4x+10=32
B.How are the solutions of the original equation and the equation in part a related? What does the term equivalent equations mean?
C.Use subtraction, multiplication, and division to form three equations equivalent to the
original equation.
D.Solve the original equation. Explain each step in finding the solution.
I rlly need help with this !!

Answer:

25.625 litros de agua por familia.

No sobrará agua.

Step-by-step explanation:

En promedio el ser humano tiene que tomar al menos 3 litros de agua al día, con esto en mente y pensando que tienes 48 familias de las cuales en promedio serían 5 personas que conforman cada familia, tendrías que son en total:

48*5=240 personas

Tienes que tener almenos 3 litros de agua para cada persona:

240*3=720

Tienes en total 1230 litros de agua, sólo para cubrir lo que las personas necesitan tomar de agua son 720, falta ver si tienen que lavar, cocinar, limpiar o bañarse, entonces con los 1230 litros conseguidos, no alcanzaría ni para dos días de sólo tomar agua.

Answer:

dang with what

Step-by-step explanation:

Answer:

Learn how to do it

Step-by-step explanation:

if you learn how to do it you won't have trouble

Answer:

\( g = \frac{2c}{q}\)

Step-by-step explanation:

\(c = \frac{1}{2} gq \\ 2c = gq \\ \huge \red{ \boxed{ g = \frac{2c}{q} }}\)

Answer:

g = 2C/q

Step-by-step explanation:

C * (2) = 1/2gq * (2)  

2C / q= gq / q

2C/q = g

Answer:

Step-by-step explanation:

To subtract the sum of a^2 - 2ab + b^2 and 2a^2 + 2ab + b^2 from the sum of a^2 - b^2 and a^2 + ab + 3b^2, you can follow these steps:

First, subtract a^2 - 2ab + b^2 and 2a^2 + 2ab + b^2 from the sum of a^2 - b^2 and a^2 + ab + 3b^2. This gives you (a^2 - b^2) + (a^2 + ab + 3b^2) - (a^2 - 2ab + b^2) - (2a^2 + 2ab + b^2).

Simplify the expression by combining like terms. This gives you 2a^2 - 3b^2 - 2ab.

Simplify the expression further by combining the remaining like terms. This gives you the final result of a^2 - 3b^2 - 2ab.

Answer:

2/9

Step-by-step explanation:

6 - 4 = 2

2 divided by 9 = 2/9

Answer:

5

Step-by-step explanation:

The number is x

3x - 3 = 12

3x = 15

x = 5

Answer: 2.214285714, probably B maybe? I'm not sure what D is.

Step-by-step explanation: (14)x + 1 = 32.

Your goal here is to get the x by itself so that you will know how much it is worth.

First step I would take is to subtract 1 from both sides to get rid of the one on the side with the x. What you do on one side is what you must do on the other side.

Now you have (14)x = 31

Next step I would take is divide both sides by 14 so that you can finally get the x by itself.

Now you have 2.214285714, so I would choose whatever answer that is closest to.

Answer:

8 miles

Step-by-step explanation:

Answer:

8 miles

Step-by-step explanation:

1 mile:63360 inches

506880 divided by 63360 = 8

The expression in the options which is equivalent to the given expression is D. (22x + 48) / (x² - 36).

Given expression is,

[15 / (x - 6)] + [7 / (x + 6)]

Cross multiplying the two fractional expressions,

= [15 (x + 6) + 7 (x - 6)] / [(x - 6) (x + 6)]

= [15x + 90 + 7x - 42] / [x² - 6²]

= (22x + 48) / (x² - 36)

Hence the equivalent expression is D.

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Answer:

Any real number could be true for this equation.

Answer:

\(2304\)\(\pi\)

Step-by-step explanation:

V = \(\frac{4}{3} \pi r^{3}\)

V = \(\frac{4}{3} *\pi * 12*12*12\)

Use 3 to divide one of the 12 which will be equal to 4

V = \(4 *\pi *4*12*12\)

V = \(2304\pi\)

Answer:

6610

Step-by-step explanation:

We have tan(X) = opposite/ adjacent

tan(QBP) = PQ/BQ

tan(35) = PQ/BQ    ---eq(1)

tan(QAP) = PQ/AQ

tan(20) = \(\frac{PQ}{AB +BQ}\)

\(=\frac{1}{\frac{AB+BQ}{PQ} } \\\\=\frac{1}{\frac{AB}{PQ} +\frac{BQ}{PQ} } \\\\= \frac{1}{\frac{230}{PQ} + tan(35)} \;\;\;(from\;eq(1))\\\\= \frac{1}{\frac{230 + PQ tan(35)}{PQ} } \\\\= \frac{PQ}{230+PQ tan(35)}\)

230*tan(20) + PQ*tan(20)*tan(35) = PQ

⇒ 230 tan(20) = PQ - PQ*tan(20)*tan(35)

⇒ 230 tan(20) = PQ[1 - tan(20)*tan(35)]

\(PQ = \frac{230 tan(20)}{1 - tan(20)tan(35)}\)

\(= \frac{230*0.36}{1 - 0.36*0.7}\\\\= \frac{82.8}{1-0.25} \\\\=\frac{82.8}{0.75} \\\\= 110.4\)

PQ = 110.4

≈110

Height above sea level = 6500 + PQ

6500 + 110

= 6610

Answer:

\( \frac{x - 9}{2} = 5 \\ x - 9 = 5 \times 2 \\ x = 10 + 9 \\ x = 19\)

Answer:

Part A:

1. Computation of Basic EPS

Basic EPS = (Net Income - Preferred Dividends) / Weighted Average Shares Outstanding²

Net Income = $120,000

Preferred Dividends = 4% x $50,000 = $2,000

Weighted Average Shares Outstanding = 100,000 (assuming no change in common stock during the year)

Basic EPS = ($120,000 - $2,000) / 100,000

Basic EPS = $1.18

2. Individual dilution/anti-dilution with decision making

We need to check if any of the convertible securities or stock options are dilutive or anti-dilutive by comparing their impact on EPS with the basic EPS.

Convertible Preferred: Each preferred share can be converted into 1.9 common shares (1,900 / 1,000). The conversion would increase the common shares outstanding by 1,900 and decrease the preferred dividends by $2,000.

EPS after conversion = ($120,000 - $0) / (100,000 + 1,900)

EPS after conversion = $1.16

Since this is lower than the basic EPS of $1.18, the convertible preferred is dilutive and should be included in the diluted EPS calculation.

Stock Options - A: Each option can be exercised at $12 to buy one common share when the average market price is $11. This means that the options are out of the money and would not be exercised by the holders. Therefore, they have no impact on EPS and are anti-dilutive.

Stock Options - B: Each option can be exercised at $7 to buy one common share when the average market price is $8. This means that the options are in the money and would be exercised by the holders. The exercise would increase the common shares outstanding by 4,000 and generate cash proceeds of $28,000 ($7 x 4,000). The cash proceeds can be used to buy back some common shares at the market price of $8. The number of shares bought back is 3,500 ($28,000 / $8). The net increase in common shares outstanding is 500 (4,000 - 3,500).

EPS after exercise = ($120,000 - $2,000) / (100,000 + 500)

EPS after exercise = $1.17

Since this is lower than the basic EPS of $1.18, the stock options - B are dilutive and should be included in the diluted EPS calculation.

Convertible Bonds: Each bond can be converted into 40 common shares (40,000 / 1,000). The conversion would increase the common shares outstanding by 40,000 and decrease the interest expense by $50,000 ($1,000,000 x 5%). The interest expense is net of tax, so we need to multiply it by (1 - tax rate) to get the after-tax amount. The tax rate is 30%.

EPS after conversion = ($120,000 - $2,000 + $50,000 x (1 - 0.3)) / (100,000 + 40,000)

EPS after conversion = $1.19

Since this is higher than the basic EPS of $1.18, the convertible bonds are anti-dilutive and should be excluded from the diluted EPS calculation.

3. Ranking of potential dilutors

We need to rank the potential dilutors from the most dilutive to the least dilutive based on their impact on EPS.

The most dilutive security is the convertible preferred with an EPS of $1.16.

The second most dilutive security is the stock options - B with an EPS of $1.17.

The least dilutive security is the convertible bonds with an EPS of $1.19.

4. Step-by-step inclusion of individual dilutors to arrive at reportable EPS with decision making.

We need to include the potential dilutors in order of their dilution until we reach a point where the next security would be anti-dilutive.

The first security to include is the convertible preferred.

EPS with convertible preferred = ($120,000 - $0) / (100,000 + 1,900)

EPS with convertible preferred = $1.16

The next security to include is the stock options - B.

EPS with stock options - B = ($120,000 - $0) / (100,000 + 1,900 + 500)

EPS with stock options

Answer:

(3^2) - n

Step-by-step explanation:

For this problem we will take it step by step to build the expression:

raise 3 to the 2nd power

= 3^2

then find the difference of the result and n

= (3^2) - n

Hence, your final expression should be (3^2) - n.

Cheers.

Answer: Discrimant is -55

I think 2 real solutions

Step-by-step explanation:

Answer:

? confused

Step-by-step explanation:

Answer:

Me too

Step-by-step explanation:

Answer:

Step-by-step explanation:

\( step - 1 : define\)

\(b + 66 = 180\)

\(step - 2 : solve\)

9514 1404 393

Answer:

  20%

Step-by-step explanation:

The percentage increase is ...

  percent change = (new/old -1) × 100% = (36/30 -1)×100% = 1/5×100% = 20%

The worker's income increased 20%.

Answer:

B.

Step-by-step explanation:

First in order to solve this problem we need to simplify the answer choices.

A. 6×8 + 6×6 = 48+ 36

B. 12×4 + 12×1=48+12

C. 4×44 + 4×3=176+12

D. 8×6 + 8×4 = 48+32

As you can see there is one expression that is equivalent to 48+12. Answer choice B is correct.

The expression that is equivalent to 48 + 12 is 12(4 + 1), Option B is correct.

An expression is combination of variables, numbers and operators.

To find the expression that is equivalent to 48 + 12, we need to simplify each of the given expressions and find the one that is equal to 60.

Because the value of 48+12 is 60

A. 6(8 + 6) = 6(14) = 84

B. 12(4 + 1) = 12(5) = 60

C. 4(44 + 3) = 4(47) = 188

D. 8(6 + 4) = 8(10) = 80

Out of the given expressions, only expression B simplifies to 60, which is equivalent to 48 + 12.

Therefore, the expression that is equivalent to 48 + 12 is 12(4 + 1), Option B is correct.

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Answer:

the last one is the only one with a y intercept of -1

Step-by-step explanation:

Answer: \($m=-\frac{1}{22}$\)   \($b=\frac{15}{22}$\)

Step-by-step explanation:

To find the equation of the tangent line to the curve \($xy^3+xy= 14$\) at the point \($(7,1)$\) we need to first find the derivative of the equation with respect to x using implicit differentiation.

Taking the derivative of both sides with respect to x:

\($\frac{d}{dx}(xy^3+xy)=\frac{d}{dx}(14)$\)

Using the product rule and chain rule:

\($y^3+x(3y^2\frac{dy}{dx}+y)=0$\)

Simplifying and solving for \($\frac{dy}{dx}$\)

\($\frac{dy}{dx}=-\frac{y}{3y^2+1}$\)

Now we can substitute x=7 and y=1 into this equation to find the slope of the tangent line at the point (7,1):

\($m=\left.-\frac{y}{3y^2+1}\right|_{(7,1)}=-\frac{1}{22}$\)

So the slope of the tangent line is \($-\frac{1}{22}$\)

To find the y-intercept, we can use the point-slope form of the equation of a line:

\($y-1 = m(x-7)$\)

\($y=mx+(1-7m)$\)

Therefore, the equation of the tangent line to the curve \($xy^3+xy=14$\) at the point (7,1) can be written as:

\($y=-\frac{1}{22}x+\frac{15}{22}$\)

So \($m=-\frac{1}{22}$\) and \($b=\frac{15}{22}$\)

Answer:

y=x

Step-by-step explanation:

Answer:

3n

Step-by-step explanation:

the output is 3 times the input

three times n equals 3n

The steps which you would take to determine if these figures are similar include the following:

2. Multiply the vertices of polygon ABCD by 1/2.

5. Reflect the intermediate image.

In Mathematics and Geometry, a dilation is a type of transformation which typically transforms the dimension (size) or side lengths of a geometric object, without affecting its shape.

Therefore, the dimension or side lengths of the dilated geometric object would be stretched or compressed (shrunk) depending on the scale factor that is applied.

By critically observing the graph representing polygon ABCD, we can logically deduce that a sequence of transformations that would polygon ABCD (pre-image) onto polygon A"B"C"D" (image) is a dilation by a scale factor of 1/2 and a reflection of intermediate image.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The value of x and y is 5 , 7

An expression consists of variables , constants and mathematical operators , when equated by any other algebraic expression or a constant it becomes an equation.

The equation given in the question is

(x + 1)/2  -(y+4)/11 = 2

(x+3) /2 + (2y+3)/17 = 5

It has to be solved for x and y ,

The simplification of the equation has to be done

and the equation is

11x-2y = 41  -----------1

and

17x +4y = 113    -------------------2

to find the solution elimination method will be followed as

Multiplying equation 1 by 2 and adding the both equations

39x = 195

x = 5

Substituting this value in equation 1

55 -2y = 41

y = 7

The value of x and y is 5 , 7

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Answer: The matrix A of the linear transformation T(f(t)) = f''(t) + 3f'(t) + 7f(t) from the space spanned by the functions cos(t) and sin(t) into itself with respect to the basis {cos(t), sin(t)} can be found by computing the images of the basis vectors under T and expressing those images as linear combinations of the basis vectors.

We have:

T(cos(t)) = -cos(t)'' - 3cos(t)' - 7cos(t) = -cos(t) - 3(-sin(t)) - 7cos(t) = -8cos(t) - 3sin(t)

T(sin(t)) = -sin(t)'' - 3sin(t)' - 7sin(t) = -sin(t) - 3cos(t) - 7sin(t) = -8sin(t) + 3cos(t)

So, with respect to the basis {cos(t), sin(t)}, the matrix A is:

A = [ -8, -3; 3, -8 ]

This is the matrix representation of the linear transformation T with respect to the basis {cos(t), sin(t)}.

Step-by-step explanation:

Answer:

50.75

Step-by-step explanation:

We have:

\(E[g(x)] = \int\limits^{\infty}_{-\infty} {g(x)f(x)} \, dx \\\\= \int\limits^{1}_{-\infty} {g(x)(0)} \, dx+\int\limits^{6}_{1} {g(x)\frac{2}{x} } \, dx+\int\limits^{\infty}_{6} {g(x)(0)} \, dx\\\\= \int\limits^{6}_{1} {g(x)\frac{2}{x} } \, dx\\\\=\int\limits^{6}_{1} {(4x+3)\frac{2}{x} } \, dx\\\\=\int\limits^{6}_{1} {(4x)\frac{2}{x} } \, dx + \int\limits^{6}_{1} {(3)\frac{2}{x} } \, dx\\\\=\int\limits^{6}_{1} {8} \, dx + \int\limits^{6}_{1} {\frac{6}{x} } \, dx\\\\\)

\(=8\int\limits^{6}_{1} \, dx + 6\int\limits^{6}_{1} {\frac{1}{x} } \, dx\\\\= 8[x]^{^6}_{_1} + 6 [ln(x)]^{^6}_{_1}\\\\= 8[6-1] + 6[ln(6) - ln(1)]\\\\= 8(5) + 6(ln(6))\\\\= 40 + 10.75\\\\= 50.74\)

Answer:

1.41 is the answer

Step-by-step explanation: