5
The equation of a line is y=-x+9.
8
(a) What is the slope of a line parallel to it?
(b) What is the slope of a line perpendicular to it?
(a) The slope of a line parallel to it is. (Simplify your answer.)
(b) The slope of a line perpendicular to it is
(Simplify your answer.)

The number of soda bottles the machine can make each minute = 40

In this question, we have been given the graph shows the relationship between time and the number of soda bottles a machine can make.

Also, we have been given two points ​(​4,160​) and ​(6​,​240)

We need to find the number of soda bottles the machine can make each minute.

i.e., we need to find the slope of line passing through points  ​(​4,160​) and ​(6​,​240)

Using the formula of slope,

m = (240 - 160) / (6 - 4)

m = 80/2

m = 40

Therefore, the number of soda bottles the machine can make each minute = 40

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Answer: 14=2x

Step-by-step explanation:

the answer is 14=2x7=14

( 0 , -1 , 5) point lies on xyz plane .

The xy-plane is the plane that houses the x- and y-axes, while the yz-plane and the xz-plane house the y- and z-axes, respectively. Space is divided into eight sections known as octants by these three coordinate planes. The positive axes determine the first octant, which is in the front.

To be expressed, everything needs a perspective and a point of view. The three spatial dimensions are represented by the X, Y, and Z coordinates. These stand for length, width, and depth. We employ the same X, Y, and Z denotations when referring to machines, but we assign them different values or meanings. Even more intriguingly, there are no clear laws defining the meaning, which makes it difficult to converse on these levels.

this given point lies on xyz plane bcz the point itself shows coordinates which is only possible in xyz plane .

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Answer:

~62.35°

Step-by-step explanation:

To find the degree of an angle from side lengths, use reverse trigonometric function.

arcsin, arccos, arctan / [tex]sin^-1, cos^-1, tan^-1[/tex]

Because we have adjacent and opposite, lets use arctan.

Set up the equation.

[tex]x = arctan\frac{21}{11}[/tex]

Use a calculator to solve.

Answer:

9 km

Step-by-step explanation:

1/2 hr = 1800 seconds

3.7 m/s * 1800s    +   1.3 m/s * 1800 s  = 9000 m in 1 hr

   ( he walked AND ran this far)

Answer:

The decemial is 7

Step-by-step explanation:

0.7. Because 04 plus 0.3 equal to 0.7

By applying the concept of rate of a reaction, The graph B never saturates because the enzyme is always in excess.

What is the enzyme substrate reaction?

The enzyme is called a catalyst as it has an active site where the substrate can bind and convert into the product. Here in the graph the enzyme is amylase, and its substrate is starch. When there is an excess of enzymes in the solution, they can convert it into a product till substrates are available. If the substrate runs out, the reaction will come stop.

As per the concept of rate of a reaction, The graph B never saturates as the enzyme in the reaction is always in excess. These excess enzymes present will convert the starch into simple glucose molecules. Hence, there will be no upper limit, as both are in abundance.

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Answer:

x = -12

Step-by-step explanation:

Get X all on one side

7x - 8x = 8x - 8x + 12

-x = 12

x = -12

Answer:

x = -12

Step-by-step explanation:

To solve this, you will need to get all of the variables on one side, and the 12 on the other. You will subtract 8x from both sides to get the equation -x = 12. You can then divide both sides by -1 to get the x alone, and thus you get x = -12.

The value of the expression in the form of k² will be (T²/4π²)-h²).

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given expression is T² = 4π² (h² + k²). The expression for the value of k² will be calculated as,

T² = 4π² (h² + k²)

(h² + k²) = T² / 4π²

k² =  (T² / 4π²) - h²

Therefore, the value of the expression in the form of k² will be (T²/4π²)-h²).

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[tex]\fbox{1.333333}[/tex]

[tex]4\frac{2}{15} \div3.1[/tex]

Simplify:

[tex]4\frac{2}{15} \div3.1[/tex]

[tex]=1.333333[/tex]

let's firstly convert the  mixed fraction to improper fraction and the decimal one to a fraction.

[tex]\stackrel{mixed}{4\frac{2}{15}}\implies \cfrac{4\cdot 15+2}{15}\implies \stackrel{improper}{\cfrac{62}{15}}\hspace{10em} 3.\underline{1}\implies \cfrac{31}{1\underline{0}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{62}{15}\div \cfrac{31}{10}\implies \cfrac{62}{15}\cdot \cfrac{10}{31}\implies \cfrac{62}{31}\cdot \cfrac{10}{15}\implies \cfrac{2}{1}\cdot \cfrac{2}{3}\implies \cfrac{4}{3}\implies 1\frac{1}{3}[/tex]

Answer:

26x-56y

Step-by-step explanation:

First you open the bracket and collect like terms

55x-29x-46y-10y

26x-56y

9% of the volume of the original volume is removed.

Given that the dimensions of solid box is 15 cm by 10 cm by 8 cm.

So the volume of solid box = 15*10*8 cubic cm = 1200 cubic centimeter

The volume of the cube with side 3 cm = 3*3*3 = 27 cubic centimeter

For each corner one cube so the number of cube is 4

So total volume removed = 4*27 = 108 cubic centimeters

The percent of volume is removed = (108/1200)*100% = 9%

Hence the percentage of volume removed is 9%.

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The probability of an event is given by dividing the favorable outcomes by total number of outcomes. The sum of all the probabilities of events is always 1.

The probability that 2 red cards and 11 black cards are dealt is .

The probability of an event is given by dividing the favorable outcomes by total number of outcomes. The sum of all the probabilities of events is always 1. If for finding probability we have to select r out of n. Combination is used to select r items out of n, the formula is as follows,

[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]

Finding the probability that 2 red cards and 11 black cards are dealt,

Number of favorable outcomes will be [tex]^{26}C_2\times^{26}C_{11}[/tex].

Total number of outcomes will be [tex]^{52}C_{13}[/tex]

Now, the probability will be,

[tex]P()=\frac{^{26}C_2\times^{26}C_{11}}{^{52}C_{13}} \\\\=\frac{325\times7726160}{635013559600} \\\\=0.00395[/tex]

Therefore, the probability that 2 red cards and 11 black cards are dealt is 0.00395.

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The volume of the cone is 15393.80 cm³

The curved surface area of a cone is 4068.36 cm²

The total surface area of the cone is 7916.81 cm²

Given parameters;

The base radius( r ) of the cone is 35cm

The height( h ) of the cone is 12cm

Case (I): To find the volume of the cone;

The volume of the cone = [tex]\pi r^{2}\frac{h}{3}[/tex]

                                        = π *(35)² * 12/3

                                        = 15393.80 cm³

Case (II): To find the curved surface area of the cone;

The curved surface area of the cone = πrl

We know that;

Slant height l = [tex]\sqrt{(r^2 + h^2)}[/tex]

By substituting the values;

l = [tex]\sqrt{35^2 + 12^2}[/tex]

l = 37

We know that;

The curved surface area of a cone = πrl

                                                          = π * 35 *37

                                                          = 4068.36 cm²

Case (III): The total surface area of the cone;

The total surface area of the cone = πr(l + r)

                                                         = π * 35 * (37 + 35)

                                                         = 7916.81 cm²

Therefore,

The volume of the cone is 15393.80 cm³

The curved surface area of a cone is 4068.36 cm²

The total surface area of the cone is 7916.81 cm²

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Answer:

g(10)=-33, x=3

Step-by-step explanation:

g(x)=-4x+7. --------(1)

a) g(10)=?

since we know function x = -4x+7 to find function g(10) we will just place 10 whenever we see x

g(10)=-4(10)+7

g(10)=-40+7

g(10)= -33

b.)find x if g(x)=-5. ---------(ii)

g(x)=-4x+7. we will place (I) in (ii)

g(x)=-5

-4x+7=-5

-4x=-5-7

-4x=-12

cancel the minus(-) sign in both sides

4x=12

x=12/4

x=3

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Answer:

I think is 50m.

Step-by-step explanation:

Is it possible to apply the conditional probability in its alternative form, P(R2|R1) is n(R1⋂R2) divided n(R1) Given that the product rule hasn't yet been taught, we have advocated this approach.

The probability of drawing a second red in the event that this red is not changed is 9/15,

hence the probability of A is 10/16 * 9/15, or 0.375.

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Answer: 60 degrees

Step-by-step explanation: Because all sides are equilateral, and in an equilateral triangle all angles are 60 degrees, hope that helps.

The given two equations are Perpendicular to each other .

What is intersection of lines ?

 It is known as an intersection of lines when two lines have exactly one point in common. A point is shared by the connecting lines. The point of intersection is the same place that may be found at the intersection of all intersecting lines. When two or more straight lines cross each other in a plane, they are said to be intersecting lines. An intersection point will be present for the two non-parallel straight lines that are coplanar. The point of intersection, which can be found on all intersecting lines, is where the intersecting lines share a common point.

Here the equation of line is y=mx+b .

Where m = slope . then,

=> y = x-7 where here slope m1= 1 and

=> y = -x+3 where here slope m2 = -1 .

Here the m1= -m2

Hence the given two equations are Perpendicular to each other .

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Answer:

(-4,-1) and (3,1), respectively.

Step-by-step explanation:

I am not quite sure if the question is necessarily asking for this, but the x and y values are switched to get the points of the inverse. (-1,-4) --> (-4,-1) and (1,3) --> (3,1). I hope that makes sense!

The given formula can be written as 5F = 9C + 160.

A measurement unit is a unit to measure certain quantities. To find the measurement of a new quantity knows units can be used in operation. As to find the unit for speed we use m/s as a unit, where, m is the unit of distance and s is the unit of time.

Given that,

The conversion formula for °C into °F is 9C  = 5(F - 32)

The given formula can be written in the form of cF = aC + b as,

9C = 5(F - 32)

⇒ 5F = 9C + 160

Hence, the given formula can be written by making F as the subject as 5F = 9C + 160.

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The level of water in the swimming pool after a specified duration of the water draining at a constant rate is found as follows;

10. a. The water level is changing (reducing) at a rate of 1.75 inches per hour.

b. After 9 hours, the change in the water ls 15.75 inches

c. The change in the water level after 23 hours is 40.25 inches

A constant rate is a rate that is fixed or steady and does not vary following a change of the other variables?

The table of values for the draining swimming pool obtained from a similar question on the internet is as follows;

Hours Draining  [tex]{}[/tex]           Change in Water Level (inches)

2   [tex]{}[/tex]                                   -35

9  [tex]{}[/tex]                                     ?

17  [tex]{}[/tex]                                    -29.75

23  [tex]{}[/tex]                                    ?

The relationship between the hours the swimming pool drains and the water level is a proportional relationship., such that the ratio of each coordinate pair in the table is a constant.

Let H represent the hours draining and let C represent the change in water level, we have;

C ∝ H

C = k·H
[tex]k = \dfrac{C}{H}[/tex]

Where;

k = The constant of proportionality, which is the rate at which the water level is changing per hour

a. The rate at which the water level changes per hour can be found from the first pair of points on the table as follows;

The first pair of points = (2, -3.5)

[tex]k = \dfrac{-3.5}{2} = -1.75[/tex]

The rate at which the water level is changing per hour is -1.75 inches per hour

The water level is decreasing at 1.75 inches per hour

b. The change in water level after 9 hours is found by using the formula;

C = k × H

Where, H = 9, we have;

Change in water level, C = -1.75 × 9 = -15.75

The change in water level after 9 hours is 15.75 inches

c. The change in water level after 23 hours is found by plugging in H = 23 as follows;

C = -1.75 × 23 = -40.25

The change in water level after 23 hours is -40.25 inches

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The solution to the expression given as 5x + 3y > 12 has the ordered pair of (3, 0)

From the question, we have the following inequality that can be used in our computation:

5x + 3y > 12

Solving further, we need to collect the like terms

So, the expression becomes

3y > 12 - 5x

Next, we divide through the inequality by 3

So, we have the following representation

y > 12/3 - 5/3x

Evaluate

The equation becomes

y > 4 - 5/3x

At this point, we assume any value for x and then solve for y

Assume that the value of x is 3

So, we have the following representation

y > 4 - 5/3 * 3

Evaluate the products

y > -1

A value greater than -1 is 0

So, we have

x = 3 and y = 0

Express as ordered pairs

(x, y) = (3, 0)

Hence, the ordered pair of the solution is (3, 0)

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The new x-coordinate must be 2-2 = 0.

acc to our question-

Finding the distance between the known endpoint and the midpoint, then applying the same transformation to the midpoint, is the quickest technique to locate the missing endpoint. The x-coordinate changes in this situation from 4 to 2, or down by 2, hence the new x-coordinate is 2-2 = 0.

Hence,The new x-coordinate must be  = 0.

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The coordinates of point N are (8.66, 21)

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.

The coordinates of a point dividing a straight line joining two coordinates in the ratio m : n is given by -

x =  [tex]$\frac{mx_2+nx_1}{m+n}[/tex]

y = [tex]$\frac{my_2+ny_1}{m+n}[/tex]

We have LMN as a straight line such that the coordinates of L are (-3,1) , coordinates of M are (4,9) and LM : MN is 2 : 3.

Assume the coordinates of point N are (a, b).

We can write -

9 =  (2b + 3)/5

4 = (-6 + 3a)/5

2b + 3 = 45

b = 21

3a - 6 = 20

3a = 26

a = 8.66

Therefore, the coordinates of point N are (8.66, 21)

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