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2 years ago

Solve for x. The triangles are similar.

Mathematics

2 answers:

erica [24]2 years ago

6 0

Answer:

D. 10

Step-by-step explanation:

We can use similar triangles to solve this question. ΔRSE ≅ ΔFGE by SAS. We can set up this similarity equations: $\frac{SE}{GE} = \frac{RE}{FE}$ . Plugging in the numbers from the diagram, we get $\frac{45}{12x-3} = \frac{55}{143}$ . Using cross multiplication, we get the following equation:

$45 * 143 = 55 *(12x-3)\\ 6435 = 660x - 165\\6600 = 660x\\x = 10$

Our final answer is D. 10

Serjik [45]2 years ago

5 0

Answer:

$\fbox {D. 10}$

Step-by-step explanation:

As the triangles are similar :

45/55 = (12x - 3)/143

9/11 = (12x - 3)/143

9 x 13 = 12x - 3

12x = 117 + 3

12x = 120

x = 10

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Find the volume and surface area of a sphere with radius 1 yards. Round your answer to two decimal places.

olga55 [171]

Answer:

Volume of the sphere up to two decimal places= $4.19$ cubic yards

Surface area of the sphere up to two decimal places $=12.56$ square yards

Step-by-step explanation:

Given:

The radius of the sphere= 1 yard

Volume of a Sphere:

$\frac{4}{3}* \pi *r^3$ : $\pi =\frac{22}{7} =3.14$

$=\frac{4}{3}*3.14*1*1*1$

$=4.187$ cubic yards

Volume of the sphere up to two decimal places= $4.19$ cubic yards

Surface area of the sphere= $4*\pi* r^2$

$=4*3.14*1*1$

Surface area of the sphere up to two decimal places $=12.56$ square yards

8 0

3 years ago

What are two numbers that has the product of 40 but has the sum of 13

Maksim231197 [3]

Answer:

8 and 5

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

An exterior angle of a triangle is 140 degrees. If the non-adjacent angles are congruent, then what are the measures of all of t

trasher [3.6K]

The measures of all of the interior angles of the triangle are 70 degrees, 70 degrees and 40 degrees

<em><u>Solution:</u></em>

Given that exterior angle of triangle is 140 degrees

The exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles

Given that adjacent angles are congruent

Let one of the non adjacent interior angles be "x"

x + x = 140

2x = 140

x = 70

So the two interior angles are 70 degrees and 70 degrees

Let us find the third interior angle

The angle sum property of a triangle states that the interior angles of a triangle always add up to 180 degrees

70 + 70 + third angle = 180

third angle = 180 - 70 - 70

third angle = 180 - 140

third angle = 40 degrees

Thus the measures of all of the interior angles of the triangle are 70 degrees, 70 degrees and 40 degrees

3 0

3 years ago

A tank initially contains 60 gallons of brine, with 30 pounds of salt in solution. Pure water runs into the tank at 3 gallons pe

adoni [48]

Answer:

the amount of time until 23 pounds of salt remain in the tank is 0.088 minutes.

Step-by-step explanation:

The variation of the concentration of salt can be expressed as:

$\frac{dC}{dt}=Ci*Qi-Co*Qo$

being

C1: the concentration of salt in the inflow

Qi: the flow entering the tank

C2: the concentration leaving the tank (the same concentration that is in every part of the tank at that moment)

Qo: the flow going out of the tank.

With no salt in the inflow (C1=0), the equation can be reduced to

$\frac{dC}{dt}=-Co*Qo$

Rearranging the equation, it becomes

$\frac{dC}{C}=-Qo*dt$

Integrating both sides

$\int\frac{dC}{C}=\int-Qo*dt\\ln(\abs{C})+x1=-Qo*t+x2\\ln(\abs{C})=-Qo*t+x\\C=exp^{-Qo*t+x}$

It is known that the concentration at t=0 is 30 pounds in 60 gallons, so C(0) is 0.5 pounds/gallon.

$C(0)=exp^{-Qo*0+x}=0.5\\exp^{x} =0.5\\x=ln(0.5)=-0.693\\$

The final equation for the concentration of salt at any given time is

$C=exp^{-3*t-0.693}$

To answer how long it will be until there are 23 pounds of salt in the tank, we can use the last equation:

$C=exp^{-3*t-0.693}\\(23/60)=exp^{-3*t-0.693}\\ln(23/60)=-3*t-0.693\\t=-\frac{ln(23/60)+0.693}{3}=-\frac{-0.959+0.693}{3}= -\frac{-0.266}{3}=0.088$

5 0

3 years ago

Which number is greater and by how much?

Lana71 [14]

Answer:

Step-by-step explanation:

first option, as the decrease percentage is applicated on a greater number than the original

e.g.

a= 10

10 + 50% = 15

15 - 50% = 7,5

A will be greater then B by 25%

4 0

2 years ago