I need help on number 14 please please

([G,G]\) is a group, which is the subgroup of \(G \times G\) generated by the set of all commutators \([g,h]\).

To fix \(G\) as a group and set \([g,h]:=g h g^{-1} h^{-1}\), and then set
\[[G,G] := \left\{\left[g_{1}, h_{1}\right] \cdots\left[g_{s}, h_{s}\right]: g_{1}, \ldots, g_{s}, h_{1}, \ldots, h_{s} \in G\right\}\), we can start by noticing that this is a subset of the Cartesian product of \(G\) with itself, and since \(G\) is a group, this subset must also be a group. Therefore, \([G,G]\) is a group, which is the subgroup of \(G \times G\) generated by the set of all commutators \([g,h]\).

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Answer:x=a

Step-by-step explanation:

Answer: -sqrt(3)/4

Step-by-step explanation:

To solve this trigonometric expression, we can use the following trigonometric identities:

sin (180 + x) = -sin x

cos (180 + x) = -cos x

Using these identities, we can rewrite the expression as:

sin(200°)cos(80°) - cos(200°)sin(80°)

= sin(180° + 20°)cos(80°) - cos(180° + 20°)sin(80°)

= -sin(20°)cos(80°) + cos(20°)sin(80°)

= (cos(20°) - sin(20°))sin(80°)

= sin(70°)sin(80°)

= (cos(20°) - cos(150°))/2

= (-sqrt(3)/2 - sqrt(3)/2)/2

= -sqrt(3)/4

Therefore, sin(200°)cos(80°) - cos(200°)sin(80°) = -sqrt(3)/4.

Answer: 8 * 8 = (distance between PQ and RS) * 8

distance between PQ and RS = 8" PQRS in units: 16 because 8 (PQ) + 8 (RS)=16, measurement type is units so 16 units

Step-by-step explanation:

*I used A.I to help explain this better.* It should make sense, just read/scan through it, as it explains the question very throughly.

"First, let's find the length of the sides of the rectangle. Since P and Q have the same x-coordinate, we know that PQ is a vertical line segment with length 8 units (since the y-coordinates of P and Q differ by 8). Similarly, since P and Q have the same y-coordinate, we know that RS is a horizontal line segment with length 8 units. Therefore, the length and width of the rectangle are both 8 units.

To find the coordinates of points R and S, we need to consider two cases:

a) Points R and S are to the left of points P and Q.

In this case, we can imagine that the rectangle is reflected across the y-axis, so that points P and Q become points P'(-1, -4) and Q'(-1, 4), respectively. Then, points R and S must lie on the line x=-2 (to the left of point P'), and the distance between them must be 8 units.

Since the area of the rectangle is 64 square centimeters, the length of RS is 8 units, and the length of PQ is 8 units, we know that the distance between PQ and RS (i.e., the height of the rectangle) is also 8 units. This means that the y-coordinates of R and S must differ by 8 units.

Let's choose a y-coordinate for point R. Since R is to the left of P', its x-coordinate is -2, and its y-coordinate must be between -4 and 4 (since the y-coordinates of P' and Q' are -4 and 4, respectively). Let's say that the y-coordinate of R is yR. Then, the y-coordinate of S must be yR + 8.

The area of the rectangle is (length)(width) = (8)(8) = 64 square centimeters. Since PQ is a vertical line segment, its length is the difference between the y-coordinates of P and Q, which is 8 units. Therefore, the length of RS is also 8 units. The distance between PQ and RS (i.e., the height of the rectangle) is also 8 units. Therefore, we can write:

8 * 8 = (distance between PQ and RS) * 8

distance between PQ and RS = 8

So, the y-coordinates of R and S differ by 8 units. Therefore, we can write:

yR + 8 - yR = 8

yR = 0

Therefore, the coordinates of R are (-2, 0), and the coordinates of S are (-2, 8).

b) Points R and S are to the right of points P and Q.

In this case, we can imagine that the rectangle is reflected across the x-axis, so that points P and Q become points P''(1, 4) and Q''(-1, 4), respectively. Then, points R and S must lie on the line y=-6 (to the right of point P''), and the distance between them must be 8 units.

Again, the area of the rectangle is (length)(width) = (8)(8) = 64 square centimeters. Since RS is a horizontal line segment, its length is the difference between the x-coordinates of R and S, which is 8 units. Therefore, the length of PQ is also 8 units. The distance between PQ and RS (i.e., the height of the rectangle) is also 8 units. Therefore, we can write:

8 * 8 = (distance between PQ and RS) * 8

distance between PQ and RS = 8"

Answer:

The lateral area of the prism is 190 square inches and the total surface area is 358 square inches.

Step-by-step explanation:

To find the lateral area and total surface area of a rectangular prism, we need to use the following formulas:

Lateral Area = perimeter of the base x height

Total Surface Area = 2 x base area + lateral area

Where the base area is simply the product of the length and width of the rectangular prism.

Let's apply these formulas to the rectangular prism with dimensions 12in x 7in x 5in:

Lateral Area:

To find the perimeter of the base, we add up the lengths of all four sides of the rectangle:

Perimeter of the base = 2(length + width) = 2(12in + 7in) = 2(19in) = 38in

Now, we multiply the perimeter of the base by the height of the prism:

Lateral Area = 38in x 5in = 190in^2

Therefore, the lateral area of the rectangular prism is 190 square inches.

Total Surface Area:

To find the base area, we simply multiply the length and width of the rectangular prism:

Base Area = length x width = 12in x 7in = 84in^2

Now, we can use the formula for total surface area:

Total Surface Area = 2 x base area + lateral area

Total Surface Area = 2(84in^2) + 190in^2

Total Surface Area = 168in^2 + 190in^2

Total Surface Area = 358in^2

Therefore, the total surface area of the rectangular prism is 358 square inches.

So the lateral area of the prism is 190 square inches and the total surface area is 358 square inches.

The ball traveled a horizontal distance of roughly 75.6*cos(theta) feet. Keep in mind that this is supposing a level, homogeneous surface and that the ball has no spin.

What is the equation?

In a math equation, two assertions are connected by the equals sign (=), which denotes equivalence. A mathematical assertion used in algebraic equations establishes the equivalence of two mathematical statements. For instance, in equation 3x + 5 = 14, the equal sign creates a space between the values 3x + 5 and 14.

To comprehend the relationship between the two sentences written on opposing sides of a letter, utilise a mathematical formula. The logo and the specific program typically correspond. An illustration would be 2x - 4 = 2.

75.6 feet are equal to ymax = 472/(2*32.2) + 4.

As the ball's motion is symmetrical, the time it takes to reach its highest point is equal to half the length of its flight. As a result, the total flight time is:

[tex]\frac{Sin(\theta)}{g} = 247;[/tex]

[tex]t_{total} = 2[/tex];

[tex]t_{max} = 247[/tex]

[tex]\frac{cos(\theta)*y_{max}}{vi^{2}},\\[/tex]

where t max is the time needed to reach the highest point. Again, we cannot precisely solve for theta, but we may leverage the knowledge that the ball's horizontal travels as follows:

[tex]Vi \ \times cos(\theta)\times t_{total} = x.[/tex]

Hence, by entering the data we are aware of, we can determine x:

x = 47cos(θ) (θ)

75.6/47 = [tex]\frac{2y_{max}}{vi}[/tex]

= 47cos(θ)75.6cos (θ).

Hence, the ball traveled a horizontal distance of roughly 75.6*cos(θ) feet. Keep in mind that this is supposing a level, homogeneous surface and that the ball has no spin.

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Answer:

16.1 is the closest asnwer

Step-by-step explanation:

if you didn't understand feel free to send me a message bro

Answer:

x=55°, y=35°

Step-by-step explanation:

The angle between x and 35° is a right angle.

A right angle equals 90°.

Therefore. 90=x+35

x=55°

Now that x is known, we can find y.

The angle made between the x and y axis is 90°.

Therefore, 90=x+y

90=55+y

y=35°

Answer:

X=55° and Y=35° ................................

For each of the given , we need to use the Law of Sines to determine whether the given information results in two triangles, one triangle, or no triangles. The Law of Sines states that for any triangle, the ratio of the length of a side to the sine of the opposite angle is the same for all three sides:

a/sin A = b/sin B = c/sin C

Let's look at each scenario and apply the Law of Sines:

Scenario 1: a = 7, b = 10, A = 50°

Using the Law of Sines, we can find the value of angle B:

7/sin 50° = 10/sin B

sin B = 10*sin 50°/7

sin B = 0.918

B = sin^-1(0.918) = 66.4°

Since the sum of the angles in a triangle must equal 180°, we can find the value of angle C:

C = 180° - 50° - 66.4° = 63.6°

Since all three angles add up to 180° and are positive, we can conclude that this scenario results in one triangle.

Scenario 2: a = 5, b = 7, A = 120°

Using the Law of Sines, we can find the value of angle B:

5/sin 120° = 7/sin B

sin B = 7*sin 120°/5

sin B = 1.209

Since the sine of an angle cannot be greater than 1, this scenario does not result in a triangle.

Scenario 3: a = 9, b = 12, A = 30°

Using the Law of Sines, we can find the value of angle B:

9/sin 30° = 12/sin B

sin B = 12*sin 30°/9

sin B = 0.667

B = sin^-1(0.667) = 41.8°

Since the sum of the angles in a triangle must equal 180°, we can find the value of angle C:

C = 180° - 30° - 41.8° = 108.2°

Since all three angles add up to 180° and are positive, we can conclude that this scenario results in one triangle.

In conclusion, scenario 1 and scenario 3 result in one triangle, while scenario 2 does not result in a triangle. We can determine this by using the Law of Sines and checking whether the values of the angles are valid and add up to 180°.

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Substituting in the given values for a and b, we can solve for d and find that it is approximately 9.48 inches.

Pythagorean Theorem is a mathematical formula that states that the square of the hypotenuse (the side opposite the right angle) of a right triangle is equal to the sum of the squares of the other two sides. It is expressed as a2 + b2 = c2, where c is the length of the hypotenuse and a and b are the lengths of the other two sides.

The given diagram is a right triangle with two of its sides labeled in inches. To find the length of the third side (d), one must use the Pythagorean Theorem. The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In this case, d is the hypotenuse, so d2 = a2 + b2. Therefore, substituting in the given values for a and b, we can solve for d and find that it is approximately 9.48 inches.

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Answer: C, 2 2/8

Step-by-step explanation: To turn a mixed number into an improper fraction, multiply the whole number by the denominator. Then, add the numerator. So in this example it would be:

4 3/8 = 35/8

2 1/8 = 17/8

Now, since the denominators are equivalent, all we need to do is subtract the numerators.

35/8 - 17/8 = 18/8

The answer needs to be changed back to a mixed number. For this problem, there is an easy way to do this.

18/8 = 8/8 + 8/8 +2/8, which as a mixed number would be 2 2/8.

So the correct choice would be (C).

The exact value of the remaining trigonometric functions of \( \theta \) are \( \sin \theta = \frac{7\sqrt{52}}{52} \), \( \cos \theta = \frac{-\sqrt{3}\sqrt{52}}{52} \), \( \tan \theta = \frac{-7\sqrt{3}}{3} \), \( \sec \theta = \frac{-\sqrt{52}\sqrt{3}}{3} \), and \( \csc \theta = \frac{\sqrt{52}}{7} \).

We can find the exact value of the remaining trigonometric functions of \( \theta \) by using the Pythagorean identity and the definition of the trigonometric functions. The Pythagorean identity states that \( \sin^2 \theta + \cos^2 \theta = 1 \). The definition of the trigonometric functions are \( \sin \theta = \frac{y}{r} \), \( \cos \theta = \frac{x}{r} \), \( \tan \theta = \frac{y}{x} \), \( \cot \theta = \frac{x}{y} \), \( \sec \theta = \frac{r}{x} \), and \( \csc \theta = \frac{r}{y} \).

Given that \( \cot \theta=-\frac{\sqrt{3}}{7} \), we can use the definition of the cotangent function to find the values of x and y. Let x = -\( \sqrt{3} \) and y = 7. Then, we can use the Pythagorean identity to find the value of r.

\( \sin^2 \theta + \cos^2 \theta = 1 \)

\( \frac{y^2}{r^2} + \frac{x^2}{r^2} = 1 \)

\( \frac{7^2}{r^2} + \frac{(-\sqrt{3})^2}{r^2} = 1 \)

\( \frac{49 + 3}{r^2} = 1 \)

\( \frac{52}{r^2} = 1 \)

\( r^2 = 52 \)

\( r = \sqrt{52} \)

Now, we can use the definition of the trigonometric functions to find the exact value of the remaining trigonometric functions of \( \theta \).

\( \sin \theta = \frac{y}{r} = \frac{7}{\sqrt{52}} = \frac{7\sqrt{52}}{52} \)

\( \cos \theta = \frac{x}{r} = \frac{-\sqrt{3}}{\sqrt{52}} = \frac{-\sqrt{3}\sqrt{52}}{52} \)

\( \tan \theta = \frac{y}{x} = \frac{7}{-\sqrt{3}} = \frac{-7\sqrt{3}}{3} \)

\( \sec \theta = \frac{r}{x} = \frac{\sqrt{52}}{-\sqrt{3}} = \frac{-\sqrt{52}\sqrt{3}}{3} \)

\( \csc \theta = \frac{r}{y} = \frac{\sqrt{52}}{7} = \frac{\sqrt{52}}{7} \)

Therefore, the exact value of the remaining trigonometric functions of \( \theta \) are \( \sin \theta = \frac{7\sqrt{52}}{52} \), \( \cos \theta = \frac{-\sqrt{3}\sqrt{52}}{52} \), \( \tan \theta = \frac{-7\sqrt{3}}{3} \), \( \sec \theta = \frac{-\sqrt{52}\sqrt{3}}{3} \), and \( \csc \theta = \frac{\sqrt{52}}{7} \).

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product of diagonal elements is 10 x -2 = -20.

To find the value of the determinant of the coefficient matrix, perform row operations to reduce it to an echelon form. First, multiply the first row by -3, the second row by 5, and the third row by 2. This yields the following matrix:

(-9)x + (0)y - 18z = -33

(25)x - 10y + 15z = 85

(4)x - (2)y - 14z = -6

Next, subtract the first row from the second row and the first row from the third row. This yields the following matrix:

(0)x + (10)y - (18)z = 52

(4)x - (2)y - (14)z = -6

Finally, subtract 4 times the second row from the third row. This yields the following matrix:

(0)x + (10)y - (18)z = 52

(0)x - (0)y - (2)z = -24

This matrix is in echelon form. The value of the determinant is simply the product of diagonal elements, which is 10 x -2 = -20.

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The sοlutiοn tο the inequality is all values οf x greater than -10. This can be represented οn a number line as shοwn in the figure attached.

A cοnnectiοn between twο expressiοns οr values that is nοt equal in mathematics is referred tο as inequality. Hence, inequity results frοm imbalance. In mathematics, an inequality establishes the cοnnectiοn between twο nοn-equal numbers. Equality and inequality are nοt the same.

Use the nοt equal symbοl mοst frequently when twο values are nοt equal (). Values οf any size can be cοntrasted using a variety οf inequalities.

By changing the twο sides until just the variables are left, many straightfοrward inequalities may be sοlved.

Nοnetheless, a variety οf factοrs suppοrt inequality: Bοth sides' negative values are split οr added. Exchange the left and the right.

5x - 15 + 15 > -65 + 15

5x > -50

5x/5 > -50/5

x > -10

Because the inequality is severe, the οpen circle at -10 shοws that it is nοt part οf the sοlutiοn set (i.e., x must be greater than -10, nοt greater than οr equal tο -10).

The right arrοw shοws that the sοlutiοn set gοes οn fοrever in that directiοn.

Hence, the sοlutiοn tο the inequality is all values οf x greater than -10. This can be represented οn a number line as shοwn in the figure attached.

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You will be able to pull out $30,956.52 each month if you want to make withdrawals for 25 years with $300,000 saved for retirement and 10% interest.

To find out how much you will be able to pull out each month if you want to make withdrawals for 25 years with $300,000 saved for retirement and 10% interest, we can use the formula:

Monthly withdrawal = (Starting balance * Interest rate) / (1 - (1 + Interest rate)^(-Number of withdrawals))

In this case, the starting balance is $300,000, the interest rate is 10% or 0.10, and the number of withdrawals is 25 years * 12 months = 300 withdrawals.

Plugging in the numbers, we get:

Monthly withdrawal = ($300,000 * 0.10) / (1 - (1 + 0.10)^(-300))

Monthly withdrawal = $30,000 / (1 - 0.031)

Monthly withdrawal = $30,000 / 0.969

Monthly withdrawal = $30,956.52

Therefore, you will be able to pull out $30,956.52 each month if you want to make withdrawals for 25 years with $300,000 saved for retirement and 10% interest.

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The end behavior of y as x goes to negative infinity in the equation y = -3x^5 + 4x^2 – 7 can be determined by looking at the leading term of the polynomial, which is -3x^5. As x goes to negative infinity, this term will dominate the other terms and determine the end behavior of the function.

Since the degree of the leading term is 5, which is an odd number, and the coefficient is negative, the end behavior of the function will be that y goes to positive infinity as x goes to negative infinity. This can be written in notation as:

lim(x→-∞) y = +∞

In conclusion, the end behavior of y as x goes to negative infinity in the equation y = -3x^5 + 4x^2 – 7 is that y goes to positive infinity.

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The solution to this system of linear equations is x = 11/3, y = -3/13, and z = 1/12.

The augmented matrix of a system of linear equations is [[1,0,5,-(11)/(3)],[-4,1,-23,(68)/(3)],[5,0,25,-(43)/(3)]]. To solve this system, we can use the process of elimination.

Step 1: Add 4 times row 1 to row 2.

[[1,0,5,-(11)/(3)],[0,1,-13,(39)/(3)],[5,0,25,-(43)/(3)]]

Step 2: Subtract 5 times row 1 from row 3.

[[1,0,5,-(11)/(3)],[0,1,-13,(39)/(3)],[0,0,15,-(32)/(3)]]

Step 3: Divide row 2 by -13.

[[1,0,5,-(11)/(3)],[0,1,1,-(3)/(13)],[0,0,15,-(32)/(3)]]

Step 4: Add 3 times row 2 to row 3.

[[1,0,5,-(11)/(3)],[0,1,1,-(3)/(13)],[0,0,12,-(1)/(13)]]

Step 5: Divide row 3 by 12.

[[1,0,5,-(11)/(3)],[0,1,1,-(3)/(13)],[0,0,1,(1)/(12)]]

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Exponent laws The abbreviated formula is -2x7y.

This leads to another exponent rule called the Power Rule for Exponents. A power of a power can be made simpler by multiplying the exponents while leaving the base fixed. In this instance, (23)5 equals 215. For any positive number x and integers a and b, (xa)b=xa b holds true.

Exponent laws comprise: Rule of the product of powers: Add the powers together when multiplying like bases. Take off the powers when separating like bases according to the quotient of powers rule. Rule of the power of powers: Add all the powers together when raising a power by another exponent.

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Complete question:

Find the Exponent law of the given formula [tex][(-2xyx^2)x^3]x^2[/tex] .

For a line perpendicular to y = - 5 x - 2 and passing through the point ( 10 , 5 ), the equation in slope-intercept form is y = (1/5)x + 3.

To write an equation for a line perpendicular to y = -5x - 2 and passing through the point (10, 5), we first need to find the slope of the new line. The slope of a line perpendicular to another line is the negative reciprocal of the original line's slope. The slope of the original line is -5, so the slope of the new line is 1/5.

Next, we can use the point-slope form of an equation to write the equation for the new line. The point-slope form is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. Plugging in the values we have, we get:

y - 5 = (1/5)(x - 10)

Finally, we can rearrange this equation to put it in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. To do this, we'll distribute the 1/5 and then add 5 to both sides of the equation:

y - 5 = (1/5)x - 2
y = (1/5)x + 3

So the equation for the new line is y = (1/5)x + 3. This is our final answer.

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As a consequence, the bolded arc is approximately 8.24 centimetres long when the bolder arc is 4cm long.

The vertex of the angle is the common endpoint shared by two rays or line segments that make up an angle in geometry. The sides or limbs of the angle are the rays or line segments that make up the angle. Angles are used to describe the amount of spin or turn between two lines or objects. They are usually measured in degrees or radians. Numerous areas of mathematics, such as geometry, trigonometry, and calculus, depend on angles.

given

We must apply the following algorithm to determine the size of the bolded arc:

arc length is equal to (angle / 360) times 2r.

where r is the radius, angle is the central angle in degrees, and is a mathematical constant roughly equivalent to 3.14.

Inputting the numbers provided yields:

(118/360) * 2 = arc length (4)

8.24 cm arc length is equal to (0.3278) × (25.12) arc length.

As a consequence, the bolded arc is approximately 8.24 centimetres long when the bolder arc is 4cm long.

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Answer:

answer is sus.

Step-by-step explanation:

sus is the correct answer to your problrm. hope this helps!

The real zeros of the polynomial p(x) are 7/2, -7, and 7. Option D is the correct answer.

According to the algebraic principle known as the Factor Theorem, if a polynomial f(x) has a factor of (x - a), then f(a) = 0. To put it another way, if (x - a) is a factor of f(x), then the polynomial f(x) is equal to zero when x equals a. By finding the components of the polynomial and computing the values of x that make each factor equal to zero, this theorem may be used to locate the roots or zeros of a polynomial. The effective factorization and solution of polynomial problems are made possible by the Factor Theorem, a potent algebraic tool.

The given polynomial can be written as follows:

p(x) = (2x - 7)(x + 7)(x - 7)

The real zeros are the values of x that make the polynomial equal to zero. Therefore, the real zeros are:

x = 7/2, -7, 7

Therefore, the real zeros of the polynomial p(x) are 7/2, -7, and 7.

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The correct measure is given as follows:

x = 6.

Vertical angles are angles that are opposite by the same vertex on crossing segments, hence they share a common vertex, thus being congruent, meaning that they end up having the same angle measure.

Over vertex C, the two angles are congruent, hence the value of x is obtained as follows:

12x - 9 = 6x + 27

6x = 36

x = 6.

(as the vertical angles are congruent, we can just equal the measures of the two angles and then solve the expression for the value of x).

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Answer:

total salary=$20000

spend%=70%

now,

spend no=70% of $20000

=70/100 ×20000

=$14000

now,

total of spend amount of each month=

spend amount×12

=140000×12

=$168000

Answer:

Step-by-step explanation:

Answer:

look down

Step-by-step explanation:

let length be" x"

accroding to question

breadth= 2x/3

we know,

Area of rectangle= l × b

384=x × 2x/3

calculate

By angle angle similarity ΔWYZ ≈ Δ WZX ≈ ΔZYX are similar.

Triangles with exactly similar corresponding angle configurations are said to be similar triangles. This implies that equiangular triangles are comparable. All equilateral triangles are thus interpretations of similar triangles.

In the given statements, thus the similar triangle are:

ΔWYZ ≈ Δ WZX ≈ ΔZYX

A,

∠Y is common

∠x = ∠z = 90°

Therefore, by angle angle similarity ΔWYZ ≈ Δ WZX ≈ ΔZYX are similar.

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Answer:

1.5

Step-by-step explanation:

See the screenshots for step by step explanation

 Use symoballab it is helpfull