What is the midpoint of a line segment connecting the points (−4,6) and (8,2)?

Answers

Answer 1

Answer:

(2,4)

Step-by-step explanation:

1. Add the 2 x-values together, then divide. The resulting number is the x-value of the midpoint. -4+8=4 and 4/2=2, so the x-value is 2

2. Do the above steps (add & divide) for the two y-values. 6+2=8 and 8/2=4, so the y-value is 4

3. put the two values together in a coordinate pair & you have your midpoint! so if x=2 and y=4, then the midpoint is (2,4)

hope this helps :)

Answer 2
the answer is 2,4 hope this helps

Related Questions

Show how 60/90 becomes 2/3

Answers

60 ÷ 30 = 2

and

90 ÷ 30 = 3

---> 60/90 = 2/3

❄ Hi there,

the way 60/90 becomes 2/3 is this:

The fraction's numerator & denominator are both divided by 30:

[tex]\sf{\dfrac{60\div30}{90\div30}=\dfrac{2}{3}}[/tex]

That's it!

A company currently pays a dividend of $2.6 per share (d0 = $2.6). it is estimated that the company's dividend will grow at a rate of 24% per year for the next 2 years, and then at a constant rate of 8% thereafter. the company's stock has a beta of 1.8, the risk-free rate is 7.5%, and the market risk premium is 4.5%. what is your estimate of the stock's current price?

Answers

The current value of the stock is $53.413455.

What is the CAMP model?The CAMP model describes the relationship between systemic risk, or the general dangers of investing, and projected return on assets, specifically stocks.

To find the current price of stock:

Stock’s current price: 53.41 dollars

First, we determine the stock's value using the CAPM model.

Ke = rf + (rm - rf)risk free, rf =  0.085.premium market = (rm - rf) = 0.045(nondiversifiable risk) = 1.3

Then, Ke = 0.085 + 1.3(0.045).

Ke = 0.14350

The current value of the future dividends must now be known:

D0 = 2.8D1 = D0 x (1 + g) = 2.8 * 1.23 = 3.444D2 =  3.444 x 1.23 = 4.2361200

The next dividends, which are at perpetuity will be solved using the dividend growth model:

dividends/return-growth = Intrinsic value

In this case, dividends will be:

4.23612 x 1.07 = 4.5326484

Return will be calculated using the CAPM and g = 7%.

plug this into the Dividend grow model,

4.53264840.1435-0.07 = Intrinsic ValueValue of the dividends at perpetuity: 61.6686857

Finally, it's crucial to remember that these statistics were calculated for the present year.

We must bring them to the present day using the present value of a lump sum:

principal/(1 + rate)time = PV3.444/(1 + 0.1435)1 = PV3.011805859 = PV4.23612/(1 + 0.1435)2 = PV3.239633762 = PV61.6686857/(1 + 0.1435)2 = PV47.16201531 = PV

We add them and get the value of the stock, 53.413455

Therefore, the current value of the stock is $53.413455.

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in april 2005, roland mailed a package from his local post office in Albermarle, NC ro a friend in fishers, Indiana for $2.76 per ounce. The first class domestic rate at the time was $.23 per ounce. Write and solve an equation to determine the weight of the package

Answers

The weight of the package is 12 ounces

How to solve an equation to determine the weight of the package?

The given parameters are

Total amount = $2.76

Domestic rate = $.23 per ounce

The equation to determine the weight of the package is represented as:

Weight = Total amount/Domestic rate

Substitute the known values in the above equation

Weight = 2.76/.23

Evaluate the quotient

Weight = 12

Hence, the weight of the package is 12 ounces

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Which equation represents y = −x2 + 4x − 1 in vertex form?

Answers

The vertex form of the equation y = -x^2 + 4x - 1 is y = -(x - 2)^2 + 3

How to determine the vertex form of the quadratic equation?

The quadratic equation is given as:

y = -x^2 + 4x - 1

Differentiate the above quadratic equation.

This is done with respect to x by first derivative

So, we have:

y' = -2x + 4

Set the derivative to 0

-2x + 4 = 0

Subtract 4 from both sides of the equation

-2x + 4 - 4 = 0 - 4

Evaluate the difference in the above equation

-2x = -4

Divide both sides of the above equation by -2

x = 2

Rewrite as

h = 2

Substitute 2 for x in the equation y = -x^2 + 4x - 1

y = -2^2 + 4 *2 - 1

Evaluate the equation

y = 3

Rewrite as:

k = 3

A quadratic equation in vertex form is represented as:

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

So, we have:

y = a(x - 2)^2 + 3

In the equation y = -x^2 + 4x - 1, a = -1

So, we have:

y = -(x - 2)^2 + 3

Hence, the vertex form of the equation y = -x^2 + 4x - 1 is y = -(x - 2)^2 + 3

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Find the area in square units of ABC△ plotted below.

Answers

Answer:

71

Step-by-step explanation:

Anyone know the anwser to this

Answers

Answer:

4112

Step-by-step explanation:

When you plug in 3 for x you get 6.

Then you just do 4^6 which is 4096.

Then add 16 which gets you 4112.

I NEED HELP WITH MY MATH PLEASE

Answers

(-5)^11

Since we have the same base for the exponent (-5) in both the numerator and the denominator, we can combine the exponents. As this is a fraction, which means dividing, we subtract the the exponents. (This is just a rule. When dividing exponents with the same base, subtract the powers.) So if we subtract 5 minus -6 we get 11. So we’re left with -5 raised to the 11th power, or (-5)^11

30 POINTS HELP PLS!!!!!!!

Answers

i really hate how we actually have to type something.

5. If a, s are the zeroes of 2 -8x +λ ,such that a – s = 2, then λ=

Answers

The value of λ = 8s + 6

What are the zeroes of a function?

The zeroes of a function f(x) are the values of x at which f(x) = 0.

How to find λ?

Given that a, s are the zeroes of 2 - 8x + λ ,such that a - s = 2.

Since we require λ,

So, let f(x) = 2 - 8x + λ.

At x = a, f(x) = 0.

So, substituting the value of x = a into f(x), we have

f(a) = 2 - 8a + λ

Since f(a) = 0, we have

2 - 8a + λ = 0   

2 + λ = 8a  (1)

Also, x = s, f(x) = 0.

So, substituting the value of x = s into f(x), we have

f(s) = 2 - 8s + λ

Since f(s) = 0,we have  

2 - 8s + λ = 0

2 + λ = 8s  (2)

Since a - s = 2

Making a subject of the formula, we have

⇒ a = s + 2

So, substituting the value of a into equation (1), we have

2 + λ = 8a  (1)

2 + λ = 8(s + 2)  (1)

2 + λ =  8s + 16

- 14 + λ = 8s   (3)

Adding equation (2) and (3), we have

-14 + λ = 8s   (3)

+

2 + λ = 8s     (2)

-12 + 2λ = 16s

2λ = 16s + 12

Dividing through by 2, we have

2λ/2 = (16s + 12)/2

λ = 4(4s + 3)/2

λ = 2(4s + 3)

λ = 8s + 6

So, the value of λ = 8s + 6

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factor this:
18x^2+39x-15

Answers

answer is:
3(2x+5)*(3x-1)

Steps for Factoring:

1) Find CM (common factor) for the expression: 3

   Factor out 3 =>

   [tex]3(6x^{2}+13x-5)[/tex]

2)Factor the above expression by grouping:

  The expression needs to be written as [tex]6x^{2} + ax+ bx -5[/tex]

 a and b should add up to 13 and multiply up to -30 (6 × -5)

By Guess & Check we find that the pair is a = -2 and b = 15 (-2+15; -2 × 15)

3) Now we can rewrite [tex](6x^{2}+13x-5)[/tex] as [tex](6x^{2} -2x)+(15x-5)\\[/tex]

Factor out 2x in the first group and 5 in the second group:

[tex]2x(3x-1)+5(3x-1)\\[/tex]

As 3x-1 is on both sides, now we can do the operation: 2x+5 (distributive property)

(3x-1) (2x+5)

The answer is 3(3x-1) (2x+5)

Hope it helps!

A savings account earns 15% interest annually. What is the balance after 8 years in the savings account when the initial deposit is 7500?

Answers

The balance after 8 years is $22,942.67

What is the balance after 8 years?

We know that the savings account earns 15% annually, and the initial deposit is $7500, then the balance as a function of time in years is:

B = $7500*(1 + 15%/100%)^t

B = $7500*(1.15)^t

The balance after 8 years is what we get when we evaluate the above function in t = 8, so we get:

B = $7500*(1.15)^8 = $22,942.67

So the correct option is the last one.

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25 Points please help me
ASAP and I will mark brainlyist

Answers

Answer:

(a)

1. 4.6... sample mean2. 4.6.. sample mean3. 4.8... sample mean4. 5.2... sample mean

(b) range of sample means =0.6

(c)

FalseFalseFalseFalse

How should I solve this?

Answers

The parallel sides AB, PQ, and CD, gives similar triangles, ∆ABD ~ ∆PQD and ∆CDB ~ ∆PQB, from which we have;

[tex] \frac{1}{x} + \frac{1}{y}= \frac{1}{z}[/tex]

Which method can be used to prove the given relation?

From the given information, we have;

∆ABD ~ ∆PQD∆CDB ~ ∆PQB

According to the ratio of corresponding sides of similar triangles, we have;

[tex] \frac{x}{z} = \mathbf{\frac{BD}{QD} }[/tex]

[tex] \frac{y}{z} = \frac{BD}{ BQ} [/tex]

Which gives;

[tex] \mathbf{\frac{y}{z}} = \frac{BD }{ BD - Q D} [/tex]

[tex] \frac{z}{y} = \frac{BD - QD }{ BD } = 1 - \frac{Q D }{ BD}[/tex]

QD × x = BD × z

BD × z = (1 - QD/BD) × y = y - (QD × y/BD)

Therefore;

BD × z = y - (QD × y/BD)

BQ × y = y - (QD × y/BD)

BQ × y = y - (z × y/x) = y × (1 - z/x)

(1 - z/x) = BQ

BD × z = y × (1 - z/x)

BD = (y × (1 - z/x))/z

Therefore;

QD × x = y × (1 - z/x)

(BD-BQ) × x = y × (1 - z/x)

(BD-(1 - z/x)) × x = y × (1 - z/x)

BD = (y × (1 - z/x))/x + (1 - z/x)

BQ + QD = (1 - z/x) + (y × (1 - z/x))/x

BD = BQ + QD

(y × (1 - z/x))/x + (1 - z/x) = (y × (1 - z/x))/z

(1 - z/x)×(y/x + 1) =(1 - z/x) × y/z

Dividing both sides by (1 - z/x) gives;

y/x + 1 = y/z

Dividing all through by y gives;

(y/x + 1)/y = (y/z)/y

1/x + 1/y = 1/z

Therefore;

[tex] \frac{1}{x} + \frac{1}{y}= \frac{1}{z}[/tex]

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The diameter of a circle graphed in the xy-plane has endpoints at (-2, -1) and (4,7). Which of the following is an equation of the circle?
A (x + 1)² + (y + 1)² = 25
B (x + 1)² + (y + 1)² = 100
C (x - 1)² + (y - 3)² = 100
D (x - 1)² + (y - 3)² = 25 ​

Answers

The required equation of the circle whose endpoint of the diameter  (-2, -1) and (4,7) is  (x - 1)² + (y - 3)² = 25 ​. Option D is correct.

Given that,

The endpoints of the circle's diameter (-2, -1) and (4,7).
The equation of the circle is to be determined.


What is a circle?

The circle is the locus of a point whose distance from a fixed point is constant i.e center (h, k). The equation of the circle is given by

(x - h)² + (y - k)² = r².

where h, k is the coordinate of the circle's center on the coordinate plane and r is the circle's radius.

Center of the circle(h, k) = (-2 + 4)/2 ,(-1+7)/2
                                  = 1  , 3
Radius of the circle,
[tex]r^2 =\sqrt{(1+2)^2+(3+1)^2}\\r^2 =\sqrt{9+16} \\r^2 = 25[/tex]


Equation of the circle with center (1, 3)
[tex]r^2 = (x - 1)^2 + (y-3)^2[/tex]
[tex]25 = (x - 1)^2 + (y-3)^2[/tex]

Thus, the required equation of the circle whose endpoint of the diameter  (-2, -1) and (4,7) is  (x - 1)² + (y - 3)² = 25 ​. Option D is correct.


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Boyle's law states that if the temperature of a gas remains​ constant, then PV​=c, where P=pressure​,V=volume ​, and c is a constant. Given a quantity of gas at constant​ temperature, if V is decreasing at a rate of 10in​^3/sec​, at what rate is P increasing when P =60​lb/in^2 and V=20in^3 in​? (do not round your answer.)

a. 30 lb/in^2 per sec
b. 120lb/in^2 per sec
c. 9 lb/in^2 per sec
d. 10/3 lb/in^2 per sec

Answers

The pressure, P if V is decreasing at a rate of 10in^3/sec is 120lb/in^2 per sec.option B

Boyle's law

PV = c

where,

P=pressure,V=volume , and c is a constant

when P =60lb/in^2 and V=20in^3

PV = c

60 × 20 = 1200 in

Find P if V is decreasing at a rate of 10in^3/sec

PV = c

P × 10 = 1200

10P = 1200

P = 1200 / 10

P = 120lb/in^2 per sec

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Show the following linear expression. Show all of your work and identify any properities used.

7-6x-9-x+3

Answers

Answer:

-7x + 1

Associative Property can be used.

Step-by-step explanation:

Hello!

We can simply the expression by combining like terms.

Like terms are terms with the same variable and degree. They may have different coefficients.

Simplify7 - 6x - 9 - x + 37 - 9 + 3 - 6x - x1 - 7x

The simplified form is 1 - 7x, or -7x + 1.

We can also represent this using the Associative property, by grouping like terms:

7 - 6x - 9 - x + 3(7 - 9 + 3) + (-6 - x)1 + (-7x)-7x + 1

Factor the GCF:-12x4y - 9x³y² + 3x²y³ (5 points)
O-3x²y(4x2 + 3xy - y²)
O 3x²y(-4x² + 3xy - y²)
O-3(4x²y + 3x³y² - x²y³)
O-3x²y(-4x2-3xy + y²)

Answers

Answer:

 A. 3x^2y(4x2 + 3xy - y^2)

Step-by-step explanation:

 -12(x^4)y - 9x³y² + 3x²y³

 -3x²y(4x² + 3xy - y²)

Find the Z-scores that separate the middle 56% of the distribution from the area in the tails of the standard normal distribution.

Answers

The z score that separate the middle 56% of the distribution from the area in the tails of the standard normal distribution is ±0.77.

Given that the z score separates the 56% of the distribution from the area in the tails of the standard normal distribution.

In a normal distribution in with mean μ and standard deviation σ, the z score of a measure X is as under:

Z=(X-μ)/σ

It is used to measure how many standard deviations the measure is from the mean.

After finding the z score we have to look at the z score table and find the p value associated with this z score, which is the percentile of X.

The normal distribution is symmetric which means that the middle 56% is between the 11th and 67th percentile. Looking at the z table the z scores are Z=±0.77.

Hence the z score that separate the middle 56% of the distribution from the area in the tails of the standard normal distribution is ±0.77.

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I need help with trigonometry
Again..

Answers

Answer: C. - √2

Step-by-step explanation:

Given requirements from the question

Find the exact value of sec 135°

Convert into common trigonometric expression

sec = secant

secx = 1 / cosx

Therefore, sec 135° = 1 / (cos 135°)

Find the reference angle

135° is quite a complicated angle, but it is possible to simplify it by finding its reference angle.

Since 135° is in the second quadrant, its reference angle will be

                                         180° - 135° = 45°

However, we need to consider the positive and negative.

In a coordinate plane, the clue is (A S T C), which corresponds to the positive values in each quadrant. In the QI, "All" are positive. In the QII, sine is positive. In the QIII, the tangent is positive. In QIV, cosine is positive.

Therefore, when the value of cosine is in QII, it is negative.

The reference angle = - (1 / cos 45°)

Determine the final value

Given that the reference angle = - (1 / cos 45°)

cos 45° = 1 / √2

Therefore:

sec 135° = - (1 / cos 45°) = - (1 / (1 / √2)) = [tex]\boxed{-\sqrt{2} }[/tex]

Hope this helps!! :)

Please let me know if you have any questions

what is 4.22 x 10^17 seconds

Answers

We can rewrite the given time as:

7.03x10^15 mins 1.17x10^14 hours.4.88x10^12 days.What is 4.22x10^17 seconds in minutes and hours?

First, remember that:

60s = 1 min

Then to write that amount in minutes, we just need to divide by 60, so we get:

(4.22x10^17)/60  mins=  7.03x10^15 mins

Now, remember that:

1 hour = 3600s

Then to get the time in hours, we need to divide by 3600:

(4.22x10^17)/3600 h = 1.17x10^14 hours.

Similarly, you can change to any time unit that you want, for example:

1 day = 24*3600 s

Then the time in days is:

(4.22x10^17)/(24*3600) days = 4.88x10^12 days.

And so on.

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On a rectangular soccer field, Sang is standing on the goal line 20 yards from the corner post. Jazmin is standing 99 yards from the same corner post on the nearest adjacent side of the field. What is the distance from Sang to Jazmin?



A. 119
B. 101
C. 10,201
D. 1,980

Answers

The distance from Sang to Jazmin is 101 yards.

What is the distance from Sang to Jazmin?

From the discussion in the question, we can see that the positions of Sang and Jazmin can be construed to give a rectangle. We know that the rectangle is a four sided figure.

The diagonal is a line that is drawn from one side of the four sided figure to another. Hence we can be able to apply the Pythagoras theorem to obtain the distance from Sang to Jazmin.

From;

c^2 = a^2 + b^2

c = √a^2 + b^2

c = √(20)^2 + (99)^2

c = 101 yards.

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please help with this i genuinely have no clue how to figure it out

Answers

Answer: c = 520

Step-by-step explanation:

     f(2) = 578 means that when x = 2, the value is equal to 578. We will plug these knowns in and then solve for c.

Given:

    f(x) = 4x³ + 7x² - x + c

Substitute:

    578 = 4(2)³ + 7(2)² - (2) + c

Distribute:

    578 = 4 * 2³ + 7 * 2² - 2 + c

Raise to the power of 3 and 2:

    578 = 4 * 8 + 7 * 4 - 2 + c

Multiply:

    578 = 32 + 28 - 2 + c

Add:

    578 = 60 - 2 + c

Subtract:

    578 = 58 + c

Subtract 58 from both sides:

    520 = c

Reflexive property:

   c = 520

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

Given:

[tex]\longrightarrow\bold{f(x) = 4x^3 + 7x2 −x + c}[/tex]

[tex]\longrightarrow\sf{578= 32+28 −2+ c}[/tex]

[tex]\longrightarrow\sf{578 =58+ c}[/tex]

[tex]\longrightarrow\sf{c = 578-58}[/tex]

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

[tex]\longrightarrow\sf{c= 520}[/tex]

magan wants to ride his bicycle 30.4 miles this week. he has already ridden 4 miles if he rides for 4 more days what is the average number of miles he would have to ride each day to meet his goal?

Answers

The average number of miles he will ride each day to meet his goal is 6.6 miles

How to find the average number of miles she will ride?

He wants to ride his bicycle 30.4 miles this week.

He has already ridden 4 miles.

He rides 4 more days.

Therefore, the average number of miles he would have to ride each day to meet his goal can be calculated as follows:

let

x = number of miles driven

Hence, the equation can be represented as follows;

4x + 4 = 30.4

Therefore,

4x + 4 = 30.4

4x + 4 - 4 = 30.4 - 4

4x = 26.4

x = 26.4 / 4

x = 6.6

Therefore, the average number of miles he will ride each day to meet his goal is 6.6 miles

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PLS HELLP ITS SO HARD

Answers

Answer:

[3,0]

[0,9]

Step-by-step explanation:

9x+3y=27

9x+3(0)=27

9x=27

x=3

9(0)+3y=27

3y=27

y=9

A mathematical prodigy wishes to put 2 of his indistinguishable IMO gold medals and 2 of his indistinguishable IPhO gold medals in one row. How many distinct arrangements are possible

Answers

This relates to combination and permutations and the number of distinct arrangements that are possible will be 6.

How to illustrate the information?

From the information, a mathematical prodigy wishes to put 2 of his indistinguishable IMO gold medals and 2 of his indistinguishable IPhO gold medals in one row.

Let 1 = IMO

Let 0 = IPho.

Therefore, the number of arrangement will be:

0011

0110

1100

1010

0101

1001

Therefore, the number of arrangement will be 6.

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The table below shows the birth rate (per 1000) per year in the United States according to data from the National Center for Health Statistics. Let x represent the number of years since 2000 with x = 0 representing the year 2000. Let y represent the birth rate per 1000 population. Write the slope-intercept form of the equation for the line of fit using the points representing 2001 and 2010. Round to the nearest hundredth.

Answers

The regression linear function, in slope-intercept form, is given by:

y = -0.07x + 14.5

How to find the equation of linear regression using a calculator?

To find the equation, we need to insert the points (x,y) in the calculator.

For this problem, the points are given as follows:

(0, 14.7), (1, 14.5), (2, 14.4), (3, 14.1), (4, 14), (5, 14.1), (6, 14.1), (7, 14.2), (8, 14), (9, 13.8), (10, 14).

Inserting these points into a calculator, the regression linear function, in slope-intercept form, is given by:

y = -0.07x + 14.5

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Answer:

y = -0.07x + 14.5

Step-by-step explanation:

Rhombus A B C D is shown. Lines are drawn from point A to point C and from point D to point B and intersect at point E. All sides are congruent.

The area of rhombus ABCD is 72 square units. EC = 8 units and DB = x – 1.

What is the value of x?
9
10
14
16

Answers

Area of rhombus = 1/2 * diagonal * diagonal

72 = 1/2 * AC * BD

Diagonals bisect each other in a rhombus so if EC is 8 then AC is 16

72 = 1/2 * 16 * x - 1
72 = 8(x-1)
9 = x-1
X = 10

Check
72 = 1/2 * 16 * 10-1
72 = 1/2 * 16 * 9
72 = 8 * 9
72=72

The rhombus ABCD has an area of 72 square units. Diagonals AC and BD intersect at E. Given EC = 8 units and DB = x - 1, the value of x is 10 units. The correct option is B).

We are given a rhombus ABCD with area 72 square units. The diagonals AC and BD intersect at point E.

Since all sides of the rhombus are congruent, we can assume that the length of each side is "s" units.

We are also given that EC (a part of diagonal AC) is 8 units long.

As diagonals of a rhombus bisect each other, we can deduce that the other half of diagonal AC is also 8 units. So, the full diagonal AC is 16 units (8 units + 8 units).

Now, we are told that DB (a part of diagonal BD) is x - 1 units long.

To find the value of x, we need to find the length of the other half of diagonal BD, which is also x - 1 units. So, the full diagonal BD is

(x - 1) units + (x - 1) units = 2x - 2 units.

The area of a rhombus is given by the formula:

Area = 1/2 × Product of Diagonals.

Substituting the given values, we have:

72 = 1/2 × 16 × (2x - 2).

Now, we can simplify the equation:

72 = 8x - 8.

Move the constant term to the right side:

8x = 72 + 8.

Combine the constants:

8x = 80.

Finally, solve for x by dividing both sides by 8:

x = 80 / 8 = 10.

So, the value of x is 10 units. The correct answer is B).

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--The given question is incomplete, the complete question is given below " Rhombus A B C D is shown. Lines are drawn from point A to point C and from point D to point B and intersect at point E. All sides are congruent.

The area of rhombus ABCD is 72 square units. EC = 8 units and DB = x – 1.

What is the value of x?

9

10

14

16 "--

The hollenbecks own a square lot with area 3600 square meters. they plan to fence just three sides of this lot. how many meters of fence must they purchase?

Answers

Answer: 180 meters

Step-by-step explanation: To solve this we need to find the square root of 3600. 6x6 = 36 so we know the square root is 60. That means that each side of the square lot is 60 meters. If they fence 3 sides they will need to purchase 60x3= 180 meters of fence.

2
5. One flight took a total of 4.6 hours. Write this number as a mixed number
and as an improper fraction. Show your work in the space below. Remember
to check your solution.

Answers

Step-by-step explanation:

4.6 hrs is 46over 10 which is

13 over 5 or 2 and 3over 5

How many ways are ther eto line up the 12 people if the bride must be next to the maid of honor?

Answers

the number of ways to line up the 12 people if the bride must be next to the maid of honor is 132 ways.

How to determine the permutation

The formula for finding the number of arrangement is given as;

Permutation = [tex]\frac{n!}{n - r!}[/tex]

Where;

n is the total number of objectr is the number of selected objects

From the question given, we can deduce that

n = 12 people

r = 2, because they must come next to each other and is taken as 2

We then have,

Permutation = [tex]\frac{12!}{12 - 2!}[/tex]

Permutation = [tex]\frac{12!}{10!}[/tex]

Permutation = 132 ways

This is to tell us that the number of ways to arrange the people is 132 ways

Thus, the number of ways to line up the 12 people if the bride must be next to the maid of honor is 132 ways.

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