A cup of hot water is left out to cool. The water is currently 19°C above room temperature. If the heat difference decreases by 5% every minute, what will the difference be in 13 minutes?

Answer:

x = 25/3; y = -5/3

Step-by-step explanation:

You did well so far by multiplying both sides of the first equation by 2.

Now notice that you have -2y in the new first equation and 2y in the second equation. -2y and 2y add to 0.

Now add the equations to eliminate y.

      2x - 2y = 20

(+)   4x + 2y = 30

-------------------------

      6x         = 50

6x/6 = 50/6

x = 50/6 = 25/3

2x - 2y = 20

2(25/3) - 2y = 20

50/3 - 2y = 60/3

-2y = 60/3 - 50/3

-2y = 10/3

-2y/2 = (10/3)/(-2)

y = -5/3

Solution: x = 25/3; y = -5/3

#1

[tex]\\ \rm\Rrightarrow \dfrac{WX}{GH}=\dfrac{UY}{JI}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{8}{14}=\dfrac{UY}{28}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{8(28)}{14}=UY[/tex]

[tex]\\ \rm\Rrightarrow UY=8(2)=16[/tex]

#2

[tex]\\ \rm\Rrightarrow \dfrac{UV}{UY}=\dfrac{FJ}{JI}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{UV}{16}=\dfrac{21}{28}[/tex]

[tex]\\ \rm\Rrightarrow UV=\dfrac{3}{4}\times 16[/tex]

[tex]\\ \rm\Rrightarrow UV=3(4)=12[/tex]

#3

[tex]\\ \rm\Rrightarrow \dfrac{WX}{XY}=\dfrac{GH}{HI}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{8}{XY}=\dfrac{14}{35}=\dfrac{2}{5}[/tex]

[tex]\\ \rm\Rrightarrow 2XY=40[/tex]

[tex]\\ \rm\Rrightarrow XY=20[/tex]

Answer:

UY = 16

UV = 12

XY = 20

Step-by-step explanation:

If UVWXY ~ JFGHI

then:

UV~JF

VW~FG

WX~GH

XY~HI

UY~JI

The only pair of sides that both have measures is WX and GH:

WX = 8

GH = 14

⇒ GH/WX = 14/8 = 1.75

Therefore, JFGHI is and enlargement of UVWXY by scale factor 1.75

As IJ = 28

⇒ UY = 28 ÷ 1.75 = 16

As JF = 21

⇒ UV = 21 ÷ 1.75 = 12

As HI = 35

⇒ XY = 35 ÷ 1.75 = 20

Answer:

3.2 kilograms

Step-by-step explanation:

1 kilograms= 1000g

so 200g =0.2kg

The triangle ABC are not similar because angle E is not equal to angle B

Similar triangles have the same corresponding angle measures and proportional side lengths.

This means that similar triangles have corresponding equal angles.

And also the ratio of the corresponding sides of Similar triangles are equal.

Since angle ACB = angle DCE

angle B = 180-( 38+94)

= 180- 132

= 48°

angle D = 180-( 94+15)

= 180-109

= 71°

Therefore;

angle A is not equal to angle D and angle B is not equal to angle E, We can therefore say that triangles ABC is not similar to triangle DEC

learn more about similar triangles from

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Answer:

A = 103.5 ft²

Step-by-step explanation:

Area = 2 rectangles + 1 triangle

R: 9 x 4 = 36 ft²

R: 6 x (15-4) = 6 x 11 = 66 ft²

T: (10-9) x (11-8) ÷ 2 = (1 x 3)/2 = 3/2 ft²

A: 36 + 66 + 1.5 = 103.5 ft²

Answer:

6

Step-by-step explanation:

once you replace the letters with numbers you get, 81/9-3 and 81/9 is equal to 9 and 9-3=6

If f is a one-to-one continuous function defined on an interval, then its inverse f−1 is also one-to-one and continuous.

Answer:

50 * 30 = 1500

Answer:

Actual Product =54*31= 1,674

Estimated Product = 50*30=1,500

Step-by-step explanation:

Answer:

x = 0.75

Step-by-step explanation:

first make the x term the subject

-7 = 12x - 16

-7 + 16 = 12x

add the like terms

9 = 12x

solve for x

9÷ 12 = 12x ÷ 12

0.75 = x

Answer:

A

Step-by-step explanation:

Answer:

35 cm²

Step-by-step explanation:

This is because the formula of the area of a parallelogram is;

area = (base) x (height)

since the base is 5, and the height is 7;

area = (5) x (7)

area = 35

Hope this helps!

Answer:

Step-by-step explanation:

The formula of area of the parallelogram is used to find the area of the parallelogram.

Area of the parallelogram formula:

[tex]\Longrightarrow: \sf{A=B*H}[/tex]

B stands for "base".

H stands for "height".

Multiply.

Solve.

5*7=35

= 35cm²

I hope this helps! Let me know if you have any questions.

Answer:

The choice 4 and 6 ;

[tex]7i(7i)[/tex]

and

[tex](9 + 3i)(9 - 3i)[/tex]

Step-by-step explanation:

[tex]7i(7i) = 49 {i}^{2} = - 49[/tex]

__o_o__

[tex](9 + 3i)(9 - 3i) \\ = 81 - 27i + 27i - 9 {i}^{2} \\ = 81 + 9 \\ = 90[/tex]

Answer:

1/4.

Step-by-step explanation:

3/4 of 1/3

= 1/3 * 3/4

= 3/12

= 1/4

The answer is in the image

Answer:

Step-by-step explanation:

Answer:

slope intercept

y=6/5x+14/5

point slope=

y-4=6/5 (x-1)

therefore y-4/x-1=6/5 is the answer

Answer:

Im stuck on this one as well lol

Step-by-step explanation:

Good luck

You find out the answer for this one? I'm stuck on it

Answer:

$68

Step-by-step explanation:

Mrs. reynolds now has 68 dollars. 153-105=48. 48+20=68

Answer:

She has $68 dollars remaining

Step-by-step explanation:

(no bar diagram needed, lol jk.)

anyways she started off with 153, right?

She then buys a bike worth $105; thats -$105  which leaves here with $48 dollars

Then ooo its her lucky day, she finds a $20 dollar bill, you add it to $48 (+$20) , now she has $68 dollars in total.

<3

Corrected question :

Solve the equation. Write your answer as an integer or simplified fraction.

Required Solution :

The given equation,

★ Multiplying -7 into (n - 2),

>> 8n - 7 × (n - 2) = 18

>> 8n - 7n + 14 = 18

★ On substracting 7n from 8n we gets,

>> n + 14 = 18

★ Now transposing 14 which is in L.H.S. into R.H.S. (Remember that sign would be . So 14 would be -14),

>> n = 18 - 14

>> n = 14

★ Therefore,

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Answer:

65

-------------------------------------------------------------------------------------------------------------

Use the A.S(or add-then-subtract) method when doing 2-value and first value unknown subtraction problems;

Answer:

[tex]\frac{9}{x-3}[/tex]

Convert the problem into split up expressions.

[tex]\frac{18}{2}(x - 6)[/tex]

Take both 6 and 18's most common factor here, 2, and divide by 2 to simplify.

[tex]\frac{18}{2} = 9\\\\\frac{6}{2} = 3[/tex]

Cancel.

18 becomes 9

6 becomes 3

The equation turns into:

[tex]\frac{9}{x - 3}[/tex]

note that because we, "canceled" 2, that also means it does not appear in the simplified form since it was a factor.

The new center is 5 units away from the original, hence we added 5 to the x-value.

If you notice the sides of the new triangle are twice the size of the original one, meaning that it was dilated by a scale factor of 2.

Answer:

$15.6

Step-by-step explanation:

Based on the given information, it is $15.6. However, it never specified how many hours she works a day and how many days of the week she works, so we must assume it is just 624/40.

Answer:

minimum amount Tamara needs to earn per hour = 15.6.

Step-by-step explanation:

40 × x = 624

x = 624/40 = 156/10 = $15.6 per hour.

please give me brainliest .:-)

Using the unit circle, it is found that the terminal point of the angle 5pi/4 is given by:

A. [tex]\left(-\frac{\sqrt{2}}{2}, -\frac{\sqrt{2}}{2}\right)[/tex]

For an angle [tex]\theta[/tex] the unit circle is a circle with radius 1 containing the following set of points: [tex](\cos{\theta}, \sin{\theta})[/tex].

The angle 5pi/4 is in the third quadrant, as it is greater than pi and less than 1.5pi, in which both the sine and the cosine are negative. Hence, considering the reference angle, we have that:

[tex](\cos{(\left(\frac{5\pi}{4}\right)}, \sin{(\left(\frac{5\pi}{4}\right)}) = (-\cos{(\left(\frac{\pi}{4}\right)}, -\sin{(\left(\frac{\pi}{4}\right)}) = \left(-\frac{\sqrt{2}}{2}, -\frac{\sqrt{2}}{2}\right)[/tex]

Hence option A is correct.

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Answer:

B. seconds

Step-by-step explanation:

We have d=rt

means that t= [tex]\frac{d}{r}[/tex]

Given the units of each:

d: feet

r: feet/second

Replace each with its unit:

 t=    [tex]\frac{feet}{\frac{feet}{second} }[/tex]   =  [tex]\frac{feet.second}{feet}[/tex]  = second

So the unit of t is seconds (option B.)

Answer:

Step-by-step explanation:

Given

To Find :

Solving :

Answer:

6/8

Step-by-step explanation:

Multiply both the denominator and numerator by 2.