How many solutions does the equation 5x + 3x − 4 = 10 have? (4 points) Zero One Two Infinitely many

A baseball is hit and its height is given by h = 29.4t – 4. 9t^2, where h is the

ioda

Answer:

44.1m

Step-by-step explanation:

we are given a quadratic function which represents the height and time of a baseball

$\displaystyle h = 29.4t - 4.9 {t}^{2}$

we want to figure out maximum height of

the baseball

since the given function is a quadratic function so we have a parabola

which means figuring out the maximum height is the same thing as figuring out the maximum y coordinate (vertex)

to do so we can use some special formulas

recall that,

$\displaystyle \rm t= \frac{ - b}{ 2a}$

$\displaystyle H_{\text{max}}=f(t)$

notice that, our given function is not in standard form i.e

$\displaystyle f(x) = a {x}^{2} + bx + c$

let's make it so

$\displaystyle h = - 4.9 {t}^{2} + 29.4t$

therefore we got

our a is -4.9 and b is 29.4

so substitute:

$\displaystyle\rm t= \frac{ -( 29.4)}{ 2 \cdot - 4.9}$

remove parentheses and change its sign:

$\displaystyle\rm t= \frac{ -29.4}{ 2 \cdot - 4.9}$

simplify multiplication:

$\displaystyle\rm t= \frac{ -29.4}{ - 9.8}$

simplify division:

$\displaystyle \: t = 3$

so we have figured out the time when the baseball will reach the maximum height

now we have to figure out the height

to do so

substitute the got value of time to our given function

$\displaystyle H_{\text{max}}=29.4\cdot 3-4.9\cdot {3}^2$

simplify square:

$\displaystyle H_{\text{max}}=29.4\cdot 3-4.9\cdot 9$

simplify mutilation:

$\displaystyle H_{\text{max}}=88.2-44.1$

simplify substraction:

$\displaystyle H_{\text{max}}=44.1$

hence,

the maximum height of the baseball is 44.1 metres

4 0

2 years ago

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Erin received the following scores on her last four spelling tests.

Tatiana [17]

The second one, 82% is Erin's highest score

4 0

3 years ago

Read 2 more answers

A cone has a height of 2.5 in. and a radius of 5 in. What is the volume of the cone? (Use 3.14 for Pi. Round the answer to two d

Stells [14]

Answer:

$V =\frac{1}{3} \pi r^2 h$

And replacing we got:

$V = \frac{1}{3} (3.14) (5in)^2 (2.5in) = 65.42 in^3$

And the best option would be:

65.42 Inches cubed

Step-by-step explanation:

For this case we have the following info given:

$h =2.5 in$ represent the height of the cone

$r = 5 in$ represent the radius

And the volume of the cone is given by;

$V =\frac{1}{3} \pi r^2 h$

And replacing we got:

$V = \frac{1}{3} (3.14) (5in)^2 (2.5in) = 65.42 in^3$

And the best option would be:

65.42 Inches cubed

6 0

2 years ago

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The graph of f(x) = 24x^2 + 63x +34/ 4x + 3 has an oblique asymptote at y =

g100num [7]

Correct answer is C). 6X+11

Step-by-step explanation:

The given function f(x)= $\frac{24x^{2} +63x + 34 }{4x+3}$

On simplying the function f(x),

f(x)= $\frac{6x(4x+3) -18x +63x + 34 }{4x+3}$

f(x)= $\frac{6x(4x+3) +45x + 34}{4x+3}$

f(x)= $\frac{6x(4x+3) +11(4x+3)+x-33 + 34 }{4x+3}$

f(x)= $\frac{6x(4x+3) +11(4x+3)+x+1}{4x+3}$

f(x)= $(6x+11)+\frac{(x+1)}{4x+3}$

From above equation

"(6x+11)" is Oblique asymptote and $\frac{(x+1)}{4x+3}$ is vertical asymptote

Therefore, Correct answer is C). 6X+11

8 0

2 years ago

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A museum has an aquarium in the shape of a right rectangular prism that is 22.9 meters long, 7.5 meters wide, and 4.6 meters hig

Vedmedyk [2.9K]

Answer:

790

Step-by-step explanation:

just multiply all of the values

8 0

3 years ago

How many solutions does the equation 5x + 3x − 4 = 10 have? (4 points) Zero One Two Infinitely many​

How many solutions does the equation 5x + 3x − 4 = 10 have? (4 points) Zero One Two Infinitely many