q=mc(T₂-T₁)
Solve for T₂

Answer:

1. Given.

2. Alternate Interior Angles Theorem.

3. m<2 + m<7 = 180 by definition of supplementary angles. By definition of congruent angles, m<2 = m<4 and m<5 = m<7, therefore m<4 + m<5 = 180 by substitution property of equality. By definition of supplementary angles, <4 is supplementary to <5.

4. Converse of Consecutive Angles Theorem.

Answer:

  (c)  2

Step-by-step explanation:

The dilation scale factor multiplies the distance from the center of dilation.

We are given that QA = 1.25, and that AA' = 1.25. By the segment sum theorem, we have ...

  QA' = QA +AA'

  QA' = 1.25 +1.25 = 2.50

The scale factor multiplies the original distance:

  QA' = k·QA . . . . . . . . . . where k is the dilation scale factor

  2.50 = k·1.25 . . . . . . . . using the known lengths

  2.50/1.25 = k = 2 . . . . divide by the coefficient of k

The scale factor is 2.

The shortest side is 130 feet, the longest side is 260 feet and the greatest possible area is 33800 square feet

The given parameter is

Perimeter, P = 520 feet

Represent the shorter side with x and the longer side with y

One side of the garden is bordered by a river:

So the perimeter is:

P = 2x + y

Substitute P = 520

2x + y = 520

Make y the subject

y = 520 - 2x

The area is

A = xy

Substitute y = 520 - 2x in A = xy

A = x(520 - 2x)

Expand

A = 520x - 2x^2

Differentiate

A' = 520 - 4x

Set to 0

520 - 4x = 0

Rewrite as:

4x= 520

Divide by 4

x= 130

Substitute x= 130 in y = 520 - 2x

y = 520 - 2 *130

Evaluate

y = 260

The area is then calculated as:

A = xy

This gives

A = 130 * 260

Evaluate

A = 33800

Hence, the shortest side is 130 feet, the longest side is 260 feet and the greatest possible area is 33800 square feet

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Answer:

1/64

Step-by-step explanation:

10 = ½

20 = ¼

30 = ⅛

40 = 1/16

50 = 1/32

60 = 1/64

Answer:

0.015625 left.

Step-by-step explanation:

If we start with say 100g of the material, in 10 years there is 100 * 1/2 =

50g left   ( = 0.5 left).

In 20 years there is 100*(1/2)^2 = 25 g  left.

In n*10 years there is  100(1/2)^2 g

So in 60 years there is 100(1/2)^6 = 1.5625 g left

This is 1.5625 %

= 0.015625 of the origin material left.

Answer:

Below in bold.

Step-by-step explanation:

a) 0.04, 0.1, 0.16

You  add 0.06 to get the next term:

The next 2 are: 0.22, 0.28.

b) 3, 9, 27

You multiply by 3 to get next term

Next 2 are: 81, 243.

c)  0.3, 1/3, 11/30

1/3 - 0.3 = 1/30

11/30 - 1/3 = 1/30

So common difference = 1/30

The next 2 terms are 12/30 and 13/30

= 2/5 , 13/30.

Answer:

[tex]3^{3}[/tex]

Step-by-step explanation:

Note: When you divide exponents with the same constant, the exponent will be subtracted, and vice-versa, when you multiply exponents with the same constant, the exponents will be added.

[tex]\frac{3^{-9} }{3^{-12} } \\= 3^{-9-(-12)} \\=3^{-9+12} \\=3^{3}[/tex]

The factors of the trinomial are:

Options C and E

This is further explained below.

Generally, A trinomial is a kind of polynomial that is used in basic mathematics. It is composed of three components, also known as monomials.

In conclusion, The following expressions are the components of the trinomial: x - 7, x + 2

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Answer:

Below in bold.

Step-by-step explanation:

9t^2 - u^2     (the difference of 2 squares)

= (3t - u) (3t + u).

2c - 4d - pc + 2pd

= 2(c - 2d) - p(c - 2d)

c -2d is common to both parts so the factors are:

(2 - p)(c - 2d)

The capital borrowed, or the principal when the interest was Q468.75 is Q7500.

The principal P, amount borrowed, at a certain rate of interest R%, for  a time of T years, giving an interest of I, can be calculated using the formula:

P = (I * 100)/(R * T).

In the question, we are asked to find the capital borrowed, that is, the principal, when the user pays Q468.75 after 15 months at 5% of income.

Thus, Interest (I) = Q468.75, rate of interest (R) = 5%, and time (T) = 15 months = 15/12 years = 1.25 years.

Thus, the principal P, can be calculated by substituting the values in the formula: P = (I * 100)/(R * T).

P = (468.75*100)/(5*1.25),

or, P = 46875/6.25,

or, P = 7500.

Thus, the capital borrowed, or the principal when the interest was Q468.75 is Q7500.

The provided question is in Spanish. The question in English is:

"After 15 months of having borrowed capital at 5% of income, I have to pay Q468.75 in interest. What capital has been borrowed?"

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Answer:

Step-by-step explanation:

Answer: 16.8°C

[tex]1+\frac{1}{6}+\frac{1}{11}+\cdots=\sum^{\infty}_{n=1} \frac{1}{5n-4} \\ \\ \frac{1}{4}+\frac{1}{9}+\cdots=\sum^{\infty}_{n=1} \frac{1}{5n-1} \\ \\ S=\sum^{\infty}_{n=1} \left(\frac{1}{5n-4} -\frac{1}{5n-1} \right) \\ \\ =\frac{\pi}{5} \sqrt{\frac{1}{5} (5+2\sqrt{5})}[/tex]

Answer:

35.56

Step-by-step explanation:

Answer:

3 cans

Step-by-step explanation:

A = lw

a = 20 x 8 = 160[tex]ft^{2}[/tex]

a = 40 x 8 = 320 [tex]ft^{2}[/tex]

Together this is 480 [tex]ft^{2}[/tex]

I would need 3 cans.

Answer:(a) 50% (b)5%

Step-by-step explanation:

For a, it's not really difficult  because the price of a jacket is 1/2 more than jeans. So it's 50%.

For b, it's similar to no. (a) because the price of the jean is 1/2 less than a jacket. So u need to divide 250 by 500 and u will get 0.5 so if u want to put in % u need to multiply with 10, so u will get 5%.

Answer:

  j = 19.6

  k = 25.9

  J = 49°

Step-by-step explanation:

The mnemonic SOH CAH TOA is intended to remind you of the relationships between sides and angles in a right triangle.

The given side is opposite the given angle. We want to find the other acute angle and the missing sides: the hypotenuse, and the adjacent side. The relations involving the opposite side are ...

  Sin = Opposite/Hypotenuse   ⇒   Hypotenuse = Opposite/Sin

  Tan = Opposite/Adjacent   ⇒   Adjacent = Opposite/Tan

Of course, the acute angles in a right triangle are complementary, so we can use that fact to find the missing angle.

  Hypotenuse = Opposite/Sin

  IJ = 17/sin(41°) ≈ 25.9

  Adjacent = Opposite/Tan

 IK = 17/tan(41°) ≈ 19.6

  Angle J = 90° -41° = 49°

In summary, ...

  j = 19.6

  k = 25.9

  J = 49°

Answer:

m = F / a is the answer

Step-by-step explanation:

F = ma

m = F / a

Answer:

x=1.08 (3SF)

Step-by-step explanation:

hope it helps!!!!

If the function is [tex](x-3)^{-2}[/tex] and  f(4) − f(1) = f '(c)(4 − 1) then there is not any answer.

Given function is [tex](x-3)^{-2}[/tex] and  f(4) − f(1) = f '(c)(4 − 1).

In this question we have to apply the mean value theorem, which says that given a secant line between points A and B, there is at least a point C that belongs to the curve and the derivative of that curve exists.

We begin by calculating f(2) and f(5):

f(2)=[tex](2-3)^{-2}[/tex]

f(2)=1

f(5)=[tex](5-3)^{-2}[/tex]

f(5)=1

And the slope of the function:

[tex]f^{1}[/tex](x)=[tex]f(5)-f(2)/(5-2)[/tex]

[tex]f^{1}[/tex](c)=0

Now,

[tex]f^{1} (x)=-2*(x-3)^{-3}[/tex]

=-2[tex](x-3)^{-3}[/tex]

=0

-2 is not equal to 0. So there is not any answer.

Hence if the function is [tex](x-3)^{-2}[/tex] and  f(4) − f(1) = f '(c)(4 − 1) then there is not any answer.

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Answer:

1. Given.

2. Reflexive Property of Congruence.

3. Alternate Interior Angles Theorem.

4. SAS

5. <4 ~= <2

6. Converse of Alternate Interior Angles Theorem.

ANSWER: 22.5 and 67.5

let, one angle be x then the another one is 3×(90-x)

x = 270 - 3x

x + 3x = 270

4x = 270

x = 270/4

x = 67.5 (first angle)

then, another angle = 90- 67.5 = 22.5

Answer: [tex]\Large\boxed{Total~area=586.17~cm^2}[/tex]

Step-by-step explanation:

Given information

[tex]Height=7~cm[/tex]

[tex]Base=18~cm[/tex]

Given formula

[tex]A=b\times h\times\dfrac{1}{2}[/tex]

[tex]A=Area\\b=base\\h=height\\[/tex]

Substitute values into the formula

[tex]A=(7)\times (18)\times\dfrac{1}{2}[/tex]

Simplify by multiplication

[tex]A=(7)\times 9[/tex]

[tex]A=63~cm^2[/tex]

Given information

[tex]Height = 18~cm[/tex]

[tex]Base=22~cm[/tex]

Given formula

[tex]A=b\times h[/tex]

[tex]A=Area\\b=base\\h=height\\[/tex]

Substitute values into the formula

[tex]A=(22)\times (18)[/tex]

Simplify by multiplication

[tex]A=396~cm^2[/tex]

Given information

Diameter = 18 cm

Given formula

[tex]A=(\dfrac{d}{2} )^2\times \pi \div2[/tex]

[tex]A=Area\\d=diameter[/tex]

Substitute values into the formula

[tex]A=(\dfrac{18}{2} )^2\times (3.14) \div2[/tex]

Simplify the fraction

[tex]A=(9 )^2\times (3.14) \div2[/tex]

Simplify the exponents

[tex]A=81\times (3.14) \div2[/tex]

Simplify by multiplication

[tex]A=254.34\div2[/tex]

Simplify by division

[tex]A=127.17~cm^2[/tex]

Given formula

[tex]Total~area=Triangle+Rectangle+circle~(half)[/tex]

Substitute values into the formula

[tex]Total~area=(63)+(396)+(127.17)[/tex]

Simplify by addition

[tex]Total~area=459+(127.17)[/tex]

[tex]\Large\boxed{Total~area=586.17~cm^2}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

The regression equation of this group of data is given as ŷ = 0.0108X - 1.98123.

ŷ = 0.0108X - 1.98123

x = 610

= 0.0108*610 - 1.98123

=  4.61 million dollars

2. the minimum number of theaters that would generate at least 7.65 million dollars in gross earnings in one week.

7.65= 0.0108x-1.98123

take like terms

x = 892

2. correlation coefficient of X and Y is r = -0.987

This shows a negative relationship

b)Linear Regression Equation =

Y = 313309 - 34740x

c) Y = 313309 - 34740x

Y = 313309 - 34740 * 3

209089

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The rate of  VAT is 10%.

In the question, we are asked to find the VAT rate, given that the market price of an article is Rs. 10000, the rate of discount and the rate of VAT are equal, and the price after VAT is Rs. 9900.

We assume the rate of discount and the rate of VAT to be r%.

Thus, discount = r% of Rs. 10000 = Rs. r/100 * 10000 = Rs. 100r.

Thus, the price after discount = Rs. 10000 - 100r = Rs. 100(100 - r)

Then, VAT = r% of (Rs. 100(100 - r)) = Rs. r/100 * 100(100 - r) = Rs. r(100 - r).

Thus, the price after VAT = Rs. 100(100 - r) + Rs. r(100 - r) = Rs. (100 + r)(100 - r).

The price after VAT is given to be Rs. 9900.

Thus, (100 + r)(100 - r) = 9900,

or, 100² - r² = 9900,

or, r² = 100² - 9900,

or, r² = 10000 - 9900 = 100,

or, r = ±√100 = ±10.

Since r is the rate of VAT, it cannot be negative, making r = 10.

Thus, the rate of  VAT is 10%.

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For sp3d hybridized central atoms, the only possible molecular geometry is trigonal bipyramidal.

Hybridisation (or hybridization) is a process of mathematically combining two or more atomic orbitals from the same atom to form an entirely new orbital different from its components and hence being called as a hybrid orbital.

In this case, if all the bonds are in place, the shape is also trigonal bipyramidal.

In chemistry, a trigonal bipyramid formation is a molecular geometry with one atom at the center and 5 more atoms at the corners of a triangular bipyramid.

Bond angle(s): 90°, 120°

Coordination number: 5

Point group: D3h

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The mass of the regular hippo at birth to that of the pygmy hippo is 49/11

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value while a dependent variable is a variable that depends on other variable.

The pygmy hippo had a mass of 5 1/2 kg at birth = 5.5 kg.

The regular hippo had a mass of 24 1/2 kg at birth = 24.5 kg

Hence:

Ratio of regular hippo to pygmy hippo = 24.5 / 5.5 = 49/11

The mass of the regular hippo at birth to that of the pygmy hippo is 49/11

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Answer:

49/11 or 4 5/11

Step-by-step explanation:

just did it on khan Academy.

Answer:

C

Step-by-step explanation:

Express functions as a ratio: put one in the numerator and the other in the denominator

[tex]\frac{12- \frac{2}{3}t}{3-\frac{1}{8}t }[/tex]

We want to get rid of the fractions which would mean multiplying top and bottom by 3 and 8. (Remember to multiply both terms). The answer would result in C.

The given expression (8h + 2w - 5h + 3w) can fully be simplified as 3h + 5w.

An expression can be defined as a type of mathematical equation which is used to show the relationship that is existing between two or more variables and numerical quantities (integers).

In this exercise, you're required to fully simplify the given expression in the lowest terms. Thus, we would simplify the given expression completely by collecting like terms and performing the necessary arithmetic operations (addition and subtraction) as follows:

Collecting like terms, we have:

8h - 5h + 3w + 2w

Subtracting and adding the like terms respectively, we have:

3h + 5w.

In conclusion, we can logically deduce that the given expression (8h + 2w - 5h + 3w) can fully be simplified as 3h + 5w.

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Complete Question:

Fully simplify 8h + 2w - 5h + 3w.

Answer:

The answer is option A SAS.We have a side,an angle and the last side.If this helps please mark me BRAINLIEST

The amount of heat (in KJ) released when 3.5 moles of CH₄ react is 3115 KJ

CH₄ + 2O₂ -> CO₂ + 2H₂O ΔH = 890 KJ

From the balanced equation above,

1 mole of CH₄ reacted to release 890 KJ of heat energy.

From the balanced equation above,

1 mole of CH₄ reacted to release 890 KJ of heat energy

Therefore,

3.5 moles of CH₄ will react ro release = 3.5 × 890 = 3115 KJ of heat energy

Thus, 3115 KJ of heat energy were released from the reaction

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