Using the function p(t)=5*2^t, estimate the boa constrictor population in 2 years, 3 years, and 4 years. Show your work.

The sum of angles of a triangle equals 180°.

Therefore:

|∠EAB| + |∠ABE| + |∠BEA| = 180°

Susbtitute

|∠EAB| = 14°

|∠ABE| = 45°

|∠BEA| = x°

14° + 45° + x° = 180°

59° + x° = 180°    |subtract 59° from both sides

∠BEA and ∠CED are vertical angles. Vertical angles are congruent, meaning that they have the same angle measure.

Therefore

In ΔCDE:

|∠CED| + |∠DCE| + |∠EDC| = 180°

Substitute:

|∠CED| =121°

|∠DCE| = 27°

|∠EDC| = y°

121° + 27° + y° = 180°

148° + y° = 180°    |subtract 148° from both sides

The equation that represent the eclipse in the image attached is option A.

We were given:

The center of an ellipse  (0, 0).

One focus is located at (12, 0),

One directrix is at x = 14 1/12.

To Find the equation of the ellipse will be:

The standard equation of an ellipse is :  [tex]\frac{(x- h )^ 2}{a^2} + \frac{(y - k)^2}{b^2}[/tex]

Note that c = 12

One need to compare the equation of directrix with the above equation:

a^2/c = 14[tex]\frac{1}{12}[/tex]

a^2/c = 169/12

Then Substitute the value c=12 and solve for a.

a^2/12 = 169/12

a² = 169

a = 13

Use the equation of  c² = a² - b² to find b.

= (12)² = (13/12)² - b²

b²= 169-144

b²= 25

b = 5

Then substitute the value of a and b into the standard equation of the ellipse.

[tex]\frac{(a- h )^ 2}{a^2} + \frac{(y - k)^2}{b^2}[/tex]

[tex]\frac{(x- 0 )^ 2}{13^2} + \frac{(y - 0)^2}{5^2}[/tex]

Therefore: [tex]\frac{(x)^ 2}{13^2} + \frac{(y)^2}{5^2}[/tex]

Hence, The equation that represent the eclipse in the image attached is option A.

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Answer:

24 and 25

Step-by-step explanation:

Angle a will be 20° because angle a+angle b=90°

angle c is 90°(right angle)

now to find the sides we will have to do a Pythagoras theorem for this indirectly therefore:

7²=49/2 sides

=24.5

therefore one side will be 24 the other side will be 25

if I am right mark as brainliest

Answer:

√41, or about 6.4 units

Step-by-step explanation:

[tex] \sqrt{ {5}^{2} + {4}^{2} } = \sqrt{25 + 16} = \sqrt{41} [/tex]

√41 is about 6.4 units

The strategy that Lucy uses to recall her phone number is what is known as Chunking.

This refers to the place where information is stored for future use and can either be a short or long-term memory.

Hence, we can see that based on the breaking down of her phone numbers of Lucy into a particular format that separates them using country/state code, she is making use of chunking.

This method of chunking is effective because it would help Lucy to recall her number quite easily.

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The constant of variation, k, is equal to 108. This is an inverse proportion and when L is 27 cm, W is 4 cm

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

The length (L) is inversely proportional to the width (W), hence:

L = k/W

18 = k/6

k = 108

When L = 27:

27 = 108/W

W = 4

The constant of variation, k, is equal to 108. This is an inverse proportion and when L is 27 cm, W is 4 cm

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Answer:

[tex]\sqrt{-3}[/tex]

Step-by-step explanation:

Since each of these answers contain a radical, you want to find the one that has a negative value, because technically sqrt(some negative number) isn't defined, or rather it has no real solution. This is because you can rewrite a radical as [tex]\sqrt{a * b} = \sqrt{a} * \sqrt{b}[/tex]. And since [tex]i = \sqrt{-1}[/tex] you can rewrite [tex]\sqrt{-3}[/tex] as [tex]\sqrt{-1} * \sqrt{3}[/tex] which becomes [tex]i\sqrt{3}[/tex]

The height of the building to the nearest foot is 121.5 ft.

The height of the building can be found using trigonometric ratios.

Therefore,

tan 59° = opposite / adjacent

tan 59°= h / 73

cross multiply

h = 73 tan 59°

h = 73 × 1.66427948235

h = 121.492402212

h = 121.5 ft

Therefore, the height of the building to the nearest foot is 121.5 ft.

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Answer:

2a^2 + 3a - 1 ,

Step-by-step explanation:

I am assuming you mean

2a^3-a^2-7a+2

By long division:

a - 2 ) 2a^3 -   a^2 - 7a +  2 ( 2a^2 + 3a - 1 <------- Quotient

          2a^3 - 4a^2

                     3a^2 - 7a

                     3a^2 - 6a

                                -a + 2

                                -a + 2

                                 . . . . .

The missing statement are:

4.  ∠B ≅ ∠B; Reflexive Property of Equality.

5.   ΔBDE ~ ΔBAC; Side-Angle-Side (SAS) Similarity Postulate.

The missing statement are number 4 and 5.

If we say that  4. ∠B ≅ ∠B; Reflexive Property of Equality then:

∠B ≅ ∠B,

Note that  there are two triangles, which are ΔABC and ΔDBE and we also have ∠BDE ≅∠BAC and ∠B ≅ ∠B,

∠BDE + ∠B + ∠BED = 180°

∠BAC + ∠B +  ∠BCA = 180°

Hence, ∠BED = ∠BCA Substitution property of equality

That  birth ΔABC ~ ΔDBE,which is Angle Angle Similarity Postulate

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Answer: 4.∠B ≅ ∠B; Reflexive Property of Equality

5. ΔBDE ∼ ΔBAC; Angle-Angle (AA) Similarity Postulate

Step-by-step explanation:

I just took the test; this exact order should be correct. :D

The table for the complete ratios between distance and time is shown below.

The ratio of distance to time, given that 280 miles will be covered in 4 hours is: 280/4 = 70 miles per hour.

Thus, for 2 hours: 2(70) = 140 miles distance.

For 350 miles, we would have: 350/70 = 5 hours time.

For 6 hours: 6(70) = 420 miles distance.

For 8 hours: 8(70) = 560 miles distance.

For 700 miles, we would have: 700/70 = 7 hours time.

The complete table is shown in the image below.

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The simplification of each form of expression is;

(6r + 7) + (13 + 7r)

= 6r + 7 + 13 + 7r

= 13r + 20

(13 - 3/2r) - (1 - r)

= 13 - 3/2r - 1 + r

= 12 - 3/2r + r

= 12 -3r+2r/ 2

= 12 - 1/2r

(-8 - r) + (2r - 4)

= -8 - r + 2r - 4

= -12 + r

(7r - 3/2) - (2/3 + 6r)

= 7r - 3/2 - 2/3 - 6r

= r -9-4/6

= r - 13/6

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Answer:

All 3 are right triangles.

Step-by-step explanation:

In a right triangle c^2 = a^2 + b^2   where c is the longest side.  ( by Pythagoras).

a) 3^2 = 9, 6^2 = 36 and √27 ^ 2 = 27

36 = 9 + 27

So this is a right triangle.

b)

17^2 = 289, 15^2 = 225 and 8^2 = 64

289 = 225 + 64

Also right triangle.

c) √50 ^ 2 = 50, 5^2 = 25 and 5^2 = 25

So also right triangle.

Answer:

Option C: y=-1/2x + 8

Step-by-step explanation:

So we have the options:

A) y=2x+5

B) y=-1/2x+4

C)y=-1/2x+8

D)y=-2x+5

But first let's define what parallel even is. When two lines are parallel it means that there slope is the same value and the same sign, while there y-intercepts are different, because if they were the same, then they wouldn't be parallel, they would just be the same exact line.

So we're given the equation in standard form. To find the slope we can change it so it's in the form of y=mx+b. This can be done by simply isolating y. The reason we want it in the slope-intercept form is because m represents the slope and b represents the y-intercept. m is the slope because as x increases by 1 the y-value will increase by m. So the "rise" will be m and the "run" will be 1, thus the slope will be m/1 or in other words m because the slope is defined as rise/run. So let's start the steps to isolating y

Original equation

2x+4y=16

Subtract 2x from both sides

4y=-2x+16

Divide both sides by 4

y = -1/2x + 4

Here we have it in slope-intercept form. In this case the slope, or m, is -1/2 and the y-intercept or b is 4. So now let's look at the other equations.

Option A: This equation has a slope of 2, which is not the same as -1/2 so it is not parallel

Option B: This equation has a slope of -1/2 which is the same as -1/2 so it might be parallel. But look at the y-intercept it's 4, that's the same y-intercept as the original equation. This means the two equations are equal and not parallel

Option C: This equation has a slope of -1/2 which is the same as -1/2 so it might be parallel. It has a y-intercept of 8 which is not the same as 4, so the two lines are parallel and not equal! This is the answer

Answer:

3.57 taps

Step-by-step explanation:

14/5 = 10/x hours (divide both sides by 10)

50/14 = x (3.57 taps)

Brainliest, please :)

Answer:

7 taps

Step-by-step explanation:

rate =    1 tank / 5 taps = 14 hr

1 tank = 70 tap-hr

70 tap -hr  / x tap  = 10 hr

x = 7 taps

Answer:  69m^2

Step-by-step explanation:

we can find the area of shaded region by  subtracting the area of removed region.

so,

area of rectangle= length*width

for area of removed region

=4m*2m=8m^2

for area of  larger region

=11m*7m=77m^2

Now final destinaltion

area of shaded region=area of lareger region-area of smaller region

                                     =77m^2-8m^2

                                    =69m^2

Answer:

m>35

Step-by-step explanation:

We have to find the least m for 65 + 0.8m > 93.

subtract 93 from each side of the inequality: 0.8m > 28

divide both sides of the inequality by 4: 0.2m > 7

multiply both sides of the inequality by 5 to find m: m>35.

The location of the fountain as described in the task content is; (-1, -0.5).

According to the task content, the locations of Fernando and Maria are given as; (-4, -2) and (4,2) respectively and the ratio of division is expected to be; 5: 3.

Hence, the coordinates of the fountain can be evaluated as;

x = (4) - (4-(-4)) × (5/8) = -1.

y = 2 - (2-(-2)) × (5/8) = -0.5

Hence, it follows that the coordinates of the fountain location is; (-1, -0.5) since the fountain is closer to Fernando than Maria.

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Answer:

-1 AND -0.5

Step-by-step explanation:

The result of the subtraction of the vectors is: [706 -3 0].

To subtract two vectors, we subtract the corresponding elements.

In this problem, the vectors are given as follows:

The subtractions of the corresponding elements are:

Hence the result is:

[706 -3 0].

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Answer: B. X = [tex]4\sqrt{6}[/tex]

Step-by-step explanation:

sec(45) = hyp/12

12sec(45) = hyp

hyp = 16.9

cot(60) = x/16.9

16.9cot(60) = x

x = 9.7

B. X = [tex]4\sqrt{6}[/tex]

Answer:

  D)  Hungary

Step-by-step explanation:

You are being asked to compare 4 pairs of numbers. The population will have decreased if the number in the 2005 column is less than the number in the 1985 column.

Whenever you compare numbers, you start with the most-significant digit. If the most-significant digit has a higher place value, the number is larger. If the digits have the same place value, the number with the larger digit is larger. If no determination can be made by these comparisons, then the digits to the immediate right are compared.

  27,... > 19,...  2 > 1 in the 10-millions place

  10,... > 9,...  1 has a greater place value

  29... > 24...  comparison shifts to the 10-thousands place: 9 > 4

  10,058,... < 10,649,... . . . . the population decreased (0 < 6)

The "population decreased" result is found on the last line of the table, identified by the Country name "Hungary."

Hungary's population decreased from 1985 to 2005.

[tex]\large\boxed{\frac{1}{1369}}[/tex]

We'll assume that there is an equal probability of any position on the wheel, so a [tex]\frac{1}{37}[/tex] chance for any given number.

We must take the probability of getting a 27, then the probability of getting a 15, and multiply them together to find the chances that they both happen in a row.

[tex]\frac{1}{37}\cdot\frac{1}{37}=\boxed{\frac{1}{1369}}[/tex]

Answer: [tex]55^{\circ}[/tex]

Step-by-step explanation:

Angles on a straight line add to [tex]180^{\circ}[/tex].

Angles around a point equal 360°, so n = 360 - 291 = 69°

Thus, as angles in a triangle add to 180°, m = 180 - 31 - 69 = 80°

Answer:

Irrational number

Step-by-step explanation:

  Prime factorize the number and then simplify.

[tex]\sf \sqrt{5}*\sqrt{5}*\sqrt{8}=\sqrt{5*5*8}[/tex]

                     [tex]\sf = \sqrt{5*5*2*2*2}\\\ = 5* 2* \sqrt{2}\\\\= 10\sqrt{2}[/tex]is an irrational number.

Answer:

D : (0 ≤t ≤6)

R : (-2 ≤d ≤0)

Step-by-step explanation:

your domain is your x and your range is your y.

this means that you start by looking at your x axis. in this problem, x goes from 0 to 6, so 0 ≤t ≤6

this is the same for y.

y goes from -2 to 0 (remember that you read the y axis down and up, so you need to have the negative number written first)  

so -2 ≤d ≤0

Answer:

(domain: 0 ≤ t ≤ 6)

(range: -2 ≤ d ≤ 0)

Step-by-step explanation:

domain of a function: all possible x-values

range of a function: all possible y-values

here, we know that we can't have negative time (note: time is along the x-axis and is x-variable; it is describing the domain)

(and yes, while time still goes on forever, this graph does not have an arrow on the end of it, meaning that is where we are considering time to stop--and because its an ≤ sign, it wouldn't be infinity)

so, time goes from 0 to 6

(domain: 0 ≤ t ≤ 6)

here, we also know that our submarine won't go above the water level (it's not going to keep floating up into space forever), so the maximum value of our range (depth) is going to be 0

we also won't be going any lower than where the toy starts--which we can see to be -2

so, the depth goes from -2 to 0

(range: -2 ≤ d ≤ 0)

hope this helps!! have a lovely day :)

We have been able to prove that the area of the triangle formed by the joining midpoints of triangle ABC is 1/4 the area of triangle ABC.

Area of triangle joining the points A, B & C is;

A₁ = ¹/₂[tex]\left[\begin{array}{ccc}1&1&1\\3&-2&5\\4&0&0\end{array}\right][/tex]

A₁ = ¹/₂(-1 * -20) + (1 * 8)

A₁ = 14

Thus;

Midpoint of AB is (¹/₂, 2)

Midpoint of BC is (³/₂, 0)

Midpoint of AC is (4, 2)

A₂ = [tex]\frac{1}{2} \left[\begin{array}{ccc}1&1&1\\\frac{1}{2} &\frac{3}{2} &4\\2&0&2\end{array}\right][/tex]

A₂ = ¹/₂(3 - 1(-7) + (1 * -3))

A₂ = ⁷/₂

Since A₁ = 14, we can equally say that;

A₂ = ¹/₄A₁

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The ray that is opposite FH in the image given is: FE.

A ray is a straight line that starts from one end and extends infinitely towards the opposite end.

We are asked to find the ray that is opposite to FH. This means the ray opposite to FH will definitely start from point B and extends to the opposite direction.

Ray FE is opposite FH.

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Answer:

Actually this question is easy. Mutual angles are equal to each other. Then 152-90=62