Answer: 7 centimeters equals 70 millimeters :)
Polynomial Functions
a) Yes, the function is in standard form.
Degree = 2
Exponent = 2
Constant term = -1
b) No, the function is not in standard form.
And it doesn't have the degree, exponent and constant term.
Firstly, let's consider the function f(x) = x(x-1). To determine if it is a polynomial function, we need to check if all of its terms have non-negative integer exponents. In this case, we see that f(x) can be written as x² - x, which has only two terms, and each term has a non-negative integer exponent. Therefore, f(x) is a polynomial function.
In this case, the degree of f(x) is 2 because the highest exponent of x is 2.
In this case, the leading term of f(x) is x², and its leading coefficient is 1.
Finally, the constant term is the term that does not have the variable in it. Here, the constant term of f(x) is -1.
Next, let's consider the function f(x) = 3 - 1/2 x. We can see that f(x) is not a polynomial function because it has a term with a negative exponent.
Polynomial functions must have non-negative integer exponents on all terms.
Therefore, the answer to the first question is 'no.'
Since f(x) is not a polynomial function, it does not have a degree, leading term, or constant term.
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At Atlas Auto Sales, 51 of the 204 cars for sale are minivans. What percent of the cars are
minivans?
Answer: 25%
Step-by-step explanation:
51/204=0.25
0.25 x 100 = 25
Answer:25%
Step-by-step explanation:
Please help with these two equations and show work as well, thank you!
13.) The simplified polynomials that can represent the area and perimeter of the large rectangle =40x + 5x² and
12X + 16 respectively.
14.)The simplified polynomials that can represent the area and perimeter of the large rectangle =21+10x + x² and 20+4x respectively.
How to determine the simplified polynomials that can be used to represent the given shape?To determine the simplified polynomials, the formula for the area and perimeter of the rectangule should be used. That is:
Area of rectangle = length×width
where;
length = 5x
width = 8+X
Area = 5x * 8+X
= 40x + 5x²
Perimeter of rectangle = 2(length+width)
= 2(5x + 8+X)
= 10x + 16 + 2x
= 12X + 16
For question 14.)
Area of rectangle = length× width
where;
length = 7+X
width = 3+X
Area = 7+X × 3+X
= 21+7x+3x +x²
= 21+10x + x²
Perimeter = 2(length+width)
= 2(7+X+3 + X)
= 2(10+2x)
= 20+4x
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Suppose a person were to breath an average of 13 times per minute. How many days would it take for them to breathe one billion times? Round your answer to the nearest single days.
Answer:
12 / min
720 / hr
17,280 / day
6,307,200 / yr
Now divide 1,000,000,000 by 6,307,200 (darn close to your 158!)
Express all real numbers greater than 2 in interval notation
The interval-notation for "all real-numbers" greater than 2 is (2, ∞).
The "Interval-Notation" is a way of expressing a set of real numbers using brackets to show which numbers are included in the set. In the case of all real numbers greater than 2, we can write this as:
(2, ∞)
The open-bracket "(" indicate that the number 2 is not included in the set, while the symbol "∞" represents all real numbers greater than 2.
This notation is used to express an open interval, meaning that the endpoints (in this case, 2 and infinity) are not included in the set.
Therefore, the required interval-notation is (2, ∞).
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please help, due in an hour !!
Answer:
Step-by-step explanation:
What is the equation of a parabola with a vertical axis, vertex (h, k), and directrix y = k – p, where p is a nonzero real number? How can the equation be simplified if the vertex is at the origin?
Note that equation of a parabola with a vertical axis, vertex (h, k), and directrix y = k – p, where p is a nonzero real number is (y-k)² = 4p(x-h).
How can the equation be simplified if the vertex is at the origin?The equation of a parabola with a vertical axis, vertex (h, k), and directrix y = k – p, where p is a nonzero real number, is:
(y - k)² = 4p( x - h)
If the vertex is at the origin (h = 0, k = 0 ), the equation an be simplified to....
y² = 4px
where p is still a nonzero real number.
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Suppose a polynomial function of degree 4 with rational coefficients has the given numbers as zeros. Find the other zeros.
1+2i, 1+√5
The other zeros are
(Use a comma to separate answers.)
Answer:
The other zeros are:
1 - 2i, 1 - √5
An oil candle globe made of hand-blown glass has a diameter of 25.8 cm. What is the volume of the globe? Use 3.14 for .
globe meaning a sphere, and since it has a diameter of 25.8, that means its radius is half that, or 12.9
[tex]\textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=12.9 \end{cases}\implies V=\cfrac{4\pi (12.9)^3}{3}\implies \stackrel{ using~\pi =3.14 }{V\approx 8987.47}[/tex]
Write an equation of a circle with the given center and radius. center (3,4) and radius 6
(x-3)^2+(y-4)^2=36
(x-3)^2+(y-4)^2=6
(x+3)^2+(y-4)^2=36
(x+3)^2+(y-4)^2=6
Answer:
[tex] {(x - 3)}^{2} + {(y - 4)}^{2} = 36[/tex]
A business manufactures and sell laptops.Each laptop is sold for R14000.the fixed monthly cost is R32000 and it cost R9000 to manufacture each laptop.let L be number of laptops manufactured and sold per monthly
The total cost equation can be written as:
Total Cost = 32000 + 9000L
What is total cost?
Total cost refers to the complete amount of money or resources that are required to produce or obtain a particular good or service. It includes all of the expenses associated with production, such as labor costs, materials costs, overhead costs, and any other costs necessary to manufacture or acquire the product.
The total cost equation can be expressed as:
Total Cost = Fixed Cost + Variable Cost
where Fixed Cost is the cost that does not vary with the number of laptops manufactured and sold, and Variable Cost is the cost that depends on the number of laptops manufactured and sold.
In this case, the fixed monthly cost is $32,000 and it does not depend on the number of laptops manufactured and sold. The variable cost is the cost of manufacturing each laptop, which is $9,000 per laptop.
If L is the number of laptops manufactured and sold per month, then the variable cost can be expressed as 9000L. Therefore, the total cost equation can be written as:
Total Cost = 32000 + 9000L
This equation represents the total cost of manufacturing and selling L laptops per month. The fixed cost of $32,000 is added to the variable cost of $9,000 per laptop multiplied by the number of laptops sold, L, to obtain the total cost.
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Complete question: A business manufactures and sell laptops. Each laptop is sold for 14000.the fixed monthly cost is 32000 and it cost 9000 to manufacture each laptop. let L be number of laptops manufactured and sold per monthly. What is the total cost equation?
To answer the question, "How do students in the United States pay for their higher education?", a questionnaire was sent out to collect 100 responses from one higher education institution per state.
The given scenario is Biased, since those who chose to respond may be systematically different than those who chose not to respond. So, the correct answer is C).
The sampling method is biased, since those who chose to respond may be systematically different than those who chose not to respond. This is known as non-response bias, where the opinions and characteristics of those who choose not to respond to the survey may differ from those who choose to respond.
Additionally, only one higher education institution per state was selected, which may not be representative of all institutions within the state. Therefore, the sample may not accurately reflect the population of students in the United States who pay for their higher education. So, the correct option is C).
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--The given question is incomplete, the complete question is given
" To answer the question, "How do students in the United States pay for their higher education?", a questionnaire was sent out to collect 100 responses from one higher education institution per state.
Is the sampling method biased or unbiased and why?
Unbiased, since a random sample was selected
Unbiased, since a large sample was selected
Biased, since those who chose to respond may be systematically different than those who chose not to respond
Biased, since all higher education institutions are represented
Unbiased, since a questionnaire was used
Biased, since every state will be represented in the sample"--
College Level Trigonometry Question!
An equation that models the trigonometric graph is:
y = 4 sin 4x
How to interpret the trigonometric graph?The general form for an equation that models a wave is this:
±a (sin/cos) (2π(x - p)/T)
where:
a is the amplitude
p is the phase shift
T is the period.
The ±ve will turn into +ve if the graph tends to start from the positive direction, and then turns -ve if it the graph tends to start from the negative direction.
The (sin/cos) will definitely become sine if the graph starts at 0 before it is being shifted. Then, it becomes cosine if the graph begins at the amplitude.
In this problem, we see that the graph begins as positive, and then at the amplitude with no phase shift, we see that the ±ve becomes +ve, (sin/cos) becomes sin, and p becomes zero. Plugging in the given values in the problem, we see that a = 4 and T = π/2.
We see that this equation becomes:
y = 4sin(2πx/(π/2)).
y = 4 sin 4x
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Which expression is equivalent to 5^3 × 10^-2?
Answer:
[tex]5 {}^{3} \times 10 {}^{ - 2} \\ = 5 {}^{3} \times \frac{1}{10 {}^{2} } \\ = 5 {}^{3} \times \frac{1}{2 {}^{2} 5 {}^{2} } \\ = 5 \times \frac{1}{4 \\ } \\ = \frac{5}{4} [/tex]
hope it helps
The sum of matrix A and B where B is the identity matrix with respect to addition will give the matrix.
Select one:
Matrix A
Matrix 0
Matrix B
Matrix AB
The sum of any matrix with the identity matrix of the same size, with respect to addition, will give the matrix itself. Therefore, the sum of matrix A and B, where B is the identity matrix, will give the matrix A.
So the answer is: Matrix A.what is twenty-five divided bye four?
Answer: The answer is 6.25
Step-by-step explanation:
Answer:
6.25
Step-by-step explanation:
pls help very much appreciate it
n/4.4 =7 Pls Help nowwwwwwwwwwwwwwwwwwwww
Answer:
n=7
Step-by-step explanation:
[tex] \frac{n}{4} \times 4 = 7 \\ \frac{4n}{4} = 7 \\ 4 \times \frac{4n}{4} = 7 \times 4 \\ 4n = 28 \\ \frac{4n}{4} = \frac{28}{4} \\ n = 7 [/tex]
solve for x, neg x over 4 = 12 A 48 or B -3 or C 3 or D -48?
The solution for x is -48, the answer is D) -48.
What is Algebraic expression ?
An algebraic expression is a mathematical phrase that contains variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. It represents a value that can change based on the values assigned to the variables.
Starting with:
x:4 = 12
Multiplying both sides by -1 gives:
(-x÷4) = -12
Simplifying the left side:
x÷4 = -12
Multiplying both sides by 4 gives:
x = -48
Therefore, the solution for x is -48, the answer is D) -48.
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Y= 1/2x+5
X _ Y
-4. ?
-2. ?
0. ?
2. ?
Answer: 0.
Step-by-step explanation:
y-(1/2*x+5)=0 STEP 1:
simplify 1/2
Equation at the end of step 1: 1
y - ((— • x) + 5) = 0
ASAP
A rectangular prism is shown in the image.
A rectangular prism with dimensions of 3 yards by 5 yards by 5 and one half yard.
What is the volume of the prism?
forty one and one fourth yd3
fifty six and one fourth yd3
eighty two and one half yd3
165 yd3
As a result, the prism's volume is given by V = lwh = 3 x 5 x 5.5 = 82.5 cubic yards. Thus, option C—eighty two and a half yards—is the correct response.
what is volume ?The quantity of room an object takes up in three dimensions is measured by its volume. It is frequently expressed in cubic units like cubic metres, cubic feet, and cubic centimetres. Mathematics formulas that are particular to the shape of the object can be used to calculate its volume, such as V = l w h for a rectangular shape or V = (4/3)r3 for a sphere.
given
V = lwh is the formula for calculating the volume of a rectangular prism, where l, w, and h stand for the prism's length, width, and height, respectively.
Here, the dimensions are 3 yards in length, 5 yards in breadth, and 5.5 yards in height.
As a result, the prism's volume is given by V = lwh = 3 x 5 x 5.5 = 82.5 cubic yards.
Thus, option C—eighty two and a half yards—is the correct response.
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Match each drawing on the left with its word description on the right , some of the answer choices on the right may not be used. Line segment AB , Line AB , Point AB , Ray AB , Ray BA
1) Line AB
2) Ray AB
3) Line segment AB
4)Ray BA
The first drawing is a line AB because a line passing through two different points A and B
The second drawing is ray AB because it started at A
The third drawing is a line segment AB because it is part of a straight line that is bounded by two distinct end points, and contains every point on the line that is between its endpoints
The fourth drawing is ray BA
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Ava uses a total of 72 bead. without dividing, how can you know if she made an even number of bracelets?
To check if the total number of beads used in each bracelet is even, we need to find out if the sum of the digits in the number 72 is even or odd.
How to know number of bracelets madeIf Ava made an even number of bracelets using the 72 beads, then the total number of beads used in each bracelet must be an even number.
One way to check if the total number of beads used in each bracelet is even is to find out if the sum of the digits in the number 72 is even or odd. If the sum of the digits is even, then it is possible that Ava made an even number of bracelets. If the sum of the digits is odd, then it is not possible that Ava made an even number of bracelets.
The sum of the digits in 72 is 7 + 2 = 9, which is an odd number. Therefore, it is not possible for Ava to have made an even number of bracelets using the 72 beads, without dividing the beads.
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What is the answer to (x^2)+(2x)-(5)=0
The solution to the given quadratic equation is [tex]=-1\pm \sqrt{6}[/tex]
What is a quadratic equation?A quadratic equation is an equation whose highest power is raised to the power of 2. Mathematically it is written in the form ax² + bx + c. There are many ways in which we can solve a quadratic equation such as:
FactoringQuadratic formulaCompleting the square methodFrom the given information, we have:
x² + 2x - 5 = 0
Using the quadratic formula method;
[tex]=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
here;
a = 1b = 2c = -5[tex]=\dfrac{-2\pm \sqrt{2^2-4(1)(-5)}}{2(1)}[/tex]
[tex]=\dfrac{-2\pm \sqrt{4+20}}{2}[/tex]
[tex]=\dfrac{-2\pm \sqrt{24}}{2}[/tex]
[tex]=\dfrac{-2\pm 2\sqrt{6}}{2}[/tex]
[tex]=-1\pm \sqrt{6}[/tex]
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State the domain, the range, and the intervals over which the graphically defined function is increasing, decreasing, or constant.
The domain will be (-∞, ∞). The range will be (-1, 1]. The function will be increasing during the intervals (0, π/2) and (3π/2, 2π), and will be decreasing at the interval (π/2, 3π/2). It will be constant only at x=0 and not at any interval.
We are given a graph in the question and we have to determine its domain, range, and the intervals over which the defined function is increasing, decreasing, and constant. If we observe this graph, we can see that this is a sin(x) graph.
The domain of this graph will be from -[tex]\infty[/tex] to [tex]\infty[/tex] as we can see in the graph that it is a repeating pattern. The range for this graph will lie between -1 and 1 as it is a sin x graph. The sin x graph increases at the intervals (0, π/2) and (3π/2, 2π) and decreases at the interval (π/2, 3π/2). As we can see from the graph, it is constant only at a point where x = 0 and there is no interval at which this graph is constant.
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What is equivalent to x^2-5x+6
Answer:
[tex]=\left(x-2\right)\left(x-3\right)\\[/tex]
Step-by-step explanation:
Given:
[tex]x^2-5x\:+6[/tex]
To find:
Equivalent to x^2-5x+6
Explanation:
[tex]x^2-5x+6\\=\left(x^2-2x\right)+\left(-3x+6\right)\\=x\left(x-2\right)-3\left(x-2\right)\\\mathrm{Factor\:out\:common\:term\:}x-2\\=\left(x-2\right)\left(x-3\right)[/tex]
Final Answer:
(x-2)(x-3)
SOMEONE, PLEASE HELP! ASAP, WILL GIVE 30 POINTS!
Using the equations given, only equation 2 has a proportional relationship.
What is a proportional and non-proportional relationship?Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other.
The difference between proportional and non-proportional linear relationships is that, although both have constant rates of change the proportional relationship has constant output to input ratios, and the non-proportional relationship does not.
In this problem, to determine the proportional relationship, we can also check for both values of x and y.
1. y = -0.75x + 5
When x = 1
y = -0.75(1) + 5
y = 4.25
when x = 2
y = -0.75(2) + 5
y = 3.5
The relationship is not proportional since as one variable increase, the other decreases.
2. y = 4x - 1
When x = 1
y = 4(1) - 1
y = 4 - 1
y = 3
when x = 2
y = 4(2) - 1
y = 8 - 1
y = 7
This relationship is proportional since the variables increases or decreases with one another.
3. y = (3/4)x
When x = 1
y = (3/4)(1)
y = 3/4
when x = 2
y = (3/4)(2)
y = 2/3
This relationship is not proportional
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Solve for x.
A
Set up the proportion.
XI7
The solution for the variable x is x = 8.4
How to determine the solution for the variable xfrom the question, we have the following parameters that can be used in our computation:
The right triangle
Using the proportion of similar triagles, we have
x/7 = 10/x
This gives
x * x = 7 * 10
So, we have
x² = 70
Next, we have
x = √70
Evaluate
x = 8.4
Hence, the solution for the variable x is x = 8.4
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What is the surface area of this composite solid?
The surface area of the given composite solid is calculated as: 200.24 square units.
How to Find the Surface Area of the Composite Solid?Surface area of the composite solid = surface area of rectangular prism + surface area of cylinder - 2(area of the base of the cylinder)
Surface area of rectangular prism = length * width * height = 10 * 3 * 5
= 150 square units.
Surface area of cylinder = 2πr(h + r)
height (h) = 4
Radius (r) = 2
Plug in the values:
Surface area of cylinder = 2 * 3.14 * 2(4 + 2) = 75.36 square units
Area of the base of the cylinder = πr² = 3.14 * 2²
= 12.56 square units
Thus, we have:
Surface area of the composite solid = 150 + 75.36 - 2(12.56) = 200.24 square units.
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Help with math problems
Answer:
Step-by-step explanation:
15.) [tex]\sqrt{12}[/tex]
[tex]\sqrt{4}[/tex] * [tex]\sqrt{3}[/tex]
Answer: 2[tex]\sqrt{3}[/tex]
17.) Distribute 3[tex]\sqrt{3}[/tex] into both sides of the parentheses
3[tex]\sqrt{3}[/tex] * 4 = 12[tex]\sqrt{3}[/tex]
3[tex]\sqrt{3}[/tex] * -3[tex]\sqrt{5}[/tex] = -9[tex]\sqrt{15}[/tex]
Answer: 12[tex]\sqrt{3}[/tex] - 9[tex]\sqrt{15}[/tex]
19.) Distribute 4[tex]\sqrt{15}[/tex] into both sides of the parentheses
4[tex]\sqrt{90}[/tex] + 4[tex]\sqrt{75}[/tex]
4*[tex]\sqrt{9}[/tex]*[tex]\sqrt{10}[/tex] + 4*[tex]\sqrt{25}[/tex]*[tex]\sqrt{3}[/tex]
4*3*[tex]\sqrt{10}[/tex] + 4*5*[tex]\sqrt{3}[/tex]
12[tex]\sqrt{10}[/tex] + 20[tex]\sqrt{3}[/tex]
21.) Distribute [tex]\sqrt{15}[/tex] into both sides of the parentheses
2[tex]\sqrt{150}[/tex] - 4[tex]\sqrt{90}[/tex]
2*[tex]\sqrt{25}[/tex]*[tex]\sqrt{6}[/tex] - 4*[tex]\sqrt{9}[/tex]*[tex]\sqrt{10}[/tex]
2*5*[tex]\sqrt{6}[/tex] - 4*3*[tex]\sqrt{10}[/tex]
10[tex]\sqrt{6}[/tex] - 12[tex]\sqrt{10}[/tex]