Find the distance between point P and line ℓ.

Line ℓ contains points (0, −3 ) and (7, 4). Point P has coordinates (4, 3).

Area of the given rectangle as per given perimeter and width is equal to 60m².

As given in the question,

Perimeter of the given rectangle = 64m

Width of the given rectangle 'w' = 2m

Let us consider 'l' be the length of the rectangle

Perimeter of the rectangle = 2 ( l + w )

Substitute the values

64 = 2 ( l + 2)

⇒32 = l + 2

⇒l = 32 - 2

⇒l = 30m

Area of the given rectangle = l × w

                                              = 30 × 2

                                              = 60m²

Therefore, the area of the given rectangle as per given dimensions is equal to 60m².

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If Richard is 13 years older than twice Teo's age. The age of Richard and Thiago will be 23 and 5 respectively.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.

It is given that, Richard and Teo have a combined age of 28. Richard is 13 years older than twice Teo’s age.

We have to find the age of Richard and Thiago.

Suppose the age of Richard and Teo be x,

If Richard and Teo have a combined age of 28,

T+R=28 --------(1)

If Richard is 13 years older than twice Teo’s age,

R=( 2T + 13) --------(2)

u

Substitute the value of R in eqation 1

T+( 2T + 13)=28

3T+13=28

3T=28-13

3T=15

T=5

Substitute the value of T in equation 1 to obtain R,

T+R=28

5+R=28

R=28-5

R=23

Thus, if Richard is 13 years older than twice Teo age. The age of Richard and Thiago will be 23 and 5 respectively.

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Answer:

14+9(x-1)=y

Step-by-step explanation:

If x is the number of pizza's being delivered and the first pizza costs $14 then that pizza is already accounted for by the 14 in the equation, so you subtract x by 1 before multiplying it by 9, then add the 14 to the product you then get the total cost: y

The value of y after solving the triangle using sine rule is 46.15.

Sine rule is a rule that relates the sides of a triangle with the sine of their opposite angles.

To calculate the value of y, we use the sine rule formula

Formula:

Where:

From the question,

Given:

Susbtitute these values into equation 1 and solve for y

Hence, the value of y is 46.15.

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The rate of change between the points (3.4, -0.1) and (3.5, 0.1) is 2.

The rate of change function is defined as the rate at which one quantity is changing with respect to another quantity.

The rate of change formula gives the relationship describing how one quantity changes in relation to the change in another quantity.

Therefore,

rate of change = Δy / Δx

rate of change = y₂ - y₁ / x₂ - x₁

Hence, let's find the rate of change of (3.4,-0.1) and (3.5,0.1).

rate of change = 0.1 + 0.1 / 3.5  - 3.4

rate of change = 0.2 / 0.1

rate of change = 2

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Answer:

slope = undefined

Step-by-step explanation:

Find the slope of the line: (5,-3), (5,8)

slope = change in y / change in x

slope = ( -3 - 8) / (5 - 5)

slope = -11/0

slope = undefined

These points graph a vertical line.

answer:

the slope is undefined.

step-by-step explanation:

there is an equation (y2-y1)/(x2-x1) that allows for you to determine the slope. since this line is vertical, the slope is defined because if you plug the points into the equation, you would be dividing by 0.

The value of x from the equation (221x3 + 154x2 + 228x + 41) / (17x + 4)-4 is 992

(221x3 + 154x2 + 228x + 41) / (17x + 4)-4

Multiplying 221*3 and 154*2 =663,308

( 663+308 + 228x + 41) / (17x + 4)-4

( 971+ 228x + 41) / (17x + 4)-4

=( 971+ 228x +41)

       (17x + 4)

=1012+228x

    (17x + 4)

-x=-992

x=992

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Rounded to the nearest tenth of a million dollars, the company made $3.2 million in profit in the year 2003.

Profit is a financial gain that occurs when the revenue from a company activity is more than the costs, costs, and taxes required to support the activity. It is, in other words, the difference between income and costs. Profit is an important aspect in a company's performance and is often quantified in monetary terms, but it may also be viewed .For example, for each consecutive year after that, their profit increased by 13%.

Profits may be divided into two categories: net profit and gross profit. After deducting all costs, taxes, and expenses, a company's net profit is the overall profit it has made. In contrast, gross profit is the profit made by a firm before expenses and costs are deducted.

How to solve?

In the year 2001, the company made $2.2 million * 1.13 = $2.486 million in profit.

In the year 2002, the company made $2.486 million * 1.13 = $2.82778 million in profit.

In the year 2003, the company made $2.82778 million * 1.13 = $3.1987314 million in profit.

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Answer:

  x = 125

Step-by-step explanation:

Given a heptagon with 60° and 90° angles marked, one marked 2x°, and the remaining angles marked x°, you want o know the value of x.

The sum of the interior angles of a heptagon is ...

  180° × (7 -2) = 900°

Using the given values, this tells us ...

  90° +x° +x° +x° +x° +60° +2x° = 900°

  6x = 750 . . . . . . . divide by °, subtract 150

  x = 125 . . . . . . divide by 6

The value of x is 125.

__

Additional comment

The attached figure is drawn with correct angles.

The sum of interior angles of an n-gon is 180°×(n -2).

The value not predicted for the given information is "how many gallons the gas tank holds".

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: (Number/variable, Math Operator, Number/variable) is an expression. An expression in mathematics is made up of numbers, variables, and functions. You can think of expressions as being similar to phrases.

Here,

How many gallons the gas tank holds is the value that could not be predicted based on the information provided.

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x=60°, y=15°, angle C is 45°, angle DBC is 105° and angle CBA is 75°.

In the given figure, ∠DBC=7y°, ∠CBA=5y°, ∠C=3y° and ∠D=x°.

Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.

Here,

∠DBC+∠CBA=180° (Sum of adjacent angles is 180°)

⇒ 7y°+5y°=180°

⇒ 12y°=180°

⇒ y°=15°

∠DBC=7y°=105°, ∠CBA=5y°=75° and ∠C=3y°=45°

Now, ∠DBC=∠C+∠A

⇒ 105°=45°+∠A

⇒ ∠A=60°

Therefore, x=60°, y=15°, angle C is 45°, angle DBC is 105° and angle CBA is 75°.

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The width of Mary's rectangular room is 5 feet.

A rectangle is a quadrilateral with four right angles in the Euclidean plane.

It can alternatively be described as a parallelogram with a right angle or an equiangular quadrilateral, where equiangular denotes that all of its angles are equal.

A square is a rectangle

So, we consider Mary's room a rectangular room:

With an area of 40ft² and a length is 8ft.

Area of rectangle: l*w

Where l stands for length and w stands for width.

Now, calculate the width using the formula as follows:

Area = l*w

40 = 8*w

w = 40/8

w = 5ft

Therefore, the width of Mary's rectangular room is 5 feet.

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Answer: 95 percent confidence interval

Step-by-step explanation: "you have a 5 percent chance of being wrong. with a 90 percent confidence interval, you have a 10 percent chance of being wrong a 99 percent confidence interval would be wider than a 95 percent confidence interval for example plus or minus 4.5 percent instead of 3.5 percent"

Using mathematical operations, we can conclude that both London and Colin will get 1/4 of strawberries each.

A mathematical function known as an operation converts zero or more input values into a precisely defined output value.

The quantity of operands affects the operation's arity.

The four basic mathematical operations, according to the majority of people, are addition, subtraction, multiplication, and division.

So, the strawberries both Landon and Colin will get are:

We know that Landon and Colin brought 1/2 strawberries.

They share is equally that is:

1/2 ÷ 2

Now, solve as follows:

1/2 ÷ 2

1/2 ÷ 2/1

1/2 * 1/2

1/4

Therefore, using mathematical operations, we can conclude that both London and Colin will get 1/4 of strawberries each.

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For 160 calories and 20 grams of carbohydrates 0.61 cups are required.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that a one-cup serving of spaghetti with meatballs contains 260 calories and 32 grams of carbohydrates. A one-cup serving of chopped iceberg lettuce contains 5 calories and 1 gram of carbohydrates.

For 160 calories the number of cups will be calculated as,

1 cup = 260 calories

160 calories = ( 160 ) / 260 cups

160 calories = 0.61 cups

Therefore, for 160 calories and 20 grams of carbohydrates 0.61 cups are required.

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The each day of the trip will cost the family $212   .

In the question ,

it is given that ,

a family is going on 3 day trip ,

the cost for hotel for 3 days is = $336 ,

So , the cost for the hotel for 1 day is = $336/3 = $112 ,

the amount budgeted for the food is one hundred dollar

the cost for the food for 1 day is = $100 .

So , the cost for each day is = cost of food + cost of hotel

Substituting the values of food and hotel ,

we get ,

= 100 + 112

Adding both the terms ,

we get ,

= 212

Therefore , the cost for each day is = $212 .

The given question is incomplete , the complete question is

A family is going to on a trip for 3 days the total cost for the hotel is $336. One hundred dollar for the day was budgeted for food. How much will each day of the the trip will cost ?

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The scientific notation of the wavelength of green light in a spectrum

is 3×10⁻⁶ feet.

In scientific notations numbers are written in the form of a base that is

0  ≤ b < 10 and multiplied by 10ⁿ where n represents integers.

We write large standard numbers in scientific form in a compact manner.

Given, The wavelength of green light in a spectrum is about 0.000003 feet.

Now, the decimal is 6 places before so we have to move the decimal 6 places to the right, and to maintain the actual value we'll raise it to 10⁻⁶.

Therefore, 0.000003 feet,

= 3×10⁻⁶ feet.

So, the wavelength of green light is 3×10⁻⁶ feet.

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Answer: y=-3/4x-3.5

Step-by-step explanation:

First, set up the equation based on the information we already know. The slope-intercept form is y=mx+b (m being the slop and b is the y-intercept)

We already know the slope, so we can substitute it.

y=-3/4x+b

Now, the only variable we need to find is b (the y-intercept)

To do this we can substitute the point that was given, (2,-5)

Substitute -5 in for y and 2 in for x.

Then you get the equation -5=-3/4(2)+b

Multiply -3/4 and 2 and you get -5=-3/2+b

Add -3/2 from both sides to isolate b

You then get b=-3.5

Substitute b back in the original equation

Your final answer is y=-3/4x-3.5

Answer:

You draw the line of the graph and every point on the line is a solution

Step-by-step explanation:

y = mx + b  You graph the b which is the y intercept.  This is where the graph crosses the x axis.  In this case it is -12.  From that point (0,-12)  You follow a pattern which is the slope.  In this case the slope is -3.  That mans that you move three units down and then 1 unit right.

I highlighted a few points on the line.  Every point on the line is a solution.

y=-x+10 is the equation of a line perpendicular to the givin equation using the given point given (8,2) and x = -4

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

In the perpendicular lines the product of slopes will be -1

m1m2=-1

y=x+4 is the given line, it has slope of 1, so the perpendicular line will have slope -1.

The line is passing through (8,2)

2=-1(8)+b

2=-8+b

2+8=b

10=b

Hence, y=-x+10 is the equation of a line perpendicular to the givin equation using the given point given (8,2) and x = -4

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The number of weeks it will take them to have saved thesame amount is 8 weeks

Simultaneous equations are two or more algebraic equations that share variables e.g. x and y . They are called simultaneous equations because the equations are solved at the same time.

if x represents the the number of weeks for saving and y represents the equal saved amount, then

42+16x = y equation 1

-70+ 30x = y equation 2

subtract equation 1 from 2

-70-42+16x- 30x= 0

-112+14x= 0

collect like terms

-112=-14x

divide both sides by 14

x= -112/-14

x= 8weeks

therefore it will take them 8 weeks to have equal savings

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Accuracy rate is equal to the difference of predicted value and true value  divide it by true value and then multiply by 100 to get the rate.

Accuracy rate = [ | Predicted value - True vale|/ true value ] × 100

Therefore, the accuracy rate is the percentage of the ratio of difference of predicted value and true value to the true value.

The given question is incomplete, I answer the question in general according to my knowledge:

How is the accuracy rate calculated?

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Answer:

b). were 18 when their parents were naturalized

Step-by-step explanation

I know I am right because I believe this is Civics or U.S History. I did Civics in 7th, and U.S History I am currently doing. hope this helps!

Answer:

16 ft

Step-by-step explanation:

The length of the ladder is 16\ ft16 ft

Step-by-step explanation:

Let

L ----> the length of the ladder

we know that

Applying the Pythagoras theorem

L^{2}=15^{2} +6^{2}L

2

=15

2

+6

2

L^{2}=261L

2

=261

L=\sqrt{261}\ ftL=

261

ft

L=16\ ftL=16 ft

The flux of  out of S is [tex]14 \pi\left(-\frac{\sqrt{2}}{2}+1\right)[/tex].

What is Flux of the Vector Field?

Solving the flux of the vector field using the divergence theorem which has the following formula [tex]$\iint_S F \cdot d S=\iiint_E div} F(x, y, z) d V$[/tex] where F is the vector field [tex]$F=P i+Q j+R k$[/tex] and div F means the divergence of F which has the formula  [tex]$F=\frac{\partial P}{\partial x}+\frac{\partial Q}{\partial y}+\frac{\partial R}{\partial z}$[/tex]

Here, we let the vector field to be [tex]$\vec{F}=x i+y j+z k$[/tex]

[tex]$\vec{F}=x i+y j+z k$[/tex]

Now solving for [tex]${div} F$[/tex]

[tex]$$\begin{aligned}& {div} F=\frac{\partial x}{\partial x}+\frac{\partial y}{\partial y}+\frac{\partial z}{\partial z} \\& {div} F=1+1+1=3\end{aligned}$$[/tex]

Thus,

[tex]\iint_S F \cdot d S=\iiint 3 d V[/tex]

From the given region the limits of integrations in spherical coordinates are,

[tex]0 \leq \theta \leq 2 \pi, 0 \leq \phi \leq \frac{\pi}{4}, 1 \leq \rho \leq 2[/tex]

Thus,

[tex]\iint_S F \cdot d S=\int_0^{2 \pi} \int_0^{\frac{\pi}{4}} \int_1^2 3 \rho^2 \sin \phi d \rho d \phi d \theta[/tex]

Integrate with respect to [tex]$\rho$[/tex]

[tex]\begin{aligned}& =\int_0^{2 \pi} \int_0^{\frac{\pi}{4}} 3\left[\frac{1}{3} \rho^3\right]_1^2 \sin \phi d \phi d \theta \\& =\int_0^{2 \pi} \int_0^{\frac{\pi}{4}} 7 \sin \phi d \phi d \theta\end{aligned}[/tex]

Integrate with respect to [tex]$\phi$[/tex]

[tex]\begin{aligned}& =\int_0^{2 \pi} 7[-\cos \phi]_0^{\frac{\pi}{4}} d \theta \\& =\int_0^{2 \pi} 7\left(-\frac{\sqrt{2}}{2}+1\right) d \theta\end{aligned}[/tex]

Integrate with respect to [tex]$\theta$[/tex]

[tex]\begin{aligned}& =7\left(-\frac{\sqrt{2}}{2}+1\right)[\theta]_0^{2 \pi} \\& =14 \pi\left(-\frac{\sqrt{2}}{2}+1\right)\end{aligned}[/tex]

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Answer:

99

Step-by-step explanation:

Since the triangles are similar, we know the ratio of the sides is a constant. We know that SQ is 55, and the corresponding side on the other triangle is 10. This lets us find the ratio for the whole triangle! The ratio is 55/10, or 5.5.

To solve for RS, consider the corresponding side on the other triangle(LS) which is 18. We multiply that by the ratio to get 18 * 5.5 = 99, which is the length of RS.

I don't know if you need to solve for x, but if you do, here it is! We have [tex]99 = 12x+3[/tex] (the equation for side RS). subtracting 3 from both sides results in [tex]96 = 12x[/tex], and dividing by x gives us that x = 8.

Thank you! Feel free to ask me any questions about my answer. I hope this helps!

Answer:

−1.3x − 15.2

Step-by-step explanation:

step 1: simplify

4x−7.2−5.3x−8

=4x+−7.2+−5.3x+−8

step 2: combine like terms

=4x+−7.2+−5.3x+−8

=(4x+−5.3x)+(−7.2+−8)

=−1.3x+−15.2

Answer:

A

Step-by-step explanation:

numerator = exponent of x (in this case is 1, so it can be omitted)

denominator = index of the root

√x