What is the solution to the following system?
(3x+2y+z = 20
X-4y-Z=-10
2x+y + 2z = 15

1) The area of a circle circumscribed about a square is 307.7 cm².

2.a.) The angle ACB is 39 degrees.°.

2b.) The value of x is 5.42.

We shall find the radius to determine the area of a circle.

First,  find the side length of the square:

Since the perimeter of the square = 56 cm, then, each side of the square is 56 cm / 4 = 14 cm.

Next, find the diagonal of the square, using the Pythagorean theorem:

Diagonal = the diameter of the circumscribed circle.

Diagonal² = side length² + side length²

= 14 cm² + 14 cm²

= 196 cm² + 196 cm²

= 392 cm²

Take the square root of both sides:

Diagonal = √392 cm ≈ 19.80 cm (rounded to two decimal places)

Then, the radius of the circle which is half the diagonal:

Radius = Diagonal / 2 ≈ 19.80 cm / 2 ≈ 9.90 cm (rounded to two decimal places)

Finally, compute the area of the circle using the formula:

Area = π * Radius²

Area = 3.14 * (9.90 cm)²

Area ≈ 307.7 cm² (rounded to two decimal places)

Therefore, the area of the circle that is circumscribed about a square with a perimeter of 56 cm is 307.7 cm².

2. a) We use the property of angles in a circle to solve for angle ACB: an angle inscribed in a circle is half the measure of its intercepted arc.

Given that arc AB has a measure of 78°, we can find angle ACB as follows:

Angle ACB = 1/2 * arc AB

= 1/2 * 78°

= 39°

Therefore, the angle ACB is 39 degrees.

2b.) To solve for the value of x, we use the information that the angle ADB =  (3x - 12)⁴.

Given that angle ADB is (3x - 12)⁴, we can equate it to the measure of the intercepted arc AB, which is 78°:

(3x - 12)⁴ = 78

Solve the equation for x, by taking the fourth root of both sides:

∛∛((3x - 12)⁴) = ∛∛78

Simplify,

3x - 12 = ∛(78)

Isolate x by adding 12 to both sides:

3x - 12 + 12 = ∛(78) + 12

3x = ∛(78) + 12

Finally, divide both sides by 3:

x = (∛(78) + 12) / 3

x = (4.27 +12) / 3

x = 5.42

So, x is 5.42

Therefore,

1) The area of the circle is 154 cm².

2a.) Angle ACB is equal to 102°.

2b.) The value of x is 5.42

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The graph of the function y = 2|x| is a vertical stretch by a factor of 2 of the parent function y = |x|.

The functions for this problem are defined as follows:

When a function is multiplied by 2, we have that it is vertically stretched by a factor of 2.

Hence the graph of the function y = 2|x| is a vertical stretch by a factor of 2 of the parent function y = |x|.

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Answer:

(- \(\frac{1}{3}\), \(\frac{3}{4}\) )

Step-by-step explanation:

9x + 8y = 3 → (1)

6x - 12y = - 11 → (2)

Multiplying (1) by 12 and (2) by 8 and adding will eliminate the y- term

108x + 96y = 36 → (3)

48x - 96y = - 88 → (4)

Add (3) and (4) term by term to eliminate y

156x = - 52 ( divide both sides by 156 )

x = \(\frac{-52}{156}\) = - \(\frac{1}{3}\)

Substitute this value into either of the 2 equations and solve for y

Substituting into (1)

9(- \(\frac{1}{3}\) ) + 8y = 3

- 3 + 8y = 3 ( add 3 to both sides )

8y = 6 ( divide both sides by 8 )

y = \(\frac{6}{8}\) = \(\frac{3}{4}\)

solution is (- \(\frac{1}{3}\), \(\frac{3}{4}\) )

Answer:

43

Step-by-step explanation:

Green:  9 - 2(-3) = 9 + 6 = 15

Red:  -2(-3) + 4 = 6 + 4 = 10

Dark blue:  7x + 5 = 19

7x = 19 - 5 = 14

x = 14/7 = 2

Light blue:  6x + 3 = 21

6x = 21 - 3 = 18

x = 18/6 = 3

Red(Lt blue) - Dk blue + Green = 10(3) - 2 + 15 = 43

The zeros with each multiplicity are given as follows:

The factor theorem is used to define the functions, which states that the function is defined as a product of it's linear factors, if x = a is a root, then x - a is a linear factor of the function.

Considering the linear factors of the function in this problem, the zeros are given as follows:

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The rule for a 270 degree rotation is the original Y value becomes the new X value and the original X value becomes the new Y value but sign becomes the opposite.

(-2,3) after a 270 degree rotation becomes (3,2)

Answer:

x=-pie/12

sinxcosx=-1/4

multiply both sides by 2

sin2x = 2sinxcosx we know

now equation will be

sin2x = -1/2

2x=-pie/6

x=-pie/12

Supposing that the other square has a length of 6 units, applying the Pythagorean Theorem, it is found that:

The length of the hypotenuse side is of 10 units.

The Pythagorean Theorem is a geometry axiom that relates the length of the legs \(l_1\) and \(l_2\) of a right triangle with the length of the hypotenuse h, stating that the hypotenuse squared is the sum of the legs squared, according to the following equation:

\(h^2 = l_1^2 + l_2^2\)

In the context of this problem, we have that the legs have lengths defined as follows:

Hence the length of the hypotenuse can be found as follows:

h² = 6² + 8²

h² = 36 + 64

h² = 100

h = sqrt(100)

h = 10 units.

This problem is incomplete and could not be found on any search engine, hence we are going to suppose that the other leg of the triangle has a length of 6 units.

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Answer:

B: -3

Step-by-step explanation:

-(-3) + 5 < 7

3 + 5 <7

8 < 7 FALSE

Answer:

-3

Step-by-step explanation:

Solve for x in the inequality, to get x > -2 (see the image below if you want to know how to solve it). Then, we can substitute the numbers for x to see which ones DO NOT make the inequality true:

-1 > -2  This is true, because -1 is greater than -2

-3 > -2  This is false, because -3 is not greater than -2

7 > -2  This is true, because 7 is greater than -2

5 > -2  This is true, because 5 is greater than -2

So you can see that -3 is the number that DOES NOT make the inequality true. So therefore:

Answer: -3

Hope this helps! :)

Answer:

the answer is b, c, d, a, respectively

Answer:

a) -22, b)14 c) -3

Step-by-step explanation:

a) -19+3(-13+4*3)

= -19+3*(-13+12)

= -19+3*(-1)

= -22

b) | -7(2)|

= | -7*2|

= -14

c) 15-3 | -4-2|

= 15-3* (-6)

= 15-18

= -3

Answer:

\(d \approx 5.8\)

Step-by-step explanation:

Just use the distance formula.

\(d=\sqrt{(x_2-x_{1})^2+(y_2-y_{1})^2}\)

\(d=\sqrt{(3-0)^2+(5-0)^2}}\)

\(d=\sqrt{(3)^2+(5)^2}}\)

\(d=\sqrt{9+25}\)

\(d=\sqrt{34\)

\(d \approx 5.8\)

Answer:

The overall expected grade point average for the semester is 3.16/3.1 or 3.2 if you round it up.

Step-by-step explanation:

To get the average, you need to add up all the numbers then divide the sum by how many numbers you added.

3.5 + 3.0 + 3.0 = 9.5

9.5 / 3 = 3.16

Given Information:

expected grade in two-credit course = 3.5

expected  grade in three-credit course = 3.0

expected grade in four-credit course = 3.0

Required Information:

Expected overall grade point average = ?

Answer:

The expected overall grade point average of this college student is 3.11

Step-by-step explanation:

The overall expected grade point average is given by

E(X) = Sum of grades/Total number of credit hours

Sum of grades = ∑ weightage*expected grades

Sum of grades = 2*3.50 + 3*3.0 + 4*3.0 = 28

Total number of credit hours = 2 + 3 + 4 = 9

E(X) = Sum of grades/Total number of credit hours

E(X) = 28/9

E(X) = 3.11

Therefore, the expected overall grade point average of this college student is 3.11 .

Need 1500 g of cornflakes

The cost

The cost

Option one is cheaper as £2.97 < £3.50

Answer:

a)  A: two 750g boxes.

b)  £2.97

Step-by-step explanation:

750g box:

500g box:

Cost of two 750g boxes:

\(\implies 1.98+\dfrac{1.98}{2}=1.98+0.99=2.97\)

Cost of three 500g boxes:

\(\implies 1.75+1.75+0=3.50\)

As 2.97 < 3.50, it is cheaper to buy two 750g boxes.

It costs £2.97 to buy 1500g of cornflakes using the cheapest way.

Answer:

X is five, 100% :D

Step-by-step explanation:

The group of individuals fitting a description is called option D: Population, this is because, in statistics, a population is seen as am entire group of individuals, items, or elements that tends to have or share a common characteristics.

The term "population" describes the complete group of people or things that you are interested in investigating. It is the group of individuals or thing(s) about which you are attempting to draw conclusions.

There are infinite and finite populations. A population with a set quantity of people or things is said to be finite. An endless population is one that has an infinite amount of people or things.

Therefore, the correct option is D

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See full text below

A group of individuals fitting a description is the _____

Which of the term below fit the description above.

A.census

B.sample

C.parameter

D.population

Answer:

A, B, & C

Step-by-step explanation:

An equilateral triangle is one that has (A) all equivalent angle measures & (B) all the sides are the same length.

since a triangle is equal to 180º, & since there are 3 angles in a triangle: (C) each angle measures 60º.

Hope this helps! Have a great day!

Answer:

Round both numbers to 1 significant figure.

400+400=800

800 is the answer.

Answer:

The inequality shown in the graph is y ≤ -3x + 3 ⇒ C

Step-by-step explanation:

The linear form of the equation of a line is y = m x + b, where

From the given graph

∵ The line passes through points (0, 3) and (2, -3)

∴ x1 = 0 and x2 = 2

∴ y1 = 3 and y2 = -3

∵ The slope of the line is m = Δy/Δx

∵ Δx = 2 - 0 = 2

∵ Δy = -3 - 3 = -6

∴ m = \(\frac{-6}{2}\)

∴ m = -3

∵ b is value y at x = 0

∴ b = 3

→ Substitute m and b in the form of the equation above

∴ y = -3x + 3

∵ The line is solid and the shading area is under the line

∴ The sign of inequality is ≤ ⇒ (smaller than or equal)

→ Change = in the equation by ≤ to get the inequality

∴ y ≤ -3x + 3

∴ The inequality shown in the graph is y ≤ -3x + 3

Ones is the place value of the digit 6 in the number 2,016 and 6 is the face value of the digit 6 in the number 2,016.

Given, a number 2,016

we have to find the place and face value of 6 in the given number 2,016.

So, the Place value of 6 in the given number is ones.

Ones is the place value of the digit 6 in the number 2,016

Also, the Face value of 6 in the given number is 6.

6 is the face value of the digit 6 in the number 2,016

Hence, Ones is the place value of the digit 6 in the number 2,016 and 6 is the face value of the digit 6 in the number 2,016.

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Step-by-step explanation:

I think it'S right......

A) The algebraic expression will be 12d + 7 = 91

B) He drives 7 miles per day to work.

For 11 days straight, Ms. Chung drove the same distance every day going to and coming from work.

The distance she drove on Saturday was; 0.9 miles.

The number of miles she drives per day:

84 miles/12

= 7 miles per day

Let the number of miles she travels be day = d

12d + 7 = 91 miles

12d + 7 = 91

12d = 91 - 7

12d = 84

d = 84/12

d = 7 miles per day

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a) The inequality for the expression 2z + 9 is 2z + 9 > 13.

b) The inequality for the expression 3(z - 4) is 3z - 12 > -6.

c) The inequality for the expression 4 + 2z is 4 + 2z > 8.

d) The inequality for the expression 5(3z - 2) is 15z - 10 > 20.

a) To write an inequality for the expression 2z + 9, we can multiply the given inequality z > 2 by 2 and then add 9 to both sides of the inequality:

2z > 2 * 2

2z > 4

Adding 9 to both sides:

2z + 9 > 4 + 9

2z + 9 > 13

Therefore, the inequality for the expression 2z + 9 is 2z + 9 > 13.

b) For the expression 3(z - 4), we can distribute the 3 inside the parentheses:

3z - 3 * 4

3z - 12

Since we are given that z > 2, we can substitute z > 2 into the expression:

3z - 12 > 3 * 2 - 12

3z - 12 > 6 - 12

3z - 12 > -6

Therefore, the inequality for the expression 3(z - 4) is 3z - 12 > -6.

c) The expression 4 + 2z does not change with the given inequality z > 2. We can simply rewrite the expression:

4 + 2z > 4 + 2 * 2

4 + 2z > 4 + 4

4 + 2z > 8

Therefore, the inequality for the expression 4 + 2z is 4 + 2z > 8.

d) Similar to the previous expressions, we can distribute the 5 in the expression 5(3z - 2):

5 * 3z - 5 * 2

15z - 10

Considering the given inequality z > 2, we can substitute z > 2 into the expression:

15z - 10 > 15 * 2 - 10

15z - 10 > 30 - 10

15z - 10 > 20

Therefore, the inequality for the expression 5(3z - 2) is 15z - 10 > 20.

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Answer:

15mg/ml

Step-by-step explanation:

Percent mass per volume ( % m/v) is unit expression that tells us how many grams of a solute that we can find 100 ml of a particular solution.

In the above question, we are asked to express 1.5%w/v Bepotastine besilate (BEPREVE) ophthalmic solution as mg/mL

Step 1

1.5% w/v = 1.5 g of Bepotastine besilate (BEPREVE) in 100ml ophthalmic solution

Hence, if

100ml = 1.5g

1 ml = y g

We Cross Multiply

100ml × yg = 1 ml × 1.5g

yg = 1 ml × 1.5g/100ml

= 0.015g

Therefore, in 1 ml we have 0.15 g.

Step 2

Since we are asked to express as mg/ml

We convert 0.015g to mg

1 gram = 1000 milligrams

0.015 grams =

Cross Multiply

0.015grams × 1000 milligrams/ 1 gram

= 15 mg

Therefore, the concentration in mg/ml of 15% m/v of Bepotastine besilate (BEPREVE) ophthalmic solution is 15mg/ml

Answer:

D. 4 units

Step-by-step explanation:

Similar figures have corresponding lengths in proportion.

\(\frac{4x}{2x}=\frac{x+1}{x} \\ \\ 2=1+\frac{1}{x} \\ \\ 1=\frac{1}{x} \\ \\ x=1\)

Therefore, the height of Figure 1 is 4.

Answer:

√221 is between 14 and 15.

√221 ≈ 14.86

Step-by-step explanation:

Perfect square:  A number made by squaring a whole number.

Perfect squares:  1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, ...

To find an approximate value of a square root, find the perfect squares above and below the number:

⇒ 196 < 221 < 225

Therefore:

\(\implies \sf \sqrt{196} < \sqrt{221} < \sqrt{225}\)

\(\implies \sf \sqrt{14^2} < \sqrt{221} < \sqrt{15^2}\)

\(\implies \sf 14 < \sqrt{221} < 15\)

Therefore, √221 is between 14 and 15 on a number line.

Drawing the number line

(see attachment 1)

Locate 221 on the number line. We can see that it is between 14.8 and 14.9.  Place a marker halfway between 14.8 and 14.9, then divide the second half into 5 equal increments (see attachment 2).

Therefore, an approx value of √221 is 14.86.

Multiply the top by -2 and just cross elimination the rest. Hope this helps.

Answer:16

Step-by-step explanation: