Solve: x - 2 = x-8

{11}
{6, 11}
{}

Given:

The piecewise function is:

[tex]f(x)=\begin{cases}x+5&x<-2\\x^2+2x+3&x\geq -2\end{cases}[/tex]

To find:

The values of [tex]f(-4),f(-2),f(0),f(3)[/tex].

Solution:

For [tex]x<-2[/tex], the function is

[tex]f(x)=x+5[/tex]

For [tex]x\geq -2[/tex], the function is

[tex]f(x)=x^2+2x+3[/tex]

a) The value of [tex]f(-4)[/tex] is:

[tex]f(-4)=-4+5[/tex]

[tex]f(-4)=1[/tex]

b) The value of [tex]f(-2)[/tex] is:

[tex]f(-2)=(-2)^2+2(-2)+3[/tex]

[tex]f(-2)=4-4+3[/tex]

[tex]f(-2)=3[/tex]

c) The value of [tex]f(0)[/tex] is:

[tex]f(0)=(0)^2+2(0)+3[/tex]

[tex]f(0)=0-0+3[/tex]

[tex]f(0)=3[/tex]

d) The value of [tex]f(3)[/tex] is:

[tex]f(3)=(3)^2+2(3)+3[/tex]

[tex]f(3)=9+6+3[/tex]

[tex]f(3)=18[/tex]

Therefore, the required values are [tex]f(-4)=1,f(-2)=3,f(0)=3,f(3)=18[/tex].

Answer:

The area of a triangle is 1/2BH, or 1/2 times the base times the height.

If the area = 6, and B and H must both be whole numbers.

The area of the triangle ΔSTU is given by A = 12 units²

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

if a² + b² = c² , it is a right triangle

if a² + b² < c² , it is an obtuse triangle

if a² + b² > c² , it is an acute triangle

Given data ,

Let the area of the triangle ΔSTU be represented as A

Now , the area of triangle ΔQTU is 6 square units, and the area of triangle ΔRSU is 6 square units

So , the base of the triangle ΔSTU = 6 units

The height of the triangle ΔSTU = 4 units

So , area of the triangle = ( 1/2 ) x Length x Base

On simplifying , we get

The area of triangle ΔSTU = ( 1/2 ) x 4 x 6

The area of triangle ΔSTU = 12 units²

Therefore , the value of A is 12 units²

Hence , the area of the triangle is 12 units²

To learn more about triangles click :

https://brainly.com/question/16739377

#SPJ3

The complete question is attached below :

The area of triangle QTU is 6 square units, and the area of triangle RSU is 6 square units. The dimensions in the figure below are labeled in units. What is the area of triangle STU in square units?

9514 1404 393

Answer:

  B.  (2, 1)

Step-by-step explanation:

As a first guess you might say the right angle will be at the point that has the x-coordinate of A (2) and the y-coordinate of B (1).

You notice that the point (2, 1) is on the list of answer choices, so that is a good choice.

The coordinates of C could be (2, 1).

__

Or, you can plot the points and see what forms a right triangle.

Answer:

8

Step-by-step explanation:

Area π 1.5^2 = 7.07cm^2

Volume = 56.52 /7  = 8cm

So go for the 4th answer = 8

Answer:

x=9

Step-by-step explanation:

55+5x=100. -subtract 55 from 100

5x=45. - divide 45 by 5

x=9

Answer: c = 2

Step-by-step explanation:

First you write out your equation: 10c + 20 = 40

Next, since the equation is adding, you can subtract 20 the constant on both sides of the equation:

10c + 20 = 40

      - 20    - 20  

The 20s cancel each other out and 40 - 20 is 20.

Our new equation looks like: 10c = 20

Now to find the value of C you are going to divide 10 on both sides because the equation is multiplying.

10c divided by 10 is just c and 20 divided by 10 is 2.

Therefore, you are left with c = 2

hope this helps have a nice day :)

Answer:

I think its - 2/3

Step-by-step explanation:

Answer:

The First One

Step-by-step explanation:

Because its dimensions are 5 by 8

Answer: I don't know if it is multiplication or addition but here are the answers.

Step-by-step explanation:  

$360 * $2.50 * $5.50= 4950

$360 + $ 2.50 + $5.50=368

9514 1404 393

Answer:

  boat speed: (7t -95)/(6t² -110t +500)

  stream speed: (37t -345)/(6t² -110t +500)

Step-by-step explanation:

The relation between time, speed, and distance is ...

  time = distance/speed

The boat speed (b) is added to the stream speed (s) going downstream. The stream speed is subtracted going upstream. The given relations tell us ...

  25/(b-s) +44/(b+s) = t

  15/(b-s) +22/(b+s) = 5

This gives us 2 equations in 3 unknowns, so we can only provide a solution in terms of one of the unknowns. Since we are asked for the speeds, they will be provided in terms of t.

Subtracting the first equation from 2 times the second gives ...

  2(15/(b-s) +22/(b+s)) -(25/(b-s) +44/(b+s)) = 2(5) -(t)

  5/(b-s) = 10 -t

  5/(10 -t) = b -s

Substituting for b-s in the second equation gives ...

  15/(5/(10-t)) +22/(b+s) = 5

  30 -3t +22/(b+s) = 5

  22/(b+s) = 3t -25

  22/(3t -25) = b+s

Adding the equations for the sum and difference of speeds, we get ...

  (b-s) +(b+s) = 5/(10-t) +22/(3t -25)

  2b = (5(3t -25) +22(10 -t))/((10-t)(3t-25)) = (95 -7t)/((10-t)(3t-25))

  b = (7t -95)/(6t² -110t +500)

Subtracting the equations for sum and difference of speeds, we get ...

  (b+s) -(b-s) = 22/(3t -25) -5/(10 -t)

  2s = (22(10-t) -5(3t -25))/((10-t)(3t-25))

 s = (37t -345)/(6t² -110t +500)

__

The speed of the boat in still water is (7t -95)/(6t² -110t +500) km/h.

The speed of the stream is (37t -345)/(6t² -110t +500) km/h.

__

Note that these solutions only make sense for values of t between 25/3 and 345/37, approximately 8.33 < t < 9.32. For t=9 hours, the boat speed is 8 km/h and the stream speed is 3 km/h.

Answer:

1/2

Step-by-step explanation:

Even numbers on the dice:

2, 4, 6

Probability of getting even:

3/6

1/2

Answer:

3 units

Step-by-step explanation:

Here, The distance between two points is 3 units

-TheUnknownScientist

Answer:

1,000

Step-by-step explanation:

1,300,000 ÷ 1,300 = 1,000

A factor of a number that, when multiplied by itself, gives the original number is called a square root.

The square root of 3 is 9.

The integer that has the nearest to the integer that has a square root of 3 is √10.

A factor of a number that, when multiplied by itself, gives the original number.

We have,

9 is a square root of 3.

The nearest square root of 3 can be 8 or 10.

The value of the square root of 8.

= √8

= 2.83

The value of the square root of 10:

= √10

= 3.16

The nearest can be determined by finding out the difference between each of its values with 3.

For √8,

= 3 - 2.83

= 0.17

For √10,

= 3.16 - 3

= 0.16

We see that √10 is nearest to the integer that has a square root of 3.

Thus the integer that has the nearest to the integer that has a square root of 3 is √10.

Learn more about square roots here:

https://brainly.com/question/3120622

#SPJ5

I hope this helps you

1) DC=60

AD=AC=60/2=30

AB=BC=30/2=15

DB=DA+AB=30+15=45

2) RQT is right triangle we can find the side

6^2+8^2=RT^2

36+64=RT^2

RT=10

Answer:

Step-by-step explanation:

The equation being shown in the question is the absolute value of x. Absolute values when graphed show up as a V-shaped graph pointing upwards. This is because whatever value is passed as an input will output a positive, regardless of whether the input is positive or negative. Meaning that both 4 and -4 will output 4. That is why the graph is a V-shaped because the outputs repeat for both positive and negative inputs. In this case since the negative is outside the absolute value brackets the positive value given from the absolute value of the input will be turned into a negative. So this will cause the V-shape graph to be reflected across the x-axis. As seen in the attached picture below.

Answer: This is the correct answer
I just took the test. :)

Step-by-step explanation:

Answer:

decay factor i think

Step-by-step explanation:

Answer:

The answer is "[tex]\bold{1920 \ in^2}[/tex]".

Step-by-step explanation:

Please find the graph file.

Rectangular solid area:

Its region comprises four rectangles, each 15 for each case 14 in each.

The rectangle field is the formula [tex]A = lw[/tex]

The four rectangles are therefore covered by a zone: [tex]\to A = 4lw = 4 \times 15 \ in \times 14 \ in = 840 \ in^2.[/tex]

square Pyramids area:

The pyramids in both squares have 8 triangular facets.

Each triangle has a 15-inch basis with a 14-inch base.

The triangle zone formulation is [tex]A = \frac{1}{2}bh[/tex]

That's it. The 8 triangles area is [tex]\to A = 8 \times \frac{1}{2}bh = 4bh = 4 \times 15 \ in \times 18 \ in = 1080 \ in^2[/tex]

Total field surface:

Strong rectangular[tex]= 840 \ in^2[/tex]

Pyramids in the Square[tex]= 1080[/tex]

Overall area [tex]= 1920 \ in^2[/tex]

The number is [tex]1920\ in^2[/tex] for a total area.

Answer:

it is B and D

Step-by-step explanation:

mark brainliest or 5 stars and heart

correct me if im wrong

Answer:

B and A

Step-by-step explanation:

Calculate distance d using the distance formula

d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

(1) with (x₁, y₁ ) = (0, 0) and (x₂, y₂ ) = (6, 8)

d = [tex]\sqrt{6-0)^2+(8-0)^2}[/tex]

   =  √(6² + 8²)

   = √ (36 + 64)

    = √ 100

     = 10  → B

(2)

Using (x₁, y₁ ) = (- 5, 3) and (x₂, y₂ ) = (3, 15)

d = √ (3 + 5)² + (15 - 3)²

   = √ 8² + 12²

   = √ 64 + 144

    = √ 208

    ≈ 14.4 ( to the nearest tenth ) → A

Answer:

11+6i

Step-by-step explanation:

vectors addition

(3+8) +(4i+2i)

11+6i

Answer:

Option C

Step-by-step explanation:

If a line passes through a point, then that point is called a solution to the line's equation. Substituting the x and y values of that solution into the equation will give a true statement. So, to find out which option is correct, we can substitute the x and y values of (-4.5, 10) into each equation and see if the result is a true statement.  

Let's try this with option C. To make things easier, convert -4.5 into decimal form: [tex]-4\frac{1}{2}[/tex]. Substitute [tex]-4\frac{1}{2}[/tex] for x and 10 for y in the equation, then solve:  

[tex]y = -\frac{2}{3} x+7\\\\10 = -\frac{2}{3} (-4\frac{1}{2} )+7\\10 = -\frac{2}{3} (-\frac{9}{2})+7\\10 = 3+7\\10 = 10[/tex]

10 does equal 10, so this is a true statement. Option C is the right answer.

Answer:

B

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Answer:a.35 degrees b. 145 degrees

Step-by-step explanation: angle 2 and angle 6 are equal they are corresponding

Angle 2 and angle 8 are supplementary they equal 180. So 180-35=145

Answer: -2.2

Step-by-step explanation:

-10 is the most possible that can be divided by 5, resulting in -2.

The leftover 1 is divided by 5, resulting in .2.

The decimal ends up being -2.2.

Answer:

-2.2 or -1.2

Step-by-step explanation:

When you want to write a decimal as a fraction, you simply divide the numerator with the denominator. So when you divide -11 by five that would be a -2.2. Or if it is -1 1/5 the answer would be -1.2. I cant really tell what that number is.

Answer:

The answer is "148 ft".

Step-by-step explanation:

Using formula:

Calculating rectangle area:

[tex]A=lw[/tex]

   [tex]=15 \times 8\\\\=120[/tex]

Calculating semicircle area:

[tex]A=\frac{1}{2} \pi r^2\\\\[/tex]

   [tex]=\frac{1}{2} \times \pi \times 7.5^2\\\\=\frac{1}{2} \times \pi \times 56.25\\\\=28.125\ \pi \\\\=28 \ \pi[/tex]

Total area:

[tex]=120+28\\\\=148[/tex]

Answer:

graph d it's your answer plz make me brainy least

Answer:

d

Step-by-step explanation: