Which of the following pairs of triangles can be proven similar through SSS similarity?

Answer:

Mr. Russo takes three minutes less than Mr. Lloyd to pack a case when each works alone.

One day, after Mr. Russo had spent six minutes in packing the case, the boss called him away, and Mr. Lloyd finished packing the case in four more minutes.

How many minutes would it take Mr. Russo alone to pack the case?

:

Let t = time required by Russo alone

then

(t+3) = time required by Lloyd alone

:

Let completed job = 1; (a packed case)

:

Russo + Lloyd = completed job

6%2Ft + 4%2F%28%28t%2B3%29%29 = 1

:

Multiply by t(t+3)

t(t+3)*6%2Ft + t(t+3)*4%2F%28%28t%2B3%29%29 = 1t(t+3)

:

Cancel the denominators, and you have:

6(t+3) + 4t = t^2 + 3t

6t + 18 + 4t = t^2 + 3t

10t + 18 = t^2 + 3t

:

Arrange as a quadratic equation on the right:

0 = t^2 + 3t - 10t - 18

t^2 - 7t - 18 = 0

Factors to

(t-9)(t+2) = 0

:

The positive solution is what we want here:

t = 9 minutes, time required by Russo alone

:

:

Check solution in original shared work equation (Lloyd requires 12 min)

Answer: no solution

Step-by-step explanation:

Answer:

10 × 0.5 x = 5x

10 × -2 = - 20

(5x-(-20)) = 5x + 20

-3x + 8x + 20 = 5x + 20

Answer:

144 minutes

Step-by-step explanation:

1 hr  = 60 minutes

5/12 of a fence in 60 mimnnutes

(5/12)x = 60

Multiply both sides by 12/5

x = 60 * 12/5

x = 144

144 minutes

If Archibald and Rasmus can paint the equivalent of 5/12 of a fence in an hour, then 144 minutes will take them to complete the job.

An algebraic expression stands for the combination of variables, coefficient, constant, or all three in a mathematical form where both sides are set equivalent to each other.

Let x be the minutes.

1 hr = 60 minutes

5/12 of a fence in 60 minutes

(5/12)x = 60

Multiply both sides by 12, and we get

[tex]$12 \cdot \frac{5}{12} x=60 \cdot 12$[/tex]

Simplifying the above equation, we get

5x = 720

Divide both sides by 5

[tex]$\frac{5 x}{5} = \frac{720}{5}[/tex]

Simplify

x = 144

The value of x = 144.

Therefore, 144 minutes will take them to complete the job.

To learn more about algebraic expression refer to:

https://brainly.com/question/19864285

#SPJ2

Answer:

x = 25.4

Step-by-step explanation:

Recall: SOHCAHTOA

Reference angle = 48°

Hypotenuse = x

Adjacent = 17

Apply the trigonometric function, CAH, since the Adj and Hyp are involved

Thus:

Cos 48° = Adj/Hyp

Cos 48° = 17/x

x*Cos 48° = 17

x = 17/Cos 48°

x = 25.4061013 ≈ 25.4 (nearest tenth)

Answer:

9300

Step-by-step explanation:

To find the total surface are of 150 boxes, all we have to do is multiply the surface area of one box ( 62 which was calculated on this question https://brainly.com/question/23446865 ) by the total amount of boxes (150)

So your answer = 150 * 62 which equals 9300

Answer:

Lets choose y

Plug in

Answer:

I'll choose 'x' variable first to eliminate because -

Step-by-step explanation:

Eqn.1 → -3x - 8y = -24

Eqn.2 → 3x - 5y = 45

If we'll add both the equations , then '3x' would be getting cancelled first.

⇒ [tex](-3x - 8y) + (3x - 5y) = (-24) + (45)[/tex]

⇒ [tex]3x - 3x - 8y - 5y = 45 - 24[/tex]

⇒ [tex]-13y = 21[/tex]

⇒ [tex]y = \frac{-21}{13}[/tex]

Putting the value of y in eqn.2 ,

⇒ [tex]3x - 5(\frac{-21}{13}) = 45[/tex]

⇒ [tex]3x + \frac{105}{13} = 45[/tex]

⇒ [tex]3x = 45 - \frac{105}{13}[/tex]

⇒ [tex]3x = \frac{585 - 105}{13} = \frac{480}{13}[/tex]

⇒ [tex]x = \frac{480}{13 \times 3} = \frac{480}{39}[/tex]

Reducing the fraction gives ,

⇒ [tex]x = \frac{160}{13}[/tex]

10.5  + 1.25x = 29.25

Answer:

The calculated value of t= -0.21 does not lie in the critical region t= ± 2.120 Therefore we accept our null hypothesis that there's no difference between strength (psi) of liner specimens when a certain fusion process was used and when this process was not used at the 0.05 significance level

Step-by-step explanation:

The given data is

No Fusion :: 2748 2700 2655 2822 2511 3149 3257 3213 3220 2753

Yes Fusion :: 3027 3356 3359 3297 3125 2910 2889 2902

The calculated Means are

x1`= 2902.8

X2`= 3108.125

The standard deviations are

s1= 277.265

s2= 205.87

We are using Student's t- test

We formulate null and alternate hypotheses are

H0 : u1 - u2= 0 against Ha: u1 - u 2≠0

The Significance level alpha is chosen to be ∝ = 0.05

The critical region t  ≥ t (0.025, 16) = ± 2.120

Degrees of freedom is calculated df = υ= n1+n2- 2= 10+8-2= 16

Here the difference between the sample means is x`1- x`2

=2902.8-3108.125

= -205.325

The pooled estimate for the common variance σ² is

Sp² = (n1-1) s1² + (n2-1) s2²/ n1+n2-2

=  9( 277.265)² + 7(3108.125)²/ 16

Sp² = 691,882.922+67,623,087.109/16

Sp= 2066.321

The test statistic is

t = (x`1- x` ) /. Sp √1/n1 + 1/n2

t= -205.325/ 2066.321 √1/10+ 1/8

t= -205.325/980.142

t= -0.2095= -0.21

Conclusion

The calculated value of t= -0.21 does not lie in the critical region t= ± 2.120 Therefore we accept our null hypothesis that there's no difference between strength (psi) of liner specimens when a certain fusion process was used and when this process was not used at the 0.05 significance level

Solution :

Let x be student will be left handed

P = 0.09

Using the normal approximation to binomial distribution,

a). n = 108,

    μ = np = 9.72

    [tex]$\sigma = \sqrt{np(1-p)}$[/tex]

       [tex]$=\sqrt{8.8452}$[/tex]

       = 2.9741

Required probability,

P(x=8) = P(7.5 < x < 8.5)

[tex]$=P\left(\frac{7.5-9.72}{2.9741}< \frac{x-\mu}{\sigma}< \frac{8.5-9.72}{2.9741}\right)$[/tex]

[tex]$=P(-0.75 < z < -0.41)$[/tex]

Using z table,

= P(z<-0.41)-P(z<-0.75)

= 0.3409-0.2266

= 0.1143

b). P(x=12) = P(11.5 < x < 12.5)

[tex]$=P\left(\frac{11.5-9.72}{2.9741}< \frac{x-\mu}{\sigma}< \frac{12.5-9.72}{2.9741}\right)$[/tex]

[tex]$=P(0.60 < z < 0.94)$[/tex]

Using z table,

= P(z< 0.94)-P(z< 0.60)

= 0.8294 - 0.7257

= 0.1006

Answer:

90 mm^2

Step-by-step explanation:

Divide it in 2 figures

Get the area of the one of 5 * 6 mm = 30mm^2

Then the one of 6 * 10 mm = 60 mm^2

Then just add it up. 90 mm^2

Answer:

The angles are vertical and x = 128*.

Step-by-step explanation:

x is the same angle as 128, because the angles are vertical.

Have a nice day! :-)

Answer:

36

Step-by-step explanation:

multiple by the length value by 3

Answer:

"0.9999" is the correct solution.

Step-by-step explanation:

The given values in the question are:

Mean,

= 55

Standard deviation,

= 9.1

Now,

⇒ [tex]z=\frac{X-mean}{sd}[/tex]

By putting the values, we get

⇒    [tex]=\frac{90-55}{9.1}[/tex]

⇒    [tex]=\frac{35}{9.1}[/tex]

⇒    [tex]=3.8461[/tex]

hence,

[tex]P(X<90)[/tex]

= [tex]P(Z<3.8461)[/tex]

= [tex]NORMSDIST(3.8461)[/tex]

then the value will be:

= [tex]0.9999[/tex]

Answer:

B

Step-by-step explanation:

surface area is finding the area of each portion of the net and adding them all up together. all the triangles are congruent, so we can start by finding the area of one of them and multiplying that area by 4 (since there are 4 triangles in this net). the formula for the area of a triangle is 1/2 bh. this is (1/2)(5.95)(5.1) which equals approximately 15.17. 4 multiplied by this is 60.68. the area of the square is length multiplied by width, which is 26.01. 60.68+26.01=86.69, which is the closest to answer choice B.

Answer:

i know this is not the option but i did the maths and the correct answer

the answer is 96.815 you dont have to give me brainliest tho since it was not an option but i got 96.815 anyways

Step-by-step explanation

1.  5.95*5.95= 35.4025

2. but since it is a triangle it should be devided by 2 which is 17.70125

3. since there are 4 triangles you have to multiply it by 4 which is 70.805

4. 5.1*5.1=26.01

5. 26.01+70.805= 96.815

john has $3.05 he subtracts $1.18 and is left over with $1.87

first john subtracts the 8 from the five but he cant do that so he takes from the 3 and makes it a 2 he then moves over that ten that he had taken away from the 3 and places it at the 0. Now john needs to move over the 10 on the 0 to the 5 so he can subtract the 8 from the 5. John moves one ten from the nine that had replaced the 0 and gave it to the 5. that 5 is now a 15 because you've added ten to it.  John now subtracts the 8 from the 15 to get 7 . next john subracts the 9 from the 1 in the tens place to get 8. Now john subracts the 1 from the 2 in the hundereds place to get a total sum of $1.87.

or

3.05

-1.18

---------

1.87

Answer:

Step-by-step explanation:

Let the first number = x

Let the second number = 8x

Let the third number = x + 100

x + 8x + x + 100 = 480              Combine like terms

10x + 100 = 480                        Subtract 100

      - 100    -100

10x = 380                                   Divide by 10

x = 380/10

x = 38

First number = 38

Second number = 8*38 = 304

The third number = 38 + 100 = 138

La respuesta es 15

31 - 16 = 15

Given:

The expression is:

[tex]\dfrac{-10v^5x+6v^5x^4}{2v^3x^2}[/tex]

To find:

The simplified form of the given expression.

Solution:

We have,

[tex]\dfrac{-10v^5x+6v^5x^4}{2v^3x^2}[/tex]

It can be written as:

[tex]=\dfrac{-10v^5x}{2v^3x^2}+\dfrac{6v^5x^4}{2v^3x^2}[/tex]

Cancel out the common factors.

[tex]=\dfrac{-5v^2}{x}+3v^2x^2[/tex]

Therefore, the simplified form of the given expression is [tex]\dfrac{-5v^2}{x}+3v^2x^2[/tex].

Step-by-step explanation:

sin 240° = -½√3 = -0.866

_______

Answer:

x= -1/5y+9/5

Step-by-step explanation:

5x+y=9

Step 1

First you need to add -y to both sides, basically subtracting y

5x+y-y= 9-y

Step 2

Divide both sides by 5, or multiply by 1/5. You want to do this because to cancel out 5, so you multiply the reciprocal, or divide the constant.

1/5*5x=-y+9/5

Then, you will get the answer

Hope this helps, sorry if it is wrong, I am just 4th grade :(

But I am sure this is correct :)

Answer

:A(2,2) _scale factor ½--A'(1,1)

B(4,6)_scale factor ½--B'(2,3)

C(6,2)_scale factor ½--C'(3,1)

is a required coordinate

Answer:

∠K ≅ ∠N

Step-by-step explanation:

Since you are given ΔJKL ≅ ΔMNO, you can say the corresponding angles are congruent:

∠J ≅ ∠M

∠K ≅ ∠N

∠L ≅ ∠O

So, the answer is ∠N

Answer:

x<-4

Step-by-step explanation:

x+9<5

-9 -9

x<-4

1. subtract the 9 on both sides to have x alone

Answer:

with what plz explain the question

Answer:

Height of slide = 5 feet (Approx.)

Step-by-step explanation:

Given:

Length of slide = 12 feet

Angle of depression = 25°

Find:

Height of slide

Computation:

Length of slide = Hypotenuse

Height of slide = Perpendicular

Using trigonometry function;

Sin θ = Perpendicular / Hypotenuse

Sin 25 = Height of slide / 12

0.422 = Height of slide / 12

Height of slide = 12 x 0.422

Height of slide = 5.064

Height of slide = 5 feet (Approx.)

wheres the picture

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let's solve your inequality step-by-step.

7 - s/2 > 3

Step 1: Simplify both sides of the inequality.

−1 /2 s + 7 > 3

Step 2: Subtract 7 from both sides.

−1 /2 s + 7 − 7 > 3 − 7

−1 /2 s > − 4

Step 3: Multiply both sides by 2/(-1).

( 2 /−1 ) * ( −1/ 2 s) > ( 2/ −1 )*(−4)

s<8

Answer:

s<8

Answer:

ω= 0.01 rad/s

Step-by-step explanation:

The given data is question is ,

Firstly let's find the linear speed. Which is

=> v = Circumference/time

=> v = 2πr/180s

=> v = 3.14 × 100ft ./ 90

=> v = 3.48 ft/s ≈ 1m/s

=> v = r[tex]\omega[/tex]

=> [tex]\omega[/tex] = v/r

=> [tex]\omega[/tex] = 1/100

=> [tex]\omega[/tex] = 0.01 rad/s