This graph shows the solutions to the inequalities y> 3x-2 and y<?x-10Does the system of inequalities have solutions? If so, which region containsthe solutions?108A84210-88441022 488BPopс-10A. There is a solution, and it is shown by region A.B. There is a solution, and it is shown by region C.C. There is no solution.D. There is a solution, and it is shown by region B.
Answers
there is no solution (option C)
Explanation:Given:
y > 3/2x - 2
y < 3/2x - 10
To find:
The solution to both graphs
To determine the solution of the graphs, we will consider their slopes
[tex]\begin{gathered} y\text{ > }\frac{3}{2}x\text{ - 2} \\ comparing\text{ with y = mx + b} \\ m\text{ = slope, b = y-intercept} \\ from\text{ the above, the slope = 3/2} \end{gathered}[/tex][tex]\begin{gathered} y\text{ < }\frac{3}{2}x\text{ - 10} \\ the\text{ slope = 3/2} \end{gathered}[/tex]The slope of both inequalities is 3/2. If the slopes of two lines are the same, the lines are said to be parallel. This means both inequalities are parallel lines
For parallel lines, there is no solution because the lines do not intersect (meet).
Since both inequalities give parallel lines, there will be no solution (option C)
Related Questions
The two options I selected was incorrect, what would the answer be?
Answers
The question gives us the following function:
[tex]f(x)=\frac{3x}{x-2}[/tex]The X-intercept is where the function crosses the x-axis and the Y-intercept is where the function crosses the y-axis.
X-intercept:
Since the graph must cross the x-axis to have an x-intercept, we should equate f(x) to zero.
[tex]\begin{gathered} f(x)=\frac{3x}{x-2}=0 \\ \\ 3x=0 \\ \therefore x=0\text{ is the x-intercept} \end{gathered}[/tex]Y-intercept:
Since the graph must cross the y-axis to have a y-intercept, we should equate x = 0.
[tex]\begin{gathered} f(x)=\frac{3x}{x-2} \\ \\ f(0)=\frac{3(0)}{0-2} \\ \\ f(0)=0\text{ is a y-intercept} \end{gathered}[/tex]Answer
Thus, the x and y-intercepts are: x = 0 and y = 0 respectively
How do i do this question
Answers
Answer:25.12
Step-by-step explanation: To find the circumference the equation is diameter time pie. Pie=3.14
Part of the graph of the function f(x) = (x – 1)(x + 7) is shown below.Which statements about the function are true? Select three options. Select three options.The vertex of the function is at (–4,–15). The vertex of the function is at (–3,–16). The graph is increasing on the interval x > –3. The graph is positive only on the intervals where x < –7 and where x > 1. The graph is negative on the interval x < –4.
Answers
The statements about the function that are true are
The vertex of the function is at (–3,–16). The graph is increasing on the interval x > –3. The graph is positive only on the intervals where x < –7 and where x > 1. How to interpret the graph?The equation of the graph is given as
f(x) = (x - 1)(x + 7)
The graph of the function is added as an attachment
On the graph, we have
Vertex = (-3, -16)
This is so because the graph has a minimum point of (-3, -16)
Also, the graph crosses the x-axis at x = 1 and x = -7
This means that the graph is positive at x >1 and x >-7
Because the vertex is a minimum, the graph is increasing at the left of its symmetry i.e. x > -3
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Which of the following numbers is a square number? Check all that apply.A. 62B. 64C. 100D. 116
Answers
the answer
a perfect square is a number that when two exact same number multiply each other, it produce
example 2 * 2 = 4
4 is a square number and the square root is 2
[tex]\begin{gathered} \text{square root of } \\ a.62=\sqrt{62}=7.87 \\ b.64=\sqrt{64}=8 \\ c.100=\sqrt{100}=10 \\ d.116=\sqrt{116}=10.77 \end{gathered}[/tex]the answer to your question is 64 and 100 which is option B and C
Find the length of the missing hypoden as a right triangle if the two legs have lengths five and 12.
Answers
To find the hypotenuse we going to use the Pythagorean theorem
[tex]c^2=a^2+b^2[/tex]being c the hypotenuse and a and b the other two sides
Replacing
[tex]c^2=5^2+12^2[/tex]Solving
[tex]\begin{gathered} c^2=25+144 \\ c^2=169 \\ c=\sqrt{169} \\ c=13 \end{gathered}[/tex]Answer: hypotenuse = 13
You have a jar of marbles in front of you 2 are green, 9 are yellow, 3 are white and 7 are red. What is e probability, as a decimal, of selecting a marble that is white or yellow, followed by a marble that is green?
Answers
Sample space = 21
Pr(White or Yellow) = Pr(White) + Pr(Yellow)
Pr(White) = 3/21 = 1/7
Pr(Yellow) = 9/21 = 3/7
Therefore,
Pr(White or Yellow)= 1/7 + 3/7 = 4/7
5x - 29.4 + 1/2x when x equals -11/5
Answers
The answer is -83/2
Decimal Form: -41.5
Mixed Number Form: -41 1/2
pnereThe radius, R, of a sphere is 5.8 m. Calculate the sphere's volume, V.Use the value 3.14 for it, and round your answer to the nearest tenth. (Do not round any intermediate computations.)
Answers
The volume of a sphere is given by the following formula:
[tex]V=\frac{4}{3}\pi r^3[/tex]Where r is the radius of the sphere r=5.8m.
Replace this value and solve for V:
[tex]\begin{gathered} V=\frac{4}{3}\cdot3.14\cdot(5.8m)^3 \\ V=\frac{4}{3}\cdot3.14\cdot195.112m^3 \\ V=\frac{2450.61m^3}{3} \\ V=816.9m^3 \end{gathered}[/tex]The volume of the sphere is 816.9 cubic meters.
Your class tried to construct a tetrahedron using four smaller congruent tetrahedra. However, the result left a gap in the center, as shown in the diagram below. If the volume of each small shaded tetrahedron is 50 in.3, what is the volume of the gap? Explain how you know.
Answers
Answer:
200 in³
Explanation:
The lengths of the sides of the constructed tetrahedron are twice the length of the side of the small tetrahedron of 50 in³. It means that the scale factor for the solid is 2. So, the complete volume of the constructed tetrahedron is equal to
Vn = 2³(50 in³)
Vn = 8(50 in³)
Vn = 400 in³
However, we only use 4 small tetrahedrons, so the volume of these four solids is
4(50 in³) = 200 in³
Then, the volume of the gap is the difference between the volume of the constructed tetrahedron and the volume of the 4 small tetrahedrons
400 in³ - 200 in³ = 200 in³
So, the answer is 200 in³
The distance between two cities on a map is 4.1 centimeters. The map uses a scale in which 1 centimeter represents 18 kilometers. What is the actual distance between these two cities in kilometers?
Answers
The actual distance between the two cities in kilometers is 73.8 kilometers.
Given:
The distance between two cities on a map = 4.1 centimeters
The Scale used by the map is, 1 centimeter is equivalent to 18 kilometers.
To find the actual distance between the two cities in kilometers,
We know, 1 centimeter = 18 kilometers.
For converting the distance in centimeters to kilometers we multiply the value in centimeters by the value of 1 centimeter i.e.18 kilometers.
So, 4.1 centimeter = (4.1 × 18) kilometers
= 73.8 kilometers
Therefore, the actual distance between the two cities calculated in kilometers is 73.8 kilometers.
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I really need help pls I’m in need of help
Answers
Let:
A be the number of pairs of Jeans Amina has.
I be the number of pairs of Jeans Idris has.
T be the total of pairs of Jeans.
Then,
A = 2
I = 3
Then, the equation that represents the total of pairs of jeans is:
[tex]T=A+I[/tex]Substituting the values we can find T:
[tex]\begin{gathered} T=2+3 \\ T=5 \end{gathered}[/tex]Answer:
The equation is: T = A + I.
And the solution is T = 5.
Please help will give Brainliest!!
Kevin took $45 with him to spend on snack for himself and his friends at the movie theater. The price for each bucket of popcorn was $4. The price of each drink was half the price of a bucket of popcorn.
Sketch the graph that represents the situation and label the intercepts. Use one axis to represent the number of bucketw of popcorn and the other axis to represent the number of drinks.
Explain your graph.
Answer:
(Score for Question 2: ___ of 5 points)
Graph the absolute value function.
f(x)=|1/3 x+2|-4
Answer:
(Score for Question 3: ___ of 4 points)
(a) Graph a linear function of your choice. On the same graph, graph a linear function transformed 2 units up and 3 units down.
(b) What was the equation of your linear function in slope-intercept form?
(c) What was the equation of the transformed function in slope-intercept form?
Answers
The required answer would be the inequality 4x + 2y ≥ 45, the graph has been attached which represents the given situation.
What is inequality?Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
We have been given that the price for each bucket of popcorn was $4. The price of each drink was half the price of a bucket of popcorn.
The total amount of spend is $45
As per the given condition, the required inequality would be as
4x + 2y ≥ 45
The situation's representation is in the attached graph with labels for the intercepts.
Here y-axis represents the number of drinks, and the x-axis represents the number of buckets of popcorn.
Thus, the required answer would be the inequality 4x + 2y ≥ 45, the graph has been attached which represents the given situation.
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Determining SimilarityAre the following triangles similar?YesNoExplain which similarity condition you used andjustify completely
Answers
Given data:
The given figure of the triangles.
In triangle STH and triangle GFH.
[tex]\begin{gathered} \angle T=\angle G \\ \angle THS=\angle GHF(vertically\text{ opposite)} \\ \end{gathered}[/tex]Thus, yes the triangles are similar by angle-angle (AA) property.
Use the number line to find the coordinate of the midpoint of
¯¯¯¯¯¯¯
M
P
.
Answers
Answer: 2.5
Step-by-step explanation:
The midpoint of the segment is the average of the coordinates.
[tex]\frac{0+5}{2}=2.5[/tex]
A. The graph of g(x) is the graph of f(x) compressed vertically.B. The graph of g(x) is the graph of f(x) compressed vertically andreflected over the x-axis.C. The graph of g(x) is the graph of f(x) stretched vertically.D. The graph of g(x) is the graph of f(x) stretched vertically andreflected over the x-axis.
Answers
The Solution:
Given:
Required:
to determine the best statement that compares the graph of g(x) with that of f(x).
Below is the graph of the given functions:
Thus, the graph of g(x) is the graph of f(x) compressed vertically and
reflected over the x-axis.
Answer:
[option B]
1/3 * 4/5 is <, >, or =,4/5
Answers
Answer:
4/15 ___ 4/5 {nothing further can be done}.
Step-by-step explanation:
1/3 * 4/5 = 4/15
4/15 = 0.26
4/15 ≠ 4/5
Thus, nothing further can be done
45. Write an inequality that represents the graph. Explain it step by step please.
Answers
Answer:
-4>x
Step-by-step explanation:
g (x)=5x-5,find g (-6)
Answers
Answer: -35
Step-by-step explanation:
set the every x in the equation to (-6)
g(-6) = 5(-6)-5
g(-6) = -30-5
g(-6) = -35
Solve the system by substitution. (If there is no solution, enter NO SOLUTION. If there are an infinite number of solutions, enter the general solution in terms of x, where x is any real number.)3x − 2y = 545x + 10y = −30(x, y) =
Answers
Solution:
Given:
[tex]\begin{gathered} 3x-2y=54 \\ 5x+10y=-30 \end{gathered}[/tex]Using the graphical method,
The solution is the point of intersection of the two lines.
Therefore, the solution is;
[tex](x,y)=(12,-9)[/tex]15. Higher Order Thinking Jane bought three sheets
of poster board and a pack of markers. Denise
bought two packs of construction paper and a
tube of glue. Who spent more? How much more?
16. If Jane buys two more sheets of poster board, how
much does she spend all together?
DATA
Poster board
Markers
Tape
Glue
8.90
Craft Supplies
Construction paper
17.MP.2 Reasoning Julene has $25 to make posters. She buys
two packs of markers, one pack of construction paper, two tubes
of glue, and a roll of tape. How many sheets of poster board can
she buy with the money she has left? Explain your answer.
:
$1.29/sheet
$4.50/pack
$1.99/roll
$2.39/tube
$3.79/pack
Answers
Answer: Denise spent more than Jane.
Step-by-step explanation: Denise spent $9.97. We know now that Denise spent more than Jane. For the second part of the question how much more? We basically just subtract the two values. $9.97-$8.37 which is $1.60. There you go.
Data Collected by the Substance Abuse and Mental Health Services Administration (SAMSHA) suggest that 69.8% of 18-20 year olds consumed alcoholic beverages in 2008?
(A) calculate the probability that exactly 4 out of 12 randomly sampled 18 to 20 year old consume an alcoholic drink?
(B) what is the probability that exactly 8 out of 1218 to20 year olds have not consumed an alcoholic beverage?
(C) What is the probability that at most two out of four randomly sampled 18 to 20 year old
have consume alcoholic beverage?
(D) what is the probability that at least one out of four randomly sample 18 to 20 years has consumed alcoholic beverage?
Answers
(a) The probability that exactly 4 out of 12 randomly sampled 18 to 20 year old consumes an alcoholic drink is 0.008127.
(b) The probability that exactly 8 out of 12, 18 to 20-year-olds have not consumed an alcoholic beverage is 0.231991.
(c) The probability that at most two out of four randomly sampled 18 to 20 year old have consumed alcoholic beverages is 0.35.
(d) The probability that at least one out of four randomly sample 18 to 20 years has consumed alcoholic beverages is 0.99168.
What is probability?The possibility of an event happening is defined by probability. We may need to forecast an event's result in a variety of real-world circumstances. The outcomes of an event may be certain or uncertain to us.
Given that 69.8% of people of 18-20 yr old consume alcohol.
Then p=0.698
Now let X is the random variable denoting the number of people who drinks alcohol.
(a) Let the sample size, n = 12, p = 0.698
It can be seen that X follows a binomial distribution
Then,
P(X=4) = ¹²C₄p⁴(1-p)⁸
= 495 × (0.698)⁴(1-0.698)⁸
=495 × 0.2373 × 0.00006919
= 0.008127
(b) P(X=8) = ¹²C₈p⁸(1-p)⁴
= 12!/ (8!)(4!)(0.698)⁸(1-0.698)⁴
=495 × 0.05634344 × 0.0083181
= 0.231991
(c) Let sample size n=4
p= 0.698
Then,
P(X≤2) = P(X=0)+P(X=1)+P(X=2)
= ⁴C₀p⁰(1-p)⁴ + ⁴C₁p¹(1-p)³ + ⁴C₂p²(1-p)²
=1 × 1× 0.0083181 + 4× 0.698 × 0.0275 + 6× 0.4872 × 0.091204
=0.3516881
=0.35
(d)
For P(X≥1)= 1-P(X<1)
=1-P(X=0)
=1-⁴C₀ p⁰(1-p)⁴
=1-1 × 1 × 0.0083181
= 0.99168
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36. Hiking You hiked 8.3 miles in Denali
National Park which is 3 miles farther than
you hiked yesterday. How far did you hike
yesterday?
Answers
Answer:
You hiked 5.3 miles yesterday
What’s 10 17/20 simplified
Answers
[tex] = 10 \frac{17}{20} \\ = \frac{20 \times 10 + 17}{20} \\ = \frac{217}{20} [/tex]
ATTACHED IS THE SOLUTION
When a rate is simplified so that it has a _ , it is called a unit rate
Answers
Answer:
When a rate is simplified so that it has a denominator of 1, it is called a unit rate
Step-by-step explanation:
Hope it helps!
Find the missing sides
Answers
The missing side and angle of the similar polygons are as follows:
∠H = 90°FI = 5.4IH = 4.8BC = 7.7What are similar polygons?Similar polygons are two polygons with the same shape, but not the same size.
Similar polygons have corresponding angles that are congruent, and corresponding sides that are proportional.
Therefore, polygon ABCD is similar to polygon FGHI. This means the corresponding angles are congruent and the corresponding sides are proportional.
Therefore,
∠C is corresponding angle to ∠H. This means they are both congruent.
Hence,
∠H = 90 degrees
Let's find FI,
10 / 6 = 9 / FI
cross multiply
FI = 54 / 10
FI = 5.4
Let's find IH
10 / 6 = 8 / IH
cross multiply
IH = 48 / 10
IH = 4.8
Let's find BC
10 / 6 = BC / 4.6
cross multiply
BC = 46 / 6
BC = 7.66666666667
BC = 7.7
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Which of the following represents the difference quotient for f of x is equal to 4 over x question mark
Answers
The difference quotient for the given function is:
[tex]-\frac{4}{x*(x + h)}[/tex]
How to get the difference quotient?For the function f(x), we define the difference quotient as:
[tex]\frac{f(x + h) - f(x)}{h}[/tex]
In this case, the function is f(x) = 4/x, replacing that in the general difference quotient:
[tex]\frac{4/(x + h) - 4/x}{h}[/tex]
Now we can simplify this to get:
[tex]\frac{4/(x + h) - 4/x}{h} = 4*\frac{1/(x + h) - 1/x}{h} \\\\4*\frac{1/(x + h) - 1/x}{h} = 4*(\frac{1/(x + h)}{h} - \frac{1/x}{h})[/tex]
[tex]4*(\frac{1/(x + h)}{h} - \frac{1/x}{h}) = 4*(\frac{1}{(x + h)*h} - \frac{1}{x*h}) = 4*\frac{x - x - h}{x*h*(x + h)} = -\frac{4}{x*(x + h)}[/tex]
So the correct option is the last one.
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Simplify the expression -3 devided by (-2/5)
Answers
Answer:-7 1/2
Step-by-step explanation:-3 divided by -2/5. -3÷-2/5. -3×-5/2. 15/2=7.5.
(3z + 2) (6-z) = 0 is there more then one solution to this if so can you tell me and use commas?
Answers
Answer:
Yes, [tex]z=-\frac{2}{3}, 6[/tex]
Step-by-step explanation:
Using the zero-product property,
[tex]3z+2=0, 6-z=0 \\ \\ \implies z=-\frac{2}{3}, 6[/tex]
Solve this system of equations by graphing. First graph the equations, and then type the solution.y=5/2x–1y=7/2x–3
Answers
System of equations:
[tex]y=\frac{5}{2}x-1[/tex][tex]y=\frac{7}{2}x-3[/tex]Using a graphing calculator we can get the graph:
As the point in which both functions meet is (2, 4), then this is the solution.
Answer: (2, 4)
Jacob bought a book that cost $11.95 and magazines that cost $4.95 each. Isabella bought a book that cost $15.79 and magazines that cost $3.99 each. Jacob spent the same amount or less money than Isabella. Write and solve an inequality to find m, the number of magazines for which Jacob spent less than or the same amount as Isabella.
Answers
Answer:
16.90≤19.78
Step-by-step explanation: