If g(x) is obtained by shifting f(x) down by 7 units, the value of k is 7.
What is a translation?In Mathematics, the translation of a geometric figure or graph downward simply means subtracting a digit from the value on the y-coordinate (y-axis) of the pre-image or function.
Mathematically, a horizontal translation to the left is modeled by this mathematical expression g(x) = f(x + k) while a vertical translation to the negative y-direction (downward) is modeled by this mathematical expression g(x) = f(x) - k.
Where:
k represents an integer.g(x) and f(x) represent a function.By comparison based on the graph of f(x) = (0.5)^x and g(x) = (0.5)^x − k, we can logically deduce that the value of k is equal to 7.
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Callen's app says they biked 8 kilometers, which is 20% of their goal. What was their goal distance?
Answer:
40KM
Step-by-step explanation:
biked=8km which is 20% of the whole distance or the goal,
so we went the goal or 100%of the distance,
and it becomes 8km/whole distance
so it becomes
8km/whole distance =20/100
,800km=20×whole distance
,whole distance or their goal =800km÷20
which is 40km
If FH =21 , and GH =6 calculate the length of FG
Answer:
42 if you mean f×g
f is 7×h is 3=21
g is 6× h is 3=21
7×6=42
Just question 10 please
a. The minimum point is located at x = 2 and y = -4. The coordinates is (2,-4).
b. The equation of the line of symmetry of the graph is x = 2.
c. The solutions are approximately x = 1.3 and x = 2.7.
d. 2x²-4x+3=0 has no solutions because when 2x²-4x is graphed, the graph never intersects the x-axis at the y-value of 3. Therefore, the equation 2x²-4x+3=0 has no solutions.
What is equation of the line of symmetry?The equation of the line of symmetry is the equation of a line that passes through the center of a geometric figure such that it divides the figure into two equal parts. The equation of the line of symmetry is usually expressed in the form of y = mx + b, where m is the slope of the line and b is the y-intercept. The slope of the line of symmetry is always equal to the opposite reciprocal of the slope of the original line, and the y-intercept is equal to the midpoint of the two end points of the original line. For example, if the equation for a line is y = 4x + 2 then the equation for the line of symmetry that would pass through the midpoint of the line would be y = -1/4x + 3, where 3 is the midpoint of the two end points of the original line. The line of symmetry is an important concept in geometry, as it divides a figure into two equal halves, allowing us to easily identify the center of the figure. It is also useful in calculus, as the line of symmetry helps us to calculate the area under the graph of a function. It is also used in other branches of mathematics, such as trigonometry and statistics.To learn more about line of symmetry refer to:
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Hayley is a hairdresser. Before her lunch break, she gave 4 haircuts and colored the hair of 1 client in 151 minutes. After lunch, she gave 3 haircuts and colored the hair of 4 clients in 370 minutes. How long does it take for Hayley to perform each type of service, assuming the amount of time doesn't vary from client to client?
Answer:1
Step-by-step explanation:
What are the 5 steps to solving a division problem?
The 5 steps in a division problem are understanding the problem, setting up the problem, dividing, finding the remainder and continuing the last two steps until the remainder is less than the divisor.
Understand the problem: Read the problem carefully and make sure you understand what is being asked. Identify the dividend, divisor, and the quotient.
Set up the problem: Write the problem using the standard division format: dividend ÷ divisor = quotient.
Divide: Begin by dividing the leftmost digit of the dividend by the divisor. Write the quotient above the dividend, to the left of the dividend, and above the divisor.
Multiply and Subtract: Multiply the divisor by the quotient digit and write the product under the corresponding digit of the dividend. Then subtract this product from the corresponding digits of the dividend.
Bring down the next digit: Bring down the next digit of the dividend to the right of the remainder. Repeat steps 3 and 4 until the remainder is zero or until you have reached the desired level of accuracy.
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How do you write 7 as a natural log?
The natural logarithm of a number is written as ln(x), where x is the number. Therefore, to write 7 as a natural log, you would write ln(7).
ln(7)
The natural logarithm of a number is written as ln(x), where x is the number. Therefore, to write 7 as a natural log, you would write ln(7).
The natural logarithm of any number is written as ln(x), where x is the number in question. Therefore, if you wanted to write 7 as a natural log, you would write ln(7). Natural logs are used in mathematics to express the logarithm of a number in a base of e, which is approximately equal to 2.718. Natural logs are useful when dealing with exponential growth or decay, and when solving certain equations. To calculate the natural log of a number, you would use the formula ln(x) = logₑx, where x is the number you are trying to calculate the natural log of. In this case, ln(7) would equal the natural log of 7.
The natural logarithm of a number is written as ln(x), where x is the number. Therefore, to write 7 as a natural log, you would write ln(7).
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X+.5x + ( x-l.25) = 4.75
Answer:
x = 2.4
Step-by-step explanation:
X+.5x + ( x- 1.25) = 4.75
1.5x + x - 1.25 = 4.75
2.5x - 1.25 = 4.75
2.5x = 6
x = 2.4
how do i solve for x on number 16. With the geometric mean
Answer:
x = 42
Step-by-step explanation:
When driving to their family reunion, River's mom drove 10 miles at a rate of x mph and then 25 miles at a rate of x+10 mph. The total driving time was 45 minutes. What were the two driving speeds at which River's mom drove?
The speed of River's mom drove for 10 miles distance is 0.234 mph
The speed of River's mom drove for 25 miles is 10.234 mph
What is speed?Speed is measured as distance moved over time. The formula for speed is speed = distance ÷ time. To work out what the units are for speed, you need to know the units for distance and time. In this example, distance is in metres (m) and time is in seconds (s), so the units will be in metres per second (m/s).
here, we have,
Given as :
The first distance cover by River's mom = 10 miles
The rate of speed = x mph
The second distance cover by river's mom = 25 miles
The rate of speed = x + 10 mph
The total driving time = 45 min
Now, According to question
Time = speed/distance
So, 45 =10/x + 25/(x+10)
Or, 9 =2/x + 5/(x+10)
Or, 9 × x × ( x + 10 ) = 2 × ( x + 10 ) + 5 x
Or, 9 x² + 90 x = 2 x + 20 + 5 x
Or, 9 x² + 90 x = 7 x + 20
Or, 9 x² + 90 x - 7 x - 20 = 0
Or, 9 x² + 83 x - 20 = 0
Solving this quadratic equation
x = 0.234 , - 9.4567
so, the value is,
I.e x = 0.234 , - 9.4567
now,
We consider x = 0.234
So, The speed for 10 miles distance = x = 0.234 mph
and The speed of 25 miles = x + 10 = 0.234 + 10 = 10.234 mph
Hence The speed of River's mom drove for 10 miles distance is 0.234 mph
and The speed of River's mom drove for 25 miles is 10.234 mph
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What are the 3 types of graphs in math?
Line graphs show relationships between two variables by plotting data points connected by a line. Bar graphs compare data by showing bars of different sizes. Pie charts show proportion or percentage of the whole by dividing a circle into sections.
Line graphs are used to show relationships between two variables. They are created by plotting data points on a graph and connecting them with a line. Line graphs can be used to show trends or changes over time, or to compare different sets of data. Bar graphs compare data by showing bars of different sizes. The bars represent different categories, and the length of each bar indicates the size of the value it represents. Pie charts are used to show proportion or percentage of the whole. The data is divided into sections and each section is represented by a different color. The size of each section is proportional to the value it represents. All three types of graphs are commonly used to visually represent data in mathematics.
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How do you find f (- 4 on a graph?
To find f (-4) on a graph, plot the point (-4, f (-4)) on the graph.
B. First, identify the point (-4, 0) on the x-axis. This is the point where the x-coordinate is -4. Then, draw a line perpendicular to the x-axis that passes through the point (-4, 0).
This line represents the function f (x). Use the equation of the line to determine the value of f (-4). For example, if the equation of the line is y = 3x + 7, then the value of f (-4) is -5.
To plot the point (-4, f (-4)) on the graph, simply draw a dot at the intersection of the line and the y-axis, with the y-coordinate being f (-4). This dot represents the point (-4, f (-4)).
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PLSSS HELLLPP
What is the domain of the function?
Answer: [-6, 8]
Explanation:
The domain is all the possible values on the x-axis, which is [-6, 8]
X
-3
-1
9
12
7
Y
16
6
16
0
7
look at this table, is this a relation a function?
No, this table does not represent a relation or a function.
What is function?Function is an action or process that produces a result. It is a set of instructions that produces an output from one or more inputs. Functions are a key building block in programming and are used to create meaningful results from a given set of data. Functions can be used to simplify complex tasks and make them more efficient. They are also used to organize and structure code, making it easier to read and debug.
A relation is a set of ordered pairs that have an established relationship between them, while a function is a relation where each input is related to only one output. This table does not establish any relationship or link between the X and Y values, so it is not a relation or a function.
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Mrs. Aika told her class that they will get a pizza if the class has an average of at least 85 out of 100 correct questions on the mid term exam.
A. Write an inequality to describe the situation where students receive a pizza
Answer:
To write an inequality to describe the situation where students receive a pizza, we need to use the concept of average.
The average of a set of numbers is equal to the sum of the numbers divided by the number of numbers. So, if the class has an average of at least 85 out of 100 correct questions on the mid term exam, we can write an inequality as:
(number of correct questions) / (number of students) ≥ 85/100
or
(number of correct questions) ≥ (85/100) * (number of students)
So the inequality that describes the situation where students receive a pizza is:
(number of correct questions) ≥ (85/100) * (number of students)
This inequality states that the number of correct questions must be greater than or equal to 85/100 multiplied by the number of students in order for them to receive a pizza.
A plumber completes 18 of a job in 29 hour. At this rate, how long does it take the plumber to complete the job?
It will take the plumber 1 hour and 1/8 hour to complete the job.
To find out how long it will take the plumber to complete the entire job, we can use the formula:
time = (job size) / (rate)
where job size is the fraction of the job that is remaining (1/8 in this case) and rate is the fraction of the job the plumber can complete in a given amount of time (2/9 in this case).
So the time to complete the job is:
time = (1/8) / (2/9)
= (9/16) / (2/9)
= (9/16) * (9/2)
= 9/8
= 1 and 1/8 hour
So it will take the plumber 1 hour and 1/8 hour to complete the job.
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Complete question :
A Plumber Completes ( 1)/(8) Of A Job In( 2)/(9) Hours. At This Rate, How Long Does It Take The Plumber Complete The Job?
Mark has 15 feet of string.He will cut the string into equal lengths of 7 inches each.How much string will be left after he cuts as many pieces of these lengths as possible.
The amount of string left after cutting 25 strings of 7 inches in length is
5 inches.
What is unit conversion?It is the conversion of one unit to another unit with its standard conversion.
Example:
1 hour = 60 minutes
1 km = 1000 m
We have,
1 feet = 12 inches
Multiply 15 on both sides.
15 feet = 15 x 12 inches
15 feet = 180 inches
Now,
Length of the string = 15 feet
Length of each string = 7 inches
The number of strings of 7 inches is 25 and 5 inches left over.
i.e
7 x 25 = 175
The string that is left over.
= 180 - 175
= 5 inches
Thus,
5 inches of the string is left after cutting 25 strings of 7 inches in length.
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the function f is defined on the closed interval [0, 1] and satisfies . on the open interval (0, 1), f is continuous and strictly increasing. which of the following statements is true? (a) f attains both a minimum value and a maximum value on the closed interval [0, 1]. (b) f attains a minimum value but not a maximum value on the closed interval [0, 1]. (c) f attains a maximum value but not a minimum value on the closed interval [0, 1]. (d) f attains neither a minimum value nor a maximum value on the closed interval [0, 1].
The statement that is true is (d) f attains neither a minimum value nor a maximum value on the closed interval [0, 1].
A function that is strictly increasing on an open interval is not bounded above or below, meaning that it does not attain a maximum or minimum value within that interval.
Since f is defined on the closed interval [0, 1], which includes the endpoints 0 and 1, it also does not attain a maximum or minimum value on the entire closed interval.
For the function f to attain a minimum value, the function must be defined for all x in the closed interval and all x in the domain and at least one point x in the domain must be a global minimum.
For the function to attain a maximum value, at least one point x in the domain must be a global maximum, in this case, the function is continuous and strictly increasing on the open interval (0, 1) which means that the function doesn't have a minimum or a maximum.
In conclusion, the statement that is true is (d) f attains neither a minimum value nor a maximum value on the closed interval [0, 1] because a function that is strictly increasing on an open interval is not bounded above or below, meaning that it does not attain a maximum or minimum value within that interval.
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Four spheres of radius 6 cm just fit inside a cylinder.
Calculate the volume inside the cylinder that is empty.
Leave your answer in terms of л.
The volume inside the cylinder that is empty will be [tex]$3883.76 \pi$[/tex].
How to estimate the volume of cylinder?A cylinder can barely accommodate four spheres with a 6 cm radius.
The cylinder and the spherical barely fit. As a result, the cylinder's height will be 2 times the sphere's diameter.
Radius R of the cylinder will be estimated as,
[tex]$$\begin{aligned}& R=\frac{\sqrt{2} \times 12+6+6}{2} \\& R=6 \sqrt{2}+6\end{aligned}$$[/tex]
Radius of the cylinder is [tex]$6 \sqrt{2}+6 \mathrm{~cm}$[/tex].
Height of the cylinder is [tex]$\mathbf{2 4} \mathbf{~ c m}$[/tex]
Volume of the cylinder,
[tex]$$\begin{aligned}& V_c=\pi r^2 h \\& V_c=\pi(6 \sqrt{2}+6)^2 \times 24 \\& V_c=5035.76 \pi\end{aligned}$$[/tex]
Volume of sphere ,
[tex]$$\begin{aligned}& V_s=\frac{4}{3} \pi r^3 \\& V_s=288 \pi\end{aligned}$$[/tex]
Volume of sphere,
[tex]$$\begin{aligned}& V_s=\frac{4}{3} \pi r^3 \\& V_s=288 \pi\end{aligned}$$[/tex]
So, the volume of empty space will be,
[tex]$$\begin{aligned}& V_c-4 V_s=5035.76 \pi-4 \times 288 \pi \\& V=3883.76 \pi\end{aligned}$$[/tex]
Therefore, the volume inside the cylinder that is empty will be [tex]$3883.76 \pi$[/tex].
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3 points
There are lots of other kinds of triangles! And Pyret has lots of other functions that make triangles!
triangle :: (size:: Number, style :: String, color :: String) -> Image
right-triangle :: (base::Number, height::Number, style::String, color::String) -> Image
isosceles-triangle :: (leg::Number, angle::Number, style::String, color::String) -> Image
Why do you think triangle only needs one number, while right-triangle and isosceles-triangle need two numbers and triangle-sas needs three?
This is a 3 point question. Please make sure you answer all of the questions.
Yes, that is correct.Additionally, programming languages such as Pyret have functions that allow for the creation of different types of triangles with various properties such as size, style, and color.
What is Pyret programming language?Pyret is a programming language that is designed to make it easy for students to learn how to code. It is based on Racket, a dialect of Lisp, and has a simple, expressive syntax that is well-suited for beginners. Pyret features a type system that can help catch errors early on, and also includes a built-in library of data structures and functions that can be used to create a wide variety of programs. It also has a web-based development environment that allows students to write and run code from their web browsers. Pyret is used in many educational settings, including schools and universities, to teach computer science concepts and programming skills to students. It is also open-source and actively maintained, allowing for a vibrant community of contributors and users.To learn more about programming refer:
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Egg weights are classified according to a set of adjectives implying size. For example, the mean weight of eggs classified as “Jumbo” is 2.5 ounces. Suppose Eggland’s Best egg weights are approximately normally distributed with a mean weight of 2.5 ounces with a standard deviation of 0.1 ounces. Which of the following represents the probability that the mean weight of a random sample of 3 eggs from this population is greater than 2.65 ounces?
A. 0.9060
B. 0.9332
C. 0.9953
D. 0.0047
E. 0.0668
The population's mean, from which the scores were drawn as samples, is the mean of the sampling distribution of the mean.
How do you find the probability of the sample mean?For samples of any size taken from a population with a normal distribution, the sample mean has a normal distribution, with a mean of X and a standard deviation of X/n, where n is the sample size.Z must be more than 1.6 in order for the sample mean to have a higher likelihood of being greater than 22. To ascertain this, we consult the Z table: P( > 22) = P(Z > 1.6) = 0.0548.The number of possible outcomes is divided by the total number of possible outcomes to determine probability. Odds are not the same as probability. Odds are calculated by dividing the chance of a given event by the probability that it won't.To learn more about population's refer to:
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Alison wants to borrow $18,000 for a new car. If annual interest rate for a 60-month loan is 3.6% , set up the equation to calculate Alison’s monthly payment.
Alison’s monthly payment is $328.26
How to calculate Alison’s monthly payment.From the question, we have the following parameters that can be used in our computation:
Rate = 3.6%
As decimal, we have
Rate = 0.036
Also, we have the values of P, n and t to be
P = 18000
n = 60
t = 12
So, we have the equation to be
P = (18,000 * (0.036/12)) / (1 - (1 + (0.036/12))^(-60))
Evaluate
P =328.26
Hence, the monthly payment is $328.26
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Question ⬇️⬇️⬇️⬇️⬇️⬇️ answer
Answer:
48
Step-by-step explanation:
Its the most logical one of them all
in the late 1840s, even though the california indian population had declined greatly, it still was far larger than the californio population. which pair of approximate figures is most accurate for this time period? fifty thousand indians and fifteen thousand californios one hundred thousand indians and seven thousand californios three hundred thousand indians and seven thousand californios one hundred thousand indians and fifteen thousand californios
One hundred thousand Indians and fifteen thousand Californios are the most accurate pair of approximate figures for the late 1840s in California
The indigenous population of California was estimated to be around 100,000 in the late 1840s, while the Californio population, which consisted of Spanish-speaking settlers, was estimated to be around 15,000.
The secularization law lead the Indians to grow crops, herd livestock, and weave clothes, live in the lands to where they migrated. Later the lands under the mission are distributed or sold for less cost to the families and friends of government officers. This mission plan happened in 1840s.
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Ella Bell operates a company that buys and sells tickets to sporting events. She deposits the day's receipts into her savings account. In bills, she had 52 one hundreds, 21 fifties, 19 tens, 71 fives, and 63 ones. Change included 6 one-dollar coins, 60 fifty-cent pieces, 32 quarters, 121 dimes, and 165 pennies. She also deposited checks for $29.44, $125.65, and $45.94. She wants to receive 5 two-dollar bills in cash.
The total deposits of Ella Bell based on the information is $ 7,107.38
How to calculate the deposit?From the information, Ella Bell operates a company that buys and sells tickets to sporting events. She deposits the day's receipts into her savings account.
In bills, she had 52 one hundreds, 21 fifties, 19 tens, 71 fives, and 63 ones. Change included 6 one-dollar coins, 60 fifty-cent pieces, 32 quarters, 121 dimes, and 165 pennies. She also deposited checks for $29.44, $125.65, and $45.94. She wants to receive 5 two-dollar bills in cash.
This will be:
= Currency + Coins + Checks - Cash received
= 6858 + 57.75 + 201.63 - 10
= 7107.38
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Sam and james saved $392 altogether. Sam had 3 times as much money as james. Sam spends $38 on a pair of shoes. How much money does sam have now?
Sam had 3 times as much money as James. After spending $38 on a pair of shoes, now Sam has $256.
To translate a math word problem into equations, assign the unknowns to variables.
Let:
s = the amount of Sam's money
j = the amount of James' money
"Sam and James saved $392 altogether" can be translated into:
s + j = 392 (Equation 1)
Sam had 3 times as much money as James, means:
s = 3j (Equation 2)
Substitute equation 2 into equation 1
s + j = 392
3j + j = 392
4j = 392
j = 392 /4 = 98
Hence,
Sam's money before he bought shoes"
s = 3j = 3 x 98 = $294
After Sam bought a pair of shoes, his remaining money:
= $294 - $38 = $256
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What is the y-intercept of y =- 1 2x?
The Slope: -1/2 and y-intercept: (0,0)
Now, According to the question:
What is slope and y-intercept examples?
In an equation in slope-intercept form (y=mx+b) the slope is m and the y-intercept is b. We can also rewrite certain equations to look more like slope-intercept form. For example, y=x can be rewritten as y=1x+0, so its slope is 1 and its y-intercept is 0.
The given equation is:
y = -1/2x
This equation is in slope intercept form
y =mx + b where m is the slope and b is the y intercept
To find the slope m and y-intercept b.
Hence, Slope: -1/2 and y-intercept: (0,0)
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Points B and D are on the perpendicular bisector of ABC. The measure of
The measure of ∠C is The solution is obtained using the properties of triangle and perpendicular bisector.
What is a perpendicular bisector?
A line that divides a line segment into two equal halves and forms a 90-degree angle at the point of intersection is called a perpendicular bisector. To put it another way, a perpendicular bisector separates a line segment at its midpoint, creating a 90-degree angle.
Assumption: The given triangle ABC is an isosceles triangle.
We are given that BD is the perpendicular bisector of triangle ABC. This means that ∠BDA and ∠BDC=90°
We know that sum of all angles of a triangle are 180°.
So, in triangle BDA,
37° + 90° + ∠BAD = 180°
127° + ∠BAD = 180°
∠BAD = 53°
Now, since the triangle ABC is an isosceles triangle, therefore AB=BC.
This implies that ∠BAC= ∠BCA
∠BAC is ∠BAD which is 53°.
So, ∠BCA = 53°
Hence, the measure of ∠C is 53°.
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la función h(x) = 3x3 + 2x2 + 5 es par, impar o ninguna de las dos.
The given function is h(x) = 3x³ + 2x² + 5 is neither even nor odd.
What are functions?In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y.The set X is called the domain of the function and the set Y is called the codomain of the function.Functions whose domain are the non - negative integers, known as sequences, are often defined by recurrence relations.Given a function as [tex]${\displaystyle f\colon X\to Y}[/tex] its graph is, formally, the set -[tex]${\displaystyle G=\{(x,f(x))\mid x\in X\}.}[/tex]
Given is the function -
h(x) = 3x³ + 2x² + 5
Let f be a real-valued function of a real variable. Then f is even if the following equation holds for all x such that x and −x are in the domain of f : f(x) = f(- x).Let f be a real-valued function of a real variable. Then f is odd if the following equation holds for all x such that x and −x are in the domain of f : - f(x) = f(- x).The given function is -
h(x) = 3x³ + 2x² + 5
Now -
h(- x) = 3(- x)³ + 2(- x)² + 5
h(- x) = - 3x³ + 2x² + 5
Now -
h(- x) ≠ h(x)
h(- x) ≠ - h(x)
Therefore, the given function is h(x) = 3x³ + 2x² + 5 is neither even nor odd.
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{Question in english -
The function h(x) = h(x) = 3x³ + 2x² + 5 is even, odd, or neither.}
1
CollegeBoard
4
Pre-AP
B
Unit 2 Learning Checkpoint 2
C
9
(10)
Question 7
Selena is the manager for the high school football team. She is responsible for organizing dinner for the team before the homecoming game. Selena is planning to get turkey sandwiches and
servings of frozen yogurt for the team dinner. The coach wants the team dinner to provide each player with between 550 and 950 total calories and no more than 1,000 milligrams of sodium. Th
table shown gives the number of calories and milligrams of sodium per turkey sandwich and serving of frozen yogurt.
Food
Turkey Sandwich
Frozen Yogurt
A 550 140t + 240f ≤ 950 and 295t +90f ≤ 1,000
Selena creates a system of inequalities to determine possible combinations for the number of turkey sandwiches, t, and the number of servings of frozen yogurt, f, a player could eat and still
remain within the coach's calorie and sodium requirements. Which of the following systems represents this scenario, for t≥ 0 and f≥ 0?
550 140t + 240f 950 and 295t +90f 1,000
Number of Calories
140
240
550 ≤ 240t + 140f 950 and 90t +295 f 1,000
M
Jackson Sween
Milligrams of Sodium
295
90
550 ≤ 140t + 240f ≤ 950 and 295t +90f ≤ 1,000 system represents the scenario, for t≥ 0 and f≥ 0. The solution is obtained using system of linear inequalities.
What is system of linear inequalities?
A system of linear inequalities is identical to a system of linear equations, but instead of equations, it is made up of inequalities. Multiple constraint scenarios are modelled using sets of linear inequalities. At least two linear inequalities in the same variables make up a system of linear inequality in two variables.
We need to find the system which represents the given scenario for which we need to take into account the standards set by the coach i.e.
Total calories must be between 550 and 950.Sodium (mg) should be less than or equal to 1000.Now, as per these conditions, we have to take into consideration that the total menu should not exceed the set standards.
This means that the combine calorie intake of turkey sandwiches, t, and the servings of frozen yogurt, f, should be more than or equal to 550 but less than or equal to 950.
As seen in the table, one turkey sandwich contains 140 calories and one serving of frozen yogurt contains 240 calories.
Thus, the equation comes out to be
550 ≤ 140t + 240f ≤ 950
Also, it is to be ensured that combine sodium intake of turkey sandwiches, t, and the servings of frozen yogurt, f, should be less than or equal to 1000.
As seen in the table, one turkey sandwich contains 295mg of sodium and one serving of frozen yogurt contains 90mg of sodium .
Thus, the equation comes out to be
295t +90f ≤ 1,000
Hence, the first system i.e. 550 ≤ 140t + 240f ≤ 950 and
295t +90f ≤ 1,000 represents the scenario, for t≥ 0 and f≥ 0.
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factor quadratics with leading coefficient 1 calculator
A monic polynomial in algebra is a non-zero univariate polynomial, or a polynomial with a single variable, whose leading coefficient (the highest degree nonzero coefficient) is equal to 1.
What is quadratic equation?Any equation in algebra that can be written in standard form as where x stands for an unknown value, where a, b, and c stand for known numbers, and where a 0 is true is known as a quadratic equation. x ax2 + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a 0. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer might be simple or complicated. In mathematics, a quadratic equation is one with degree 2, which means that its highest exponent is 2. A quadratic has the standard form y = ax2 + bx + c, where a, b, and c are all numbers and a cannot be zero.
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In algebra, a monic polynomial is a non-zero univariate polynomial (i.e., a polynomial with a single variable) in which the leading coefficient (the nonzero coefficient of highest degree) is equal to 1.
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