In a parallelogram ABCD point K belongs to diagonal BD so that BK:DK=1:4. If the extension of AK meets BC at point E, what is the ratio of BE:EC?

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:

C. 75°

The sum of the three angles is 180°, as it is for the angles in any triangle.

35° + 70° + x° = 180° . . . . an equation expressing the relationship of the angles

x° = 180° -35° -70° . . . . . subtract 35° and 70°

x° = 75°

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:

-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

Answer:

[tex]\ast=16a^2[/tex]

Step-by-step explanation:

Use formula for  a square of a sum:

[tex](x+y)^2=x^2+2xy+y^2.[/tex]

Note that

Then instead of * should be the square of the term 4a that is [tex](4a)^2=16a^2.[/tex]

Then

[tex]16a^2+56a+49=(4a+7)^2.[/tex]

To complete the pattern in the expression ∗ +56a+49 to make it a square of a sum or a difference, we can use the formula for (a+b)² as a guide. If 49 is b² and 56a is 2ab, the missing part would be a². On solving, we find that the value of a² is 16a².

The subject of this question is finding a monomial such that the given expression can be rewritten as a square of a sum or a difference. The expression is ∗ +56a+49. We can think of the square of a sum or a difference as the result of the formula (a+b)² = a² + 2ab + b² which gives a hint that we can structure our expression in a similar way.

Let's rearrange the given expression a bit using this hint. If we look at 49, it is equal to 7². This could be our b². Additionally, 56a can be written as 2*7*a or 2ab. So the missing part would be a² which completes the pattern of the formula.

To find the value of a², we need to know the value of a. Here's where 56a comes into play. It is 2ab (or in this case, 2*7*a). Solving this equation for a, we get a=4. So, a²=16. Therefore, the monomial that completes the pattern in the expression is 16a².

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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:

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:

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%.

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.

There is an infinite number of numbers between 1 and 1.01 on the number line. The correct answer should theoretically be: 1 < n < 1.01.

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

_____

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."

Answer:

Add 78 to 54 to get 132 total patrons, then divide the number of females into the total number of patrons. Therefore, 78/132 = .5909 = 59%

Step-by-step explanation:

Answer:

Thats simple!

Step-by-step explanation:

G.o.o.g.l.e.

(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

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

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:

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]

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.

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

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:

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

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:

0.471

Step-by-step explanation:

The mnemoic SOH CAH TOA reminds you that ...

... Sin = Opposite/Hypotenuse

... sin(S) = 32/68 ≈ 0.471

∠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:

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

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:

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.