Which of the following is the graph of the following system of equations? { 2x - 3y>12 {y< -1 x + 5 2
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SOLUTION
The graph of the inequality
[tex]\begin{cases}2x-3y\ge12{} \\ y<-\frac{1}{2}x+5\end{cases}[/tex]is shown below
The darkest part is the required region
Comparing with the options,
the answer is the graph below
Related Questions
If the rate of inflation is 2.5% per year, the future price P(T) in dollars of a certain item can be modeled by the following exponential function, where T is the number of years from today
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Solution:
The future price p(t), in dollars, can be modelled by the exponential function;
[tex]p(t)=800(1.025)^t[/tex](a) The current price is;
[tex]\begin{gathered} t=0; \\ \\ p(0)=800(1.025)^0 \\ \\ p(0)=800(1) \\ \\ p(0)=800 \end{gathered}[/tex]ANSWER: $800
(b) The price 8 years from today;
[tex]\begin{gathered} t=8 \\ \\ p(8)=800(1.025)^8 \\ \\ p(8)=800(1.2184) \\ \\ p(8)=974.72 \\ \\ p(8)\approx975 \end{gathered}[/tex]ANSWER: $975
Which triangle congruence postulate or theorem proves that these triangles are congruent?
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The AAS triangle congruence postulate proves that these triangles are congruent .
In the question,
two triangles are given that are triangle ABC and triangle PQR .
Consider the triangle ABC and triangle PQR .
we can see that
(i) angle C = angle R .....given in the figure
(iii) angle B = angle Q .... given in the figure
(ii) side BC = side QR ....given in the figure
From the above three statements we conclude that
ΔABC ≅ ΔPQR
both the triangles KLM and PQR are congruent by AAS Congruence Postulate .
Therefore , The AAS triangle congruence postulate proves that these triangles are congruent .
Learn more about Congruence Postulate here
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f(×) = 3× + 7 f(1) =
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f(1) = 10
Explanation:Given f(x) = 3x + 7
To find f(1), replace x by 1 in the equation above
f(1) = 3(1) + 7
= 3 + 7
= 10
Solve: 9x 2+ 2x = –3 using the quadratic formula. step by step please to understand better
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Explanation: To solve the following equation
[tex]9x^2+2x=-3[/tex]We can use the following quadratic formula
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]Step 1: Let's compare our equation with a generic quadratic equation as follows
As we can see above, first we move -3 from the second term to the first term and when we do that we change its sign to +3. Now we know that a = +9, b = +2 and c = +3.
Step 2: Now all we need to do is to substitute the values of a, b and c into our quadratic formula and solve it to find the roots as follows
[tex]\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ x=\frac{-2\pm\sqrt[]{2^2-4\cdot9\cdot3}}{2\cdot9} \\ x=\frac{-2\pm\sqrt[]{4^{}-108}}{18} \\ x=\frac{-2\pm\sqrt[]{-104}}{18} \\ x=\frac{-2\pm\sqrt[]{-104}}{18} \end{gathered}[/tex]Final answer: As we can see above inside the square root there is a negative number -104 which means this quadratic equation has no real solutions.
9.A piece of wood is cut into 3 pieces. The lengths are 8'15, 634 and953/8".If 1/4" is used up for each saw cut (kerf), what is the length of the original board?HINT: 2 kerfs are made in cutting the board. Reduce fraction to simplest terms.
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The Solution.
First, we shall convert the given lengths to inches.
[tex]undefined[/tex]Given two vectors,find y so that a and b are orthogonal,
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In they are orthogonal the their scarlar product will be zero.
So
[tex]a\cdot b=0[/tex][tex]\begin{gathered} (9,-7,-7)\cdot(6,y,-4)=0 \\ 54-7y+28=0 \\ -7y=-82 \\ y=11.714 \end{gathered}[/tex]Hence, [tex]y=11.714[/tex] when the [tex]a[/tex] and [tex]b[/tex] are orthogonal.
What is the vectors?
Vectors in math is a geometric entity that has both magnitude and direction. Vectors have an initial point at the point where they start and a terminal point that tells the final position of the point.
Various operations can be applied to vectors such as addition, subtraction, and multiplication.
Here given that,
[tex]a=(9,-7,-7)\\b=(6,y,-4)[/tex]
If they are orthogonal the their scarlar product will be zero.
So,
[tex](9,-7,-7).(6,y,-4)=0\\54-7y+28=0\\-7y=-82\\As,\\a.b=0\\y=\frac{82}{7}\\y=11.714[/tex]
Hence, [tex]y=11.714[/tex] when the [tex]a[/tex] and [tex]b[/tex] are orthogonal.
To know more about the vectors
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Write the point-slope form of the equation of the line through the points (-1, -1) and (2, 4)
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The point-slope form of (-1, -1) and (2, 4) is y = 5/3(x+1) - 1.
The point-slope form is simply writing an equation of a line so that the slope or steepness and x-intercept i.e. where the line crosses the vertical x-axis are immediately apparent.
The slope-intercept equation is y - y1 = m(x - x1), where x and y are two variables, and m is the slope.
Slope m = (y2-y1) / (x2-x1)
Let,
(x1, y1) = (-1, -1)
(x2, y2) = (2, 4)
Slope (m) = ((4) - (-1)) / ((2) - (-1))
= 5/3
y - y1 = m(x - x1) => (y - (-1)) = 5/3(x - (-1))
=> y+1 = 5/3(x + 1)
=>y = 5/3(x+1)-1
Therefore, the point-slope form of (-1, -1) and (2, 4) is y = 5/3(x+1)-1.
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The population of Boom town is 775,000 and is increasing at a rate of 6.75% each year. How many years will it take to reach a population of 1,395,000?
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To study population growth, we use the following formula
[tex]P=P_0\cdot e^{rt}[/tex]Where,
[tex]\begin{gathered} P=1,395,000 \\ P_0=775,000 \\ r=0.0675 \end{gathered}[/tex]Let's replace the values above, and solve for t.
[tex]\begin{gathered} 1,395,000=775,000\cdot e^{0.0675t} \\ e^{0.0675t}=\frac{1,395,000}{775,000} \\ e^{0.0675t}=1.8 \\ \ln (e^{0.0675t})=\ln (1.8) \\ 0.0675t=\ln (1.8) \\ t=\frac{\ln (1.8)}{0.0675} \\ t\approx8.7 \end{gathered}[/tex]Hence, it would take 8.7 years to reach a population of 1,395,000.(10,-3),(5,-4)i need help finding the midpoint
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The given points are (10, -3) and (5, -4).
The midpoint formula is
[tex]M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})_{}[/tex]Where,
[tex]\begin{gathered} x_1=10 \\ x_2=5 \\ y_1=-3 \\ y_2=-4 \end{gathered}[/tex]Replacing these coordinates, we have
[tex]\begin{gathered} M=(\frac{10+5}{2},\frac{-3-4}{2}) \\ M=(\frac{15}{2},-\frac{7}{2}) \end{gathered}[/tex]Therefore, the midpoint is M(15/2, -7/2).I have 3 more questions but it didn’t fir here
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Probability = number of required outcome/number of the possible outcome
(a) To determine the theoretical probability for mary
[tex]\begin{gathered} \text{ Probability of spinner landing on grey = }\frac{\text{ number of grey}}{Total\text{ colour}} \\ \text{Probability of spinner landing on grey = }\frac{593}{1000} \\ \text{Probability of spinner landing on grey = 0.}593 \end{gathered}[/tex](b) To determine the experimental probabiity for mary's result
[tex]\begin{gathered} \text{Experimental probabil}ity\text{ = }\frac{\text{ number of grey}}{Total\text{ number}} \\ \text{Experimental probabil}ity\text{ = }\frac{3}{5\text{ }} \\ \text{Experimental probabil}ity=\text{ 0}.600 \end{gathered}[/tex](c) Assuming the spinner is fair, with a large number of spins there might be a difference between the experimental and theoretical probability but the difference will be small.
the density of aluminum is 2700 kg/m3. what is the mass of a solid cube of aluminum with side lengths of 0.5 meters?
Answers
SOLUTION
Density is calculated as
[tex]\begin{gathered} Density=\frac{mass}{volume} \\ \end{gathered}[/tex]The side lengths of the aluminium cube has been given as 0.5 m
The volume becomes
[tex]\begin{gathered} volume=length\times length\times length \\ V=L\times L\times L \\ V=0.5\times0.5\times0.5=0.125m^3 \end{gathered}[/tex]so the volume is 0.125 cubic-meters.
The mass becomes
[tex]\begin{gathered} Density=\frac{mass}{volume} \\ mass=density\times volume \\ mass=2700\times0.125 \\ =337.5 \end{gathered}[/tex]Hence the answer is 337.5 kg
Mia made a pencil box in the shape of a right rectangular prism what's the surface area of the box 20cm,6cm,7cm
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1) Let's visualize it to better understand:
A right rectangular prism is made from
2 faces 6 x 7
4 faces 20 x 6
Since we have rectangles, we can write calculating the area of each rectangle.
S base = 2 (6x 7) ⇒ S base = 84 cm²
S faces = 2 (20 x 6) ⇒ S faces = 240 cm²
S faces = 2 (20 x 7) ⇒ S faces = 280 cm²
2) Then the total surface area
84+240+280=604 cm²
Aubrey paints 4 square feet of her house each minute. How many square feet does she paint in 20 seconds? Round to the nearest tenth.
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We were told that Aubrey paints 4 square feet of her house each minute.
Recall that 1 minute = 60 seconds.
The statement can be written as
Aubrey paints 4 square feet of her house each 60 seconds
If x represents the number of square feets that she paints in 20 seconds, it means that
4 = 60
x = 20
By cross multiplying, it becomes
60 * x = 4 * 20
60x = 80
x = 80/60
x = 1.333
Rounding to the nearest tenth, it becomes 1.3 square feet
She paints 1.3 square feet in 20 seconds
A standard pair of six sided dice is rolled what is the probability of rolling a sum greater than or equal to 11
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The diagram below shows all the possible outcomes from rolling a pair of six sided dice.
The first row and first columns represents the numbers on each die. The numbers in the other rows and columns are outcomes for each roll. Thus, the total number of outcomes is the total number of pairs in the other rows and columns.
Total number of outcomes = 36
Number of outcomes with sum greater than or equal to 11 are the circled pairs. They are 3
Thus, the probability of rolling a sum greater than or equal to 11 is
3/36 = 1/12
Write the slope-intercept (y = mx + b) form of an equation for a line with y-intercept-5 and slope 2.
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The slope-intercept form of the line is
[tex]y=mx+b[/tex]where m is the slope and b is the y-intercept
so we only need to substitute the values into the equation
m=2
b= -5
the equation is
[tex]y=2x-5[/tex]points a,b, and are b lies between a and c. if ac=48,ab =2x+2and bc =3x+6, what is bc?
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Given that A, B, and C are collinear and B lies between A and C, then:
AB + BC = AC
Replacing with data:
(2x + 2) + (3x + 6) = 48
(2x + 3x) + (2 + 6) = 48
5x + 8 = 48
5x = 48 - 8
5x = 40
x = 40/5
x = 8
Then,
BC = 3x + 6
BC = 3(8) + 6
BC = 24 + 6
BC = 30
Question #10: Given triangle A is the pre image and B is the image, state the scale factor of the dilation from A to B. * 4 B 10 18 А 7.2 15
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To find the acale factor we need to solve the following equation:
[tex]\begin{gathered} 18k=7.2 \\ k=\frac{7.2}{18} \\ k=0.4 \end{gathered}[/tex]This comes from the fact that the biggest sides of both triangles have to be realted.
Therefore the dilation factor is 0.4.
A randomly generated list of integers from O to 4 is being used to simulate anevent, with the number 3 representing a success. What is the estimatedprobability of a success?
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We have that:
• A randomly generated list of, integers from 0 to 4 i,s being used to simulate an event.
• The number 3 represents a success.
And we need to find the estimated probability of success.
We can achieve that if we know that:
1. We have the following sample space for the experiment - we have a list of integers from 0 to 4:
[tex]\Omega=\lbrace0,1,2,3,4\rbrace[/tex]2. Then the probability of having a 3 is:
[tex]P(3)=\frac{1}{5}=0.2\Rightarrow20\%[/tex]We have one possibility of getting a 3 (one possibility) out of 5 possibilities (0, 1, 2, 3, 4).
Therefore, the estimated probability of success is 20% (option D.)
Two jets leave harrisburg at the same time, one flying east at a speed of 20 km/h greater than the other, which is flying west. After 4 h, the planes are 6000 km apart. Find their speeds. A tourist bus leaves Richmond at 1:90 PM for New York City. Exactly 24 minutes later, a truck sets out in the same direction. The tourist bus moved at a steady 60 km/h. The truck travels at 80 km/h. How long does it take the truck to overtake the tour bus?
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We know that two jets leave Harrisburg at the same, time, one flying east, and another flying west.
We will denote the speed of the second jet by x (in km/h). Thus, the speed of the first jet is x+20. Remembering that:
[tex]v=\frac{d}{t}[/tex]where v is speed, d is distance and t is time, we know that for the first jet:
[tex]x+20=\frac{d_1}{4}\Rightarrow4x+80=d_1[/tex]Where d₁ represents the distance of the first jet from the starting point. For the second jet:
[tex]x=\frac{d_2}{4}\Rightarrow4x=d_2[/tex]Where d₂ represents the distance of the second jet from the starting point.
We also know that:
[tex]d_1+d_2=6000[/tex]As:
Thus, we have that:
[tex]\begin{gathered} (4x+80)+(4x)=6000 \\ \text{And solving for x, we get:} \\ 8x+80=6000 \\ 8x=5920 \\ x=\frac{5920}{8}=740 \end{gathered}[/tex]This means that the second jet has a speed of 740km/h, and the first jet has a speed of 760km/h (20km/h greater than the second one).
I am having a hard time finding the apt for this question pls help me?
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The APR, that is Annual Percentage Rate, is calculated using the formula below;
[tex]undefined[/tex]I need help with fractions and word problem can you help me
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Grace wants to bring a small wedge of cheese for the next 12 days, but there are three small rounds of cheddar cheese in Grace's refrigerator, That is to say, that Grace needs to buy cheese to fulfill this purpose, the small wedge of cheese that Grace needs are:
[tex]12-3=9[/tex]but we must represent this infraction, for this, we will take the 12 small wedges of cheese as a unit, which is formed by having the 12 portions.
That is, out of 12/12 portions, we only have 3/12, To do this we do subtraction and see how many we need in fractional form.
[tex]\begin{gathered} \frac{12}{12}=1 \\ \frac{12}{12}-\frac{3}{12}=\frac{9}{12} \end{gathered}[/tex]In conclusion, Grace need 9 portions i.e. 9/12
Now, that we know this fraction, this is a correct answer, however, we can simplify this fraction.
[tex]\frac{9}{12}=\frac{3}{4}[/tex]In conclusion, Grace needs 3/4 small wedge of cheese.
Note: the answer can be 9/12, but also its simplified form which corresponds to the same, this simplified form is 3/4.
4x + 8 = 28Describe a real-world situation the equation could represent.
Answers
In a club, the entrance ticket is $8. And every time you order a soda you have to pay $4 per can. Since you only have $28 in your pocket, how many sodas can you afford?
The equation 4x +8=28 could be used to describe a scenario like this below:
In a club, the entrance ticket is $8. And every time you order a soda you have to pay $4 per can. Since you only have $28 in your pocket, how many sodas can you afford?
Notice the fixed amount (8) and the variable (4x) and the total of money you have (28). So the sum above describes the amount of money for that club.
With that equation you can find that:
4x +8=28
4x+8 -8 =28-8
4x=20
x=5
5 cans of soda.
What is the slope for this equation y = -2.5x + 92
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EXPLANATION
Given the equation y = -2.5x + 92
The slope is equal to -2.5
i need to know which one is the answer , i’m having a hard time figuring it out
Answers
Answer:
Explanation:
Here, we want to know the table that represents a function
For a relationship to represent a function, no two y values can have a single x value but two x values can have a single y value.
What this means is that two independent variable values can take a single dependent variable value but no two dependent variable values can take a single independent variable value
Now, looking at the table given:
4. Tickets for a carnival cost $6 for adults and $4 for children. The school has abudget of $120 for a field trip to the carnival. An equation representing thebudget for the trip is 120 = 6x + 4y. Here is a graph of this equation:
Answers
Given:
The equation is 6x + 4y = 120.
Explanation:
The points that lies on the line satifies the equation. So point (0,30) lies on the number which 0 adults and 30 children could go to school. So "if no adult chaperons were needed, 30 students could go to school is true.
For ten students and 15 adults point is (15,10). The point (15,10) does not lie on number line and not satifies the equation so second statement is false.
The cost of tickets for 4 adults is,
[tex]4\cdot6=24[/tex]and cost of tickets for six students is,
[tex]6\cdot4=24[/tex]Both costs are equal, means for six fewer students 4 additional adults can go to the zoo. Thus third statement is correct.
The cost of tickets for two children is,
[tex]4\cdot2=8[/tex]The cost of tickets for 3 adults is,
[tex]6\cdot3=18[/tex]Since cost of tickets for 3 adults is more than cost of tickets for two children which means two children can not go to the zoo for 3 fewer adults in the trip. Thus fourth statement is wrong.
For 16 adults and 6 students point is (16,6). The point (16,6) lies on the number line, which point (16,6) satifies the equation. So fifth statement is correct.
Find anequation for the perpendicular bisector of the line segment whose endpointsare (5,-4) and (-9, -8).
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First, we need to find the slope of the line:
Let:
(5, -4) = (x1,y1)
(-9, -8) = (x2,y2)
m = (y2-y1)/(x2-x1) = (-8-(-4))/(-9-5) = -4/-14 = 2/7
Also, we need to find the midpoint:
let:
MP = (xp,yp)
xp= (x1+x2)/2 = (5-9)/2 = -2
yp = (y1+y2)/2 = (-4-8)/2 = -6
MP = (-2, -6)
Now, the slope for the perpendicular bisector is -m = -7/2
y = -mx + b
Using the midpoint
-6 = -7/2(-2) + b
-6 = 7 + b
Solving for b:
b = -13
Therefore, the equation for the perpendicular bisector is:
y = -7x/2 - 13
what does translation mean?
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translation means moving a geometric object in the cartesian plane without rotating it.
Determine if the triangles, △YPQ and △NPD, are similar. if so, Identify criterion.
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Answer:
Yes, they are similar.
Criterion: AA Similarity
Explanation:
Looking at triangles YPQ and NPD, we can see that angles NPD and YPQ are vertically opposite angles and are congruent since vertically opposite angles are always congruent;
[tex]\angle YPQ\cong\angle NPD\text{ (vertically opposite angles)}[/tex]We can also observe that angles N and Y are congruent since they are alternate angles;
[tex]\angle N\cong\angle Y\text{ (alternate angles)}[/tex]From the AA similarity rule, we know that two triangles are said to be similar if two angles in one triangle are equal to two triangles in the other triangle.
Therefore, from the AA rule, we can say that triangles YPQ and NPD are similar.
Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form. 4)-1 and 3 + 2i A) (x)= x3 + 5x2 +7x + 13 B)(x) = x3 - 5x2 + 7x - 13 C)(x)= x3 - 5x2 + 7x + 13 D) f() = x3 - 5x2 + 7x + 14
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A sample was done, collecting the data below. Calculate the standard deviation, to one decimalplace.х24726573
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We have the following data
[tex]24,7,26,5,13[/tex]The standard deviation is given by
[tex]\sigma=\sqrt[]{\frac{\sum(x_i-\mu)^2}{N}}[/tex]Where μ is the mean and N is the number of data points
Let us first find the mean of the data.
[tex]\mu=\frac{\text{sum}}{number\text{ of data points}}=\frac{24+7+26+5+13}{5}=\frac{75}{5}=15[/tex]Finally, the standard deviation is
[tex]\begin{gathered} \sigma=\sqrt[]{\frac{(24-15)^2+(7-15)^2+(26-15)^2+(5-15)^2+(13-15)^2}{5}} \\ \sigma=\sqrt[]{\frac{(9)^2+(-8)^2+(11)^2+(-10)^2+(-2)^2}{5}} \\ \sigma=\sqrt[]{\frac{81^{}+64^{}+110^{}+100^{}+4^{}}{5}} \\ \sigma=\sqrt[]{\frac{359}{5}} \\ \sigma=\sqrt[]{71.8} \\ \sigma=8.5 \end{gathered}[/tex]Therefore, the standard deviation of the data set is 8.5