In the figure, the ratio of the area of rectangle ABEF to the area of rectangle ACDF is .
If the coordinates of point A are (0,6), the area of rectangle ABEF is square units, and the area of rectangle ACDF is square units.
The perimeter of rectangle BCDE is units.

Answer:

∠ABC =   52°

∠BCA =  48°

∠CAB = 80°

Step-by-step explanation:

Angle sum property of triangle: Sum of all the angles of a triangle is 180.

13x² + 12x² + 20x² = 180

Combine like terms,

                 45x²  = 180

                     x² = 180 ÷ 45

                     x² = 4

                     x = √4

                     x = ± 2

x = 2 ; -2

∠ABC = 13x² = 13*4 = 52°

∠BCA = 12x² = 12 *4 = 48°

∠CAB = 20x² = 20 *4 = 80°

The value of x is +2 and -2 and the angles will be given as ∠ABC = 52 ∠ACB = 48 and ∠CAB = 80.

The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.

Given that:-

∠ABC = 13x² ∠ACB = 12x² and ∠CAB = 20x²

The angles will be calculated as follows:-

13x² + 12x² + 20x² = 180

45x²  =  180

x²  =  4

x   =  ±2

The angles will be:-

∠ABC = 13x²  = 13 x ( 2² ) = 52

∠ACB = 12x²  = 12 ( 2² )    = 48

∠CAB = 20x²  = 20 ( 2² )  = 80

Therefore value of x is +2 and -2 the angles will be given as ∠ABC = 52 ∠ACB = 48 and ∠CAB = 80.

To know more about Trigonometry follow

https://brainly. com/question/24349828

#SPJ1

Answer:

Step-by-step explanation:

(√6 - √2)/4

Answer:

10.33332

Step-by-step explanation:

-6.77777 is 6.77777 units away from 0. So there's 6.77777+3.55555 which is 3.55555 units away from 0.

Add those two numbers together and it's 10.33332

Answer:

10.33332

Step-by-step explanation:

distance between -6.77777 and 3.55555 is 10.33332

Answer: cosecant

Formula's are:

Secant:

1/cos(x) = sec(x)

Cosecant:

1/sin(x) = cosec(x)

Cotangent:

1/tan(x) = cos(x)/sin(x) = cot(x)

If BCD was reflected over the x axis then the coordinates will be B(-1,0) C(-1,2) and D(-4,1).

Given BCD is a triangle having coordinates (-1,0),(-1,-2),(-4,-1).

When the triangle is reflected over the x axis then all the values of y will change from negative to positive and the values of x remains same because in the second and third quadrant the values of x remains same and in the second quadrant the values of y used to  be positive  and in the third quadrant the values of y used to be negative.

So coordinates of B will change from (-1,0) to (-1,0)

coordinates of C will change from (-1,-2) to (-1,2)

coordinates of D will change from (-4,-1) to (-4,1)

New coordinates will be (-1,0) (-1,2) (-4,1).

Hence if BCD was reflected over x axis the new coordinates will be (-1,0) (-1,2) (-4,1).

Learn more about coordinates at https://brainly.com/question/17206319

#SPJ10

Answer:

P=3.5

P=2.667

Step-by-step explanation:

p=f/a

P=70/20

P=3.5

then f is increased by 10

f=70+10=80

and a is increased by 10

a=20+10

a=30

therefore; P=f/a

P=80/30

P=2.667

Answer:

[tex]x \approx 2.740646096[/tex]

Step-by-step explanation:

Given:

[tex]x\log_{10}x=1.2[/tex]

Rewrite so that it's equal to zero:

[tex]\implies x\log_{10}x-1.2=0[/tex]

Therefore:

[tex]\implies f(x)=x\log_{10}(x)-1.2[/tex]

Differentiate the function:

Use the product rule to differentiate [tex]x\log_{10}(x)[/tex]:

[tex]\textsf{Let }u=x \implies \dfrac{du}{dx}=1[/tex]

[tex]\textsf{Let }v=\log_{10}(x) \implies \dfrac{dv}{dx}=\dfrac{1}{x \ln 10}[/tex]

[tex]\begin{aligned}\implies \dfrac{dy}{dx} & = u\dfrac{dv}{dx}+v \dfrac{du}{dx}\\& = \dfrac{x}{x \ln 10}+\log_{10}(x)\\& = \dfrac{1}{\ln 10}+\log_{10}(x)\end{aligned}[/tex]

[tex]\implies f'(x)=\dfrac{1}{\ln 10}+\log_{10}(x)[/tex]

[tex]\implies f'(x)=\dfrac{1+\ln 10 \log_{10}(x)}{\ln 10}[/tex]

Newton-Rhapson iteration formula

[tex]x_{n+1}=x_n-\dfrac{f(x_n)}{f'(x_n)}[/tex]

Substitute the function and its derivative into the formula, replacing x with [tex]x_n[/tex]:

[tex]\implies x_{n+1}=x_n-\dfrac{x_n\log_{10}(x_n)-1.2}{\dfrac{1+\ln 10 \log_{10}(x)}{\ln 10}}[/tex]

[tex]\implies x_{n+1}=x_n-\dfrac{x_n\ln 10\log_{10}(x_n)-1.2\ln 10}{1+\ln 10 \log_{10}(x_n)}[/tex]

Therefore, the iteration formula is:

[tex]x_{n+1}=x_n-\dfrac{x_n\ln 10\log_{10}(x_n)-1.2\ln 10}{1+\ln 10 \log_{10}(x_n)}[/tex]

Let [tex]x_0=3[/tex]

Substitute this into the formula and carry out 3 iterations:

[tex]\implies x_{1}=3-\dfrac{3\ln 10\log_{10}(3)-1.2\ln 10}{1+\ln 10 \log_{10}(3)}=2.746149035[/tex]

[tex]\implies x_2=2.740648841[/tex]

[tex]\implies x_3= 2.740646096[/tex]

Answer:  [tex]x^2[/tex]  and  [tex]-2[/tex]

Step-by-step explanation:

original :

[tex](10x^3+3x^2)+(-20x-6)[/tex]

factored :

[tex]x^2(10x+3)+-2(10x+3)[/tex]

Answer :

[tex]x^2[/tex]  and  [tex]-2[/tex]

Answer:

8

Step-by-step explanation:

If the only zero for this function is at x = - 4 it looks like this:

f(x)  = (x+4)(x+4)        =    x^2 +8x + 16         so j = 8

Answer:

Step-by-step explanation:

x² +jx +k = 0

If there is only one root ( - 4 ), then (x + 4)² = 0

or

x² + 8x + 16 = 0

j = 8 and k = 16

Answer:

see below

Step-by-step explanation:

2: letter at the vertex,  placing a letter or number inside .... , or by using 3 letters

3:

WXY

WXZ

YXZ

4: X

Using the given information, the smallest possible value of x - z is 12

From the question, we are to determine the smallest possible value of x - z

From the given information,

w and x are whole numbers

and

w > 60

x < 50

∴ w = 61, 62, 63, 63, 65, ...

x = 49, 48, 47, 46, 45, ...

Then,

The smallest possible value of x - z is

x - z = 61 - 49

x - z = 12

Hence, the smallest possible value of x - z is 12

Learn more on Evaluating an expression here: https://brainly.com/question/21245378

#SPJ1

Answer:

x=10, y=14

Step-by-step explanation:

added in the picture

Answer: B. 4x-2y=2

Step-by-step explanation:

We will work this out one by one. Plug in the x and y values of the solution to the equations and you will see which one is true or false.

A. [tex]2(1)+y(1)=2\\2+1\neq 2[/tex]     B. [tex]4(1)-2(1)=2\\4-2=2[/tex]

C. [tex]2(1)-2(1)=2\\2-2\neq 2[/tex]     D. [tex]x(1)+y(1)=4\\1+1\neq 4[/tex]

With this information, we see that B is the correct answer.

I hope this helped!! Pls mark brainliest!! :))

Answer:

14

Step-by-step explanation:

First divide 24 and 6 to find how much 6's there are in 24.

24/6=4

Now, we take that number and multiply it by 3.5 to find how long it will take the group to walk 24km.

3.5*4=14.

It will take the group 14 hours to walk 24 km.

Hope this helps!

If not, I am sorry.

The attached graph represents the function h(x), where h(x) = f(x)g(x)

Consider the functions f(x) = x - 6 and g(x) = x + 6. Which graph shows h(x) = f(x)g(x)?

We have

f(x) = x - 6

g(x) = x + 6

The equation h(x) = f(x)g(x) means

h(x) = f(x) * g(x)

So, we have:

h(x) = (x - 6) * (x + 6)

Expand

h(x) = x² - 36

See attachment for the graph of function h(x)

Read more about functions at:

https://brainly.com/question/3791183

#SPJ1

Answer:

A on edg. 2020

Step-by-step explanation:

Which graph shows h(x) = f(x)/g(x)

Answer:

Decreases

Step-by-step explanation:

A negative correlation means the y is big when the x is small. As x gets bigger, y gets smaller.

Answer:.

Step-by-step explanation:

If quadrilateral JKLM were in third quadrant then the coordinates will be (-1,0),(-4,-1),(-4,-2)(-1,-2)

Given Quadrilateral JKLM is in fourth quadrant and coordinates (1,0),(4,-1),(4,-2)(1,-2)

We know that the coordinates of x used to negative in third quadrant and positive in fourth quadrant. Coordinates of y used to negative in third and fourth quadrant.

So in order to change the coordinates from fourth to third we need to change the coordinates of x axis to negative and the coordinates will be :

Coordinates of J will change from (1,0) to (-1,0)

Coordinates of  K will change from(4,-1) to (-4,-1)

Coordinates of L will change from (4,-2) to (-4,-2)

Coordinates of M will change from (1,-2) to (-1,-2).

Learn more about coordinates at https://brainly.com/question/17206319

#SPJ10

Answer:

30 dollars

Step-by-step explanation:

25/5 = 5 dollars per hour

so 6 hours would be 5 * 6 = 30 dollars

Answer:

It would be B

Step-by-step explanation:

First, we need to find out the unit rate

5/25=1/5

Therefore, that means in one hour the cost would be $5

Since you are going from one hour to 6 hours you need to multiply both numbers by 6

Since 5x6=30, it would be 30$ :)

Answer: To solve a system of equations by substitution, we can rewrite a two-variable equation as a single variable equation by substituting the value of a variable from one equation into the other. Let’s start by solving the system of equations that we looked at above: x=4 x = 4 y+x=12 y +x = 12

Step-by-step explanation:

Answer:

Isolating a variable in one of the equations.

Step-by-step explanation:

x = the quantity of 3 plus or minus the square root of 29 all over 2. Then the correct option is B.

The quadratic equation is given as ax² + bx + c = 0.

Then the solution is given as

[tex]\rm x = \dfrac{-b\pm \sqrt{b^2 - 4ac}}{2a}[/tex]

The quadratic equation is given below.

x² – 3x – 5 = 0

Then the solution of the equation will be

[tex]\rm x = \dfrac{-(-3)\pm \sqrt{(-3)^2 - 4 *1*(-5)}}{2*1}\\x = \dfrac{3 \pm \sqrt{29}}{2}[/tex]

Then the correct option is B.

More about the solution of the quadratic equation link is given below.

https://brainly.com/question/17376136

#SPJ1

Answer:

a

Step-by-step explanation:

Answer:

27/4

Step-by-step explanation:

added in the picture

Answer:

4 hours

Step-by-step explanation:

First we need to subtract the one pay fee (the helmet rental fee, $15)

So 51 - 15 = 36

Then we need to divide 36 by the amount of money it costs for each hours to find how many hours he rented the bike

So 39/9 = 4

A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.

Here we have.

-3(2x - 5) < 5*(2 - x)

First, we need to isolate x in one side, let's expand both sides:

-6x + 15 < 10 - 5x

15 - 10 < 6x - 5x

5 < x

This will be represented with a number line where we have an open circle at 5, and an arrow that goes to the right. So the correct option is:

"A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right."

If you want to learn more about inequalities:

https://brainly.com/question/18881247

#SPJ1

If [tex]x=p+2[/tex] and [tex]y=p-3[/tex], then

[tex]x+y = (p+2) + (p-3) = 2p - 1 \implies x+y+1=2p[/tex]

and

[tex]x-y = (p+2)-(p-3) = 5 \implies x-y-5=0[/tex]

as required.

The solution of the equation -x^2 + 2x + 3 = x^2 - 2x + 3 are the x-coordinates of common points on the graphs are x=0 and x=2.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

As we can see from the attached graph these graphs intersect at points (0,3) and (2,3).

The system of equation are;

[tex]y = x^2 + 2x + 3 \\y = x^2 - 2x + 3[/tex]

So,

[tex]-x^2 + 2x + 3 = x^2 - 2x + 3 \\\\2x^2 - 4x = 0\\\\2x ( x - 2) = 0[/tex]

Then the solutions of the equation are x=0 and x=2.

Learn more about equations here;

https://brainly.com/question/10413253

#SPJ1

Answer:

0 and 2

Step-by-step explanation:

b on edge