Given that ABCD is a rhombus, what is the value of x? ​

Answer: f(x) = x - 2x² + 1

              x=-b/2a

              (1/4,9/8

   2.      f'(x) = 4x³ - 4x

            ((\sqrt(3))/(3),-(8\sqrt(3))/(9))is a local minima

             (-(\sqrt(3))/(3),(8\sqrt(3))/(9))is a local maxima

Step-by-step explanation: hopes this help

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Answer:

66

Step-by-step explanation:

6(n² + 2)

6(3² + 2)

6(9 + 2)

6(11)

66

Answer:

slope = - [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

given f(4) = 6 and f(- 2) = 8 , then 2 points on the line are

(4, 6 ) and (- 2, 8 )

calculate slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (4, 6 ) and (x₂, y₂ ) = (- 2, 8 )

m = [tex]\frac{8-6}{-2-4}[/tex] = [tex]\frac{2}{-6}[/tex] = - [tex]\frac{1}{3}[/tex]

Since the paper representing her desk is 1 1/4 inches by 2 1/4 inches, the actual dimensions of her desk are D: 2 ¹/₂ ft by 4 ¹/₂ ft

To answer the question, we need to know what scale is

A scale is the ratio of two dimension and it is given on a scale drawing.

Given that Chelsea makes a scale drawing of the room and cuts out pieces of paper to represent her furniture, and the paper representing her desk is 1 1/4 inches by 2 1/4 inches.

Since on the scale, we have 1/2 in = 1 foot ⇒ 1 in = 2 ft

So, the actual dimensions of her desk are

1 ¹/₄ in by 2 ¹/₄ in = 5/4 in by 9/4 in

= 5/4 × 1 in by 9/4 × 1 in

= 5/4 × 2 ft by 9/4 × 2 ft

= 5/2 ft by 9/2 ft

= 2 ¹/₂ ft by 4 ¹/₂ ft

So, the actual dimensions of her desk are D: 2 ¹/₂ ft by 4 ¹/₂ ft

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Answer:

a

Step-by-step explanation:

anything less than 18 is wrong

I used exemplar. the mean means add all the numbers and divide it buy how many there are.

5 + 7 + 9 = 21

21/3 = 7

0 3 4 6 6 7 7 7 9

Median = 6  (the middle number)

Mode = 7 (the most common number)

Range = 9 (Biggest number - smallest number)

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Answer:

Step-by-step explanation:

~1

Given Polynomial:

To Find:

Solution:

Substitute x = -2 onto the given polynomial,as we need to find f(-2),so x = -2.

Simplify using PEMDAS,then.

Hence, f(6) = -14

[tex] \rule{225pt}{2pt}[/tex]

~2

Given polynomial:

To Find:

Solution:

g(x) = -4x-1

Substitute x = 7 onto the given polynomial,as we need to find g(7),so x = 7.

Simplify using PEMDAS.

Hence, g(7) = -29.

[tex] \rule{225pt}{2pt}[/tex]

Answer:

You will be 55

Step-by-step explanation:

[tex]~~~~~~~c = \dfrac{a^2 +3b}{4}\\\\\implies 4c = a^2 +3b\\\\\implies 3b = 4c-a^2\\\\\implies b = \dfrac{4c-a^2}{3}[/tex]

Answer:

b = [tex]\frac{(4c-a^2)}{3}[/tex]

Step-by-step explanation:

[tex]c=\frac{a^{2}+3b }{4}[/tex]

First, let us multiply both sides by 4.

4c = a² + 3b

Now let us take a² to the left side.

4c - a² = 3b

Now to make b as the subject let us divide both sides by 3.

[tex]\frac{(4c-a^2)}{3} =\frac{3b}{3}[/tex]

Therefore,

b = [tex]\frac{(4c-a^2)}{3}[/tex]      

Answer:

Step-by-step explanation:

Proof

AB||CD                          Given

<1 = <2                           Given

<2 = <3                          Alternate interior angles of Parallel lines

<1 =  <3                          Substitution for <2 from Given.

AC = AB                        the sides opposite equal angles are equal

The volume of the rectangular piece with sides of lengths of 7.08 × 10–3 m, 2.18 × 10–2 m, and 4.51 × 10–3m is 6. 96 × 10^ -7 m

Volume is defined as the amount of space or capacity occupied by a three-dimensional shape.

It is represented in cubic units.

Formula:

Volume, V = length × breadth × height

Given the values;

7. 08 × 10 ^-3m , 2.18 × 10^ -2m and 4. 51 × 10^-3m

Multiply all the lengths

Volume = 7. 08 × 10 ^-3 × 2.18 × 10^ -2 × 4. 51 × 10^-3

= 69.6 × 10^-8

= 6. 96 × 10^ -7 m

Therefore, the volume of the rectangular piece is 6. 96 × 10^ -7 m

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Answer:

A

Step-by-step explanation:

trust

Answer:

2 feet

Step-by-step explanation:

1 foot = 12 inches

2 feet=24 inches

Answer:

2 feet

Step-by-step explanation:

12 x 2 is 24.

The number of winners that Heather can expect is 300.

The first step is to determine the total number of winners to the total number of players using the information in the table.

Ratio = 180 / 450 = 0.40

Number of winners if there are 750 players = 0.40 x 750 = 300 winners

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Answer:

x = 1

Step-by-step explanation:

-33 + 8x = -9x - 18 + 2

8x+ 9x = -18 + 2 + 33

17x = -16 + 33

17x = 17

x = 1

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Answer:

3 and 4

Step-by-step explanation:

given that the difference is 7, two numbers that add up to 7 are 3 and 4.

Answer:

B: r² + 2r = 4

Explanation:

[tex]\rightarrow \sf 3x^2+6x=12[/tex]

divide both sides by 3

[tex]\rightarrow \sf x^2+2x=4[/tex]    ← This is the result of the first step.

factor out the common term

[tex]\rightarrow \sf x(x+2) = 4[/tex]

set to 0

[tex]\rightarrow \sf x = 4, \ x+2 = 4[/tex]

simplify

[tex]\rightarrow \sf x = 4, \ x= 2[/tex]

Divide all terms by a i.e 3

We get

Or

Option B is correct

The measure of angle b is 112° and the measure of angle c is 68°

From the question, we are to determine the measures of the missing angles

From the diagram,

b = 112° (Vertically opposite angles)

∴ b = 112°

Also,

112° + c = 180° (Sum of angles on a straight line)

c = 180°- 122°

∴ c = 68°

Hence, the measure of angle b is 112° and the measure of angle c is 68°

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To solve this, we need to use our trigonometric equations:

 ⇒ look at the diagram attached

Let's examine what the problem wants:

Let's examine what the problem gives us:

Let's solve:

  [tex]tan(27)=\frac{x}{15} \\x=15*tan(27)\\x=7.64[/tex]

Answer: 7.6 (rounded to the nearest tenth)

Hope that helps!

Answer:

[tex]6n \geq -24[/tex]

Step-by-step explanation:

First let's provide a variable for "a number" and call it [tex]n[/tex].

So "six times a number" could be written as [tex]6*n[/tex].

"Is at least" in mathematical terms means "greater than or equal to" or

≥

Putting this altogether gives the expression:

[tex]6n\geq -24[/tex]

Answer:

The correct answer is 742,000

Step-by-step explanation:

Answer:

742,000

Step-by-step explanation:

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The worth of the cd at the end of 7 years will be $384,101.79.

When an investment earns an interest that is compounded continuously, it means that it earns interest continuously.

The formula for calculating future value when there is continuous compounding is : A x e^r x N

Where:

2375 x (e^3.14) x 7 = $384,101.79

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The cuboid can hold 27.2 cubic inches of popcorn

A right rectangular prism is also called the cuboid. it is a solid three dimensional shape with 6 faces, 12 edges and 8 vertices.

Analysis:

Volume of cuboid = length x width x height

                              = 5 x 3 x 29/4 = 108.75 cubic inches

When it is quarter full, volume = 1/4 x 108.75 = 27.2 cubic inches

In conclusion, the volume of the cuboid is 27.2 cubic inches.

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Answer:

See below

Step-by-step explanation:

mx + b = y           subtract 'b' from both sides of the equation

mx = y - b            now, divide both sides by 'x'

m  = (y-b)/x

An equation is formed of two equal expressions. The number of seats in row 18 will be 119.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

A.) Given the number of seats that the first row can have is 11, while the number of seats that the next row should have is six more than the previous one. Therefore, the number of seats will increase linearly.

Thus, the equation for the number of seats in any row can be given as y=11+6x, where y is the number of seats and x is the number of row.

B.) The number of seats in row 18 will be equal to,

y = 11 + 6x

y = 11 + 6(18)

y = 11 + 108

y = 119

Hence, the number of seats in row 18 will be 119.

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Answer:

D) 65°

Step-by-step explanation:

Use Snell's Law

[tex]n_1\sin\theta_1=n_2\sin\theta_2\\\\1.00\sin\theta_1=1.47\sin38^\circ\\\\\sin\theta_1=1.47\sin38^\circ\\\\\theta_1=\sin^{-1}(1.47\sin38^\circ)\\\\\theta_1\approx64.83^\circ[/tex]

Thus, the angle of incidence is D) 65°

Answer: A.) y=4+x

Step-by-step explanation:

if the "d"iameter of the pie is 30, then its radius must be half that, or 15.

[tex]\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=15\\ \theta =42 \end{cases}\implies \begin{array}{llll} A=\cfrac{(42)\pi (15)^2}{360}\implies A=\cfrac{105\pi }{4} \\\\\\ \stackrel{using~\pi =3.14}{A\approx 82.43} \end{array}[/tex]

The answer is:
   " m∠BAC = 45° ;  m∠ABC, = 64° ; and:  m∠ACB = 70° ."
__________

Step-by-step explanation:

To find the measure of ∠BCA {"m∠BCA"} :

<BCA is supplementary to " 110 " ; that is, both, or all, of all the measurements that form a "line or line segment";  or any portions thereof,

that can be written in:  "slope-intercept format"

  that is, on Cartesian plane:  " y = mx + b " ;

  in which:  "y" is isolated on the "left-hand side" of the equation; as a single, isolated variable;

  and in which:  "m" is the "slope" (if applicable); and the coefficient to the "x"  value'

  and in which "b" is the "y-intercept"; or more precisely"
    the value of the "y-coordinate"—in: "(x, y)" format —at which:
    " x = 0" ; that is, in the format:  " (0, b)."
_________________
So, to find
m∠BCA :  Subtract our given value, "110" ; from "180" ; as follows:
_________________

  " (180 − 110) = 70" ;
__________________
Now:   Note a triangle, by definition, has 3 (three) sides and 3 (three) angles—and all three (3) angles of a triangle add up to 180°.

So:  We just solved for  m∠ACB ; which is:  70° .

Now shall solve for the value of "x" ; & then find the value of all 3 (three) sides of this triangle

Since all angles within a triangle add up to 180: Let's add them up:
  " 70  +  3x + 20 + 3x = 180 " ;

 Combine the "like terms" on the "left-hand side" of the equation:
  " +3x + 3x = 6x " ;  "+ 70 + 20 = 90 ";
And rewrite the equation:
  "  6x + 90 = 180 " ;

Now, subtract "90" from Each Side of the equation:
  "  6x + 90 − 90 = 180 − 90 " ;
to get:   " 6x = 90 " ;

Now, divide Each side of the equation by "6" ;

  to isolate "x" on one side of the equation ;
    and to solve for "x" :
   " 6x / 6 = 90 / 6 ;

to get:  " x = 15 " ;
________________
Now, we are asked to find:
1)  " m∠BAC = 3x " ;  Plug in "15" for "x" ; and solve:
                     "3x = 3(15) = 45 " ;
2)  " m∠ABC = "(3x + 20)" ; Plug in "15" for "x"; and solve:
                     "3(15) + 20 = 45 + 20 = 65 " ;
3)  " m∠ACB  = 70 " ; (as per our calculated value);

To check our work—do these 3 (three) numbers add up to 180?

   "45 + 65 + 70 =? 180 ? " ;

   " 110 + 70 = " 180 "? Yes!
__________
So: The answer is as follows:
   " m∠BAC = 45° ;  m∠ABC, = 64° ; and:  m∠ACB = 70° ."
__________
Hope this is helpful to you!  Best wishes!

The possible values of N from the given probability parameters is; N equals 15 or 21

We are told that;

Number of pens in the box = N

Let the number of red pens be x

Thus; number of black pens = x + 3

Thus;

x + x + 3 = N

x = (N - 3)/2

The probability that she will take a black pen followed by a red pen is;

P(she will take a black pen followed by a red pen) = (x + 3)/N * x/(N - 1)

Plugging in he relevant values and solving for N gives ;

Solving for N gives N equals 15 or 21

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