Lenght of a rectangle: L
Widht of the rectangle: W
Perimeter of the rectangle: P
length of a rectangle is four times it's width: L = 4W
Perimeter is at most 106: P <= 106
Perimeter is 2L + 2W: P = 2L + 2W
P <= 106
if we use the value of P = 2L + 2W, we can write:
2L + 2W <= 106
Since L = 4W, then we can write this equation:
2L + 2W <= 106
2(4W) + 2W <= 106
8W + 2W <= 106
10W <= 106
W <= 106/10 = 10.6
W <= 10.6
Therefore, the greatest possible value for the width is 10.6
Answer:
10.6
Circle whether the point is a solution to the inequality. Show work to support the answer.y ≤ 1/3x + 4 is (-6,2) a solution?Yes/No
Answer:Explanation:
Yes
The point is a solution if it satisfies the inequality.
In this case, the inequality is y ≤ (1/3)x + 4, so replacing (x, y) = (-6, 2), we get:
y ≤ (1/3)x + 4
2 (1/3)(-6) + 4≤
2 ≤ -2 + 4
2 ≤ 2
Since 2 is equal to 2, the inequality is satisfied and (-6, 2) is a solution.
So, the answer is Yes.
Chef Kim baked his famous casseroles for a company holiday party. The casseroles had different shapes and different delicious fillings. Spinach Cheese Rectangle 3 8 Circle 3 4 What is the probability that a randomly selected casserole is shaped like a rectangle giver that the casserole is filled with spinach? Simplify any fractions.
Explanation
The probability of an event is the number of favorable outcomes divided by the total number of outcomes possible
[tex]P=\frac{favorable\text{ outcomes}}{\text{total outcomes}}[/tex]then
Step 1
Let
rectangle filled with spinach= favorable outcomes=3
total outcomes= total casseroles= 3+8+3+4=18
Now, replace.
[tex]\begin{gathered} P=\frac{favorable\text{ outcomes}}{\text{total outcomes}} \\ P=\frac{3}{18} \\ P=0.1666 \\ \text{rounded} \\ P=0.17 \end{gathered}[/tex]therefore, the answer is 0.17
I hope this helps you
find two rational numbers lying between 1 and 1.2
Answer:
1.1 and 1.12
Step-by-step explanation:
a rational number is any number that can be written as a fraction or a decimal that does not go on forever (unless it is a repeating decimal, ex: 3.454545..)
so any decimal that can be written as a fraction that is between 1 and 1.2 works
6. The following observations are arranged in ascending order. The median of the data is 25 find the value of x. 17, x, 24, x + 7, 35, 36, 46 (3 Points)
The value of x = 18.
What is median?
The median is the value that divides a data sample, a population, or a probability distribution's upper and lower halves in statistics and probability theory. It could be referred to as "the middle" value for a data set.
Median = [tex]\frac{n+1}{2} ^{th}[/tex] term
Given that,
The median of the data is 25.
The observations are 17, x, 24, x+7, 35, 36, 46.
Here, n = 7
Median = 25
Median = [tex]\frac{7+1}{2} ^{th}[/tex] term
Median = [tex]\frac{8}{2}^{th}[/tex] term
Median = 4[tex]^{th}[/tex] term
Median = x+7
25 = x+7
X = 25-7
X = 18
Here, x+7
X+7 = 18+7
X+7 = 25.
Therefore, the value of x is 18.
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Find the area of a rectangle that is 2 7/9 m long and 4 4/5 m wide. Enter your answer as a mixed number and reduce if possible.
Answer:
13 ⅓.
Step-by-step explanation:
The area of a rectangle is given by
Area = Length × Breadth
Length = 2 7/9 = 25/9 and breadth = 4 4/5 = 24/5
.: Area = 25/9 × 24/5 = 600/45 (15 can go to both the numerator and denominator)
We have 40/3 but to convert it to a mixed fraction we get 13 ⅓ as your area.
Homany zeros are in the product (6×5)×10^3
6.07 X 10^7 in standard form
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{6.07 \times 10^7}\\\mathsf{= 6.07(10^7)}\\\mathsf{= 6.07(10\times10\times10\times10\times10\times10\times10)}\\\mathsf{= 6.07(100\times100\times100\times10)}}\\\mathsf{= 6.07(10,000\times1,000)}\\\mathsf{= 6.07(10,000,000)}\\\mathsf{= 60,700,000 \rightarrow 6.07\times 10^7}\\\\\huge\text{Therefore, your answer should be: }\boxed{\mathsf{60,700,000}}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
Find an equation for the line perpendicular to the line −7x+2y=3 having the same y-intercept as 9x+3y=−2.
The equation of the line perpendicular to the line −7x+2y=3 having the same y-intercept as 9x+3y=−2 is y = - 2 / 7x - 2 / 3
How to find equation of a line?The equation of a line can be represented as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore, the equation of the line is perpendicular to −7x+2y=3.
−7x+2y=3
2y = 7x + 3
y = 7 / 2 x + 3 / 2
Perpendicular lines follows the rule below:
m₁ m₂ = -1
7 / 2 m₂ = -1
7m₂ = -2
m₂ = - 2 / 7
Therefore, the equation of the line also haver the same y-intercept as
9x + 3y = −2.
3y = - 9x - 2
y = -3x - 2 /3
The y-intercept of the equation is - 2 / 3.
Hence
the equation of the line is y = - 2 / 7x - 2 / 3
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On a coordinate plane, a graph curves up through (negative 2, negative 5) to inflection point (0, 1), and then curves up through (1, 4). Consider the graph shown. Which ordered pairs are on the inverse of the function? Check all that apply.
The ordered pairs are on the inverse function are (-5, -2) and (4, 1)
What are inverse functions?Inverse functions are the opposite of an original equation. This means that for a function f(x), the inverse of the function f(x) is f-(x); it also represents the opposite function
How to determine the ordered pairs on the inverse of the function?From the question, we have the following coordinate points
Point (negative 2, negative 5)Inflection point (0, 1)Curves up through (1, 4)Rewrite the points as:
Point (-2, -5)Inflection point (0, 1)Curves up through (1, 4)Remove the inflection point.
So, we have
Point (-2, -5)Curves up through (1, 4)The next step is to switch/swap the positions of x and y in the above equation ordered pairs
So, the points become:
Inverse point (-5, -2)Another inverse point (4, 1)Hence, the ordered pairs that are on the inverse function of the function are (-5, -2) and (4, 1)
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Answer:
its
A(-5,-2),
B(0,-1),
E(1,0),
F(4,1).
Step-by-step explanation:
i took one for the team
Tickets for the monster truck rally cost $12 for children and $20 for adults. Last
night 400 total tickets were sold for a total of $6000. Use c for the child tickets and
a for adult tickets. If one of the equations for this system is a + c = 400, write
the second equation for this system below.
Answer:
20a + 12c = 6000
Step-by-step explanation:
a = adult tickets
c = child tickets
$20 for adults, $12 for children, for a total of $6000
20a + 12c = 6000
a + c = 400
[tex]\sqrt{6} +2\sqrt{3} +\sqrt{12}[/tex]
[tex] = \sqrt{6} + \sqrt{12} + \sqrt{12} \\ \\ = \sqrt{6} + 2 \sqrt{12} \\ = \sqrt{6} + 2 \sqrt{4 \times 3} \\ = \sqrt{6} + 2 \times \sqrt{4} \times \sqrt{3} \\ = \sqrt{6} + 2 \times 2 \sqrt{3} \\ = \sqrt{6} + 4 \sqrt{3} [/tex]
ATTACHED IS THE SOLUTION
Miguel pays $68 biweekly for health insurance which is 14% of the total cost his employer pays the rest what is the total annual cost to the nearest dollar of Miguel's health insurance
Cost of the health insurance is $11657.14
What is cost?
A cost is the worth of money that has been used up to create something or supply a service and is thus no longer accessible for use in production, research, retail, or accounting. In business, the cost might be one of acquisition, in which case the money spent to obtain it is recognized as cost. In this situation, money is the input that is used to purchase the item. This acquisition cost might be the total of the original producer's production expenses and the acquirer's additional transaction costs over and above the amount paid to the producer. Typically, the price includes a profit margin above the cost of manufacture.
14% of x = 68
x = 68 x 100/14
= $485.71
Total cost = $485.71 x 24 months = $11657.14
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Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
A system of linear equations is given by the tables. One of the tables is represented by the equation y = -x + 7.
X
0
3
6
9
y
5
6
7
8
X
-6
-3
0
3
y
9
8
7
6
The equation that represents the other equation is y=
The solution of the system is (
)
4
X +
Reset
Next
y = 1 / 3 x + 5 is the linear equation for the first table.
The system of equations' answer is (3, 6).
Linear Equation: What Is It?A linear equation is an algebraic equation of the form y= mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The previous equation, which has the variables y and x, is sometimes referred to as a "linear equation with two variables."
based on the available facts;
Equation of a point slope:
y = mx + b,
where m = slope and b = y-intercept
As a result, the equation for the second table is y = - 1 /3 x + 7.
With the help of the table's (0, 5)(3, 6) values, the equation for the first table may be solved. Therefore,
m = 6 - 5 / 3 - 0 = 1 / 3
let's find b using (0, 5)
5 = 1 / 3(0) + b
b = 5
Therefore, the equation of the first table is as follows:
y = 1 / 3 x + 5
The solution to the system of equation can be calculated as follows:
y + 1 /3 x = 7
y - 1 / 3 x = 5
2y = 12
y = 12 / 2
y = 6
6 - 1 / 3 x = 5
- 1 / 3 x = 5 - 6
- 1 / 3 x = - 1
x = 3
Therefore, the solution to the system of equation is (3, 6)
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assume that each of the n trails
Given,
The value of n is 8.
The value of x is 0.
The value of p is 0.6.
The binomial expression is,
[tex]P(X=x)=^nC_x\times(p)^x\times(1-p)^{n-x}[/tex]Subsituting the values then,
[tex]\begin{gathered} P(X=0)=^8C_0\times(0.6)^0\times(1-0.6)^{8-0} \\ P(X=0)=\frac{8!}{0!\times8!}\times1\times(0.4)^8 \\ P(X=0)=1\times1\times(0.4)^8 \\ P(X=0)=0.000655 \\ P(X=0)=0.0007 \end{gathered}[/tex]ence, the probability is 0.0007.
What is the equation of the line that is perpendicular to y = 3x + 3 and passes through the point (−6, 9)?
The equation of the line will be equal to 3y = -x + 21.
A line may be defined as the straight figure drawn which has no end points. The equation of a line can be written in slope intercept form as y = mx + c where m is the slope of line, c is y intercept an x and y are independent and dependent variables. If a point (x₁, y₁) is given then equation of line is (y - y₁) = m (x - x₁). The slope of line which is perpendicular to a given line having slope m is equal to -1/m.
Now, equation of line is y = 3x + 3. If we compare with slope intercept form then, m = 3. Now, slope of line perpendicular to this line is equal to -1/3. Now, equation of line passing through point (-6, 9) is given as
(y - 9) = -1/3 (x + 6)
3y - 27 = -x - 6
=> 3y = -x + 21 which is the required equation of line.
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QUESTION DOWN BELOW PLEASE HELP!! ITS DUE SOON!
The unknown angles of the triangle and trapezium are as follows:
∠1 = 110°, ∠2 = 40°∠1 = 120°, ∠2 = 60°How to find angles in a triangle and trapezium?A triangle is a polygon with three sides.
The sum of angles in a triangle is 180 degrees.
Therefore, angle 1 can be found as follows:
∠1 = 180 - 40 - 30
∠1 = 180 - 70
∠1 = 110 degrees.
Therefore, angle 2 can be found as follows:
∠2 = 180 - 40 - 40 - 30 - 30
∠2 = 180 - 80 - 60
∠2 = 180 - 140
∠2 = 40 degrees.
A quadrilateral is a polygon with 4 sides. The sum of angles in a quadrilateral is 360 degrees.
Therefore, the triangle in the trapezium is an isosceles triangle. The base angles are equal.
Hence,
∠1 = 180 - 30 - 30
∠1 = 180 - 60
∠1 = 120 degrees
Sum of angles in the same transversal is supplementary.
Therefore,
90 + 30 + ∠2 = 180
∠2 = 180 - 120
∠2 = 60 degrees
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Write in all missing angles.
Answer:
The answers are all there. 50° + 22°= 77°
180° - 77° = 103°
Step-by-step explanation:
All the rest is just mirrored.
Use Gaussian elimination or Gauss-Jordan elimination.
Mike works a total of 58 hr per week at his two jobs. He makes $7 per hour at job A and $8 per hour at job B. If his total
pay for one week is $424 before taxes, then how many hours does he work at each job?
Mike works 40 hours at job A and 18 hours at job B.
What are simultaneous equations?Simultaneous equations are two or more algebraic equations that share the same unknown variables and have the same solution for each of them. This suggests that the equations are simultaneous and have a single solution.
Given:
Mike makes $7 per hour at job A and $8 per hour at job B.
Let x be the number of hours Mike spends working at job A and y be the number of hours he spends working at job B.
Since he works a total of 58 hours per week,
x + y = 58
His total pay for one week is $424.
7x + 8y = 424
Solving both equations simultaneously we get,
From the first equation, we have, y = 58 - x
Putting the value of y in the second equation,
7x + 8(58 - x) = 424
7x + 464 - 8x = 424
8x - 7x = 464 - 424
x = 40
So, now calculate y = 58 - 40 = 18
Therefore, Mike spends 40 hours working at job A and 18 hours working at job B.
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Mom and Dad have decided to put themselves on a strict budget so that the family can save money to go onvacation. For breakfast, the family decides to spend no more than $20.00 for the week.Each day, the family eats 1/3 of a pound of granola and drinks 2/7 of a liter of milk for breakfast.Milk costs $4,49 per liter, but different types of granola have different prices.If the family only buys one type of granola for the week, what is the price per pound of the most expensivegranola they can afford?Explain your solution using logic, tables, graphs, and/or algebraic reasoning.
For breakfast, the family decides to spend no more than $20.00 for the week.
Each day, the family drinks 2/7 of a liter of milk for breakfast.
For the entire week, the amount of milk consumed is
[tex]7\times\frac{2}{7}=2\; \text{liters}[/tex]Milk costs $4,49 per liter, so the cost of the total amount of milk consumed is
[tex]2\times\$4.49=\$8.98[/tex]So, the amount left for the granola is
[tex]\$20.00-\$8.98=\$11.02[/tex]Each day, the family eats 1/3 of a pound of granola for breakfast.
For the entire week, the amount of granola consumed is
[tex]7\times\frac{1}{3}=\frac{7}{3}\; \text{pounds}[/tex]Let x be the price per pound of the most expensive granola they can afford.
[tex]\begin{gathered} \frac{7}{3}\cdot x=\$11.02 \\ x=\$11.02\cdot\frac{3}{7} \\ x=\$4.72 \end{gathered}[/tex]Therefore, the most expensive granola they can afford is $4.72
The mean of the values in a data set is b. If each of the values in the data set
were multiplied by 8, what would be the mean of the resulting data?
A. 9b
B. 7b
C. b
D. 8b
Answer:
The answer is D.
Step-by-step explanation:
I hope 'm not too late answer your question good luck.
Find the midpoint of the segment with the following endpoints.
(9, 2) and (5,5)
Answer:
(7,3.5)
Step-by-step explanation:
Midpoints
x = (x1 + x2)/2 = (9 + 5)/2 = 14/2 = 7
y = (y1 + y2)/2 = (2 + 5)/2 = 7/2 = 3.5
Given f(x) = 2x² -x+3
Find f(x)
The function f(x) = 2x² - x + 3 equals to 9 when x is equal to 2.
What is function in mathematics?
In mathematics, a function is an expression, rule, or law that establishes the connection between an independent variable and another variable (the dependent variable). In mathematics, functions exists everywhere, and they are crucial for constructing physical links in the sciences.
The function given in the question is:
f(x) = 2x² - x + 3
We have to find f(x) when x = 2,
We are replacing x with 2 in given function, we get:
f(x) = 2(2)² - 2 + 3
f(x) = 2(4) -2 + 3
f(x) = 8 -2 +3
f(x) = 9
Hence the given function equals to 9 when x is equal to 2.
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Complete question
Given f(x) = 2x² -x+3
Find f(x) when x = 2
Gabe is paid semi monthly and contributes 9% of the total cost of his individual healthcare coverage he pays $48.47 per paycheck towards this contribution what is the total value of Gabes healthcare coverage for the year
Cost of the health insurance is $12925.33
What is cost?
A cost is the worth of cash that has been used up to create it or supply a function and is thus no longer accessible for use in manufacturing, research, commerce, or bookkeeping. In business, the cost might be one of procurement, in which case the money being spent to obtain it is recognized as cost. In this situation, money is the input that is used to purchase the item. This acquisition cost might be the total of the original producer's production expenses and the acquirer's direct capital costs above and beyond the amount paid to the producer. Typically, the package includes a gross margin above the cost of manufacture.
9% of x = 48.47
x = 48.47 x 100/9
= $538.55
Total cost = $538.55 x 24 months = $12925.33
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What is the correct evaluation of 3x - x + 2, when x is equal to -4?
Answer:
When x = -4, the equation's answer is -6.
Hope this helps!
Step-by-step explanation:
3(-4) - ( -4 ) + 2
-12 - (-4) +2 ( negative times negative is positive )
-12 + 4 + 2
-8 + 2 or -12 + 6
is -6
how do you solve this?
According to the given values, the length of the arc is 1 cm approx.
What is an arc?An arc is, in general, any straight curve that connects two points. The term "arc length" refers to an arc's length. A graph arc is an ordered pair of adjacent vertices in a graph. An arc is specifically any section of a circle's circumference (other than the entire curve).So, the formula to find the length of the arc:
Arc Length = θ × (π/180) × rNow, substitute the values in the formula as follows:
Arc Length = θ × (π/180) × rArc Length = 8π/9 × (π/180) × 16.5Arc Length = 8π/9 × π/180 × 16.5Arc Length = 2π/9 × π/45 × 16.5Arc Length = 2π × π/45 × 1.8Arc Length = 6.28 × 3.14/45 × 1.8 (π = 3.14)Arc Length = 11.304 × 3.14/45Arc Length = 1.256 × 3.14/5Arc Length = 3.94384/5Arc Length = 0.788768Rounding off: 1.00 cmTherefore, according to the given values, the length of the arc is 1 cm approx.
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factorise 3^2-16x +5
Answer:
3²- 16x +5
9-16x+5
-16x+9+5
-16x + 14
Step-by-step explanation:
I hope this will be helpful for you.
PART F Write the equation of a line that goes through the coordinate (5, 3) and has a slope of 3
I got y=3x-12 I am not sure if it's right
Your answer is correct.
Four friend must give a 7 minute presentation.each friend must speak for an equal amount of time. How long will each friend speak?
Answer:
1 minute and 75 seconds
Step-by-step explanation:
you take 4 and divide it by 7 minutes there for getting 1.75
I need help on this question please and thank you
It is proved that the line c is parallel to line d.
What is defined as the supplement angles?If two angles add up to 180 degrees, they are described as supplementary angles. When supplementary angles are combined, they establish a straight angle (180 degrees). In other words, if Angle 1 + Angle 2 = 180°, angles 1 and 2 are supplementary. Supplementary angles can be either adjacent or not. As a result, there are two kinds of supplementary angles. Every one of these kinds of supplementary angles is discussed further below.supplementary angles adjacentNon-contiguous supplementary anglesFor the given question;
Angle 2 and angle 3 are supplement;
∠2 + ∠3 = 180 ......eq 1
See from figure.
∠4 = ∠3 (vertically opposite angles)
Thus, replacing ∠3 with ∠4 in eq 1.
∠2 + ∠4 = 180 (linear pair)
As ∠2 and ∠4 form the linear pair. Thus, line c is parallel to line d.
Therefore, line c proved to be parallel to line d.
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Urgenttt!!!!!!!!!!!!!
Which of the following expressions is accurate for angle 8 that intersects the unit circle at point (-0.949, 0.314).
Cos(0) = - 0.949 this expression is accurate for the unit circle which is intersected at point by angle 8 according at point (-0.949, 0.314).
What is circle ?An elliptical plane figure is a circle. From a fixed location known as the circle's center, each point on the circle is equally distant. It has a two-dimensional (2D) shape and a radius value. The Latin word "circulus" (which means little ring) is the root of the English word "circle."A circle is a two-dimensional shape that is made up of a collection of points that are spaced out from the center of the circle (its fixed point) on the plane by a fixed or constant distance (radius). The radius of a circle is the fixed distance between points that is fixed from the fixed point, which is known as the origin or center of the circle.
The terminal side of angle 0 intersects the unit circle at point P(- 0.949, 0.314) That means, OQ = 0.949 and PQ = 0.314
Here, OP is the radius of the unit circle. So, OP = 1
In respect of angle 0, the adjacent side is OQ and the hypotenuse is OP.
We know that,
cos= [tex]\frac{adjacent}{hpotenusey}[/tex]
So,
cos(0) = - [tex]\frac{OQ}{OP}[/tex] [As the angle is in quadrant II, so cos is negative]
cos(0) = - [tex]\frac{-0.949}{1}[/tex]
cos(0) = - 0.949
Cos(0) = - 0.949 this expression is accurate for the unit circle which is intersected at point by angle 8 according at point (-0.949, 0.314).
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