Answer:
[tex]x = -8[/tex]
Step-by-step explanation:
Let [tex]x[/tex] be the integer, then the consecutive integer is [tex]x + 1[/tex]. "3 times the next consecutive integer" means we should multiply [tex]x + 1[/tex] (the consecutive integer) by 3, giving us [tex]3 ( x + 1)[/tex].
We are told that the sum of [tex]x[/tex] and [tex]3(x + 1)[/tex] gives -29. Therefore, we can build an equation.
The sum of [tex]x[/tex] and [tex]3(x + 1)[/tex] can be expressed as [tex]x + 3(x + 1)[/tex].
Therefore,
[tex]x + 3(x + 1) = -29 \text{ // Distribute 3(x + 1)}\\x + 3 \times x + 3 \times 1 = -29\\\to x + 3x + 3 = -29 \text{ // Simplify}\\\to 4x + 3 = -29 \text{ // Subtract 3 from both sides}\\4x + 3 - 3 = -29 - 3\\\to 4x = -32 \text{ // Divide by 4 on both sides}\\\frac{4x}4 = -\frac{32}4\\\to x = -8[/tex]
8) Consider the following sets,
A = {x | x ≤ N}
B = {x-5 < x < 105, x ≤ R}
C = {x|x is a rational number, 10 < x < 80}
Find the cardinality of the set (A − C) n B.
The cardinality of the set (A − C) n B is 35 .
Cardinality of a set is defined as the number of elements in the mathematical set. It can be finite or infinite. For example, the set A = {1, 2, 3, 4, 5, 6} has cardinality 6. Because the set A has 6 elements. Set cardinality is also known as set size. A real number can be defined as a combination of rational and irrational numbers. They can be both positive and negative, denoted by the symbol "R". Natural number all count numbers starting at 1. N = {1 ,2 , 3 ,4, .....}We have given three sets A = {x | x ≤ N} where N is a natural number .
Then , set A will get values [tex]A= \{1,2,3,4,5......\}[/tex]
B = {x-5 < x < 105, x ≤ R} where R is a real number whose values is in domain of (- ∞ ,∞)
Then , set B will get values [tex]B=(-5,105)[/tex]
C = {x|x is a rational number, 10 < x < 80} rational number which can expressed in [tex]\frac{p}{q}[/tex] where [tex]q\neq 0[/tex] .
Then , set C will get values [tex]=(10,80][/tex]
According to the question
(A − C) n B [tex]=(\{1,2,3,4,5 ........\}-(10,80] \sqcap (-5,105)[/tex]
[tex]=\{1,2,3,4,5,6,7,8,9,10,81,82,83 .......\} \sqcap (-5,105)\\[/tex]
={1,2,3,4,5,6,7,8,9,10,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103, 104 ,105}
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I would appreciate the help please!!
The graph of y = x2 –7x +12 is a parabola with x-intercepts at: {-3 and -4, or 3 and 4} and a vertex that is the: {lowest or highest} point on the curve.
Thanks in advance!
The graph of y = x2 –7x +12 is a parabola with x-intercepts at: {-3 and -4, or 3 and 4} and a vertex that is the: the x-intercepts are 3 and 4
The vertex is the lowest point on the curve
we know that
The equation of a vertical parabola in vertex form is equal to
y = a [tex](x-h)^{2}[/tex] + k
where
(h,k) is the vertex of the parabola
if a>0 -----> then the parabola opens upward (a vertex is a minimum)
if a<0 -----> then the parabola opens downward (a vertex is a maximum)
In this problem we have
y = [tex]x^{2}[/tex] - 7x +12
a = 1
so
the parabola opens upward (a vertex is a minimum)
Find the x-intercepts of the quadratic equation
Equate the equation to zero
y = [tex]x^{2}[/tex] - 7x +12
Group terms that contain the same variable, and move the constant to the opposite side of the equation
[tex]x^{2}[/tex] - 7x = -12
Complete the square. Remember to balance the equation by adding the same constants to each side
[tex]x^{2}[/tex] - 7x + 12.25 = -12 + 12.25
[tex]x^{2}[/tex] - 7x + 12.25 = 0.25
Rewrite as perfect squares
[tex](x-3.5)^{2}[/tex] = 0.25
square root on both sides
(x - 3.5) = (+/-) 0.5
x =3.5(+/-) 0.5
x = 3.5+0.5=4
x = 3.5-0.5=3
therefore
the x-intercepts are 3 and 4
A parabola is an approximately U-shaped, mirror-symmetrical plane curve in mathematics. It corresponds to a variety of seemingly unrelated mathematical descriptions, all of which may be shown to define the same curves.
One definition of a parabola includes a line and some extent (the focus) (the directrix). The directrix isn't the main focus. The locus of points therein plane that is equally spaced apart from the directrix and the focus is known as the parabola. A right circular conical surface and a plane parallel to a different plane that is tangential to the conical surface intersect to form a parabola, which is additionally known as a conic section.
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a vacuum cleaner dealership sold 360 units in 2011 and 347 units in 2012 .
The number of units sold decreased and it decreased by
%decrese =4.23%
This is further explained below.
What percent did it decrease or increase?Generally, the equation for is mathematically given as
Number of sold 450 units in 2011
431 units in 2012
No of Sold units decrease, so the Percentage decreased.
[tex]\% \text { decrease } &=\frac{450-431}{450} \times 100 \\\\&=\frac{19}{450} \times 100 \\[/tex]
=4.23%
In conclusion, the percentage decrease is
%decrese =4.23%
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CQ
A vacuum cleaner dealership sold 450 units in 2011 and 431 units in 2012. Find the percent increase or decrease in the number of units sold.
Did the number of units sold decrease or increase?
What percent did it it decrease or increase?
can someone help it only 2 qestions 20 points
= 0.45
= 9/20
= (9 x 10)/(20 x 10)
= 90/200
1/2= (1 x 100)/(2 x 100)
= 100/200
0.045= 9/200
Descending order: 100/200, 90/200, 9/200 1/2, 45%, 0.04514)125%= 1.25
= 5/4
1 1/2= 3/2
1.26= 63/50
Descending order: 3/2 > 63/50 > 5/4 1 1/2 > 1.26 > 125%Lila makes a chart that has 8 tows and 4 columns. How many spaces are in her chart? Explain why Lila can use 8s facts or 4s facts to solve
Based on the fact that Lila made a chart that had 8 rows and 4 columns, the number of spaces in the chart is 32 spaces.
Lila can use 8s factors or 4 factors to solve because both 8 and 4 are factors of 32.
How to find the spaces created?The number of spaces can be found by the formula:
= Number of rows x Number of columns
= 8 x 4
= 32 spaces
Factors of 8 and 4 can be used for 32 because when a number is a factor of another number, then all the factors of the first number, are also the factors of the other number.
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Part A: What does CPI-W stand for?
Consumer Price Index for Urban Wage Earners and Clerical Workers (CPI-W) .
Describe the CPI-W?
The Consumer Price Index for Urban Wage Earners and Clerical Workers (CPI-W) is a monthly indicator of how prices for a market basket of goods and services have changed on average over time for urban wage earners and clerical workers.
What distinguishes the CPI-U from CPI-W?
In order to track retail prices as they effect all urban consumers, the CPI-U is a more comprehensive index. It includes around 87 percent of the population of the United States. The CPI-W, a more specialized indicator, tracks retail prices as they relate to hourly wage earners and office workers in metropolitan areas.Learn more about CPI-U
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what pair of numbers does the squared root of 23 fall between
The total payroll for a baseball team is 2.44 × 109 dollars, and the total payroll for a football team is 2.9 × 1011 dollars. How many more dollars is the football team's total payroll than the baseball team's total payroll?
l
which one of these are the answer /
0.46 × 109 dollars
2.8756 × 109 dollars
4.6 × 1011 dollars
2.8756 × 1011 dollars
The final answer is 2.8756 × [tex]10^{11}[/tex] is the football team's total payroll than the baseball team's total payroll.
The total payroll for a baseball team is 2.44 × [tex]10^{9}[/tex] dollars
The total payroll for a football team is 2.9 × [tex]10^{11}[/tex] dollars
How many more dollars is the football team's total payroll than the baseball team's total payroll
The total payroll for a football team = 2.9 × [tex]10^{11}[/tex] dollars = 290 × [tex]10^{9}[/tex]
The total payroll for a baseball team = 2.44 × [tex]10^{9}[/tex] dollars
To find the differentiate between foodball team payroll and the baseball team payroll subtract their payroll.
How many more dollars is the football team's total payroll = The total payroll for a football team - The total payroll for a baseball team
How many more dollars is the football team's total payroll = 290 × [tex]10^{9}[/tex] - 2.44 × [tex]10^{9}[/tex] = 287.56 × [tex]10^{9}[/tex] = 2.8756 × [tex]10^{9}[/tex] dollars
The main answer is 2.8756 × [tex]10^{11}[/tex] is the football team's total payroll than the baseball team's total payroll.
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-3 -2 -1 0 1 2 3 4 How can you find the length of CD
Number line
Answer:
3
Step-by-step explanation:
Because C is 1 and D is 4, so 4-1=3.
What is the next number
7, 11, 2, 18, -7, ?
Complete the model to find -9 + 9 Show your work
A 56-inch board is to be cut into three pieces so that the second piece is twice as long as the first piece and the third piece is 4 times as long as the first piece. If x represents the length of the first piece,
find the lengths of all three pieces?
The lengths of the 3 parts of the board x,y,z would be 7 inch, 14 inch, and 35 inch.
What exactly is proportion?A proportion is a mathematical equation that is predicated on the equality of two parameters.A proportion is a calculation that can be solved; a proportion is two ratios that are set equal to each other.Once I say that such a proportion is 2 ratios that really are equal to the other, I imply two fractions that really are equal to each other.If 3 pieces of 56 in. board have been cut into the ratio x: y: z,
The second piece y equals 2x and,
The third piece z equals 5x.
Now calculate the value of x:
x + y + z = 56
x + 2x + 5x = 5
8x = 56
x = 7 inches
Then, 2nd piece;
2x = 2(7)
2nd piece = 14 inches.
Now, the 3rd piece;
5x = 5(7)
3rd piece = 35 inches.
As a result, the lengths of the 3 parts x,y,z are 7 inches, 14 inches, and 35 inches, respectively.
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The admission fee to a carnival is $5.00, and each game costs an additional $1.50 to play. The carnival also has a
special admission price of $14 that includes unlimited games. What is the minimum number of games a customer
must play to make the special admission price less than paying for each game separately?
10 point for this. Simplify: 3x^2y^4\times 2x^6y
Answer:
[tex]6x^8y^5[/tex]
Step-by-step explanation:
[tex]3x^2y^4 \times 2x^6y \text{ // We should remind ourselves of the rule: }a^m \times a^n = a^{m + n}\\\\\to (3 \times 2)(x^2 \times x^6)(y^4 \times y^1)\\\\\to 6(x^{2 + 6})(y^{4 + 1})\\\\\\\to 6x^8y^5[/tex]
Find the exact value of each expression if 0° < θ < 90°
A. If cosθ = 5/13, find sin θ.
B. If cosθ = 4, find sec θ.
The values of the trigonometry will be:
If cosθ = 5/13, sin θ = 12 / 13.
If cosθ = 4, sec θ = 1/4.
How to illustrate the information?Adjacent = 5
Opposite = 12
Hypothenuse = 13
It should be noted that cosθ = 5/13. This implies that adjacent / hypothenuse = 5/13.
The sin θ will be:
= Opposite / Hypothenuse
= 12 / 13
When cosθ = 4, sec θ will be the reciprocal. This will be = 1/4.
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is this equivaleent with 9:15?????????????
Answer:yes
Step-by-step explanation:
yes, the ratio 36:60 is equivalent to the ratio 9:15.
if you really liked my answer, please rate, thanks, and award brainliest
hope this helped :)
Cuanto es:
5/6 x 2 =
Porfa es para una tarea
Answer: 1.66
For next time you can use calculator
Answer:
1.666
Step-by-step explanation:
5/6 × 2=5/3
=1.6666...
or you can use your calculator
Find the sum of 1 2/5 and the product of 3 and 8, and divide the result by 6
please help me im so lost
Using it's concepts, the domain of the composite functions are given as follows:
Domain of f(g(x)): x > 0.Domain of g(f(x)): x > 0 and x ≠ 1.What are the domain and the range of a function?The domain of a function is the set that contains all the values of the input of the function.The range of a function is the set that contains all the values of the output of the function.In a graph, the domain and the range are found as follows:
The domain is given by the values of x, present in the horizontal axis of the graph.The range is given by the values of y, present in the vertical axis of the graph.For the composite functions in this graph, we have that:
g(x) is defined only for x > 0, due to the asymptote, hence f(g(x)) will also be defined only for x > 0, meaning that the domain of f(g(x)) is x > 0.f(x) is defined for all real values, assuming all real values expect y = 1 as range. g(x) is defined for all values of x > 0, hence, considering the two restrictions, the domain of g(f(x)) is x > 0 and x ≠ 1.More can be learned about the domain of a relation at https://brainly.com/question/10197594
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The length of a rectangle is three times its width. If the perimeter is 132 inches, what is the length of the rectangle?
1. 48 inches
2. 16.5 inches
3. 49.5 inches
4. 18 inches
Please give an explanation (Do not just give an answer and take points or you will get reported)
Thank you :D
Given the perimeter, the numerical length of the rectangle is 49.5 inches.
Hence, option 3) 49.5 inches is the correct answer.
What is the length of the rectangle?The perimeter of a rectangle is expressed mathematically as;
P = 2( l + w )
Given the data in the question;
Let "x" represent the width of the rectangle.
Width w = xLength l = 3 × x = 3xPerimeter P = 132 inchesTo determine the length of the rectangle, first plug the given values into the formula above and solve for x.
P = 2( l + w )
132 = 2( 3x + x )
Apply distributive property
132 = 2(3x) + 2(x)
132 = 6x + 2x
132 = 8x
8x = 132
x = 132/8
x = 16.5
Now, the length of the rectangle will be;
Length l = 3x
Length l = 3( 16.5 )
Length l = 49.5 inches
Given the perimeter, the numerical length of the rectangle is 49.5 inches.
Hence, option 3) 49.5 inches is the correct answer.
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P and Q are points on the line 3y - 4x = 12 a) Complete the coordinates of P and Q. P (0, )) Q (,0) b) Plot points P and Q on the graph. Use the tool to plot the coordinates. c) Draw the line 3y - 4x = 12 for values of x from -3 to 3. -3-2 8 7 6 5 4 3 2 4 O -1 X
a) The coordinates of P and Q are; P = (0 , 4) , Q = ( -3 , 0).
b) The graph of points P and Q is plotted.
c) The line 3y - 4x = 12 for values of x from -3 to 3 is drawn.
What is defined as the coordinates?Coordinates are numerical distances or angles that uniquely defines points on two-dimensional (2D) surfaces or in three-dimensional (3D) space ( 3D ). Mathematicians, researchers, and engineers use a variety of coordinate schemes.The equation of line is given as;
3 y - 4 x = 12
a) To calculate the coordinates on the line are P and Q.
Let x = 0
3 y - 4 × 0 = 12
3 y + 0 = 12
y = 4
So, points P = (0 , 4)
Now, For y = 0;
3 × 0 - 4 × x = 12
0 - 4 × x = 12
x = - 3
So, points Q = ( -3 , 0)
Thus, points are P = (0 , 4) , Q = ( -3 , 0)
b) points P and Q on the graph.
The graph of the points P and Q for the coordinates of P = (0 , 4) , Q = ( -3 , 0) is plotted.
c) Draw the line 3y - 4x = 12 for values of x from -3 to 3.
The straight line for the values of x are drawn.
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2+2=6 why?
[tex]2 + 2 [/tex]who can answer this?
Answer:
2+2=4, not 6
Step-by-step explanation:
3 and 1/4 + 1 and 1/2
Answer:3 and 1/4 +1 is 4 and 1/4 assuming the and means plus then it’s
4 and 3/4
Does this help?
Step-by-step explanation:
five and five hundred sixty -two thousandths
Five and five hundred sixty -two thousandths written in expanded form, the result is 5 + (5 x 0.1) + (6 x 0.01) + (2 x 0.001).
What is expanded form?Writing in expanded form means that we add the digits of a number after they are multiplied by the power of 10 that corresponds with their position.
Tens will be multiplied by 10
Tenths will be multiplied by 0.1
Hundredths will be multiplied by 0.01
Thousandths will be multiplied by 0.001
These numbers are then added to each other.
Five and Five hundred sixty -two thousandths is 5.562 and when written in expanded form it becomes:
5 + (5 x 0.1) + (6 x 0.01) + (2 x 0.001)
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Simplify
5^3
5^7
leaving your answer in index form.
5x5=25 , 25x5= 125.
5x5=25, 25x5= 125, 125x5=625, 625x5=3125, 3125x5=15625, 15625x5= 78125.
Answer:
5^10
Step-by-step explanation:
When multiplying exponents with the same base, we add the exponents
5^3 * 5^7
5^(3+7)
5^10
cuales son las caracteristicas de las "diferencias de cuadrados perfectos'
It should be noted that the the characteristics of perfect square trinomial include:
A perfect square trinomial is a special polynomial consisting of three terms.
A perfect square trinomial is created by multiplying a binomial to itself.
Two of the terms in a perfect trinomial are perfect squares.
They can be used to solve quadratics by completing the square
What is a perfect square trinomial?It should be noted that a perfect square trinomial is an algebraic expression that is of the form ax² + bx + c, that has three terms.
It should be noted that it is obtained by the multiplication of a binomial with itself.
For example, it should be noted that x² + 6x + 9 is a perfect square polynomial that is obtained by multiplying the binomial (x + 3) by itself.
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What are the characteristics of perfect square trinomial
What two numbers are 3 away from -2 on the number line? Write the two answers in the space provided.
Answer:
-5, 1
Step-by-step explanation:
For every [tex]a[/tex] and [tex]x[/tex], the two numbers that are [tex]x[/tex] away from [tex]a[/tex] are [tex]a - x[/tex] and [tex]a + x[/tex].
Therefore, the two numbers that are 3 away from -2 are [tex]-2 - 3 = -5[/tex] and [tex]-2 + 3 = 1[/tex]
Construct a sample of 6 measurements whose mean is 15
Answer can not create a sample 2
Step-by-step explanation:
The number0.000000675 can be written in scientific notation as 6.75 x 10x . What is the value of x?
Answer:
-7
Step-by-step explanation:
The decimal 0.000000675 can be written as 6.75 x 10^-7 in scientific notation. To write a decimal in scientific notation, you need to count how many decimal places the decimal needs to be moved in order to get a number with 2 decimals after it (if that makes sense). In this case, you need to move the decimal point 7 places to the right, so the value of x is -7. The x value is negative if you need to move the decimal to the right and positive if you need to move the decimal to the left.
SOMEONE HELP PLEASE I NEED THIS QUESTION TO BE ANSWERED. PICTURE ALREADY ATTACHED.
Answer: Day 50
:-]
Step-by-step explanation: 20/0.4
Step-by-step explanation:
she starts with 20 pounds of rice (1 bag).
every day she uses 0.4 pounds.
to have 1.6 pounds left means she used 20-1.6 = 18.4 pounds.
so, the question really is : how many days until she used 18.4 pounds ?
that is
18.4 / 0.4 = 46
that means at the end of day 46 she will need to order a new bag.