x + y ≤ -4 and 3x + 2y ≤ -5
======================================================
Explanation:
The given point has coordinates of x = 3 and y = -7.
Let's plug those coordinates into the first inequality of choice A.
x+y < -4
3 + (-7) < -4
-4 < -4
The last statement is false. A number cannot be smaller than itself.
Since the last inequality is false, it causes the first to be false for those x,y values. Therefore, we rule out choice A.
--------------
We'll do the same idea for the first inequality in choice B
x + y ≤ -4
3 + (-7) ≤ -4
-4 ≤ -4
This time we get a true statement at the end. The key difference is the "or equal to" portion.
Let's check the other inequality of choice B
3x + 2y < -5
3(3) + 2(-7) < -5
9 - 14 < -5
-5 < -5
We run into a similar issue as we did with choice A. We have no choice but to cross choice B off the list as well.
--------------
Choice C is eliminated for the same reason choice A was.
Choice D is the final answer because both inequalities involve "or equal to". So the -5 < -5 is now -5 ≤ -5 which is true.
It turns out that (3, -7) is on the boundary of each shaded region. It's at the intersection of the two boundary lines x+y = -4 and 3x+2y = -5.
D. x + y ≤ -4
3x + 2y ≤ -5
To see if (3, -7) satisfies both inequalities.
x + y ≤ -4:
Substitute x = 3 and y = -7 into the first inequality:
3 + (-7) ≤ -4
-4 ≤ -4
Since -4 is less than or equal to -4, the first inequality is true for the point (3, -7).
3x + 2y ≤ -5:
Substitute x = 3 and y = -7 into the second inequality:
3(3) + 2(-7) ≤ -5
9 - 14 ≤ -5
-5 ≤ -5
Since -5 is equal to -5, the second inequality is also true for the point (3, -7).
(✿◕‿◕✿)
The time it takes to wash all the windows on a large building w(z) varies inversely with the number of workers assigned to the job x.
It takes 6 hours to complete the job when 4 workers are assigned to it.
Which equation can be used to find the time to complete the job when x workers are assigned to it?
a.)w(x) = 24/x
b.)w(x)= 1.5x
c.)w(x)=10/x
d.)w(x)=24
The equation that can be used to find the time to complete the job can be expressed as w (x) = 1.5x, so option B is correct.
What is the equation?A formula known as an equation uses the equals sign to denote the equality of two expressions.
Given:
The time taken to complete the work = 6 hrs,
The no of worker = 4,
The no of workers = The time taken by four workers / no of workers,
w (x) = 6 /4x
w (x) = 1.5x
Therefore, the equation that can be used to find the time to complete the job can be expressed as w (x) = 1.5x.
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X
The following question has two parts. First, answer part A.
Then, answer part B.
Part A
Hailey is making floral centerpieces for a wedding. Each
centerpiece has 17 flowers. She has 430 flowers for the project.
She estimates that she can make between 20 and 30 complete
centerpieces. Is her estimate reasonable?
Use your knowledge of place value and division to explain the
reasonableness of her answer.
18
▾ Math symbols
centerpieces
+
010
II
=
LA
I
08 (-)
v
X
O
>
?
+
[-]
H
Part B
How many complete centerpieces can she make? Find the
exact answer.
Use a model in 2006, the average ticket price for a national football league game was $62. 38. Since then the cost has increased an average of $2. 54 per year. Write a linear equation to represent the cost c of an nfl ticket y years after 2006.
The linear equation to represent the cost of C of an NFL ticket y years after 2006 is y=2.54x+62.38.
Given that the average ticket price for a national football league game was $62. 38 and the cost has increased an average of $2. 54 per year.
we want to write a linear equation to represent the cost c of an nfl ticket y years after 2006.
A linear equation is an equation in which the greatest power of a variable is always 1. Also called the 1 degree equation. The equation can be written in the form y=mx+b.
Let us assume x represent the duration or stipulated years after the year 2006, y represent the amount of ticket that is sold and m represent the average increase in the price every year.
y=mx+c
y=2.54x+62.38
Hence, a linear equation to represent the cost c of an nfl ticket y years after 2006 is y=2.54x+62.38 when the average ticket price for a national football league game was $62. 38 and the cost has increased an average of $2. 54 per year.
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what's 3× (-4) × (-5)
Answer: 60
Step-by-step explanation:
first multiply like terms,
-4 x -5 = 20 [Multiplying two negative signs equal to positive]
3 x 20= 60
what kinds of images are based on mathematical instructions that define lines, curves, text, ovals, and other geometric shapes?
The mathematical instructions that define lines, curves, text, ovals, and other geometric shapes is vector graphics
The vector graphics is defined as the computer graphics that the visual images are created directly from geometric shapes. It is defined on the Cartesian plane such as lines, curves, texts, ovals and other geometric shapes
The vector artworks are the artwork that created by vector graphics. There will be lines curves, text, oval and other geometric shapes according to the mathematical expression
Therefore, the vector graphics is the mathematical instruction that defines the geometric shapes
Hence, the mathematical instructions that define lines, curves, text, ovals, and other geometric shapes is vector graphics
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please help me answer this worksheet (Geometry Worksheet 3.3)
As per the reference document attached thereby along with the question statement, if (∠SOX = 160°), [∠1 = (x + 14)], and [∠2 = (3x – 10)], then the measure of ∠2 in degrees will be 113°
As per the reference document attached thereby along with the question statement, (∠SOX = 160°), and it's constituent angles
[∠1 = ∠SOW = (x + 14)], and [∠2 = ∠WOX = (3x – 10)],
And we are required to determine the measure of ∠2.
Since, [(∠SOW + ∠WOX) = ∠SOX],
Therefore, [{(x + 14) + (3x – 10)} = 160°]
Or, [{(x + 3x) + (14 - 10)} = 160°]
Or, [(4x - 4) = 160°]
Or, [4x = (160 + 4)°]
Or, (4x = 164°)
Or, [x = (164/4)°]
Or, (x = 41°)
Or, [(3x – 10) = {(3 * 41) - 10}°]
Or, [∠2 = (123 - 10)°]
Or, (∠2 = 113°)
That is, if (∠SOX = 160°), and it's constituent angles (∠1) and (∠2) measure as [∠1 = ∠SOW = (x + 14)], and [∠2 = ∠WOX = (3x – 10)], then the measure of ∠2 in degrees will be 113°
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suppose the family wise error rate is 0.05, if there are ten levels of one factor but only 5 comparisons are of importance, what would the individual error rate need to be for each of those 5 comparisons?
The individual error rate needs to be for each of those 5 comparisons is Option B which is 0.01.
Individual error rate = α/m = 0.05/5 = 0.01
The individual error rate is the most extreme likelihood that at least one correlation will inaccurately infer that the noticed contrast is essentially unique in relation to the invalid speculation.
Individual error rates are careful in all cases. Family error rates are careful with equivalent gathering sizes. Assuming that gathering sizes are inconsistent, the true family error rate for Tukey, Fisher, and MCB will be somewhat more modest than expressed, bringing about moderate certainty spans. The Dunnett family error rates are careful with inconsistent example sizes.
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Bao is the oldest of four siblings whose ages are consecutive even integers. If the sum of their ages is 60, find Bao's age.
Answer:
:)......................
Bao's age is 12 years old.
What are Integers?Integers are defined as the collection of Whole Numbers and the negative values of Natural Numbers make up an integer. Fractional numbers are not included in integers. Integers are represented by the symbol Z.
Let's call Bao's age "x".
Since their ages are consecutive even integers, the next sibling's age would be x + 2, the next one x + 4, and the last one x + 6.
The sum of all their ages is x + (x + 2) + (x + 4) + (x + 6) = 4x + 12 = 60.
Solving for x, we get 4x + 12 = 60, and subtracting 12 from both sides gives 4x = 48.
Dividing both sides by 4 gives x = 12.
Therefore, Bao's age is 12 years old.
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Subtract -9x² - x + 9 from 8x² - 6x - 8.
Answer:
17x^2-5x-17
Step-by-step explanation:
(8x^2-6x-8)-(-9x^2-x+9)
8x^2-6x-8+9x^2+x-9
17x^2-5x-17
Evaluate the expression when c=12 and d=112. 3(14 c2) 2d enter your answer as a mixed number in simplest form in the box.
The value of the expression is 698.
What is an expression?
A mathematical expression is a phrase containing a minimum of two numbers or variables and a minimum of one mathematical operation. It is possible to multiply, divide, add, or subtract in math. An expression has the following structure: (Mathematical Operator, Number/Variable, Expression)
The order of operations is a rule that specifies the right procedure to follow when evaluating a mathematical equation. Using the acronym PEMDAS, we can memorize this order: parentheses, exponents, multiplication, and division (left to right), addition and subtraction (from left to right).
Given expression 3*(14+c²) +2d
3*(14+12²)+2*112
= 42+3*12²+224
= 42+3*144+224
= 42+432+224
= 698
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a subset bb of the set of integers from 11 to 100100, inclusive, has the property that no two elements of bb sum to 137137. what is the maximum possible number of elements in bb?
The maximum possible number of elements in B = 68.
A subset B of the set of integers from 1 to 100, inclusive, has the property that no two elements of B sum to 137.
Maximum possible number of elements in B =?
Set of integers = {1, 2, 3, 4, 5......100}
If we divide 137/2 = 68.5
If we add 68+69 = 137
So, we cannot consider number 69 in the subset, it gives us the total numbers we can consider are till 68.
Set B = {1,2,3,4,5,6,7....60,61,68}.
The maximum possible number of elements in B = 68.
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Please anyone I need and explanation and just h and c solving them and explaining how that it please.
Answer: h = 19, c = 132
Step-by-step explanation:
Oooh! This is a toughie!
Okay, first of all, there's a straight line on top. A straight line is 180 degrees.
This means we have to subtract 48 from 180.
180 - 48 = 132.
This means both a and b are 132.
F is equal to 151.
180 - 151 = e
e = 29
d = 29
g = 29
132 + 29 = 161
180 - 161 = 19
h = 19
19 + 29 = 48
180 - 48 = 132
c = 132
Sorry that this answer isn't so clear...
(BTW, it'd make me happy if you gave me the brainliest reward)
help asaap
7.2.1 Prove that AABC and ALMN are congruent.
7.2.2 Given that AFGH|||ALMN.
Calculate the value of x.
The triangles ΔABC and ΔLMN are congruent triangles by the SAS postulate. And the value of the variable 'x' will be 6 cm.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180 °.
The ratio of the matching sides will remain constant if two triangles are comparable to one another.
In triangles ΔABC and ΔLMN, we have
AB = LM = 8 cm
∠B = ∠M = 90°
AC = LN = 12 cm
The triangles ΔABC and ΔLMN are congruent triangles by the SAS postulate.
The triangles ΔFGH and ΔLMN are similar triangles, then we have
x / 12 = 4 / 8
x / 12 = 1 / 2
x = 12 / 2
x = 6 cm
The triangles ΔABC and ΔLMN are congruent triangles by the SAS postulate. And the value of the variable 'x' will be 6 cm.
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3. Because it is so popular, a store owner increases the cost of a toy by $4.99. The new cost of the toy is $14.84. (a) Write an equation that represents the situation. Use c to represent the original cost of the toy. (b) Solve the equation using a related equation. Show your work. (c) What does the solution of the equation represent? HELP ASAPPP
The equation that represents the situation is c + 4.99 = 14.84, and the store owner increased the original price of the toy by adding $5.
What is the percent increase?
The formula for percentage increase is the ratio of the increased value to the original value multiplied by 100. It is expressed as a percentage. If the price of something rises, the percentage rises as well.
a) c + 4.99 = 14.84.
c = 14.84.- 4.99
c = 9.84
(b) 14.84 - 9.84 = 5
(c) Store owner increased the original price of the toy by adding $5.
hence, the equation that represents the situation is c + 4.99 = 14.84, and the store owner increased the original price of the toy by adding $5.
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-69/-11 as a quotient
Answer: 69/11
Step-by-step explanation:
-69/-11=
-69*(-1)/(-11*(-1))=
69/11
Distance (km) 10 9 8 3 2 1 0 20 40 60 Time (min) 80 100 120 Sara and Sam went for a two-hour drive. According to the graph, between 40 minutes and 80 minutes into their trip, they-- M KO a €
The correct option regarding Sara's and Sam's position between 40 minutes and 80 minutes is given as follows:
C. Were not moving since there was not a change in position.
What is stated by the graph?The graph is given by the image shown at the end of the answer, and the relation graphed is defined as follows:
Distance x Time.
Hence the input and the output variables are given as follows:
Input variable: Time.Output variable: Distance.Between 40 minutes and 80 minutes, which is a symmetric period around the time of one hour, the graph is constant.
The constant graph means that the position was not changed, that is, they were not moving, hence the correct statement is given by option C.
Missing InformationThe problem is given by the image shown at the end of the answer.
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Help please! Find the slope of the line that goes through these two points.
(–6, −3), (–19, 16)
The slope of the line that goes through these two points is -19/13.
Given points:
(–6, −3), (–19, 16)
slope:
Slope is the steepness of a line as it moves from LEFT to RIGHT. Slope is the ratio of the rise, the vertical change, to the run, the horizontal change of a line. The slope of a line is always constant (it never changes) no matter what 2 points on the line you choose.
slope m = y2-y1 / x2-x1
= 16-(-3) / -19-(-6)
= 16+3/-19+6
= 19/-13
= -19/13
Therefore The slope of the line that goes through these two points is -19/13.
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(x+5) is a factor of R(x)=x^4+5x^3-16x^2-80x. What are the zeros of the function R(x)?
A) 2, 3, -4, -5 B) 0, 3, -3, -5
C) 0, 3, 4, -5 D) 0, 4, -4, -5 E) 0, 16, -16, -5
The zeros of the function R(x) will be 0 , 4 , -4 , -5.
The equation given to us is
[tex]x^{4}[/tex] + 5[tex]x^{3}[/tex] - 16[tex]x^{2}[/tex] - 80x = 0
Take x common
x( [tex]x^{3}[/tex] + 5[tex]x^{2}[/tex] - 16x - 80 ) = 0
from here we get one factor of x as 0.
Now
[tex]x^{3}[/tex] + 5[tex]x^{2}[/tex] - 16x - 80 = 0
It is given that x + 5) is a factor of this equation. so we will divide the equation by (x + 5).
After dividing it by (x + 5) we get [tex]x^{2}[/tex] - 16
Which can be written as [tex]x^{2}[/tex] - [tex]4^{2}[/tex] = (x + 4) (x - 4)
From here we get rest of the two roots of the equation.
Therefore four zeros of the function will be 0 , 4 , -4 , -5.
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Answer:
D) 0, 4, -4, -5
Step-by-step explanation:
Given polynomial:
[tex]R(x)=x^4+5x^3-16x^2-80x[/tex]
Given (x + 5) is a factor of R(x), use long division to find the other factor:
[tex]\large \begin{array}{r}x^3-16x\phantom{)}\\x+5{\overline{\smash{\big)}\,x^4+5x^3-16x^2-80x\phantom{)}}}\\{-~\phantom{(}\underline{(x^4+5x^3)\phantom{-b))))))))))))}}\\-16x^2-80x\phantom{)}\\-~\phantom{()}\underline{(-16x^2-80x)\phantom{}}\\0\phantom{)}\\\end{array}[/tex]
Therefore:
[tex]R(x)=(x^3-16x)(x+5)[/tex]
Factor out x from the first factor:
[tex]R(x)=x(x^2-16)(x+5)[/tex]
Apply the Difference of Two Square Formula: a²-b²=(a-b)(a+b)
[tex]\begin{aligned}\implies x^2-16&=x^2-4^2\\&=(x-4)(x+4)\end{aligned}[/tex]
Therefore:
[tex]R(x)=x(x-4)(x+4)(x+5)[/tex]
Zero Product Property
If a ⋅ b = 0 then either a = 0 or b = 0 (or both).
To find the zeros of the function, apply the zero-product property by setting each factor equal to zero and solving for x:
[tex]\implies x=0[/tex]
[tex]\implies x-4=0 \implies x=4[/tex]
[tex]\implies x+4=0 \implies x=-4[/tex]
[tex]\implies x+5=0 \implies x=-5[/tex]
Therefore, the zeros of the function R(x) are:
0, 4, -4, -51. Which is the solution of 8 -3(1-x) = 2(x + 1)-3? Ax=-6 B © x= D x = 9/10 6550 x=4 204
We are given the following:
[tex]8-3(1-x)=2(x+1)-3[/tex]
To solve for x, simplify both sides of the equation, then isolate the variable.
Option A; [tex]x = -6[/tex] ← Our Solution
Hope this helps!
an ostrich farmer wants to enclose a rectangular area and then divide it into six pens with fencing parallel to one side of the rectangle (see the figure below). there are 900 feet of fencing available to complete the job. what is the largest possible total area of the six pens?
The largest possible total area of the six pens is 33750 square feet.
Given:
An ostrich farmer wants to enclose a rectangular area and then divide it into six pens with fencing parallel to one side of the rectangle (see the figure below). there are 900 feet of fencing available to complete the job.
Let L and W be the length and width.
900 = L + 6W
L = 900 -6W
Area = A = LW = (900-6W)W = 900W -6W^2
A' = 990-12W = 0
W = 900/12 = 75 feet wide
L = 900 -6W = 900 - 6(75)
L = 900 - 450 = 450 feet.
Maximum area = 450 * 75
= 33750 square feet.
Therefore the largest possible total area of the six pens is 33750 square feet.
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What do you do for this question
Answer:
= 197.5 [tex]cm^{2}[/tex]
Step-by-step explanation:
1) first split the shape into two shapes (a rectangle and trapezium)
2. find the area of the rectangle
10 x 6 = 60 [tex]cm^{2}[/tex]
3. find the missing sides for the trapezium and substitute it into the formula for finding the area of trapezium
([tex]\frac{a+b}{2}[/tex])xh
a=10
b= 15
h = 11 (17-6=11)
( [tex]\frac{10+5}{2}[/tex])x 11
this gives you 137.5 [tex]cm^{2}[/tex]
4. add both the areas together
60 [tex]cm^{2}[/tex] + 137.5 [tex]cm^{2}[/tex] = 197.5 [tex]cm^{2}[/tex]
5 so your final answer is 197.5 [tex]cm^{2}[/tex]
Determine whether the quadrilateral is a parallelogram, answer Yes or No below
The quadrilateral is a parallelogram so it is Yes.
What are the properties of a parallelogram?If a quadrilateral has a pair of parallel opposite sides, it’s a special polygon called parallelogram .The properties of a parallelogram are as follows:
The opposite sides are parallel and equal
The opposite angles are equal
The consecutive or adjacent angles are supplementary
If any one of the angles is a right angle, then all the other angles will be at right angle.
The quadrilateral is a parallelogram since the adjacent interior angles 75° and 105° are supplementary meaning they sum up to 180°
In conclusion, yes, the figure is a parallelogram.
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Graph AXYZ with vertices X(2, 4), Y(6, 0) and Z(7, 2) and its image after the composition.
Translation: (x,y) → (x-6.y)
Translation: (x, y) → (x+2y+7)
After 1st Translation (x,y) → (x-6.y) = X(-4,4), Y(0,0), Z(1,2)
After 2nd Translation (x, y) → (x+2y+7) = X(4,11), Y(8,7), Z(9,9)
What is translation?
Translation is a transformation where all points of the figure are moved the same distance in the same direction. The distance and direction are indicated by a ray sometimes called the translation vector. A vector is a quantity that has both length and direction, and can be thought of as a line segment with a starting point and an endpoint. A translation is an isometry, so the image of a translated figure is congruent to the preimage.And image After Composition means resultant image after you plot the translated points.
So, Given Vertices are X(2,4), Y(6,0), Z(7,2)
Then after 1st Translation = X(-4,4), Y(0,0), Z(1,2)
After 2nd Translation = X(4,11), Y(8,7), Z(9,9)
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Kayden invested $6,300 in an account in the year 2006, and the value has been growing exponentially at a constant rate. The value of the account reached $8,200 in the year 2010. Determine the value of the account, to the nearest dollar, in the year 2019.
The answer to the expositional growing account will be $14838.
What is exponential function?
The mathematical formula for an exponential function is f (x) = ax, where x is a variable and a constant known as the base of the function, which must be greater than zero. The transcendental number, or e, which is roughly equivalent to 2.71828, is the most frequently used exponential function base.
Let suppose in the xth year, the value of the money is 6300* [tex]a^{4}[/tex]
⇒8200 = 6300* [tex]a^{4}[/tex]
⇒a = 1.068
So 6300 *[tex]a^{13}[/tex]
= $14838
Hence the value of the account will be $14838.
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if the rvr equipment is inoperative for an iap that requires a visibility of 2,400 rvr, how should the pilot expect the visibility requirement to be reported in lieu of the published rvr? a. as an rvr of 2,400 feet. b. as a ground visibility of 1/2 sm. c. as a slant range visibility of 2,400 feet.
The correct answer is the pilot should expect the visibility required to be reported in lieu of the published RVR as a ground visibility of 1/2SM.
Visibility is half of a statute mile (SM). Persuading visibility is described in statute miles and fractions. The visibility having 15+ is encrypted as 15SM. Lower visibilities which are half or less of the visibility are detailed in the remarks section. Low visibility procedures (LVP) refer to procedures related to an aerodrome for the cause of ensuring safe operations in the course of lower-than-standard value and low visibility take-offs.
Reduced visibility operations are operations that take place at an aerodrome during the visibility is lower than Runway Visual Range which is 2600 RVR and 1/2 statute mile sm down to and including 1200 RVR and 1/4 statute mile sm.
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4
Convert the mixed number to an improper fraction. -5-
5
=
Answer:
+1
Step-by-step explanation:
So, you just first multiply the denominator to whole then add to the numerator after that the denominator will remain the same and the numerator will be the remainder
A one-year membership to a swim club is $170. This cost includes a $20 registration fee and 12 monthly payments. The equation 12m+20=170 can be used to find the amount m of each monthly payment. Solve the equation and interpret the solution.
The cost of a swim club membership for a year is $170. The price consists of 12 monthly payments of $20 and a $20 registration fee. From equation, the mth payment is $12.5 per month.
Finding the value m of each monthly payment can be done using the equation 12m+20=170.
To find the amount(m), solve the equation 12m+20=170.
12m=150
M = 150/12
M= $12.5
Consequently, each monthly payment will cost 12.5 in total.
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The point (1, 2), translated 4 units to the right, becomes (
around the origin it becomes (
becomes
not the same.
then rotated 90° clockwise
). The point (1, 2) rotated 90° clockwise around the origin
), which is
then translated 4 units to the right it becomes (
The point (2,3) translated 2 units to the right is (4,3)
Rotated 90 degrees clockwise around the origin becomes (3,-4)
Then (2,3) is translated 2 units to the right and rotated 90 degrees counterclockwise to become (3,-2). (5,-2)
What is meant by coordinates ?One of two numbers and/or letters indicating a point's precise location on a map or graph: Zoom in on the map after entering the GPS coordinates.
In two dimensions, points are represented as coordinates (x, y) with respect to the x- and y-axes. An object's x-coordinate, also referred to as the abscissa, is its perpendicular distance from the y-axis as measured along the x-axis.
The domain refers to the first coordinate, which is typically the x-coordinate, and the range refers to the second coordinate, which is typically the y-coordinate.
You do the opposite to determine a point's coordinates in a coordinate system. Starting at the point, move vertically up or down until you reach the x-axis.
The complete question is : The point (2, 3), translated 2 units to the right, becomes (___, ____), then rotated
90° clockwise around the origin it becomes (___, ____). The point (2, 3) rotated
90° clockwise around the origin becomes (____, ____), then translated 2 units to the right it becomes (___,____), which is not the same.
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Some campers are starting a 7-mile hike. If they stop to take pictures every ⅕-mile, how many stops will they make?
Answer:
35
Step-by-step explanation:
I did 1/5 into a decimal which is 0.2 and then i did 7/0.2 because 7 miles and 0.2 miles they stop and then you divide them and get 35
Which problem can be solved by determining 5 ÷ 1/4?
Answer:
[tex]20[/tex]
Explanation:
[tex]5[/tex] ÷ [tex]\frac{1}{4}[/tex]
To change the division sign into a multiplication sign, you need to change (1/4) into its reciprocal.
[tex]5[/tex] × [tex]\frac{4}{1}[/tex]
[tex]5[/tex] × [tex]4[/tex]
[tex]20[/tex]
