Write the equation of line in slope-intercept form. Line parallel to y=0.5x+3 that passes through the point (−9,12)

Divide 100 from 2000

2000/100 = 20

20 counted to get to 2000 by skip counting by 100

hope this helps

There are a variety of methods of performing this subtraction, and corresponding different methods of regrouping.

If you're taught (as I was) to do the subtraction right-to-left, then the first regrouping you need to do is when you try to subtract 500 from 100. You must regroup the 8 thousands and 1 hundred to 7 thousands and 11 hundreds. Then, when you subtract 5 hundreds, you end with 7 thousands and 6 hundreds.

The next regrouping you need to do is when you try to subtract 6 ten-thousands from 5 ten-thousands. You must regroup the 2 hundred-thousands and 5 ten-thousands to 1 hundred-thousand and 15 ten-thousands. Then, when you subtract 6 ten-thousands, you end with 1 hundred-thousand and 9 ten-thousands.

The end result is

... 258,197 - 64,500 = 193,697

_____

If you use an abacus or soroban or similar tool to help you keep track of the numbers, you were likely taught to do the subtraction left-to-right. In this case, the first regrouping  comes when you want to subtract 6 ten-thousands. Practitioners of this method know that -6 = -10 +4, so the number represented on the tool becomes (2-1) hundred-thousands and (5+4) ten-thousands plus the rest of the initial number, or 198,197 after subtracting the 6 ten-thousands.

The subtraction proceeds until you find you need to subtract 500 from 100. At this point, the tool is representing the partial result as 194,197. Again, if you practice this method, you know that -5 = -10 +5, so you reduce the thousands digit by 1 (to 3) and add 5 to the hundreds digit to get 193,697.

_____

An attempt is made to show the regroupings in the attachment. In each case there are two of them. However, working left-to-right, the result of the first subtraction of 6 ten-thousands is 19 ten-thousands, so you never actually write down anything else. Of course, if you're using an abacus or soroban, you don't write down anything—you simply change the position of the beads on the tool.

We can treat inequalities like standard algebraic equations.

7x - 9 > 2x + 6

Add 9 to both sides.

7x > 2x + 15

Subtract 2x from both sides.

5x > 15

Divide both sides by 5.

x > 3

Answer:

x>3 is the answer

Step-by-step explanation:

We are given one inequality

7x-9>2x+6

To solve this we can do additions and subtraction as we do for equations.

Only for multiplication if negative number is used inequality changes

So let us add 9 to both the sides

7x>2x+6+9

Now subtract 2x from both the sides

7x-2x >15

5x>15

We divide by a positive number 5 without disturbing inequality sign.

X>3 is the answer

In interval notation we can write this as open interval

(3,∞)

In number line this is the region to the right of 3, not includig 3

The angle of elevation of the ladder is approximately 70.35°

How do we find the angle of elevation?

To find the angle of elevation of the ladder, we can use trigonometric functions.

The angle of elevation can be found using the tangent function, which is the ratio of the opposite side to the adjacent side in a right triangle.

opposite side is the height from the ground to the window = 14 feet,

adjacent side is the distance from the house to the base of the ladder= 5 feet.

tan(θ) = opposite/adjacent

tan(θ) = 14/5

θ = arctan(14/5)

θ =  70.35 degrees

​

Full question
Jack is using a ladder to hang lights up on his house. He places the ladder 5 feet from the base of his house and leans It so it reaches a window 14 feet above the ground. Find the angle of elevation of the ladder.
A) 65.5

B) 68.4

C) 70.3

D) 71.5

E) 72.9

We won't have a function if for same value of x in (x,y) we get different values y.

So first step: figure out k so that the first coordinate (x) is the same:

3k-4=4k    | solve for k

k = -4

no check the values y for the elements of the relation

x = 3k-4 = -12-4=-16

so at -16 we get (-16,16) and (-16, 32), which mean for k=-4 the relation is not a function.

Let me know if you have any questions.

Answer:

K= -4

Step-by-step explanation:

Since it isn't possible that (3k-4, 16) is going to be equal to (4k, 32) in terms of positive numbers, you will have to go to the negative side of the number line.

K has to equal 4 because 3 · -4 = -12, and -12 minus 4 is equal to -16.

And since 4 · -4 = -16, K has to equal - 4.

Consider the ordering

... -2 < -1

Now consider the ordering of their absolute values:

... 1 < 2

_____

Hopefully, you see that changing the sign reflects the sequence across the origin, so that the ordering is reversed when the signs are changed.

Note that the graph shows 8 dots with associated x-values 1 through 8.  The domain is the set of integers {1, 2, 3, 4, 5, 6, 7, 8}.  The range is the set of all y-values associated with this domain, a bit harder to read off the graph.  One by one, I will approximate the y-value associated with each x value and present these 8 y-values as the range:  {7.5, 9, 12, 15. 18, 22, 23}.

You need to pick from each column depending on what makes sense - they are mixed (some numbers are roots, some cubes, in the same column).

On the order:

3 - 27

4 - 64

5 - 125

512 - 8

8 - 2

729 - 9

216 - 6

1 - 1

Answer:

as>JDKFas;lkdjfsa;lkdfjas;kldfjlakdjfalsdkfjakdkdkdlddd

Step-by-step explanation:

Angles DCE and ACB are vertical angles, hence equal. Both have the value 3x.

Angles ACH and HCB (x) add to give ange ACB, so they sum to 3x. That makes ACH have the value 2x. (2x +x = 3x)

The angles in triangle ACH add to 180°. This sum is ...

... 2x +2x +100° = 180°

... 4x = 80° . . . . . . . . subtract 100°, then divide by 4 to get ...

... x = 20°

Yes ,

side ×side×side= side^3 =volume of cube  

=>side^3=30

=>side = 30^1/3-answer

Amount of down payment = $650.

Jordan gets money by mowing lawns = $25 per lawn.

Sharla gets money by selling handmade necklaces for = $15 each necklace.

The number of lawns Jordan mows = x.

The number of necklaces Sharla sells = y.

A) Total money raised by Jordan to move x lawns at the rate $25 per lawn = 25x.

Total money raised by Sharla by selling y handmade necklaces for $15 per necklace = 15y.

Total money Sharla can raise by selling 40 necklaces at the rate $15 each = 40 × 15 = $600.

If s = 1/4 unit and A = 80s^2

A = 80 (1/4)^2

A = 80 (1/16)

A = 5

Answer

5 square units

5 square units

substitute s = [tex]\frac{1}{4}[/tex] into the equation

A= 80 × ([tex]\frac{1}{4}[/tex])² = 80 × [tex]\frac{1}{16}[/tex] = [tex]\frac{80}{16}[/tex]= 5 square units

slope = [tex]\frac{1}{12}[/tex]

the slope is the value of f' (36)

f(x) = √x = [tex]x^{\frac{1}{2} }[/tex]

f'(x) = [tex]\frac{1}{2}[/tex] [tex]x^{-\frac{1}{2} }[/tex] = [tex]\frac{1}{2\sqrt{x} }[/tex]

f'(36) = [tex]\frac{1}{2(6)}[/tex] = [tex]\frac{1}{12}[/tex]

Answer:

[tex]slope = \frac{1}{12}[/tex]

Step-by-step explanation:

Here is another method to solve your problem. I am showing this method because this is the first method normally taught and a student might not of had the chance yet to learn the other methods

We can solve this problem by using limits and the following function

[tex]\lim_{h\to 0} \frac{f(x+h) - x}{h}[/tex]

[tex]\lim_{h\to 0} \frac{\sqrt{x+h} - \sqrt{x}}{h}[/tex]

Next multiply by the conjugate of the numerator.

[tex]\lim_{h\to 0} \frac{\sqrt{x+h} - \sqrt{x}}{h} * \frac{\sqrt{x+h} + \sqrt{x}}{\sqrt{x+h} + \sqrt{x}}[/tex]

[tex]\lim_{h\to 0} \frac{x + h - x}{h(\sqrt{x+h} + \sqrt{x})}[/tex]

Cancel the x - x

[tex]\lim_{h\to 0} \frac{h}{h(\sqrt{x+h} + \sqrt{x})}[/tex]

Divide out the h

[tex]\lim_{h\to 0} \frac{h}{h(\sqrt{x+h} + \sqrt{x})}[/tex]

[tex]\lim_{h\to 0} \frac{1}{(\sqrt{x+h} + \sqrt{x})}[/tex]

Plugin 0 where h is located

[tex]\lim_{h\to 0} \frac{1}{(\sqrt{x+h} + \sqrt{x})}[/tex]

[tex]\lim_{h\to 0} \frac{1}{(\sqrt{x+0} + \sqrt{x})}[/tex]

[tex]\lim_{h\to 0} \frac{1}{(\sqrt{x} + \sqrt{x})}[/tex]

Combine Like terms in denominator

[tex]\lim_{h\to 0} \frac{1}{(\sqrt{x} + \sqrt{x})}[/tex]

[tex]\lim_{h\to 0} \frac{1}{2\sqrt{x}}[/tex]

Now lets use our derivative and plugin 36 where x is located and solve

[tex]\frac{1}{2\sqrt{x}}[/tex]

[tex]\frac{1}{2\sqrt{36}}[/tex]

[tex]\frac{1}{2(6)}[/tex]

[tex]\frac{1}{12}[/tex]

Note, this is a harder method but it is normally the first method taught in Calculus 1.

The only answer choice involving powers of prime numbers is ...

... 2^8

The surface area of an open cylinder can be expressed as 2πrh + πr^2. The cost of building the open cylinder can be calculated using the surface area and the cost per square foot. If the volume of the cylindrical container is known, the cost of building the cylinder can be expressed in terms of the cylinder's radius.

(a) The surface area of an open cylinder consists of the sum of the lateral surface area and the area of the bottom. The lateral surface area is given by the formula 2πrh, and the area of the bottom is πr^2. Therefore, the surface area of the open cylinder, S, can be expressed as:

S = 2πrh + πr^2

(b) The cost of building the open cylinder can be calculated by multiplying the surface area by the cost per square foot. Let C be the cost of building the cylinder:

C = 6(2πrh + πr^2) + 9πr^2

(c) If the volume of the cylindrical container is 500 cubic feet, we can express the cost of building the cylinder, C, in terms of the cylinder's radius, r. We already know that the volume of a cylinder is given by the formula V = πr^2h, so we can solve for h and substitute it into the equation for C:

C(r) = 6(2πr(V/πr^2) + πr^2) + 9πr^2

(d) If the volume of the cylindrical container is V cubic feet, we can express the cost of building the cylinder, C, in terms of the cylinder's radius, r:

C(r) = 6(2πr(V/πr^2) + πr^2) + 9πr^2

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Surface area S of the open cylinder is 2πrh + πr². The cost C to build the cylinder is 12πrh + 9πr². Given the volume V, cost C(r) can be expressed as 12V/r + 9πr².

Building a Cylindrical Container without a Top

The problem involves calculating the surface area and cost of a cylindrical container with no top. Here are the detailed steps:

(a) Surface Area Calculation

The surface area S of a cylindrical container with radius r and height h (with no top) includes:

The lateral surface area: 2πrh

The bottom area: πr²

Thus, the total surface area S is given by:

S = 2πrh + πr²

(b) Cost Calculation

The cost C to build the cylindrical container is calculated as:

Cost of lateral sides: $6 per square foot

Cost of the bottom: $9 per square foot

Therefore, the cost C is:

C = 6(2πrh) + 9(πr²) = 12πrh + 9πr²

(c) Cost in Terms of Radius r (Volume = 500 cubic feet)

Given the volume V = 500 cubic feet, we have:

Volume V = πr²h = 500

Rearranging for h, we get:

h = 500 / (πr²)

Now, substitute h in the cost equation:

C(r) = 12πr(500 / πr²) + 9πr² = 6000/r + 9πr²

(d) Cost in Terms of Radius r (Volume = V cubic feet)

For a general volume V, we have:

Volume V = πr²h = V

Rearranging for h, we get:

h = V / (πr²)

Now, substitute h in the cost equation:

C(r) = 12πr(V / πr²) + 9πr² = 12V/r + 9πr²

Hello...

Z = total area (1)

___-z___0.9544___z

z = 0.0288

Normal,

z = 2

The value of z is 2.  the probability that is closest to 0.0228, where the outliner is a -2 and z equals 2.

The decimal numeral system is widely used to express both integer and non-integer numbers. It is the expansion of the Hindu-Arabic numeral system to non-integer values. Decimal notation is the term used to describe the method of representing numbers in the decimal system.

A number that has been divided into a whole and a fraction is called a decimal. Between integers, decimal numbers are used to express the numerical value of complete and partially whole quantities.

The word decimus, which means tenth in Latin, is derived from the base word decem, or 10. As a result, the decimal system, often known as a base-10 system, has 10 as its fundamental unit. A number expressed using the decimal method is also referred to as being "decimal."

Given ,

0.9544/2= 0.4772

.5- 0 .4772=0.0228

the probability that is closest to 0.0228, where the outliner is a -2 and z equals 2.

Therefore value of z is 2.

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If you add the two purchases, you find 9 hotdogs and 9 hamburgers cost 24.75. One hotdog and one hamburger will cost 1/9 of that total, or 2.75.

... One hotdog and one hamburger costs $2.75.

_____

This is what your question asks. Usually, we want to know the individual costs of the items. If we multiply this total by 5, then we have the cost of 5 hotdogs and 5 hamburgers: 13.75. This $1.75 more than the cost of 5 hotdogs and 4 hamburgers, so the cost of a hamburger must be $1.75

... One hotdog costs $1.00

... One hamburger costs $1.75

D

to divide 2 fractions

• leave the first fraction

• change division to multiplication

• turn the second fraction upside down

• simplify if possible

= - [tex]\frac{3}{8}[/tex] × - [tex]\frac{7}{6}[/tex] = [tex]\frac{3(7)}{8(6)}[/tex] = [tex]\frac{7}{16}[/tex]

In y years, the loss is ...

... loss = 15y

Then in 6 years, the loss will be ...

... loss = 15·6 = 90

The loss of students for those 6 years will be 90 students.

The roots of equation are: x= -3+ √29/2 and x= -3-√29/2.

Quadratic equation's roots The roots of a quadratic equation are the values of the variables that fulfil the equation. In other words, if f(a) = 0, then x = a is a root of the quadratic equation f(x). The x-coordinates of the sites where the curve y = f(x) intersects the x-axis are the real roots of an equation f(x) = 0.

given:

x² + 3x - 5 = 0

So, solving for x

x² + 3x - 5 = 0

D= (3)² - 4(1)(-5)= 9 + 20= 29

Now, using the quadratic equation

x= -b ± √ b² -4ac/ 2a

x= -3 ±√(3)² -4(1)(-5) / 2

x= -3±√29/2

x= -3+ √29/2 and x= -3-√29/2

Hence, the roots of equation are: x= -3+ √29/2 and x= -3-√29/2.

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you can use a calculator and plug n 989x49 which equals 48461

989 times 49 is 48461

Hope this helps :)

E is located at (-2,-4)

F is located at (2,2)

To find the midpoint, add the 2 X values together and divide by two, then do the same with the y values:

X = -2 + 2 = 0/2 = 0

Y = -4 + 2 = -2/2 = -1

The midpoint is located at (0,-1)

Answer:

not a rectangle

Step-by-step explanation:

There are several ways to determine whether the quadrilateral is a rectangle. Computing slope is one of the more time-consuming. We can already learn that the figure is not a rectangle by seeing if the midpoint of AC is the same as that of BD. (It is not.) A+C = (-5+4, 5+2) = (-1, 7). B+D = (1-2, 8-2) = (-1, 6). (A+C)/2 ≠ (B+D)/2, so the midpoints of the diagonals are different points.

___

The slope of AB is ∆y/∆x, where the ∆y is the change in y-coordinates, and ∆x is the change in x-coordinates.

... AB slope = (8-5)/(1-(-5)) = 3/6 = 1/2

The slope of AD is computed in similar fashion.

... AD slope = (-2-5)/(-2-(-5)) = -7/3

The product of these slopes is (1/2)(-7/3) = -7/6 ≠ -1. Since the product is not -1, the segments AB and AD are not perpendicular to each other. Adjacent sides of a rectangle are perpendicular, so this figure is not a rectangle.

___

Our preliminary work with the diagonals showed us the figure was not a parallelogram (hence not a rectangle). For our slope calculation, we "magically" chose two sides that were not perpendicular. In fact, this choice was by "trial and error". Side BC is perpendicular to AB, so we needed to choose a different side to find one that wasn't. A graph of the points is informative, but we didn't start with that.

(1)

C

d + q = 250 ( total number of coins ) and

d + 0.25q = 137.50 ( total value of coins )

(2)

G

consecutive integers have a difference of 1 between them

let the integers be n and n + 1 then

2n + 3(n + 1) = 153 (distribute and simplify )

2n + 3n + 3 = 153

5n + 3 = 153 ( subtract 3 from both sides )

5n = 150 ( divide both sides by 5 )

n = 30 and n + 1 = 31

the 2 consecutive integers are 30 and 31

(3)

E

let x be the shortest side then longest side = 2x and middle side = x + 4

2x + x + 4 + x = 52

4x + 4 = 52 ( subtract 4 from both sides )

4x = 48 ( divide both sides by 4 )

x = 12

the longest side = 2x = 2 × 12 = 24

The system of equations for a parking meter are -

d + q = 250

100d + 25q = 137.50

What is Equation Modelling?

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We have a a parking meter in downtown Seattle takes dollar coins and quarters only.

Assume that there are [d] dollar coins and [q] quarter coins. Then, we can write the system of equations as -

d + q = 250

100d + 25q = 137.50

Therefore, the system of equations for a parking meter are -

d + q = 250

100d + 25q = 137.50

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Answer:

x can take any value less than 3.

Step-by-step explanation:

This is an inequality.

[tex]2x < 6[/tex]

Lets solve the inequality for x

[tex]x < 3[/tex]

This means x can take any value less than 3.

We can show this by using a number line.

Notice how number 3 is not fully shaded, this means x cannot be 3. And all the numbers less than 3 to infinity is shaded, meaning x can take any value in that range.

All the numbers shown are real.

The answers to problems 4, 7, 11 are irrational, because they are square roots of numbers that are not perfect squares.

The remaining numbers are rational because they are terminating decimals or the square root of a square number.

The two points on the graph of the function - 7y + 8 = 21x - 6 are;

⇒ (0, 2) and (2, -4)

What is Coordinates?

A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.

Given that;

The function is,

⇒ - 7y + 8 = 21x - 6

Now,

We can draw the graph of the function - 7y + 8 = 21x - 6 as shown in figure.

And, The points on the graph are;

⇒ (0, 2) and (2, -4)

Thus, The two points on the graph of the function - 7y + 8 = 21x - 6 are;

⇒ (0, 2) and (2, -4)

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7/3 = 2 1/3.  Rounded to the nearest hundredth, we get 2.33.

depth = 3.3 cm

the volume (V ) of a cuboid is

V = Ah ( A is the area and h the depth )

A = 20 × 28 = 560 cm², thus

h = [tex]\frac{V}{A}[/tex] = [tex]\frac{1843}{560}[/tex] ≈ 3.3 cm