What is the answer for -3i²

Answer:

x=16 and y=9

Step-by-step explanation:

(x+19)+(9x+1)=180

Combine Like Terms

10x+20=180

Subtract 20 from both sides

10x=160

Divide 10 by both sides

x=16

Fill in for x in (9x+1) to help find y

9*16+1

145

3y+8+145=180

Combine like terms

3y+153=180

Subtract 153 from both sides

3y=27

Divide 3 by both sides

y=9

We need to add 225 ml of water to the 90 ml of concentrate to make lemon squash.

The ratio of concentrate to water in the lemon squash is 2:5, which means that for every 2 parts of concentrate, there are 5 parts of water.

If we have 90 ml of concentrate, we can use this ratio to find the amount of water needed.

We can set up a proportion as follows:

2/5 = 90/x

Where x is the amount of water needed.

To solve for x, we can cross-multiply:

2x = 5 * 90

2x = 450

x = 225

Therefore, we need to add 225 ml of water to the 90 ml of concentrate to make lemon squash.

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On Saturday evening, there were 520 covers. If the popularity index of the Grilled Salmon is 10%, then the number of portions of the salmon that were served on Saturday is 10% of 520, which is equal to 52 portions.

To calculate this, you can use the following formula:

Number of portions of salmon = popularity index of salmon * number of covers

= 10% * 520

= 0.10 * 520

= 52 portions

Therefore, 52 portions of the Grilled Salmon were served on Saturday.

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Answer:

180

Step-by-step explanation:

Answer: 180.2

Step-by-step explanation: 85% of 212 is 180.2

The value of  ∂u∂f​​(u,v)=(−2,−2) = -20 and ∂v∂f​​(u,v)=(−2,−2) = -45.

To evaluate the partial derivatives ∂u∂f​​(u,v)=(−2,−2) and ∂v∂f​​(u,v)=(−2,−2), we can use the Chain Rule. We first take the partial derivatives of f(x,y,z) with respect to x, y, and z, and then substitute in x = u2 + v, y = u + v2, and z = 4uv.

First, ∂f∂x​=3x2, ∂f∂y​=yz and ∂f∂z​=y2.

Substituting in x = u2 + v, y = u + v2, and z = 4uv gives us: ∂f∂x​=3(u2 + v)2, ∂f∂y​=(u + v2)(4uv) and ∂f∂z​=(u + v2)2.

Next, we use the Chain Rule to find ∂u∂f​​(u,v)=(−2,−2) and ∂v∂f​​(u,v)=(−2,−2):

∂u∂f​​(u,v)=(−2,−2)= ∂f∂x​•∂x∂u​​ + ∂f∂y​•∂y∂u​​ + ∂f∂z​•∂z∂u​​ = 3(u2 + v)2•(2u) + (u + v2)(4uv)•(1) + (u + v2)2•(4v) = 6u2 + 8uv + 4uv + 4v2 = 10uv + 6u2 + 4v2

∂v∂f​​(u,v)=(−2,−2)= ∂f∂x​•∂x∂v​​ + ∂f∂y​•∂y∂v​​ + ∂f∂z​•∂z∂v​​ = 3(u2 + v)2•(1) + (u + v2)(4uv)•(2v) + (u + v2)2•(4u) = 3 + 8uv + 8u2 = 8u2 + 8uv + 3

When (u,v)=(−2,−2), we have ∂u∂f​​(u,v)=(−2,−2) = 10(-2)(-2) + 6(-2)2 + 4(-2)2 = 20 - 24 - 16 = -20 and ∂v∂f​​(u,v)=(−2,−2) = 8(-2)2 + 8(-2)(-2) + 3 = -32 - 16 + 3 = -45.

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The answer is 3y.

Repeat the question in your answer. "We need to subtract the polynomials (7y+5)-(4y+5)."

Subtract the terms with the same variable and the same degree. In this case, you need to subtract 7y and 4y, and 5 and 5.

Write the subtraction in the form of an equation.

"7y - 4y = 3y" and "5 - 5 = 0"

Write the final answer. "The result of subtracting the polynomials is 3y + 0, or simply 3y."

So the final answer is 3y.

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Answer:

4 : 2 : 5

Step-by-step explanation:

To find the ratio of silver to brown to pink counters in simplest form, we need to divide the number of each type of counter by their greatest common factor.

The greatest common factor of 16, 8, and 20 is 4.

So, we divide each of the numbers by 4:

Silver counters: 16 ÷ 4 = 4

Brown counters: 8 ÷ 4 = 2

Pink counters: 20 ÷ 4 = 5

Therefore, the ratio of silver to brown to pink counters in simplest form is:

4 : 2 : 5

or

2 : 1 : 2.5 (if we prefer to express the ratio in decimal form)

Answer:

= 1/2

Step-by-step explanation:

the slope or the gradient (m)

[tex] \frac{y1 - y2}{x1 - x2} [/tex]

the points is (6,1) and (-6,-5)

therefore

[tex] \frac{1 - ( - 5)}{6 - ( - 6)} \\ = \frac{1 + 5}{6 + 6} \\ = \frac{6}{12} \\ = \frac{1}{2} [/tex]

therefore the slope of the line is 1/2

The perpendicular distance between the two parallel sides, height h of the trapezium is 8cm

It is important to note the properties of a trapezium;

the formula for area of  trapezium is;

Area = a + b/ 2 ·(h)

Substitute the value

80 = (4 + 16)/ 2  (h)

Add the values

80 = 10h

Divide by the coefficient of h

h = 8cm

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Complete question:

The area of a trapezium is  80cm^2

The lengths of its parallel sides are  4cm and 16cm respectively. Find the perpendicular distance between the two parallel sides.

As a result, 25% of chlorine is present in solution B.

It's 100 × 20 / 100 = 20% ! In this circumstance, percentages are useful. When describing a change from one % to another, we use percentage points. The difference between 10% and 12% is two percent respectively (or 20 percent).

Let x represent the chlorine content of solution B.

The entire quantity of chlorine inside the combination can be used to create the following equation as a starting point:

3 cups of solution A × 10% chlorine + 6 cups of solution B × x% chlorine = (3+6) cups of new solution × 20% chlorine

When we simplify this equation, we obtain:

0.3 + 6x = 1.8

By taking 0.3 away both from sides, we get at:

6x = 1.5

When we multiply both parts by 6, we get:

x = 0.25

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The complete table is

Whose card Length Width Perimeter Area

Sanya          10 cm 8cm               36cm         80 cm²

The perimeter of a shape is the distance around its edges. For a rectangle, like Sanya's greeting card, the perimeter can be found by adding up the lengths of all four sides. In this case, we have:

Perimeter = 2 × Length + 2 × Width

Perimeter = 2 × 10 cm + 2 × 8 cm

Perimeter = 20 cm + 16 cm

Perimeter = 36 cm

So, the perimeter of Sanya's greeting card is 36 centimeters. This means that if you were to walk all the way around the edges of the card, you would cover a distance of 36 centimeters.

The area of a shape is the amount of space it takes up. For a rectangle, the area can be found by multiplying its length by its width. In this case, we have:

Area = Length × Width

Area = 10 cm × 8 cm

Area = 80 cm²

So, the area of Sanya's greeting card is 80 square centimeters. This means that if you were to cover the card completely with paint or ink, you would need 80 square centimeters of paint or ink.

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Complete Question:

Sanya made greeting cards. Complete the table for their cards:

Whose card Length Width Perimeter Area

Sanya          10 cm 8cm              

Answer:

9 [tex]cm^{2}[/tex]

Step-by-step explanation:

All the sides have the same length, so if the perimeter.  The distance around the figure is 24, then each side is 6 (24 divided by 4 is 6)

The area of a triangle is

a = 1/2 bh

a = 1/2(6)(3)

a = 1/2(18)

a = 9

Helping in the name of Jesus.

Substituting the values into the formula gives us Angle XZY = 180° - angle XYZ - angle YXZ = 180° - 95° - 50° = 35°. Thus, the measure of angle XZY in triangle XYZ is 35 degrees

We use the knowledge that the total of the angles in any triangle is always 180 degrees to determine the size of angle XZY in triangle XYZ. Angle YXZ is known to measure 50 degrees, while angle XYZ is known to measure 95 degrees. In order to determine the measure of angle XZY, we can subtraction the measurements of these two angles from 180 degrees. We obtain Angle XZY = 180° - angle XYZ - angle YXZ = 180° - 95° - 50° = 35° by substituting the values into the formula. As a result, the angle XZY in triangle XYZ has a measure of 35 degrees.

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The answers are a.(f∘g)(x) = x^2+2x+1 and b. (g∘f)(x) = x^2+1.

Let f(x)=x^2 and g(x)=x+1. We are asked to find a.(f∘g)(x) and b. (g∘f)(x).

a. (f∘g)(x) = f(g(x)) = f(x+1) = (x+1)^2 = x^2+2x+1

b. (g∘f)(x) = g(f(x)) = g(x^2) = x^2+1

Therefore, the answers are a.(f∘g)(x) = x^2+2x+1 and b. (g∘f)(x) = x^2+1.

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The numbers in the cards are:

From the question, we have the following parameters that can be used in our computation:

Cards = 45, 45 and 46

Next, we have

Multiples of 2, 3 and 4

Using the above as a guide, we have the following:

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Answer:

You need to add 50 gallons of the 3% solution to the 50 gallons of the 7% solution and that will give 100 gallons of a 5% solution.

Answer:

Step-by-step explanation:

The answer is 11.61

The comparison of the population shows that the correct option is C.

Class A: median = 90, IQR = 12.5

Class B: median = 80, IQR = 10 The variation in the test scores is about the same, but Class A has greater test scores.

The variation in test scores is about the same between Class A and another group, but Class A has greater test scores, it means that Class A as a group performed better on the test than the other group.

It should be the total score for A is 2200 while the score for B is 2110.

Therefore, it should be noted that the correct option is C.

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Total SUM Sq is 22623.933

To address the research question of whether there were any statistically significant differences on the rated levels of trustworthiness across the three conditions, a one-way ANOVA test was conducted in JAMOVI, using a significance criterion of 5%. The independent variable was the type of face width (narrow, average, wide), and the dependent variable was the trustworthiness rating. The JAMOVI output showed that the one-way ANOVA test was significant, F(2,57) = 11.203, p < 0.001, η2 = 0.281. Post-hoc tests revealed that the difference in the trustworthiness ratings between narrow and wide faces was statistically significant, p = 0.001, d = 1.121, 95% CI [0.579, 1.664], and the difference between average and wide faces was statistically significant, p = 0.025, d = 0.556, 95% CI [0.039, 1.074]. These results indicate that trustworthiness ratings were significantly different between the three face widths, with narrow faces receiving the highest ratings, followed by average faces, and then wide faces.

JAMOVI Output:
One-Way ANOVA
Source df Sum Sq Mean Sq F p
Between 2 6409.933 3204.967 11.203 0.000
Error 57 16214.000 284.532
Total 59 22623.933

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Answer:

Awnser "y = 10x + 60"

Step-by-step explanation:

So, the chart coordinate should looks like this:

(1, 75)

(2, 70)

(3, 80)

(4, 95)

(4, 100)

And there is a line passing (0, 60) and (2, 80)

So we just need to find the y-intercept and the slope by the line:

Slope: [change in x over change in y] = 20 ÷ 2 = 10

y-intercept: [the value of y when x equal 0] = 60 (because the line passed through (0, 60) )

Step-by-step explanation:

Answer; 10; for each additional hour a student studies, their grade is predicted to increase by 10% on the test

Step-by-step explanation:

For subspace (a.1) basis for Col(A) is the first four columns of A and dimension is 4. For (a.2) basis for Row(A) is the first four rows of A and dimension is 4. A basis for (a.3) Nul(A) is the set of vectors obtained by setting one free variable to 1 and the others to 0 and dimension is 7.

A basis for a subspace is a set of vectors that are linearly independent and span the subspace. The dimension of a subspace is the number of vectors in a basis for that subspace.

(a.1) Col(A) is the subspace of R^4 spanned by the columns of A. To find a basis for Col(A), we can reduce A to its reduced row echelon form (RREF) and find the columns of A that correspond to the pivot columns in the RREF. The RREF of A is:

1 0 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 0 0
0 0 0 1 0 0 0 0 0 0 0

The pivot columns are the first four columns, so a basis for Col(A) is the first four columns of A:

{[1, 1, 1, 1], [1, 1, -1, -1], [1, -1, 1, -1], [1, -1, -1, 1]}

The dimension of Col(A) is the number of vectors in the basis, which is 4.

(a.2) Row(A) is the subspace of R^11 spanned by the rows of A. To find a basis for Row(A), we can reduce A to its RREF and find the nonzero rows. The RREF of A is the same as above, so a basis for Row(A) is the first four rows of A:

{[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2], [0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0], [0, 0, 0, 0, 0, 0, 1, -3, 3, 0, 0]}

The dimension of Row(A) is the number of vectors in the basis, which is 4.

(a.3) Nul(A) is the subspace of R^11 consisting of all vectors x such that Ax = 0. To find a basis for Nul(A), we can reduce A to its RREF and find the solutions to the homogeneous equation Ax = 0. The RREF of A is the same as above, and the general solution to Ax = 0 is:

x1 = 0
x2 = 0
x3 = 0
x4 = 0
x5 = free
x6 = free
x7 = free
x8 = free
x9 = free
x10 = free
x11 = free

A basis for Nul(A) is the set of vectors obtained by setting one free variable to 1 and the others to 0:

{[0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]}

The dimension of Nul(A) is the number of vectors in the basis, which is 7.

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Answer:

1+1= 2

Step-by-step explanation:

im a genuis

Answer:

A

Step-by-step explanation:

sorry if it is wrong

The solutions to the equation x^2 + 8x +4 = 0 are x1 and X2.

(a) Without solving the equation write down the value of
(i) x1 + x2 = -8 (The sum of the roots of a quadratic equation ax^2 + bx + c = 0 is -b/a, so in this case, -8/1 = -8)
(ii) x1x2 = 4 (The product of the roots of a quadratic equation ax^2 + bx + c = 0 is c/a, so in this case, 4/1 = 4)

The solutions to the equation ax^2 + bx+c=0 where a,b,c E Z are 1/x1 and 1/x2

(b) Use part (a) to find the value of
(i) b/a = -(1/x1 + 1/x2) = -(-8) = 8 (The sum of the roots of a quadratic equation ax^2 + bx + c = 0 is -b/a, so in this case, -b/a = -8)
(ii) c/a = 1/x1 * 1/x2 = 1/4 (The product of the roots of a quadratic equation ax^2 + bx + c = 0 is c/a, so in this case, c/a = 4)

Find the values of a, b, and c where a is the smallest possible positive value.
Since a is the smallest possible positive value, let a = 1. Then, b = 8 and c = 4. So the values of a, b, and c are 1, 8, and 4, respectively.

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The height of the Eiffel Tower is approximately 311.6 meters.

Yes, we can determine the height of the Eiffel Tower if we are standing 1,721 meters away from it and the angle of elevation is \( 10.37^{\circ} \). We can use the tangent function to find the height of the Eiffel Tower. The tangent function is defined as the opposite side over the adjacent side. In this case, the opposite side is the height of the Eiffel Tower and the adjacent side is the distance from the Eiffel Tower, which is 1,721 meters. The equation for the tangent function is:

tan( \( 10.37^{\circ} \) ) = height / 1,721

We can rearrange the equation to solve for the height of the Eiffel Tower:

height = tan( \( 10.37^{\circ} \) ) * 1,721

Using a calculator, we can find the value of tan( \( 10.37^{\circ} \) ) and multiply it by 1,721 to get the height of the Eiffel Tower:

height = 0.181 * 1,721

height = 311.6 meters

Therefore, the height of the Eiffel Tower is approximately 311.6 meters.

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The probability of getting 4 heads is 0.205078125, the probability of getting 6 heads is 0.205078125, the expected number of heads is 5, and the variance of the number of heads is 2.5.

The probability of getting 4 heads or 6 heads in 10 coin tosses can be calculated using the binomial probability distribution formula:

P(X=x) = nCx * p^x * (1-p)^(n-x)

Where:
n = number of trials (10)
x = number of successes (4 or 6)
p = probability of success (0.5)
1-p = probability of failure (0.5)
nCx = combination of n things taken x at a time

For 4 heads:
P(X=4) = 10C4 * 0.5^4 * 0.5^(10-4)
P(X=4) = 210 * 0.0625 * 0.015625
P(X=4) = 0.205078125

For 6 heads:
P(X=6) = 10C6 * 0.5^6 * 0.5^(10-6)
P(X=6) = 210 * 0.015625 * 0.0625
P(X=6) = 0.205078125

The expected number of heads can be calculated using the formula:
E(X) = n * p
E(X) = 10 * 0.5
E(X) = 5

The variance of the number of heads can be calculated using the formula:
Var(X) = n * p * (1-p)
Var(X) = 10 * 0.5 * 0.5
Var(X) = 2.5
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47. The identity that expresses cot(x) in terms of csc(x) is: cot(x) = 1/sin(x) = csc(x)/sin(x) * sin(x)/sin(x) = csc(x)cos(x)

48. The identity that expresses sec(x) in terms of tan(x) is: sec(x) = 1/cos(x) = 1/cos(x) * sin(x)/sin(x) = sin(x)/(cos(x)sin(x)) = sin(x)/sin(x)cos(x) = 1/cos(x) = sec(x)

49. The identity that expresses sin(x) in terms of cot(x) is: sin(x) = 1/csc(x) = 1/csc(x) * cos(x)/cos(x) = cos(x)/(csc(x)cos(x)) = cos(x)/cos(x)csc(x) = 1/csc(x) = sin(x)

50. The identity that expresses cos(x) in terms of tan(x) is: cos(x) = 1/sec(x) = 1/sec(x) * cos(x)/cos(x) = cos(x)/(sec(x)cos(x)) = cos(x)/cos(x)sec(x) = 1/sec(x) = cos(x)

51. The identity that expresses tan(x) in terms of csc(x) is: tan(x) = sin(x)/cos(x) = sin(x)/cos(x) * 1/csc(x) = sin(x)csc(x)/cos(x) = 1/cos(x) = sec(x)

52. The identity that expresses cot(x) in terms of sec(x) is: cot(x) = 1/tan(x) = 1/(sin(x)/cos(x)) = cos(x)/sin(x) = cos(x)/sin(x) * 1/sec(x) = cos(x)sec(x)/sin(x) = 1/sin(x) = csc(x)

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The solution set of the given inequality is (164/18, ∞).

To solve the inequality symbolically, we first need to isolate the variable x on one side of the inequality. We can do this by multiplying both sides by 8 and then subtracting 4 from both sides. Finally, we can divide both sides by 6 to solve for x. Here are the steps:

(6x + 4)/8 > 22/3

6x + 4 > (22/3)(8)

6x + 4 > 176/3

6x > (176/3) - 4

6x > 164/3

x > (164/3)(1/6)

x > 164/18

Now we can express the solution set x > 164/18 in interval notation: (164/18, ∞)

So the solution set is all values of x greater than 164/18.

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The side of figure WXYZ corresponds with QR is XY

In mathematics, mirror images are often used in the study of symmetry and geometry. A mirror image, also known as a reflection, is a transformation that flips an object over a line called the mirror line.

An image appears to be reversed from left to right. Therefore, the left side of the object appears to be on the right side of the image, and the right side of the object appears to be on the left side

Here we have

Parallelogram PQRS and WXYZ which are two mirror images

Here the corresponding side of the two figures are

=> PQ and WX

=> QR and XY

=> RS and YZ

=> PS and WZ

Therefore,

The side of figure WXYZ corresponds with QR is XY

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