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3 years ago

Tell whether it is possible to draw a triangle with the given side lengths.

Mathematics

1 answer:

expeople1 [14]3 years ago

4 0

Answer:

Step-by-step explanation:

Since the 2 shorter sides are greater than the longest side when added, it meet the triangle inequality thoerem. Triangle Inequality Theorom: The longest side of a triangle is less then the 2 shorter sides added.

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The function f(x) = x2 is transformed to f(x) = −1.4x2. Which statement describes the effect(s) of the transformation on the gra

Romashka-Z-Leto [24]

Answer:

C) The parabola is narrower and reflected across the x-axis.

Step-by-step explanation:

The original parabola has equation:

$f(x) = {x}^{2}$

The transformed parabola has equation

$f(x) = - 1.4 {x}^{2}$

How wide the graph is can be determined by the absolute value of the coefficient.

The smaller the absolute value of the coefficient, the wider the graph.

Since

$|1| \: < \: | - 1.4|$

The original graph is wider than the transformed graph.

Also the negative factor tells us there is a reflection in the x-axis.

3 0

3 years ago

How many roots does the equation 3x² = 1 - 7x have and what is the nature of the roots

AnnyKZ [126]

Answer:

Step-by-step explanation:

Rewrite this quadratic in standard form: 3x^2 + 7x - 1.

The coefficients of x are {3, 7, -1}, and so the discriminant is b^2 - 4ac, or

7^2 - 4(3)(-1), or 49 + 12, or 61. Because the discriminant is positive, this quadratic has two real, unequal roots

7 0

3 years ago

Which is an equation of the line that passes through the point(2,3) and has a slope of 1/3

777dan777 [17]

Y = 1/3x + b
Plug in the point
3 = 1/3(2) + b
3 = 2/3 + b, b = 7/3
Solution: y = 1/3x + 7/3

7 0

3 years ago

Can someone help me figure out the answer?

Marina86 [1]

Answer:

f(t) = 5×0.87^t

Step-by-step explanation:

The general form for an exponential function described in this fashion is ...

... f(t) = (starting value) × (1 + (percent change))^t

Here, the "percent change" is -13%, or -0.13.

Then the value (1 + percent change) is (1 + (-0.13)) = 0.87. Putting this and the starting value into the form above, we have ...

... f(t) = 5 × 0.87^t

3 0

3 years ago

According to data from a medical association, the rate of change in the number of hospital outpatient visits, in millions, in

GaryK [48]

Answer:

a) $f(t)=0.001155[\frac{2}{3}t(t-1980)^{3/2}-\frac{4}{15}(t-1980)^{5/2}]+264,034,000$

b) f(t=2015) = 264,034,317.7

Step-by-step explanation:

The rate of change in the number of hospital outpatient visits, in millions, is given by:

$f'(t)=0.001155t(t-1980)^{0.5}$

a) To find the function f(t) you integrate f(t):

$\int \frac{df(t)}{dt}dt=f(t)=\int [0.001155t(t-1980)^{0.5}]dt$

To solve the integral you use:

$\int udv=uv-\int vdu\\\\u=t\\\\du=dt\\\\dv=(t-1980)^{1/2}dt\\\\v=\frac{2}{3}(t-1980)^{3/2}$

Next, you replace in the integral:

$\int t(t-1980)^{1/2}=t(\frac{2}{3}(t-1980)^{3/2})- \frac{2}{3}\int(t-1980)^{3/2}dt\\\\= \frac{2}{3}t(t-1980)^{3/2}-\frac{4}{15}(t-1980)^{5/2}+C$

Then, the function f(t) is:

$f(t)=0.001155[\frac{2}{3}t(t-1980)^{3/2}-\frac{4}{15}(t-1980)^{5/2}]+C'$

The value of C' is deduced by the information of the exercise. For t=0 there were 264,034,000 outpatient visits.

Hence C' = 264,034,000

The function is:

$f(t)=0.001155[\frac{2}{3}t(t-1980)^{3/2}-\frac{4}{15}(t-1980)^{5/2}]+264,034,000$

b) For t = 2015 you have:

$f(t=2015)=0.001155[\frac{2}{3}(2015)(2015-1980)^{1/2}-\frac{4}{15}(2015-1980)^{5/2}]+264,034,000\\\\f(t=2015)=264,034,317.7$

3 0

3 years ago