Answer: For the linear relationship in A, the y-intercept is the point where the line crosses the y-axis. This point represents the starting balance on Ailee's gift card before she makes any purchases.
The y-intercept of this linear relationship is the point (0, 20), which represents the fact that Ailee's gift card has a starting balance of $20 before she makes any purchases.
For the linear relationship in B, the y-intercept is the point where the line crosses the y-axis. This point represents Duncan's starting elevation before he begins to hike.
The y-intercept of this linear relationship is the point (0, 1000), which represents the fact that Duncan starts his hike at an elevation of 1000 feet.
Step-by-step explanation:
What are the 14 types of angles?
Fourteen types of angles are Acute Angles, Obtuse Angles, Right Angles, Straight Angles, Reflex Angles, Positive Angles, Negative Angles, Complementary angles, Supplementary angles, Linear Pair, Adjacent angles, Vertically Opposite angles, Alternate interior angles and Alternate exterior angles.
There are mainly 5 types of angles based on their magnitude. They are Acute Angles, Obtuse Angles, Right Angles, Straight Angles and Reflex Angles.
Positive Angles and Negative Angles are the angles based on the direction of measurement or the direction of rotation.
When two angles are paired, then there exist different angles, such as Complementary angles, Supplementary angles, Linear Pair, Adjacent angles, Vertically Opposite angles, Alternate interior angles and Alternate exterior angles.
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A boat heading out to sea starts out at Point AA, at a horizontal distance of 862 feet from a lighthouse/the shore. From that point, the boat’s crew measures the angle of elevation to the lighthouse’s beacon-light from that point to be 15^{\circ}
∘
. At some later time, the crew measures the angle of elevation from point BB to be 8^{\circ}
∘
. Find the distance from point AA to point BB. Round your answer to the nearest tenth of a foot if necessary
The distance from point A to point B is 781.5 ft.
Since the angle of elevation from point A to the lighthouse is 15 degrees, use the tangent function to find the height of the lighthouse. Let x be the height of the lighthouse,
tan(15°) = x / 862
Solve for x.
x = 862 (tan(15°))
Similarly, let y be the distance from point B to the lighthouse,
tan(8°) = x / y
Solve for y.
tan(8°) = 862 (tan(15°)) / y
y = 862 (tan(15°)) / tan(8°)
y = 1643.45 feet
Subtract 862 from 1643.45 to get the distance from point A to point B.
distance from point A to point B = 1643.45 - 862 = 781.45 ft = 781.5 ft
Therefore, the distance from point A to point B is 781.5 ft.
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Pls help
(3 x 8 x 5)⁷
To evaluate (3 x 8 x 5)⁷, you need to first multiply 3, 8, and 5 together to get the base, then raise that result to the seventh power.
What does a math exponent mean?
The number of times a number has been multiplied by itself is referred to as an exponent. For instance, the expression 2 to the third (written as 23) signifies 2 x 2 x 2 = 8. 23 and 2 x 3 = 6 are not equivalent. Keep in mind that any number is itself when raised to the power of 1.
So,
(3 x 8 x 5)⁷ = (120)⁷ = 120 x 120 x 120 x 120 x 120 x 120 x 120
= (1.2 x 10^2)^7 = 1.2 x 10^2 x 1.2 x 10^2 x 1.2 x 10^2 x 1.2 x 10^2 x 1.2 x 10^2 x 1.2 x 10^2
=1.2^7 x 10^14 = 1.2^7 x 10^14
=4096 x 10^14
=4.096 x 10^17
Therefore (3 x 8 x 5)⁷ = 4.096 x 10^17
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4382 round 1 significant figure
Answer:
4382 contains 4 significant figures, 4382 round to 1 significant figure is 4000.
Improper fraction for 4 1/5
How do u solve this?
Answer: [tex]3x^4 / 2y^4[/tex]
Step-by-step explanation: [tex](3x7x^6y^5)divide(2x7x^2y^9)[/tex] then [tex]x^6 divided by x^2 = x(^6 ^- ^2) = x^4[/tex] then
[tex]y^5 divided by y^9 = y(^5 ^- ^9) = y(^-^4) = 1/y^4[/tex] then
Canceling out 7 as it appears on both sides of the fraction line.
Hope this is clear and is helpful
A quantity with an initial value of 7800 decays continuously at a rate of 0. 1%
per hour. What is the value of the quantity after 1. 25 days, to the nearest
hundredth?
The question is asking for the value of a quantity that decays continuously at a rate of 0.1% per hour. We are given that the initial value of the quantity is 7800 and are asked to find the value after 1.25 days (30 hours).
What is a ratio in mathematics?
A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ratio 4:3).
We can use the following formula to find the final value of the quantity after a certain amount of time:
final value = initial value * (1 - decay rate)^time
Where decay rate is given as a decimal (0.1% = 0.001)
Plugging in the given values, we get:
final value = 7800 * (1 - 0.001)^30
The final value is around 7396.65
Rounding the final value to the nearest hundredth, the final value after 1.25 days is:
7396.65 ≈ 7396.66
The value of the quantity after 1.25 days, to the nearest hundredth is 7396.66.
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What is the answer of 7x 5 2x?
The answer to the given that is 7x 5 2x question is 70
Explanation: In this case the answer is calculated by performing the operations in the order they are written. First, we multiply 7 and 5, which gives us 35. Then, we multiply 2 and x, which gives us 2x. Finally, we add 35 and 2x, resulting in 70
Multiplication is an arithmetic operation that involves multiplying two numbers together to produce a third number. It is usually represented by the multiplication sign (×) and is one of the four basic operations in mathematics. Hence the correct answer is 70.
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Owen is designing a rectangular garden whose length is 25 feet he needs to put fencing all around the exterior of the garden and wants to use less than 8 feet of fencing
Answer:
To enclose the rectangular garden, Owen will need to put fencing along the length of the garden, which is 25 feet, and along the width of the garden. He wants to use less than 8 feet of fencing, so the width of the garden must be less than 8 feet.
The total amount of fencing needed will be equal to the length of the garden plus the width of the garden, multiplied by 2 (since there are two sides to the garden for each of the length and width).
For example, if the width of the garden is 5 feet, the total amount of fencing needed will be 25 + 5 + 25 + 5 = 60 feet, which is less than 8 feet.
So, the width of the garden can be any value less than 8 feet.
Step-by-step explanation:
You can read 12 pages of a book in 15 minutes.
How many hours will it take you to read a 312-page book?
It will take you 6.5 hours to read a 312-page book
How many hours will it take you to read a 312-page book?From the question, we have the following parameters that can be used in our computation:
Rate = 12 pages of a book in 15 minutes
This means that
Rate = 12 pages/15 minutes
Convert to per hour
Rate = 12 pages/0.25 hour
Evaluate
Rate = 48 pages per hour
For a 312-page book, we have
Time = 312 pages/48 pages per hour
Evaluate
Time = 6.5 hours
Hence, the time is 6.5 hours
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Nikki shovel snow at a constant rate Nikki plot points on the coordinate plane below to show how many scoops of snow they can shovel in different lengths of time which of the following ordered pairs could Nikki add to the graph
Answer:
2,30
the difference between 3,45 and 4,60 is 1,15. So if you add 1,15 and 1,15 it will be 2,30. you can't do 1,10 because the rate is 1,15 neither can you do 6,85 because 5,75 plus 1,15 is 6,90 not 6,85 so 2,30 is the final choice.
Give an example of a radical expression and a rational exponent. Convert each to the other form. Simplify one example that utilizes at least one exponent rule.
Radical expression can be defined as the expression containing square root and rational exponent , which is in the form of p/q form.
What is an Algebraic expression ?
Algebraic expression can be defined as combination of variables , constants and exponents.
Radical expression, in which if the expression contains square root than it called as the radical expression.
Examples are : - [tex]\sqrt{7}[/tex] , [tex]\sqrt{x}[/tex] and etc .
Rational exponent , in which it is in the form of p/q is called as the rational exponent .
Examples are :- 5/8 , 6/9,8/7 and etc .
Hence, Radical expression can be defined as the expression containing square root and rational exponent , which is in the form of p/q form.
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I need help on this question. I dont understand it.
a. The system of equations is given as follows:
35x = 15 + 32x.
The solution is given as follows:
x = 5.
b. The meaning of the solution is that the cost to purchase 5 jackets in each company is the same.
c. Gabriela should choose Anastasia's Monogram, as the function has a lower numeric value when x = 10.
How to model the situation?The cost per jacket for each company is constant, hence a linear function is used to model the situation.
The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
m is the slope, representing the cost paid per each jacket.b is the y-intercept, representing the design fee, which is a one-time payment.Hence the functions for each company are given as follows:
Anastasias's Monograms: y = 15 + 32x.Monograms Unlimited: y = 35x.The system of equations is used to find when both will have the same cost, as follows:
35x = 32x + 15
3x = 15
x = 5 jackets.
For 10 jackets, the costs are given as follows:
Anastasias's Monograms: y = 15 + 32(10) = $335 -> lower cost.Monograms Unlimited: y = 35(10) = $350.More can be learned about linear functions at https://brainly.com/question/24808124
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The football team would like to purchase tickets to see a U of M football game. StubHub is charging $45 per ticket along with a handling fee of $4 per ticket. The shipping charge for all of the tickets is a flat fee of $20. How many players can attend the game if their budget is $1500? Write and solve an inequality that models this situation
Answer: Let x be the number of players who can attend the game. The total cost for the tickets is $45 per ticket * x tickets + $4 per ticket * x tickets + $20 flat fee = $49x + $20. We can write this as an inequality as follows:
49x + 20 <= 1500
To solve this inequality, we need to isolate the x term on one side of the inequality. We can do this by subtracting 20 from both sides:
49x <= 1480
Then, we can divide both sides by 49 to find the value of x:
x <= 30
Thus, if their budget is $1500, the football team can purchase tickets for at most 30 players to attend the game.
Step-by-step explanation:
35PTS 35PTS answer the whole question, don’t explain.
The equation of the straight line in slope - intercept form will be y = (1/4)x - 2.
What is the slope - intercept form of a line?The slope - intercept form of a line is -
y = mx + c ... { 1 }
where -
{m} is slope of line.
{c} is y - intercept of the line.
Given is the slope of the line as {m} = 1/4 and the y - intercept as {c} = -2.
From Eq { 1 }, we can write the slope - intercept form as -
y = mx + c
y = (1/4)x - 2
Therefore, the equation of the straight line in slope - intercept form will be y = (1/4)x - 2.
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EMERGENCY i need thissss helpp. tysmm <33
In a closed system, an object with a mass of 1.5 kg collides with a second object. The two objects then move together at a velocity of 50 m/s. The total momentum of the system is 250 kg⋅m/s. What is the mass of the second object?
The mass of the second object will be 3.5 kg.
What is momentum?In Newtonian mechanics, momentum is calculated as the sum of an object's mass and velocity. It has both a magnitude and a direction, making it a vector quantity.
According to the collision theory, for a chemical reaction to take place, the reacting particles must come into contact with one another. The frequency of collisions affects the reaction's rate. According to the idea, responding particles frequently encounter without reacting.
The final momentum will be calculated by the expression given below,
(m₁ + m₂ ) V=250
( 1.5 + m₂ 0 x 50 = 250
1.5 + m₂ = 5
m₂ = 5 - 1.5
m₂ = 3.5 kg
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The ff. test scores were recorded by job applicants: 65, 68, 70, 75, 88, 90, 90, 91, 92. What is the mode
In the recorded test scores 90 is the mode, as it appears most frequently in the set of ff test scores.
What do you meant by mode?Job applicants submitted their ff test results, which were as follows: 65, 68, 70, 75, 88, 90, 90, 91, and 92. Following that, the Mean (Average) is 81, Median (Middle) is 88, and Mode (Most Common) is 90. The mode can be calculated quite easily.
After sorting the numbers in a set according to their order—lowest to highest or highest to lowest—count how many times each number appears in the group.
The mode is the one that is most prevalent. the quantity that happens the most frequently, or the quantity that appears the most frequently overall. The mode of the numbers 4, 2, 4, 3, 2, and 2 is 2, since it appears three times, more than any other number. The most frequent number in a set of numbers is called the mode.
To find the mode, we first need to put the test scores in order from lowest to highest:
65, 68, 70, 75, 88, 90, 90, 91, 92
Then we can count how many times each number appears:
65: 1 time
68: 1 time
70: 1 time
75: 1 time
88: 1 time
90: 2 times
91: 1 time
92: 1 time
As we can see, the number 90 appears the most with 2 times, so the mode of this set of data is 90.
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what is the quotient of 6x^3+2x-x/x where x≠0
Answer:
6[tex]x^{2}[/tex] + 1
Step-by-step explanation:
[tex]\frac{6x^{3}+ 2x-x }{x}[/tex] combine 2x -x = x
[tex]\frac{6x^{3} + x}{x}[/tex]
[tex]\frac{x(6x^{2} + 1) }{x}[/tex] the x's cancel out
6[tex]x^{2}[/tex] + 1
1.) what is the length of the apothem in this regular pentagon?
2.) What is the area of the regular pentagon?
3.)What is the length of the apothem in this regular pentagon ?
On solving the provided question, we can say that - the each angle of pentagon is x = 108
what is a pentagon?A pentagon is a polygon with five sides that is used in geometry. The inner angles of a straightforward pentagon add up to 540°. Simple or self-intersecting pentagons are both possible. A pentagram is a self-intersecting regular pentagon. Five angles and all sides of a regular pentagon are equal. It is referred to as an irregular pentagon if the side lengths and angle measurements do not match. All outside angles, as far as we are aware, balance out inside angles. The polygon's exterior angle total is therefore equal to n(360°/n). There are five sides to a pentagon, therefore n must equal five. Consequently, 5(360°/5) = 360° is the sum of the pentagon's outer angles.
since all sum of pentagon is 540
so, 5x = 540
x = 108
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How would I do this?
[tex]~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{28p^5-8p^4 + 40p^2}{4p^3}\implies \cfrac{28p^5}{4p^3}-\cfrac{8p^4 }{4p^3}+\cfrac{ 40p^2}{4p^3}\implies 7p^5 p^{-3}-2p^4 p^{-3}+10p^2p^{-3} \\\\\\ 7p^{5-3}-2p^{4-3}+10p^{2-3}\implies 7p^2-2p+10p^{-1}\implies 7p^2-2p+\cfrac{10}{p}[/tex]
Where does the line 2x 3y 6 will intersect Y axis at?
The graph of the given line 2x+3y=6 intersects the Y-axis at (0,2).
For the graph of linear equation to intersect the Y-axis, its X-co-ordinate should be zero or the abscissa is zero as Y-axis as the equation of Y-axis is x=0. Also the set of coordinates should satisfy the equation.
According to the first condition the x-coordinate of the equation should be zero so in equation 2x+3y=6 substituting the value of x as zero 2(0)+3y=6
3y=6
y=6/3=2
So at point (0,2), the graph of the given line 2x+3y=6 intersects the Y-axis.
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Circumference question
1. Suppose a bottle of Buckley's has a radius of 2cm. You need to
create a label for this product. What is the length of this label?
2. Assumes the company uses 22cm x 12cm boxes for delivery to stores. How many vials will be in each box?
suppose the price of each vial is $5.00. What is the cost of a box?
12.57 cm is the length of the label on bottle.
What is Circle?A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.
Given that a bottle of Buckley's has a radius of 2cm
You need to create a label for this product
We need to find the length of this label.
Means we need to find the circumference of the bottle.
The formula for circumference is
C=2πr
Given radius is 2cm
C=2×3.14×2
C=12.57 cm
Hence, 12.57 cm is the length of the label on bottle.
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Freddy is helping buy ingredients for salads for the school spaghetti dinner he bought 10 pounds of onions at $0.69 per pound 100 pounds of tomatoes at $0.99 pound 1,000 pounds of break cumbs at $0.09 per pound and 100 pounds of lettuce at $0.69 per pound which of the items he bought cost the most?
Answer:
Answer: Tomatoes If you multiply 10 x 0.69 (for onions) it would be 6.9If you multiply 100 x 0.99 (for tomatoes) it would be 99Lastly, if you multiply 100 x 0.69 (for lettuce) if would be 69Which are the most? Tomatoes.~ Hope this helps
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C is the centroid of △ABD. find the following:
1. If CD = 12, find FC.
2. If BG= 15, find BC.
3. If AE = 21, find EC.
4. If FA = 6, find BA.
5. If CG = 3.5, find BC.
Answer:
1. FC = 6
2. BC = 10
3. EC = 7
4. BA = 12
5. BC = 7
Step-by-step explanation:
⭐What is the centroid of a triangle?
the intersection of the medians of a trianglethe medians bisect each side in halfeach median is split in the ratio of 2:1each median has a segment from the vertex to the centroid. that segment is 2/3 the distance from said vertex to the opposite side of said vertexeach median has a segment from the centroid to a side opposite of a vertex. that segment is 1/3 the distance from said vertex to said opposite sideUsing the properties of a centroid, we can determine the lengths the problem is asking us for.
1. If CD = 12, find FC.
each median is split in the ratio of 2:1So if the median we need to look at is FD,
then CD : FC = 2:1
[tex]\frac{CD}{FC} = \frac{2}{1}\\\\\\\\[/tex] . . . . . . . . write the proportion
[tex]\frac{12}{FC} = \frac{2}{1}[/tex] . . . . . . . . . substitute the known values
[tex]12 = 2FC[/tex] . . . . . . cross multiply
[tex]FC = 6[/tex] . . . . . . divide both sides by 2 to isolate FC
∴ FC = 6
2. If BG = 15, find BC
each median has a segment from the vertex to the centroid. that segment is 2/3 the distance from said vertex to the opposite side of said vertexSo if BG = 15, and BC is the distance from a vertex to the centroid, then BC is 2/3 of BG.
[tex]BC = \frac{2}{2}BG[/tex] . . . . . write equation
[tex]BC = \frac{2}{3}(15)[/tex] . . . . . substitute known values
[tex]BC = \frac{30}{3}[/tex] . . . . . . . . multiply numerators
[tex]BC = 10[/tex] . . . . . . . . compute
∴ BC = 10
3. If AE = 21, find EC
each median has a segment from the centroid to a side opposite of a vertex. that segment is 1/3 the distance from said vertex to said opposite sideSo if AE is the full median, and EC is the distance from the centroid to the opposite side of a vertex, then EC is 1/3 of AE.
[tex]EC = \frac{1}{3}AE[/tex] . . . . . . . . write equation
[tex]EC = \frac{1}{3}(21)[/tex] . . . . . . . . substitute known values
[tex]EC = \frac{21}{3}[/tex] . . . . . . . . . . . multiply the numerators
[tex]EC = 7[/tex] . . . . . . . . . . . . compute
∴ EC = 7
4. If FA = 6, find BA
the medians bisect each side in halfIf BA is a side length that is bisected by a median, then FA is 1/2 of BA.
[tex]FA = \frac{1}{2}BA[/tex] . . . . . . . make equation
[tex]FA = \frac{1}{2}(6)[/tex] . . . . . . . . substitute known values
[tex]FA = \frac{6}{2}[/tex] . . . . . . . . . . . multiply the numerators
[tex]FA = 3[/tex] . . . . . . . . . . . compute
∴ FA = 3
5. If CG = 3.5, find BC
each median is split in the ratio of 2:1each median is split in the ratio of 2:1So if the median we need to look at is BG,
then BC : CG = 2:1
[tex]\frac{BC}{CG} = \frac{2}{1}[/tex] . . . . . . . . . . create the proportion
[tex]\frac{BC}{3.5} = \frac{2}{1}[/tex] . . . . . . . . . . substitute the known values
[tex]BC = 2(3.5)\\[/tex] . . . . . . . . cross multiply
[tex]BC = 7[/tex] . . . . . . . . . . . . . compute
∴ BC = 7
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To arrive at his appointment on time, Mr. Jones needs to drive from his home at the average speed of 60 mph. But traffic is heavy, so Mr. Jones drives 15 mph slower than planned and arrives at the appointment 20 minutes late. How many miles from his home is the appointment
On solving the provided question, we can say that by equation 60 miles from his home is the appointment
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
for d and t
60 = d/t
45 = d / t + 0.33
60t = d
45( t + 0.33) = d
60t = 45t + 15
t = 1 hour
d = 60 X 1 miles = 60 mile
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Product sales by month (in thousands) Month Product 1 Product 2 Product 3 Product 4 Product 5 January 228 964 429 169 456 February 188 784 414 238 520 March 222 816 422 235 562 April 222 738 414 214 624 May 176 710 420 303 670 June 120 697 486 768 342 Popular products are often placed in the window to attract customers into the store. Based on this information, which product should be displayed in the window in July?
Based on the information provided, it seems that the product that should be displayed in the window in July is Product 5.
What is mean?A dataset's mean is the sum of all values divided by the total number of values, often known as the arithmetic mean (as opposed to the geometric mean). Often referred to as the "mean," this is the most often used measure of central tendency. Simply dividing the dataset's total number of values by the sum of all of those values yields this result. Both raw data and data that have been combined into frequency tables can be used for calculations. Average refers to a number's average. It is straightforward to calculate:
Divide by how many digits there are after adding up all the digits. the total divided by the count.
Based on the information provided, it seems that the product that should be displayed in the window in July is Product 5. This can be determined by looking at the sales data for each product over the months of January through June.
In every month, Product 5 has the highest sales figures among all the products. This suggests that Product 5 is the most popular among customers and would likely attract the most attention if it were to be placed in the window.
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Katie plans to paint four toy chests that have the given net. She will buy 10-oz cans of paint that cover 933 square inches each
Two cans of paint are needed to cover the toy chest of 1866 in²
Area:
The area is the amount of space occupied by a two-dimensional object or figure. Area (A) of the rectangle is:
A = length * breadth.
Area of A = 13 * 16 = 208 in²
Area of B = 13 * 25 = 325 in²
Area of C = 25 * 16 = 400 in²
Area of D = 13 * 25 = 325 in²
Area of E = 13 * 16 = 208 in²
Area of F = 25 * 16 = 400 in²
1) Combined Area = 208 + 208 = 416 in²
2) Combined Area = 325 + 325 = 650 in²
3) Combined Area = 400 + 400 = 800 in²
4) Combined Area = 416 + 650 + 800 = 1866 in²
5) Amount of paint = 1866 in² / 933 in² = 2
Therefore, Two cans of paint are needed to cover the toy chest of 1866 in²
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1. Rewrite the equation 5(x – 3) = x + 13 with 6 substituted for x. Write a question mark over the equal sign to show that you're testing to see if the equation is true. (2 points)
x = 6 does not satisfy the given equation.
What is an equation?An equation is a mathematical statement that shows that two mathematical expressions are equal.
Given that an equation, 5(x – 3) = x + 13
Checking if x = 6 satisfy the equation or not,
5(x – 3) ? x + 13
5(6-3) ? 6+13
5×3 ? 19
15 ≠ 19
Hence, x = 6 does not satisfy the equation.
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What is undecidable language?
Therefore , the solution of the given problem of algorithm comes out to be when the language L of all yes cases to a decision problem P cannot be decided, the problem is said to be "undecidable."
Describe an algorithm.Algorithms exist to identify, solve, and frequently automate a solution to a particular problem; regardless of the situation, they are essentially problem solvers of expression.
In area of beginning textbooks, algorithms are typically introduced as "a set of phases to solve a problem."
Here,
Alternatively, a Turing computer that halts for all inputs cannot recognize a language for whose membership cannot be determined by an algorithm.
It is known as undecidable language.
There is no Turing Machine for an undecidable language that accepts the language and decides on each input string (TM can make decision for some input string though).
When the language L of all yes cases to a decision problem P cannot be decided, the problem is said to be "undecidable."
Therefore , the solution of the given problem of algorithm comes out to be when the language L of all yes cases to a decision problem P cannot be decided, the problem is said to be "undecidable."
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