

step 2

The perimeter of a rectangle is equal to

$P=2(L+W)$

we have

$L=5(a^2)(b^4)\ units$

$W=3(a)(b^2)\ units$

substitute in the formula

$P=2(5(a^2)(b^4)+3(a)(b^2))$

$P=10a^2b^4+6ab^2\ unit$

Part 24) Find the perimeter and area

step 1

The area of triangle is equal to

$A=\frac{1}{2}bh$

where

$b=8mn\ units$

$h=4m^2\ units$

Remember that

When multiply exponents with the same base, adds the exponents and maintain the base

substitute the given values

$A=\frac{1}{2}(8mn)(4m^2)$

$A=16m^3n\ units^2$

step 2

Find the perimeter

I will assume that is an equilateral triangle (has three equal length sides)

The perimeter of an equilateral triangle is

$P=3b$

where

$b=8mn\ units$

substitute

$P=3(8mn)$

$P=24mn\ units$

Part 26) Find the area

The area of a circle is equal to

$A=\pi r^{2}$

where

$r=3x^3y\ units$

Remember the property

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

substitute in the formula the given value

$A=\pi (3x^3y)^{2}$

$A=9\pi x^6y^{2}\ units^2$

6 0

2 years ago

The sum of 2x+7 and −x+12 is equal to 14 what is x?

Alekssandra [29.7K]

Answer:-5

Step-by-step explanation:

2x+7-x+12=14

x+19=14

x=-5

4 0

3 years ago

Help please! I need answers quickly :((

Rzqust [24]

Answer:

y = - $\frac{1}{2}$ x + 2

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, 2) and (x₂, y₂ ) = (4, 0) ← 2 points on the line

m = $\frac{0-2}{4-0}$ = $\frac{-2}{4}$ = - $\frac{1}{2}$

The line crosses the y- axis at (0, 2) ⇒ c = 2

y = - $\frac{1}{2}$ x + 2 ← equation of line

5 0

2 years ago

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A bakery uses 25 cups of flour to make 8 loaves of bread. What is true about the number of cups of flour in each loaf?

Levart [38]

So basically we need to divide

25/8=3.125

they need 3.125 cups of flour in each loaf

I hope I've helped!

6 0

3 years ago

What is the range of the fraction f(x) = -2(6^x)+3?​

What is the range of the fraction f(x) = -2(6^x)+3?