Which conditional statement is true?

A. If two angles are acute, then they are complementary

B. If an angle is acute, then it’s measure is less then 90.

Answer:

[tex]\frac{dL}{dt}=30 \frac{ft}{s}[/tex]

Step-by-step explanation:

In order to solve this it is always a good idea to start by drawing a diagram of the situation (See attached picture).

From the diagram we can see that we are dealing with similar triangles. We can use similar triangles to build an equation that relates the length of the shadow with the height of the lamp, so we get:

[tex]\frac{L}{6}=\frac{10+L}{h}[/tex]

the height of the lamp can be found by subtracting the [tex]16t^{2}[/tex] distance the lamp falls in a given time t from the original 30ft the lamp was located at.

So the equation will now lok like this:

[tex]\frac{L}{6}=\frac{10+L}{30-16t^{2}}[/tex]

So now we can solve the equation for L, we can start by multiplying by the LCD SO WE GET:

[tex]L(30-16t^{2})=6(10+L)[/tex]

next, we can distribute the right side of the equation so we get:

[tex]L(30-16t^{2})=60+6L[/tex]

and subtract 6L from both sides so we get:

[tex]L(30-16t^{2})-6L=60[/tex]

and factor L, so we get:

[tex]L(30-16t^{2}-6)=60[/tex]

and solve for L:

[tex]L=\frac{60}{24-16t^{2}}[/tex]

now, we can differentiate this equation by using the chain rule, so we get:

[tex]dL=-\frac{60}{(24-16t^{2})^{2}}(-32t)dt[/tex]

which can be simplified to:

[tex]\frac{dL}{dt}=\frac{1920t}{(24-16t^{2})^{2}}[/tex]

and now we can substitute t for 1s so we get:

[tex]\frac{dL}{dt}=\frac{1920(1)}{(24-16(1)^{2})^{2}}[/tex]

[tex]\frac{dL}{dt}=30 \frac{ft}{s}[/tex]

hello :

2x+7y=1 ...(*)

y=4x−8...(**)

(4;8) means x= 4 and y= 8

put this values in (*) and(**) :

2(4)+7(8) =1           62=1    false

8=4(4)-8          8=8   true

so :(4;8)  is not solution for this system.

Answer:.

Step-by-step explanation:

Answer:

The correct answer is A

Step-by-step explanation:

I think you are trying to find corresponding sides. In the answer that you think it is, it says BC = DF. Well, is you look triangle ABC you see that BC is at the bottom. However, this differs from triangle DEF because EF is the bottom line. So if you look at the answer A, you see that it has the correct corresponding sides. I hope that helps :))

Answer:

The answer should be b: x=-9

Answer:

b. -9

Step-by-step explanation:

-8x+10=82

     -10   -10

-8x=72

divide both side by -8

x=-9

Answer:1+3=4 4+2=6 5+6=11

Step-by-step explanation:

Answer:

1+3=4, 2+4=6, 5+6=11

Step-by-step explanation:

when made into a cube, (assuming 2 is on the top,) 1 is on the left side and 3 is on the right. 2 is on the top and 4 is on the bottom. 5 is on the north side (the front I guess, but north is the way I can explain it best) and 6 is on the south (the back).

Answer:

D. c - 2 = 25 + c + 10√c

Step-by-step explanation:

Hope this helps!! Have a great day!! ❤

Answer:

49050

Step-by-step explanation:

(5 x 109)x (9 x 10)

545×90

49050

So the answer is 49050

Answer:

100000

Step-by-step explanation:

Maths class

Answer:

500.000 cos it's firstly multiplies by 5

Answer:

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

General Formulas and Concepts:

Pre-Algebra

Algebra I

Step-by-step explanation:

Step 1: Define

Find points from graph.

Point (-3, 1)

Point (2, -3)

Step 2: Find slope m

Answer:  y = -7

graph attached.

Step-by-step explanation:

This is a horizontal line passing through -7 in the y-axis. It passes through all x-values

x ≤ -2    OR  x ≥ 4

__________________________________________________________

We are given the inequality:

|2x - 2| ≥ 6

Getting rid of the Modulus:

Since 2x-2 is in modulus:

|2x-2| =  -(2x-2)    OR   2x-2

(since the modulus of both these values is 2x-2)

Hence, our inequality can be written in 2 different ways:

__________________________________________________________

Solving these 2 inequalities:

Solving inequality 1:

2x - 2 ≥ 6                

2x ≥ 8                     [adding 2 on both sides]

x ≥ 4                       [dividing both the sides by 2]

This is the solution of the inequality if: 2x-2 ≥ 0

Solving Inequality 2:

-(2x-2) ≥ 6

It can be rewritten as:

2 - 2x ≥ 6                

2 ≥ 6 + 2x                [adding 2x on both the sides]  

-4 ≥ 2x                     [Subtracting 6 from both sides]

x ≤ -2                       [Dividing both sides by 2]

This is the solution of the given inequality if: 2x-2 < 0

__________________________________________________________

Solution of the given Inequality:

Therefore, the solution of the given inequality |2x-2| ≥ 6 are:

x ≥ 4   (if 2x-2 ≥ 0)

x ≤ -2  (if 2x-2 < 0)

Hence, option C is correct!

Answer:

4 hour

Step-by-step explanation:

The time it takes to fly from Los Angeles to New York varies inversely as the speed of the plane i.e.

[tex]t\propto v^2[/tex]

Here, t₁ = 5 h, v₁ = 950 km/h, v₂ = 850 km/h, t₂=?

[tex]\dfrac{t_1}{t_2}=\dfrac{v_1^2}{v_2^2}\\\\t_2=\dfrac{t_1v_2^2}{v_1^2}\\\\t_2=\dfrac{5\times (850)^2}{(950)^2}\\\\t_2=4\ h[/tex]

If the speed is 850 km/h then the time is 4 h.

Answer: x= 13/3

Step-by-step explanation: solve x

by simplifying both sides of the equation, then isolating the variable.

Answer:

[tex]x=\frac{13}{3}[/tex]

Step-by-step explanation:

The explanation on how to solve it is from the attached picture.

Hope this helps! :)

Answer:

200 ft

Step-by-step explanation:

Answer:

220

Step-by-step explanation:

60 times 2 equals 120

50 times 2 equals 100

120 plus 100 equals 220

Answer:

1681

Step-by-step explanation:

In a four digit perfect square, the first two digits and last two digits taken seperately are also perfect squares.

Therefore, the answer is 1681 because 1681=41*41 and

16=4*4 and 81=9*9

Answer:

Area of ΔXYZ = 10 square units

Step-by-step explanation:

Area of the triangle XYZ = [tex]\frac{1}{2}(\text{Height})(\text{Base})[/tex]

Height of the triangle = AY

Base of the triangle = XZ

To get the length of any segment we will use the formula,

d = [tex]\sqrt{(y_2-y_1)^2+(x_2-x_1)^2)}[/tex]

Here [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are the endpoints of the segment.

Length of AY = Distance between (-1, 4) and (3, 6)

                      = [tex]\sqrt{(6-4)^2+(3+1)^2}[/tex]

                      = [tex]\sqrt{20}[/tex]

Length of XZ = [tex]\sqrt{(6-2)^2+(-2-0)^2}[/tex]

                      = [tex]\sqrt{20}[/tex]

Area of ΔXYZ = [tex]\frac{1}{2}(\sqrt{20})(\sqrt{20})[/tex]

                       = 10 square units                      

Answer:

1430000000

Step-by-step explanation:

9514 1404 393

Answer:

  12 units

Step-by-step explanation:

Reflection over two lines x units apart is equivalent to a translation of 2x units. Since the given lines are 6 units apart, ...

  the equivalent translation is of 12 units.

___

Example:

Lines at x=0 and x=6. Point (x, 0). After reflection over x=0, the point is located at (2·0 -(x), 0) = (-x, 0). After reflection of that over x=6, the point is located at (2·6 -(-x), 0) = (12 +x, 0). That is, 12 has been added to the x-coordinate, meaning the point was translated 12 units. (The translation is in the direction the second line is from the first.)

Answer:

5/8 quart

Step-by-step explanation:

Answer:

ob

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

i did flvs

Answer: 61

Step-by-step explanation:

[tex]\sqrt{x+20}=9\\\\x+20=81\\\\x=\boxed{61}[/tex]

The value of x will be 61.

What is mathematical expression?

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 mathematical expression is,

⇒ √x + 20 = 9

Now,

Solve the expression for the value of x as;

The mathematical expression is,

⇒ √x + 20 = 9

Take square on both side, we get;

⇒ (√x + 20 )² = 9²

⇒ x + 20 = 81

Subtract 20 both side, we get;

⇒ x + 20 - 20 = 81 - 20

⇒ x = 61

Therefore, The value of x will be 61.

Learn more about the mathematical expression visit:

https://brainly.com/question/16583268

#SPJ2

Answer:

Step-by-step explanation:

tan 26° = [tex]\frac{x}{90}[/tex] ⇒ x = 90tan26° ≈ 43.9 ft. (This answer for the picture)

sin 26° = [tex]\frac{h}{100}[/tex] ⇒ h = 100sin26° ≈ 43.9 ft (This answer for the text)

h = √(100² - 90²) ≈ 43.589 ft. (Pythagorean theorem)

Answer:

Explanation below

Step-by-step explanation:

First Degree Equations

A first-degree equation can have one, none, or infinitely many solutions.

An equation like

2x + 3 = -x + 6

Has one solution: x=1

An equation like:

4x + 2 = 4x + 1

Has no solutions because when trying to solve for x we get:

2 = 1

This equality is false and no value of x can make it true

Finally, the equation:

3x + 2 = x + 2x + 2

Has infiniteyl many solutions, because when trying to solve it, we get:

2 = 2

Which is true regardless of the value of x

3x + 9 + 4x + x = ??

can be simplified as:

8x + 9 = ??

For this equation not having solutions, we should have 8x plus any number but 9 on the right side of the equation:

8x + 9 = 8x -3, or

8x + 9 = 8x + 4

3x + 9 + 4x + x = ??

can be simplified as:

8x + 9 = ??

If the equation has one solution, the only condition is that we should not have 8x on the right side. Thus any of those will do:

8x + 9 = 3x + 9

8x + 9 = -x + 5

8x + 9 = 0

3x + 9 + 4x + x = ??

can be simplified as:

8x + 9 = ??

For this equation to have infinitely many solutions, the right side must be exactly equal to the left side:

8x + 9 = 8x + 9

Answer:

1.) 0.95

2.) 0.25

3.) 5.13

4.) 0.04

5.) 0.02

6.) 0.5

7.) 0.22

8.) 0.12 cents

9.) 5.11 feet long

10.) $41.29 per day

Step-by-step explanation:

Answer:

The domain of the graph must be [tex]x\ge \:-4[/tex].

Therefore,

[tex]x\ge \:-4\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x\ge \:-4\:\\ \:\mathrm{Interval\:Notation:}&\:[-4,\:\infty \:)\end{bmatrix}[/tex]

Hence, option a is true.

Step-by-step explanation:

From the graph, it is clear that the graph is heading towards positive infinity from x=-4.

The point x=-4 is included in the graph as the starting point of the graph i.e. x=4 is showing a closed circle on x=4, and heading towards positive infinity onward.

i.e. [-4, ∞)

Hence, the domain of the graph must be [tex]x\ge \:-4[/tex].

Therefore,

[tex]x\ge \:-4\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x\ge \:-4\:\\ \:\mathrm{Interval\:Notation:}&\:[-4,\:\infty \:)\end{bmatrix}[/tex]

Hence, option a is true.

Answer:

b = 7

Step-by-step explanation:

Add 4b to both sides

You then get -b = -7

You want to multiply both sides by -1 because you can't have a negative variable

Answer:

b = 7

Step-by-step explanation:

^^^

^

h

g

h

h

h

h

h

hh

h

h

h

h

h

h

h