[tex](\stackrel{x_1}{-12}~,~\stackrel{y_1}{15})\qquad (\stackrel{x_2}{18}~,~\stackrel{y_2}{-13}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-13}-\stackrel{y1}{15}}}{\underset{\textit{\large run}} {\underset{x_2}{18}-\underset{x_1}{(-12)}}} \implies \cfrac{-28}{18 +12} \implies \cfrac{ -28 }{ 30 } \implies - \cfrac{14 }{ 15 }[/tex]
6 TH GRADE MATH , WHAT IS THE SLOPE? TY
Answer:
Step-by-step explanation:
The slope of a line is the measure of the steepness and the direction of the line. Finding the slope of lines in a coordinate plane can help in predicting whether the lines are parallel, perpendicular, or none without actually using a compass.
The slope of any line can be calculated using any two distinct points lying on the line. The slope of a line formula calculates the ratio of the "vertical change" to the "horizontal change" between two distinct points on a line. In this article, we will understand the method to find the slope and its applications.
That is what Slope is.
Answer:
Step-by-step explanation:
Slope :( 1,1)
You start on the y-axis point which is (0,1) as you can see it is going up so I used the “up left” strategy. You go up 1 to the left 1 since the line intersects at point (1,2)
Martin has a spinner that is divided into four sections labeled A, B, C, and D. He spins the spinner twice. PLEASE ANSWER RIGHT HELP EASY THANK UU
Drag the letter pairs into the boxes to correctly complete the table and show the sample space of Martin's experiment..
The diagram included shows the letter pairs that should go into each box to appropriately finish the table and display the sample area of Martin's experiment.
Explain about the sample space of an event?A common example of a random experiment is rolling a regular six-sided die. For this action, all possible outcomes/sample space can be specified, but the actual result on any given experimental trial cannot be determined with certainty.
When this happens, we want to give each event—like rolling a two—a number that represents the likelihood of the occurrence and describes how probable it is that it will occur. Similar to this, we would like to give any event or group of outcomes—say rolling an even number—a probability that reflects how possible it is that the occurrence will take place if the experiment is carried out.Martin features a spinner with four compartments marked A, B, C, and D.
To get the correct result of the filling, first take the value of the horizontal bar and write the value from the corresponding vertical bar where both column are meeting.
Thus, the diagram included shows the letter pairs that should go into each box to appropriately finish the table and display the sample area of Martin's experiment.
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What percentage decrease in profits from 2021 to 2022 would imply that profits were equal in 2020 and 2022?
This means that in order for the profits in 2022 to match those in 2020, the profits in 2021 would also need to match those in 2020.
[tex]r = 0[/tex] % is the percentage drop in earnings from 2021 to 2022 that would indicate that profits were equal in both 2020 and 2022.
What does “mean profit” mean?Profits for mesne. According to Section 2(12) C.P.C., the term “mesne profit” refers to any earnings that the person who is in wrongful possession of a piece of property has actually received or may obtain in the future. High Court of Telangana.
The earnings in 2022 must match the profits in 2020, hence we must choose the value of r such that:
[tex]P \times(1-r/100)^² = P[/tex]
By simplifying and dividing both sides by P, we obtain:
[tex](1-r/100)^² = 1[/tex]
Taking the square root of both sides, we get:
1-r/100 = ±1
Each time we solve for r, we obtain:
[tex]1-r/100 = 1[/tex] , which implies [tex]r = 0[/tex]
and
[tex]1-r/100 = -1,[/tex] which implies [tex]r = 200[/tex]
We reject the [tex]r = 200[/tex] Option because a percentage drop cannot be larger than 100%.
Therefore, [tex]r = 0[/tex] % is the percentage drop in earnings from 2021 to 2022 that would indicate that profits were equal in both 2020 and 2022.
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First-year students at a university must take history or philosophy during their first semester. 400 are enrolled in both out of a total of 1200 first-year students. If 600 are enrolled in philosophy, how many are taking history?
Answer: I really don't know I'm just trying to get a quest done sorry
5. Briefly define the following terminologies: (A) Degeneracy; (B) Slack variable; (C) Project; (D) Critical path; (E) Optimistic time; (G) Artificial variable; (H) Alternative optimal solution
This circumstance may happen if one of the RHS coefficients is 0. The objective value and solution remain the same in this situation, but there are still variables. Degeneracy describes this condition.
What is Degeneracy?The energy levels in a three-dimensional box are provided by the formula E = (h2/8m) [(n x2/a2) + (n y2/b2) + (n z2/c2)].
where n x, n y, and n z are the quantum numbers for the x, y, and z dimensions, respectively, and h is Planck's constant, m is the particle'smass, a, b, and c are the dimensions of the box.
The amount of various quantum number combinations that result in the same energy is the degeneracy of an energy level.
The degeneracies of the first four energy levels for a three-dimensional box with a=b=1.5c are as follows:
1 degeneracy at first energy level (n=1)
Third degeneracy at second energy level (n=2)
6 degeneracies at third energy level (n=3)
10 degeneracies at energy level four (n = 4)
Hence, This circumstance may happen if one of the RHS coefficients is 0. The objective value and solution remain the same in this situation, but there are still variables. Degeneracy describes this condition.
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Use Synthetic Division to find the quotient of the division between
x4-2x3+2x2-9x +10 and (x-2).
x^3 + 2x - 5
x^3 + x + 4
x^4 + 2x - 5
x^2 - 2x + 5
Using synthetic division for the given dividend and divisor the required quotient is given by option a. x^3 + 2x - 5.
Dividend is equal to,
x^4-2x^3+2x^2-9x +10
Divisor is equal to,
( x - 2 )
Using synthetic division we have,
Use double equals to method to simplify the dividend we have,
x^4-2x^3+2x^2-9x +10
= x^4 - 2x^3 + 2x^2 - 4x -5x + 10
= x^3 (x -2) + 2x ( x -2 ) - 5 ( x - 2 )
= ( x - 2 ) ( x^3 + 2x - 5 )
Now ,
Simplify by dividing it,
( x^4-2x^3+2x^2-9x +10 ) ÷ ( x - 2 )
= ( x - 2 ) ( x^3 + 2x - 5 ) ÷ ( x -2 )
= ( x^3 + 2x - 5 )
Therefore, the quotient of the synthetic division for the given dividend is equal to option a . ( x^3 + 2x - 5 ).
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1 The contractor is still paying for the truck (water tanker) and it is covered for insurance. 1.1 nights Write down the Loan term of the truck in years
Answer:
Unfortunately, the provided statement does not contain sufficient information to determine the loan term of the truck.
Step-by-step explanation:
The loan term refers to the length of time over which the loan for the truck is scheduled to be repaid. It is typically determined at the time of purchase and specified in the loan agreement.
To determine the loan term of the truck, we would need to know additional information such as the date of purchase, the loan agreement terms, the payment schedule, and any other relevant details about the loan.
Mark is going to an awards dinner and wants to dress appropriately. He is running behind schedule and asks his little brother to randomly select an outfit for him.
Mark has one blue dress shirt, one white dress shirt, one black dress shirt, one pair of black slacks, one pair of grey slacks, and one red tie. All six of his possible outfits are listed below.
Let
A
AA be the event that Mark's little brother selects an outfit with a white shirt and grey slacks and
B
BB be the event that he selects an outfit with a black shirt.
What is
P
(
A
or
B
)
P(A or B)P, left parenthesis, A, start text, space, o, r, space, end text, B, right parenthesis, the probability that Mark's little brother selects an outfit with a white shirt and grey slacks or an outfit with a black shirt?
Question 1 (2 points)
In a survey of 500 people, 65% said they like dogs. How many people in the survey
said they like dogs?
65
35
325
175
Answer: 325
Step-by-step explanation:
65% is more than half of the 500 people. Half of the number of people is 250. 325 is the only answer over 250
help plssss explainnn!!
Answer:
[tex]xy^8[/tex]
Step-by-step explanation:
Notice if you have the same base you can ADD the exponent, for example:
[tex]x^{-6} x^{7} =x^{-6+7}=x^{1 }=x[/tex]
[tex]y^{6} y^{2} =y^{6+2}=y^{8 }\\[/tex]
so the answer is
[tex]xy^8[/tex]
18% of 50 is what percent of 24
Answer:
37.5%Step-by-step explanation:
please make me brainalist and keep smiling dude I hope you will be satisfied with my answeridentify whether 1352 is perfect square number if not then find the smallest number by which is given number should be multiplied not make them perfect square number .
please help me !!!!!
Answer:
The number by which the given number should be multiplied is 2.--------------------------
Find the prime factors of 1352:
1352 = 2*2*2*13*13 = 2³*13²We need another factor of 2 as a minimum added in order to have even number of same factors:
2⁴*13² = (2²*13)² = (4*13)² = 52²Hence we need to multiply the given number by 2.
(the ine on top) The drawing below shows similar triangles representing a boy and his shadow compared to a tree and its shadow
A.27.4
B.37.3
C.40.0
D.42.0
(on bottom) if the sun is at an angle of 30• from the horizontal and a tree casts a 15- meter shadow in ground which is closest to the height of the tree
A. 7.5
B. 8.7
C. 13.0
D 26.0
The height of the tree is closest to 8.66 meters (option B).
What is angle of elevation?Angle of elevation is the angle between a horizontal line of sight and an object above the line of sight, as measured from the observer's eye.
In other words, it is the angle formed between the observer's line of sight and the line drawn from the observer's eye to the object being observed, when the object is above the observer's eye level.
To solve this problem, we can use the property of similar triangles, which states that the ratios of corresponding sides of similar triangles are equal.
For the boy and his shadow, we have:
height of boy / length of boy's shadow = height of tree / length of tree's shadow
Substituting the values given, we get:
56 / 48 = height of tree / x, where x is the length of the tree's shadow
Solving for the height of the tree, we get:
height of tree = (56 / 48) * x
We are not given the length of the tree's shadow, but we can use the information given in the second part of the problem to find it.
For the tree and its shadow, we have:
height of tree / length of tree's shadow = tan(30)
Substituting the value of the length of the tree's shadow as 15 meters and solving for the height of the tree, we get:
height of tree = 15 * tan(30)
height of tree ≈ 8.66 meters
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10.5.PS-18 Question content area top Part 1 The diagram shows a track composed of a rectangle with a semicircle on each end. The area of the rectangle is square meters 11200. What is the perimeter of the track? Use 3.14 for pi.
divide 1350 into 5:4 and then do the same for 261
Answer:
a) 750 and 600,
b) 145 and 116.
Step-by-step explanation:
A) For 1350 divided to two as 5 : 4, we need to add 5 and 4 first = 9:
Then, with the following, calculate the amount for 5:
[tex]\frac{1350}{9}[/tex] x 5
150 x 5
= 750 for 5, then for 4:
150 x 4
= 600 for 4.
B) For 261 divided with into 5 : 4, we need to add 5 and 4 = 9:
Then, with the following, calculate the amount for 5:
[tex]\frac{261}{9}[/tex] x 5
29 x 5
= 145 for 5. Finally, for 4:
29 x 4
= 116 for 4.
Estimate 61.604-48.44 by first rounding each number to the nearest whole number
Answer:
14
Step-by-step explanation:
When we round 61.604 to the nearest whole number, we get 62, and when we round 48.44 to the nearest whole number, we get 48.
Therefore, we can estimate 61.604 - 48.44 by subtracting 48 from 62:
62 - 48 = 14
So, the estimated answer is 14.
How do you find the slope of (-4, 8) and (4, 2)
To find the slope of a line that passes through two points, you can use the slope formula. The slope formula is:
Slope = (y2 - y1) / (x2 - x1)
Using the points given in your question, the slope formula to find the slope of the line is:
Slope = (2 - 8) / (4 - (-4))
Using the order of operations, the calculation of the slope formula is as follows:
Slope = -6 / 8
Therefore, the slope of the line passing through (-4, 8) and (4, 2) is -3/4.
I will mark you brainiest!
What are the values of each of the exterior angles?
A) 30º, 30º, 60º, 60º
B) 90º, 90º, 180º, 180
C) 60º, 60º, 120º, 120º
Answer:
C) 60º, 60º, 120º, 120º
Step-by-step explanation:
We know the sum of all the angles in a rectangle is 360 degrees, whether it's irregular or not.
Given: x + 2x + 2x + x = 360
Calculate the linear equation, to find x.
x + 2x + 2x + x = 360
3x + 3x = 360
6x = 360 (Divide both sides by 6)
x = 60 degrees.
Then you can calculate the polygons.
x + 2x + 2x + x
For the first x, = 60.
Then for 2x, 60 * 2 = 120.
Then for 2x again, = 120.
Finally for the last x, = 60.
Therefore, the answer is C) 60º, 60º, 120º, 120º.
A car travelling north at 48 km/hr is approaching an intersection. A truck travelling East at 60 km/hr is moving away from the same intersection. How is the distance between the car and the truck changing when the car is 9 m from the intersection and the truck is 40 m from the intersection?
The rate at which the distance between the car and the truck is changing when the car is 9 m from the intersection and the truck is 40 m from the intersection is about 19.187 m/s
What is the rate of change of a function?The rate of change of a function is an indication of how fast the function's output changes per unit change in the input of the function.
Let y represent the distance of the car from the intersection, and let x represent the distance of the truck from the intersection, we get;
The distance between the car and the truck, d, can be obtained from Pythagorean Theorem as follows;
d² = y² + x²
2·d·d/dt = 2·y·dy/dt + 2·x·dx/dt
dy/dt = The speed of the car = 48 km/h = 40/3 m/s
dx/dt = The speed of the truck = 60 km/h = 50/3 m/s
y = The distance of the car from the intersection = 9 m
x = The distance of the truck from the intersection = 40 m
d² = 9² + 40² = 1681
d = √(1681) = 41
d = 41 m
Therefore;
2×41×d/dt = 2×9 × 40/3 + 2 × 40 × 50/3 = 4720/3
d/dt = 4720/3/(2 × 41) = 2360/123 ≈ 19.187
d/dt ≈ 19.187 m/s
The rate of change distance between the car and the truck d/dt is about 19.187 m/s
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- The table shows the number of
miles Michael ran each day over
the past four days. How many
more miles did he run on day 3
than on day 2? Determine if there
is extra or missing information.
By conducting subtraction we know that Michael ran 5 miles more on day 3 than on day 2.
What is subtraction?The four arithmetic operations are addition, multiplication, division, and subtraction.
Removal of items from a collection is represented by the operation of subtraction.
For instance, in the following image, there are 5 2 peaches, which means that 5 peaches have had 2 removed, leaving a total of 3 peaches.
The number that the other number is deducted from is known as a minuend.
Subtrahend: The amount that needs to be deducted from the minuend is known as a subtrahend.
Difference: A difference is an outcome obtained by deducting a subtractor from a minimum.
So, more miles Michael ran on day 3 than on day 2:
= 7 - 2
= 5 miles
Therefore, by conducting subtraction we know that Michael ran 5 miles more on day 3 than on day 2.
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instead of using the values {1, 2, 3, 4, 5, 6} on dice, suppose a pair of dice have the following: {1, 2, 2, 3, 3, 4} on one die and {1, 3, 4, 5, 6, 8} on the other. find the probability of rolling a sum of 6 with these dice. be sure to reduce
Answer:
your answer to the lowest terms
The probability of rolling a sum of 6 with these dice is 1/12.
What percentage of 23 miles is 27 miles
taking 23(origin amount) as the 100%, what is 27 off of it in percentage?
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 23 & 100\\ 27& x \end{array} \implies \cfrac{23}{27}~~=~~\cfrac{100}{x} \\\\\\ 23x=2700\implies x=\cfrac{2700}{23}\implies x\approx 117.39[/tex]
What is the correct numerical expression for "multiply the sum of 7 and 6 by the sum of 4 and 5?"
7 + 6 x 4 + 5
(7 + 6) x (4 + 5)
7 + (6 x 4) + 5
7 + 6 x (4 + 5)
The correct numerical expression for the given statement "multiply the sum of 7 and 6 by the sum of 4 and 5" is (7 + 6) x (4 + 5).
What is an expression?Mathematical statements are called expressions if they have at least two words that are related by an operator and contain either numbers, variables, or both. There are two sorts of expressions in mathematics: numerical expressions, which only contain numbers, and algebraic expressions, which also include variables. A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation.
The given statement, "multiply the sum of 7 and 6 by the sum of 4 and 5", can be represented as:
sum of 7 and 6 = (7 + 6)
sum of 4 and 5 = (4 + 5)
multiply: (7 + 6) x (4 + 5)
Hence, the correct numerical expression for the given statement is (7 + 6) x (4 + 5).
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Answer:
(7 + 6) x (4 + 5).
Step-by-step explanation:
hope this helps!
What’s 9 X 3/9 answer…………………………………….
Answer:
9 x 3/9
= 39 ⋅ 3= 2727/9
27 ÷ 9
= 3Step-by-step explanation:
You're welcome.
A plane is located at C on the diagram. There are two towers located at A and B. The distance between the towers is 7,600 feet, and the angles of elevation are given.
a. Find BC, the distance from Tower 2 to the plane, to the nearest foot.
b. Find CD the height of the plane from the ground, to the nearest foot.
The distance BC from Tower 2 to the plane is equal to 18,674 feet.
The height of the plane from the ground is equal to 7,595 feet.
How to determine the distance from Tower 2 to the plane?In order to determine the distance from Tower 2 to the plane (BC), we would apply the law of sine (sine law) because we have two angles and one side length.
In Mathematics and Geometry, the law of sine is modeled or represented by this mathematical equation:
[tex]\frac{sinA}{a} =\frac{sinB}{b} =\frac{sinC}{c}[/tex]
[tex]\frac{sin8}{7600} =\frac{sin20}{BC}[/tex]
BCsin8 = 7600sin20
BC = 2599.35/0.1392
Distance, BC = 18,673.50 ≈ 18,674 feet.
Next, we would determine the height of the plane from the ground (CD);
sin24 = CD/18,674
CD = 18,674sin24
Height, CD = 7,595.40 ≈ 7,595 feet.
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Answer:
a) The length of BC is 15,052 ft to the nearest foot.
b) The length of CD is 6,122 ft to the nearest foot.
Step-by-step explanation:
Part aAngles on a straight line sum to 180°. Therefore:
[tex]\implies m \angle ABC +24^{\circ}=180^{\circ}[/tex]
[tex]\implies m \angle ABC =156^{\circ}[/tex]
Interior angles of a triangle sum to 180°. Therefore:
[tex]\implies m \angle BCA+16^{\circ}+156^{\circ}=180^{\circ}[/tex]
[tex]\implies m \angle BCA=8^{\circ}[/tex]
[tex]\boxed{\begin{minipage}{7.6 cm}\underline{Sine Rule} \\\\$\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}$\\\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are the angles. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides opposite the angles.\\\end{minipage}}[/tex]
Use the Sine Rule to find the length of BC.
[tex]\implies \dfrac{AB}{\sin BCA}=\dfrac{BC}{\sin CAB}=\dfrac{AC}{\sin ABC}[/tex]
[tex]\implies \dfrac{7600}{\sin 8^{\circ}}=\dfrac{BC}{\sin 16^{\circ}}[/tex]
[tex]\implies BC=\dfrac{7600\sin 16^{\circ}}{\sin 8^{\circ}}[/tex]
[tex]\implies BC=15052.0746...[/tex]
[tex]\implies BC=15052\; \sf ft\;(nearest\;foot)[/tex]
Therefore, the length of BC is 15,052 ft to the nearest foot.
Part bInterior angles of a triangle sum to 180°. Therefore:
[tex]\implies m \angle BCD+24^{\circ}+90^{\circ}=180^{\circ}[/tex]
[tex]\implies m \angle BCD=66^{\circ}[/tex]
[tex]\boxed{\begin{minipage}{9 cm}\underline{Sine trigonometric ratio} \\\\$\sf \sin(\theta)=\dfrac{O}{H}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]
To find the length of CD, use the sine trigonometric ratio.
[tex]\implies \sin 24^{\circ}=\dfrac{CD}{BC}[/tex]
[tex]\implies CD=BC\sin 24^{\circ}[/tex]
Substitute the found value of BC into the equation:
[tex]\implies CD=\left(\dfrac{7600\sin 16^{\circ}}{\sin 8^{\circ}}\right)\sin 24^{\circ}[/tex]
[tex]\implies CD=6122.23031...[/tex]
[tex]\implies CD=6122\; \sf ft\;(nearest\;foot)[/tex]
Therefore, the length of CD is 6,122 ft to the nearest foot.
true/false. The p-value of a test is the probability of observing a test statistic at least as extreme as the one computed, given that the null hypothesis is true.
True. The p-value is a probability value that measures the power of evidence in against to the null hypothesis in a statistical test.
Mainly, it represents the possibility of staring at a test statistic as a minimum as extreme as the one computed, assuming that the null hypothesis is genuine.
If the p-value is small, commonly less than a chosen significance stage (e.g., 0.05), it shows that the determined data is unlikely to have took place by danger alone and provides proof against the null hypothesis. alternatively, a large p-value suggests that the determined information is consistent with the null speculation, and the evidence isn't sturdy enough to reject it.
Consequently, the p-value is an critical tool in statistical inference, permitting researchers to draw conclusions about the population based totally on pattern information and degree the extent of uncertainty in their outcomes.
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Mia has a collection of vintage action figures that is worth $190. If the collection appreciates at a rate of 6% per year, which equation represents the value of the collection after 5 years?
The equation that represents the value of the collection after 5 years is:
Value of collection after 5 years = 190 x (1 + 0.06)^5
Explanation:
To calculate the value of the collection after 5 years, we need to use the compound interest formula. This formula is represented as A = P x (1 + r)^n, where P is the principal amount (initial value of the collection), r is the rate of interest (in this case, 6%), and n is the number of years (in this case, 5).
Therefore, the equation for the value of the collection after 5 years is:
Value of collection after 5 years = 190 x (1 + 0.06)^5
This can also be written as:
Value of collection after 5 years = 190 x 1.31 (1.31 is the result of (1 + 0.06)^5)
Therefore, the value of the collection after 5 years is $246.90.
Answer: 254.26
Step-by-step explanation:
FAST
Write two expressions to represent the following situation. Then, find the answer.
When Nathan went to bed, the outside temperature was 28°F. When he woke up the next morning, the temperature had decreased to -13°F. By how many degrees did the temperature change during the overnight hours
The temperature changed by 41°F during the overnight hours, decreasing from 28°F to -13°F.
How is an expression determined?The difference in temperature from 28°F to -13°F can be shown in one of two ways:
Temperature change equals final temperature - The starting temperatureTemperature change: (-13°F) - (28°F)Temperature change: -41°FTemperature change = final temperature minus initial temperature; temperature change = -13°F minus 28°F; temperature change = -41°F; temperature change = 41°F.To calculate the change in temperature, the first exponent equation subtracts the initial temperature from the end temperature. The change in this instance is negative and points to a drop in temperature.
The absolute value function is employed in the second statement to guarantee a positive result regardless of whether the temperature rose or fell. The result is the same as the first expression in this instance, but with a positive sign.
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which statements are true about the reflectional symmetry of a regular heptagon? select two options. it has only 1 line of ref
the regular heptagon has only one line of reflectional symmetry, and it passes through the center of the heptagon. This property is common to all regular polygons, and it is related to their rotational symmetry.
The statements that are true about the reflectional symmetryof a regular heptagon are:
It has only one line of reflectional symmetry.
The line of reflectional symmetry passes through the center of the heptagon.
A regular heptagon is a polygon with seven equal sides and angles. Each vertex of the heptagon is equidistant from the center of the heptagon, and the lines connecting the center to the vertices divide the heptagon into seven congruent triangles.
To understand the reflectional symmetry of the regular heptagon, we need to define what it means. Reflectional symmetry is a type of symmetry where a figure is symmetric with respect to a line. In other words, if we fold the figure along this line, one half will coincide with the other half.
In the case of the regular heptagon, we can observe that if we draw a line passing through the center of the heptagon and perpendicular to any of its sides, we obtain a line of reflectional symmetry. This line divides the heptagon into two congruent halves. However, if we draw any other line of reflectional symmetry, it will not coincide with the sides of the heptagon, and therefore, it will not divide the heptagon into congruent halves.
Therefore, we conclude that the regular heptagon has only one line of reflectional symmetry, and it passes through the center of the heptagon. This property is common to all regular polygons, and it is related to their rotational symmetry.
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A rectangular picture is 7 inches by 5 inches and has a border of uniform width surrounding it. If the area of the picture and the border is 80 square inches find the width of the border
The width of the rectangle border is 3 in.
What is area of rectangle?
The area a rectangle occupies is the space it takes up inside the limitations of its four sides. The dimensions of a rectangle determine its area. In essence, the area of a rectangle is equal to the sum of its length and breadth.
Here We know that ,
Area of the rectangle = length* width square unit.
Here area of the picture and border is 80 [tex]in^2[/tex] Then,
=> (7+w)*(5+w)=80
=> [tex]35+5w+7w+w^2=80[/tex]
=> [tex]12w+w^2=45[/tex]
=> [tex]w^2+12w-45=0[/tex]
=> [tex]w^2+15w-3w-45=0[/tex]
=> w(w+15)-3(w+15)=0
=> (w-3)(w+15)=0
=> w=3 , w=-15( negative is neglected)
Hence the width of the rectangle border is 3 in.
To learn more about area of the rectangle refer the below link
https://brainly.com/question/2607596
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