A perpendicular bisector of DC is AB and a perpendicular bisector of AB is DC. the intersection of AB and DC is at E. Which equation is true?

EB =CD
AE= DE
DE = CE
CD= CE
AB=CD

The hotel charge in city one is $767 and the hotel charge in city two is $2276.

Let x = the charge in 1st city before taxes and

Let y = the charge in 2nd city before taxes

The equation before taxes:

y = x ₊ 1500 ..eq(1)

The equation for total tax paid:

0.075x ₊ 0.055y = 700 ..eq(2)

Substitute equation 1 that is y value in equation 2.

0.075x ₊ 0.055(x₊1500) = 700

0.075x ₊ 0.055x ₊ 82.5 = 700

add the variables and subtract the constants.

0.805x = 700 ₋ 82.5

0.805x = 617.5

x = 617.5/0.805

x = 767

now substitute x value in equation 1.

y = 767 ₊ 1500

y = 2267

Hence the hotel charge before the tax in the first city was $767 and in the second city was $2267.

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Answer:





Find the multiplicative inverse of the following

(i) -13    (ii) -13/19    (iii) 1/5    (iv) -5/8 × -3/7    (v) -1 × -2/5

(vi) -1

Solution:

The reciprocal of a given rational number is known as its multiplicative inverse. The product of a rational number and its multiplicative inverse is 1.

(i) The Multiplicative inverse of -13 is -1/13

∵ -13 × (-1/13) = 1

(ii) The Multiplicative inverse of -13/19 is -19/13

∵ -13/19 × (-19/13) = 1

(iii) The Multiplicative inverse of 1/5 is 5

∵ 1/5 × 5 = 1

(iv) The Multiplicative inverse of -5/8 × -3/7 is 56/15

∵ -5/8 × (-3/7) = 15/56 and 15/56 × 56/15 = 1

(v) The Multiplicative inverse of -1 × -2/5 is 5/2

∵ -1 × (-2/5) = 2/5 and 2/5 × 5/2 = 1

(vi) The Multiplicative inverse of -1 is -1

∵ -1 × (-1) = 1

The logical function that represents the amount of workout Laura does in each week along with her simultaneous increase in workout can be given by Arithmetic Progression.

It is represented as An = A + (n-1)d. Here, A represents the first term, or the amount of workout done in first week, d represents common difference or the difference in workout done in next week to its previous week, n represents the number of terms or the number of weeks for which data is to be calculated and An represents the workout done in nth week.

Arithmetic progression refers to the sequence of numbers such that each succeeding number increases with respect to previous number by fixed/ constant value. Thus, there exists constant amount of difference between each consecutive pair of number.

Since, Laura's workout pattern varies such that the amount of workout she does in one week increases by same amount in next week, so we get an arithmetic progression of her workout pattern.

Hence, her workout pattern can be traced as A, A+d, A+2d, A+3A, ..., An.

Thus, An = A + [(n-1)*d]

A3 = A +[(3-1)*d] = A + [2d] = 20 ...(1)

A9 = A +[(9-1)*d] = A + [8d] = 50 ...(2)

A11 = A +[(11-1)*d] = A + [10d] = 60 ...(3)

Solving equation (1) and (2), we get d = 5 and A = 10.

Thus, we conclude by saying that the function of her exercise routine is given by arithmetic progression and the amount of workout that she increases each week is given by 'd' that is 5 minutes.

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Answer:

Mixed fractions is equivalent to improper fraction both A and C

A. 12 1/3

C. 10 7/3

The inequality shown by a number line which describes that 12 is to the right of -2 is; 12 > -2.

It follows from the task content that the inequality which represents the number line as described in the task content is to be determined

On this note, it follows that since, numbers are arranged from left to right in increasing order on the number line, then;

Since 12 is to the right of -2, the inequality which represents the situation is; 12 > -2.

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Required answer:

Detailed explanation:

To find the slope of the line, given that it passes through two points, use the formula:

[tex]\bf{m=\dfrac{y_2-y_1}{x_2-x_1}}[/tex]

Where:

Plug in the data:

[tex]\bf{m=\dfrac{6-6}{3-(-4)}=\dfrac{0}{3+4}=\dfrac{0}{7}=\boxed{\bf{0}}[/tex]

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

Given the pair of points: (-5,8) and (-5,-6), plug them into the slope formula:

[tex]\bf{m=\dfrac{y_2-y_1}{x_2-x_1}}[/tex]

Evaluate:

[tex]\bf{m=\dfrac{-6-8}{-5(-5)}=\dfrac{-14}{-5+5}=\dfrac{-14}{0}=\boxed{\bf{Not\:De fined}}[/tex]

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

Answer: The number of ribbons used to trim the Curtains are 72 inches.

Step-by-step explanation:

Let us convert all numbers into inches.

Then, 1 yard= 36 inches

Given data, 5/2yards

So, 5/2 yards means.,

5/2= 2.5 yards

We can write: 2.5yards=2.5x36inches

=90inches

We convert feet into inches

1feet=12inches

We consider 1feet=12inches

In this question she had 1feet 6 inches of ribbons left.

Then 1x12=12inches

More 6 inches: 12+6=18inches

Now subtract 18 inches from 90 inches to get the inches used to trim curtains

Then, 90inches-18inches=72 inches

Thus, the number of ribbons used to trim the Curtains are 72 inches.

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Venn diagram{image attached},2000 people didn't cast their vote and 1000 votes are not valid in the election

Given that In a municipal election, two candidates, A and B, ran for the position of Mayor, and 25000 people voted. Voters were supposed to vote for only one candidate. A received 12000 votes, B received 10,000 votes, and 1000 cast votes for A and B both.

Number of votes for A=12,000

Number of votes for B=10,000

1000 cast votes to Both A and B, these votes are not valid because each one is supposed to vote only for one.

Therefore, the number of votes not valid is 1000

Total people cast vote= sum of votes for every party

Total people cast vote=12,000+10,000+1000

Total people casted vote=23,000

Therefore, Venn diagram{image attached},2000 people didn't cast their vote and 1000 votes are not valid in the election

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Answer:

x=-8

Step-by-step explanation:

8x-2=3x+5x

1. Combine Like Terms

3x+5x=8x

Now your equation looks like this:

8x-2=8x

+8x   +8x

2. Move Variables to one side

Now this is your equation:

-2=16x

3. Divide to isolate "x"

16/-2

x=-8

Let me know if this helped! :)

Answer:

3

Step-by-step explanation:

Think of "f(a)" like "y" in this context.   You can set that equal to 11 and solve for a:

f(a) = 3a + 2

11 = 3a + 2

9 = 3a

3 = a

Answer:factors

Step-by-step explanation:

The value of x in the angles is 20

The angles are given as

4x - 12 and 7x - 28

These angles are same side interior angles

So, we have

4x - 12 + 7x - 28 = 180

Collect the like terms

So, we have

4x + 7x  - 12 - 28 = 180

Evaluate the like terms

So, we have

11x  = 220

Divide both sides by 11

x= 20

Hence, the value of x in the angles is 20

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Answer:

x = c / (7 - h)

Step-by-step explanation:

c = 7x - hx

c = x(7 - h)

x = c / (7 - h)

The actual problem will be  9000 % 700, with the remainder 600 and quotient 12.

Since we are with the actual problem, which is 8,950 % 695, here the dividend is 8950  and the divisor is 695, the actual division we come up with the 12 as quotient and remainder 620. Now making the expression simple  using the round-off rule, here  in  the dividend  8950, the last two digits are 50, so we can round off it to 9000 and in the  divisor  695,  the last digit is 5, so we add 1 in the preceding  number converting it to 700, after the actual division of the estimated expression, the quotient we come up with is 12, and the remainder is 600.

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Answer:

41

Step-by-step explanation:

because if m=-4 that means (-4)2+6(-4)+9=41

Answer:

3

Step-by-step explanation:

32 - 20 = 12

12/4 = 3

This assumes that by remainder they mean they twelve feet left over and not the twenty feet removed. This is likely what it means.

Answer:

1440

Step-by-step explanation:

3(4+4)(4+1)(4+2)(4-2)

3*8*5*6*2

1440

From the steps below, it has been proved that  by transitive property of congruence, we can say that; ∠CON ≅ ∠BOM

We are given;

∠AOM ≅ ∠DON

To prove that;

∠CON ≅ ∠BOM

Now, from the image attached, we can say that;

∠BOM ≅ ∠DON because of vertical angles theorem

Similarly, we can say that ∠AOM ≅ ∠BOM due to transitive property of congruence.

Also, we can say that from vertical angles theorem, ∠AOM ≅ ∠CON

Finally, since  ∠AOM ≅ ∠BOM, then by transitive property of congruence, we can say that;∠CON ≅ ∠BOM

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If A line of best fit for the data is  B= 0.45m + 1.93. The value that is the best estimate of the amount of money in the jar at the end of the first month is: D.  $2.38.

Given:

B= 0.45m + 1.93.

Where:

m= 1 month (First month)

Hence:

B= 0.45(1) + 1.93

B= 0.45+ 1.93

B=$2.38

Therefore if A line of best fit for the data is  B= 0.45m + 1.93. The value that is the best estimate of the amount of money in the jar at the end of the first month is: D.  $2.38.

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Using the Venn sets, the amounts are given as follows:

a) 1358 students.

b) 688 students.

c) 1758 students.

d) 746 students.

e) 371 students.

f) 771 students.

For this problem, we consider the following sets:

235 students said they were taking all three courses, hence:

(A ∩ B ∩ C) = 235.

457 students said they were taking Dance and Psychology, hence:

(B ∩ C) + (A ∩ B ∩ C) = 457

(B ∩ C) = 222.

466 students said they were taking Psychology and History, hence:

(A ∩ C) + (A ∩ B ∩ C) = 466

(A ∩ C) = 231.

474 students said they were taking Dance and History, hence:

(A ∩ B) + (A ∩ B ∩ C) = 474

(A ∩ B) = 239.

1012 students said they were taking Psychology, hence:

C + (A ∩ C) + (B ∩ C) + (A ∩ B ∩ C) = 1012

C + 231 + 222 + 235 = 1012

C + 688 = 1012

C = 324.

987 students said they were taking Dance, hence:

B + (A ∩ B) + (B ∩ C) + (A ∩ B ∩ C) = 987

B + 239 + 222 + 235 = 987

B + 696 = 987

B = 291.

921 students said they were taking History, hence:

A + (A ∩ B) + (A ∩ C) + (A ∩ B ∩ C) = 921

A + 239 + 231 + 235 = 921

A + 705 = 921

A = 216.

The number of students who took no courses is given as follows:

None + A + B + C + (A ∩ B) + (A ∩ C) + (B ∩ C) + (A ∩ B ∩ C) = 2129

None + 216 + 291 + 324 + 239 + 231 + 222 + 235 = 2129

None + 1758 = 2129

None = 2129 - 1758

None = 371.

For item a, the amount is:

Dance + None = 987 + 371 = 1358 students.

For item b, the amount is:

(B ∩ C) + (A ∩ B ∩ C) + (A ∩ C) = 457 + 231 = 688 students.

For item c, the amount is the total subtracted by none, hence:

2129 - 371 = 1758 students.

For item d, the amount is:

A + B +  (A ∩ B) = 216 + 291 + 239 = 746 students.

For item e, the amount is of 371, as we found previously.

For item f, the amount is:

A + C +  (A ∩ C) = 216 + 324 + 231 = 771 students.

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Answer:

noun. Britannica Dictionary definition of SELLING PRICE. [singular] : the price for which something actually sells. They asked $200,000 for the house, but the eventual selling price was $175,000.

Answer:

[tex]\begin{array}{|l|l|c|c|c|}\cline{1-5} \textbf{Equation} & \textbf{Standard Form} & \textbf{a} & \textbf{b} & \textbf{c}\\\cline{1-5} \text{1.}\:\:x^2+x=20 & x^2+x-20=0 & 1 & 1 & -20\\\cline{1-5} \text{2.}\:\:4x^2-2x=28 \phantom{)))}& 4x^2-2x-28=0 \phantom{)))}& 4 & -2 & -28\\\cline{1-5} \text{3.}\:\:5x^2=225 & 5x^2-225=0 & 5 & 0 & -225\\\cline{1-5} \text{4.}\:\:x^2-x=36 & x^2-x-36=0 & 1 & -1 & -36\\\cline{1-5} \text{5.}\:\:3x^2-4=7x & 3x^2-7x-4=0 & 3 & -7 & -4 \\\cline{1-5}\end{array}[/tex]

Step-by-step explanation:

Standard form of a quadratic equation:

[tex]\boxed{ax^2+bx+c=0}[/tex]

Question 1

Given:

[tex]x^2+x=20[/tex]

Rearrange to standard form by subtracting 20 from both sides:

[tex]\implies x^2+x -20=20-20[/tex]

[tex]\implies x^2+x -20=0[/tex]

Therefore:

Question 2

Given:

[tex]4x^2-2x=28[/tex]

Rearrange to standard form by subtracting 28 from both sides:

[tex]\implies 4x^2-2x-28=28-28[/tex]

[tex]\implies 4x^2-2x-28=0[/tex]

Therefore:

Question 3

Given:

[tex]5x^2=225[/tex]

Rearrange to standard form by subtracting 225 from both sides:

[tex]\implies 5x^2-225=225-225[/tex]

[tex]\implies 5x^2-225=0[/tex]

Therefore:

Question 4

Given:

[tex]x^2-x=36[/tex]

Rearrange to standard form by subtracting 36 from both sides:

[tex]\implies x^2-x-36=36-36[/tex]

[tex]\implies x^2-x-36=0[/tex]

Therefore:

Question 5

Given:

[tex]3x^2-4=7x[/tex]

Rearrange to standard form by subtracting 7x from both sides:

[tex]\implies 3x^2-4-7x=7x-7x[/tex]

[tex]\implies 3x^2-4-7x=0[/tex]

[tex]\implies 3x^2-7x-4=0[/tex]

Therefore:

The estimation of the value is A. 40000.

Based on the information, we are to estimate the sum by rounding to the nearest ten thousand. 18,789 + 19,019.

It should be noted that 18789 to the nearest ten thousand is 20000.

Also, 19019 to the nearest ten thousand will be 20000.

Therefore, the addition will be:

= 20000 + 20000

= 40000

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Answer:

Please see picture below.

Step-by-step explanation:

Answer:

no, in a function x can not repeat so points (2,-1) and (2,-2) makes it wrong bc 2 is your x

The area of triangle XYZ is of 13.3 units².

The missing information are the vertices of the triangle, given as follows:

The area of a triangle is given by half the base multiplied by the height, that is:

A = 0.5bh

For this problem, the have that the base is the length of segment XZ, which is found applying the distance between two points as follows:

[tex]b = \sqrt{(1 + 3)^2+(-1 - 2)^2}[/tex]

b = sqrt(25)

b = 5.

The height is the distance between the midpoint of XZ and Y. The midpoint of XZ(mean of the coordinates) is (-1, 0.5), hence the height is:

[tex]h = \sqrt{(-1 - 3)^2+(4 - 0.5)^2}[/tex]

h = sqrt(4² + 3.5²)

h = 5.32.

Thus the area of the triangle is given by:

A = 0.5 x 5 x 5.32 = 13.3 units².

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The profit function is P(x) = ( - x² / 5000 ) + 11.9x - 95000.

35,000 baseball game tickets were sold at $5 per ticket.

When the price is raised to $6, then 30,000 tickets were sold.

The variable and fixed costs for the ballpark owners are $0.10 and $95,000 respectively.

Let's say x is the number of tickets sold, and P is the profit.

Then,

P = ax + b

At P = 5,

5 = (35000)a + b                                                                                  ---------(1)

At P = 6,

6 = (30000)a + b                                                                                  --------(2)

Subtracting (2) from (1),

5 - 6 = (35000)a + b - (30000)a - b

- 1 = 5000(a)

a = ( - 1/5000)

So if a = ( - 1/5000),

Then,

5 = (35000)a + b

5 = (35000)( - 1 / 5000 ) + b

5 = - 7 + b

b = 12

Therefore,

P(x) = ( - x /5000) + 12

Now, the profit function is:

Profit = Revenue - Costs

P(x) = R(x) - C(x)

Now, R(x) =  xp(x)

R(x) = x[ ( - x/5000) + 12]

R(x) = ( - x² / 5000 ) + 12x

The fixed cost is F(x) = $95000

Hence, the costs will be:

C(x) = 95000 + (0.10)x

Therefore the profit function is:

P(x) = R(x) - C(x)

P(x) = ( - x² / 5000 ) + 12x - 95000 - (0.10)x

P(x) = ( - x² / 5000 ) + 11.9x - 95000

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Answer:

$127975, $182875

Step-by-step explanation:

Let the salary in state A be x. Then, the salary in state B is x+54900.

[tex]x+x+54900=310850 \\ \\ 2x=255950 \\ \\ x=127975 \\ \\ x+54900=182875[/tex]