Square ABCD has vertices at A(−1,3), B(0,7), C(4,6), and D(3,2).

What is the area of the square when rounded to the nearest whole number?

Answer:

[tex]\displaystyle [CQF]=5[/tex]

Step-by-step explanation:

Note that [tex][n][/tex] refers to the area of some polygon [tex]n[/tex].

Diagonal [tex]\overline{AC}[/tex] forms two triangles, [tex]\triangle ABC[/tex] and [tex]\triangle ADC[/tex]. Both of these triangles have an equal area, and since the area of parallelogram [tex]ABCD[/tex] is given as [tex]210[/tex], each triangle must have an area of [tex]105[/tex].

Furthermore, [tex]\triangle ADC[/tex] is broken up into two smaller triangles, [tex]\triangle ADF[/tex] and [tex]\triangle ACF[/tex]. We're given that [tex]\frac{DF}{FC}=2[/tex]. Since [tex]DF[/tex] and [tex]FC[/tex] represent bases of [tex]\triangle ADF[/tex] and [tex]\triangle ACF[/tex] respectively and both triangles extend to point [tex]A[/tex], both triangles must have the same height and hence the ratio of the areas of [tex]\triangle ADF[/tex] and [tex]\triangle ACF[/tex] must be [tex]2:1[/tex] (recall [tex]A=\frac{1}{2}bh[/tex]).

Therefore, the area of each of these triangles is:

[tex][ACF]+[ADF]=105,\\[][ACF]+2[ACF]=105,\\3[ACF]=105,\\[][ACF]=35 \implies [ADF]=70[/tex]

With the same concept, the ratio of the areas of [tex]\triangle AQE[/tex] and [tex]\triangle DQE[/tex] must be [tex]2:1[/tex] respectively, from [tex]\frac{AE}{ED}=2[/tex], and the ratio of the areas of [tex]\triangle DQF[/tex] and [tex]\triangle CQF[/tex] is also [tex]2:1[/tex], from [tex]\frac{DF}{FC}=2[/tex].

Let [tex][DQE]=y[/tex] and [tex][CQF]=x[/tex] (refer to the picture attached). We have the following system of equations:

[tex]\displaystyle \begin{cases}2y+y+2x=70,\\y+2x+x=35\end{cases}[/tex]

Combine like terms:

[tex]\displaystyle \begin{cases}3y+2x=70,\\y+3x=35\end{cases}[/tex]

Multiply the second equation by [tex]-3[/tex], then add both equations:

[tex]\displaystyle \begin{cases}3y+2x=70,\\-3y-9x=-105\end{cases}\\\\\rightarrow 3y-3y+2x-9x=70-105,\\-7x=-35,\\x=[CQF]=\frac{-35}{-7}=\boxed{5}[/tex]

9514 1404 393

Answer:

  u = 7√2; v = 7

Step-by-step explanation:

The ratios of side lengths in an isosceles right triangle are ...

  1 : 1 : √2 = 7 : v : u

Then v = 7 and u = 7√2.

Answer:

Step-by-step explanation:

The cross-section is an 8”×13” rectangle.

Area = 104 square inches

Answer:

This is what you asked me just now.

Step-by-step explanation:

Answer:

correct me if I'm but i think the net cash flow is 3,790 because 2,040 a month income and 1,750 a month for other stuff. 2,040+1,750=3,790

Step-by-step explanation:

Answer: 7 miles/h and 1 miles/h

Step-by-step explanation:

With the speed of current = x + 1

Against the speed of current = x - 1

ATQ

4(x-1) = 3(x+1)

4x-4 = 3x+3

4x - 3x = 3+4

x = 7

Speed of boat = 7miles/h

Current of river = 1 miles/h

please click thanks and mark brainliest if you like :)

Answer:

Hello,

Boat speed=7 miles/h

Current speed = 1 mile/h

Step-by-step explanation:

I am going to try to explain.

Let say V the speed of the boot (V like vitesse in french)

Let say v the speed of the current.

distance=24 miles

[tex]\left\{\begin{array}{ccc}V-v&=&\dfrac{24}{4} \\V+v&=&\dfrac{24}{3} \\\end{array}\right.\\\\\left\{\begin{array}{ccc}V-v&=&6 \\V+v&=&8 \\\end{array}\right.\\\\Adding\ the\ 2\ equations\ and\ substracting\ them \\\\\\\left\{\begin{array}{ccc}2V&=&14 \\2v&=&2 \\\end{array}\right.\\\\\\\left\{\begin{array}{ccc}V&=&7 \\v&=&1 \\\end{array}\right.\\\\[/tex]

Boat speed=7 miles/h

Current speed = 1 mile/h

Answer:

-25

Step-by-step explanation:

First, add 5 to -23 since the temperature is getting hotter.

so -23 +5= -18

Second, minus the answer by 7 since the temperature is now falling down after the sunset.

so -18 -7 = -25

or...

this step can be simplified as:

-23 +5 -7 =. -25

The equation has two real and equal roots for [tex]k = \frac{5}{6}[/tex]

In this question, we use the concept of the solution of a quadratic equation to solve it, considering that a quadratic equation in the format:

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

has two equal solutions if [tex]\Delta = b^2 - 4ac[/tex] is 0.

------------------------------------

In this question:

The equation is:

[tex](2k+1)x^2 + 2x = 10x - 6[/tex]

Placing in the correct format:

[tex](2k+1)x^2 + 2x - 10x + 6 = 0[/tex]

[tex](2k+1)x^2 - 8x + 6 = 0[/tex]

Thus, the coefficients are: [tex]a = 2k + 1, b = -8, c = 6[/tex]

------------------------------------

Delta:

We want it to be positive, so:

[tex]\Delta = b^2 - 4ac[/tex]

[tex]\Delta = 0[/tex]

[tex]b^2 - 4ac = 0[/tex]

[tex](-8)^2 - 4(2k+1)(6) = 0[/tex]

[tex]64 - 48k - 24 = 0[/tex]

[tex]-48k + 40 = 0[/tex]

[tex]-48k = -40[/tex]

[tex]48k = 40[/tex]

[tex]k = \frac{40}{48}[/tex]

[tex]k = \frac{5}{6}[/tex]

The equation has two real and equal roots for [tex]k = \frac{5}{6}[/tex]

A similar question is found at https://brainly.com/question/12144265

The quadratic equation that could be solved using the given application of the quadratic formula is x² + 2x - 1 = 3, which in standard form is x² + 2x - 4 = 0. Hence, option C is the right choice.

A standard quadratic equation of the form ax² + bx + c = 0, can be solved using the quadratic formula, which is given as:

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

In the question, we are asked for the quadratic equation, which could be solved using this application of the quadratic formula:

[tex]x = \frac{-2\pm\sqrt{2^2-4(1)(-4)} }{2(1)}[/tex]

To find the quadratic equation for which we use the quadratic formula

[tex]x = \frac{-2\pm\sqrt{2^2-4(1)(-4)} }{2(1)}[/tex]

we compare this equation with the standard quadratic formula,

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

to get a = 1, b = 2, and c = -4, to get the standard quadratic equation, ax² + bx + c = 0, as (1)x² + (2)x + (-4) = 0, or x² + 2x - 4 = 0.

Now, we convert the given options in the standard form to check for the correct choice:

Thus, the quadratic equation that could be solved using the given application of the quadratic formula is x² + 2x - 1 = 3, which in standard form is x² + 2x - 4 = 0. Hence, option C is the right choice.

Learn more about the quadratic formula at

https://brainly.com/question/1214333

#SPJ2

Answer:

y = -5/14 -13/7

Step-by-step explanation:

First find the slope

m = (y2-y1)/(x2-x1)

m = (1 - -4)/(-8 - 6)

    = (1+4)/(-8-6)

   = 5/-14

   =-5/14

Point slope form is

y-y1 = m(x-x1)

y - -4 = -5/14(x-6)

y+4 = -5/14(x-6)

We want the equation in slope intercept form y = mx+b

Distribute

y+4 = -5/14x + 15/7

Subtract 4 from each side

y+4 -4= -5/14x + 15/7-4

y = -5/14x +15/7 - 28/7

y = -5/14 -13/7

Answer:

4,000mm

Step-by-step explanation:

I tryed my best

Answer:

mate...

cm to mm is by multiplying 10

400 * 10 = 4000mm

brainliest l m a o

Answer:

Hshushahhahaa

Hdhddjkddjdkjd

Answer:

Front = 30

Back = 30

Right = 30

Left = 30

Bottom = 25

Top = 16

Total = 161

Let me know if this helps!

Answer:

Step-by-step explanation:

a) 3x^2

b) (512)^-2/3=2^n

1/64=2^n

n=-6

Answer:

i: -1.3

ii: 1.3

Step-by-step explanation:

You literally have it.

I hope this helps!

pls ❤ and give brainliest pls

Answer: it wll be thursday at 7:30PM

Answer: (b)

Step-by-step explanation:

Given

There are five consecutive integers and the least minus twice the greatest equals to -3

Suppose [tex]x,x+1,x+2,x+3,x+4[/tex] are the five consecutive integers

According to the question

[tex]\Rightarrow x-2(x+4)=-3\\\Rightarrow x-2x-8=-3\\\Rightarrow -x=8-3\\\Rightarrow x=-5[/tex]

option (b) is correct.

Answer:

MZ = 10

ZO = 10

MO = 20

XZ = 9

YZ = 7

Step-by-step explanation:

Triangles are all the same, proportionally.

X is midpoint of 14, so 7

Y for 18, so 9

Triangle with 10 is 7, 9, 10

Full triangle is double at 14, 18, MO

Since angle N is same angle, MO is double 10, so 20

Z is midpoint, so both halves are 10

Because of midpoints, XZ and YZ with 10 form same triangle as half triangle at 9, 7, and 10 respectively.

Answer:

[tex]\displaystyle d \approx 15.8768[/tex]

Step-by-step explanation:

We want to find the distance of d or AB.

From the right triangle with a 35° angle, we know that:

[tex]\displaystyle \tan 35^\circ = \frac{50}{PB}[/tex]

And from the right triangle with a 42° angle, we know that:

[tex]\displaystyle \tan 42^\circ = \frac{50}{PA}[/tex]

AB is PA subtracted from PB. Thus:

[tex]\displaystyle d = AB = PB - PA[/tex]

From the first two equations, solve for PB and PA:

[tex]\displaystyle \frac{1}{\tan 35^\circ } = \frac{PB}{50} \Rightarrow PB = \frac{50}{\tan 35^\circ}[/tex]

And:

[tex]\displaystyle \frac{1}{\tan 42^\circ } = \frac{PA}{50} \Rightarrow PA = \frac{50}{\tan 42^\circ}[/tex]

Therefore:

[tex]\displaystyle d = AB = \frac{50}{\tan 35^\circ} - \frac{50}{\tan 42^\circ}[/tex]

Using a calculator:

[tex]\displaystyle d= AB \approx 15.8768[/tex]

Answer:

63,70

Step-by-step explanation:

7 x 8 = 56

7 x 11 = 77

multiples of 7 and 9, 7 x 10

63 and 70

7×9 = 63

7×10 = 70

Answered by Gauthmath must click thanks and mark brainliest

Answer:

4/5 or 0.8

Step-by-step explanation:

this problem description is not very precise. it leaves out the definition what corners or sides of JKLM correspond to corners and sides of ABCD.

I assume J and K correlate to A and B, and JK is a long side of JKLM.

so, we are going from JKLM to ABCD.

that means we are going from larger to smaller (as JK = 15 and therefore larger than AB = 12).

what is the scale factor to go from 15 to 12 ?

15 × x = 12

x = 12/15 = 4/5 or 0.8

Answer:

y+1/2-2y-1/2=4​

y-2y=4

-y=4

y=-4

Let  me know if this helps!

Answer:

B

Step-by-step explanation:

area=1/2×32×6.1=16×6.1=97.6 yd²

Answer:

Choice B. 97.6 yd^2

Step-by-step explanation:

B×W×.5= A

Answer:

Area of a complete circle = PI * r^2

The shaded area is 1/3 of the circle so

Area = (PI * 9^2) / 3

Area = (254.4690049408) / 3

Area = 84.8230016469

Area = 84.82 square feet (rounded)

Step-by-step explanation:

Answer:

1.92 m³

hopefully this answer can help you to answer the next question.

Answer:

area = 8 × 18 = 144 cm^2

volume 8×18×5 = 720cm^3

Answer:

105 frames

Step-by-step explanation:

Given that 25 frames are played per second

25 frames= 1 sec

The video already played 3 and 2/5 seconds before the player started to count 0

Write 3 and 2/5 seconds as an improper fraction

=(5*3)+2 / 5 = 17/5 seconds

Multiply by 25 frames

17/5 *25 =85 frames

So according to the video counter,after 17/5 seconds,it should count 85 frames.However,at 0 seconds,it indicated a count of 190 frames.Thus,to get the number of frames that were already in count you subtract 85 frames from the 190 frames.

190-85=105 frames.

Step-by-step explanation:

Answer:

3 11/15 miles

Step-by-step explanation:

4 1/3 - 3/5

4 5/15 - 9/15

3 20/15 - 9/15

3 11/15 miles

Answer:

The answer is the Second Option

Step-by-step explanation:

Answer:

the second one sqrt(10) + sqrt(15) -sqrt(14) - sqrt(21)

Step-by-step explanation: