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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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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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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what is 10% of 70% and what is 25% of 160%
PLEASE HELP!!
I NEED TO GET MY GRADES UP
If c =⟨6,2⟩ and d =⟨ – 9,7⟩, find the sum c + d .
Answer:
[tex]c+d=\langle-3,9\rangle[/tex]
Step-by-step explanation:
We simply add the respective horizontal and vertical components:
[tex]c+d=\langle 6,2 \rangle+\langle-9,7\rangle=\langle6+(-9),2+7\rangle=\langle6-9,9\rangle=\langle-3,9\rangle[/tex]
2/3(6a+9)+19.2
step by step equation
Answer:
4a + 25.2.
Step-by-step explanation:
2/3(6a+9)+19.2
= 2/3 * 6a + 2/3 * 9 + 19.2
= 4a + 6 + 19.2
= 4a + 25.2.
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 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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What is the solution set of the following equation 8x x 15 7x 12 Ã {} all reals?
The solution set of the following equation (- 8x + x + 15) = ( - 7x + 12) is zero i.e this equation does not have any solution.
Equation is (- 8x + x + 15) = (-7x + 12)
Now solving
(-8x + x + 7x ) = ( 12 - 15 )
( - 7x +7x) = (-3)
( 0 )= ( - 3)
Since 0 = -3 is not correct, therefore, the equation does not have any solution.
So it is stated that the equation (- 8x + x + 15) = ( - 7x + 12) does not have any solution in its solution set.
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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:
Rectangle abcd is similar to rectangle wxyz. If the length of ab is 50 inches and the length of bc is 40 inches, what is the length of wx if xy is 32 inches?.
The length of the side WX of the rectangle WXYZ, which is similar to the rectangle ABCD, is 40 inches.
According to the information provided, the rectangles ABCD and WXYZ are very similar to one another, which means they have the same ratio or proportional. If the ratio between two amounts is directly proportional, then as one quantity increases, the other amount also increases, and when one amount decreases, the other amount also decreases.
In this case, we are given that:
AB = 50 inches
BC = 40 inches
XY = 32 inches
To calculate the length of WX, we may apply the formula that is as follows =
AB/WX = BC/XY
50/WX = 40/32
40WX = 50x32
WX = 40
As a result, the length of WX in rectangle WXYZ is 40 inches
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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.
Which of the following statement is not a statement?Every set is a finite set.Every square is a rectangle.The sun is a star.Shut the window.
all are statement except shut the window because sets are statement
square is a rectangle .The sun is a star is a statement
Describe finite set using an example.
What is the set in math?
Sets, in mathematics, are an organized collection of objects and can be represented in set-builder form or roster form. Usually, sets are represented in curly braces {}, for example, A = {1,2,3,4} is a set.
A1 = { 1} A2 = { 2 } A3 = { 3 }..
U Ai = { 1 , 2 , ,,}
= N is not a finite set
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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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Why are there 2 answers for quadratic equations?
Due to the fact that the solutions lie where the parabola crosses the x-axis, quadratic equations frequently have two solutions.
Any equation in algebra that can be written in standard form as
ax^2+bx+c=0,
where x stands for an unknown integer and a, b, and c are known quantities, where a 0, is considered a quadratic equation.
The coefficients of the equation are the numbers a, b, and c, which can be separated by naming them, respectively, the quadratic coefficient, the linear coefficient, and the constant coefficient or free term.
Due to the fact that the solutions lie where the parabola crosses the x-axis, quadratic equations frequently have two solutions. The graph will cross twice if the vertex is below the x-axis and the parabola opens up, and it will cross twice again if the vertex is above the x-axis and the parabola opens down.
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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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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:
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.
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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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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54 biscuits from 9 batches
Answer: 6 in each batch
Step-by-step explanation: 54/9 = 6
A microscope magnifies an object 10 $^5$ times. The length of an object is 10 $^{-7}$ meter. What is its magnified length? write your answer as a decimal.
The magnified length of the objects is 0.01 meters in decimal form, based on the height of object and magnification power.
The formula to find magnified length is -
Magnification = image height ÷ object height. Here image height is magnified length.
Keep the values in formula -
Image height = 10⁵ × [tex] {10}^{-7} [/tex]
Performing multiplication on Right Hand Side of the equation. Note that power of products will be used to find the magnified length. The exponents will be added.
Image height = [tex] {10}^{5 + (-7)} [/tex]
Performing addition of exponents to find the image height
Image height = [tex] {10}^{-2} [/tex] meters
Writing the image height in decimal form - 0.01 meters
Therefore, the height of image or magnified length is 0.01 meters.
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You are given that Z>2.
Write an inequality for each expression
a) 2z+9
b) 3(z-4)
c) 4+2z
d) 5(3z-2)
Part (a)
Multiply both sides by 2, then add 9 to both sides.
z > 2
2z > 2*2
2z > 4
2z+9 > 4+9
2z+9 > 13 is the final answer for part (a)
--------------------------------------------------------------
Part (b)
We'll start with subtracting 4 from both sides, and then triple each side.
z > 2
z-4 > 2-4
z-4 > -2
3(z-4) > 3*(-2)
3(z-4) > -6 is the final answer for part (b)
--------------------------------------------------------------
Part (c)
Follow similar steps to that of part (a).
z > 2
2z > 2*2
2z > 4
2z+4 > 4+4
2z+4 > 8 is the final answer to part (c)
--------------------------------------------------------------
Part (d)
For now let's ignore the 5 out front and focus on 3z-2
z > 2
3z > 3*2
3z > 6
3z-2 > 6-2
3z-2 > 4
Now multiply each side by 5.
5(3z-2) > 5*4
5(3z-2) > 20 is the final answer to part (d)
--------------------------------------------------------------
Side note: The inequality signs did not flip when multiplying both sides by a positive number. The flip would only happen if we multiplied both sides by a negative number.
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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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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(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:
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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I need some help on here
Answer:
[tex]\huge\boxed{\sf Yes.}[/tex]
Step-by-step explanation:
Given Equations:y = 6x - 9 ---------------(1)
y = 2x + 3 --------------(2)
Coordinate point:(x, y) = (3, 9)So,
x = 3, y = 9
Put this in Eq. (1) to verify.
9 = 6(3) - 9
9 = 18 - 9
9 = 9 [Equation satisfied]
Now, put x = 3, y = 9 in Eq. (2)
9 = 2(3) + 3
9 = 6 + 3
9 = 9 [Equation satisfied]
Since, both the equations are satisfied by the values of x and y, we can say that x = 3 and y = 9 is the solution to the system.
[tex]\rule[225]{225}{2}[/tex]
Answer: Yes, it is a solution
Step-by-step explanation:
Plug (x,y) values into the equations.
Plug in (3,9)
y=6x-9 ---->. (9)=6(3)-9 ----> 9=18-9 -----> 9=9
y=2x+3 ------>. (9)=2(3)+3 ----> 9=6+3 ----> 9=9
When know (3,9) is a solution because each side has the same value.
Example:
8=9 Not a solution
5=5 A solution
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 2798 in Roman numerals
Answer: MMDCCLXXXIX
Step-by-step explanation:
Answer:
Step-by-step explanation:
2000=MM, 700=DCC, 90=XC, 8=VIII