Parallel lines p and q are cut by transversal r. On line p where it intersects with line r, 4 angles are created. Labeled clockwise, from the uppercase left, the angles are: 1, 2, 4, 3. On line q where it intersects with line r, 4 angles are created. Labeled clockwise, from the uppercase left, the angles are: 5, 6, 8, 7. m∠3 is (3x + 4)° and m∠5 is (2x + 11)°. Angles 3 and 5 are . The equation can be used to solve for x. m∠5 = °

Answer:

a. 16; b. aₙ = 4ⁿ⁻¹; c. predation and carrying capacity will limit the population

Step-by-step explanation:

a. The first female had 4 pups.

If each of them had 4 pups, there would be 4 × 4 = 4² = 16 pups.

b. 1st generation                        =     1 pup

2nd generation = 4 ×  1 pup      =    4 pups

3rd generation  = 4 ×  4 pups    =  16 pups

4th generation  = 4 × 16 pups    = 64 pups

5th generation  = 4 × 64 pups = 256 pups

The sequence is           1,   4, 16, 64, 256, …

We can also write it as 4⁰, 4¹, 4²,  4³,   4⁴, …

Note that the exponent is one less than the number of the generation.

Thus, the general formula for the nth term, aₙ, is

aₙ = 4ⁿ⁻¹, where

n = the number of the generation

a = the number of pups in that generation.

c. a₂₅ = 4²⁵⁻¹ = 4²⁴ ≈ 281 000 000 000 000 or 281 trillion

The population would not reach that number because there would not be enough food for all those pups. Pups would die of starvation until their numbers equalled the carrying capacity of the ecosystem and would level off at that point.

There would also be increased predation by coyotes, bobcats, etc. This would also keep the population growth in check,

Answer:

27π Sq in.

Step-by-step explanation:

Circle A is equal to 9π sq inches. (Radius squared times Pi), Segment BC is a radii of Circle B and the diameter of Circle A. Meaning Circle B's radius is 6 inches. The area of circle B would be 36π sq inches. Now we subtract Circle A's area from Circle B's area(36π sq in. - 9π sq in.), the area of the shaded region is 27π sq in.

Answer:

the height that represents the 99th percentile is 69.324  inches

Step-by-step explanation:

Given that :

the mean height =  62.8 inches

standard deviation = 2.8  inches

For 99th percentile;

Let X be the random variable;

SO, P(Z≤ z)  = 0.99

From the standard normal z tables

P(Z )= 2.33

The standard z score formula is :

[tex]z = \dfrac{X- \mu}{\sigma}[/tex]

[tex]2.33 = \dfrac{X- 62.8}{2.8}[/tex]

2.33 × 2.8 = X - 62.8

6.524 = X - 62.8

6.524 +62.8 =  X

69.324  = X

X = 69.324

Therefore; the height that represents the 99th percentile is 69.324  inches

Answer:

Step-by-step explanation:

5 * 45 = 225

225+75=300

300/500=0.6

The tank will be 60% full.

If this helped, make sure to mark it as brainliest :D

Answer:

C.60%

Step-by-step explanation:

45 x 5 = 225  225 + 75 = 300

300 / 500 = 0.6 = 60%

Answer:

18

Step-by-step explanation:

Each interior angle of a regular pentagon is 108 degrees. So Angle AED is 108 degrees. Since Angle AEF is a straight line (180 degrees), Angle FED is 72. This is because 180-108 = 72. Now, since a triangle has a total of 180 degrees, we add 72 and 90, because those are the 2 degrees we have calculated. This gives us a total of 162. Now, we subtract 162 from 180 to find out the degree of Angle FDE. This is 18. So our final answer is 18.

Sidenote: I hope this answer helps!

The properties of a pentagon and the given right triangle formed by

segments EF and FD give the measure of ∠FDE.

Response:

The given parameters are;

A, E, F are points on the same line.

ABCDE is a regular pentagon

∠EFD = 90°

Required:

The measure of ∠FDE

Solution:

The points A and E are adjacent points in the pentagon, ABCDE

Therefore;

line AEF is an extension of line side AE to F

Which gives;

∠EFD = 90°, therefore, ΔEFD is a right triangle, from which we have;

The sum of the acute angles of a right triangle = 90°

Therefore;

∠DEF + ∠FDE = 90°

Which gives;

72° + ∠FDE = 90°

∠FDE = 90° - 72° = 18°

Learn more about the properties of a pentagon here:

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Answer:

I dont give you the answer right away so you will read what i write and fully understand :D

Step-by-step explanation:

We are picking 3 balls from 30 balls, so its C(30,3) because the order of picking the balls doesnt matter. We also need to pick 2 balls from 20 balls, which is C(20,2). So the answer is C(30,3) * C(20,2).

Answer :Answer: Did you get helped on this one?          

Step-by-step explanation: okay yup yup have a good day OKAY

Step-by-step explanation: HAVE A GOOD ONE OKAY

Answer:

96

Step-by-step explanation:

We simply need to plug in a = 4 so 6a² = 6 * 4² = 6 * 16 = 96.

Answer:

A

Step-by-step explanation:

With this one, you can just plug in 3 into each of the equations until the answer is 1.

When u plug 3 into x for solution A.

(1/3)×3=1

1^2=1

Answer:

[tex]\boxed{ \mathrm{A} }[/tex]

Step-by-step explanation:

The point is given (3, 1)

x = 3

y = 1

y = (1/3x)²

Plug x as 3 and y as 1.

The equation should be equal.

1 = (1/3(3))²

1 = 1²

1 = 1 True

Answer:

It took 31 days for the patch to cover half the lake

Step-by-step explanation:

The patch grows to double its size everyday

the patch completely covers the lake in 32 days

Since the patch doubles itself everyday, this means that the previous day before the 32nd day, the lake was just half covered.

Therefore, the the patch covered half the lake on the 31st day, i.e it took 31 days for the patch to cover half the lake

Answer:

The function has a maximum value of 3 that occurs at x = 1.

Step-by-step explanation:

First, note that the leading coefficient is negative. This means that the parabola will curve downwards. Because of this, the function has a maximum. The maximum value will simply be the vertex.

The formula for the x-coordinate of the vertex is -b/2a.

a=-3, b=6, c=0

Plug in the numbers:

x=-(6)/2(-3)

=-6/-6=1

Now, plug 1 back into the original function:

-3x^2+6x

-3(1)^2+6(1)

=-3(1)+6

=-3+6

=3

Answer:

18m square

Step-by-step explanation:

Formula for rectangular- based pyramid is L x W x H divided by 3

= 3 x 5 x 3.6 divided by 3 = 18

So you would need 18 m square for the sculpture

Answer:

(E) including reminders to watch the endorsement, compare signatures, and view

Step-by-step explanation:

The principle features that will help the company to confirms checks authenticity. It include endorsements and compare the signatures with the designated signatories. If the signatures are matched correctly with the assigned signatories the check is hold in light to view the watermark on it.

Answer:

D

Step-by-step explanation:

Given

y = x² + 1

y = x

Equating gives

x² + 1 = x ( subtract x from both sides )

x² - x + 1 = 0

Consider the discriminant Δ = b² - 4ac

with a = 1, b = - 1 and c = 1

b² - 4ac = (- 1)² - (4 × 1 × 1) = 1 - 4 = - 3

Since b² - 4ac < 0 then there are no real solutions

Answer:

D.

Step-by-step explanation:

A function is when each x-value has only 1 y-value.

A: When x = 5, there are two values for y.

B: When x = -3, there are two values for y.

C: When x = -4, there are two y-values.

D: Each x-value has exactly one y-value.

So, your answer should be D.

Hope this helps!

Option (D) is accurate since the fourth option's x value has exactly one y value.

D. {(₋7,9), (₋4,₋9), (5,15), (7,19)}

What are functions?

Each element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and co-domain, respectively.

When we say that a variable quantity y is a function of a variable quantity x, we indicate that y depends on x and that x's value determines what y's value will be. This reliance can be expressed as follows: y = f (x)

Given,

In the first case, y has two different values of 13 and 17, which is not permitted in a function, with the same value of x = 5. The first case is not a function as a result.

For the same value of x = 3 in the second case, y has two different values of 1 and 1, which is not permitted in a function. The second example is therefore not a function.

In the third case, for the same value of x = ₋4, y has two different values of 52 and 16 which is not allowed in a function. Therefore, third case is not a function.

Here, in the fourth situation, no x value is identical and there is only one possible y value.

Hence we get the answer as {(₋7,9), (₋4,₋9), (5,15), (7,19)} which represents the function.

Learn more about "functions" here-

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Answer:

48.

Step-by-step explanation:

[tex]\frac{24\sqrt{72} }{3\sqrt{2} }[/tex]

= (24 / 3) * [tex]\frac{\sqrt{72}} {\sqrt{2} }[/tex]

= 8 * [tex]\frac{\sqrt{72} * \sqrt{2}} {\sqrt{2} * \sqrt{2} }[/tex]

= 8 * [tex]\frac{\sqrt{144}} {2}[/tex]

= 8 * (12 / 2)

= 8 * 6

= 48.

Hope this helps!

Answer:

Step-by-step explanation:

Let the points be A and B

A ( - 2 , 3 ) -------> ( x1 , x2 )

B ( -4 , -9 ) -------> ( x2 , y2 )

Now, finding the slope:

[tex]slope \: (m) = \frac{y2 - y1}{x2 - x1} [/tex]

Plug the values

[tex] = \frac{ - 9 - 3}{ - 4 - ( - 2)} [/tex]

Calculate

[tex] = \frac{ - 12}{ - 4 - ( - 2)} [/tex]

When there is a (-) in front of an expression in parentheses , change the sign of each term in expression

[tex] = \frac{ - 12}{ - 4 + 2} [/tex]

Calculate

[tex] = \frac{ - 12}{ - 2} [/tex]

Reduce the fraction with -2

[tex] = 6[/tex]

Hope this helps..

Best regards!!

Answer:

-2

Step-by-step explanation:

Hello,

First of all, let's check the denominator.

[tex]x^2-x-6 \ \ \text{ *** How to factorise it ...? ***}\\\\\text{*** The product of the roots is -6=-2*3 and their sum is 1 ***}\\\\x^2-x-6=x^2-3x+2x-6=x(x-3)+2(x-3)=(x+2)(x-3)[/tex]

Now, let's see the numerator.

[tex]x^2+8x+4 \ \text{ *** -2 is not a zero as ***}\\\\(-2)^2+8*(-2)+4=4-16+8=-4\\\\\text{*** 3 is not a zero as ***}\\\\3^2+8*3+4=9+24+4=37\\[/tex]

So we cannot factorise the numerator with (x+2) or (x-3)

Then, -2 and 3 are the the discontinuities of the expression.

There is only -2 in the list, this is the correct answer.

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

890 m^3 to the nearest whole number.

Step-by-step explanation:

Volume = volume of the cylinder + volume of the hemisphere:

= π r^2 h + 1/2 * 4/3 π r^3

= π*5^2 * 8 + 1/2 * 4/3  π 5^3

= 890.12

There are 18 rectangles inside the playing field.  And if you include the fence around the field, that makes 19.

Answer:

Its the last option. On the bottom.

Step-by-step explanation:

You need to Solve for x to find the zeroes of the equation.

x-1=0 So one x is at 1.

x+4=0 So the other x is at -4.

This graph is also not negative so it does not get flipped across the x-axis

The graph of the function [tex]f(x) = (x - 1)(x + 4)[/tex] is graph (d)

The equation of the function is given as:

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

From the above function, we have the zeros of the function to be:

1 and -4

This means that:

Hence, the graph is graph (d)

Read more about quadratic functions at:

https://brainly.com/question/1214333

Answer:

Four unique planes

Step-by-step explanation:

Given that the points are non co-planar, triangular planes can be formed by the joining of three points

The points will therefore appear to be at the corners of a triangular pyramid or tetrahedron such that together the four points will form a three dimensional figure bounded by triangular planes

The number of triangular planes that can therefore be formed is given by the combination of four objects taking three at a time as follows;

₄C₃ = 4!/(3!×(4-3)! = 4

Which gives four possible unique planes.

Answer:

7 3/8 + (-4 1/2) ÷ (-5 2/3) = 8 23/136

Step-by-step explanation:

1) First I turned all the mix numbers into improper fractions:

7 3/8 ----> ( 7(8)+3/8) = 59/8, 4 1/2 ----> (4(2)+1/2) = 9/2, 5 2/3 ---->  (5(3)+2/3) = 17/3

So now it should look like this: 59/8 + (-9/2)÷(-17/3)

2) Now our goal is to divide both of the improper fractions (-9/2)÷(-17/3),

- We first apply our fraction rule:  -a/-b = a/b (when we have two negatives they cancel out each other and make a positive)

Our Case, From this:-9/2 ÷ -17/3 = To This: 9/2 ÷ 17/3

3) Now we can divide the fractions using this rule: a/b ÷ c/d = a times d / b times

Our Case, From This: 9/2 ÷ 17/3 To This: 9(3)/2(17) Which Gives Us: 27/34

(9 x 3 = 27, 2 x 17= 34)

So now it looks like this: 59/8 +27/34

4) Our look goal is to have the same denominator (which is the bottom part of the fraction)  which are 8 and 34

To find it we find the LCM or Least Common Multiple of 8 and 34

(The LCM of a, b is the smallest positive number that is divisible by both a and b) which in this case a and b are 8 and 34  

LCM is 136

5) We adjust our two fractions based on the LCM,

(Multiply each numerator ( top part of the fraction)  by the same amount of needed to multiply its corresponding denominator to turn it to the LCM 136.

From This: 59/8  and 27/34 To This: 1003/136 and 108/36 ( 59(17)/8 (17) = 1003/136, 27(4)/34(4) = 108/306

6) Finally we can add the numerator (1003 and 108) together: 1003+108= 1111 and now we are left with 1111/136

Then we turn our improper fraction back into a mix number: 1111/138= 8 23/136

Answer:

[tex]\frac{1111}{136} = 8 \frac{23}{136}[/tex]

Step-by-step explanation:

We want to simplify:

[tex]7 \frac{3}{8} + \frac{ -4 \frac{1}{2} }{ -5 \frac{2}{3} }[/tex]

First, convert all the fractions to improper fractions:

[tex]\frac{59}{8} + \frac{ - \frac{9}{2} }{ - \frac{17}{3} } \\\\= \frac{59}{8} + \frac{27}{34}[/tex]

Find the LCM of the denominators:

[tex]\frac{(17 * 59) + (4 * 27)}{136} \\\\ = \frac{1003 + 108}{136}\\ \\= \frac{1111}{136} \\\\= 8 \frac{23}{136}[/tex]

Answer:

[15, ∞).

Step-by-step explanation:

–3(6 – 2x) ≥ 4x + 12

-18 + 6x ≥ 4x + 12

6x - 4x ≥ 12 + 18

2x ≥ 30

x ≥ 15

This means that the minimum of x is 15, and the most is infinity, which is the same thing as [15, ∞).

Hope this helps!

Answer:

[tex]\dfrac{74}{20}=3.7 meters[/tex]

Step-by-step explanation:

Hello!

1) Since no other data has been given. Suppose Natasha is in the center and the beagle is to the right.

[tex]\dfrac{25}{4} \:meters[/tex]  

2) The labrador is [tex]\dfrac{51}{20}\: to\: the\: left.[/tex]

[tex]\dfrac{25}{4} -\dfrac{51}{20} =\dfrac{(5*25)-51}{20} \\\dfrac{(125-51}{20} =\dfrac{74}{20}[/tex]

Answer:

The answer is B :D hope this helps

Step-by-step explanation:

Answer:

B 2.5 Gal

Step-by-step explanation:

Answer:

I think the correct answer may be B.

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

If Dan earns $x then Bob earns $3x ( 3 times as much as Dan ), then

x + 3x = 72 , that is

4x = 72 ( divide both sides by 4 )

x = 18

Thus

Dan earns $18 and Bob earns 3 × $18 = $54

The earning of Bob will be 54 dollars and the earning of Dan will be 18 dollars.

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

Let the earning by Bob be x and the earning by Dan be y.

Bob and Dan earned a total of $72 shoveling snow. Then the equation will be

x + y = 72 ...1

If Bob earned 3 times as much as Dan. Then the equation will be

x = 3y   ...2

Substitute the value of x in equation 1, then the equation will be

3y + y = 72

     4y = 72

       y = $18

Then the money earned by Bob will be

x = 3y

x = 3(18)

x = $54

Thus, the earning of Bob will be 54 dollars and the earning of Dan will be 18 dollars.

More about the linear system link is given below.

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Answer:

Are you asking what the value of x is if [tex]n^{x} * n^2 = 343[/tex] ?

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

For the first triangle which is triangle <KJL

Hypotenuse= 8✓2

Angle=30°

Opposite = ?

Therefore we will use Sine formula

Sin30° = Y/8✓2

Y=4✓2

For the second triangle which is triangle <JML

Hypotenuse= 4✓2

Opposite=X

Angle=45°

Therefore we will use Sine formula again

Sin45°=X/4✓2

X=4

Answer:

Step-by-step explanation:

ΔJKL is half of equilateral triangle and ΔJML is half of square.

We can use properties of these triangles (picture):

m∠KJL=90° and m∠JKL = 30° ⇒  JL = 0.5KL = 0.5•8√2 = 4√2

m∠JML=90° and m∠MJL = 45° ⇒  JL = ML√2

                                                        4√2 = x√2

                                                             x = 4