Given:
The graph of a linear inequality.
The boundary line passes through the points (0,-2) and (1,1), and the shaded region lies above the boundary line.
To find:
The inequality for the given graph.
Solution:
The boundary line passes through the points (0,-2) and (1,1), so the equation of the boundary line is:
[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
[tex]y-(-2)=\dfrac{1-(-2)}{1-0}(x-0)[/tex]
[tex]y+2=\dfrac{1+2}{1}(x)[/tex]
[tex]y+2=3x[/tex]
Subtract 2 from both sides.
[tex]y=3x-2[/tex]
The boundary line is a solid line and the shaded area lies above the boundary line, so the sign of inequality must be [tex]\geq [/tex].
[tex]y\geq 3x-2[/tex]
Therefore, the required inequality is [tex]y\geq 3x-2[/tex].
Answer:
y>3x-2
Step-by-step explanation:
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what is 8/9 divide 2/3?
Answer:
4/3
Step-by-step explanation:
8/9 ÷ 2/3
Simplify the complex fraction.
4/3
Step-by-step explanation:
8/9 ÷ 2/3
Simplify
4/3 is the correct answer
6 – x + = 6 minus StartFraction 3 Over 4 EndFraction x plus StartFraction 1 Over 3 EndFraction equals StartFraction one-half EndFraction x plus 5.X + 5 2 3 6 12
Answer:
x = 16/15
Step-by-step explanation:
Given:
6 - 3/4x + 1/3 = 1/2x + 5
Collect like terms
6 + 1/3 - 5 = 1/2x + 3/4x
(18+1-15)/3 = (2x+3x)/4
4/3 = 5/4x
x = 4/3 ÷ 5/4
x = 4/3 × 4/5
x = (4 * 4) / (3 * 5)
x = 16/15
What is the measure of ∠
A. 6°
B. 42°
C. 60°
D. 49°
Answer:
<XYZ is equal to 49°
Step-by-step explanation:
Set the two expressions equal to each other so 7x+7=5x+19. Subtract 5x from 7x and 7 from 19 which is equal to 2x=12 that means x is 6. then plug 6 into (7x+7) which is equal to 49.
Oscar bought 15 gallons of water at $1.98 per gallon. He wants to divide this water in bottles of 1/8 gallon each. What is the cost of a bottle of water?
Answer:
Step-by-step explanation:
James' truck uses 8 gallons of gas per day. He filled his tank up with 36 gallons of gas. How many days will James be able to drive using 36 gallons of gas?
Answer:
4.5
Step-by-step explanation:
36 ÷ 8 = 4.5
James will be able to drive for 4.5 days.
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James will be able to drive [tex]=4\frac{1}{2}[/tex] days.
What is arithmetic maths ?Arithmetic is the fundamental of mathematics that includes the operations of numbers like addition, subtraction, multiplication and division.
We have,
James' truck uses gas per day [tex]=8[/tex] gallons
Tank has gas [tex]=36[/tex] gallons
Now,
According to the question,
Number of days James will drive [tex]= \frac{Total\ gas}{Gas\ used\ per\ day}[/tex]
[tex]=\frac{36}{8}[/tex]
Number of days James will drive[tex]=4\frac{1}{2}[/tex] days
Hence, we can say that James will be able to drive [tex]=4\frac{1}{2}[/tex] days.
To know more about arithmetic maths click here
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Choose the one that is FALSE. *
A. 1/4 = 2/8
B. 3/4 = 10/12
C. 5/10 = 1/2
D. 10/12 = 5/6
Answer:
B. 3/4 = 10/12
Step-by-step explanation:
A. 1/4*2/2 = 2/8
B. 3/4*3/3 = 9/12 not10/12
C. 5/10*5/5 = 1/2
D. 10/12 divided by 2/2 = 5/6
Select the correct answer.
What is the value of x in the triangle?
Answer:
The answer is A. 21
Hope it helps.
Step-by-step explanation:
• • •
What is -3 over 9 in standard form
Answer:
-1/3
Step-by-step explanation:
-3/9
= -1/3
what is the surface area of a sphere if the volume is 3000 pi
Answer:
228.95 cm2 / 229 cm2
Step-by-step explanation:
Volume of a sphere is given by;
V = (4/3)πr3
So in this question we have to find the radius of the sphere to enable us find the surface area.
Therefore let's find the radius using the volume formula;
3000π = (4/3)πr3
Divide through by (4/3)π
r3 = 2250
r =3√2250 (cube root of 2250)
r = 13.104cm2
Since we have gotten the radius, let's calculate the surface area using the formula;
A = (4/3)πr^2
= (4/3) × π × 13.104^2
= 228.95 π cm2 or 229 cm2
What is the recursive formula for this geometric sequence?
-4, -24, -144, -864, ...
= -4
O A.
an =
2n-1 • 30
OB.
la = -4
ar = 2n-16
fa
= -6
C.
= 2n-1 • 30
= -6
O D.
lan
ar = 2n-1.4
Answer:
a1 = -4
an = an-1 * 6
Step-by-step explanation:
-4, -24, -144, -864, ...
First find the common ratio
Take the second term and divide by the first term
-24/-4 = 6
The common ratio is 6
The recursive formula is
a1 = -4
an = an-1 * 6
which of the following equations are perpendicular
N is the centriod of triangle. Find XN if XG = 33
Answer:
22
Step-by-step explanation:
The centroid divides a median in two parts that have this ratio = 1/3 and 2/3
In particular the part between the vertex and the centroid is 2/3 of the median.
So we have:
XN = (33 * 2)/3 = 22
What is the solution to this equation?
7x - 2(x - 10) = 40
O A. x = 4
O B. x = 12
O C. x = 6
D. X = 10
Answer:
A. x = 4
Step-by-step explanation:
[tex]7x-2(x-10)=40\\7x-2x+20=40\\5x+20=40\\5x=20\\x=4[/tex]
Ashish deposite rs 1000 every month is a recurring deposit account for period of 12 months. If the bank pays interest at a certain rate p.A. And ashish gets 12715 as the maturity value of this account at what rate of interest did he pay every month
Solution :
Given :
Principal amount, P = Rs. 1000
Time period = 12 months
The maturity value = Rs. 12,715
We know that,
[tex]$ SI = \frac{PTR}{100}$[/tex]
[tex]$SI = 1000 \times \frac{n(n+1)}{2 \times 12} \times \frac{R}{100}$[/tex]
[tex]$SI = 1000 \times \frac{12(12+1)}{2 \times 12} \times \frac{R}{100}$[/tex]
SI = 65 R
So we know,
maturity value = principal amount + SI
12715 = 1000 + 65 R
65 R = 12715 - 1000
65 R = 11715
R = 18%
So the rate is 18%
Answer:
[tex]R=11\%[/tex] p.a.
Step-by-step explanation:
Given:
the principal amount deposited each month, [tex]P=Rs. 1000[/tex]
amount after maturity of one year, [tex]A=Rs. 12715[/tex]
We have the formula as:
[tex]I=\frac{PR}{100}\times\frac{T(T+1)}{2\times 12}[/tex]
where:
R = rate of interest per annum
T = time in months
[tex]A-12P=\frac{PR}{100}\times\frac{T(T+1)}{2\times 12}[/tex] [since the principal is deposited each month]
[tex]715=\frac{1000\times R}{100}\times \frac{12\times 13}{24}[/tex]
[tex]R=11\%[/tex] p.a.
the hypotenuse of a right angled triangular field is 50ft and the legs are in the ratio 7:24, find the area of the right angled triangular field triangular field also find the cost of paving the field with brick at the rate of rs.20per square ft
Answer:
Step-by-step explanation:
If one leg is 7x than other leg is 24x
Using Pythagoras
50² = (7x)² + (24x)²
2500 = 49x² + 576x²
2500 = 625x²
x² = 2500/625 = 4
x = +2 or -2 ; x is positive
Means 7 x = 14 and 24x = 48
The two sides are 14cm and 48cm
Test: 14² + 48² = 196 + 2304 = 2500= 50²
for each relation, decide whether or not it is a function
Answer:
Relation 1,2,and 4 are functions, but relation 3 not is a function.
Step-by-step explanation:
function 1 input, no function with the same input like m in relation 3.
Explain why y +1 = 1.2(x + 2) and y- 5 = 1.2(x – 3) represent the same line, despite having
different equations.
Answer:
They have the same slope
Step-by-step explanation:
The standard equation of a line in point-slope form is expressed as;
y-y0 = m(x-x0)
We can see that both equations given are written in this form with a slope of 1.2. For two lines to be equal, they must have the same slope no matter the point on the lines. Hence the two equations are equal since they have different slopes.
I having a hard time figuring this out.
Answer:
33
Step-by-step explanation:
Start by adding the 3 to the other side (2/3x=22)
Then, you divide 2/3 to cancel it out. To do that, multiply 22 by 3/2 which equals to 33.
Answer:
2/3x - 3 = 19
We first isolate the variable and solve for x, (we get rid of any constants first in the process)
2/3x - 3 = 19 the three is the constant so we get rid of it by adding three to both sides.
2/3x - 3 = 19
+3 +3
2/3x = 22
Now we divide by 2/3 on both sides
X = 33
a bag contains 3 red marbles, 5 yellow marbles, and 2 green marbles. what is the probability that you will select 2 green marbles in a row if you do not replace the first marble? A) 0.020 B) 0.02 C) 0.040 D) 0.200
Answer:
B
Step-by-step explanation:
find the probability of picking the first green marble, which would be 2/10
then afterwards once the marble is removed, it would be 1/9
Multiply both 2/10 and 1/9 to get 0.022, which rounds to 0.02
Answer:
0.02
Step-by-step explanation:
3+5+2 = 10
to choose 1 green the probability is 2/10 = 1/5
if we do not replace it, then there are now 9 marbles left and only 1 green left, so 1/9
to find them both in a row, multiply
1/5 * 1/9 = 1/45 = 0.02222
Which is the angle of elevation from C to B?
Answer:
Angle of elevation = ∠4
Step-by-step explanation:
Angle of elevation of a point point from another point is the angle formed between the line joining these points and the horizontal line.
Therefore, angle of elevation of point B from a point C = ∠4
Option with angle 4 will be the answer.
help help............
Answer:
please send the pic again clearly
Answer:
I hope it will help you
Step-by-step explanation:
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Which number is rational?
√2
Pi
Square root of 10
Square root of 16
Answer:
[tex]\sqrt{16}[/tex] is rational number
Step-by-step explanation:
Rational number is of the form p/q, where q ≠ 0. It may be a terminating number or non terminating repeating number.
√2 is irrational number as it is non terminating non repeating number
π is irrational number as it is non terminating non repeating number
√10 is irrational number as it is non terminating non repeating number.
[tex]\sqrt{16}=\sqrt{4*4}=4[/tex]
[tex]\sqrt{16}[/tex] is a rational number
the length of a photograph is 11.4 inches if the photo is enlarged so that its length is increased by 2.25 inches what the new length
We know
[tex] \\ \sf \longmapsto \: new \: length = length + increased \: length \\ \\ \sf \longmapsto \: new \: length = 11.4 + 2.25 \\ \\ \sf \longmapsto \: new \: length = 13.65in[/tex]
Two linear equations are shown.
A coordinate grid with 2 lines. The first line is labeled y equals StartFraction one-third EndFraction x plus 2 and passes through (negative 6, 0) and (0, 2). The second line is labeled y equals StartFraction 4 over 3 EndFraction minus 5.
What is the solution to the system of equations?
(7, 4)
(7, StartFraction 13 over 3 EndFraction)
(8, StartFraction 14 over 3 EndFraction)
(9, 7)
Answer:
(7, 13/3)
Step-by-step explanation:
Given the expressions
y = 1/3x + 2 and the second line y = 4/3x - 5
Equating both expressions
1/3x + 2 = 4/3x - 5
1/3x - 4/3x = -5 - 2
-3/3x = -7
-x = -7
x = 7
Substitute x = 7 into any of the equations
Using y = 1/3 x + 2
y = 1/3(7) + 2
y = 7/3 + 2
y = (7+6)/3
y = 13/3
Hence the solution to the system of the equation is (7, 13/3)
Answer:
(7,13/3) is your answer, otherwise known as answer choice B.
Step-by-step explanation:
PLEASE HELP ASAP 30 POINTS
Answer:
I don't know how to do please let me I will try solve the question
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Answer:
bka bla bla bla sorry I newbie
sin pi/3 __ __ pi/6 = 1/2(sin pi/2 + sin pi/6)
I think I’m just supposed to fill in the blank? (question off of a p e x) please give explanation!
Notice that
• π/2 = π/3 + π/6
• π/6 = π/3 - π/6
Recall the angle sum identities for sine:
sin(x + y) = sin(x) cos(y) + cos(x) sin(y)
sin(x - y) = sin(x) cos(y) - cos(x) sin(y)
By adding these together, we get
sin(x + y) + sin(x - y) = 2 sin(x) cos(y)
==> sin(x) cos(y) = 1/2 (sin(x + y) + sin(x - y))
Now take x = π/3 and y = π/6 :
sin(π/3) cos(π/6) = 1/2 (sin(π/2) + sin(π/6))
So the blank should be filled with cos.
I only need the answer
Answer:
1
Step-by-step explanation:
The given equation of the function is y = -a·(x - h)² + 1
The positive constants of the equation = a, and h
The points the function crosses the x-axis = 2, and 4
Where the function crosses the x-axis, y = 0, and x = 2, and 4, therefore, when x = 2, we have;
y = 0 = -a·(2 - h)² + 1
When x = 4, we have;
0 = -a·(4 - h)² + 1
-a·(2 - h)² + 1 = -a·(4 - h)² + 1
-a·(2 - h)² = -a·(4 - h)²
(2 - h)² = (4 - h)²
±(2 - h) = +#±(4 - h)
When
(2 - h) is negative, and (4 - h) is positive, but the same magnitude, we have';
-(2 - h) = +(4 - h)
2·h = 4 + 2 = 6
h = 3
0 = -a·(4 - h)² + 1 = -a·(4 - 3)² + 1 = -a + 1
Therefore, a = 1
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Not enough information to solve..... Please make your question more clear
Which system of linear inequalities is graphed?
Answer:
The first one.
Step-by-step explanation:
Graph lines as if the inequalities were equal signs.
X = -3 is a vertical line at x = -3, because it's less than we shade to the left. All numbers less than -3 are to the left. The line is dashed because there is no equal to. Only less than. The line is not included in the solution set.
y = -x - 1 is a line with a y-intercept of -1 and a slope of -1. All values that are less that y are below the line. Because it's less than or equal to the line is solid.
Answer:
A
Step-by-step explanation:
The vertical line is dotted at -3 and shaded to the left
x < -3
This gives us two choices left
A and C
The other line has a y intercept at -1 and is solid and shaded to the left
It is of the form
y ≤ mx+1
We know the slope is negative since is goes down from left to right
The only Choice is A
