An object was dropped off the top of a building. The function
f
(
x
)
=
−
16
x
2
+
256
f(x)=−16x
2
+256 represents the height of the object above the ground, in feet,
x
x seconds after being dropped. Find and interpret the given function values and determine an appropriate domain for the function.

f(−1)= , meaning that seconds after the object was dropped, the object was feet above the ground. This interpretation in the context of the problem.
f
(
1.5
)
=
f(1.5)= , meaning that seconds after the object was dropped, the object was feet above the ground. This interpretation in the context of the problem.
f
(
6
)
=
f(6)= , meaning that seconds after the object was dropped, the object was feet above the ground. This interpretation in the context of the problem.
Based on the observations above, it is clear that an appropriate domain for the function is .

Answer:

y = 3/5x + 3/5.

Step-by-step explanation:

the /'s are division symbols.              3            3

                                                  y =     _   +       _

                                                           5            5

Answer:

12

Step-by-step explanation:

For ΔDEF similar to ΔRST, the value of x is 12. So, option a) is correct.

Two triangles are said to be similar if corresponding angles are equal or  corresponding sides are in the same proportion.

Given triangles are similar:

ΔDEF ~ ΔRST

Therefore, using the property of similar triangle that corresponding sides of a similar triangle are in same proportion.

[tex]\dfrac{EF}{ST}=\dfrac{ED}{SR}\\\\\dfrac{x}{16}=\dfrac{3}{4}\\\\x=\dfrac{3}{4}\times 16\\\\x=12[/tex]

Thus, the value of x is 12. So, option a) is correct.

Learn more about similar triangles, here:

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Answer:

B- y=-3

Step-by-step explanation:

Answer:

x=19

Step-by-step explanation:

subtract 12 from each side: 50-12=2x+12-12

38=2x

divide by 2

38/2=2x/2

19=x

Answer:

x=19

Step-by-step explanation:

50=2x+12

50-12=2x+12-12

38=2x

38/2=2x/2

x=19

Answer:

0.749

Step-by-step explanation:

We start by calculating the z-score

Mathematically:

z-score = (x-mean)/SD

z-score = (75-77)/3 = -2/3 = -0.67

The probability we want to calculate is;

P( X > -0.67)

we can use the standard normal distribution table for this

Using this table, the probability has a value 0.74857 which is 0.749 to the nearest thousandth

Answer:

5:1

Step-by-step explanation:

The ratio 10: 2 will be equivalent to ratios 20:4, 30:6, 40:8, and 50:10. Then all the options are correct.

A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.

The equivalent is the expression that is in different forms but is equal to the same value.

The ratio is given below.

Ratio = 10 / 2

Multiply and divide the ratio by 2. Then we have

Ratio = 10 x 2 / 2 x 2

Ratio = 20 / 4

Multiply and divide the ratio by 3. Then we have

Ratio = 10 x 3 / 2 x 3

Ratio = 30 / 6

Multiply and divide the ratio by 4. Then we have

Ratio = 10 x 4 / 2 x 4

Ratio = 40 / 8

Multiply and divide the ratio by 5. Then we have

Ratio = 10 x 5 / 2 x 5

Ratio = 50 / 10

The ratio 10: 2 will be equivalent to ratios 20:4, 30:6, 40:8, and 50:10. Then all the options are correct.

More about the ratio and the proportion link is given below.

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The missing options are given below.

20:4

30:6

40:8

50:10

Transformations are used to change the position of a function from one point to another. When f(x) is reflected over the y-axis, the new function g is [tex]g(x) = x + 8[/tex]

Given that:

[tex]f(x) = -3+|x - 11|[/tex]

To reflect across the y-axis, we use the following transformation rule:

[tex](x,y) \to (-x,y)[/tex]

So, the new function is:

[tex]g(x) = f(-x)[/tex]

If [tex]f(x) = -3+|x - 11|[/tex], then:

[tex]f(-x) = -3+|-x - 11|[/tex]

Factor out -1

[tex]f(-x) = -3+|-1(x + 11)|[/tex]

Remove absolute sign

[tex]f(-x) = -3+1 \times (x + 11)[/tex]

[tex]f(-x) = -3+x + 11[/tex]

Collect like terms

[tex]f(-x) = x + 11-3[/tex]

[tex]f(-x) = x + 8[/tex]

Hence, the new function is:

[tex]g(x) = x + 8[/tex]

Read more about transformations at:

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Answer:

X=$7

Step-by-step explanation:

Answer:

El ángulo entre el piso y la escalera está cambiando a una razón de -1 radian por segundo.

Step-by-step explanation:

Sea [tex]x[/tex] la distancia horizontal entre la pared y la base de la escalera y [tex]l[/tex] la longitud de la escalera, medidas en metros. Además, tenemos que [tex]\theta[/tex] es el ángulo entre la escalera y el piso, medido en radianes.

Si la pared y el piso son ortogonales entre sí, entonces podemos utilizar la siguiente relación trigonométrica que relaciona las variables anteriores:

[tex]\cos \theta = \frac{x}{l}[/tex]  (1)

Por diferenciación implícita y la definición de razón de cambio tenemos que:

[tex]-\sin \theta \,\dot \theta = \frac{\dot x}{l}[/tex] (2)

Donde:

[tex]\dot x[/tex] - Razón de cambio de la distancia horizontal entre la pared y la base de la escalera, medida en metros por segundo.

[tex]\dot \theta[/tex] - Razón de cambio del ángulo entre el piso y la escalera, medida en radianes por segundo.

Pero tenemos que el seno del ángulo está definido por:

[tex]\sin \theta = \frac{\sqrt{l^{2}-x^{2}}}{l}[/tex] (3)

Si aplicamos (3) en (2), expandimos la ecuación como sigue:

[tex]-\frac{\sqrt{l^{2}-x^{2}}}{l}\,\dot \theta = \frac{\dot x}{l}[/tex]

[tex]\dot \theta = - \frac{\dot x}{\sqrt{l^{2}-x^{2}}}[/tex] (4)

Si tenemos que [tex]\dot x = 5\,\frac{m}{s}[/tex], [tex]l = 13\,m[/tex] y [tex]x = 12\,m[/tex], entonces la razón de cambio del ángulo es:

[tex]\dot \theta = -\frac{\left(5\,\frac{m}{s} \right)}{\sqrt{(13\,m)^{2}-(12\,m)^{2}}}[/tex]

[tex]\dot \theta \approx -1\,\frac{rad}{s}[/tex]

El ángulo entre el piso y la escalera está cambiando a una razón de -1 radian por segundo.

Answer:

12.6 cups

Step-by-step explanation:

each liter has 4.2 cups so if you just multiply it by 3 you will get 12.6. cups.

Answer:

280 miles

Step-by-step explanation:

So, 420 miles=12 gallons

That means that for 1 gallon you would be able to go 35 miles.

Just multiply that by 8. 35*8=280

Answer:

Length=3x^3+6x^2+10x+10

Step-by-step explanation:

given that the area A of a rectangle is A=L*W, we can find length L=A/W

Answer:

6 divided by 2 =p (a made a little graph at the bottom to demonstrate)

Step-by-step explanation:

.  .  .  .  .  .          Graph←

.  .  .  .  .  .

Answer:

The slope is 6 and the y intercept is -5

Step-by-step explanation:

y=6x-5

The equation is in slope intercept form

y = mx+b where m is the slope and b is the y intercept

The slope is 6 and the y intercept is -5

Answer:

[tex]slope=6\\\\y-intercept=-5[/tex]

Step-by-step explanation:

The given equation is written in slope-intercept form:

[tex]y=mx+b[/tex]

where:

Find the values:

[tex]y=(slope)x+(y-intercept)\\\\y=6x-5[/tex]

6 is in the slope place, so the slope is 6.

5 is in the y-intercept place. Note how this number has a negative sign when the original equation says "+b". This means that the y-intercept is -5.

:Done

Answer:

1 mile every 6 minutes because 30 divided by 5 is 6 and 5 divided by 5 is 1

Step-by-step explanation:

I hoped this helped and if it did I would appreciate it if you marked me brainliest. Thank you and have a nice day!

Answer:

[tex]\%Increase = 4\%[/tex]

Step-by-step explanation:

Given

[tex]Initial\ Population = 625[/tex]

[tex]Final\ Population = 650[/tex]

Required

Determine the percentage population increase

This is calculated using the following formula:

[tex]\%Increase = \frac{Final - Initial}{Initial} * 100\%[/tex]

[tex]\%Increase = \frac{650 - 625}{625} * 100\%[/tex]

[tex]\%Increase = \frac{25}{625} * 100\%[/tex]

[tex]\%Increase = \frac{25* 100\%}{625}[/tex]

[tex]\%Increase = \frac{2500\%}{625}[/tex]

[tex]\%Increase = 4\%[/tex]

Hence, there is a 4% increment from 2014 to 2015

Answer:

I got x = -3/7, y = 20/7. Hope this helps :)

Answer:

Option 1: -2

Step-by-step explanation:

Take the rise over the run, where rise is the number of units vertically up the graph and run is the number of units horizontally across the graph

This is a topic on coordinate geometry. If you wish to explore more into this topic you can give me a follow on Instagram (learntionary). I'll be uploading notes on this topic soon. At the meantime, you can take a look at other topics or some tips as well!

Answer:

1 months

Step-by-step explanation:

Given

Anaconda

[tex]Length = 5.23m[/tex]

[tex]Growth = 1.27m[/tex] monthly

Python:

[tex]Length = 4.76m[/tex]

[tex]Growth = 2.04m[/tex] monthly

Required

Determine when their length will be equal

First, we need to write equations that determines the growth of each snake in m months.

For both snakes;

[tex]Expression = Length + Growth * m[/tex]

For the Anaconda, the expression is:

[tex]5.23 + 1.27 * m[/tex]

[tex]5.23 + 1.27 m[/tex] --- (1)

For the Python, the expression is

[tex]4.76 + 2.04 * m[/tex]

[tex]4.76 + 2.04m[/tex] ---- (2)

Both snakes will have equal length when both expressions (1 & 2) are equal

[tex]4.76 + 2.04m = 5.23 + 1.27 m[/tex]

Collect Like Terms

[tex]2.04m - 1.27 m= 5.23 - 4.76[/tex]

[tex]0.77 m= 0.47[/tex]

Solve for m

[tex]m = \frac{0.47}{0.77}[/tex]

[tex]m = 0.61[/tex]

[tex]m = 1[/tex] --- Approximated

Hence, the zookeeper will wait for 1 month

Answer:

Step-by-step explanation:

Aakash body temperature during the day = 99.2°F.

If by evening his body temperature increases by 3.4°F, then his body temperature in the evening will be expresses as the sum of his temperature in the day and the increment.

Temperature in the evening = 99.2°F+3.4°F.

Temperature in the evening = 102.6°F.

Hence his body temperature in the evening is 102.6°F.

Answer:

102.6

I hope this helps

Answer:

if the points are in a straight line going upward then they are corect

but if the points are scattered they are wrong its hard to answer this question he graph to look at

Answer:

8.5

Step-by-step explanation:

8.5 is the coefficient in front of x

Answer:

answer is -1/2 .i think it will be helpful for you

Answer:

Equation of y in terms of x is: [tex]y = \frac{7}{4}x[/tex]

Step-by-step explanation:

Proportion means that the change in one quantity causes change in other quantity.

Given that A proportional relationship exists between x and y.

It can be expressed mathematically as:

y ∝ x

When the proportionality symbol is removed, constant of proportionality is introduced which is usually denoted as k

[tex]y = kx[/tex]

Given that y=14 when x=8

Putting in equation

[tex]14 = k * 8\\k =\frac{14}{8}\\k = \frac{7}{4}[/tex]

Putting the value of k in equation

[tex]y = \frac{7}{4}x[/tex]

Hence,

Equation of y in terms of x is: [tex]y = \frac{7}{4}x[/tex]

Answer:

12

Step-by-step explanation:

can you please answer my question too? it is due soon

Answer:

x = 12

Step-by-step explanation:

1/2x-5=10-3/4x

add 5 to both sides

1/2x=15-3/4x

add 3/4x to both sides

1/2x + 3/4x = 15

2/4x + 3/4x = 15

5/4x = 15

divide both sides by 5/4

x = 15 * 4/5

x = 60/5

x = 12

Answer:

A rectangular visual model resembling a piece of tape with divisions used to assist mathematical calculations. Also known as a divided bar model, fraction strip, length model or strip diagram. In mathematics education, it is used to solve word problems.

Step-by-step explanation:

Answer:

Tape diagrams are visual models that use rectangles to represent the parts of a ratio.

Here's what it looks like