A line has a slope of 1/2 and includes the points (-4,-7) and (w,-3) What is the value of w?

1) The bus took a 30-minute stop in the interval between D and E

2) The bus traveled the fastest in the interval between C and D

3) The bus was traveling at 60 miles per hour during this interval.

4) The average rate of speed of the bus over the entire journey is 35 miles /hr

Speed is the rate at which an object's position changes, measured in meters per second. For example, if an object starts at the origin, and then moves three meters in three seconds, its speed is one meter per second. The equation for speed is simple: distance divided by time

Given here for the first question we have there was no change in the distance in the interval between D and E thus bus must have stopped for 30 minutes.

2) The interval in which the bus travelled the fastest is between C and D

3) The Speed of the bus in this interval is S = 90/1.5

                                                                         = 60 miles/hr

4) The average speed of the bus over the entire trip is Sₐ = 140/4

                                                                                                = 35 miles/hr

Hence the above answers are correct ones.

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Answer:

For the first graph:

Domain: -∞ [tex]\leq[/tex] x [tex]\leq[/tex] ∞

Range: y [tex]\geq[/tex] 3

For the second graph:

Domain: 0 [tex]\leq[/tex] x [tex]\leq[/tex] 4

Range: y [tex]\leq[/tex] 64

Step-by-step explanation:

For the second graph, I'm assuming that that point are stopping at (0,0) and (4,0) that's why I wrote that for the domain. If it doesn't stop, then the domain would be the same and the first graph.

The speed of the current of the river will be 4.47 km per hour.

Speed is defined as the length traveled by a particle or entity in an hour. It is a scale parameter. It is the ratio of length to duration.

We know that the speed formula

Speed = Distance/Time

A riverboat goes at a normal of 14km each hour in still water. the riverboat voyages 110km east up the Ohio waterway and 110km west down a similar stream in a sum of 17.5 hours.

Let 'y' be the speed of the current of the river. Then the equation is given as,

T = T₁ + T₂

17.5 = [110 / (14 + y)] + [110 / (14 - y)]

17.5 / 110 = (14 - y + 14 + y) / (196 - y²)

196 - y² = 176

y² = 20

y = 4.47 km per hour

Then the speed of the current of the river will be 4.47 km per hour.

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A) 3x+9y-1 = 3(x+3y) -1, here distributive property is used the 3 is multiplied with each term inside the bracket.

What is algebraic operations?
Any of the common arithmetic operations, such as addi - tion, subtraction, multiplication, division, raising to a complete number power, and taking roots, are considered basic algebraic operations in mathematics (fractional power). These operations could be applied to numerical data, in which case people are frequently referred to as arithmetic operations. Similar operations can be carried out on factors, algebraic expressions, and, more generally, on components of algebraic structures like groups and fields. Another way to describe an algebraic operation is as a function from the Cartesian power of the a set to the same set. The dot product is an example of an operation that can be described by compounding simple algebraic operations, and is referred to as an algebraic operation.

b) 7x+5y-5y = 7x

Here the Additive inverse of 5y is used which is -5y .

c) (x-4)(x+3) = 0

here distributive property of addition over multiplication is used.

d) 4x+5x = 5x+4x

here commutative property is used.

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By resolving an equation, we may determine that Uan needs to sell 12 or more goods in order to generate a profit of $60 or more.

A formula that describes how two expressions on each side of a sign are connected.

It typically has an equal sign and one variable.

Similar to this: 2x - 4 = 2.

Graphing, substitution, or elimination are the three methods that can be used to solve systems of equations.

To answer a problem by graphing, just plot the given equations on a graph and identify the point(s) where they all intersect.

So, a number of items Uan should sell to earn a profit of $60 or above:
We know that Uan earns $5 for each item he sells.

So, let x be the number of items Uan should sell.

Then, the equation will be:

5x = 60

Now, solve as follows:
5x = 60

x = 60/5

x = 12

Profit of $60: 12 items to sell

Profit more than $60: More than 12 items to sell

So, by resolving an equation, we may determine that Uan needs to sell 12 or more goods in order to generate a profit of $60 or more.

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The graph line for function d = 0.25t is added as an attachment

The equation of the function is given as

d = 0.25t

The above function is a linear function

One way to create the graph is to make a list of ordered pairs

So, we have

When t = 0, d = 0.25 * 0 = 0

When t = 1, d = 0.25 * 1 = 0.25

When t = 2, d = 0.25 * 2 = 0.5

So, the ordered pairs are (0, 0), (1, 0.25) and (2, 0.5)

We plot these points on a graph and connect them through a line

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The solution is y will increase by 2 units with every unit increase in x1

A single dependent variable and several independent variables can be analyzed using the statistical technique known as multiple regression. In order to predict the value of the single dependent value, multiple regression analysis uses independent variables whose values are known.

X and Y variables are the sole ones in simple linear regression. Two or more x variables and one y variable make up multiple linear regression. For instance, basic linear regression is used when we forecast rent using only square footage.

In the above question:-

Interpretation of b1=2

it means that y will increase every 2 units for every unit increase in x1

holding x2 constant.

Hence option B is the correct answer.

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The length of the other leg of the given right triangle is [tex]\sqrt{70}[/tex].

A triangle is classified as a right triangle when it presents one of your angles equal to 90º.  The greatest side of a right triangle is called the hypotenuse. And, the other two sides are called legs.

The math tools applied for finding angles or sides in a right triangle are the trigonometric ratios or the Pythagorean Theorem.

The Pythagorean Theorem says (hypotenuse)²= (leg1)²+(leg2)². And the main trigonometric ratios are: sin (x) , cos  (x) and tan  (x) .

The question gives:

Therefore, from the Pythagorean Theorem, you will find the value of the other leg. See below.

[tex]9^2={\sqrt{11}^2 +{leg_2}^2[/tex]

[tex]81=11 +{leg_2}^2[/tex]

[tex]{leg_2}^2=81-11\\ \\ {leg_2}^2=70\\ \\ leg_2=\sqrt{70}[/tex]

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The value of x for the given equation is 1.

What is solving an equation?

A General Rule for Equation Solving

Remove parentheses from each side of the equation and combine similar phrases to make it simpler.

To separate the variable term on one side of the equation, use addition or subtraction.

To find the variable, use division or multiplication.

Consider the given expression

0.2(x + 1) + 0.5x = -0.3(x - 4)

Simplifying,

0.2x + 0.2 + 0.5x = -0.3x + 1.2

0.7x + 0.2 = -0.3x + 1.2

Add 0.3x on both sides,

0.7x + 0.2 + 0.3x = -0.3x + 1.2 + 0.3x

x + 0.2 = 1.2

Subtract 0.2 from both sides,

x + 0.2 - 0.2 = 1.2 - 0.2

x = 1

Hence, the value of x for the given expression is, 1.

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The slope and y-intercept of this function is

B. The slope is 5/6, The y-intercept is (0, -3

Linear function is a function of the form y = mx + c

m = slope

c = intercept

The slope is represented as m, The slope by definition is the ratio change of the output values to the input values

the slope, m calculated using the points (0, -3) and  (6, 2)

m = (y₀ - y₁) / (x₀ - x₁)

m = (2 - -3) / (6 - 0)

m = (5) / (6)

m = 5/6

c = y intercept, from the table

c = -3

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By solving a quadratic equation, it can be calculated that

Length of the plot = 85 ft.

Width of the plot = 100 - 85 = 15 ft.

What is a quadratic equation?

Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.

A two degree equation is known as quadratic  equation.

Here a quadratic equation needs to be solved.

Let the length be l ft. and the width be b ft.

Perimeter = 2(l + b) ft.

By the problem,

2(l + b) = 200

l + b = [tex]\frac{200}{2}[/tex]

l + b = 100

b = (100 - l) ft.

Now,

Area = l [tex]\times[/tex] b sq. ft.

        = [tex]l \times (100 - l)[/tex]

By the problem,

[tex]l \times (100 - l) = 1275\\100l - l^2=1275\\l^2 -100l+1275 = 0\\l^2 - 85l -15l + 1275 = 0\\l(l -85) - 15(l - 85) = 0\\(l -85)(l -15) =0\\l -85 = 0 \ or \ l -15 = 0\\l =85 \ or \ l =15[/tex]

If l = 15 ft.

b = 100 - 15 = 85 ft.

Which is not possible as length is always greater than the width

So, length of the plot = 85 ft.

Width of the plot = 100 - 85 = 15 ft.

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The value of x = 6cm.

What is surface area?

The area is the area occupied by a two-dimensional flat surface. It has a square unit of measurement. The surface area of a three-dimensional object refers to the space occupied by its outer surface.

From the given figure,

Surface area(A) = [tex]192cm^{2}[/tex]

Height = 8cm

a base side = 6 cm

b base side = 10 cm

c base side = x cm

Therefore,  TSA= 2B +Px = [tex]2 \times\frac{1}{2} \times8\times6 +(6+10+8)x[/tex]

                                          =48+24x

Thus, 60+24x=192

                     [tex]x=\frac{192-48}{24}[/tex]

                      x= 6cm

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Answer:

[tex]S=\{-2,-3\}[/tex]

Step-by-step explanation:

Required integers are: -2 and -3

A comparison of multiple treatments and the use of the double-blind method are two fundamental components of all statistically designed experiments. (6) Compare various treatments; assign patients to treatments at random.

What is double-blind method?

A kind of clinical experiment in which neither the participants nor the researcher is aware of the treatment or intervention that each participant is receiving until the trial is complete.

                      This reduces the likelihood of skewed study outcomes.

What is a sample of a double-blind study?

Imagine, for instance, that researchers are looking into the effects of a novel medication.

                            The participants in a double-blind study would not be aware of who was receiving the real medication and who was receiving a placebo, and neither would the researchers who interact with them.

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The complete question is -

Two essential features of all statistically designed experiments are (2 Points) O use enough subjects; always have a control groups O always have a placebo group; use the double - blind method O use a block design; use chance to assign subjects to treatments O compare several treatments; use the double - blind method O compare several treatments; use chance to assign subjects to treatments.

The average rate of change over the interval x = -2 and x = 1 is 4

The equation is given as

f(x) = x² + 5x - 12

The interval is given as:

x = -2 to x = 1

Start by calculating the functions f(-2) and f(1)

So, we have

f(-2) = (-2)² + 5(-2) - 12 = -18

f(1) = (1)² + 5(1) - 12 = -6

So, the average rate over these intervals is calculated as:

Average rate = [f(1) - f(-2)]/[1 - -2]

This gives

Average rate = [-6 - -18]/[1 - -2]

Evaluate

Average rate = 4

Hence, the average rate of change is 4

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The simplest expression of the ratio of circles to squares is 5:3.

Describe ratio.

A relationship between two quantities is called a ratio, and it is expressed as one quantity divided by the other.

There are 6 circles and 10 squares.

These steps can be used to determine the ratio of two quantities:

Finding the quantities of both scenarios for which we are calculating the ratio is the first step. There are 10 squares and 6 circles in this instance.

It should be expressed as a fraction, a/b. Thus, we represent it as 10/6.

If you can, make the fraction even simpler. The ultimate ratio will be shown by the simple fraction.

In this case, 10/6 can be reduced to 5/3.

As a result, the simplest expression of the ratio of circles to squares is 5:3.

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The balance due on the note at the date of maturity is ​$1010.13.

The offering of a payment by cheque for less than the whole amount sought by the creditor is known as partial payment. It is standard practice to grant debt forgiveness in exchange for the tender of a "payment-in-full" check.

Given permission to apply the US rule

In the United States, a year is deemed to have 360 days for the purposes of calculating interest.

Given that the principal is $ 2000,

Interest rate = 4% = 0.04

The effective date is April 1.

The whole amount is $1,000.

May 1 = partial payment

Duration = 30 days (May 1 - April 1)

Therefore, interest = PTR = 2000 * 0.04 * 30/360 = $6.67

So value = $ 2000 + $6.67 = $6.67

Partial payment received = $1,000

As a result, value = $ 1006.67 = $2006.67 - $ 1000

Time T= 31

Interest = PTR * 31/360 * 0.04 = 3.46

So the total value is $1006.67 + $3.47 = $1010.13.

The note's outstanding balance at maturity is $1010.13.

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Answer: [tex]x=-1, 2[/tex]

Step-by-step explanation:

If [tex]ab=0[/tex], then [tex]a=0[/tex] and/or [tex]b=0[/tex].

So, [tex]x+1=0[/tex] or [tex]2x-4=0[/tex].

[tex]x+1=0 \implies x=-1\\\\2x-4=0 \implies x=2\\\\\therefore x \in \{-1, 2\}[/tex]

The journey along Line segment X Y is longer than the path along Line segment Z Y, and the path along Line segment Z Y is longer than the path along Line segment A B, hence Option-A is the correct answer.

Given that,

He makes paths that follow Line segments A and B, X and Y, and Z and Y through the garden.

We have to find which accurately compares the pathways' lengths.

We know that,

The length of the third side in a triangle is proportional to the angle Ф  if the lengths of the two sides that make up the angle Ф are fixed.

XY > YZ because XY's opposing angle (79°) is greater than YZ's (65°).

As before, YZ > AB because the opposing angle of YZ (65°) is greater than that of AB (36°).

Since both sides of the angle are the same length (8 feet),

As a result, assertion A. is accurate. (Answer)

Therefore, The journey along Line segment X Y is longer than the path along Line segment Z Y, and the path along Line segment Z Y is longer than the path along Line segment A B, hence Option-A is the correct answer.

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Answer:

It's A

Step-by-step explanation:

I got 100 on the quiz

Answer: 2/11

Step-by-step explanation: there are 11 letters and 2 of them are p so the chances of getting p is 2/11

Answer:

2/11

Step-by-step explanation:

The total amount of tiles is 11. There are only 2 tiles that have the letter P on them.

Theoretical probability is the probability that should occur over many, many trials.

Theoretical probability = favorable outcomes / total outcomes.

In this scenario, the favorable outcome is the letter P. which there are two of. The total outcomes would be all the letters that make up the word MISSISSIPPI, or 11.

So your theoretical probability would be 2/11.

The height of the kite assuming that there is no slack in the string is 86.6 m.

We have given that,

the string of a kite is 100 meters long and it makes an angle of 60°.

and we have to find the height of the kite.

So therefore we know the formula for right angled triangle,

i.e. sinθ = Opposite side/ Hypotenuse

Here θ = 60°

Opposite side = height of the kite = h (say)

Hypotenuse = length of string = 100 m

⇒ sin60° = [tex]\frac{h}{100}[/tex]

           h = 100sin60°

              = 100 × [tex]\frac{\sqrt{3} }{2}[/tex]

              = 50 × 1.732

           h = 86.6 m

Hence the height of the kite is 86.6 m.

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The statemet 2, the variable K represent carrying capacity and the variable N represent population size, is correct.

In the given question we have to review the video to determine whether each statement about the following equation is true or false.

The given equation is:

[tex]\frac{dN}{dt}=rN(\frac{K-N}{K})[/tex]

The given equation is used to find the annual growth of population.

In which, dN/dt = the annual increase for the population,

r = the annual growth rate,

N = the population size, and

K = the carrying capacity.

So the statemet two, the variable K represent carrying capacity and the variable N represent population size, is correct.

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Answer: How Weather Exists

Step-by-step explanation:

~I think you mean, how weather exists.

You see, "Weather" exists because of the atmosphere. Evidently, weather  is the movement of the atmospheric gases around the planet that creates weather. Places like the Moon or Mercury do not have weather - only temperature changes.

~Hope this helped :)

The simplification of the expression (3√-5 + 2)(4√-5 -1) gives 5√-5 - 62

Simplification is a way of determining an answer for a complex calculation that may involve numbers on division, multiplication, square roots, cube roots, plus and minus, etc.

Given: the expression (3√-5 + 2)(4√-5 -1)

(3√-5 + 2)(4√-5 -1)

Clear the parenthesis:

(3√-5 + 2)(4√-5 -1) = 3√-5(4√-5) + 3√-5 (-1) + 2(4√-5) + 2(-1)

                             = -60 - 3√-5 + 8√-5 -2

                            = 5√-5 - 62

Therefore, the expression (3√-5 + 2)(4√-5 -1) simplifies to 5√-5 - 62

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Answer:

Slope-intercept form: y = 3x + 5

Slope: 3

y-intercept: 5

Step-by-step explanation:

When the equation of a line is written in the slope-intercept form, we can easily identify the slope from the coefficient of x and the y-intercept from the constant.

The slope-intercept form is expressed as y = mx + c, where m is the slope and c is the y-intercept. Note that other textbooks might use y = mx + b instead, but both have the same meaning as both m and b or c will be replaced by a certain value.

To rewrite an equation in the slope-intercept form, isolate the y term on the right-hand side of the equation and divide the whole equation by the coefficient of y.

Working

[tex]y - ( - 7) = 3(x - ( - 4))[/tex]

Expand:

[tex]y + 7 = 3(x + 4)[/tex]

[tex]y + 7 = 3x + 12[/tex]

Subtract both sides by 7:

[tex]y = 3x + 12 - 7[/tex]

[tex]\bf{y = 3x + 5}[/tex]

Since the coefficient of y is already 1, we have arrived at our final answer.

When the equation is in the slope-intercept form, the slope can be identified from the coefficient of x. This refers to the number that comes before x which is multiplied to x.

Thus, the slope is 3.

The y-intercept is the value of the constant in the slope-intercept form. This refers to the number that is not attached to any variables.

Hence, the y-intercept is 5.

Note that the y-intercept can also be found by substituting x = 0 into the equation.

The x-intercept occurs at y = 0. Since we have the equation of the line, we can substitute y = 0 into the equation to find the value of x when y = 0.

Working

y = 3x + 5

When y = 0,

0 = 3x + 5

3x = -5

Divide both sides by 3:

[tex]x = - \frac{5}{3} [/tex]

I have attached the graph as an image. If only a sketch is required, there are 3 pieces of information that needs to be labelled on the graph:

Additional resources:

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From knowledge of numerals the answer to the given Question is: a = 3 b = 6 c = 5

What are Numerals?

Numerals are symbols or numerals used to represent numbers. They are used in math and other fields to represent quantities and measurements. Numerals can be written in different forms, such as Arabic numerals (1, 2, 3, etc.) or Roman numerals (I, II, III, etc.). Numerals are also used to label items, such as dates (e.g. May 4th, 2020), addresses (e.g. 1234 Main Street), and telephone numbers (e.g. 555-123-4567). Numerals are an important part of our everyday lives, used to count, measure, and express amounts.

Numerals are just a combination of digits that we know
for example if 0,1,2,3,4,5,6.....9

are the fundamental digits then numbers from these like

12,34,668,389,23,39 etc are called numerals

We can also conclude that all numbers have originated from numerals itself and numerals are basic unit of formation of numbers

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By using the concept of maxima, it can be calculated that

Volume is maximum if the radius of the cone is 40 cm

What is maxima of a function?

Maxima of a function gives the maximum value of the function on a certain interval or on the whole domain.

Let the height of the cylinder be h and radius be r

Sum of height and circumference = h + 2πr

By the problem,

h + 2πr = 60

h = 60 -2πr

Volume(V) = π[tex]r^2[/tex] h

             = π[tex]r^2[/tex](60 - r)

             = 60π[tex]r^2[/tex] - π[tex]r^3[/tex]

[tex]\frac{dV}{dr} = 120\pi r - 3 \pi r^2[/tex]

For maximum volume

[tex]\frac{dV}{dr} = 0[/tex]

[tex]120\pi r - 3 \pi r^2 = 0\\[/tex]

[tex]3 r^2 = 120 r\\3r = 120 [r \neq 0]\\r = \frac{120}{3}\\r = 40 \ cm[/tex]

[tex]\frac{d^2V}{dr^2} = 120 \pi - 6 \pi r\\[/tex]

Putting r = 40

[tex]\frac{d^2V}{dr^2} = 120 \pi - 6 \pi \times 40\\\frac{d^2V}{dr^2} =120\pi - 240 \pi\\\frac{d^2V}{dr^2} = -120\pi < 0[/tex]

Hence Volume is maximum

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The angles ∠BCD and ∠BAD are opposite interior angles of a parallelogram. in which the alternate interior angles  ∠BAC  and  ∠ACD and ∠BCA and ∠DAC are congruent, from which by angle addition property, ∠BCD ≅ ∠BAD

Alternate interior angles are angles formed by the transversal to two parallel lines on the inside of the parallel lines, and on opposite sides of the transversal.

The two column-method used to  prove that ∠BCA is congruent to ∠DAC can be presented as follows;

Step       [tex]{}[/tex]         Statement                                          Reason

1.        [tex]\overline{BC}[/tex]║ [tex]\overline{AD}[/tex],  [tex]\overline{AB}[/tex]║[tex]\overline{CD}[/tex]   [tex]{}[/tex]       Given

2. [tex]{}[/tex]    ∠BCA ≅ ∠DAC                  ║ lines cut by a trans. form ≅ int.  ∠s

3. [tex]{}[/tex]    [tex]\overline{AC}[/tex]║[tex]\overline{CA}[/tex]     [tex]{}[/tex]                         Reflexive Property

4.     ∠BAC ≅ ∠ACD [tex]{}[/tex]                  Alternate interion angles

5.     ∠BCA = ∠DAC[tex]{}[/tex]                    Definition of congruency

[tex]{}[/tex]        ∠BAC = ∠ACD

6.    ∠BCD = ∠BCA + ∠ACD[tex]{}[/tex]       Angle addition property

      ∠BAD = ∠BAC + ∠DAC

7.    ∠BCD = ∠BCA + ∠ACD  [tex]{}[/tex]       Substitution property

8. [tex]{}[/tex]   ∠BCD = ∠BAD   [tex]{}[/tex]                    Substitution property

9.    ∠BCD ≅ ∠BAD   [tex]{}[/tex]                    Definition of congruency

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Answer:

The three numbers are 3, 7 and 13

Step-by-step explanation:

Considering the 3 numbers: x, y and z

x + z = 16

z=16-x

3x=z-4

3x=16-x-4

4x=12

x=3

3+z=16

z=16-3

z=13

3+13+y=23

y=23-13-3

y=7

Hope this helps :)

Answer:

[tex]\huge\boxed{\sf 3 \ baskets}[/tex]

Step-by-step explanation:

Let the baskets missed in game 2 be x.

Says that, the shooting of both the games were accurate.

So,

[tex]\displaystyle \frac{Baskets \ made \ in \ game \ 1}{Baskets \ missed \ in \ game \ 1 } =\frac{Baskets \ made \ in \ game \ 2}{Baskets \ missed \ in \ game 2} \\\\\frac{15}{5} =\frac{x}{1} \\\\Cross \ Multiply\\\\15 \times 1 = 5 \times x\\\\15 = 5x\\\\Divide \ 5 \ to \ both \ sides\\\\3 = x\\\\x = 3\\\\\rule[225]{225}{2}[/tex]