Consider this system of inequalities.
x + y ≤ –3
y < StartFraction x Over 2 EndFraction
Which graph shows the solution for this system?
Answers
The line x + y ≤ –3 will be solid and shaded below the graph and the line y < x/2 will be dashed and shaded below the graph.
Graphing linear inequalities.Inequalities is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.
When graphing the inequalities x + y ≤ –3, the line will intersects the y-axis at the coordinate point (0, -3) and the line will be solid and shaded below the graph.
When graphing the inequalities y < x/2, the line will intersects the y-axis at the coordinate point (0, 0) and the line will be dashed and shaded below the graph.
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Related Questions
evaluate the polynomial function at x=-2 using direct and synthetic substitution f(x)=3x⁵-x³+6x²-x+1
Answers
Answer:
-61
by both methods
Step-by-step explanation:
Let's first see what the terms direct substitution and synthetic substitution mean.
Direct Substitution
In direct substitution, to find the value of a polynomial f(x) at any point x = k. we simply substitute the value of k into the polynomial function and solve for f(k)
Synthetic Substitution
In synthetic substitution we make use of the Remainder Theorem..
The Remainder Theorem states that when we divide a polynomial [tex]f(x)[/tex] by [tex]x-c[/tex], the remainder [tex]R[/tex] equals [tex]f(c)[/tex]
Solving using direct substitution
The given polynomial is
[tex]f(x) = 3x^5 - x^3 + 6x^2 - x + 1[/tex]
and we are asked to evaluate this function at [tex]x = - 2[/tex]
Using Direct Substitution,
[tex]f(-2) = =3\left(-2\right)^5-\left(-2\right)^3+6\left(-2\right)^2-\left(-2\right)+1\\\\=3\left(-32\right)-\left(-8\right)+6\left(-2\right)^2-\left(-2\right)+1\\\\=- -96 + 8 + 6(4) + 2 + 1\\=-96 + 8 + 24 + 2 + 1\\\\= -61\\\\[/tex]
Using direct substitution we get [tex]\bold{f(-2)= -61}[/tex]
Using Synthetic Substitution
Since the remainder when [tex]f(x)[/tex] is divided by [tex]x - c[/tex] is [tex]f(c)[/tex] , we will divide the polynomial [tex]f(x) = 3x^5 - x^3 + 6x^2 - x + 1[/tex] by [tex]x -(-2) = x + 2[/tex] and find out the remainder which will give f(-2)
This is the technique used in synthetic division
Step 1. Write only the coefficients of [tex]x[/tex] in the dividend inside an upside-down division symbol. Write -2 as the divisor on the left of this row
[tex]\begin{matrix}\texttt{\:\:-2|\:\:\:3\:\:\:0\:\:-1\:\:\:6\:\:-1\:\:\:1}\\ \;\;\;\;\;\;\;\texttt{\:\:\:\:|\underline{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\;\;\;\;\;\;\;\;\;\;\;\;\;}}\\ \texttt{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:}\end{matrix}[/tex]
Step 2
Carry down the leading coefficient as is to below the division symbol
[tex]\begin{matrix}\texttt{\:\:-2|\:\:\:3\:\:\:0\:\:-1\:\:\:6\:\:-1\:\:\:1}\\ \;\;\;\;\;\;\;\texttt{\:\:\:\:|\underline{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\;\;\;\;\;\;\;\;\;\;\;\;\;}}\\ \texttt{\:\:\:\:\;\;\;\;3\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:}\end{matrix}[/tex]
Step 3
Multiply the above carry-down value by -2 and carry that result to the next column:
[tex]3\left(-2\right)=-6[/tex]
[tex]\begin{matrix}\texttt{\:\:\:\:\:\:-2|\:\:\:3\:\:\:\:\:\:\:0\:\:-1\:\:\:6\:\:-1\:\:\:1}\\\texttt{\:\:|\ensuremath{\underline{\;\;\;\;\;\:\:\:-6\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:}}}\\\texttt{\:3\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:}\end{matrix}[/tex]
Step 4
Add down the column
[tex]\begin{matrix}\texttt{\:\:\:\:\:\:-2|\:\:\:3\:\:\:\:\:\:\:0\:\:-1\:\:\:6\:\:-1\:\:\:1}\\\texttt{\:\:|\ensuremath{\underline{\;\;\;\;\;\:\:\:-6\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:}}}\\\texttt{\:3\:\:\:\:\:\:\:\:-6\:\:\:\:\:\:\:\:\:\:\:\:}\end{matrix}[/tex]
Step 5
Multiply the above carry-down value by -2 and carry that result to the next column:
(-6)(-2) = 12
2 | 3 0 -1 6 -1 1
| -6 12
-------------------------------------------------
3 -6
Step 6
Add down the column
-1 + 12 = 11
2 | 3 0 -1 6 -1 1
| -6 12
-------------------------------------------------
3 -6 11
Repeat this process for the other two coefficients
The final result is
2 | 3 0 -1 6 -1 1
| -6 12 -22 32 -62
-------------------------------------------------
3 -6 11 -16 31 -61
The last carry-down value s the remainder and the value of f(-2) = - 61
The difference of 7 and the product of 2 and a number.
Answers
estimate the slope of the tangent line at p by averaging the slopes of the two adjacent secant lines corresponding to the two points closest to p.
Answers
The secant line connects two points on a graph's curve:
Secant lines PQ have slopes of -213.5, -187, -145, -113.5, and -85.The tangent line's average slope is -166.Point P: (15, 1257)
(a) The secant lines' slopes PQ.
The points are as follows:
Q = {(5, 3410), ( 10, 2210), (20, 550), (25, 145), (30, 0)}The slope (m) is calculated using:
Therefore, the secant line connects two points on a graph's curve:
Secant lines PQ have slopes of -213.5, -187, -145, -113.5, and -85.The tangent line's average slope is -166.The slope (m) is calculated as follows:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
So far, we have:
The slope of the secant line for Q = (5,3410) is:
[tex]\begin{aligned}m_1 &=\frac{1275-3410}{15-5} \\m_1 &=\frac{-2135}{10} \\m_1 &=-213.5\end{aligned}[/tex]
The slope of the secant line for Q = (10, 2210) is:
[tex]\begin{aligned}&m_2=\frac{1275-2210}{15-10} \\&m_2=\frac{-935}{5} \\&m_2=-187\end{aligned}[/tex]
The slope of the secant line for Q = (20, 550) is:
[tex]\begin{aligned}&m_3=\frac{1275-550}{15-20} \\&m_3=\frac{725}{-5} \\&m_3=-145\end{aligned}[/tex]
The slope of the secant line for Q = (25, 145) is:
[tex]\begin{aligned}&m_4=\frac{1275-140}{15-25} \\&m_4=\frac{1135}{-10} \\&m_4=-113.5\end{aligned}[/tex]
The slope of the secant line for Q = (30, 0) is:
[tex]\begin{aligned}&m_5=\frac{1275-0}{15-30} \\&m_5=\frac{1275}{-15} \\&m_5=-85\end{aligned}[/tex]
(b) The average slope of the tangent.
The secant lines that are closest to tangent P are:
Q = {( 10, 2210), (20, 550)}This is because point P (15, 1275) is located between the two previous points.
The slopes of secant lines at Q = {( 10, 2210), (20, 550)} are:
[tex]\begin{aligned}&m_2=-187 \\&m_3=-145\end{aligned}[/tex]
The average slope (m) is as follows:
[tex]\begin{aligned}&m=\frac{m_2+m_3}{2} \\&m=\frac{-187-145}{2} \\&m=\frac{-332}{2} \\&m=-166\end{aligned}[/tex]
Hence, the average slope is -166.
Therefore, the secant line connects two points on a graph's curve:
Secant lines PQ have slopes of -213.5, -187, -145, -113.5, and -85.The tangent line's average slope is -166.Know more about slopes here:
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The complete question is given below:
a tank holds 5000 gallons of water, which drains from the bottom of the tank in half an hour. The values in the table show the volume V of water remaining in the tank (in gallon) after t minutes.a) If P is the point (15,1275) on the graph of V, find the slopes of hte secant lines PQ when Q is the point on the graph with the following values.(5, 3410) -427/2(10, 2210) -187(20, 550) -145(25, 145) -113(30, 0) -85B) estimate the slope of hte tangent line at P by averaging the slopes of two adjacent secant lines. (Round your answer to one decimal places).
How do I remember my timetables easily? Any advice?
Answers
Answer:
Study a Times Tables map each day if you can soon you will get the hang of it
How do you regular divide
Answers
Answer:
These are dividend, divisor, quotient and remainder.
Step-by-step explanation:
Determine the first digit or set of digits your divisor will go into at least once.
Determine the maximum number of times your divisor will go into the said digit or digits.
Place the answer over the corresponding digit. For multiple digits, place it over the last digit.
Multiply the answer from above by your dividend.
Place the result under your dividend starting from the left most digit.
Subtract the result from your dividend. Only subtract the digits that line up. For instance, if you have a five digit dividend, but the result is only two digits, only subtract using the first two digits of your dividend.
Bring down the next digit of your dividend beside the result.
Repeat the process using the new set of digits. Each time, bring down the next digit of your dividend.
1
T
school 1 H
school 2
2
✓
✓
468 10 12 14 16 18
hours in the weight room
The two box plots summarize the number of hours
spent in the weight room for all the players on the
football team for two different high schools. Determine
whether the following statements are true or false.
d) School 1 had the player that spent the most time
in the weight room.
M
True
O
False
Sep 16
3:00
Answers
true!!!
school 1 spent 13 hours in the weight room whereas school 2 spent 11 hours in the weight room
need help i dont know how to solv
Answers
Answer:
It's learn proper English. I'll rewrite your statement. I need help, I do not understand how to solve this. Thank you!
can someone answer 2 1/2 x 1 3/5 =
Answers
First, multiply 2 by and add that one to get 5/2. Then, multiply 1 by 5 and add the 3 to get 8/5
write a function g whose graph is a reflection in the x axis of the graph of f(x)=|x|-5
please help
Answers
A function g whose graph is a reflection in the x axis of the graph of f(x) = |x| - 5 is g(x) = 5 - |x|
The question asks to find a function g, that is, g(x)
The graph of g(x) is a reflection in the x axis of the graph of f(x) = |x| - 5
Reflection of a function in the x-axis gives us
y = g(x) = - f(x)
=> g(x) = - ( |x| - 5 )
=> g(x) = - |x| + 5
=> g(x) = 5 - |x|
Therefore, using the concept of reflection of a function in x axis of the graph of the given function, we get a function g whose graph is a reflection in the x axis of the graph of f(x) = |x| - 5 as g(x) = 5 - |x|
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Amir has 2 checking accounts. The first has a balance of -$20 and the
second has a balance of $160. What is the sum of the two sum balances
Answers
Answer:
D. 140. ....,.....
Step-by-step explanation:
160-20=140
Find the least common denominator for these fractions. Enter your answer in the space provided. 1/2 and 2/9
Answers
Answer:
18.
Step-by-step explanation:
2 = 2
9 = 3*3
So, the LCD = 2*3*3 (no duplicates in the 2 lists).
= 18.
Express this number in scientific notation.
0.00067
Answers
I cant find my answer help needed
Answers
Step-by-step explanation:
the domain is the interval or set of all valid x (input) values.
the range is the interval or set of all valid y (function result) values.
so, we see here, x goes from -2 to +2.
and y stays between -5 and -1.
the hole point at (-2, -1) means the point itself is not included. the full point (2, -1) means the point itself is included.
the domain is
-2 < x <= +2
"-2 < x" because (-2, -1) is not included.
"x <= +2" because (2, -1) is included.
the range is
-5 <= y <= -1
"y <= -1" because for the included point (2, -1) y can reach -1, even though (-2, -1) is excluded.
HELP!!
What is the volume of this solid?
A. 39
B. 108
C. 27
D. 63
Answers
Answer: B
Step-by-step explanation:
4 times 3 times 3 times 3 times 3=108
Answer:
A. 39
Step-by-step explanation:
Given:
Length of a pyramid (lpy ) = 4 cm
Width of a pyramid (wpy ) = 3 cm
Height of a pyramid (hpy ) = 3 cm
It is given that the rectangular pyramid fits exactly on top of the prism, the length and width of the prism are the same for the base of the pyramid.
So, Length of a prism (lpr) =3 cm, width of a prism (wpr) = 3cm and height of a prism (hpr) = 3 cm
Volume of Prism (Vpr) = lpr × wpr × hpr
⇒ Vpr = 3 cm × 3 cm × 3 cm
⇒ Vpr = 27 cm³ ....(eq 1)
Volume of Rectangular Pyramid Vpy
= (lpy × wpy × hpy ) / 3
⇒ Vpy = (4 × 3 × 3) ÷ 3
⇒ Vpy = 12 cm³ ....(eq 2)
From 1 and 2, Volume of composite space,
Volume of composite space = Volume of prism + Volume of Pyramid
⇒ V = 27 cm³ + 12 cm³ = 39 cm³
⇒ V = 39cm³
A kite of area 252 m² has one diagonal of length 9 m. Find the length of the other diagonal
Answers
Answer:
The other diagonal of the kite is 56 meters
Step-by-step explanation:
To find the length of the other diagonal you find to know the formula for finding the area of a kite which is A = (p×q)/2. It is given that the area is 252m² and one diagonal is 9m.
Place your given numbers in the formula for the area of the kite. With your numbers given the formula is 252 = (9q)/2 or alternatively 252 = (9p)/2Multiply both sides by 2 the reason being is that we are trying to islolate the unknown variable (weather it is p or q) so we are doing the inverse operation. So you will have 252 × 2 = (9p)/2×2 or (9q)/2×2. At the end of this step it is 504 = 9q or 504 = 9pDivide by 9 on both sides remember that the point is to islolate the variable. 504/9 = 9q/9 or 504/9 = 9p/9. The final answer is that your unknown diagonal (whether it was q or p) is 56 mFactorise x^2+4x+3=0
Answers
Check the image below for working
What is the greatest common factor of 27 and 36?
Answers
Answer:
9!
Step-by-step explanation:
Answer: 9
Step-by-step explanation:So you look at whatever can be multiplied to get 27 or 36. When you do that 9 is your biggest number
Answer both questions please [ brainliest ]
-
1. The measure of an angle is 84°. The measure of its complementary angle is ___
degrees.
2. The measure of an angle is 29°. The measure of its supplementary angle is ___ degrees.
Answers
For question 1 the answer is
6 degrees
For question 2 the answer is
151 degrees
I got #1 by taking 90 and subtracting 84 to get 6 degrees
I got #2 by taking 180 and subtracting 29 to get 151 degrees
help, i’ll give you brain list sh or wtv if it’s correct. !!
Answers
the combinations that work are "A" and "B" as they both equal to 80
Wayne placed an order for 1 2/3 sacks of brown lentils and 1/2 of a sack of green lentils. How much more brown lentils did Wayne order?
Answers
Answer:
1 1/6
Step-by-step explanation:
1 2/3 - 1/2 =
1 2/3 = 1 4/6
1/2 = 3/6
1 4/6 - 3/6 =
1 1/6
Write the equation of a line that passes through point (16,7) with slope 5/4 in point slope form
Answers
Answer: y = 5x/4 - 13
Step-by-step explanation:
y=mx+b
7=5/4 *16+b
7=5*16/4 +b
7=80/4+b
7=20+b
b=-13
y = 5x/4 - 13
Write a numerical expression for the verbal expression. eighteen divided by the sum of two and seven
Answers
The numerical expression for the verbal expression is 18 ÷ (2+7).
Given,
Verbal expression = Eighteen divide by the sum of two and seven
we know that ,
We can write any verbal expression to numerical expression by using playing with numbers.
Playing with numbers:
Playing with numbers involves activities like arranging the numbers, understanding , finding out whether a given number is a factor of another number or a multiple of another number, and understanding the properties of factors and multiples
Now, According to question
Eighteen divided by the sum of two and seven
18÷(2+7)
Therefore,
The numerical expression is 18÷(2+7).
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The points L, M, N and O all lie on the same line segment, in that order, such that the ratio of LM:MN:NOLM:MN:NO is equal to 5:1:2.5:1:2. If LO=48,LO=48, find NO.NO.
Answers
The length of the line segment NO is 12 units
How to determine the length of NO?The ratios of the line segments are given as:
LM : MN : NO = 5 : 1 : 2
The length of LO is given as:
LO = 48
The above means that
NO = (NO Ratio)/(Total Ratio) * LO
So, we have
NO = 2/(5 + 1 + 2) * 48
Evaluate the product
NO = 12
Hence, the length of NO is 12 units
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The Shah family's pancake recipe uses 2 teaspoons of baking powder for every
1
3
of a teaspoon of salt. How much baking powder would they need if they used 1 teaspoon of salt?
Answers
The baking powder that they would need if they used 1 teaspoon of salt will be illustrated will be 6 baking Powder.
How to illustrate the information?It should be noted that from the information given, the Shah family's pancake recipe uses 2 teaspoons of baking powder for every 1/3 of a teaspoon of salt.
Therefore, the baking powder that they would need if they used 1 teaspoon of salt will be illustrated thus:
= Pancake recipe ÷ Teaspoon
= 2 ÷ 1/3
= 2 × 3
= 6
Therefore, the baking powder that they would need if they used 1 teaspoon of salt will be illustrated will be 6 baking Powder.
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(8x-4)+(4x-90)
also simplify
Answers
Answer:
12x-94
---------------------
Hope this helps!
Have a great day and God bless! :)
A snack recipe calls for 1 1/4 cups of dip and 1/5 cup of chips. charlie wants to make the same recipe using 1 cup of chips. how many cups of dip will charlie need?
Answers
Using the concept of ratio the number of cups of chips Charlie needs can be found out.
What is ratio?A ratio in mathematics shows how many times one number is contained in another. The ratio symbol is represented by a colon (:).A ratio is still valid if all of the quantities are multiplied by the same number. By dividing each quantity by the sum of all the numbers' common factors, ratios can be lowered (much like fractions are). The simplest version of a fraction is one in which the ratio's numbers are the smallest feasible integers.
Amount of dip required by the recipe be 'a' =[tex]1\frac{1}{4}[/tex] cups=[tex]\frac{5}{4}[/tex]cups
Amount of chips required by the recipe be 'b'= [tex]\frac{1}{5}[/tex]cups
Amount of chips to be used be 'c'= 1 cup
Number of cups of chips Charlie needs
=[tex]\frac{c*a}{b}[/tex]
=[tex]\frac{1*\frac{5}{4} }{\frac{1}{5} }[/tex]
=[tex]\frac{5*5}{4}[/tex]
=[tex]\frac{25}{4}[/tex] cups
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Singing star bitsy carlyle isnt as popular as she used to be at her latest concert she was only able to sell 910 tickets for a total of 15620 barely enough to pay her agent if regular seats cost 18.50 and mezzanine seats the only other option cost 16.25 how many mezzanine tickest were sold
Answers
The number of mezzanine tickets sold = 540
Total number of tickets sold = 910
Total number of tickets sold is the sum of the number of regular seats and the number of the mezzanine seats sold.
Let 'x' be the number of regular seats and 'y' be the number of mezzanine seats.
Then x + y = 910 ----------(1)
Cost of a regular seat = $ 18.50
So cost of x regular seats = 18.50x dollars
Cost of a mezzanine seat = $ 16.25
So cost of y mezzanine seats = 16.25y
Total amount of money she got by selling tickets = $ 15620
Therefore, 18.5x + 16.25y = 15620 ----------------(2)
Solve equations (1) and (2) for x and y.
Multiplying (1) with 18.5 throughout,
18.5x + 18.5y = 16835 ---------------(3)
Subtracting (2) from above equation (3), we get,
(18.5 - 16.25)y = 16835 - 15620
⇒ 2.25y = 1215
⇒ y = 1215/2.25
⇒ y = 540
Hence 540 mezzanine tickets were sold.
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The triangles are congruent by SSS and HL.
Triangles R S T and V W X are shown. Triangle R S T can be rotated about point S and then shifted down and to the left to form triangle V W X.
Which transformation(s) can be used to map △RST onto
△VWX?
Answers
Using translation concepts, the transformations that are used to map △RST onto △VWX are:
Rotation, then a translation.
What is the missing information?The two triangles are given at the end of the answer.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
Looking at the image, we have that:
The orientation of the triangle changed, hence it underwent a rotation.After the function underwent the rotation, it was moved up and right, then it underwent a translation.More can be learned about translation concepts at https://brainly.com/question/4521517
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A 1971 Indian Motorcycle is worth 30 times its original cost. Today it is worth $3000. How much did it originally cost in 1971?
Answers
Answer: $100
Step-by-step explanation:
3,000 divided by 30 is 100
Answer: 100
Step-by-step explanation: divide 3,000 by 30
HELP...................................! !
Answers
Answer:
Your answer would be 3.075.
Step-by-step explanation:
15 - 6.8 = 8.2
8.2 - 5 1/8 = 3.075
--------------------------------
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Have a great day and God bless! :)