f(x)>=-7
Functions:
Function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable). Functions are ubiquitous in mathematics.
If a variable y is so related to a variable x that whenever a numerical value is assigned to x, there is a rule according to which a unique value of f(x)is determined, then f(x) is said to be a function of the independent variable x
Given :
f(x) = -3|x+1|-4
using the table of values for g(x) = |x|
Solution :
f(x) = -3|x+1|-4
f(x) = -3|g(x)+1|-4
f(x) = -3||x|+1|-4
which means |x| is always positive |x|>0
f(x) = -3||x|+1|-4
f(x) = -3x-3-4
f(x) = -3x-7
f(x)>=-7
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What is the answer for this question
The values for the net change and average change is given as-
7. Net change = 2 , Average change = 2/3.
8. Net change = -2, Average change = -1/2.
9. Net change = -4, Average change = 4/5.
10. Net change = 4, Average change = 2/3.
What is defined as the net change and the average change?Given two points on the graph of f(x), (a,f(a)) and (b,f(b)), the net change would be the contrast between the different f(x) values.
So, net change is estimated by f(b)−f(a).The ratio of the net change to a change between the 2 input values is equal to the average net change and average rate of change. Taking the same two points, the following formula can be used to calculate the average rate of change: [f(b)−f(a)]/(b - a)In other words, the average rate of change is the slope of the line connecting any two points.Part 7:
The points on x axis are;
a = 1 and b = 4
f(b) = f(4) = 5
f(a) = f(1) = 3
Thus, net change is; f(b)−f(a)
= f(4) - f(1)
= 5 - 3
net change = 2
The average change;
= [f(b)−f(a)]/(b - a)
= [f(4) - f(1)]/(4 - 1)
net change = 2/3.
Part 8:
The points on x axis are;
a = 1 and b = 5
f(b) = f(5) = 2
f(a) = f(1) = 4
Thus, net change is; f(b)−f(a)
= f(5) - f(1)
= 2 - 4
net change = -2
The average change;
= [f(b)−f(a)]/(b - a)
= [f(5) - f(1)]/(5 - 1)
net change = -2/4 = -1/2
Part 9:
The points on x axis are;
a = 0 and b = 5
f(b) = f(5) = 2
f(a) = f(0) = 6
Thus, net change is; f(b)−f(a)
= f(5) - f(0)
= 2 - 6
net change = -4
The average change;
= [f(b)−f(a)]/(b - a)
= [f(5) - f(0)]/(0 - 5)
net change = -4/-5 = 4/5
Part 10:
The points on x axis are;
a = -1 and b = 5
f(b) = f(5) = 4
f(a) = f(-1) = 0
Thus, net change is; f(b)−f(a)
= f(5) - f(-1)
= 4 - 0
net change = 4
The average change;
= [f(b)−f(a)]/(b - a)
= [f(5) - f(-1)]/(5 + 1)
net change = 4/6 = 2/3
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B. locate and plot (square root of)15 on a number line. find a better approximation using decimals.
The number line for √15 is shown in the figure and the value of √15 is approximately 3.87298.
Number line:
Number line used for visual representation of numbers on a straight line.
Given:
Here we need to locate and plot √15 on a number line.
Steps for the construction:
Step 1) Draw a line AB that is 15 in length, and then add 1 to C so that the distance from A to C is 16.
Step 2) From the midpoint of A C on the line, use your compass and make a half circle from A to C.
Step 3) Draw a vertical line up from B until it touches the red half circle you made in Step 2.
Step 4) From B on the number line, use your compass and make a quarter circle from D to E.
The square root of 15 is the distance from B to E. To make things clearer, we have also created the illustration below showing where B, E, and the square root of 15 are located on the number line, labeled with numbers instead of the half circle, quarter circle and vertical line.
Based on the steps the number line is looks like,
Therefore, The square root of 15 (√15) is approximately 3.87298.
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I need Help please :(
Step-by-step explanation: See attached step by step
A rate is a type of ratio. It uses quantities that are not measured the same way,
like miles and hours. In a unit rate, the number in the denominator is 1. For
example, a speed of 60 miles per hour is written as number of miles traveled
thr
Express 55 miles per hour as a unit rate.
ог
55
55
60 mi
1 hr??
The 55 miles can be written as 24.4m/s.
A Rate is a special kind of ratio that is used to show the comparison of two different units of measurments. a ratio compares the same units
A rate is a ratio because it compares two numbers yet a ratio cannot be a rate because it only compares the same unit.
one common type of rate is per unit time
1 mile has 1600 meters.
distance= 55×1600= 88000m
Time= 1 hour= 3600 second.
speed is euqal to distance upon time.
88000÷ 3600 = 24.4m/s
so the 55 miles can be written as 24.4m/s.
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Geometry -Triangle
Screenie attached
Answer:102
Step-by-step explanation:
The interior angles of a triangle have to measure 180 degrees, which is an isosceles triangle, and 39+39=78.
180-78=102.Therefore the answer is 102
g(n)=n+3
f(n)=-n-5
Find g(3)-f(3)
Answer:
14
Step-by-step explanation:
g(3)=(3)+3
g(3)=6
f(3)=-(3)-5
f(3)=-8
6-(-8)=14
IM GIVING 100 PTS TO WHOEVER ANSWERS THE FASTEST
Jayden went to the grocery store and purchased cans of soup and frozen dinners. Each can of soup has 200 mg of sodium and each frozen dinner has 650 mg of sodium. Jayden purchased a total of 13 cans of soup and frozen dinners which collectively contain 4400 mg of sodium. Write a system of equations that could be used to determine the number of cans of soup purchased and the number of frozen dinners purchased. Define the variables that you use to write the system.
A system of equations that could be used to determine the number of cans of soup purchased and the number of frozen dinners purchased is;
c + f = 13
200c + 650f = 4400
where; c is the number of cans of soup and f is the number of frozen dinners.
How to create a system of equations?Let us denote c as the number of cans of soup and f is the number of frozen dinners.
The total number of items is 13 and so, we can write;
c + f = 13
The total amount of sodium is 4400 mg. Each can of soup has 200 mg, and each frozen dinner has 650 mg.
200c + 650f = 4400
We can use substitution or elimination to solve the equation for c and f but we are not asked to find it. Thus, we will conclude that;
A system of equations that could be used to determine the number of cans of soup purchased and the number of frozen dinners purchased is;
c + f = 13
200c + 650f = 4400
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Answer:
Step-by-step explanation:
11970658976
Solve the simultaneous equation
-4x+3y=1
6x-y=2
Step-by-step explanation:
multiply 6x - y = 2 by 3 and subtract the first equation from the second
18x-3y=6 - (-4x+3y=2
3y is cancelled and after the others are subtracted the equation becomes
22x = 4
x = 2/11
Answer:
The value of x = 1/2
The value of y = 1
Step-by-step explanation:
Let's change the equation,
→ 6x - y = 2
→ y = 6x - 2
Then the value of x will be,
→ -4x + 3y = 1
→ -4x + 3(6x - 2) = 1
→ -4x + 18x - 6 = 1
→ 14x = 1 + 6
→ x = 7/14
→ [ x = 1/2 ]
Hence, the value of x is 1/2 (or) 0.5.
Now the value of y will be,
→ y = 6x - 2
→ y = 6(1/2) - 2
→ y = 3 - 2
→ [ y = 1 ]
Hence, the value of y is 1.
what is the reference angle for 202 degrees
Answer: 22 degrees
Step-by-step explanation:
Since the angle 180° is in the third quadrant, subtract 180° from 202°.
Find the indicated measure
I will give brainliest to the right answer with solution
Answer:
∠ N = 10° , arc RS = 134°
Step-by-step explanation:
the measure of an inscribed angle is half the measure of its intercepted arc.
(5)
∠ N is an inscribed angle and we require arc LM
the measure of the arcs in a circle = 360°
note LN is the diameter so arc LN = 180°
Then
LM + MN + LN = 360°
LM + 160° + 180° = 360°
LM + 340° = 360° ( subtract 340° from both sides )
LM = 20°
then
∠ N = [tex]\frac{1}{2}[/tex] LM = [tex]\frac{1}{2}[/tex] × 20° = 10°
(6)
∠ Q is an inscribed angle so its intercepted arc is twice its measure
arc RS = 2 × 67° = 134°
In a standard normal distribution the probability of z being less than or equal zero is?
In a standard normal distribution the probability of z being less than or equal zero is 0.5.
What is standard normal distribution?The standard normal distribution, also known as the z-distribution, is a type of normal distribution with a mean of zero and a standard deviation of one.
Some key features regarding the standard normal distribution are-
Any normal distribution's values can be standardized by converting them to z-scores. Z-scores indicate how so many standard deviations each value is from the mean.Transforming a normal distribution to a z-distribution enables you to compute the likelihood of specific values occurring and compare various sets of data.Every normal distribution is a stretched or squeezed version of the standard normal distribution that has been moved horizontally right or left.The mean determines the center of the curve. Increasing the mean shifts the curve to the right, whereas decreasing it shifts the curve to the left.The standard deviation either stretches or compresses the curve.Now, as per the given question;
The mean of a standard normal distribution is 0.
Because this distribution is symmetric, the median is also equal to 0.
So, P ( z ≤ 0 ) = P ( z ≤ median ) = 0.5
Therefore, the standard normal distribution the probability of z being less than or equal zero is 0.5.
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A new go-cart track has opened up in your neighborhood. They charge $10 for a license and $3 for each ride . If you paid in total of $22 , how many rides did you take
Answer:
Step-by-step explanation:
4 rides
Answer:
4 rides is the answer to this question
Need help before 10:30
Answer: I will really try to get answers just wait
Step-by-step explanation:
Please help :(
Use PEMDAS to find the surface area.
81 + 72(4) =
157 km²
369 km²
612 km²
Solve the system of inequalities by graphing.
3x + 4y ≥ 16
-4x+6y < 30
x= -0.706, y= 4.529
The mathematical expression with unequal sides is known as an inequality in mathematics. Inequality is referred to in mathematics when a relationship results in a non-equal comparison between two expressions or two numbers. In this instance, 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 (), is used in place of the equal sign "=" in the expression. Polynomial inequality, rational inequality, and absolute value inequality are the various types of inequalities that can exist in mathematics.
3x+4y z 16
-4x+6y< 30
Solving the two equations we get,
x=-0.706, Y= 4.529
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Please answer this !!!!!! will give brainliest !on first down, the vultures lost 6 yd. on second down, they lost 5yd. on third down, they lost 8 yd. use an integer to express their overall change in position as a result of the three plays.
As per given condition first they lost 5yd , second lost 6yd , third lost 8 yd ,so change in position shows lost 19 yd.
As given,
Let x be the total number of yards in the beginning
First down they lost 5 yards, second 6 yd and third 8 yd.
Required equation,
x-5-6-8
= x-19
Negative sign represent the lost of 19 yads.
Therefore, as per given condition first they lost 5yd , second lost 6yd , third lost 8 yd ,so change in position shows lost 19 yd.
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Revision 1. Find the value of the variable that makes these number sentences true: a) h+8=19 b) 2p-6=4 c) y = 12 2. Substitute the value for x in order to find the value of y in the following: a) y=3x+2 ifx=8 b) y=4x-1 ifx=! c) y=0,2x+5 ifx=10 d) y = 10x+12 if x=0,3 3. Write the following as number sentences: a) The difference between two numbers is 25 b) The product of 5 and p is equal to the quotient of q and 2 c) The difference between 14 and 2y is equal to 6 d) The product of 15 and 4 is equal to four less than the sum of x and y. that represent these word problems.
1. The values which the given number sentences true are:
a) 11 b) 5 c) 36
2. After substituting the value of x we get the value for y as :
a) 6 b) 0 c) 7 d) 15
3. The number sentences are :
a) x ₋ y = 25
b) 5 × p = q ÷ 2
c) 2y ₋ 14 = 6
d) 15 × 4 = 4 ₋ (x₊y)
Given in the first bit we need to find the variables:
a) h ₊ 8 = 19
arrange the constants on one side.
h = 19 ₋ 8
h = 11
b) 2p ₋ 6 = 4
arrange the constants on one side.
2p = 4 ₊ 6
2p = 10
p = 10/2
p = 5
c) 1/3 y = 12
cross multiply.
y = 36
Now in the second exercise we are asked to substitute the x value and get the value of y.
a) y = 3x ₊ 2 if x =8
substitute x value in the equation.
y = 3(8) ₊ 2
y = 24 ₊ 2
y = 26
b) y = 4x ₋ 1 if x = 1/4
y = 4(1/4) ₋ 1
y = 1 ₋ 1
y = 0
c) y = 0.2x ₊ 5 if x = 10
y = 0.2(10) ₊ 5
y = 2 ₊ 5
y = 7
d) y = 10x ₊ 12 if x = 0.3
y = 10(0.3) ₊ 12
y = 3 ₊ 12
y = 15
In the last third bit we need to frame equations for the given word problems.
a) The difference between two numbers is 25.
let the two numbers be x and y.
x ₋ y = 25.
b) The product of 5 and p is equal to quotient of q and 2.
5 × p = q ÷ 2
c) The difference between 14 and 2y is equal to 6.
2y ₋ 14 = 6
d) The product of 15 and 4 is equal to four less than the sum of x and y.
15 × 4 = 4 ₋ (x₊y)
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13. Which function includes the data set below?
{(2, -2), (6, 10), (13, 31)) (Lesson 2-1)
A. f(x)=2x-3
B. f(x) = -2x + 2
C. f(x) = 3x8
D. f(x) = 4x 10.
-
Answer:
C. 3x-8
Step-by-step explanation:
To solve this, we put the x values into the functions and calculate the y values.
A
y = (1/2)x - 3
test for (2, -2)
-2 = 1/2 × 2 - 3 = 1 - 3 = -2 correct
test for (6, 10)
10 = 1/2 × 6 - 3 = 3 - 3 = 0 wrong
so, A cannot be right.
B
y = -2x + 2
test for (2, -2)
-2 = -2×2 + 2 = -4 + 2 = -2 correct
test for (6, 10)
10 = -2×6 + 2 = -12 + 2 = -10 wrong
so, B cannot be right.
C
y = 3x - 8
test for (2, -2)
-2 = 3×2 - 8 = 6 - 8 = -2 correct
test for (6, 10)
10 = 3×6 - 8 = 18 - 8 = 10 correct
test for (13, 31)
31 = 3×13 - 8 = 39 - 8 = 31 correct
so, C is a right answer.
D
y = 4x - 10
test for (2, -2)
-2 = 4×2 - 10 = 8 - 10 = -2 correct
test for (6, 10)
10 = 4×6 - 10 = 24 - 10 = 14 wrong
so, D cannot be right.
I hope this helped! Have a good day! :D
find the midpoint of the line segment with the given points.
Answer:
[tex]\displaystyle (-\frac{5}{2}, 4)[/tex]
Step-by-step explanation:
We will use the midpoint formula to solve.
[tex]\displaystyle (\frac{x_{1}+x_{2} }{2}, \frac{y_{1}+y_{2} }{2} )[/tex]
[tex]\displaystyle (\frac{0+-5 }{2}, \frac{3+5}{2} )[/tex]
[tex]\displaystyle (\frac{-5 }{2}, \frac{8}{2} )[/tex]
[tex]\displaystyle (-\frac{5}{2}, 4)[/tex]
Find the equation of the line shown.
Answer:
y = -2x + 9
Step-by-step explanation:
The standard form of a linear function is y = mx + b, where m is the slope and b is the y-intercept.
The line intersects the y-axis at 9, thus b = 9.
The slope formula is rise/run. The line falls 2 and runs 1, thus m = -2/1, or -2.
y = -2x + 9
what is the lcm of 12,27,30
Answer:
The least common multiple of 12, 27 and 30 is 540.
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Your friend eats 25 strawberries less than 5 times the
amount of strawberries you do. If you eat 10 strawberries,
find out how much your friend eats?
Answer:
25
Step-by-step explanation:
The required amount of strawberries eaten by the friend is given as 25 strawberries.
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Let the number of strawberries he eat be x,
According to the question,
Strawberries that his friend eat = 5x - 25
Put x = 10
Strawberries that his friend eat = 50 - 25 = 25
Thus, the required amount of strawberries eaten by the friend is given as 25 strawberries.
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use the diagram to find bc.
Answer:
BC = 12
Step-by-step explanation:
from the diagram
AB + BC = AC , that is
18 + BC = 30 ( subtract 18 from both sides )
BC = 12
Use substitution to solve the system.
y = 2x+14
3x+2y = -7
Answer: x=-5, y=4 (-5,4)
Step-by-step explanation:
Match each business message to the best delivery method.
We are writing to thank you for providing the support we
needed to meet our delivery targets last week.
Listen up: The Big Shoe store is announcing a storewide
clearance sale!
All employees must obey these updated company Internet
usage policies.
Follow us to learn more about our scuba diving classes for
beginning and advanced divers!
letter
arrowRight
memo
arrowRight
social media
arrowRight
radio
arrowRight
Answer:
The correct pair matching each type of letter to its correct description would be as follows:
send it to favorably influence employers’ decision on hiring you - thank you letter
state how you meet the job requirements - cover letter
send 3-5 days after submitting your application or résumé - follow-up letter
express your desire to work for a particular company - letter of interest
A 'thank you' letter is a letter written to admit gratefulness for a favor that has been done. It can also be written in anticipation of a favor to be done. Hence, writing it to a potential employer after an interview is a way of trying to influence the employer's decision on hiring you.
A cover letter, as it relates to job application, is a letter written to express how one meets the requirement for a job. In it, a job seeker would state their qualifications, skills, and experience as it relates to the job they are applying for.
A follow-up letter is usually written to follow up with a situation that one expects that a response should have been given or written just to further emphasize one's interest in something. Writing a follow-up letter after submitting an application for a job is a way of reminding potential employers of one's desire to take up a job in their firm.
A letter of interest is written to show a desire to work in a particular organization or company irrespective of whether they have got a vacancy.
Step-by-step explanation:
Answer:
Step-by-step explanation:
I need some help please
Step-by-step explanation:
[tex] = \frac{ {2}^{4} }{ {2}^{7} } [/tex]
[tex] = {2}^{4 - 7} [/tex]
[tex] = {2}^{ - 3} [/tex]
[tex] = \frac{1}{ {2}^{3} } [/tex]
[tex] = \frac{1}{2 \times 2 \times 2} [/tex]
[tex] = \frac{1}{8} [/tex]
The answer is not 8, but 1/8.
Create a polynomial that has 4 term, a degree of 6, a leading coefficient of -1 and a
Constant term of -5.5
Answer: Theorems About Roots of Polynomial Equations
Step-by-step explanation:
Theorems About Roots of Polynomial Equations
In the given case we can conclude that the polynomial is [tex]-x^6 + bx^5 + cx^4 + dx^3 + ex^2 + fx - 5.5.[/tex]
To create a polynomial with 4 terms, a degree of 6, a leading coefficient of -1, and a constant term of -5.5, we can use the general form of a polynomial:
A "polynomial" is a mathematical expression consisting of variables (or indeterminates) raised to non-negative integer powers, combined using addition and multiplication. Polynomials are fundamental objects in algebra and are used to represent a wide range of mathematical relationships, including functions, curves, and various mathematical concepts.
P(x) = [tex]ax^6 + bx^5 + cx^4 + dx^3 + ex^2 + fx + g[/tex]
Plugging in the given values, we have:
P(x) = [tex]-x^6 + bx^5 + cx^4 + dx^3 + ex^2 + fx - 5.5[/tex]
Remember that the degree of a polynomial is determined by the highest exponent of x.
In this case, the degree is 6.
The leading coefficient is the coefficient of the term with the highest degree, which is -1. The constant term is -5.5.
So, the polynomial is [tex]-x^6 + bx^5 + cx^4 + dx^3 + ex^2 + fx - 5.5.[/tex]
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If the odds against debroah's winning first prize are 3 to 5, what is the probability that she will win 1st prize?
Answer:
See below
Step-by-step explanation:
Odds AGAINST are 3 to5 then odds FOR are 2 to 5
2/5 = .4 = 40% chance of winning
The maximum of a function is the highest point on a graph (identified as an ordered pair). For the function below, what is the x-value of its maximum.
For the graphed parabola we can see that the maximum is at (3, 2), then the x-value is x = 3.
What is the x-value of the maximum?For a function f(x), we define the maximum as a value y = f(x₀), such that:
f(x₀) ≥ f(x) for every value in the domain.
In the case of the graph is really easy to identify the maximum, in this case, it is in the vertex of the parabola.
We can see that the maximum is on the point (3, 2)
Then it is at x = 3, y = 2, from that, we can see that the x-value of the graphed function is x = 3.
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Your hourly wage is $10.05 per hr when you work during the day and $12.01 per hr when you work the night shift .what is your gross pay for one week if you worked 24 hrs at night and 16 hrs during the day.
The gross income over the whole week upon working during the day and at night is; $449.04.
What is the gross pay for one week if you worked 24 hrs at night and 16 hrs during the day?Since, the pay rates during the day and night according to the task content are; $10.05 per hour and $12.01 per hr respectively.
It then means that the total gross total income can be calculated as follows;
(10.05 × 16) + (12.01 × 24)
= 160.8 + 288.24
= $449.04.
Therefore, the gross income over the whole week upon working during the day and at night is; $449.04.
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