Answer:
[tex]Max\ z = 1[/tex]
[tex]Min\ z = -9[/tex]
Step-by-step explanation:
Given
[tex]z = 4x + 5y[/tex]
[tex]x \ge -1[/tex]
[tex]y \le 2x +3[/tex]
[tex]y \le -1[/tex]
Required
The maximum and minimum of z
To do this, we make use of the graphical method
See attachment for graphs of
[tex]x \ge -1[/tex]
[tex]y \le 2x +3[/tex]
[tex]y \le -1[/tex]
The corner points of the function are:
[tex](x,y) = (-1,1)[/tex]
[tex](x,y) = (-1,0)[/tex]
[tex](x,y) = (-1,-1)[/tex]
We have:
[tex]z = 4x + 5y[/tex]
Calculate z with the above values
[tex]z = 4(-1) + 5(1) = 1[/tex]
[tex]z = 4(-1) + 5(0) = -4[/tex]
[tex]z = 4(-1) + 5(-1) = -9[/tex]
So, we have:
[tex]Max\ z = 1[/tex]
[tex]Min\ z = -9[/tex]
17’4” multiply by 17’5”
Its awpicture please help if you can
What is the explicit rule for the geometric sequence?
400, 200, 100, 50,...
(I'll put the answers in a screenshot) Plzz help :(
Answer:
an = 400*(1/2)^(n - 1) which is C is the most common answer.
Step-by-step explanation:
What did you have to do to get 400 as the first term?
There are two answers.
an = 400 * (1/2)^(n - 1)
an = 400 * (1/2)^n
Which one is the answer?
The answer is the one that leaves 400 as the first term.
a1 = 400*(1/2)^(n-1) should be the answer.
400*(1/2)^n is unfortunately sometimes used. In which case, the first term is a^0
A1 = 400 (1/2)^(n - 1) is the usual for that describes the series.
The rule of the following sequence is k = 3n − 1. What is the tenth term of the sequence?
2, 5, 8, 11, ...
b. Analyze What pattern do you recognize in this sequence?
Answer:
a. 29
b. 3 is added each time
Step-by-step explanation:
In the given rule, n represents the term number. So, when k=2, n would be 1 because it is the first term. Therefore, to find the 10th term, plug 10 in for n, then solve. The equation would look like [tex]k=3(10)-1[/tex] which equals 29.
The pattern for this type of sequence is known as the common difference because it is the amount that is added each term. You know this because when reading the sequence you can see that it is increasing by 3. Additionally, in the rule, 3 is being multiplied by n, this shows that 3 is the common difference/pattern.
Answer:
29
Step-by-step explanation:
29. If (x, 5) is a solution to the equation 3x + 5y = -5, what is the value of x?
A.-10
B.-4
C. 2
D. 6
Answer:
the answer is -10
Step-by-step explanation:
x=x
y=5
then
3x+5y=-5
3x+5*5=-5
3x=-5-25
3x=-30
x=-30/3
•°•x=-10
Answer:
A
Step-by-step explanation:
3x+5*5=-5
x=-10
Hamid had gained weight he is now 88k which is 10% more then he uses to be what was his original weight
Answer:
80k
Step-by-step explanation:
let the previous weight be x
88=x + 10%of x
88=x+(10/100)of x
8800=110x
8800/110=x
x=80k
Answer: Original weight = 80 kg
Step-by-step explanation:
Given:
Current weight = 88 Kg
Gain weight rate = 10%
Solve:
Original weight = Current weight / Gain rate
Original weight = (88) / (1 + 10%)
Original weight = 80 Kg
Hope this helps!! :)
Please let me know if you have any questions
Will give brainliest to the first person
. Ram solved 2/7 part of an exercise while Shyam solved 1/5 of it. Who solved greater part and by how much?
fast please
Step-by-step explanation:
LCM of 7 and 5 is 35
now will make the denominator equal,
10+7/35
So, Ram's work = 10/35
Shyam's work = 7/35
so
Ram > Shyam
hope it helps
CAN SOMENE PLESAE ANSWER B ITS URGERT MARKING BRAINLIEST
prove it if you know
(please no spam answers)
Answer:
....ans
hope it helps you
hope this help you
have a great day
What am i supposed to type here tho, just look at the photo pls
slope is just "how much up or down" for one step to the right.
its clearly negative here
only -3 seems to be remotely plausible looking at the graph in your screenshot
Answer:
The slope is [tex]-3[/tex]
Step-by-step explanation:
The slope of a line, [tex]m[/tex], that passes through points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is given by:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
To find the slope of a line, choose two points that it clearly passes through.
In the given graph, the line clearly passes through points (2, 2) and (0, 8).
Let:
[tex](x_1, y_1)\implies (2, 2)\\(x_2, y_2)\implies (0, 8)[/tex]
Substitute into the slope formula:
[tex]m=\frac{8-2}{0-2}=\frac{6}{-2}=\boxed{-3}[/tex]
Therefore, the slope of the line is -3.
Find two fractions, when multiplied together make 3/4
Answer:
3/1 times 1/4, 3/2 times 1/2, 9/8 times 2/3
Answer:
1/2 & 3/2
Step-by-step explanation:
1/2 X 3/2 = 3/4
To get this answer, you need to think of two numbers which we can multiply to get 3 and two numbers which we can multiply to get 4.
Answer from Gauthmath
Radius of circle is 6 and I need help finding the angles, SUT is 39 and MOP is 49 degrees
Answer:
a. i) ∠TUV = 39°
ii) The measure of arc VTS (the minor arc) = 102°
b. The diameter OT of the circle = 12
c. The angle which we can calculate, given ∠MOP, is angle ∠OTM = 51°
i) Arc MVT = 98° and arc MO = 82°
Step-by-step explanation:
The given parameters are;
The radius of the circle = 6
∠SUT = 39°, ∠MOP = 49°
a. i) According to two tangent theory, two tangents that meet at a given point are congruent
Therefore, VU is congruent to SU
Given that PU is congruent to PU by reflexive property and PV = PS = The radius of the circle, we have;
ΔPVU is congruent to ΔPSU by Side Side Side (SSS) rule of congruency
∠SUT ≅ ∠TUV by Congruent Parts of Congruent Triangles are Congruent (CPCTC)
Therefore, ∠SUT = ∠TUV = 39° by transitive property of equality
ii) Arc VTS is the minor arc while arc VOS is the major arc by size
The arc measure that describes arc VTS is the minor arc
iii) From circle theorem, we have that the sum of the angle formed by two tangents and the minor arc equals 180°
Therefore, ∠SUT + ∠TUV + arc VTS = 180°
∴ Arc VTS = 180° - (39° + 39°) = 102°
b. The line segment length that can be calculated based on knowing the radius length includes the length of the diameter OT of the circle
The diameter OT = 2 × The length of the radius
∴ The diameter OT = 2 × 6 = 12
c. The angle ∠MOP, is an interior angle of the right triangle ΔTMO formed by the diameter of the circle, OT, therefore, given that ∠MOP = 39°, we have;
∠OTM = 90° - ∠MOP
∴ ∠OTM = 90° - 39° = 51°
∠OTM = 51°
Therefore, given ∠MOP, we can calculate angle ∠OTM
i) The arc that we can calculate, given ∠MOP are arc MVT and arc MO
Arc MVT = 2 × ∠MOP
∴ Arc MVT = 2 × 49° = 98°
Arc MO = 2 × ∠OTM
∴ Arc MO = 2 × (90° - 49°) = 82°
Can someone answer all these questions
If the perimeter is 16' the sum of the length and width must be 8'. Assuming that area is non 0 possible dimensions are:
1x7 2x6 3x5 4x4 5x3 6x2 7x1
Giving brainliest! View the image!
Answer:
a- 15 b- 1292^cm this is the answer
Solve for x. Solve for x.
Answer:
4√3
Step-by-step explanation:
This is a right triangle. When two sides are given in a right triangle, we need to use the Pythagorean Theorem to solve for the third side.
Pythagorean Theorem: a² + b² = c²
The a here is 11, while the b is x. The c is always the hypotenuse (the longest side), which is 13.
Now we substitute:
11² + x² = 13²
121 + x² = 169
-121 -121
x² = 48
√x² = √48
x = √48 <-- We can simplify that.
√48 = 12 * 4 = 3 * 4 * 4 = 4√3
Hello !
Answer:
[tex]\boxed{\sf x=4\sqrt 3}[/tex]
Step-by-step explanation:
It is a right-angled triangle. To find the value of x, we will have to use the Pythagorean theorem which says that the lengths of the sides of a right-angled triangle satisfy the following equality :
[tex]\boxed{\sf c^2=a^2+b^2}[/tex]
Where :
c represents the length of the hypotenuse.a,b represents the lengths of the other two sides.In this triangle, we can consider a = 11, b = x, and c = 13.
Let's substitute the values of a, b, and c into the formula.
[tex]\sf 13^2=11^2+x^2[/tex]
Now we have to solve the equation to find the value of x.
Let's subtract 11² from both sides and calculate.
[tex]\sf 13^2-11^2=11^2-11^2+x^2\\x^2=13^2-11^2\\x^2=169-121\\x^2=48[/tex]
Reminder : if x² = a (a ≥ 0), then x = ±√a.
Let's apply that to our equation.
[tex]\sf x=\pm \sqrt{48}[/tex]
x represents a distance, it must be positive. The unique solution is:
[tex]\sf x=\sqrt{48}\\\boxed{\sf x=4\sqrt 3}[/tex]
Have a nice day ;)
What is the length of segment FH?
Answer:
FH ≈ 15.20
Step-by-step explanation:
Using the Altitude- on- Hypotenuse theorem
(leg of large triangle)² = (part of hypotenuse below it ) × (whole hypotenuse )
FH² = 11 × (11 + 10) = 11 × 21 = 231 ( take the square root of both sides )
FH = [tex]\sqrt{231}[/tex] ≈ 15.20 ( to 2 dec. places )
Factor the polynomial expression 4x3 - 4.
==================================================
Work Shown:
4x^3 - 4
4(x^3 - 1)
4(x - 1)(x^2 + x + 1)
In the last step, I used the difference of cubes factoring formula which is
a^3 - b^3 = (a - b)(a^2 + ab + b^2)
The length, breadth and thickness of a brick is 18 cm, 8 cm, and 5 cm respectively. Find the area of the widest part of the brick. Also find the volume of the brick.
Answer:
area = 8 × 18 = 144 cm^2
volume 8×18×5 = 720cm^3
Which expression is equivalent to d - 8 - 8d?
Answer:
−7d−8
Step-by-step explanation:
Subtract 8d from d.
4 = t/2.5
t=?
i am not sure how to divided this... also what is t?
Answer:
"t" is not a specific thing, this is just the sign of your variable.
t = 4 × 2.5
t = 10
Rewrite the expression in the picture in the form y^n.
Step-by-step explanation:
here's the answer to your question
Answer:
y^(2/3)
Step-by-step explanation:
( y ^ ( 7/3) * y^ ( 1/3) ) ^ 1/4
Combine the terms in side the parentheses
a^b* a^c = a^(b+c)
( y ^ ( 7/3+ 1/3) ) ^ 1/4
( y^( 8/3) )^1/4
We know a^b^c = a^(b*c)
y ^(8/3*1/4)
y^(2/3)
In need of desperate help it’s due in a few hours plssss!!
Answer:
x = -6 and y = -9
y = 0
Step-by-step explanation:
A vertical line is an x = equation. No matter what y equals, x will always be -6, so it's x = -6. A horizontal line is a y = equation. No matter what x equals, y will always be -9, so it's y = -9. Finally the equation of the x axis is simply y = 0 since any point on that horizontal line has a y coordinate of 0.
Answer:
x = -6 and y = -9
thectgod ig
What is an equation of the line that passes through the points ( − 7 , 7 )and( 3 , 7 )
Answer:
Y=7
Step-by-step explanation:
x1 y1 x2 y2
-7 7 3 7
(Y2-Y1) (7)-(7)= 0 ΔY 0
(X2-X1) (3)-(-7)= 10 ΔX 10
slope= 0
B= 7
Y =0X +7
Answer:
y = 7
Step-by-step explanation:
(x₁, y₁) = (-7 , 7) & (x₂, y₂) = (3 , 7)
y-co-ordinate are same for both points. So, the line parallel to x-axis and it's slope =0
A line that is parallel to x-axis and has a y-intercept 'c' has the equation y = c
y = 7
Write an inequality and show on a number line all numbers:
less than 4 but greater than or equal to 0
Answer:
the inequality is 0<x<4
Step-by-step explanation:
(0,4)
In a 4-digit perfect square, the first two digits are the same, and the last two digits are also the same. What is the value of this 4-digit number?
Answer:
7744Step-by-step explanation:
Let the number is in the form of aabb.
We can put it as:
aabb = 11*(100a + b) = 11*(99a + a + b)The number is a perfect square so it must be divisible by 11.
It is divisible by 11 if (a + b) is divisible by 11..
On the other hand, b = 0, 1, 4, 5, 6, 9 as the last digit of a perfect square.
Also, both a and b must be within (0,9) interval.
Considering the above conditions we have options:
a,b = 2,9 or 5,6 or 6,5 or 7,4The numbers are:
2299556666557744By testing we confirm only one of them is a perfect square:
7744What is the area of the circle?
Answer:
363
Step-by-step explanation:
Formula for area of a circle
A = πr^2
Where r = radius
The circle has a given radius of 11
To find the area of the circle we simply substitute r in the formula with the value of the radius (11)
( Also note that the question says to use 3 for π )
A = πr^2
π = 3
r = 11
Substitute values in formula
A = (3)(11)^2
11^2 = 121
A = 121(3)
121(3) = 363
A = 363
In the following diagram, ABCD is a parallelogram. Is AC the bisector of angle BAD? Show calculations and explain
Answer:
yes
Step-by-step explanation:
in parallelogram ,<A=<C
<C=<D
then <D=115=<C=115
X+115+30=180....TRIANGLE THEROME
X=35
so that,<A=65
<C=65
If the length of the shorter arc AB is 22cm and C is the center of the circle then the circumference of the circle
is:
Answer:
22= 2(pi)(r)(45/360)
28.01
C=176
Step-by-step explanation:
without using tables or calculator, evaluate
[tex] \frac{ \sin(20 \degree) }{ \cos(70\degree) } + \frac{ \cos(35\degree) }{ \sin( 65\degree)} [/tex]
Answer->[tex] \frac{ \sin(20 \degree) }{ \cos(70\degree) } + \frac{ \cos(35\degree) }{ \sin( 65\degree)} [/tex]
we know:-[tex] \sin( \theta) = \cos(90 - \theta) \\ \\ \cos( \theta) = \sin(90 - \theta) [/tex]
So putting down the value
[tex] \frac{ \cos(90 - 20 \degree) }{ \cos(70\degree) } + \frac{ \sin(90 - 35\degree) }{ \sin( 65\degree)} [/tex]
[tex] \frac{ \cos(70\degree) }{ \cos(70\degree) } + \frac{ \sin(65\degree) }{ \sin( 65\degree)} [/tex]
[tex]\frac{\cancel{\cos(70\degree)}}{ \cancel{\cos(70\degree)}} + \frac{\cancel{\sin(65\degree)}}{\cancel{\sin( 65\degree)}} [/tex]
[tex] \frac{1}{1} + \frac{1}{1} \\ 1 + 1 = 2 \: \: ans[/tex]