the cost $C of transporting goods is directly proportional to the distance, d km. Given that C=100 when d=60 find

a) an equation connecting C and d

b) the cost of transporting goods for 45km

c) the distance if the cost of transporting goods is $120

Answer:

16

Step-by-step explanation:

8-4x times y^2, x=3 and y=-2

First, plug in both variables. Since x=3, you would substitute 4x in the equation to 4(3). You would do the same to y, but instead it would be in replace of y^2. So it would be -2^2. You now have a new equation:

8-4(3) times -2^2

Next, you start solving the equation. You should follow PEMDAS (Parenthesis, Exponent, Multiplication, Division, Addition, Subtraction). This method is sometimes controversial, but it still works for this problem.

Start by multiplying 4 times 3 which equals 12. Then I solve the exponent. The exponent -2^2 is the same as -2 times -2. The -2 is the number that gets multiplied, and the exponent is how many times -2 gets multiplied times itself. -2 times -2 is 4. You can plug your new numbers back in the equation now.

8-12 times 4

The equation is much easier to solve now. 8-12 is -4. -4 times 4 is 16.

The answer is 16.

Answer:

1: 254 inches

2: 100.8 mi

3: 64 yards

4: 128 yards

Step-by-step explanation:

1: 4x7=28 4x7=28 9x7=63 9x7=63 9x4=36 9x4=36

28+28+63+63+36+36=

254

2: Dunno exactly, but my guess is: 6x5=30. 3x6=18. 2.8x3=8.4 3x6=18. 3x6=18. 2.8x3=8.4

8.4+8.4+18+18+18+30=

100.8

3: 2x1=2 2x1=2 10x2=20 10x2=20 10x1=10 10x1=10

2+2+20+20+10+10=

64

4: 6x8/2=24 6x8/2=24 10x5=50 6x5=30

24+24+50+30=

128 yards

Pls give brainliest :)

Answer:

The capacity of the big vase is half times bigger than the capacity of the middle sized vase, which means it is 1 + 1/2 times the capacity of the middle vase.

So, the capacity of the big vase in terms of x is:

1/2x + x = 3/2x

Therefore, the capacity of the big vase in x is 3/2x.

The capacity of the middle sized vase is four times bigger than the capacity of the small vase, which means it is 4 times the capacity of the small vase.

So, the capacity of the small vase in terms of x is:

x/4

Therefore, the capacity of the small vase in x is x/4.

The total capacity of the three vases is 5.5 liters. We can set up an equation based on this information:

x + 3/2x + x/4 = 5.5

Multiplying both sides by 4 to eliminate the fraction:

4x + 6x + x = 22

11x = 22

x = 2

Therefore, the capacity of the middle sized vase is 2 in terms of x. To find the capacity in liters, we can substitute x = 2 into any of the expressions we found earlier:

Capacity of the big vase: 3/2x = 3/2 * 2 = 3 liters

Capacity of the small vase: x/4 = 2/4 = 0.5 liters

So, the capacities of the three vases are 3 liters, 2 liters, and 0.5 liters, and their total capacity is 5.5 liters.

To solve the equation x^(2)-5x-5=0 using the quadratic formula, we can use the formula x = (-b ± √(b^(2)-4ac))/(2a), where a, b, and c are the coefficients of the equation. In this case, a=1, b=-5, and c=-5.

Plugging in the values into the formula, we get:

x = (-(-5) ± √((-5)^(2)-4(1)(-5)))/(2(1))

Simplifying the equation, we get:

x = (5 ± √(25+20))/2

x = (5 ± √45)/2

x = (5 ± 3√5)/2

Therefore, the solution set in exact simplest form is x = (5 ± 3√5)/2.

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The amount of money in the account after 9 years is $2549.68.

The formula A=P(1+(r)/(n))^(nt) is used to calculate the amount of money in an account after a certain amount of time, given the principal amount (P), the interest rate (r), the number of times interest is compounded per year (n), and the number of years (t).

To find A when P=2000, r=3%, n=12, and t=9, we can plug these values into the formula and simplify:

A = 2000(1+(0.03)/(12))^(12*9)

A = 2000(1+0.0025)^(108)

A = 2000(1.0025)^(108)

A = 2000(1.2748)

A = 2549.68

Therefore, $2549.68 is the amount of money in the account after 9 years.

"

Correct question

Ulas and Applications:

If A=P(1+(r)/(n))^(nt)

Find A when P=2000,r=3%,n=12, and t=9.

"

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Answer: false

Step-by-step explanation:

since you do not know if EF and DG are the same it is not possible to know if it is true yet

The simplified expression to (49(2w-5))/(7(w-8)(2w-5)) is 7/(w-8).

To simplify the given expression, we can factor out common terms from the numerator and denominator and then cancel them out. This will give us the simplest form of the expression.

The given expression is: (49(2w-5))/(7(w-8)(2w-5))

First, we can factor out the common term (2w-5) from the numerator and denominator:
= (49 * (2w-5))/(7 * (w-8) * (2w-5))

Next, we can cancel out the common term (2w-5) from the numerator and denominator:
= (49)/(7 * (w-8))

Finally, we can simplify the expression by dividing the numerator and denominator by the common factor 7:
= 7/(w-8)

Therefore, the simplified expression is 7/(w-8).

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The equation of a parabola with zeros at 3 and 9 and goes through the point \( (6,-18) \) is
y = 2x^2 - 24x + 54.

To write the equation in general form of a parabola with zeros of 3 and 9 and goes through the point (6,-18), we can use the fact that the equation of a parabola can be written in the form y = a(x - h)^2 + k, where (h,k) is the vertex of the parabola and a determines the width of the parabola.

First, we can use the zeros to find the vertex of the parabola. The vertex is located halfway between the zeros, so the x-coordinate of the vertex is (3 + 9)/2 = 6. We can plug this value into the equation to find the y-coordinate of the vertex:

y = a(6 - 6)^2 + k = k

Since the parabola goes through the point (6,-18), we know that k = -18.

Now we can plug in the zeros and the vertex into the equation to find the value of a:

0 = a(3 - 6)^2 - 18

0 = a(9) - 18

18 = 9a

a = 2

So the equation of the parabola is y = 2(x - 6)^2 - 18.

To write this equation in general form, we can expand the squared term and simplify:

y = 2(x^2 - 12x + 36) - 18

y = 2x^2 - 24x + 72 - 18

y = 2x^2 - 24x + 54

So the equation in general form is y = 2x^2 - 24x + 54.

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The interest rate will be 7%

A quick and simple way to figure out interest on money is to use the simple interest technique, which adds interest at the same rate for each time cycle and always to the initial principal amount.

Any bank where we deposit our funds will pay us interest on our investment. One of the different types of interest charged by banks is simple interest. Now, before exploring the idea of basic curiosity in further detail,

The formula for simple interest is:

S = p*t*r/100

the simple interest on ​$7000 for 7 years is ​$3430

r = S*100/(p*t)

r = (3430*100)/(7000*7)

r = 7%

Hence the interest rate will be 7%

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The following solutions with regard to resolving or simplifying the radii of circular ponds are given below.

Part A: 5√100 + √164 meters = 5 × 10 + 2√41 meters

Part B: 5 × 10 + 2√41 meters = 50 + 2√41 meters
Part C: The radius of Pond B is 10√2 meters.
Part D: the radius of Pond B is greater than the radius of Pond A.

Part A: The mistake is in Step 1. To simplify the square root of 164, we need to find its prime factors:

164 = 2 × 2 × 41

So, we can write:

√164 = √(2 × 2 × 41) = 2√41

Using this, we can rewrite Step 1 as:

5√100 + √164 meters = 5 × 10 + 2√41 meters

Part B: Using the corrected step from Part A, we can simplify the radius of Pond A as:

5 × 10 + 2√41 meters = 50 + 2√41 meters

So, the radius of Pond A is 50 + 2√41 meters.

Part C: The radius of Pond B is already simplified, so we don't need to do any additional steps. It is:

25√200/5 meters = 5√200 meters

We can simplify this further by finding the prime factorization of 200:

200 = 2 × 2 × 2 × 5 × 5

So, we can write:

√200 = √(2 × 2 × 2 × 5 × 5)

= 2 × 5√2

Using this, we can rewrite the expression for the radius of Pond B as:

5 × 2 × √2 meters

= 10√2 meters

Thus, the radius of Pond B is 10√2 meters.

Part D: We can compare the radii of the ponds using the original expressions by writing:

√164 < 25√200/5

Simplifying both sides:

2√41 < 10√2

Dividing both sides by 2:

√41 < 5√2

Squaring both sides (since both sides are positive):

41 < 25 × 2

41 < 50

So, the inequality is true. Therefore, the radius of Pond B is greater than the radius of Pond A.

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Full Question:

Two circular ponds at a botanical garden have the following radii:

Pond A: Sqrt(164) meters;

Pond B: 25Sqrt(200)/5 meters:

Todd simplified the radius of pond A this way:

5sqrt(164)

Step 1: 5sqrt(100) + Sqrt(164) meters

Step 2: 5(10 + 8)

Step 3: 5(18)

Step 4: 90

One of the steps above is incorrect.

Part A: Rewrite the steps so that it is correct

Part B: Using the corrected step from Part A, simplify the radius of Pond A.

Part C: Simplify the expression for the radius of pond B.

Part D: Write an inequality to compare the radii of the ponds, using the original expressions.

The values of {y} less than 3.7 on the number line represent the solution set of the given inequality.

An inequality is used to compare two or more expressions or numbers.

For example -

2x > 4y + 3

x + y > 3

x - y < 6

Given is that Tania began a graph to show the inequality → y < 3.7.

Given is the inequality as -

y < 3.7

For all the values of {y} less than 3.7 on the number line represent the solution set of the given inequality.

Therefore, the values of {y} less than 3.7 on the number line represent the solution set of the given inequality.

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{Question in english -

Tania began a graph to show the inequality y < 3.7. Finish labeling the number line and draw the graph.}

The algebraic expression for "r squared minus the product of 6 and d plus 5" is r2 - 6d + 5.

An algebraic expression is an expression that contains at least one variable and uses mathematical operations such as addition, subtraction, multiplication, and division. It can also include exponents and/or roots. Algebraic expressions are used to represent mathematical relationships between different variables or constants. They can be used to represent real-world problems, such as finding the area of a rectangle.

In this expression, r2 represents "r squared", - 6d represents "minus the product of 6 and d", and + 5 represents "plus 5".

So, the final algebraic expression is r2 - 6d + 5.

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The f(g(x))=−4x3​and g(f(x))=x3​−15x2​+25x−125x3​.

To find f(g(x)), we need to substitute the function g(x) into the function f(x). This means that wherever we see an "x" in f(x), we replace it with the function g(x). So, f(g(x))=g(x)−5g(x)=x3​−5x3​=−4x3​. Similarly, to find g(f(x)), we substitute the function f(x) into the function g(x). So, g(f(x))=f(x)3​=(x−5x)3​=x3​−15x2​+25x−125x3​.

Therefore, f(g(x))=−4x3​and g(f(x))=x3​−15x2​+25x−125x3​.

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The solution to the compound inequality is x > -3 and x <= -4, or (-4, -3] in interval notation.

A compound inequality contains at least two inequalities that are separated by either "and" or "or.  The graph of a compound inequality with an "and" represents the intersection of the graph of the inequalities.

The compound inequality 8x - 6 > -30 OR -2x + 4 >= 12 can be solved by solving each inequality separately and then combining the results.

Solve 8x - 6 > -30:
8x - 6 > -30
8x > -24
x > -3

Solve -2x + 4 >= 12:
-2x + 4 >= 12
-2x >= 8
x <= -4

The solution to the compound inequality is x > -3 and x <= -4, or (-4, -3] in interval notation.

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Answer:-4.5

Step-by-step explanation:

-6+-30=-36

-36 divided by 8= -4.5

The corresponding value of D is 15 defective genes in 100 cc of kidney tissue.

The Poisson distribution is used to model the occurrence of rare events in a fixed interval of time or space. In this case, the geneticist is using the Poisson process to model the occurrence of defective genes in kidney tissue exposed to a toxin. The average rate of occurrence is given as 3 defective genes per 20 cc of kidney tissue.

To simulate the number of defective genes in 100 cc of kidney tissue, we need to scale the average rate accordingly. Since 100 cc is five times the size of 20 cc, the average rate for 100 cc would be 15 defective genes.

The geneticist uses a uniform distribution on (0,1) to generate a random observation, U = 0.71. To obtain the corresponding value of D, we can use the inverse transform method. Let X be the number of defective genes in 100 cc of kidney tissue, then we have:

P(X = k) = e^(-λ) (λ^k / k!)

where λ is the average rate of occurrence, which is 15 in this case.

By plugging in λ = 15 and solving for k, we get:

P(X = k) = e^(-15) (15^k / k!) = 0.71

Using a calculator or a statistical software, we can find that the value of k that satisfies this equation is k = 15. Therefore, the corresponding value of D is 15 defective genes in 100 cc of kidney tissue.

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Answer: True

Step-by-step explanation:

Answer: No

Step-by-step explanation:

Definitely not.

The expression when evaluated is p^21/200

From the question, we have the following parameters that can be used in our computation:

[tex]5^{-2} x 125 x p^{15} / 10^{3} x p^{-6}[/tex]

Express properly

So, we have the following representation

(5^-2 * 125 * p^15)/(10^3 * p^-6)

Evaluate the products of common factors

This gives

(5 * p^15)/(10^3 * p^-6)

Apply the law of indices

(5 * p^21)/10^3

So, we have

5p^21/1000

Divide 5 and 1000 by 5

p^21/200

Hence, the expression is p^21/200

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Complete Question

Evaluate the expression:

[tex]5^{-2} x 125 x p^{15} / 10^{3} x p^{-6}[/tex]

The simplified expression is -22 degrees (rounded to the nearest degree).

What is Trigonometry?

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles, and the functions that describe those relationships. It has applications in fields such as engineering, physics, astronomy, and navigation.

We can use the following trigonometric identity to simplify the expression:

arctan(x) + arctan(y) = arctan[(x+y) / (1-xy)]

In this case, we can substitute x = 5 and y = 6 to get:

arctan 5 + arctan 6 = arctan[(5+6) / (1 - 5*6)]

Simplifying the denominator, we get:

arctan 5 + arctan 6 = arctan(11/-29)

To find the degree measure of this angle, we can use a calculator to evaluate the inverse tangent of -11/29 and convert the result to degrees.

The result is approximately -22 degrees (rounded to the nearest degree).

Therefore, the simplified expression is:

arctan 5 + arctan 6 = -22 degrees (rounded to the nearest degree).

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Answer:

Step-by-step explanation:

based on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole number based on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole number based on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole number

The value of  sin(θ/2) is √6/4.

We can start by using the identity:

sin(θ/2) = ±√[(1 - cosθ)/2]

However, before we apply this identity, we need to determine the quadrant in which θ lies, so that we can determine the sign of sin(θ/2).

From the given information, we know that cos θ = 1/4. Using the unit circle or a trigonometric table, we find that θ is a first quadrant angle whose reference angle is arc cos(1/4) ≈ 75.52°.

Since csc > 0, we know that sinθ > 0, which means that θ is either in the first or second quadrant.

However, since cosθ is positive (i.e., in the first or fourth quadrant), we know that θ must be in the first quadrant, and so sinθ > 0.

Now we can use the half-angle identity:

sin(θ/2) = ±√[(1 - cosθ)/2]

Plugging in cosθ = 1/4, we get:

sin(θ/2) = ±√[(1 - 1/4)/2] = ±√(3/8) = ±(√3/2)(√2/2) = ±(√3/2)(1/√2)

Since θ is in the first quadrant, we know that sin(θ/2) > 0, so we take the positive root:

sin(θ/2) = (√3/2)(1/√2) = √3/2√2 = √6/4

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Answer:

X=7    Y=2

I will lead you through it and show you how you can find x through eliminating y, and finding y through eliminating x! So, both ways! :)

Step-by-step explanation:

When looking to use the elimination method, either all x OR y  coefficients must be equal before finding one or another. That might sound a little confusing so let me explain!

Finding x by eliminating y: (they already set it up for us, this way!)

6x+6y=54              6y and -6y will cancel each other out!

2x - 6y= 2

6x=54                   Add both lines!

2x=2

8x=56                   Now, divide 8 on both sides to find x!

x=7                       The product is x equals 7! Plug into a line to find y!

6(7)+6y=54          

42+6y=54          Subtract both sides by 42

6y=12                  Divide both sides by 6

y=2

So, X=7 and Y=2 ! To check that this is true, plug both variables into one line!

2(7)-6(2)=2

14-12=2

2=2                2 equals 2, so this is true! Lets check the other line to make

                      sure!

6(7)+6(2)=54

42+12=54

54=54             Yes, this is also true! That means we found the true value of the variables. :)

Finding y by eliminating x: Now, how do we find X and Y using the elimination method if the terms are not equal? We will continue to use this problem since it meets the standards of unequal terms! However, we will find y by eliminating x!

We must get the x terms to be equal to they can cancel each other out! So, we will multiply a line by a certain variable until it matches the x term on the other line. We will multiply line 2 until it matches line 1's x term, but make sure the signs (positive/negative) are opposite so they cancel out! In other problems, one line's term may not be able to be multiplied until it reaches its term since it is not a factor of it! So, both lines would be multiplied b a specific number until they have a common multiple! Confusing? Just focus on the underlined portion of this paragraph as that is what you will need for this question. Lets work hard now! :)

6x+6y=54    Multiply line 2 by -3 so the x term will be cancel out line 1's x!

2x - 6y= 2

6x+6y=54

(2x - 6y= 2) -3           Yes, all of it!

6x+6y=54

-6x+18y=-6              Add both lines

24y=48                 Divide 24 by both sides!

y=2                       y is equivalent to 2! Plug value into a line!

6x+6(2)=54

6x+12=54        Subtract 12 on both sides!

6x=42       Divide 6 on both sides.

x=7           X is equal to 7!

So, X=7 and Y=2 , just like we found and even checked before! I hope this helped. Elimination method is my favorite method and overall favorite lesson in Algebra, for me, since it is pretty easy once you get a hang of it! Goodluck all! :)

Five copies of a textbook are placed in a travel bag by Jada's instructor. 17 pounds are made up of the bag and the books. Each copy of the textbook weighs 2.8 pounds.

To find the weight of each book, we can start by using algebra. Let's call the weight of each book "b".

The weight of the bag and books together is 17 pounds, and we know the empty bag weighs 3 pounds. So the weight of the books alone is:

17 - 3 = 14 pounds

Since there are 5 copies of the textbook in the bag, we can write an equation:

5b = 14

To solve for "b", we can divide both sides by 5:

b = 2.8 pounds

It's worth noting that this is an example of a simple algebraic equation that can be solved using basic arithmetic. However, algebra is a powerful tool for solving more complex problems in math, science, and other fields. By understanding how to use variables and equations to represent real-world situations, we can gain deeper insights and make more accurate predictions about the world around us.

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a. The values of p = 8, UV = 70 and VW = 34

b. The property that we can use is "Opposite sides of the parallelogram are equal"  

A parallelogram is a quadrilateral with two pairs of parallel sides. The opposite sides of a parallelogram are equal in length and parallel to each other, and the opposite angles are also equal.

Here we have

Quadrilateral UVWX is a parallelogram

Here UV = 8p + 6, VW = 5p - 6, and XW = 9p - 2

Here the property that we can use is

The opposite sides of the parallelogram are equal

=> 8p+ 6 = 9p - 2

=> 9p - 8p = 6 + 2

=> p = 8

Hence, the lengths of UV and VW are calculated as

UV = 8p + 6 = 8(8) + 6 = 64 + 6 = 70

VW = 5p - 6 = 5(8) - 6 = 40 - 6 = 34

Therefore,

a. The values of p = 8, UV = 70 and VW = 34

b. The property that we can use is "Opposite sides of the parallelogram are equal"  

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a. The scale factor is 2.

b. The lengths of GH, HJ, and JF are 13 m, 4 m, and 8 m respectively.

A scale factor is a number that is used to resize, a geometric figure. When a figure is scaled, all of its dimensions are multiplied by the scale factor.

The resulting figure is similar to the original figure, but it may be larger or smaller, depending on the value of the scale factor.

Here we have

ABCD ∼ FGHJ

Since both figures are similar

The ratio of the corresponding sides will be equal

a. Scale factor = AB/FG = 8m/ 4m = 2

b. Calculating JF, HJ, and GH  

As we know the ratio of the corresponding sides is equal

=> AB/FG = BC/GH = CD/HJ = AD/JF

From the figure,

=> 8 m /4 m = 26 m/GH = 8 m/HJ = 16/JF  

=>  26 m/GH = 8 m/HJ = 16/JF = 2

=> 26 m/GH = 2

=> GH = 13 m

=> 8 m/HJ = 2  

=> HJ = 4

=>  16/JF = 2  

=> JF = 8 m

Therefore,

a. The scale factor is 2.

b. The lengths of GH, HJ, and JF are 13 m, 4 m, and 8 m respectively.

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if f(x) = 3*2ˣ + 2 is vertically stretched by a factor of 2, then the new function g(x) is 6*2ˣ + 4.

To vertically stretch the function f(x) by a factor of 2, we need to multiply the entire function by 2.

This will stretch the function vertically, making it twice as tall as before.

Therefore, if f(x) = 3*2ˣ + 2 is vertically stretched by a factor of 2, then the new function g(x) is:

g(x) = 2*f(x)

g(x) = 2*(3*2ˣ + 2)

g(x) = 6*2ˣ + 4

So the new function g(x) is 6*2ˣ + 4.

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Answer:

Step-by-step explanation:

A=[tex]\frac{1}{2}[/tex]bh

  =[tex]\frac{1}{2}[/tex]×34×14

  =238 in²

Alisha's total earnings for the week would be $650.

Why it is and what is selling?

Alisha's total earnings for the week can be calculated as follows:

Commission earned on sales = 15% of $2000 = 0.15 x $2000 = $300

Total earnings for the week = Base salary + Commission earned

= $350 + $300

= $650

Therefore, Alisha's total earnings for the week would be $650.

Selling refers to the exchange of goods or services for money or other valuable consideration. It is the process of convincing or persuading potential customers to purchase a product or service. Selling involves various activities, including advertising, marketing, negotiating, and closing a sale.

The goal of selling is to create a relationship with the customer that leads to repeat business and referrals. It is an essential aspect of commerce and business, as it generates revenue and helps companies grow and expand.

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Answer:  x= [tex]\sqrt{x=15i} or \sqrt{x=-5[/tex]

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