Identify the graph of m(x)=√x+5.

Determine when the function is nositive. negative, increasing. or decreasing. Then describe the end behavior of the function..

Answer:

M=(-5,-4)

Step-by-step explanation:

The midpoint of the line segment AB with coordinates A = (-3, -1) and B = (-7, -7) is (-5, -4).

To find the midpoint of a line segment AB, we can use the midpoint formula. The midpoint formula states that the x-coordinate of the midpoint is the average of the x-coordinates of A and B, and the y-coordinate of the midpoint is the average of the y-coordinates of A and B.

Given A = (-3, -1) and B = (-7, -7), we can use the midpoint formula as follows:

Therefore, the midpoint M of AB is (-5, -4).

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Answer:

D) 25 : 1

Step-by-step explanation:

[tex]\boxed{\bf Volume \ of \ cylinder = \pi r^2h}[/tex]

Cylinder 1:

         [tex]h_1 = 5 \ cm\\\\r_1 = 3 \ cm[/tex]

Cylinder 2:

           [tex]h_2 = 5 \ cm\\\\r_2 = 15 \ cm[/tex]

[tex]Volume \ of \ cylinder2 : Volume \ of \ cylinder1 = \dfrac{\pi * 15 * 15 * 5}{\pi *3*3*5}[/tex]

                                                                       = 25 : 1

Answer:

The hypotenuse is 13 cm

The longest leg is 12 cm

The shortest leg is 5 cm

Step-by-step explanation:

Given:

A right triangle

Let's assume, that the longest leg is x, the shortest leg is y and the hypotenuse is z

Let's write 2 equations according to the given information and put them into a system (use the Pythagorean theorem):

[tex]z = \sqrt{ {x}^{2} + {y}^{2} } [/tex]

{√(x^2 + y^2) = x + 1,

{x - y = 7;

Let's make x the subject from the 2nd equation:

x = 7 + y

Replace x in the 1st equation with its value from the 2nd one:

[tex] \sqrt{( {7 + y)}^{2} + {y}^{2} } = (7 + y) + 1[/tex]

[tex] \sqrt{49 + 14y + {2y}^{2} } = 8 + y[/tex]

Square both sides of the equation:

[tex]2 {y}^{2} + 14y + 49 = {(8 + y)}^{2} [/tex]

[tex]2 {y}^{2} + 14y + 49 = 64 + 16y + {y}^{2} [/tex]

Move the expression to the left and collect like-terms:

[tex] {y}^{2} - 2y - 15 = 0[/tex]

a = 1, b = -2, c = -15

Solve this quadratic equation:

[tex]d = {b}^{2} - 4ac = ({ - 2})^{2} - 4 \times 1 \times ( - 15) = 64 > 0[/tex]

[tex]y1 = \frac{ - b - \sqrt{d} }{2a} = \frac{2 - 8}{2 \times 1} = \frac{ - 6}{2} = - 3[/tex]

y must be a natural number, since the length of a triangle's side cannot have negative units

[tex]y2 = \frac{ - b + \sqrt{d} }{2a} = \frac{2 + 8}{2 \times 1} = 5[/tex]

We found the length of the shortest leg

Now, we can find the rest of the dimensions:

x = 7 + 5 = 12

[tex]z = \sqrt{ {12}^{2} + {5}^{2} } = \sqrt{144 + 25} = \sqrt{169} = 13[/tex]

The correct option is A) 20.2.

What is triangle sum?

The triangle sum is a property of triangles that states that the sum of the interior angles of a triangle is always equal to 180 degrees. In other words, if you add up the measures of the three angles inside a triangle, the result will always be 180 degrees.

Using the given information and the fact that the angles in a triangle sum to 180 degrees, we can find the value of x as follows:

Start by finding the measure of angle K by subtracting the measures of angles A and B from 180 degrees:

K = 180 - A - B

= 180 - 84 - 65

= 31 degrees

Use the law of sines to set up an equation relating the side lengths and corresponding angle measures:

sin(A)/x = sin(K)/17

Substitute the values we know into the equation and solve for x:

sin(84)/x = sin(31)/17

x = sin(84)*17/sin(31)

Using a calculator, we get:

x ≈ 20.2

Therefore, the value of x in the triangle is approximately 20.2.

So, the correct option is A) 20.2.

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Answer:

a. The Ferris wheel has a diameter of 30 meters, which means the radius is 15 meters. Since the wheel is boarded from a platform that is 2 meters above the ground, the center of the Ferris wheel is 2 + 15 = 17 meters above the ground.

The function h(t) gives a person's height in meters above the ground t minutes after the wheel begins to turn. Since the Ferris wheel completes one revolution in 10 minutes, the period of h(t) is 10 minutes.

The midline is the average value of the function h(t) over one period, and it is equal to the vertical displacement of the graph from the x-axis. Since the center of the Ferris wheel is 17 meters above the ground, the midline is h = 17 meters.

The amplitude of the function h(t) is the distance between the midline and the maximum or minimum value of the function. The maximum height a person can reach on the Ferris wheel is when they are at the very top of the wheel, which is 17 + 15 = 32 meters above the ground. The minimum height a person can reach on the Ferris wheel is when they are at the very bottom of the wheel, which is 17 - 15 = 2 meters above the ground. So the amplitude of h(t) is 15 meters.

Therefore, the amplitude is 15 meters, the midline is h = 17 meters, and the period is 10 minutes.

b. To find the height of a person after 5 minutes, we can plug t = 5 into the function h(t):

h(5) = 15 sin(2π/10 * 5) + 17

h(5) = 15 sin(π) + 17

h(5) = 2 meters

Therefore, a person is 2 meters above the ground after 5 minutes on the Ferris wheel.

Step-by-step explanation:

The shaded area is the same in both circumstances, implying that 4/5 equals 8/10.

We can use a visual representation of a rectangle divided into five equal segments to understand why 4/5 equals 8/10.

If we shade four of those portions, we have shaded four-fifths of the rectangle.

Let's now divide the same rectangle into ten equal sections, each half the size of one of the five parts we started with.

If we shade in eight of these smaller areas, we will have shaded eight-tenths of the rectangle.

We can observe that the shaded area is the same in both circumstances, implying that 4/5 equals 8/10.

In other words, when we divide a whole into equal parts, we can always discover a fraction of those parts.

another fraction that is equivalent to it by splitting the same total into more or less equal-sized parts. In this scenario, 4/5 and 8/10 represent the same portion of the entire rectangle, simply divided into a different number of portions.

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The three successive positive numbers are 3, 4, and 5.

The largest of these 5.

Integers are made up of zeros, natural numbers, and their additive inverses. Except for the fractional part, it can be represented on a number line.

Let's call the smallest of three successive positive numbers x. The following two consecutive integers would then be x + 1 and x + 2.

The product of the two smaller integers (x and x + 1) is eight times that of the largest integer (x + 2). This can be written as an equation:

x(x + 1) = 8 + (x + 2)

By enlarging and simplifying the left side, we get:

[tex]x^2 + x = x + 10[/tex]

When we subtract x and 10 from both sides, we get:

[tex]x^2 - 9 = 0[/tex]

After factoring in, we get:

(x - 3)(x + 3) = 0

As a result, x = 3 or x = -3. We can disregard the negative solution because we're seeking positive integers and infer that x = 3.

As a result, the three successive positive numbers are 3, 4, and 5.

The largest of these 5.

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Answer:

216

Step-by-step explanation:

Answer:

216

Step-by-step explanation:

3(5x² - 9x)

3(5(-3)² - 9(-3))

3(5(9) - 9(-3))

3(45 + 27)

3(72)

216

Best approximation of the mass of an African elephant is 8 ×10³kg

In physics, mass is a fundamental property of matter that measures the amount of substance in an object. It is a scalar quantity that describes an object's resistance to acceleration when a force is applied. Mass is usually measured in kilograms (kg) and can be calculated by dividing an object's weight by the acceleration due to gravity.

Given;

Mass of elephant=8139kg

Dividing the mass by 1000 and multiplying it by 10³, we get

Mass of elephant=8.139 ×10³kg

Estimating the mass of elephant, we get

Mass of elephant=8 ×10³kg

hence, best approximation of the mass of an African elephant is 8 ×10³kg.

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The expression for the total combined profit that John made from the sales of MP3 and DVD players last week is: 18x + 35(128 - x) dollars.

To arrive at the expression, we should first note that if x is the number of DVD players sold by John last week, then the number of MP3 players sold by John last week would amount to:

(128 - x), because the total number of players sold for both MP3 and DVD was 128.

Next, the total profit made by John from selling x DVD players is 18x dollars, since he makes a profit of $18 for a unit of DVD player sold.

In the same vein, the total profit made by John from selling (128 - x) MP3 players is 35(128 - x) dollars, since he makes a profit of $35 for each MP3 player sold.

In conclusion, the expression for the total combined profit John made from selling the DVD and MP3 players last week is: 18x + 35(128 - x) dollars.

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Step-by-step explanation:

Assuming   18 cm and 12 cm sides are parallel ( you are not told this) , this is just a trapezoid

  area = height * averge of bases = 7 * ( 12+18)/2 = 105 cm^2

Answer:

Step-by-step explanation:

If principal is $2,658 and rate of interest 9% then the value of  the account balance is approximately $10,253 by using continuous compound interest formula.

Recurring interest is interest calculated on principal plus all interest and other interest. The idea is that lenders always receive interest, not individually at specific times.

The formula for continuous compound interest :

  A=    Peˣⁿ                          

Where,

A =Amount of money  after a certain amount of time

P= principal or the amount of money you start with

e =Napier's number, which is approximately 2.7183

x =Interest rate

n =Amount of time in years.

Use the continuous compound interest formula :

Given  P= 2658

x =9% =   = 0.09

n = 15

e = 2.7183

By using

A=    Peˣⁿ  

A= (2658)(2.7183)⁰°⁰⁹¹⁵

A =10,253 (approximately)

Hence, the value of account balance after 15 years is approximately $10,253

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Answer:

1.15

Step-by-step explanation:

To figure out how many miles she walked in 5 days, we can multiply the number from just one day and multiply that by 5 and we will get our answer!

0.23 * 5 = 1.15

After applying the difference of squares procedure , the factors  we get =(7y + 5z)(7y - 5z)

Finding the factors of a given statement is a procedure known as factoring.

For instance,  the factors of 12 are 1, 2, 3, 4, 6, and 12 are. The components of x²+ 5x + 6 are (x + 2) and (x + 3), respectively.

Factorization of polynomials is a specific instance of the difference of squares formula. It claims that the product of two squares' sum and differences may be calculated using their difference.

A difference of squares expression is, for instance, a² - b² = (a + b)(a - b).

the phrase 49y² - 25z² can be factored, where

a² - b² = (a + b).(a - b).

Where a=49  ,  b = 25

After applying the difference of squares procedure, the phrase 49y² - 25z² can be factored, where a² - b² = (a + b).(a - b).

Consequently, 49y - 25z

= 7y + 5z(7y - 5z).

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Using density, we can find the following:

There are about 0.00032 grizzly bears per acre.

There are about 0.0090 elks per acre.

There are about 0.00085 mule deer per acre.

There are about 0.0015 bighorn sheep per acre.

A measurement of the amount of data stored on a medium (tape or disk). The amount of data stored on magnetic tape is measured in bits per inch or millimetre; for discs, it is measured in a defined number of bits per sector, sectors per track and tracks per disc.

Density is calculated mathematically by dividing mass by volume.

Here in the question,

The national park is 2.22 million acres.

= 2,220,000 acres.

Now given,

Grizzly bears population = 728.

Elks' population = 20,000

Mule deer's population = 1900

Bighorn sheep's population = 345.

Now, to find density:

Density of Grizzly bears = 728/2220000

= 0.00032

Density of elk = 20,000/2220000

= 0.0090

Density of mule deer = 1900/2220000

= 0.00085

Density of bighorn sheep = 345/2220000

= 0.0015

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1) The future value of $460 in 8 months, with an annual interest rate of 12% is $496.10.

2) The present value that must be deposited now so that its value will be $3,500 after 9 months is $3,350.34.

3a) The total amount to be repaid, including accumulated interest, for Zach's purchase of furniture worth $2,800 with a $400 down payment, is $2,552.87.

3b) The monthly payment is $106.37.

An online finance calculator can be used to determine the future value, present value, and monthly payments for 1), 2), and 3).

The future value is the present value compounded into the future at an interest rate.

The present value is the future value discounted to the present period at an interest rate.

N (# of periods) = 0.6667 years (8/12 months)

I/Y (Interest per year) = 12%

PV (Present Value) = $460

PMT (Periodic Payment) = $0

Results:

Future Value (FV) = $496.10

Total Interest = $36.10

N (# of periods) = 0.75 years (9/12 years)

I/Y (Interest per year) = 6%

PMT (Periodic Payment) = $0

FV (Future Value) = $3,500

Results:

Present Value (PV) = $3,350.34

Total Interest = $149.66

The cost of furniture bought by Zach = $2,800

Down payment = $400

Loan amount - $2,400 ($2,800 - $400)

Interest rate = 6%

Loan period = 2 years.

N (# of periods) = 24 months (2 years x 12)

I/Y (Interest per year) = %6

PV (Present Value) = $2,400

FV (Future Value) = $0

Results:

Monthly Payment (PMT) = $106.37

Sum of all periodic payments = $2,552.87

Total Interest = $152.87

The total amount to be repaid = Loan amount + Accumulated Interest

= $2,552.87

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The midpoint of the line segment connecting the endpoints of the diameter is the center of the circle. We can find the midpoint by averaging the coordinates of the endpoints:

$\sf\implies\:Midpoint\:=\:\left(\frac{-6\:-\:14}{2},\:\frac{3\:+\:13}{2}\right)\:=\:(-10,\:8)$

The radius of the circle is half the length of the diameter, which we can find using the distance formula:

$\sf\implies\:Radius\:=\:\frac{\sqrt{(-6\:-\:(-14))^2\:+\:(3\:-\:13)^2}}{2}\:=\:\frac{\sqrt{160}}{2}\:=\:4\sqrt{10}$

Thus, the equation of the circle is

$\sf\implies\:(x\:+\:10)^2\:+\:(y\:-\:8)^2\:=\:(4\sqrt{10})^2$

Simplifying and rearranging, we get:

$\sf\implies\red\bigstar\:(x\:+\:10)^2\:+\:(y\:-\:8)^2\:=\:160$

[tex]\huge{\colorbox{black}{\textcolor{lime}{\textsf{\textbf{I\:hope\:this\:helps\:!}}}}}[/tex]

[tex]\begin{align}\colorbox{black}{\textcolor{white}{\underline{\underline{\sf{Please\: mark\: as\: brillinest !}}}}}\end{align}[/tex]

[tex]\textcolor{blue}{\small\textit{If you have any further questions, feel free to ask!}}[/tex]

[tex]{\bigstar{\underline{\boxed{\sf{\textbf{\color{red}{Sumit\:Roy}}}}}}}\\[/tex]

Answer:

Step-by-step explanation:

A. The individual events are dependent. The probability of the combined event is:

The probability of drawing a red piece of candy on the first draw is 10/51. Since we do not replace the candy after the first draw, the probability of drawing another red piece of candy on the second draw depends on what happened on the first draw. If a red piece of candy was drawn on the first draw, then there are 9 red pieces of candy left out of 50 total pieces of candy for the second draw. If a non-red piece of candy was drawn on the first draw, then there are still 10 red pieces of candy left out of 50 total pieces of candy for the second draw. Therefore, the probability of drawing two red pieces of candy in a row is:

(10/51) x (9/50) + (41/51) x (10/50) = 0.0698

Rounded to three decimal places, the probability of the combined event is 0.070.

Answer:

Step-by-step explanation:

What you'll want to do is add the three numbers on top to get 6/5. If you need the answer in decimal form, it's 1.2, and if you need it as a mixed number, your answer will be 1 1/5 :)M Hope this helped.

Answer:

[tex]1\frac{3}{5}[/tex] meter is the difference in depths of locations diver dove.

Step-by-step explanation:

Answer:

z = -1.5

6.68%

More than 2.5 standard deviations:  X > 125 mg/dl

Less than 2.5 standard deviations:  X < 75 mg/dl

Step-by-step explanation:

If a continuous random variable X is normally distributed with mean μ and variance σ², it is written as:

[tex]\boxed{X \sim\text{N}(\mu,\sigma^2)}[/tex]

Given:

Therefore, if the blood sugar levels are normally distributed:

[tex]\boxed{X \sim\text{N}(100,10^2)}[/tex]

where X is the blood sugar level in milligrams per deciliter.

Converting to the Z distribution:

[tex]\boxed{\textsf{If }\: X \sim\textsf{N}(\mu,\sigma^2)\:\textsf{ then }\: \dfrac{X-\mu}{\sigma}=Z, \quad \textsf{where }\: Z \sim \textsf{N}(0,1)}[/tex]

If David has a blood sugar of 85 mg/dl then X = 85:

[tex]\implies Z=\dfrac{85-100}{10}=-1.5[/tex]

To calculate the percentile, find the area associated with the z-score on the Z Table (attached).  Multiply the area by 100 and add a percentage sign:

[tex]z=-1.5 \implies 0.0668=6.68\%[/tex]

The calculations of the blood sugar readings that would be more than or less than 2.5 standard deviations from the mean are:

[tex]\implies \mu + 2.5 \sigma=100+2.5(10)=100+25=125[/tex]

[tex]\implies \mu -2.5 \sigma=100-2.5(10)=100-25=75[/tex]

The blood sugar readings that would be more than 2.5 standard deviations from the mean are:

The blood sugar readings that would be less than 2.5 standard deviations from the mean are:

Answer:

Options B and C

Step-by-step explanation:

First, we have to find out the unit rates

Matte Paint

7.56 ÷ 4

= $1.89 per paint

Glossy Paint

26.16 ÷ 2

= $13.08 per gallon

Paint Brushes

18 ÷ 4

= $4.5 per brush

Now we have to check for each statement.

Option A

If he buys 1 [tex]\frac{1}{2}[/tex] gal on matte paints

1 [tex]\frac{1}{2}[/tex] = 1.5 gal

1.5 × 1.89 = $2.84

So therefor statement A is not true.

Option B

We have to convert quart to gal

1 quart = 0.25 gal

6 quarts = 1.5 gal

1.5 × 13.08 = $19.62

so statement B is true

Option C

They got 2 paintbrushes so we have to mutiply

2 × 4.5=$9

1 gal matte paint

We have to convert gal to pint

1 gal = 8 pint

8 × 1.89 = $15.12

Then we add them

15.12 + 9 = $24.12

Which means statement C is true

Option D

13 pints of glossy paint

$13.08 per gallon

1 gal =8 pint

13 pints = [tex]\frac{13}{8}[/tex] gal

[tex]\frac{13}{8}[/tex] × 13.08 = $21.26

so statement D is not true

That leaves us with Option B and C

Answer:

third

Step-by-step explanation:

both the points are negative therefore they would be in the third quadrant

The value of x by the use of the laws of trigonometry is 94 degrees.

Vertically opposite angles are a pair of angles formed by the intersection of two straight lines. When two lines intersect at a point, four angles are formed, and the angles that are opposite each other and not adjacent are called vertically opposite angles. Vertically opposite angles are always equal in measure, which means that they have the same angle degree or radian measure.

We know that the interior angle is vertically opposite to 39 degrees and the exterior angle is equal to the sum of the opposite interior angles.

Hence;

55 + 39 = 94 degrees

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The cost of 14 peaches will be 14/114 the of the price of 114 peaches. Therefore, the answer is 14/114 x 50.95 ≈ $6.26.

The fraction 3/8 is equivalent to 37.5% as a percentage.

A percentage can be used to represent a number as a portion of 100.. It is frequently employed to convey ratios, rates, and proportions in a more intelligible manner. One part in one hundred is represented by the percentage sign, which is %.

A fraction is a measure of a ratio between two numbers or a portion of an entire. It has a horizontal line between the numerator and denominator. The denominator reflects the total number of pieces in the whole, whereas the numerator specifies how many parts are being taken into account.

To convert the fraction 3/8 to a percentage, we need to multiply it by 100.

So,

3/8 x 100 = 37.5%

Therefore, the fraction 3/8 is equivalent to 37.5% as a percentage.

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Let's assume that the area of the rectangular field is x square meters, and the width of the field is y meters. Then we know that:

x = y * 4 (since the length of the rectangular field is 4 times the width)

And we also know that the area of the rectangular field is equal to the area of a square. Therefore:

x = y^2

Combining these two equations, we get:

y^2 = y * 4

y = 4 meters

So the width of the rectangular field is 4 meters. Using this, we can find the length:

x = y * 4 = 4 * 4 = 16 square meters

Now, to find the perimeter of the rectangular field:

Perimeter = 2 * (length + width) = 2 * (16 + 4) = 40 meters

Therefore, the perimeter of the rectangular field is 40 meters.

Next, we need to find the number of papaya plants that can be sown in the area of the field. The total area of the field is 16 square meters. If one papaya plant is sown in every 4 square meters, then the number of plants required would be:

Number of plants = Total area / Area per plant

Number of plants = 16 / 4 = 4 plants

Therefore, 4 papaya plants can be sown in the rectangular field.