2x+y=8
y+3z=5
z+2w=1
5w+3x=9

Find the solution to each variable

Answer:

5 cm

Step-by-step explanation:

ΔABC is equilateral, so BC = AB = 5 cm.

____

AO is the perpendicular bisector of BC and the angle bisector of angle A, so ∠OAC = ∠OAB = 30°. Then vertex angle BAC of isosceles triangle ABC is 60°, which means all angles in the triangle are 60° and the triangle is equilateral.

The length of BC is 5cm

Given that line AB is tangent to circle K at point B, and line AC is tangent to circle K at point C, we know that the radius of the circle at the point of tangency is perpendicular to the tangent line. Therefore, OB is perpendicular to AB, and OC is perpendicular to AC. This forms two right triangles,[tex]$\triangle OAB$ and $\triangle OAC$.[/tex]

Let's denote OB as the side opposite the 30° angle and OA as the hypotenuse. Then we have:

[tex]OB = $\frac{1}{2}$AB = $\frac{1}{2} \times 5$ cm = 2.5 cm[/tex]

OA = AB = 5 cm (since AB is the hypotenuse of the right triangle)

Now, since the circle is the same, OA is also the radius of the circle, and thus OB = OC = 2.5 cm.

Therefore [tex], $\triangle OBC$[/tex] is an equilateral triangle because all angles are 60° and the sides opposite these angles are equal. Hence, BC = OB = OC = 2.5 cm.

Thus, BC = OB + OC' = 2.5 cm + 2.5 cm = 5 cm.

But this is not the final answer. We have to consider that the length of the chord BC is equal to the diameter of the circle because the tangents from a common external point to a circle are equal in length. Therefore, the diameter of the circle is twice the length of the radius OB (or OC').

Diameter = 2 * OB = 2 * 2.5 cm = 5 cm

BC = 5cm

Answer:

Failing to pay debt

Step-by-step explanation:

Final answer:

Defaulting on a debt, failing to pay debt, and building a credit history are crucial aspects of managing one's financial health.

Explanation:

Defaulting on a debt occurs when a borrower fails to repay the loan according to the terms agreed upon with the lender. This can lead to serious consequences such as damage to one's credit score and possible legal actions taken by the lender.

One of the contributing factors to defaulting is failing to pay debt on time. This affects a person's credit history and the lender's trust in the borrower's ability to repay borrowed money.

It is important to build a credit history by responsibly managing credit accounts, paying bills on time, and avoiding opening too many accounts rapidly to maintain a good credit score and prevent defaulting.

Answer:

a: 27 apples

b: $0.40 apples

Step-by-step explanation:

a: another way of saying that the price of an apple one-third that of an orange is that you can get 3 apples for the price of 1 orange. If he bought 5 oranges, he could have gotten 15 apples, so 27 apples total.

b:  $10.80/27 = $0.40 per apple

Answer:

C. 2

Step-by-step explanation:

Point B is 6-(-4) = 10 units up from point A. A point (F) that partitions that distance in the ratio 3:2 will be 3/(3+2) = 3/5 of the distance from A to B. That is, it will be ...

3/5 · 10 units = 6 units

above A. The y-coordinate of F will be 6 units added to the y-coordinate of point A, -4 +6 = 2.

Answer:

D. (2, 5)

Step-by-step explanation:

On a graph, (2, 5) is the only point in the solution space.

___

You can evaluate the inequality for each of the points to see which works.

A. 4 > 2·4 -3 . . . . false

B. 12 > 2·9 -3 . . . . false

C. 2 > 2·3 -3 . . . . false

D. 5 > 2·2 -3 . . . . TRUE

Answer:

1) 17p + 45.99 = 200

2) 200 > 45.99 + 17p

Step-by-step explanation:

Total Budget = $200

Cost of Party Room = $45.99

Cost of movie ticket for one person = $12.50

Cost of one small bag of popcorn = $4.50

Part 1: Possible Equation by Tomas

The possible equation that can be set up will have the total budget equal to total expenses.

So,

200 = Total Cost of party

200 = Cost of Party Room + Cost of Movie Tickets + Cost of popcorns

If p people attend the party, the cost of movie tickets will be $12.50p and cost of popcorns will be $4.50p, assuming that each person get a small popcorn bag.

So, now the equation will be:

200 = 45.99 + 12.50p + 4.50p

200 = 45.99 + 17p

or

17p + 45.99 = 200

This is a possible equation that Tomas might have used to represent the cost of the party.

Part 2: Possible Inequality by Emilio

Emilio might want to keep the cost below $200 of the entire party. So the possible inequality will be of the form:

200 > Total Cost of party

200 > Cost of Party Room + Cost of Movie Tickets + Cost of popcorns

200 > 45.99 + 12.50p + 4.50p

200 > 45.99 + 17p

This is a possible inequality that Emilio might have used to represent the cost of the party.

Answer:

  √13 units

Step-by-step explanation:

Find points B and C on the figure and locate the line between those points. The number next to the line is its length. Read the length from the diagram.

In a right triangle, the hypotenuse is the side across from the 90 degree angle. Without more information, we can't determine the length of the hypotenuse (BC), but if the lengths of the other two sides or the measurements of the other angles are known, the Pythagorean theorem or trigonometry can be used.  It is expressed as BC^2 = AB^2 + AC^2.

In a right triangle, the hypotenuse is the side that is opposite to the 90 degrees angle. In your right triangle, as you mentioned the sides as BC, I assume you have a triangle ABC where B and C are the two base angles and A is the right angle (90 degrees).

Without additional information such as the lengths of the other two sides (AB, AC), or the measurements of angles B or C, it is impossible to determine the length of the hypotenuse (BC). However, if you do have this information, you can use the Pythagorean theorem or trigonometric ratios to find the length. Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (BC) is equal to the sum of the squares of the lengths of the other two sides. It is expressed as BC^2 = AB^2 + AC^2.

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Answer:

184

Step-by-step explanation:

1st step

we simplify (5-1) which is just 4 and (3+7) which is 10

and we also simply 6^2 which is 36

now we plug the simplified terms back in

(4)(36+10)

(4)(46)

184

Answer:

184

Step-by-step explanation:

Subtract: 5 - 1 = 4

Power: 6 ^ 2 = 36

Add: 36 + 3 = 39

Add: 39 + 7 = 46

Multiple: 4 * 46 = 184

Please mark as brainiest

Answer:

Since 2 inches represent 8 feet then 2.5 would represent x feet so  

2/8 = 2.5/x  

By doing cross multiplication :  

2 x = 20 --> x = 10 feet

Step-by-step explanation:

Answer: it should be will receive a refund of $278

Step-by-step explanation:

That’s just what was on my test though

Hope that helps somebody

The amount Ms. Wilson will receive after she figures out her tax for the year is; $999.88

The tax bracket Ms. Wilson falls into demands that she pays 12% of her taxable income in tax.

Hence, the tax she's supposed to pay is;

Hence, she will receive after she figures her taxes for the year is; $5344 - $4,344.12 = $999.88

Read more on federal tax rate;

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Answer:

b

Step-by-step explanation:

100%

The explicit formula for the sequence -5, -3, -1, 1, 3 is a_n = -5 + (n - 1)2.

Each term of an arithmetic sequence can be found using the formula:

a_n = a + (n-1)d

The given sequence is 5, -3, -1, 1, 3.

From this, we can see that the value of:

a = -5

d = -3 - (-5) = -3 + 5 = 2

∴ The explicit formula can be written as:

a_n = -5 + (n - 1)2

Therefore we have found the explicit formula for the sequence -5, -3, -1, 1, 3 as a_n = -5 + (n - 1)2.

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Answer:

(x, y) ⇒ (-x, y)

Step-by-step explanation:

Any transformation that multiplies a variable by something other than ±1 is not a rigid transformation — it involves some sort of dilation. Constants can be added or subtracted to effect translation, but none of the transformations shown here do any translation.

The first transformation is a reflection across the y-axis, hence the rigid transformation you're looking for.

_____

Comment on rotations

A rotation about the origin can be written in the form ...

(x, y) ⇒ (ax -by, bx +ay)

where a^2 +b^2 = 1 and b/a = tan(angle of rotation)

This rigid transformation is an exception to the statement above about multiplication by something other than ±1.

Answer:

[tex]\sum_{x=0}^{15}2(\frac{1}{3})^x=3.0[/tex]

Step-by-step explanation:

We want to evaluate:

[tex]\sum_{x=0}^{15}2(\frac{1}{3})^x[/tex]

When x=0, we obtain the first term of the geometric series as

[tex]a_0=2(\frac{1}{3})^0[/tex]

The common ratio of this geometric series is [tex]r=\frac{1}{3}[/tex]

The sum of the first n-terms of a geometric series is

[tex]S_n=\frac{a(1-r^n)}{1-r}[/tex]

From x=0 to x=15, we have 16 terms.

The sum of the first 16 terms of the geometric series is

[tex]S_{16}=\frac{a(1-(\frac{1}{3})^{16})}{1-\frac{1}{3}}=2.99999993031[/tex]

[tex]\sum_{x=0}^{15}2(\frac{1}{3})^x=3.0[/tex] to the nearest tenth.

Answer:

6a. -8

8b. 1/125

Step-by-step explanation:

If you know powers of 2 and the squares and cubes of small integers, you can work these in your head. There is no "work" to show. Of course, a calculator can evaluate these easily. (see attached)

___

6a. (-128)^(3/7) = ((-2)^7)^(3/7) = (-2)^3 = -8

___

8b. (27^(2/3) +8^(4/3))^(-3/2) = ((3^3)^(2/3) +(2^3)^(4/3))^(-3/2)

= (3^2 +2^4)^(-3/2) = (9+16)^(-3/2) = 25^(-3/2)

= (5^2)^(-3/2) = 5^(-3) = 1/5^3

= 1/125

I think the last one is maybe ten, maybe

Answer:

Step-by-step explanation:

no

Answer:

5/2

Step-by-step explanation:

The multiplicative inverse is what me need to multiply by to get 1

2/5 * what = 1

Multiply by the reciprocal

5/2 *2/5 * what = 1 *5/2

what = 5/2

The multiplicative inverse is 5/2

5/2 is the multiplicative inverse

Given dimensions:

Height of the cylinder = 2 m

Volume is increasing at a rate of = 10 m³/min

Radius = 4 inches

Converting radius in meters.

1 inch = 0.0254 meters

4 inches = [tex]4\times0.0254=0.1016[/tex] meters

[tex]\frac{dv}{dt}=10[/tex]

we have to find, [tex]\frac{dr}{dt}=?[/tex]

Volume of the cylinder is given by [tex]\pi r^{2} h[/tex]

= [tex]\pi r^{2} *2 = 2\pi r^{2}[/tex]

Now differentiating with respect to 't'

[tex]\frac{dv}{dt} = \frac{d}{dt} (2\pi r^{2})[/tex]

[tex]\frac{dv}{dt} = 2\pi (2r)(\frac{dr}{dt})[/tex]

[tex]10=2\pi (2*0.1016)\frac{dr}{dt}[/tex]

[tex]10=2*3.14(0.2032)\frac{dr}{dt}[/tex]

[tex]\frac{dr}{dt}=\frac{10}{1.276}[/tex]

= 7.83 meter per minute.

100:40

=2.5

1200 : 2.5

=480

About 480 people out of the 1,200 customers are likely satisfied with their service.

To determine how many of the company's customers are likely satisfied with their service based on the survey results, we can use the concept of proportions. This involves simple multiplication and understanding ratios in percentages.

Find the proportion of satisfied customers in the survey:

Number of satisfied customers in the survey: 40

Total number of people surveyed: 100

Proportion of satisfied customers = (Number of satisfied customers) / (Total number of people surveyed)

Proportion of satisfied customers = 40 / 100 = 0.4 or 40%

Apply this proportion to the entire customer base:

Total number of the company's customers: 1,200

Estimate of satisfied customers = Proportion of satisfied customers × Total customers

Estimate of satisfied customers = 0.4 × 1,200 = 480

Answer:

Step-by-step explanation:

Let n represent the number of laps that Alan completes in 9 minutes. Then n-1 is the number of laps Brian completes, and the difference in their lap times in minutes per lap is ...

  9/(n -1) - 9/n = 3/4 . . . . . minutes

Multiplying by (4/3)n(n -1), we get

  12n -12(n -1) = n(n -1)

  12 = n(n -1)

Solutions to this are n=4 and n=-3. We are only interested in the positive solution, n = 4. Then Alan's speed in m/min is ...

  (4·450 m)/(9 min) = 200 m/min

Brian completes 3 laps in that 9-minute time, so his rate is ...

  (3·450 m)/(9 min) = 150 m/min

To find out how many games Natalie and her friends played, we subtracted the total shoe rental cost for 6 people from the $21 spent and divided the remainder by the cost per game, which gave us a result of 3 games played.

The question asks us to solve a real-world math problem where Natalie and her friends go bowling and spend a total of $21. The cost to play one game is $3 and shoe rental is $2 per person.

To determine the number of games they played, we need to calculate the cost of shoe rental for all people and then figure out how much of the $21 was left for the games.

First, we calculate the shoe rental for 6 people (Natalie and her 5 friends):

Next, we subtract the shoe rental cost from the total amount spent to find the amount spent on games:

Finally, we divide the amount spent on games by the cost per game to find the number of games played:

Natalie and her friends played 3 games of bowling.

Answer:

x ≈ -0.93, x ≈ 1.06

Step-by-step explanation:

A graphing calculator can show you the approximate solutions. (It is also capable of refining those solutions to full calculator precision, if you need.)

_____

Comment on the graphical solution

I prefer to have the calculator show me the zeros of a function, where the zeros correspond to solutions of the original equation. For the purpose, it is sufficient to define the function as the difference between the sides of the original equation.

__

The definition of g(x) in the attachment corresponds to the iterator of Newton's Iteration method for finding zeros of a function. When the input and output values of that iteration function match, the value of x is a zero of the function f(x).

Answer: OPTION D

Step-by-step explanation:

To solve this problem you must apply the proccedure shown below:

- Convert from 48 inches to foot. You know that 12 inches=1 foot. Then you have:

 [tex](48inches)(\frac{1foot}{12inches})=4feet[/tex]

- Therefore, keeping on mind that 48 inches is 4 feet, and you must find the ratio that  correctly compares 2 feet to 48 inches, you can write:

[tex]ratio=\frac{2feet}{4feet}[/tex]

- Reduce the fraction, then:

[tex]ratio=\frac{1}{2}[/tex]

- You can rewrite it as following:

[tex]ratio=1:2[/tex]

Answer:

D

Step-by-step explanation:

Answer:

Step-by-step explanation:

27

Answer: function b has a greater rate of change

Answer:

1282.82ft³

Step-by-step explanation:

To find the volume of the entire shape, we first need to find the volume of the cone and the cylinder separately.

Let's begin by getting the volume of the cylinder.

The formula to find the volume of a cylinder is:

[tex]V=\pi r^{2}h[/tex]

r = 7 ft

h = 6 ft

Let's plug in our values into the formula.

[tex]V=\pi (7)^{2}6[/tex]

[tex]V=\pi (49)6[/tex]

[tex]V=\pi (294)[/tex]

[tex]V=923.63[/tex]ft³

Now that we have the volume of our cylinder we need to find the volume of the cone.

The volume of the cone can be found by using the formula:

[tex]V=\dfrac{1}{3}\pi r^{2}h[/tex]

Our variables for the cone are:

r = 7 ft

h = 7 ft

[tex]V=\dfrac{1}{3}\pi (7)^{2}(7)[/tex]

[tex]V=\dfrac{1}{3}\pi (49)(7)[/tex]

[tex]V=\dfrac{1}{3}\pi (343)[/tex]

[tex]V=\dfrac{1}{3}1077.57[/tex]

[tex]V=359.19[/tex]ft³

Now that we found both of the volumes of the two shapes, we can then simply get the sum of both volumes to get the total volume of the shape.

Total Volume = 923.63ft³ + 359.19ft³

Total Volume = 1282.82ft³

Answer:

x = 2

Step-by-step explanation:

The minimum occurs where the value being squared is zero. x-2 = 0 when x=2.

Answer: c. Exponential

Answer:77

32+27+22+17+12+7+2-3-8-13-15-18=77

Answer:

54

Step-by-step explanation:

The first twelve terms would be, in decreasing order, 32, 27, 22, 17, 12, 7,2, -3, -8,-13,-18,-23.

1. -23+22 = -1

2. -13+12 = -1

3. -18+17 = -1

4. -8+7 = -1

5. -3+2 = -1

Using these five facts, we can simplify this to 32+27 -5(1) = 32+27-5 = 54

Answer:

1800

Step-by-step explanation:

Given in the question a polygon of 12 sides

Formula to calculate sum of interior angles of 12-gon is

where n is the number of sides

which in this case = 12

plug values in the formula above

(12 - 2)180

12*180 - 180(2)

2160 - 360

1800

Sum of measurements of the interior angles of a 12sided polygon is 1800

Answer:

=1800°

Step-by-step explanation:

A 12 sided figure is called a do-decagon or a 12-gon. The general formula for calculating the sum of all interior angles of a regular polygon is=180(n-2)

n represents the number of sides of the polygon.

Therefore, the sum of all angles= 180(12-2)

=1800°

Answer:

x = 45, y = 24.

Step-by-step explanation:

If the 2 numbers are x and y:

x + y = 69...........(1)

x = 2y - 3

x - 2y = -3...........(2)

Subtract: (1) - (2):

x - x + y - (-2y) = 69 - (-3)

y + 2y = 72

3y = 72

y = 24.

From equation 1:-

x + 24 = 69

x = 45.

The numbers are x = 24 and y = 45 respectively.

An algebraic expression in mathematics is a combination of terms both constant and variable. For example, we can write the expressions as -

2x + 3y + 5

2z + y

x + 3y

Given is that the sum of two numbers is 69. The larger number is three less than twice the smaller number.

Assume that the numbers are {x} and {y}. So, we can write the equations as -

x + y = 69

y = 2x - 3

Rewriting equation {1}, we get -

x + y = 69

x + 2x - 3 = 69

3x = 72

x = 24

and

y = 2 x 24 - 3

y = 45

Therefore, the numbers are x = 24 and y = 45 respectively.

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