Answer:
dividimos los 42 dejando 12 para cada 1 sobran 6 pies para el primero le aumentamos 4 al segundo 2 y el ultimo se quedaria asi y asi tendria 2 pies de longitud mas que el anterios y el mas largo tendria 16 pies el mediano 14 y el mas pequeño 12
What is the solution to the inequality |2x + 3| < 7?
4 < x < 10
–5 < x < 2
x < 4 or x > 10
x < –5 or x > 2
The solution of the given inequality is x < –5 or x > 2
What are Inequality equations:Equations are not always balanced on both sides using an "equal to" symbol in mathematics. Sometimes it can be about a "not equal to" relationship, meaning that something is greater than or lower than another.
In mathematics, an inequality is a relationship between two numbers or other mathematical expressions that results in an unequal comparison. Inequalities are the name given to certain algebraic mathematical expressions.
Here we have
|2x + 3| < 7
=> 2x + 3 > 7 or 2x + 3 < - 7
Take 2x + 3 > 7
Add - 3 on both sides
=> 2x + 3 - 3 > 7 - 3
=> 2x > 4
Divide by 2 into both sides
=> 2x/2 > 4/2
=> x > 2
Take 2x + 3 < - 7
Add - 3 on both sides
=> 2x + 3 - 3 < - 7 - 3
=> 2x < -10
Divide by 2 into both sides
=> 2x/2 < -10/2
=> x < -5
Therefore,
The solution of the given inequality is x < –5 or x > 2
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19) The function C(x) = 25x+75 represents the labor cost (in dollars) for Bob's Auto Repair to replace
your alternator, where x is the number of hours. The table below shows sample labor costs from its main
competitor, Budget Auto Repair. The alternator is estimated to take 5 hours of labor. Which company
would you hire? Explain.
Hours 1,2,3
Cost
$90 $130 $170
we can see that the function C(x) = 25x + 75 represents the labor cost (in dollars) for Bob's Auto Repair to replace your alternator, where x is the number of hours. We can use this function to find the cost of replacing an alternator that is estimated to take 5 hours of labor.
C(5) = 25(5) + 75 = 125 + 75 = 200
We also have the labor cost for the main competitor, Budget Auto Repair, in a table format.
Hours Cost
1 $90
2 $130
3 $170
We can see that the cost of labor increases as the number of hours increases. From the information provided it's hard to say which company would be cheaper to hire, however the company with the function C(x) = 25x + 75 would be cheaper if the alternator takes more than 4 hours of labor, otherwise Budget Auto Repair would be cheaper.
It's important to check the warranty, prices of parts, and reputation of both companies. If a company has a good reputation and a good warranty, it may be worth paying a little more for labor.
It's also a good idea to get a second opinion or ask for a quote from both companies before making a decision.
In conclusion, it's hard to say which company would be cheaper to hire based on the information provided, but it's recommended to check the warranty, prices of parts, and reputation of both companies, and to get a second opinion or quote from both companies before making a decision.
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What are alternative forms of genes found on chromosomes called?
Allele are alternative forms of genes found on chromosomes. Humans are known to be diploid organisms because they have two alleles at each genetic locus, with one allele inherited from each parent.
What are chromosomes?Chromosomes are long molecules of DNA that contain some or all of an organism's genetic material. In most chromosomes, very long, thin strands of DNA are coated with packaging proteins. In eukaryotic cells, the histones are the most important of all proteins. These proteins, with the help of chaperone proteins, bind and condense DNA molecules to maintain their integrity. These chromosomes have complex three-dimensional structures that play important roles in transcriptional regulation.
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Somebody help please I don’t understand!!
A rate is a ratio comparing quantities of different items. A unit rate is a rate with 1 in the denominator.
How to calculate unit rate?A rate is a ratio comparing quantities of different items. A unit rate is a rate with 1 in the denominator. If you have a rate, such as price per some number of items, and the quantity in the denominator is not 1, you can calculate unit rate or price per unit by completing the division operation: numerator divided by denominator.
Examples of How to Find Unit Rate or Unit Price
We want to know the price per apple unit so we set up a ratio with the number of apples in the denominator. The total price goes in the numerator. So the fraction is 1.80/3.Complete the division: 1.80 ÷ 3 = .60. You can conclude that the per apple price unit rate is $0.60/1. Ryan paid a unit price of $0.60 per apple (60 cents per 1 apple = .60/1).We want to know the number of mugs made per hour unit so we set up a ratio with hours in the denominator. The total number of mugs made per day goes in the numerator. So the fraction is 176/8.Complete the division: 176 ÷ 8 = 22. You can conclude that the per hour mug-making unit rate is 22/1. The pottery store makes 22 mugs per hour (22 mugs per 1 hour = 22/1).To learn more about unit rate refers to;
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What is an inequality statement in math?
A statement of an order relationship between two numbers or algebraic expressions is known as an inequality in mathematics. It can be greater than, greater than or equal to, less than, or less than or equal to.
Using the inequality symbol, a mathematical statement known as an inequality depicts the relationship between two expressions. An inequality symbol denotes that the terms on each side are not equal.
It indicates that the expressions on the left and right should be bigger or less than one another, or vice versa. Literal inequalities are those where the relationship between two algebraic expressions is described by the inequality symbols.
According to the definition, a relationship is considered to be an inequality if it involves two real numbers or algebraic expressions and uses the symbols “>”, “<”, “≥”, “≤”.
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A young umo wretler decided to go on a pecial high-protein diet to gain weight rapidly. After
11
1111 month, he weighed
140
140140 kilogram. He gained weight at a rate of
5. 5
5. 55, point, 5 kilogram per month. Let
y
yy repreent the umo wretler' weight (in kilogram) after
x
xx month. Complete the equation for the relationhip between the weight and number of month
The linear equation for the relationship between the weight and number of months is y = 5.55x + 78.95.
First-order equations include linear equations. In the coordinate system, linear equations are defined for lines. A linear equation in one variable is one in which there is a homogeneous variable of degree 1 (i.e., just one variable). Multiple variables may be present in a linear equation. Linear equations with two variables, for example, are used when a linear equation contains two variables.
We know that the sumo wrestler's weight is 140 kilograms after 11 months and he gained weight at a rate of 5.55 kilograms per month.
The equation for the relationship between the weight and number of months can be represented as:
y = 5.55x + b
Where y is the sumo wrestler's weight (in kilogram) after x month, 5.55 is the rate at which he gained weight per month, x is the number of months and b is the y-intercept.
To find the value of b, we can use the point (11, 140) which represents that after 11 months the sumo wrestler's weight is 140 kg, and substitute it into the equation:
y = 5.55x + b
140 = 5.55(11) + b
Solving for b:
b = 140 - (5.55 * 11)
b = 140 - 61.05
b = 78.95
So the complete equation is:
y = 5.55x + 78.95
Where y is the sumo wrestler's weight (in kilogram) after x months.
Therefore, The linear equation for the relationship between the weight and number of months is y = 5.55x + 78.95.
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Lorene says summer is 1/4 of the year minus the summer is 3/12 of the year who is correct
Both statement by Lorene and Maria is correct because it has a common factor is "1/4".
What type of fraction are 1/4 and 3/12?Both fraction are called proper fraction. Basically, a fractions represent the parts of a whole or collection of objects.
Under fraction, proper fraction is one in which the numerator is less than the denominator. It is in contrast to improper fraction, that numerator equals or exceeds the denominator. Proper fractions are 3/4, 2/11, and 7/19, while improper fractions are 5/2, 8/5, and 12/11.
The statements of Laurie and Maria can be compared as follows:
In the fraction 1/4, the denominator and numerator have no common factors.In the fraction 3/12, the denominator and numerator have a common factor as 3.It can be written as,
3/12 = (3 ÷ 3)/(12 ÷ 3)
= 1/4
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If AY= 7cm , what is the length of BY?
Answer:
BY = 9.90 cm
Step-by-step explanation:
from the figure the triangle has a right angle and one of 45°, therefore it is a right isosceles triangle, 2 equal sides and 2 equal angles, we solve with Pythagoras
AY = 7cm
AB = 7cm
BY = ?
BY = [tex]\sqrt{7^2+7^2}[/tex]
BY = [tex]\sqrt{98}[/tex]
BY = 9.89cm (round to 9.90cm)
How many degrees is a 10 to 1 slope?
The degree value, when rounded to the nearest decimal, is 6. Therefore, the slope's angle of 1 in 10 is 6 degrees.
1 in 10 in geometry refers to the ratio of one unit of vertical drop or rise for every ten units of horizontal distance crossed. This slope's value is calculated using the angle of tan. Let x represent the tan-using angle.
tan x = horizontal distance/vertical distance
tan x = 1/10
tan x = 0.1
Now taking the inverse
x = [tex]\tan^{-1}(0.1)[/tex]
x = 5.71 degree
The degree value, when rounded to the nearest decimal, is 6.
Therefore, the slope's angle of 1 in 10 is 6 degrees.
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The right question is:
How many degrees angle is a 1 in 10 slope?
What would you make the size of the hypotenuse of a right tria gle to make if its other two size measure 2 and 5 cm?
a. 7 squared.
b. 29 squared.
C. 29.
d. 29 squared by 3.
Answer: To find the length of the hypotenuse of a right triangle, you can use the Pythagorean theorem. The theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides (the legs).
So, if the legs of the right triangle measure 2 cm and 5 cm, the hypotenuse c can be calculated as follows:
c² = a² + b²
c² = 2² + 5²
c² = 4 + 25
c² = 29
Therefore, the length of the hypotenuse c is the square root of 29.
c = √29
The answer is c = √29 which is the only one that is not squared, So the answer is (C) 29.
Step-by-step explanation:
Decribe the ditribution of the following data et. 388,217,317,361,350,298,400,147,254,101,336,387,14,256
The mean of the distribution of the given data set is equal to 273.33.
As given in the question,
Given distribution of the data set is :
388, 217, 317, 361, 350, 298, 400, 147, 254, 101, 336, 387, 14, 256.
Mean of the given data set
= ( Sum of all the distribution of the data set ) / ( number of observations)
= [tex]\sum x_{i}[/tex] / n
Where x represents the value of each distribution of the given data set.
and 'n' represents the number of data set
Here n = 14
Mean
=(388+217+317+361+350+298+400+147+254+101+ 336+387+14+ 256)/ 14
= 3826/ 14
=273.328
=273.33
Therefore, the mean of the given data set is equal to 273.33.
The given question is incomplete, I answer the question in general according to my knowledge:
Calculate the mean of the distribution of the following data set.
388, 217, 317, 361, 350, 298, 400, 147, 254, 101, 336, 387, 14, 256.
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Given the function h(x)=-x²+4x+12, determine the average rate of change of the function over the interval -1≤x≤8
The average rate of change of the function over the interval -1≤x≤8 is -3.22.
How do you determine the average rate?The average rate of change of a function over an interval is given by the formula (f(b) - f(a)) / (b - a) where f(x) is the function, a is the starting point of the interval, and b is the ending point of the interval.
In this case, the function is h(x) = -x² + 4x + 12, the interval is -1≤x≤8.
Plugging in the values we have:
Average rate of change = (h(8) - h(-1)) / (8 - (-1)) = (h(8) - h(-1)) / 9
h(8) = -8² + 4(8) + 12 = -64 + 32 + 12 = -20
h(-1) = -1² + 4(-1) + 12 = 1 - 4 + 12 = 9
So the average rate of change = (-20 - 9) / 9 = -29/9 = -3.22
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Which expressions are equivalent to 2(b+3c)2(b+3c)2, left parenthesis, b, plus, 3, c, right parenthesis ?
The equivalent expressions are (b+3c)+(b+3c) and 2(b)+2(3c) or 2b+6c. Options B and C
What is an algebraic expression?An algebraic expression is simply described as an expression consisting of variables, coefficients, terms, constants, and factors.
Algebraic expressions are also made up of mathematical operations, such as;
BracketParenthesesDivisionMultiplicationSubtractionAddition, etcGiven the expression;
2(b+3c)
expand the bracket
2(b)+ 2(3c)
2b + 2×3×c
Multiply the values, we get;
= 2b +6c
It can also be written as the sum of b+3c as (b+3c)+(b+3c)
Hence, the expressions are (b+3c)+(b+3c) and 2(b)+2(3c) or 2b+6c
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The complete question:
Which expressions are equivalent to 2(b+3c)2(b+3c)2, left parenthesis, b, plus, 3, c, right parenthesis ?
Choose all answers that apply:
A 3(b+2c)3(b+2c)3, left parenthesis, b, plus, 2, c, right parenthesis
B (b+3c)+(b+3c)(b+3c)+(b+3c)left parenthesis, b, plus, 3, c, right parenthesis, plus, left parenthesis, b, plus, 3, c, right parenthesis
C 2(b)+2(3c)2(b)+2(3c)2,
What is substitution simple?
Substitution refers to the process of replacing one group with another. We can say that it refers to replacing a variable with another given value.
For example, given that x = 17, we can substitute the value of 17 in for x and evaluate the obtained expression to get the value of x.
We can name the expression: F (x) = 17 + 3x - 4.
here , let's say x = 2
then , F (x) = 17 + 6 + 2 = 25
The algebraic method which is used for solving simultaneous linear equations is known as the substitution method. The value of one variable from one equation is substituted in the second equation, as the name implies.
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MODELING WITH MATHEMATICS: The function f(t)=-16t^2+10 models the height (in feet) of an object t seconds after it is dropped from a height of 10 feet on Earth. The same object dropped from the same height on the moon is modeled by g(t)=-8/3t^2+10.
Describe the transformation of the graph of f to obtain g.
The graph of g is a horizontal stretch by a factor of (blank) of the graph of f. Round your answer to the nearest hundredth.
From what height must the object be dropped on the moon so it hits the ground at the same time as on Earth? Round your answer to the nearest hundredth.
The object must be dropped from a height of (blank) feet.
The transformation of the graph of f to obtain g is described as follows:
The graph of g is a vertical compression of the graph of f by a factor of 6 units.
The object must be dropped at a height of 1.66 feet from the moon so it hits the ground at the same time as on Earth,
What is the transformation?The functions in the context of this problem are given as follows:
f(t) = -16t² + 10.g(t) = -8/3t² + 10.The multiplier that was applied to function f(t) to obtain function g(t) is given as follows:
-16x = -8/3
16x = 8/3.
x = 8/48
x = 1/6.
The leading coefficient was divided by 6, meaning that the graph of g is a vertical compression of the graph of f by a factor of 6 units.
When does the object hits the ground?The object hits the ground when the output of the quadratic function assumes a value of zero.
For the Earth, we have that the time to hit the ground is obtained as follows:
-16t² + 10 = 0
16t² = 10
t² = 5/8
[tex]t = \sqrt{\frac{5}{8}}[/tex]
t = 0.79 seconds.
For the Moon, the function is given as follows:
g(t) = -8/3t² + h.
In which h is the initial height.
We want that g(t) = 0 when t = 0.79, hence the initial height is obtained as follows:
0 = -8/3(0.79)² + h
h = 8/3(0.79)²
h = 1.66 feet.
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An online video game rental site has a Frequent Gamers Plan. It costs $30 to join and each video game rental for members costs $2. Non-members pay a rental fee of $3.50 per rental. For what number of rentals would both plans cost the same amount?
The number of rentals would be 20 so that both plans cost the same amount.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
It costs $30 to join and each video game rental for members costs $2.
Non-members pay a rental fee of $3.50 per rental.
let the number of rentals they both pay same amount be x.
So, 30 + 2x = 3.5x
30 = 3.5x - 2x
30 = 1.5x
x= 30/1.5
x = 20
Hence, number of rentals should be 20.
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What is 2798 in Roman numerals
Answer: MMDCCLXXXIX
Step-by-step explanation:
Answer:
Step-by-step explanation:
2000=MM, 700=DCC, 90=XC, 8=VIIIwhat is 10% of 70% and what is 25% of 160%
PLEASE HELP!!
I NEED TO GET MY GRADES UP
I -6 -8 I divided by 2 x -6 (9-7)^3
Answer:
Step-by-step explanation:
−6−8÷2x−6(9−7)
3
Divide 8 by 2 to get 4.
−6−4x−6(9−7)
3
Subtract 7 from 9 to get 2.
−6−4x−6×2
3
Calculate 2 to the power of 3 and get 8.
−6−4x−6×8
Multiply 6 and 8 to get 48.
−6−4x−48
Subtract 48 from −6 to get −54.
−54−4x
Solve for x
I need help
The value of x, in the triangle shown is: C. 5.25.
How to Solve for x in Similar Triangle?In the image given, the triangles shown are similar to each other, which means that their corresponding side lengths are proportional to each other.
Therefore, we would have the following proportion:
x / 2 = 16.8 / 6.4
Cross multiply:
6.4 * x = 16.8 * 2
6.4x = 33.6
6.4x/6.4 = 33.6/6.4
x = 5.25
The correct value of x is: C. 5.25.
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LIt cost Sophia $530 to make wind chimes. How many
chimes must she sell at $12 apiece to make a profit?
Answer:
c = number of chimes
12c = amount gotten from the sale of the chimes.
To make a profit what she gets from the sales must be greater than her expenses.
12c > 530
c > 44.166666
She must sell each chime for more than 44 an one-sixth cent.
Step-by-step explanation:
Please I need help!!!
Find the measure of each missing angle.
The measures of the missing angles are given as follows:
m < 1 = 4º. m < 2 = 88º.m < 3 = 124º.m < 4 = 88º.m < 5 = 36ºHow to obtain the angle measures?First we consider that when two angles form a ray, they are supplementary, meaning that the sum of their measures is of 180º.
Then the measures of angles 3 and 5 are given as follows:
m < 3 + 56 = 180 -> m < 3 = 124º.m < 5 + 144 = 180 -> m < 5 = 36º.The sum of the internal angles of triangle is of:
S(3) = (3 - 2) x 180º = 180º.
Hence the measure of angle 4 is obtained as follows:
m < 4 + 36 + 56 = 180
m < 4 = 180 - (36 + 56)
m < 4 = 88º.
Angles 2 and 4 are congruent, hence the measure of angle 2 is given as follows:
m < 2 = m < 4 = 88º.
The sum of the internal angles of a quadrilateral is of:
S(4) = (4 - 2) x 180º = 360º.
Hence the measure of angle 1 is obtained as follows:
m < 1 + 88 + 144 + 124 = 360
m < 1 = 360 - (88 + 144 + 124)
m < 1 = 4º.
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A trucking company sets up contracts with various manufacturing companies to ship their freight. One contract has the following points: A charge of 6.5% of the total value of the freight for each delivery. A charge of $70 per delivery regardless of the amount of freight. Your responsibility is to determine the lowest values of combinations of total freight value and number of deliveries each month that will be necessary in order for the trucking company to make AT LEAST $102,000 each month.
Using concept of linear inequality, number of least deliveries is 30 and value of freight is $60000.
What are linear inequalities?
Inequality represents the mathematical expression in which both sides are not equal. If the relationship makes the non-equal comparison between two expressions or two numbers, then it is known as inequality in Maths. In this case, the equal sign “=” in the expression is replaced by any of the inequality symbols such as greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤) or not equal to symbol (≠). The different types of inequalities in Maths are polynomial inequality, rational inequality, absolute value inequality.
The symbols ‘<‘ and ‘>’ express the strict inequalities and the symbols ‘≤’ and ‘≥’ denote slack inequalities. A linear inequality seems exactly like a linear equation but there is a change in the symbol that relates two expressions.
e.g. y>x+2
Now,
Given charge of $70 per delivery and A charge of 6.5% of the total value of the freight for each delivery and least amount is $102,000.
Let only one delivery is possible per day and no. of deliveries=n
amount of each freight=x
Therefore,
Linear inequality will be n(6.5/100**x+70)>102000
So least values of n and x will be
n=30 and x=$60000
Hence,
number of least deliveries is 30 and value of freight is $60000.
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How do you determine if a function is an exponential function?
Answer:
How can you tell if a function is an exponential function? If your function can be written in the form y = a b x , where and are constants, a ≠ 0 , b > 0 , and b ≠ 1 , then it must be exponential. In quadratic equations, your functions were always to the 2nd power. In exponential functions, the exponent is a variable.
How do you find the roots of a factor?
By setting each factor to 0, you can get the roots, or solutions, of the polynomial equation P(x) = 0 by figuring out what x is. Factor the polynomial equation to find the solution.
What are polynomials?Constants and indeterminates are parts of polynomial algebraic expressions.
One could consider polynomials to be a subset of mathematics.
They are used to express numbers in almost all areas of mathematics, and calculus is one of those areas where they are particularly important.
A polynomial is a specific sort of expression.
An expression is a mathematical statement that does not contain the equals sign (=). Let's look at the following descriptions of polynomials' definition and applications.
All the exponents of an algebraic expression called a polynomial must be whole numbers.
Any polynomial must have non-negative integer variable exponents. We cannot divide a polynomial by a variable even though it contains variables and constants.
Hence, By setting each factor to 0, you can get the roots, or solutions, of the polynomial equation P(x) = 0 by figuring out what x is. Factor the polynomial equation to find the solution.
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(8.) A person must be at least 52 inches tall in order to ride the power train ride at Cedar Point Ohio. Write an inequality statement that describes the required height if x is a persons height.
Answer: x [tex]\leq[/tex] 52 inches.
Step-by-step explanation:
Samantha earned $700 thi ummer. If he depoit the money in a aving account, how many year will it take her to earn $196 in interet at a imple annual rate of 4%?
A. 6
B. 7
C. 8
D. 9
Answer:
B. 7
Step-by-step explanation:
[tex]I=Prt \\ \\ 196=700(0.04)t \\ \\ 196=28t \\ \\ t=7[/tex]
What is the slop intercept form of the equation
Answer:
The slope intercept form in math is one of the forms used to calculate the equation of a straight line, given the slope of the line and intercept it forms with the y-axis. The slope intercept form is given as, y = mx + b, where 'm' is the slope of the straight line and 'b' is the y-intercept.
What is exponential form formula?
Answer:
f(x)=a(b)^x
Step-by-step explanation:
exponential functions are usually growth or decay,
a represents the base, b is the change, and x is how much time (depending on the question). if b is larger than 1 ex: 1.08, it is growth. if it is less than 1 ex: 0.4, it is decay
The exponential form formula is a^b = c, where a is the base, b is the exponent, and c is the result. In this formula, a is raised to the power of b, resulting in the value c.
What is the base of an exponential term?
The base of an exponent is a number that is increased to a definite power. So, the base of an exponent defines the number that is multiplied by itself.
The exponent means how many times the base number is multiplied.
The power can be expressed as the number obtained by increasing the base number to the exponent.
So, in the power [tex]a^{n}[/tex], the letter “a” is the base. The letter n is the exponent.
It says, a is multiplied by itself n number of times.
If the base is a negative and an exponent is an even number, the power is positive.Example - (-5) ² = (-5) × (-5) = 25
If the base is negative and an exponent is an odd number, the power is negative.Example: (-5)³ = (-5) × (-5)× (-5) = -125
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