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3 years ago

Help please !! I’m am struggling with this lol

Mathematics

1 answer:

tatyana61 [14]3 years ago

4 0

Answer:

x ≈ 3.9

Step-by-step explanation:

Call the segment shared by the two triangle "y". The Pythagorean theorem tells you ...

sum of squares of sides = square of hypotenuse

y² +6² = 10²

x² +7² = y²

Substituting for y² using the second equation, we get ...

x² +7² +6² = 10²

x² = 10² -7² -6² = 100 -49 -36 = 15

Taking the square root, we find ...

x = √15 ≈ 3.9

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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

4 years ago

The mass is 500 grams and the volume is 40 cubic centimeters.

Paha777 [63]

Answer: is there a question for/to the numbers gjven

4 0

3 years ago

Pleaseee help meee struggling currently

lisabon 2012 [21]

Answer: 2908.92435 inches.

Step-by-step explanation for shape 1: A = 2(wl + hl + hw) = 2 · (30 · 13 + 13 · 13 + 13 · 30) = 1,898 inches.

Step-by-step explanation for shape 2:

Using the formulas:

A=2AB+(a+b+c)h

AB=s(s﹣a)(s﹣b)(s﹣c)

s=a+b+c

Solving for A:

A=ah+bh+ch+1

2﹣a4+2(ab)2+2(ac)2﹣b4+2(bc)2﹣c4=9·30+13·30+9·30+1

2·﹣94+2·(9·13)2+2·(9·9)2﹣134+2·(13·9)2﹣94≈1010.92435

Step-by-step explanation for total volume: 2908.92435 inches.

5 0

3 years ago

Read 2 more answers

Each day a commuter takes a bus to work, the transportation system has a phone app that tells her what time the bus will arrive.

Paraphin [41]

Answer:

Step-by-step explanation:

Hello!

The commuter is interested in testing if the arrival time showed in the phone app is the same, or similar to the arrival time in real life.

For this, she piked 24 random times for 6 weeks and measured the difference between the actual arrival time and the app estimated time.

The established variable has a normal distribution with a standard deviation of σ= 2 min.

From the taken sample an average time difference of X[bar]= 0.77 was obtained.

If the app is correct, the true mean should be around cero, symbolically: μ=0

a. The hypotheses are:

H₀:μ=0

H₁:μ≠0

b. This test is a one-sample test for the population mean. To be able to do it you need the study variable to be at least normal. It is informed in the test that the population is normal, so the variable "difference between actual arrival time and estimated arrival time" has a normal distribution and the population variance is known, so you can conduct the test using the standard normal distribution.

$Z_{H_0}= \frac{X[bar]-Mu}{\frac{Sigma}{\sqrt{n} } }$

$Z_{H_0}= \frac{0.77-0}{\frac{2}{\sqrt{24} } }= 1.89$

d. This hypothesis test is two-tailed and so is the p-value.

p-value: P(Z≤-1.89)+P(Z≥1.89)= P(Z≤-1.89)+(1 - P(Z≤1.89))= 0.029 + (1 - 0.971)= 0.058

e. 90% CI

$Z_{1-\alpha /2}= Z_{0.95}= 1.645$

X[bar] ± $Z_{1-\alpha /2}* (\frac{Sigma}{\sqrt{n} } )$

0.77 ± 1.645 * $(\frac{2}{\sqrt{24} } )$

[0.098;1.442]

I hope this helps!

4 0

3 years ago

The mean hourly salary of the 10 employees at a fast-food restaurant is $8.25. One of the employees earning $6.50 an hour leaves

Travka [436]

You would add $8.25 + $5.50, which equals $13.75. Then you would divide that number by the number of employees currently working at the fast food restaurant; $13.75 / 2 = $6.875. So, $6.88 would be the new mean salary of the employees.

5 0

3 years ago