Write the linear inequality shown in the graph. The gray area represents the shaded region
The inequality from the given graph is y≤-3x+5.
What are inequalities?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
From the graph, the coordinate points are (2, -1) and (1, 2).
Here, slope (m)=(2+1)/(1-2)
m=-3
Substitute m=-3 and (x, y)=(2, -1) in y=mx+c, we get
-1=-3(2)+c
-1=-6+c
c=5
Substitute m=-3 and c=5 in y=mx+c, we get
y=-3x+5
So, the inequality is y≤-3x+5
Therefore, the inequality is y≤-3x+5.
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What is the value of the expression 2 + 32 ⋅ (4 − 1)?
Please help answer this questionnnn
y=5
5=1/4x^2+1
4=1/4x^2
16 = x^s
x = square root (16) = 4
x=3
y= 1/4(3)^2+1 = 3 1/4 = 13/4
Given the following functions f(x) and g(x), solve for (f ⋅ g)(2) and select the correct answer below:
f(x) = 3x2 + 2
g(x) = x − 8 (1 point)
Answer:
Given the functions:
[tex]f(x) = 3x^2+2[/tex]
[tex]g(x) = x-8[/tex]
we have to find [tex](f \cdot g)(2)[/tex]
[tex](f \cdot g)(2) = f(2) \cdot g(2)[/tex] ....[1]
Substitute the value of x = 2 in f(x) and g(x) we have;
[tex]f(2) = 3(2)^2+2 =12+2 = 14[/tex] and
[tex]g(2) = 2-8 = -6[/tex]
Substitute these in [1] we have;
[tex](f \cdot g)(2) = 14 \cdot -6 = -84[/tex]
Therefore, the value of [tex](f \cdot g)(2)[/tex] is, -84
-5/4x -5= -35 solve for x
How to write x2+y2+2x-12y-9 in Standard form
Can u help idk how to write it ?
What is the sum of 4.2•10^5 and 5.3• 10^5
Nicole Tobin receives a salary of $250 per week plus a commission of 15% on all sales over $1500. Find her earnings during a week in which sales totaled $3000.
Final answer:
To calculate Nicole Tobin's earnings for a week in which her sales totaled $3000, we first determine the total sales eligible for commission and then calculate 15% commission on that amount. Adding the resulting commission to her weekly salary of $250 gives us Nicole's total earnings for the week, which are $475.
Explanation:
Nicole Tobin receives a salary of $250 per week plus a commission of 15% on all sales over $1500. To calculate her earnings during a week in which her sales totaled $3000, we need to find out the commission on the sales exceeding $1500 and then add it to her weekly salary.
First, we calculate the amount eligible for commission:
Sales = $3000
Threshold for commission = $1500
Eligible amount for commission = Total sales - Threshold for commission = $3000 - $1500 = $1500
Next, we calculate the commission:
Commission rate = 15%
Commission = Eligible amount for commission × Commission rate = $1500 × 0.15 = $225
Finally, we find Nicole's total earnings:
Weekly salary = $250
Total earnings = Weekly salary + Commission = $250 + $225 = $475
Nicole's earnings for the week are $475.
Derek owns a landscape business. He charges a fixed fee of $30 plus $1 per 1,000 square feet of lawn mowed. Derek's earnings (in dollars) in the past five weeks are {204, 344, 450, 482, 504}. To find the corresponding square footage of lawn mowed, construct a function that models the total area of lawn that Derek mows based on his earnings. Based on Derek's earnings, the corresponding square footage of the lawns he mowed in the past five weeks is
Answer:
{174,000, 134,000, 420,000, 452,000, 474,000}
is 3 sin(alpha)+4 cos(beta)=8 possible
Answer:
No, it's not possible
Step-by-step explanation:
We know that for various values of x , [tex]-1\leq \sin x\leq 1[/tex]
and [tex]-1\leq \cos x \leq 1[/tex]
For values of [tex]\alpha[/tex], [tex]-1\leq \sin \alpha\leq 1[/tex]
On multiplying all sides by 3, we get
[tex]-3\leq 3\sin \alpha\leq 3[/tex]
For values of [tex]\beta[/tex], [tex]-1\leq\cos \beta\leq 1[/tex]
On multiplying all sides by 4, we get
[tex]-4\leq 4\cos \beta\leq 4[/tex]
On adding all sides of [tex]-3\leq 3\sin \alpha\leq 3\,\,,\,\,-4\leq 4\cos \beta\leq 4[/tex] , we get
[tex]-3-4\leq 3\sin \alpha+ 4\cos \beta\leq 3+4\\-7\leq 3\sin \alpha+ 4\cos \beta\leq 7[/tex]
Therefore, maximum value of [tex]3\sin \alpha+ 4\cos \beta[/tex] is 7.
So, it's not possible that [tex]3\sin \alpha+ 4\cos \beta=8[/tex]
Selma uses a jogging trail that runs through a park near her home. The trail is a loop that is 3/4 of a mile long. On Monday, Selma ran the loop in 1/6 of an hour. What is Selma's unit rate in miles per hour for Monday's run?
Pittsburgh international airport had approximately 714,587 passengers in august 2009. Write a number that is greater than 714,587.
given A = {a, e, i, o, u} and B = {a, l, g, e, b, r}, find A ∪ B.
{}
{a,e}
{a, b, e, g, i, l, o, r, u}
Emily made 75% of the baskets that she attempted if she may nine baskets how many attempts did you make?
Julia wrote 14 letters to friends each month for y months in a row. Write an expression to show how many total letters she wrote.
The ratio between the number of cats (c) and the number of dogs (d) in the shelter is 3. There are 27 cats in the shelter. How many dogs are in the shelter?
What is the value of z in the equation 5z − 9 = 36? 4 5 6 9
What is 10 times 7 thousands
Solve for x. Rs/x =1/4 A. X=rs/4 B. X=4/rs C. X=1/4rs D. X=4rs
Answer:
The correct option is D.
Step-by-step explanation:
The given equation is
[tex]\frac{Rs}{x}=\frac{1}{4}[/tex]
We need to solve the given equation for x.
On cross multiplication we get
[tex]Rs\times 4=1\times x[/tex]
On further simplification we get
[tex]4Rs=x[/tex]
The value of x is 4 times of Rs. Only option D represents this situation.
Therefore, the correct option is D.
Which of the following numbers has a value that is between 10% and 1/9? (a) 0.151 (b) 0.112 (c) 0.108 (d) 0.019
Among the given options, (c) 0.108 is the only number that lies between 0.10 (which is the decimal equivalent of 10%) and 0.111 (which is approximate decimal equivalent of 1/9).
Explanation:To answer the question "Which of the following numbers has a value that is between 10% and 1/9?", we first need to convert 10% and 1/9 into decimal form. 10% is equivalent to 0.10, and 1/9 is approximately 0.111. We are therefore looking for a number between 0.10 and 0.111.
Reviewing the options, (a) 0.151, (b) 0.112, (c) 0.108, and (d) 0.019, we see that only (c) 0.108 fits because it falls between 0.10 and 0.111.
Therefore, the correct answer is (c) 0.108.
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Find two numbers that have 2,3 and 5 as factors. What other factors do the two numbers have in common?
Two numbers are 30 and 60 that have 2,3 and 5 as factors.
What is LCM ?LCM is the least common multiple of two or more that two given numbers which is exactly divisible by these given numbers.
According to the given question we have to find two numbers that have 2, 3 and 5 as common factors.
To find least such number which have common factor of 2, 3 and 5 we have to take LCM of 2, 3 and 5.
The LCM of 2, 3 and 5 is 30.
The next such possible higher numbers will be of the form 30k, where k is an integer.
At k = 2,
The number 30k will be 30(2) which is
= 60.
We can find any such form of numbers by putting different integer value of k.
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Which statement is false? A.The all them of a regular polygon is perpendicular to the side. B.the radius of a regular polygon is always greater than the all them. C.the perimeter of a regular hexagon is 6r. D.the perimeter of a regular n-gob is the area divided by the all them.
four times the square of a non-zero number is equal to twelve times the number.
3 is the number whose four times the square is equal to twelve times 3.
What is equation?An equation is a relationship between two or more variables expressed in equal to sign. It is solved to find the value of variables. Equation of two variables will look like ax+ by=c.
How to find number?Let the required number be x.
According to question we have to form an equation which will be:
4[tex]x^{2}[/tex]=12x
[tex]4x^{2} -12x=0[/tex]
4x(x-3)=0
4x=0, x-3=0
x=0, x=3
Non negative number=3
Hence 3 is the number whose 4 times square is equal to 12*3.
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The best length of a triangle is 4 feet and the height is 2 feet. What is the area of the triangle?
Tess and Dan have $24.00 each to spend at a book fair, where all students receive a 15% discount. They both want to purchase a copy of the same book, which normally sells for $24.50 plus 10% sales tax. To check if she has enough to purchase the book, Tess takes 15% of $24.50 and subtracts that amount from the normal price. She takes 10% of the discounted selling price and adds it back to find the purchase amount. Dan takes 85% of the normal purchase price and then computes 110% of the reduced price. Is Tess correct? Is Dan correct? Do they have enough money to purchase the book? Explain your answer using complete sentences, and show your work.
Answer:
Tess is wrong and Dan is correct because the tax is calculated after discount.
Step-by-step explanation:
Add 3 7/12 +2 7/9. Simplify the answer and write as a mixed number.
3 7/12 = 43/12
2 7/9 = 25/9
both denominators must be the same to add together.
(25/9)x 12
(43/12) x 9
300/108 + 387/108 =
687/108
which in its simplest form is 229/36
and in a mixed number is 6 13/36
You run 6 miles in 1 hour. At this rate how long will it take you to run a marathon of 26 miles?
During an 8 hour car ride to Georgia, my dog Pepper whined for 1/3 of the ride. How many hours did she whine
multiply 8 by 1/3
8* 1/3 = 8/3 =2 2/3 hours