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2 years ago

If a truck traveled 75.648 miles per year how many miles did it travel monthly

Mathematics

1 answer:

aev [14]2 years ago

7 0

The answer is 6.304 :D

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Remember to show work and explain. Use the math font.

MrMuchimi

Answer:

$\large\boxed{1.\ f^{-1}(x)=4\log(x\sqrt[4]2)}\\\\\boxed{2.\ f^{-1}(x)=\log(x^5+5)}\\\\\boxed{3.\ f^{-1}(x)=\sqrt{4^{x-1}}}$

Step-by-step explanation:

$\log_ab=c\iff a^c=b\\\\n\log_ab=\log_ab^n\\\\a^{\log_ab}=b\\\\\log_aa^n=n\\\\\log_{10}a=\log a\\=============================$

$1.\\y=\left(\dfrac{5^x}{2}\right)^\frac{1}{4}\\\\\text{Exchange x and y. Solve for y:}\\\\\left(\dfrac{5^y}{2}\right)^\frac{1}{4}=x\qquad\text{use}\ \left(\dfrac{a}{b}\right)^n=\dfrac{a^n}{b^n}\\\\\dfrac{(5^y)^\frac{1}{4}}{2^\frac{1}{4}}=x\qquad\text{multiply both sides by }\ 2^\frac{1}{4}\\\\\left(5^y\right)^\frac{1}{4}=2^\frac{1}{4}x\qquad\text{use}\ (a^n)^m=a^{nm}\\\\5^{\frac{1}{4}y}=2^\frac{1}{4}x\qquad\log_5\ \text{of both sides}$

$\log_55^{\frac{1}{4}y}=\log_5\left(2^\frac{1}{4}x\right)\qquad\text{use}\ a^\frac{1}{n}=\sqrt[n]{a}\\\\\dfrac{1}{4}y=\log(x\sqrt[4]2)\qquad\text{multiply both sides by 4}\\\\y=4\log(x\sqrt[4]2)$

$--------------------------\\2.\\y=(10^x-5)^\frac{1}{5}\\\\\text{Exchange x and y. Solve for y:}\\\\(10^y-5)^\frac{1}{5}=x\qquad\text{5 power of both sides}\\\\\bigg[(10^y-5)^\frac{1}{5}\bigg]^5=x^5\qquad\text{use}\ (a^n)^m=a^{nm}\\\\(10^y-5)^{\frac{1}{5}\cdot5}=x^5\\\\10^y-5=x^5\qquad\text{add 5 to both sides}\\\\10^y=x^5+5\qquad\log\ \text{of both sides}\\\\\log10^y=\log(x^5+5)\Rightarrow y=\log(x^5+5)$

$--------------------------\\3.\\y=\log_4(4x^2)\\\\\text{Exchange x and y. Solve for y:}\\\\\log_4(4y^2)=x\Rightarrow4^{\log_4(4y^2)}=4^x\\\\4y^2=4^x\qquad\text{divide both sides by 4}\\\\y^2=\dfrac{4^x}{4}\qquad\text{use}\ \dfrac{a^n}{a^m}=a^{n-m}\\\\y^2=4^{x-1}\Rightarrow y=\sqrt{4^{x-1}}$

6 0

3 years ago

Rationalize the denominator of each of the following 4 by (root7+root3)

Solnce55 [7]

Answer:

4/(√7 + √3)

Step-by-step explanation:

=> Multiply and divide by (√7-√3)

=> 4(√7 - √3)/((√7 + √3)(√7 - √3)

=> 4(√7 - √3)/((√7)² - (√3)²)

=> 4(√7 - √3)/((7) - (3))

=> 4(√7 - √3)/4

=> √7 - √3

7 0

1 year ago

Read 2 more answers

ABC is isosceles with AB=AC=8 units and BC=6 units. D and E are midpoints of AB and BC respectively. Calculate the length of DE?

Allushta [10]

The triangle is drawn and is shown in the image attached with.

We get two similar triangles. Triangle ABC and Triangle ADE. Since the triangles are similar the ratio of their corresponding sides will be the same.

D and E are the midpoints of AB and BC, therefore, AD and AE are both 4 units in length. Using the property of similar triangles, we can say:

AD : DE= AB : BC
AD = 4 units
AB = 8 units
BC = 6 units
DE = unknown = x units

So,

$4 :x = 8 : 6 \\ \\ 
 \frac{4}{x} = \frac{8}{6} \\ \\ 
x=4* \frac{6}{8}=3 
$

Therefore, the length of DE will be 3 units

6 0

2 years ago

If the radius and the slant height of a right circular cone are each multiplied by 9, by what factor is the surface area of the

goblinko [34]

Answer:

the answer is D) 81

7 0

3 years ago

Helppp i’ll give brainliest if it’s right :)

BigorU [14]

Answer:

2 real solutions

Step-by-step explanation:

7 0

2 years ago