Which polygon is a convex heptagon?

The angle that the vector "v = 9i + 8j - 4k" makes with the vector "u = 6i - 4j - k" is Acute Angle .

To determine the angle between two vectors, we need to find the dot product of the vectors and divide it by the product of their magnitudes.

If the result is positive, the angle between the vectors is acute, if it's negative the angle is obtuse, and if it's zero, the angle is a right angle.

In this case, the dot product of vectors "u" and "v" is:

⇒ (6i - 4j - k) . (9i + 8j - 4k) = 54 - 32 + 4 = 26  ;

The magnitude of vector "u" is = √(6² + (-4)² + (-1)²) = √(36 + 16 + 1) = √53

The magnitude of vector "v" is = √(9² + 8² + (-4)²) = √(81 + 64 + 16) = √161

So, the Cosine (Cos) of angle between two vectors "u" and "v" is:

⇒ Cos(θ) = 26/(√37 × √145) = 26/√5365  .

Since the value of Cos(θ) is positive, the angle between the vectors is acute. This means the vectors "u" and "v" are pointing in somewhat similar directions, but not exactly the same direction.

The given question is incomplete , the complete question is

Determine whether the angle vector "v" makes with vector "u" is acute, obtuse, straight, a right angle, or whether "v" is a vector in the same direction as "u" . u=6i-4j-k  and  v=9i+8j-4k .

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The given expressions in the expanded form are 2x² + 6x + 4, 8x² + 28x + 24 and x² + 24x + 144.

a. (x + 1)(2x + 4) =

Expanding the product:

2x² + (2 × 1 + 4 × 1)x + 4 × 1 = 2x² + 6x + 4

b. (2x + 3)(4x + 8) =

Expanding the product:

8x² + (4 × 3 + 8 × 2)x + 8 × 3 = 8x² + 28x + 24

c. (x + 12)² =

Expanding the square:

x² + 2 × x × 12 + 12² = x² + 24x + 144

So, for each expression, the expanded form is given by ax² + bx + c.

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The total surface area of the cardboard in square inches is option B. 6 × 5 × 5.

The area of a three dimensional object on it's outer surface is called the surface area of the object.

From the given figure, there are 6 squares with each square having the side length equals 5 inches.

Area of a square = a × a, where a is the length of a side.

Area of a 5 inch square = 5 × 5

There are total of 6 squares.

Total surface area = 6 × 5 × 5

Hence the total surface area of the given figure is option B. 6 × 5 × 5.

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Answer:

Hi, I'm Za'Riah! I will gladly assist you with your problem! (see explanation)

Step-by-step explanation:

[tex]\frac{x-4}{3} \leq 5[/tex]

[tex]\frac{1}{3}x + \frac{-4}{3} \leq 5[/tex]

[tex]\frac{1}{3}x+ \frac{-4}{3} + \frac{4}{3} \leq 5+ \frac{4}{3} \\\frac{1}{3}x\leq \frac{19}{3}[/tex]

[tex]3*\frac{1}{3}x\leq 3*( \frac{19}{3} )[/tex]

Answer:

x [tex]\leq[/tex] 19

(Hope this helped!)

(see image for number line graph)

The equation of the parabola graphed is given as follows:

(x - 3)² = 5(y + 1)

The equation of a vertical parabola is given as follows:

(x - h)² = 4p(y - k)

In which:

The vertex is at the coordinate (3,-1), hence the parameters h and k are given as follows:

h = 3, k = -1.

The directrix is at the coordinate y = -2.25, hence the value of p is obtained as follows:

-1 - p = -2.25

p = 1.25.

Meaning that the equation of the parabola is given as follows:

(x - 3)² = 5(y + 1)

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Step-by-step explanation:

a) h−¹(x) = (x-13)/ (5x+7)

b) h-¹(x) cannot be found when x = 7.

The common region to both the inequalities would be the solution region.

Given is the compound inequality as -

–x + y ≤ –1

x + 2y ≥ 4

Refer to the graph of the inequalities attached. The common region to both the inequalities would be the solution region.

Therefore, the common region to both the inequalities would be the solution region.

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The required steps to show that circle A is similar to circle B are,
1. Dilate circle A by a scale factor of 0.5.
2. Translate circle A using the rule (x − 5, y − 5).

The circle is the locus of a point whose distance from a fixed point is constant i.e center (h, k). The equation of the circle is given by

(x - h)² + (y - k)² = r²

where h, k is the coordinate of the center of the circle on the coordinate plane and r is the radius of the circle.

Here,
Circle A = Center of −2, −2 and a radius of 4,
Circle B = Center of 3, 3, and a radius of 2.

Steps to show circle A is similar to circle B
1. Dilate circle A by a scale factor of 0.5

2. Translate circle A using the rule (x − 5, y − 5)

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The expressions are evaluated to 7 and -6

Algebraic expressions are mathematical expressions comprising of terms, coefficients, variables, constants and factors.

These expressions are also comprised of mathematical or arithmetic operations. These operations are;

From the information given, we have that;

a. -4d + 3

b. k - m

Given that d= ,-1. k = 4 and m = -10

Now, substitute the values, we get;

a.-4(-1) + 3

expand the bracket

4 + 3 = 7

b. k - m

4 - 10

-6

Thus the values are 7 and -6

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The angular velocity in rpm of a point on its rim is equals to the 4224 rad/min.

We have, a cylinder with Radius , R = 6 inch. Spining velocity, S = 24 miles per hour

We have to calculate the the angular velocity in rpm of a point on its rim. To calculate Angular and Linear Speed from Linear velocity :

Step 1: Identify which speed we are asked to calculate and Identify the radius and the velocity. We already identified all this in above.

Step 2: To calculate the angular speed when the linear speed and the radius of the circular object use : angular velocity = linear velocity/radius

First, we need to reconcile the unit of the radius of the wheel/rim and the unit of the speed of the car. Also, we are asked to give the answer in radians per minute. So, let's convert the speed to inches per minutes. So, the linear velocity of spining = 24 miles per hour × 5280 ft. per miles× 12 inches per ft. × 1 hour / 60 minutes

= 25,344 inches per minute

Now, the angular velocity is written as

angular velocity = linear velocity /radius

= 25,344 inches per minute / 6 inches

= 4224 /min. Hence, the angular velocity of the rim is 4224 rad/min.

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If a cylinder with a 6 in. radius is spinning at 24 mph, The angular velocity of a point on the rim of the cylinder is 672.27 rpm.

Angular velocity is a measure of the speed at which an object is rotating around a central axis. It is measured in units of radians per second (rad/s) or revolutions per minute (rpm). To find the angular velocity of a point on the rim of the cylinder, we need to first convert the linear velocity (24 mph) to linear velocity in feet per second (ft/s). We can use the formula:

where v is the linear velocity, r is the radius of the cylinder, and ω is the angular velocity.

Due to the 6 in. = 0.5 feet,

ω = v χ 1 r = 24 miles hr 1 0.5 ft χ 5280 ft mile = 253,440 (rad) hr

Then, 672.27 rpm at 253,440 (rad) hr  1 2pi rev rad  1 60 hr min

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Answer:

[tex]\Huge \boxed{\textbf{B. \$33}}[/tex]

Step-by-step explanation:

To solve this problem, we first need to find the daily rental rate for the midsize sedans. Since the luxury sedans rent for $45 per day and their daily rate is 50% greater than the midsize sedans, we can set up the following equation:

[tex]\Large \boxed{\texttt{45 = 1.5 $\times$ Midsize daily rate}}[/tex]

Now, we can solve for the midsize daily rate:

So, the midsize sedans rent for $30 per day. There are 16 midsize sedans (20 total cars - 4 luxury sedans) and 4 luxury sedans. To find the average daily rental fee for all 20 cars, we can use the following formula:

[tex]\Large\boxed{\texttt{Average daily rental fee} = \frac{\texttt{Total rental fees}}{\texttt{Total number of cars}}}[/tex]

The total rental fees can be calculated as follows:

Now, we can find the average daily rental fee:

So, the average daily rental fee for all 20 cars at this agency is $33, which corresponds to option B.

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________________________________________________________

The paragraph above describes a/an c. controlled experiment.

The participants who drink beer are the b. control group, the participants who drink soda are the a. treatment group.

Flipping a coin to decide which player gets which drink is an example of g. randomization.

A controlled experiment is a type of study in which the researcher manipulates one or more independent variables to observe the effect on a dependent variable. In this case, the independent variable is the type of drink (beer or soda) and the dependent variable is the score achieved in a dart-throwing task.

The purpose of randomly assigning the players to drink either beer or soda is to control for any other factors that could affect the scores, such as the individual's dart-playing ability or the amount of alcohol consumed.

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Complete Question:

A researcher is looking at the effect of drinking alcohol on the ability to play darts. He recruits 20 dart players from the nearby pub and has them come to a lab where he flips a coin for each player. If the coin comes up heads, he has the player drink a pint of beer. If the coin comes up tails, he has the player drink a pint of soda. Each player then throws three darts at a dartboard and the score is recorded. The researcher calculates that the soda-drinkers score, on average, 2.5 points more than the beer-drinkers.

The paragraph above describes a/an _____________.The participants who drink beer are th_____________, the participants who drink soda are the _____________. Flipping a coin to decide which player gets which drink is an example of _____________.

Choose from the list below to fill in the blanks.

a. treatment group

b. control group

c. controlled experiment

d. observational study

e. placebo

f. confounding factor

g. randomization

Answer:

To find the volume of a prism, use the formula V = A * h, where A is the area of the base of the prism and h is its height. For example, for the first prism, the area of the base is 8 and the height is 4, so the volume is 8 * 4 = 32. For the second prism, the area of the base is 6 and the height is 9, so the volume is 6 * 9 = 54. The first prism has a volume of 32 and the second prism has a volume of 54.

Answer:um it dose not show the thing i downloded  the file if u  try again i will anser it for  tho

Step-by-step explanation:

Alexa scored g + 4 goals in the last soccer season.

Expression in mathematics is a combination of symbols, such as numbers and operators, which produces a mathematical result. An expression can involve a single term or multiple terms and usually consists of a combination of constants, variables, operators, functions and parentheses. In an expression, operators are used to perform operations on terms, allowing one to solve equations and other problems. Examples of mathematical expressions include 3 + x = 5, sin(x) + 4, and (x + 2y)^2.

The expression that shows how many goals Alexa scored is: Alexa scored (g + 4) goals.

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Answer:

x = 15º

Step-by-step explanation:

you see they are complementary angles in a straight line (180º), so:

6x - 5 + 6x + 5 = 180

12x = 180

x = 180 / 12

x = 15

And 6x - 5 is not equal 6x + 5 and will never be, I don't know where you got that from.

For the recursive definition F(0) = 0, F(1) =1 , F(n+2) = 2F(n) + F(n+1) , n ≥ 0 ; the first six values are  0 , 1 , 1 , 3 , 5 and 11 .

The first six values of the function F can be computed step by step as follows:

the recursive definition is F(0) = 0, F(1) =1 , F(n+2) = 2F(n) + F(n+1) , n ≥ 0 ;

it is already known that : F(0) = 0  and  F(1) = 1    ;

So , F(2) = 2×F(0) + F(1) = 2×0 + 1 = 1  ;

Similarly ; F(3) = 2×F(1) + F(2) = 2×1 + 1 = 3  ;

⇒ F(4) = 2×F(2) + F(3) = 2×1 + 3 = 5  ;

⇒ F(5) = 2×F(3) + F(4) = 2×3 + 5 = 11 .

Therefore , first six values of F are 0 , 1 , 1 , 3 , 5 and 11 .

The given question is incomplete , the complete question is

Let F be a function defined for all the nonnegative integers by the following recursive definition.

F(0) = 0, F(1) =1 , F(n+2) = 2F(n) + F(n+1) , n ≥ 0 .

Compute the first six values of F .

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16 is the number which is one-fifth of a number when one-fourth of that same number is 20.

As per the given data:

One-fourth of the number is resulted to 20.

Here we have to determine the result of one-fifth of the same number from the given options.

An expression for a portion of a whole is a fraction.

For any real numbers, the fractional component of x is defined.

Let the number be X.

One-fourth of a number is 20 which means:

Multiply the one-fourth fraction with an unknown number which results in the number 20.

[tex]$\frac{1}{4}[/tex]  (X) = 20

X = 20 × 4

X = 80

Now we have to determine that one-fifth of the same number.

Multiply the one-fifth fraction by 80.

We get:

= [tex]$\frac{1}{5}[/tex] (80)

= [tex]$\frac{1}{5}[/tex]   × 5 × 16

= 16

One-fifth of the number 80 is 16

Therefore Option (D) - 16 is the correct answer.

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At 25 mph, stopping distance = 22.56 feet

At 110 mph, stopping distance = 436.81 feet

Now, According to the question:

Let d represents the stopping distance required by an alfa romeo.

The stopping distance is proportional to the square of velocity is equivalent to the equation,

[tex]d = kv^2[/tex]

Here, k is proportionality constant.

We have,

d = 177 feet and v = 70 mph.

So, proportionality constant

[tex]k =\frac{177}{(70mph)^2}[/tex] ≈ 0.0361

Thus, the stopping distances required by an alfa Romeo going at 25 mph and at 110 mph,

[tex]d_2_5=0.0361[/tex] × [tex](25mph)^2[/tex] = 22.56 feet

[tex]d_1_1_0[/tex] = 0.0361 × [tex](110mph)^2[/tex] = 436.81 feet

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Answer: A: 9 galloons and then

Step-by-step explanation:

Answer: the only clear answer i can think of would be, NO, the work she did was not clear i would say she did 4/10days she needed to work

Step-by-step explanation:

A two-sample z-test for a difference in population proportions is the appropriate method for analyzing the results.

Z-test is a statistical test often utilizes to find the difference in mean. It is coupled with variances and sample size to find the appropriate results. It is a hypothetical test where normal distribution is seen.

z-test holds numerous advantages such as it indicates difference in small size groups making it more usable. Moreover, it is also reliable in non-normal distribution of data and is efficient while taking multiple groups in a single analysis. The question has two different popular proportion and hence the two sample z-test will suitable to compare the means.

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The measure of the angle DEF is 39.5 and thus option C is correct.

A circle is simply a round shape that has no corners or line segments. It is a closed curve shape in geometry. The points of circle are at a fixed distance from the center.

Given here: The arc angle as 79

But we know The measure of the angle is equal to half the sum of the intercepted arcs. The angle x is equal to half the sum of the intercepted arcs.

∴∠ DEF= 79/2

           =39.5°

Hence, The measure of the angle is 39.5

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If x denotes the width (in feet) of the billboard, find a function in the variable x giving the area of the printed region of the billboard as a function of x is (150/x - 10)(x - 4).

A billboard designer has decided that a sign should have 5-ft margins at the top and bottom and 2-ft margins on the left and right sides.

x = width of the billboard designer

Total Area including margin = 150 ft^2

Height of the billboard = Area/width

Height of the billboard = 150/x

Before the height of the billboard = (150/x - 5 × 2)

Before the height of the billboard = (150/x - 10) ft

The width of the printed region billboard = (x - 2 × 2)

The width of the printed region billboard = (x - 4) ft

The area of the printed region of the billboard = The width of the printed region billboard × The height of the printed region billboard

The area of the printed region of the billboard = (150/x - 10)(x - 4)

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The complete question is:

A billboard designer has decided that a sign should have 5-ft margins at the top and bottom and 2-ft margins on the left and right sides. Furthermore, the billboard should have a total area of 150 ft^2 (including the margins).

If x denotes the width (in feet) of the billboard, find a function in the variable x giving the area of the printed region of the billboard.

Area as a function of x =

The required probability that a randomly selected bird is a parakeet given that it is green is 54.1%.

Probability can be defined as the ratio of favorable outcomes to the total number of events.

Here,
From the table,
Total green birds = 37
Total green parakeets = 20

Now,
The probability that a randomly selected bird is a parakeet given that it is green,
= 20 / 37 = 54.1%

Thus, the required probability that a randomly selected bird is a parakeet given that it is green is 54.1%.

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Lexi made more than 400 fluid ounces of punch.

According to the mathematical definition of inequality, neither side is equal. When a relationship leads to a non-equal comparison between two expressions or numbers, it is known as an inequality in mathematics. The equal sign "=" in this phrase can be replaced by any of the inequality symbols, such as greater than (>), less than (<), more than or equal to (≥), less than (≤), or not equal to (≠).

Given Lexi made fruit punch for her Fourth of July party and split it equally among 50 cups There were more than 8 fluid ounces of punch in each one.

let x be the total punch Lexi made,

linear inequality for the condition is,

x/50 > 8

multiply both sides by 50

(x/50)*50 > 8*50

x > 400

Hence she made more than 400 ounces of punch.

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Here, the degree of the numerator, 2, is equal to the degree of the denominator, 2, so r(x) has a nonzero horizontal asymptote

Asymptote is a line taken in relation to curve. The line is always far apart from the curve irrespective of distance. Taking the definition in sense of curve, then the curve tries to reach this line while moving towards infinity. Horizontal asymptote indicates the behaviour of function at graph edge.

The equation to be considered for formation of horizontal asymptote is y = mx + b, where u is y-axis, m is slope, x is axis and b is constant. If the two values, that are numerator and Denominator are equal, then y = b.

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Answer:

The expression "84 × 7 = ( + 4) × = 80 × || + 28 + x 7" is not a valid mathematical equation and has errors in syntax. I suggest rephrasing it to a clear and well-formed equation for me to help solve.

If dropped from a height of 20 feet, the ball will travel a vertical distance of 39 feet.

We know that a ball if dropped will bounce back to 95% of its original height.

This means that when a ball is dropped from a distance of 100 m, it will travel 95 meters up.

Here we have been given that the ball is dropped from a height of 20 feet.

Hence, it will bounce back to a height of

95% of 20 = 19 feet.

Hence, the total vertical distance traveled by the ball is

The height at which it was dropped from + distance it bounced back to

20 feet + 19 feet

= 39 feet.

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