A notebook has a perimeter of 36 inches. It’s area is 80 square inches. What are the dimensions of the notebook
__inches by___ inches
Final answer:
To solve for the dimensions of the notebook, we set up equations based on the perimeter and area, then solved the quadratic equation to find that the dimensions are 10 inches by 8 inches.
Explanation:
To find the dimensions of a notebook with a perimeter of 36 inches and an area of 80 square inches, we will use the formulas for the perimeter and area of a rectangle. The perimeter (P) of a rectangle is 2 times the length (l) plus 2 times the width (w), or P = 2l + 2w. The area (A) of a rectangle is length times width, or A = lw.
Given P = 36 and A = 80, we can set up two equations:
2l + 2w = 36l × w = 80First, we simplify the perimeter equation to l + w = 18 by dividing everything by 2. We can then express w in terms of l: w = 18 - l. Now, we substitute w into the area equation: l(18-l) = 80. Expanding this gives us a quadratic equation: l2 - 18l + 80 = 0.
To solve the quadratic equation, we look for factors of 80 that add up to 18. The factors are 10 and 8, meaning the length is 10 inches and the width is 8 inches, since l = 10 and w = 8 satisfy both the area and perimeter equations.
Therefore, the dimensions of the notebook are 10 inches by 8 inches.
There are 100 students in a drawing contest, and 58 of them are girls. What percent of the students in the contest are girls?
There are 100 students in a drawing contest and 58 of students are girls. What percent of students in the drawing contest are girls?
The fraction [tex]\frac{58}{100}[/tex] represents the number of girls in the drawing contest out of all the students.
To find out what percent of the students are in the drawing contest, we can change [tex]\frac{58}{100}[/tex] into a percent.
We can first reduce the fraction by dividing both the numerator and denominator by the Greatest Common Factor of 58 and 100 using 2.
58 ÷ 2 = 29
100 ÷ 2 = 50
Our reduced fraction is [tex]\frac{29}{50}[/tex].
29 ÷ 50 = 0.58
0.58 × 100 = 58%
Therefore, 58% of the students in the drawing contest are girls.
Divide £770 in the ratio of 4:3 plsss
Every day for two full weeks (14 days) jimmy records the number of coins in his pocket. he finds that the mean is 27. he decides to remove one sunday's total because it was an outlier. his new mean is 18 coins. how many coins did he have in his pocket on the sunday he removed?
a.18
b.27
c.126
d.144
Answer:
It is D.)144
Step-by-step explanation:
Use the mid-point rule with n = 4 to approximate the area of the region bounded by y = x3 and y = x. (10 points)
Using the mid-point rule with n = 4, we approximate the area bounded by y = x³ and y = x b as 0.2578125.
To approximate the area of the region bounded by y = x³ and y = x using the mid-point rule with n = 4, we follow these steps:
Determine the points of intersection between y = x³ and y = x. Solving x³ = x, we get the points of intersection at x = 0 and x = 1.
Divide the interval [0, 1] into 4 subintervals, each of width Δx = (1 - 0)/4 = 0.25.
Calculate the midpoint of each subinterval: 0.125, 0.375, 0.625, and 0.875.
Evaluate the functions y = x³ and y = x at these midpoints:
At x = 0.125: y = x³ = 0.125³ = 0.001953125 and y = x = 0.125At x = 0.375: y = x³ = 0.375³ = 0.052734375 and y = x = 0.375At x = 0.625: y = x³ = 0.625³ = 0.244140625 and y = x = 0.625At x = 0.875: y = x³ = 0.875³ = 0.669921875 and y = x = 0.875Determine the heights of the rectangles by finding the difference between the values of y:
At x = 0.125: Δy = 0.125 - 0.001953125 = 0.123046875At x = 0.375: Δy = 0.375 - 0.052734375 = 0.322265625At x = 0.625: Δy = 0.625 - 0.244140625 = 0.380859375At x = 0.875: Δy = 0.875 - 0.669921875 = 0.205078125Compute the area of each rectangle (height × width) and then sum them up:
Area at x = 0.125: 0.123046875 × 0.25 = 0.03076171875Area at x = 0.375: 0.322265625 × 0.25 = 0.08056640625Area at x = 0.625: 0.380859375 × 0.25 = 0.09521484375Area at x = 0.875: 0.205078125 × 0.25 = 0.05126953125Add the areas to get the total approximate area:
0.03076171875 + 0.08056640625 + 0.09521484375 + 0.05126953125 ≈ 0.2578125
Therefore, the approximate area of the region bounded by y = x³ and y = x using the mid-point rule with n = 4 is 0.2578125.
Ronald and Tim both did their laundry today. Ronald does laundry every 666 days and Tim does laundry every 999 days.
How many days will it be until Ronald and Tim both do laundry on the same day again?
Answer:
18
Step-by-step explanation:
Which of the following choices is the value of cscΘ?
a) 12/15
b) 9/15
c) 15/12
D) 15/9
A basketball player has a 50 chance of making each free throw. what is the probability that the player makes at least eleven out of twele free throws
What is the equation of a circle with center (8, 4) and radius 7?
The standard form of the equation of a circle is given by (x-h)² + (y-k)² = r², where (h, k) are the center and r is the radius. For a circle with center at (8, 4) and radius 7, the equation of the circle becomes (x - 8)² + (y - 4)² = 49.
Explanation:The equation of a circle in standard form is given by (x-h)² + (y-k)² = r², where (h, k) are the coordinates of the center of the circle and r is the radius. This formula comes from Pythagorean theorem and how a circle is defined as the locus of points equidistant from a given point (the center).
By substituting the given center and radius into this formula, we can write the equation of the specific circle you're asking about. The center of this circle is (h, k) = (8, 4), and its radius is r = 7. Therefore, the equation of the circle is (x - 8)² + (y - 4)² = 7² or (x - 8)² + (y - 4)² = 49.
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The equation of the circle is (x-8)^2 + (y-4)^2 = 49.
Explanation:The equation of a circle with center (h, k) and radius r is given by the formula:
(x-h)2 + (y-k)2 = r2
In this case, the center is (8, 4) and the radius is 7. So, the equation of the circle is:
(x-8)2 + (y-4)2 = 72
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The total number of points scored by each player throughout a season are listed on a roster by the player's jersey number. is this a function? explain your reasoning.
A)Yes, it is a function because each player's jersey number will have only one number for the points scored during the season.
Each jersey number has exactly one number for the total points scored by the player.
In a function, every input has exactly one output. In this situation, each jersey number is an input, and the total points scored for the season by the player is the output.
Which compound inequality can be used to solve the inequality |3x+2|>7
Answer:
x>[tex]\frac{5}{3}[/tex].
Step-by-step explanation:
We have given an inequality |3x+2|>7.
We need to solve this inequality |3x+2|>7, and find the compound which can solve this.
We know that, inequality :
|3x+2|>7
Subtrating 2 from both sides,
|3x+2-2|>7-2
3x>5
Dividing by 3 both sides,
[tex]\frac{3x}{3} > \frac{5}{3}[/tex]
x>[tex]\frac{5}{3}[/tex]
Therefore, we can see that on the inequality |3x+2|>7, we find x>[tex]\frac{5}{3}[/tex] compound.
Answer:
D. 3x + 2 < –7 or 3x + 2 > 7
Step-by-step explanation:
Aaron solved an inequality and then graphed the solution as shown below. Anwser: A
A student found the solution below for the given inequality lx-9l less than 4
Anwser: D
Amber is solving the inequality lx+6l - 12 less than 13 by graphing. Which equations should Amber graph?
Anwser: A
What is the solution, if any, to the inequality l3xl greater than or equal to 0?
Anwser: A
Which compound inequality is equivalent to lax-bl greater than c for all real numbers a, b, and c, where c is greater than or equal to 0?
Anwser: D
Which compound inequality is equivalent to the absolute value inequality lbl greater than 6?
Anwser: D
What is another way to write the absolute value inequality lpl less than or equal to 12?
Anwser: A
What is the solution to the inequality lx-4l less than 3?
Anwser: B
Which inequality is equivalent to lx-4l less than 9?
Anwser: B
Hope This Helps!
if 3x+2y=12 and -4x+6y=24 what is the value of -x+2y
The volume of a cylinder is given by the formula v=pi r^2h, where r is the radius of the cylinder and h is the height. Which expression represents the volume of this cylinder? h=2x+7, r=x-3.
Simplify the questions that aren't crossed on the attachment, thank you
Find the base area of a rectangular pyramid whose pyramid height is 5 cm and slant height of one side of the base is 13 cm and another side of the base is 7 cm.
a. 92√6 cm^2
b. 96√6 cm^2
c. 180√6 cm^2
d. 100√6 cm^2
e. 198√6 cm^2
Chiara pays $21 for 3 DVDs that she finds in a one-price bin. Gunther wants to know how much he would spend for 1 DVD in this bin. Chiara wants to know how many dollars she will need to purchase 9 DVDs the next time she goes.
use formulas to find the lateral and surface are of the given prism the numbers are 5.39m 26m 5m 2m
Suppose f(x) = x. Find the graph of f(x+1)
A family drove 2,275 miles from Los Angeles to Atlanta in a time span of 35 hours . Calculate their average speed in miles per hour .
The family drove at an average speed of 65 mph from Los Angeles to Atlanta with a span length of 2275 miles
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
The equation for average speed is given as:
Average speed = Total distance / total time
Hence:
Average speed = 2275 miles / 35 hour = 65 mph
The family drove at an average speed of 65 mph from Los Angeles to Atlanta
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Find the coordinate of the point (x,y) shown on the unit circle
Here the angle is
[tex]\frac{4 \pi}{3}[/tex]
And radius is 1 units .
And
[tex]x = r cos \theta, y = r sin \theta[/tex]
Substituting the values of theta and r, we will get
[tex]x = 1 cos(\frac{4 \pi}{3} ) = -1/2 \\ y=1 sin( \frac{4 \pi}{3} ) =\sqrt3 /2[/tex]
So we will get
[tex]x = \frac{-1}{2} , y = -\frac{ \sqrt 3}{2}[/tex]
The coordinate of the point (x,y) shown on the unit circle is therefore: (-1/2, -√3/2)
The circle given is a unit circle.
In essence, the radius as indicated by the blue line is 1.
The angle subtended by the line is; 4π/3.
Therefore, from trigonometry of right-angled triangles; we have;
x = r Cos(4π/3)y = r Sin(4π/3)where, r = 1
Therefore,
x = -1/2y = -√3/2Read more:
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Question 19 Unsaved
Ann office building has the same number and size of office units per floor. If there are 21 units on the first 3 floors, then what is the total number of offices in the 10 story building?
Question 19 options:
7
24
63
70
Write x2 − 2x − 3 = 0 in the form (x − a)2 = b, where a and b are integers.
A.(x − 4)2 = 3
B.(x − 3)2 = 2
C.(x − 2)2 = 1
D.(x − 1)2 = 4
Give the dimensions of a cuboid with a volume of 18cm to the power 3.
A. 3
B. 5
C. 6
D. 10
One of the mutually exclusive results of an activity conditional probability 2. a combination of one or more outcomes independent events 3. a measure of likelihood of a given result event 4. compound events whose outcomes do not affect each other outcome 5. events involving two or more activities compound events 6. probability of one event given that another has occurred probability
From the information given about the probability, the appropriate terms that denotes them will be:
outcome - one of the mutually exclusive results of an activity.probability - a measure of the likelihood of a given result.compound events - events involving two or more activities.event - a combination of one or more outcomes.independent events - compound events whose outcomes do not affect each other.conditional probability - the probability of one event given that another has occurred,ProbabilityIt should be noted that probability is the branch of mathematics that deals with numerical descriptions of how likely an event is to occur.
The probability of an event occuring is a number between 0 and 1. 0 indicates the impossibility of the event while 1 indicates certainty.
The outcome is one of the mutually exclusive results of an activity.
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In 2010, 100 japanese yen purchased .88 u.s. dollars and in 2013, it purchased .93 u.s. dollars. how much was 1 u.s. dollar worth in japanese yen, in 2010 and 2013?
A sphere has a diameter of 12 ft. What is the volume of the sphere? Give the exact value in terms of pi
______________ is process that you can do over and over, where each result does not affect the next.
Ex. Flipping a coin, rolling dice, choosing a card, etc.
Sue Baker is given a prescription of MECLIZINE 25MG to be taken three times daily. She was given enough for ten days. She has been given her pills following the six "rights" (right resident, right drug, right dosage, right time, right route, right record/documentation). On the start of day four, how many pills should be in the bottle?
Christopher is analyzing a circle, y^2 + x^2 = 121, and a linear function g(x). Will they intersect?
A. Yes, at the positive x coordinates.
B. Yes, at negative x coordinates.
C. Yes, at the negative and positive x coordinates.
D. No, they will not intersect
Yes, they will intersect at the positive x coordinates.
What is the equation of the circle?The standard equation of a circle is: (x-h)^ 2 + (y-k) ^2 =r ^2 Where (h, k) is the coordinates of the center, and r is the radius of the circle.
Christopher is analyzing a circle, y^2 + x^2 = 121, and a linear function g(x). Will they intersect?
The given equation of the circle is;
[tex]\rm x^2+y^2=121\\\\x^2+y^2=11^2[/tex]
The circle with center at (0,0) and radius r = 11 units and g(x) points (-1,14) (0,12) (1,10).
The linear function is;
[tex]\rm y=mx+b[/tex]
From the graph on drawing all the co-ordinates lies in positive x and y axis.
Hence, they will intersect at the positive x coordinates.
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