A pattern of rectangles is formed by decreasing the length and increasing the width, each by the same amount. The relationship between x, the amount of increase, and A, the area of the rectangle represented by the increase, is quadratic.

Which graph could represent the area of each rectangle in terms of the change in the length and width?

A graph shows change in dimensions (units) labeled 1 to 10 on the horizontal axis and area (square units) on the vertical axis. A straight line decreases from 0 to 9 units.
A graph shows change in dimensions (units) labeled 1 to 10 on the horizontal axis and area (square units) on the vertical axis. A line decreases from 0 to 3 units, increases from 3 to 6 seconds, and decreases from 6 to 9 seconds.
A graph shows change in dimensions (units) labeled 1 to 10 on the horizontal axis and area (square units) on the vertical axis. A line increases from 0 to 3 seconds then decreases from 3 to 9 seconds.
A graph shows change in dimensions (units) labeled 1 to 10 on the horizontal axis and area (square units) on the vertical axis. A curved line decreases from 0 to 9 units.

The simplified equation equivalent to the total distance in miles is given as,

[tex]x^{2} +5x[/tex]

What is the equation representing the total distance?

It is given that in a road test of a geared bike,

The distance covered on a flat road = (3x - 2)

The distance covered uphill = (x² - 5)

The distance covered downhill = (2x + 7)

Total distance covered in miles as equation,

(3x - 2) + (x² - 5) + (2x + 7)

= 3x - 2 + x² -5 + 2x + 7

= 5x - 7 + x² + 7

= x² + 5x

Thus, the final equation representing the total distance covered in miles by the bike is (x² + 5x)

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The sequence of transformation is; B. A translation 2 units to the right and 1 unit up followed by a counter-clockwise rotation 90° about the origin.

From the given image in the transformation, we can see that the pre image which is the original image is on the right hand side while the image after transformation is on the left hand side.

Now it will be noticed that in the pre image, all the x and y coordinates are positive while the image after transformation has all the x-coordinates as negative with the y-coordinates as positive.

This transformation when critically examined is seen to be a translation 2 units to the right and 1 unit up followed by a counter-clockwise rotation 90° about the origin.

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Answer: its B

Step-by-step explanation:

Answer:

240 students

Step-by-step explanation:

     To find the minimum number of students, we have to find the LCM of 10, 12, 16

10 = 2 * 5

12 = 2 * 2 * 3

16 = 2 * 2 * 2 * 2

LCM = 2 * 2 *  2 * 2 * 3 * 5

       = 240

Answer:

0.

Step-by-step explanation:

-6+6=0 because any negative number plus the same positive number cancels each other out.

Answer:

5/7

Step-by-step explanation:

Note that the highest common factor to the numbers are 5. Therefore, to simplify will be:

= 25/35

= 5/7

The proof does the fourth statement and reason represent It is an argument.

AB≅ BC and BC≅EF

 a = b  and b = c then, a =c

ABC is the side of the triangle

⇒AB≅EF

AB = EF                               [def of  segment]

By Segment Addition Postulate states that given  two points A and C, and a third point B lies on the line segment AC if and only if the distances between the  points satisfy the equation

AB + BC = AC.

Since, the line segment EG, F lies on the line segment;

then, by segment addition postulates we have;

EG = EF + FG

By substitution AB=EF

⇒ EG = AB + FG                    hence proved!

In the fourth statement, the reason is:  It is an argument.

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Answer:

60 degrees

Step-by-step explanation:

Since all three sides are the same length, all three angles must be the same size.  This means the triangle is an equilateral triangle

The angles are 60 degrees

Answer:

Hello! The answer is 60°.

Step-by-step explanation:

As marked by the dashes on each side, the sides are congruent. If the sides are congruent, this means that the angle measures are equal.

Having three equal sides is an equilateral triangle, and the total angle measure sum is 180.

To find the measure of angle y, you will have to divide the total angle measure by the number of angles:

180 ÷ 3 = 60

The measure of angle y = 60°

The cone has a greater height because the bases are the same, but the volume of the cylinder is less than 3 times the volume of the cone.

The volume of a cylinder is three times that of a cone.

Volume of a cylinder = πr²h

Volume of a cone = 1/3πr²h

If the height of the cylinder would be greater than that of the cone, the volume of the cylinder should be at least 3 times that of the cone.

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Answer:

Proof explained below

Step-by-step explanation:

Tan trigonometric ratio

[tex]\sf \tan(\theta)=\dfrac{O}{A}[/tex]

where:

Draw a diagram to help visualize the scenario (see attached).

If the angles are complementary, their sum is 90°.

Therefore, let one of the angles be [tex]x[/tex] and the other angle be [tex]90^{\circ}-x[/tex].

Use the tan trig ratio to create two equations with the missing side length.

Right triangle ACD

Given:

Substituting the given values into the tan trig ratio:

[tex]\implies \tan (x)= \dfrac{\textsf{CD}}{9}[/tex]

Right triangle BCD

Given:

Substituting the given values into the tan trig ratio:

[tex]\implies \tan (90^{\circ} - x)= \dfrac{\textsf{CD}}{4}[/tex]

[tex]\textsf{As }\:\tan(90^{\circ} - x)= \cot (x):[/tex]

[tex]\implies \cot(x)= \dfrac{\textsf{CD}}{4}[/tex]

[tex]\implies \dfrac{1}{\tan(x)}= \dfrac{\textsf{CD}}{4}[/tex]

[tex]\implies \tan(x)= \dfrac{4}{\textsf{CD}}[/tex]

Therefore, the two equations are:

  [tex]\textsf{Equation 1}: \quad \tan (x)= \dfrac{\textsf{CD}}{9}[/tex]

  [tex]\textsf{Equation 2}: \quad \tan(x)= \dfrac{4}{\textsf{CD}}[/tex]

Substitute one equation into the other and solve for CD:

[tex]\implies \sf \dfrac{CD}{9}=\dfrac{4}{CD}[/tex]

[tex]\implies \sf CD \cdot CD= 4 \cdot 9[/tex]

[tex]\implies \sf CD^2=36[/tex]

[tex]\implies \sf CD=\sqrt{36}[/tex]

[tex]\implies \sf CD= \pm 6[/tex]

As distance cannot be negative, CD = 6 m only, thus proving that the height of the tower is 6 m.

Using the margin of error for the z-distribution, the sample sizes are given as follows:

a) 822.

b) 1068.

A confidence interval of proportions is given by:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

The margin of error is given by:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which:

We have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

Item a:

The estimate is of [tex]\pi = 0.26[/tex], hence we solve for n when M = 0.03.

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.03 = 1.96\sqrt{\frac{0.26(0.74)}{n}}[/tex]

[tex]0.03\sqrt{n} = 1.96\sqrt{0.26(0.74)}[/tex]

[tex]\sqrt{n} = \frac{1.96\sqrt{0.26(0.74)}}{0.03}[/tex]

[tex](\sqrt{n})^2 = \left(\frac{1.96\sqrt{0.26(0.74)}}{0.03}\right)^2[/tex]

n = 821.2

A sample of 822 is needed.

Item b:

No prior estimate, hence [tex]\pi = 0.5[/tex].

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.03 = 1.96\sqrt{\frac{0.5(0.5)}{n}}[/tex]

[tex]0.03\sqrt{n} = 1.96\sqrt{0.5(0.5)}[/tex]

[tex]\sqrt{n} = \frac{1.96\sqrt{0.5(0.5)}}{0.03}[/tex]

[tex](\sqrt{n})^2 = \left(\frac{1.96\sqrt{0.5(0.5)}}{0.03}\right)^2[/tex]

n = 1067.11

A sample of 1068 is needed.

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Answer:

im gonna say circle or even a hour glass

Step-by-step explanation:

Based on trigonometric formulas, we can find that the options that applies to the given trigonometric relationship are tan θ = 5/12 and cos θ = 12/13.

There six trigonometric functions, which are related by a group of expressions, which will be used in this question:

[tex]\cos \theta = \frac{1}{\sec \theta} = \frac{12}{13}[/tex]

[tex]\sin \theta = \sqrt{1 - \cos^{2}\theta}[/tex]

[tex]\sin \theta = \sqrt{1 -\left(\frac{12}{13} \right)^{2}}[/tex]

[tex]\sin \theta = \frac{5}{13}[/tex]

[tex]\csc \theta = \frac{1}{\sin \theta} = \frac{13}{5}[/tex]

[tex]\tan \theta = \sqrt{\sec^{2}\theta - 1}[/tex]

[tex]\tan \theta = \sqrt{\left(\frac{13}{12} \right)^{2}-1}[/tex]

[tex]\tan \theta = \frac{5}{12}[/tex]

Based on trigonometric formulas, we can find that the options that applies to the given trigonometric relationship are tan θ = 5/12 and cos θ = 12/13.

The statement is incomplete. Complete form is shown below:

Check all that apply:

If sec θ = 13/12, then:

a) sin θ = 12/13

b) tan θ = 5/12

c) cos θ = 12/13

d) csc θ = 12/13

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Answer:

Step-by-step explanation:

The computation shows that the number of ways that this can be done is 64.

From the information given, it's was stated that a 3x2 flag is divided into six squares and that each square is to be coloured green or blue.

In this case, the number of ways that this can be illustrated will be:

= 2^n

= 2^6

= 64

Therefore, there are 64 ways.

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Answer:

The answer is C

Step-by-step explanation:

First if you look at the problem you will notice the triangles aren't the same size so if it's neither rotation nor translation then the shapes do not

The first function isn't decreasing over the largest interval, so the box in the wrong spot is the first one.

Here we have 3 cubic functions.

A function is decreasing when reading from left to right, the curve goes downwards.

Now, if you look at the graph, you can see that the interval where the function decreases is really small (the graph is small so I can't see the exact interval).

While if you look at g(x), you can see that, at least in the interval [-2, 2] the function is decreasing.

So the box in the wrong spot is the first box.

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Answer:

[tex]p = 52.942259755149776[/tex]

Step-by-step explanation:

This is basic trigonometry.

[tex] \cos(39) = \frac{e}{22} [/tex]

[tex]e = \cos(39) \times 22[/tex]

[tex] \sin(39) = \frac{d}{22} [/tex]

[tex]d = \sin(39) \times 22[/tex]

And finally perimeter (p):

[tex]p = 22 + e+ d[/tex]

Answer:

-30

Step-by-step explanation:

The scuba driver is below the sea and ground level which is 0 ft, and he dives down 30 ft so it should be negative.

Hope it helps!

No, the friend is not correct.

The equation of a line is a single b of numerous points on the line. The general form of the equation of a line is of the form ax + by + c = 0 and any point on the line satisfies this equation.

slope= 2/4= 1/2

Now,

y-(-2)= 1/2(x-0)

y+2= 1/2x

y= 1/2x - 2

Hence, the equation is incorrect.

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It would take 1.5 seconds for the diver standing on a spring board 24 feet above the pool to hit the water.

An equation is an expression that shows the relationship between two or more numbers and variables.

Given that d represent the height of the diver above the water and t is the time in seconds.

d(t) = -16(2t - 3)(t + 1)

The diver hit the water at d(t) = 0, hence:

0 = -16(2t - 3)(t + 1)

2t - 3 = 0; or t + 1 = 0

t = 1.5 seconds

It would take 1.5 seconds for the diver standing on a spring board 24 feet above the pool to hit the water.

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The information given about fables and myths is correct. Therefore, the correct option is true.

It should be noted that a fable simply illustrates a story that's considered false or fictional.

In this case, fable derives from the Latin word fabula, which originally meant about the same as the Greek mythos.

Myths are typically not presented as fictitious or untrue. Therefore, the correct option is true.

Complete question:

The word fable derives from the Latin word fabula, which originally meant about the same as the Greek mythos. Like mythos, it came to mean a fictitious or untrue story. Myths, in contrast, are not presented as fictitious or untrue. Fables, like some myths, feature personified animals or natural objects as characters. True or false.

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There are 84 sets of pictures she can post on her wall.

Since Alyssa has taken a picture with every single athlete individually. It means she has taken 9 pictures.

Now she wants to post 3 pictures on her wall.

We need to use Combination for arranging pictures. A combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter. In combinations, we can select the items in any order.

Therefore, The number of different sets of pictures = Selecting 3 pictures from a set of 9 pictures

9C3  =  (9!)/((9-3)!*3!)

(9*8*7)(3*2*1)= 84 ways

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The given statement about normal score that it is expected z score of a data value is true.

Given A statement that a normal z score is the expected z score of a data value, assuming the distribution of the random variable is normal.

We have to tell whether the given statement is true or false.

In z test the z score or standard score is the number of standard deviations by which the value of a raw score is above or below the mean value of what is observed or measured.

A normal distribution is arrangement of a data set in which most values cluster in the middle of the range and the rest taper off symmetrically toward either extreme.

A random variable is a variable which is identified without following any criteria.

A Z test is any statistical test for which the distribution of the test statistic under the null hypothesis ca be approximated by a normal distribution.

Hence the given statement about normal score is absolutely true.

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Answer:

Step-by-step explanation:

Hello and Good Morning/Afternoon!

To determine whether a sequence is arithmetic or geometric:

   ⇒ must consider their definitions

Let's test out this sequence to see what kind of sequence it is:

             3 ⇒ 4, 3 + 1  

             4 ⇒ 7, 4 + 3

             7 ⇒ 11, 7 + 4

              NOT AN ARITHMETIC SEQUENCE

              3 ⇒ 4,  3 * (4/3)

              4 ⇒ 7,  4 * (7/4)

              7 ⇒ 11,  7 * (11/7)

               NOT AN GEOMETRIC SEQUENCE

Answer: Neither arithetic nor geometric

Hopefully that helps!

The probability that the mean weight of the sample babies would be less than 3631 grams is 0.1591 or 15.91%.

The mean weight of the babies (μ) = 3685 grams.

The variance (σ²) = 330625.

Therefore, the standard deviation (σ) = √330625 = 575.

The sample size (n) = 113.

The sample mean = μ - 3685 grams.

The sample standard deviation (s) = σ/√n = 575/√113 = 54.09145.

We are asked to find the probability that the mean weight of the sample babies is less than 3631 grams, that is,

P(X < 3631)  = P(Z < {(3631 - 3685)/54.09145})

Using the formula: Z = (x - μ)/s,

or, P(Z < -0.9983) = 0.1591 or 15.91%.

From the table of area under the z-score.

P(X < 3631) can also be calculated using calculator function:

Normalcdf(-100000000,3631,3685,54.0195), which gives the value 0.1591 or 15.91%.

Thus, the probability that the mean weight of the sample babies would be less than 3631 grams is 0.1591 or 15.91%.

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Answer:

A

Step-by-step explanation:

(f - g)(x)

= f(x) - g(x)

= 3x² + 4x - 6 - (6x³ - 5x² - 2) ← distribute parenthesis by - 1

= 3x² + 4x - 6 - 6x³ + 5x² + 2 ← collect like terms

= - 6x³ + 8x² + 4x - 4

Answer:

nothing

a point

a segment

Step-by-step explanation:

nothing

a point

a segment

Answer:

28 legs are on the floor once again

There are no legs on the floor.

Hence answer is zero.

According to the question,

For 2 dogs: Each dog has 4 legs.

Therefore, 2 dogs have a total of 8 legs.

For 4 horses: Each horse has 4 legs.

Therefore, 4 horses have a total of 16 legs.

For 1 giraffe: A giraffe has 4 legs.

For 1 duck: A duck has 2 legs.

For 3 hens: Each hen has 2 legs.

Therefore, 3 hens have a total of 6 legs.

To get the total number of legs on the bed,

we simply add up all the legs of the animals on the bed,

⇒ 8 legs + 16 legs + 4 legs + 2 legs + 6 legs = 36 legs.

Now, to get the number of legs on the floor,

We need to subtract the number of legs on the bed from the total number of legs of all the animals,

For 2 dogs with a total of 8 legs.

For 4 horses with a total of 16 legs.

For 1 giraffe with 4 legs.

For 1 duck with 2 legs.

For 3 hens with a total of 6 legs.

So, the total number of legs of all the animals is,

⇒ 8 legs + 16 legs + 4 legs + 2 legs + 6 legs = 36 legs.

Since all the animals are on the bed,

There are no legs on the floor.

Therefore, the answer is 0 legs on the floor.

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Answer:

The answer is c) 73

Step-by-step explanation:

The angle 146 and (-39 + x) lie on the same line, so that means their sum is 180 degrees because a straight line has 180 degrees.

180 = 149 - 39 + x

180 = 107 + x

180 - 107 = x

73 = x

Answer:

73

Step-by-step explanation:

The two angles form a straight line  and a straight line is 180 degrees

-39+x + 146 = 180

Combine like terms

107 +x = 180

Subtract 107 from each side

107+x-107 = 180-107

x =73