slope and rate of change
help please on card 7 an 8

70 m * .54=37.8 METERS

Answer:

a) (x, y, z) = (1, -1, 0)

b) a = 0; L = {t, t, 0}

c) a = 1 . . or . . a = 3

d) No

Step-by-step explanation:

a) The solution using row-reduction techniques is shown in the first attachment, part (a). The generic solution is shown evaluated for a=2, the result being (1, -1, 0).

You will note that the solution gives indeterminate values for a=1 and a=3, which make the denominators zero.

b) For this, we use the point solution of part (a) together with the cross product of the normal vectors of planes 1 and 2. Said cross product will be in the direction of their line of intersection. We substitute the parametric equation for that line into the equation for plane 3 and solve for a. The result is a = 0.

The simplification of the resulting equation also gives a=1 and a=3, but we treat those as extraneous solutions because the corresponding common point of intersection of the planes does not exist.

c) The values a = 1 and a = 3 were found in part (a). These are values of a that make the common point indeterminate.

d) Substituting the given values for (x, y, z) gives three equations for a that have 3 different solutions. Hence there cannot be a value of a that makes this be a common point of intersection.

e) The second attachment illustrates part (a), with a=2. The third attachment illustrates part (b) with a=0.

The fourth attachment illustrates part (c). The first picture has the triangular tunnel between the planes in a vertical orientation (a=1). The second picture has the triangular tunnel extending from lower front to upper back (a=3).

we are given

A ball rolling down a hill was displaced 19.6 m

so,

[tex]h=19.6m[/tex]

the final velocity was 5.00m/s

so, [tex]v=5m/s[/tex]

Since, a ball rolling down a hill was displaced

so, we get

[tex]u=0m/s[/tex]

we can use kinematic equation formula

[tex]v^2-u^2=2ah[/tex]

Here ,

v is final velocity

u is initial velocity

a is acceleration

h is height from which ball is dropped

now, we can plug our values

[tex]5^2-0^2=2a(19.6)[/tex]

[tex]2a\left(19.6\right)=5^2[/tex]

[tex]2a\left(19.6\right)=25[/tex]

[tex]a=0.63776m/s^2[/tex]................Answer

Using the equation of Motion, the rate of acceleration of the ball is 0.638 m/s²

Using the 2nd equation of Motion :

v² = u² - 2gh (downward motion)

5² = 0 - 2(19.6)a

25 = 0 - 39.2a

39.2a = 25

a = 25/39.2

a = 0.638 m/s²

Therefore, the rate of acceleration is 0.638 m/s²

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find the perimeter of a triangle with sides 15 inches, 15 inches, and 21 inches length

To find the perimeter of a triangle we add all the sides of the triangle

The length of the sides of the triangle are given as 15 inches, 15 inches, and 21 inches

Perimeter of a triangle =

15 inches + 15 inches +   21 inches = 51 inches

So 51 inches is the perimeter

- a³m³

each term inside the parenthesis is raised to the power of 3

note that (- 1 )³ = - 1, thus

(-am)³ = - a³m³

Answer:

[tex]12a^{3}-15a^{2}+36a[/tex]

Step-by-step explanation:

To solve this problem you must apply the procccedure shown below:

1. You have the following expression:

[tex]3a(4a^{2}-5a+12)[/tex]

2. Then, you must apply the Distributive property. In other words, you need to multiply [tex]3a[/tex] by each term inside the parentheses.

3. You need to remember the properties of exponents. When you have equal base, you only need to multiply the coefficients, write the base and add the exponents. Therefore, you have:

[tex]3a(4a^{2}-5a+12)=12a^{(2+1)}-15a^{(1+1)}+36a=12a^{3}-15a^{2}+36a[/tex]

Answer:

B. (2a +3b)(4a -c)

Step-by-step explanation:

Group the terms pairwise, then factor each pair.

... (8a² -2ac) +(12ab -3bc)

2a is a common factor in the first pair of terms; 3b is a common factor in the second pair of terms. We can factor those out.

... = 2a(4a -c) +3b(4a -c)

Then we see that (4a-c) is a common factor in the result. We can factor that out.

... = (2a +3b)(4a -c) . . . . matches selection B

co·ef·fi·cient

ˌkōəˈfiSHənt/Submit

noun

1.

MATHEMATICS

a numerical or constant quantity placed before and multiplying the variable in an algebraic expression (e.g., 4 in 4x y).

So your answer is 3

3 because the number 3 in 3x is a coefficient and the x is the variable.

hope that helps :)

The equation of a parallel line will have the same x-term, but a different constant (y-intercept). The required value can be found by putting the given point values in to the equation to see what it needs to be.

... y = 5x + ___

... 8 = 5·4 + ___

... 8 - 20 = -12 = ___

Your equation is ...

... y = 5x -12

For quadratics, these formulas are used mainly for factoring.

Your equation can be written as ...

... 2(x² +2x -3) = 0

You factor this by looking for factors of -3 (c=x1·x2) that add to give +2 (b=-(x1+x2)). These are {-1, +3}, so the factorization is ...

... 2(x -1)(x +3) = 0

The roots are then 1 and -3, which sum to -b = -2.

(You will note that the numbers used in the binomial factors are the opposites of the roots x1 and x2 in the Viete's Formulas. That is how we can look for them to sum to "b", rather than "-b".)

We have a rectangular garden. The length of the garden is 7 feet longer than its width.

Lets say the width of the garden is 'x' feet. So, the length of the garden must be [tex](x+7)[/tex] feet.

Length [tex]=(x+7)[/tex] feet

Width [tex]=x[/tex] feet

We have been given that the perimeter of the garden is 186 feet.

Now as we know that the perimeter of the rectangle is:

[tex]2(length+width)[/tex]

Plugging the values of length and width in the equation, we get:

Perimeter [tex]= 2((x+7)+x)=2(2x+7)=4x+14[/tex]

We know that perimeter of the garden is equal to 186 feet,

So,

[tex]186=4x+14[/tex]

Solving for 'x' we get:

[tex]4x+14=186[/tex]

[tex]4x=186-14=172[/tex]

[tex]x=\frac{172}{4} =43[/tex]

We had assumed that the width of the garden is 'x' feet and now that we have the value of 'x'. We can say that:

The width of the rectangular garden is 43 feet.

The width of the garden is found by using the perimeter formula for a rectangle and the given information that the length is 7 feet longer than the width. Solving the resulting equation gives a width of 43 feet.

To find the width of the garden, we use the fact that the perimeter (P) of a rectangle is given by the formula P = 2l + 2w, where l is the length and w is the width. We are told that the length is 7 feet longer than the width, so we can express the length as w + 7. Substituting the given perimeter of 186 feet, we set up the equation as follows: 186 = 2(w + 7) + 2w. Simplifying further, we get 186 = 4w + 14. Subtracting 14 from both sides gives us 172 = 4w and dividing both sides by 4, we find w = 43. Therefore, the width of the garden is 43 feet.

x = 4 is the solution

given [tex]\sqrt{x+12}[/tex] = x ( square both sides )

x + 12 = x² ( rearrange into standard form )

x² - x - 12 = 0 ← in standard form

(x - 4 )(x + 3 ) = 0 ← in factored form

equate each factor to zero and solve for x

x - 4 = 0 ⇒ x = 4

x + 3 = 0 ⇒ x = - 3

substitute these values into the original equation and if both sides are equal then they are the solutions

x = 4 : [tex]\sqrt{4+12}[/tex] = [tex]\sqrt{16}[/tex] = 4 = x ← correct

x = - 3 : [tex]\sqrt{-3+12}[/tex] = [tex]\sqrt{9}[/tex] = 3 ≠ - 3 ← false

the solution is x = 4

Answer: x= 4

Step-by-step explanation:

n = 4.06

isolate the term in n by subtracting 11.57 from both sides of the equation

- n = 7.51 - 11.57 = - 4.06

multiply both sides by - 1

n = 4.06

As written, the inequality has a negative coefficient for the variable n. It can be convenient to add the opposite of the right side of the inequality to both sides, so the comparison is to zero:

... 25 +3(4n -3) > 0

... 25 + 12n -9 > 0 . . . . . . eliminate parentheses using the distributive property

... 12n + 16 > 0 . . . . . . . . . collect terms

... n + 4/3 > 0 . . . . . . . . . . divide by 12*

... n > -4/3 . . . . . . . . . . . . add the opposite of the constant (first of answer choices)

_____

6w -8 ≥ 22 . . . . . . . given

6w ≥ 30 . . . . . . . . . add 8

w ≥ 5 . . . . . . . . . . . .divide by 6* (second of answer choices)

_____

* When solving inequalities, solution can proceed in the same way it does for solving equations, with one exception. When multiplying or dividing by a negative number, the direction of the comparison changes. Consider the inequality

... 1 < 2

Now, see what happens when we multiply by -1:

... -1 > -2

You may note that we were always dividing by a positive number in the solutions above. That is intentional. In other words, we specifically chose the solution method for problem 3 so that we would avoid dividing by a negative number.

Part--1:

We know that a equation in point-slope form is represented by:

               [tex]y-y_1=m(x-x_1)[/tex]

where m is the slope of the line and [tex](x_,y_1)[/tex] is a point through which the line passes.  

  Consider a equation in a point-slope form as:

           [tex]y-5=2(x-1)[/tex]

This means that the slope of the line is: 5

and the line  passes through the point (1,5).

Part--2:

Now as we know that if a line has a slope as m then the perpendicular line has a slope: -1/m

Since,

[tex]m\times \text{Slope\ of\ second\ line}=-1\\\\i.e.\\\\\text{Slope\ of\ second\ line}=\dfrac{-1}{m}[/tex]

Let this perpendicular line passes through (2,6)

Hence, the equation of a line in point slope form is given by:

             [tex]y-6=\dfrac{-1}{2}(x-2)[/tex]

Answer:

Equation:

y-y1=m(x-x1)

y-2=4(x-1)

Part 2:

y=-1/4x +b

Step-by-step explanation:

Answer:

The answer will be 3.55

Step-by-step explanation:

Answer:

3.55

Step-by-step explanation:

26.30 - 22.75 = 3.55

So, you got it right.

[tex]Echy[/tex]

We need to find the unit price of each box.

So, a box that weighs 30 Oz costs $4.50.

lets say that 30 Oz box is named box 1. We can use unitary method to find out the unit price of box 1.

Unitary method is a process to find the value of a single unit.

Now,

30 Oz costs $4.50

therefore, 1 Oz should cost:

[tex]\frac{4.50}{30} =0.15[/tex] dollars

So, the unit price of box 1 is $0.15.

Now, lets say the 20 Oz box is named box 2. Again we can use unitary method to find out the unit price of box 2.

Now,

20 Oz box costs $3.60

therefore, 1 Oz should cost:

[tex]\frac{3.60}{20} =0.18[/tex] dollars

So, the unit price of box 2 is $0.18.

Angle 1 is in the northwest corner of the intersection of lines. Other (corresponding) angles that are in the northwest corner are ∠5, ∠9, and ∠13.

The appropriate choice is ...

... ∠5 and ∠13

Answer:

1887

Step-by-step explanation:

You can do this by putting the value -5 where x is in the expression, using synthetic division, or letting a calculator evaluate the function. (Likely a calculator is involved, regardless.)

Shown in the attachments are a couple of these methods.

Answer:

286.1 people per mile^2

Step-by-step explanation:

there are 11.69 million people in ohio

and ohio is 44,825 mi^2

so if you do 11.69 million / 44,825 = 268.1

Population density is calculated by dividing the population of an area by its size. The actual population density of Ohio can vary from estimates due to factors like population changes and migration. Researchers use various methods to calculate population size and density, especially for large areas.

The subject of this question deals with population density, which in the context of geography, refers to the number of people per unit of area. To calculate the population density of Ohio, you would need to first find the actual area of Ohio, and then find the actual population of Ohio. Once you have these two pieces of information, you can calculate the population density by dividing the population by the area. The difference between your initial estimate and the actual population density could be due to various factors, such as fluctuations in population size, migration patterns, or changes in the area's ">demographic data.

Population size can often be estimated using life tables, but this can be a complex process. A straightforward way to estimate population size is to count all the inhabitants in a certain area. However, for large areas like Ohio, this isn't always feasible, which is why researchers often use other methods or statistics to make these estimations. Understanding how population densities are calculated and how they can vary is important in fields like urban planning, sociology, and environmental science.

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Answer:

 So the water level of pond reduces by 8.16 centimeter over 25.5 days.

Explanation:

 Average change in pond's water level = -0.32 centimeter.

 Duration considered for taking the average of change in pond's water level = 25.5 days.

 Total change in the pond's water level = -0.32*25.5 = -8.16 centimeter

So the water level of pond reduces by 8.16 centimeter over 25.5 days.

I don't like algebra masquerading as geometry.  Algebra and geometry are connected in interesting ways, but this is boring.

It just says the two little angles add to the big angle,

(2x + 6) + (10x - 5) = 73

Solving,

12x + 1 = 73

12x = 72

x = 6

SQR = 2x+6 = 18 degrees

PQR = 10x -5 = 55 degrees

Answer:

x intercept is the point (0.3, 0)

Step-by-step explanation:

Just read it off the graph The line passes through the horizontal x axis halfway between 0.2 and 0.4  which is  0.3. Here x = 0.3 and y = 0.

the x-intercept is the point where the line crosses the x- axis.

From the graph this is where x = 0.3 or (o.3, 0 )

Remark

On the right, the deposits will build up and the river will have trouble depositing more material and still follow the path it is on. Eventually the river will want to take a short cut across the narrowest part or the neck.

Usually during flooding the water will cut across the narrowest part and an oxbow lake is formed. I think you are intended to answer B, but 50 years may not be enough time in which case D is the answer.

If you have notes on this event, find out what they say. I will choose B, but if you agree don't be surprised if it is D.

It is -1, at least thats what i got i hope this helped

The slope of a line can be found, given two points, as follows:

[tex]P_{1}(-5.5,6.1) \\ \\ P_{2}(-2.5,3.1) \\ \\ m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ \\ m=\frac{3.1-6.1}{-2.5-(-5.5)}=-1[/tex]

So this slope tells us the direction of a line and represents the vertical change divided by the horizontal change.

d because 0.7 is larger than 0.007

Answer:

The equation that can be used to solve for a is 1 = a(0=1)²-3.

Explanation:

In this case, I would model the parabola in vertex form.  Vertex form is y = a(x-h)²+k, where (h,k) is the vertex of the parabola.  Using the information from the question, we can plug in values to get 1 = a(0+1)²-3.  (This could be simplified as 1 = a(1)²-3 ⇒ 1 = a-3 ⇒ a = 4, but we are only interested in finding the equation that can solve for a.)

Answer:

The correct answer is A, 1 = a(0 + 1)^2 – 3

Step-by-step explanation:

The verified guy made a typo, putting = instead of + :P

c = 2b

a = [tex]2\sqrt{3}[/tex]

b = ?

Use Pythagorean equality:

[tex]c^2 = a^2 + b^2\\b^2 = c^2 - a^2\\b^2 = 4b^2 - 12\\b^2 = 4\\[/tex]

b can be only positive so the solution is b=2