What is X = to in -3x+4x=2•4-x​

Answer:

12 km/h

Step-by-step explanation:

Given: Distance covered by boat downstream = 50 km

           Distance covered by boat upstream = 30 km

           Time taken by boat in down stream and upstream are equal.

           Speed of the stream = 3 km/h

Let x be the speed of boat in still water.

∴ Speed of boat in downstream [tex](s_1)[/tex] = [tex](x+3)\ km/h[/tex]

Speed of boat in upstream [tex](s_2)[/tex] = [tex](x-3)\ km/h[/tex]

As we know, [tex]Time = \frac{Distance}{speed}[/tex]

And time remain same for both upstream and downstream

∴ [tex]\frac{50}{(x+3)} = \frac{30}{(x-3)}[/tex]

Now, cross multiply both side

⇒  [tex]50\times (x-3) = 30\times (x+3)[/tex]

⇒ [tex]50x-30x = 150+90[/tex]

∴ [tex]x= 12\ km/h[/tex]

∴ Speed of boat in still water is 12 km/h

1) Find the solution to each equation.

A) 4(2x - 1) = -3x + 32

The solution to the equation 4(2x - 1) = -3x + 32 is x = 3.273

Need to find the solution of following equation

4(2x - 1) = -3x + 32

Let use BODMAS rule to solve the expression

According to Bodmas rule, if an expression contains brackets ((), {}, []) we have to first solve or simplify the bracket followed by of (powers and roots etc.), then division, multiplication, addition and subtraction from left to right.

On opening the bracket of left hand side we get

[tex]4 \times 2x-4 \times 1=-3 x+32[/tex]

Now perform multiplication,

8x – 4 = -3x + 32

On bringing terms having variable x in left hand side and constant term on right hand side we get

8x + 3x = 32 + 4

=> 11x  = 36

On dividing both sides by 11, we get

[tex]\begin{array}{l}{\Rightarrow \frac{11 x}{11}=\frac{36}{11}} \\\\ {\Rightarrow x=\frac{36}{11}=3.273}\end{array}[/tex]

Hence solution of equation 4(2x - 1) = -3x + 32 is 3.273

A function that gives the amount that the plant earns per man-hour t years after it opens is [tex]\mathrm{A}(\mathrm{t})=80 \times 1.05^{\mathrm{t}}[/tex]

Given that  

A manufacturing plant earned $80 per man-hour of labor when it opened.

Each year, the plant earns an additional 5% per man-hour.

Need to write a function that gives the amount A(t) that the plant earns per man-hour t years after it opens.  

Amount earned by plant when it is opened = $80 per man-hour

As it is given that each year, the plants earns an additional of 5% per man hour

So Amount earned by plant after one year = $80 + 5% of $80 = 80 ( 1 + 0.05) = (80 x 1.05)

Amount earned by plant after two years is given as:

[tex]=(80 \times 1.05)+5 \% \text { of }(80 \times 1.05)=(80 \times 1.05)(1.05)=80 \times 1.052[/tex]

Similarly Amount earned by plant after three years [tex]=80 \times 1.05^{t}[/tex]

[tex]\begin{array}{l}{\Rightarrow \text { Amount earned by plant after } t \text { years }=80 \times 1.05^{t}} \\\\ {\Rightarrow \text { Required function } \mathrm{A}(t)=80 \times 1.05^{t}}\end{array}[/tex]

Hence a function that gives the amount that the plant earns per man-hour t years after it opens is [tex]\mathrm{A}(t)=80 \times 1.05^{t}[/tex]

Answer:

Mr. Winking 87.9%

Ms. Sand 88.55%

Ms. Sand's class is better

Step-by-step explanation:

Step 1: Average in Mr. Winking's Class 87.9%

Convert each weight factor to a decimal.

Homework 10% = 0.1

Quiz 25% = 0.25

Test 45% = 0.45

Exam 20% = 0.2

Multiply your grades by the weight factors:

Homework 0.1 X 95% = 9.5%

Quiz 0.25 X 85% = 21.25%

Test 0.45 X 87% = 39.15%

Exam 0.2 X 90% = 18%

Add all of these values:

9.5% + 21.25% + 39.15% + 18%

= 87.9%

Step 2: Average in Ms. Sand’s Class 88.55%

Convert each weight factor to a decimal.

Homework 15% = 0.15

Quiz 20% = 0.2

Test 40% = 0.4

Exam 25% = 0.25

Multiply the weight factors by your grades:

Homework 0.15 X 95% = 14.25

Quiz 0.2 X 85% = 17

Test 0.4 X 87% = 34.8

Exam 0.25 X 90% = 22.5

All all these values:

14.25 + 17 + 34.8 + 22.5

= 88.55%

Step 3:

I would rather be in Ms. Sand's class. My average in her class would be 88.55%, whereas in Mr.Winking's Class, my average would be 87.9%. 88.55% is a higher mark than 87.9% and I want higher marks. Therefore, I would get higher marks in Ms. Sand's class.

Answer: 90

Step-by-step explanation: You equation is 4(3*7) + 2(1*3). To solve this, you first solve what is on the inside of the parenthesis. so 3 times 7 is 21. And 1 times 3 is 3. So now your equation looks like this 4(21) + 2(3). 4 times 21 is 84 and 2 times 3 is 6. So now your equation is 84 + 6 which equals 90.

Answer:

90

Step-by-step explanation:

4(3*7)+2(1*3)=4(21)+2(3)=84+6=90

Answer:

30 hours

Step-by-step explanation:

Let the small pipe take time "t" to fill up the tank alone

Since larger pipe takes 15 HOURS LESS, so it will take "t - 15" time to fill up the tank alone

Let the whole tank be equal to "1" and each pipe fills up a fraction of the tank.

Smaller Pipe fills up 10/t, and

Larger Pipe fills up 10/(t-15)

Totalling "1". So we can write:

[tex]\frac{10}{t}+\frac{10}{t-15}=1[/tex]

Now, we solve for t. First, we multiply whole equation by (t)(t-15), to get:

[tex]t(t-15)*[\frac{10}{t}+\frac{10}{t-15}=1]\\(t-15)(10)+10t=t(t-15)[/tex]

Now we multiply out and get a quadratic and solve by factoring. Shown below:

[tex](t-15)(10)+10t=t(t-15)\\10t-150+10t=t^2-15t\\20t-150=t^2-15t\\t^2-35t+150=0\\(t-30)(t-5)=0\\t=5,30[/tex]

Since, this time is for the smaller pipe (which takes longer than 15 hours), so we disregard t = 5 and take t = 30 as our solution. So,

Smaller pipe takes 30 hours to fill up the tank alone

The smaller pipe takes 30 hours to fill the tank on its own, determined by solving the equation derived from the combined and individual rates at which each pipe fills the tank.

Since they can jointly fill the tank in 10 hours, we can use the rates at which they fill the tank to set up the equation: 1/x + 1/(x - 15) = 1/10. To find the solution, we multiply each term by 10x(x - 15) to clear the denominators, which gives us 10(x - 15) + 10x = x(x - 15). This simplifies to 20x - 150 = x^2 - 15x. Rearranging the terms yields x^2 - 35x + 150 = 0, which can be factored into (x - 30)(x - 5) = 0. Thus, x could be either 30 hours or 5 hours. Since x - 15 must also be positive, x = 30 hours is the correct solution, meaning the smaller pipe takes 30 hours to fill the tank alone.

Answer:

n = -2

Step-by-step explanation:

Distribute first.

-32 - 32n = 8n + 48

Subtract 8n.

-32 - 40n = 48

Add 32

-40n = 80

n = -2

Answer: download Photomath is the best!! The answer is n=-2

Step-by-step explanation:

Answer:

The length of VW is [tex]25\ m[/tex]

Step-by-step explanation:

we know that

The perimeter of triangle TVW is equal to

[tex]P=VW+TV+TW[/tex]

we have

[tex]P=74\ m[/tex]

so

[tex]74=VW+TV+TW[/tex] -----> equation A

[tex]VW=TV+3[/tex] ----> equation B

[tex]TW=(VW+TV)-20[/tex] ----> equation C

substitute equation B in equation C

[tex]TW=(TV+3+TV)-20[/tex]

[tex]TW=2TV-17[/tex] ----> equation D

substitute equation B and equation D in equation A

[tex]74=(TV+3)+TV+(2TV-17)[/tex]

solve for TV

[tex]74=4TV-14[/tex]

[tex]4TV=74+14[/tex]

[tex]4TV=88[/tex]

[tex]TV=22\ m[/tex]

Find the value of VW

[tex]VW=TV+3[/tex] -----> [tex]VW=22+3=25\ m[/tex]

Find the value of TW

[tex]TW=2TV-17[/tex] -----> [tex]TW=2(22)-17=27\ m[/tex]

Answer:

30x+45

Step-by-step explanation:

5*6x=30x

5*9=45

Answer:

30x + 45

Step-by-step explanation:

We distribute the 5 to the variable 6x and the constant 9:

5(6x+9)

5 x 6x = 30x

5 x 9 = 45

The answer is 30x + 45

Answer:

-1/2

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(0-(-3))/(-5-1)

m=(0+3)/(-6)

m=3/-6

simplify

m=-1/2

Answer:

The error Tara made is she rewrote incorrectly 3 3/8 as 17/8 and 4 1/9 as 13/9,

the corrected number can be rewrote as 3 3/8 as 27/8 and 4 1/9 as 37/9.

Step-by-step explanation:

To find the Product of:

[tex]3\frac{3}{8}\times 4\frac{1}{9}[/tex]

The Number can be rewrote as,

[tex]\frac{3\times8+3}{8}\times \frac{4\times9+1}{9}\\\\\frac{24+3}{8}\times \frac{36+1}{9}\\\\\frac{27}{8}\times \frac{37}{9}[/tex]

Tara made error here she rewrote the number incorrectly 3 3/8 as 17/8 amd 4 1/9 as 13/9.

Now multiplying the fraction we get

[tex]\frac{999}{72}[/tex]

Because she rewrote incorrectly which led her answer to multiplication of fraction, the product too was incorrect which she wrote as 221/72.

Answer:

16a^4

Step-by-step explanation:

You do 4a^2*4a^2= 16a^4 because area of square is length times width and we know that that length and width in a square is equal.

4*4= 16

a^2*a^2= a^4 (because when you multiply powers with the same base like a in this case, you add the powers up. So in this example it would be 2+2= 4)

Put them together to give you 16a^4

Final answer:

The area of a square with a side length of 4a² is A = 16a⁴, showcasing the area's proportionality to the fourth power of side length a.

Explanation:

The expression for the area of a square with a side length of 4a squared is found by squaring the side length. Since the side of the square is 4a², the area A is given by:

A = (4a²) × (4a²) = 16a⁴

The simplified expression for the area is 16a to the fourth power, which indicates that the area is proportional to the fourth power of the side length a.

Answer: B

Step-by-step explanation: The equation of the line in Slope-intercept form is:

Where "m" is the slope of the line and "b" is the intersection of the line with the y-axis.

For the graph of the line, you can identify that:

And for, you can identify that:

Therefore, you can observe that the slope does not change, but now the line cuts the y-axis at . In other words, it was moved from to (3 units on the y-axis)

Then, it is the graph of translated 3 units upward, which means that the graph of g(x) is 3 units above the graph of f(x).

The graph of g is 3 units above the graph of f(x), the correct option is A.

The graph is a mathematical representation of the relation between two objects.

It helps in determining the function that fits best for the data obtained.

A function is a mathematical statement that defines a relationship between a dependent and an independent variable.

A function always has a defined range and domain, domain is all the value a function can have as input and range is all the value that a function can give as output.

The function f(x) = 2x

g(x) = 2x+3

Both functions are a straight line, an equation of a straight line is given by y =mx +c, m is the slope of the line and c is the y intercept.

In the function f(x), the slope is 2 and the intercept is 0

In the function g(x), the slope is 2 and the intercept is 3.

As the intercept is 3, the g(x) is 3 units above the graph f(x).

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Answer:

The y-intercept is (0,-26)

Step-by-step explanation:

Given two points P(a,b) and Q(c,d), the line that passes for both points can be found with the expression

[tex]\displaystyle y-b=\frac{d-b}{c-a}(x-a)[/tex]

We'll take the first two points P(34,-52) and Q(51,-65) to find

[tex]y=-\frac{13}{17}(x-34)-52\\ \\y=-\frac{13}{17}x-26[/tex]

Let's verify if the third point is on the line:

[tex]y=-\frac{13}{17}68-26=-52-26=-78[/tex]

It belongs to the line. To find the y-intercept of the line, we set x to 0

[tex]y=-\frac{13}{17}(0)-26=-26[/tex]

The y-intercept is (0,-26)

Answer:

[tex]\displaystyle 5b^{-4}[/tex]

Step-by-step explanation:

[tex]\displaystyle 5b^{-4} = (-5a^4b^{-7})(-a^{-4}b^3) \\ \\ \frac{5}{b^4} = 5b^{-4}[/tex]

According to the Negative Exponential Rule [part II], you bring the denominator to the numerator WHILE ALTERING THE INTEGER SYMBOL FROM POSITIVE TO NEGATIVE:

[tex]\displaystyle b^{-n} = \frac{1}{b^n}[/tex]

I am joyous to assist you anytime.

984 members of club would be in favor of used-gear sale based on results of survey.

Step-by-step explanation:

Number of people surveyed = 72

People in favor of sale = 63

Percentage of people in favor = [tex]\frac{People\ in\ favor\ of\ sale}{No.\ of\ people\ surveyed}*100[/tex]

Percentage of people in favor = [tex]\frac{63}{72}*100 = \frac{6300}{72}\\[/tex]

Percentage of people in favor = 87.5%

It means that 87.5% members of club will be in favor of sale.

Total members of club = 1125

Total members in favor = 87.5% of total members

[tex]Total\ members\ in\ favor=\frac{87.5}{100}*1125 = \frac{98437.5}{100}\\Total\ members\ in\ favor=984.3[/tex]

Rounding off to nearest whole number

Total members in favor = 984

984 members of club would be in favor of used-gear sale based on results of survey.

Keywords: percentage, division

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Answer:

C = [tex]$ \frac{1}{10} $[/tex]

D = [tex]$ \frac{1}{10^2} $[/tex]

Step-by-step explanation:

78.09 = 7 [tex]$ \times A + 8 \times B + 0 \times C + 9 \times D $[/tex]

78.09 = 7 [tex]$ \times 10^1 + 8 \times 10^0 + 0 \times \frac{1}{10} + 9 \times \frac{1}{10^2}[/tex]

⇒ C = [tex]$ \frac{1}{10} $[/tex]

   D = [tex]$ \frac{1}{10^2} $[/tex]

Hence, the answer.

Do:

3x6

(3)(6)

6+6+6

Do not:

(3)-(6)

3/6

3+6

For this case we must simplify the following expression:

[tex](2x ^ 3 + 6x-1) + (3x ^ 2-7x)[/tex]

We eliminate the parentheses taking into account that:

[tex]+ * + = +\\+ * - = -[/tex]

So, we have:

[tex]2x ^ 3 + 6x-1 + 3x ^ 2-7x =[/tex]

We add similar terms taking into account that:

Different signs are subtracted and the sign of the major is placed:

[tex]2x ^ 3 + 3x^2-x-1[/tex]

Answer:

[tex]2x ^ 3 + 3x^2-x-1[/tex]

The equation to represent Juan's pay is P = 2300 + 90N. If he sells 21 copies of the book, his total pay would be $4190.

Pay Calculation

Given that Juan's base salary is $2300 and he makes an additional $90 for every copy of Math is Fun he sells, we can write an equation relating P (total pay) to N (number of sales) by adding together his base pay and his earnings from selling the books. This can be written as P = 2300 + 90N. We can then use this equation to calculate Juan's total pay if he sells 21 copies of the Math is Fun book. By substituting N = 21 into our equation, we get P = 2300 + 90*21, which simplifies to P = 2300 + 1890 = $4190. So, if Juan sells 21 copies of Math is Fun, his total pay would be $4190.

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The expression x=20-3D will present the amount Amy has left after buying D sodas.

Step-by-step explanation:

Given,

Total amount = 20 quarters

Cost of sodas = $0.75 = 0.75*100 = 75 cents

25 cents = 1 quarter

1 cent = [tex]\frac{1}{25}\ quarter[/tex]

75 cents = [tex]\frac{1}{25}*75[/tex] = 3 quarters

Amount of D sodas = 3D

Let x be the amount left with Amy.

Amount left = total amount - Amount of D sodas

[tex]x=20-3D[/tex]

The expression x=20-3D will present the amount Amy has left after buying D sodas.

Keywords: fractions, subtraction

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Answer:

b. y = 27x

Step-by-step explanation:

When you talk about "per" it means multiplication, and 27 is being multiplied by (x) gallons of gas.

Answer:

-4/5

Step-by-step explanation:

slope = m = (difference in y)/(difference in x) = (-3 - 1)/(3 - (-2)) =-4/5

Answer:

198

Step-by-step explanation:

-511 + (+709) =

709 - 511 = 198

Answer:

-511 + 709 = 198

Step-by-step explanation:

-511+709 is the same as 709-511

Answer:

The coordinates are x = -1 and y = -2.

Step-by-step explanation:

Given:

Equations are 2x-4y=6 and 3x+y=-5.

Now, to find the coordinates.

[tex]2x-4y=6[/tex]...........(1)

[tex]3x+y=-5[/tex]...........(2)

So, first we solve the equation 1 to get the value of [tex]x[/tex].

[tex]2x-4y=6[/tex]

Subtracting both sides by [tex]-4y[/tex] we get:

[tex]2x=6+4y[/tex]

Dividing both sides by 2 we get:

[tex]x=3+2y[/tex]

Now, we put the value of [tex]x[/tex] in equation 2 to get [tex]y[/tex].

[tex]3x+y=-5[/tex]

[tex]3(3+2y)+y=-5[/tex]

[tex]9+6y+y=-5[/tex]

[tex]9+7y=-5[/tex]

On solving the whole equation we get :

[tex]y=-2[/tex]

And, now putting the value of [tex]y[/tex] in equation (1) we get [tex]x[/tex]:

[tex]2x-4y=6[/tex]

[tex]2x-4(-2)=6[/tex]

[tex]2x+8=6[/tex]

[tex]2x=6-8[/tex]

[tex]2x=-2[/tex]

on solving we get:

[tex]x=-1[/tex]

Therefore, the coordinates are x=-1 and y=-2.

Final answer:

By solving a system of equations, we find that the cost of one squash is $0.18 and the cost of one zucchini is $0.21.

Explanation:

The question involves solving a system of linear equations to determine the cost of each vegetable. Let's define x as the cost of one squash and y as the cost of one zucchini. We have the two equations based on the information provided:

We can solve this system using either substitution or elimination methods. For this example, I'll use the substitution method:

Therefore, the cost of one squash is $0.18 and the cost of one zucchini is $0.21.

Final answer:

To find the cost of each vegetable, a system of linear equations was set up and solved, revealing the cost of one squash to be $0.18 and the cost of one zucchini to be $0.21.

Explanation:

The cost of 5 squash and 2 zucchini is $1.32, and the cost of 3 squash and 1 zucchini is $0.75. To find the cost of each vegetable, we can set up a system of linear equations and solve for the unknowns.

Let 's' represent the cost of one squash and 'z' represent the cost of one zucchini. We can then create two equations based on the information given:

5s + 2z = $1.32

3s + 1z = $0.75

Now, we need to solve this system of equations. An effective way to do this would be using the substitution or elimination method. For simplicity, let's use the elimination method:

Multiply the second equation by 2 to align the coefficients of z:

6s + 2z = $1.50

Now subtract the modified second equation from the first:

(5s + 2z) - (6s + 2z) = $1.32 - $1.50

-s = -$0.18

s = $0.18

With the cost of one squash known, substitute 's' back into one of the original equations to find 'z':

3(0.18) + z = $0.75

0.54 + z = $0.75

z = $0.75 - $0.54

z = $0.21

So, one squash costs $0.18, and one zucchini costs $0.21.

Answer:

d.every word in the first sentence of the first page of every chapter.

Step-by-step explanation