The city plans a new road that will be parallel to Village Way and pass through the intersection of Gray Dr and Canon Rd. What is the equation of the road in slope-intercept form?

Sarah's company started out with a $350 value and is currently changing at a rate of $100 annually.

The annual fee is expressed as an equation in slope-intercept form:

y = 100x + 350.

y = mx + b, where m is the line's slope and b is its y-intercept, is the formula for a straight line.

Given details:

The table displays the prices that Sarah charged each client during the course of her business's first two years:

Year                            Annual Dog-walking Fee

2010                            $350

2014                            $750

A.

Sarah has so increased the cost by $400 over the past four years.

For Sarah's company, its rate of change called slope will be,

m = 750 - 350 / 4

m = 100

Therefore, Sarah is raising the cost by $100 yearly.

Due to the payment she received for the first year, the calculated values of a business is $350.

B. Define x as the period of time that has passed since she began her business in 2010.

Consequently, the annual fee equation can be expressed in slope-intercept form as,

y = mx + c

where y stands for the cost she must pay after x years.

Her company's baseline value is therefore $350, and its rate of change is $100 annually.

The annual fee is expressed as an equation in slope-intercept form.: y = 100x + 350.

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The equation of the plane orthogonal to the line (x, y, z) = (9, 5, 7) + t(-2, -4, 4) and passing through the point (5, 7, 9) can be written as -2x - 4y + 4z = 36.

To find the equation of a plane orthogonal (perpendicular) to a line, we need a direction vector of the line and a point that lies on the plane. In this case, the given line has a direction vector of (-2, -4, 4) and passes through the point (9, 5, 7).

We can start by finding a normal vector to the plane by taking the cross product of the direction vector of the line and a vector formed by subtracting the given point (5, 7, 9) from any point on the line (9, 5, 7). The cross product of (-2, -4, 4) and (4, 2, 2) gives us a normal vector of (4, 0, 0).

Using the normal vector (4, 0, 0) and the coordinates of the point (5, 7, 9), we can write the equation of the plane in the form ax + by + cz = d. Plugging in the values, we get -2x - 4y + 4z = 36.

Therefore, the equation of the plane orthogonal to the given line and passing through the point (5, 7, 9) is -2x - 4y + 4z = 36.

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Answer:

Step-by-step explanation:

2.00/5= 0.40 an orange

12*.40= $4.80

Answer:

The correct answer is:

||u|| = 18.439; θ = 130.601°

The magnitude of the vector u is 18.439 and its direction is 130.601°. These values come from the formulae for the magnitude and direction of a vector, given its initial and terminal points.

The initial and terminal points of vector u decide its magnitude and direction. The magnitude of the vector ||u|| can be calculated using the distance formula which is √[(x2-x1)²+(y2-y1)²]. The direction of the vector can be found using the inverse tangent or arctan(y/x), but there are adjustments required depending on the quadrant.

Given the initial point (4, 8) and terminal point (–12, 14), we derive the magnitude as √[(-12-4)²+(14-8)²] = 18.439, and the direction θ as atan ((14-8)/(-12-4)) = -49.399°. However, since the vector is in the second quadrant, we add 180° to the angle to get the actual direction, which becomes 130.601°. Therefore, ||u|| = 18.439; θ = 130.601°.

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Answer: its 11.2 my good sir

Step-by-step explanation:

Im jsut smort trust me its right

Answer:

11.25 miles

Step-by-step explanation:

To figure out how many miles John will travel in 1/2 an hour, we can use the following formula:

distance = rate x time

We know the rate, which is the number of miles John can travel per hour. We can find this by dividing the total distance by the total time:

rate = distance / time

rate = 45 miles / 2 hours

rate = 22.5 miles per hour

Now we can use this rate and the given time of 1/2 an hour to find the distance:

distance = rate x time

distance = 22.5 miles per hour x 1/2 hour

distance = 11.25 miles

Therefore, John will travel 11.25 miles in 1/2 an hour at this rate.

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Let's solve ~

\(\qquad \sf  \dashrightarrow \: ( - 3 {p}^{3} + 5 {p}^{2} - 2 p) + ( - p {}^{3} - 8 {p}^{2} - 15p)\)

\(\qquad \sf  \dashrightarrow \: - 3 {p}^{3} + 5 {p}^{2} - 2 p - p {}^{3} - 8 {p}^{2} - 15p\)

\(\qquad \sf  \dashrightarrow \: - 3 {p}^{3} -p³+ 5 {p}^{2} - 8 {p}^{2} -2p - 15p\)

\(\qquad \sf  \dashrightarrow \: - 4{p}^{3} -3 {p}^{2} - 17p \)

The  area of triangle is 21 yd².

The region contained by a triangle's sides is known as the area of the triangle. The length of the sides and internal angles affect a triangle's area differently from one triangle to the next.

Area of triangle = 1/2 × base × height

Given:

Base= 6 yd

Height = 7 yd

So, Area of Triangle

= 1/2 x base x height

= 1/2 x 6 x 7

= 3 x 7

= 21 yd²

Hence, the area of triangle is 21 yd².

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The linear factors of the polynomial function are f(x) = - (1/1500) · (x + 20) · (x + 5) · (x - 15).

Cubic equations are polynomials of third grade, whose standard and factor forms are shown below:

Standard form

y = a · x³ + b · x² + c · x + d

Factor form

y = (x - r₁) · (x - r₂) · (x - r₃)

Where r₁, r₂, r₃ are the zeros of the cubic equation.

There are several approaches to find the roots of the polynomial, in this question we decided to use the graphical approach, which offers sufficiency and quickness for analysis. The roots of the polynomials are the points that pass through the x-axis.

In accordance with the image attached below, the polynomial has three real roots: r₁ = - 20, r₂ = - 5, r₃ = 15. Then, the linear factors of the polynomial function are f(x) = - (1/1500) · (x + 20) · (x + 5) · (x - 15).

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Answer: 45 minutes for BOTH workouts

Step-by-step explanation:

Let time for plan a be x

Let time for plan b be y

On Wednesday

# of clients for plan a are 5

# clients for plan b are 3

On Thursday

# of clients for plan a are 7

# of clients for plan b are 9

Wednesday eqn --> 5x+3y=6

Thursday eqn --> 7x+9y=12

Multiply Wednesday equation by -3 and use elimination to solve

-15x-9y=-18

7x+9y=12

-8x=-6

x=6/8

Reduce: x=3/4 hour

Substitute x=3/4 into Thursday equation

7(3/4)+9y=12

9y=27/4

y=3/4

Therefore, the length of BOTH the plan a and plan b workouts were 45 minutes

In order to evaluate the expression, we must first understand the order of operations. The ^ symbol indicates an exponential, which takes precedence over division. the expression.343 ^ { 4 / 3 } is 7,625

In order to evaluate the expression, we must first understand the order of operations. The ^ symbol indicates an exponential, which takes precedence over division. Therefore, we will first calculate 343^4 and then divide the result by 3. 343^4 = 7,741,675. 7,741,675 divided by 3 is equal to 2,580,558.33. When rounded to the nearest whole number, the answer is 7,625.The expression 343^ {4/3} can be broken down into 343 to the power of 4 divided by 3. Before we evaluate the expression, we must understand the order of operations. The ^ symbol indicates an exponential, which takes precedence over division. Therefore, we will first calculate 343^4 and then divide the result by 3. 343^4 can be calculated using the formula 343 x 343 x 343 x 343. This results in 7,741,675. 7,741,675 divided by 3 is equal to 2,580,558.33. When rounded to the nearest whole number, the answer is 7,625.

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Answer:

  10 minutes

Step-by-step explanation:

You want to know how much longer 2/3 hour is than the sum of 1/5 hour and 3/10 hour.

Each fraction of an hour can be expressed in minutes:

The time difference of interest is ...

  (2/3 - 1/5 -3/10) h = (40 -12 -18) min = 10 min

Jacob spent 10 minutes more reading than doing housework.

9514 1404 393

Answer:

  1. HA is equivalent to AAS when the triangle is a right triangle.

  2. AM = BM, so the triangles are congruent by HL. CPCTC

  3. The triangles are congruent by HL. CPCTC

Step-by-step explanation:

1. The acute angle of the triangle together with the right angle comprise two angles of the triangle. When two corresponding angles and a corresponding side (the side opposite the right angle) are congruent, the right triangles are congruent by the AAS theorem. (This can be referred to as the HA theorem.)

__

2. CM = DM; MA = MB; ∠A = ∠C = 90°, so all of the requirements for the HL theorem are met. ΔCMA ≅ ΔDMB, so AC ≅ BD by CPCTC.

__

3. TS = TV, TR = TR, ∠S = ∠V = 90°, so all requirements for the HL theorem are met. ΔTSR ≅ ΔTVR, so RS ≅ RV by CPCTC.

Answer:

Axioms or postulates are universal truths. They cannot be proved. Theorem are statements which can be proved.

To use a compound inequality calculator, follow these steps:

1. Open the compound inequality calculator on your device or web browser.

2. Input the two inequality expressions you want to combine with the appropriate inequality symbols.

3. Check that the inequality symbols are facing the same direction. If not, rearrange the expressions to make them face the same direction.

4. Click on the "Calculate" or "Solve" button to get the solution for the compound inequality.

5. The calculator should display the solution in either interval notation or set-builder notation.

For example, let's say you want to solve the compound inequality "2x + 1 > 5 and 3x - 2 < 7".

You would input the two inequalities like this:

2x + 1 > 5

3x - 2 < 7

Since the inequality symbols are facing the same direction, you can proceed to solve the compound inequality by clicking on the "Calculate" button.

The calculator might display the solution in interval notation or set-builder notation, depending on the calculator.

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Given, Total amount, $4,200

Time, 18years

Concept used

An amount that a borrower must pay to a lender as interest during the course of a loan, stated as a percentage of the loan amount.

All interest is a percentage that is added to or collected from a one-time payment. A type of interest known as compound interest is based on multiplying the original.

The answer is 6.2%.

If the interest rate i is = x

$4,200× (1+x/365)^18 ×365= $5,600

= (1+x/365)^6570= 100/38.2

=0.4712

x= 9/365

=0.0246× 100

= 2.46%

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Answer: About -4.604.

Step-by-step explanation:

    To solve, we will isolate the x variable.

Given:

    \(5e^{(2x+11)}=30\)

Divide both sides of the equation by 5:

    \(e^{(2x+11)}=6\)

Natural log of both sides:

    \(Ln(e^{(2x+11)})=Ln(6)\)

Power property:

    (2x + 11)(Lne) = Ln(6)

Simplify:

➜ \(Lne = Log_ee = 1\)

    2x + 11 = Ln(6)

Subtract 11 from both sides of the equation:

    2x = Ln(6) - 11

Divide both sides of the equation by 2:

    \(\displaystyle x=\frac{Ln(6) - 11}{2}\)

Compute:

    x = -4.60412 ≈ -4.604

Answer:

approximately 6.6 yards :)  

Step-by-step explanation:

Answer:

6.6

Step-by-step explanation:

take pi as 3.14

formula for circumfurence is 2*pi*r

so 2r=20.724/pi

2r=6.6

since diameter is 2 radius, the diameter is 6.6

A rectangular prism in which BA = 20 and h = 6 has a volume of 120 units³; therefore, Shannon is correct. The correct option is A.

To compare the volumes of the rectangular pyramid and the rectangular prism, we need to find the base area (BA) of the pyramid. The volume (V) of a pyramid is given by the formula:

\(V = \dfrac{1}{3} \times BA \times h\)

where BA is the base area and h is the height.

Given that the volume of the pyramid is 40 units³ and the height is 6 units, we can find the base area:

40 = (1/3) x BA x 6

Now, solve for BA:

\(BA = \dfrac{(40 \times 3)} { 6}\\BA = 20\ units^2\)

Now, let's check the options:

A rectangular prism in which BA = 20 and h = 6 has a volume of 40 units³; therefore, Shannon is incorrect.

The volume of the rectangular prism with BA = 20 and h = 6 is (20 x 6) = 120 units³, not 40 units³. So, this statement is incorrect.

A rectangular prism in which BA = 6.67 and h = 6 has a volume of 40 units³; therefore, Shannon is incorrect.

We have already determined that the base area of the pyramid is 20 units², not 6.67 units². So, this statement is incorrect.

A rectangular prism in which BA = 20 and h = 6 has a volume of 120 units³; therefore, Shannon is correct.

This statement matches our calculations. The volume of the rectangular prism with BA = 20 and h = 6 is (20 x 6) = 120 units³, which is three times the volume of the pyramid. So, this statement is correct.

A rectangular prism in which BA = 6.67 and h = 6 has a volume of 120 units³; therefore, Shannon is correct.

The base area of the pyramid is 20 units², not 6.67 units². So, this statement is incorrect.

A rectangular prism in which BA = 20 and h = 6 has a volume of 120 units³; therefore, Shannon is correct.

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The complete question is attached below:

A rectangular pyramid has a height of 6 units and a volume of 40 units3. Shannon states that a rectangular prism with the same base area and height has a volume that is three times the size of the given rectangular pyramid. Which statement explains whether Shannon is correct?

A rectangular prism in which BA = 20 and h = 6 has a volume of 40 units3; therefore, Shannon is incorrect.

A rectangular prism in which BA = 6.67 and h = 6 has a volume of 40 units3; therefore, Shannon is incorrect.

A rectangular prism in which BA = 20 and h = 6 has a volume of 120 units3; therefore, Shannon is correct.

A rectangular prism in which BA = 6.67 and h = 6 has a volume of 120 units3; therefore, Shannon is correct.

Answer:

0.0225

Step-by-step explanation:

Have a great rest of your day or night hope this helps

The quantity of substance remains after 850 years is 8.98g if the half life of radioactive radium is 1,599 years.

The time taken by substance to reduce to its half of its initial concentration is called half life period.

We will use the half- life equation N(t)

N e^{(-0.693t) /t½}

Where,

N is the initial sample

t½ is the half life time period of the substance

t2 is the time in years.

N(t) is the reminder quantity after t years .

Given

N = 13g

t = 350 years

t½ = 1599 years

By substituting all the value, we get

N(t) = 13e^(0.693 × 50) / (1599)

= 13e^(- 0.368386)

= 13 × 0.691

= 8.98

Thus, we calculated that the quantity of substance remains after 850 years is 8.98g if the half life of radioactive radium is 1,599 years.

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Answer:

the time spent

Step-by-step explanation:

\(\boxed{\underline{\bf \: ANSWER}}\)

\( \sf\frac { 3 + p } { 2 } = 6 \\ \)

Multiply both sides by 2.

\( \sf \: 3+p=6\times 2 \)

Multiply 6 and 2 to get 12.

\( \sf \: 3+p=12 \)

Subtract 3 from both sides.

\( \sf \: p=12-3 \)

Subtract 3 from 12 to get 9.

\( \boxed{\bf \: p=9} \)

____

Hope it helps.

RainbowSalt2222

Answer:

the answer is 111

Step-by-step explanation:

\(180 - 36 - 75 = 69\)

\(180 - 69 = 111\)

Answer:

x = 111°

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

x is an exterior angle of the triangle, thus

x = 75° + 36° = 111°

The amount that Roxana has left is $7560.

Total Amount = $12000

She spent 12% on meat and 25% on vegetables.

Therefore, the amount left will be:

= (100 - 12% - 25%) × 12000

= 63% × 12000

= 63/100 × 12000

= 0.63 × 12000

= $7560

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The possible outcomes of getting 6 different face values out of 52 playing cards is equal to 5,271,552.

Total number of cards in a deck of cards = 52

Number of cards draw = 6

To determine the number of possible outcomes of getting 6 different face values.

when drawing 6 cards from a deck of 52 playing cards.

There are 13 different face values in a deck of cards .

Choose 6 of these face values and then choose one card of each of the chosen face values.

The order in which we choose the face values or the order in which we choose the cards of each face value does not matter.

To choose 6 face values out of 13, use the combination formula,

C(13, 6) = 13! / (6! × (13-6)!)

           = 13! / (6! × 7!)

           = 1716

Once chosen the 6 face values, choose one card of each face value.

There are 4 cards of each face value in a deck of cards.

Since choosing one card of each face value,

choose 4 cards for the first face value,

3 cards for the second face value since already chosen one card of that face value.

2 cards for the third face value since we have already chosen two cards of that face value and so on.

The total number of possible outcomes of getting 6 different face values is.

C(13, 6) × (4×3×2×1)(4×2 ×2 ×2×2× 2)

= 1716 × 24 × 128

= 5,271,552

Therefore, there are 5,271,552 possible outcomes of getting 6 different face values when drawing 6 cards from a deck of 52 playing cards simultaneously.

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The graph of y= √x-1 is given by the image presented at the end of the answer.

A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.

The four translation rules for functions are defined as follows:

The parent function in the context of this problem is given as follows:

y= √x

Which has vertex at the origin.

The translated function is given as follows:

y = √x-1

Which is a translation down one unit of the parent function, hence it will have vertex at (0,-1).

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Answer:

c

Step-by-step explanation:

c will be the answer g g g t g

Answer of the following questions for given mean and standard deviation along with sample size are:

a. Null hypothesis , H₀: μ = 4.00

   Alternative hypothesis, H₁ : μ > 4.00

b. Value of test statistic is 1.647

c. Conclusion is no evidence to conclude mean wait time for customer is longer than 4.00 minutes.

As given in the question,

Wait time for customer is at most 4.00 minutes

a. Null hypothesis is given by

H₀: μ = 4.00

Mean time is not exceeding the requirement

Alternative hypothesis is given by:

H₁ : μ > 4.00

b. Value of test statistic is given by :

(\(\bar{x}\) - μ₀) ÷ ( s/√n )

Sample mean \(\bar{x}\) = 4.14

Population mean μ₀ = 4.00

Standard deviation 's' = 0.55 minutes

Sample size 'n' = 42

Substitute the value in the formula we get,

(4.14 - 4.00) ÷ (0.55/ √42)

= 0.14 / (0.55/ 6.5)

=0.14/ 0.085

= 1.647

c. α = 1 - 98%

   = 1 - 0.98

   = 0.02

Decision value limit :

Reject H₀ ; if P value < α

Using table ,

P value = P(Z < 1.647)

              = 0.04997

⇒P value = 0.04997

0.04997 > 0.02

Here P value > α

Fail to reject Null hypothesis .

Therefore, from the given standard deviation and mean conclusion is that there is no sufficient evidence to prove that mean wait time for customers is longer than 4.00.

The complete question is:

The board of a major credit card company requires that the mean wait time for customers when they call customer service is at most 4.00 minutes. to make sure that the mean wait time is not exceeding the requirement, an assistant manager tracks the wait times of 42 randomly selected calls. the mean wait time was calculated to be 4.14 minutes. assuming the population standard deviation is 0.55 minutes, is there sufficient evidence to say that the mean wait time for customers is longer than 4.00 minutes with a 98% level of confidence?

1. State the null and alternative hypotheses for the test.

2. Compute the value of the test statistic.

3. Draw a conclusion and interpret the decision.

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