Back to Ten Facts -When subtracting two integers when the digit in the ones place is the same and the larger number has a 1 in the tens place, the result is 10 (for example, 15-5=10, 13-3=10, 12-2=10, etc.).
Subtraction:
Subtraction symbolizes the process of removing elements from a collection. The negative sign represents subtraction. If, for example, four of the nine oranges that are stacked together (as in the figure above) are then relocated to a basket, the stack will now only contain five oranges as opposed to nine. Thus, 5 is equal to 9 less 4 and is the difference between 9 and 4. In addition to natural numbers, other kinds of numbers can also be subtracted. The symbol for subtraction is the letter "-." The difference, the minuend, and the subtrahend are the three numerical components that make up the subtraction operation.
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What is the variable in this expression?
4b + 2b + 1⁄4
The variable in this expression 4b + 2b + 1⁄4 is b
How to determine the variable?From the question. we have the following expression
4b + 2b + 1⁄4
Take for instance, we have an expression
Ax
Where A is a number
It means that the expression x is a variable
This is so because the value of x can change
Similarly, the variable in 4b + 2b + 1⁄4 is b
This is so because the value of b can change
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1. The unit price of an item is how much it costs for one item. It's useful to know the unit price when buying in bulk. If we're buying 100 items, then you'll save quite a bit of money if you buy the unit priced item that costs $10 per item compared to the unit price of $12 per item!
You can calculate a unit price by dividing the total amount of money you spent for items by the number of items you purchased. For instance: $7.99 per oz of goldfish is $ 7.99 / 30= 0.26$ per ounce.
Which purchase has the lower unit price - $\$ 200$ for 15 flower arrangements, or $70 for 5 flower arrangements?
What is division?
Division is the process by which value of single unit can be calculated from the value of multiple unit.
The number to be divided is known as dividend, the number by which the dividend is divided is the divisor, the result obtained is the quotient and the remaining part is the remainder.
There is a well known formula for division
Divisor x Quotient + Remainder = Dividend.
This is a problem sum of division
Cost of 15 flowers = $200
Cost of 1 flower = $200 [tex]\div[/tex] 15 = $13.33
Cost of 5 flowers = $70
Cost of 1 flower = $70 [tex]\div[/tex] 5 = $14
So unit price of 15 flower arrangement of $200 is lower than unit price of 5 flower arrangement of $70
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"Even in winter, the roadsides were places of beauty, where countless birds came to feedon the
berries and on the seed heads of the dried weeds rising above the snow. The countryside was, in
fact, famous for the abundance and variety of its bird life, and when the flood of migrants was
pouring through in spring and fall, people came from great distances to observe them"
(paragraph 5).
Why most likely does the author give a detailed description of a healthy ecology (the
study of organisms and how they interact to the environment around them) as noted in
paragraph 5?
A. To promote birdwatching to people visiting the town
B. To give the natural history of a specific region
C. To describe different tourist activities of people pouring through the town
D. To contrast how the town changed once the ecology was compromised with the use of
harmful pesticides
The author gives a detailed description of a healthy ecology D. To contrast how the town changed once the ecology was compromised with the use of harmful pesticides.
What is the ecology about?
Ecology also teaches us about the benefits of ecosystems and how to use the Earth's resources in a way that protects the environment for future generations. We can learn more about our surroundings thanks to the various fields of ecology, which include statistical ecology, marine ecology, and vegetation ecology.
With the help of this information, we can manage our natural resources, protect human health, and improve the environment. In this case, the author give a detailed description of a healthy ecology.
The correct option is D.
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When two angles and a non-included side of a triangle are equal to the corresponding angles and sides of another triangle it means that we are going to use what postulate?
The used postulate is explained below.
What is congruent triangles?
Two triangles are stated to be congruent if the 3 facets and the 3 angles of each the angles are same in any orientation.
When angles and facet blanketed in among those angles of 1 triangle are identical as any other one, each those triangle are Congruent.
This standards of congruency is is aware of as ASA criterion as a facet blanketed among angles are all identical.
Two triangles are congruent, if angles and the facet blanketed among them in a single triangle is same to the 2 angles and the facet blanketed among them of the alternative triangle.
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What would the answer be? I tried 4 and -4 and a lot more.
Answer:
-2
Step-by-step explanation:
a is -3
d is -1
you subtract the two
-3 - (-1)
when you have two negatives they cancel each other out and become positive
-3 + 1
-3 + 1 = -2
that is your answer
How do you solve an isosceles triangle problem?
Isosceles triangle problem can be solved by given steps
what is isosceles triangle ?
An isosceles triangle in geometry is a triangle with two sides that are the same length. Sometimes it is stated as having exactly two sides that are the same length, and other times it is specified as having at least two sides that are the same length, the latter form containing the equilateral triangle as a particular case.
explanation:
In isosceles triangle
1. Two sides of the triangle are congruent
2. The angle opposite those sides are congruent
x + 72 +72 = 180
x = 180 -144
x = 36
Hence the isosceles triangle problem can be solved by above steps and explanation
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Is it true that 5 2/3 - 3 3/4 = 1+ 2/3 + 3/4?
The fraction 5 2/3 - 3 3/4 is not equal to 1+ 2/3 + 3/4.
What is a fraction?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.
In this case, 5 2/3 - 3 3/4 will be:
= 5 2/3 - 3 3/4
= 5 8/12 - 3 9/12
= 1 11/12
Therefore 1 + 2/3 + 3/4
= 1 + 2/3 + 3/4
= 1 + 8/12 + 9/12
= 2 5/12
They are not the same.
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Toby created a sculpture for art class using different-sized cubes. The smallest cube is 1.5 inches along each edge. The largest cube is 7.5 inches along each edge.
How many of the smallest cubes would it take to fill the largest cube?
Write your answer as a whole number or decimal. Do not round.
There are 125 of the smallest cubes that will fill the largest cube using the size of their respective volume
Volume of cubeThe volume of cube is calculated by using a × a × a = a³ where "a" is the edge.
The volume of the smallest cube = 1.5inches × 1.5inches × 1.5inches
The volume of the smallest cube = 3.375inches³
The volume of the largest cube = 7.5inches × 7.5inches × 7.5inches
The volume of the largest cube = 421.875inches³
Thus, the number of the smallest cubes it would take to fill the largest cube is derived by
421.875inches³/3.375inches³ = 125.
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The perimeter of a rectangle is 204 centimeters. Find the length and width if the length is an even integer and the width is 3 times the next consecutive even integer.
Step-by-step explanation:
2×length + 2×width = 204 cm
length = x
width = 3×(x + 2)
as consecutive even integers are always spaced out by 2 (2, 4, 6, ...).
we are using these 2 equations in the first main equation :
2×x + 2×3×(x + 2) = 204
2x + 6x + 12 = 204
8x + 12 = 204
8x = 192
x = 192/8 = 24
length = x = 24 cm
width = 3(x + 2) = 3×26 = 78 cm
In Exercises 13-16, find the area of the polygon with the given vertices. (See Example 3.)
13. E(3,1), F(3,-2), G(-2,-2)
14. J(-3,4), K(4,4), L(3,-3)
The area of the polygon EFG with given vertices is, 7.5 units.
What is area of triangle?
The area of a triangle is the area that it completely encloses in a two-dimensional plane. A triangle is a closed shape that, as we all know, has three sides and three vertices. As a result, the total area occupied by a triangle's three sides is known as its area. The general formula for calculating a triangle's area is the product of the triangle's base and height divided by half.
Let the given vertices are,
E(3, 1), F(3, -2), G(-2, -2)
There are three vertices, so the polygon is a triangles.
Since,
Area of triangle = 1/2 x base x height.
If we draw the given vertices on the coordinate plane then the base is FG and the height of the triangle is EF.
Now to find the lengths of side FG and EF.
By using the distance formula,
[tex]d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\EF =\sqrt{(3-3)^2+(-2-1)^2} = \sqrt{9} = 3\\ FG = \sqrt{(-2-3)^2 + (-2-(-2))^2} = \sqrt{25+0} = 5[/tex]
⇒ Area = 1/2 x 5 x 3
= 1/2 x 15
Area = 7.5
Hence, the area of the polygon EFG is 7.5 units.
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at a field trip for every 8 students there is 1 chaperone. if the teacher purchased 108 total tickets, how many tickets were for students?
First, 108/9=12
This means that are 12 groups of people.
If there are 8 students in each group, 12 x 8 = 96.
96 should be your answer.
How do you find the range on a graph?
The range of a graph can be found using the values depicted on the y-axis.
According to the question,
We have the following information:
We have a graph and we need to know how do we find the range of that graph.
We know that the domain of a graph is the collection or in other words set of input values depicted on x -axis and the range of a graph is the set of possible output values portrayed on y-axis of the graph.
In noting down the range of a graph, we first list down the down value and then the up value or in other words we move from down to up in order to find the range of a graph.
Hence, the range of a graph can be found using the values depicted on the y-axis.
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Write the equation of the line in all three forms that is perpendicular to the line 6x+18y=36 and goes through the point (-5,4) Point-Slope Form, Slope-Intercept Form, and Standard Form
Answer:
Step-by-step explanation:
SLOPE OF THE GIVEN LINE
6x + 18y = 36
x + 3y = 6
3y = -x + 6
3/3 y = -1/3 x + 6/3
y = -1/3 x + 2
Slope = -1/3
slope of a perpendicular line = 3
POINT SLOPE FORM
y-4 = 3(x-(-5)
y - 4 = 3(x+5)
SLOPE INTERCEPT FORM
y-4 = 3x + 15
y = 3x + 15 + 4
y = 3x + 19
STANDARD FORM
3x - y + 15 + 4 = 0
3x - y + 19 = 0
Equation of line in point slope form is y-4= 3 (x+5), y=3x+19 is equation in slope intercept form and equation in standard form is 3x-y+19=0.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
6x+18y=36
18y=-6x+36
Divide both sides by 18
y=-6/18x+36/18
y=-1/3x+2
Slope of given line is -1/3, so slope of perpendicular line is 3.
The equation of line in point slope form with slope 3 and goes through the point (-5,4) is given below
y-4= 3 (x+5)
To find the equation in slope intercept form we need to find y intercept
4=3(-5)+b
4=-15+b
19=b
y=3x+19 is equation in slope intercept form.
The equation in standard form is 3x-y+19=0
Hence, equation of line in point slope form is y-4= 3 (x+5), y=3x+19 is equation in slope intercept form and equation in standard form is 3x-y+19=0.
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How do you find a polynomial?
Answer:
To find a polynomial, you must identify the terms, coefficients, and degrees. The degree of a polynomial is the highest exponent of the variable in the equation. The coefficients of a polynomial are the values that are multiplied by the variables. The terms of a polynomial are the pieces of the equation, including the coefficients and the variables. After identifying the terms, coefficients, and degree of the polynomial, you can write it in standard form.
Step-by-step explanation:
What is a proof formula?
A mathematical proof is an inferential justification for a mathematical claim that demonstrates how the premises logically support the conclusion.
Result for an image A proof formula:
There are numerous techniques to demonstrate something; we'll talk about three of them: direct proof, proof by contradiction, and proof by induction. We'll discuss each of these proofs, including what they are and when and how to use them.
Proof: If n is an integer, then. We shall demonstrate the converse statement, "if n is divisible by 4, then n is divisible by 2," in order to demonstrate that "if n is not divisible by 2, then n is not divisible by 4." Let's say n can be divided by 4.
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When a transversal cuts parallel lines, how can one angle measurement be used to determine all of the other measurements?
Answer: If two parallel lines are cut by a transversal, then corresponding angles are congruent.
Step-by-step explanation:
Eight workers are hired to harvest strawberries from a field. Each is given a plot with an area of 72 ft² What is the total area
strawberry field?
Answer:
576 ft squared
Step-by-step explanation:
8 x 72 ft= 576 total area
Hope this helps!
The table shows that the total cost of a ride-sharing trip, y, is a function of the distance traveled, a.
What is the rate of change and what does it mean?
2; the ride costs $2 per mile.
43; the ride costs $3 per mile.
2; it costs $2 as soon as you start the ride.
4) 3; it costs $3 as soon as you start the ride.
Distance (mi), Total Cost ($). y
2
5
8
11
14
0
1
2
3
4
Answer:3; the ride costs $3 per mile
Step-by-step explanation:
Rate of Change of the function is 3. then the ride costs $3 per mile.
What is the average rate of change?The average Rate of Change of the function f(x) can be calculated as;
[tex]f(x) = \dfrac{f(b) - f(a)}{b-a}[/tex]
We are given the total cost of a ride-sharing trip, y, is a function of the distance traveled,
Distance (mi), Total Cost ($). y
2 0
5 1
8 2
11 3
14 4
Therefore,
Rate of Change of the function
(5 - 2) / (1- 0)
= 3 / 1
Hence, we can conclude that the ride costs $3 per mile.
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What are the 5 ways triangles are congruent?
The correct answer is the 5 ways to find if two triangles are congruent are SSS, SAS, ASA, AAS and HL.
Two triangles are congruent if and only if they have the same three sides and angles.
SSS (side, side, side): SSS, which stands for "side, side, side," denotes that there are two triangles with identical angles on all three sides. The triangles are congruent if their third sides are the same as those of another triangle.
SAS (side, angle, side): "Side, Angle, Side" stands for two triangles whose two sides and one included angle are known to be equal. The triangles are congruent if two sides and the included angle of one triangle equals the corresponding sides and angle of another triangle.
ASA (angle, side, angle): ASA, which stands for "angle, side, angle," denotes the existence of two triangles whose included side and two known angles are equal. The triangles are congruent if two angles and the included side of one triangle match the corresponding angles and side of another triangle.
AAS (angle, angle, side): AAS, which stands for "angle, angle, side," denotes the equality of the non-included side and two angles in two triangles. The triangles are congruent if two of one triangle's angles and its excluded side are equal to the corresponding angles and sides of another triangle.
HL (hypotenuse, leg): The two triangles are congruent if one right-angled triangle's hypotenuse and one of its legs are equal to its corresponding hypotenuse and leg in another right-angled triangle.
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A certain forest covers an area of 2,000 square kilometers. Suppose that each year, this area decreases by 6%. What is the equation that best represents the area of the forest each year?
Hint: Use the formula y = P(1 + r)x.
y = 2,000(0.94)x
y = 2,000(1.06)x
y = 2,000(0.06)x
y = 2,000(1.94)x
The equation that best represents the area of the forest each year is A. y = 2,000(0.94)^x.
What is an equation?An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.
Since the certain forest covers an area of 2,000 square kilometers and each year, this area decreases by 6%.
The equation will be:
= 2000(1 - 6%)^x
= 2000(0.94)^x
In conclusion, the correct option is A.
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Directions: Find the value of each variable.
11) x=?
y=?
12) x=?
y=?
13) x=?
y=?
14) x=?
y=?
15) x=?
y=?
z=?
The value of the variables x and y are,
11) x = 13, y = 18.4
12) x = 6.9, y = 8.
What is right angle triangle?
A right triangle is a triangle with one angle at a right angle, meaning that two of its sides are perpendicular. It is also known as a right-angled triangle, an orthogonal triangle, or more commonly as a rectangled triangle. Trigonometry's foundation is the right triangle's relationship between its sides and other angles.
11)Let the given triangle is a right angle triangle.
So we can use trigonometric ratio,
[tex]tan(45) = \frac{x}{13} \\x = 13(tan(45))\\x = 13[/tex]
Using this to find the value of y.
[tex]sin(45) = \frac{x}{y} \\sin(45) = \frac{13}{y} \\y = \frac{13}{sin(45)} \\y = 18.4[/tex]
So, the values of x and y are x = 13 and y = 18.4.
12) The given triangle is a right angle triangle.
So we can use trigonometric ratio,
[tex]tan(30) = \frac{4}{y}\\ y = \frac{4}{tan(30)} \\y = 6.9[/tex]
Now to find the value of x.
[tex]sin(30) = \frac{4}{x} \\x = \frac{4}{sin(30)} \\x = 8[/tex]
Hence, the values of x and y are, x = 6.9 and y = 8.
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(1 point)
Solve this inequality, and write your answer in interval notation.
|x|>-5
Please type:
- int for oo,
- no solution if there are no real solutions
- U for the union symbol U
You have attempted this problem 8 times.
Your overall recorded score is 0%
You have unlimited attempts remaining.
Answer: [tex](-\infty, \infty)[/tex]
Step-by-step explanation:
Absolute value is always non-negative.
Think back to our discussion on Negative Exponents. Why do we follow the steps that we do, specifically, why do we flip the number (reciprical)? Use the other laws of exponents to help gauge your thinking, but I want you to try to determine the meaning behind the process instead of just memorizing the steps. This might be a tough question to answer, so just do your best and we can discuss this again in class.
By using the law of exponents, it has been proved that
[tex]a^{-n} = \frac{1}{a^n}[/tex]
What are exponent?
Exponent tells us how many times a number is multiplied by itself.
For example : In [tex]2^4 = 2 \times 2 \times .... \times 2[/tex]
Here, 2 is multiplied by itself 4 times.
If [tex]a^m = a \times a \times a \times ..... \times a[/tex] (m times),
a is the base and m is the index.
The laws of exponents are
[tex]a^m \times a^n = a^{m+n}\\\\a^ m \div a^n = a^{m - n}\\\\a^ 0 =1\\\\a^{-m} = \frac{1}{a^m}\\\\(ab)^m = a^m \times b^m\\\\(\frac{a}{b})^m = \frac{a^m}{b^m}\\\\(a^m)^n = a^{mn}[/tex]
We know this law
[tex]a^p \times a^q = a^{p + q}[/tex]
Putting p = n and q = -n
[tex]a^n \times a^{-n} = a^{n + (-n)} = a^{n - n} = a^0 = 1[/tex]
So,
[tex]a^n \times a^{-n} = 1\\a^{-n} = \frac{1}{a^n}\\a^{-n} = \frac{1^n}{a^n}\\a^{-n} = (\frac{1}{a})^n[/tex]
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Using the unit circle, determine the value of sin 930°
Answer: -1/2
Step-by-step explanation:
Because the degrees given is greater than 360, we must find out what its simplest degree is. The easiest way to do this is to find the remainder of the argument divided by 360.
So let's start by doing 930 / 360. This will give you a remainder of 210 degrees. So now we are finding sin 210 degrees.
Remember that sin is the y-values of the unit circle. From 0 < θ < 180, sin θ is positive, so we automatically know it must be a negative answer. Now, 210 is 30 degree below the x-axis, meaning that coordinate pair of (cos 210 degrees, sin 210 degrees) is (-sqrt(3)/2 , -1/2). Tje y-value, -1/2, is your answer.
Answer:
c
Step-by-step explanation:
Fing
the lowest torm of the following fraction
1. 6-42
2. 14-28
The lowest form of 6/42 is 1/7 and,
the lowest form of 14/28 is 1/2.
What is the lowest form of fraction?
When there is no common factor between the fraction's numerator (top) and denominator (bottom), the fraction is said to be in its simplest form. This is also known as its Lowest form.
In fraction 6/42, both denominator and numerator have common factor as 6, So we divide the denominator and numerator by 6.
Hence, we get 1/7.
Similarly, In fraction 14/28, both denominator and numerator have common factor as 14, So we divide the denominator and numerator by 14.
Hence, we get 1/2.
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What is a prime multiple?
The multiples of a number are numbers found by multiplying the original number by any whole number. Prime multiples are number which multiply each other and form a prime
What are Prime Numbers ?
A prime number is a number that is only divisible by 1 and itself. So, prime numbers have only two factors, 1 and the number itself.
This means these numbers cannot be divided by any number other than 1 and the number itself without leaving a remainder.
Numbers that have more than 2 factors are known as composite numbers.
For example :
The factors of 3 are 1 and 3.
Therefore, the prime multiples of 3 are 1 and 3.
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please somebody help me!!! this assignment is called; Factor Quadratic when a=1
The quadratic equations and their factors are simplified below
Quadratic EquationA quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax² + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term. The first condition for an equation to be a quadratic equation is the coefficient of x² is a non-zero term(a ≠ 0). For writing a quadratic equation in standard form, the x² term is written first, followed by the x term, and finally, the constant term is written. The numeric values of a, b, c are generally not written as fractions or decimals but are written as integral values.
1) (x - 5)(x - 5) = x² - 5x - 5x + 25 = x² -10x + 25
2) (x + 2)(x + 9) = x² + 2x + 9x + 18 = x² + 11x + 18
3) (x + 2)(x + 3) = x² + 2x + 3x + 6 = x² + 5x + 6
4) (x + 1)(x + 2) = x² + x + 2x + 2 = x² + 3x + 2
5) (x - 3)(x - 3) = x² - 3x - 3x + 9 = x² - 6x + 9
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I need help bxbcbcbcbcbcbcbcbcbcb
The shape of Keisha's rectangular shaped planter would be the shape with the dimensions shown in the image below.
What is the Volume of a Rectangular Box?The volume of a rectangular box = length × width × height.
The shape of the planter is a rectangular box.
Given that the rectangular shaped planter would be filled first by 4 in. of rocks, it means the height of the rectangular shaped planter that the rock will occupy up to would be 4 in.
Find the volume the rock would fill:
Height = 4 in.Length = 10 inWidth = 10 in.Volume occupied by the rocks in the rectangular shaped planter = (10)(10)(4) = 400 in.²
If the soil to be filled must be exactly 800 in.², then the total volume of the shape of the rectangular planter that would be used would be: 400 + 800 = 1,200 in.².
From the options given, the last shape that has a height of 12 in., length of 10 in, and width of 10 in will have a volume = (12)(10)(10) = 1,200 in.².
Therefore, the last shape in the diagram below could be the shape of Keisha's rectangular shaped planter.
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what is the range of a square root function
There is no fixed range for a square root function.
Range is the set of all the output values that a function can take. In other words, it is simply the set of all values that the dependent variable can take for the function to exist. It is also known as the co-domain.
Let us take a simple square root function given as-
y = [tex]\sqrt{x}[/tex]
Here, y is the dependent variable. We know that the square root of any number cannot be negative. Thus, y can take only positive values. Therefore, the range of a square root function is [0, ∞)
However, this is not always the case, there are various translations of a square root function for which the range might differ. For example, if we have a function as follows-
y = [tex]-\sqrt{x}[/tex]
Here, because of the minus sign, y will always be negative and thus the range will be (-∞, 0]
Hence, we conclude that there is no fixed range for a square root function.
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Please help will mark Brainly
The rate of change in the given interval would be 1.25 ft/s.
What is the rate of change?
The slope of a graphed function is determined using the average rate of change formula. Divide the change in y-values by the change in x-values to find the average rate of change.
By observation, we can take the points from the graph in between the given interval.
The points would be (3, 2.5) and (5, 4)
Then the rate of change = y2 - y1/ x2 - x1
= 4 - 2.5/5 - 3
= 2.5/2
= 1.25 ft/s.
Hence, the rate of change in the given interval would be 1.25 ft/s.
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