Find all values of y such that the distance between (3,y) and (-2,2) is 8.

Answer:

a.42/98 b.52/98

Step-by-step explanation:

its easy

The Value of CD from the second equation into the first equation:2AC = AB + OC + OD⇒ 2AC = AB + AB (By substituting OC = OA and OD = OB)⇒ 2AC = 2AB⇒ AC Therefore, AC is Congruent to c .

Since AC and BD bisect each other at O, we can say that AO = OC and BO = OD.

We need to prove that AC = CD.To do this, we can use the segment addition postulate which states that if a line segment is divided into two parts, the length of the whole segment is equal to the sum of the lengths of the two parts.

Let us draw a diagram to represent the given information:From the diagram, we can see that:AO + OB = AB (By segment addition postulate)OC + OD = CD (By segment addition postulate)AO = OC (Given)BO = OD (Given)

Now, we can substitute the values of AO and OC as well as BO and OD into the equations above:AO + OB = AB ⇒ OC + OB = AB (Substituting AO = OC)OC + OD = CDNow, we can add both equations:OC + OB + OC + OD = AB + CD ⇒ 2(OC + OD) = AB + CDWe know that OC = AO and OD = BO.

Therefore, we can write:2(AO + BO) = AB + CDSince AO = OC and BO = OD, we can write:2(OA + OD) = AB + CDNow, substituting AO = OC and BO = OD, we can write:2AC = AB + CD

Finally, we can substitute the value of CD from the second equation into the first equation:2AC = AB + OC + OD⇒ 2AC = AB + AB (By substituting OC = OA and OD = OB)⇒ 2AC = 2AB⇒ AC

Therefore, AC is congruent to c .

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The binomial factors of x³- 4x²+x+6​ are (x+2), (x+3), and (x-1).

Using the splitting and grouping the terms:

x³ + 4x² + x - 6

= x³ + 2x² + 2x² + x - 6  [Splitting 4x² = 2x² + 2x²]

= (x³ + 2x²) + (2x² + x - 6)

= x² (x + 2) + (2x² + 4x - 3x - 6)

= x² (x + 2) + [ 2x (x + 2) - 3 (x + 2)]

= x² (x + 2) + (x + 2) (2x - 3)

= (x + 2) ( x² + 2x - 3)

= (x + 2) ( x² + 3x - x - 3)

= (x + 2) [x (x + 3) - 1 (x + 3)]

= (x + 2) (x + 3) (x - 1)

Hence, the binomial factors are (x + 2), (x + 3) and (x - 1)

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Answer:

Thank you,Hope you like it and it will help you

Answer:

  see attached

Step-by-step explanation:

No doubt you have examples showing the wording that is expected to be used here. We have made a guess.

power of a ratio: the numerator is raised to the power, as is the denominator. (a/b)^c = (a^c)/(b^c)

power of a product: each factor is raised to the power. (ab)^c = (a^c)(b^c)

power of a power: the powers are multiplied. (a^b)^c = a^(bc)

quotient of powers: the result when one power is divided by another is the difference of the numerator and denominator powers. (a^b)/(a^c) = a^(b-c)

_____

Additional comment

The order of operations tells you to simplify inside parentheses first. Doing that reduces the work somewhat.

  \(\left(\dfrac{-3x^3y}{x^2}\right)^4=(-3xy)^4=(-3)^4x^4y^4=81x^4y^4\)

The solution to the inequality expression is n < -9

The inequality expression is given as

4n - 6(n + 1) > 12

Open the bracket in the above inequality expression

4n - 6n - 6 > 12

Evaluate the like terms

-2n > 18

Divide both sides by -2

n < -9

Hence, the solution to the inequality expression is n < -9

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The minimum number of unique charms that must be available is 18

The given parameters are

Offers = minimum of 30000

Different charms, r = 9

Represent the minimum number of unique charms that must be available with n

So, we have the following combination equation

nCr = Total offers

Apply the combination formula

So, we have

n!/(r!(n- r)!) = Total offers

Substitute the known values in the above equation

n!/(9!(n- 9)!) >= 30000

Multiply through by 9!

So, we have

n!/(n- 9)! >= 10886400000

Next, we divide the left-hand side by (n - 9)!

So, we have

n x (n - 1) x ..... x (n-8) >= 10886400000

Next, we continue solving by trial by error

After several trials, we have:'

n = 18

To check:

18 x (18 - 1) x ..... x (18 - 8) >= 10886400000

17643225600 >= 10886400000 --- true

Assume n = 17, we have

17 x (17 - 1) x ..... x (17 - 8) >= 10886400000

8821612800 >= 10886400000 --- false

Hence, the minimum number of unique charms that must be available is 18

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Answer:

Step-by-step explanation:

2x3−34x2+131x+11

2x3−34x2+131x+11

=(x−11)(2x2−12x−1)

Answer:

(x−11)(2x2−12x−1)

The domain of the function above is [-2, 3].

The range of the function above is [-2.5, 2].

The intervals over which the function is increasing is [-2, 1.5] U [-2.5, 2].

The intervals over which the function is decreasing is [1.5, -2.5].

In Mathematics and Geometry, a domain refers to the set of all real numbers for which a particular function is defined.

Furthermore, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

By critically observing the graph of this rational expression (function)   shown in the image attached below, we can reasonably and logically deduce the following domain and range:

Domain = [-2, 3] or -2 ≤ x ≤ 3.

Range = [-2.5, 2] or -2.5 ≤ y ≤ 2.

Additionally, the intervals over which the function is increases over the interval [-2, 1.5] and [-2.5, 2], while it decreases over the interval [1.5, -2.5].

In conclusion, the given function is not constant over any interval.

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Group B has lower range.

Group A shows variability.

Mean is the best to make concussion about age of Salsa students.

Upon visual examination, it appears that Group A is likely to have a lower average age of music students compared to Group B.

This inference is supported by the observation that the majority of data points in Group B are concentrated around younger ages.

In contrast, Group A exhibits a more dispersed distribution of data points across a wider range of ages, including higher.

So, Group B has lower range.

and, Group A shows variability.

Lastly, Mean is the best to make concussion about age of Salsa students.

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Answer:

Step-by-step explanation:

b- base of the triangle = 6

h - height of the triangle = 4

L = length of the rectangles = 7

s₁ = breadth of the base rectangle = 6

S₂ = breadth of the right rectangle = 5

s₃ = breadth of the left rectangle = 5

Surface area of the prism = bh + L*(s₁ + s₂ + s₃)

                                          = [ 6*4 ] + 7 * (6+5+5)

                                          = 24 + 7*16

                                          = 24 + 112

                                           = 136 square units

Answer:

A = 2184 cm²

Step-by-step explanation:

the area (A) of the figure is calculated as

A = \(\frac{1}{2}\) h(b₁ + b₂)

where h is the perpendicular height between the bases b₁ and b₂

here h = 42 , b₁ = 52 , b₂ = 52 , then

A = \(\frac{1}{2}\) × 42 × (52 + 52) = 21 × 104 = 2184 cm²

Answer:

A = 2184 cm2

Step-by-step explanation:

Area of a parallelogram:

\(A = b*h\)

\(b=52,h=42\)

\(A=(42)(52)=2184cm^{2}\)

Hope this helps.

The probability that four batteries connected in series will have a combined voltage of 60.8 or more volts is approximately 0.0228 or 2.28%.

To find the probability that four batteries connected in series will have a combined voltage of 60.8 or more volts, we need to use the concept of the Central Limit Theorem.

In this case, we know that the mean voltage of a single battery is 15 volts and the standard deviation is 0.2 volts. When batteries are connected in series, their voltages add up.

The combined voltage of four batteries connected in series is the sum of their individual voltages. The mean of the combined voltage will be 4 times the mean of a single battery, which is 4 * 15 = 60 volts.

The standard deviation of the combined voltage will be the square root of the sum of the variances of the individual batteries. Since the batteries are connected in series, the variance of the combined voltage will be 4 times the variance of a single battery, which is 4 * (0.2)^2 = 0.16.

Now, we need to calculate the probability that the combined voltage of four batteries is 60.8 or more volts. We can use a standard normal distribution to calculate this probability.

First, we need to standardize the value of 60.8 using the formula:

Z = (X - μ) / σ

Where X is the value we want to standardize, μ is the mean, and σ is the standard deviation.

In this case, the standardized value is:

Z = (60.8 - 60) / sqrt(0.16)

Z = 0.8 / 0.4

Z = 2

Next, we can use a standard normal distribution table or calculator to find the probability associated with a Z-score of 2. The probability of obtaining a Z-score of 2 or more is approximately 0.0228.

Therefore, the probability that four batteries connected in series will have a combined voltage of 60.8 or more volts is approximately 0.0228 or 2.28%.

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we can identify a few things to rule out options

the highest point of the graph is at y = 3k, this means that there must be a constant 3 adding

then first and second option are discarded

now we take a point from the graph and we will replace in the last two options

the point is (-4,3)

x=-4, the solyution must be 3

Option D

Step-by-step explanation:

The equation x = 7 has only one solution, which is x = 7.

Therefore, none of the options given in the question (OA, OB, OC, OD) are correct

Answer:

Step-by-step explanation:

a + c  = 147

2.50a + 1.50c = 297.50

-2.50a - 2.50c = -367.50

 2.50a + 1.50c = 297.50

   -c = -70

 c = 70 children

a + 70 = 147

a = 77 adults

\(f(x)=x\) for \(x\leq0\), therfore \(f(0)=0\).

the first domain is true for f(0) so we substitute value of x in the first function

\(f(x) = x \\ f(0) = 0\)

The appropriate test statistic is approximately 1.89.

To determine if there is evidence that 20 to 29-year-old drivers have a higher mean accident claim compared to 30 to 49-year-old drivers, we can perform a two-sample t-test.

The test statistic can be calculated using the following formula:

\(t = (mean1 - mean2) / \sqrt{(s1^2 / n1) + (s2^2 / n2)}\)

where:

mean1 and mean2 are the sample means of the two populations,

s1 and s2 are the sample standard deviations of the two populations,

n1 and n2 are the sample sizes of the two populations,

Given the following information:

For population 1 (20 to 29-year-old drivers):

Sample mean (mean1) = $4586

Sample standard deviation (s1) = $2302

Sample size (n1) = 40

For population 2 (30 to 49-year-old drivers):

Sample mean (mean2) = $3669

Sample standard deviation (s2) = $2029

Sample size (n2) = 40

Calculate the test statistic (t):

\(t = (4586 - 3669) /\sqrt{ (2302^2 / 40) + (2029^2 / 40))\)

Calculating this expression:

t ≈ 917 / √(132360.1 + 102996.025)

t ≈ 917 / √(235356.125)

t ≈ 917 / 485.086

t ≈ 1.89

Therefore, the appropriate test statistic is approximately 1.89.

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Answer:

Using the data under D1 and D2, calculate the cross elasticity of demand for golf at all three prices. (To do this, apply the midpoints approach to the cross elasticity of demand.) At $50, cross elasticity = -2.40 ± 0.05At $35, cross elasticity = -3.00 ± 0.05At $20, cross elasticity = -4.00 ± 0.05Is the cross elasticity the same at all three prices? No. Are movies and golf substitute goods, complementary goods, or independent goods? Complementary goods.b. Using the data under D2 and D3, calculate the income elasticity of demand for golf at all three prices. (To do this, apply the midpoints approach to the income elasticity of demand.) At $50, income elasticity of demand = 1.40 ± 0.05At $35, income elasticity of demand = 2.33 ± 0.05At $20, income elasticity of demand = 3.00 ± 0.05Is the income elasticity the same at all three prices? No. Is golf an inferior good? No, it is a normal good.

The required statement is given as the data tends to the normal good.

Statistics is the study of mathematics that deals with relations between comprehensive data.

Calculate the cross elasticity of demand for golf at each of the three prices using the information under D1 and D2.

At $50, the cross elasticity is equal to -2.40 ± 0.05;
At $35, it is - 3.00± 0.05;
At $20, it is - 4.00 ±0.05.
No golf and movies complementary, independent, or alternative goods complementing products b.

Calculate the income elasticity of demand for golf at each of the three prices using the information under D2 and D3.
At $50, the income elasticity of demand is equal to 1.40±0.05
At $35, it is 2.33± 0.05
At $20, it is 3.00± 0.05

Thus, the required statement is given as the data belong to the normal good.

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floor plan => It is the scale drawing that show the relationship between rooms, spaces, and physical features viewed from the above

THIS PIC WILL ALSO HELP U

Answer:

6x+1

Step-by-step explanation:

3x+3x=6x

-5+6=1

Answer:

6x+1

Step-by-step explanation:

First remove the parentheses

the combine like terms!

6x+1

Hoped it help!

One angle measure provided (27 degrees), to determine the lengths of the sides or the measures of the other Angles.

The triangle, we need more information about the triangle, such as the lengths of the sides or the measures of other angles. The given information, "27 degrees," only specifies one angle of the triangle, but it is not sufficient to solve the triangle completely.

To solve a triangle, we typically need at least three pieces of information, which can include side lengths, angle measures, or a combination of both. With only one angle measure provided (27 degrees), we are unable to determine the lengths of the sides or the measures of the other angles.

To fully solve the triangle, we would need additional information such as the lengths of the sides or measures of at least two more angles. Without this additional information, it is not possible to provide a complete solution or determine the lengths of the sides or the measures of the other angles in the triangle.

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The quadratic equation is:

then what we need to do is to complete the square for x, we add in both sides of the inequality (18/2)^2=81

then the vertex will be (-9,-49)

Answer:

y= 22 + 187 – 32 Vertex form

The genotype ratio is:  1   TT : 1   Tt : 0  tt

The phenotype ratio is :  4   Tall :   0   Short

100 percent of the offspring will be tall.

Genotypic ratio is the ratio between the genetic makeup among the offspring population.

On the other hand, the ratio between the offspring population for an observable characteristic is the phenotype ratio.

The given test cross is between a homozygous tall parent and a heterozygous tall parent.

Using a Punnett square,

The result will be as shown below.

                     T                   t

          T        TT                 Tt

           T       TT                 Tt

Genotype :  1   TT : 1   Tt : 0  tt

Phenotype :  4   Tall :   0   Short

100 percent of the offspring will be tall.

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Answer:

ff

Step-by-step explanation:

fff

The sine equation for the object's height is given as follows:

d = -5sin(0.24t).

The standard definition of the sine function is given as follows:

y = Asin(Bx) + C.

The parameters are given as follows:

The amplitude for this problem is of 5 inches, hence:

A = 5.

The period is of 1.5 seconds, hence the coefficient B is given as follows:

2π/B = 1.5

B = 1.5/2π

B = 0.24.

The function starts moving down, hence it is negative, so:

d = -5sin(0.24t).

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The height of Jim's house is needed.

The height of Jim's house is 5.8 m.

Jim's office building is 19 times the height of his house.

The height of the office building is 110.3 m

Let \(o\) be height of office

\(h\) be height of house

So,

\(o=19h\\\Rightarrow h=\dfrac{o}{19}\\\Rightarrow h=\dfrac{110.3}{19}\\\Rightarrow h=5.8\ \text{m}\)

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