Use the distributive property to fill in the blanks below. 6×(7 + 2) = (_ × 7) + ( _ × 2)

Answer:

D

Step-by-step explanation:

Check the picture below.

\(\cfrac{17.5+14}{17.5}~~ = ~~\cfrac{x}{12.5}\implies \cfrac{(17.5+14)(12.5)}{17.5}~~ = ~~x\implies 22.5=x\)

The triangles are necessarily congruent by the ASA congruence rule.

The ASA, which is an acronym for Angle-Side-Angle, congruence rule states that if two angles and an included side of one triangle are congruent to two angles and an included side of another triangle, then the two triangles are congruent.

The angle markings on the triangles ΔJLK and ΔZXY indicates;

∠J ≅ ∠Z, ∠K ≅ ∠Y

The side markings on the triangles indicates

Side JK in triangle ΔJLK is congruent to side ZY in triangle ΔZXY

Therefore, two angles and an included side in triangle ΔJLK are congruent to two angles and an included side in triangle ΔZXY, therefore, triangle ΔJLK is congruent to triangle ΔZXY by Angle-Side-Angle, ASA congruence rule.

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The conical surface is the correct answer as it allows for slopes ranging from 20:1 to 50:1. The FAR Part 77 imaginary surface that has slopes that may range from 20:1 to 50:1 is the conical surface.

The conical surface is a three-dimensional surface defined by a combination of horizontal and inclined planes. It extends upward and outward from the end of the primary surface and has varying slope requirements. The slope of the conical surface represents the ratio of the change in elevation to the horizontal distance. A slope of 20:1 indicates that for every 20 units of horizontal distance, there is a 1-unit increase in elevation.

Similarly, a slope of 50:1 means that for every 50 units of horizontal distance, there is a 1-unit increase in elevation. Therefore, the conical surface is the correct answer as it allows for slopes ranging from 20:1 to 50:1.

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Answer:

X=4

I’m pretty sure

Answer:

1. City A
2. Exponential Growth
3. Linear

Step-by-step explanation:

The equation for exponential growth is f(x)=a(1+r/100)^x, where a is the initial growth/starting population, r is the growth rate, and x is the time intervals.

City A
f(x)=200(1+1.05/100)^x
Simplify:
f(x)=200(1.105)^x

City B
An increase in 20 people each year is NOT exponential but linear:
f(x)=20x+200

Now we plug in x for 1 to stand for 1 year and see which city has a greater number:
City A:
f(1)=200(1.105)^1
f(1)=200 x 1.105
f(1)=221

City B:
f(1)=20(1)+200

f(1)=20+200

f(1)=220

City A will have more people.

City A is an exponential function because there's a percent increase every year, and there will be more people every year because there are more people. This is kind of how compound interest also works

City B is a linear equation because a set number of people are added every year and doesn't change based on the amount of people already in it.

1. City B will have more population after 1 year.

In this case, we have been given of both the cities A and B with each year's growth factor and we have been told to find out, which city will have more population after 1 year. So to find out the comparison, first we need to find out the individual popoulation of both the cities after 1 year of interval.

So, population of City A after 1 year will be 200 * 1.05 = 210

Similarly,  population of City B after 1 year will be 200 + 20 = 220

It is clear that City B has more population as compared to City A.

Therefore, after 1 year City B has more population.

2. equation for City A is Exponential Growth Equation.

Exponential growth is the growth which takes place when a particular quantity increases at a constant rate over a fixed time period. It is given in the form of \(P = P_{0} * (1 + r)^t\), where P is population, \(P_{0}\) is initial population, r is the growth rate, and t is time period.

3. equation for City B is Linear Equation.

Linear equation is a representation of a straight line when graphed on paper. It has constant coefficients and variables raised to power 1. It is given in the form of \(P = P_{0} + rt\), where P is population, \(P_{0}\) is initial population, r is the growth rate, and t is time period.

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The least number of pieces that she needs to tie together to make a length of at least 12 yards long is 8 pieces.

Staci has 13 pieces of rope, each piece is 5 feet long. Therefore, the  least number of pieces that she needs to tie together to make a length that is at least 12 yards long can be calculated as follows:

Therefore,

1 piece = 5 feet

13 piece = ?

Therefore,

13 piece = 65 feet

Hence,

1 yard = 3 feet

12 yards = ?

cross multiply

number of feet = 36 feet

Number of pieces to get at least 12 yards(36 feet) = 36 / 5

Number of pieces to get at least 12 yards = 8 pieces

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Answer:

the slope is 2

Step-by-step explanation:

slope = m = rise/run

m=4/2

it can be simplified so

m= 2/1

it can be simplified again

m=2

(a) To prove the equation ||u' - v|| = √2√(1 - u · v) in R², where u and v are unit vectors, we can use the properties of the dot product and vector norms.

First, let's expand the norm on the left side of the equation:

||u' - v||² = (u' - v) · (u' - v)

Expanding the dot product, we have:

||u' - v||² = (u' · u') - 2(u' · v) + (v · v)

Since both u and v are unit vectors, their norms are equal to 1:

||u' - v||² = (1) - 2(u' · v) + (1)

Simplifying, we have:

||u' - v||² = 2 - 2(u' · v)

Now, let's focus on the right side of the equation:

√2√(1 - u · v) = √2√(1 - (u' · v))

Taking the square of both sides, we have:

2 - 2(u' · v) = 2 - 2(u' · v)

Therefore, the equation ||u' - v|| = √2√(1 - u · v) holds in R².

(b) To prove that if x'ui = ||ui|| for all i, 1 ≤ i ≤ n, where U = {u₁, ..., un} is an orthonormal basis for Rⁿ and x ∈ Rⁿ, then x = u₁ + ... + un.

Since U is an orthonormal basis, each ui is a unit vector, and they are linearly independent, forming a basis for Rⁿ. We can write any vector x ∈ Rⁿ as a linear combination of the basis vectors:

x = c₁u₁ + c₂u₂ + ... + cnun

Now, let's calculate the dot product of x with each basis vector ui:

x · ui = (c₁u₁ + c₂u₂ + ... + cnun) · ui

= c₁(u₁ · ui) + c₂(u₂ · ui) + ... + cn(un · ui)

Since the basis vectors are orthonormal, the dot product of any two distinct basis vectors is zero:

(uj · ui) = 0 (for j ≠ i)

Therefore, the dot product simplifies to:

x · ui = ci(u · ui)

Given that x · ui = ||ui|| for all i, we have:

ci(u · ui) = ||ui||

Since ui is a unit vector, the dot product (u · ui) is equal to the norm of u:

ci ||ui|| = ||ui||

This equation holds for all i, 1 ≤ i ≤ n. Since ||ui|| is non-zero (as ui is a unit vector), we can divide both sides of the equation by ||ui||:

ci = 1

Hence, each coefficient ci is equal to 1. Therefore, we can rewrite x as:

x = u₁ + u₂ + ... + un

If x'ui = ||ui|| for all i, 1 ≤ i ≤ n, where U = {u₁, ..., un} is an orthonormal basis for Rⁿ, then x can be written as the sum of the basis vectors: x = u₁ + u₂ + ... + un.

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The cosine of angle J is given as follows:

\(\cos{J} = \frac{14\sqrt{2}}{49}\)

The three trigonometric ratios are the sine, the cosine and the tangent of an angle, and they are obtained according to the rules presented as follows:

For the angle J in this problem, we have that:

Hence the cosine of angle J is given as follows:

\(\cos{J} = \frac{4}{\sqrt{98}} \times \frac{\sqrt{98}}{\sqrt{98}}\)

\(\cos{J} = \frac{4\sqrt{98}}{98}\)

\(\cos{J} = \frac{2\sqrt{98}}{49}\)

As 98 = 2 x 49, we have that \(\sqrt{98} = \sqrt{49 \times 2} = 7\sqrt{2}\), hence:

\(\cos{J} = \frac{14\sqrt{2}}{49}\)

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x = 127°

Step-by-step explanation:

The sum of the interior angles of an n-sided polygon is (n - 2)×180°. For a 5-sided polygon (pentagon), the sum is 540°. From the diagram,

90 + 90 + 90 + 143 + x = 540

Solving for x,

x = 127°

Answer:

It is 5:45

- Fifteen minutes before six

- Fifteen minutes until six

- Fifteen minutes till six

- A quarter before six

- A quarter until six

- A quarter till six

- Eight forty-five

- Forty-five after five

- Forty-five past five

It is 8:15

- A quarter past eight

- A quarter after eight

It is 1:35

- one thirty-five

- thirty-five after one

-  thirty-five past one

It is 9:10

- nine ten

- ten past nine

- ten after nine

It is 11:30

- Half past eleven

- eleven thirty

Change in concentration = c(5/6) - c(2/3). To estimate the change in concentration (C) in mg/ml of a certain drug in a person's bloodstream when t changes from 40 to 50 minutes,

we will use the given model: c(t) = 2t / (3 + e^(-0.01t)).

First, let's convert the time from minutes to hours since the model uses hours:
40 minutes = 40/60 = 2/3 hours
50 minutes = 50/60 = 5/6 hours
Next, we will calculate the concentration at these times using the model:
1. For t = 2/3 hours:
c(2/3) = 2(2/3) / (3 + e^(-0.01(2/3)))

2. For t = 5/6 hours:
c(5/6) = 2(5/6) / (3 + e^(-0.01(5/6)))
Now, estimate the change in concentration by subtracting the concentrations at these two times:
Change in concentration = c(5/6) - c(2/3)

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Answer:

F

Step-by-step explanation:

Answer:

4 ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

Step-by-step explanation:

12÷3=4

Courtney rides for two hours on a bicycle, traveling 24 miles from her home. She has ridden for nine hours and is now 101 miles away. Courtney travels at a speed of 6 mph.

Let x represent the duration in hours and y the distance in miles.

Courtney travels 24 miles from her home after a two-hour ride.

She has traveled 101 miles after riding for nine hours.

rate is the slope

We divide the change in hours by the change in miles to find the rate.

\(Slope=\frac{y_{2} - y_{1} }{x_{2}-x_{1} } \\Slope=\frac{101-24}{9-2} \\Slope= \frac{77}{7} \\Slope=11\)

Therefore, Courtney's speed is 11 mph.

The speed of something or someone is shown to us. If you know how far and how long it took, you can find the average speed of an object.

The distance covered in a given amount of time would also double if one were to speed up. We need to know how far an object has traveled in order to determine its speed, and the slowest speeds are measured over the longest time periods.

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Step-by-step explanation:

mid point=(1+(-4),(-3+(-0.5)

------ ------------

2 2

.mid point =-³/2,3.5/2

Answer:

-2c^13

hopefully i helped :)

Answer:

y = 841.25 feet

Step-by-step explanation:

Given that,

The height of the rocket, y in feet, is  related to the time after launch, x in seconds, by the given equation as follows:

\(y = -16x^2 + 212x + 139\) ....(1)

We need to find the maximum height reached by the rocket.

For maximum height, put dy/dx = 0

So,

\(\dfrac{d(-16x^2 + 212x + 139)}{dx}=0\\\\-32x+212=0\\\\x=\dfrac{212}{32}\\\\x=6.625\ s\)

Pu x = 6.625 in equation (1).

\(y = -16(6.625)^2 + 212(6.625) + 139\\\\y=841.25\ feet\)

So, the maximum height reached by the rocket is equal to 841.25 feet.

The area of the parallelogram with vertices (0,0), (3,6), (8,2), and (11,8) is 0 square units.

To find the area of a parallelogram with given vertices, we can use the formula:

Area = |(x1y2 + x2y3 + x3y4 + x4y1) - (y1x2 + y2x3 + y3x4 + y4x1)| / 2

Given the vertices:

A = (0, 0)

B = (3, 6)

C = (8, 2)

D = (11, 8)

We can plug these coordinates into the formula to calculate the area:

Area = |(0*6 + 3*2 + 8*8 + 11*0) - (0*3 + 6*8 + 2*11 + 8*0)| / 2

Area = |(0 + 6 + 64 + 0) - (0 + 48 + 22 + 0)| / 2

Area = |70 - 70| / 2

Area = 0 / 2

Area = 0

Therefore, the area of the parallelogram with vertices (0,0), (3,6), (8,2), and (11,8) is 0 square units.

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Let the width be x.

Then,length = 2x + 3

Area of rectangle = 560 [ Given ]

⇒ l × b = 560

⇒ ( 2x + 3 ) x = 560

⇒ 2x² + 3x - 560 = 0

⇒ 2x² + 35x - 32x - 560 = 0

⇒ x ( 2x + 35 ) - 16 ( 2x + 35 ) = 0

⇒ ( x - 16 ) = 0 and ( 2x + 35 ) = 0

⇒ x = 16 and x = -35/2 [ Ignore negative number ]

★ Width = x = 16 cm

★ Length = 2x + 3 = 2 × 16 + 3 = 32 + 3 = 35 cm

Step-by-step explanation:

this is what i according to the calculator

Option (A): "As the degrees of freedom increases the shape of the Chi-Square Distribution becomes more skewed" is a false statement.

Now, amongst the considered options, "As the degrees of freedom increases the shape of the Chi-Square Distribution becomes more skewed." (Option A) is not true, because:

As the degrees of freedom increases, the shape of the Chi-Square Distribution approaches a normal distribution and the graph of the Chi-Square Distribution looks more symmetrical.

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A state function is a property that depends only on the current state of the system, and not on the path taken to reach that state.

Examples of state functions include temperature, pressure, volume, and internal energy, and they can only be measured if a substance undergoes a phase change.

A state function is a property of a system that depends only on the current state of the system, and not on the path taken to reach that state. In other words, a state function is a property that is path-independent. This means that the value of a state function does not depend on how the system arrived at its current state, only on the current state itself.

One way to think about state functions is to compare them to non-state functions, also known as path functions. A non-state function, such as work or heat, depends on the path taken to reach the current state of the system. For example, the amount of work done on a gas in a piston can be different depending on the path taken to compress the gas. If the gas is compressed slowly, the amount of work done will be less than if it were compressed quickly. However, the internal energy of the gas, which is a state function, will be the same regardless of the path taken to compress it.

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The cartesian vector form of \(F\) is \(F = (-31cos(\alpha )i + 102sin(\alpha )j)\). We call x + yi the Cartesian form for a complex number.

Given that \(i,j,p\) and \(q\) are unit vectors and the angle \(\alpha = 222\)°, we can express the cartesian vector form of \(F\) as \(F = (-31cos(\alpha )i + 102sin(\alpha )j)\).

To calculate the components of \(F\) , we use the trigonometric functions \(cos(\alpha )\) and \(sin(\alpha )\) with the given angle \(\alpha = 222\)°.

\(cos(222) = -0.766\\sin(222) = -0.643\)

Substituting these values into the cartesian vector form, we have:

\(F = (-31cos(222)i + 102sin(222)j)\\F = (-31 * -0.766i + 102*-0.643j)\\F = (23.746i - 65.586j)\)

Therefore, the cartesian vector form of \(F\) is \(F = (23.746i - 65.586j)\).

The cartesian vector form of \(F = (23.746i - 65.586j)\)

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