The hypotenuse of a right angle triangle measures 12 units. what is the maximum possible area in square units, of the triangle ?

Answer: 1  5/12

Step-by-step explanation: You need to find a common denominator 3 and 4 are the denominators you can do 3 times 4 is 12 and 4 times 3 is 12, but whatever you do to the denominator needs to be done to the numerator so 2 times 4 is 8 and 1 times 4 is 4 then you have the fractions 8/12 and 3/12 then you just subtract and you get 1  5/12.

*Hard to explain*

[tex]\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{-3}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{11}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{5-3}{2}~~,~~\cfrac{11+5}{2} \right)\implies \left(\cfrac{2}{2}~,~ \cfrac{16}{2}\right)\implies \stackrel{center}{(1,8)} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ \stackrel{endpoint}{(\stackrel{x_1}{-3}~,~\stackrel{y_1}{5})}\qquad \stackrel{center}{(\stackrel{x_2}{1}~,~\stackrel{y_2}{8})}\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ \stackrel{radius}{r}=\sqrt{[1-(-3)]^2+[8-5]^2}\implies r=\sqrt{(1+3)^2+(8-5)^2} \\\\\\ r=\sqrt{16+9}\implies r=\sqrt{25}\implies r=5[/tex]

Do the midpoint formula. Which will give you (1,8)

Answer:

A. How can the equation be used in temperature conversion?

You take the conversion equation C = (5/9) (F - 32) and you replace the F by the value of Fahrenheit degrees...  then solve the calculations to get the degrees in Celsius.

For example, if you have 80°F to convert in °C:

C = (5/9) (80 - 32) = (5/9) (48) = 26.66 °C

B. How can you use the graph to find the body temp in C?

Using the graph will give a very imprecise measure due the scale of the graph.

But you would have to find 98.6 on the axis of X (it represents the °F), then go upwards until you find the line....

Then report that position on the line on the Y-axis (representing the °C) to get your measure.

Answer:

For A: The linear equation is [tex]C=\frac{5}{9}F-\frac{32}{9}[/tex]

For B: The temperature of normal body in degree Celsius is 37° C.

Explanation:

Linear equations are defined as the equations in which the highest power of a variable is '1'. The general equation for a linear equation is:

[tex]y=mx+c[/tex]

where,

y = Y-coordinate

m = slope of the line

x = X - coordinate

c = intercept on y-axis

For the given equation:

[tex]C=\frac{5}{9}(F-32)[/tex]

The linear equation representation for the given equation is:

[tex]C=\frac{5}{9}F-\frac{32}{9}[/tex]

We are given a value of temperature in degree Fahrenheit. To calculate its value in degree Celsius, we use the equation above.

Putting value of F = 98.6 in above equation, we get:

[tex]C=(\frac{5}{9}\times 98.6)-\frac{32}{9}\\\\C=37[/tex]

Hence, the temperature of normal body in degree Celsius is 37° C.

The function rule for the situation is none of the given options

From the question, we have the following parameters that can be used in our computation:

Membership = $20

Payment each time = $300 per visit

using the above as a guide, we have the following:

f(x) = Membership + Payment each time * x

substitute the known values in the above equation, so, we have the following representation

f(x) = 20 + 300* x

Evaluate

f(x) = 20 + 300x

Hence, the expression is f(x) = 20 + 300x

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none of the given options

None of the provided options in the question are correct.

The function rule that correctly represents Rex's situation, given that he paid a $20 membership fee and pays $300 each time he goes to the pool, would be a linear equation that includes a one-time fee (membership) and a per-visit cost. Let's define x as the number of times Rex goes to the pool and y as the total cost. Therefore, the equation should include the initial membership fee and the per-visit cost multiplied by the number of visits.

The correct function rule is y = 20 + 300x, where 20 represents the one-time membership fee and 300 represents the cost per pool visit. None of the provided options are correct. The equation signifies that for every visit to the pool, the total cost increases by $300, and the initial membership cost is $20.

Answer:

[tex]6z^{4}[/tex]

Step-by-step explanation:

Given in the question an expression,

[tex]\frac{ (2z^5)(12z^3)}{4z^4}[/tex]

Step 1

Apply exponential "product rule"

[tex]x^{m}x^{n}=x^{m+n}[/tex]

[tex]\frac{ 12(2)z^5)(z^3)}{4z^4}[/tex]

[tex]\frac{ (24)z^5)(z^3)}{4z^4}[/tex]

[tex]\frac{ 24(z^{(5+3)})}{4z^4}[/tex]

[tex]\frac{ 24(z^{8})}{4z^4}[/tex]

Step 2

Apply exponential " divide rule"

[tex]\frac{x^{m}}{x^{n}}=x^{m-n}[/tex]

[tex]\frac{24/4(z^{8})}{z^4}[/tex]

[tex]\frac{6(z^{8})}{z^4}[/tex]

[tex]\frac{6(z^{8-4})}{1}[/tex]

[tex]6z^{4}[/tex]

QUESTION 11

Given : [tex]\ln(3x-8)=\ln(x+6)[/tex]

We take antilogarithm of both sides to get:

[tex]3x-8=x+6[/tex]

Group similar terms to get:

[tex]3x-x=6+8[/tex]

Simplify both sides to get:

[tex]2x=14[/tex]

Divide both sides by 2 to obtain:

[tex]x=7[/tex]

12.  Given; [tex]\log_3(9x-2)=\log_3(4x+3)[/tex]

We take antilogarithm to obtain:

[tex](9x-2)=(4x+3)[/tex]

Group similar terms to get:

[tex]9x-4x=3+2[/tex]

[tex]5x=5[/tex]

We divide both sides by 5 to get:

[tex]x=1[/tex]

13.  [tex]\log(4x+1)=\log25[/tex]

We take antilogarithm to get:

[tex](4x+1)=25[/tex]

Group similar terms

[tex]4x=25-1[/tex]

[tex]4x=24[/tex]

Divide both sides by 4

[tex]x=6[/tex]

14. Given ; [tex]\log_6(5x+4)=2[/tex]

We take antilogarithm to get:

[tex](5x+4)=6^2[/tex]

Simplify:

[tex](5x+4)=36[/tex]

[tex]5x=36-4[/tex]

[tex]5x=32[/tex]

Divide both sides by 5

[tex]x=\frac{32}{5}[/tex]

Or

[tex]x=6\frac{2}{5}[/tex]

15. Given: [tex]\log(10x-7)=3[/tex]

We rewrite in the exponential form to get:

[tex](10x-7)=10^3[/tex]

[tex](10x-7)=1000[/tex]

[tex]10x=1000+7[/tex]

[tex]10x=1007[/tex]

Divide both sides by 10

[tex]x=\frac{1007}{10}[/tex]

16. Given:   [tex]\log_3(4x+2)=\log_3(6x)[/tex]

We take antilogarithm to obtain:

[tex](4x+2)=(6x)[/tex]

[tex]2=6x-4x[/tex]

Simplify

[tex]2=2x[/tex]

Divide both sides by 2

[tex]1=x[/tex]

17. Given [tex]\log_2(3x+12)=4[/tex].

We rewrite in exponential form:

[tex](3x+12)=2^4[/tex]

[tex](3x+12)=16[/tex]

[tex]3x=16-12[/tex]

[tex]3x=4[/tex]

Divide both sides by 3

[tex]x=\frac{4}{3}[/tex]

18. Given [tex]\log_3(3x+7)=\log_3(10x)[/tex]

We take antilogarithm to get:

[tex](3x+7)=(10x)[/tex]

Group similar terms:

[tex]7=10x-3x[/tex]

[tex]7=7x[/tex]

We divide both sides by 7

[tex]x=1[/tex]

19.  Given: [tex]\log_2x+\log_2(x-3)=2[/tex]

Apply the product rule to simplify the left hand side

[tex]\log_2x(x-3)=2[/tex]

We take antilogarithm to obtain:

[tex]x(x-3)=2^2[/tex]

[tex]x^2-3x=4[/tex]

[tex]x^2-3x-4=0[/tex]

[tex](x-4)(x+1)=0[/tex]

x=-1 or x=4

But x>0, therefore x=4

20. Given  [tex]\ln x+ \ln (x+4)=3[/tex]

Apply product rule to the LHS

[tex]\ln x(x+4)=3[/tex]

Rewrite in the exponential form to get:

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

[tex]x^2+4x=e^3[/tex]

[tex]x^2+4x-e^3=0[/tex]

This implies that:

[tex]x=-6.91[/tex] or [tex]x=2.91[/tex]

Check the picture below.

Answer:

[tex]\large\boxed{A.\ 2^0}[/tex]

Step-by-step explanation:

[tex]\text{Use}\ \dfrac{a^n}{a^m}=a^{n-m}:\\\\\dfrac{2^6}{2^6}=2^{6-6}=2^0=1[/tex]

Add the ratio to get total shares: 4 +1 = 5

Divide the total amount to share by the total shares:

150 / 5 = 30

Now multiply each set of shares by that:

4 x 30 = 120

1 x 30 = 30

120-30 = 90 more

A two-dimensional shape with less than four sides and all straight sides is a triangle. Triangles are basic geometric shapes with three edges and three vertices.

If you are a two-dimensional shape with less than four sides and all your sides are straight, the shape you are describing is a triangle. A triangle is a simple polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with all three sides of equal length is an equilateral triangle, if only two sides are equal it's called an isosceles triangle, and if all sides are of different lengths, it is called a scalene triangle.

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the answer is z=7 (as 3z-4=17)

Answer:

A. 5

Step-by-step explanation:

Answer:

The Great Barrier Reef is located in Australia.

The Great Barrier Reef is located off the northeastern coast of Australia.

It stretches for approximately 1,600 miles and is home to a diverse range of sea creatures and fish, attracting millions of tourists, scuba divers, and water enthusiasts each year.

This natural wonder is a significant tourist attraction and plays an important role in the Australian economy.

Additionally, the Great Barrier Reef has been designated as a United Nations World Heritage Site due to its ecological importance.

Given.

Radius of the Half sphere is 3 inches.

From the figure;

Radius of half sphere= Radius of cylinder= Radius of cone=3inches

Height of cone= 4inches.

Height of cylinder=6inches.

Volume of cone=(πr²h)/3

=(π3²×4)/3

=(12π) inch³

volume of cylinder= πr²h=π3²6=54π inch³

Volume of half sphere= (4/3) π r³=π(4×3³)/3 (1/2)=π×4×9/2=18π inch³

Total area of Composite figure=(12π +54π +18π) inch³

=84π inch³

=(84)× 22/7inch³

=12×22 inch³

=264inch³

Hope it helps...

Regards;

Leukonov/Olegion.

Answer:

The volume of the composite figure is 84π ≅ 263.89 inches³

Step-by-step explanation:

Lets revise the rules of the volume of some figures

- The composite figure consists of :

# Half sphere with radius 3 inches

# Cylinder with radius 3 inches and height 6 inches

# Cone with radius 3 inches and height 4 inches

- The volume of the sphere is 4/3 π r³

∴ The volume of the half sphere = 1/2 × 4/3 π r³ = 2/3 π r³

- The volume of the cylinder is π r² h

- The volume of the cone is 1/3 π r² h

* Now lets solve the problem

- The volume of the half sphere

∵ The radius of the half sphere = 3 inches

∵ The volume of it = 2/3 π r³

∴ The volume = 2/3 × π × (3)³ = 18π inches³

- The volume of the cylinder

∵ The radius of the cylinder = 3 inches

∵ The height of the cylinder = 6 inches

∵ The volume of it = π r² h

∴ Its volume = π × (3)² × 6 = 54π inches³

- The volume of the cone

∵ The radius of the cone = 3 inches

∵ The height of the cone = 4 inches

∵ The volume of it = 1/3 π r² h

∴ Its volume = 1/3 π × (3)² × 4 = 12π inches³

- Add all the volumes to find the volume of the composite figure

∴ The volume = 18π + 54π + 12π = 84π = 263.89 inches³

* The volume of the composite figure is 84π ≅ 263.89 inches³

Answer:

[tex]g(3x-2) = (3x-2)^{2}[/tex]

Step-by-step explanation:

[tex]g(x)=x^{2}[/tex]

To do this, you must substitute [tex]3x-2[/tex] for x in the equation g(x)

[tex]g(3x-2) = (3x-2)^{2}[/tex]

Simplified this would be

[tex]9x^{2} -12x+4[/tex]

Answer

a. [tex]\frac{1}{m}(6)+\frac{1}{12} (6)+\frac{1}{15} (6) =1[/tex]

b. 60hrs

Step-by-step explanation:

Let the time Molli will take to pint the room to be = t

Thus the amount of room that Molli can paint in 1 hour= 1/m

The amount of room John can paint is 1 hour= 1/12

The amount of room Rick can paint in 1 hour = 1/15

The equation for working together at a rate x time per work done will be;

[tex]\frac{1}{m} *6+\frac{1}{12} *6+\frac{1}{15} *6=1[/tex]

You multiply by 6 in the three terms of the equation because it takes 6 hours for John, Rick and Molli to complete painting.

[tex]\frac{6}{m} +\frac{1}{2} +\frac{2}{5} =1[/tex]

multiply by 10m in every part of the expression because 10m is the Least Common Multiple(LCM) is this case

Collect like terms and find value of m

[tex]60+5m+4m=10m\\\\60+9m=10m\\\\60=10m-9m\\\\60=m[/tex]

Molli will take 60 hours to paint the room if working alone

For this case we must solve the following equation:

[tex]-17+ \frac {n} {5} = 33[/tex]

Adding 17 to both sides of the equation we have:

[tex]\frac {n} {5} = 33 + 17\\\frac {n} {5} = 50[/tex]

Multiplying by 5 on both sides of the equation:

[tex]n = 50 * 5\\n = 250[/tex]

Thus, the value of n is 250

ANswer:

[tex]n = 250[/tex]

The solution to the equation -17 + n/5 = 33 is n = 250.

We have,

To solve the equation, we can start by isolating the variable term.

Here's the step-by-step solution:

-17 + n/5 = 33

First, let's get rid of the constant term (-17) by adding 17 to both sides of the equation:

-17 + 17 + n/5 = 33 + 17

Simplifying, we have:

n/5 = 50

To isolate n, we can multiply both sides of the equation by 5:

5 * (n/5) = 5 * 50

This simplifies to:

n = 250

Therefore,

The solution to the equation -17 + n/5 = 33 is n = 250.

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Answer:

x-8>-3 {x|R, x>5 is right answer

For this case we must find the solutions of the following inequality:

[tex]x-8> -3[/tex]

Adding 8 to both sides of the inequality we have:

[tex]x> -3 + 8\\x> 5[/tex]

Thus, the solutions of the variable "x" are given by all the real numbers greater than 5.

Answer:

Option C

It’s the fourth one

Answer:

None of these

Step-by-step explanation:

This is because the answer can't have anything to do with perpendicular because you don't know if any of the angles are 90 degrees (and honestly none of them look right anyways... pun intended) and the only answer that isn't perpendicular is wrong because the lines are intersececting.

Answer: answer is d

Step-by-step explanation: input in calculator or set both equal to y and then set them equal to each other

Answer:

32x + 48y - 16z

Step-by-step explanation:

The given data set is:

37, 4, 53, 79, 25, 48, 78, 65, 5, 6, 42, 61

We arrange the data set in ascending order of magnitude {4,5,6,25,37,42,48,53,61,65,78,79}

The median is 45.

The lower half of the data set is

{4,5,6,25,37,42}

The first quartile is the median of the lower half set;

[tex]Q_1=15.5[/tex]

The upper half of the data set is:

{48,53,61,65,78,79}

The median of the upper half is [tex]Q_3=63[/tex].

The inter-quartile range  [tex]Q_3-Q_1=63-15.5=47.5[/tex]

8. The given data set is 112, 149, 112, 148, 139, 121, 116, 134, 148.

The mean of the data set is [tex]\bar X =\frac{\sum x}{n}[/tex]

[tex]\bar X =\frac{112+149+112+148+139+121+116+134+148}{9}[/tex]

[tex]\bar X =\frac{179}{9}=131[/tex]

The standard deviation is given by:

[tex]s=\sqrt{\frac{\sum (x-\bar X)^2}{n} }[/tex]

[tex]s=\sqrt{\frac{(-19)^2+(18)^2+(-19)^2+(17)^2+(8)^2+(-10)^2+(-15)^2+(3)^2+(18)^2}{9} }[/tex]

[tex]s={\frac{\sqrt{2022}}{3}=14.98888477[/tex]

The standard deviation is 15.0 to the nearest tenth.

Answer:

3300

Step-by-step explanation:

100 * 33

Answer:

81

Step-by-step explanation:

Assuming the pigeons are either male or female, the 45% of them that are not female are male. Of those, there are 40% that are not white, so 60% are white. Then the number of white male pigeons is ...

60% of 45% of 300 = 0.60 · 0.45 · 300 = 81

For this case we have that the area of a circle is given by:

[tex]A = \pi * r ^ 2[/tex]

Where:

r: It is the radius of the circle

By clearing the radio we have:

[tex]r = \pm \sqrt {\frac {A} {\pi}}[/tex]

We take the positive value:

[tex]r = \sqrt {\frac {A} {\pi}}\\r = \sqrt {\frac {95.03} {\pi}}\\r = 5.50 \ ft[/tex]

The diameter is twice the radius:

[tex]d = 11[/tex]

Answer:

[tex]11 \ ft[/tex]

Answer:

11 feet

Step-by-step explanation:

We are given the area of a circle and we are to find the diameter of this circle.

We know that the area of a circle is given by [tex]\pi r^2[/tex] so equating its given value to get:

[tex]\pi \times r^2 = 95.03[/tex]

[tex] r ^ 2 = \frac {95.03} {\pi } [/tex] [tex] r = \sqrt {30.25} [/tex]

[tex] r = 5 . 5 [/tex]

Therefore, our required diameter will be [tex]5.5 \times 2[/tex] = 11 feet

Answer:

$142500

Step-by-step explanation:

We are given that the resident of a certain University receives a salary that is three times the salary of one of the department heads.

If the sum of the two salaries is $190000, we are to find the salary of the president of the University.

Let [tex]x[/tex] to be the department head's salary, we can write an equation:

[tex]3x+x=190000[/tex]

[tex]4x=190000[/tex]

[tex]x=47500[/tex]

Salary of the president of the University = [tex]3(47500)[/tex] = $142500

Answer:

$142,500

Step-by-step explanation:

Let's say x is the salary of the department head.... so the salary of the president of the university can be described as 3x.

Then, we know the total of the two salaries is 190,000.  We can express this as:

3x + x = 190,000

4x = 190,000

x = 47,500

x is for the department head.  To get the president's salary, we have to multiply that by 3:

p = 3 (47,500) = 142,500

The salary of the president is then of $142,500.

First make a table of values of the function’s coordinates, and try to avoid coordinates that include decimals.

Second, find the first differences from the table you constructed. ( it should be 1)

There should be a 2 point gap in the x column if you chose the points (2,-4)(4,-3)(6,-2) (8,-2) and that is your denominator

Last, the y intercept (-5) is your b variable (y=mx +b)

The equation is

Y= x/2 -5

Sorry about my English

Assuming that the probability of a car being colored blue is not equal to 0 or 1, then the most logical answer would be the smallest probability.

P= 0.001

Answer:

0.001

Step-by-step explanation:

gradpoint

I believe I am correct.

Multiply the side values together to get the volume of the prism.

1 x 2 2/3x 2/3 = 1.7(repeating)

Then divide 1.7(repeating) by 1/3 and you end up with 5 1/3.

Hope this helps!

Check the picture below.

so the net once folded up, will look more or less like the box there on the bottom-right.

Length = 2, Width = 10, Height = 6.

volume is then 2*10*6 = 120.

Answer:10,126,272 units

Step-by-step explanation:

184*184*184=6,229,504

120*120*120=1,728,000

124*124*124=1,906,624

64*64*64=262,144

6,229,504+1,728,000+1,906,624+262,144=10,126,272

Answer:

9

Step-by-step explanation:

2-2+5+5+5+5+5+5-6

the answer is 9. ——-