A 117.3 cm²
B 104.8 cm²
C 97.3 cm²
D 71.1 cm²

[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{14}~,~\stackrel{y_1}{21})\qquad (\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ x +14}{2}~~~ ,~~~ \cfrac{ y +21}{2} \right) ~~ = ~~\stackrel{midpoint}{(41~~,~~50)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ x +14}{2}=41\implies x+14=82\implies \boxed{x=68} \\\\\\ \cfrac{ y +21}{2}=50\implies y+21=100\implies \boxed{y=79}[/tex]

The simplification of the given expression using laws of Indices is :

[tex]\frac{y^{14}}{z^{14}}[/tex]

How to use Laws of Indices?

We want to simplify the expression y raised to the negative second power times z raised to the third power end quantity over quantity z raised to the negative fourth power times y raised to the fifth power end quantity all raised to the negative second power.

The above can be expressed as :

[(y⁻² * z³)/(z⁻⁴ * y⁵)]^(-2)

Collecting like terms and When two terms that are divided have the same base and different exponents, we keep the base and subtract the exponents, hence :

= [(y⁻² * z³)/(z⁻⁴ * y⁵)]²

= [(z⁻⁴ * y⁵)/(y⁻² * z³)]²

= [(z⁻⁴/z³) x (y⁵/y⁻²)]²

= [z^{-4-3} x y^{5+2}]²

= [z^{-7} x y^{7}]²

Then both numerator and denominator exponents multiply by 2, hence the equivalent expression is :

= [tex][\frac{y^{7}}{z^{7}}]^{2} = \frac{y^{14}}{z^{14}}[/tex]

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An object that appears to be 4 inches on a scale illustration actually measures 32 feet.

A representation of a real thing with correct sizes that has been scaled back or blown up slightly (called the scale).

The scale is represented by the length in the drawing, a colon (":"), and then the actual length that corresponds to it.

A measurement of 150 mm on the picture would be 1500 mm on the actual horse since this drawing has a scale of "1:10," meaning that everything represented with a size of "1" would have an the actual world, a size of "1" corresponds to a size of "10."

based on the facts provided;

4 in =1/4 in 2ft

= 16*2 ft

= 32 ft

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The elephant can move 53.2 meters if it is charged for 1 minute.

Given,

The time that the elephant charged = 15 seconds

The distance that the elephant can travel by this charge = 13.3 meters

We have to find the distance moved by the elephant if it is charged for 1 minute:

That is,

15 seconds = 13.3 meters

Then,

1 minute (60 seconds) = x

Therefore;

15 × x = 13.3 × 60

x = (13.3 x 60) / 15

x = 798 / 15

x = 53.2

That is, the elephant can move 53.2 meters if it is charged for 1 minute.

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The value of f (1) is 5.

The value of f (-7) is - 35.

The value of f (y + 2) is (-y²- 5y + 1).

What is Function?

A relation between a set of inputs having one output each is called Function.

The function is given as;

⇒ f(x) = -x² - x + 7

Now, To find value of f (1), substitute the value of x = 1 in given function and then calculate as;

⇒ f(x) = -x² - x + 7

⇒ f (1) = - (1)² - 1 + 7

⇒ f (1) = - 1 - 1 + 7

⇒ f (1) = 5

Hence, The value of f (1) is 5.

To find value of f (-7), substitute the value of x = -7 in given function and then calculate as;

⇒ f(x) = -x² - x + 7

⇒ f(-7) = -(-7)² - (-7) + 7

⇒ f(-7) = -49 + 7 + 7

⇒ f(-7) = - 35

Hence, The value of f (-7) is - 35.

To find value of f (y + 2), substitute the value of x = y+2 in given function and then calculate as;

⇒ f(x) = -x² - x + 7

⇒ f(y + 2) = -(y + 2)² - (y + 2) + 7

⇒ f(y + 2) = - (y² + 4y + 4) - y - 2 + 7

⇒ f(y + 2) = - y² - 4y - 4 - y - 2 + 7

⇒ f(y + 2) = -  y² - 5y + 1

Hence, The value of f (y + 2) is (-y²- 5y + 1).

So, The value of f (1) is 5.

The value of f (-7) is - 35.

The value of f (y + 2) is (-y²- 5y + 1).

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Answer:

i’m pretty sure it’s 6,039

Step-by-step explanation:

12,078 divided by 2

The equation of this straight line is y = 50x + 100.

A linear function can be defined as a type of function whose equation is graphically represented by a straight line on the cartesian coordinate.

In order to determine the equation from this graph of a linear equation, we would find the slope of the straight line by using this formula as follows:

[tex]Slope,\;m = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope,\;m = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]

Slope, m = 100/2

Slope, m = 50.

Mathematically, the standard form of the equation of a straight line is given by;

y = mx + c

Where:

At point (4, 300), we have:

y = mx + c

300 = 50(4) + c

300 = 200 + c

c = 300 - 200

c = 100.

Therefore, the equation of this straight line is y = 50x + 100.

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for the equation - 7 + 4 u = - 35, we get the value of u after solving it as - 7.

We are given the equation:

- 7 + 4 u = - 35

We need to solve the equation for u.

- 7 + 4 u = - 35

Add 7 to both the sides, we get that:

- 7 + 4 u + 7 = - 35 + 7
4 u = - 28

Divide both the sides by 4, we get that:

4 u / 4 = - 28 / 4

u = - 7

Therefore, for the equation - 7 + 4 u = - 35, we get the value of u after solving it as - 7.

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Answer: 6.30

Step-by-step explanation:

Since no line segment or reference diagram is provided in the question statement, considering ourselves a line as shown in the picture attached hereby, another name of the line "l" is UM.

As per the question statement, we are required to determine another name of the line, but no no line segment or reference diagram is provided, on whose basis, we were supposed to answer. Hence, we consider a line ourselves, as shown in the picture attached hereby, and then try to answer as per the question statement,

From the picture attached hereby, we can clearly see that, although the line "l" is a ray, it has two points "U" and "M" at the extremes, i.e., points U and M lie on the line. Hence, line "l" can be referred to as "UM" also.

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Answer:

1651

Step-by-step explanation:

Add up the numbers, and you get your answer. [tex]1585+16.25+49.75=1651[/tex]

Answer:

No solution.

Step-by-step explanation:

There is not an number that I can put in for x and y and get the answer 4 and -4.

Answer:

No solutions

Step-by-step explanation:

Given system of equations:

[tex]9x - y = 4 \\ 9x - y = -4[/tex]

Let us substitute the equation 9x - y = 4 into the second equation:

[tex]\implies 9x - y = -4[/tex]

[tex]\implies 4 = -4 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [9x - y} = 4} ][/tex]

But 4 = -4 is not possible, as they are opposite integers. Since 4 ≠ -4, there are no solutions for the given system of equations.

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The sun is [(1.974) * (10^1)] times farther from Neptune, than Mercury, mentioned in scientific notation.

As per the question statement, there is no information provided about the actual distance of the sun from Neptune, or from Mercury. Hence, let us consider that the actual distance of the sun from Neptune is [4.5 * (10^9)] kilometers, while that from Mercury is [2.28 * (10^8)] kilometers.

We are required to calculate the number of times, which the sun is times farther from Neptune, than Mercury, and express our desired answer in proper scientific notation.

Considering that, the sun is "x" times farther from Neptune, than Mercury, we can state that,

[{2.28 * (10^8)} * x] = {4.5 * (10^9)}

or, x = [{4.5 * (10^9)}/{2.28 * (10^8)}]

or, x = [{4.5 * 10 * (10^8)}/{2.28 * (10^8)}]

or, x = [{45 * (10^8)}/{2.28 * (10^8)}]

or, x = (45/2.28)

or, x = 19.7368

or, x = 19.74

or, x = [(1.974) * (10^1)]

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t = 5.48 in ln (t - 1)² = 3, by properties of logarithm.

Now,

In ln ( t -1 )² = 3, by property of logarithm ( [tex]log_b(a)^m=m(log_b(a))[/tex]),

=> 2 ( ln (t -1) ) = 3

=> ln (t - 1) = [tex]\frac{3}{2}[/tex]

=> t - 1 = [tex]e^\frac{3}{2}[/tex]

=> t = [tex]e^\frac{3}{2}[/tex] + 1 = 4.48 + 1 = 5.48

Hence, t = 5.48 in ln (t - 1)² = 3, by properties of logarithm.

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Step-by-step explanation:

the range of a function is the interval or set of all valid y (function result) values.

so, what values is this function creating ?

we see that y never gets larger than -4.

but it will clearly go and go and go ... further down without any limit.

so, the range is

-infinity < y <= -4

The sweets in jar B in the box with Amir will be 190 sweats.

From the information, Jar A contains 205 sweets. Jar c contains 175 sweet. Also, jar a has the most sweets and Jar c has the least of sweets.

The deets in jar B will be:

= (205 + 175) / 2

= 380 / 2

= 190

Therefore, the sweets in jar B in the box with Amir will be 190 sweats.

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The logarithmic expression changed by the base formula is ㏒₁₀9/㏒₁₀4.

A number's logarithm is the exponent that a fixed value known as the base should be raised in order to generate that number. For example, because 1000 is 10 to a third power, the log of 1000 to base 10 is 3.

Some rule of the logarithmic functions are-

Now, as per the sated condition of the log function;

= log₄9

Now, use the Base Rule to re-write the expression;

= ㏒ₓ9/㏒ₓ4

or, for the base 10 this could be written as;

= ㏒₁₀9/㏒₁₀4

Therefore, the given logarithmic expression converted by the base formula is ㏒₁₀9/㏒₁₀4.

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In [tex]e^{2x}=12[/tex], x = 1.24, by the properties of logarithm.

Now,

In  [tex]e^{2x}=12[/tex], taking natural logarithm on both side.

=>  [tex]log_e(e^{2x})=log_e(12)[/tex]

=> 2x = 2.48 (approx)

=> x = 1.24

Hence, In [tex]e^{2x}=12[/tex], x = 1.24, by the properties of logarithm.

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4 9/10

explanation:

1: Simplify both sides of the equation.

x+−2/5=9/2

2: Add 2/5 to both sides.

x+−2/5+2/5=9/2+2/5

x=4 9/10

On reflecting f(x) = 9x in the x-axis and vertical compression by a factor of 1/3 we get the transformation g(x) where, g(x) = -3x

Transformation of the function means that the curve representing the graph either moves to the left or right or up or down or expansion , compression or reflection of graph happens.

Rules for reflection over x axis  :  for an curve y = f(x) , replace y by -y and keep x as it is, we get -y = f(x) or y = - f(x)

Rules for vertical compression by a factor α : y becomes αy .If f(x) is compressed by a factor of 1/2 the the transformations becomes 1/2(f(x))

Given function is f(x) = 9x

When we reflect f(x) over x axis then the transformations becomes some h(x) where h(x) = -f(x) =-9x

Now we want to vertically compress it by a factor of 1/3 , then this transformation will become g(x) = 1/3(h(x)) = 1/3(-9x) =(-9/3)x =-3x

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Answer:

C - 1/81

Step-by-step explanation

There are 6 sides on a standard die (1, 2, 3, 4, 5, 6). Out of these numbers, only 3 and 6 are divisible by 3. Therefore, 2/6 numbers would be divisible by 3. As the die is rolled 4 times, we multiply 2/6 4 times - (2/6)(2/6)(2/6)(2/6) to get 1/81. The probability that the die shows a number divisible by three all four times is 1/81. Hope that helps!

The distance between base of tree and swing set is 24 feet.

We are given the angle of depression and the vertical height. Joining the three points, which are top and base of tree and swing set forms a right angled triangle. The height of tree will be perpendicular of triangle and base will be the distance between base of tree and swing set.

The angle at the swing set will be equal to 30.26°, as alternate angles are equal.

So, the angle formed can be related with perpendicular and base by -

tan theta = perpendicular ÷ base

Keep the values in formula to find the value of base

Base = perpendicular ÷ tan theta

Base = 14 ÷ tan 30.26°

Base = 14 ÷ 0.5834

Performing division

Base = 24

Hence, the distance between  base of tree and swing set is 24 feet.

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Answer to this question is:

Domain of given function is (-∞,0),{x|x<0}

Range of given function is (0,∞),{y|y>0}

Inverse of given function is -1/2x²

The domain is all values of x that make the expression defined.The entire range of independent variable values is the domain of a function.

This definition can be stated simply as follows: The domain is the collection of all x-values that can be used to make the function "work" and produce actual y-values.

When choosing the domain, keep in mind that a fraction's denominator (bottom) cannot be 0.

Interval Notation:(-∞,0)

Set-Builder Notation:{x|x<0}

The set of all valid y values constitutes the range.

Interval Notation:(0,∞)

Set-Builder Notation:{y|y>0}

For calculation of inverse:

∴Domain of given function is (-∞,0),{x|x<0}

Range of given function is (0,∞),{y|y>0}

Inverse of given function is -1/2x²

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Answer: C.

Step-by-step explanation:

The length of the segment when J is between H and K will be HJ = 21 and JK = 12.

From the information given, J is between H and K and we want to use the segment addition Postulate to solve for x.

It should be noted that:

HJ=4x+9,

Jk=3x+3,

HK=33

Therefore, we will equate the values. This will be:

4x + 9 + 3x + 3 = 33

7x + 12 = 33

Collect like terms

7x = 33 - 12

7x = 21

Divide

x = 21 / 7

x = 3

HJ=4x+9, = 4(3) + 9 = 21

Jk=3x+3 = 3(3) + 3 = 12

Therefore, the length of the segment when J is between H and K will be HJ = 21 and JK = 12.

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The questions tests on indices. Write 27 in form of its prime factors. Apply the power rule (a^m)^(1/n)=a^(m/n). In prime factor form 27 = 3×3×3

27 = 3^3

(27^3)^(1/3) = 3^(3×1/3) = 3

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Answer: 6912

Step-by-step explanation:

96x12=1,152

1,152x6=6912

x = 78

The equation given is

   3[tex](x + 3)^{3/4}[/tex]= 81

first we will divide 3 of the right side to left side number which is 81

i.e 81/3 = 27

So we get the equation

[tex](x + 3)^{3/4}[/tex] =27

We can also write the equation as

[tex](x + 3)^{3/4}[/tex]= [tex]3^{3}[/tex]

[tex][(x + 3)^{1/4]^{3}[/tex]= [tex]3^{3}[/tex]

So from, this we get

[tex](x + 3)^{1/4}[/tex] = 3

Now we have to side with the multiply both power of four(4)

[tex][ (x + 3)^{1/4}]^{4}[/tex]= [tex]3^{4}[/tex]

we get

x + 3 = 81

x = 78

So the value of x is 78.

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Answer: 6

Step-by-step explanation: