ALOT KF POINTS PLEASE HELP The measures of two exterior angles are given in the figure below.
Choose an equation that could be used to represent one of the exterior
angles and a logical conjecture about the exterior angles of a triangle.

Answer:

16

Step-by-step explanation:

18,903

[tex] \huge\mathbb{ \underline{SOLUTION :}}[/tex]

[tex]\small\leadsto\bold{Substitute:}[/tex]

[tex]\longrightarrow\sf{ \dfrac{6}{7}= Ce^{k*0}}[/tex]

[tex]\longrightarrow\sf{\dfrac{6}{7}= C*e^0}[/tex]

[tex]\longrightarrow\sf{e^0=1}[/tex]

[tex]\therefore\sf{C= \dfrac{6}{7} }[/tex]

[tex]\therefore\sf{5=Ce^{k*5}}[/tex]

[tex]\\[/tex]

[tex] \bold{Solve \: to \: find \: k:}[/tex]

[tex]\longrightarrow\sf{5 = \dfrac{6}{7} *e^{k5}}[/tex]

[tex]\longrightarrow\sf{ \dfrac{7*5}{6} *e^{5k}}[/tex]

[tex]\longrightarrow\sf{In=( \dfrac{35}{6} ) = 5k}[/tex]

[tex]\longrightarrow\sf{1.76=5k}[/tex]

[tex]\longrightarrow\sf{k=\dfrac{1.76}{5} = 0.352}[/tex]

[tex]\huge \mathbb{ \underline{ANSWER:}}[/tex]

[tex]\large\sf{\boxed{\sf \dfrac{6}{7}= e^{0.352*t}}}[/tex]

5x-30y=-35

Divide both the side by 5 and we get

x-6y = -7

x = 6y -7

Answer:

x=-7+6y

You simply need to add 30y and then divide by 5 to isolate the variable.

Answer:

5,000

[tex]50000 \div 10 = 5000[/tex]

Answer:

C. 8√3

Step-by-step explanation:

* = multiply or times

To find √192 in its simplest form we need to divide it by a square number like 64.

192/64 = 3

√192 = √64 * √3 = 8√3

Answer:

400$

Step-by-step explanation:

Let C.P. of the watch = Rs. 100

When profit =5%; S.P. = Rs. (100+5)

= Rs. 105

and when profit = 11%;

S.P. = Rs. (100+11)

=Rs.111

Difference of two selling prices

= Rs. 111-Rs.105 = Rs.6

When watch sold for Rs. 6 more; then C.P. of the watch = Rs.

100

6

When watch sold for Rs. 24 more; then C.P. of the watch = Rs.

100

6

×

24

= Rs.

100

×

24

6

=400

[tex]\begin{cases} -5x+y=-3\\ 3x-8y=24 \end{cases} \\\\\\ \stackrel{\textit{using the 1st equation}}{-5x+y=-3}\implies \underline{y=-3+5x} \\\\\\ \stackrel{\textit{substituting on the 2nd equation}}{3x-8(\underset{y}{-3+5x})=24}\implies 3x+24-40x=24\implies 3x-40x=0 \\\\\\ -37x=0\implies \boxed{x=0}~\hfill \underline{y=-3+5(\stackrel{x}{0})}\implies \boxed{y=-3} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill (0~~,~~-3)~\hfill[/tex]

Answer:

( 0, -3 )

Step-by-step explanation:

-5x + y = -3 ⇒ ( 1 )

3x - 8y = 24 ⇒ ( 2 )

We can make y the subject of equation 1.

y = 5x - 3 ⇒ ( 3 )

Now let us take equation 2.

Here we can replace y with ( 5x - 3 ) to find the value of x.

Value of x.

3x - 8y = 24

3x - 8 (5x - 3) = 24

3x - 40x + 24 = 24

-37x = 0

x = 0

Now let us take equation 3 to find the value of y.

Here we can replace x with 0.

Let us find it now.

y = 5x - 3

y = 5 × 0 - 3

y = 0 - 3

y = -3

Now, let us write the answer as an ordered pair.

( x, y )

( 0, -3 )

Answer:Sanjay has 8

Step-by-step explanation: Because 8x4 equals 32 so thats how much tanya has a 32+8 equals 40. This is what I did I knew 10x4 is 40 so that couldn't be it so then I tried 8 because nine x four is 36 which would be to high so I tried 8 and it was perfect hope this helps.

If Combined, Tanya and Sanjay have 40 pens. If Tanya has four times as many pens as Sanjay, then Sanjay have 8 pens.

Two or more expressions with an equal signs is called as Equation.

Given that Tanya and Sanjay have 40 pens. If Tanya has four times as many pens as Sanjay, We need to find how many pens sanjay has.

Let sanjay has x number of pens.

Tanya has four times as many pens as Sanjay

So 4 times means four multiple of sanjay pens.

Tanya has four times as many pens as Sanjay can be write as 4x.

Combined of tanya and sanjay has 40 pens.

Combined means adding.

x+4x=40

Add the like terms

5x=40

Divide both sides by 5.

x=8

So Sanjay has eight pens and Tanya has 4(8)=32 pens.

Hence Sanjay have eight pens.

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The total income and expenditure in September are "Income is R 106 360.00 and expenditure is R 4 850.00." Option C. This is further explained below.

Generally, the equation for  Insurance and investment  is  mathematically given as

II= 42% of the balance

II = 0.42*0.64A

II= 0.2688A

Generally, the equation for Total After All other exp is  mathematically given as

Texp = 0.64A – 0.2688A

Texp= 0.3712A

Total After All other exp = 111210

subbing ahead and equating we have

111210 = 0.3712 A

Therefore

A = 299596

The total income is 299596

Therefore, the calculation for the expense is given as

Expense = 0.25A + 0.11A + 0.2688A + 4850

Expense= 0.6288A + 4850 = (0.6288*299596) + 4850

Expense= 193236

The Expense is 299596

In conclusion,  At the end of September, Agri-Small Business's minimal spending on gasoline for their fleet amounted to R 4 850.00, and they still had a balance of R106 360.00 in their account. The majority of the remaining revenue was allocated to insurance and investments by the business, which accounted for 42% of the total. Wages and salaries accounted for 25% of the company's income in September. The overall revenue and expenses for the month of September were as follows: the income was R 106 360.00, and the expenses were R 4 850.00. Option C.

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Answer:

Step-by-step explanation:

find the prime factors of given numbers:

126= 2*3*3*7- this side can be cut into any number here or combination of numbers as per factors

108= 2*2*3*3*3 - same as above

As per prime factors, the squares can be of  sizes:

2×2, 3×3, 6×6, 9×9 and 18×18

The least number can be obtained with the biggest size option 18×18, this will give 7*6=42 square

Answer:

x = 31

Step-by-step explanation:

Given:

f(x) =

[tex]2 {x}^{2} - 1[/tex]

g(x) = x + 2

We will first find g(2).

g(2) = 2 + 2 = 4

Next we will find f(g(2)).

f(g(2))= f(4) =

[tex]2( {4}^{2} ) - 1 \\ = 2(16) - 1 \\ = 32 - 1 \\ = 31[/tex]

The number of years it would take sales to reach $1,750,000 is 14.65 years.

The formula that can be used to determine the number of years it would take for the sales to reach $1,750,000 is:

Number of years : In (FV / PV) / r

Where:

Number of years : In ($1,750,000 / 850,000) / 0.04931998

Number of years : In (2.06) / 0.04931998

Number of years : 14.65 years

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If Caisse can download a maximum of 1000 mb of songs or movies then the inequality that represents the number of movies and songs that Caisse downloads each month is 85x+4y<1000.

Given that Caisse can download a maximum of 1000 mb of songs or movies to her smartphone each month. the file of each movie is 85mb, and the file of each song is 4mb.

We are required to find the inequality that represents the number movies and songs that Caisse downloads each month.

Inequality is like an equation that shows the relationship between variables that are expressed in greater than, less than , greater than or equal to , less than or equal to sign.

let the number of movies be x and the number of songs be y.

According to question Caisse cannot download more than 1000 mb, so we will use less than towards equation.

It will be as under:

85x+4y<1000.

Hence if Caisse can download a maximum of 1000 mb of songs or movies then the inequality that represents the number of movies and songs that Caisse downloads each month is 85x+4y<1000.

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The circumference of the pad to the nearest tenth is 39.6 meters

The circumference of a circle is the arc length of the circle, as if it were opened up and straightened out to a line segment. It is also known as the perimeter of a circle.

The formula for calculating the circumference of a circle is expressed as;

C = 2πr

where

π = 3.14

r is the radius of the circle

Given the following parameters

π = 3.14

r = 6.3m

Substitute to have:

C = 2 * 3.14 * 6.3

C = 6.28 * 6.3

C = 39.564

Hence the circumference of the pad to the nearest tenth is 39.6 meters

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The limit of j (x) as x approaches 3 is 4.

According to the question, A line begins at an open circle (2, 6) on a coordinate plane and descends through ( -2, 2). At, a complete circle is (3, 6). From a solid circle (2, 3), a curve leads to an open circle (3, 4). From the open circle to the closed circle, a line runs (6, 5).

From the graph, it can be seen that the limit of the function j(x) as the value of x approaches 3 is 4.

A diagram or pictorial representation that organizes the depiction of data or values is known as a graph.

The relationships between two or more items are frequently represented by the points on a graph.

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Answer:

4

Step-by-step explanation:

egg 2023

Based on the given entries that Jonathan Shaw owes and owns, the Balance Sheet can be drawn below.

The assets will go to the right side of the sheet and the liabilities and equity will go to the left.

                                            Jon's Shop of Gifts Balance Sheet

Assets                                                                                          Liabilities

Cash                                    $2,556           Bank loan                    $19,000

Accounts Receivable:         $450             Accounts Payable -           $900

R. Gregory                                                 Ceramic supply

Accounts Receivable:         $1,860          Accounts Payable -           $2,900

R. Gregory                                                 Jose's Art Co.

Supplies                               $1,000         Total liabilities                 $22,800

Furniture                              $10,300       Equity

Equipment                           $20,000       Jonathan Shaw capital  $51,166

Automobiles                       $37,800         Total equity                   $51,166

Total assets                       $73,966        Total liabilities and          $73,966

                                                                  equity

The equity can be found as:

= Assets - liabilities

= 73,966 - 22,800

= $51,166

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The volume of the solids are 240 cubic yards and 125.6 cubic cm

The complete question is added as an attachment

Solid 1

The shape is a rectangular prism.

The volume of a rectangular prism is

Volume = Length * Width * Height

So, we have

Volume = 8 yd * 5 yd * 6 yd

Evaluate

Volume = 240 cubic yards

Hence, the volume of the solid is 240 cubic yards

Solid 2

The shape is a cylinder.

The volume of a rectangular prism is

Volume = πr²h

So, we have

Volume = 3.14 * 2^2 * 10

Evaluate

Volume = 125.6 cubic cm

Hence, the volume of the solid is 125.6 cubic cm

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Divide the interval [3, 5] into [tex]n[/tex] subintervals of equal length [tex]\Delta x=\frac{5-3}n = \frac2n[/tex].

[tex][3,5] = \left[3+\dfrac0n,3+\dfrac2n\right] \cup \left[3+\dfrac2n,3+\dfrac4n\right]\cup\left[3+\dfrac4n,3+\dfrac6n\right]\cup\cdots\cup\left[3+\dfrac{2(n-1)}n, 3+\dfrac{2n}n\right][/tex]

The right endpoint of the [tex]i[/tex]-th subinterval is

[tex]r_i = 3 + \dfrac{2i}n[/tex]

where [tex]1\le i\le n[/tex].

Then the definite integral is given by the Riemann sum

[tex]\displaystyle \int_3^5 \sqrt{8+x^2} \, dx = \lim_{n\to\infty} \sum_{i=1}^n \sqrt{8+{r_i}^2} \Delta x = \boxed{\lim_{n\to\infty} \frac2n \sum_{i=1}^n \sqrt{17 + \frac{12i}n + \frac{4i^2}{n^2}}}[/tex]

Answer:

choice C. Yes, this image proves the pythagorean theorem is true because 9 + 16 = 25

Step-by-step explanation:

The equation that can be used to determine after how many years the town will have of 900 acres of undeveloped land is 900 = 3400 * (0.827)^t

From the question, the given parameters are:

Initial value = 3400 acres

Rate, r = 17.3%

Final value = 900

An exponential function is represented using the following equation

y = a(1 - r)^t

Substitute the known values in the above equation

y = 3400 * (1 -17.3%)^t

Express 17.3% as decimal

y = 3400 * (1 -0.173)^t

Evaluate the difference

y = 3400 * (0.827)^t

Recall that:

Final value = 900

So, we have

900 = 3400 * (0.827)^t

Hence, the equation that can be used to determine after how many years the town will have of 900 acres of undeveloped land is 900 = 3400 * (0.827)^t

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Considering the definition of conditional probability, the probability that the team will win the second game given that they have already won the first game is 45.33%.

Probability is the greater or lesser chance that a given event will occur.

In other words, the probability establishes a relationship between the number of favorable events and the total number of possible events.

Conditional probability is the probability that a given event will occur given that another event occurs. The conditional probability operator is the │ sign.

In other words, the conditional probability is the probability of some event A , given the occurrence of some other event B and is denoted by P(A|B) and is read “the probability of A , given B ”.

Then, when an event influences the outcome of a second event, the probability of the second event is said to be a conditional probability and is calculated using the expression:

P(A|B)= P(A∩B) ÷ P(B)

where:

In this case, you know that:

Replacing in the definition of conditional probability:

P(A|B)= 0.34 ÷ 0.75

P(A|B)= 0.4533= 45.33%

Finally, the probability that the team will win the second game given that they have already won the first game is 45.33%.

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The mass of the CO2 produced IS 630 Kg

Gasoline is a kind of fuel that is composed mostly of isooctane. In most engines, gasoline is widely used hence the demand for the product is high. We know that the combustion of an alkane (of which gasoline is one) would produce carbon dioxide and water according to a balanced reaction equation.

The balanced reaction equation for the combustion of gasoline is shown in the image attached to this answer.

Since  a Puerto Rico hospital uses 3 gallons of gasoline per hour, and there are 24 hours in a day, it the follows that 72 gallons of gasoline are used per day. This 72 gallons is the equivalent of 272.88 L

Now;

Given that the density of gasoline = 748.9 g/L

Mass of gasoline = 748.9 g/L * 272.88 L = 204 Kg

Number of moles of gasoline =  204 * 10^3/114 g/mol = 1789.5 moles

If 2 moles of gasoline produces 16 moles of CO2

1789.5 moles produces  1789.5 moles * 16 moles/2 moles = 14316 moles

Mass of CO2 =  14316 moles * 44 g/mol = 630 Kg

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Based on the angle-angle similarity theorem (AA), the pair of ratios that are equal is: AE/EC = AD/DB.

The angle-angle similarity theorem (AA) states that two triangles are similar to each other if they have two corresponding congruent angles, and therefore, the ratios of their corresponding side lengths are equal. This means their corresponding side lengths are proportional in measure.

Given that angle ADE ≅ angle ABC, we also know that:

Angle EAD ≅ CAB.

Thus, this implies that triangle EAD is similar to triangle CAB based on the angle-angle similarity theorem (AA). Therefore, the ratios of their corresponding side lengths are equal.

Thus, the ratios that are equal to each other would be:

AE/EC = AD/DB.

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A  value of 24 is 2.5 standard deviations away from the mean

The given parameters about the distribution are:

Mean = 18

Standard deviation = 4

Value = 24

Let the number of standard deviations away from the mean be x.

The value of x is calculated using

Mean + Standard deviation * x = Value

Substitute the known values in the above equation

18 + 4 * x = 24

Subtract 18 from both sides of the equation

4 * x = 6

Divide both sides of the equation by 4

x = 1.5

Hence, a value of 24 is 2.5 standard deviations away from the mean

So, the complete parameters about the distribution are:

Mean = 18

Standard deviation = 4

Value = 24

24 is 2.5 standard deviations away from the mean

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Answer:

  x = {π/6, π/2, 5π/6, 3π/2}

Step-by-step explanation:

The equation can be solved using a double-angle trig identity and factoring.

Dividing the equation by 7 and substituting for sin(2x), we have ...

  7sin(2x) = 7cos(x)

  sin(2x) = cos(x)

  2sin(x)cos(x) = cos(x)

  2sin(x)cos(x) -cos(x) = 0

  cos(x)(2sin(x) -1) = 0

The product of factors is zero when one or more of the factors is zero.

  cos(x) = 0   ⇒   x = {π/2, 3π/2}

  2sin(x) -1 = 0   ⇒   x = arcsin(1/2) = {π/6, 5π/6}

Solutions in the given interval are ...

  x = {π/6, π/2, 5π/6, 3π/2}

__

Additional comment

When the equation is of the form f(x) = 0, then the x-intercepts of f(x) are its solutions. We can rearrange this one to ...

  sin(2x) -cos(x) = 0

The solutions identified above match those shown in the graph.

Answer:

we write in form of (a x 10^n)

5.702 x 10⁷

Answer:

5.702 x 10^7

Step-by-step explanation:

In scientific notation, a number in the ones place is raised to a power of 10: the power will be positive if the original number is huge, and negative if the original number is small.

The number 57,020,000 is a huge number. We simply move the decimal 7 places to the left to get 5.072, and since we moved the decimal 7 places, 10 is raised to the power of 7.

Brainliest, please :) Hope this helps!

Step-by-step explanation:

It is just where it crosses the x axis

6) -3, -4

7) 1, -6

8) -5, -6

9) 3, -2.5

Based on the calculations, the interest rate on the stock in four (4) years is equal to 7.1%.

Given the following data:

Amount borrowed (Principal) = $22,000.

Simple interest, I = $78.40.

Time = 4 year.

To determine the interest rate on the stock in four (4) years:

Mathematically, simple interest can be calculated by using this formula:

I = PRT

Where:

Making R the subject of formula, we have:

R = I/PT

Substituting the given parameters into the formula, we have;

R = 6260/(22,000 × 4)

R = 6260/(88,000)

Interest rate = 0.071 = 7.1%.

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Answer:

The intervals represent the domain, or the values on the horizontal axis.

When x ≤ -3, the graph should form a straight line at y = 3. Because the interval includes x = -3, the rightmost part of the line should be capped with a closed dot. The line should continue for infinity to the left.

When -3 < x < 4, the graph should form a line with the equation (2x + 1). Because the interval does not include the endpoints, the endpoints should have open dots.

When x ≥ 4, the graph should form a straight line at y = -4. Because the interval includes x = 4, the leftmost endpoint should be a closed dot. The right of the line should continue for infinity.

**The included graph does not take the endpoints into account

Answer:

See attached for graph.

Step-by-step explanation:

Piecewise functions have multiple pieces of curves/lines where each piece corresponds to its definition over an interval.

Given piecewise function:

[tex]f(x)=\begin{cases}3 & \textsf{if }x\leq -3\\2x+1 & \textsf{if }-3 < x < 4 \\ -2 & \textsf{if } x\geq 4 \end{cases}[/tex]

Therefore, the function has three definitions:

[tex]f(x)=3 \quad \textsf{when x is less than or equal to 3}[/tex]

[tex]f(x)=2x+1 \quad \textsf{when x is more than -3 and less than 4}[/tex]

[tex]f(x)=-2 \quad \textsf{when x is more than or equal to 4}[/tex]

When graphing piecewise functions:

First piece of function

Substitute the endpoint of the interval into the corresponding function:

[tex]\implies f(-3)=3 \implies (-3,3)[/tex]

Place a closed circle at (-3, 3).

As this piece of the function is f(x) = 3 for any value of x that is less than or equal to -3, draw a horizontal straight line to the left from the closed circle.  Add an arrow at the end.

Second piece of function

Substitute the endpoints of the interval into the corresponding function:

[tex]\implies f(-3)=2(-3)+1=-5 \implies (-3,-5)[/tex]

[tex]\implies f(4)=2(4)+1=9 \implies (4,9)[/tex]

Place an open circle at (-3, -5) and (4, 9).

Join the points with a straight line.

Third piece of function

Substitute the endpoint of the interval into the corresponding function:

[tex]\implies f(4)=-2 \implies (4,-2)[/tex]

Place a closed circle at (4, -2).

As this piece of the function is f(x) = -2 for any value of x that is more than or equal to 4, draw a horizontal straight line to the right from the closed circle.  Add an arrow at the end.

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