If you make $20 per hour, how many hours did you work if you earned
$160? I worked hours. Just write the numeric hours you worked.

6 ≤ 1 - 5x can be written as -5x ≤ -5, which can be further simplified to x ≥ 1.

An equation is a mathematical statement that states that two expressions are equal. It is written using an equals sign, ‘=’, to show that the two expressions being compared have the same value. Equations are used in many areas of mathematics, including algebra, calculus and geometry.

2) -6.9 < 8.1 - 1.5x can be written as 1.5x > 14.9, which can be further simplified to x > 9.93.

3) 7/9 × -2/3 > 1/6x + 3 can be written as -2/3x > 15/2, which can be further simplified to x < -10.

4) 3(x + 1) > 5x + 7 can be written as 3x + 3 > 5x + 7, which can be further simplified to x > 4.

5) 4(3 - 0.1x) ≤ 15 - 0.6x can be written as -0.4x ≤ 12, which can be further simplified to x ≥ 30.

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Answer:

30.8

Step-by-step explanation:

2(4) +3.4(2)=30.8

The equation - 28 · (y + 2) = x² represents the parabola in vertex form.

In this question we find the directrix, the axis of symmetry and the y-coordinate of the vertex of a parabola. The vertex form of the parabola is introduced below:

4 · p · (y - k) = (x - h)²

Where:

Please notice that the axis of symmetry passes through the vertex of the parabola.

First, determine the least distance:

p = - 2 - 5

p = - 7

Second, find the x-coordinate of the vertex:

h = 0

Third, write the complete function:

- 28 · (y + 2) = x²

The equation of the parabola is - 28 · (y + 2) = x².

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We have transformed the first expression, x∧z∨¬(¬y∨z)∨x∧¬z, into the second expression, x∨y∧¬z, using the properties of Boolean algebra. Therefore, the two expressions are equivalent.

To show that the two Boolean expressions are equivalent, let's transform the first expression, x∧z∨¬(¬y∨z)∨x∧¬z, into the second expression, x∨y∧¬z, using the properties of Boolean algebra:

1. Distributive Property (a∨(b∧c) ≡ (a∨b)∧(a∨c)): Apply the distributive property to the first term, x∧z, in the first expression: x∧z∨¬(¬y∨z)∨x∧¬z ≡ (x∨¬(¬y∨z))∧(z∨¬(¬y∨z))∨x∧¬z

2. De Morgan's Law (¬(a∨b) ≡ ¬a∧¬b): Apply De Morgan's Law to the negation, ¬(¬y∨z), in the first expression: (x∨¬(¬y∨z))∧(z∨¬(¬y∨z))∨x∧¬z ≡ (x∨(¬¬y∧¬z))∧(z∨(¬¬y∧¬z))∨x∧¬z

3. Double Negation (¬¬a ≡ a): Simplify the double negation, ¬¬y, in the expression: (x∨(¬¬y∧¬z))∧(z∨(¬¬y∧¬z))∨x∧¬z ≡ (x∨(y∧¬z))∧(z∨(y∧¬z))∨x∧¬z

4. Associative Property ((a∧b)∨c ≡ a∧(b∨c)): Apply the associative property to the second term, (y∧¬z), in the expression: (x∨(y∧¬z))∧(z∨(y∧¬z))∨x∧¬z ≡ (x∨y∧¬z)∧(z∨y∧¬z)∨x∧¬z

5. Absorption Law (a∨(a∧b) ≡ a): Apply the absorption law to the first term, (x∨y∧¬z), in the expression: (x∨y∧¬z)∧(z∨y∧¬z)∨x∧¬z ≡ x∨y∧¬z∧(z∨y∧¬z)∨x∧¬z

6. Idempotent Property (a∧a ≡ a): Apply the idempotent property to the second term, (z∨y∧¬z), in the expression: x∨y∧¬z∧(z∨y∧¬z)∨x∧¬z ≡ x∨y∧¬z∨x∧¬z

7. Commutative Property (a∨b ≡ b∨a): Apply the commutative property to reorder the terms: x∨y∧¬z∨x∧¬z ≡ x∨x∧¬z∨y∧¬z

8. Idempotent Property (a∨a∧b ≡ a): Apply the idempotent property to the second term, (x∧¬z), in the expression: x∨x∧¬z∨y∧¬z ≡ x∨y∧¬z

Thus, we have transformed the first expression, x∧z∨¬(¬y∨z)∨x∧¬z, into the second expression, x∨y∧¬z, using the properties of Boolean algebra. Therefore, the two expressions are equivalent.

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Answer: 35%

Step-by-step explanation:

Answer:

HL

Step-by-step explanation:

The hypotenuses and the long legs of the right triangles are congruent, therefore using the rule HL, the triangles are congruent.

Answer:

The correct answer is 7/20

The polynomials span P₂ implies any polynomial of degree 2 written as linear combination of these polynomials.

To determine whether the given polynomials span P₂,

Check whether any polynomial of degree 2 can be written as a linear combination of these polynomials.

Let us consider a general polynomial of degree 2.

p(x) = ax² + bx + c

We need to find coefficients k₁, k₂, k₃, and k₄ such that.

p(x) = k₁(1-x+2x²) + k₂(3+x) + k₃(5-x+4x²) + k₄(-2-2x+2x²)

Expanding the right side and collecting like terms, we get,

p(x) = (2k₁+4k₃+2k₄)x² + (-k₁-k₂+k₃-2k₄)x + (k₁+3k₂+5k₃-2k₄+1)

This equation must hold for any value of x.

Equate the coefficients of the powers of x on both sides,

2k₁ + 4k₃ + 2k₄ = a

-k₁ - k₂ + k₃ - 2k₄ = b

k₁ + 3k₂ + 5k₃ - 2k₄ + 1 = c

Solve this system of linear equations for k₁, k₂, k₃, and k₄.

Write this in matrix form as,

\(\left[\begin{array}{cccc}2&0&4&2\\-1&-1&1&-2\\1&3&5&-2\end{array}\right]\)\(\left[\begin{array}{ccc}k_{1} \\k_{2}\\k_{3}\end{array}\right]\)  \(= \left[\begin{array}{ccc}a \\b\\c-1\end{array}\right]\)

Solve this system using Gaussian elimination or other methods.

However, a simpler way to check whether the polynomials span P₂ is to check whether the matrix of coefficients is invertible.

If the matrix is invertible, then there is a unique solution for any value of a, b, and c.

If the matrix is not invertible,

Then there are some values of a, b, and c for which there is no solution.

And the polynomials do not span P₂.

To check whether the matrix is invertible, compute its determinant,

\(\left|\begin{array}{cccc}2&0&4&2\\-1&-1&1&-2\\1&3&5&-2\end{array}\right|\)

= 12

Since the determinant is non-zero,

The matrix is invertible, and the polynomials span P₂.

Therefore, matrix is invertible implies polynomials span P₂, any polynomial of degree 2 written as linear combination of these polynomials.

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The above question is incomplete, the complete question is:

Determine whether the following polynomials span P₂ (polynomial of degree 2):

p₁=1−x+2x²,

p₂=3+x,

p₃=5−x+4x²,

p₄=−2−2x+2x²

To Construct the box-and-whisker plot: Draw a number line, mark the quartiles (Q1, Q2, Q3), and represent the data points with dots or small vertical lines. Connect the lower and upper quartiles with a box, and extend lines (whiskers) from the box to the minimum and maximum values that are not considered outliers.

(a) Data set 1: {0.87, 0.88, 0.91, 0.92, 0.86, 0.91, 0.90, 0.93, 0.82, 0.89, 0.87}

1. Arrange the data in ascending order: 0.82, 0.86, 0.87, 0.87, 0.88, 0.89, 0.90, 0.91, 0.91, 0.92, 0.93.

2. Calculate the quartiles:

  - Q1: The median of the lower half of the data set: Q1 = 0.87.

  - Q2: The median of the entire data set: Q2 = 0.89.

  - Q3: The median of the upper half of the data set: Q3 = 0.91.

3. Calculate the interquartile range (IQR): IQR = Q3 - Q1 = 0.91 - 0.87 = 0.04.

4. Identify any outliers based on the lower and upper fences (values outside Q1 - 1.5 * IQR and Q3 + 1.5 * IQR, respectively).

5. Construct the box-and-whisker plot: Draw a number line, mark the quartiles (Q1, Q2, Q3), and represent the data points with dots or small vertical lines. Connect the lower and upper quartiles with a box, and extend lines (whiskers) from the box to the minimum and maximum values that are not considered outliers.

(b) Data set 2: {98.0, 74.1, 121.2, 103.5, 79.4, 89.3, 79.9, 80.2, 76.4, 109.7, 86.8, 82.1}

Follow the same steps as above to construct the box-and-whisker plot for Data set 2.

The box-and-whisker plots visually represent the distribution of the data sets, providing information about the minimum and maximum values, quartiles, and any outliers present in the data.

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Answer:

If you spent $56 on candy, she'd buy 8 pounds.

Step-by-step explanation:

The answer is b

In this image is the explanation, just click on it

Answer:

The value of X is 6.

Step-by-step explanation:

5 + 3 + 7 + 9 = 24

30 - 24 = 6

X = 6

The difference is 6.  

Answer:

Step-by-step explanation:

You want the translation that maps f(x) = x² to g(x) = x² -6x +6.

A graph of the two functions shows g(x) is right 3 units and down 3 units from f(x).

We know the vertex of f(x) = x² is the origin (0, 0). The vertex of g(x) will tell us the translation. Putting that function in vertex form, we have ...

  g(x) = x² -6x +6

  g(x) = (x² -6x) +6

  g(x) = (x² -6x +9) +6 -9 . . . . . add and subtract 9 to complete the square

  g(x) = (x -3)² -3

Compare this to ...

  y = (x -h)² +k . . . . . . has vertex (h, k)

We see that (h, k) = (3, -3).

g(x) is translated right 3 units and down 3 units.

Answer:

75 * 1000 = 75000

75000 gram

Step-by-step explanation:

1 kg = 1000g, so the answer is simple (kg * 1000 = g)

Answer:

F

Step-by-step explanation:

b = 3 5/8 × x < -- Times

x is a variable that uses for the representation of the number of pies

Example : 3 pies there

b = 3 5/8 × 3

therefore b = 5.625 pounds

Answer:

y = - 2x + 9

Step-by-step explanation:

From y = -2x + 1

comparing with y = mx + c

slope (m) = - 2

Writing in point slope form

y - y1 = m(x - x1)

y - 1 = -2( x - 4)

y - 1 = -2x + 8

Now writing in slope intercept form

y = - 2x + 8 + 1

y = -2x + 9

Hope it will help :)

In step 2 addition property is used.

2x + (1 ÷ 4) - (3 ÷ 5)x = 55 ÷ 4

Simplifying x,

2x - (3 ÷ 5)x - (1 ÷ 4) = 55 ÷ 4

(10x - 3) ÷ 5 - (1 ÷ 4) = 55 ÷ 4

(7x ÷ 5) - (1 ÷ 4) = 55 ÷ 4

Add (1 ÷ 4) on both sides,

(7x ÷ 5) - (1 ÷ 4) + (1 ÷ 4) = 55 ÷ 4 + (1 ÷ 4)

(7x ÷ 5) = (55 + 1) ÷ 4

(7x ÷ 5) = 56 ÷ 4

Multiplying (5 ÷ 7) on both sides,

(7x ÷ 5) × (5 ÷ 7) = (56 ÷ 4) × (5 ÷ 7)

x = 10

In step 2 - Add (1 ÷ 4) on both sides, the addition property is being used.

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Answer:

its c step three

Step-by-step explanation:

Answer:

The student didn't fully factorize out the terms to the least factor. He only collected some like terms but there was still more to collect and that's why the Teacher didn't give him full credit

Step-by-step explanation:

The original polynomial is;

4x²y^(5) - 8xy³

Now, if we want to completely factor this properly, we have to do it to the barest minimum.

Thus;

4xy³ is common to both terms so we can bring them out;

4xy³(xy² - 2)

Now this complete factorization is different from the one the student gave which is 2xy³(2xy³ - 4)

Thus, the student at best has factorized but only partly as it has not been reduced to the least of like terms.

(A) Table of values

x              y

1              22

2             29

3              36

4              43

5              50

6               57

(C) The function which represents the statement is y(x) = 7x + 15 where x is the number of weeks.

Anthony has $15 and wants to save $7 per week.

Let the number of weeks be x and the amount he saved be y.

Then, the function that represents the situation is:

y = 7x + 15

Therefore,

y(1) = 7(1) + 15 = 22

y(2) = 7(2) + 15 = 14 + 15 = 29

y(3) = 7(3) + 15 = 21 + 15 = 36

y(4) = 7(4) + 15 = 28 + 15 = 43

y(5) = 7(5) + 15 = 35 + 15 = 50

y(6) = 7(6) + 15 = 42 + 15 = 57

So, the table of values is:

x             y(x) = 7x + 15

1                   22

2                  29

3                  36

4                  43

5                  50

6                   57

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The calculated perimeter of the shape is 4x + 9

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

The shape

Calculating the side lengths, we have

Area = Base * Height

This gives

Base * Height = x

So, we have

Base = x and Height = 1

The perimeter of the shape is the sum of the side lengths

So, we have

P = x + x + 1 + 1 + 1 + 1 + 1 + 1 + 1 + x + x + 1 + 1

Evaluate

P = 4x + 9

Hence the perimeter is 4x + 9

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Answer: 14,48,50

Step-by-step explanation:

We can use the pythagorean theorem on right triangles

Take the 2 smaller values and put them into the theorem

The theorem is a^2+b^2=c^2 or a squared plus b squared equals c squared

Start by inserting values

3^2+5^2=6^2

9+25=36 is false

Next Value

9^2+12^2=13^2

81+144=169? certainly not!

Third Value

14^2+48^2=50^2

196+2304=2500? Looks right to me!

Answer: x=-1

Step-by-step explanation:

3x+2(2x+8)=9

Answer:

3x+2y=9

3x+2(2x+8)=9

3x+4x+16=9

7x=-7

x=-1

y=2(-1)+8

y=-2+8

y=6

Step-by-step explanation:

Answer:

216 and 64

Step-by-step explanation:

Answer:

1 ) Yes

2) No

perfect cubes are 216 and 64

³√64=4 } not have fraction so it's perfect cubes

³√216=6 } not have fraction so it's perfect cubes

Hope this helps

Answer:

Hence, x=28.

Step-by-step explanation:

Answer:

4:3

Step-by-step explanation:

240:180=

60(4):60(3)=

4:3

Hope this helps!

Answer:

4:3

Step-by-step explanation:

24:18

4:3

The expected value for the complete pairs of socks that make it out alive from the washing machine is calculated based on the probability of losing a sock and the number of pairs. The expected value for the complete pair of socks is 2.

Let's denote the random variable X as the number of complete pairs of socks that make it out alive. To calculate the expected value of X, we need to consider the probability of losing a sock and the total number of pairs.

In this case, there are 20 pairs of socks, which means there are a total of 40 socks. The washing machine eats four socks at random, which means there will be 36 socks remaining.

The probability of losing a sock can be calculated by dividing the number of socks lost by the total number of socks. In this scenario, four socks are lost out of 40 socks, so the probability of losing a sock is 4/40 = 1/10.

To calculate the expected value, we multiply the probability of losing a sock by the total number of pairs. In this case, the expected value is (1/10) * 20 = 2.

Therefore, the expected value for the number of complete pairs of socks that make it out alive from the washing machine is 2.

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The area of triangle varies jointly as its base and height. Given that the area of a triangle with a height of 24 cm and a base of 4 cm is 48 cm, we can find the area of a triangle with a height of 16 cm and a base of 6 cm.

Let A represent the area of the triangle, b represent the base, and h represent the height. According to the given information, the area A varies jointly as the base b and the height h, which can be expressed as A = k * b * h, where k is a constant of variation.

We are given that when h = 24 cm and b = 4 cm, the area A is 48 cm. Substituting these values into the equation, we get 48 = k * 4 * 24. Simplifying this equation, we find that k = 1.

Now, we can use the value of k to find the area of the triangle when h = 16 cm and b = 6 cm. Plugging these values into the equation A = k * b * h, we get A = 1 * 6 * 16. Simplifying, we find that the area is 96 cm.

Therefore, the area of a triangle with a height of 16 cm and a base of 6 cm is 96 cm.

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The name given to this type of design is a factorial design. A factorial design is a design in which researchers investigate the effects of two or more independent variables on a dependent variable.

In this study, two independent variables were used: room color (yellow, blue) and room temperature (20, 24, 28 degrees Celsius), while the dependent variable was happiness.

Each level of each independent variable was tested in conjunction with each level of the other independent variable. There are a total of six experimental conditions (two colors × three temperatures = six conditions), and twenty students were randomly assigned to each of the six conditions.

The researcher then examined how each independent variable and how the interaction of the two independent variables affected the dependent variable (happiness). Therefore, this study is an example of a 2 x 3 factorial design.

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