Find the domain of the following piece wise function

Answer:

110.5 units²

Step-by-step explanation:

The area (A) of a rhombus is calculated as

A = [tex]\frac{1}{2}[/tex] product of diagonals, that is

A = 0. 5 × MK × JL = 0.5 × 13 × 17 = 110.5

The area of the rhombus will be 110.5 square units.

The area of the rhombus can be calculated by half of the product of its two diagonals.

Here given,

JKLM is a rhombus.

The length of its diagonals will be MK=13

JL=17

The diagonal MK and JL intersect each other by 90° at point O.

Now the rhombus is divided by 4 right-angled triangle,

Area of the rhombus will be 4 times of the right-angled triangle ΔMJO

Area of the rhombus= 4*Area of right-angled triangle ΔMJO

=4*(1/2)*MO*JO

= 4*(1/2)*(MK/2)(JL/2)

=(1/2)*MK*JL

=(1/2)*the product of its two diagonals

=(1/2)*13*17

=110.5 Square unit

Therefore the area of the rhombus will be 110.5 square units.

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Answer:

122.2 in^2.

Step-by-step explanation:

WE can divide a regular octagon into 8 triangles with height ( = the apotherm) = 6.5 and  base = 4.7.

The area of each triangle is 1/2 * 4.7 *6.5 so #the area of the octagon

= 8 * 1/2 * 4.7 * 6.5

= 122.2 in^2.

For this case we have by definition, that the area of an octagon is given by:

[tex]A = \frac {p * a} {2}[/tex]

Where:

p: perimeter

a: apothem

We have that the perimeter is given by the sum of the sides of the octagon:

[tex]p = 8 * 4.7 = 37.6 \ in\\a = 6.5 \ in[/tex]

Substituting:

[tex]A = \frac {37.6 * 6.5} {2} = 122.2[/tex]

So, the area of the octagon is[tex]122.2 \ in ^ 2[/tex]

Answer:

[tex]122.2 \ in ^ 2[/tex]

Answer:

The option A,D and E are correct.

Step-by-step explanation:

Given: 2x^3-250x^2

Factor : 2x^2(x-125)

So, GCF = 2x^2

Now a = 1 and b= 5

we know that a^3-b^3 = (a-b)(a^2+ab+b^2)

(x)^3 - (5)^3 = (x-5)(x^2+5x+25)

So, the option A,D and E are correct.

Answer:

x^2-16 goes with (x+4)(x-4)

x^2+10x+16 goes with (x+8)(x+2)

Step-by-step explanation:

The first one you got wrong is known as a difference of squares.

To factor a difference of squares, a^2-b^2, you just write it as (a-b)(a+b) or (a+b)(a-b) would work too.

So x^2-16=(x-4)(x+4) or (x+4)(x-4).

Let's check (x+4)(x-4) using foil!

First: x(x)=x^2

Outer: x(-4)=-4x

Inner: 4(x)=4x

Last: 4(-4)=-16

----------------------Add

x^2-16

Bingo! (x+4)(x-4) definitely corresponds to x^2-16.

Here are more examples of factoring a difference of squares:

Example 1:  x^2-25  = (x+5)(x-5)

Example 2: x^2-81   = (x+9)(x-9)

Example 3: x^2-100 =(x+10)(x-10)

Onward to the next problem:

x^2+10x+16

When the coefficient of the leading term of a quadratic is 1, all you have to do is find two numbers that multiply to be c=16 and add up be b=10.

Those numbers would be 8 and 2

because 8(2)=16 and 8+2=10.

So the factored form of x^2+10x+16 is (x+2)(x+8) or (x+8)(x+2).

Here is another example of when the leading coefficient of a quadratic is 1:

Example 1:  x^2+5x+6=(x+2)(x+3) since 3(2)=6 and 3+2=5.

Example 2: x^2-x-6=(x-3)(x+2) since -3(2)=-6 and -3+2=-1.

Answer:

For    [tex]x^x > 500,000[/tex]  [tex]x=7[/tex]

For  [tex]x^{(-x)} > 500,000[/tex]  [tex]x=-7[/tex]

Step-by-step explanation:

We need to find the smallest positive whole number that satisfies the inequality:

[tex]x^x > 500,000[/tex]

We tested with x = 6

[tex]6^6=46,656\\\\46,656 > 500,000[/tex]

Inequality is not met because  [tex]46,656 < 500,000[/tex]

We test with the following integer x = 7

Then we have that:

[tex]7^7=823,543\\\\823,543 > 500,000[/tex]

Then the smallest positive integer that will make  [tex]x^x > 500,000[/tex]  is 7 because Inequality is met.

In the same way the largest negative integer that will make  [tex]x^{(-x)} >500000[/tex] is [tex]x=-7[/tex] Beacuse   [tex]7^{-(-7)}=823,543>500,000[/tex]

Answer:

Smallest positive integer value for [tex]x^x>500000[/tex] is,

x = 7,

Largest negative integer value for [tex]x^{-x}>500000[/tex] is,

x = -8

Step-by-step explanation:

If [tex]x^x>500000[/tex]

By graphing calculator,

[tex]x>6.83[/tex]

Thus, the smallest possible positive integer value of x is 7,

Now,

[tex]x^{-x}>500000[/tex]

Possible negative integer values of x are -6, -7 and -8,

If x = -6, -7, and -8,

[tex](-6)^{6}=46656[/tex]

[tex](-7)^{7}=-823543[/tex]

[tex](-8)^{8}=16777216[/tex]

[tex]\because 16777216 > 500000[/tex]

Thus, the largest negative integer value of the inequality [tex]x^{-x}>500000[/tex] is,

x = -8.

Answer:

A 54

Step-by-step explanation:

RC = 126

WC = 72

RC = WC + RW

126 = 72+RW

Subtract 72 from each side

126-72 = 72-72+RW

54 = RW

Answer: First option

[tex]RW=54[/tex]

Step-by-step explanation:

Notice in the image that the distance from R to C is equal to 126.

Then we write:

[tex]RC = 126[/tex]

Also note that the distance between W and C is 72.

We know that:

[tex]RC=RW + WC[/tex]

In this case we want to find RW, so we solve the equation for RW

[tex]RC-WC=RW + WC-WC[/tex]

[tex]RC-WC=RW[/tex]

[tex]RW=RC-WC[/tex]

Now we substitute the values of RC and WC into the equation

[tex]RW=126-72[/tex]

[tex]RW=54[/tex]

Answer:

C. 1307 ft

Step-by-step explanation:

Given:

Angle = 48.4 degrees

Height, opposite side= 1472 feet

his distance from the Empire State Building, base=x

Now as per the trigonometric ratios:

Tan∅= Opposite/base

tan(48.4)= 1472/x

x=1472/(1.13)

x=1302.65

his distance from the Empire State Building is 1302.65 feet!

Answer:

The correct answer is option C.

Step-by-step explanation:

Height of Empire State Building = 1,472 feet

Angle formed by the line segment from the point of ground on which Dante is positioned to the top of the building is  48.4°.

Distance of Dante from the Empire State Building =?

In the fig ,ΔABC

AB = 1,472 feet, BC = ? , θ= 48.4°

[tex]\tan\theta =\frac{Perpendicular}{base}[/tex]

[tex]\tan 48.4^o=\frac{AB}{BC}[/tex]

[tex]BC=\frac{AB}{\tan 48.4^o}=\frac{1,472 feet}{1.1263}=1,306.9 feet\approx 1,307 feet[/tex]

Distance of Dante from the Empire State Building is 1,307 feet.

Answer:

126 units

Step-by-step explanation:

the lateral area of a regular pyramid with a square base of 126 units has a slant height of 9 units and base side lengths of 7 units.

Answer:

39 meat patties

Step-by-step explanation:

Given,

The Big Burger recipe calls for 3 meat patties, 2 slices of cheese and 4 pickles,

That is, the ratio of meat patties, cheese and pickles in the recipe = 3 : 2 : 4

Let in a recipe,

Meat patties = 3x, Cheese = 2x, pickles = 4x

Where, x is a positive real number,

If there are 52 pickles,

⇒ 4x = 52 ⇒ x = 13

Hence, meat patties = 3 (13) = 39

Answer:

The zeros are x=1, x=-6

Step-by-step explanation:

f(x) =x^2+5x-6

Factor:  What two numbers multiply to -6 and add to 5

-1 *6 = -6

-1 +6 = 5

f(x) = (x-1) (x+6)

Using the zero product property

0 = (x-1) (x+6)

  x-1 =0  x+6=0

x=1         x=-6

The zeros are x=1, x=-6

Answer:

AH

Step-by-step explanation:

we know that

A cube has 6 faces and on each face there are two diagonals joining nonadjacent vertices and there are 4 diagonals through the interior of the cube. Thus in total there are 6×2+4=16 diagonals in a cube.

In this cube, the diagonals through the interior of the cube are

AH, CF, DE and BG  

therefore

The answer is AH

Answer:

The correct answer is first option. AH

Step-by-step explanation:

From the figure we can see a cube ABCDEFGH.

In a cube thee are 4 interior diagonals

To find the diagonal of the cube

AH, BG, CF   and DE

There are 4 interior diagonals.

The given options contain only one interior diagonal.

Therefore the correct answer is first option. AH

Answer:

[tex]x=k=117\°[/tex]

Step-by-step explanation:

Givens

AB || CD

EF || GH

These parallels gives us certain pair of angles which are congruent.

The given angle 63° is congruent with its corresponding angles. The image attached shows all corresponding angles that are equal to 63° (red angles).

Basically,

[tex]x+63=180[/tex] and [tex]k+63=180[/tex], by suplementary angles and straight angle definition.

Then, solving for [tex]x[/tex] and [tex]k[/tex], we have

[tex]x=180-63\\x=117\°[/tex]

[tex]k=180-63\\k=117\°[/tex]

Therefore, both angles are equal to 117°.

The measure of each angle are:

Given:

AB || CD

EF || GH

As, the lines are parallel and parallel line have following properties

So, <m = 63 {Corresponding angle}

Now, <m + <n = 180 {Linear pair}

63 + <n =180

<n =180 - 63

<n = 117

and, <k = 63 {Vertical opposite angle}

and, <k = <x = 63  {Corresponding angle}

and, <w = <x = 63  (alternate Interior angle}

and, <p = <w = 63 {Vertical opposite angle}

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Answer:

B. A(w)=w∧2+4w

Step-by-step explanation:

Let the width of the rectangle be w.

The length is  4 feet longer than the width= w+4

Area of a rectangle= length× width

A=L×W

=(w+4)×w

Opening the brackets gives the:

A=w²+4w

Therefore the expression for the area in terms of width is A(w)=w∧2+4w

[tex]34+3\cdot5=34+15=49[/tex]

Hope this helps.

r3t40

Answer:

[tex]\huge \boxed{49}\checkmark[/tex]

Step-by-step explanation:

Order of operations

PEMDAS

Parenthesis

Exponent

Multiply

Divide

Add

Subtract

Do multiply first.

[tex]\displaystyle 34+3\times5[/tex]

[tex]\displaystyle 3\times5=15[/tex]

Add from left to right to find the answer.

[tex]\displaystyle 34+15=49[/tex]

[tex]\huge \boxed{49}[/tex], which is our answer.

Hope this helps!

Answer:

1) 95

2) -12

3) 7

4) 1,700

5) 57

6) 3,070

Answer:

Texting speed

Step-by-step explanation:

It's the dependent variable

Answer:

B

Step-by-step explanation:

I has the most numbers varied and has bigger numbers which means it can't be the time which is either 1 2 or 3. The number of words will almost never be the answer!

Answer:

3x - 5

Step-by-step explanation:

Perform the indicated multiplication.  We get:

7x - 14 - 4x + 9.

Combining like terms, we get 3x - 5

Answer:

1010

Step-by-step explanation:

There are a whole class of questions that rely on the method to this one.

First add up what you know

1270 + 1150 + 870 + 1450 = 4740

Now add on the 5th month (which you don't know. Call it x)

4740 + x

Divide by 5

(4740 + x)/5 = 1150 and that is your equation    

Solution

Multiply both sides by 5

5*(4740 + x) / 5 = 1150 * 5

4740 + x = 5750

Subtract 4740 from both sides

4740 - 4740 + x = 5750 - 4740

x = 1010

Which seems kind of low, but that's what the numbers come to.

The circumcenter O, formed by the intersection of the perpendicular bisectors of sides AB and BC, is equidistant from all vertices, with OA = OB = OC. Here option B is correct.

In a triangle, the circumcenter is the point where the perpendicular bisectors of its sides intersect. In this case, the circumcenter O is formed by the intersection of the perpendicular bisector of side AB and the perpendicular bisector of side BC.

The circumcenter is equidistant from all three vertices, making OA, OB, and OC equal, and these distances represent the radius of the circumcircle.

This line not only bisects side AB but also intersects with the perpendicular bisector of side BC at the circumcenter O. The equality of OA, OB, and OC ensures that the circumcircle passes through all three vertices of the triangle, making it a significant point in the context of the triangle's geometry. Here option B is correct.

Answer:

A.  d = 0.75.

Step-by-step explanation:

The z-score =( x - m) / d  where m = the mean and d = the standard deviation.

So we have

(3 - m) / d = 1

3   -  m =  d.............(1)

and

(3.75 - m) / d = 2

3.75 - m = 2d....... (2)

Subtract (2) - (1):

0.75 = d.

Answer: A 0.75

Step-by-step explanation:

Formula for z-score :

[tex]z=\dfrac{x-\mu}{\sigma}[/tex]

, where x= random variable

[tex]\mu[/tex] = Population mean

[tex]\sigma[/tex] = Standard deviation

As per given , we have

[tex]+1=\dfrac{3-\mu}{\sigma}\\\\\Rightarrow\ \sigma=3-\mu\\\\\Rightarrow\ \mu=3-\sigma---(i)[/tex]

[tex]+2=\dfrac{3.75-\mu}{\sigma}\\\\\Rightarrow\ \mu=3.75-2\sigma---(ii)[/tex]

From (i) and (ii) , we have

[tex]3-\sigma=3.75-2\sigma\\\\\Rightarrow\ 2\sigma-\sigma=3.75-3\\\\\Rightarrow\ \sigma=0.75[/tex]

Hence, the standard deviation of the length of candy bars produced at Carl's Candies is 0.75.

Thus , the correct answer is A.  0.75.

Answer:

<AED = 60

Step-by-step explanation:

Since triangle ADE is similar to triangle ABC

Angle ADE equals angle ADC

The angles of a triangle add to 180 degrees

<A + <ADE + <AED = 180

36 + 84+ <AED = 180

Combine like terms

120 + <AED = 180

Subtract 120 from each side

120-120 +<AED = 180-120

<AED = 60

Answer:

58°

Step-by-step explanation:

Since DE and BC are parallel, ADE will be equal to ABC.

So ADE is 84°.

And, the sum of the angles of a triangle is 180°. So AED will be equal to 180-(38 + 84),which is 58°

[Only if Angle A is 38°]

Answer:

Step-by-step explanation:

Good idea to review quadratic functions and the quadratic formula.

Quadratics have three coefficients:  ax² + bx + c, and the "discriminant" is defined as b²-4ac.  Please review these rules:

1) if the discriminant is +, the quadratic equation has two real, unequal roots.

2) if the disc. is 0, the equation has two real, equal root.

3) If the disc. is - , the equation has two complex roots.

Here a = 1, b  = -3 and c = 4.  Therefore the discriminant is (-3)²-4(1)(4), or

-7.  Rule 3) applies:  the equation has two complex roots, but no real ones.  Thus we know that the graph does not cross the x-axis.

Graphing the given quadratic, x² - 3x + 4, using a dashed "line," is helpful.  As you can see in the illustration of this graph, the graph neither touches nor crosses the x-axis.  Thus, y = x² - 3x + 4 is greater than 0 for all x.  The answer:  All real numbers.

Answer:

The answer is C; (5, 1).

Step-by-step explanation:

2(5) - 1 = 9

10 - 1 = 9

9 = 9

9 = 9 is a true statement so the answer is C.

[tex]\bf y-0=\cfrac{1}{4}(x-3)\implies y=\cfrac{1}{4}(x-3)\implies \stackrel{\textit{distributing}}{y=\cfrac{1}{4}x-\cfrac{3}{4}}[/tex]

For this case we have that by definition, the equation of a line in the slope-intersection form is given by:

[tex]y = mx + b[/tex]

Where:

m: It's the slope

b: It is the cut-off point with the y axis

According to the data we have to:

[tex]m = \frac {1} {4}[/tex]

Then, the equation is of the form:

[tex]y = \frac {1} {4} x + b[/tex]

We substitute point (3.0):

[tex]0 = \frac {1} {4} (3) + b\\b = - \frac {3} {4}[/tex]

Finally, the equation is:

[tex]y = \frac {1} {4} x- \frac {3} {4}[/tex]

Answer:

Option B

Answer:

The approximate value of arc cos(0.87) is 29.54°

Step-by-step explanation:

we know that

The arc cosine of x is defined as the inverse cosine function of x

so

if y=cos(x)

then

arc cos (y)=x

In this problem we have

y=0.67

so

x=arc cos(0.87)

using a calculator

x=29.54°

So, the approximate value of arccos(0.67) is about 0.84108 radians.

To approximate arccos(0.67) using a calculator, we find it to be approximately 0.84108 radians. This value represents the angle whose cosine is 0.67. Arccos, or inverse cosine, returns the angle in radians between 0 and π (approximately 3.14159) whose cosine is the input value. In this case, 0.67 is the cosine of the angle 0.84108 radians. This angle is commonly used in trigonometric calculations, such as determining the angle of a vector or solving geometric problems involving cosine functions.Let's use a calculator to find the approximate value of arccos(0.67).

Using a calculator:

[tex]arccos(0.67) \approx 0.84108 radians[/tex]

Answer:

168.558

Step-by-step explanation:

       168.58

34√5731.0

    -34 ↓3

     23 3

    -204 ↓1

       28  1

     - 272 ↓0

       19  0

       -170  ↓0

         20 0

        -170  ↓0

           30 0

          -272 ↓0

            28  0

and just goes on..

Answer:

3

Step-by-step explanation:

3 is the greatest possible number of stops she made at traffic lights.

A distance-time graph suggests how the distance an item has traveled in a given time. it's far a simple line graph that denotes distance as opposed to time findings the graph. Distance is plotted on the Y-axis.

In a distance-time graph, the gradient of the line is equal to the velocity of the object. The more the gradient (and the steeper the road) the faster the object is transferring.

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Answer:

So first blank=6

Second blank=0

Third blank=-5

Fourth blank=6

Step-by-step explanation:

It is a horizontal line so the equation is just going to be

[tex]y=\text{ whatever y-coordinate they gave you in that one point}[/tex].

So it will be [tex]y=6[/tex]

We are going to do the point-slope form too as I requested.

Point-slope form is [tex]y-y_1=m(x-x_1)[/tex].

We have m=0 since you said the slope was 0 and since it said your have a horizontal line (which means the slope slope or m is 0).

You also that it contains the point [tex](-5,6)=(x_1,y_1)[/tex].

So our line in point-slope form is [tex]y-6=0(x-(-5))[/tex].

Answer:

4800 miles

Step-by-step explanation:

Answer:

axis of symmetry is [tex]x=\frac{-9}{2}[/tex].

The ordered pair of the vertex is [tex](\frac{-9}{2},\frac{-145}{4})[/tex].

Step-by-step explanation:

Your function is a quadratic.

Compare [tex]x^2+9x-16[/tex] to [tex]ax^2+bx+c[/tex].

You should see that [tex]a=1,b=9,c=-16[/tex].

The x-coordinate of the vertex or the axis of symmetry since the axis symmetry goes through the vertex can be found by computing [tex]\frac{-b}{2a}[/tex].

So here we go!

The axis of symmetry is [tex]x=\frac{-9}{2(1)}=\frac{-9}{2}[/tex].

When you write your axis of symmetry be sure to write it as an equation.

That is the axis of symmetry is [tex]x=\frac{-9}{2}[/tex].

Now that was also the x-coordinate of your vertex.  To find the corresponding y-coordinate of the vertex, plug your value for [tex]x[/tex] into

[tex]y=x^2+9x-16[/tex].

[tex]y=(\frac{-9}{2})^2+9(\frac{-9}{2})-16[/tex]

Put into calculator:

[tex]y=\frac{-145}{4}[/tex] when [tex]x=\frac{-9}{2}[/tex]

The ordered pair of the vertex is [tex](\frac{-9}{2},\frac{-145}{4})[/tex].

Answer:

Vertex: [tex](h,k)\rightarrow(-4.5,-36.25)[/tex]

Axis of symmetry: [tex]x=-4.5[/tex]

Step-by-step explanation:

First I'll find the axis of symmetry. This formula lets us find the a.o.s: [tex]x=\frac{-b}{2a}[/tex].

In [tex]x^2+9x-16[/tex], the values of a, b, and c are:

We only need a and b to find the axis of symmetry. Substitute these values into the formula.

Simplify this fraction.

The axis of symmetry of this quadratic function is x = -4.5.

Now to find the vertex, we have to take into account that this quadratic is in standard form, making it a little harder. We have to convert this function into vertex form.

Start by changing f(x) to 'y' and adding 16 to both sides.

Use the completing the square formula: [tex](\frac{b}{2} )^2[/tex]

Keep the balance by adding 20.25 on the left side and adding it on the right side of the equation.

Combine like terms.

Factor the right side of the equation. Ask yourself, "What two numbers multiply to 20.25 (c) and add up to 9 (b)?" These two numbers are 4.5 and 4.5. Rewrite the right side with factors.

Isolate y by subtracting 36.25 from both sides of the equation.

Now this quadratic function is in vertex form, making it super simple to find the vertex using [tex](h, k)[/tex].

Vertex form of a quadratic is:

Compare [tex]y=(x+4.5)^2-36.25[/tex] with the original vertex form and find where h and k are. Those are the x (h) and y (k) values of the vertex.

Since the original vertex form has x - h, the h value in [tex]y=(x+4.5)^2-36.25[/tex] would be a negative since two negatives make a positive. The k value would stay "normal"---negative would mean it is a negative and positive would mean it is a positive number.

Therefore the h value is -4.5, and the k value is -36.25.

The ordered pair of the vertex is [tex](-4.5, -36.25)[/tex].