The polynomial below is a perfect square trinomial of the form A^2 - 2AB + B^2

9x^2 - 12x + 4

A. True

B. False

Answer:

The exact perimeter is [tex]18\sqrt{2}[/tex] meters.

This is approximately 25.5 meters (nearest tenth).

The area of the rectangle is 36 square meters.

Step-by-step explanation:

Area of a rectangle = width × length

Perimeter of a rectangle = (2 × width) + (2 × length)

Given:

Perimeter

[tex]\textsf{Perimeter}=2 \sqrt{18} +2\sqrt{72}[/tex]

               [tex]=2 \sqrt{9 \cdot 2} +2\sqrt{36 \cdot 2}[/tex]

               [tex]=2 \sqrt{9} \sqrt{2}+2\sqrt{36}\sqrt{2}[/tex]

               [tex]=2 \cdot 3 \sqrt{2}+2\cdot 6\sqrt{2}[/tex]

               [tex]=6 \sqrt{2}+12\sqrt{2}[/tex]

               [tex]=18\sqrt{2} \textsf{ m}[/tex]

The exact perimeter is [tex]18\sqrt{2}[/tex] meters.

This is approximately 25.5 meters (nearest tenth).

Area

[tex]\textsf{Area}=\sqrt{18} \times \sqrt{72}[/tex]

       [tex]=\sqrt{9 \cdot 2} \times \sqrt{36 \cdot 2}[/tex]

       [tex]=3\sqrt{2} \times 6\sqrt{ 2}[/tex]

       [tex]=18\sqrt{2}\sqrt{ 2}[/tex]

       [tex]=18 \cdot 2[/tex]

       [tex]=36 \textsf{ m}^2[/tex]

The area of the rectangle is 36 square meters.

Answer:

5/9

Step-by-step explanation:

Let the probability of getting a multiple of 3 is "A"

Let the probability of getting an even number is "B"

Total number of outcomes=36

Total number of favourable outcomes of either a multiple of 3 or an even number are

(1,1) ,(1,2) ,(2,1) ,(1,3) ,(3,1) ,(2,2) ,(1,5) (5,1) ,(3,3) ,(2,4) ,(4,2) ,(2,6) ,(6,2) ,(3,5) ,(5,3) ,(4,4) ,(6,4) ,(4,6) ,(5,5) ,(6,6)

That is we have 20 favourable outcomes

Hence, Probability=\frac{\text{favourable outcomes}}{\text{total number of outcomes}}Probability=

total number of outcomes

favourable outcomes

Therefore, after substituting the values we get

probability=\frac{20}{36}probability=

36

20

After simplification we will get

probability=\frac{5}{9}probability=

9

5

Answer:

6

Step-by-step explanation:

Longer than 49 is only 25% percentile.

27  X .25 = 6.75

Employees are whole numbers, therefore the answer is 6.

Answer:

6

Step-by-step explanation:

Answer:

Step-by-step explanation:

The mean is calculated by adding up their values, and then dividing them into elements of a set.

All of them should first be added together.

21.2+15.3+20.5+16.8+30.2

Solve.

[tex]\sf{21.2+15.3+20.5+16.8+30.2=104}[/tex]

The sum of the data set is 104.

The number of terms in the data set is n=5.

Therefore, the mean of the data set is 20.8, which is our answer.

I hope this helps you! Let me know if my answer is wrong or not.

Answer:

C. 61 degrees

Step-by-step explanation:

a line is 180 degrees

so e and 119 degrees makes a line

so you subtract 180-119= 61 degrees

18 females, 13 males, total: 31 students.

•female french students: 2

•male french students: 5

probability: male french = 5/31,

total students

edit: as a percentage, 16.129 %

Let the original price be x.

x * (1 - 0.25) = $41.25

0.75x = $41.25

x = $41.25 / 0.75 = $55

Answer:

$55

Step-by-step explanation:

____ decrease by 25%= $41.25, which the unknown number is $55.

Answer:

58

Step-by-step explanation:

its basically saying that pam spent 24 dollars less than you. soo 82 - 24 = 58

Step-by-step explanation:

width is 6 units

P=2(l+w)

p=2(l+6)

l+6=p/2

l= (p/2)-6

The length of the reactangle with a width of 6 units and perimeter p units is (P/2)-6 units.

A perimeter is a closed route that surrounds, outlines, or embraces a rectangle. The perimeter of a rectangle is given by the formula,

[tex]\rm Perimeter= 2(Length +width)[/tex]

As it is given that the width of the rectangle is 6 units, while the perimeter of the rectangle is P. Now if we write about the perimeter of the rectangle, it can be written as,

[tex]\rm Perimeter= 2(Length +width)[/tex]

[tex]P = 2(l+6)\\\\\dfrac{P}{2} = (l+6)\\\\l = \dfrac{P}{2}-6[/tex]

Hence, the length of the reactangle with a width of 6 units and perimeter p units is (P/2)-6 units.

Learn more about Perimeter:

https://brainly.com/question/2142493

Answer:

$1225

$33,775

Step-by-step explanation:

Given:

To find a percentage of an amount, convert the percentage into a decimal and multiply it by the amount:

3.5% = 3.5/100 = 0.035

⇒ Decrease in price = 0.035 × 35000 = $1225

Price of next model = price of current model - decrease in price

                                 = 35000 - 1225

                                 = $33,775

Decrease amount:-

So

New price:-

The exponential equation that correctly models the ball's peak height, h, in meters, after b bounces is given by:

[tex]H(b) = 4(0.79)^b[/tex]

A decaying exponential function is modeled by:

[tex]A(t) = A(0)(1 - r)^t[/tex]

In which:

In this problem:

Thus, the equation is given by:

[tex]H(b) = 4(0.79)^b[/tex]

More can be learned about exponential equations at https://brainly.com/question/25537936

Answer:

Domain = [-7,4]

Range = [-4,8]

Step-by-step explanation:

Domain= all values of x

Range= all values of y

becuase there are no values going to infinity and they all end, we can just look at our end points.

Answer:

400

Step-by-step explanation:

48 is 12% of x

12/100 = 48/x

3/25 = 48/x

1/25 = 16/x

x = 25 × 16

x = 400

Answer: 400

Answer:

400

Step-by-step explanation:

(48 x 100) / 12 = 400

      Answer: [tex]\frac{4}{75}[/tex]

      To Know: A percent (%) divided by 100 becomes a decimal / fraction.

      Step-by-step explanation:

[tex]5\frac{1}{3}[/tex]% [tex]/100[/tex]

[tex]5\frac{1}{3}[/tex]%[tex]*\frac{1}{100}[/tex]

[tex]\frac{16}{3}[/tex]%[tex]*\frac{1}{100}[/tex]

[tex]\frac{16*1}{3*100} =\frac{16}{300} =\frac{8}{150}=\frac{4}{75}[/tex]

     Leaving us with an answer of [tex]\frac{4}{75}[/tex]

Answer:

Part-A= C

Part-B= B

Step-by-step explanation:

153-39=114

114+28=142

39+28=67

Answer:

Part A is b and Part B is c good luck

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

⇒ Find the slope of the line that is perpendicular to y = 2x + 7 :

     ↓

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

I hope this helps you

:)

Answer:

a) 37º

b) 143º

c) 2x - 5 = 143

Step-by-step explanation:

a) Angles 5 and 7 are vertical angles and therefore have the same measurements.

b) Angles 5 and 6 form a straight line and are therefore supplementary (add up to 180º). 180 - 37 = 143.

c) We found the measure of angle 6 is 143º in part b. We can set that equal to 2x - 5. Therefore the equation is 2x - 5 = 143.

Answer:

True

Determine whether x+2 is a factor of x³-3x²-7x+6:

↓

[tex]True[/tex]

I hope this helps you

:)

Answer:

0.75mg

Step-by-step explanation:

6 years is its half life, meaning that half of it will have iradiated by that point. 1.5 / 2 = 0.75

Answer:

For me I think it is a number 3

Step-by-step explanation:

The statement about these triangles which is true there are exactly three isosceles triangles, the correct option is B.

A right-angle triangle is a triangle that has a side opposite to the right angle the largest side and is referred to as the hypotenuse. The angle of a right angle is always 90 degrees.

We are given that;

4 triangle figure

we can answer the question by counting how many triangles belong to each category. We have:

Three acute triangles: B, D, and E.

Three isosceles triangles: A, D, and E.

Two right triangles: A and C.

Two scalene triangles: B and C.

Therefore, the statement that is true about these triangles is:

Therefore, by the given triangle answer will be There are exactly three isosceles triangles.

Learn more about a right angle triangle;

https://brainly.com/question/7116550

#SPJ2

Volume of the bead = Volume of the sphere - volume of the cylindrical hole = 242.95 mm³.

Volume of the bead = Volume of the sphere - volume of the cylindrical hole

= 4/3π(4³) - π(1²)(8)

= 268.08 - 25.13

Volume of the bead = 242.95 mm³

Learn more about volume of sphere on:

https://brainly.com/question/22807400

We will see that for Stuart the maximum height is 30ft, and for Francisco it is 46.0625 ft

In the case of Stuart it is simple, as we have a graph, we just need to see the largest y-value on the graph. We can see that it is y = 30, then for Stuart, the largest distance from the ground is 30ft.

In the case of Francisco, we need to find the maximum of:

g(x)= -16x^2 + 50x +7

Notice that this is a quadratic of negative leading coefficient, so the maximum is at the vertex.

x = -50/(2*-16) = 25/16

Evaluating the function in 25/16 we get:

g(25/16) = -16*(25/16)^2 + 50*(25/16) +7 = 46.0625 ft

If you want to learn more about quadratic functions, you can read:

https://brainly.com/question/1214333

Answer:

[tex]90^{\circ}[/tex]. In other words, these two vectors are perpendicular (orthogonal) to one another.

Step-by-step explanation:

Let [tex]\|a\|[/tex] and [tex]\|b\|[/tex] denote the magnitudes of vector [tex]a[/tex] and vector [tex]b[/tex]. The dot product between these two vectors is represented as [tex]a^{T}\, b[/tex].  Let [tex]\theta[/tex] denote the angle between the two vectors. The cosine of this angle would be equal to:

[tex]\begin{aligned}\cos(\theta) &= \frac{a^{T}\, b}{\|a\| \|b\|}\end{aligned}[/tex].

The dot product between vector [tex]a = \langle 1,\, 2\rangle[/tex] and [tex]b = \langle 1,\, -1/2\rangle[/tex] is:

[tex]\begin{aligned}a^{T}\, b &= {\begin{bmatrix}1 \\ 2\end{bmatrix}}^{T}\, \begin{bmatrix}1 \\ -1/2\end{bmatrix} \\ &= 1 \times 1 + 2 \times \left(-\frac{1}{2}\right) \\ &= 0\end{aligned}[/tex].

The magnitudes of the two vectors are:

[tex]\begin{aligned}\| a \| &= \sqrt{1^{2} + 2^{2}} \\ &= 5\end{aligned}[/tex].

[tex]\begin{aligned}\| b \| &= \sqrt{1^{2} + \left(-\frac{1}{2}\right)^{2}} \\ &= \frac{1}{2}\, \sqrt{5}\end{aligned}[/tex].

Therefore:

[tex]\begin{aligned}\cos(\theta) &= \frac{a^{T}\, b}{\|a\| \|b\|} \\ &= \frac{0}{5 \times (\sqrt{5} / 2)} \\ &= 0\end{aligned}[/tex].

Among all angles between [tex]0^{\circ}[/tex] and [tex]180^{\circ}[/tex], the only angle with a cosine of [tex]0[/tex] is [tex]90^{\circ}[/tex]. Therefore, the angle between vector [tex]a[/tex] and vector [tex]b[/tex] must be [tex]90^{\circ}\![/tex]. Hence, these two vectors are perpendicular to one another.

Answer:

y+4

Step-by-step explanation:

Apply Thales theorem

[tex]\\ \rm\rightarrowtail \dfrac{MR}{RN}=\dfrac{MQ}{QP}[/tex]

[tex]\\ \rm\rightarrowtail \dfrac{10}{RN}=\dfrac{8}{5}[/tex]

[tex]\\ \rm\rightarrowtail 8RN=50[/tex]

[tex]\\ \rm\rightarrowtail RN=50/8[/tex]

[tex]\\ \rm\rightarrowtail RN=6.25[/tex]

Answer:

RN = 6.25

Step-by-step explanation:

Triangle Proportionality Theorem: If a line parallel to one side of a triangle intersects the other two sides, then it divides the two sides proportionally.

Therefore,

MQ : MP = MR : MN

⇒ 8 : (8 + 5) = 10 : (10 + RN)

⇒ 8 : 13 = 10 : (10 + RN)

⇒ [tex]\sf\dfrac{8}{13}=\dfrac{10}{10+RN}[/tex]

Cross multiply and solve:

⇒ 8(10 + RN) = 10 × 13

⇒ 80 + 8RN = 130

⇒ 8RN = 130 - 80

⇒ 8RN = 50

⇒ RN = 50 ÷ 8

⇒ RN = 6.25

Answer:

Step-by-step explanation:

To solve for x, you have to isolate it on one side of the equation.

First, subtract by 15 from both sides.

[tex]\sf{5x+15-15=28-15}[/tex]

Solve.

28-15=13

Rewrite the problem down.

5x=13

Divide by 5 from both sides.

[tex]\sf{\dfrac{5x}{5}=\dfrac{13}{5} }[/tex]

Solve.

You can also divide the numbers from left to right.

13/5=2.6

[tex]\boxed{\sf{x=\dfrac{13}{5}=2.6 }}[/tex]

I hope this helps you! Let me know if my answer is wrong or not.

[tex]\rightarrow \sf 5x + 15 = 28[/tex]

[tex]\rightarrow \sf 5x + 15 -15= 28-15[/tex]

[tex]\rightarrow \sf 5x = 13[/tex]

[tex]\rightarrow \sf \dfrac{5x}{5} = \dfrac{13}{5}[/tex]

[tex]\rightarrow \sf x = \dfrac{13}{5}[/tex]

[tex]\rightarrow \sf x = 2\dfrac{3}{5}[/tex]

[tex]\rightarrow \sf x = 2.6[/tex]

Answer:

depends on how much each thing costs

Step-by-step explanation:

Answer:

1. A = 40 units²

2. A = 72 units²

3. B) 45

Step-by-step explanation:

1.  This shape comprises 4 congruent triangles with base of 5 units and height of 5 units.

Area of a triangle = 1/2 x base x height

Therefore, area of polygon = 4(1/2 x 5 x 4)

                                             = 40 units²

2.  This shape comprises two pairs of congruent triangles.

Area of a triangle = 1/2 x base x height

Therefore, area of polygon = 2(1/2 x 2 x 6) + 2(1/2 x 10 x 6)

                                             = 72 units²

3.  Count the number of shaded squares:

9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 45 units²