In rectangle FGHI, diagonals FH and GI intersect at E. G F E H I • IE = 3x + 4 • EG = 5x - 6 What is the length of FH ?​

Answer:

I) The roots are:

First Case:

[tex]x=-2\text{ or } x=-6[/tex]

Second Case:

[tex]x=2\text{ or } x=6[/tex]

II) Possible values of p are:

First Case:

[tex]p=-12[/tex]

Second Case:

[tex]p=4[/tex]

Step-by-step explanation:

We have the equation:

[tex]x^2-(4+p)x+12=0[/tex]

We know that one of the roots is three times the other.

And we want to find the roots of the equation and the possible values for p.

To find our solutions, we can use the process of factoring.

If we have an equation in the form:

[tex]x^2+bx+c=0[/tex]

We want to find two numbers, say, k and j, such that:

[tex]\displaystytle kj=c\text{ and } k+j=b[/tex]

After finding them, we can factor as such:

[tex](x+k)(x+j)[/tex]

So, -k and -j will be our zeros.

Therefore, for our equation, we will find two numbers k and j such that:

[tex]\displaystyle kj=12\text{ and } k+j=-(4+p)[/tex]

Notice that for the first criterion, we can simply list all the factors of 12.

So, according to the first equation, possible values of k and j are:

1 and 12; 2 and 6; or 3 and 4.

Then, our roots will be -1 and -12; -2 and -6; or -3 and -4, respectively.

However, remember that one of our roots is three times the other.

Therefore, the only candidates that work will be the second option.

Hence, k and j are 2 and 6.

Therefore:

[tex]k=2\text{ and } j=6[/tex]

With this information, we can now determine p. Since:

[tex]k+j=-(4+p)[/tex]

Then it follows that:

[tex]\begin{aligned}(2)+(6)&=-(4+p)\\8&=-(4+p)\\-8&=4+p\\p&=-12\end{aligned}[/tex]

Hence, our equation is:

[tex]x^2-(4+-12)x+12=0[/tex]

Or, factored:

[tex]x^2+8x+12=0 \text{ or } (x+6)(x+2)=0[/tex]

So, our roots are x=-6 and x=-2 when p=-12.

However, we also need to consider the negative factors of 12.

Factors of 12 also include -2 and -6.

Hence, our k and j can also be k=-2 and j=-6.

Then, in this case, our p is :

[tex]\begin{aligned} (-2)+(-6)&=-(4+p)\\-8&=-(4+p)\\8&=4+p\\p&=4\end{aligned}[/tex]

Therefore, for our second case, k=-2 and j=-6. Then p=4. So, our equation is:

[tex]x^2-(4+4)x+12=0[/tex]

Or, factored:

[tex]x^2-8x+12\text{ or } (x-2)(x-6)=0[/tex]

Hence, when p=4, our roots are x=2 and x=6.

Answer:

G

Step-by-step explanation:

(x)0 months: (y)15 toys, 1:17, 2:19, 3:21, 4:23, 5:25, 6:27, 7:29, 8:31, etc.

The equation that represents best shows this relationship between the number of toys Rudolfo has will be y = 2x + 15. Then the correct option is G.

A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

Rudolfo has 15 toys in his toy box, and he adds 2 new toys every month.

Let x be the number of months and y be the total number of toys. Then the equation is given as,

y = 2x + 15

The equation that represents best shows this relationship between the number of toys Rudolfo has will be y = 2x + 15. Then the correct option is G.

More about the linear equation link is given below.

https://brainly.com/question/11897796

#SPJ2

Answer:

the one after 5

Step-by-step explanation:

press the one after 5

The point -5 1/4 is plotted on the number line in the graph as shown.

A graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner. A graph consists of some points and lines between them.

For the given situation,

The point is -5 1/4.

We need to plot this point on the number line shown.

In the graph below, the point -5 1/4 is plotted on the number line.

Hence we can conclude that the point -5 1/4 is plotted on the number line in the graph as shown.

Learn more about graphs here

https://brainly.com/question/15295094

#SPJ2

Answer:

$2.85

Step-by-step explanation:

Answer:

$22.23

Step-by-step explanation:

7.8 x 2.85 = 22.23 :D

Answer:

15 components.

Step-by-step explanation:

There is one Carbon, 11 hydrogen, 2 hydrogen, and one oxygen... Add it all tg and thats what you get... Hope this helped you!! Give brainliest..

Answer:

4

Step-by-step explanation:

to find the slope, you have to do rise/run.

you rise up from the first dot 4 times,

then you run once.

4/1

so the answer is 4

Answer:

b:-15

Step-by-step explanation:

There are 9 num in the set sowe add all the num and the we divide the answer we got

Answer:

The answer is:

b) - 15

Hope it helps:D

Answer:

120

Step-by-step explanation:

a^2 + b^2 = c^2

48^2 + x^2 = 52^2

2304 + x^2 = 2704

x^2 = 2704-2304

x^2 = 400

x = 20

52 + 48 + 20 =

120

Answer:

x = c/(A + b)

A + b ≠ 0

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define

Ax + bx = c

Step 1: Solve for x

We know that we cannot divide by 0, so A + b cannot equal 0.

Answer:

(8,6) and (10,4)

Step-by-step explanation:

solutions to the system of inequalities are in the purple shaded area, coordinates not landing in the purple shaded area are incorrect. The purple shaded area represents solutions for both lines red and blue.

Incorrect answers:

(0,10) because it lands in the blue shaded area ( meaning its the solution for only line blue and not line red)

(5,12) because it lands in the red shaded area ( meaning its the solution for only line red and not line blue)

(12,5) in red only

(15,2) in red only

Answer:

B) Domain 0, 1, 2, 3; Range -3, -2, -1, 0

Step-by-step explanation:

The x-axis number in an ordered pair is the domain. The y-axis number is the range.

Hope it helps!

ehhhhhhhhhhhhhhhhh sorrry i just wanna points

Answer:

The first one and the last two

Answer:

the first one and the 2 last ones!

Answer:

B. 68

Step-by-step explanation:

Solution :

The null and alternative hypothesis is given by

[tex]$H_0: \mu = 11$[/tex]

[tex]$H_a: \mu \ne 11$[/tex]

Assume that the level of significance, α = 0.05

The t-test statistics is, t = 1.484

Degree of freedom :

df = n - 1

   = 14 - 1

   = 13

The P-value is given by

P-value = 2P (T>|t|)

            = 2P(T>|1.484|)

            = 2P(T>1.484)

            = 2(=T.DIST.RT(1.484,13))

            = 0.05

Answer:

D

Step-by-step explanation:

The answes D kiddo cuz

10 x 3 = 30 and 17 x 3 = 51

Answer:

a

TRUST ME

Step-by-step explanation:

PLEASE MAKE ME BRANLIEST

Answer:

[tex]\boxed {\boxed {\sf A. \ 0.60 \ km}}[/tex]

Step-by-step explanation:

Distance (how far the submarine travelled) can be found by multiplying the speed by the time.

[tex]d=s*t[/tex]

The speed is 2.4 kilometers per hour.

The time is 0.25 hours.

[tex]s= 2.4 \ km/hr \\t= 0.25 \ hr[/tex]

Substitute the values into the formula.

[tex]d= 2.4 \ km/hr * 0.25 \ hr[/tex]

Multiply. Note that the hours (hr) will cancel each other out.

[tex]d= 0.6 \ km/hr *hr[/tex]

[tex]d= 0.6 \ km[/tex]

The submarine travelled 0.6 kilometers in 0.25 hours.

Answer:

A is the best buy.

Step-by-step explanation:

A

All trees 42 dollars.

B

1 foot   6

7 1/2 feet = x

x = 7 1/2 * 6

x = 45

C

First 4 feet = 22

3 1/2 feet * 6 = 21

Total = 43

Answer:

It is A.

Step-by-step explanation:

Hope this helped have an amazing day!

Answer:

b

Step-by-step explanation:

Answer:

Henry's cousin went to an audition.

Step-by-step explanation:

Answer:

x is 20 and y is 23

Step-by-step explanation:

Answer:

x = 15

y = 4

Step-by-step explanation:

In a triangle a line parallel to any of the sides of the triangle divides the remaining two sides in the proportion. Therefore,

[tex] \frac{12}{y} = \frac{x}{5} = \frac{18}{6} \\ \\ \frac{12}{y} = \frac{x}{5} = \frac{3}{1} \\ \\ \implies \:\frac{x}{5} = \frac{3}{1} \\ \\ x = 5 \times 3 \\ \\ x = 15 \\ \\ \\ \frac{12}{y} = \frac{3}{1} \\ \\ 3y = 12 \\ \\ y = \frac{12}{3} \\ \\ y = 4[/tex]

Answer:

.003411

Step-by-step explanation:

Is the OBJ box supposed to mean something?

Answer:

Step-by-step explanation:

1/4a + 1/3a + 8 = 22

Collect like terms

1/4a + 1/3a = 22 - 8

Simplify

3a+4a/12 = 14

7/12a = 14

Divide both sides by 7/12

a = 14 ÷ 7/12

= 14 × 12/7

= 168/7

= 24

a = 24

Check:

1/4a + 1/3a + 8 = 22

1/4(24) + 1/3(24) + 8 = 22

24/4 + 24/3 + 8 = 22

6 + 8 + 8 = 22

22 = 22

Answer: D

Step-by-step explanation:

Answer:

Honestly i dont even know

Step-by-step explanation:

Answer:

x                f(x)

-9               9

-6               4

-3               -1

0                 -6

Step-by-step explanation: