solve for x
2 + x^2 = 18​

Valid dimensions for the rectangular pen that satisfy the given constraints are: L = 20 feet, W = 10 feet; L = 40 feet, W = 20 feet; L = 80 feet, W = 75 feet.

To find the possible dimensions for the rectangular pen, we need to consider the constraints given: the fence should be at least 60 feet long and the distance around it should be no more than 310 feet.

Let's assume the length of the rectangular pen is L and the width is W.

The perimeter of a rectangle is given by the formula: P = 2L + 2W.

According to the constraints:

The fence should be at least 60 feet long, so we have the inequality: 2L + 2W ≥ 60.

The distance around the fence should be no more than 310 feet, so we have the inequality: 2L + 2W ≤ 310.

We can solve these inequalities to determine the possible dimensions.

2L + 2W ≥ 60:

We can rearrange this inequality as L + W ≥ 30.

2L + 2W ≤ 310:

We can simplify this inequality as L + W ≤ 155.

The possible dimensions for the rectangular pen are any values of L and W that satisfy both inequalities:

L + W ≥ 30

L + W ≤ 155

This means the length and width must be positive numbers that add up to 30 or more, but no more than 155. Since there are infinitely many possible combinations, here are a few examples of valid dimensions that satisfy the constraints:

- L = 20 feet, W = 10 feet (perimeter: 60 feet)

- L = 40 feet, W = 20 feet (perimeter: 120 feet)

- L = 80 feet, W = 75 feet (perimeter: 310 feet)

These are just a few examples, and there are many other combinations that would satisfy the given constraints.

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Circle with center C and point D. Triangle CDE and triangle CDF are both equilateral, and we have DE = EF = FD.

What is construction?

In the context of geometry, construction refers to the process of creating geometric figures or shapes using only a compass and straightedge (also called a ruler). The goal of construction is to create accurate and precise geometric figures using only these two tools and a given set of instructions.

To construct an equilateral triangle DEF with points E and F on circle C, we will follow the following steps:

Step 1: Draw a circle with center C and point D on it.

Step 2: Draw a line through points C and D. This line will be the base of our equilateral triangle DEF.

Step 3: Construct the perpendicular bisector of line CD. This can be done by drawing two circles with centers at C and D, both with radius greater than half the length of CD. The two circles will intersect at two points, and the line passing through these two points will be the perpendicular bisector of CD.

Step 4: Let G be the intersection point of the perpendicular bisector and circle C that is closest to point D. Draw lines from G to points C and D. These lines will intersect circle C at points E and F, respectively.

Step 5: Check that the length of CE is equal to the length of CF. This can be done using a compass and ruler.

Step 6: Finally, draw lines from points E and F to point D. The resulting triangle DEF will be equilateral.

To prove that triangle DEF is equilateral, we can show that DE = EF = FD. We already know that CE = CF from step 5. Since C is the center of the circle, CE = CF = CD. By construction, angle ECD and angle FCD are both 60 degrees, since they are inscribed angles that intercept the same arc.

Therefore, triangle CDE and triangle CDF are both equilateral, and we have DE = EF = FD.

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In Chloe's risk information forms, the key item she should document is the probability and impact of each identified risk.

To effectively monitor risks and obtain early warnings, Chloe should document the probability and impact of each identified risk in her risk information forms. Let's break down why this information is critical in risk management.

The impact of a risk represents the potential consequences or severity of its occurrence. By documenting the impact, Chloe can understand the potential damage or disruption a risk could cause. This allows her to prioritize risks based on their potential impact on the project or objective. By assigning an impact rating or value to each risk, Chloe can identify high-impact risks that require careful consideration and robust mitigation strategies.

Once Chloe has established the probability and impact for each risk, she can set thresholds or triggers for early warning signs. These thresholds act as indicators that a risk is approaching or crossing a critical level.

Chloe can track these thresholds regularly and set up a monitoring system that alerts her when a risk reaches or surpasses the specified levels. This allows her to take timely action and implement mitigation strategies before the risk escalates and negatively impacts the project.

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In this case, the experimental probability is D. 0.860

First, note that Experimental probability, also known as Empirical probability, is founded on real experiments and adequate documentation of events.

In the table we can see that he rolled the cube 1000 times, and he recorded that 140 of those times he rolled a 5.

Then, the probability of rolling a 5 will be equal to:

P1 = 140/1000 = 0.14

Now, the probabilty of NOT rolling a 5, is equal to the rest of the probabilities, this is:

P2 = 1 - 0.14 = 0.86

then the correct option is D

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Full Question:

Although part of your question is missing, you might be referring to this full question:

Jimmy rolls a number cube multiple times and records the data in the table above. At the end of the experiment, he counts that he had rolled 140 fives. Find the experimental probability of not rolling a five, based in Jimmy’s experiment. Round the answer to the nearest thousandth.

A. 0.140

B. 0.167

C. 0.667

D. 0.860

The sum of three non-contiguous segments is the same as the sum of the other three.

The Theorem of Menelaus states that six segments are cut off on either side of every line that transverses (crosses) a triangle's three sides (one of them must be extended). This theorem only applies to plane geometry. The sum of three non-contiguous segments is the same as the sum of the other three.

Menelaus' theorem relates ratios that can be derived by cutting a triangle in half. The inverse of the theorem, which states that three points on a triangle are only coincident if and only if they meet certain requirements, is also accurate and very effective in demonstrating the existence of three congruent points.

By using Menelaus' Theorem for triangle ADC and line F - E - B:

\($$\begin{gathered}\frac{A F}{F C} \cdot \frac{C B}{B D} \cdot \frac{D E}{E A}=1 \\\frac{A F}{F C} \cdot \frac{2}{1} \cdot \frac{1}{1}=1 \\\frac{A F}{F C}=\frac{1}{2}\end{gathered}$$\)

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Answer:

perpendicular

Step-by-step explanation:

both lines meet at a 90 degree angle

The missing statement in Step 5 include the following: B. AC/DC = BC/EC.

In Mathematics and Geometry, two triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.

Based on the angle, angle (AA) similarity theorem, we can logically deduce the following congruent triangles:

ΔABC ≅ ΔDEC  ⇒ Step 4

By the definition of similar triangles, we can logically deduce the following proportional and corresponding side lengths:

AC/DC = BC/EC ⇒ Step 5

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

x≤4

Step-by-step explanation:

uh i did this wrong so uh just ignore what i said

Answer:

82°

Step-by-step explanation:

Angle C and B equal the measure of angle A so,

143 - 61 = 82

Angle B is 82°

To approximate the integral ∫2.4 to 2 f(x) dx using Simpson's rule, we divide the interval [2, 2.4] into subintervals and approximate the integral within each subinterval using quadratic polynomials.

Given the data points (x, f(x)) = (2, 0.6931), (2.2, 0.7885), and (2.4, 0.8755), we can use Simpson's rule to approximate the integral.

Step 1: Determine the step size, h.

Since we have three data points, we can divide the interval [2, 2.4] into two subintervals, giving us a step size of h = (2.4 - 2) / 2 = 0.2.

Step 2: Calculate the approximations within each subinterval.

Using Simpson's rule, the integral within each subinterval is given by:

∫f(x)dx ≈ (h/3) * [f(x₀) + 4f(x₁) + f(x₂)]

where x₀, x₁, and x₂ are the data points within each subinterval.

For the first subinterval [2, 2.2]:

∫f(x)dx ≈ (0.2/3) * [f(2) + 4f(2.1) + f(2.2)]

≈ (0.2/3) * [0.6931 + 4(0.7885) + 0.8755]

For the second subinterval [2.2, 2.4]:

∫f(x)dx ≈ (0.2/3) * [f(2.2) + 4f(2.3) + f(2.4)]

≈ (0.2/3) * [0.7885 + 4(0.4545) + 0.8755]

Step 3: Sum up the approximations.

To obtain the approximation of the total integral, we sum up the approximations within each subinterval.

Approximation ≈ (∫f(x)dx in subinterval 1) + (∫f(x)dx in subinterval 2)

Calculating the values, we get the final approximation of the integral ∫2.4 to 2 f(x) dx using Simpson's rule.

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Answer:

-3231a-5326b

Step-by-step explanation:

I subtracted the a's but you can't subtract the b with anything so .....yea

Answer:

Adriana= $960

Tania= $1080

Step-by-step explanation:

Please see the attached pictures for the full solution.

• Do note that you could also use 'x' or other variables to represent the amount of money either Adriana or Tania brought for shopping. A unit was used in this case since I used model method to represent the given situation.

\(\pink{\bigstar}\) The larger number is \(\large\leadsto\boxed{\tt\purple{78}}\)

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

Let the two numbers be 'x' and 'y' respectively.

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

According to the question:-

✯ Sum of two numbers is 100.

➪ \(\sf x + y = 100 \dashrightarrow\bold\red{[equation \: 1]}\)

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

Also,

✯ Difference between the numbers is 56.

➪ \(\sf x - y = 100 \dashrightarrow\bold\red{[equation \: 2]}\)

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• Adding equation [1] and equation [2]:-

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

➪ \(\sf (x + y) + (x - y) = 100 + 56\)

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

➪ \(\sf x + y + x - y = 156\)

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

➪ \(\sf 2x = 156\)

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

➪ \(\sf x = \dfrac{156}{2}\)

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

★ \(\large{\bold\red{x = 78}}\)

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• Substituting the value of x in equation [1]:-

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

➪ \(\sf x + y = 100\)

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

➪ \(\sf 78 + y = 100\)

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

➪ \(\sf y = 100 - 78\)

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

★ \(\large{\bold\red{y = 22}}\)

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

Therefore, the numbers are 78 and 22.

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

The larger number is 78.

Answer:

\(here \: given \: that \: sum = 100 \\ diffrence = 56 \\ take \: the \:large \: number = x \\another = y \\ thenx - y = 56 \\ y = x - 56 \\ here \: x + y = 100 \\ x + x - 56 = 100 \\ 2x - 56 = 100 \\ 2x = 156 \\ x = \frac{156}{2} \\ x = 78 \\ large \: number \: = 78 \\ thank \: you\)

Given:

The coordinate of point R in quadrilateral RUST are (2,4).

R is dilated by a scale factor of 3, centered at the origin, followed by the translation \((x, y)\to (x+4,y)\).

To find:

The coordinates of R' after dilation and translation.

Solution:

If a figure is dilated by a scale factor of 3, centered at the origin, then

\((x,y)\to (3x,3y)\)

We value R(2,4).

\(R(2,4)\to R_1(3(2),3(4))\)

\(R(2,4)\to R_1(6,12)\)

The rule of translation is:

\((x, y)\to (x+4,y)\)

Using this rule, we get

\(R_1(6,12)\to R'(6+4,12)\)

\(R_1(6,12)\to R'(10,12)\)

Therefore, the coordinates of point R' are (10,12) and the correct option is B.

Answer:

The answer is A and C

Step-by-step explanation:

Supplementary angles added together = 180.

Answer:

The sixth rod is 35.20 cm.

Step-by-step explanation:

Get the total length of the 6 rods.

Total length = 6(44.2cm)

= 265.20 cm

Get the total length of 5 rods

Length of 5 rods = 5(46cm)

=230cm

The length of the sixth rod is the difference between the two.

Length of the sixth rod = 265.20 cm - 230 cm

length = 35.2 cm

Answer: Utmostly Irrefutably true my good sir!

Answer:

C

Step-by-step explanation:

RATATATATATATATATATATATATTATATATATATAAT

Answer:

C

Step-by-step explanation:

9-5=4

3-1=2

4/2=2

The nurse should infuse argatroban at a rate of approximately 42.41 ml/hr.

To calculate the infusion rate of argatroban in ml/hr, we need to convert the weight of the patient from pounds to kilograms and then use the ordered dose to determine the infusion rate. Here are the steps:

1. Convert patient weight from pounds to kilograms:

  187 lbs * (1 kg / 2.2046 lbs) = 84.82 kg (rounded to two decimal places)

2. Calculate the total dose per minute:

  2 mcg/kg/min * 84.82 kg = 169.64 mcg/min

3. Convert the total dose from micrograms to milligrams:

  169.64 mcg/min * (1 mg / 1000 mcg) = 0.16964 mg/min

4. Determine the infusion rate in ml/hr:

  Since the pharmacy provided argatroban in a concentration of 100 mg/250 ml, we can set up a proportion:

  0.16964 mg/min * (250 ml / 100 mg) * (60 min / 1 hr) = 42.41 ml/hr (rounded to two decimal places)

Therefore, the nurse should infuse argatroban at a rate of approximately 42.41 ml/hr to provide the desired dose for JK.

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Answer:

(4i+1)^2

4i^2 + 2(4i) + 1

16(-1) + 8i + 1

-15+8i

8i-15

(x+1) + (x-2)(x+3)

(x+1) + (x^2-2x+3x-6)

(x+1)+x^2+x-6

x+1+x^2+x-6

x^2+2x-5

Let me know if this helps!

The statement that describes when the plans are based on the same number of aerobic exercise sessions is:

The number of strength-training exercises and aerobic exercises per week is calculated as follows:

Let a be the number of strength-training exercises and b be the number of aerobic exercises per week respectively.

For the beginner plan:

15a + 20b = 90  eqn. (1)

For the advanced plan:

20a + 30b = 130 eqn. (2)

Solving the simultaneous equation by elimination method:

Multiply eqn. (1) by 3 and eqn. (2) by 2

45a + 60b = 270 eqn. (3)

40a + 60b = 260 eqn. (4)

Subtract eqn. (4) from eqn. (3)

5a = 10

a = 2

Substitute a = 2 in eqn (2)

b = 3

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Complete question:

A personal trainer designs exercise plans based on a combination of strength-training and aerobic exercise. A beginner plan has 15 minutes per session of strength training and 20 minutes per session of aerobic exercise for a total of 90 minutes of exercise in a week. An advanced plan has 20 minutes per session of strength training and 30 minutes of aerobic exercise for a total of 130 minutes of exercise in a week.

Which statement describes when the plans are based on the same number of aerobic exercise sessions?

Each plan utilizes a combination of 2 strength-training sessions and 2 aerobic exercise sessions per week.

Each plan utilizes a combination of 2 strength-training sessions and 3 aerobic exercise sessions per week.

Each plan utilizes a combination of 3 strength-training sessions and 2 aerobic exercise sessions per week.

Each plan utilizes a combination of 3 strength-training sessions and 3 aerobic exercise sessions per week.

Answer:

The mean increases from 9 to 10 when there are 15 students at the next meeting of the club. This is because the mean is calculated by adding all the data values together and then dividing by the total number of students. When the number of students increases from 9 to 15, the sum of the data points increases while the total number of students also increases, resulting in an increase in the mean.

Including the 15 students in the data may increase or decrease the mean. This is because the mean is calculated by adding all the numbers in a set and dividing by the quantity. Adding a new number to the set (in this case 15) thus changes the mean. If the new number is greater than the current mean, the mean will increase; if it's less, the mean will decrease.

The question is related to the concept of mean in mathematics which is the average of a set of numbers. If there are more students attending the club meeting, including this value can cause the mean to change.

Consider a set of values. The mean of these values is calculated by adding all these values together and dividing by the number of values. If we add a new value (in this case the 15 students) to our set, it will affect the calculation of the mean. If the new value is higher than the current mean, it would increase the mean. If it's less, it would decrease the mean. Therefore, the mean could increase or decrease when including the 15 students in the data set.

Let's say the mean value before adding 15 was 9 and we had 10 values in our set. The total would be 9*10=90. When we add 15, the total becomes 105 and the new mean becomes 105/11, which is close to 9.5. Thus, by adding 15 to our data set, the mean has increased from 9 to 9.5.

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Answer:

92

Step-by-step explanation:

E is the midpoint of AC.

F is the midpoint of BC.

FE and AB are parallel by a theorem.

m<DBF = m<EFC = 92 by corresponding angles of parallel lines cut by a transversal.

Answer:

92°

Step-by-step explanation:

The probability that the first failed inspection occurs on Fatima's 5th inspection i.e P(c = 5) is 0.05..

In probability and statistics,the geometric distribution defines the probability of the first success occurring after k trials. The probability of success is p

P r ( X = k ) = ( 1 − p )⁽ᵏ⁻¹⁾ p.

We have given that,

An emissions inspections on cars is conducted by Fatima.

Probability that car fail the inspection, p = 6% = 0.06

let c denoted the number of cars that are inspected until one car fail to inspection.

The random variable c here. Here c follow geometric probability distribution with probability of success (0.06).

Plugging all known values in above formula we get, p(c= 5) = (1-0.06)⁴ × 0.06

= (0.94)⁴ (0.06)

=0.0468449376~ 0.05

so, the answer is 0.05

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Complete question:

Fatima conducts emissions inspections on cars. She finds that 6%, percent of the cars fail the inspection. Let C be the number of cars Fatima inspects until a car fails an inspection. Assume that the results of each inspection are independent.

Required:

Find the probability that the first failed inspection occurs on Fatima's 5th inspection

Answer: $4,000

Step-by-step explanation:

If you have $1,000 dollars, and take ad ten percent ($100) interest you would get $1,100. But If you take away 30 percent ($300) away from 1,100 dollars you would get $800 dollars. The over all balance on the account after five years is, $4,000.

Hope this answer helps! :)

The length of the diagonal from one corner to the opposite corner is larger because it includes the prism's height as well as the length and width of the base.

A prism is an n-sided quadrilateral polyhedron with an n-sided quadrilateral base, a second base that is a relocated copy of the first base, and n extra heads (necessarily all parallelograms), generally with two connecting the corresponding sides of the base. Any cross sections that appear parallel to the base are translations. A prism is a solid, three-dimensional object having numerous faces. It has identical cross-sections, horizontal flanks, and bases. A prism's faces are parallelograms or quadrilaterals with no bases. A prism is a refracting object that is homogeneous, solid, and transparent, and it is surrounded by planes that are just slightly inclined to one another. A prism typically has two triangular heads and two parallel rectangular faces.

The Pythagorean theorem can be used to compute the length of the diagonals. Assume the rectangular prism's length, width, and height are a, b, and c, respectively. Then:

\(\sqrt(a^2 + b^2)\)) is the length of the diagonal at the base.

The diagonal length from one corner to the opposite corner is \(\sqrt(a^2 + b^2 + c^2)\).

The length of the diagonal from one corner to the opposite corner is larger because it includes the prism's height as well as the length and width of the base.

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Answer:

1. With the height and base of a triangle given, we can use the Pythagorean Theorem to find the length of the hypotenuse (the third side) of the right triangle.

Given:

Height (a) = 6

Base (b) = 8

We can plug these values into the Pythagorean Theorem formula:

a^2 + b^2 = c^2

Substituting the values:

6^2 + 8^2 = c^2

Simplifying:

36 + 64 = c^2

100 = c^2

Now, we can take the square root of both sides to solve for c:

√100 = √c^2

10 = c

So, the length of the hypotenuse (c) of the right triangle is 10 units.


2.
Given:

Base (b) = 8

One side (a or c) = 12

We can use the Pythagorean Theorem to find the length of the remaining side (either a or c) of the right triangle.

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Using the formula:

a^2 + b^2 = c^2

Substituting the values:

a^2 + 8^2 = 12^2

Simplifying:

a^2 + 64 = 144

Next, we can isolate a^2 by subtracting 64 from both sides of the equation:

a^2 = 144 - 64

a^2 = 80

Finally, we can take the square root of both sides to solve for a:

√(a^2) = √80

a ≈ 8.94 (rounded to two decimal places)

So, the length of the remaining side (either a or c) of the right triangle is approximately 8.94 units. Please note that depending on the context of the problem, you may need to use the positive square root value for a or c, depending on which side is relevant in the specific scenario.

Answer:

X = 10^2

Y = /80

Step-by-step explanation:

Pythagorean theorem = A^2 +B^2= C^2

Fist triangle

6^2+8^2

36 + 64= 100

/100 = 10^2

X= 10^2

Second triangle

Pythagorean theorem = C^2 - A^2= B^2

12^2 - 8^2

144 - 64= 80

/80 = /80

X = /80

If henry can  70 words in 5 minutes and that in 8 minutes he can type 112 words the rate of change is 14.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

Henry can type 70 words in 5 minutes and that in 8 minutes he can type 112 words.

m=112-70/8-5

=42/3

=14

Hence, the rate of change is 14.

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