a 13-foot ladder is leaning against a wall. if we pull the ladder away from the wall at a rate of 6ft/s, how fast is the top of the ladder moving down the wall when the bottom of the ladder is 12ft from the wall?

Answer:

j= 118 pounds

Step-by-step explanation:

d+j = 226     d = 226-j

j+b = 210      b = 210 - j

d+b = 200     Sub in the values above

           226-j    +  210 -j  = 200

               - 2j = -236

                   j = 118 pounds

The linear function that represents the profit earned is: C. y = 2x − 48.

The linear Function can be written as y = mx + b, which is in slope-intercept form, where we have:

From the information given, we have:

x = number of hot dogs sold

y = Profit earned

m = unit rate = 2

b = starting value = -48 (this is negative because the profit on each hot dog sold must be deducted from the cost for each morning.)

Therefore, substitute m = 2 and b = -48 into y = mx + b to write the linear function:

y = 2x - 48

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Answer:

C

Step-by-step explanation:

i said so

The price of one senior citizen ticket is $8 and that of a child ticket is $3.

Let the price of one senior citizen ticket be x

and the price of one student ticket be y

Thus, for the first day, we can make the following equation-

7x + 6y = 69

and similarly, we can make an equation for the second day as-

7x + 4y = 53

Now, we can solve these two linear equations to find the value of x and y.

Subtracting equation 2 from 1 we get-

(7x + 6y) - (7x + 4y) = 69 - 53

7x - 7x + 6y - 4y = 16

6y - 4y = 16

2y = 16

y = 16/2

y = 8

Substituting the value of y in any of the two equations we can find the value of x-

7x + 6(8) = 69

7x = 69 - 48

x = 21/7

x = 3

Thus, the price of one senior citizen ticket is $8 and that of a child ticket is $3.

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Answer:

y = sqrt(-2 x - 1/4) + 1/2 (2 i x + i) or y = 1/2 (2 i x + i) - sqrt((-2 x - 1/4))

x = sqrt((-2 i) y + 1/4) + 1/2 (-2 i y + 1) or x = 1/2 (-2 i y + 1) - sqrt(((-2 i) y + 1/4))

Step-by-step explanation:

Solve for y:

(x + (0 + i) y)^2 = x + (0 - i) y

Subtract -i y + x from both sides:

-x + (i y + x)^2 + i y = 0

Expand and collect in terms of y:

-x + x^2 + y (2 i x + i) - y^2 = 0

Multiply both sides by -1:

x - x^2 + y (-2 i x - i) + y^2 = 0

Subtract -x^2 + x from both sides:

y (-2 i x - i) + y^2 = x^2 - x

Add 1/4 (-2 i x - i)^2 to both sides:

1/4 (-2 i x - i)^2 + y (-2 i x - i) + y^2 = 1/4 (-2 i x - i)^2 - x + x^2

Write the left hand side as a square:

(1/2 (-2 i x - i) + y)^2 = 1/4 (-2 i x - i)^2 - x + x^2

Take the square root of both sides:

1/2 (-2 i x - i) + y = sqrt(1/4 (-2 i x - i)^2 - x + x^2) or 1/2 (-2 i x - i) + y = -sqrt(1/4 (-2 i x - i)^2 - x + x^2)

Subtract 1/2 (-2 i x - i) from both sides:

y = 1/2 (2 i x + i) + sqrt((((-2 i) x - i)^2)/4 - x + x^2) or 1/2 (-2 i x - i) + y = -sqrt(1/4 (-2 i x - i)^2 - x + x^2)

1/4 (-2 i x - i)^2 - x + x^2 = -2 x - 1/4:

y = 1/2 (2 i x + i) + sqrt((-2 x - 1/4)) or 1/2 (-2 i x - i) + y = -sqrt(1/4 (-2 i x - i)^2 - x + x^2)

Subtract 1/2 (-2 i x - i) from both sides:

y = sqrt(-2 x - 1/4) + 1/2 (2 i x + i) or y = 1/2 (2 i x + i) - sqrt((((-2 i) x - i)^2)/4 - x + x^2)

1/4 (-2 i x - i)^2 - x + x^2 = -2 x - 1/4:

Answer: y = sqrt(-2 x - 1/4) + 1/2 (2 i x + i) or y = 1/2 (2 i x + i) - sqrt((-2 x - 1/4))

________________________

Solve for x:

(x + (0 + i) y)^2 = x + (0 - i) y

Subtract -i y + x from both sides:

-x + (i y + x)^2 + i y = 0

Expand and collect in terms of x:

x^2 + x (2 i y - 1) + i y - y^2 = 0

Subtract -y^2 + i y from both sides:

x^2 + x (2 i y - 1) = y^2 - i y

Add 1/4 (2 i y - 1)^2 to both sides:

x^2 + x (2 i y - 1) + 1/4 (2 i y - 1)^2 = 1/4 (2 i y - 1)^2 - i y + y^2

Write the left hand side as a square:

(x + 1/2 (2 i y - 1))^2 = 1/4 (2 i y - 1)^2 - i y + y^2

Take the square root of both sides:

x + 1/2 (2 i y - 1) = sqrt(1/4 (2 i y - 1)^2 - i y + y^2) or x + 1/2 (2 i y - 1) = -sqrt(1/4 (2 i y - 1)^2 - i y + y^2)

Subtract 1/2 (2 i y - 1) from both sides:

x = 1/2 (-2 i y + 1) + sqrt((((2 i) y - 1)^2)/4 - i y + y^2) or x + 1/2 (2 i y - 1) = -sqrt(1/4 (2 i y - 1)^2 - i y + y^2)

1/4 (2 i y - 1)^2 - i y + y^2 = -2 i y + 1/4:

x = 1/2 (-2 i y + 1) + sqrt(((-2 i) y + 1/4)) or x + 1/2 (2 i y - 1) = -sqrt(1/4 (2 i y - 1)^2 - i y + y^2)

Subtract 1/2 (2 i y - 1) from both sides:

x = sqrt((-2 i) y + 1/4) + 1/2 (-2 i y + 1) or x = 1/2 (-2 i y + 1) - sqrt(((2 i y - 1)^2)/4 - i y + y^2)

1/4 (2 i y - 1)^2 - i y + y^2 = -2 i y + 1/4:

Answer: x = sqrt((-2 i) y + 1/4) + 1/2 (-2 i y + 1) or x = 1/2 (-2 i y + 1) - sqrt(((-2 i) y + 1/4))

Answer:

Step-by-step explanation:

The symbol that creates a true sentence for the expression is (16 - 8) ÷ 2 < 16 – 8 ÷ 2.

It should be noted that an expression is used to show the relationship between the values or the data given. This will be illustrated as thus:

It should be noted that (16 - 8) ÷ 2 will be:

(16 - 8) ÷ 2

= 2 ÷ 2

= 1

On the other hand, 16 - 8 ÷ 2 will be;

= 16 - 8 ÷ 2

= 16 - 4

= 12

It should be noted that 1 is less than 12. The symbol will be less than.

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Answer:

the fraction is 2/5

Step-by-step explanation:

4/5 + 1/2

=2/5

The mean number of days employees were sick is 3 days.

Mean is the average of numbers. The calculation is easy. Add all the digits and then divide by the number of digits. That is, the sum divided by the count.

As We have count for number of days by each employee given as follows

Kailynn 4days

Josh 5days

Brian 1days

Bill 3days

Jacob 2days

Pete 2days

Sasha 3days

∴ Total number of days will = 4 + 5 + 1 + 3 + 2 + 2 + 3 = 20 days

∴ Total employee count is 7.

∴ Mean Will be [tex] \frac{20}{7} [/tex]

= 2.85714

≈ 3 --(rounding to nearest hundred).

∴ The mean number of days employees were sick is 3 days.

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The scale of a map exists 1: 250000 the actual distance between two cities exists 80km then the two cities exists 72 cm apart on the map.

Given that the representative fraction exists 1/250000.

We know that the representative fraction exists the ratio of map distance to the corresponding ground distance exists independent of units of measurement.

This implies that 1 cm on the map exists actually 250000 cm distance.

We will convert this 250000 cm into m as 1 m = 100 cm.

[tex]\[250000 \times \dfrac{1}{{100}}[/tex] m = 2500 m

To convert this into km as 1 km = 1000 m.

[tex]\[2500 \times \dfrac{1}{{1000}}[/tex] km = 2.5 km

So, 1 cm on the map exists 2.5 km actual distance.

To find the distance on the map corresponding to 180 km on ground.

[tex]\dfrac{{180}}{{2.5}}[/tex] cm = [tex]$\frac{{1800}}{{25}}[/tex] cm = 72 cm

Therefore, the two cities exists 72 cm apart on the map.

We exists supposed to scale the representative fraction properly to avoid any miscalculation. Also, we will take care of the scales properly i.e. kilometers, meters and centimeters.

The complete question is:

The scale of a map is 1: 250 000.

(a) The actual distance between two cities is 80 km. Calculate this distance on the map. Give your answer in centimeters.

(b) On the map a large forest has an area of 6 cm?

Calculate the actual area of the forest. Give your answer in Square kilometres. ​

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If during the sale, cans of soup sell for $0.55 less than full price. Tiana pays a total of $13.20 for the cans of soup. The equation that can you use to find the amount, f, each can of soup costs at full price is 12(f−0.55)=13.20 and the amount that each can of soup cost at full price is $1.65.

Given data:

Number of cans = 12 can

Cost of can less than full price = $0.55

Total amount paid = $13.20

Let f represent the full price

Now let formulate an equation that will be use to  find the amount:

Equation :

12(f−0.55)=13.20

Let let determine the amount that each can of soup cost at full price using the equation

12(f−0.55)=13.20

12f−6.6=13.20

Collect like terms

12f = 19.8

Divide both side by 12f

f = 19.8 / 12

f = $1.65

Therefore the can of soup at full price costs is $1.65.

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If f(x) = 1/x, then the function representing the graph plotted will be -

y = f(x + 2) - 1.

The function f(x) = 1/x is called the multiplicative inverse function, because for each input it returns the multiplicative inverse or reciprocal of that input.

Given is function f(x) = 1/x.

The graph of the function f(x) = 1/x is plotted in the graph. If we plot the graph for f(x + 2) = 1/(x + 2), than the graph will shift towards left. If we subtract 1 from the f(x + 2), than the graph will shift downwards.

Therefore, if f(x) = 1/x, then the function representing the graph plotted will be -

y = f(x + 2) - 1

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Answer:

Since both lines are parallel, they must have the same slope, which in this case is -5.

Answer:

It has one line of folding symmetry

When a transversal crosses parallel lines corresponding angles are congruent.

What are corresponding angles?

Two lines are parallel if and only if the two angles of any pair of transversal corresponding angles are congruent (equal in measure). Proposition 1.28 of Euclid's Elements, an absolute geometry theorem (therefore true in both hyperbolic and Euclidean Geometry), demonstrates that if the angles of two transversals are corresponding, the two lines are parallel (non-intersecting). According to Euclid's parallel postulate, if two lines are parallel, the angles of a pair of corresponding angles are congruent (Proposition 1.29 of Euclid's Elements). If the angles of one pair of related angles are congruent, the angles of the remaining pairs are likewise congruent.

The correct option is (D) When a transversal crosses parallel lines corresponding angles are congruent.

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Answer:

y = 2.50× + 3.25

Step-by-step explanation:

For example if Melissa rode 8 miles:

y = 2.50(8) + 3.25

y = 20.00 + 3.25

y = $23.25

I think the answers are 2/3 and 1/3

The domain and range of the function f(x) = |x-1| +3 are-

For the given expression for the function;

f(x) = |x-1| +3.

Domain: Unless the expression is undefined, the domain of the representation is all real numbers. Because there is no real number in this case, the expression is undefined.

Interval Notation:(−∞,∞)

Set-Builder Notation:{x| x ∈ R}

Range: The range is indeed the collection of all possible y values. To determine the range, consult the graph.

Interval Notation:[3,∞)

Set-Builder Notation:{y| y ≥ 3}

Thus, the domain and the range of the function is estimated.

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4 - 7k = 3 - 6k

⇒ 4 - 3 = 7k - 6k

⇒ k = 1

The value of k is 1.

In this equation, k is a variable.

In an experimental study, the independent variable can be changed, manipulated, or adjusted.

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Answer:

12

Step-by-step explanation:

because you can see that in the first column, the y value is 4 times the x value

and in the third column, the y value is still 4 times greater than the x value

meaning that you need to find a number that is 4 times the value of 3 (because that is the x value)

3 times 4 is 12

[tex]\cfrac{1}{6}x=\cfrac{1}{3}-y\implies 0=-\cfrac{1}{6}x+\cfrac{1}{3}-y \\\\\\ y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{1}{6}} x\stackrel{\stackrel{b}{\downarrow }}{+\cfrac{1}{3}}\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

Answer:

$14.82/hr

It depends on where you are though.

An easy way to estimate would be to choose numbers close such as 90x400, which equals 36,000.

The true answer is 87*403 = 35,061.

3 600

Step-by-step explanation:

First multiply 87 to the nearest ten then multiply 403 to the nearest hundred which will give you 90 and 400. Multiply the two to get your answer

Answer:

-7

Step-by-step explanation:

Answer:

Step-by-step explanation:

-4 + (-3) is basically -4 - 3

-4 - 3 = -7

Answer:

216

Step-by-step explanation:

gof(6) means g(f(6))

f(6)=2(6)-6=6

g(6)=6^3=216

According to the geometric diagram and the definition of the area for a rectangle, the area of the rectangle is 16√3 + 32 square milimeters.

In this problem we find a geometric system formed by a rectangle and three inscribed triangles. The detailed geometric diagram is introduced in the image attached below, in which we find that the triangle formed by the centers of the three circles is equilateral.

The area of the rectangle is equal to the product of its height and its width, whose dimensions are:

Height: h = 2 · 0.5√3 · (2 mm) + 2 · (2 mm) = 2√3 + 4 mm

Width: w = 4 · (2 mm) = 8 mm

A = h · w

A = (2√3 + 4 mm) · (8 mm)

A = 16√3 + 32 mm²

The area of the rectangle is 16√3 + 32 square milimeters.

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The expression representing the base is b = 2(10x² - 4x)/x

It is important to note that the formula for area of a triangle is expressed as;

Area = 1/2 bh

Where;

Given the parameters as;

Area = 10x² - 4x

Height = x

Substitute the values into the formula

10x² - 4x = 1/2(x)b

10x² - 4x = xb/2

cross multiply

2(10x² - 4x) = xb

Now, to determine the expression, make 'b' the subject of formula by dividing both sides by the coefficient of b, we have;

b = 2(10x² - 4x)/x

Hence, the expression is 2(10x² - 4x)/x

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Answer:

a

Step-by-step explanation: