A box without a top is made from a rectangular piece of cardboard, with dimensions 25 inches by 20 inches, by cutting out square corners with side length x inches. which expression represents the volume of the box in terms of x?

In this given equation, any value of x and y will work, which will cause it to have infinite number solutions

What is an equation?

An equation is a mathematical statement showing that two or more values or mathematical expressions are equal or equivalent.

We represent an equation with the equation symbol (=).

Given the equation:

3x + 2y = 5

The lineear equation has infinitely many solutions

We know the standard form of a linear equation is:

ax + by = C

In this given equation, any value of x and y will work, which will cause it to have infinite number solutions

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The value of a is ( x - 5 ) factor of f (x) = x ³ - 3x²  + ax -10 is found to be 8 .

A factor is a number that divides another number, leaving no remainder. In other words, if multiplying two whole numbers gives us a product, then the numbers we are multiplying are factors of the product because they are divisible by the product.

There are two methods of finding factors: multiplication and division. In addition, rules of divisibility may also be used.

Let f (x) = x ³ - 3x²  + ax -10 be the given polynomial.

By factor theorem,  ( x - 5 ) is the factor of f (x) , if f ( 5 ) = 0

Therefore,

f ( 5 ) = 3 ( 5 )²  + a ( 5 ) - 10 = 0

           125 - 75 + 5a - 10 = 0

            5a = -40

            a = -8

Hence, a = -8

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Yes, you can use the Side-Side-Angle (SSA) Congruence Theorem to prove that two triangles are congruent.

The SSA Congruence Theorem states that if two sides of one triangle have the same length as two sides of another triangle, and the included angle in the first triangle is congruent to the included angle in the second triangle, then the two triangles are congruent.

Here is an example of how you can use the SSA Congruence Theorem to prove that two triangles are congruent:

Let's say you have two triangles, triangle ABC and triangle DEF. You are given that the length of side AB is equal to the length of side DE, the length of side AC is equal to the length of side DF, and angle A is congruent to angle D.

To prove that triangle ABC is congruent to triangle DEF, you would need to show that all of the corresponding parts of the triangles are congruent. Since the lengths of two sides (AB and DE) and the included angle (angle A and angle D) are congruent, you can use the SSA Congruence Theorem to conclude that triangle ABC is congruent to triangle DEF.

It's worth noting that the SSA Congruence Theorem is not always sufficient to prove that two triangles are congruent. If the conditions of the theorem are not met, you may need to use other methods, such as the ASA Congruence Theorem or the HL Congruence Theorem, to prove congruence.

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If a local park is open for biking every 12 day open for paddling every 8 day and if today the park is open for both options, then the next date when the park will be open will be on the 24th day. So Hana should pick 24th day from today next.

Every 12 day the local park is open its path for biking and every 8 day they open their lake or paddling. That is in every multiple of 12 days the biking option is available and every multiple of 8 days the paddling option is available.

If today both the biking and paddling option are open, then the next day where both options will be open can be determined by calculating the least common multiple of 12 and 8.

12 = 2×2×3

8 = 2×2×2

LCM (12, 8) = 2×2×2×3

LCM(12, 8) = 24

LCM of 12 and 8 is 24. So 24 days from today, the park will be open for both options.

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Answer:

4 is correct

Step-by-step explanation:

The product rule must be used to find the number of strings of four decimal digits, that have exactly three digits that are 9s.

What is product rule ?

The Product Rule says that the derivative of a product of two functions is the first function times the derivative of the second function plus the second function times the derivative of the first function.

To obtain the number of strings of 4 decimal digits that have exactly 3 digits that are 9s ; we use the product rule,

In first digit 1 possible way between 0 to 9

In second digit 1 possible way between 0 to 9

In third digit 1 possible way between 0 to 9

In fourth digit 9 possible ways between 0 to 9

That's mean 1 * 1* 1* 9* 4 = 36

Thus 36 possible ways.

The product rule must be used to find the number of strings of four decimal digits.

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The Pythagorean Theorem states that because a pyramid's height, slant height, and apothem form a right triangle with slant height as its longest side:  (apothem)² + (height)² = (slant height)².

A pyramid is a three shape having a base that is a polygon and triangular sides that come together at the apex, which is located directly just above center of the base.

Let's start by taking a look at a pyramid with both the height, slant height, the apothem shown in order to demonstrate how to use the Pythagorean Theorem to get a pyramid's height.

a² + b² = c².

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g(x)=-x^2 is the reflection of your function f(x) over the x-axis.

What is function?

The function f(x)=x2 is a parabola facing upward with its vertex at (0,0), and including the points (1,1), (2,4), (-1,1), and (-2,4).

A function that is a reflection across the x-axis compared to f(x) would be the mirror image of f(x). It would have the opposite y-values for each x-value. It would also have its vertex at the same place as f(x).

Therefore, it would be a parabola pointing downward, with the points (1, -1), (2,-4), (-1,-1), and (-2,-4).

To get the opposite values for y, you simply need to place a negative in front of the x2. So the function would be g(x) = - x2.

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Shawna finds The correct answer as "explanatory variable: weight response variable: calories burned per minute."

In this scatterplot, the explanatory variable is the weight of the individuals and the response variable is the number of calories burned per minute. The explanatory variable is the variable that is being manipulated or tested in the study, while the response variable is the variable that is being measured or observed.

In this case, the study is examining the relationship between weight and calories burned per minute, with weight being the explanatory variable and calories burned per minute being the response variable. The other answer choices do not correctly identify the explanatory and response variables in the scatterplot.

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Answer:

14: 15 or 2: 15 pm

Step-by-step explanation:

1/2 times 60 = 30 minutes

2 1/2 hours = 2 hours and 30 minutes

Take

11:45

+ 2:30

13:75

1 hour only has 60 minutes, so 13:75 = 14:15 or 2:15 pm

So, his appointment was at 2:15 pm

The number of zeros for each function is given as follows:

1. Three zeros.

2. One zero.

3. Two zeros.

The number of zeros for each function is obtained looking at the graph of the function, counting the number of times that the function either touches or crosses the x-axis, which is the horizontal axis.

Thus the graph for each function is plotted, using a graphing calculator, as shown by the image at the end of the answer, and the number of zeros for each of the functions is given by the number of times that the function touches or crosses the x-axis.

The colors of each function are given as follows:

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Answer:

we know that

The rule of the translation is

That means

The translation is  units to the right and   units down

therefore

the answer in the attached figure

Step-by-step explanation:

Answer:

infinite, no solutions, and uniquely solution

Step-by-step explanation:

In grade 11 math, the slope is a concept that is typically introduced in the study of linear equations and graphing.

The slope of a line serves as a gauge for its steepness. It is defined as the change in y (the vertical distance) divided by the change in x (the horizontal distance) between two points on the line.

A line's slope might be zero, positive, negative, or undefinable. A line with a positive slope rises as it goes from left to right, while a line with a negative slope falls as it goes from left to right. A line with a slope of zero is horizontal, while a line with an undefined slope is vertical.

The slope is often represented by the letter m in the equation of a line, which is written in the form y = mx + b. The slope of the line is the coefficient of the x term (the m in the equation).

For example, the slope of the line represented by the equation y = 3x + 4 is 3, while the slope of the line represented by the equation y = -2x + 1 is -2.

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The table that shows the correct t and d values is

Distance Covered (m)           Time Taken (hr)

8                                               6

32                                              15

How to determine the correct values for t and d

The table of values is given as:

Distance Covered (m)           Time Taken (hr)

8                                               6

16                                              12

32                                              15

48                                              18

The distance covered in 15 hours is 32 m and the time taken to cover 8 m is 6 hours

When these values are extracted, we have:

Distance Covered (m)           Time Taken (hr)

8                                               6

32                                              15

The above represents the table that shows the correct t and d values

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The steps of the  step method are:

Problem solving is an essential skill in life. It helps us to find solutions to difficult situations and can be applied to almost any area of life. One effective way to approach problem solving is to use the 4-step method. This method is designed to help you analyze a situation, plan an action, execute the plan, and evaluate the results. In this essay, we will discuss the benefits of using the 4-step method to solve problems.

The first step of the 4-step method is to analyze the situation. This involves identifying the problem and its causes. Taking the time to understand the problem before attempting to solve it can help ensure that the solution is effective. By analyzing the situation, you can determine the most effective solution and avoid wasting time and resources on ineffective solutions.

The second step of the 4-step method is to plan an action. This involves developing a plan of action to address the problem. Taking the time to plan ahead can help ensure that the solution is tailored to the specific situation. It can also help to minimize the risk of unexpected problems or delays during the execution of the plan.

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Real roots and distinct roots are the two types of roots of quadratic function.

Given,

Real roots;-

We are aware that anytime we resolve a linear or quadratic equation, we obtain the equation's value variable, or in other words, we identify the equation's solution. We refer to this "solution" as the real roots. For instance, when we solve the equation x27x+12=0, the real roots come out to be 3 and 4.

Distinct roots;-

Whenever the answers to a quadratic equation have two distinct values that may be represented by real numbers on a number line. It is known as distinct roots.

Here,

How do you tell which roots are distinct and real?

The discriminant is the expression b² - 4ac for the quadratic equation ax² + bx + c = 0. The discriminant's value reveals how many roots f(x) has: - The quadratic function has two unique real roots if b² - 4ac > 0, otherwise it does not. The quadratic function has one repeating real root if b² - 4ac = 0.

That is,

The quadratic function has real roots and distinct roots.

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Answer:

Binomial,Trinomial,Monomal,Linear equation

Step-by-step explanation:

It is a AAA similarity theorem If and only if the corresponding sides of two triangles are in proportion, they will have identical corresponding angles.

According to the fundamental theorem of similarity, a line segment can divide two triangle sides into proportionate segments if and only if it is parallel to the third side of the triangle.

Theorem: Two triangles have identical corresponding angles if and only if their corresponding sides are proportionate.

It can also be rephrased as the AAA (angle-angle-angle) similarity theorem.

A triangle is said to be comparable to another triangle if any two of its three angles are equal to any two of its three angles.

Therefore, it is a AAA similarity theorem If and only if the corresponding sides of two triangles are in proportion, they will have identical corresponding angles.

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The fraction 2.666666666667 equals   [tex]\frac{8}{3}[/tex] .

A fraction is used to represent a portion/part of something larger. It symbolises the equal parts of the whole. A fraction is comprised of two components the numerator and the denominator. The top number is referred to as that of the numerator, and the bottom number is known as the denominator. The denominator specifies the total number of equal parts in a whole, whereas the numerator describes the number of equal parts taken.

1. Assume that x = 2.666667 (1)

2. Six is the repeating digit.

To the left of the decimal point, put the repeating digit.

In this instance, multiply the decimal point by 10 to move it one place to the right.

Thus,

(x = 2.666667) * 10

Equation 10x = 26.66667 (2)

4. Take Eq. (1) away from Eq (2)

10x - x = 26.66667 - 2.666667

9x = 24

9 divided by both sides

x = [tex]\frac{24}{9}[/tex] or [tex]\frac{8}{3}[/tex]

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Without using a calculator, the square root of an integer is

1. Use multiplication to calculate the ideal square root.

2. Use division to calculate the ideal square root.

3. Use nearest perfect square number to find the square root of non-perfect squared numbers.

Given that,

We need to figure out how to calculate a number's square root without a calculator.

We know that,

There are some ways to find

First

Use multiplication to calculate the ideal square root.

A number that, when multiplied by itself, equals the first number is the number's square root.

3 is therefore the square root of 9.

Because 3 multiply by 3 is 9

That is 3×3=9

√9=3

Second

To calculate the square root, we use division.

A whole number can also be divided by a number until you get an answer that is the same as the number you used to divide the whole number in order to determine its square root.

For instance: Four is the square root of sixteen.

Because 16 divided by 4 is 4

That is 16÷4=4

√16=4

Third

We must compare the number with a nearly perfect squared number in order to determine the square root of non-perfect squared numbers.

For example: the square root of 63 is not a perfect square.

So,

The closest perfect square integer right now is 64, and its square root value is 8.

So, we can say the square root of 63 as 7.98.

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at least 67 inches, but at most 73 inches if  Jed can be 67 inches or

shorter

The  inequality in which involves one or more rational expressions is Rational inequality.

What is inequality?

Using the terms greater than, larger than or equal to, less than, or less than or equal to as a declaration of the order connection between two integers or algebraic expressions is known as inequality. Economic inequality comes in many forms, most notably wealth inequality measured by the distribution of wealth and income inequality measured by the distribution of income (the amount of money people are paid) (the amount of wealth people own). There are significant forms of economic inequality amongst various groups of people in addition to economic disparity between nations or states.

An inequality with a rational expression is said to be rational. Inequalities with rational expressions, such as 32x>1, 2xx34, 2x3x6x, and 142x23x, are referred to as rational inequalities.

67 ≤ x ≤ 73 are the solutions to the absolute value inequality |x − 70| ≤ 3

the complete question is

What are the solutions to the absolute value inequality |x − 70| ≤ 3? Remember, the inequality can be written as −3 ≤ x − 70 ≤ 3 or as x − 70 ≤ 3 and x − 70 ≥ −3.

Answer: 67 ≤ x ≤ 73

Remember, Jed's height is within 3 inches of Pablo's height.

Describe the solutions in words.

Jed can be

67 inches or shorter.

at least 67 inches, but at most 73 inches.

73 inches or taller.

67 inches or shorter, or 73 inches or taller.

Just found out it's the 2nd choice.

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Answer:

B: at least 67 inches, but at most 73 inches.

Step-by-step explanation:

Answer:

23

Step-by-step explanation:

Given in the picture below (BODMAS rule is applied)

I hope my answer helps you

Answer:

Step-by-step explanation:

5 + 2 x 3² =                         (remember PEMDAS)

5 + 2 x 9 =

5 + 18 =

23

The statement is "a car wash operator wants to see if offering a discount to local residents would create a greater income." This is an observational study.

A method of study in which participants are observed or certain outcomes are measured. There is no attempt made to change the outcome (for example, no treatment is given).

Experimental investigations include introducing an intervention and observing its results. Experimental investigations are frequently randomized, which means that the individuals are assigned to groups at random. People who qualify are randomly allocated to one of two or more groups in a randomized controlled experiment (RCT).

Cohort studies, case-control studies, and cross-sectional studies are the three different kinds of observational research.

In an observational study, the researchers just observe the participants without interfering with them or attempting to sway the results. In other words, neither the researchers nor the individuals are placed in experimental groups or in charge of the therapies.

Thus, the above mentioned statement is an observational study.

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The linear inequality represented by the graph is given as follows:

y < 1/4x + 2.

The dashed line is a linear function, hence the slope-intercept format of the inequality is given as follows:

y < mx + b.

(the sign is < because the line is dashed and not solid).

In which the coefficients are given as follows:

The line crosses the y-axis at y = 2, hence the intercept b is given as follows:

b = 2.

When x = -8, y = 0, thus when x increases by 8, y increases by 2, meaning that the slope is given as follows:

m = 2/8

m = 1/4.

Thus the inequality is given as follows:

y < 1/4x + 2.

The graph of the linear inequality is given by the image shown at the end of the answer.

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Answer:

total number of votes = 5696

Step-by-step explanation:

the 5 part of the ratio relates to 3560 no votes , then

3560 ÷ 5 = 712 ← value of 1 part of the ratio , then

3 × 712 = 2136 ← number of yes votes

total number of votes = yes + no = 2136 + 3560 = 5696

Step-by-step explanation:

that means that we need to transform the equation so that we get a form

h = ...

A = ½h(b1 + b2) | multiply both sides by 2

2A = h(b1 + b2) | divide both sides by (b1 + b2)

2A/(b1 + b2) = h

that's it.

The height of the yield sign is 15.5 inches.

The total amount of space allotted to a triangle's three sides in a two-dimensional plane is known as the area of a triangle. The fundamental formula for a triangle's area is A = [tex]\frac{1}{2}*b*h[/tex], which states that the area of a triangle is equal to half the product of its base and height.

To find the height of the yield sign, we need to use the following formula, which is:

area= length*height

The result of substituting in the data we are aware of is:

558=36*h

h= [tex]\frac{558}{36}[/tex]

h= 15.5

Therefore the height of a standard yield sign when the area is 558 square inches and each side is 36 inches is 15.5 inches.

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A binomial expression is of the form (x + y)ⁿ. The given binomial expression (2x + 3)⁵ has 6 terms in it.

Binomial is said to be the algebraic expression containing exactly two terms.

Examples of binomials are 4x² + 5y², xy² + xy, x + y, x² + 3, etc.

The number of terms in the binomial expression (x + y)ⁿ is given as,

Number of terms = n + 1

where, n is the power of ( x + y )

In the above given binomial expression, (2x + 3)⁵, n = 5.

N = n + 1 = 5 + 1 = 6

Thus, there are a total of 6 terms in the above expansion.

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Bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to find the result.

Now, According to the question:

The algebraic expression should be any one of the forms such as addition, subtraction, multiplication and division. To find the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to find the result.

Standard Equation

The standard form to find the value of X in multiplication operation is

Multiplicand × Multiplier = Product

Let us take Multiplier as x,

Multiplicand × x = Product

Then the formula to find the value of x is

X = product / Multiplicand

Example of how to find the value of x.

Find the value of x for the given expression: 10x = 50

Given: 10x = 50

X = 50/10

X = 5

Therefore, the value of x is 5.

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