Marc is 46 years old. He is 4 years older than 3 times his sons age, find the age of his son.

Answer:

32 posts

Step-by-step explanation:

In terms of fence-post spaces, the corral is 10 by 6, so its perimeter is ...

P = 2(10 +6) = 32 . . . . . fence post spaces.

Patrick intends to paint 32 fence posts.

Final answer:

Patrick needs to paint a total of 32 fence posts around the rectangular corral. This total counts the posts for both pairs of sides after considering that the four corner posts have been counted twice.

Explanation:

The question involves calculating the total number of fence posts needed to surround a rectangular corral. Since the corral is 50 ft by 30 ft, and fence posts are spaced 5 feet apart, we must calculate how many posts are needed on each side of the rectangle and then add them together.

To begin with, for each of the longer sides (50 ft), we would need 50 ft ÷ 5 ft/post = 10 posts per side. However, we need to add one more post to close the rectangle, so we have 10 + 1 = 11 posts on each of the longer sides. For the shorter sides (30 ft), it would be 30 ft ÷ 5 ft/post = 6 posts per side, plus the extra post to close the rectangle, resulting in 6 + 1 = 7 posts on each of the shorter sides.

To get the total number of posts, we add up the posts on all sides: (11 posts × 2) + (7 posts × 2) = 22 + 14 = 36 posts. However, we must consider that we have counted the corner posts twice, once for each side they join. Since there are four corners, we subtract four posts from our total, resulting in 36 - 4 = 32 posts that Patrick needs to paint.

Answer:

  [tex]\log_{9}{\dfrac{13}{x}}=\log_{9}{\boxed{13}}-\log_{9}{x}[/tex]

Step-by-step explanation:

The rule is ...

  log(a/b) = log(a) -log(b) . . . . all logs to the same base

Then for a/b = 13/x, this becomes ...

  log(13/x) = log(13) -log(x)

If the base of logarithms is 9, then this is ...

  log9(13/x) = log9(13) -log9(x)

Answer:

B, C, D, and F

Step-by-step explanation:

The graph is an exponential curve rising upwards. By looking at the graph we can tell that the graph is only increasing, it touches the y-axis at 30 and it lies in the 1st quadrant.

So, option A is wrong, as the graph is increasing.

Option B is correct. The point where graph crosses/touches the y-axis is the y-intercept. So the y-intercept is 30.

Option C is correct. As the graph lies in 1st quadrant and is positive over the entire range of values.

Option D is also correct as the graph is increasing over entire range of values.

Option E is incorrect as y-intercept is 30.

Option F is correct. Since the graph is increasing, this means with every passing year the number of dolphins is increasing.

Therefore, the correct options are: B, C, D, and F

Answer:

a) R = 3.6

b) A = 2

Step-by-step explanation:

To find the value, start by modeling the inverse proportionality by using the base equations with the original givens.

y = k/x

12 = k/1.5

18 = k

Now we use that to model the equation

R = 18/A

And we can now use that to solve parts a) and b)

a)

R = 18/A

R = 18/5

R = 3.6

b)

R = 18/A

9 = 18/A

2 = A

Answer:

  x² + y² = 1

Step-by-step explanation:

x and y are the leg lengths of a right triangle with hypotenuse 1. The Pythagorean theorem says the relationship is ...

  1² = x² + y²

___

Of course, 1² = 1.

The equation for the line of reflection is x = 0 if the polygon ABCDE is reflected to produce polygon A'B'C'D'E'

It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.

We have a polygon ABCDE is reflected to produce polygon A'B'C'D'E' in the picture.

As we know, the reflection is the geometric transformation which create a mirror image of the object, but size or shape does not change.

The y-axis is the axis of reflection in this case.

The equation for the y-axis is x = 0

Thus, the equation for the line of reflection is x = 0 if the polygon ABCDE is reflected to produce polygon A'B'C'D'E'

Learn more about the geometric transformation here:

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s=√\frac{n}{n-1} [tex]n∑(x₁-x⁻)^2

                                  i=1

Ok so we know that consecutive angles are supplementary and the diagonals bisect the angels so

2x-15+3x=90

5x=105

X=21

Answer:

Step-by-step explanation:

To prove that Circle X is similar to Circle Y, we need to show that their corresponding angles are equal and their corresponding sides are proportional. We can compare the ratios of the circumference to the diameter for both circles, which are equal, implying that the angles in the two circles are equal and Circle X is similar to Circle Y.

To prove that Circle X is similar to Circle Y, we need to show that their corresponding angles are equal and their corresponding sides are proportional. Since the radii of the two circles are different (r for Circle X and s for Circle Y), we cannot directly compare their sides. However, we can compare their ratios. If we divide the circumference of Circle X by its diameter, we get the value of pi (π), which is approximately 3.14. Similarly, if we divide the circumference of Circle Y by its diameter, we would also get pi (π). This means that the ratios of the circumference to the diameter for both circles are equal, which implies that the angles in the two circles are equal and therefore, Circle X is similar to Circle Y.

Answer:

Option D.  11.

Step-by-step explanation:

121 = 11 * 11.  These are the only factors.

So its 11.

11 is a factor of 121.

A factor of a number is a number that makes up the former number. When a number is factorized, it gives us the factors of the number.

The number 121 can also be written as:

121 = 11*11

This means that when 11 is multiplied by itself, it gives 121.

This also means that 11 is the only factor of the given number.

Now observe the given options. We can see that only one option is correct and that option is 11.

Therefore, we have found the factor of 121 is 11. The correct answer is option D.

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Answer:

9 servings of meat.

Step-by-step explanation:

The first ratio you are given is 8:36. You are trying to figure out what 2:__ is.

8/36 x  2/X

Multiply 2 x 36 and get 72. Now divide 72 by 8 to get 9.

Answer:

The answer really is 9 servings of meat.

Step-by-step explanation:

I had the same question and I got it right...but mine said: Write a proportion that could be used to solve this problem. Do not solve it.

The point-slope form of the line with slope 6 that contains the point (1, 2) is y - 2 = 6(x - 1).

The point-slope form of a line is given by:

[tex]\[ y - y_1 = m(x - x_1) \][/tex]

where m is the slope of the line and [tex]\( (x_1, y_1) \)[/tex] is a point on the line.

Given that the slope m = 6 and the point [tex]\( (x_1, y_1) = (1, 2) \)[/tex], we can substitute these values into the point-slope form:

y - 2 = 6(x - 1)

So, the point-slope form of the line with slope 6 that contains the point (1, 2) is y - 2 = 6(x - 1).

[tex]GT=\frac{HF.TS}{SF}=\frac{4.8\times 21}{12}=8.4 [/tex]

Answer: 15 cubic inches.

Step-by-step explanation:

The volume of rectangular prism is given by :-

[tex]V=l\times w\times h[/tex], where l is length , w is width and h is height.

Given :  Hamsta' snacks box has a width of 1.5 inches,a length of 2.5 inches,and a height of 4 inches.

Then, the volume of the box will be :-

[tex]V=2.5\times 1.5\times 4=15\text{ cubic inches}[/tex]

Hence, the  volume of this Hamsta' snacks box is 15 cubic inches.

domain and range are both infinite

Answer:15

Step-by-step explanation:he has 3 packs of model cars. 15 is in each pack if he gave away four he would have 11 left.

Answer:

$0.61

Step-by-step explanation:

1. Find the sales price of each store by multiplying the regular price by the % off to find the discount - then subtract.

    store A: 24.95*20% (or 0.20) = 4.99 (discount)

                   24.95 - 4.99 = 19.96 (sales price)

    store B: 25.80 * 25% (or 0.25) = 6.45 (discount)

                  25.80 - 6.45 = 19.35

To find the difference of sales price, subtract 19.96 - 19.35 = 0.61

Answer:)

THE ANSWER IS A) $0.61

Answer:

I'm pretty sure it'd be set {3,6}

Answer:

A

Step-by-step explanation:

Answer:

D.2

Step-by-step explanation:

Slope is given by the ratio of change in y to change in x.

Taking two points on the table;

(-5, 15) and (1, 3)

Slope = (3-15)/ (1- (-5))

         = 12/6

         = 2

Answer:

A)  -2

Step-by-step explanation:

See the attached photo for explanation

Answer:

The 10! means 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 ⇒ answer C

Step-by-step explanation:

* Lets explain how to solve the problem

- Factorial number means a number which is multiply itself to its

 decreasing numbers

- In mathematics, the factorial of a non-negative integer n, denoted by

 n! is the product of all positive integers less than or equal to n

- That means n! = n × (n-1) × (n-2) × (n-3) × ...........× 1

- Ex: 5 ! = 5 × 4 × 3 × 2 × 1 = 120

* Lets solve the problem

- There was 10 factorial 10! possible different orders

- The meaning of 10! is the multiplication of all the numbers from

 10 to 1

∴ 10! = 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1

* The 10! means 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1

The correct choice is C, 10(9)(8)(7)(6)(5)(4)(3)(2)(1). The expression 10! (ten factorial) means the product of all integers from 1 to 10, which is calculated as 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1.

Therefore, the correct choice is C. For example, 4! equals 4 × 3 × 2 × 1 = 24.

The expression 10!, read as 'ten factorial', represents the product of all integers from 1 to 10. It is calculated as follows:

10! = 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1

So, the correct choice for what 10! means is:

C- 10(9)(8)(7)(6)(5)(4)(3)(2)(1)

For example, the factorial of 4 is calculated as 4! which equals 4 × 3 × 2 × 1 = 24.

Similarly, for 10!, you multiply all integers from 10 down to 1.

Answer:

30.9 ft

Step-by-step explanation:

Answer:

Step-by-step explanation:

you take 5280( How many feet are in a mile) and dived it by 3. The equals 1760 and that is the answer because 1760 is 1/3 of 5280

Answer:1760  

Answer:

The length of the cut is [tex]17\ ft[/tex]

Step-by-step explanation:

we know that

To calculate the length of the cut apply the Pythagoras Theorem

Let

x----> the length of the cut (hypotenuse of a right triangle)

[tex]x^{2}=L^{2} +W^{2}[/tex]

substitute the given values

[tex]x^{2}=15^{2} +8^{2} \\ \\x^{2}= 289\\ \\x=17\ ft[/tex]

To find the length of the diagonal cut on the rectangular board, use the Pythagorean Theorem by square rooting the sum of the squares of the length and width. In this case, the cut will be 17 feet long.

A construction worker is cutting along the diagonal of a rectangular board 15 feet long and 8 feet wide.

To find the length of the cut:

Answer:

[tex]x^2+y^2=25[/tex]

Step-by-step explanation:

The given circle is centered at the origin;

The radius of the circle is

[tex]r=|5-0|=5[/tex] units.

You could also count the boxes from the center to any of the given points to get the radius.

The equation of a circle centered at the origin is given by;

[tex]x^2+y^2=r^2[/tex]

We substitute the radius to obtain;

[tex]x^2+y^2=5^2[/tex]

The required equation is

[tex]x^2+y^2=25[/tex]

Answer:

dx/dy =  (x^4 -  2x^5y -  6xy^2) /  (5x^4y^2 - 4x^3y +  2y^3).

Step-by-step explanation:

x^5y^2 − x^4y + 2xy^3 = 0

Applying the Product and Chain Rules:

y^2*5x^4*dx/dy + 2y*x^5 - (y*4x^3*dx/dy + x^4) + (y^3* 2*dx/dy + 3y^2*2x) =0

Separating the terms with derivatives:

y^2*5x^4*dx/dy - y*4x^3*dx/dy + y^3* 2*dx/dy =  x^4 -  2y*x^5 -  3y^2*2x

dx/dy =  (x^4 -  2x^5y -  6xy^2) /  (5x^4y^2 - 4x^3y +  2y^3)

Answer:

[tex]\frac{dx}{dy}=\frac{-2x^5y+x^4-6xy^2}{5x^4y^2-4x^3y+2y^3}[/tex]

Step-by-step explanation:

The given equation is

[tex]x^5y^2-x^4y+2xy^3=0[/tex]

Differentiate with respect to y.

[tex]\frac{d}{dy}(x^5y^2)-\frac{d}{dy}(x^4y)+\frac{d}{dy}(2xy^3)=0[/tex]

Using product rule we get

[tex]x^5\frac{d}{dy}(y^2)+y^2\frac{d}{dy}(x^5)-x^4\frac{d}{dy}(y)-y\frac{d}{dy}(x^4)+2x\frac{d}{dy}(y^3)+2y^3\frac{d}{dy}(x)=0[/tex]           [tex](fg)'=fg'+gf'[/tex]

[tex]x^5(2y)+y^2(5x^4\frac{dx}{dy})-x^4(1)-y(4x^3\frac{dx}{dy})+2x(3y^2)+2y^3\frac{dx}{dy}=0[/tex]

[tex]2x^5y+5x^4y^2\frac{dx}{dy}-x^4-4x^3y\frac{dx}{dy}+6xy^2+2y^3\frac{dx}{dy}=0[/tex]

Isolate [tex]\frac{dx}{dy}[/tex] terms on left side.

[tex]5x^4y^2\frac{dx}{dy}-4x^3y\frac{dx}{dy}+2y^3\frac{dx}{dy}=-2x^5y+x^4-6xy^2[/tex]

[tex](5x^4y^2-4x^3y+2y^3)\frac{dx}{dy}=-2x^5y+x^4-6xy^2[/tex]

Isolate [tex]\frac{dx}{dy}[/tex] term.

[tex]\frac{dx}{dy}=\frac{-2x^5y+x^4-6xy^2}{5x^4y^2-4x^3y+2y^3}[/tex]

Therefore the value of [tex]\frac{dx}{dy}[/tex] is [tex]\frac{-2x^5y+x^4-6xy^2}{5x^4y^2-4x^3y+2y^3}[/tex].

Answer:

true!! :)) please mark brainliest

Answer:

False

Step-by-step explanation:

The given inequality is [tex]-3\:<\:x\:<\:14[/tex].

The boundaries of the inequality are not inclusive.

We use the "()" to indicate that the interval is open.

The required interval notation is [tex](-3,14).[/tex]

Answer:

2/4

Step-by-step explanation:

1/4 = 0.25

3/4 = 0.75

0.75 - 25 = 0.50

0.50 is your answer

Answer:

See the highlighted values below.

Step-by-step explanation:

The following right angled triangle will have an angle whose cosine is 5/13.

Hypotenuse = 13 and the 2 legs  will be 5 and 12 units long. The 12 is found using the Pythagoras theorem ( 13^2 = 5^2 + 12^2).

cos O = adjacent / hypotenuse = 5/13.

So sin O = opposite / hypotenuse = 12/13.

tan O =  opposite / adjacent = 12/5.

csc O = 1 / sin O =  13/12.

sec O = 1 /cos O = 13/5.

cot O = 1 / tan O = 5/12.

Answer:

b.  secx

Step-by-step explanation:

We have given a trigonometric expression.

csc(x)/cot(x)

We have to simplify it.

Since we know that

csc(x) is reciprocal to sin(x).

cscx = 1/sinx

cot(x) is ratio of cos(x) and sin(x).

cotx = cosx/sinx

Then, given expression becomes,

[tex]\frac{1/sinx}{cosx/sinx}[/tex]

[tex]\frac{1}{sinx}[/tex] × [tex]\frac{sinx}{cosx}[/tex]

[tex]\frac{1}{cosx}[/tex]

csc(x)/cot(x)   = secx