the midpoint formula
12a − 8 = 11a + 3(solve for a)
HELP!!!!!!! I GIVE BRAINLEST AND THANKS!!!!!! + 5 POINTS!!!!
Factor the polynomial.
4x7+32x+5-24x^4
A. 4x^4(x^3+8x-6)
B. 2x^4(2x^3+16x-12)
C. 2x^4(x3+8x-6)
D. 4x^4(2x^3+16x-12)
1. Explain a method of determining the correct degree and classification of a polynomial.
2. Why is the polynomial, 4x^2y + 5xy classified as a 3rd degree binomial?
A gas station is 12 kilometers away. How far is the gas station in miles? Use the following conversion: 1 mile is 1.6 kilometers.
Whole numbers are _____ integers. Help please!
always
sometimes
never
P.S. (I think it is always because if it were switched around, integers are ? whole numbers, it would have been sometimes)
Whole numbers are sometimes integers. Correct option is b.
Integers include both positive and negative whole numbers, as well as zero. Whole numbers are a subset of integers, but they do not include negative numbers. So, while all whole numbers are integers, not all integers are whole numbers.
Relationship between Whole Numbers and Integers:
Every whole number is an integer: Since whole numbers include zero and all positive counting numbers, they are also part of the set of integers.
Not every integer is a whole number: Integers also include negative numbers, which are not part of the set of whole numbers.
To know more about Whole numbers:
https://brainly.com/question/28262778
#SPJ2
What does it mean when a greater than sign is underlined?
An underlined greater than sign in mathematics represents a strict inequality, indicating that one value is significantly greater than another.
Explanation:In mathematics, an underlined greater than sign usually represents an inequality. When a greater than sign (>) is underlined, it indicates a strict inequality, meaning that the value on the left side is significantly greater than the value on the right side.
For example, if we have the underlined inequality 5 > 3, it means that 5 is larger than 3 and there is a clear distinction between the two values.
It's important to note that this is just one possible interpretation of an underlined greater than sign, as the context in which it is used can vary.
What must be true of f(x) and g(x) if both are antiderivatives of f(x)?
They can differ only by a constant is true of f(x) and g(x) if both are antiderivatives of f(x) Hence, option D is correct.
When two functions, F(x) and G(x), are antiderivatives of the same function f(x), it means that their derivatives are equal to f(x).
This relationship can be represented as:
F'(x) = G'(x) = f(x)
However, it's important to note that if F(x) and G(x) are both antiderivatives of F(x), then their difference, F(x) - G(x), will have a derivative of zero.
Consequently, F(x) and G(x) can differ only by a constant.
So, the correct option is D.
Complete question:
What must be true of f(x) and G(x) if both of them are antiderivatives of f(x)?
A. They are the same function
B. They can differ by a factor of x
C. If is not possible for two functions to be antiderivatives of the same function
D. They can differ only by a constant
12.5% of what is 130?
According to the text, which is not a main component of drawing?
Perspective
Vanishing point
Horizon
The volume of oil in four different containers is shown below: container
a.5.25 milliliters container
b.5.29 milliliters container
c.5.27 milliliters container
d.5.23 milliliters sue has a measuring cup that can measure to the nearest tenth of a milliliter. if sue measures the oil in each container, the least amount of oil would measure ____ milliliters.
Answer:
5.2
Step-by-step explanation:
In how many different ways can five elements be selected in order from a set with three elements when repetition is allowed?
There are 243 ways to select five elements in order from a set of three elements with repetition allowed.
When selecting five elements in order from a set with three elements and repetition is allowed, each selection can include any of the three elements, repeated as necessary. Here's the breakdown:
1. For the first position, there are 3 choices.
2. For the second position, there are also 3 choices, as repetition is allowed.
3. Similarly, for the third, fourth, and fifth positions, there are 3 choices each.
To find the total number of ways, we multiply the number of choices for each position:
3 choices for the first position × 3 choices for the second position × 3 choices for the third position × 3 choices for the fourth position × 3 choices for the fifth position = [tex]\(3^5 = 243\)[/tex] ways.
Therefore, there are 243 different ways to select five elements in order from a set with three elements when repetition is allowed.
The correct naswer is 21.
The number of ways to select five elements in order from a set with three elements when repetition is allowed can be represented in LaTeX as:
[tex]\binom{5+3-1}{5} = \binom{7}{5} = \frac{7!}{5!(7-5)!} = \frac{7!}{5!2!} = 21[/tex]
Explanation:
- When repetition is allowed, the problem can be treated as finding the number of ways to arrange 5 objects with 3 distinct types.
- This can be solved using the combination formula, where we choose 5 positions out of 7 (5 elements + 3 distinct types - 1).
- The binomial coefficient [tex]\binom{n}{r}[/tex] represents the number of ways to choose [tex]$r$[/tex] items from a set of [tex]$n$[/tex] items.
- In this case, we are choosing 5 positions (elements) from a set of 7 positions (5 elements + 3 distinct types - 1).
- The binomial coefficient can be expanded using factorials: [tex]\binom{n}{r} = \frac{n!}{r!(n-r)!}[/tex]
- Substituting [tex]n = 7$ and $r = 5[/tex], we get[tex]\binom{7}{5} = \frac{7!}{5!(7-5)!} = \frac{7!}{5!2!} = 21[/tex]
Therefore, there are 21 different ways to select five elements in order from a set with three elements when repetition is allowed.
Evaluate.
8m - 4 + 3n
n = 5 and m = 2
Is the square root of 12 - 2 rational or irrational
Assume that month is an int variable whose value is 1 or 2 or 3 or 5 ... or 11 or 12. write an expression whose value is "jan" or "feb or "mar" or "apr" or "may" or "jun" or "jul" or "aug" or "sep" or "oct" or "nov" or "dec" based on the value of month. (so, if the value of month were 4 then the value of the expression would be "apr".).
The expression that satisfies the given condition is using if-else conditional statements to check the value of the variable 'month' and assign the corresponding month name.
Explanation:The expression that satisfies the given condition is:
if (month == 1) { answer = "jan"; } else if (month == 2) { answer = "feb"; } else if (month == 3) { answer = "mar"; } // ... continue this pattern for the remaining months
This code uses conditional statements (if-else) to check the value of the variable 'month' and assigns the corresponding month name to the variable 'answer'.
Learn more about Conditional Statements here:https://brainly.com/question/36974334
#SPJ2
Read the following statement: If the sum of two angles is 90°, then the angles are complementary. The hypothesis of the statement is:
there are two angles.
the sum of two angles is 90°.
the angles are complementary.
Angles are complementary if their sum is 90°.
The hypothesis in the given mathematical conditional statement 'If the sum of two angles is 90°, then the angles are complementary.' is 'the sum of two angles is 90°'.
Explanation:In a conditional statement in mathematics, the 'if' part of the statement is called the hypothesis and the 'then' part is termed the conclusion. Given the statement 'If the sum of two angles is 90°, then the angles are complementary.', the hypothesis of this statement is 'the sum of two angles is 90°'.
Learn more about Hypothesis here:https://brainly.com/question/39619836
#SPJ12
In a conditional statement, the hypothesis is the condition that needs to be met. In this case, the hypothesis of the statement 'If the sum of two angles is 90°, then the angles are complementary,' is 'the sum of two angles is 90°.'
Explanation:In the context of the given conditional statement, 'If the sum of two angles is 90°, then the angles are complementary,' the hypothesis refers to the clause immediately after 'if.' This indicates the condition that needs to be fulfilled for the conclusion to be considered valid. Therefore, the hypothesis for this statement is 'the sum of two angles is 90°'.
After the 'if,' the hypothesis is given, and after the 'then,' you find the conclusion. The conclusion in this case is 'the angles are complementary.'
Learn more about Hypothesis here:https://brainly.com/question/39619836
#SPJ12
eight times the sum of a and b
The question concerns a basic algebraic expression 'eight times the sum of a and b' which is represented as 8(a + b). The expression emphasizes the operation order: sum first, then multiply, which results in a value eight times greater than the original sum.
Explanation:The question 'eight times the sum of a and b' is a mathematical expression that can be represented as 8(a + b). This expression means you first add the numbers 'a' and 'b' and then multiply their sum by eight. The result you get after the multiplication will be eight times greater than the original sum of 'a' and 'b'. For instance, if 'a' is 2 and 'b' is 3, their sum is 5, and when this is multiplied by eight, it becomes 40, which is the desired expression's value.
To understand this concept further, we can refer to the exponentiation rule mentioned, which states that (xa)b = xa.b. Although this is a different type of operation—exponentiation—it demonstrates a similar principle of first performing the operation inside the parentheses and then applying the outside operation.
Finally, when performing algebraic operations, it's essential to remember that whatever you do to one side of the equation, you should do to the other side to maintain balance. This is a fundamental principle in algebra that helps to solve equations, such as the example provided showing how to isolate 'a' by subtracting 'x' from both sides of the equation a b.
How to factor 2p^4+9p^3-18p^2
the answer to number 3
What are the center and radius of the circle defined by the equation ?
A. Center (3, -4); radius 2
B. Center (-3, 4); radius 2
C. Center (-3, 4); radius 4
D. Center (3, -4); radius 4
Determine the zeros of the function f(x) = 3x2 – 7x + 1.
Zeros of the given equation [tex]3x^{2} -7x+ 1[/tex] are [tex]\frac{7+\sqrt{37} }{6} \ or \frac{7-\sqrt{37} }{6}[/tex].
What are the zeros of a quadratic equation?The zeros of a quadratic equation f(x) are all the x-values that make the polynomial equal to zero.
What is quadratic method?The quadratic formula helps us solve any quadratic equation. First, we bring the equation to the form ax²+bx+c=0, where a, b, and c are coefficients. Then, we plug these coefficients in the formula:
[tex]x = \frac{-b \pm \sqrt{b^{2} -4ac} }{2a}[/tex]
According to the given question.
We have a function.
[tex]f(x) = 3x^{2} -7x+1[/tex]
To find the zeros of the function equate f(x) = 0.
[tex]3x^{2} -7x+1 = 0\\[/tex]
Solve the above equation by quadratic method.
[tex]x = \frac{7\pm\sqrt{(7)^{2} -4(3)(1)} }{2(3)}[/tex]
[tex]\implies x = \frac{7\pm\sqrt{49-12} }{6}[/tex]
[tex]\implies x = \frac{7\pm\sqrt{37} }{6}[/tex]
[tex]\implies x = \frac{7+\sqrt{37} }{6} \ or \frac{7-\sqrt{37} }{6}[/tex]
Hence, zeros of the given equation [tex]3x^{2} -7x+ 1[/tex] are [tex]\frac{7+\sqrt{37} }{6} \ or \frac{7-\sqrt{37} }{6}[/tex].
Find out more information about zeros of a quadratic equation and quadratic method here:
https://brainly.com/question/27349171
#SPJ2
Write the number in the form a +bi
Zeus Industries bought a computer for $2857. It is expected to depreciate at a rate of 24% per year. What will the value of the computer be in 3 years?
Round to the nearest penny. Do not type the "$" sign in your answer
******PLEASE HELP******
Which statements are true for solving the equation 0.5 – |x – 12| = –0.25? Check all that apply.
The equation will have no solutions.
A good first step for solving the equation is to subtract 0.5 from both sides of the equation.
A good first step for solving the equation is to split it into a positive case and a negative case.
The positive case of this equation is 0.5 – |x – 12| = 0.25.
The negative case of this equation is x – 12 = –0.75.
The equation will have only 1 solution
we have
[tex]0.5-\left|x-12\right|=-0.25[/tex]
we know that
The absolute value has two solutions
Subtract [tex]0.5[/tex] both sides
[tex]-\left|x-12\right|=-0.25-0.5[/tex]
[tex]-\left|x-12\right|=-0.75[/tex]
Step 1
Find the first solution (Case positive)
[tex]-[+(x-12)]=-0.75[/tex]
[tex]-x+12=-0.75[/tex]
Subtract [tex]12[/tex] both sides
[tex]-x+12-12=-0.75-12[/tex]
[tex]-x=-12.75[/tex]
Multiply by [tex]-1[/tex] both sides
[tex]x=12.75[/tex]
Step 2
Find the second solution (Case negative)
[tex]-[-(x-12)]=-0.75[/tex]
[tex]x-12=-0.75[/tex]
Adds [tex]12[/tex] both sides
[tex]x=-0.75+12[/tex]
[tex]x=11.25[/tex]
Statements
case A) The equation will have no solutions
The statement is False
Because the equation has two solutions------> See the procedure
case B) A good first step for solving the equation is to subtract 0.5 from both sides of the equation
The statement is True -----> See the procedure
case C) A good first step for solving the equation is to split it into a positive case and a negative case
The statement is False -----> See the procedure
case D) The positive case of this equation is 0.5 – |x – 12| = 0.25
The statement is False
Because the positive case is [tex]0.5-(x-12)=-0.25[/tex] -----> see the procedure
case E) The negative case of this equation is x – 12 = –0.75
The statement is True -----> see the procedure
case F) The equation will have only 1 solution
The statement is False
Because The equation has two solutions------> See the procedure
The equation 0.5 - |x - 12| = -0.25 has no solutions because an absolute value cannot be negative. Attempting to split the equation into positive and negative cases or solving for x is fruitless because the left side of the equation will always be at least 0.5.
Explanation:When solving the equation 0.5 - |x - 12| = -0.25, we can immediately notice that it will have no solutions because the absolute value is always non-negative, and therefore the left-hand side cannot be less than 0.5. Hence, subtracting 0.5 from both sides is not a good first step. Instead, you would typically isolate the absolute value on one side, but given that the equation equals a negative number, we know it has no solutions without additional steps.
Additionally, splitting the equation into a positive case and a negative case isn't useful here, because no matter what's inside the absolute value, the output cannot lead to a negative result, thus making both cases moot.
The statements that say "The positive case of this equation is 0.5 - |x - 12| = 0.25" and "The negative case of this equation is x - 12 = -0.75" are incorrect as they misinterpret how the absolute value works. Lastly, the equation does not have any solution, so it cannot have only one solution.
Learn more about Absolute Value Equations here:https://brainly.com/question/35209059
#SPJ3
For an angle θ with the point (–20, –21) on its terminating side, what is the value of cosine?
Answer:
-20/29
Step-by-step explanation:
How many solutions does the equation 6s − 3s − 9 = −2 + 3 have?
Only one
None
Two
Infinitely many
14÷420 long division
A circle of radius 1 centered at (4, 0) is rotated about the y-axis.
1) Draw a picture of the three-dimensional shape that is produced when the circle is rotated about the y-axis.
2) In two or more complete sentences, describe the three-dimensional shape.
please help and thank you.
The variable Z is directly proportional to X. When X is 15, Z has the value 45.
What is the value of Z when X = 23
Below are the steps to solve an equation: Step 1: |x − 5| + 2 = 5 Step 2: |x − 5| = 5 − 2 Step 3: |x − 5| = 3 Which of the following is a correct next step to solve the equation?
Answer: [tex]x-5=\pm 3[/tex] will be the next step of the given expression.
Step-by-step explanation:
Since, Given expression is |x-5|+2=5
On solving the above expression,
Step 1. [tex]|x-5|+2=5[/tex]
step 2. [tex]|x-5| = 5-2[/tex]
Step 3. [tex]|x-5| = 3[/tex]
Step 4. [tex]x-5=\pm 3[/tex] (because mode takes both positive and negative values)