(05.06 MC)
Graph the system of inequalities presented here on your own paper, then use your graph to
answer the following questions:
y > 5x + 5
y>-2x+1
Part A: Describe the graph of the system, including shading and the types of lines graphed.
Provide a description of the solution area. (6 points)
Part B: Is the point (-2, 5) included in the solution area for the system? Justify your answer
mathematically. (4 points)
(10 points)
Answers
The point (-2, 5) is not included in the solution area
The graph of the inequalitiesThe system of inequalities is given as:
y > 5x + 5
y > -2x+1
See attachment for the graph.
Since the inequalities use the greater than symbol, then the lines of the inequalities would be a dotted line and the upper part would be shaded
The solution areaThe point is given as:
(-2, 5)
The point (-2, 5) is not in the shaded area of the system of inequalities
Hence, the point is not included in the solution area
Mathematically, we have:
5 > 5 * -2 + 5 ⇒ 5 > -5 --- true
5 > -2 * -2 +1 ⇒ 5 > 5 --- false
Since both inequalities are not true, then the point is justified
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Related Questions
There are three square gardens whose lengths of the sides are 3 ft, 7ft, and 2 ft respectively. Find the total area of the three gardens in square feet.
65
60
62
64
Answers
Answer:
62
Step-by-step explanation:
1. To find the total area, we must find the area of the three individual gardens and sum them together
2. Since the gardens are square, the area is equal to the side length squared
3. Therefore, square the sides and sum:
3^2 = 9
7^2 = 49
2^2 = 4
4+9+49 = 62
PLS HELP I REALLY NEED HELP
Answers
Answer:
a) AB = 10 unitsb) Midpoint is (2, 6)===================
GivenPoints A( - 1, 10) and B(5, 2)To finda) The length of ABb) The midpoint of ABSolutiona) Use the distance formula:
[tex]d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Substitute the coordinates and calculate:
[tex]d=\sqrt{(5-(-1))^2+(2-10)^2} =\sqrt{6^2+(-8)^2} =\sqrt{36+64} =\sqrt{100} =10[/tex]
The distance is AB = 10 units
b) Use midpoint formula and find x and y- coordinates of this point:
[tex]x= \cfrac{x_1+x_2}{2}[/tex] and [tex]y= \cfrac{y_1+y_2}{2}[/tex]
Substitute coordinates and find the midpoint:
[tex]x= \cfrac{-1+5}{2} =2[/tex] and [tex]y= \cfrac{10+2}{2}=6[/tex]
The midpoint is (2, 6)
Answer:
Length of line segment AB = 10 units
Midpoint of line segment AB = (2, 6)
Step-by-step explanation:
To find length, apply the distance formula :
AB = √(5 - (-1))² + (2 - 10)²AB = √36 + 64 = √100[tex]\fbox {AB = 10 units}[/tex]To find the midpoint :
M = (-1 + 5 / 2, 10 + 2 / 2)[tex]\fbox {Midpoint = (2, 6)}[/tex]Amy is x years old. Ben is 2 years older than Amy. Alice is six years younger than Amy.
a) Write an expression for Ben's age and Alice's age in terms of x.
Answers
Answer:
Step-by-step explanation:
Amy = x years
Ben = x + 2 (years)
Alice = x - 6 (years)
Answer:
a)
Amy's age is x.
• Ben's age is 2 more than Amy's age.
∴ Ben's age = x + 2
• Alice's age is 6 less than Amy's age.
∴ Alice's age = x - 6
The number of bacteria in a culture is expected to grow 82% per hour over the next several hours. The predicted change in the number of
bacteria can be represented by P= 120(1.82) where P is the predicted number of bacteria t hours from now.
To the nearest tenth of a percent, by what percent is the number of bacteria expected to grow by each minute?
O .1%
O 1.0%
O 1.1%
O 1.4%
Answers
1.4 % growth each minute
I don’t feel like the representation
P = 120(1.82) is important in this certain problem.
So P the predicted number of bacteria is not practical with this problem.
Use the 82% per hour and divide it by 60 because there are 60 minutes in an hour.
When doing this you find the rate in which bacteria grows which is about 1.4%.
The prediction is about 1.82 percent for 120 something it’s not clarified, but I’m guessing that’s minutes.
So you can prove that the prediction is over the rate in which bacteria grows per minute.
the number of men is five eights of the number of women working in a factory if there is 24 more women than men how many workers are all together
Answers
Answer:
104
Step-by-step explanation:
women = 8/8
men = 5/8
all workers = 8/8 + 5/8 = 13/8
extra women workers = 8/8 - 5/8 = 3/8
so...
3/8 = 24
13/8 = x
( cross multiplication method)
3/8 x = 39
x = 104
Hence, there are 104 workers
Answer:
104 workers
Step-by-step explanation:
w = women
m = men = 5/8 w
w - 5/8 w = 24
w = 64 then m = 5/8 * 64 = 40 total = 104
f(x)=x^2(x+2)(x-2)(x-5) has zeros at x=-2, x=0, x=2 and x=5. what is the sign of f on the interval -2
Answers
Answer:
f is sometimes positive and sometimes negative on the interval
Step-by-step explanation:
So if you were to expand out the x's you would have x^2 * x * x * x which will result in x^5. and because the leading coefficient is positive, it will be going towards positive infinity as x goes towards positive infinity, and because the degree is odd the end behaviors will be opposite, so as x goes towards negative infinity the value of f(x) will be going towards negative infinity. One other thing to note is that because x^2 technically is two zeroes, with the same value, the zero at x=0 has a multiplicity of 2, meaning that it will not cross the x-axis, but rather have a turning point, once it intersects the x-axis, because the zero has an even multiplicity. Given this information we can draw a graph. So as you can see in the graph, it will sometimes be negative and sometimes positive
A farmer must add the areas of two plots of land to determine the amount of seed to plant. The area of Plot A can be represented by 3x^2 +7x - 5, and the area of Plot B can be represented by 5x^2 - 4x + 11. Write a polynomial that represents the total area of both plots of land.
Answers
Step-by-step explanation:
Combine common terms
(3x²+5x²)+(7x-4x)+(-5+11)
8x²+3x+6
The polynomial that represents the total area of both plots of land will be; 8x²+3x+6
What is a polynomial?They are mathematical expressions involving variables raised with non negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non negative exponentiation of variables involved.
We are given that ;
The area of Plot A can be represented by 3x² +7x - 5, and the area of Plot B can be represented by 5x² - 4x + 11.
So the polynomial that represents the total area of both plots of land
Now Combine common terms;
(3x²+5x²)+(7x-4x)+(-5+11)
Then we get;
8x²+3x+6
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Which equation correctly describes the relationship between the measure of the inscribed angle and the measure of the intercepted arc in the figure? m∠PQR=360°−mPR⏜ m∠PQR=12mPR⏜ m∠PQR=2(mPR⏜) m∠PQR=mPR⏜ Circle with two chords. Point Q at 10 o clock, point P at 3 o clock, and point R at 6 o clock are on the circle. Segment Q R and Q P share a common end-point at point Q.
Answers
Answer:
Your answer is ∠PQR=(1/2)* m arc PR.
Step-by-step explanation:
The Angle Described is one that has its vertex in the circumference. The inscribed angle measures half of the arc it comprises.
So, in this problem, The inscribed angle=∠PQR
The arc it comprises=m arc PR too.
So therefore:
∠PQR=(1/2)* m arc PR is the answer
M angle A=
M angle B=
M angle C=
Help me please Stuck on this question thanks
Answers
m<A = 28
m<B = 96
m<C = 56
Can someone help me please?
Answers
Answer:
1. y ax
|
A-------------------------------B
|
------------C---------------------
|
|__________________x ax
for this, your A might be (0,5), B (5,5), C (2,2).
parallel means railroad tracks: same slope, different intercepts.
line AB in this case has a slope of 0, intercept (0,5), so y₁=0x+5 or just y₁=5
the line passing through C also has slope 0, but intercept (0,2), so y₂=0x+2 or just y₂=2
2. perpendicular means that the slopes of two lines multiply out to -1. If line AB has, for example, a slope of 2/3, then the line passing through C would have slope -3/2 (negative reciprocal). To make things easier have either point A or B be on the x or y axis
khan academy has some helpful videos :)
https://www.khanacademy.org/math/geometry/hs-geo-analytic-geometry/hs-geo-parallel-perpendicular-eq/v/perpendicular-lines
Point O is the center of dilation. Triangle A B C is dilated to create triangle A prime B prime C prime. The length of O A is 3. The length of A A prime is 9.
Triangle ABC is dilated to create triangle A'B'C' using point O as the center of dilation.
What is the scale factor of the dilation?
1/3
3
4
1/4
Answers
Answer:
3
Step-by-step explanation:
9 divided by 3 is 3...
hope this helped
Answer:
its 3
Step-by-step explanation:
im doing summer school rn lol
Theodore started watching a movie at 19:30.
The movie was 1 hour and 56 minutes long, but part-way through he
paused it for 12 minutes.
What was the time when the movie finished?
Give your answer using the 24 hour clock.
Answers
The time when movie finished was 21 : 38.
It is given that Theodore started watching movie at 19:30 and length of movie was 1 hour and 56 minutes.
We have to find the time when the movie finished if there was a break of 12 minutes also between movie.
What is algebra ?
Algebra is the branch that deals with various symbols and the arithmetic operations and the symbols are called variables.
As per the question ;
Theodore started watching movie at 19:30.
The length of movie = 1 hour and 56 minutes
Break = 12 minutes
So ;
Total length of running of movie = 2 hours and 8 minutes
The time when movie finished will be ;
= 19 :30 + 2:08
= 21 : 38
Thus , the time when movie finished was 21 : 38.
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help me i dont understand this
Answers
The equation of the line passing through the coordinates but with its coordinates interchanged i.e (5, 7) and (9, 11)
Equation of reciprocal of a functionGiven a linear function that contains the coordinate point on its line (5, 7) and (9, 11)
The equation of its reciprocal can be determine by finding the equation of the line passing through the coordinates but with its coordinates interchanged i.e (5, 7) and (9, 11)
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Please help ASAP
Please help ASAP
Please help ASAP
Please help ASAP
Answers
The volume of the rectangular box is 12 cubic inches
Volume of a boxThe formula for measuring the volume of a rectangular box is expressed as:
V = lwh
l is the length
w is the width
h is the height
Given the following
l = 2in
w = 3in
h = 2in
Substitute
V = 2* 3 * 2
V = 12 cubic inches
Hence the volume of the rectangular box is 12 cubic inches
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(5 - 1/2- 2)x^2 + ( 1/5 + 1/2 - 1/3 )x + (5/2 - 1/3 - 1/6 ) =
Answers
Answer:
Step-by-step explanation:
Answer:
The answer is
5/2x^2+11/30x+2
[tex] \frac{5}{2}x ^{2} + \frac{11}{30} x + 2[/tex]
if (p,4) is mapped into (q,-3) under a rotation through+90° about origin . then find the values of p and q
Answers
Answer:
p = 3
q = 4
Step-by-step explanation:
Rotation by +90° (clockwise) about the origin: (x, y) → (y, -x)
Therefore, (p, 4) rotated by +90° about the origin:
(p, 4) → (4, -p)
Therefore:
(4, -p) = (q, -3)
⇒ p = 3
⇒ q = 4
Therefore, (3, 4) is mapped into (4, -3) under a rotation by +90° about the origin.
Which of the following equations describes the graph? Urgent lol
Answers
Answer : I think 3rd is the answer
Write pqqqqrr in exponential form.
Answers
p^1
q^4
r^2
Is this what your asking for and also can you please mark me as brainlist. Thank you
help help help help??
Answers
Answer:
a b f would all be the correct answers
Step-by-step explanation:
Less than looks to the left
Greater than looks right
What is the range of y equals square root of x +7+5?
Answers
The range of a function are the dependent variables for which the function exists. The range of the function will be y ≥ 5
Range of a function
The range of a function are the dependent variables for which the function exists
Given the function below;
f(x) = √x+7 + 5
The function can only exist for values less than or equal to -7 that is x ≤ -7.
Substitute
f(-7) = √-7+7 + 5
f(-7) = 5
The range of the function will be y ≥ 5
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0.65 more than -4.35
Answers
Answer:
-3.7
Step-by-step explanation:
1. More = Addition
2. 0.65 + -4.35 = -3.7
[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]
0.65 more than -4.35
[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]
The word more means addition, thus
-4.35+0.65=
[tex]\bf{-3.7}[/tex]
[tex]\cline{1-2}[/tex]
[tex]\bf{Result:}[/tex]
[tex]\bf{=-3.7}[/tex]
[tex]\LARGE\boxed{\bf{aesthetic\not1\theta\ell}}[/tex]
what are the possible numbers of positive, negative, and complex zeros of f(x)=x^6+x^5+x^4+4x^3-12x^2+12?
Answers
The number of zeros are; Positive; 2 or 0; Negative: 4 or 2 or 0; Complex; 0, 2, 4, 6
How to find the zeros of a Polynomial?We are given the polynomial function as;
f(x) = x⁶ + x⁵ + x⁴ + 4x³ - 12x² + 12
Use Descartes Rule rule of signs allows us to determine the possible number of positive, negative, and complex roots.
For the function f(x), the number of sign changes that occur from term to term will give us the number of positive possible roots.
For the function f(-x), the number of sign changes that occur from term to term will give us the number of negative possible roots.
The numbers of complex roots is the difference between the degree of function and total number of positive and negative roots.
For f(x), the signs change 2 times. Thus, there can only be a possibility of 2 positive roots
For f(-x), we have;
x⁶ - x⁵ + x⁴ - 4x³ - 12x² + 12
Thus, the sign changes 4 times and so we have a possibility of 4 negative roots.
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the area of 4 walls of a room is 120 m^2. if the length and breadth are 7m and 5m respectively, find the height.
Answers
=========================================================
Explanation:
The floor is a 7 meter by 5 meter rectangle. The perimeter is
P = 2(L+W)
P = 2(7+5)
P = 2(12)
P = 24
The perimeter of the floor is 24 meters.
Multiply this perimeter by the unknown height h to get 24h
This expression represents the lateral surface area. This is the combined wall area. Set this equal to 120 and solve for h.
24h = 120
h = 120/24
h = 5
-----------------
Check:
One pair of walls is 7 meters by 5 meters, giving an area of 7*5 = 35 square meters each. So far that's 2*35 = 70 square meters for these two walls combined.
The other pair of walls is 5 by 5. Each has an area of 5*5 = 25 which doubles to 2*25 = 50
The total wall area is 70+50 = 120 to confirm the answer.
Can someone help me please
measure of angle B = 37 degrees, a = 12, b = 15. Find the measure of angle A to the nearest degree.
Answers
Answer: 28.78
Step-by-step explanation:
[tex]\frac{\sin A}{a}=\frac{\sin B}{b}\\\\ \sin A=\frac{a \sin B}{b}\\\\\sin A=\frac{12 \sin 37^{\circ}}{15}\\\\\sin A=0.481452...\\\\A \approx 28.78^{\circ}, 151.21^{\circ}[/tex]
However, we disregard the second case, giving 28.78 degrees.
Add: (-5u5 + 5) + 7u5
Answers
Answer:
2u^5+5
Step-by-step explanation:
Drop parenthesis and add like terms.
[tex]7u^{5}-5u^{5}+5=2u^{5}+5[/tex]
Hope this helps!
If not, I am sorry.
Solve the rational equation quantity 3 times x minus 5 end quantity divided by 7 equals four sevenths.
Answers
Answer:
3
Step-by-step explanation:
If we write it out, the equation will be 3x-5/7 = 4/7. So first, we can multiply 7 by both sides to get 3x - 5 = 4. Next, we can add 5 to both sides to get 3x = 9. Lastly, we'll divide 3 by both sides to get x = 3.
Anna has been studying a type of bacteria that triples every month. originally, there were 4 bacterial cells. she wants to know how many there will be after 15 months. which equation should she use?
Answers
Anna should use the following equation,
[tex]a_{15} = 4(3)^{15}[/tex]
Equation for Determining the Number of Bacterial Cells
Initially, the count of bacterial cells = 4
It is given that the bacterial cell triples every month.
Hence, the equation for the count of bacterial cells after first month is,
a₁ = 4(3)
This count of 4(3) triples again in the second month.
So, after the second month, the equation for the count of bacterial cells is given by,
a₂ = 4(3)(3) = 4(3)²
Calculating the Count of Bacterial Cells For Each Month
Again, this count triples in the third month.
Therefore, the equation for the count of bacterial cells after the third month becomes,
a₃ = 4(3)(3)(3) = 4(3)³
This count triples again in the fourth month and this process continues till 15 months.
Hence, the equation for determining the number of bacterial cells comes out to be as follows,
a₁₅ = 4(3)¹⁵
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Lisandro fabrica juguetes. Si tiene 100 ruedas ¿Cuantos autos puede armar?
Me aydan porfa
Answers
Answer:
25
Step-by-step explanation:
un carro tiene 4 ruedas, entonces divide 100 por 4
100÷4=25
can someone help me solve this problem?
Answers
Answer:
13
Step-by-step explanation:
cos17 = x/14
x = 14cos17
x= 13.38826658
to the nearest hundredth
x=13
line L has a slope of 9/8 the line through which of the following pair of points is perpendicular to line L
Answers
A pair of points which is perpendicular to line L is: D. (3, -5),(-6, 3).
How to calculate the slope of a line?Mathematically, the slope of any straight line can be calculated by using this formula;
[tex]Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]
For points A, we have:
[tex]Slope = \frac{3\;-\;(-6)}{3\;-\;(-9)}\\\\Slope = \frac{9}{12}[/tex]
Slope = 9/12.
For points B, we have:
[tex]Slope = \frac{6\;-\;(-2)}{-6\;-\;(-9)}\\\\Slope = \frac{8}{-3}[/tex]
Slope = -8/3.
For points C, we have:
[tex]Slope = \frac{3\;-\;(-6)}{3\;-\;(-5)}\\\\Slope = \frac{9}{8}[/tex]
Slope = 9/8.
For points D, we have:
[tex]Slope = \frac{3\;-\;(-5)}{-6\;-\;3}\\\\Slope = \frac{-8}{9}[/tex]
Slope = -8/9.
In Mathematics, the condition for perpendicularity of two lines is:
m₁ × m₂ = -1
9/8 × 8/9 = -1
Thus, points (3,−5) and (−6,3) are perpendicular to line L.
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Complete Question:
Line L has a slope of 9/8. The line through which of the following pair of points is perpendicular to L?
A. (−9,−6),(3,3)
B. (9,−2),(−6,6)
C. (−5,−6),(3,3)
D. (3,−5),(−6,3)