Given the following figure, what is the measure of angle B?

Let x represent the number of adults who swam at the pool. Then (262-x) is the number of children. Multiplying these numbers by the corresponding admission charge will give the associated receipts. We are given the total of receipts, so we can write the equation ...

... 2.00x +1.50(262-x) = 470.00

... 0.50x +393.00 = 470.00 . . . . . simplify

... 0.50x = 77.00 . . . . . . . . . . . . . . .subtract 393

... 77.00/0.50 = x = 154 . . . . . . . . . divide by the coefficient of x

... (262-x) = 108 . . . . . . . . . . . . . . . .find the number of children admitted

Answer:

x ≈ 0, x ≈ 2.5

Step-by-step explanation:

The left point of intersection is very near the y-axis, where x=0.

The right point of intersection is somewhat below the midpoint between x=2 and x=4. It seems to be just about at the midpoint between that midpoint (x=3) and the line at x=2. We estimate the value at about x=2.5.

_____

If we knew the actual function definitions, we could solve for the points of intersection.

Answer:

When dealing with VOLUME, an increase in a linear quantity, produces a third power result in the volume.

Increase the sides of a cube by 2 produces an 8 times effect in the volume.

Increasing each side of a cube by 4 produces a chnage of 4 * 4 * 4 or

64 times in the volume.

Step-by-step explanation:

Increasing the length of each side of a cube by a factor of 4 results in the volume increasing by a factor of 64, since volume is proportional to the cube of the linear dimensions.

When the length of each side of a cube is increased by a factor of 4, the effect on the volume of the cube is that it increases by a factor of [tex]4^3[/tex], or 64. This is because volume is a three-dimensional measure, and when each dimension (length, width, height) of a cube is multiplied by a factor, the volume is multiplied by the factor raised to the third power (since volume is calculated by length  *width * height).

Therefore, if the original length of one side of the cube is L, the original volume is L3. After increasing each side by a factor of 4, the new length becomes 4L, making the new volume [tex](4L)^3 = 4^3 \times L^3 = 64L^3[/tex]. Hence, the new volume is 64 times the original volume, not simply 4 times because the increase happens in each of the three dimensions.

Answer:

4x-2=0

5x-3=0

Step-by-step explanation:

Answer:

Step-by-step explanation:

The question will look like (3b)/(a^-2)

To simplify, note the (a^-2). It is a negative, so flip the placement of the monomial. Note that the term is located in the decimal, so when it is flipped, it goes to the numerator (vice versa if it is opposite)

(3b)/(a^-2) = (3b)(a²)

3a²b, or (A) is your answer choice

~

Answer:

Option A) 3a2b

Step-by-step explanation:

Answer:

615

Step-by-step explanation:u make $20 a week and u worked 40 hours u jus do 40*20=$800

800-185=615 im pretty sure hope this helps

Answer:

Weekly net pay is $36790

Weekly gross pay is  $41600

Step-by-step explanation:

Net pay  is the gross pay minus taxes

Net pay = gross pay - taxes

Gross pay =  hours worked * hourly rate

Net pay = hours worked * hourly rate - taxes

We know the  

hours worked = 40

Hourly rate = 20

tax rate = 185 bi weekly  = 185/2 = 92.5 weekly

Net pay = 40 * 20 - 92.5

Net pay = 800-92.5

Net pay = 707.5

This is the weekly net pay

Assuming we work 52 weeks a year

Weekly net pay is 52* 707.5 = 36790

Weekly gross pay is  40*20 * 52 = 41600

Answer:

3/√2

Step-by-step explanation:

find the details in the attachment (this is not the shortest way).

The shortest way is: to prove ED=AB, then to calculate x=AB/√2=3/√2.

∠BDC and ∠AED are right angles

Because ∠C ≅ ∠C, the additional bit of information above can be used to show AA similarity.

____

None of the other offered choices says anything about both triangles. In order to show similarity, you need information about corresponding parts of the two triangles. Information about one triangle alone is not sufficient.

Answer:

I think it's A. ∠BDC and ∠AED are right angles

Step-by-step explanation:

I hope this helps.

Answer:

0.471

Step-by-step explanation:

The mnemoic SOH CAH TOA reminds you that ...

... Sin = Opposite/Hypotenuse

... sin(S) = 32/68 ≈ 0.471

Answer:

-9

Step-by-step explanation:

(x-2) is 3 more than (x-5), because -2 is 3 more than -5.

3 more than -12 is -9.

_____

If you like, you can solve for x.

... x -5 = -12

... x = -7 . . . . . add 5

Now find the value of x-2

... x -2 = -7 -2 = -9

12 in

If the dilation is uniform, both height and width will be multiplied by 4.

New height = (1 in) × 4 = 4 in

New width = (3 in) × 4 = 12 in

DE = 1.5 cm, EF = 2.25 cm, FD = 3 cm

Side DE corresponds to side AB and is (1.5 cm)/(2 cm) = 3/4 the length of it.

Because the triangles are similar, all pairs of corresponding sides have the same ratio. That is, the side lengths in ΔDEF are 3/4 of those in ΔABC.

... EF = (3/4)×BC = (3/4)×(3 cm)

... EF = 2.25 cm

... FD = (3/4)×CA = (3/4)×(4 cm)

... FD = 3 cm

The lengths of the sides of triangle △DEF, given that AB=2 cm, BC=3 cm, CA=4 cm, and DE=1.5 cm, would be EF = 2.25 cm and DF = 3 cm.

If triangles △ABC and △DEF are similar, then the ratio of the corresponding sides is the same. We know AB = 2 cm which corresponds to DE = 1.5 cm in the triangle △DEF. The ratio of AB to DE is 2cm:1.5cm or 4:3. Let's compute the sides of the triangle △DEF using this ratio:

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Answer:

13

Step-by-step explanation:

65=5x(because number A is four times number B therefore, it is really B five times)

Then divide both sides by 5.

13=x

To find two numbers when their sum is 65 and one number is 4 times the other, the smaller number is 13, and the larger number is 52.

number, and 4x be the larger number.

Write an equation: x + 4x = 65.

Solve the equation: 5x = 65, x = 13.

The smaller number is 13, and the larger number is 4 times 13, which is 52.

Answer:

The solution for u is:

[tex]u = \frac{mpq}{q+p}[/tex]

Step-by-step explanation:

The first step to solve this problem is finding the least common multiplicator between p and q, that is pq, so:

[tex]\frac{u}{p} + \frac{u}{q} = m[/tex]

[tex]\frac{uq + up}{pq} = m[/tex]

[tex]uq + up = mpq[/tex]

[tex]u(q + p) = mpq[/tex]

[tex]u = \frac{mpq}{q+p}[/tex]

The required solution of the given equation for u is equal to

(m(p × q)) / (q + p).

Given that:

Equation: u/p + u/q = m, if p ≠ -q

To solve for u in the equation u/p + u/q = m, use the method of finding a common denominator and simplifying the expression.

First, need to find a common denominator for the fractions u/p and u/q. The common denominator in this case would be (p × q).

Multiplying the equation by (p × q) to get,

u(q) + u(p) = m(p × q)

Next, combine the terms with u as:

u × q + u × p = m(p × q)

Now, factor out u as:

u(q + p) = m(p × q)

To solve for u, divide both sides of the equation by (q + p):

u = (m(p × q)) / (q + p)

Therefore, the solution for u is u = (m(p × q)) / (q + p).

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Answer:

40

Step-by-step explanation:

36 = 90% × (number of questions)

36/0.90 = (number of questions) = 40 . . . . . divide by the coefficient of the variable

There were 40 questions on the test.

Answer:

5400 mi²

Step-by-step explanation:

The area is half the absolute value of the sum of the determinants of the points taken pairwise in some consistent order around the polygon. For a triangle, this sum of determinants can also be written as the determinant of a 3×3 matrix of the coordinates with the third column being 1.

... Area = (1/2)|D|

where D = ...

[tex]\left|\begin{array}{ccc}0&-1&1\\-3&-9&1\\3&-2&1\end{array}\right|=\left|\begin{array}{cc}0&-1\\-3&-9\end{array}\right|+\left|\begin{array}{cc}-3&-9\\3&-2\end{array}\right|+\left|\begin{array}{cc}3&-2\\0&-1\end{array}\right|\\\\=-3+33-3=27[/tex]

Then the area is (in grid squares) ...

... Area = (1/2)|27| = 13.5 . . . . grid squares

Each grid square is (20 mi)² = 400 mi², so 13.5 grid squares is ...

... 13.5 × 400 mi² = 5400 mi²

Answer:

36

Step-by-step explanation:

The length of 1 1/2 units is equivalent to 3/2 = 6/4 = 6×(1/4) = 6 cubes.

The width of 1/2 units is equivalent to 2/4 = 2×(1/4) = 2 cubes.

The height of 3/4 units is equivalent to 3×(1/4) = 3 cubes.

Then, in terms of cubes, the dimensions are 6 × 2 × 3. The volume is the product of these dimensions, so is ...

... 6 × 2 × 3 = 36 . . . . cubes

Answer:

Step-by-step explanation:

Answer:

120 cm^3

Step-by-step explanation:

The surface areas are in the ratio 60 to 135  so the single dimensions are in the ratio √60 to √135.

Therefore the volumes are in the ratio (√60)^3 to  (√135)^3  or 60^3/2 to  135^3/2.

So  Volume of  Pyramid B / Volume of Pyramid A

= 60^3/2 / 135^3/2.

Therefore we have the equation  60^3/2 / 135^3/2 =  V / 405  where V is the volume of pyramid B.

V = (60^3/2 * 405) / 135^3/2

=  120  cm^3

Answer:

120cm³

Step-by-step explanation:

√135/√60=3/2

3/2=1.5

1.5³=3.375

405/3.375=120

120cm³

Scientific notation has exactly one non-zero digit to the left of the decimal point in the mantissa. The numbers listed above do not.

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Comment on these numbers

There may be good reasons for writing the numbers in this form. For example, in engineering, it is often useful to have the exponent be a multiple of 3. In other instances, writing the number in these forms may facilitate arithmetic. However good the reasons may be, these numbers are not in in the form defined as "scientific notation."

(2π-5) radians ≈ 1.2831853 radians

The reference angle is the magnitude of the acute angle made with the x-axis. The value of θ is greater than 3π/2, so the reference angle is ...

... θ' = abs(θ -2π) = 2π-5 . . . . radians

We know that :

✿  [tex]\mathsf{Cos\theta = \frac{Adjacent\;Side}{Hypotenuse}}[/tex]

✿  [tex]\mathsf{Sin\theta = \frac{Opposite\;Side}{Hypotenuse}}[/tex]

✿  [tex]\mathsf{Tan\theta = \frac{Opposite\;Side}{Adjacent\;Side}}[/tex]

From the Figure :

✿  [tex]\mathsf{Cosx = \frac{4}{5}}[/tex]

✿  [tex]\mathsf{Sinx = \frac{3}{5}}[/tex]

✿  [tex]\mathsf{Tanx = \frac{3}{4}}[/tex]

Only 1st Statement is True

1st Option is the Answer

Answer:

Step-by-step explanation:

a) p(1) = 1³ -3·1² +2·1 -1 = 1 -3 +2 -1 = -1 . . . . not zero

b) Dividing p(x) by x-1 gives x² -2x +0 with a remainder of -1 (as found in part (a)). So the function can be written as ...

... p(x) = (x -1)(x² -2x +0) -1

_____

Polynomial division can be done using synthetic division or long division. The latter can be done by hand or by using any of several on-line calculators. Attached is output from one of them.

Answer:

x = 100

Step-by-step explanation:

Answer:

the solutions are x = -100,100

Step-by-step explanation:

The given logarithmic equation is [tex]\log x^2 +1=5[/tex]

Subtract 1 to both sides

[tex]\log x^2=4[/tex]

Remove logarithm, we get

[tex]x^2=10^4[/tex]

Take square root both sides

[tex]\sqrt{x^2}=\pm\sqrt{10^4}\\\\x=\pm10^2\\\\x=\pm100[/tex]

Therefore, the solutions are x = -100,100

System

Solution

(a) Generally, the equations of interest are one that models the total amount of mixture, and one that models the amount of one of the constituents (or the ratio of constituents). Here, there are two constituents and we are given the desired ratio, so three different equations are possible describing the constituents of the mix.

For the total amount of mix:

... p + m = 10

For the quantity of peanuts in the mix:

... p + 0.2m = 0.6·10

For the quantity of almonds in the mix:

... 0.8m = 0.4·10

For the ratio of peanuts to almonds:

... (p +0.2m)/(0.8m) = 0.60/0.40

Any two (2) of these four (4) equations will serve as a system of equations that can be used to solve for the desired quantities. I like the third one because it is a "one-step" equation.

So, your system of equations could be ...

___

(b) Dividing the second equation by 0.8 gives

... m = 5

Using the first equation to find p, we have ...

... p + 5 = 10

... p = 5

5 lb of peanuts and 5 lb of mixture are required.

2x + 10 can be simplified using the distributive property by factoring a 2 out of each term.

2(x + 5)

2(3x + 5) can be solved by applying the distributive property, by multiplying each term inside the parentheses by 2.

6x + 10

Answer:

The unit rate is [tex]\frac{2}{5}[/tex] km per minute. It means sarah bikes [tex]\frac{2}{5}[/tex] km in 1 minute or the speed of sarah is [tex]\frac{2}{5}[/tex] km per minute.

Step-by-step explanation:

It is given that Sarah bikes [tex]\frac{4}{5}[/tex] km in 2 min. It means Sarah covers [tex]\frac{4}{5}[/tex] km in 2 min.

The units rate is defined as

[tex]\text{Unit rate}=\frac{\text{Distance covered}}{\text{Time Taken}}[/tex]

[tex]\text{Unit rate}=\frac{(\frac{4}{5})}{2}[/tex]

[tex]\text{Unit rate}=\frac{4}{5}\times \frac{1}{2}[/tex]

[tex]\text{Unit rate}=\frac{2}{5}[/tex]

Therefore the unit rate is [tex]\frac{2}{5}[/tex] km per minute. It means sarah bikes [tex]\frac{2}{5}[/tex] km in 1 minute or the speed of sarah is [tex]\frac{2}{5}[/tex] km per minute.

400%

Suppose sales in 1994 were 100 of some unit. Then in 1995, they were ...

... 100 - 80% × 100 = 100 × (1 - 0.80) = 100 × 0.20 = 20 . . . . units

Then the percent increase to sales of 100 units in 1996 can be found from ...

... percent change = ((new value) - (old value))/(old value) × 100%

... = (100 -20)/20 × 100%

... = 80/20 × 100%

... = 400%

The increase from 1995 to 1996 was 400%.

Answer:

A. x^2 = y^2/3 -2

Step-by-step explanation:

Add 3x^2 to both sides of the equation. We do this so that the coefficient of x^2 is positive. It can be less confusing that way.

... y^2 = 3x^2 +6

Divide by 3.

... y^2/3 = x^2 +2

Subtract 2.

... y^2/3 -2 = x^2 . . . . . matches selection A.

Answer:

A. x^2 = y^2/3 -2

Step-by-step explanation:

Answer:

3(t+2)

Step-by-step explanation:

As with any problem involving division of fractions, you can invert the denominator and multiply.

Your knowledge of the factoring of the difference of squares helps. If that doesn't work for you, you can always use synthetic division or polynomial long division to find the quotient of (t^2-4) and (t-2).

[tex]\displaystyle\frac{\frac{4t^2-16}{8}}{\frac{t-2}{6}}=\frac{4(t^2-4)}{8}\cdot\frac{6}{t-2}\\\\=\frac{3(t+2)(t-2)}{t-2}=3(t+2)[/tex]