What is the degree of (2x + 45)

The standard form of the equation of the ellipse is (x - 2)^2 / 4 + (y - 3)^2 / 7 = 1

To find the standard form of the equation of the ellipse, we first need to determine some of its properties.

The foci of the ellipse are given as (2, 0) and (2, 6). This tells us that the center of the ellipse is at the point (2, 3), which is the midpoint of the line segment connecting the foci.

The major axis of the ellipse is given as a length of 8. Since the major axis is the longest dimension of the ellipse, we can assume that the length of the major axis is 2a = 8, so a = 4.

Next, we need to determine the length of the minor axis. We know that the distance between the foci is 2c = 6, so c = 3. Since c is the distance from the center of the ellipse to each focus, we can use the Pythagorean theorem to find the length of the minor axis

b^2 = a^2 - c^2

b^2 = 4^2 - 3^2

b^2 = 7

b = sqrt(7)

Now we have all the information we need to write the standard form of the equation of the ellipse. The standard form is

(x - h)^2 / a^2 + (y - k)^2 / b^2 = 1

where (h, k) is the center of the ellipse. Plugging in the values we found, we get

(x - 2)^2 / 4 + (y - 3)^2 / 7 = 1

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Answer:

\(x\geq 7\\\)

\(x\) ∈ \([7,\) ∞ \()\)

Step-by-step explanation:

In this problem, one is given the following function,

\(f(x)=(x-7)^2\)

The problem asks one to find the interval for which the function is one-to-one and non-decreasing.

A one-to-one function is when every element in the range corresponds to every element in the range. Moreover, no element in the range will correspond to more than one element in the domain. In essence, every input pairs to only one output, and every output pairs to only one input. In a quadratic equation (an equation with a term to the second degree (exponent of (2)), half of the graph will form a one-to-one function. This is because when one has the full graph, for every output there are two inputs. However, with half of the graph, there is only one input for every output. Therefore, a function with a domain of all values less than the (x-coordinate) of the vertex will form a one-to-one function. The same conclusion can be drawn for any value greater than the (x-coordinate) of the vertex.

The given function is in vertex form. This means that one can find the vertex using the given information. The general format for the vertex form of a quadratic equation is as follows,

\(y=k(x-h)^2+k\)

Where vertex is the following,

\((h,k)\)

Applying this logic here, one can state that the vertex of the given equation (\(f(x)=(x-7)^2\)) is as follows,

\((7, 0)\)

Since the coefficient of this equation is positive (no coefficient means that it is (1)) outside of it, one can conclude that the graph of the equation is increasing after the (x) value of (7). Therefore, the function is one-to-one and increasing on the interval (\(x\geq 7\\\)).

The measure of the inscribed angle G in the circle is 85 degree.

An inscribed angle is simply an angle with its vertex on the circle and whose sides are chords.

The relationhip between an an inscribed angle and intercepted arc is expressed as:

Inscribed angle = 1/2 × intercepted arc.

Since the circle equals 360 degrees, we can determine the intercepted arc DF.

Hence:

Arc DF = 360 - ( 70 + 120 )

Arc DF = 360 - 190

Arc DF = 170°

Now, plug the value into the above formula:

Inscribed angle = 1/2 × intercepted arc.

Inscribed angle G = 1/2 × 170°

Inscribed angle G = 85°

Therefore, angle G has a measure of 85 degree.

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Answer:

Indeed. The system of equations has a solution at point (0, -7).

Step-by-step explanation:

A system of linear equations is consistent only if exist a solution. Let equalize each expression to eliminate y and determine if a solution for x exist. That is:

\(2\cdot x - 7 = x - 7\)

\(2\cdot x - x = 7 - 7\)

\(x = 0\)

Therefore, the system of linear equations has a solution at point (0, -7).

Sample Response/Explanation: Yes, the lines will intersect because the slopes are different. Also, both lines have a y-intercept of -7, so they both include the point (0, –7).

Which did you include in your response? Check all that apply.

The lines will intersect.

The slopes are different.

The point (0, –7) lies on both lines.

Answer:

6

Step-by-step explanation:

Answer:

Yes, he is correct

Step-by-step explanation:

d = sqrt[(6-2)² + (3-4)²]

d = sqrt[4² + (-1)²]

d = sqrt(16 + 1)

d = sqrt(17)

Answer:

A

Step-by-step explanation:

Yes he is correct.

he didn't substitute the values in the wrong places.

he did use the proper order of operations.

he didn't evaluate the powers incorrectly.

Therefore, A is correct.

Answer:

1/9

Step-by-step explanation:

probability equals number of desired outcomes over total possible outcomes

Total possible outcomes = 36

possible sums of 5:

2,3   1,4  3,2.  4,1

4/36= 1/9

Answer:

The son is 12, The father is 45

Step-by-step explanation:

Let x=son's age now

Then x-2=son's age two years ago

And 4(x-2)=father's age two years ago

So 4(x-2)+2=4x-8+2=4x-6=father's age now

Also x+3=son's age three years for now

And 3(x+3)=father's age three years from now

Now if we subtract 5 years from father's age three years from now, then that will equal father's age two years ago. So:

3(x+3)-5=4(x-2) get rid of parents

3x+9-5=4x-8

3x+4=4x-8 subtract 4 and also 4x from both sides

3x-4x+4-4=4x-4x-8-4 collect like terms

-x=-12 divide both sides by -1

x=12 - son's age now

------------------------------------------------------------------------------------------------------------

4x-6=4*12-6=48-6=42 - father's age now

Two years ago, father was 4 time as old as his son:

4(12-2)=42-2

40=40

also

Three years from now father will only be three times as old as his son

3(12+3)=42+3

45=45

Answer:

45

Step-by-step explanation:

45 daw sagot sabi,, la

Answer:

2nd option

Step-by-step explanation:

The estimate (to one decimal place) of the average rate of change f is 1.7

The interval is given as

x = 1 to x = 4

This can be represented as

(a, b) = (1, 4)

From the attached graph, we have

f(1) = 2

f(4) = 7

The estimate (to one decimal place) of the average rate of change f is

Rate = [f(b) - f(a)]/[b - a]

This gives

Rate = [f(4) - f(1)]/[4 - 1]

So, we have

Rate = [7 - 2]/[4 - 1]

Evaluate

Rate = 1.7

Hence, the estimate (to one decimal place) of the average rate of change f is 1.7

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The triangle which could be drawn as per the given description is only option b. isosceles triangle with measure 20° and 80°.

An acute triangle with sides measuring 7, 4, and 2

In an acute triangle, the sum of the squares of the two shorter sides must be greater than the square of the longest side .

According to the Pythagorean Theorem.

Here, 7² is greater than (4² + 2²).

So this is not possible.

An isosceles triangle with angles measuring 20° and 80°

In an isosceles triangle, two angles are equal, so if two angle measures 20° and 80°,

Then the third angle measures is

180° - 20° - 80°= 80°

Two angles are congruent implies two sides are congruent.

It is possible to form isosceles triangle.

An obtuse triangle with sides measuring 5, 10, and 15

In an obtuse triangle, the longest side is opposite the largest angle.

Sum of squares of two shorter sides is less than square of longest side according to Pythagorean Theorem.

However, 15²is greater than (5²+ 10²),

so this is not possible.

A scalene triangle with angles measuring 110° and 35°

The sum of the angles of any triangle is 180°,

so the third angle must measure

180° - 110° - 35° = 35°.

Two angles are congruent so it is isosceles triangle.

It is not possible to form scalene triangle.

Therefore, the triangle possible to draw as per the given condition is only option b. isosceles triangle with measure 20° and 80°.

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To solve this problem, we can use the binomial probability formula. Let's break it down:

Given information:

Total number of people surveyed (n) = 1369

Number of people who said they voted (x) = 912

Probability of an eligible voter actually voting (p) = 0.64

(a) To find the probability that at least 912 people actually voted, we need to calculate the probability of x being 912 or more. We can use the cumulative binomial probability for this.

P(X ≥ 912) = 1 - P(X < 912)

Using the binomial probability formula, we can calculate P(X < 912):

P(X < 912) = ∑[from k=0 to 911] (nCk) * p^k * (1-p)^(n-k)

Calculating this summation may be complex, but we can use statistical software or calculators to compute it. The result is:

P(X < 912) ≈ 0.0003

Therefore, to find P(X ≥ 912), we subtract this value from 1:

P(X ≥ 912) = 1 - P(X < 912) ≈ 1 - 0.0003 ≈ 0.9997

Rounded to four decimal places, the probability that among 1369 randomly selected voters, at least 912 actually voted is approximately 0.9997.

(b) The result from part (a) suggests that some people may not be honest about whether they actually voted. The probability of observing at least 912 people who said they voted, given the true voting rate of 64%, is extremely high (approximately 0.9997). This suggests that either the voting records are inaccurate or some individuals may have misrepresented their voting behavior in the survey. The high probability implies that the reported number of voters may not align with the actual voting participation. Therefore, option C is the most appropriate:

C. Some people are being less than honest because P(X) is less than 5%.

Please note that the interpretation and implications may vary depending on the context and additional factors involved.

Answer:

$21.15

Step-by-step explanation:

(235)(.045)(2)

The value of K = 0.044999999 and the initial value of Machine Vo = 949999.9952

The value of a machine is depreciating using the exponential function = 0 − where k is a constant, 0 is initial value of the machine and t is time in years. The value of the machine after 5 years is Sh. 758,590.4078 and its value after 8 years is Sh. 662,792.5098.

According to Exponential function

\(V = Voe^-Kt\)

where K = constant

Vo = Initial value

At = t = 5

V = 758590.4078

At = t = 8

V = 662792.5098

\(V_{Q} = Voe^{-Kt}\)

758590.4078 = \(Voe^-5t\)   --- equation 1

662792.5098 = \(Voe^{-8k}\)   --- equation 2

Dividing equation 1 by 2

1.144536784 = \(e^{3k}\)

Taking log on both the sides

3k = 0.134999999

K = 0.044999999

At t = 5 years

\(V = Voe^{-5k}\)

758590.4078 = \(Voe^{-5k}\)

\(Vo = \frac{758590.4078}{e^{-5(0.044999999)}}\)

Vo = 949999.9952

Hence the answer is the value of K = 0.044999999 and the initial value of Machine Vo = 949999.9952

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Using central angle theorem,

The measure of the arc BC = 110°.

An angle with its vertex in the middle of the circle it creates with its two radii is said to be central.

Here in the question,

As per the central angle theorem:

(2x -30) ° + x° = 180°

⇒ 2x - 30 + x = 180

⇒ 3x - 30 = 180

Adding 30 on both sides:

⇒ 3x = 180 + 30

⇒ 3x = 210

Dividing both sides by 3.

⇒ x = 70°

Now BC = 2x-30

= 2 × 70 -30

= 140 - 30

= 110°

Therefore, the measure of BC = 110°.

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The value of a where the Limit of g(x) as x approaches alpha not exist are -1 and 1

The limit of a function is the limit of a function as x tends to a value.

From the given graph, you can see that the function g(x) goes large at the point where the arrows orange and purple point down from the x-coordinates -1 and 1.

Hence the value of a where the Limit of g(x) as x approaches alpha not exist are -1 and 1

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The number of turns the wheel makes is 1.93 ≈ 2.

What is Turns?

This is referred to as a cycle. It is a unit of plane angle measurement that is equivalent to 2π radians, 360 degrees, or 400 gradians.

formular for calculating Turns:

Turns =         Lenght

              Circumference

Circumference of a circle, C= πD

Where,

Diameter=D

            π =22/7

Calculating Circumference;

C= 22  * 66

            7

    =207.4

From the question:

D= 66cm

L  =400m

Calculating Turns:

Turns =  Lenght

              Circumference

          =   400m

               207.4

      Turns =1.93

Turns =1.93≈ 2

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Answer:

Step-by-step explanation:

To classify the quadrilateral formed by the given points, we need to find the length of each side and the measure of each angle.

Using the distance formula, we can find the length of each side:

AB = sqrt((4 - (-3))^2 + (2 - 1)^2) = sqrt(49 + 1) = sqrt(50)

BC = sqrt((9 - 4)^2 + (-3 - 2)^2) = sqrt(25 + 25) = 5sqrt(2)

CD = sqrt((2 - 9)^2 + (-4 - (-3))^2) = sqrt(49 + 1) = sqrt(50)

DA = sqrt((-3 - 2)^2 + (1 - (-4))^2) = sqrt(25 + 25) = 5

Using the slope formula, we can find the measure of each angle:

Angle ABC: m1 = (2 - 1)/(4 - (-3)) = 1/7

m2 = (-3 - 2)/(9 - 4) = -1/5

tan(ABC) = |(m2 - m1)/(1 + m1m2)| = 3/4

ABC = arctan(3/4) ≈ 36.87°

Angle BCD: m1 = (-3 - 2)/(9 - 4) = -1/5

m2 = (-4 - (-3))/(2 - 9) = 1/7

tan(BCD) = |(m2 - m1)/(1 + m1m2)| = 3/4

BCD = arctan(3/4) ≈ 36.87°

Angle CDA: m1 = (-4 - 1)/(2 - (-3)) = -1

m2 = (1 - (-3))/(-3 - 9) = 1/2

tan(CDA) = |(m2 - m1)/(1 + m1m2)| = 7/5

CDA = arctan(7/5) ≈ 54.46°

Angle DAB: m1 = (1 - (-4))/(4 - (-3)) = 5/7

m2 = (-4 - (-3))/(-3 - 2) = 1/5

tan(DAB) = |(m2 - m1)/(1 + m1m2)| = 3/4

DAB = arctan(3/4) ≈ 36.87°

Therefore, the quadrilateral formed by the given points is a kite, because adjacent sides are congruent and one diagonal bisects the other diagonal at a right angle.

(9) The slope of a line perpendicular to the line, f(x) = 0.75x + 6 is - 4/3.

(10) The slope of a line parallel to this line, y = 10 -8x is -8.

The slope of a line perpendicular to the line is the negative reciprocal of the slope of the line equation.

Question 9.

f(x) = 0.75x + 6

where;

The slope of a line perpendicular to this line = -1/0.75 = -100/75 = -4/3

Question 10.

For the equation of another line, y = 10 - 8x

The slope of a line parallel to this line is equal to the slope of this line and it is calculated as follows;

y = 10 - 8x

where;

slope of a line parallel to the line = -8

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Answer:

b

Step-by-step explanation:

to prove if NP is tangent to MN

we could prove if NPM is a right triangle

By pythagorean theorem

a^2+b^2=c^2

where a=MN=33

b=NP=180

c=MP=MQ+QP=152+33=185

so

33^2+180^2=185^2

but

1089+32400 is not equal to 34225

33489 is different from 34225

Answer:4

Step-by-step explanation:

replace x with -3

f(x) = 2x-2

find f(-3)

f(-3) = 2(-3) - 2

f(-3) = -6 -2

f(-3) = -8

Answer:

See below

Step-by-step explanation:

For the second step, \(\angle T\cong\angle R\) by Alternate Interior Angles. The rest of the steps appear to be correct.

Step-by-step explanation:

here is the ans

please check

Answer:

31

Step-by-step explanation:

the bottom go's up 6 every space

Answer:

I think the answer is 31.

Step-by-step explanation:

It is 5 times 5 plus 6.

The area of triangle ADE is,

⇒ A = 48 square units

We have to given that,

In the diagram , DE is a midsegment of triangle ABC.

And, The area of triangle ABC is 96 square units

Now, We know that,

Since DE is a midsegment of triangle ABC, it is parallel to AB and half the length of AB. Therefore, DE is half the length of AB.

Hence, the area of triangle ADE is half the area of triangle ABC,

That is,

A = 96 / 2

A = 48 square units

Thus, The area of triangle ADE is,

⇒ A = 48 square units

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The straight-line distance between Akira's house and Cooper's house is 6.13 kilometers (rounded to the nearest tenth)

Given that,To get from home to his friend Akira's house, Jaden would have to walk 2.8 kilometers due east.The straight-line distance between Akira's house and Cooper's house is given by the distance between two points in a coordinate plane. Let the home be the origin (0, 0) of the coordinate plane and Akira's house be represented by the point (2.8, 4.7). Similarly, let Cooper's house be represented by the point (8.3, 7.4).The distance formula between the two points (2.8, 4.7) and (8.3, 7.4) is given by:distance = √[(8.3 - 2.8)² + (7.4 - 4.7)²]= √[5.5² + 2.7²]= √(30.25 + 7.29)= √37.54= 6.13 km (rounded to the nearest tenth)

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Answer:

Since the calculated value of z= 1.869 does not fall in the critical region we accept the null hypothesis H0: p1≠ p2  the data provides evidence that the proportion of high school students in metropolitan areas who have internet access during school hours is different than the proportion of rural high school students who have internet access during school hours.

Step-by-step explanation:

Let p1= proportion of the high school students having internet access

p2= proportion of the rural school students having internet access

1) The null and alternate hypothesis are

H0: p1≠ p2  against the claim   Ha: p1= p2

2) We choose significance level ∝ =0.05

3) The test statistic under H0 is

z= p1^- p2^/√ p^q^( 1/n1 + 1/n2)

Now

p1^= 768/850= 0.9035

p2^= 308/355= 0.8670

p^= 768+ 308/850+ 355= 1076/1205

p^= 0.8929

q^= 1-p^= 0.1070

Putting the values

z= p1^- p2^/ √p^q^( 1/n1 + 1/n2)

Z= 0.9035-0.8670/sqrt [0.8929*0.1070( 1/850 + 1/355)]

z= 0.0365/ sqrt [ 0.0955403 (0.001176 + 0.002816)]

z= 0.0365/ 0.019531

z= 1.8688

The critical region is  z∝/2 = ± 1.96

The value of z is 1.8666. The value of p is 0.06148 which is greater than 0.05

Conclusion:

Since the calculated value of z= 1.869 does not fall in the critical region we accept the null hypothesis H0: p1≠ p2  the data provides evidence that the proportion of high school students in metropolitan areas who have internet access during school hours is different than the proportion of rural high school students who have internet access during school hours.

Answer:  first choice is correct

Step-by-step explanation:

\(\sqrt{10} = 3.16\\\\ \sqrt{13} = 3.6\)

22/9 = 2.44

Therefore Point A is 22/9, Point B is \(\sqrt{10}\),  Point C is \(\sqrt{13}\)

The amount Aman paid to clear the debt, at last, was Rs. 25,773, including compounded interest of Rs.10,773.

Compound interest is a type of interest system in that accumulated interest attracts interest.

With compounding, interest is paid on interest, unlike the simple interest system.

To compute compound interest, we use the following formula: CI = P( 1 + r/100)^n - P, where CI is compound interest, P is the principal, r is the compound interest rate and n is the number of years.

The amount of the loan = Rs.30,000

Loan period = 4 years

Annual percentage rate = 10%

Compounding period = Annual

Amount after two years = P( 1 + r/100)^n

= Rs. 30,000 x (1 + 0.1)^2

Rs. 36,300 (Rs. 30,000 x 1.21)

Payment after two years = Rs.15,000 (Rs. 30,000 x 50%)

Balance = Rs. 21,300 (Rs. 36,300 - Rs. 15,000)

Amount after another two years = Rs. 21,300 x (1 + 0.1)^2

= Rs. 25,773 ($21,300 x 1.21)

Total payments = Rs. 40,773 (Rs. 25,773 + Rs. 15,000)

Compounded interest = Rs. 10,773 (Rs. 40,773 - Rs. 30,000)

Thus, to settle the loan, lastly, Aman paid Rs. 21,300.

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The store owner needs to mixed 100 pounds of pistachios and 100 pounds of walnuts if the store owner will charge 5 dollars for the mixture.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

Let's suppose the store owner mixed x pounds of pistachios and

(200-x) pounds of walnuts, then a linear equation can be framed:

The total mixture cost = 200×5 = 1000

Now,

6x + 4(200-x) = 1000

x = 100 pounds

200 - 100 = 100 pounds

Thus, the store owner needs to mixed 100 pounds of pistachios and 100 pounds of walnuts if the store owner will charge 5 dollars for the mixture.

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