Answers
Given:
The graph of system of inequalities.
To find:
The system of inequalities.
Solution:
From the given graph it is clear that the shaded region is lies below the line y=10 and the boundary line y=10 is a solid line. So, the sign of inequality must be [tex]\leq[/tex].
[tex]y\leq 10[/tex].
The shaded region lies on the right side of the y-axis. So, [tex]x\geq 0[/tex].
Another boundary line passes through the point (0,1) and (1,2). So, the equation of the line is:
[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
[tex]y-1=\dfrac{2-1}{1-0}(x-0)[/tex]
[tex]y=1(x)+1[/tex]
[tex]y=x+1[/tex]
The boundary line [tex]y=x+1[/tex] is a dotted line and the shaded region lies above the boundary line, so the sign of inequality must be [tex]>[/tex].
[tex]y> x+1[/tex]
So, the required system of inequalities is:
[tex]y> x+1[/tex]
[tex]y\leq 10[/tex]
[tex]x\geq 0[/tex]
Therefore, the correct option is B.
Related Questions
If A = [tex]\left[\begin{array}{ccc}cosx&-sinx\\sinx&cosx\end{array}\right][/tex], then show that [tex](A^{-1} )^{-1}[/tex]
Answers
Given:
The matrix is:
[tex]A=\begin{bmatrix}\cos x&-\sin x\\\sin x&\cos x\end{bmatrix}[/tex]
To show:
[tex](A^{-1})^{-1}=A[/tex]
Solution:
If a matrix is:
[tex]M=\begin{bmatrix}a&b\\c&d\end{bmatrix}[/tex]
Then,
[tex]M^{-1}=\dfrac{1}{ad-bc}\begin{bmatrix}d&-b\\-c&a\end{bmatrix}[/tex]
We have,
[tex]A=\begin{bmatrix}\cos x&-\sin x\\\sin x&\cos x\end{bmatrix}[/tex]
Using the above formula, we get
[tex]A^{-1}=\dfrac{1}{(\cos x)(\cos x)-(-\sin x)(\sin x)}\begin{bmatrix}\cos x&\sin x\\-\sin x&\cos x\end{bmatrix}[/tex]
[tex]A^{-1}=\dfrac{1}{\cos^2x+\sin^2x}\begin{bmatrix}\cos x&\sin x\\-\sin x&\cos x\end{bmatrix}[/tex]
[tex]A^{-1}=\dfrac{1}{1}\begin{bmatrix}\cos x&\sin x\\-\sin x&\cos x\end{bmatrix}[/tex]
[tex]A^{-1}=\begin{bmatrix}\cos x&\sin x\\-\sin x&\cos x\end{bmatrix}[/tex]
Now, the inverse of [tex]A^{-1}[/tex] is:
[tex](A^{-1})^{-1}=\dfrac{1}{(\cos x)(\cos x)-(\sin x)(-\sin x)}\begin{bmatrix}\cos x&-\sin x\\\sin x&\cos x\end{bmatrix}[/tex]
[tex](A^{-1})^{-1}=\dfrac{1}{\cos^2x+\sin^2x}\begin{bmatrix}\cos x&-\sin x\\\sin x&\cos x\end{bmatrix}[/tex]
[tex](A^{-1})^{-1}=\dfrac{1}{1}A[/tex]
[tex](A^{-1})^{-1}=A[/tex]
Hence proved.
What is important to remember when multiplying radicals?
Answers
Answer:
A radical is basically a fractional exponent and is denoted by the radical sign (√). The expression x2 means to multiply x by itself (x × x), but when you see the expression √x, you're looking for a number that, when multiplied by itself, equals x. Similarly, 3√x means a number that, when multiplied by itself twice, equals x, and so on. Just as you can multiply numbers with the same exponent, you can do the same with radicals, as long as the superscripts in front of the radical signs are the same. For example, you can multiply (√x × √x) to get √(x2), which just equals x, and (3√x × 3√x) to get 3√(x2). However, the expression (√x × 3√x) can't be simplified any further.
What is the slope of the line? What is the y-intercept of the line? y = 2x + 5
Answers
Slope intercept form of a line is, y = mx + c where m is the slope and c is constant.
Judging the given equation y = 2x + 5
Slope (m) of the line is 2,
y-intercept of the line,
y = 2x + 5
y = 2×0 + 5
y = 5
Answered by GAUTHMATH
Answer:
m = 2
y intercept = 5
Step-by-step explanation:
The given equation of the line is ,
[tex]\implies y = 2x +5[/tex]
We know that the Standard equation of Slope Intercept Form of the line is,
[tex]\implies y = mx + c[/tex]
Where ,
m is slope c is y interceptOn comparing to the Standard form of the line we get ,
[tex]\implies Slope = 2 [/tex]
[tex]\implies y - intercept= 5[/tex]
Can someone help with this?
Answers
Answer:
(a) is 8 x 7 x 3 = 168
(b) is 8 x 7 = 56
(b2) is weird I don't know what it's asking
Answer:
FOR LETTER A
Volume of prism (expression) = Length x Width/Breadth x Height
Volume of prism (expression) = 8 units x 7 units x 3 units = 168 cubic units
FOR LETTER B
Area of the shaded base = 8 x 7 = 56 square units
Volume of prism = Area of the shaded base x Height
Volume of prism = 56 square units x 3 units = 168 cubic units
Step-by-step explanation:
To find the volume of rectangular prism, we multiply the length of the prism by the width of the prism by the height of the prism.
Volume of rectangular prism = length × width × height
To get the area of the shaded base, when the base is in rectangular shape:
Definition: Area of rectangle is the region occupied by a rectangle within it's four sides or boundaries.
The area of a rectangle depends on its sides. Basically, the formula for area is equal to the product of length and breadth of the rectangle. Whereas when we speak about the perimeter of a rectangle, it is equal to the sum of all its four sides. Hence, we can say, the region enclosed by the perimeter of the rectangle is its area. But in the case of a square, since all the sides are equal, therefore, the area of the square will be equal to the square of side-length.
Area of rectangle = Length × Breadth
A = l × b
Select all of the equations below that are equivalent to:
w + 13 = –8
Answers
Answer:
w= -21
Step-by-step explanation:
How many marbles do you need to be able to arrange them into the shape of an equilateral triangle with 75 rows
Answers
Answer:
2850
Step-by-step explanation:
1+2+3+4+5+6+7...74+75
just add up all the numbers from 1 to 75
26
Which defines a circle?
Answers
Answer:
a round figure that has no corners or vertices.
Step-by-step explanation:
Answer:
A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre; equivalently it is the curve traced out by a point that moves in a plane so that its distance from a given point is constant. The distance between any point of the circle and the centre is called the radius. This article is about circles in Euclidean geometry, and, in particular, the Euclidean plane, except where otherwise noted.
Step-by-step explanation:
Center of a Circle
The center of a circle is the center point in a circle from which all the distances to the points on the circle are equal. This distance is called the radius of the circle.
Here, point P is the center of the circle.
center of the circle center point
Semicircle:
A semi-circle is half of a circle, formed by cutting a whole circle along a line segment passing through the center of the circle. This line segment is called the diameter of the circle.
find the highest common factor and lowest common multiple of 152 and 266
Draw a factor tree for each
Answers
Answer:
the highest common factor of 152 and 266 is 38 and the lowest common multiple is 1064
Answer:
Explanation is in the attachment
hope it is helpful to you
Which polynomial function has a leading coefficient of 3 and roots 4, I, and 2, all with multiplicity 1? Of(x) = 3(x + 4)(x - 1)(x - 2) O f(x) = (x - 3)(x + 4)(x - 1)(x - 2) f(x) = (x - 3)(x + 4)(x - 1)(x + 1)(x - 2) O f(x) = 3(x + 4)(x - 1)(x + 1)(x - 2) N
Answers
Note: There must be -4 instead of 4 otherwise all options are incorrect.
Given:
A polynomial function has a leading coefficient of 3 and roots -4, 1, and 2, all with multiplicity 1.
To find:
The polynomial function.
Solution:
The general polynomial function is defined as:
[tex]P(x)=a(x-c_1)^{m_1}(x-c_2)^{m_2}...(x-c_n)^{m_n}[/tex]
Where, a is the leading coefficient, [tex]c_1,c_2,...,c_n[/tex] are the zeros with multiplicity [tex]m_1,m_2,...,m_n[/tex] respectively.
It is given that a polynomial function has a leading coefficient of 3 and roots 4, 1, and 2, all with multiplicity 1. So, the polynomial function is defined as:
[tex]P(x)=3(x-(-4))^1(x-1)^1(x-2)^1[/tex]
[tex]P(x)=3(x+4)(x-1)(x-2)[/tex]
Therefore, the correct option is A.
A point P(3, k) is first transformed by E¹[0, 2] and then by E²[0,3/2] so that the final image is (9, 12), find the value of k.
Answers
Hello,
The first transform E1 is the homothetie of center (0,0) and ratio=2
The second transform E2 is the homothetie of center (0,0) and ratio=3/2
P=(3,k)
P'=E1(P)= E1((3,k))=(2*3,2*k)=(6,2k)
P''=E2(P')=E2(6,2k)=(3/2*6,3/2*2*k)=(9,3k)=(9,12)
==> 3k=12
k=4
Ava’s gross pay is $2,500 per month. Her deductions include the following:
Federal income tax $290
State income tax $85
Social Security $112
Medicare $35
What is Ava’s net pay each month?
Answers
Explanation:
Gross pay is what’s made before taxes and necessary deductions, net pay is after taxes and necessary deductions. So we minus the deductions to find the net pay. The equation is 2,500 - 290 - 85 - 112 - 35 = ? . The answer is $1,978.
I hope this helps. Please mark me the Brainliest, it’s not necessary but I put time and effort into every answer and I would appreciate it greatly. Have a great day, stay safe and stay healthy ! :)
through: (4,- 4), perp. to y = -4x - 2
Answers
Answer:
Step-by-step explanation:
y = -4x - 2
slope of line = -4
slope of perpendicular to line = ¼
Point-slope equation for line of slope ¼, passing through (4,-4):
y+4 = ¼(x-4)
In slope-intercept form:
y = ¼x - 5
what is lockdown
what is lockdown
Answers
Answer:
lockdown is a restriction policy for people or community to stay where they are, usually due to specific risks to themselves or to others if they can move and interact freely.
lockdown is when a country or a state closes and prevent entry or exit from one state or country to another in order to avoid the spread of for example a disease.
Determine which statement or statements are true. If none write “none”.
SOMEONE PLSSSS HELP ME WITH 4-6 THANK YOU SO MUCH!!!! LIFE SAVER!!!!
Answers
Answer:
4. D.
5. C.
6. A.
Step-by-step explanation:
It's just simple ratios... It's been a while since I learned it so I don't really remember how to explain the answers.
5) C
6) A
hope this helped ! :)
PLEASE HELP !!!!!!!!!!!!
9. The approximate height, h, in metres, travelled by golf balls hit with two different clubs over a horizontal distance of d metres is given by the following functions:
-Seven Iron: h= -0.002d^2+0.3d
-Nine Iron: h=-0.004d^2+0.5d
a) At what distances is the ball at the same height when either of the clubs is used?
B) What is this height?
(I need to use a ti-84 calculator in order to find the answer)
Answers
Answer:
The ball will reach the same height of 10 meters after 100 meters.
Part A)
100 meters.
Part B)
10 meters.
Step-by-step explanation:
The golf-ball hit by the Seven-Iron is modeled by the equation:
[tex]h=-0.002d^2+0.3d[/tex]
And the ball hit by the Nine-Iron is modeled by the equation:
[tex]h=-0.004d^2+0.5d[/tex]
Where h is the height of the ball after d meters.
When they are at the same height, the two equations will equal each other.
Graphically, this is where the two graphs will intersect.
To solve this using a Ti-84, you can follow these steps (I'm using the Ti-84 Plus Silver Edition):
1) Using [Y=], write and then [GRAPH] the two equations.
2) Press [ZOOM] and [ZOOM OUT] until you can see both graphs clearly.
3) To find the intersection point, press [2ND] and then [CALC] (above [TRACE]).
4) Choose [5) Intersect].
5) Using the arrow keys, click on one graph to choose it as your first curve and the other to choose it as your second curve. (In this case, it doesn't matter which one is which.)
6) When it asks you to guess, put the cursor to as close to the intersection point as possible. Ignore the intersection at the origin point.
7) Press [ENTER], and it should give you your solution.
Therefore, the intersection point (not counting (0,0)) is at (100, 10).
Therefore, the ball will reach the same height of 10 meters after 100 meters.
find the size of each of the unknown angles
plz give me solution
Answers
Answer:
80°Step-by-step explanation:
See the picture
It should be self-explanatory
The top part of the angle a is:
35° + 165° - 180° = 20°The bottom part of the angle a is:
180° - 120° = 60°The measure of angle a is:
20° + 60° = 80°Firstly, draw a line parallel to UT
Something like in the picture
Now,
a = BNU
Also,
BNU + BNM = 165°
Find the HCF of
[tex] 4x {}^{2} y \: and \: 12xy {}^{3} [/tex]
Answers
Answer:
I hope the pic i gave is helpful!!!
Darryl is finding the product of -5y(-4y^3+6y^2-5) Is he correct? If not, what changes should be made?
Answers
A. Yes, Darryl’s work is correct.
Step-by-step explanation:
-5y(-4y^3 + 6y^2 -5)
Darryl used distributive property
Where the outside number (-5y) is being multiplied by all of the numbers in parentheses
-5y • -4y^3 = 20y^4
Two negative numbers multiplied makes a positive number and an extra y on -5y makes y^4
-5y • 6y^2 = -30y^3
Since -5y is being multiplied by a positive number, the product becomes negative. Extra y^3 comes from the y in -5
-5y • -5 = 25y
Two negatives are being multiplied causing the product to be a positive number and keeping the variable the same value.
Finally, add all of the results!
20y^4 + -30y^3 + 25y =
20y^4 - 30y^3 + 25y
Line b has a slope of -2/7. Line c is perpendicular to b. What is the slope of c?
Answers
Perpendicular lines have negative reciprocal slopes.
This is just a fancy way of saying flip the fraction and change the sign.
So the slope of line c is 7/2.
solve the following problems
Answers
Answer:
135°
Step-by-step explanation:
∠AOB = ∠COB = 90°
∠BOK = 45°
90 + 45 = 135°
Sort each function into the correct category.
Linear Functions
Quadratic Functions
Exponential Functions
f(x) = 0.45X-1
f(x) = 5
f(x) = 4.5x +18
Rx) = 19x2
f(x) = x² – 3x+4
f(x) = 2x - 6
Answers
Answer:
Linear functions are
f(x) = 0.45 x - 1
f(x) = 5
f(x) = 4.5 x + 18
Quadratic function is
R(x) = 19x^2
Step-by-step explanation:
The linear function is a function in which the degree of function is 1.
So,
f(x) = 0.45 x - 1
f(x) = 5
f(x) = 4.5 x + 18 are the linear functions.
The quadratic function is a function in which the degree of function is 2.
So,
R(x) = 19 x^2 is a quadratic function.
The exponential function is a function which involves the exponents.
Answer:
pic
Step-by-step explanation:
I would appreciate the help on all of these :)
Answers
Answer:
Pythagoras theorem states that c²=a²+b²
14²=12²+x²
14²-12²=x²
196-144=x²
52=x²
√52=√x²
7.2111025509279785=x
rounded up to the nearest hundredth=7.21
Ashvin want to replace the carpet in your living room and hallway with laminate flooring.
Find the total area of the hallway and living room.
Answers
Answer:
I’m sorry but you need to edit this question, it is incomplete.
Step-by-step explanation:
I see nothing, if there is supposed to be an image attached, please i attach it again, tnx!
I could help you though
which algebraic expressions are polynomials
Answers
Answer:
last option
Step-by-step explanation:
3.9x3 -4.1x2+7.3
What is the slope of the line? What is the y-intercept of the line? y = 1/2x + 7
Answers
Answer:
slope= 1/2
y-intercept= 0,7
Answer:
slope = 1/2 or 0.5, the y-intercept is (0,7)
Step-by-step explanation:
A store charges 7% sales tax. Which expression can be used to find the total cost of an item with a price of p?
0.07p
0.93
1.07
7.000
HELP PLS SMb!
Answers
Answer:
0.07.
Step-by-step explanation:
Below. Lets say 1 is 100 dollars sale tax. If 1 is 100 7 would be 7.00
Write an equation of the line that passes through the point (4, -5) with slope 2.
a) y+5=-2(x-4)
b) y+5=2(x-4)
c) y-4=-2(x+5)
d) y-4=2(x+5)
Answers
Answer:
y + 5 = 2(x - 4)
Step-by-step explanation:
y + 5 = 2(x - 4)
4 is added to two-thirds of d
Answers
Answer:
ayan po answer nasa picture po
Step-by-step explanation:
where
x
is the number you are trying to compute the (2/3) rds of
Two dogs run around a circular track 300 m long. One dog runs at a steady rate of 15m per second, the other at a steady rate of 12 m per second. Suppose they'd tart at the same point and time. What is the least number of seconds that will elapse before they are again together at the starting point?
Answers
Answer:
300 seconds
Step-by-step explanation:
The first dog run at v₁ = 15 m/sec the second one run at v₂ = 12 m/sec
we know that d = v*t then t = d/v
Then the first dog will take 300/ 12 = 25 seconds to make a turn
The second will take 300 / 15 = 20 seconds to make a turn
Then the first dog in 12 turns 12*25 will be at the start point, and so will the second one at the turn 15.
To check first dog 12 * 25 = 300
And the second dog 15 * 20 = 300
That means that time required for the two dogs to be at the start point together is
300 seconds, in that time the first dog finished the 12 turns, and the second had ended the 15.
Another procedure to solve this problem is as follows:
between 12 m/sec and 15 m/sec the minimum common multiple is 300 ( 300 is the smaller number that accept 12 and 15 as factors 12*15 = 300) Then when time arrives at 300 seconds the two dogs will be again in the starting point
Find the highest common factor (HCF) for 36, 84 and 108
Answers
Answer:
Check your question one time
