You have a rectangular prism whose cross section is a square with side length
3 cm. You need to know its length, but you do not have a ruler. Luckily, you have a calibrated container of water nearby. The container has marks that measure cubic centimeters of liquid. It appears to have 70 cubic centimeters of water in it, but when you submerge the prism into the water, the water level rises to the 115-cubic-centimeter mark. Determine how long your prism is.

1. x = 8 -8      When the number that is the sum or answer, the number that is in the lines is usually the same but is the opposite, os if it is positive, then it is negative.

2. x = 7, -7

3. A = 6, -10     8 - 2 = 6     8 + 2 = 10  Switch it up, put the negative sign with the 10.

This is all that I can do right now I hope this helped I will try to answer more later.

The required expression is  "8+x" .

When integer variables, constants, and algebraic operations are used to create an expression, it is said to be algebraic (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number)

The required expressions are:

19) 8 + x

20) x - 10

21) 3 + x = 10

22) 4 > 6t

23) d > 3/2 p

24) 4s ≥ 70 + 5

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I will give an example on an equation with variables on both sides, then explain.

Example : 20-x = 5x - 4

→the first step in solving an equation with a variable on both sides is to get the variable on one side. This is done by reversing the addition or subtraction of one of the terms with the variable.

20-x =

It takes four (4) comedy routines to hear 360 jokes

A proportion can be defined as an equation which is typically used to represent (indicate) the equality of two (2) ratios. This ultimately implies that, proportions can be used to establish that two (2) ratios are equivalent and solve for all unknown quantities.

By applying direct proportion, we have:

1 minute = 3 jokes

X minutes = 360 jokes

Cross-multiplying, we have:

3X = 360

X = 360/3

X = 120 minutes

Now, we can determine the number of comedy routines required for 360 jokes as follows:

Number of comedy routines = 120/35

Number of comedy routines = 3.42 ≈ 4 comedy routines.

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Answer:

Monica sells one more book (12) than Carlos (11).

Step-by-step explanation:

Carlos: $60.50/$5.50 = 11

Monica: $57.00/$4.75 = 12

Monica sells one book more than Carlos.

The variable "b" is greater than or equal to −37/76.

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Answer: 50.24ft²

Step-by-step explanation:

Total area of square = 8 * 8 = 64 ft²

Diameter of circle = 8 ft

The formula of area of circle = π r²

(4 = r)

(r² = 16)

3.14 * 16

50.24ft²

The results of the logical expressions are

Logical expressions are expressions that have a result of true or false.

These results are generally classified as boolean values

We start by solving the first expression

Logic expression (3)

¬ q v p

The above expression uses the or operator

The rule of the or operator is that:

This means that the expression ¬ q v p evaluates to false if q is true and p is false; otherwise, it evaluates to true

Logic expression (4)

¬ p ∧ ¬ q

The above expression uses the and operator

The rule of the and operator is that:

This means that the expression ¬ p ∧ ¬ q evaluates to true if q is false and p is false; otherwise, it evaluates to false

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Answer:The results of the logical expressions are¬ q v p: false if q is true and p is false¬ p ∧ ¬ q: true if q is false and p is falseWhat are logical expressions?Logical expressions are expressions that have a result of true or false.These results are generally classified as boolean valuesHow to solve the logical expressions?We start by solving the first expressionLogic expression (3)¬ q v pThe above expression uses the or operatorThe rule of the or operator is that:It evaluates to true, if at least one of the terms is trueOtherwise, it is falseThis means that the expression ¬ q v p evaluates to false if q is true and p is false; otherwise, it evaluates to trueLogic expression (4)¬ p ∧ ¬ qThe above expression uses the and operatorThe rule of the and operator is that:It evaluates to true, if both terms are trueOtherwise, it is falseThis means that the expression ¬ p ∧ ¬ q evaluates to true if q is false and p is false; otherwise, it evaluates to false

Step-by-step explanation:

1) Using order of operations, the solution to the given expression is; 12

2) The estimated cost of groceries if the prices are estimated to the nearest dollar is; $42

In mathematics , the acronym for the right order of operations is PEMDAS which denotes;

P- Parentheses

E- Exponents

M- Multiplication

D- Division

A- Addition

S- Subtraction.

3) From the given statement, we are to add 6 to 12, then divide the sum by 4. Thereafter, we divide the quotient by negative nine and then multiply by twenty-four. This is expressed as;

[(6 + 12)/4] = 18/4 = 9/2

Then divide by -9 to get;

(9/2) ÷ 9 = 1/2

Then we multiply by 24 to get;

1/2 * 24 = 12

4) Let us first estimate each cost to the nearest dollar to get;

$6.47 ≈ $6

$14.72 ≈ $15

$7.99 ≈ $8

$9.40 ≈ $9

$2.79 ≈ $3

Total estimated cost = 6 + 15 + 8 + 9 + 3 = $42

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1. If Alex runs a mile in under 6 minutes, then he will have a new personal record. Alex ran a mile in 5 minutes and 45 seconds. Therefore, Alex set a new personal record. - law of Detachment

2. If you go to the water park, then you will need to bring sunscreen. If you do not bring sun screen, then you will burn. Therefore, when you go to the water park you will get a sunburn. - law of contrapositive

3. If two lines are parallel, then they never intersect. Line a and line b intersect. Therefore, line a and line b are not parallel - Law of Syllogism

4. If the measures of two angles in a triangle are 30° and 60°, then the third angle is 90°. If a triangle has a 90° angle, then it is a right triangle.  Therefore, if a triangle has two angles that measure 30° and 60°, then it is a right triangle. - Not a valid conclusion

According to the law of contrapositive, the initial assertion is accurate if and only if the contrapositive is accurate. The original assertion is untrue if the contrapositive is false. A conditional assertion that may or may not depend on another is a contrapositive.

Using deductive reasoning, a syllogism is a three-part logical argument in which two premises are joined to get a conclusion.

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Answer:

a) -2/9

Step-by-step explanation:

2/3 - 5/6, you would need to start by making the denominators the same, so 2/3 would become 4/6. 4/6-5/6 = -1/6.

-1/6 ÷ 3/4, use the keep change flip rule

-1/6 × 4/3 then multiply directly across:

-1×4=-4

6×3=18

-4/18 reduces to -2/9

Given expression is

Among the given options the simplication that applies the power rule is

This can be simplified as

Hence the corresponding simplification is D.

The statements that are true regarding the temperature include:

1. At noon, the temperature is - 9 1/2°F.

2. The temperature at 5pm is - 15 3/4°F.

3. The change in temperature from noon to 5pm is - 6 1/4°F.

From the information, the temperature at 6A.M is -14°D and the temperature increases at an average of 3/4°F each hour until noon. Then it drops at 1 1/4°F until 5P.M.

The temperature at noon will be:

= -14 + (3/4 × 6)

= -14 + 4.5

= -9.5°F

The temperature at 5pm will be:

= -9.5 - (1 1/4 × 5)

= -9.5 - 6.25

= -15.75

The total change in temperature will be:

= Ending temperature - Starting temperature

= -15.75°F - (-14°F)

= 1.75°F

The temperature change from noon to 5 pm will be:

= -15.75 - (-9.5)

= -6.25 = 6 1/4°F

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Answer:

No

Step-by-step explanation:

No because it says purple to green buttons and the student put green to purple so the answer would be 4:3 not 3:4

Answer:

  20 mi/h

Step-by-step explanation:

You want the speed of separation after 3 hours between two cars that started from the same point. One is moving at 16 mi/h south, the other is moving at 12 mi/h west.

Since both cars started from the same point, the speed of separation is the magnitude of the difference between the respective velocity vectors. A graphical representation of the velocity vectors shows them to be the legs of a right triangle. Their difference is the length of the hypotenuse, which can be found using the Pythagorean theorem.

  s = √(16² +12²) = √(256 +144) = √400

  s = 20

The speed of separation is a constant 20 mi/h.

__

Additional comment

If the cars did not start at the same point, then the speed of separation would be changing with time. It could be found using the derivative of the distance between the cars, or by considering the car speeds in the direction each car is from the other at the time of interest.

We note that the problem here makes use of a 3-4-5 right triangle, with a multiplier of 4 mph.

We have following:

The sine of the angle is given by the quotient of the opposite side and the hypotenuse

replacing:

The answer is the option C. 0.38

An equation of the function in standard form for the given table of values is equal to -2x² - 7x - 6 = 0.

In Mathematics, the standard form of a quadratic equation is given by;

y = f(x) = ax² + bx + c = 0

In order to write an equation of the quadratic function in standard form, we would formulate a system of equations from the data provided in the table above as follows:

-6 = a(-3)² + b(-3) + c  ⇒ -6 = 9a - 3b + c      .......equation 1.

0 = a(-2)² + b(-2) + c  ⇒   0 = 4a - 2b + c      .......equation 2.

-2 = a(-1)² + b(-1) + c  ⇒   -2 = a - b + c          .......equation 3.

From equation. 2, we derive:

c = -4a + 2b   .....equation 4.

Substituting equation 4 into equation 1 and 3, we derive the following equations:

-2 = a - b - 4a + 2b          ⇒ -2 = -3a + b

-6 = 9a - 3b - 4a + 2b     ⇒ -6 = 5a - b

By using the elimination method, the value of a is given by:

[-2 + (-6) = (-3a + 5a) + (b + (-b)]

-2 - 6 = -3a + 5a + b - b

-8 = 2a

a = -4

Next, we would determine the value of b as follows:

-2 = -3a + b

b = -2 + 3a

b = -2 + 3(-4)

b = -2 - 12

b = -14

For the value of c, we have:

c = -4a + 2b

c = -4(-4) + 2(-14)

c = 16 - 28

c = -12.

Substituting the respective values of a, b and c into the standard form of a quadratic equation:

ax² + bx + c = 0

-4x² - 14x - 12 = 0

Dividing all through by 2, we have the following quadratic function:

-2x² - 7x - 6 = 0

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Complete Question:

The table represents a quadratic function. Write an equation of the function in standard form.

X -3, -2, -1, 0

f(x)-6, 0, -2, 0

Q: 23The side opposite to larger angles is always larger than angle oppostie to smaller side.

a sideangle the

Since side opposite to angle 68 is AB and side opposite to angle 65 is CD. The angle of measure 68 is more than angle 65. So,of measure

The degree of the polynomial is even.

Algebraic expressions called polynomials include indeterminates and constants. Polynomials can be considered a particular type of mathematics. In practically all areas of mathematics, including calculus, they are used to express numbers. They are also regarded as being crucial in several areas of mathematics. Examples of polynomials include 2x + 9 and [tex]x^{2}[/tex] + 3x + 11. The "=" sign is absent from all of these samples, as you may have observed.

The polynomial's degree is even since the final behavior is the same in both directions (for -x and for +x, y→∞).

The y-intercept is the fixed term. Since it is not an integer, evenness and oddness cannot be determined.

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Answer:

3(2x+1)+2(x+4)

3x2x and 3x1

6x+3+2(x+4)

2xx and 2x4

6x+3+2x+8

and the like terms

6x+2x and 3+8

8x+11

Step-by-step explanation:

Answer:

8x +11

Step-by-step explanation:

3(2x+1)+2(x+4)

Use the distributive property to multiply 3 by 2x+1.

6x+3+2(x+4)

Use the distributive property to multiply 2 by x+4.

6x+3+2x+8

Combine 6x and 2x to get 8x.

8x+3+8

Add 3 and 8 to get 11.

8x+11

Answer:

Step 1: DAB

Step 2: rotated triangle 180° using AC as center of rotation

Step 3: EAC

Step 4: now all 3 angles…

Step 5: a + b + c = 180°

Step-by-step explanation:

The total number of 8780 minutes was spent on the assembly and packaging of the wagons in June at these two stores.

Matrix A shows the number of wagons sold at two different locations during the month of June.

[tex]A =\begin{bmatrix}50 & 90 & 30\\25 & 5 & 50\\\end{bmatrix}[/tex]

Matrix B shows the number of minutes required for the assembly and packaging of the three different-sized wagons.

[tex]B = \begin{bmatrix}15 & 5\\20 & 8 \\30 & 12 \end{bmatrix}[/tex]

We have to multiply Matrix A by Matrix B

[tex]AB =\begin{bmatrix}50 & 90 & 30\\25 & 5 & 50\\\end{bmatrix}\begin{bmatrix}15 & 5\\20 & 8 \\30 & 12 \end{bmatrix}[/tex]

[tex]AB =\begin{bmatrix}3450 & 1330 \\2875 & 1125 \\\end{bmatrix}[/tex]

So the time is 3450 + 1330 + 2875 + 1125 = 8780 minutes

Therefore, a total number of 8780 minutes was spent on the assembly and packaging of the wagons in June at these two stores.

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Answer:

Step-by-step explanation:

Took the quiz

The height of the soccer ball after 1.8 seconds will be 372.47 feet.

A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.

An air kick is made with a soccer ball. The table displays the ball's height y (in feet) after x seconds.

The function is given as,

y = 0.06x² + 17.82x + 32.27

The height of the soccer ball after 1.8 seconds will be given as,

y = 0.06(18)² + 17.82(18) + 32.27

y = 19.44 + 302.76 + 32.27

y = 372.47

The height of the soccer ball after 1.8 seconds will be 372.47 feet.

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Answer:

24.06................

Answer:

B

Step-by-step explanation:

[tex]( - 20.16) + ( - 3.9) \\ [/tex]

=

[tex] - 20.16 - 3.9[/tex]

=

[tex] \frac{ - 1203}{50} or - 24.06[/tex]

Considering the linear relationship between the variables, we have that:

a) The function is: y = 500t - 500.

b) The factory should operate for 10 hours to have a production of 4500 units.

c) The graph for the first 20 hours of the function is given at the end of the answer.

A linear function, in slope-intercept format, is modeled according to the following rule:

y = mx + b

In which:

For the given linear relationship, we have two points, as follows:

(5,2000) and (8,3500).

The slope is given by change in y divided by change in x, hence:

m = 1500/3 = 500.

Then:

y = 500t + b.

When t = 5, y = 2000, hence we solve for the intercept as follows:

2000 = 500(5) + b

b = -500.

Then the function is:

y = 500t - 500.

For 4500 units, the time is found as follows:

4500 = 500t - 500

500t = 5000.

t = 5000/500

t = 10 hours.

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As the line intersected the y-axis at x = 4, the equation of the line which represents planet Drive to the community garden is x = 4.

The shortest distance that separates two points is represented by a line. A line can be horizontal, slanted, or straight. A equation of a line in slope-intecept form has been expressed as:

y = mx + b

where,

m is called the slope

b is the y-intercept

From the graph shown, you recognize that the planet drive line is a horizontal as well as the general equation of the a horizontal line is represented as x = a where;

'a' is indeed the x-intercept of a line, which is the point at which the line intersects the y-axis.

Because, the line intersected the y-axis at x = 4, the equation of the line which reflects planet Drive to community garden  is x = 4.

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Answer:

  the slope is 3/4

  the y-intercept is 4

Step-by-step explanation:

You want the slope and y-intercept of the line defined by the equation 3x -4y = -16.

The values of interest can be found easily from the slope-intercept form of the equation of the line. Solving for y puts the equation in that form.

  3x -4y = -16 . . . . . . given

  -4y = -3x -16 . . . . . subtract 3x

  y = 3/4x +4 . . . . . . divide by -4

Compare this to the slope-intercept form equation:

  y = mx + b . . . . . . . line with slope m and y-intercept b

We see that ...

  m = 3/4, b = 4

  The slope is 3/4

  The y-intercept is 4

Two different expressions that represent the total bill, including both tax and tip for the meal sold by the restaurant, are:

To arrive at the amount to be paid by the customer, we first have to get the original amount that they should pay for the meal. Next, they are meant to apply the 16% tip for the total meal and this is gotten by calculating 16% of the total meal.

Next, we ought to get 5% of the sales tax which will also be applied to the total bill. When all of these are summed up, we will arrive at the total amount to be paid by the customer. Another way will be, to sum up, all of the percentages and apply them to the total bill.

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For the linear function y = 2/3x + 1, we have that:

a) The slope is of 2/3 and the intercept is of 1.

b) The y-intercept is marked at y = 1 on the y-axis.

c) Using the slope and the intercept, point (3,3) is the second point used to graph the function.

d) The graph of the linear function y = 2/3x + 1 is given at the end of the answer.

A linear function, in slope-intercept format, is modeled as follows:

y = mx + b

In which:

For this problem, the function is:

y = 2/3x + 1.

Then, form item a, we have that:

For item b, the y-intercept of b = 1 means that the function crosses the y-axis at b = 1.

For item c, we have to consider that the slope is of 2/3, meaning that when y increases by 2, x increases by 3. Point (0,1) is on the graph of the function, hence point (3,3) will also be, as x increases by 3 from 0 to 3 and y increases by 2 from 1 to 3.

Considering the discussion above, the graph of the function is given at the end of the answer, with the intercept and point (3,3) labeled.

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B. The polynomial can be simplified. 6[tex]x[/tex]³ + 5[tex]x[/tex]³ + 4[tex]x[/tex] + 5 = 11[tex]x^3[/tex] + 4[tex]x[/tex] + 5