[tex] \longmapsto \: 2(2x - 1 + x + 9) = 103 \\ \\ \longmapsto \: 2(3x + 8) = 106 \\ \\ \longmapsto \: 6x +16 = 106 \\ \\ \longmapsto \: x = \frac{90}{6} \\ \\ \longmapsto \: x = 15 [/tex]
So,
[tex]l = 2 \times 15 - 1 = 29 \\ \\ b = 2 + 15 = 17[/tex]
The perimeter of a rectangle is given by the formula P = 2(l + w), where P is the perimeter, l is the length, and w is the breadth (or width) of the rectangle.
In this case, we know that the perimeter is 106 cm, so we can set up the equation:
106 = 2(l + (X + 9))
106 = 2l + 2X + 18
We also know that the length of the rectangle is 2X - 1, so we can set this equal to l:
2X - 1 = l
Now we have a system of two equations with two unknowns (l and X). We can substitute the value of l from the second equation into the first equation and solve for X:
106 = 2(2X - 1 + (X + 9))
106 = 2(3X + 8)
106 = 6X + 16
90 = 6X
X = 15
Now that we know the value of X, we can substitute it back into the equation for the length of the rectangle to find the length:
l = 2X - 1 = 2(15) - 1 = 29 cm
And then we can use the value of X again to find the breadth:
w = X + 9 = 15 + 9 = 24 cm
So the length of the rectangle is 29 cm and the breadth is 24 cm.
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You lose 0.3 point for stepping out of bounds during a gymnastics floor routine. Your final score is 9.124. Write and solve an equation to find your score $x$ without the penalty.
Your score without the penalty is 9.424.
To find your score without the penalty, we need to add 0.3 points back to your final score of 9.124. We can use the linear equation:
x = 9.124 + 0.3
This equation represents the original score, represented by x, plus the penalty of 0.3. To solve for x, we need to add 0.3 to 9.124:
x = 9.124 + 0.3
x = 9.424
So your score without the penalty is 9.424.
In this equation, x is being used to represent the original score, before the 0.3-point penalty was applied. The equation x = 9.124 + 0.3 represents that the original score was 9.124 and 0.3 points were taken off due to stepping out of bounds. By solving the equation, we are able to find the original score without the penalty which is 9.424
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Charlie runs laps around a track. The table shows how long it takes him to run different numbers of laps. How long would it take Charlie to run 5 laps?
Number of laps 2 4 6 8 10
Time (min) 18 36 54 72 90
It will take Charlie ___
minutes to run 5 laps.
270 mins - 10 laps
xmins -5 laps
(cross multiply)
270*5=10x
10x=1350
x= 1350/10
x=135 mins
Its pre-algebra. I need it fast
Answer:
Obtuse and isosceles
Step-by-step explanation:
obtuse because an angle is more than 90* and isosceles because two sides are equal.
Hope this helps!
In 1800, the slave population in the United States of America was 893,602. By 1860, the slave population rose to about 1,953,760. How large of a percentage did the slave population increase by from 1800 to 1860?
To find the percentage increase of the slave population from 1800 to 1860, we can use the following formula:
What does math's % mean?
In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).
percentage increase = (new value - original value) / original value x 100
We know that in 1800 the slave population was 893,602 and in 1860 the slave population was 1,953,760. So we can plug in these values into the formula:
percentage increase = (1,953,760 - 893,602) / 893,602 x 100
percentage increase = (1,060,158) / 893,602 x 100
percentage increase = 1.1885 x 100
percentage increase = 118.85
So, the slave population increased by 118.85% from 1800 to 1860.
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What is the midpoint of the x intercepts of x 4 )( x 4?
The midpoint of the x-intercepts of f(x) = (x - 4)(x + 4) is (0, 0).
The midpoint of a line segment is known as the midpoint in geometry. It is the centroid of the segment and of the ends, and it is equally distant from both of them. It cuts the section in half.
A compass and straightedge setup can be used to locate the midpoint of the line segment they determine given two points of interest. By initially building a lens out of circular arcs with equal radii centered at the two endpoints and joining the cusps of the lens, one can determine the midpoint of a line segment immersed in a plane. The midpoint of the segment is then the place where the line joining the cusps intersects the segment.
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How do you solve 3 equations with 3 unknowns on a Casio calculator?
The process to solve 3 equations with 3 unknown is explained below.
The term equation is known as a mathematical statement that is made up of two expressions connected by an equal sign.
The process of 3 equation with 3 unknown variable is explained step by step as follows:
First of all we have to write all the equations in standard form cleared of decimals or fractions.
And then we have to choose a variable to eliminate them then we have to choose any two of the three equations and eliminate the chosen variable.
After that we have to select a different set of two equations and eliminate the same variable as in Step 2.
Now, we have to solve the two equations from steps 2 and 3 for the two variables they contain.
And then we have to substitute the answers from Step 4 into any equation involving the remaining variable.
And then finally we have to check the solution with all three original equations.
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Clara and erin volunteered at an animal shelter a of 9 1/5 hours. Clara worked for 41/3 hours. How many hours did erin work?Yon can use fraction strips to solve this problem
If $10,000 is invested at x percent simple annual interest for n years, the total amount of interest would be F = 10,000n(x/100)
What is simple interest?Simple interest is calculated based on the principle of a loan or the initial deposit into a savings account. Simple interest doesn't compound, so a creditor will only charge interest on the principal sum, and a borrower will never be required to pay interest on interest that has already accrued.
F = P(1+rt), formula for simple rate of interest
Here,
=> Future value is F
Present value is P
=> Rate is R
=> Time is t
Substituting x for r
And, n for t
Also, 10,000 in for P
F = 10,000(1+xn)
The formula tells us principal + interest,
F = 10,000(xn)
Now, to get the x into terms of a percentage,
F = 10,000(n * x/100)
F = 10,000n(x/100)
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There is a line that includes the point (9,–8) and has a slope of –19. What is its equation in point-slope form?
Answer:
y +8 = -1/9(x -9)
Step-by-step explanation:
You want the point-slope form of the equation of the line through point (9, -8) with slope -1/9.
Point-slope formThe equation of the line through point (h, k) with slope m is ...
y -k = m(x -h)
You have (h, k) = (9, -8), and m = -1/9. Using these values, the equation is ...
y +8 = -1/9(x -9)
store a charges $8 per movie plus a $10 shipping fee for each order (no matter how many movies are in the order). An order of movies from store z always costs the same as ordering the same number of movies from store A. How much does store Z charge per movie
Store Z charges $8 per movie.
What is an expression?
An expression is the mathematical statement that is formed by numerical and variable terms along with operators. It represents the method of a mathematical operation in a symbolic form.
How much does store Z charge per movie?
given, store A charges $8 per movie.
for each order shipping fee = $10
if store A is ordered x movie at a time than the total cost for one order
represented by the expression, $8 x + $10.
As per question, store Z cost always the same as store A for one order.
so, cost for one order in case of store Z = $8x + $10
if x denotes the number of movies that is ordered at a time, then the Z store charges $ 8 per movie.
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Stella measures the diameters of a nickel, a dime, and a quarter. They are 21.2 mm, 17.8 mm, and 24.5 mm, respectively. Find the areas of each coin. Round to the nearest tenth.
The area of nickel is 353.0 mm²
The area of a dime is 248.8 mm²
The area of a quarter is 471.4 mm²
Given that,
The diameter of a nickel, a dime, and a quarter are 21.2 mm, 17.8 mm, and 24.5 mm, respectively.
Diameter = 2r (r=radius)
or, r = d/2
so, the Radius of a nickel, a dime, and a quarter are 10.6 mm, 8.9 mm, and 12.25 mm, respectively.
Thus, the area of a nickel, a dime, and a quarter => A= πr²
So, the area of the nickel = 3.14*10.6*10.6 = 353.0 mm²
The area of the dime = 3.14*8.9*8.9 = 248.8 mm²
The area of a quarter = 3.14*12.25*12.25 = 471.4 mm²
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there's no explanation for it either sh trippin
solving for "xx"
[tex]\sqrt{xx - 2}=7\implies \sqrt{xx - 2}=7\implies (\sqrt{xx - 2})^2=(7)^2 \\\\\\ xx-2=49 \implies xx=51[/tex]
find the ratio of 15 min and 1 hrs.
Evaluate the expression!!
The given expression is equivalent to 22 for x = 17 and y = 12.
What is expression?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context. Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is the expression as follows -
2x - y
For x = 17 and y = 12, we can evaluate the expression as -
2 x 17 - 12
34 - 12
22
Therefore, the given expression is equivalent to 22 for x = 17 and y = 12.
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Last week, a dairy farm produced n kg of cheese.
The dairy farm also produced 30 kg more yoghurt than cheese and 4 times
as much ice cream as cheese.
The dairy farm produced more kilograms of ice cream than yoghurt last
week.
Write and solve an inequality to work out the possible values of n.
Answer:
The dairy farm produced 30 + n kg of yoghurt, where n is the number of kilograms of cheese produced.
The dairy farm also produced 4n kg of ice cream, where n is the number of kilograms of cheese produced.
Since the dairy farm produced more kilograms of ice cream than yoghurt, we can write the following inequality:
4n > 30 + n
Subtracting n from both sides gives us:
3n > 30
Dividing both sides by 3 gives us:
n > 10
Therefore, the possible values of n are any value greater than 10, such as 11, 12, 13, 14, and so on.
Step-by-step explanation:
Range of 63, 42, 28, 45, 36, 48, 32, 40, 57, 49
Please help!! Find the area of the circle use 3.14 for pi
Answer:
when pi = 3.14, A = 63.535
when pi = pi, A = 63.61725
Step-by-step explanation:
Area of a circle = pi × radius (4.5) squared (^2)
auggie bought 8 books. Some books cost $13 each and the rest of the books cost $24 each. They spent a total of $159. Write a system of linear equations that could represent the given situation
Answer: Let x be the number of $13 books that Auggie bought and y be the number of $24 books. Then we can represent the given information in the following system of linear equations:
x + y = 8 (the total number of books Auggie bought is 8)
13x + 24y = 159 (the total amount of money Auggie spent is $159)
This system of linear equations represents the given situation. We can use this system to find out how many books Auggie bought of each price by solving the system of equations.
The equation (1) represents the number of books that Auggie bought is 8, and equation (2) represents the amount of money he spent $159. This system of equations is a valid representation of the given situation because the values of x and y that satisfy the system of equations will be the number of $13 books and the number of $24 books that Auggie bought.
Step-by-step explanation:
It takes a train of a certain length 15 seconds to pass under a sign, and it takes the same train 40 seconds to pass under a bridge that is 100 meters wide.What is the length (in meters) of the train
After solving, the length of the trains in meters is 60 meters.
In the given question, it takes a train of a certain length 15 seconds to pass under a sign, and it takes the same train 40 seconds to pass under a bridge that is 100 meters wide.
We have to find the length (in meters) of the train.
Let the length of the train is x.
The length of the bridge is 100 meters.
As we know that the formula of the speed is the ratio of distance that he traveled in the certain duration of time.
So Speed = Distance/Time
So according to the question;
(x + 100)/40 = x/15
Now solving the expression using the cross multiplication
15x + 1500 = 40x
Subtract 15x on both side, we get
25x = 1500
Divide by 25 on both side, we get
x = 60 meters
Hence, the length of the trains in meters is 60 meters.
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Find four consecutive odd integers such taht 4 times the sum of the first and third is 4 larger than 4 times the fourth
The four consecutive odd integers = 15, 17, 19, 21
What are integers ?Positive, negative, and zero are all examples of integers.
The Latin word "integer" signifies "whole" or "intact."
As a result, fractions and decimals are not included in integers.
All whole numbers and negative numbers are considered integers.
This means that if we combine negative numbers with whole numbers, a collection of integers results.
An integer, which can comprise both positive and negative integers, including zero, is a number without a decimal or fractional portion.
Here are a few instances of integers: -5, 0, 1, 5, 8, 97, and 3,043. a collection of numbers, denoted by the symbol Z.
According to our question-
x + x + 6 = -(x + 4) + 55
x + x+6 = (-x - 4) + 55
2x + 6 = -x + 51
Collect like terms
2x + x = 51 - 6
3x = 45
x = 15
Second integer = x + 2 = 15 + 2 = 17
Third integer = x + 4 = 15 + 4 = 19
Fourth integer = x + 6 = 15 + 6 = 21
The four consecutive odd integers = 15, 17, 19, 21
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Olivia tries to cut a piece of metal 45 inches long the piece of metal ends up being 43. 5 inches long what is the approximate orecent error in this situation
When Olivia tries to cut a piece of metal 45 inches long, the piece of metal ends up being 43.5 inches long, then there is an approximate percent error of 3.33% in this situation.
Therefore the answer is 3.33%.
To calculate the approximate percent error in this situation, we can use the formula:
Percent Error = (|Experimental Value - Theoretical Value| / Theoretical Value) x 100
In this case, the experimental value is 43.5 inches and the theoretical value is 45 inches. Plugging these values into the formula, we get:
Percent Error = (|43.5 - 45| / 45) x 100
= (1.5 / 45) x 100
= 0.033 x 100
= 3.33%
So the approximate percent error in this situation is 3.33%.
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Show youR WORK please send. A photo it could help
Answer:
Step-by-step explanation:
1 ft= 12 inches
So 5ft = 60 Inches
4= 0.3
Thus, Its 60.3
How do you write no solution?
No solution is when a system of equations has no solution. This means that the equations are inconsistent, and there is no set of values that can make the equations true.
For example, if the system of equations is 2x + 3y = 4 and 2x + 3y = 5, then there is no solution. This is because no matter what values are chosen for x and y, the equations cannot both be true. This means that the system of equations is inconsistent, and there is no solution.
To symbolically represent no solution, you can use the following notation:
2x + 3y = 4, 2x + 3y = 5 No solution
This notation is used to indicate that the equations are inconsistent and that there is no solution.
Complete question: What is the solution to the equation 2x + 3y = 4 and 2x + 3y = 5?
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What is the solution of the equation 8x 3y 5 and 3x 2y 5 answer?
The solution of the equation is x = 1 and y = 0.
We can solve this equation using the substitution method.
First, subtract 5 from both sides of the equation to isolate the x and y terms:8x - 3y = 0
3x - 2y = 0
Next, divide both sides of the first equation by 8:
x = (3/8)y
Substitute this expression for x into the second equation:
3(3/8)y - 2y = 0
Simplify:
(-13/8)y = 0
Divide both sides by -13/8:
y = 0
Now, substitute y = 0 into the first equation:
8x - 3(0) = 0
Simplify:
8x = 0
Divide both sides by 8:
x = 0
Therefore, the solution of the equation is x = 1 and y = 0.
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please help me find the surface area of this triangular prism
The area is measurement of the surface of a shape. To find the area of a rectangle or a square you need to multiply the length and the width of a rectangle or a square. Area, A, is x times y.
How do you find the area of a prism?The surface area of a triangular prism is defined as the sum of the area of its five faces. To calculate the surface area, we need the values of the base, length, and height of the triangular prism. Its formula equals the sum of two times the base area and three times the product of the base and length of the prism.Triangular prisms have their own formula for finding surface area because they have two triangular faces opposite each other. The formula A = 1 2 b h is used to find the area of the top and bases triangular faces, where A = area, b = base, and h = height.To find the surface area of a prism, use the formula SA=2B+ph, where SA stands for surface area, B stands for area of the base of the prism, p stands for the perimeter of the base, and h stands for the height of the prism.Two triangles' area: 18×24÷6x3 = 432cm^2
The widest rectangle's area: 30×7 = 210cm^2
The rectangle facing the left's area: 18×7= 126cm^2
The rectangle facing the ground's area: 24×7= 168cm^2
Total Surface Area: 432+210+126+168 = 936cm^2
=936cm^2
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HELP 50 points :D
1. You have $25 to spend on snacks for movie night with 4 of your friends. If individual boxes of raisins are $1.50, find the amount of money that remains per person for popcorn and a drink.
2. The cost for a town’s soccer league banquet is $960. There are 60 players in the soccer league. Determine the cost per player for the town if each player pays $5 to attend the banquet.
3. To solve the equation 2/3(x−4)=−10, Izzy wants to multiply both sides of the equation by the reciprocal of the fraction. Name the reciprocal.
__/__
4. There are 2 types of tickets to attend an awards dinner—silver and gold. The gold tickets are $8 more than the silver. If Patrick bought 10 tickets at each level and spent a total of $140, find the price of each ticket.(1 point)
$___ for each silver ticket and $___ for each gold ticket
5. Kendra is making bread, but the recipe she’s using makes 4 loaves. She only wants to make one loaf. The changed recipe calls for 2 1/2 cups of flour and sugar combined. If the original recipe calls for 2 cups of sugar, find the amount of flour (in cups) in the original recipe.
1. You have $25 to spend on snacks for movie night with 4 of your friends. If individual boxes of raisins are $1.50, find the amount of money that remains per person for popcorn and a drink.
To find the amount of money that remains per person after buying raisins, we first need to find the total cost of the raisins. If 4 boxes of raisins cost $1.50 each, then 4*1.50 = $6 is spent on raisins.
To find the amount of money that remains for popcorn and drinks, we subtract the cost of the raisins from the total amount of money: 25-6 = $19.
Since there are 5 people in total (you and 4 friends), we divide the remaining money by 5 to find the amount per person: 19/5 = $3.80 per person.
How calculate the cost?2. The cost for a town’s soccer league banquet is $960. There are 60 players in the soccer league. Determine the cost per player for the town if each player pays $5 to attend the banquet.
To find the cost per player, we divide the total cost of the banquet by the number of players: 960/60 = $16 per player
3. To solve the equation 2/3(x−4)=−10, Izzy wants to multiply both sides of the equation by the reciprocal of the fraction. Name the reciprocal.
The reciprocal of the fraction 2/3 is 3/2
4. There are 2 types of tickets to attend an awards dinner—silver and gold. The gold tickets are $8 more than the silver. If Patrick bought 10 tickets at each level and spent a total of $140, find the price of each ticket.
Let's call the cost of a silver ticket x.
The cost of a gold ticket is x + 8.
We know that Patrick spent 10x + 10(x+8) = $140
We can simplify that: 10x + 10x + 80 = 140
Then we have 20x + 80 = 140
Then we have 20x = 60
And x = 3
Then the price of a silver ticket is $3 and the price of a gold ticket is $3+8 = $11
5. Kendra is making bread, but the recipe she’s using makes 4 loaves. She only wants to make one loaf. The changed recipe calls for 2 1/2 cups of flour and sugar combined. If the original recipe calls for 2 cups of sugar, find the amount of flour (in cups) in the original recipe.
If the original recipe calls for 2 cups of sugar and the changed recipe calls for 2 1/2 cups of flour and sugar combined, then the original recipe calls for 2 1/2 - 2 = 1/2 cup of flour.
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What is the median of the distinct positive values of all of the fractions less than or equal to 1 with positive integer denominators less than or equal to 5
The median of the distinct positive values of all of the fractions less then or equal to 1 with positive integer denominators less than or equal to 5 is 11/20.
In the statistics, the median is the value in the middle of a data set. It means that 50% of data points have a value smaller or equal to the median and 50% of data points have a value higher or equal to the median. The middle number is found by ordering all data points and picking out the one in the middle or if there are two middle numbers, taking the mean of those two numbers. We have to arrange data values from lowest to highest value. The median is the data value in the middle of the set. If there are 2 data values in the middle the median is the mean of those 2 values.
The set of numbers are,
1 /5, 1/4, 1/3, 2/5, 1/2, 3/5, 2/3, 3/4, 4/5, 1
we have to take the average of middle two .
The middle of the set are 1/2 and 3/5. and the average of these two is 11/20.
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PLEASE HELP!!! WILL MARK ANSWER BRAINLIEST!!!!!!! The manager of a hardware store took a random sample of 4.5 pounds of nails from a delivery of 350 pounds of nails. The manager found that 0.3 pounds of nails in the sample were defective. They were either bent, the heads were damaged, or they had been clipped too short during manufacture. How many pounds of defective nails should the manager expect the 350-pound delivery to contain? Round your answer to the nearest tenth of a pound.
The manager should expect the defective nails of 350-pound delivery to contain 23.3 pounds .
How to find defective rate?The defect rate is a measurement of the proportion of production units that are flawed or useless relative to a certain number of units. Businesses use this assessment to assess the quality of their products and how they affect their bottom line. Although lower rates are desired, no industry has a set acceptable fault rate. Therefore, businesses must choose their goal defect rate.
Defect rate is crucial because it enables firms to calculate the proportion of output units that fail quality checks. This assists the firms in identifying any issues with quality control or manufacturing and estimating the cost of each fault. To estimate the profitability of a product, businesses can also compare failure rates among comparable or dissimilar products.
In ever 4.5 pounds of nail defective nails are = 0.3 pounds
In ever 1 pounds of nail defective nails are = 0.3/4.5 pounds
In ever 350 pounds of nail defective nails are = (0.3/4.5)*350 pounds
⇒ the defective nails in 350 pounds of nails= 105/4.5
⇒ the defective nails in 350 pounds of nails= 23.3 pounds
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n \triangle NOP,△NOP, \overline{PN}\cong \overline{OP}
PN
≅
OP
and \text{m}\angle P = 50^{\circ}.m∠P=50
∘
. Find \text{m}\angle O.m∠O.
The value of the measure of ∠O in the given triangle will be 65°
What is triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
In ΔNOP;
PN ≅ OP
So, ∠O = ∠N
And, Measure of ∠P = 50°
Now,
In the ΔNOP;
The sum of all the three angles are 180°.
The value of the measure of ∠O = x
We get;
∠O + ∠N + ∠P = 180°
Substitute ∠P = 50° and ∠O = ∠N = x we get;
x + x + 50 = 180
2x + 50 = 180
2x = 180 - 50
2x = 130
x = 65
Thus, The value of the measure of ∠O will be 65°.
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PLEASE HELP!!!
Will give brainliest!
The value of h'(2) = 50.
What do you mean by function?
A relation between a collection of inputs and outputs is known as a function. In other word, it is a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.
here we are given a function h(x)
here h(x) = - 5f(g(x)) ------(i)
and we are given the value of
g(2) =3 ; f(2) = 1 ; g'(2) = -2
f(3) = 4 ; f'(3) = 5 ; f'(2) = 6.
and we need to find the value of h'(2).
here f(x), g(x) and h(x) are the function of x and f'(x), g'(x) and h'(x) denotes the derivative of f(x), g(x) and h(x) respectively.
so we are given ,
h(x) = - 5f(g(x))
differentiating with respect to x both side
h'(x) = -5 f'(g(x).g'(x).
at x =2,
h'(2) = [tex]-5*f'(g(2))*g'(2)[/tex]
and we know g(2) = 3 and g'(2) = -2.
so,
h'(2) = [tex]-5*f'(3)*-2[/tex]
h'(2) = [tex]-5*5*-2\\[/tex] ( as f'(3) = 5 )
h'(2) = 50
so Option C is correct, the value of h'(2) = 50.
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Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options. x2 + (y – 3)2 = 36 x2 + (y – 5)2 = 6 (x – 4)² + y² = 36 (x + 6)² + y² = 144 x2 + (y + 8)2 = 36
The circle equations for circles with diameters of 12 units that lie on the y-axis are:
x^2 + (y – 3)^2 = 36x^2 + (y + 8)^2 = 36Which equations represent circles?We want to find the equations that represent circles that have a diameter of 12 units and a center that lies on the y-axis, now, remember that the general equation for a circle of radius R and a center (a, b) is:
(x - a)^2 + (y - b)^2 = R^2
If we want a circle that lies on the y-axis, then a = 0, and if the diameter is 12 units, then the radius is R = 6 units.
Then the equation is something like:
x^2 + (y - b)^2 = 6^2 = 36
The two circle equations with this form are:
x^2 + (y – 3)^2 = 36x^2 + (y + 8)^2 = 36Learn more about circle equations:
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