Russo and Frederica want to find out if the parallelogram formed by connecting points
A, B, C, and D is a rhombus.
Russo's plan:
• Use the distance formula to find the lengths of the sides.
• See if the sides are all the same length.
Frederica's plan:
• Find the slopes of the two diagonals.
• See if the two slopes are negative reciprocals of each other.
Which student's plan will work?

9514 1404 393

Answer:

  2.  (b) 6 feet by 18 feet

  3.  -5, -1

Step-by-step explanation:

2. Perhaps the easiest way to answer this is to check to see what the areas are of the offered choices:

  a) 7·19 = 133 . . . . numbers are odd, so the answer is odd, incorrect

  b) 6·18 = 108 . . . . correct choice

  c) 12·24 = 288

  d) 5·17 = 85 . . . . again an odd number

__

If you were to solve this by factoring, you would be looking for factors of 108 that have a difference of 12.

  108 = 1·108 = 2·54 = 3·36 = 4·27 = 6·18 = 9·12

The differences are 107, 52, 33, 23, 12, 3. The dimensions you want are 6 and 18 feet.

_____

3. Completing the square is easier if the quadratic has a leading coefficient of 1. Here, all of the coefficients are divisible by 2, so we can simplify this to ...

  x^2 +6x = -5 . . . . . . divide both sides by 2

Now, we complete the square by adding the square of half the linear term coefficient.

  x^2 +6x +9 = 4 . . . . add (6/2)^2 = 9 to both sides

  (x +3)^2 = 4 . . . . .  write as a square

  x +3 = ±2 . . . . . . . take the square root

  x = -3 ±2 = -5, -1 . . . . add -3 to both sides

The solutions are -5 and -1.

Answer:

x= 30/7

Step-by-step explanation:

See image below:)

Answer:

Step-by-step explanation:

2/3x = - 1/2x + 5

2/3x + 1/2x = - 1/2x + 1/2x + 5

[tex]1\frac{1}{6}x=5[/tex]

[tex]\frac{1\frac{1}{6}x}{1\frac{1}{6} } =\frac{5}{1\frac{1}{6} }[/tex]

Answer:

Answer:

option D :

f(-8) = -2 ; f(4) = 3

Step-by-step explanation:

f(-8) = ³√-8 = -2

f(4) = 3 (the constant function)

Answer:

option A

Step-by-step explanation:

∠WPS +∠OPW  = 180   {straight line}

∠WPS +110 = 180

∠WPS = 180 - 110

∠WPS = 70°

∠RWQ + ∠QWT +∠TWU = 180   {straight line}

∠RWQ + 60 + 50 = 180

∠RWQ + 110 = 180

∠RWQ = 180 - 110

∠RWQ= 70°

∠PWU +  ∠USP + ∠ WPS = 180  {angle sum property of triangle}

∠PWU + 40 + 70 = 180

∠PWU + 110 = 180

∠PWU = 180 - 110  

∠PWU = 70°

Answer:

A

Step-by-step explanation:

∠WPS +∠OPW  = 180 (adj angles on a str line)

       ∠WPS +110 = 180

                ∠WPS = 180 - 110

                            = 70°

∠RWQ + ∠QWT +∠TWU = 180 (adj angles on a str line)

            ∠RWQ + 60 + 50 = 180

                   ∠RWQ + 110 = 180

                             ∠RWQ = 180 - 110

                                         = 70°

∠PWU +  ∠USP + ∠ WPS = 180 (adj angles on a str line)  

            ∠PWU + 40 + 70 = 180

                     ∠PWU + 110 = 180

                              ∠PWU = 180 - 110  

                                          = 70°

[tex] \frac{x {}^{0}y {}^{ - 3} }{x {}^{2}y {}^{ - 1} } \\ = \frac{1y {}^{ - 3} }{ {x}^{2}y {}^{ - 1} } \\ = \frac{1 \times 1}{ {x}^{2} y {}^{2} } \\ \\ = \frac{1}{ {x}^{2}y {}^{2} } [/tex]

Step by Step Explanation:

#CarryOnLearning

Answer:

5 =x

Step-by-step explanation:

The top and the bottom are the same length

17 = 3x+2

Subtract 2 from each side

17-2 = 3x+2-2

15 =3x

Divide by 3

15/3 = 3x/3

5 =x

Answer:

x = 5

Step-by-step explanation:

3x + 2 = 17

3x + 2 - 2 = 17 - 2

3x = 15

3x ÷ 3 = 15 ÷ 3

x = 5

Answer:

5250

Step-by-step explanation:

a. 7/8 of 60,00

a [tex]\frac{7}{8} * 60,00[/tex]

[tex]\frac{7*60,00}{8}[/tex]

[tex]\frac{42,000}{8}[/tex]

[tex]5250[/tex]

Answer:

1 9 3

Step-by-step explanation:

i think only this much

Answer:

1,3 and 9

As Nine is divisible by 1,3 and 9

Answer:

arc AB = 45°

Step-by-step explanation:

The central angle ABC is equal to the measure of the arc that subtends it, so

AB = ∠ ABC = 45°

Answer:

9/8 x 9/8 = 81/64 in fraction form.

Hi there!  

»»————-　★　————-««

I believe your answer is:  

[tex]\frac{81}{64}[/tex]

»»————-　★　————-««  

Here’s why:

⸻⸻⸻⸻

[tex]\boxed{\text{Calculating the answer...}}\\\\(\frac{9}{8})^2\\\\\text{Recall the power of a fraction rule: } (\frac{a}{b})^x =\frac{a^x}{b^x}\\\\\rightarrow (\frac{9}{8})^2 =\frac{9^2}{8^2} =\boxed{\frac{81}{64}}[/tex]

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

Answer:

21

Step-by-step explanation:

what are the best ways for your business and how do they get neck debt from the air and to get rid from a good or

Answer:

B =53.15010235

Step-by-step explanation:

Since this is a right triangle, we can use  trig functions

tan theta = opp / adj

tan B =  20 /15

Take the inverse tan of each side

tan ^ -1 ( tan B) = tan ^-1( 20/15)

B =53.15010235

Answer:

It has 5 Faces.

The 4 Side Faces are Triangles.

The Base is a Square.

It has 5 Vertices (corner points)

It has 8 Edges.

Step-by-step explanation:

btw you can choose 3

Answer:

832.6lbs

Step-by-step explanation:

Answer:

120 - 4.5t= 75

t = 10 minutes

Step-by-step explanation:

the equation :

120 - 4.5t= 75

the solution:

-4.5 t = 75-120

-4.5t = -45

t = -45/(-4.5) = 10 minutes

The equation to model the given situation is 120 - 4.5t= 75 and the  solution to the equation is 10 minutes.

Given that, a hot air balloon is cruising at an altitude of 120 meters above the ground when it begins its descent.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The balloon will reach an altitude of 75 meters above the ground.

Now, 120-75 =45 meters

Let t be the time to descends 45 meters

So, 120 - 4.5t= 75

⇒ -4.5 t = 75-120

⇒ -4.5t = -45

⇒ t = -45/(-4.5)

⇒ t = 10 minutes

Hence, the equation to model the given situation is 120 - 4.5t= 75 and the  solution to the equation is 10 minutes.

To learn more about an equation visit:

https://brainly.com/question/14686792.

#SPJ2

Answer:

The slope of the line reflects the actual d.

Answer:  0.0766

Step-by-step explanation:

Let x be the random team scores.

Given: Mean = 76

Standard deviation = 8.4

We assume that x follows normal distribution.

The probability that a random team scores less than 64 points = P(x<60)

[tex]=P(\frac{x-\mu}{\sigma}<\frac{64-76}{8.4})\\\\=P(z<-1.4286) \ \ \ [Z=\frac{x-\mu}{\sigma}]\\\\= 1-P(z<1.4286)\\\\=1-0.9234\\\\=0.0766[/tex]

Hence, the probability that a random team scores less than 64 points =0.0766

Answer:

(2x-4()(x-2)

Step-by-step explanation:

this is how it looks when factorised

Answer:

y=-2x^2-8x

you can use a factor form helper and from that it can show you examples on how to solve it

Step-by-step explanation:

the answer is in the above image

Answer:

Step-by-step explanation:

8 .) Probability of students has no pets in senior = No. of outcomes favourable / Total no.of outcome

= 15 / 24

9.) Probability of students has pets in junior = No.of outcomes favourable / Total no. of outcomes

= 37/52

Answer:

Point Form:

(6,18), (-3,-9)

Equation Form:

x=6, y=18

x=-3, y=-9

Step-by-step explanation:

Solve for the first variable in the first equation, then substitute the result into the other equation.

Answer:

x=-3 , x=6

so

y=-9 or y=18

Answer: The game will end at 3:27 pm.

Step-by-step explanation: 50 minutes from 11:37 am is 12:27 pm, and 3 hours from 12:27 pm is 3:27 pm.

Answer:

Step-by-step explanation:

The key here is to find out how long it will take Justin to triple his money, and then use that number of years in Hailey's equation. If Justin starts with $940, he will triple his money when he has $2820 (940*3). We need to find out how long it takes him to do this using the equation

[tex]A(t)=P(1+\frac{r}{n})^{nt}[/tex]where A(t) is the tripled amount of money, P is the initial investment, r is the interest rate in decimal form, n is the number of compoundings done per year, and t is the time in years. Filling in and solving for t:

[tex]2820=940(1+\frac{.07625}{12})^{12t[/tex] which simplifies a bit to

[tex]2820=940(1+.0063541667)^{12t[/tex] and a bit more to

[tex]2820=940(1.0063541667)^{12t[/tex] Begin to solve for t by dividing both sides by 940 to get:

[tex]3=(1.0063541667)^{12t[/tex] and then take the natural log of both sides to get the t alone eventually. Taking the natural log on the right side enables us to move the 12t down in front. So doing all of that at the same time:

[tex]ln3=12tln1.0063541667[/tex] and divide both sides by ln(1.0063541667):

[tex]173.4450855=12t[/tex] then finally divide both sides by 12 to get

t = 14.5 years. Now we use that number of years to find out how much Hailey will have.

[tex]A(t)=940(1+\frac{.0825}{4})^{(4)(14.5)}[/tex] which simplifies a bit to

[tex]A(t)=940(1+.020625)^{58[/tex] and a bit more to

[tex]A(t)=940(1.020625)^{58[/tex] and

A(t) = 940(3.26768151) so in 14.5 years, Hailey will have

A(t) = $3071.62

Answer:

x=25

Step-by-step explanation:

43=2x-7 (since the midpoint separate a line into two equal halves)

43+7=2x

50/2=x

25=x

Answer:

x=25

Step-by-step explanation:

Since M is the midpoint, you can set your formula up as

43 = 2x-7

43+7=2x

50/2=x

25=x

Answer:

x=41/4

Step-by-step explanation:

According to the Secant Theorem, a(a+b)=c(c+d)

Therefore, 3(3+4x+12)=2(2+8x),  12x+45=16x+4, x=41/4

Step-by-step explanation:

f(x) =x-1 and when we put 0 from x our answer is -1 and put 1 answer is 0 ........ for this f(x) must be x-1. g(x)= f(x)+ 4