The area of a right triangle is 5 in 2. If the length of a leg is x, write the function h(x) that describes the length of the hypotenuse.

The correct statement about the given function is: The function is increasing for all real values of x where x < –4.

In this question, we have been given the graph of the function

f(x) = -(x + 6)(x + 2)

According to description of the graph of given function f(x), the graph of function is a parabola and on a coordinate plane, a parabola opens down.

Also, the parabola goes through (-6, 0), has a vertex at (-4, 4), and goes through (-2, 0).

We need to find to the correct statement about the function.

f(x) = -(x + 6)(x + 2)

The function is increasing until it reaches the vertex x = -4.  

The function will decrease after the vertex, so after x = -4 function decreases.

increasing: -∞ < x < -4

decreasing : -4 < x < ∞

Therefore, the correct statement about the given function is: The function is increasing for all real values of x where x < –4.

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The area of the polygon is approximately 24.497 square units.

In accordance with the statement, we have a polygon with three vertices set on Cartesian plane, that is, a triangle. We need to find the side lengths first and later to calculate the area by Heron's formula. First, determine the lengths of each line segment by Pythagorean theorem:

JK = √[[4 - (- 3)]² + (4 - 4)²]

JK = 7

KL = √[(3 - 4)² + (- 3 - 4)²]

KL = √[(- 1)² + (- 7)²]

KL = 5√2

JL = √[[3 - (- 3)]² + (- 3 - 4)²]

JL = √85

Second, calculate the area of the triangle:

s = (JK + KL + JL) / 2

s = (7 + 5√2 + √85) / 2

s ≈ 11.645

A = √[s · (s - JK) · (s - KL) · (s - JL)]

A = √[11.645 · (11.645 - 7) · (11.645 - 5√2) · (11.645 - √85)]

A ≈ 24.497

The area of the polygon is approximately 24.497 square units.

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Answer:

Step-by-step explanation:

-9x - 45 = -7x - 15  (Distribute -0.75 to (12x+60))        (x-8x = -7x)

-30 = 2x   (add 15 to both sides and add 9x to both sides)

-15 = x (divide both sides by 2)

Answer:

h=sqrt2*5i, h=-sqrt 2*5i

Step-by-step explanation:

Answer:

DNE

No real solutions

Step-by-step explanation:

This Quadratic Equation: 2h² + 100 = 0

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$1024\\ r=rate\to 100\%\to \frac{100}{100}\dotfill &1\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{half-yearly, thus twice} \end{array}\dotfill &2\\ t=years\dotfill &3 \end{cases}[/tex]

[tex]A=1024\left(1+\frac{1}{2}\right)^{2\cdot 3} \implies A=1024(1.5)^6\implies A = 11664~\hfill \underset{earned~interest}{\stackrel{11664~~ - ~~1024}{10640}}[/tex]

This is an arithmetic sequence

The nth term of an arithmetic sequence is Tn = a + (n-1)d

a is the first term.

n is the number of terms

d is the common difference

Given that 19th term of the sequence is:

         gn=gn−1⋅(−12) if g17=162

Suppose a=12

Then,

The 17th term g17=a+(n-1)d

                           = 12+(17-1)d

'n' means number of terms

                        12+(17-1)d=162    because g17=162

                        12+16d=162

                         16d=162-12

Subtract the values,

We can write,

                         16d=150

                           d=150/16

Divide the values,

We can write,

                           d=25

To get the sixth term g6

      g6=12+(6-1)d

           =12+5d

     Replace with d value in above equation,

Then,       g6=12+5(25)

              g6=12+125

               g6=137

So, the sixth term is g6=137.

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The value of the functions f(6), f(- 10), f(0) are 9, 7 and 3 respectively.

A function can be defined as an expression, rule or law that shows the relationship between a dependent and an independent variable.

Given the function;

f(x) = |x+3|

To determine f(6)

Substitute the value of x as 6

We have;

f(6)  = | 6 + 3 |

f(6) = 9

To determine f(-10)

Substitute the value of x as - 10

We have;

f(-10) = | -10 + 3 |

f(-10) = | -7|

f(-10) = 7

To determine f(0)

Substitute the value of x as 0

We have;

f(0) = | 0 + 3|

f(0) = 3

Thus, the value of the functions f(6), f(- 10), f(0) are 9, 7 and 3 respectively.

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The angle of depression of the meat from the top of the table is 40°

This situation makes a right-angle triangle with the height of table being the perpendicular to the right-angle triangle and the distance of meat from the foot of the table becomes the base of the imaginary right-angle triangle

to know the angle of depression of the meat from the top of the table

we need to find the ratio between the perpendicular and the base of the triangle to use trigonometry.

Tan  is the ratio of perpendicular and base of the triangle

which is = 96/114.4

          tan Ф=0.8392

To solve for Ф , a tan would move from the left-hand side to the right-hand side and would become tan inverse.

            Ф  = tan-1 0.8392

             Ф = 40°

 The correct question is a cat on a table 96cm views a piece of meat on the ground 114.4cm away from the foot of the table. find the angle of depression of the meat from the top of the table.

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Answer:

Your answer should be 90 degrees for angle one. For angle two, 58 and angle three 32.

Step-by-step explanation:

This is because they are supplementary angles! I hope this helps. Xx

Answer: ∠1 = 90°

Step-by-step explanation:

∠1 = ∠4

∠2 = ∠5

∠3 = ∠6

reason = vertically opposite angle

∠1 = 90°

∠2 = 58°

∠3 = 32°

checking :

total angles = 360°

360° = ∠1 + ∠2 + ∠3 + ∠4 + ∠5 + ∠6

360° = 90° + 58° + 32° + 90° + 58° + 32°

360° = 360°

Answer:

area of the arrow is 36inches^2

Step-by-step explanation:

Area of rectangle= lw

10x3=30

Area of triangle = bh/2

3x4=12/2=6

30+6=36 inches^2

The solution set of the inequality for R is given by [tex]-\frac{1172}{85} \leq x\leq \frac{1228}{55}[/tex] .

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way.  It is frequently used to compare two numbers on the number line based on their sizes. Different types of inequalities are represented by a variety of notations such as < ,> ,≤ and ≥.

The modulus function takes the absolute value of a function.

To solve the given inequality we have simplify the inequality first.

[tex]x-\frac{7}{9} |(\frac{12}{5} -6x)|+50\ge -30[/tex]

[tex]or, x-\frac{7}{9}\times \frac{6}{5} |(2-5x)|+50\ge -30\\or,x-\frac{14}{15}|2-5x|\ge-80\\[/tex]

Now we separate the inequalities:

[tex]x-\frac{14}{15}(2-5x)\ge-80[/tex]  for 2x-5 ≥ 0

[tex]x-\frac{14}{15}(-(2-5x))\ge-80[/tex]  for 2x-5 ≤ 0

Now we will solve the two inequalities separate and find the intersection.

[tex]x-\frac{14}{15}(2-5x)\ge-80\\or,15x-28+70x\ge-1200\\or,x\ge -\frac{1172}{85}[/tex]

Again

2x-5 ≥ 0

or, [tex]x\le\frac{2}{5}[/tex]

hence [tex]-\frac{1172}{85}\le x\le\frac{2}{5}[/tex]

Similarly solving the other inequality we get

[tex]\frac{2}{5}\le x\le\frac{1228}{55}[/tex]

Now we find the intersection of the two inequalities:

[tex]-\frac{1172}{85}\le x\le\frac{1228}{55}[/tex]

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Answer:

1728

Hope this helps :)

[tex]\cfrac{12}{16}\implies \cfrac{4\cdot 3}{4\cdot 4}\implies \cfrac{4}{4}\cdot \cfrac{3}{4}\implies 1\cdot \cfrac{3}{4}\implies \boxed{\cfrac{3}{4}}~\hfill \cfrac{8\cdot 3}{8\cdot 4}\implies \boxed{\cfrac{24}{32}}[/tex]

The amount of water a bag of salt can treat is 47, 250 cubic feet

The formula for volume of a rectangle is expressed as;

Volume = length × width × height

From the information given, we have the following parameters;

Substitute the values into the formula

Volume = 25 × 14 × 5

Find the product

Volume = 1750 cubic yards

Covertoing cubic yard to cubic feet

I cubic yard = 27 cubic foot

1750 yards = x

x = 27 × 1750

x = 47, 250 cubic feet

Thus, the amount of water a bag of salt can treat is 47, 250 cubic feet

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Answer:

v = 13

Step-by-step explanation:

because they are supplementary angles they add up to 180

so

add them

and put them equal to 180

9v + 3 + 60 = 180

combine like terms

9v + 63 = 180

now subtract 63 to both sides

9v = 117

divide 9 to both sides

v = 13

that is your answer

Based on the temperature readings, the average recorded temperature in the 20 days was 10.15°

The average temperature can be found by adding all the temperatures and then dividing by the number of temperatures taken which is 20.

The average is therefore:

= 24° + (−10°) +  9° +  18° +  23° +  27° +  8° +  17° +  3° +  7° + ( −2°) +  (−6°) +  2° + (−9°) +  (−8°) +  21° +  25° +  15° +  10° +  29°) / 20

= 203 / 20

= 10.15°

In conclusion, the average temperature was  10.15°.

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Answer: -4x²-11x-7

Step-by-step explanation:

[tex]-3x^2-3x-7-(x^2+8x)=\\-3x^2-3x-7-x^2-8x=\\-4x^2-11x-7[/tex]

Answer:

1.45 dollars per quart.

0.69 quarts per dollar.

Explanation:

To find dollars per quart,

5.79 ÷ 4 = 1.4475

Round to the nearest hundredth; 1.4475 -> 1.45

-

To find quarts per dollar,

4 ÷ 5.79 = 0.6908462867

Round to the nearest hundredth; 0.6908462867 -> 0.69

Dividing was all you needed!

The cost of each hamburger is $8, the cost of each French fry is $5 while the cost of each Soda is $3.

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

Let x represent the cost of hamburger, y represent the cost of french fries and z represent the cost of soda, hence:

x + y = 13   (1)

Also:

x + 2z = 14    (2)

And:

x + y + z = 16    (3)

From the three equations:

x = 8, y = 5, z = 3

The cost of each hamburger is $8, the cost of each French fry is $5 while the cost of each Soda is $3.

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The car will take 15 minutes to drive to the next stop which is 16 miles away.

As per the question statement, we are supposed to find the time taken by the car to drive to the next stop which is 16 miles away if it is driving on the interstate with cruise control on at a constant speed of 64 miles per hour.

Before solving the question, we need to know the concept of relation between time, distance and speed, which states that

[tex]speed=\frac{distance}{time}[/tex]

In the question [tex]speed = 64 mph\\distance = 16 miles\\time taken = t[/tex]

Substituting values in the formula above,

[tex]64=\frac{16}{t} \\t=\frac{16}{64} \\t=0.25 hours =0.25 *60\\t=15 minutes[/tex]

Hence the time taken by car  to drive to the next stop which is 16 miles away is 15 minutes or [tex]\frac{1}{4}[/tex] hours.

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The quotient of the given problem using laws of exponents is; 6 * 10⁰

We want to express the quotient of the quantity 30 times ten raised to the negative twenty fourth power end quantity divided by the quantity 5 times ten raised to the negative twenty fourth power end quantity.

This is;

(30 * 10⁻²⁴)/(5 * 10⁻²⁴)

Now, we can break this down into like terms to get;

(30/5) * (10⁻²⁴/10⁻²⁴)

= 6 * 1

Now, 1 can also be written as;

10⁰ = 1

Thus, the solution of the given problem is; 6 * 10⁰

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The graphing is achieved as follows:

On the graph the third sign counting from the left is used.

This is placed on the first mark of the three marks between 3 and 4. This point equivalent to 3 1/4 or 3.25

Given data

the graph

and the equation  1/2 x - 3 < -1 3/8

solving for x gives

1/2 x - 3 < -1 3/8

1/2 x < 3 -11/8

x/2 < 13/8

x < 13 / 4

x < 3 1/4

On the graph the third sign counting from the left is used.

The arrow is facing left, this is to show the sign less than.

The tail has a hollow not a solid point to show that equality sign is not included.

This is placed on the first mark after point 3 as this is the point equivalent to 3 1/4 or 3.25

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The equivalent income in City A given the average annual cost of living in City A and city B is $163,658.

The first step is to determine the ratio of the average cost of living in State A and State B. Ratio is used to show the relationship that exists between two or more values.

Cost of Living in City B / Cost of Living in City A

$62,000 / $44,400 = 1.39640

Multiply the ratio gotten in the previous step by the offered salary in State B : 1.39640 x $117,200 = $163,658

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Answer:B

Step-by-step explanation:because she might buy more cookies but we dont know she we dont multiply it by anything but the cookies we multiply that by 3 so thats why it doesn't have p because we know how much she's getting the reason its not a is because it says greater or equal to we dont want to go over 30 we want to be equal or less than 30

hope this helps :}

Answer: 5

Step-by-step explanation:

Answer: 1st is positive 2nd is negative 3rd and 4th are undefined or 0

Step-by-step explanation:

Answer:

1.positive

2.undefine

3.positive

4.negative

Answer- D = (equal sign)

Explanation-

When you see two straight lines in math | | with number inside, regardless if the number inside is positive or negative, the outcome will be positive. This is called the absolute value. After we solve our absolute value however, there is a negative on the outside, which means that 61 will become negative again. Our equation is now -61 _____ -61. Your correct choice will be the equal sign, since -61 is equal to -61.

HOPE THIS HELPS GOOD LUCK!

The vehicle will get speed of approximately 15 mph and -210 mph.

Science's most important concept is measurement. Many measurable quantities are measured in fundamental or base units. One such measurable quantity is speed, which is defined as the ratio of an object's distance travelled to the time required to travel that distance. Let us learn about speed in depth during this session.

The ratio of distance to time taken to cover a distance is used to calculate speed. Because it only has one direction and no magnitude, speed is a scalar quantity.

Given the equation for gas mileage = 0.02x² + 3.9x  - 43 where x means speed

We have been asked to find x if gas mileage = 20 that is

0.02x² + 3.9x  - 43 = 20

Lets simplify

⇒ 0.02x² + 3.9x  - 43 = 20

⇒ x² /50 + 39x/10  - 63 = 0

⇒ x²/ 50 + 195x/50 - 3150 = 0

⇒ 1/50 (x + 195x - 3150 ) = 0

⇒ 1/50 (x + 210x - 15 x - 3150 ) = 0

⇒ 1/50 (x (x+210) −15 (x+210)) = 0

⇒ 1/50 (x−15)(x+210) = 0

⇒  (x−15)(x+210)  = 0 × 50

⇒ (x − 15)(x + 210)  = 0

⇒ x = 15, x = -210

So, try using 15 mph and -210 mph, that might work.

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Answer: 207936 millimeters squared

Step-by-step explanation:

57 * 57 = 3249

3249 * 64 = 207936

Answer: 207936 millimeters^2

Step-by-step explanation: 57*57=3249

3249 64 times is 207936.

Answer: 15

Explanation:

The length of the segment is 10 plus 5 which is fifteen because you need to know how long it is. Just ignore the negatives.