A trapezoid has a base of 4.5 inches, a height of 6 inches, and an area of 21 square inches. The equation below can be used to determine b2, the length in inches of the second base of the trapezoid.
12(4.5+b2)(6)=21

The x-intercepts of an equation are simply the zeros of the equation

The equation [tex]\mathbf{y = bx(x - a)(x -a)(x + b)(x - b)}[/tex] has 4 distinct x-intercepts

The equation is given as:

[tex]\mathbf{y = bx(x - a)(x -a)(x + b)(x - b)}[/tex]

Set the equation to 0; i.e. calculate the zeros

[tex]\mathbf{bx(x - a)(x -a)(x + b)(x - b) = 0}[/tex]

Divide both sides by constant b

[tex]\mathbf{x(x - a)(x -a)(x + b)(x - b) = 0}[/tex]

Split the above equation, as follows

[tex]\mathbf{x= 0\ or\ x - a = 0\ or\ x -a = 0\ or\ x + b = 0\ or\ x - b = 0}[/tex]

Solve for x in each of the equation

[tex]\mathbf{x= 0\ or\ x = a\ or\ x = a\ or\ x= -b\ or\ x = b}[/tex]

Remove repeated solutions

[tex]\mathbf{x= 0\ or\ x = a\ or\ x= -b\ or\ x = b}[/tex]

The count of solutions above is 4

Hence, the equation has 4 distinct x-intercepts

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Answer:

$57.84

Step-by-step explanation:

Balloons needed = 168

Cost of 36 balloons per pack = $11.88

Cost of 12 balloons per pack = $5.16

cost per balloon

36 per pack = $11.88 / 36

= $0.33

12 per pack = $5.16 / 12

= $0.43

In order to minimize cost, she should buy as many packs of 36 per pack balloon

36 per pack × 1 pack = 36

36 per pack × 2 packs = 72

36 per pack × 3 packs = 108

36 per pack × 4 packs = 144

36 per pack × 5 packs = 180

The required number of balloons is 168

So, the number of possible 36 packs to buy is 4, that is, 144 balloons

Balloons remaining = 168 - 144

= 24

Possible packs of 12 balloons per pack possible is

12 per pack × 1 pack = 12

12 per pack × 2 packs = 24

Therefore, Megan needs to buy 4 packs of 36 balloons per pack and 2 packs of 12 balloons per pack

Cost of 4 packs of 36 balloons per pack = 4 × $11.88

= $47.52

Cost of 2 packs of 12 balloons per pack = 2 × $5.16

= $10.32

Total cost = $47.52 + $10.32

= $57.84

Answer:

B. x = −3, x = −11

Step-by-step explanation:

−3|x + 7| = −12

-3x - 21 = -12 and -3x - 21 = 12

-3x - 21 = -12

      -3x = 9

          x = -3

-3x - 21 = 12

      -3x = 33

         x = -11

Answer: 48

Step 1: Find how much 12 is of 48.

12 = 1/4 of 48

Step 2: Multiply 12 by 3 for 3/4.

12 x 3 = 36.

Step 3: Add the numbers.

12 + 36 = 48

Answer = 48

Approximately, 48 hot dogs did he eat during the 12-minute contest.

One strategy to promote uniformity in work efforts, costs, and time is to simplify procedures. It lessens diversity and variation that is damaging, unnecessary, or meaningless. PEMDAS stands for parenthesis, exponents, multiplication, division, addition, and subtraction. Given two or more operations in a single statement, the order of the letters in PEMDAS tells you what to compute first, second, third, and so on, until the computation is complete.

As a result, Takeru Kobayashi broke the record for eating the hottest dogs in a 12-minute period.

Since,

In the first three minutes, he consumed 12 hot dogs.

in three minutes, he ate = 12 hot dogs

in 1 minute, he ate = 12/3

in 1 minute, he ate = 4

So,

in 12 minutes, the total number of hot dogs he ate = 4*12

in 12 minutes, the total number of hot dogs he ate = was 48

therefore, Approximately, 48 hot dogs did he eat during the 12-minute contest.

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Answer:

so the correct statement is;

The equation 2 ( 3 w − 6 ) + 2 w = 36 can be used to find the width of the rectangle, and the width is 6 feet

Step-by-step explanation:

Here, we want to select the statement which is true

Let the width be w

the length is 6 ft less than 3 times the width

The length will be (3w - 6) ft

Mathematically, the perimeter of a rectangle can be calculated using the formula;

2( l + b) = P

Thus;

2(3w -6 + w) = 36

divide both sides by 2

3w -6 + w = 36/2

3w -6 + w = 18

4w -6 = 18

4w = 18 + 6

4w = 24

w = 24/4

w = 6

Answer:

Step-by-step explanation:

for 2.2 you would still have 5^2 in brackets still

same kind of error for 2.1

Answer:

A, C, E, F

Step-by-step explanation:

Answer:

hello

Step-by-step explanation:

Slope, sometimes referred to as gradient in mathematics, is a number that measures the steepness and direction of a line, or a section of a line connecting two points, and is usually denoted by m. Generally, a line's steepness is measured by the absolute value of its slope, m.

m = slope

Answer:

m=56kx-6

Step-by-step explanation:

Answer:

D.) y=-x-2

Step-by-step explanation:

Answer:

D.) y=-x-2

Step-by-step explanation:

Trust me I just know

Answer:

John: 18 years old

Mikayla: 6 years old

Step-by-step explanation:

Please see the attached picture for the full solution.

Answer:

360 degrees

Step-by-step explanation:

We know that the sum of all the (ordered) exterior angles of any polygon is 360 degrees. As shown in the figure that, x,y and z recognise themselves as  the exterior angles of the given triangles, their sum will be 360 degrees as well.

Answer:

[tex]n = \frac{49}{2x}[/tex]

Step-by-step explanation:

1) Simplify [tex]\frac{4}{7}[/tex] xn to [tex]\frac{4xn}{7}[/tex]

[tex]\frac{4xn}{7}[/tex] = 14

2) Multiply both sides by 7.

4xn = 14 × 7

3) Simplify 14 × 7 to 98.

4xn=98

4) Divide both sides by 4.

[tex]xn = \frac{98}{4}[/tex]

5) Simplify [tex]\frac{98}{4}[/tex] to [tex]\frac{49}{2}[/tex]

[tex]xn = \frac{49 }{2}[/tex]

6) Divide both sides by x.

[tex]n = \frac{49}{2} / x[/tex]

7) Simplify [tex]\frac{49}{2} /x[/tex] into [tex]\frac{49}{2x}[/tex]

[tex]n = \frac{49}{2x}[/tex]

9514 1404 393

Answer:

  x = 4c-3d

Step-by-step explanation:

Cross multiply, separate variables terms and constant terms.

  [tex]3(x-d)=4(x-c)\\\\3x-3d=4x-4c\\\\4c-3d=x\qquad\text{add $4c-3x$}\\\\\boxed{x=4c-3d}[/tex]

Answer:

(7, -6)

Step-by-step explanation:

You will graph it at this point because the point is basically the origin and when you rotate it clockwise 90° it will end up in Quadrant IV.

Answer:

1.)47.022

2.)8.032

3.)2.436

4.)61.92

Step-by-step explanation:

Answer:

[tex]\boxed {x = -\frac{1}{7}}[/tex]

Step-by-step explanation:

Solve for the value of [tex]x[/tex]:

[tex]6(4x + 5) = 3(x + 8) + 3[/tex]

-Use Distributive Property:

[tex]6(4x + 5) = 3(x + 8) + 3[/tex]

[tex]24x + 30 = 3x + 24 + 3[/tex]

-Combine like terms:

[tex]24x + 30 = 3x + 24 + 3[/tex]

[tex]24x + 30 = 3x + 27[/tex]

-Take [tex]3x[/tex] and subtract it from [tex]24x[/tex]:

[tex]24x + 30 -3x = 3x - 3x + 27[/tex]

[tex]21x + 30 = 27[/tex]

-Subtract both sides by [tex]30[/tex]:

[tex]21x + 30 - 30 = 27 - 30[/tex]

[tex]21x = -3[/tex]

-Divide both sides by [tex]21[/tex]:

[tex]\frac{21x}{21} = \frac{-3}{21}[/tex]

[tex]x = \frac{-3}{21}[/tex]

-Reduce the fraction to the lowest term by extracting and canceling out [tex]3[/tex]:

[tex]x = \frac{-3\div3}{21 \div 3}[/tex]

[tex]\boxed {x = -\frac{1}{7}}[/tex]

Therefore, the value of [tex]x[/tex] is [tex]-\frac{1}{7}[/tex].

Answer:

so

box1 = x

box2= 9

Step-by-step explanation:

5(x+9)  

distribute

5(x) + 5(9)

5x + 45

Answer:

24

Step-by-step explanation:

Answer:

C. None of these

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

-(-x) ^3-x^3

x^3-x^3

=0

Answer:

The radius of the track is 32 meters

Step-by-step explanation:

Circumference

The circumference of a circle can be defined as the distance around the circle or the length of a circuit along the circle.

Given a circle of radius r, the circumference of the circle can be calculated as follows:

[tex]L=2\pi r[/tex]

If we already know the length of the circle, we can solve the above expression for r:

[tex]\displaystyle r=\frac{L}{2\pi}[/tex]

The distance given around a circular running track is L=200 m, thus:

[tex]\displaystyle r=\frac{200}{2\pi}=31.830989\ m[/tex]

Rounding to the nearest meter:

r= 32 meters

The radius of the track is 32 meters

Answer:

Step-by-step explanation:

BD divides CBA into two angles. The add to 90 degrees. Therefore they are complementary.

The key word is complementary. The angles are <CBA and <DBA are complementary.

Answer:

Right angle or adjacent angle. I'm not sure if there was a vocabulary bank.

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

When dividing two negative numbers, the negatives cancel out, leaving you with simply 21/3. As you probably know, 21/3 is 7.

Answer:

50 dollars an hour

Step-by-step explanation:

Answer:

(x^3y)/2

Step-by-step explanation:

Answer:

81 cm square

Step-by-step explanation:

the answer is 121.5cm^2