Prove triangle ABC is congruent to triangle CDA

Answer:

[tex]y=3750 \cdot 1.0215^t[/tex]

(where [tex]y[/tex] is the population and [tex]t[/tex] is time in years after 2021)

5159

Step-by-step explanation:

Part (a)

General form of an exponential function:  [tex]y=ab^x[/tex]

where:

If [tex]b > 1[/tex]  then it is an increasing function

If [tex]0 < b < 1[/tex] then it is a decreasing function

We are told that the initial population is 3750.  Therefore, [tex]a=3750[/tex]

We are told that the farm grows at a rate of 2.15% annually.  Therefore, if it grows then every year it is 100% + 2.15% = 102.15% of the previous year.

Convert the percentage into a decimal:

102.15% = 102.15/100 = 1.0215

Therefore, [tex]b=1.0215[/tex]

We are told that the independent variable is [tex]t[/tex] (in years).

Therefore, the equation is  [tex]y=3750 \cdot 1.0215^t[/tex]

(where [tex]y[/tex] is the population and [tex]t[/tex] is time in years after 2021)

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Part (b)

The year 2036 is 15 years after 2021.  Therefore, substitute [tex]t = 15[/tex] into the equation and solve for [tex]y[/tex]:

[tex]\implies y=3750 \cdot 1.0215^{15}[/tex]

[tex]\implies y=5159.49068...[/tex]

Therefore, an estimate of the population of the town in 2036 is 5159.

Answer:

[tex]\frac{17}{6}[/tex] or in mixed form = 2[tex]\frac{5}{6}[/tex]

Step-by-step explanation:

5 2/3 divide by 2 = 17/6 of 2 5/6

9514 1404 393

Answer:

  14,400 people

Step-by-step explanation:

The area is the product of length and width:

  A = LW

  A = (300 ft)(120 ft) = 36,000 ft^2

Then the number of people is the area divided by the area per person:

  (36,000 ft^2)/(2.5 ft^2/person) = 14,400 persons

Answer: b

Step-by-step explanation: the answer is B i think

Answer:

yes

Step-by-step explanation:

Answer:

Except d. Rotate 120 degrees around center c then rotate 220 degrees around again.

Step-by-step explanation:

Let's choose an arbitrary shape to work with the exercise.

For example a square (All the conclusions that we will make can be use with any shape).

For a. Translate 3 units up, then 3 units down is easy to see that this will return the square to its original position. Wherever we translate up and then down the same units a particularly shape this will return to its original position.

For b. Reflect over line p, then reflect over line p again

Wherever we have any particularly shape and we reflect over an arbitrary line twice, the shape will return to its original position. Particularly, the composition of two reflections over the same line is the identity function.

The identity function is the function that doesn't change the shape (It is the analogy of the multiplication by 1 with the common product between real numbers).

c. Translate 1 unit to the right, then 4 units to the left, then 3 units to the right.

The composition of this three translation will return the square to its original position (Same reasoning as a.)

d. Rotate 120 degrees around center c then rotate 220 degrees around c again.

Given that we choose an arbitrary center c and then chosen an arbitrary rotation sense (counterclockwise or clockwise), the composition of the two rotations is a 340 degrees rotation (given that we sum the degrees).

This transformation will not return a shape to its original position

(Of course, it exists some exceptions such as a rotation of a circle around its center. For any value of degrees, the rotation of a circle around its center will return the circle to its original position).

Generally, option d. is the correct option.

Answer:

8

Step-by-step explanation:

Answer:

2.47 × 10^-6

Step-by-step explanation:

The negative power is in coorilation to how many decimal spots it was moved.

Ex: The 2 in 2.47 was moved left 6 spots.

Answer: 7

Step-by-step explanation: 6/2 is 3, 3+4 is 7

Answer: 8?

Step-by-step explanation: because 6/2 has 4 extra so I guess you add those and get "8"

[tex]\begin{array}{lcccl} &\stackrel{lbs}{Qty}&\stackrel{\$}{price}&\stackrel{total}{value}\\ \cline{2-4}&\\ \textit{1st candy}&x&0.9&0.9x\\ \textit{2nd candy}&y&0.4&0.4y\\ \cline{1-4} mix&50&0.85&42.5 \end{array}\qquad \qquad \begin{cases} x+y=50\\\\ 0.9x+0.4y=42.5 \end{cases} \\\\[-0.35em] ~\dotfill[/tex][tex]\stackrel{\textit{using the 1st equation}}{x+y=50\implies y=50-x}\qquad \qquad \stackrel{\textit{substituting on the 2nd equation}}{0.9x~~ + ~~0.4(50-x)~~ = ~~42.5} \\\\\\ 0.9x+20-0.4x=42.5\implies 0.5x+20=42.5\implies 0.5x=22.5 \\\\\\ x=\cfrac{22.5}{0.5}\implies \boxed{x=45}\qquad \qquad \qquad \boxed{\stackrel{50~~ - ~~45}{y=5}}[/tex]

Answer:

6 1/2 minutes per miles

2/13 miles per minutes

Step-by-step explanation:

Distance travelled = 2 1/2 miles

Time taken = 16 1/4 minutes

Average: minutes per mile

= 16 1/4 minutes / 2 1/2 miles

= 65/4 ÷ 5/2

= 65/4 × 2/5

= 13/2

= 6 1/2

Average time per mile in minutes

= 6 1/2 minutes per mile

Average (miles per minutes)

= 2 1/2 ÷ 16 1/4

= 5/2 ÷ 65/4

= 5/2 × 4/65

= 20 / 130

= 2/13 miles per minutes

Answer:

it's not showing the question so how will I tell you

Answer:

59

Step-by-step explanation:

You know the measures of the 2 angle values. you add

52+69=121

Since the interior has to be 180 degrees, you subtract

180-121=59 degrees is the measure of I.

Answer:

im too slow i thought this was a gta cheat code

Answer:

I only know the first question and it's f(x)=3x^2+24x-6.

Answer:

n + 35

Step-by-step explanation:

Let's convert the words to math:

"a number" we can define as n.

"increases" we can define as addition, or sum (+).

"thirty-five" we can define as 35.

We then combine all the translations:

n + 35

Answer: 12.9

Step-by-step explanation:

[tex]\textit{circumference of a circle}\\\\ C=2\pi r~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ C=82.21 \end{cases}\implies 82.21=2\pi r\implies \cfrac{82.21}{2\pi }=r \\\\[-0.35em] ~\dotfill\\\\ \textit{area of a circle}\\\\ A=\pi r^2\qquad \qquad A=\pi \left( \cfrac{82.21}{2\pi } \right)^2\implies A=\cfrac{82.21^2}{4\pi }\implies A\approx 538.1[/tex]

Answer:

6p + 7c = 50

4p + 5c = 34

(where p is the number of pizzas and c is the number of bags of chicken wings)

We need to buy 6 pizzas and 2 bags of chicken wings in order to spend a total of $50, AND for each of the 17 people to have 2 servings of food.

Step-by-step explanation:

Let p = number of pizzas

Let c = number of bags of chicken wings

Equation 1

Given:

⇒ 6p + 7c = 50

Equation 2

Given:

⇒ 4p + 5c = 34

Equation 3

Multiply Equation 2 by 1.5:

⇒ 6p + 7.5c = 51

Subtract Equation 1 from Equation 3 and solve for c:

⇒ 0.5c = 1

⇒ c = 2

Substitute found value of c into Equation 2 and solve for p:

⇒ 4p + 5(2) = 34

⇒ 4p + 10 = 34

⇒ 4p = 24

⇒ p = 6

Therefore, we need to buy 6 pizzas and 2 bags of chicken wings in order to spend a total of $50, AND for each of the 17 people to have 2 servings of food.

Answer:

A. $32

Step-by-step explanation:

Normal price

1 chair cost = $79.99

2 chairs = $79.99 × 2

= $159.98

Discount price of 2 chairs

40% of $79.99

= 40/100 × 79.99

= 0.4 × 79.99

= 31.996

Approximately

$32

A. $32

Answer:

y = 2/3x + 3

Step-by-step explanation:

Use rise over run (y2 - y1) / (x2 - x1)

Plug in the points:

(3 - 1) / (0 + 3)

= 2/3

So, the slope is 2/3

Plug this and another point into y = mx + b to find b:

y = mx + b

3 = 2/3(0) + b

3 = b

Then, plug b and the slope into y = mx + b

y = 2/3x + 3 is the equation of the line

Answer:

d₃ = 803.9 Miles

Step-by-step explanation:

d₁ = 560 Miles

R₁ = N35⁰E

d₂ = 410 Miles

R₂ = S76⁰E

d₃ = ?

α = 35⁰+76⁰ = 111⁰

We can apply the Law of Cosines as follows

d₃ = √(d₁² + d₂² - 2*d₁*d₂* Cos α)

⇒  d₃ = √(560² + 410² - 2*560*410* Cos 111⁰) = 803.9 Miles

Answer: C the price of a water bottle

Step-by-step explanation: The problem states that the energy bar is $2 so it can’t be D. The math problem also states how many players they have so it’s not B. The math problem says how much they paid which is $77 so it’s not A. However the problem doesn’t state how much the price of a water bottle is so therefore it is C.

Answer:

c

Step-by-step explanation: i got it right on the quiz

Answer:

P=L10(2)+W4(2)=28ft

the perimeter of the rectangle is L(2)+w(2)=perimeter.

Answer:

25

Step-by-step explanation:

14 x 25 gives you 350

Answer:

25 is the answer for people that are in k12

Answer:

Slope: [tex]\boxed {7}[/tex]

Y-intercept: [tex]\boxed {-4}[/tex]

Step-by-step explanation:

About the Slope-Intercept Form equation, the variable [tex]m[/tex] is the slope and variable [tex]b[/tex] is the y-intercept. So, according to the following expression, the slope would be [tex]7[/tex] and the y-intercept would be [tex]-4[/tex]:

-Slope-Intercept Equation:

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

Slope: [tex]m[/tex]

Y-intercept: [tex]b[/tex]

-The following expression:

[tex]y = 7x - 4[/tex]

Slope: [tex]\boxed {7}[/tex]

Y-intercept: [tex]\boxed {-4}[/tex]

Answer:

281.15 cm²

Step-by-step explanation:

semi perimeter ( s ) = ( a + b + c ) / 2

=( KL + LM + KM ) / 2

=(32+21+27)/2

= 80/2

=40

Area of triangle =

[tex] \sqrt{s \: (s - a) \: (s - b)(s - c)} [/tex]

[tex] \sqrt{40(40 - 32)(40 - 21)(40 - 27)} [/tex]

[tex] \sqrt{40 \times 8 \times 19 \times 13} [/tex]

[tex] \sqrt{79040} [/tex]

[tex]281.15cm {}^{2} [/tex]

Answer:

40 carnations

Step-by-step explanation:

Using the principle of proportional relationship, the number of carnations to be used in the bouquet is 40

Setting up the proportional relationship thus :

2 roses = 5 carnations ----(1)

16 roses = P carnations - - - - - 2)

Solve for p :

Cross multiply :

2p = 16 × 5

2p = 80

p = 80 /2

p = 40

Therefore, the Number of carnations to be used is 40

Learn more : https://brainly.com/question/18581754

Answer:

it is 6.5

Step-by-step explanation:

Answer:

6 people per car

Step-by-step explanation:

divide 18 people by 3 cars to get people per cars.

please rate and mark as brainlest.

Answer:

1.75

Step-by-step explanation:

Answer:

Step-by-step explanation:

11/4 / 5/7 = 11/4 x 7/5 = 11x7 / 5x4 = 77/20