16. AQRS is an equilateral triangle. If QR is seventeen more than twice x, RS is 19 less than six times x,
and QS is one less than four times x, find x and the measure of each side.
Topic 4: Congruent Triangles
18. Write three valid congruency statements given the triangles below.
P
17. In AJKL, if JK = JL, m/J = 23x - 4, m/K = 4x - 1, and m/L = 9x - 31, find x and the
measure of each angle.
¥
Q
R
S
|||
T
U
19. If AKPLAACM, complete each part.
a) KL =
d)

b) AC=
e) ZK =
c) PL=
f) ZM =
a)
b)
c)
W
15 m
Topic 5: Triangle Congruence & Proofs
21. What are the methods to prove triangles are congruent?
20. If AWXY AHJI, complete each part.
a) JI =
b) JH =
c) m/W=
d) m/J=
e) m/I=
114°
X
16 m
J
Y
37°
X:
H
QR=
RS =
QS =
22. Determine if the triangles below are congruent. If yes, state which method.
a)
b)
c)
=
X =
m/J=
m/K=
m/L=
d)
40

We are given the following inequality.

[tex]5x+38 \leq 4(2-5x)[/tex]

Apply the distributive property on the right side:

[tex]5x+38\leq 8-20x[/tex]

Add both sides by 20x:

[tex]5x+38+20x\leq 8-20x+20x[/tex]

[tex]25x+38\leq 8[/tex]

Subtract both sides by 38:

[tex]25x+38-38\leq 8-38[/tex]

[tex]25x\leq -30[/tex]

Divide both sides by 25:

[tex]25x/25\leq -30/25[/tex]

[tex]x\leq -6/5[/tex]

Out of all the options, only option A accurately depicts this inequality. Thus, the answer is option A.

Let me know if you have any questions, thanks!

Answer:

2. $240.50

3. See below

Step-by-step explanation:

2.

I = Prt

where I = interest

P = principal amount (amount of investment)

r = annual interest rate

t = time in years

t = 4 months = 4/12 year = 1/3 year

r = 9.25% = 0.0925

I = Prt

I = $7800 × 0.0925 × 1/3

I = $240.50

3. Exact interest takes into account every day of the year. In a regular year, there are 365 days. in a leap year, there are 366 days. Exact interest uses the exact number of days of the specific year for interest calculations of less than a year.

Ordinary interest rounds off a year to 360 days, and calculations are based on a year having 360 days, not 365 of 366 days.

Answer:its a cool song

Step-by-step explanation:

listening, listened to it, its good

Answer:

400×30= 12000 in 30yrs

12000

Step-by-step explanation:

12000÷.08= 150000

The value of the 'm' and 'b' will be negative 1.44 and 3.61, respectively.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + b

Where m is the slope of the line and b is the y-intercept of the line.

The linear equation is given below.

r(t)= √3 - 0.4t√13

r(t)= √3 - (0.4√13) t

Compare the equation with the standard equation. Then we have

m = - (0.4√13)

m = - 1.44

b = √13

b = 3.61

The value of the 'm' and 'b' will be negative 1.44 and 3.61, respectively.

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The solution is, the system represents the situation is, x+y= 20

and, 2x+3y = 48.

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

here, we have,

Each button has a diameter of either 2 or 3 centimeters.

The combined diameters of all buttons is 48 cm.

If x is the number of 2 cm buttons,

and y is 3 cm buttons.

Kate has a collection of 20 buttons.

So, the system represents the situation is,

x+y= 20

and, 2x+3y = 48.

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The difference between the median is 0.5. option D

Getting the sets of values that we have in order, we can see that we have;

12, 15, 33, 45, 46, 51, 52, 93

We can find the median between  4th and 5th numbers this is now going to give us that;  (45+46)/2 =  45.5

Median value  = 45.5

We can see that 93 is the outlier in the data set so if we remove it we would have;

12, 15, 33, 45, 46, 51, 52

The median of the data set in this case is 45.

The difference is;

45.5 - 45 = 0.5

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Missing parts;

The number of lattes sold daily for two coffee shops is shown in the table:

Lattes

12

52

93

33

51

15

46

45

Based on the data, what is the difference between the median of the data, including the outlier and excluding the outlier?

A.46

B.45.5

C.45

D.0.5

Answer:

Step-by-step explanation:

The amount of money he will need to purchase the paper and ink is $299.04.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Cost of 1 ream = $5.89

Cost of 1 ink cartridge = $29.30

Now,

Number of reams to buy = 6

Number of ink cartridges to buy = 9

The amount needed to buy.

= 6 x 5.89 + 9 x 29.30

= 35.34 + 263.7

= $299.04

Thus,

The amount of money needed is $299.04.

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The equation that can be used to represent the cost of 4 markers is y = k × 4

5 markers = $6.5

Unit cost of each marker = $6.5 / 5

= $1.3 per marker.

If

y = kx

Where,

y = total cost of markers

k = unit cost of marker

x = number of markers

The equation for the cost of 4 markers:

y = kx

y = 1.3 × 4

y = $5.2

Ultimately, y = k × 4 represents the equation for total cost of 4 markers.

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On solving the provided question, we cans ay that ratio is 2:3=> 2x + 4x = 4 => x = total fat is 6.6666666667

Ratios show how often one number is contained in another in mathematics. For instance, the ratio of oranges to lemons in a fruit dish is 8 to 6 if there are 8 oranges and 6 lemons present. In a similar vein, the proportion of oranges to whole fruit is 8, while that of lemons to oranges is 6:8. A ratio is an ordered pair of numbers a and b that is expressed as a / b, with b not equal to zero. An equation equating two ratios is known as a ratio. The ratio can be expressed as 1:3, for instance, if there is 1 boy and 3 girls (for every boy she has 3 girls) 3/4 are girls, while 1/4 are boys.

The ratio of saturated fat to total fat in a caramel frappucino is 2 to 3

There are 4 more grams of total fat than saturated fat

ratio is 2:3

2x + 4x = 4

x = 4/6*10

x = 6.6666666667

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The expressions that are completely factored are:

The expressions are considered correct because they have been completely factored, meaning they have been written in the form of "a common factor times another expression". This means that the expression on the right side of the equal sign can be simplified into its simplest form.

For example, in the expression 16a5−20a3=4a3(4a2−5), the 4a3 factor is common to both 16a5 and 20a3, so it can be factored out. The expression then becomes 4a3 times (4a2−5), which is the completely factored form.

Similarly, in the expression 12a3+8a=4(3a3+2a), the factor of 4 is common to both the expressions on the right side, so it can be factored out. This results in the completely factored form of 4 times (3a3+2a).

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Answer:

16a^5−20a^3=4a^3(4a^2−5)

and

24a^4+18=6(4a^4+3)

Step-by-step explanation:

The solution is,

a) Melissa's monthly payment on the promissory note is $133.10.

b) The total of Melissa's monthly payments is $6,388.80.

c) The total finance charge is $388.80.

Using an online finance calculator, we can compute the promissory note's monthly payments and finance charges (cost of credit).

The sum of the monthly payments is the total payments made by Melissa, consisting of the amount of the promissory note and the finance charges.

here, we have,

N (# of periods) = 48 months (4 years x 12)

I/Y (Interest per year) = 3.11%

PV (Present Value) = $6,000

FV (Future Value) = $0

Results:

PMT = $133.10

Sum of all periodic payments = $6,388.80

Total Interest = $388.80

Thus, Melissa's finance charge on the promissory note is $388.80, with a monthly payment of $133.10 for 4 years.

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The length of the spring stretched is given by the proportion A = 42 meters

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

The proportional equation is given as y ∝ x

And , y = kx where k is the proportionality constant

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Given data ,

Let the length of the spring stretched when 56 kg weight is attached be A

Now , the equation will be

The length of the spring when 8 kg is attached to it = 6 meters

So , the proportion is

A / 56 = 6 / 8

On simplifying the equation , we get

Multiply by 56 on both sides of the equation , we get

A = ( 6 x 56 ) / 8

On further simplification , we get

A = 6 x 7

A = 42 meters

Therefore , the value of A is 42 meters

Hence , the equation is A = 42 meters

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The solution to the inequality in this problem is given as follows:

b. x < -17 or x > 15.

The inequality for this problem is defined as follows:

0.25|x + 1| > 4.

Isolating the absolute value, we have that:

|x + 1| > 4/0.25

|x + 1| > 16.

The absolute value of a number represents it's distance from the origin, meaning that the inequality can be written as follows:

x + 1 < -16 or x + 1 > 16.

Then the first interval in the solution of the inequality is given as follows:

x + 1 < -16

x < -17.

The second interval in the solution of the inequality is given as follows:

x + 1 > 16

x > 15.

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Answer:

B

Step-by-step explanation:

There are two types in this good ol' world, Salary and Hourly.

Hourly gets paid by, well, the hour

Salary has a set amount. Let's say there around is $1000 a week. If they work 70 hours, they get paid $1000, if they work 30 hours, they get paid $1000

The missing coordinates of the cubic equations are filled out as ordered pairs as follows

function                coordinates

y = x³                     (-1, -1),  (0, 0)

f(x) = (x - 4)³ - 6      (-1, -131), (0, -70)

The coordinates of the cubic equation is sought by substituting the values of x in the function and solve for y.

for x = -1

y = x³ = (-1)³ = -1

f(x) = (x - 4)³ - 6 = (-1 - 4)³ - 6 = -131

for x = 0

y = x³ = (0)³ = 0

f(x) = (x - 4)³ - 6 = (0 - 4)³ - 6 = -70

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The piecewise function will be f(x) = - 0.5x - 1.5 if -6 ≤ x ≤ - 1, f(x) = -2 if - 1 < x ≤ 3, and f(x) = (5/3)x + 7 if 3 < x ≤ 6.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The equation of the line in the interval [-6, -1] whose points are (-3, 0) and (-1, -1) is given as,

(y - 0) = [(0 + 1) / (- 3 + 1)](x + 3)

y = - 0.5x - 1.5

The equation of the line in the interval (1, 3] whose points are (0, -2) and (3, -2) is given as,

(y + 2) = [(-2 + 2) / (3 - 0)](x + 0)

y = - 2

The equation of the line in the interval (3, 6] whose points are (3, -2) and (6, 3) is given as,

(y + 2) = [(3 + 2) / (6 - 3)](x + 3)

y + 2 = (5/3)(x + 3)

y = (5/3)x + 7

The function is given as,

f(x) = - 0.5x - 1.5 if -6 ≤ x ≤ - 1

f(x) = -2 if - 1 < x ≤ 3

f(x) = (5/3)x + 7 if 3 < x ≤ 6

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The total amount of Investment A is $6,348.58.

What is the compound interest?

Compound interest is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periods.

To find the total amount of investment A, you can use the formula for compound interest:

A = P * (1 + r/n)⁽ⁿᵗ⁾

Where P is the initial investment ($5,000), r is the annual interest rate (6%), n is the number of times interest is compounded per year (2 times), and t is the number of years invested (4).

A = 5000 * (1 + 0.06/2)⁽²*⁴⁾

= 5000 * (1 + 0.03)⁸

= 5000 * 1.03⁸

= 5000 * 1.269716

= $6,348.58

Hence, The total amount of Investment A is $6,348.58.

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what made the time ater sugauli treaty politically instable and complicated

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[tex](\stackrel{x_1}{7}~,~\stackrel{y_1}{8})\hspace{10em} \stackrel{slope}{m} ~=~ - 6 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{8}=\stackrel{m}{- 6}(x-\stackrel{x_1}{7})[/tex]

The actual cost per pound of potatoes for the 5-pound bag is $0.76 per pound.

A rate in arithmetic is a ratio that contrasts two separate values with various unit systems. For instance, if John types 50 words per minute, that means he types 50 words per minute. We are dealing with a rate because the word "per" is there. The symbol "/" can be used in place of the word "per" in issues.

When two or more similar amounts or numbers are being compared using the same units, a ratio is utilized. When referring to the ratio of one quantity "to" the second quantity in spoken language, it is frequently written with a colon.

A 5-pound bag of potatoes costs  $.3.80.

So the rate of the potato per pound is: 3.80/5 = 0.76

Therefore, the cost of potatoes per pound will be $0.76.

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Complete question:

A 5 pound bag of potatoes costs  $.3.80. How much do the potatoes cost per pound?

The actual cost per pound of potatoes for the 5-pound bag is             per pound.

The equation of a line perpendicular to the line y = 1/4x + 2 and passing through a point (x1, y1) is given by:

y - y1 = -4(x - x1)

This is because the slope of the original line is 1/4, so the slope of the perpendicular line must be -4 (the negative reciprocal).

A perpendicular line is a line that forms a 90-degree angle with another line. In other words, it is a line that is perpendicular to another line at their point of intersection. The slope of two perpendicular lines are negative reciprocals of each other, meaning that if one line has a slope of m, the slope of the perpendicular line is -1/m.

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The additional charge per minute is given as follows:

$1.1.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

From the table, when the time in minutes increases by 3, from 3 to 6, the cost increases by $3.3, from $10.30 to $13.60, hence the slope m is obtained as follows:

m = 3.3/3

m = $1.1.

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The length of JM is 24 units.

In general, the term "proportion" refers to a part, share, or amount that is compared to a total.

Two ratios or fractions are equal when an equation or a declaration to that effect is utilised.

A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.

Given:

<H= <K=  <N= 90

and, GH || JK || MN

then, Using proportion

GL/ GM = HK/ HN

18/ (18+ x) = 15/ (15+20)

18(15+20) = 15(18+x )

18 . 20= 15 x

x= (18)(20)/ 15

x= 24

Hence, the length is 24 units.

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Answer: The definition of a solution is a value or values which, when substituted for a variable in an equation, make the equation true. For example, the solutions to the equation x2 = 4 are 2 and -2. I hope this helped!

The different student number possible if a student I.D number consisting of seven digits (the first digits may be repeated) Followed by three of the letters A,B,C,D and E is 32659200.

A permutation is an arrangement of items in a specific direction or sequence. One should consider both the selection and the arrangement while dealing with permutation. In permutations, ordering is crucially important. The permutation is seen as an ordered combination, in other words.

The college ID consists of a total of 10 elements in which the first 7 can be a number and the last three are letters A, B, C, D, E.

Since, the number cannot start with a 0, we have the following combination of numbers:

9 * 9 * 8 * 7 * 6 * 5 * 4 * 5 * 4 * 3 = 32659200

where the first seven places represent digits, and the last three represent letters.

Hence, the different student number possible if a student I.D number consisting of seven digits (the first digits may be repeated) Followed by three of the letters A,B,C,D and E is 32659200.

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Step-by-step explanation:

the new cocrfinations are

K' (-1, 7)

H' (-1, 5)

J' (5, 7

I' (2, 2)

Step-by-step explanation:

The rate of change of the population is proportional to the population, so we can use the exponential growth formula:

P(t) = P0 * e^(kt)

Where P0 is the initial population (300), k is the constant of proportionality, and t is the time in hours. We can use the data from t=24 hours to solve for k:

1000 = 300 * e^(24k)

Dividing both sides by 300 and taking the natural logarithm of both sides:

ln(1000/300) = 24k

ln(3.33) = 24k

k = ln(3.33) / 24

Now that we have k, we can plug it into the formula and solve for t when P(t) = 500:

P(t) = 300 * e^(kt)

500 = 300 * e^(kt)

e^(kt) = 500/300

e^(kt) = 5/3

kt = ln(5/3)

t = ln(5/3) / k

Substituting k = ln(3.33) / 24:

t = ln(5/3) / (ln(3.33) / 24)

t ≈ 11.7 hours.