The length of a rectangular sign is 12 ft less than twice its width. Its perimeter is 144 ft. Find the length and the width of the sign.

Answer:

4x - 5y = 30

4x - 5(0) = 30

x1 = 7.5 y1 = 0

Find y-intercept

The y-intercept is where the graph crosses the y-axis. To find the y-intercept, we set x2=0 and then solve for y.

4x - 5y = 30

4(0) - 5y = 30

y2 = -6 x2 = 0

(x1,y1) and (x2,y2)

(7.5,0) and (0,-6)

Solve for x

To solve for x, we solve the equation so the variable x is by itself on the left side:

4x - 5y = 30

x = 1.25y + 7.5

Solve for y

To solve for y, we solve the equation so the variable y is by itself on the left side:

4x - 5y = 30

y = 0.8x - 6

Answer:

1     8    6

9    4    2

5    3    7

Step-by-step explanation:

1) When solving problems like this it is best to start with the smallest number. In this case the smallest number was 1, so that was placed in the top left corner.

2) The smallest number must be next to the two largest numbers so, 8 and 9 can be placed on its sides

1    8

9

3) solve for the final spots in the first row and the first column.

Row:

    1 + 8 = 9

    15 - 9 = 6

Column:

   1 + 9 = 10

   15 - 10 = 5

So,

1    8    6

9

5

3) Looking at the largest unused number, number 7, we can see that it is too large to go in the second row or the second column. This means it must be placed in the lower right corner

1    8    6

9

5          7

4) At this point you have enough information to solve for the rest of the numbers using simple addition and subtraction

Answer:

distance: 11

there are 11 points between 12 and 23, they are:

12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22 and 23.

Step-by-step explanation:

Answer:

0.00578034682

Step-by-step explanation:

9/1557

keep on adding .0 to the end of your number.

You will eventually get the answer.

Answer:

173.

Step-by-step explanation:

Answer:

4 2/3

Step-by-step explanation:

1 3/4 x 2 2/3

We need to change the mixed numbers to improper fractions

1 3/4 = ( 4*1+3) /4 = 7/4

2 2/3 = ( 3*2 +2) /3 = 8/3

7/4 * 8/3

Rewriting

7/3 * 8/4

Simplify

7/3 *2

14/3

Make this a mixed number

4 goes into 14 4 times with 2 left over

4 2/3

Answer:

[tex]4\frac{2}{3}[/tex]

Step-by-step explanation:

[tex]1\frac{3}{4} *2\frac{2}{3}[/tex]

First, make fractions as improper fractions.

[tex]\frac{7}{4} *\frac{8}{3}[/tex]

Now multiply the answers.

[tex]\frac{56}{12}[/tex]

Now make the answer a mixed number.

[tex]4\frac{8}{12}[/tex]

To write the answer in its simplest form, divide the numerator and denominator by 4.

[tex]4\frac{2}{3}[/tex]

The expression is multiplied to give 1728x^6

Index forms are simply defined as the power or exponent of a variable, number or element.

It is also seen as an arithmetic method of writing numbers that are too large or too small into simpler forms.

The rules of exponents are;

Given the expression;

2^3x^3.6^3x^3

We have to determine the product of the index forms

First, we have to multiply the numbers, we have;

2^3 = 2 × 2 × 2 = 8

6^3 = 6 × 6 × 6 = 216

Now, substitute the values

8x³ × 216x³

Multiply through

1728x^3 + 3

1728x^6

Thus, the value is 1728x^6

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Answer: [tex](-\infty, 0][/tex]

Step-by-step explanation:

This is a parabola that opens down (because of the negative leading coefficient).

So, the average rate of change (i.e., the slope of the secant) is negative when the function is decreasing.

The function is decreasing to the left of the vertex, which is at (0, 7).

So, the function has a negative average rate of change for [tex](-\infty, 0][/tex].

From the characteristics of the given cylinder, we have that:

a) The equation is h = 15 - 2r.

b) The volume of the cylinder is of V = πr²(15 - 2r).

c) The values of r should be in the range of 0 < r < 7.5.

The volume of a cylinder of radius r and height h is given according to the following equation:

V = πr²h.

The sum of the height and the diameter is of 15 feet, hence:

h + d = 15.

The diameter is twice the radius, hence:

h + 2r = 15.

For item a, the solution of h in terms of r is:

h = 15 - 2r.

Hence, in item b, the equation is:

V = πr²h.

V = πr²(15 - 2r).

For item c, there are two constraints, as follows:

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Hey! Your question was incomplete because I have double-checked my work, and even checked reliable sources to see if I missed something in my work, but I keep getting –238. I did play around with the question by switching the negative symbol around in the equation to see if I would get a balanced answer. I say this because when you solve the question you posted, the answer I got was w = –238, but when I went back to check my work by plugging that number in as the value of w, I got –238 ≠ 238 (or something like that. The number is the same, but the signs are not). If the signs and numbers don't both equal each other something is wrong with the problem. I believe I figured out where your question went wrong. Instead of the question being 34 = –w/7, I believe that the correct question should have been –34 = w/7. What I think happened was that when you typed your question, you swapped the negative on the 34 with the variable of w. If I am incorrect, and you typed your question correctly, I am sorry in advance because my work wasn’t matching what I got for w. But for now, I will solve what I think the question should have said. Again, sorry in advance. Solve for w in the following equation: –34 = w/7.

Write the equation:

–34 = w/7

Multiply both sides by 7:

7 × –34 = w/7 × 7

Multiply:

–238 = 1w

Divide:

–238/1 = 1w/1

–238 = w or w = –238

Check your work by plugging –238 back into the equation as w:

–34 = w/7

–34 = –238/7

Multiply both sides by 7:

–34 × 7 = –238/7 × 7

–238 = –238 ✔

Thus, w = –238

Hope that helps! Have an amazing rest of your day!! :)

The number of pie each got-

For the given question;

Let the number of pie eaten by Alex be 'a'.

Let the number of pie eaten by Bob be 'b'.

Let the number of pie eaten by Chuck be 'c'.

Then, for the given condition.

If you add Alex’s and bobs pie total together, they ate 22 pies,

a + b = 22 .....eq 1.

Bobs and chucks pies sum to 24.

b + c = 24   .......eq 2

Alex and chucks pie together be 16.

a + c = 16      .......eq 3

Solving equation 1 and 3 by elimination.

Subtract eq 3 from 1.

c = b - 6 .....eq 4

Solving equation 4 and 2.

b = 15

Put in eq 4

c = 9

Put the values of b and c in eq 1.

a = 7

Thus, the number of pie shared by Alex, Bob and Chuck are 7, 15 and 9 respectively.

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y = x + 6 and 3x - 3y = -18 will have no solution (parallel lines)

y = −4x + 11 and −6x + y = 11 will have unique solution (intersecting lines)

y = -2x + 5 and 2x + y = -7 will have no solutions (parallel lines)

taking first set of equations,

y = x + 6 and 3x - 3y = -18

rearranging it in the ax+by=c form we get,

x - y = 6

3x - 3y = -18

a1=1, b1= -1, c1= 6

a2=3, b2= -3, c2= -18

now comparing,

1/3 = 1/3 ≠ 6/(-18) 0r -1/3

thus, we get a1/a2=b1/b2≠c1/c2, which satisfies the condition for parallel lines, thus there will be no solution.

taking second set of equations,

y = −4x + 11 and −6x + y = 11

rearranging it in the ax+by=c form we get,

4x+y=11

-6x+y=11

a1=4, b1= 1, c1= 11

a2=-6, b2= 1, c2= 11

4/6 or 2/3≠1/1

thus, we get a1/a2≠b1/b2, which satisfies the condition for intersecting lines, so there will be a unique solution.

taking third set of equations,

y = -2x + 5 and 2x + y = -7

rearranging it in the ax+by=c form we get,

2x+y=5

2x+y=-7

a1=2, b1= 1, c1= 5

a2=2, b2= 1, c2= -7

2/2 or 1/1 =1/1≠ -5/7

thus, we get a1/a2=b1/b2≠c1/c2, which satisfies the condition for parallel lines, thus there will be no solution.

What are intersecting and parallel lines?

Parallel lines never cross, always have distinct ends, and are always spaced at the same distance from one another. Lines that intersect are lines that have a common point and do cross.

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Answer:146,600,000

1.496*10^8

Step-by-step explanation:

Answer:

$1560.60

Step-by-step explanation:

PV (1+V)^n

= 1500 (1+2%)² = 1560.6

As a result of this definition, vertices are intersection of two lines that create an angle as well as the corners of polygons and polyhedra.[tex]f(x)=x^2-2x-10[/tex]  general form to vertex form is y=[[tex](x-1)^{2}[/tex]-9]

The intersection of two or more curves, lines, or edges is known as a vertex in geometry (plural: vertices or vertexes), which is frequently represented by the letters S, P, Q, or R. As a result of this definition, vertices are intersection of two lines that create an angle as well as the corners of polygons and polyhedra.

The point where two rays start or meet, where two line segments join or meet, where two lines intersect (cross), or any other suitable arrangement of rays, segments, and lines that results in two straight "sides" coming together at one location is the vertex of an angle.

[tex]f(x)=x^2-2x-10[/tex]

      = [[tex](x-1)^{2}[/tex]-9]

Use the form, [tex]ax^{2} + bx+c[/tex]

a=1

b=2

c=-10

Consider a vertex form of parabola,

[tex]a(x+d)^{2} + e[/tex]

find the value of d, using the formula d=[tex]\frac{b}{2a}[/tex]

d=[tex]\frac{2}{2*(-1)}[/tex]

simplify the right side,

d= -1

find the value of e, using e= [tex]c-\frac{b^{2} }{4a}[/tex]

e= [tex]-10\frac{2^{2} }{4*(-1)}[/tex]

simplify the right side,

e= -9

substitute the value of a, d and e into vertex form.

y=  [[tex](x-1)^{2}[/tex]-9]

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The ratios 9:6 and 12:8 does not form a proportion, since the products of the two are not equal.

Given we have two ratios:

9:6 and 12:8

An equation in mathematics that shows that two ratios expressed in fraction form are equivalent is known as a proportion. The rule that says a/b= c/d if and only if ad=bc allows us to assess whether two ratios, a: b and c: d, constitute a proportion.

To determine if 9:6 and 12:8 form a proportion, we use the rule of proportion.

That is, 9/12 = 8/6

If only if 9×6=12×8

Therefore,  9×6=54

and 12×8=96

since these two products are not equal, we have that 9:12 and 8:6 do not form a proportion.

Hence the ratios 9:6 and 12:8 are not in proportion.

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Inequality - Trevor needs to tutor more than 6 hours in order to make at least $180.

What is inequality?

inequality, A declaration of an order relationship between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to. Either questions or theorems can be used to express inequality problems, and both can be solved using methods similar to those used to solve equations. The triangle inequality, for instance, states that the length of the remaining side of a triangle is greater than or equal to the sum of the lengths of any two of its sides. Many of these inequalities, including the Cauchy-Schwarz inequality, are used by mathematical analysis to prove some of its most significant theorems.

Total number of hours = 15

Let the hours spent tutoring French is x

Therefor, hours spent in scooping ice cream = (15-x)

Tutoring French is $15 an hour, total for x hours = 15x

Scooping ice cream is $10 an hour, 10×(15-x)= 150-10x

To make more than $180,

= 15x+ (150-10x)> 180

= 15x+150-10x>180

=15x-10x>180-150

=5x>30

=x>6

So, Trevor needs to tutor more than 6 hours.

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Answer:

f= -g/3

Step-by-step explanation:

Answer:

Step-by-step explanation:

<B, <ABC, <CBA

based off the image

Point slope form of the equation through the points (6, 10) and (3, 5)  is y - 5 = 5/3 (x - 3)

Point slope form:

The point slope form of equation is used to find the equation of the straight line which is inclined at a given angle to the x-axis and passes through a given point.

The general form of the equation is

(y - y1) = m (x - x1)

y = y coordinate of second point

y1 = y coordinate of point one

m = slope

x = x coordinate of second point

x1 = x coordinate of point one

Given,

Here we have the points  (6, 10) and (3, 5).

Through the given points we have to find the point slope form of the equation.

To find the point slope of the equation, first step is to find the slope of those points,

It can be calculated using the formula,

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

Where the values of (x1,y1) is (6,10) and the values of (x2,y2) is (3,5).

Then the value of slope after applying the values,

m = (5 - 10)/(3-6)

m = -5/-3

m = 5/3

Use the slope and a given point (3,5) to substitute for x1 and y1 in the point-slope form

y−y1=m(x−x1),

which is derived from the slope equation.

Then we get the equation as,

y - 5 = 5/3 (x - 3)

Therefore, the point slope form equation is y - 5 = 5/3 (x - 3).

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Answer: $3.55

Step-by-step explanation:

5 oranges * $2.84/4 oranges =

5 oranges * $0.71/1 orange=

5 oranges/1 orange * $0.71=

5/1 * 0.71=

5*0.71=$3.55

Using the sine rule we estimate the value of b to be approximately 4.6 units.

The sine law, often referred to as the sine formula, sine rule, or law of sines, is a trigonometrical equation that connects the lengths of any triangle's sides to its sines.

The sine rule states that [tex]\frac{a}{sinA} =\frac{b}{sinB} =\frac{c}{sinC}[/tex] , where A ,B and C are the three vertices of the triangle and a, b and c are the three side lengths.

Given A = 50° and B = 62 ° and a = 4 .

Now we use the given values to :

[tex]\frac{4}{sin50} =\frac{b}{sin62}[/tex]

or, b = 4.6104...

or , b ≈ 4.6

Hence the length of b is 4.6

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Answer:

Step-by-step explanation:

The initial depth is 100 feet below sea level or 100 ft.

Diving rate is 50 feet per minute or 50 ft/min.

The diving rate is the independent variable, which is:

The depth at any point is the dependent variable, which is different after number of minutes, in ft.

The equation of the line is:

Answer:

Independent variable: Time in minutes

Dependent variable: The elevation in feet

Slope: -50

Y-Intercept: -100

Step-by-step explanation:

Just did the assignment

Answer: 4b+6a+3c

Step-by-step explanation:

[tex]\displaystyle\\Answer:\ (0,-\frac{29}{13} )[/tex]

Step-by-step explanation:

[tex]\displaystyle\\A(-3,-5)\ \ \ \ \ B(10,7) \ \ \ \ \ \lambda=3/10=0.3\ \ \ \ \ C(x_C,y_C)=?\\\\\boxed {x_C=\frac{x_A+\lambda x_B}{1+\lambda} }\ \ \ \ \ \ \ \ \ \ \boxed {y_C=\frac{y_A+\lambda y_B}{1+\lambda} }\\\\x_C=\frac{-3+0.3(10)}{1+0.3} \\\\x_C=\frac{-3+3}{1.3} \\\\x_C=\frac{0}{1.3}\\\\x_C=0\\[/tex]

[tex]\displaystyle\\y_C=\frac{-5+0.3(7)}{1+0.3} \\\\y_C=\frac{-5+2.1}{1.3} \\\\y_C=\frac{-2.9}{1.3} \\\\y_C=-\frac{2.9(10)}{1.3(10)} \\\\y_C=-\frac{29}{13}[/tex]

[tex]\displaystyle\\Thus,\ C(0,-\frac{29}{13} )[/tex]

Solution of the given equation -3x =2x² -4,using quadratic formula is (-3 ±√41) /4.

As given in the question,

Given equation is:

-3x =2x² -4

Rearrange the terms in proper order:

2x² + 3x -4 =0

Solve it using quadratic formula

x = (-b ±√b²-4ac)/ 2a

Here compare the given equation with general quadratic equation:

a =2 , b=3 , c=-4

Substitute the values in the quadratic formula we get,

x = [ -3± √(3)² -4(2)(-4)]/2(2)

  = (-3 ± √9+32)/4

  = (-3 ±√41) /4

Therefore, Solution of the given equation -3x =2x² -4, using quadratic formula is (-3 ±√41) /4.

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Answer:

6

Step-by-step explanation:

let the number be equal to x

The sum of twice a number= 2x

The value of x based on the equation given as 3(4x + 6) = 9x + 12 is -2.

It should be noted that an equation shows that relationship between the variables that are given or illustrated in the data.

The value for x based on the equation will be:

3(4x + 6) = 9x + 12

Open bracket

12x + 18 = 9x + 12

Collect like terms

12x - 9x = 12 - 18

3x = -6

Divide

x = -6/3

x = -2

Therefore, x is -2.

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Answer:

Step-by-step explanation:x=-2x