Answer:
S1 = 294 square mm
Step-by-step explanation:
7 * 7 = 49
49 mm per side on the large cube
a cube has 6 faces, or sides
so
49 * 6 = 294 mm
Place the numbers in order from least to greatest.
the inequality x>3 is read as x is greater than 3.The solution set of this equality is represent by the blue ray and includes all numbers greater than 3.
How many numbers are greater than 3?
The amount of numbers that are greater than 3 is given as follows:
Infinity.
How to model the inequality?The four inequality symbols, along with their meaning, are presented as follows:
> x: greater than x.< x: less than x.≥ x: at least x.≤ at most x.The inequality for this problem is defined as follows:
x > 3.
Meaning that the graph is composed by all the values that are greater than 3.
Perhaps the biggest difference between an equality and an inequality is the number of solutions. While an equality has a fixed number of solutions, an inequality has infinity solutions, as all the values in the solution set are solutions to the inequality.
(the solution set in this problem is all the values to the right of x = 3).
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Mario and Russell plot a triangle on a coordinate grid and then perform a
rotation and a translation. Russell thinks the original triangle and final triangle
are congruent but Mario disagrees. Which student is correct and why?
Russell is correct. Since neither rotations no translations preserve distance, the
triangles are congruent.
O Mario is correct. Since neither rotations not translations preserve distance, the
triangles are not congruent.
Mario is correct. Since both rotations and translations preserve distance, the triangles
are congruent.
►
Russell is correct. Since both rotations and translations preserve distance, the
triangles are congruent.
Since two triangle are considered to be congruency if each of their 3 sides, and Mario is correct, the correct response is SSS.
How may a triangle's congruence be demonstrated?If a triangle's size and shape are a perfect match, it is said to be congruent. The symbol is contained in the word "congruent". The three sides and three angles of two triangle are said to be congruent when their three sides and three angles coincide.
Here,
As illustrated below, start by writing the names of the triangles' vertices, starting with triangles DAB and BCD.
AB = CD
DA = BC
Side BD is the same in both triangles, therefore
BD = BD
The fact that the triangle DAB & BCD have the same number of angles on each side indicates that they are congruent and utilise the SSS property of a congruence triangle.
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Add the expreion (-4/5t 5/3) and (-3 2t)
a)-19/5t 11/3
b)13/15t - 1
c)-4/3t 1
d)6/5t - 4/3
The addition of the algebraic expression is = [tex]\frac{6}{5} t - \frac{4}{3}[/tex], so option (d) is correct.
Given that,
The expression (-4/5t + 5/3) and (-3 + 2t)
The addition of algebraic expressions requires categorizing the terms in an algebraic expression into two types - like and unlike terms.
An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.). ...
These expressions are represented with the help of unknown variables, constants and coefficients.
Then, take up the like terms and add them.
The addition of algebraic expression is;
= [tex]-\frac{4}{5} t + \frac{5}{3} -3+2t[/tex]
= [tex]-\frac{4}{5} t+2t+\frac{5}{3} -3[/tex]
= -0.8t + 2t + 1.66 - 3
= 1.2t - 1.34
= [tex]\frac{6}{5} t - \frac{4}{3}[/tex]
Therefore,
The addition of the algebraic expression is = [tex]\frac{6}{5} t - \frac{4}{3}[/tex], so option (d) is correct.
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Can somebody help me?
The function g is given in three equivalent forms. Which form most quickly reveals the vertex?
Choose 1 answer:
(Choice A) A g(x)=3(x+3)(x-1),
(Choice B) B g(x)=3x^2+6x-9
(Choice C) C g(x)=3(x+1)^2-12
What is the vertex?
Since the function g is given in three equivalent forms, a form which most quickly reveals the vertex is: C. g(x) = 3(x + 1)² - 12.
The vertex is equal to (-1, -12).
What is the vertex form of a quadratic equation?In this exercise, you are required to determine and select the vertex form of a function g that is written in three equivalent forms. Mathematically, the vertex form of a quadratic equation is given by this formula:
y = a(x - h)² + k
Where:
h and k represents the vertex of the graph.a represents the leading coefficient.Based on the information provided, we can reasonably infer and logically deduce that a mathematical expression which quickly reveals the vertex of the quadratic equation is given by g(x) = 3(x + 1)² - 12.
Since the directrix is horizontal, the axis of symmetry would be vertical. Additionally, the distance (a) from directrix to vertex on the axis of symmetry is equal to 3.
In conclusion, the vertex of this quadratic equation is given by the ordered pair (-1, -12).
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I just need to know what kind of polynomial expression and the amount of terms
For the given bi-quadratic polynomial with 4 terms, the constant is -1/6, the leading term is -9x⁴ and the leading coefficient is -9.
What is a polynomial?When two or more algebraic terms are added, subtracted, or multiplied (no division), the result is a mathematical expression known as a polynomial. Constants, positive exponents, and at least one variable are all commonly present in polynomial expressions.
Consider the given polynomial,
The highest power of the variable is 4. Therefore this type of polynomial is called a bi-quadratic polynomial.
The portions of the equation that are often separated by "+" or "-" signs are known as polynomial terms. The number of terms in the above equation is 4.
The term which does not contain any variables are called constant. For the given polynomial the constant is -1/6.
The term with the largest power of the variable is the leading term. The leading term's coefficient is the leading coefficient.
For the above polynomial, the leading term is -9x⁴ and the leading coefficient is -9.
Therefore the above for the given bi-quadratic polynomial with 4 terms, the constant is -1/6, the leading term is -9x⁴ and the leading coefficient is -9.
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How do you find the length of a segment with the midpoint and endpoint?
To find the length of a line segment given the coordinates of the midpoint and one endpoint, you can use the distance formula. The distance formula is:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Where (x1, y1) and (x2, y2) are the coordinates of two points, and d is the distance between the points.
Given the midpoint (mx, my) and one endpoint (ex, ey) you can use the following steps to find the length of the segment:
Calculate the difference in the x-coordinates and square it: (ex - mx)^2Calculate the difference in the y-coordinates and square it: (ey - my)^2Add the two values from steps 1 and 2Take the square root of the result from step 3. This is the length of the line segment.For example, if the midpoint of a segment is (5,7) and one endpoint is (7,10), the length of the segment is:
d = √((7-5)^2 + (10-7)^2)
d = √((2)^2 + (3)^2)
d = √(4+9)
d = √13
the length of the segment is √13 units.
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In a certain city, each block is about 275
meters long. If the post office is 13 blocks
away from the library, approximately how
many miles is it from the post office to the
library? Round your answer to the nearest
tenth.
Using linear equations, it is 3570metre from the post office to the
library
What is a linear equation ?
A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form
Ax + B = 0
e.g. x-10=0. Here, x is a variable, A is a coefficient and B is constant.
The standard form of a linear equation in two variables is of the form
Ax + By = C
e.g. 2x-4y=10. Here, x and y are variables, A and B are coefficients and C is a constant.
Now,
Length of each block=275 meter
let's Create a linear equation from this i.e. 275x where x=number of blocks.
No. of blocks from post office to the library = 13 (x=13)
so, distance of post office to the library= 275*13
=3575meter
≈3570 meter (round to nearest 10th)
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7 1/3t - (10 2/3t - 6)
Answer:
[tex]-3 \frac{1}{3}t+6[/tex]
Step-by-step explanation:
Given expression:
[tex]\sf 7\frac{1}{3}t-\left(10 \frac{2}{3}t-6\right)[/tex]
Remove the parentheses:
[tex]\implies \sf 7\frac{1}{3}t-10 \frac{2}{3}t+6[/tex]
Factor out the common term t:
[tex]\implies \sf \left(7\frac{1}{3}-10 \frac{2}{3}\right)t+6[/tex]
Change the mixed numbers into improper fractions:
[tex]\implies \sf \left(\dfrac{7 \cdot 3+1}{3}-\dfrac{10 \cdot 3+2}{3}\right)t+6[/tex]
[tex]\implies \sf \left(\dfrac{22}{3}-\dfrac{32}{3}\right)t+6[/tex]
Subtract the fractions:
[tex]\implies \sf \left(\dfrac{22-32}{3}\right)t+6[/tex]
[tex]\implies \sf \left(\dfrac{-10}{3}\right)t+6[/tex]
Convert the improper fraction back into a mixed number:
[tex]\implies -3 \frac{1}{3}t+6[/tex]
Could the points A(-2,1), B(4,7), and C(1,4) be three vertices of rectangle ABCD?
O No, since AB and BC are not perpendicular.
OYes, since a fourth point can always be determined to form a rectangle.
OYes, since AB and BC form a right angle.
O No, since AB and BC are not parallel.
Since, AB and BC are not perpendicular,
No, Points A(-2,1), B(4,7), and C(1,4) cannot be three vertices of rectangle ABCD.
The correct option is A.
What is rectangle?A rectangle is a quadrilateral in which all the angles are equal and the opposite sides are equal and parallel.
A rectangle is a closed two-dimensional figure with four sides, all the angles of a rectangle are equal to 90°.
Given points
A(-2,1),
B(4,7), and
C(1,4)
For being vertices of rectangle
Angle between line segment AB and BC should be 90°.
Slope of line AB
m = (y - y')/(x-x')
m = (7 - 1)/(4 - -2)
m = 6/6
m = 1
Slope of line BC
m' = (y - y")/(x - x")
m' = (7 - 4)/(4-1)
m' = 3/3 = 1
Since slope of the two lines is same that is both are parallel, which is only possible when A, B, C are in a straight line.
Hence, points A(-2,1), B(4,7), and C(1,4) cannot be three vertices of rectangle ABCD.
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What is the area of the triangle?
2 m
4 m
3 m
square meters
first
Semi perimeter (S)=(2+4+3)/2
=9/2=4.5
now
area=
[tex] \sqrt{4.5(4.5 \times 2)(4.5 \times 4)(4.5 \times 3)} [/tex]
[tex] \sqrt{s( s- a)( s-b )( s- c)} [/tex]
which is equal to
99.20
What is the value of 9^−6/9^−4?
Answer:
[tex]\frac{1}{81}[/tex]
Step-by-step explanation:
using the property of exponents
• [tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]\frac{1}{a^{(n-m)} }[/tex] , then
[tex]\frac{9^{-6} }{9^{-4} }[/tex]
= [tex]\frac{1}{9^{(-4-(-6))} }[/tex]
= [tex]\frac{1}{9^{(-4+6)} }[/tex]
= [tex]\frac{1}{9^2}[/tex]
= [tex]\frac{1}{81}[/tex]
Answer:
1/81
Steps:
move 9^-6 to the denominator using the negative exponent rule
b^-n=1/b^n
1/9^-4 x 9^6
Multiply 9^-4 by 9^6 by adding the exponents
1/9^2
Raise 9 to the power of 2
1/81
Please help it’s argent
Answer:
40%
Step-by-step explanation:
no of children = 16
no of adult = 24
total = 40
percentage of people who are children =
[tex] \frac{16 \\ }{40} \times 100\%[/tex]
[tex] = \frac{1600 \\ }{40} \%[/tex]
[tex]40\% \\ [/tex]
i hope this helped
Equation to represent lengths of triangle DEF
Answer:
Step-by-step explanation:
watch the other parralleles cotés
The Pythagorean Theorem, one of the most well-known mathematical formulas, tells us how a right triangle's sides relate to one another. The hypotenuse, along with the two legs, make up a right triangle. The hypotenuse, the longest side of the right triangle and the side opposite the right angle, is where the two legs of a right triangle come together at a 90° angle.
Equation to represent the length -
a2 + b2 = c2
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Isabella spends $4.87 on paintbrushes and paint. How many of each item does she buy? $0.99 each for a jar of paint. $0.95 each for a paintbrush
Answer:
Isabella can buy together 5 paintbrushes ( p ) and jars of paint ( p ) : j + p = 5, She can`t buy 4 items ( because 4 * $0.99 = $3.96 < $4.87 ) and she also can`t buy 6 items ( 6 * $0.95 = $5.70 > $4.87 ). So: p = 5 - j. Another equation is: 0.95 * ( 5 - j ) + 0.99 j = 4.87, 4.75 - 0.95 j + 0.99 j = 4.87; 0.04 j = 0.12; j = 0.12 : 0.04; j = 3, p = 5 - 3 = 2. We can prove it: 0.95 * 2 + 0.99 * 3 = 1.90 + 2.97 = 4.87. Answer: Isabella buys 2 paintbrushes and 3 jars of paint.
Urgent help needed urgent urgent
The polynomial for x2 -4 in function notation is (x+2)(x-2) since a function produces an output from an input.
what is function ?Mathematics deals with numbers and their variants, equations and related structures, shapes and their locations, and locations where they might be found. The term "function" describes the connection between a group of inputs, each of which has a corresponding output. A function is an association between inputs and outputs where each input results in a single, unique output. A domain and a codomain, or scope, are assigned to each function.The input is an x. On functions, one-to-one functions, many-to-one functions, within functions, and on functions are the four main categories of functions that are available.
given
A function creates an output from an input.
The name of the function, f (x) f(x) f(x)f, left parenthesis, x, right parenthesis, and the output, f (x) f(x) f(x)f, left parenthesis, x, right parenthesis, are all enclosed in parentheses.
x2 -4
(x2 - 2*2)
= (x+2)(x-2)
The polynomial for x2 -4 in function notation is (x+2)(x-2) since a function produces an output from an input.
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help please and thank you
The product of a, b and c would be 6.
What is an expression?
An expression is a mathematical phrase that can contain numbers, variables, and operators. Expressions do not contain an equal sign and they can't be solved for a single value. They are used to represent a value or a set of values.
The given expression is [tex]\frac{\sqrt[4]{16xy^4}}{x^{\frac{1}{2}}y^{\frac{1}{2}}}[/tex]
In order to write the expression in the form of [tex]ax^by^c[/tex], we need to simplify it.
First, we simplify the fourth root of [tex]16xy^4[/tex] by taking the fourth root of 16, which is 2. So, the expression becomes
[tex]2\frac{xy^4}{x^{\frac{1}{2}}y^{\frac{1}{2}}}[/tex]
Next, we simplify the fraction by canceling out the[tex]x^{\frac{1}{2}} $$ and $ y^{\frac{1}{2}}[/tex] from the numerator and denominator. This gives us [tex]2xy^3[/tex]
So the expression in the form of [tex]ax^by^c[/tex] is [tex]2xy^3[/tex], where a = 2, b=1, and c=3.
the product of a, b, and c is 2 * 1 * 3 = 6.
Hence, the product of a, b and c would be 6.
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3 1/2k + 3/4 = -7/8
50 points reward! I need help immediately.
The value of k in the given equation is -0.104839
What is the equation in maths?A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is utilized.The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.Finding an equation's solutions, which are values (numbers, functions, sets, etc.) that satisfy the equation's condition and often consist of two expressions connected by an equals sign, is known as solving an equation in mathematics.The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.Evaluate
[tex]\frac{31}{2}[/tex]k + [tex]\frac{3}{4}[/tex] = - [tex]\frac{7}{8}[/tex]
Move the constant to the right side
[tex]\frac{31}{2}[/tex]k = [tex]-\frac{7}{8} - \frac{3}{4}[/tex]
Subtract the terms
[tex]\frac{31}{2}[/tex]k = [tex]-\frac{13}{8}[/tex]
Multiply both sides
[tex]\frac{31}{2}[/tex]k x [tex]\frac{2}{31} = - \frac{13}{8} * \frac{2}{31}[/tex]
k = [tex]-\frac{13}{124}[/tex]
k = - 0.104839
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How would you classify angle 1 and angle 5?
Answer: Alternate Exterior Angles
Step-by-step explanation:
Simply, both angles are outside the paralell lines.
Alex has 2/4 quarts of chocolate milk left in a jug. In another jug he had 2 1/2 pints of chocolate milk . Can Alex pour the milk from both jugs into a third jug that has a capacity of 2 gallons.
Answer:
Yes, he can
Step-by-step explanation:
We have to find the total of Chocolate milk Alex has by taking
2 1/2 = 5/2
2/4 + 5/2 = 2/4 + 10/4 = 12/4 = 3 quarts of chocolate milk
1 gallon = 4 quart
And here, Alex only has 3 quarts of chocolate milk, so he can pour the milk from both jugs into a third jug.
What is an inequality Class 7?
An inequality is a mathematically explicable relationship between two expressions that can be represented by any of the following symbols: >, <, ≤, ≥, and ≠.
A mathematical statement known as an inequality uses the inequality symbol to represent the connection between two expressions. The terms on each side are not equal when there is an inequality sign present.
It suggests that the left and right expressions should be greater or smaller than one another, or the opposite. Literal inequalities are ones where the inequality symbols indicate the connection between two algebraic expressions.
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What two events are independent
The equation that must be true for event C and D to be independent are P(C│D) = P(C) and
P(D│C ) = P(D).
What are independent event ?Two events are independent if the occurrence of one event does not affect the chances of the occurrence of the other event. The mathematical formulation of the independence of events A and B is the probability of the occurrence of both A and B being equal to the product of the probabilities of A and B (i.e., P(A and B)
For two events C and D. For the two events to be independent events then;
P(C│D) = P(C∩ D)/ P(D) = P(C)
or
P(D│C) = P(D∩ C)/ P(C) = P(D)
For example if a fair die is rolled,
P(D ) = Probability of getting a 3
P(C) = Probability of getting an even number
P(C│D) = P(C∩ D)/ P(D)
P(C∩ D)= 1/3 × 1/2 = 1/6
P(C│D) = P(C∩ D)/ P(C) = 1/6 ÷ 1/3 = 1/2
therefore P(C│D) = P(C) and
P(D│C ) = P(D).
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-8r-3(-6-5r)=8-5(4-2r) show work pleaseeeee
Answer:
[tex]r=-2[/tex]
Step-by-step explanation:
First, apply the distributive property: A(B + C) = AB + AC
[tex]-8r-3(-6-5r)=8-5(4-2r)[/tex]
[tex]-8r+18+15r=8-20+10r[/tex]
Then, get all of the r's on one side.
[tex]-8r+18+15r=8-20+10r[/tex]
↓ subtract 18 from both sides
[tex]-8r+15r=8-2+10r[/tex]
↓ subtract 10r from both sides
[tex]-8r+5r=8-2[/tex]
Finally, solve for r by combining like terms, then dividing by -3.
[tex]-3r = \ 6\\\overline{\, -3 \: } \ \ \ \ \overline{-3}[/tex]
[tex]r = -2[/tex]
What if these particles is able to leave the atom?
1.Electrons
2.Protons
3.Neutrons
A chemical element's atom is a particular type of particle of substance. A positively charged electron or many negatively charged electrons encircle the central nucleus of an atom.
What if these particles is able to leave the atom?Electrons: If an electron leaves an atom, it is said to be ionized. Ionization can occur through various processes, such as collision with another particle or exposure to electromagnetic radiation.
Protons: Protons are found in the nucleus of an atom, and are held in place by the strong nuclear force. If a proton were to leave the nucleus, it would no longer be a stable atom and it would become an ion.
Neutrons: Neutrons are also found in the nucleus of an atom and are held in place by the strong nuclear force. If a neutron were to leave the nucleus, it would no longer be a stable atom, and it would become a different element.
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3 Look at the equation below.
y = 2x - 2
Which situation is best described by the
equation?
The temperature at 2:00 A.M. is 2°C and
rises 2° each hour for x hours.
The temperature at 2:00 A.M. is -2°C and
rises 2° each hour for x hours.
The temperature at 2:00 A.M. is 2°C and
drops 2° each hour for x hours.
The temperature at 2:00 A.M. is -2°C and
drops 2° each hour for x hours.??
Answer:the temperature at 2:00 am is 2C and drops 2 each hour for X hours
Step-by-step explanation:
A virus is spreading around Brookfield. At the moment, 685 people are infected. If the virus is
spreading at a rate of 13% each day, how many people in all will have caught the virus in 3
days?
If necessary, round your answer to the nearest whole number.
A virus spreading around Brookfield will infect 988 people in the next 3 days.
What is an equation?
A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").
Number of people infected by the virus = 685
The rate at which the virus is infecting = 13%
The virus is spreading at 13% rate each day.
To deduce the number of people who will get infected in next 3 days.
The final equation will be -
= 685 × ( 1 + 13%)³
= 685 × (113/100)³
= 685 × (1.13)³
= 685 × 1.442
= 987.77 ≈ 988
Therefore, the number of people who will get infected is 988.
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What is equality for Class 7?
In mathematics, equality refers to the relationship between two expressions or values, indicating that they are equivalent or have the same value.
For example, the equation "2 + 3 = 5" states that the left side of the equation (2 + 3) is equal to the right side of the equation (5). Equality can be represented using the symbol "=", which is called the equality sign or equal sign.
Equality can also be used in other mathematical concepts such as congruence, similarity, and equivalence. For example, two triangles are congruent if they have the same shape and size, two figures are similar if they have the same shape but different sizes, and two equations are equivalent if they have the same solutions.
Equality in mathematics is transitive, meaning that if a = b and b = c, then a = c, and reflexive, meaning that a = a for any value of a.
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what is three fourths plus one third
Answer:
3/4 + 1/3 = 13/12 = 1 1/2
Step-by-step explanation:
Why are all the multiples of 8 even?
All the multiples of 8 represents they are even numbers because of the following property:
Odd × even = Even
As given in the question,
Given number is equal to 8,
Multiples are those numbers which we get after multiplying the given number to any of the integer.
Multiples of 8 are equal to:
8, 16, 24, 32, 40, 48, 56, ..... so on.
Even numbers are those numbers which get divided by 2 without leaving the remainder.
Odd × odd = Odd
Even × even = even
Odd × even = Even
When we multiply any number by an even number result is always an even number.
Example:
2 (even) × 2(even) = 4(even)
2 (even) × 3 (odd ) = 6 (even)
Here
8 is an even number multiplying any integer to 8 is always an even number.
Therefore, all the multiples of given number 8 are always an even number as Odd × even = Even.
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