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2 years ago

A car drives 5 1/2 miles in 1/12 hour. What is the speed of the car in miles per hour?

Mathematics

2 answers:

horrorfan [7]2 years ago

8 0

Answer:

The car is going 66 miles per hour.

Step-by-step explanation:

If in 1/12 of an hour, the car has gone 5.5 miles, then you must find how far it would go in an hour. To do this, multiply 5.5 by 12 to get 66, how far it went in miles in an hour. This would be the speed it is going: 66 miles per hour.

Klio2033 [76]2 years ago

5 0

Answer: 66

Step-by-step explanation:

5 1/2= 5.5 and 5.5 times 12=66

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You invest 4,100 in an account that pays an interest rate of 7.25% ,compounded continuously. Calculate the balance of your accou

levacccp [35]

$\bf ~~~~~~ \textit{Continuously Compounding Interest Earned Amount}
\\\\
A=Pe^{rt}\qquad 
\begin{cases}
A=\textit{accumulated amount}\\
P=\textit{original amount deposited}\to& \$4100\\
r=rate\to 7.25\%\to \frac{7.25}{100}\to &0.0725\\
t=years\to &8
\end{cases}
\\\\\\
A=4100e^{0.0725\cdot 8}\implies A=4100e^{0.58}\implies A\approx 7322.757566075$

8 0

3 years ago

Given functions f ( x ) = 1 √ x and m ( x ) = x 2 − 4 , state the domains of the following functions using interval notation.

babunello [35]

The domain of a function f(x)/m(x) = 1/√x(x² - 4) is (0, ∞) - {0, 2, -2} for other function is shown in the solution.

<h3>What is a function?</h3>

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have:

f(x) = 1/√x

m(x) = x² - 4

Domain of f(x)/m(x):

f(x)/m(x) = (1/√x)/(x² - 4)

f(x)/m(x) = 1/√x(x² - 4)

The denominator cannot be zero:

√x(x² - 4) ≠ 0

x(x - 2)(x+2) ≠ 0

x ≠ 0, 2, -2

and x > 0

Domain of f(x)/m(x) is: (0, ∞) - {0, 2, -2} or $\:\left(0,\:2\right)\cup \left(2,\:\infty \:\right)$

Domain of f(m(x)):

f(m(x)) = 1/√(x² - 4)

x² - 4 > 0

Domain: $\rm \left(-\infty \:,\:-2\right)\cup \left(2,\:\infty \:\right)$

Domain of m(f(x)):

= ((1/√x)² - 4)

Domain: $\:\left(0,\:\infty \:\right)$

Thus, the domain of a function f(x)/m(x) = 1/√x(x² - 4) is (0, ∞) - {0, 2, -2} for other function is shown in the solution.

Learn more about the function here:

brainly.com/question/5245372

#SPJ1

7 0

2 years ago

Mateo reproducira una foto que mide 5 cm por lado a una escala de 3/4

Aneli [31]

the question in English

Mateo will reproduce a photo measuring 5 cm per side on a scale of 3/4

How much will the square side of the copy measure?

Will the size of the copy be larger or smaller than the original?

we know that

the scale factor is equal to $\frac{3}{4}$

Let

x----------> the original length side

y--------> the copy length side

$y=\frac{3}{4}*x$

we have that

$x=5\ cm$

substitute the values

$y=\frac{3}{4}*5=3.75\ cm$

therefore

the answer Part a) is

the length side of the copy measure is $3.75\ cm$

Part b)

we know that

the size of the original photo is------> $5*5=25\ cm^{2}$

the size of the copy is------> $3.75*3.75=14.06\ cm^{2}$

$14.06\ cm^{2} < 25\ cm^{2}$

therefore

the answer part b) is

The size of the copy be smaller than the original

3 0

3 years ago

an isosceles triangle has congruent sides of 20cm. the base is 10cm. find the height of the triangle.

dolphi86 [110]

Answer:

$\large\boxed{A_\triangle=25\sqrt{15}\ cm^2}$

Step-by-step explanation:

Look at the picture.

The formula of an area of a triangle:

$A_\triangle=\dfrac{bh}{2}$

b - base

h - height

We need a length of a height.

Use the Pythagorean theorem:

$leg^2+leg^2=hypotenuse^2$

We have:

$leg=5,\ leg=h,\ hypotenuse=20$

Substitute:

$5^2+h^2=20^2$

$25+h^2=400$ subtract 25 from both sides

$h^2=375\to h=\sqrt{375}\\\\h=\sqrt{(25)(15)}\\\\h=\sqrt{25}\cdot\sqrt{15}\\\\h=5\sqrt{15}\ cm$

Calculate the area:

$A_\triangle=\dfrac{(10)(5\sqrt{15})}{2}=\dfrac{50\sqrt{15}}{2}=25\sqrt{15}\ cm^2$

8 0

3 years ago

Plssssss help fast!!!!Launching From a Tower

aleksandrvk [35]

Answer:

A. h = 64

B. t = 4 -> 4 seconds

C. t = 1.5 -> 1.5 seconds

D. maximum height is 100 ft

E. The domain that makes sense for the function in this context is t

is any positive real number since time can not be negative.

Step-by-step explanation:

h = -16t2 + vt + 64

A. What tower platform height was the projectile launched from?

when the projectile was not launched, t = 0

h = -16(0)^2 + v(0) + 64 = 64

B. How long was the projectile in the air?

if the projectile lands, its height = 0 so substitute 0 for h

0 = -16(t)^2 + 48(t) + 64

= -16(t^2 - 3t - 4)

= -16(t - 4)(t + 1)

t = 4 or t = -1

Since time can not be negative, t = -1 can not be the answer. Therefore, the projectile lands when t = 4 or 4 seconds.

C. When did it reach its maximum height?

maximum -> t=-b/2a where in -16(t)^2 + 48(t) + 64, b = 48 and a = -16

t = -48/-32 = 1.5

D. What was its maximum height?

plug t = 1.5 into -16(t)^2 + 48(t) + 64

-16(1.5)^2 + 48(1.5) + 64 = -36 + 72 + 64 = 100

E. The domain that makes sense for the function in this context is t

is any positive real number since time can not be negative.

6 0

2 years ago