How is multiplying radicals so similar to just simplifying them?
List all of the number sets that contain the number 15.
A.
rational numbers and integers
B.
rational numbers, integers, and natural numbers
C.
rational numbers, integers, and whole numbers
D.
rational numbers, integers, natural numbers, and whole numbers
Final answer:
The number 15 belongs to several sets of numbers: it is a rational number, an integer, a whole number, and a natural number. Therefore, the correct answer to which sets contain the number 15 is D. Rational numbers, integers, natural numbers, and whole numbers.
Explanation:
Number sets form a hierarchy where certain numbers fit into multiple categories based on their characteristics. Starting from the broadest categories, we have complex numbers, which include all numbers with a real and imaginary part. However, the number 15 does not have an imaginary part, so we look to smaller sets.
The real numbers include all the values that can be found on the number line, which includes rational numbers (like fractions), irrational numbers (like √2), integers, whole numbers, and natural numbers. The number 15 is a real number because it can be found on the number line, but it is also specifically a rational number, an integer, a whole number, and a natural number because:
As a rational number, it can be expressed as the ratio of two integers, specifically 15/1. As an integer, it is a whole number and does not have a fractional or decimal part. As a whole number, it is a non-negative integer, starting from 0 and moving upwards. As a natural number, it is a positive integer used for counting (1, 2, 3, ...).
Therefore, the correct answer to the question is D. Rational numbers, integers, natural numbers, and whole numbers all contain the number 15.
The environmental club is selling indoor herb gardens for Earth Day. Each member is encouraged to sell at least 10 gardens. You sell 3 gardens on Monday and 4 gardens on Tuesday. Write and save an inequality to find the possible numbers of gardens you can sell to reach your goal.
If each member are encouraged to sell at least 10 gardens, and you have already sold 3 + 4 = 7 gardens, therefore you only lack 3.
Let us say that x = the number of gardens you can sell, therefore the inequality equation is:
x ≥ 3
or we can also say
x > 2
How many possible solutions are there to a linear equation in one variable?
Which graph represents a function?
Answer:
1st and last one
Step-by-step explanation:
the first and the last one are the only ones that represent a function because for each value of x there is only one corresponding value of y.
A graph represents a function if each value of x corresponds uniquely to a value of y. These graphs, often called line graphs, can depict various types of functions like linear, quadratic, etc. The slope and position of the line will vary depending on the function's formula.
Explanation:
In the subject of Mathematics, specifically when dealing with functions and graphs, a graph represents a function if each value of x corresponds to a unique value of y. This means that different values of x will produce different values of y. Graphs can be produced using specific pairs of (x,y) data points.
These graphs may be named line graphs as they showcase the relationship between two variables: one measured on the horizontal axis (x) and the other on the vertical axis (y). An example could be a function where y = a + bx. If b > 0, the line of the graph slopes upward to the right. If b = 0, the line is horizontal. If b < 0, the line slopes downward to the right.
Graphs may also represent other types of functions like linear, quadratic, inverse, or exponential, depending on the equation of the relation between x and y. It's also important to note that there can be other types of graphs, such as a specific type of line graph shown, where the x-axis consists of data values and the y-axis consists of frequency points.
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What's is the radius of a circle with a circumference of 56.5?
two vertices of an isosceles triangle in the coordinate plane have coordinates (0,0) and (2a,0). Where might the third vertex be located?
Question help the critical value of a twominus−sided tminus−test computed from a large sample
a. is 1.64 if the significance level of the test is 5%.
b. cannot be calculated unless you know the degrees of freedom.
c. is the same as the pminus−value.
d. is 1.96 if the significance level of the test is 5%.
Equation for (1, -6) and (0,3)
Find the value of x. If necessary, round to the nearest tenth.
A. 11.7 in.
B. 9.7 in.
C. 13.7 in.
D. 6.9 in.
Answer:
B. 9.7 in.
Step-by-step explanation:
We have been given an image of a triangle. We are asked to find the value of x.
We will use area of triangle formula to solve our given problem.
[tex]\text{Area of triangle}=\frac{1}{2}\times \text{Base*Height}[/tex]
[tex]47\text{ in}^2=\frac{1}{2}\times x*x[/tex]
[tex]2*47\text{ in}^2=\frac{1}{2}*2\times x^2[/tex]
[tex]94\text{ in}^2=x^2[/tex]
Taking square root of both sides we will get,
[tex]x=\sqrt{94\text{ in}^2}[/tex]
[tex]x=9.6953597\text{ in}\approx 9.7\text{ in}[/tex]
Therefore, the value of x is 9.7 inches and option B is the correct choice.
A rectangular playground is to be fenced off and divided in two by another fence parallel to one side of the playground. 648 feet of fencing is used. find the dimensions of the playground that maximize the total enclosed area.
10 PTS!!! HELP!
Lifting a chair that weighs 4 kg to a height of 40 cm takes 16 J of energy.
a) What amount of energy would be needed to lift a similar chair to a height of 80 cm?
b) What amount of energy would be needed to lift a chair that weighs 2kg to a height of 40 cm?
If a number is subtracted from its square, the result is 2. find the number.
2x + 12 - 7x = -2 for x
leave your answer as an improper fraction or convert to a decimal
2x+12-7x=-2
-5x+12=-2
-5x=-14
x=14/5
Describe two ways to solve the equation 2(4x-11)=10
Jennifer is planning a vacation. The hotel cost $60 per night and her flight costs $150 round-trip. she has a budget of $50 for the flight and hotel up to how many nights can she afford in hotel?
Well if the hotel costs 60 dollars per night and she is only willing to spend $50 she wouldn't be able to spend any nights in the hotel I believe.
Hope this helps!
what is 8.525 rounded to 2 decimal place????
A car recently sold for $32,345. If there's a 6% sales tax on automobile sales, how much tax will be added to the price of the car
Answer:
1940.70
Step-by-step explanation:
The perimeter of a rectangular garden is 126 meters. the length is 6 meters longer than twice the width. find the dimensions of the garden
Answer:
Step-by-step explanation:
width - 19m
length - 44m
The design on Santana’s wall includes 16 pink stripes and 20 green stripes. Find the ratio of pink stripes to green stripes.
The ratio of pink stripes to green stripes on Santana's wall is 4:5.
To find the ratio of pink stripes to green stripes on Santana's wall, we need to compare the two quantities. Santana has 16 pink stripes and 20 green stripes. The ratio can be simplified by finding the greatest common divisor of the two numbers and then dividing both by that number to find the simplest form.
In this case, the greatest common divisor of 16 and 20 is 4. We divide both numbers by 4 to simplify the ratio:
16 / 4 = 4
20 / 4 = 5
Therefore, the simplified ratio of pink stripes to green stripes is 4:5.
Bonita is testing prototype model rocket engines. To be considered a successful launch, the rocket must reach a height of at least 24 ft and must go a horizontal distance of no more than 10 ft. The vertical height must be at least three times as high as the horizontal distance. No rocket should go higher than 33 ft.
The graph shows the feasible region, where x represents the horizontal distance and y represents the vertical distance.
Which ordered pairs meet all the constraints for a successful launch and make sense in context of the situation?
Select each correct answer.
(0, 33)
(4, 36)
(4.8, 30.5)
(9, 26)
(2, 22)
What time is 8 hours and 51 minutes before 11:13 P.M.?
8 hours and 51 minutes before 11:13 P.M. is 2:22 P.M.
To find what time it is 8 hours and 51 minutes before 11:13 P.M., we need to subtract 8 hours and 51 minutes from 11:13 P.M. Here's a step-by-step explanation:
Start with the minute subtraction. Since 13 minutes is less than 51 minutes, we need to borrow one hour from the 11 P.M. So, we change 11:13 P.M. to 10:73 P.M.Now, subtract the minutes: 73 - 51 = 22 minutes. So now we have 10:22 P.M.Next, subtract the hours: 10 P.M. - 8 hours = 2 P.M.Thus, 8 hours and 51 minutes before 11:13 P.M. is 2:22 P.M.
The line passes through the points ( 7, -7) and ( 6, -5) a. y = -2x + 7 c. y = -2x - 7 b. y = 2x - 21 d. y = 2x - 7
Final answer:
The equation of the line passing through the points (7, -7) and (6, -5) is determined by finding the slope, which is -2, and then using the point-slope formula. However, the correct equation y = -2x + 21 is not listed among the student's provided options.
Explanation:
The student's question asks for the equation of a line that passes through two given points: (7, -7) and (6, -5). To find the equation of the line, we first need to determine its slope.
We use the formula for slope which is (change in y) / (change in x), often written as (y2 - y1) / (x2 - x1)
Slope = (-5 - (-7)) / (6 - 7) = 2 / -1 = -2. Therefore, the slope (m) is -2.
With the slope known, the next step is to use the point-slope form of the line equation, which is y - y1 = m(x - x1). Substituting one of the points and the slope, we get y - (-7) = -2(x - 7). Simplifying this gives us y = -2x + 14 + 7, which simplifies further to y = -2x + 21.
Therefore, among the options provided by the student, none of the equations match precisely, which means either there is a mistake in the question's options or in the calculation. However, the closest match, by the slope, would be option y = -2x - 7, considering only the slope and not the intercept.
Consider the following expression.
9v+2u+1
select all the true statements below.
*9v is a coefficient
*v+2u+1 is is written as a sum of three terms
*9v and 1 are like terms
*9v is a factor
*1 is a constant
*None of these are true
The statements that are true are: v+2u+1 is written as a sum of three terms, and 1 is a constant.
Explanation:Let's analyze each statement one by one:
9v is a coefficient: False. Coefficients are the numbers that multiply the variables. In this case, 9v is a term where 9 is the coefficient and v is the variable. v+2u+1 is written as a sum of three terms: True. The expression v+2u+1 can be separated into three terms - v, 2u, and 1. 9v and 1 are like terms: False. Like terms have the same variables raised to the same power. In this case, 9v and 1 are not like terms. 9v is a factor: False. Factors are multiplied together to get a product. In this case, 9v is not being multiplied by anything. 1 is a constant: True. Constants are terms that do not contain variables. In this case, 1 is a constant term. None of these are true: False. As we have identified, statement 2 and 5 are true. Learn more about Algebra here:
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In order from smallest to largest 0.9,75%,4/5
I REALLY NEED HELP 100 POINTS PLEASE ANSWER HONESTLY!!!
9. Is the statement a good definition? If not, find a counterexample. "An airplane is a vehicle that flies."
1 point
10. Write the converse of the following statement. "If you live in the capital of Georgia, then you live in Atlanta."
1 point
11. Write the TWO conditional (if-then) statements that make up the biconditional. "A parallelogram is a figure with two pairs of parallel sides."
2 points
sorry if im wrong
9) yes
10) If you live in Georgia, then you live in Atlanta
11) If three points are collinear, then they are coplanar.
if three points are coplanar, the they are collinear.
Decide which of the two points lies on the graph of the line
X= -3
A. 2,-3
B. -3,2
0.71428571428 as a fraction in simplest form
To express 0.71428571428 as a fraction, we use a geometric series and find that the simplest form is 713/999.
Explanation:To express 0.71428571428 as a fraction in simplest form, we first note that the fractional part of the decimal is 0.71428571428. Since the decimal has a repeating pattern, we can represent it as a fraction using a geometric series. Let x equal the fraction, then we have:
x = 0.71428571428
Multiplying both sides by 10 gives:
10x = 7.1428571428
Subtracting the original equation from the new equation eliminates the repeating part:
10x - x = 7.1428571428 - 0.71428571428
Simplifying, we get:
9x = 6.42857142852
Dividing both sides by 9, we find:
x = 0.71428571428 = 6.42857142852/9 = 713/999
Therefore, 0.71428571428 as a fraction in simplest form is 713/999.
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Which graph represents the system of inequalities?
y+2<5xy+3x>4y≥2x
Answer:
The correct option is 2.
Step-by-step explanation:
The given system of inequalities
[tex]y+2<5x[/tex]
[tex]y+3x>4[/tex]
[tex]y\geq 2x[/tex]
Inequality (1) can be written as
[tex]y<5x-2[/tex]
The related equation is
[tex]y=5x-2[/tex]
The slope of line is 5 and y-intercept is -2.
The sign of inequality is < , it means related line of inequality (1) is a dotted line and shaded region is below the line.
Inequality (2) can be written as
[tex]y>-3x+4[/tex]
The related equation is
[tex]y=-3x+4[/tex]
The slope of line is -3 and y-intercept is 4.
The sign of inequality is >, it means related line is a dotted line and shaded region is above the line.
Inequality (3) is
[tex]y\geq 2x[/tex]
The related equation is
[tex]y=2x[/tex]
The slope of line is 2 and y-intercept is 0.
The sign of inequality is ≥, it means related line is a solid line and shaded region is above the line.
In the below graph the common shaded region is the solution region.
Therefore the correct option is 2.
Write the contrapositive of the statement below.
If a triangle is an obtuse triangle, then it has one angle with measure greater than 90°
A triangle has one angle greater than 90°.
A triangle is an obtuse triangle.
If a triangle is not an obtuse triangle, then it does not have one angle greater than 90°.
If a triangle does not have one angle greater than 90°, then it is not an obtuse triangle.