Which linear inequality is represented by the graph?y ≤ x − 1y ≥ x − 1y < 3x − 1y > 3x − 1
Answers
Equation of a straight line graph is given in the form [tex]y = mx+c[/tex] where [tex]m[/tex] is the slope of the line and [tex]c[/tex] is the y-intercept.
The graph given shows the line intercept y-axis at (0, -1)
To work out the slope, choose any two coordinates then find their vertical and horizontal distance. Say we choose (0, -1) and (3, 0)
The vertical distance is 1 and the horizontal distance is 3, so the slope is
[tex]m = \frac{-1-0}{0-3}= \frac{-1}{-3}= \frac{1}{3} [/tex]
Then form the equation for the line
[tex]y=mx+c[/tex]
[tex]y= \frac{1}{3}x-1 [/tex]→ Multiply each term by 3
[tex]3y = x - 3[/tex]
Now the inequality part, the shaded region is above the line, so the values intended are 'greater than' and the line is a bold line, so the inequality is 'greater than or equal to' and the symbol is ≥
The inequality is then
3y ≥ x - 3
Note: None of the options show this answer. Maybe check if the original options have been copied correctly.
Solution: As the line shown in the graph passes through (3,0) and (0,-1).
So, equation of line passing through (3,0) and (0,-1) is given by two point formula i.e equation of line passing through (p,q) and (a,b) is given by
→[tex]\frac{y-q}{x-p}=\frac{q-b}{p-a}[/tex]
→[tex]\frac{y-0}{x-3}=\frac{0+1}{3-0}[/tex]
So ,the equation of line is ,→3 y = x-3
→ x- 3 y -3= 0 or y=x/3 -1
take point (0,0) and putting in the above equation, we see that ,L.H.S>R.H.S
Similarly if you take other points , like (1,0).(0,1) we see that ,L.H.S>R.H.S.
it means the above equation can be written as , y≥x/3 -1.
None of the option is correct.
Related Questions
A club with 15 women and 12 men need to form a committee that consists of a president, a vice president, a secretary, and a treasurer. how many committees are possible…
a. if the committee must have two women and two men?
Answers
where [tex]\displaystyle{ C(n, r) = \frac{n!}{r!(n-r)!} [/tex], r! being [tex]1\cdot2\cdot...\cdot r[/tex].
Thus, 2 women out of 15 can be selected in a total of C(15, 2) many ways, and 2 men out of 12, can be selected in C(12, 2) many ways.
Any possible pair of women can be combined with any pair of men, thus there are a total of [tex]C(15, 2)\cdot C(12, 2)[/tex] many ways of forming the committee.
[tex]C(15, 2)\cdot C(12, 2)= \displaystyle{ \frac{15!}{2!13!}\cdot \frac{12!}{2!10!}= \displaystyle{ \frac{15\cdot14\cdot13!}{2!13!}\cdot \frac{12\cdot11\cdot10!}{2!10!}[/tex]
[tex]\displaystyle{ = \frac{15\cdot14}{2}\cdot \frac{12\cdot11}{2}=15\cdot 7\cdot6\cdot11= 6,930[/tex]
Answer: 6,930
What is the Solution of the following system?
{-3x -2y = -12
{9x + 6y= -9
Imagine those two bracket things are one big one connecting both equations, and the answers are A (2,1) B No Solutions C (-2, -1) D Infinitely Many Solutions
@Emma11234
Answers
One of the methods we can use to solve the system is the elimination method. In this method we multiply one of the equations with a certain value, such that when the this equation is added to the other one, one of x or y cancels out:
Notice that we can eliminate the variable y by multiplying the first equation by 3, and adding it to the second equation:
the system becomes:
-9x-6y=-36
9x+6y=-9
adding the left hand sides, and the right hand sides of the equations we have:
0=-45, which is not true. This means that the system has no solutions because all the operations we used are valid, but the result is absurd.
Answer: B. No solutions.
Remark:
we could have noticed that the coefficients of x and y in both equations are proportional. (-3*(-3)=9, -2*(-3)=6)
In such situations, if the numbers in the right hand side are also proportional, then the solution has infinitely many solutions,
if not, as in our case, the system has no solution.
At a charity bike rally, 2/3 of the student population of Heartsworth Middle School participated. If there are 1,200 students in Heartsworth, how many participated?
Answers
(2÷3)×(1200)= 800
800 students participated at a charity bike rally
What are mathematics operations?
• A mathematical operation is a function that converts a set of zero or more input values (also called "b" or "arguments") into a defined output value. The number of operands determines the operation's arity. Most commonly studied operations are binary operations (i.e., operations of arity 2), such as addition and multiplication, and unary operations (i.e., operations of arity 1), such as additive and multiplicative inverses.
• Zero-arity operations, or nullary operations, are constants, and mixed products are arity three operations, or ternary operations.
It is given that :
there are 1200 students population of Heartsworth Middle School.
and, 2/3 of the student participated in a charity bike rally That is :
(2 x 1200)/ 3 = 2400/3 = 800 students
Therefore, 800 students participated at a charity bike rally.
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Find a formula for the sum of the first n even positive integers.
b.prove the formula that you conjectured in part (a)
Answers
(a) The formula for the sum of the first n even positive integers is n(n+1) and (b) the formula has been proved with an example.
What is an arithmetic progression?Arithmetic progression is the sequence of numbers that has a fixed common difference between any two consecutive numbers.
For the given situation,
Part (a):
The sum of even numbers formula is obtained by using the sum of terms in an arithmetic progression formula.
Sum of Even Numbers Formula = n(n+1),
where n is the number of terms in the series.
Part (b):
Let us consider the even positive numbers,
2,4,6,8,10,.......
Now take first 5 positive numbers 2,4,6,8,10
By using the formula, n=5
Sum of n even positive integers = [tex]n(n+1)[/tex]
⇒ [tex]5(5+1)[/tex]
⇒ [tex]5(6)[/tex]
⇒ [tex]30[/tex].
Now add the first 5 positive numbers without the formula,
⇒ [tex]2+4+6+8+10=30[/tex]
Hence we can conclude, that the formula for the sum of the first n even positive integers is n(n+1) and the formula has been proved with an example.
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The formula for the sum of the first n even positive integers is S = n(n+1). This was derived by recognizing the pattern of the series and using the formula for the sum of an arithmetic series. The proof by induction confirms the validity of our formula.
Explanation:The problem asks us to find and prove a formula for the sum of the first n even positive integers. To find the formula, we recognize that the first n even integers can be represented as 2, 4, 6, ..., 2n. Hence, the sum S of the first n even integers can be written as S = 2 + 4 + 6 + ... + 2n. This is an arithmetic series with the first term a = 2 and the common difference d = 2. The sum of an arithmetic series can be given by the formula S = n/2 [2a + (n-1)d], substituting a = 2 and d = 2, we get S = n/2 [2*2 + (n-1)2] = n[2 + 2(n-1)], which simplifies to S = n(n+1).
To prove this formula, we use induction. For n=1, the sum is 2, which matches our formula 1(1+1) = 2. Assuming the formula holds for n = k, for n = k+1, the sum would include one more term, 2(k+1), so the new sum is S + 2(k+1) which upon simplification, verifies our formula for all n.
: A bookstore owner is conducting market research to forecast sales for the coming year. The bookstore is open 360 days a year and out of the 1,200 people who pass the store each day, 8% of them enter the store and make a purchase. The average amount of each sale is $18. What is the estimated amount of sales for the coming year?
Answers
Answer:
622,080
Step-by-step explanation:
thanks me later
(Fill in the blank )
Zero pairs are two numbers that ______ to get zero.
A. Subtract
B. Add
C. Divide
D. Multiply
Answers
B. Add
Helena needs 3.5 cups of flour per loaf of bread and 2.5 cups of flour per batch of muffins. She also needs 0.75 cup of sugar per loaf of bread and 0.75 cup of sugar per batch of muffins. Helena has 17 cups of flour and 4.5 cups of sugar available for baking.
Which combination of loaves of bread and batches of muffins could Helena bake?
Answers
Answer:
Helen can make 2 loaves of bread and 4 batches of muffins.
Step-by-step explanation:
Let x be the number of loaves of bread
Let y be the number of batches of muffins
As per the given requirement of flour, the equation becomes:
[tex]3.5x+2.5y=17[/tex] .......(1)
As per the given requirement of sugar, the equation becomes:
[tex]0.75x+0.75y=4.5[/tex] .....(2)
Multiplying equation (1) with 0.3 and subtracting (2) from (1)
[tex]1.05x+0.75y=5.1[/tex] now subtracting (2) from this we get
=> [tex]0.3x=0.6[/tex]
So, x = 2
And as [tex]3.5x+2.5y=17[/tex] ; so substituting x = 2 here we get
[tex]3.5(2)+2.5y=17[/tex]
[tex]7+2.5y=17[/tex]
[tex]2.5y=17-7[/tex]
[tex]2.5y=10[/tex]
So, y = 4
Hence, there will be 2 loaves of bread and 4 batches of muffins.
the total cost of a bus ride and a ferry ride is $8.00. in one month, bus fare will increase by 10% and ferry fare will increase by 25%. the total cost will then be 9.25. how much is the current bus fare?
Answers
x + y = 8
The bus fare will increase by 10% and the ferry fare will increase by 25%.
1.1x + 1.25y = 9.25
Multiply the first equation by -1.1:
-1.1x - 1.1y = -8.8
Add this to the original second equation.
0.15y = 0.45
y = 3
x + y = 8
x + 3 = 8
x = 5
The bus fare is $5, and ferry fare is $3.
1. What is the area of a parallelogram whose vertices are A(−1, 12) , B(13, 12) , C(2, −5) , and D(−12, −5) ?
2.
Each small square on the grid is 1 ft².
Which estimate best describes the area of this figure?
25 ft²
35 ft²
50 ft²
65 ft²
Answers
Write the equation in the slope-intercept form. 7x − 4y + 8 = 0
Answers
Final answer:
To convert the equation 7x - 4y + 8 = 0 to slope-intercept form, solve for y to get y = (7/4)x + 2, with a slope of 7/4 and a y-intercept of 2.
Explanation:
To write the equation 7x − 4y + 8 = 0 in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept, we want to solve for y. The steps are as follows:
Subtract 7x and 8 from both sides of the equation to isolate terms involving y: -4y = -7x - 8.Divide every term by -4 to solve for y: y = (7/4)x + 2.Thus, the equation of the line in slope-intercept form is y = (7/4)x + 2. Here, the slope is 7/4 and the y-intercept is 2.
What is the perimeter of the triangle shown on the coordinate plane, to the nearest tenth of a unit? 20.6 units 22.7 units 25.6 units 27.6 units
Answers
we know that
the perimeter of a polygon is the sum of the length sides
in this problem we have a triangle
so
the polygon has three sides
Let
[tex]A(-5,4)\\B(1,4)\\C(3,-4)[/tex]
the perimeter is equal to
[tex]P=AB+BC+AC[/tex]
The formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
Step 1
Find the distance AB
[tex]A(-5,4)\\B(1,4)[/tex]
substitutes the values in the formula
[tex]d=\sqrt{(4-4)^{2}+(1+5)^{2}}[/tex]
[tex]d=\sqrt{(0)^{2}+(6)^{2}}[/tex]
[tex]dAB=6\ units[/tex]
Step 2
Find the distance BC
[tex]B(1,4)\\C(3,-4)[/tex]
substitutes the values in the formula
[tex]d=\sqrt{(-4-4)^{2}+(3-1)^{2}}[/tex]
[tex]d=\sqrt{(-8)^{2}+(2)^{2}}[/tex]
[tex]d=\sqrt{68}[/tex]
[tex]dBC=8.25\ units[/tex]
Step 3
Find the distance AC
[tex]A(-5,4)\\C(3,-4)[/tex]
substitutes the values in the formula
[tex]d=\sqrt{(-4-4)^{2}+(3+5)^{2}}[/tex]
[tex]d=\sqrt{(-8)^{2}+(8)^{2}}[/tex]
[tex]d=\sqrt{128}[/tex]
[tex]dAC=11.31\ units[/tex]
Step 4
Find the perimeter
the perimeter is equal to
[tex]P=AB+BC+AC[/tex]
substitutes the values
[tex]P=6+8.25+11.31=25.56\ units=25.6\ units[/tex]
therefore
the answer is
[tex]25.6\ units[/tex]
Ricardo is constructing a line through point P that is perpendicular to line m. He has already constructed the arc shown.
He places his compass on point X to construct an arc.
What must be true about the width of the compass opening when Ricardo draws the arc?
It must be less than 1/2XY.
It must be equal to XY .
It must be equal to PX .
It must be greater than 12XY.
Answers
Answer:
It must be greater than 1/2XY.
Step-by-step explanation:
We draw an arc from point X below the arc that passes through X and Y. Keeping our compass the same width, we will draw another arc from point Y below, intersecting the first arc.
If the width of the compass is not set to more than 1/2XY, then the two arcs will not intersect and we will not complete our construction.
Perpendicular lines are lines that meet at 90 degrees.
The true statement about the width of the compass is that: (d) It must be greater than 1/2XY.
From the question, we understand that he has drawn arc XY already.
The next step is to draw an arc less than the width of XY, but greater than half width XY.
This will ensure that the arcs bisect one another.
Hence, the true option is (d).
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Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. write the polynomial in standard form. (1 point) 4, -14, and 5 + 8i
Answers
for the zero 4 you can write (x-4)
for the zero -14 you can write (x+14)
for the zero 5+8i since it is complex it will be accompanied with its conjugate 5-8i so you can write (x-(5+8i) and (x-(5-8i)) =(x^2-10x+89)
so
(x-4)(x+14)(x^2-10x+89)
expanding
x^4-67x^2+1450x-4984=0
The required polynomial function is x⁴ - 67x² + 1450x - 4984 = 0 with 4 degrees with real coefficients.
What is a polynomial?A polynomial is defined as a mathematical expression that has a minimum of two terms containing variables or numbers. A polynomial can have more than one term.
The zeros are given in the question as 4, -14, and 5 + 8i
The required polynomial function of minimum degree with real coefficients whose zeros include those listed above.
For the zero 4, you can write (x-4)
For the zero -14, you can write (x+14)
For the zero 5+8i since it is complex it will be accompanied by its conjugate 5-8i
So, you can write (x-(5+8i) and (x-(5-8i)) =(x²-10x+89)
(x - 4)(x + 14)(x² - 10x + 89)
Expanding the expression, we get
x⁴ - 67x² + 1450x - 4984 = 0
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Write log3 6 as a logarithm of base 2.
log base 2 of 3 over log base 2 of 6
log base 2 of 6 over log base 2 of 3
log base 3 of 2 over log base 6 of 2
log base 6 of 2 over log base 3 of 2
Answers
Using the change-of-base formula:
log3(x)=logb(x)/logb(a)
to write log3(6) as a logarithm of base 2: a = 3, x = 6, b = 2:
log3(6)=log2(6)/log2(3)
hope this helps ^-^
Answer:
Option 2 - log base 2 of 6 over log base 2 of 3
Step-by-step explanation:
Given : Expression [tex]\log_3 6[/tex]
To find : Write the expression as a logarithm of base 2?
Solution :
Expression [tex]\log_3 6[/tex]
Applying the change-of-base formula,
[tex]\log_a(x)= \frac{\log_b(x)}{\log_b(a)}[/tex]
On comparing, a = 3, x = 6, b = 2
Substitute in the formula,
[tex]\log_3 (6)= \frac{\log_2(6)}{\log_2(3)}[/tex]
Therefore, Option 2 is correct.
Option 2 - log base 2 of 6 over log base 2 of 3
Martin drives to work at a speed of 45 miles per hour. It takes him about 2 hours and 15 minutes to get to work. If gas costs $2.75 per gallon and Martin’s car gets 25 miles per gallon, about how much does Martin spend on gas to get to work?
Answers
2.25 * 45 = 101.25 miles to work
101.25 / 25 = 4.05 gallons of gas
4.05 * 2.75 = $11.14 total cost of gas
PLEASE HELP ME :( I DONT UNDERSTAND! A teacher already had a certain number of canned goods for the food drive. Each day of the food drive, the class plans to bring in 10 cans. The total number of canned goods for 10 is 205. Assume the relationship is linear. Find and interpret the rate if change and the initial value.
Answers
A scuba diver descends at a rate of 40 feet per minute. How many feet will the scuba diver move in 2 minutes?
Answers
40 feet x 2 minutes = 80 feet
On a particular road map 1/2 inch represents 18 miles about how many miles apart are 2 towns that are 21/2 inches apart on this map
Answers
(21/2) / (1/2) = 21
So we know that there are 21 sets of 1/2 in 21/2, and since 1/2 and 18 are equal, we can say we know there are 21 sets of 18.
We can multiply to find this.
21 * 18 = 378
So two towns are 378 miles apart.
prove that x-s-t is a factor of x^3 - s^3 -t^3 -3st(s+t)
Answers
To prove that (x-s-t) is a factor of the polynomial $x^3 - s^3 - t^3 -3st(s+t)$, we applied the factor theorem which states that (x-c) will be a factor of a polynomial if f(c) equals zero. By substituting x with (s+t) into the polynomial, we got a value of zero, confirming that (x-s-t) is indeed a factor.
Explanation:To prove that (x-s-t) is a factor of $x^3 - s^3 -t^3 -3st(s+t)$, we can use the factor theorem. According to the factor theorem, a polynomial f(x) has a factor (x-c) if and only if f(c) equals zero.
Given the polynomial $x^3 - s^3 - t^3 -3st(s+t)$, we substitute (x = s + t) into the polynomial, thus:
$f(s + t) = (s + t)^3 -s^3 -t^3 - 3st(s + t)$.
After simplifying the equation, we obtain:
$s^3 + 3s^2t +3st^2 + t^3 - s^3 - t^3 - 3st^2 - 3s^2t$.
When we cancel out the like terms, the result is 0. Therefore,
$(x - s - t)$ is a factor of the given polynomial $x^3 - s^3 -t^3 -3st(s+t)$. This proves our result according to the Factor theorem.
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Tom went to his car in the morning and saw that a car or truck had bumped into it during the night, causing a lot of damage. What is the most likely outcome of this situation?
His finance company will reduce his interest.
His insurance company will lower his monthly payments.
His insurance company will pay for damages.
His finance company will increase his interest.
Answers
Answer:
His insurance company will pay for damages.
Step-by-step explanation:
An insurance is a form of contract that permits an individual to transfer the responsibilities of a financial loss to an insurance company. The company bears the risk of the financial loss. Small amount of money are collected from their clients and summed together to pay for losses that the client may encounter in the future. Insurance safeguards an individual and his property from losses, misfortune, hazards or theft. Covered losses are paid for by the insurance company thereby reducing the financial costs for the individual. Examples include auto insurance , health insurance, disability insurance, and life insurance.
Kesia knows that 1/4=0.25. Explain how she could use this fact to determine the decimal equivalent of 5/8
Answers
[tex]0.25 = \frac{1}{4} = \frac{2}{8} [/tex]
[tex] \frac{5}{8} = \frac{2}{8} + \frac{2}{8} + \frac{1}{8} = \\ 0.25 + 0.25 + \frac{0.25}{2} = \\ 0.25 + 0.25 + 0.125 = 0.625 [/tex]
Answer:
0.625
Step-by-step explanation:
We are given that
Kesia knows =[tex]\frac{1}{4}=0.25[/tex]
We have to determine the decimal equivalent to [tex]\frac{5}{8}[/tex] using given decimal value.
[tex]\frac{5}{8}[/tex] can be written as
[tex]\frac{5}{8}=\frac{2}{8}+\frac{2}{8}+\frac{\frac{1}{4}}{2}[/tex]
[tex]\frac{5}{8}=\frac{1}{4}+\frac{1}{4}+\frac{\frac{1}{4}}{2}[/tex]
[tex]\frac{5}{8}=0.25+0.25+\frac{0.25}{2}[/tex]
[tex]\frac{5}{8}=0.50+\frac{0.25}{2}[/tex]
[tex]\frac{5}{8}=0.625[/tex]
Hence,[tex]\frac{5}{8}=0.625/tex]
which overlapping triangles are congruent by ASa
Answers
The graph of the function B is shown below. If B(x) = -1, then what is x?
A. -1
B. 1
C. 2
A is NOT The answer, the answer is either B or C!!!
Answers
If it takes Ashley 3 seconds to run from the batters box to first base at an average speed of 6.5 m/sec, what is the distance that she covers in that time?
Answers
Which set of statements always have the same truth value
A) Conditional and Converse
B) Conditional and Inverse
C) Inverse and Contrapositive
D) Conditional and Contrapositive
Answers
The set of statements always have the same truth value will be Conditional and Contrapositive i.e. Option [tex](D)[/tex] .
What is Conditional and Contrapositive?
Conditional and Contrapositive : If the conditional statement is “If P then Q.” Then converse of the conditional statement is “If Q then P.” The contrapositive of the conditional statement is “If not Q then not P.” The inverse of the conditional statement is “If not P then not Q.”
So,
As per given options,
Option [tex](B)[/tex] and [tex](C)[/tex] have inverse, so they have nothing to do with inverse.
Now,
So, according to the above mentioned definition,
Option [tex](D)[/tex] Conditional and Contrapositive is the correct option.
Hence, we can say that the set of statements always have the same truth value will be Conditional and Contrapositive Option [tex](D)[/tex] .
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How do I write the height h of the rectangle as a function of x.
Answers
(4x-x^2)-2x=2x-x^2
To write the height h of the rectangle as a function of x, you need to understand the relationship between the height and the other variables involved.
To write the height h of the rectangle as a function of x, you need to understand the relationship between the height and the other variables involved. In a rectangle, the height is typically perpendicular to the base.
So, if we assume that x represents the base length, then the height h can be written as a function of x using an equation.
For example, if the rectangle has a fixed width, the height can be calculated using the following equation: h = f(x), where f is the function that describes the relationship between the base length x and the height h.
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What is h(10) equal to?
Answers
h(10) = 10^2 - 10. 100 - 10 = 90
h(10) = 90.
89.87 is 215% of what number
Answers
89.87 is 215% of approximately 41.8. This is found by converting 215% to a decimal (2.15) and dividing the given number (89.87) by this decimal.
Explanation:
The student's question relates to an application of percentages. To work out this problem, we must first understand that in this context, 215% is equivalent to 2.15 when transformed into a decimal. We then divide the given number, 89.87, by 2.15 to find the original value. The calculation would be as follows: 89.87 ÷ 2.15, which equates to approximately 41.8. Therefore, 89.87 is 215% of the number 41.8.
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Number 28 plz?????!!?!???
Answers
64 - 4 divided by 4 is
60 div by 4 = 15. No, 65 is not correct.
Let's try again, following Order of Operations rules:
Anything within parentheses is done first, followed by exponentiation. After that it's mult. or div., and after that it's addn. or subtr.
8^2 - 4 divided by 2 + 2 = 65
Do 8^2 first; correct result is 64.
"-4 div by 2" is -2; adding 2 results in zero.
Then we have 64 = 65 (which is false.
Are you positive that the original problem included a '65,' not a '64?'
graph and solve the system
3x+6y-12= 0
x + 2y = 8
Answers
Y-intercept: 2
Slope: -1/2
Y-intercept:4
hope this helped :)