Answer:
(0,-22)
Step-by-step explanation:
Plug in 0 for x and solve for y
1
Apply the Linear Programming Theorem and interpret the results.
2) Answer the questions below for the following situation:
For a certain lawn, a landscaping contractor plans to use the least expensive combination of two brands of
fertilizer. A package of Brand X costs $16 and contains 12 oz of phosphates and 10 oz of nitrates. A package of
Brand Y costs $7 and contains 10 oz of phosphates and 5 oz of nitrates. The lawn requires at least 60 oz of
phosphates and 40 oz of nitrates. Which combination of the two brands should be used?
a. Translate the constraints into a system of inequalities.
b. Graph the system and label the vertices of the feasible set.
c. Apply the Linear Programming Theorem and interpret the results.
X
The minimum cost will be at (2.5 , 3) and the minimum cost be $25.
Given, a landscaping contractor plans to use the least expensive combination of two brands of fertilizer.
A package of Brand X costs $16 and contains 12 oz of phosphates and 10 oz of nitrates.
A package of Brand Y costs $7 and contains 10 oz of phosphates and 5 oz of nitrates.
The lawn requires at least 60 oz of phosphates and 40 oz of nitrates.
Let the number of Brand X packages be, x
the number of Brand Y packages be, y
According to the question,
12x + 10y ≥ 60 = 6x + 5y ≥ 30
10x + 5y ≥ 40 = 2x + y ≥ 8
x ≥ 0
y ≥ 0
Z = 16x + 7y
On solving the equations, we get
6x + 5y = 30
6x + 3y = 24
On subtracting, we get
2y = 6
y = 3
and x = 2.5
So, minimum cost will be at (2.5 , 3) and the minimum cost be
Z = 16(2.5) + 7(3)
Z = 4 + 21
Z = 25
Hence, the minimum cost will be at (2.5 , 3) and the minimum cost be $25.
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At the beginning of spring, Sophia planted a small sunflower in her backyard. When
it was first planted, the sunflower was 25 inches tall. The sunflower then began to
grow at a rate of 3 inches per week. How tall would the sunflower be after 9 weeks?
How tall would the sunflower be after w weeks?
Height after 9 weeks:
Height after w weeks:
The height of the sunflower after 9 weeks is 52 inches and the function that represent the height of the sunflower after w weeks = 25 + 3w weeks.
Sophia planted a tiny sunflower in her backyard at the start of spring.
When she planted the sunflower,
The height of the sunflower = Initial height of the sunflower = 25 inches.
Now, The sunflower then began to grow at a rate of 3 inches per week.
Thus, the growth rate of the sunflower = 3 inches/week
The growth in 9 weeks = 3*9 = 27 inches,
The height of the sunflower after 9 weeks = initial height + growth = 25 +27 = 52 inches.
The growth in w week = 3w inches,
The height of the sunflower after w weeks = initial height + growth = 25 + 3w inches.
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Q8.
The area of this rectangle is 28 cm²
(x+2)cm
(x+2)cm
(6x-1)cm
(6x-1)cm
Work out the perimeter of the rectangle.
using a similar argument to solve teh hw problem 1, show that if a is an integer, then 7 divides a^7 -a
The expression a⁷- a is divisible by 7 if a is an integer.
Given that,
7 divides a^7−a
To find that if a is an integer, then 7 divides a^7 -a or a⁷- a is divisible by the number 7
We can write, where k is an integer
a^7−a=7k
a(a^6−1)=7k
Now if a=k then
a^6−1=7
a^6=8
and a=±1.414 so a^7−a=9.898
If a is not equal to k then
a(a^6−1)=a(a^3+1)(a^3−1)=7k
since a(a+1)(a−1) is the not product of 3 consecutive integers, the expression is divisible by 7.
Hence, The expression a⁷- a is divisible by 7 if a is an integer.
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what does the solution of equality look like?
Answer:no image I can’t see on mobile
Step-by-step explanation:
h
Does each pair of expressions form an equation when joined with an equals sign?
Solving each pair of expression shows that
(1/5)^2 + 1 ≠ 2 * 12 / 25
( 1 + 1/4 )^2 = 2 - 7/16
Analysis of the expressionPutting equals sign implies that the the expression in left hand side of the equation is equal to the expression on the right hand side
If they are not equal the sigh to be used is not not equal to
(1/5)^2 + 1 & 2 * 12 / 25
1/25 + 1 & 24/25
26/25 ≠ 24/25
( 1 + 1/4 )^2 & 2 - 7/16
(5/4)^2 & 25/16
25/16 = 25/16
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SOLVE CORRECTLY FOR 83 POINTS AND BRAINLIEST
The transformation rule used to transform Triangle PQR to P'Q'R' is; (x, y) → (⁵/₂x, ⁵/₂y)
How to Interpret Mathematical Transformations?We are told that the triangle P'Q'R' has been transformed from triangle PQR.
Now, the coordinates of triangle PQR are;
P(-1, 1)
Q(2, 0)
R(-1, -2)
The coordinates of the transformed triangle P'Q'R' are;
P(-5/2, 5/2)
Q(5, 0)
R(-5/2, -5)
Thus, this is clear that the transformation rule used is;
(x, y) → (⁵/₂x, ⁵/₂y)
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Tariq is going to invest in an account paying an interest rate of 5.8% compounded quarterly. How much would Tariq need to invest, to the nearest hundred dollars, for the value of the account to reach $600 in 20 years?
The amount to be invested today in order to have $600 in 20 years is $189.66.
How much should be invested today?When an account pays interest that is compounded quarterly, it means that both the amount invested and the interest that has already been earned increases in value four times in a year.
In order to determine the amount to be invested today, determine the present value of $600.
The formula for calculating present value:
P = FV / [(1 + r)^nm]
Where:
FV = Future value P = Present value R = interest rate = 5.8 / 4 = 1.45% m = number of compoundingN = number of yearsP = 600 / [(1.0145)^80] = $189.66
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Answer: it is 200
Step-by-step explanation:
Hi! I can’t seem to figure out this proof can anyone help me? I tried labeling the sides and angles.
Answer:
3. line XZ is congruent to line XZ | reflexive property
4. triangle WXZ is congruent to triangle YZX | HL (i think)
5. angle WXZ is congruent to angle YXZ | CPCTC
Step-by-step explanation:
WILL GIVE BRAINLIEST
A farmer has 300 yards of fencing. He is trying to figure out how to build his fence so that he has a rectangle with the greatest square footage inside. What are the side lengths of the fence he can build with the greatest area inside?
60 yards and 60 yards
60 yards and 75 yards
75 yards and 75 yards
75 yards and 80 yards
The side lengths of the fence he can build with the greatest area inside are of:
75 yards and 75 yards.
What are the area and the perimeter of a rectangle?Considering a rectangle of length l and width w, we have that the area and the perimeter of the rectangle are given as follows:
The area is given by the multiplication of the dimesions, that is, A = lw.The perimeter is given by twice the sum of the dimensions, that is, P = 2(l + w).A farmer has 300 yards of fencing, hence the perimeter is:
P = 300.
Then:
2(l + w) = 300
l + w = 150
l = 150 - w.
Then the equation giving the area of the fence is:
A = lw
A = w(150 - w)
A = -w² + 150w.
Which is a quadratic equation with coefficients given by:
a = -1, b = 150.
The width that will give the highest possible area is the x-coordinate of the vertex, hence:
w = -150/(2(-1)) = 75 yards.
The length is of:
l = 150 - w = 150 - 75 = 75 yards.
Which means that the third option is correct.
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Your mother made some pumpkin cookies and put half of them on a
plate for your brother and you. Your dog Gobbles ate six! Your
brother ate half of what was left, and you ate the last four.
How many cookies did your mother bake altogether?
The total cookies she baked altogether is 28 cookies
What are word problems?A word problem is a math problem written out as a short story or scenario. Basically, it describes a realistic problem and asks you to imagine how you would solve it using math.
Half of the cookies is placed on the table, 6 is eaten by my dog, half is eaten by my brother and I ate the last 4, the means my brother ate 4 cookies too.
Therefore the total cookies put on the plate is 6+4+4= 14cookies
half of all the cookies were put in the plate,
therefore the total cookies made is 14×2= 28cookies.
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The perimeter of an isoceles triangle is 392cm and its unequal sides are 195 cm.Find the area
9,603.75 cm² is the area of the given triangle.
What are triangles?A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. △ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane. Equilateral, isosceles, scalene and right-angled triangles are the four different forms of triangles.So, the perimeter of the triangle is 392 cm.
The unequal side is 195.Then, let the rest 2 sides be x, where x = x.
x + x + 195 = 3922x + 195 = 3922x = 392 - 1952x = 197x = 197/2x = 98.5Now, we know that the rest 2 equal sides are of length 98.5 cm.
Area of triangle: 1/2 × base × heightNow, calculate the area as follows:
1/2 × base × height1/2 × 98.5 × 1951/2 × 19,207.59,603.75Therefore, 9,603.75 cm² is the area of the given triangle.
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Write the equation in standard form using integers
(no fractions or decimals): y= -2/3 x-1
The standard form of the equation y = -2/3 x - 1 is 2x + 3y = -3.
How to write linear equation in standard form?The standard form for linear equations in two variables is Ax + By = C. Where,
A, B and C are constant.x and y are the variables.The equation is represented in slope intercept form. So, let' represent it in standard form.
Therefore,
y = - 2 / 3 x - 1
add 2 / 3 x to both sides of the equation
y = - 2 / 3 x - 1
y + 2 / 3 x = - 2 / 3 x + 2 / 3 x - 1
y + 2 / 3 x = - 1
Let's multiply all through by 3 to eliminate the fraction
y + 2 / 3 x = - 1
3y + 3(2 / 3 x) = -3
Therefore, the standard form equation is 2x + 3y = -3
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what is the image point of (0, 2) after a translation left 5 units up to 1 units
The image of the given point after the translation will be (-5,1).
The given point is (0,2).
We have to find out the image of the given point after a translation left 5 units and up to 1 units.
Since it is given that there is a translation left 5 units, starting from point (0,2), the image will be on the negative side of x-axis at point 3.
Similarly, it is given that there is also a translation up to 1 units. This implies starting from point (0,2), the image will be on the positive side of y-axis at point 1.
So, the image of the given point after the translation will be (-3,1).
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Statements 1 and 2 are true conditional statements.
Statement 1: If a figure is a parallelogram, then it is a quadrilateral.
Statement 2: If a figure is a quadrilateral, then its angles sum to 360°.
Which conclusion is valid?
Multiple choice question.
A)
If Figure A is a quadrilateral, then Figure A is a parallelogram.
B)
If Figure A is not a parallelogram, then Figure A’s angles do not sum to 360°.
C)
If Figure A’s angles do sum to 360°, then Figure A is a parallelogram.
D)
If Figure A is a parallelogram, then Figure A’s angles sum to 360°.
The valid conclusion about statement A and statement B is "If Figure A is a parallelogram, then Figure A’s angles sum to 360°".
The correct answer option is option D.
What is conditional statement?A conditional statement can be defined a statement that is written in the form “If A then B,” where A and B are sentences.
For this conditional statement:
Sentence A is called the hypothesis
Sentence B is called the conclusion.
Hypothesis: This is an assumption taken to be true for the purpose of argument or investigation.
Conclusion: This is the proposition that follows as a necessary consequence of the premises in an argument or syllogism.
Hence, “If A then B” means that B must be true whenever A is true.
Therefore, if a figure is a parallelogram, then it is a quadrilateral; If a figure is a quadrilateral, then its angles sum to 360°.
It can be concluded that if a figure is a parallelogram, then it's angles must sum to 360°.
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Select the correct answer.
What is the inverse of function f?
f(x)=10 9x+11
A.f−1(x)=9x+11 /10
B. f−1(x)=9 10x+11
C. f−1(x)=9x−99 /10
D. f−1(x)=10x−110/ 9
Edmuntem btw
PLEASEEE ANSWERRRRR ASAP!!!!
The inverse function of the given function will be f(x)⁻¹ = ( 10 ) / ( 9x - 99).
From the question, we have
f(x) = ( 10/9x) + 11
x = ( 10 / 9y ) + 11
x - 11 = ( 10 / 9y )
9y / 10 = ( 1 / ( x - 11 )
9y = 10 / ( x - 11 )
y = ( 10 ) / ( 9x - 99 )
Inverse function :
The expression that established the relationship between the dependent variable and the independent variable is referred to as a function. An inverse function is a function that is applied to the value of y after switching the values of two variables, x and y.
Complete question:
What is the inverse of function f?
f(x) = 10/9x+11
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Write the following as an inequality.
8 is greater than x, and x is greater than 2.
use x only once in your inequality
Using x only once in the inequality, the inequality expression is 8 > x > 2
How to determine the inequality expression?The mathematical statement is given as
8 is greater than x, and x is greater than 2.
In mathematical expressions, greater than can be represented as >
So, we have the following representations
8 > x, and x > 2
Next, we combine the inequality expressions
This becomes
8 > x > 2
Hence, the inequality expression is 8 > x > 2
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the angle measures of a quadrilateral are in a ratio of 4 : 5 : 6 : 9. find the measure of the smallest angle.
The measure of the smallest angle of the quadrilateral is 60° .
In the question ,
it is given that ,
the angle measure of the quadrilateral are in the ratio 4 : 5 : 6 : 9 .
So , the measure of the largest angle is = 9x
and the measure of the smallest angle is = 4x .
we know that the sum of the measure of all the angles of the quadrilateral is 360° .
that means ,
4x + 5x + 6x + 9x = 360°
24x = 360
dividing both sides by 24 ,
x = 360/24
x = 15 .
the smallest angle is = 4(15) = 60°
Therefore , The measure of the smallest angle of the quadrilateral is 60° .
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2. If m angle EFD = 75°, then m angle JAB = ??
C
B
A
1.
2.
Answer:
If m angle EFD = 75°, then m angle JAB = ??
C
B
A
1.
2.
What is the slope NEED HELP PLEASEEEEEEEE
The slope of the graph above is [tex]-\frac{4}{3}[/tex]
How to find the slope of a line?The slope of a line is the change in the dependent variable with respect to the change in the independent variable. The slope of a line is rise over run.
Therefore,
slope = m = y₂ - y₁ / x₂ - x₁
Hence, using the coordinates on the graph let's find the slope of the graph.
(-2, 1)(1, -3)
Therefore,
x₁ = - 2
x₂ = 1
y₁ = 1
y₂ = - 3
Hence,
[tex]slope = \frac{-3-1}{1-(-2)}[/tex]
[tex]slope = \frac{-4}{1+2}[/tex]
[tex]slope = \frac{-4}{3}[/tex]
Therefore, the slope of the line is [tex]-\frac{4}{3}[/tex]
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describe and correct the error in graphing the function y = x - 1 with the domain 1 , 2 , 3 ,4 ,and 5
The graph of the function is y - 1 = x, not y = x - 1.
What is a graph?The set of ordered pairings (x, y) where f(x) = y makes up the graph of a function.
These pairs are Cartesian coordinates of points in two-dimensional space and so constitute a subset of this plane in the general case when f(x) are real values.
Given, y = (x - 1).
When x = 1, y = 0 ⇒ (1, 0).
When x = 2, y = 1 ⇒ (2, 1).
When x = 3, y = 2 ⇒ (3, 2).
When x = 4, y = 3 ⇒ (4, 3).
When x = 5, y = 4 ⇒ (5, 4)
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I need help please!!!!!!
Answer: -1
Step-by-step e
What is the greatest number of rectangles 6 cm x 4cm that can be cut from a piece of metal that measures 16 cm x 20 cm?
The greatest number of rectangles 6cm×4cm that can be cut from a metal that measure 16cm×20cm is 13 rectangles.
What is a rectangle?A rectangle is a plane shape that has pair of opposite sides equala and parallel.
To calculate the greatest number of rectangles, we use the formula below.
Formula:
n = LW/lw.................... Equation 1Where:
n = Number of rectangleL = Lenght of the metalW = Width of the metall = Length of the small rectanglew = Width of the small rectangleFerom the question,
Given:
L = 20 cmW = 16 cml = 6 cmw = 4 cmSubstitute these values into equation 1
n = (20×16)/(6×4)n = 13.33n ≈ 13 rectangles.Hence, the greatest number of rectangles is 13 rectangles.
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An arithmetic sequence has this recursive formula: What is the
explicit formula?
Answer:
the correct answer is -32+43
Step-by-step explanation:
I just know
Subtract. Put you answer in lower terms.
47/50 - 3/10
A. 44/40
B. 32/50
C. 13/60
D. 16/25
The required simplified solution of the given subtraction is 16/25. Option D is correct.
Given that,
To Subtract. and determine the lower terms,
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Given expression,
= 47/50 - 3/10
= [47 - 3×5] / 50
= [47 - 15] /50
= 32 / 50
= 16 / 25
The required simplified solution of the given subtraction is 16/25. Option D is correct.
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Answer:
d) 16/25
Step-by-step explanation:
The problem is,
→ (47/50) - (3/10)
Let's solve the problem,
→ (47/50) - (3/10)
→ (47/50) - (15/50)
→ (47 - 15)/50
→ 32/50
→ (32 ÷ 2)/(50 ÷ 2)
→ 16/25
Hence, answer is 16/25.
What number (let's call it x ) must be added to the numerator and denominator of the fraction 6/29 so that the new fraction is equal to 2/3 ?
Answer:
add 54 to the numerator and 61 to the denominator because after you add it the fraction, it should be 60/90: simplified to 2/3 if you divide the numerator and denominator by 30.
The number that must be added to the numerator and denominator is 40.
What is a fraction?A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.
Example: 1/2, 1/3 is a fraction.
We have,
Fraction = 6/29
The new fraction = 2/3
Now,
(6 + x)/(29 + x) = 2/3
3(6 + x) = 2(29 + x)
18 + 3x = 58 + 2x
3x - 2x = 58 - 18
x = 40
Thus,
The number x is 40.
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Can someone please help me I need the ones that are ticked
Answer:
*Note: Perimeter is equal to the sum of all side lengths
1. 3cm + 3cm + 5cm + 4cm = 6cm + 9cm = 15cm
2. 3.5cm + 3cm + 3.5cm + 3.5cm + 3cm + 3.5cm
= 6cm + 7cm + 7cm = 6cm + 14cm = 20cm
3. 2cm + 3cm + 3cm + 3cm + 5cm + 6cm = 5cm + 6cm + 11cm
= 11cm + 11cm = 22cm
7. 9cm + 9cm + 9cm = 27cm
8. Perimeter of a rectangle = 2 times the length plus 2 times the width
P = 2(60m) + 2(48m) = 120m + 96m = 216m
9. 1 roll of 16m of wire = $3,214
216m/16m = 13.5 rolls of wire
13.5 rolls($3,214) = $43,389
Name the postulate or theorem that proves the pair of triangles is congruent. List the vertices of the congruent tri-
A
B
с
D
E
F
Y
AABC Ayxz by the AAS Postulate/Theorem.
X
i
Z
G
H
Answer:1712
Step-by-step explanation: is 1712
3-6n-4<17
What is the Answer for this??
Answer:
-6n-4+3<17
-6n-1<17
-6n<17+1
-6n<18
DIVIDE BOTH SIDE WITH THE COEFFICIENT OF n WHICH IS (-6)
-6n =18
-6 -6
n= -3
Can you help me PLEASE,
The answers are:
Q1 = x < -1
Q2 = x ≤ 2
Q3 = x > -2
Q4 = x > 0
Code = 4776
What is inequality?It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal = ≤
Greater than and equal = ≥
We have,
Solve for x.
3 < -5x + 2x
3 < -3x
Divide both sides by 3.
1 < -x
Change sign.
x < -1
18 ≥ 5x + 4x
18 ≥ 9x
Divide both sides by 9.
2 ≥ x
-6x - 16 < 2x
Add 16 on both sides.
-6x < 2x + 16
Subtract 2x on both sides.
-6x - 2x < 16
-8x < 16
Divide both sides by 8.
-x < 2
Change sign.
x > -2
(1/2)x - 4 > -4
1/2x > -4 + 4
1/2x > 0
x > 0
Code = 4776
Thus,
The answers are:
Q1 = x < -1
Q2 = x ≤ 2
Q3 = x > -2
Q4 = x > 0
Code = 4776
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