If EF = 5w + 20, FG = 7w + 28, and EG = 72, find the value of w. Find EF and FG

Answer:

We can not solve for a unique cost for each soldier.

Step-by-step explanation:

Let x be the daily cost for legionaries and y be the daily cost for archers.  

Upon using our given information we will get a system of linear equations as:

[tex]3x+3y=10...(1)[/tex]

[tex]x+y=3...(2)[/tex]

Now we will solve for x from our 2nd equation,

[tex]x = 3-y[/tex]

Now we will substitute this value in our 1st equation.

[tex]3(3-y)+3y=10[/tex]

[tex]9-3y+3y=10[/tex]

We can see that -3y cancels out with 3y  and 9 is not equal to 10. So this is an unsolvable system. Therefore, we can not find a unique cost for each soldier.

Answer: No solutions

Step-by-step explanation:

The order from greatest to least is 56.011, 56.10, 56.01.

23 miles

hope this helps :)

If there is 45 angle from the south to the east α= 45° then the distance of d=32miles is

the diagonal of the square and your question how far south has it sailed is the side of the square let's call it x.

The relation is

d = x √2 => x= d/√2 = 32/1.41 ≈ 22.69 ≈ 22.7 miles

The correct answer is 22.7 miles

Good luck!!

Answer: B) is the right answer→the distance between points a and b is equal to the distance between points b and c.

Step-by-step explanation:

As Kerry drew a number line starting at 0, point a, and ending at 1, point c and halfway between points a and c, he added point b.

.⇒ab=1/2 of ac and bc= 1/2 of ac or b is the mid point of line segment ac.

⇒ ab=bc(∵things which are equal to the same thing are equal to one another....→Euclid's first postulate)

Therefore, option B) the distance between points a and b is equal to the distance between points b and c is correct.

If 8 of the picks are orange, then 6 of the picks will be green

if you traveled at 40 mph you would go 240 miles in 6 hours. your answer is 40 mph

To calculate the number of years it would take for $1200 to earn simple interest of $324 at an annual interest rate of 6%, we use the simple interest formula. Substituting these values into the formula and solving for time, we find that it would take 4.5 years to earn the aforementioned interest.

The subject of this problem revolves around the concept of simple interest, a foundational topic in financial mathematics. To find the number of years it will take for $1200 to earn a simple interest of $324 at an annual interest rate of 6%, we need to use the simple interest formula: I = PRT, where I is interest, P is principal amount (initial investment), R is rate of interest per year, and T is time in years.

In this example, the interest (I) is $324, the principal (P) is $1200, and the annual interest rate (R) is 6% or 0.06 in decimal form.

Substitute these values into the formula to solve for T (the number of years):

I = PRT

324 = 1200 * 0.06 * T

To solve for T, divide 324 by the product of 1200 and 0.06. Doing this calculation gives you:

T = 324 / (1200 * 0.06) = 4.5 years

Therefore, "it will take 4.5 years to earn $324 of simple interest on an initial deposit of $1200 at an annual interest rate of 6%".

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The 59th term of the sequence 29, 37, 45 is 493. The sequence is arithmetic with a common difference of 8. Applying the formula for the nth term of an arithmetic sequence, we calculate the 59th term as 493.

Finding the 59th Term of an Arithmetic Sequence

To find the 59th term of the sequence (29, 37, 45), we first need to determine the common difference of the sequence. We do this by subtracting any term from the term that follows it. For example:

37 - 29 = 8
45 - 37 = 8

The common difference is 8.

This sequence is an arithmetic sequence where each term increases by 8 from the previous term. The formula to find the nth term of an arithmetic sequence is:

an = a1 + (n - 1) * d

where:

Plugging in the values for the 59th term:

a59 = 29 + (59 - 1) * 8
a59 = 29 + 58 * 8
a59 = 29 + 464
a59 = 493

Therefore, the 59th term of the sequence is 493.

All we have to do here is multiply how many liters of water they drink in a day (225) by 2

225 x 2 = 450

Therefore, elephants drink 450 liters of water in 2 days

Hope this helps you

-AaronWiseIsBae

let

x-------> the number of Lucy's orders

y-------> the number of Sam's orders

z-------> the number of Bob's orders

we know that

[tex]x+y+z=72[/tex]----> equation A

[tex]z=3x[/tex]-----> equation B

[tex]x=8+y-----> y=x-8[/tex] -----> equation C

substitute equation B and C in equation A

[tex]x+(x-8)+3x=72\\ 5x=72+8\\ 5x=80\\x=16\\[/tex]

find z

[tex]z=3*16=48[/tex]

find y

[tex]y=x-8------> y=16-8=8[/tex]

therefore

the answer is

the number of Lucy's orders is [tex]16[/tex]

the number of Sam's orders is [tex]8[/tex]

the number of Bob's orders is [tex]48[/tex]

Perimeter (P) = 2L + 2w

68 = 2L + 2w

68 - 2L = 2w

2(34 - L) = 2(w)

34 - L = w

********************                                

Area (A) = L * w

     240 = L (34 - L)

     240 = 34L - L²

L² - 34L + 240 = 0

(L - 10)(L - 24) = 0

L = 10  or  L = 24

w = 34 - L   = 34 - 10   = 24      or      w = 34 - 24   = 10

Answer: width = 10, length = 24  assuming length is bigger than the width

Perimeter (P) = 2L + 2w

68 = 2L + 2w

68 - 2L = 2w

2(34 - L) = 2(w)

34 - L = w

********************                                

Area (A) = L * w

     240 = L (34 - L)

     240 = 34L - L²

L² - 34L + 240 = 0

(L - 10)(L - 24) = 0

L = 10  or  L = 24

w = 34 - L   = 34 - 10   = 24      or      w = 34 - 24   = 10

Answer: width = 10, length = 24   assuming length is bigger than the width

To solve this, you first have to find the number of yards in one mile.

If three feet = 1 yard, and 5280 ft = 1 mile, all you have to do to find the number of yards in a mile is divide 5280 feet by 3 feet.

You end up with 1760 yards in 1 mile.

To find the number of yards in 2 miles, all you would have to do is multiply 1760 by 2

To convert 2 miles into yards, first change miles to feet (2 miles * 5,280 feet/mile = 10,560 feet). Then, convert feet to yards (10,560 feet ÷ 3 feet/yard = 3,520 yards). So, 2 miles is equal to 3,520 yards. therefore, option b is correct

To calculate the number of yards in 2 miles, we must first know the relationship between miles, feet, and yards. As the question mentioned, 1 mile = 5,280 feet and 1 yard = 3 feet.

So the first step is to convert 2 miles into feet: 2 miles * 5,280 feet/mile = 10,560 feet.

The second step is to convert feet into yards: 10,560 feet ÷ 3 feet/yard = 3,520 yards.

Therefore, there are 3,520 yards in 2 miles.

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Let's apply the given values into equation x(y-5), which becomes 2(7-5). Subtract 5 from 7 which is 2, making equation 2*2. Multiply 2's together resulting in 4.

To evaluate this math problem, we can first substitute the given values into the equation. In other words, we would place '2' where we see 'x', and '7' where we see 'y'.

So our equation becomes: 2(7-5)

Then, we resolve the operation inside the parentheses first, as per the order of operations (PEMDAS/BODMAS). So, you subtract 5 from 7, which equals 2.

So our equation now becomes: 2 * 2

Lastly, you just multiply the 2's together. The final result is: 4

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Mom's view is that she loses 50 dollars, but gains back 17.85 dollars as change from her daughter.

Olivia's view is that she gained 50 dollars from her mom, spent 32.15 dollars, then gave back the 17.85 change to her mom, so she didn't gain any money.

Mom's point of view: -$50 + $17.85 and Mom's point of view: -$50 + $17.85 are the correct answers, but technically, Olivia still owes her mom 32.15 dollars.

From the information given, Olivia paid her mom back $17.85 and still owes her $32.15.

Since Olivia borrows $50 from her mom to buy some art supplies and spends $32.15 on art supplies, then it can be inferred that the amount that she'll give her mom will be:

= $50 - $32.15

= $17.85 change

On the other hand, her mom will still expect her to balance her $32.15. In this case, Olivia paid her mom back $17.85 and still owes her $32.15.

The mom will expect $32.15 from her later whenever she has it.

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Tony and Mike, factored the trinomial [tex]8x^2 - 12x - 8[/tex]

Tony factored it as 4(x - 2)(2x + 1) and

Mike factored it as (x - 2)(8x + 4)

[tex]8x^2 - 12x - 8[/tex]

GCF is 4. We factor out 4

[tex]4(2x^2 - 3x - 2)[/tex]

2*-2=-4. We find out two factors whose product is -4  and sum is -3

two factors are -4  and 1. Split middle term -3x using two factors

[tex]4(2x^2 - 4x + 1x - 2)[/tex]

Group first two terms and last two terms

[tex]4[(2x^2 - 4x) + (1x - 2)][/tex]

Factor out GCF from each group

[tex]4[2x(x - 2) + 1(x - 2)[/tex]

4(2x+1)(x-2)

Tony factored it correctly

Mike factored it as (x − 2)(8x + 4)

Mike factor 8x+4 further. GCF of 8 and 4 is 4

So it becomes 4(2x+1)

Mike not factored it completely

When Riley dove 8 feet further down from her initial position of 12 feet below sea level, her new location is 20 feet below sea level.

Riley was initially scuba diving 12 feet below sea level. This can be represented as a negative number, so we start with -12. Then, she dove 8 feet further down. In mathematical terms, this means we subtract another 8 from -12.
Thus, her elevation now is -12 - 8 = -20. Therefore, Riley is now 20 feet below sea level.

Hence, it is proved here completely.

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The answer is (C)

[tex]xy (x + 1), x(x+2)[/tex]

By multiplying x in equation

[tex]y(x^2 + x), x^2 + 2x[/tex]

[tex]y(x^2 + x), x(x+2)[/tex]

All the 4 factors are (x^2 + x), y, x, (x + 2)

So, the LCM is

[tex]xy(x + 1)(x + 2)[/tex]

Final answer:

The LCM of xy(x + 1) and x(x + 2) is found by including the highest powers of all variables and unique factors from both expressions, yielding x²y(x + 1)(x + 2).

Explanation:

The Least Common Multiple (LCM) of two algebraic expressions is the smallest expression that both original expressions can divide into evenly without leaving a remainder. To find the LCM of xy(x + 1) and x(x + 2), we look for the highest power of all the variables and factors included in both expressions.

The factor x appears in both expressions, but with different powers. The highest power of x in the given expressions is x² as seen in the second expression.

The factor y appears only in the first expression, so it must also be included in the LCM.

Next, the factors (x + 1) and (x + 2) are both unique, so they are also included in the LCM.

Therefore, the LCM of xy(x + 1) and x(x + 2) is x²y(x + 1)(x + 2), which corresponds to choice C. Hence, the correct answer is C.xy(x + 1)(x + 2).



3 × 4 × 3 - 2 × 4²

36 - 2 × 4²

36 - 2 × 16

36 - 32

The answer is 4

Is that right? I hoped it helped...

Let's assume

independent variable is x

dependent variable is h

A linear function h models a relationship in which the dependent variable increases 1 unit for every 5 units the independent variable decreases.

so, we can use formula of linear function

[tex]h=mx+b[/tex]

where

m is slope

[tex]m=-\frac{1}{5}[/tex]

now, we can plug values

[tex]h=-\frac{1}{5}x+b[/tex]

The value of the function at 0 is 3

so, at x=0 , h=3

we can use it and find b

[tex]3=-\frac{1}{5}*0+b[/tex]

[tex]b=3[/tex]

now, we can plug back

[tex]h=-\frac{1}{5}x+3[/tex]

now, we can draw graph

Graph:

Answer:The y-intercept is 3,The slope is [tex]-\frac{1}{5}[/tex],and the x-intecept is 15.

Step-by-step explanation: Credit:The answer is above me.

To find the unit price of each item you want to divide:

Fresh water:

$1.76 / 16 = $0.11

Spring water:

$2.40 / 20 = $0.12

So the statement that is true is B) Fresh water has a lower unit price of $0.11/ounce.

Hope this Helps!!

When a function is reflected over the x-axis, the positive y-values become negative and the negative y-values become positive.

When a function is reflected over the x-axis, the positive y-values become negative and the negative y-values become positive. In the case of f(x)=2/3(6)^x, when it is reflected over the x-axis, the positive y-values will become negative and the negative y-values will become positive. This means that the range of the reflected function will be the opposite of the original range. Since the original range is all positive y-values, the reflected range will be all negative y-values.

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Answer:

The measure of angle RAN is 39 degrees.

Step-by-step explanation:

Given:

To Find:

Measure of angle RAN

Calculations:

STEP 1 : We note that angle RAN = angle RAI + angle IAN (by the construction of the angles given in the problem).

So, we need to individually find the angles RAI and IAN in order to find the angle RAN

STEP 2 : Finding angle RAI

Given that AR if the bisector of angle KAI, therefore angle KAR = angle RAI

Also given that angle KAR = 13 degrees.

Therefore, angle RAI = 13 degrees.

STEP 3 : Finding angle IAN

Given that AI is the bisector of angle KAN, therefore angle KAI = angle IAN

Now,

angle KAI = angle KAR + angle RAI

= 13 + 13 degrees (using what we found out in STEP 1)

= 26 degrees

Therefore angle IAN = angle KAI = 26 degrees

STEP 4 : Finding angle RAN

As we noted in STEP 1,

angle RAN = angle RAI + angle IAN

= 13 + 26 degrees (using Steps 2 and 3)

= 39 degrees

Therefore, angle RAN = 39 degrees

NOTE - A hand-drawn diagram has been attached so that it is easier to picture the solution. I hope this helps!

We are given: The number of bands in the chicken soup county battles of the bands = 40.

The percentage of the all virus state finals will compete = 15% of the total number of bands given.

We have given 40 number of bands.

Therefore, the bands will compete in the finals = 15% of 40.

15% can be written as 0.15.

Therefore, 15% of 40 = 0.15 × 40 = 6.

Answer: 14

Step-by-step explanation:

The ______ is asking what 140 ÷ 10 is

140 ÷ 10 = 14

I'm ASSUMING that we're talking about Three Ordered Ordered Pair Solutions.

If so, the answer is (0,−1),(1,2),(2,5).

The solution of equation are,

(0, - 1) ( 1, 2) and (2, 5)

We have to given that,

To find the solution of equation y = 3x - 1

Here, The equation is,

y = 3x - 1

Now, We can put x = 0 in above equation,

y = 3 (0) - 1

y = - 1

Put x = 1;

y = 3 (1) - 1

y = 3 - 1

y = 2

Put x = 2;

y = 3 (2) - 1

y = 6 - 1

y = 5

Thus, The solution of equation are,

(0, - 1) ( 1, 2) and (2, 5)

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Answer: (-∞, -4)

To find the interval(s) over which the function is constant,

We look at the graph and pick the interval where the graph is neither increasing nor decreasing

When the graph is neither increasing nor decreasing means it should be a straight line

From the given graph , we have a straight line starts at -4  and goes to infinity

So constant interval is (-∞, -4)

The function is constant over the interval [0, 20].

The function is constant when its graph is a horizontal line. In this case, the graph is a horizontal line between x = 0 and x = 20, inclusive. Therefore, the function is constant over the interval [0, 20].

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A) False because it is not a line (it is a parabola)

B) False  because it fails the horizontal line test

C) False because it passes the vertical line test.

D) True because it passes the vertical line test but fails the horizontal line test.

Answer: D

[tex]f(x)=4^x-8,\ g(x)=5x+6\\\\(f-g)(x)=f(x)-g(x)=(4^x-8)-(5x+6)=4^x-8-5x-6=4^x-5x-14[/tex]