Complete the two-column proof using the answers in the bank.

Answer:

Step-by-step explanation:

[tex]\sqrt[3]{b^{27}}=\sqrt[3]{b^{(9)(3)}}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=\sqrt[3]{(b^9)^3}\qquad\text{use}\ \sqrt[n]{a^n}=a\\\\=b^9[/tex]

Answer:

b^9 :)

Step-by-step explanation:

The dimension of the rectangle is 25 by 40

Let :

Area of rectangle = x * (x + 15)

1000 = x² + 15x

x² + 15x - 1000 = 0

solving the quadratic equation

x(x - 25) +40(x - 25)

x = 25 or x = -40

The width cannot be negative.

Hence,

Therefore, the dimension of the rectangle is 25 by 40

Answer:

[tex]W_{f}  = 90 - 1.2w[/tex]

Step-by-step explanation:

I want to cut back on my calorie intake so that I can lose weight.

I plan to lose 1.2 kg a week from my current weigh 90 kg until I reach my goal.

Therefore, I can model my weight loss for the next several weeks by the equation  

[tex]W_{f}  = 90 - 1.2w[/tex]  

where [tex]W_{f}[/tex] is my final weight after w weeks of treatment. (Answer)

To model your weight loss, you can create a linear equation using your current weight as the starting point, and representing your weekly weight loss as a negative rate of change. The equation W(t) = 90 - 1.2t will allow you to predict your future weight based on this rate of weight loss.

To develop an equation to model your weight loss, you need to translate the information about your weight loss goals into mathematical terms. You mentioned that your current weight is 90 kilograms and you plan to lose 1.2 kilograms per week.

Imagining that each week is a step forward in time, we can say time is represented by the variable 't' in weeks. Likewise, your weight, which will change as time increases, can be represented by 'w' in kilograms.

Giving weight loss a negative sign (since you are losing, not gaining weight), the amount of weight you will lose per week is -1.2 kilograms. When we start, at time t = 0, your weight is 90 kilograms. So we could represent your weight as a function of time with the equation W(t) = 90 - 1.2t.

In this equation, simply substitute 't' for the number of weeks to predict your weight loss. For example, if you want to find out your weight after 3 weeks, you would calculate W(3) = 90 - 1.2 * 3 = 86.4 kilograms. This is a simplified model and actual weight loss may vary due to factors like metabolic rate, type of food ingested and the amount of calories burned per day.

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Answer:

42/100

The drawings will help

Answer:

42/100

Step-by-step explanation:

Just looking at the fraction, you could guess that one of the fractions is larger. So my guess would be the first one, but I'm guessing which really is only a guess. I like to guess at things like this; it's a little like playing monopoly. Let's find out what the answer really is. So get out your calculator.

29/71: 29 ÷ 71 = 0.4085

42/100: 42/100 = 0.4200

Well if you guessed the second one you are a better guesser than I am

42/100  is larger that 29/71

Answer:

A-1 Rentals

hopefully that helps!!

Answer:

rent all

Step-by-step explanation:

Answer:

x = 3.576 and x = - 3.076

Step-by-step explanation:

Two functions are given to be, g(x) = 2x² + 3x + 10 and k(x) = 2x + 16.

Now, we have to solve the equation g(x) = 2k(x)  

⇒ 2x² + 3x + 10 = 4x + 32

⇒2x² - x - 22 = 0

The expression in the left hand side can not be factorized and therefore we have to use Sridhar Acharya formula which gives the solutions of the equation in the form ax² + bx + c = 0 are given by  

[tex]x = \frac{-b + \sqrt{b^{2} - 4ac} }{2a}[/tex] and [tex]x = \frac{-b - \sqrt{b^{2} - 4ac} }{2a}[/tex]

Therefore, the solutions of the given equation are  

[tex]x = \frac{-(- 1) + \sqrt{(- 1)^{2} - 4 (2)(-22)}  }{2(2)} = 3.576[/tex]

and [tex]x = \frac{-(- 1) - \sqrt{(- 1)^{2} - 4 (2)(-22)}  }{2(2)} = -3.076[/tex] (Answer)

Final answer:

To solve the equation g(x) = k(x) for x, we simplify it to 2x² + x - 6 = 0 and factor it, resulting in x = 1.5 or x = -2. The method used is factoring due to the simplicity of the equation.

Explanation:

To solve the equation g(x) = k(x) algebraically for x, we set the given functions equal to each other. Given the functions g(x) = 2x² + 3x + 10 and k(x) = 2x + 16, the equation becomes 2x² + 3x + 10 = 2x + 16. To solve for x, we must first simplify the equation by moving all terms to one side and then using the quadratic formula or factoring, if possible.

Step 1: Subtract 2x and 16 from both sides to obtain the quadratic equation 2x² + x - 6 = 0.

Step 2: Factor the quadratic equation if possible. In this case, it factors to (2x - 3)(x + 2) = 0, so the possible solutions for x are x = 1.5 or x = -2.

The chosen method for solving this quadratic equation is factoring because the equation simplifies nicely and the factors are easily observable.

Answer:

Tommy and Manuel are 16 ft apart

Step-by-step explanation:

The locations of all three players are shown in the image below

They form a right triangle where the hypotenuse is 20 ft, and one of the legs is 12 ft. We must find the other leg.

We must use Pythagoras's theorem. Being a and b the legs of a right triangle and c its hypotenuse, then

[tex]c^2=a^2+b^2[/tex]

Knowing c and one of the legs, say b:

[tex]a^2=c^2-b^2[/tex]

Using the values c=20, b=12 we find

[tex]a^2=20^2-12^2=400-144=256[/tex]

[tex]a=\sqrt{256}=16[/tex]

So, Tommy and Manuel are 16 ft apart

Answer:

 The chance that positive response obtained for program 1 is 65.90

And  The chance that positive response obtained for program 2 is 87.50  

Step-by-step explanation:

Given data as :

The positive response for program of different cities in percentage

Now, The positive response is obtained from Chicago for program 1 is 65.90

The total positive response for program 1 in % = 68.80

So, The chance that positive response obtained = 65.90

Again ,

The positive response is obtained from Chicago for program 2 is 87.50

The total positive response for program 1 in % = 81.70

So, The chance that positive response obtained = 87.50

Hence   The chance that positive response obtained for program 1 is 65.90

And  The chance that positive response obtained for program 2 is 87.50  answer

Answer:from calculator

0.9333333333

Answer: 3.3

Step-by-step explanation:

49 divided by 15 =3.26

Rounding 3.26 to the nearest tenth gives you 3.3

Answer:

c = 10 , d = 26

Step-by-step explanation:

In the rectangular prism, we know the fact that the three faces are mutually perpendicular to each other. So, it has a rectangular base.

Given, the length and breadth of the rectangle are 8 and 6 units, and the diagonal is c.

Since it is a rectangle, length , breadth and diagonal from a right angled triangle.

So we have, c² = 6² + 8² = 36 + 64 = 100

⇒           c = 10 units

For the side face:

Length = 24 units.

As we can see, the edge of the side face is perpendicular to the base of the prism. Which means, any line on the base of the prism is perpendicular to the 24units side edge.

So we can say that , the diagonal of the rectangular base of the prism (c) is perpendicular to the 24 units side face edge.

Hence, 24 , d and c (which is 10units) form a right angled triangle

From pythagoras theorem:

   d² = 24² + 10² = 576 + 100 = 676

⇒ d = 26 units

Answer:

-3

Step-by-step explanation:

We must do the subtraction -3 + 2 BEFORE anything else, because any operations inside parenthesis always take first priority.

We end up with:

-3(-1) - 6.  

We must multiply before addiing or subtracting.  Therefore, multiply (-3)(-1), obtaining 3 and complete result 3 - 6.

Finally do that subtraction; the result is -3.

Answer:

?=13/6

Step-by-step explanation:

5/2-?+?=1/3+?

5/2-1/3=?

?=15/6-2/6=13/6

Answer:

13/6???

Step-by-step explanation:

I turned 5/2 into 15/6 and 1/3 into 2/6. I multiplied both their numerators and denomonators by 3. I then subtracted the two numbers and got 13/6.

Answer:

Julie weighs 35 lbs, Ted weighs 70 lbs, Mike weighs 105 lbs.

Step-by-step explanation:

Let the weight of Julie be [tex]x[/tex]

Given:

Ted weighs twice as much as Julie

Weight of Ted = [tex]2x[/tex]

Mike weighs three times as much as Julie.

Weight of Mike = [tex]3x[/tex]

Together, Ted, Mike, and Julie weigh 210 lbs.

[tex]x+2x+3x=210[/tex]

Solving above we get;

[tex]6x=210\\x=\frac{210}{6}=35\ lbs[/tex]

Hence Julie weight is 35 lbs.

Weight of Ted = [tex]2x=2\times 35 = 70 \ lbs[/tex]

Hence Ted weight is 70 lbs.

Weight of Mike = [tex]3x=3\times 35 = 105 \ lbs[/tex]

Hence Mike weight is 105 lbs.

Answer:

Julie weighs 35 lbs, Ted weighs 70 lbs, Mike weighs 105 lbs.

I hope this helps you

Answer:

answer should be x = 18.

Step-by-step explanation:

25 = x + 7

we can also write it as

x + 7 = 25

as we see 7 is positive(+) on LHS( left hand side) so if we move it to RHS( right hand side) the sign will change so the equation will be:

x = 25 - 7

now just simplify it:

x = 18.

Answer:

x=-5.4

Step-by-step explanation:

0.6+0.2x=-0.48

0.2x=-0.48-0.6

0.2x=-1.08

x=-1.08/0.2

x=-5.4

Answer:

The apothem is also the radius of the incircle of the polygon. For a polygon of n sides, there are n possible apothems, all the same length of course. The word apothem can refer to the line itself, or the length of that line. So you can correctly say 'draw the apothem' and 'the apothem is 4cm'.

Final answer:

To find the apothem in geometry, one must utilize trigonometry, knowing the polygon's side length. In astronomy, calculating distances such as the semi-major axis involves understanding celestial mechanics and requires knowing the aphelion and perihelion distances. The problem content combines concepts from geometry and astronomy to discuss angles and distances.

Explanation:

Calculating the Measure of the Apothem

When attempting to find the measure of the apothem of a geometric figure, you're essentially looking for a segment that connects the center of the figure to the midpoint of one of its sides and is perpendicular to that side. This is especially common in regular polygons. However, this particular problem seems to blend geometry and astronomy, discussing the apparent width of the Moon and comparing it using similar triangles.

To calculate the apothem in a regular polygon, you can use trigonometry if you know the length of one of the sides and the number of sides. On the other hand, if the setting involves celestial bodies like the moon and planets, determining an apothem-like distance would involve understanding the object's orbit, size, and distance from the observer.

To compute the semi-major axis of an elliptical orbit, like that of a planet around a sun, you would use the sum of the aphelion and perihelion, divided by two. For instance, if we know the perihelion (rp) and aphelion (ra), we calculate the semi-major axis (a) as (ra + rp)/2.

Remember, an angle is used in astronomy to measure the apparent separation between celestial objects as seen from Earth. Astronomers use degrees to describe these angles, and knowing the angular size can help in estimating distances in space.

To find the aphelion or semi-major axis of an orbit, certain equations are used that involve these distances. Such calculations are essential for understanding celestial mechanics and the movement of objects in our solar system.

Answer:

Part a) [tex]7.536\ m[/tex]

Part b) [tex]\$34.14[/tex]

Step-by-step explanation:

Part 6)

a) How much edging is needed?

we know that

To find out how much edging is needed determine the circumference of the circular garden

The circumference of the circular garden is equal to

[tex]C=\pi D[/tex]

where

D is the diameter

we have

[tex]D=2.4\ m[/tex]

assume

[tex]\pi =3.14[/tex]

substitute

[tex]C=(3.14)(2.4)[/tex]

[tex]C=7.536\ m[/tex]

Part b) we know that

To find out the cost to edge the garden, multiply the length of edging plastic needed by the cost of $4.53 per meter

so

[tex](7.536\ m)(4.53\ \$/m)=\$34.14[/tex]

Answer:

5/100• X = 3.5

X=3.5÷5/100

X=70

The answer is 5% x 70 = 3.5

To solve for the blank in the equation 5% x __ = 3.5, we need to find a number that, when multiplied by 5%, equals 3.5.

First, express 5% as a decimal: 5% = 0.05.

Set up the equation:

0.05 x x = 3.5

Next, solve for x by dividing both sides by 0.05:

x = 3.5 / 0.05

x = 70

Thus, the blank should be filled with 70.

Final answer:

The rule for determining the cost based on the number of tickets is Cost = 30 × Tickets. Using this rule, the cost for 10 tickets is calculated to be 300 dollars.

Explanation:

The question requires us to determine a rule for the output based on the given input of tickets and then use this rule to find the cost for 10 tickets. By examining the input and output values provided, we see a consistent pattern: the cost increases by 30 dollars with each additional ticket. Given this pattern, the rule can be formulated as an algebraic expression: Cost = 30 × Tickets.

Applying this rule to an input of x tickets, the expression becomes Cost = 30 × x. To find the cost for 10 tickets, we replace x with 10: Cost = 30 × 10 = 300 dollars.

Yeah, I think it is C...

I don't really have an explanation though.

If I'm wrong, correct me. Hope I helped! ☺☼

Answer:

Option D is the nearest answer.

Elizabeth invested = $45,714

Step-by-step explanation:

Given that:

Total amount = $80,000

Ratio given = 3:4

As the total is divided into 7 parts (3+4) so,

Each part equals = 80,000/7

Each part equals = 11,428.57

Now steive invested = 11,428.57 * 3 = $34,286

Elizabeth invested= 11,428.57*4 = $45,714

i hope it will help you

Answer:

[tex]\$16,990.62[/tex]  

Step-by-step explanation:

we know that    

The compound interest formula is equal to  

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

[tex]t=5\ years\\ P=\$15,000\\ r=2.5\%=2.5/100=0.025\\n=4[/tex]  

substitute in the formula above

[tex]A=15,000(1+\frac{0.025}{4})^{4*5}[/tex]  

[tex]A=15,000(1.00625)^{20}[/tex]  

[tex]A=\$16,990.62[/tex]  

Answer:

The solution for the given system of equations is ( 4,-3).

Step-by-step explanation:

Here, the given set of equations is:

7 x - 3 y = 37    ....  (1)

14 x + 11 y = 23   .... (2)

Now, we solve this equation by ELIMINATION METHOD,

Multiply the first given equation with ( -2), we get:

(-2) [7 x - 3 y = 37 ] ⇒   -14 x + 6 y = -74  .... (3)

Adding equation (2) and (3), we get:

14 x + 11 y  +   -14 x + 6 y  = 23 -74

or, 17 y = - 51

or, y = -51/17 = 3

⇒ y = -3

Now, out the value of y in the given second equation,we get:

14 x + 11 (-3)  = 23

or, 14 x  = 23 + 33 = 56

or, x =  56/14 =  4

⇒ x = 4

Hence, the solution for the given system of equations is ( 4,-3).

194 children, 92 students, and 97 adults attended

Step-by-step explanation:

The given is:

We need to find how many children,

students, and adults attended

Assume that x represents the number of children, y represents the number of students, and z represents the number of adults

∵ There were x children, y students and z adult attended

∵ The movie theater has a seating capacity of 383

∴ x + y + z = 383 ⇒ (1)

∵ The theater charges $5 for children, $7 for students, and

   $12 for adults

∵ The total ticket sales was $2778

∴ 5x + 7y + 12z = 2778 ⇒ (2)

∵ There are half as many adults as there are children

- Half means 0.5

∴ z = 0.5x ⇒ (3)

Substitute equation (3) in equations (1) and (2)

∵ x + y + 0.5x = 383

- Add like terms

∴ 1.5x + y = 383 ⇒ (4)

∵ 5x + 7y + 12(0.5x) = 2778

∴ 5x + 7y + 6x = 2778

- Add like terms

∴ 11x + 7y = 2778 ⇒ (5)

Let us solve equations (4) and (5) to find x and y

Multiply equation (4) by -7 to eliminate y

∴ -10.5x - 7y = -2681 ⇒ (6)

- Add equations (5) and (6)

∴ 0.5x = 97

- Divide both sides by 0.5

∴ x = 194

Substitute the value of x in equations (4) and (3) to find y and z

∵ 1.5(194) + y = 383

∴ 291 + y = 383

- Subtract 291 from both sides

∴ y = 92

∵ z = 0.5 (194)

∴ z = 97

194 children, 92 students, and 97 adults attended

Learn more:

You can learn more about the system of linear equations in brainly.com/question/6075514

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Answer:

Step-by-step explanation:

[tex]\bold{METHOD\ 1:}\\\\p\%=\dfrac{p}{100}\to16.5\%=\dfrac{16.5}{100}=\dfrac{16.5\cdot10}{100\cdot10}=\dfrac{165}{1000}=\dfrac{33}{200}\\\\16.5\%\ of\ 33=\dfrac{33}{200}\cdot33=\dfrac{1089}{200}=5.445[/tex]

[tex]\bold{METHOD\ 2:}\\\\\begin{array}{ccc}100\%&-&33\\\\16.5\%&-&x\end{array}\qquad\text{cross multiply}\\\\\\100x=(16.5)(33)\\\\100x=544.5\qquad\text{divide both sides by 100}\\\\x=\dfrac{544.5}{100}\\\\x=5.445[/tex]

First find slope.

slope=change in y/change in x (y2-y1/x2-x1)

slope=4-3/-2-(-4)=1/2

Now we need to find the x intercept.

y=mx+b

3=1/2(-4)+b

b=5

So the equation is y=1/2x+5.

The domain of this function is first restricted to all nonnegative integers because the ferry can carry only a whole number number of cars.

The domain is restricted to number less than or equal to 42  because the ferry cannot carry more cars than capacity .

The domain of this function is the set of non-negative integers.

The domain of a function represents the set of possible input values for that function. In this case, the function represents the revenue collected by the ferry, which depends on the number of cars. The number of cars, denoted as c, must be a non-negative integer because the ferry cannot transport a fraction of a car. Therefore, the domain of this function is the set of non-negative integers, or {0, 1, 2, 3, ...}.

Answer:

-20a+12b

Step-by-step explanation:

Answer:

-20a+12b

Step-by-step explanation:

-4(5a-3b)=-20a+12b

Answer:

Divide 85 by 9.24

Step-by-step explanation:

The answer is B I believe, because the parallelogram b is half parallelogram a and is reflected across the y axis, NOT the x.