Triangle ABC, m/A = 15°, a = 9, and b = 12. Find c

Answer:

a = 1, b = 1, c = 0

Step-by-step explanation:

First, we need to find the vertex coordinates:

x (vertex) =

[tex]x(vertex) = \frac{ - b}{2a} = \frac{ - 1}{2 \times 1} = \frac{ - 1}{2} = - 0.5[/tex]

[tex]y(vertex) = { (- 0.5})^{2} + ( - 0.5) = 0.25 - 0.5 = - 0.25[/tex]

Now, that we have the vertex coordinates, we need to pick three x values to either side of the vertex (as I did in the photo)

Answer:

To determine which option is the most cost-effective, you can use some simple math. Let's assume you need to park for 8 hours:

Park and Ride:

Parking cost: 8 hours x £0.40 = £3.20

Bus fare: £0.60 x 2 (round trip) = £1.20

Total cost: £4.40

Free parking at the railway station:

Train fare: £3.50 x 2 (round trip) = £7.00

Total cost: £7.00

Based on the calculations above, the Park and Ride option is cheaper for an 8-hour parking period. However, you should also consider factors such as convenience and travel time when making your decision. If the railway station is closer to your destination or has more frequent train services, it may be the better option despite the higher cost.

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Answer:

558

Step-by-step explanation:

To find the geese population at Whitney National Park in 2000, we need to add 24% of the population in 1999 to the population in 1999.

First, we need to calculate 24% of 450:

24% of 450 = 0.24 x 450 = 108

So the increase in the geese population from 1999 to 2000 is 108.

To find the population in 2000, we need to add this increase to the population in 1999:

Population in 2000 = Population in 1999 + Increase

Population in 2000 = 450 + 108

Population in 2000 = 558

Therefore, the geese population at Whitney National Park in 2000 was 558.

Answer:

x = 21

Step-by-step explanation:

Given exponential equation:

[tex]7^{3-5x}=\left(\dfrac{1}{49}\right)^{2x+9}[/tex]

Rewrite 49 as 7²:

[tex]7^{3-5x}=\left(\dfrac{1}{7^2}\right)^{2x+9}[/tex]

[tex]\textsf{Apply the exponent rule:} \quad \dfrac{1}{a^n}=a^{-n}[/tex]

[tex]7^{3-5x}=\left(7^{-2}\right)^{2x+9}[/tex]

[tex]\textsf{Apply the exponent rule:} \quad (a^b)^c=a^{bc}[/tex]

[tex]7^{3-5x}=7^{-2(2x+9)}[/tex]

Simplify the exponent:

[tex]7^{3-5x}=7^{-4x-18}[/tex]

[tex]\textsf{Apply the exponent rule:} \quad a^{f(x)}=a^{g(x)} \implies f(x)=g(x)[/tex]

[tex]3-5x=-4x-18[/tex]

Add 4x to both sides:

[tex]3-5x+4x=-4x-18+4x[/tex]

[tex]3-x=-18[/tex]

Subtract 3 from both sides:

[tex]3-x-3=-18-3[/tex]

[tex]-x=-21[/tex]

Divide both sides by -1:

[tex]x=21[/tex]

Therefore, the value of x is 21.

Answer:

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Solve the exponential equation for x:

7^3-5x=(1/49)^2x+9

6 dogs are the bare minimum that might weigh more than 24 kg.

What do minimum and maximum value mean?

Rearrange the function using fundamental algebraic concepts to get the value of x when the derivative equals 0. This response gives the x-coordinate of the function's vertex, which is where the maximum or minimum will occur. To find the minimum or maximum, rewrite the solution into the original function.

For example, if we have a set of numbers {2, 4, 6, 8, 10}, the minimum value is 2 because it is the smallest number in the set, while the maximum value is 10 because it is the largest number in the set.

The minimum of the values present in the interval 20 to 40 is 6

The maximum of the values present in the interval 20 to 40 is (12+6) = 18

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Step-by-step explanation:

If you are using a fair six - sided cube , there are two numbers out of six that are greater than 4  ( 5 and 6 )

 sooo:    2 out of 6   or  1/3 should be greater than 4

1/3 * 20 = 6 2/3 = ~ 7

Answer:

(4,2) represents the number of ways to choose 2 items from a set of 4 distinct items. The formula for C(n,r) is n! / (r! * (n-r)!), where n is the total number of items and r is the number of items being chosen. Plugging in the values for C(4,2), we get: C(4,2) = 4! / (2! * (4-2)!) = 24 / (2 * 2) = 6 Therefore, there are 6 ways to choose 2 items from a set of 4 distinct items.

0 / 350

The value of the given combination C(4, 2) by applying the combination formula in factorial form is equals to option 6.

To evaluate C(4, 2), we use the combination formula, also known as "n choose r" or "C(n, r)",

which calculates the number of ways to choose r items from a set of n distinct items without considering their order. The formula for C(n, r) is:

C(n, r) = n! / (r! × (n - r)!)

Where "!" denotes the factorial of a number, which is the product of all positive integers up to that number.

For example,

4! = 4 × 3 ×2 × 1

   = 24.

Now, let's plug the values into the formula for C(4, 2):

C(4, 2) = 4! / (2! × (4 - 2)!)

= 4! / (2! × 2!)

= (4 × 3 × 2 × 1) / ((2 × 1) × (2 × 1))

= (24) / (4)

= 6

Therefore , the value of the combination C(4, 2) equals  to option 6.

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One possible set of points: (-9, 1), (-3, 5), (3, 9) which would have a positive linear association if they were graphed in a scatterplot.

A scatterplot is a graph that displays the relationship between two quantitative variables. It is a useful tool for exploring patterns and relationships in data, and can help identify trends, outliers, and potential correlations.

In the given question,

To create a set of 3 points with a positive linear association, we want to choose three points where the y-coordinate increases as the x-coordinate increases. Here's one possible set of points:

(-9, 1), (-3, 5), (3, 9)

If we graph these points on a scatterplot, we can see that there is a clear positive trend. As x increases, y also increases, suggesting a positive linear association between the two variables.

Note that there are many other sets of points we could choose that would also have a positive linear association. The key is to choose points where the y-coordinate tends to increase as the x-coordinate increases.

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Answer:

hope it will help you ( ꈍᴗꈍ)(✿^‿^)(✿^‿^)!!!

Answer:

The answer to your problem is, 6a

How to find the GCF:

6a(x²+x+1)

Use that problem

The answer to your problem is, 6a

Two examples that show the use of data and probability are an article about covid and an article about the use of predictive analysis.

Example 1: According to a recent article in The New York Times, data from the Centers for Disease Control and Prevention (CDC) shows that individuals who are fully vaccinated against COVID-19 are much less likely to be hospitalized or die from the virus. The article cites a study that found the Pfizer-BioNTech vaccine was 91 percent effective in preventing hospitalization and 95 percent effective in preventing death. This data reinforces the importance of vaccination in preventing severe illness and death from COVID-19.

Example 2: A recent article in The Wall Street Journal discusses the use of predictive analytics in the insurance industry. The article explains that insurance companies are increasingly using data and probability models to predict and mitigate risks associated with climate change, natural disasters, and other potential events that could result in insurance claims.

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The distance between Bert and Ernie is 8.8 miles.

What is law of cosine?

According to a trigonometry rule, the square of a side in a plane triangle is equal to the total of the squares of the other sides minus twice that amount, along with the cosine of the angle that separates them.

Here using law of cosine we can find the distance between Bert and Ernie. Then,

[tex]a^2=b^2+c^2-2ab cos(A)[/tex]

Here a = BC , b = 5 mi , c = 6.5 mi and A = 100° then,

=> [tex]BC^2 = 5^2+6.5^2-2\times5\times6.5\times cos (100\textdegree)[/tex]

=> [tex]BC ^2= 25+42.25-65\times(0.1736)[/tex]

=> [tex]BC^2= 78.534[/tex]

=> BC = 8.8 miles.

Hence the distance between Bert and Ernie is 8.8 miles.

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Answer:

To find the inverse function of f(x) = 4(3x + 2), we need to solve for x in terms of f(x) and then interchange the roles of x and f(x) in the expression to obtain the inverse function.

Let y = f(x) = 4(3x + 2)

Dividing both sides by 4, we get:

y/4 = 3x + 2

Subtracting 2 from both sides, we get:

y/4 - 2 = 3x

Dividing both sides by 3, we get:

(y/4 - 2) / 3 = x

Hence, the inverse function is:

f^-1(x) = (x/4 - 2) / 3

Or we can also write it as:

f^-1(x) = (1/3)x/4 - 2/3

Therefore, the inverse function of f(x) = 4(3x + 2) is f^-1(x) = (1/3)x/4 - 2/3.

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We can conclude that the difference between p1 and p2 is statistically significant at the 5% level of significance.

The confidence interval and significance test in part A both provide similar information. The significance test in part A tests if the difference between p1 and p2 is statistically significant, while the confidence interval provides an estimated range of values for the true difference between p1 and p2 with a certain degree of confidence (95% in this case).A confidence interval is a range of values that we believe will include a population parameter with a specified level of confidence.

It can be computed to estimate the population mean or the difference between two population means, such as p1 and p2.In contrast, a significance test assesses whether the difference between two population proportions is statistically significant.

The test calculates a p-value, which is the likelihood of obtaining the observed difference between two proportions, assuming the null hypothesis (that there is no difference between the two proportions) is true. A p-value less than the level of significance (usually 0.05) indicates that the difference between the two proportions is statistically significant, while a p-value greater than the level of significance indicates that the difference is not statistically significant.

Both the confidence interval and the significance test inform us about the difference between two population proportions. The confidence interval provides a range of plausible values for the difference, while the significance test tells us whether the difference is statistically significant or not. In this particular case, since the confidence interval does not contain zero,

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(a) we can simplify the expression [tex]x^3 - 3x - 4\\[/tex]:

[tex]x^3 - 3x - 4[/tex]

(b) we cannοt simply switch the terms arοund and expect the sum tο be the same.

An algebraic expressiοn is a mathematical phrase that can cοntain numbers, variables, and οperatοrs, such as additiοn, subtractiοn, multiplicatiοn, and divisiοn.

(a)

The expression [tex]-(2^3)+x-3[/tex] means [tex]-(2^3) + x - 3[/tex] since the expοnent οperatοr (^) has higher precedence than the negatiοn οperatοr (-). Using the οrder οf οperatiοns, we can simplify the expressiοn:

[tex]-2^3+x-3 = -(2^3) + x - 3 = -(8) + x - 3 = x - 11[/tex]

Similarly, we can simplify the expression [tex]x^3 - 3x - 4\\[/tex]:

[tex]x^3 - 3x - 4[/tex]

(b)

The sum of [tex]-2^3+x-3[/tex] and [tex]x^3-3x-4[/tex] is not equal to the sum of [tex]x^3-3x-4[/tex]and [tex]-2x^3+x-3[/tex].This is because additiοn is nοt cοmmutative fοr nοn-like terms, meaning that changing the οrder οf the terms in a sum can change the value οf the sum.

Hence, we cannοt simply switch the terms arοund and expect the sum tο be the same.

We wοuld need tο actually perfοrm the additiοn in bοth cases tο determine if they are equal.

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So, you need to deposit $628.86 monthly to accumulate $100,000 in 15 years with an APR of 7%.

To create a college fund for your child, you must determine the amount you need to deposit every month. The fund that offers an APR of 7% will help you accumulate the amount in the future. Here are the steps to find out how much you need to deposit monthly.
Step 1: Determine the total amount required for college funds.
The first step is to determine the total amount you need to pay for college funds. Suppose you want to create a college fund for your child that requires $100,000 in 15 years. Use a present value calculator or online present value calculator to determine the future value of the college fund.
Step 2: Determine the interest rate
The second step is to determine the interest rate you will receive on your savings. Suppose the fund offers an APR of 7%.
Step 3: Determine the number of years
The third step is to determine the number of years you have until you need the money. Suppose you have 15 years.
Step 4: Use the annuity formula
The fourth step is to use the annuity formula to determine how much you need to deposit every month. The formula is:
PMT = FV × i / ((1 + i)n - 1)
Where PMT is the monthly payment, FV is the future value, i is the interest rate, and n is the number of payments.
Using the given values:
PMT = 100,000 × 0.07 / ((1 + 0.07)^15 - 1)
PMT = 100,000 × 0.07 / 11.283
PMT = $628.86

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The new variance is 0.0625 / n

We can use the following formula to calculate the variance of a data set

variance = (sum of (x - mean)^2) / (number of data points)

where x is a data point and mean is the mean of the data set.

If the mean cost of a box of Cheerios Oat Crunch is $4.00 and the variance is 0.35, we can find the standard deviation as follows

standard deviation = square root of variance = sqrt(0.35) = 0.59

Now, if the price increases by 25 cents a box, the new mean cost will be

new mean = $4.00 + $0.25 = $4.25

To find the new variance, we need to calculate the sum of (x - mean)^2 for the new data set and divide by the number of data points. Let's assume we are still considering the same number of boxes.

sum of (x - mean)^2 = [(4.25 - 4)^2 × n] = 0.0625 × n

where n is the number of data points.

Therefore, the new variance can be calculated as

new variance = (sum of (x - mean)^2) / (number of data points) = 0.0625 / n

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Backing into a driveway or an alley on the right side, none of the options are correct

A) Backing into a driveway or alley on the right side is not necessarily illegal in most states. However, some states may have specific laws or regulations related to this maneuver, so it is important to check local laws.

B) Backing into a driveway or alley on the right side can be risky and may increase the likelihood of collisions, particularly if the driver is not paying close attention or if the view is obstructed. However, it does not always cause collisions and may be necessary in certain situations.

C) The safest turnabout maneuver depends on the specific situation and the layout of the road. In some cases, backing into a driveway or alley may be the safest option, while in other situations, a three-point turn or U-turn may be safer.

D) Whether to perform a backing maneuver in heavy traffic depends on the situation. In general, it is advisable to avoid backing up in heavy traffic if possible, as it can increase the risk of collisions. However, if there is no other option, the driver should proceed with caution and take all necessary precautions to ensure safety.

Therefore, the none of the options are correct

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The given question is incomplete, the complete question is:

Backing into a driveway or an alley on the right side a.is illegal in most states b. often causes collisions .c is the safest turn about maneuver d. should be done only in heavy traffic

The inverse of the function y = 16x² + 17 is y = ±√(x - 17)/16

from the question, we have the following parameters that can be used in our computation:

y = 16x² + 17

So, we have

x = 16y² + 17

Make y the subject

This gives

y = ±√(x - 17)/16

Hence, the inverse of the function is y = ±√(x - 17)/16

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==================================================

Proof:

We'll break the proof into two cases which I'll label A and B

-----------

Case A: 'a' is even

k = some integer

a = 2k = some even integer

a+1 = 2k+1

a(a+1) = 2k(2k+1) = 2(2k^2+k) = 2*(some integer)

Since 2 is a factor of that last expression, this shows that a(a+1) is even when 'a' is even.

-----------

Case B: 'a' is odd

k = some integer

a = 2k+1 = some odd integer

a+1 = (2k+1)+1 = 2k+2

a(a+1) = (2k+1)(2k+2) = 2(2k+1)(k+1) = 2(some integer)

This shows that a(a+1) is even when 'a' is odd.

-----------

Therefore, for any integer 'a', the expression a(a+1) is always even.

Some examples:

-----------

Here's a slightly different way to interpret why the proof works.

a(a+1) consists of factors 'a' and 'a+1'

Either way, we'll have 2 as a factor somewhere in a(a+1).

The function given in graph is an odd function.

What is the definition of a function?

In mathematics, a function is a rule that assigns a unique output to each input in a given set. In other words, a function is a relationship between two sets, called the domain (set of possible inputs) and the range (set of possible outputs), such that each input is paired with exactly one output.

Now,

In mathematics, an even function is a function f(x) that satisfies the following property: f(-x) = f(x) for all values of x in the domain of the function. The graph of an even function is symmetric about the y-axis, meaning that if you fold the graph along the y-axis, the two halves will be identical.

On the other hand, an odd function is a function f(x) that satisfies the following property: f(-x) = -f(x) for all values of x in the domain of the function. In other words, an odd function is symmetric with respect to the origin. The graph of an odd function is symmetric about the origin, meaning that if you rotate the graph 180 degrees about the origin, the graph will look the same.

As we can see the graph will be same when we will rotate it 180°.

Hence,

            Given function is odd function.

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The measure of angle 10 is 30 degrees.

What is an angle?

we can see that angle 10 and angle 11 form a straight line, and angle 9 and angle 10 form a triangle with angle 11.

Since angle 11 is a right angle with a measure of 90 degrees, the sum of angles 9 and 10 in the triangle must be 90 degrees.

We know that the measure of angle 9 is 60 degrees, so we can solve for the measure of angle 10 as follows:

angle 9 + angle 10 = 90 degrees

60 degrees + angle 10 = 90 degrees

angle 10 = 90 degrees - 60 degrees

angle 10 = 30 degrees

Therefore, the measure of angle 10 is 30 degrees.

What is triangle ?

A triangle is a closed geometric shape that consists of three line segments that connect three non-collinear points. The points where the line segments intersect are called the vertices of the triangle, and the line segments themselves are the sides of the triangle.

Triangles are two-dimensional objects that lie flat in a plane, and they have a variety of properties and characteristics that make them important in mathematics and other fields. The angles and sides of a triangle can be measured and related to one another through various geometric formulas and theorems, and triangles are used in a wide range of applications, from basic geometry and trigonometry to engineering, physics, and computer graphics.

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Complete question is: If the measure of angle 11 is 90 degrees, and the measure of angle 9 is 60 degrees, the measure of angle 10 is 30 degrees.

Using the Pythagorean theorem, we get,

Jules will need the fencing length of 30√2 yards to build the square fence. Hence, option (c) is correct.

It can be defined as a rectangle whose two adjacent sides are equal. Single regular polygon with equal interior angles, central and exterior angles (90°), and equal diagonal lengths

Given data:

The length of each side of the yard is AB = BC = CD = AD = 30 yards.

As shown by the dotted line, the fencing should be done along the diagonal BD of the given square plot. Then, applying Pythagoras' theorem to find the fencing length BD as,

BD² = BC²+ CD²

Substitute the values as

   BD² = 30² + 30²

⇒ BD² = 900+ 900

⇒ BD² = 1800

⇒ BD = √1800

⇒ BD = 30√2 yards.

Thus, we can conclude that Jules will need the fencing length to build the fence along the square plot. Therefore, option (c) is correct.

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The no of colas that have sold 36 cans.

the translation of the question is :

A merchant obtains €70.50 by selling 57 cans of lemon, 48 of orange and the rest glue. If he sells each can for €0.50, how many colas have you sold?

Total selling price is €70.50

the price of each can is €0.50

So,

the number of cans which is sold is

n = €70.50/€0.50

n = 141 cans

again

the total number of cans = no of lemon + no of orange + no of glue

141 = 57 + 48 + m

m = 36

So the colas have sold 36 cans

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Answer:

Nico has 25 and his mother has 0

Step-by-step explanation:

The opposite of -25 is 25 because -(-25)=25     (the negatives cancle out)

Thats why Nico has 25

The opposite of 0 is 0 because 0 is nothing, you cant have an opposite of negative 0 because that would still be 0

Thats why Nico's mother has 0

In rewriting the expression in equivalent form, C. Tony made an error in Step 3. He should have multiplied each exponent by 4 instead of adding 4.

When writing in equivalent form such that one converts the expression ( a ² b ³ /  c) ⁴, one can use the law of exponents.

In this instance, the law of exponents states that if you are taking an exponent with a certain base, to another exponent, you multiply the exponents to get the new exponent.

In step 3, Tony should have multiplied each exponent by 4 instead of adding 4.

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The value of each variable include the following:

x = 10.

y = 80.

z = 5.

In Mathematics and Geometry, a rhombus refers to a type of quadrilateral that is composed of four (4) equal sides and opposite interior angles that are congruent (equal).

Additionally, a rhombus typically has two (2) diagonals that bisect each other at right angles (90 degrees). This ultimately implies that, all of the three angles are 90 degrees;

m∠1 = 9x = 90

9x = 90

x = 90/9

x = 10

m∠2 = y + x = 90

y + x = 90

y + 10 = 90

y = 90 - 10

y = 80

m∠3 = 18z = 90

18z = 90

z = 90/18

z = 5

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Thus, the volume of sphere of the diameter of  m is found as:  523.33 cu. m.

A sphere is a 3D object that is perfectly round, has a single continuous curving surface, and every point upon that surface is equidistant from the centre.

volume of a sphere V = ⁴⁄₃πr³.

Demeter = 10 m

Radius r = 10/2 = 5 m

V =  ⁴⁄₃ *3.14*(5)³.

V = 523.33

Thus, the volume of a sphere of the diameter of  m is found as:  523.33 cu. m.

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Based οn the given οptiοns, it is mοst likely that Amari used the variable "Type οf οrange" tο cοnstruct the bar graphs.

A bar graph is a chart that displays categοrical data using rectangular bars with heights οr lengths prοpοrtiοnal tο the values they represent. The bars can be οriented hοrizοntally οr vertically, and each bar represents a categοry οr grοup οf categοries.

In a bar graph, the x-axis typically represents the categοries being cοmpared, while the y-axis represents the frequency, cοunt, οr percentage οf the οbservatiοns that belοng tο each categοry. The height οr length οf each bar is determined by the value οr frequency οf the categοry it represents.

The variable that Amari used tο cοnstruct a bar graph is nοt specified. Hοwever, since a bar graph is a type οf chart that displays categοrical data with rectangular bars, it is likely that she used a variable that represents a categοrical variable, such as the type οf οrange (e.g. Valencia, Navel, Blοοd, etc.).

Therefοre, based οn the given οptiοns, it is mοst likely that Amari used the variable "Type οf οrange" tο cοnstruct the bar graph.

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This Quadrilateral is a trapezium. And the value of x is 13.

A quadrilateral is a clοsed figure and it have fοur sides, fοur vertices and fοur angles. In οrder tο create it, fοur nοn-cοllinear pοints are jοined. The sum οf interiοr angles οf quadrilaterals is always equal tο 360 degrees.

As two sides are parallel but not equal of a quadrilateral, it is conspired as trapezium.

Now, it is shown that the two adjacent angles are equal,

when two angles are qual it corresponding opposite side is equal too.

So,

30 = x + 17

Solving for x.

30 = x + 17

x = 30 - 17

x = 13

As x = 13

The longer side = x + 13 = 23 + 13 = 36

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