given the function f(x)=5x-3/4,which of the following is correct?

Answer:

A

Step-by-step explanation:

We are given a right triangle with a base of x feet and a height of h feet, where x is constant and h changes with respect to time t.

The angle in radians is defined by:

[tex]\displaystyle \tan(\theta)=\frac{h}{x}[/tex]

And we want to find the relationship that describes dθ/dt and dh/dt.

So, we will differentiate both sides with respect to t where x is a constant:

[tex]\displaystyle \frac{d}{dt}[\tan(\theta)]=\frac{d}{dt}\Big[\frac{h}{x}\Big][/tex]

Differentiate. Apply the chain rule on the left. Again, remember that x is just a constant, so we can move it outside the derivative operator. Therefore:

[tex]\displaystyle \sec^2(\theta)\frac{d\theta}{dt}=\frac{1}{x}\frac{dh}{dt}[/tex]

Since we know that tan(θ)=h/x, h is the opposite side of our triangle and x is the adjacent. Therefore, by the Pythagorean Theorem, our hypotenuse will be:

[tex]\text{Hypotenuse}=\sqrt{h^2+x^2}[/tex]

Since secant is the ratio of the hypotenuse to adjacent:

[tex]\displaystyle \sec(\theta)=\frac{\sqrt{h^2+x^2}}{x}[/tex]

So:

[tex]\displaystyle \sec^2(\theta)=\frac{x^2+h^2}{x^2}[/tex]

By substitution, we have:

[tex]\displaystyle \Big(\frac{x^2+h^2}{x^2}\Big)\frac{d\theta}{dt}=\frac{1}{x}\frac{dh}{dt}[/tex]

By multiplying both sides by the reciprocal of the term on the left:

[tex]\displaystyle \frac{d\theta}{dt}=\frac{1}{x}\Big(\frac{x^2}{x^2+h^2}\Big)\frac{dh}{dt}[/tex]

Therefore:

[tex]\displaystyle \frac{d\theta}{dt}=\frac{x}{x^2+h^2}\frac{dh}{dt}[/tex]

Our answer is A.

Answer:

[tex]-\frac{5}{4}[/tex]

Step-by-step explanation:

Parallel lines always have equal slopes. Therefore any parallel line to a given line will share the same slope.

Answer:

-5/4

Step-by-step explanation:

Parallel lines have the same slope but a different y intercepts, because if you think about parellel lines, they'll never intersect-- if two lines have the same slope, that means they won't be able to intersect. However, if they have the same slope, they would be coinciding (the same). That's why the y intercepts are different.

Since the slope of the first line is -5/4, the slope for the line parallel to it would also be -5/4

hope this helps!

Answer:

hope this hlp u

Step-by-step explanation:

the last one shows the radius

Answer:

figure 4 shows the radius

Answer:

G=23/16

Step-by-step explanation:

Answer:

The given statement  Y = 7, x = 4 is False.

Step-by-step explanation:

We are given:

Y is inversely proportional to x, when Y = 7, x = 4.

We need to tell if the statement is True or False: the constant of proportionality, k, is 20.

Y is inversely proportional to x

We can write it as: [tex]y\:\alpha \:\frac{1}{x}\\y=\frac{k}{x}[/tex]

Now, we need to check when Y=7, x = 4 is true or false

We are given k = 20

Now, I can find value of y, by putting values of k and x in the equation:

[tex]y=\frac{k}{x}\\y=\frac{20}{4}\\y=5[/tex]

When we put x = 4, and k =20, we get Y=5 and not Y=7

So, The given statement  Y = 7, x = 4 is False.

Answer:

"The product of thirty and a number is six".

30n=6 is the right answer.

the answer is K it's parallel

Step-by-step explanation:

the answer is A

Answer:

y = ⅓x - 3

Step-by-step explanation:

First, find the slope using two points on the line, say (0, -3) and (6, 0):

[tex] \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - (-3)}{6 - 0} = \frac{3}{6} = \frac{1}{3} [/tex]

Slope (m) = ⅓

Find the y-intercept (b):

The line intercepts the y-axis at y = -3. So b = -3

Next, substitute m = ⅓ and b = -3 into y = mx + b (slope-intercept form):

y = ⅓(x) + (-3)

y = ⅓x - 3

Answer:

The slope is 2

Step-by-step explanation:

The slope that connects the two points (0, 4) and (-2, 0) is 2.

Answer:

x

Step-by-step explanation:

The definition of a variable is an unknown quantity, usually represented by a letter.

The variable in the algebraic expression 5x + 13 will be 'x'.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The algebraic expression is,

⇒ 5x + 13

Now,

Since, The algebraic expression is,

⇒ 5x + 13

Hence, The variable of the algebraic expression = x

Therefore, The variable in the algebraic expression 5x + 13 = x

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ2

Answer:

Volume of the prism =  280 ft^3

Step-by-step explanation:

Recall that the volume of a prism is given by the  following formula:

Volume = B * H

where B is the area of the base (in our case a right angle triangle), and H is the prism's height (in our case 16 ft)

Then we estimate the area of the triangle at the base as base* height/2 :

Area triangle = 5 * 7 / 2 = 35/2 ft^2

and multiply by the prism's height to get its volume:

Volume = 35/2 * 16 = 280 ft^3

Answer:

find the value

Step-by-step explanation:

duhhhhhhhhh

Answer:

Step-by-step explanation:

6x+8+4x+2=180

the sum of interior angles =180

10x+10=180

10x=180-10

10x=170

x=17

by the Angle sum property of triangle,

55+75+(-6+7x) = 180

=> 130 +(-6+7x) = 180

=> (-6+7x) = 180-130

=> (-6+7x) = 50

=> 7x = 50+6

=> 7x = 56

=> x= 56/7

=> x = 8

Answer:

100 answer is correct

Step-by-step explanation:

2×10-3×-12+4×11

20+36+44

100 answer is correct

Step-by-step explanation:

2x-3y+4z

x=10

y=12

z=11

2(10)-3(-12)+4(11)

20+36+44

and the answer is 100

(made a lot of mistakes so edited answer!)

good day :)

Answer:

(29x + 9)

Step-by-step explanation:

Perimeter of a polygon = Sum of measures of all sides of the polygon

Therefore, Perimeter of the given polygon = (9 + 12x + 2x + 2x + 12x + x)

                                                                       = (9 + 29x)

Expression (29x + 9) will represent the perimeter of the polygon.

Answer:15

Step-by-step explanation: 7 and a half times 2 is 15

the answer to that question is 15.

Answer:

-2[tex]x^{2}[/tex] + 9

Step-by-step explanation:

   0[tex]x^{2}[/tex] + (-7x) + 1

+ -2[tex]x^{2}[/tex]  + 7x + 8

  -2[tex]x^{2}[/tex] + 0x + 9

or

-2[tex]x^{2}[/tex] + 9

This is not the correct answer.

1. 2.30 is not even close to the point given in the number line.

2. My guess for the correct answer would be 0.23 because in between 0.2 and 0.3 is 0.25, so the best answer would be 0.23.

Answer

always

Step-by-step explanation:

Answer:

208

Step-by-step explanation:

this is what I did. 348×.6

60% of 580 is 348 is the answer you're looking for

If you divide .6 by 348 you get 580.

To check your answer, you can do .4 (40%) multiplied by 580 to get 232

232+348=250 which is 100%

Answer:

Segment J’K lies on line g and has a slope of -1/3

Step-by-step explanation:

Im taking the test but I need step 4 but step 5 is filled in for me

Answer:

In case you get the same question

Step-by-step explanation:

Answer:

Step-by-step explanation:

16(1/4)^2 - 4(6)

16(1/16) - 24

1 - 24 = -23

Answer:

look below ⏬

Step-by-step explanation:

you can see there is a pattern

0.40

0.70

1.00

so you keep adding three (30)

1.30

1.60

1.90

And for 0

0.10

All in oder now

0- 0.10

10- 0.70

20- 1.00

30- 1.30

40- 1.60

50- 1.90

60- 2.20

Answer: 2/3

Step-by-step explanation: