Opposite sides are congruent.
Diagonals are perpendicular.
Exactly one pair of opposite angles are
congruent.
Diagonals are congruent.
Diagonals bisect opposite interior angles.
Consecutive interior angles are
supplementary.

Answer:

<

Step-by-step explanation:

Negative numbers are always smaller than positive numbers, and "<" is the smaller than symbol, so < is the correct choice. We can eliminate = immediately because a negative number can't equal a positive number (excluding the weird number 0)

Jorge mowed 18 lawns.

Let the number of lawns mowed by Jorge =x

So according to the question

Number of lawns mowed by sandra = x/3

Number of lawns mowed by Danny =x/2

Number of lawns mowed by Valeria =16

sum of total lawns mowed = lawns mowed by Jorge + lawns mowed by sandra + lawns mowed by Danny + lawns mowed by Valeria.

[tex]x+\frac{x}{3} +\frac{x}{2} +16=49[/tex]

taking LCM as 6 and solving further we get

[tex]\frac{6x+2x+3x+96}{6} =49[/tex]

By cross Multiplying we get

11x+96=294

11x=198

Solving further for x,

x=198/11

x=18

Therefore,  the number of lawns mowed by Jorge is 18 .

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Norma's family spends 120 mins at Mount Rushmore

The question is based on the concept of linear equations where 1/3 of an hour spent watching a movie equals 1/6 of the total time spent at Mount Rushmore by Norma and her family.

The time they watched the movie = 1/3 of an hour

Time spent at Mount Rushmore = 1/6 of the whole time

The equations will be as follows:

1/3 of an hour = 1/6 of the whole time

20 mins = 1/6 of the whole time

120 mins = The time they spent at Mount Rushmore

So, Norma's family spends 120 mins at Mount Rushmore

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Answer:

$18 less than the cost of 5 hot dog combos

Step-by-step explanation:

First, we see from the minus sign that this will be subtraction.  PEMDAS (order of operations) says we do the multiplication first, then the subtraction.

We get the fractions in ascending order as -2350 / 1000, -1640 / 1000, 1225 / 1000 and 2050 / 1000.

We are given the daily changes in four stock prices as shown in the table.:

-2 35/100

-1.64

2.05

1 9/40

We have to arrange them from least to greatest in fraction form with a common denominator.

We can write -2 35/100 as:

-235 / 100 ( mixed fraction converted into the improper fraction)

= -2350 / 1000

We can write -1.64 as:

- 1.64 = -164 / 100 ( decimal into fraction)

= -1640 / 1000

We can write 2.05 as:

2.05 = 205 / 100 (decimal into fraction)

= 2050 / 1000

We can write 1  9/40 as:

1 9/40 = 49 / 40 ( mixed fraction converted into the improper fraction)

49 / 40 × 25 / 25

= 1225 / 1000

Arranging it from least to greatest, we get that:

-2350 / 1000, -1640 / 1000, 1225 / 1000 and 2050 / 1000

Therefore, we get the fractions in ascending order as -2350 / 1000, -1640 / 1000, 1225 / 1000 and 2050 / 1000.

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The results of the equations are listed below:

In this problem we must make use of given formulas and substitute all known variables to determine all the required information:

Case 1

The temperature in Celsius scale in terms of the temperature in Fahrenheit scale is defined by the following formula:

T' = (5 / 9) · (T - 32)

T' = (5 / 9) · (68 - 32)

T' = 20 °C

Case 2

The area of the circle in terms of its radius is presented below:

A = π · r²

A = π · (6 m)²

A ≈ 113.097 m²

Case 3

The area of the triangle as a function of its base and its height is shown in the following formula:

A = 0.5 · b · h

A = 0.5 · (8 ft) · (25 ft)

A = 100 ft²

Case 4

The traveled distance is the product of the velocity and time:

s = v · t

s = (62.5 mi / h) · (5 h)

s = 312.5 mi

Case 5

The simple interest formula is equal to the product of the invested amount, interest rate and time divided by 100:

C' = (C · r · t) / 100

C' = [(300) · (5) · (8)] / 100

C' = $ 120

Case 6

C' = (C · r · t) / 100

C' = [(200) · (2) · (10)] / 100

C' = $ 40

Case 7

s = v · t

s = (45 mi / h) · (0.5 h)

s = 27.5 mi

Case 8

T' = (5 / 9) · (T - 32)

T' = (5 / 9) · (212 - 32)

T' = 100 °C

Case 9

C' = (C · r · t) / 100

C' = [(1200) · (2.5) · (2)] / 100

C' = $ 60

Case 10

The area of the rectangle is equal to the product of its base and its height:

A = b · h

A = (14 ft) · (8 ft)

A = 112 ft²

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Hence the required expression is Proved.

Given the expression is 2 1/4 ₋ 6/7 = 39/28

Consider L.H.S 2 1/4 ₋ 6/7

Convert improper fraction to proper fraction.

2 1/4 = 9/4

take LCM of the denominators.

The LCM is 28.

9×7/28 ₋ 6×4/28

63/28 ₋ 24/28

Now subtract.

63 ₋ 24/28

39/28

Hence proved.

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Your question is incomplete. Please find the missing content here.

Show that 2 1/4 ₋ 6/7 = 39/28

Answer:

T9=60

Step-by-step explanation:

step 1: solve for x

it is an arithmetic pattern,so the 1st difference is the common difference (d)

therefore...9x+199x+11-(4x+44x+4)=14x+18-(9x+199x+11)

128x+11-48x-4=14x+18-128x-11

80x+7=-144x+7

80x+144x=7-7

224x=0

224x/224=0/224

X=0

step 2: substitute for x

4(0)+44(0)+4=4[1st term]

9(0)+119(0)+11=11(2nd term)

14(0)+18=18(3rd term)

step 3:find the common difference

d=3rd term- 2nd term, 2nd term-1st term

3rd term-2nd term

18-11=7

2nd term-1st term

11-4=7

therefore...d=7

step 4:find the general formula

we use the formula Tn=a+(n-1)d to find the general formula/ nth term

where: Tn is the nth term

a is the first term

n is the number of term

d is the common difference

Tn=a+(n-1)d

=4+(n-1)7

=4+7n-7

=7n-3

step 5:find the 9th term

Tn=a+(n-1)d

=7n-3

=7(9)-3

=60

The result obtained are-

A frequency table is merely a "t-chart" or two-column table that illustrates the numerous possible outcomes and associated frequencies demonstrated in a sample.

Part 1: Smallest value;

As the frequency table is continuous distribution with a initial value of 4.

Thus, the smallest value of the table is 4.

Part 2: largest value;

As the frequency table is continuous distribution with a final value of 48.

Thus, the largest value of the table is 48.

Part 3: Median

The median is the number in the middle of a sorted list of numbers, and it is more descriptive of the data set than that of the average.

For even number of frequencies.

median = n/2

median = 12/2 = 6

Thus, the 6th term is the median.

median = 24.

Part 4: first quartile {Q1}

When data points are organized in increasing order, the lower quartile, or the first quartile (Q1), is indeed the value at which 25% of them are found.

Thus, Q1 = 12.

Part 3: third quartile {Q3}

When arranged in increasing order, the upper quartile, as well as third quartile (Q3), has been the value at which 75% of data points are found.

Q3 = 36.

The result for the frequency distribution is obtained.

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The Arithmetic sequences are-

The common difference must be same for the sequence to be arithmetic;

d₁ = a₂- a₁

d₂ = a₃ - a₂

Thus, d₁ = d₂

Check the common differences for given sequences are-

A. -5, 5, -5, 5, - 5, 5....

d₁ = 5 - (-5) = 10

d₂ = -5 - 5 = -10

d₁ ≠ d₂, not a Arithmetic sequences

B. 96, 48, 24, 12, 6...

d₁ = 48 - 96 = -48

d₂ = 24 - 48 = -24

d₁ ≠ d₂, not a Arithmetic sequences

C. 18, 5.5, -7, -19.5, -32...

d₁ = 5.5 - 18 = -12.5

d₂ = -7 - 5.5 =  - 12.5

d₁ = d₂,  Arithmetic sequences

D. -1, -3, -9, -27, -81....

d₁ = -3 -(-1) = -2

d₂ = -9 - (-3) = -6

d₁ ≠ d₂, not a Arithmetic sequences

E. 16, 32, 48, 64.....

d₁ = 32 - 16 = 16

d₂ = 48 - 32 = 16

d₁ = d₂,  Arithmetic sequences

Thus, the common difference must be equal for Arithmetic sequences.

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So S.P of the product is 10.4% .

We have been given C.P of a product is E950 and loss percentage is 6%,.

So the starting price is the the price for which something actually sells.

And the cost price represents the specific value that represents unit price purchased. This value is used as a key factor in determining profitability, and in some stock market theories it is used in establishing the value of stock holding.

A saving account has a rate of interest of 10 denoted by our which we can write equal to 0.1 in decimal form and we have to calculate the effective annual yield yield if the interest is calculated quarterly, that means we have the number of compounds per year denoted by M equal to four. The effective yield denoted by capital Y is given by the formula one plus are divided by M. Hold raised to the Power M -1. After putting in the values of R and M we get one plus 0.1 divided by four. Hold raised to the Power 4 -1, equal to one plus 0.25 raised to the power four minus one which is equal to 1.025 raised to the Power 4 -1. On simplifying this further, we get the value equal to 0.1038. Now this value is in the decimal form to convert it into percentage. We will multiply this value by 100. That means we have like 0.1038 multiplied by 100 Which gives us 10.38. And after rounding it off to one decimal place, we get the value 10.4%.

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we get the sum of (a b² + 26² ) + ( - 6 c a b² + 26² ) as a b² ( 1 - 6 c) + 1352.

We are given the expression:

(a b² + 26² ) + ( - 6 c a b² + 26² )

We need to find its sum.

a b² + 26² - 6 c a b² + 26²

a b²  - 6 c a b² + 26² + 26²

a b²  - 6 c a b² + 676 + 676

a b²  - 6 c a b² + 1352

a b² ( 1 - 6 c) + 1352.

Therefore, we get the sum of (a b² + 26² ) + ( - 6 c a b² + 26² ) as a b² ( 1 - 6 c) + 1352.

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2ⁿ integers can be represented and the range would be 0 to (2ⁿ) -1.

So, if n bits are given then 2ⁿ integers can be represented.

And the range is the difference between the largest number by the smallest number. So, the range of 2ⁿ integers will be from 0 to (2ⁿ) -1.

Therefore, 2ⁿ integers can be represented and the range would be 0 to (2ⁿ) -1.

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Answer:

y = -5/4x + 1

Step-by-step explanation:

Answer:

6.913339

Step-by-step explanation:

a) the formula for r is r = (a/p - 1)/r

b) The interest rate for the principal is $1000, the time is 2 years and simple inters $1080 is 0.04

c) The formula for p is p = a/1+rt

Simple Interest:

Simple interest is the process of multiplying the daily interest rate by the principal by the number of days that elapse between payments.

Given,

the amount a of money in an account after simple interest has been earned is given by the formula

=> a = p + prt

where

p is the principal,

r is the annual interest rate in decimal form, and

t is the time in years.

Here we need to find the following:

a. solve the formula for r

b. the amount of money in an account after interest has been earned is $1080, the principal is $1000, and the time is 2 years. what is the annual interest rate?

c. solve the formula for p.

a) The formula for r is calculated by moving the other elements and hold on r.

Then, the given formula,

=> a = p + prt

=> a = p (1 + rt)

=> a/p = 1 + rt

=> a/p - 1 = rt

=> r = (a/p - 1)/r

b) The given values are

p = $1000

t = 2

a = $1080

Now apply the values on the formula r to find the value of it,

=> r = ([1080/1000] - 1)/2

=> r = (1.08 - 1) /2

=> r = 0.08/2

=> r = 0.04

c) The formula for p can be derived as follows:

=> a = p + prt

=> a = p(1+rt)

=> p = a/1+rt

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Answer:

102

Step-by-step explanation:

x = 5th test

(82 + 76 + 90 + 0 + x) /5 = 70

248 + x = 70*5

x = 350 - 248

x = 102

Answer:

{y | 0 ≤ y < 9}

Step-by-step explanation:

The range is all the y-values; all the y's on the graph, or if you had an equation, all the y's that could be produced by that equation.

Right away, you know if the question is RANGE, the sets showing x are NOT the answer.

On the graph shown the lowest point is at (0,0) and it IS actually on the graph, so we use a >= symbol that has the "or equal to" bar under the > symbol.

The biggest y-value on the graph is the 9, but it's an open point, so exactly9 is technically NOT on the graph. So we use a < symbol without the bar underneath.

Lines can be perpendicular or parallel to one another.

What do we mean by linear equation?

So,

A linear equation is written as:  y = mx + b

Where, m = slope.

(A) Parallel equation:

The slope of a line parallel to y = mx + b is the same as the slope of y = mx + b, that is the slope is the equation in m.

The equation is then solved as follows:

Where:

Now, put (x₁,y₁) = (a,c) in y = m(x - x₁) + y₁ as follows:

y = m (x - a) + c

y = mx - am + c

So, the equation of a line is y = mx - am + c.

(B) Parallel equation:

The slope (m2) of a perpendicular line to y = mx + b is:

The equation is then solved as follows:

Where:

Now, put (x₁,y₁) = (a,c) in y = m(x - x₁) + y₁

The perpendicular line's equation is y = -(x/m) + a/m + c.

Therefore, lines can be perpendicular or parallel to one another.

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The correct question is given below:
Find the equations for the lines through the point (a,

c.that are parallel to and perpendicular to the line y = mx + b where m ≠ 0. use y for the dependent variable and all letters in lower case.

Answer:

[tex]x=-3[/tex]

Step-by-step explanation:

[tex]-4\left(1.5x-5\right)+4x=26[/tex]
Subtract 20 from both sides.
[tex]-2x+20-20=26-20[/tex]
-2x=6
[tex]\frac{-2x}{-2}=\frac{6}{-2}[/tex]
[tex]x=-3[/tex]

The equation would use to determine how long he drove each way is 2x - 8 = 60.

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

We have been given that Lots took one hour to drive from his apartment to Philips arena and back. the return drive took 8 minutes less than the trip to the arena.

Since the return trip took 8 minutes less, the complete equation must be written in minutes.

Here x - 8 represents the time it took to return to Philips Arena.

The total travel time, including both directions, was 60 minutes;

thus, add x and x - 8 and set them both equal to 60.

So 2x - 8 = 60

Therefore, the equation would use to determine how long he drove each way is 2x - 8 = 60.

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Answer:

x = 27

Step-by-step explanation:

(5x - 32) + (3x - 4) = 180

8x - 36 = 180

x = 216

x = 27

m<NQR = 5x - 32 = 5*27 - 32 = 103

m<QRP = 3x - 4 = 3*27 - 4 = 77

Answer:200

Step-by-step explanation:1,090

Answer:

https://www.omnicalculator.com/math/slope

Step-by-step explanation:

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Answer: -7/24

Step-by-step explanation:

move 2/3 to the opposite side of the equal sign which then changes the equation to...

3/8-2/3 = r

then change the denominators for both of them to 24.

so it would be 9/24 - 16/24

9-16 = -7

so it would be -7/24

It should be noted that the seat number is C

Jean received seat number 108.

It should be noted that from the information, The seat numbers were either 53, 64, 108, or 216. Candice received the only seat number with a factor of 16. This is 64.

Bill received the seat number that is the greatest multiple of 8 from the group of seats. This is 216.

Rose received the.only seat number that is a prime number. This is 53

Therefore, the remaining number is 108.

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The amount of water that should be added to 30 mL of 18​% alcohol solution to reduce the concentration to 15​% is: 6ml.

Let x represent the amount of water

Hence,

15% = .18(30)/(30+x)× 100          

Solve for x

.15 = 5.4/(30+x)

.15(30+x) = 5.4

30 + x = 5.4/.15= 36

x = 36 - 30

x = 6 ml

Therefore the amount of water that should be added to 30 mL of 18​% alcohol solution to reduce the concentration to 15​% is: 6ml.

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