The area of the walkway around the garden is 2.5(6x+6) - 2(3.5x +2.5).
Define area.A sketch or a picture is an example of a flat shape, which is a two-dimensional geometric shape. The interior space of the shape is how area is defined in mathematics. The area of a two-dimensional shape must take into account the units, which are squared units (units2). All of the shapes shown in the diagram below are flat, two-dimensional shapes. The quantity of square units that occupy any form determines its area.
Given
A rectangular garden has a walkway around it
Area of garden 2(3.5x +2.5)
Combined area 2.5(6x+6)
Walkway area = A
2(3.5x +2.5) + A = 2.5(6x+6)
A = 2.5(6x+6) - 2(3.5x +2.5)
The area of the walkway around the garden is 2.5(6x+6) - 2(3.5x +2.5).
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how to simplify this equation
Answer:
25x^2√(2x)
Step-by-step explanation:
2√(50x^5) + 5x√(18x^3) =
2√((2*25) * x^(4+1)) + 5x√((2*9) * x^(2+1)) =
2√(2 * 5^2 * x^4 * x^1) + 5x√(2 * 3^2 * x^2 * x^1) =
5*2√(2 * 1 * x^(2^2) * x) + 3*5x√(2 * 1 * x^2 * x) =
10√(2 * x^(2^2) * x) + 15*x*x√(2 * 1 * x) =
10√(2x * (x^2)^2) + 15*x^2√(2x) =
10x^2√(2x) + 15x^2√(2x) = 25x^2√(2x)
Analise's resting heart rate is 75 beats per minute. When she sleeps, it slows to 60 beats per minute. What percent decrease is this?
Answer:
20% decrease
Step-by-step explanation:
[tex]\frac{75-60}{75}[/tex]
[tex]\frac{15}{75}[/tex] = .2 to make a percent, multiply by 100 = 20%
does anyone know what -x/3 ≥ 15 is?
After solving the given inequality, the obtained value will be x ≤ -45.
What is inequality?Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare the two values. Less than (or less than and equal to), larger than (or greater or equal to), or not similar to signs are used in place of the equal sign in between.
As per the given inequality in the question,
-x/3 ≥ 15
-x ≥ 45
Multiply the equation with a minus sign, due to which the sign of inequality will change.
So, the inequality will be,
x ≤ -45
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James has $2,000 saved for a vacation his airplane ticket cost 637 his hotel costs 175 per night how many full night can he stay on vacation without going over his savings
He can spend $2000 on a 7-day vacation without going over his budget.
What is equation?In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical statement made up of two expressions joined by an equal sign is known as an equation. 3x - 5 = 16 is an example of an equation. We get the value of the variable x as x = 7 after solving this equation.
Here,
175x+637=2000
175x=1363
x=7.78
x=7.8
He can stay on vacation for 7 days with $2000 without going over his savings.
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lonzo borrowed 15000$ at 1.2% simple interest to buy a car . after 9 months how much will lonzo owe the bank in interest
The simple interest implies that Lonzo owes $1513.5
How to determine the amount Lonzo owes?The given variables can be represented as:
Loan amount P = $1500
Rate of interest, R = 1.2%
Time to pay back the loan, t = 9 months i.e. 0.75 year
The amount from a simple interest can be calculated using:
A = P(1 + RT)
Substitute the known values in the above equation, so, we have the following representation
A = 1500 * (1 + 1.2% * 0.75)
Evaluate
A = 1513.5
Hence, the amount owed is $1513.5
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Given the equation 7m − 11 = 5m + 43 and the possible solution set S: {2, 27, 54, 86}:
Part A: Determine which integer(s) in the solution set makes the equation false. Show all work. (8 points)
Part B: Use a complete sentence to explain how you were able to determine which values make the equation false. (4 points)
A) The integers that make the equation false are {2, 54, 86}
B) We found that by solving the linear equation.
Which integer makes the equation false?
Here we have the following linear equation:
7m - 11 = 5m + 43
And the set of the possible solutions is S: {2, 27, 54, 86}
The simplest way to see which integer makes the equation false, we just need to replace the values of the possible solution sets and see which ones give a false equation.
Another method is to simplify the equation, and i will do that:
7m - 11 = 5m + 43
7m - 5m = 43 + 11
2m = 54
m = 54/2
m = 27
So the equation has a single solution, m = 27.
Then the integers that make the equation false are {2, 54, 86}
B) We determined the only true solution for the linear equation, and thus, all the other possible integers aren't solutions, thus, make the equation false.
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Given the function f(x) = 3(x – 5) + 8, which of the following represents f–1(x)?
Step-by-step explanation:
f(x) = 3(x - 5) + 8
f-1(x) = -1(3(x - 5) + 8)
= -3(x - 5) - 8
= -3x + 15 -8
= -3x + 7
A new streaming service sent out a survey to 350 households to see who would be interested in its service. The company found that it could charge $55 per month, with a margin of error of ±1.3. If 1,000 people signed up for the service, what is the least amount of monthly revenue the company should expect?
$52,815
$53,700
$54,915
$56,300
Answer:
B) $53700-------------------------------------
The charge of $55 with error margin of ± 1.3 results in the least value of $(55 - 1.3) = $53.7 and greatest value of $(55 + 1.3) = $56.3.
If 1000 people signed up for the service, then the least total amount is:
$53.7*1000 = $53700Correct choice is B.
I need help with this problem if you can help me !!
Answer:
C - 52.50
Step-by-step explanation:
49 Euros To dollars
Answer:
C) 52.50
Step-by-step explanation:
[tex]\frac{15}{14}[/tex] = [tex]\frac{x}{49}[/tex] Cross multiply and solve for x
14x = 15(49)
14x = 735 Divide both sides by 14
[tex]\frac{14x}{14}[/tex] = [tex]\frac{735}{14}[/tex]
x = 52.50
Heather, Kareem, and Chris served a total of 81 orders Monday at the school cafeteria, Chris served 2 times as many orders
as Heather, Kareem served 5 more orders than Heather How many orders did they each serve?
Answer: Heather served 15 orders, Kareem served 20 orders, and Chris served 30 orders.
Step-by-step explanation: Let H be the number of orders that Heather served, K be the number of orders that Kareem served, and C be the number of orders that Chris served.
We are given that C = 2*H and K = H + 5.
We are also given that H + K + C = 81.
Substituting the expressions for C and K into the equation, we get:
H + (H + 5) + (2*H) = 81
5*H + 5 = 81
5*H = 76
H = 15
Since Heather served 15 orders, Kareem served 15 + 5 = 20 orders and Chris served 2*15 = 30 orders.
Therefore, Heather served 15 orders, Kareem served 20 orders, and Chris served 30 orders.
a pizza parlor offers six toppings. what is the greatest number of four-topping pizzas that can be made such that no two pizzas have the same topping combination? (all four toppings must be different.)
On solving the provided question, we can say that - there are 120 distinct pizza topping combinations that may be created if the maximum number of toppings is 3.
What is combination?Regardless of the sequence in which the items were chosen, a mathematical approach known as a combination may be used to calculate the number of alternative arrangements within a collection of objects. Any order can be chosen by a combination. Combinations in mathematics are ways to choose elements from a collection, and the order in which they are chosen is irrelevant. Let's say we have a trio of numbers: P, Q, and R. The amount of possible combinations for two integers from each set is determined by combinations.
Given: Six toppings in all.
There are three toppings to choose from.
Additionally, if topping repetition is prohibited, the number of viable combinations is equal to 6 × 5 x 4. [We select one out of six first, then one out of the remaining five, then one out of four, and finally we multiply the options for three toppings]
= 120
As a result, there are 120 distinct pizza topping combinations that may be created if the maximum number of toppings is 3.
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If A=45° B = 30°, prove that
Sin (A-B) = sinAcos B - Cos Asin B
To prove that Sin (A-B) = sinAcos B - Cos Asin B, we can use the angle subtraction formula for sine:
Sin (A-B) = Sin A Cos B - Cos A Sin B
This formula is derived from the identity:
Sin (A-B) = Sin A Cos B - Cos A Sin B
which can be derived by using the double angle identities for sine and cosine:
Sin (2A) = 2 Sin A Cos A
Cos (2A) = Cos^2 A - Sin^2 A = 2 Cos^2 A - 1 = 1 - 2 Sin^2 A
Substituting these identities into the identity above, we get:
Sin (A-B) = Sin A Cos B - Cos A Sin B
What is an angle subtraction?Angle subtraction formulas is otherwise known as angle subtraction identities. This angle subtraction formulas permit us to find the exact values of less common trigonometric angles by expressing the less common angle as the difference of two common angles. For example, 15 degrees = 45 degrees - 30 degrees.
Therefore, Sin (A-B) = sinAcos B - Cos Asin B.
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what is r 156 ÷ r = 26
Answer:
r=6
Step-by-step explanation:
156/r=26
All terms are shifted to the left:
156/r-(26)=0
We divide every term by the denominator.
-26*r+156=0
All the numbers and variables are added together.
-26r+156=0
All terms containing r are shifted to the left, and all other terms are shifted to the right.
-26r=-156
r=-156/-26
r=6
what is the value of the expression 3^{2}*(2^{3} +4)-22
Answer:
86
Explanation:
3² × (2³ + 4) - 22
9 × (8 + 4) - 22
9 × 12 - 22
108 - 22
86
the sum of the sequence 7+21+63..... to the 9th term
68,887 is the sum of the sequence (7+21+63...) to the 9th term.
That is, the sequence (as far as we are given) has a common ratio r=3, between successive terms. The initial term a= 7 and we are interested in the sum to N = 9 terms.
and the sum of the 9th term is
[a^n = a( 1 - r^N)/1 - r ]
=[7 ( 1 - 3^9 )/ 1 - 3 ]
=7 ( 1 - 19683) / -2
= - 137,774 / -2
= 68,887
9th term = 68,887
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The half-life of a substance is how long it takes for half of the substahce to decay or become
harmless (for certain radioactive materials). The half-life of a substance is 235 years, and there is anamount equal to 100 grams now. This function can be modeled by the expression A(t) = 100(0.5)
t/235
Part A: Discuss collaboratively: How can the expression for the amount, A(t), that remains after t
years, be rewritten using a base of 2 instead of a base of 0.5? Explain.
Part B: Using either one of the exponential models, what is the amount of substance remaining
(rounded to the nearest tenth) after 1,000 years?
I
a) Using a base 2, the exponential function can be written as follows:
A(t) = 100(2)^(-t/235)
b) The amount of substance remaining after 1000 years is given as follows: 5.2 grams.
What is the exponential function?The exponential function for this problem is defined as follows:
A(t) = 100(0.5)^(t/235).
Which gives the amount of a substance after t years, considering a half life of 235 years.
The base can be changed to 2 as follows:
A(t) = 100(2)^(-t/235).
As exchanging the sign of the exponent, the numerator and the denominator of the base are exchanged, and 0.5 = 1/2.
The amount of the substance after 1000 years is calculated as follows:
A(1000) = 100 x (0.5)^(1000/235) = 5.2 grams.
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two thirds of a number b is no more than 12.
two thirds of a number b which is no more than 12, is b ≤ 18
What is inequality ?
In mathematics, an inequality represents the connection between two values in an imbalanced algebraic statement. A sign of inequality can be used to show that one of the two variables is larger than, greater than or equal to, less than, or equal to another value.
According to question
two thirds of a number b = (2/3)b
Given two thirds of number b is no more than 12
⇒ (2/3)b ≤ 12
⇒ 2b ≤ 12*3
⇒ b ≤ (12*3)/2
⇒ b ≤ 36/2
⇒ b ≤ 18
hence the number b whose 2/3 is no more than 12 is, b ≤ 18
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Seven days a year, Tiger Stadium becomes the fifth largest city in the state of Louisiana. Over 92,000 fans pack the stadium to watch the Tigers play. After the game, if the fans leave at a rate of 10% per minute, how long will it take before the stadium is half empty?
It will take 5 minutes before the stadium is half empty
Given that:
Over 92,000 fans pack the stadium to watch the Tigers play
The fans leave at a rate of 10% per minute
The number of fans that leave per minute will be:
10% of 92,000 = 10/100 × 92, 000 = 9,200
The stadium will be fully empty in:
time = 92,000/9,200 = 10 minutes
The stadium will be half empty in:
time = 10 minutes / 2 = 5 minutes
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help me pleasee asappp
The median of the data sets 10, 11, 13, 18, 19, 21, 22, 25, 27, 30, 32 is 21.
How to find median?The Median is the "middle" of a sorted list of numbers. In other words, Median, in statistics, is the middle value of the given list of data when arranged in an order.
Therefore, let's find the median of the data sets.
Firstly, we have to sort the data in ascending order before we can find the median in the data set.
10, 11, 13, 18, 19, 21, 22, 25, 27, 30, 32
Hence, the sorted data set is 10, 11, 13, 18, 19, 21, 22, 25, 27, 30, 32.
Therefore,
median = 21
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an item is regularly priced at . it is on sale for off the regular price. how much (in dollars) is discounted from the regular price?
An item is regularly priced at, 1.98$ is discounted from the regular price.
A percentage is a portion of a whole expressed as a number between 0 and 100 rather than as a fraction. All of something is 100 percent, half of it is fifty percent, none of something is zero percent. To determine a percentage, you divide the portion of the whole by the whole itself and multiply by 100.
Given that,
First, change the percentage into decimal:
Let us assume,
Sale of regular price = 1%
1% = 1/100 = 0.01
Assume, item regular price is = 2$
Multiply 2 with 0.01:
2 * 0.01 = 0.02
Note that this number 0.02 (0.01 of 2) is the amount off from the original price (2). Subtract 2 from 0.02
2 - 0.02 = 1.98
Therefore,
An item is regularly priced at, 1.98$ is discounted from the regular price.
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Find the slope passing through the point -8,-4 and 3,-4
Answer:
0
Step-by-step explanation:
(-8, -4) and (3, -4)
m = y2-y1 / x2-x1
m = -4+4 / 3+8
m = 0 / 11
m = 0
May I please have a brainliest for this? Thank you!
please help me out with my math
Answer:
4
Step-by-step explanation:
√64 = 8
√4 = 2
8/2 = 4
Answer:4
Step-by-step explanation:
[tex]\sqrt{64[/tex] = 8
[tex]\sqrt{4[/tex] = 2
8÷2=4
A company has two manufacturing plants with daily production levels of 8x + 15 items and 3x-7 items, respectively. The first plant produces how many more items daily than the second plant?
The first plant produces more items daily than the second plant
(Simplify your answer)
CETTE
What’s the answer
To find the difference in the number of items produced by the two plants, we can subtract the production level of the second plant from that of the first plant. This gives us:
[tex]8x + 15 - (3x - 7) = 5x + 22[/tex]Therefore, the first plant produces [tex]5x + 22[/tex] more items daily than the second plant.
The table shows the scores of two teams at the end of the first half of a trivia challenge.
Team Points Scored
Bobcats 2x−7
Huskies 5x−3
How many more points did the Huskies score than the Bobcats?
The point difference between Huskies and Bobcats are 3 x + 4.
What is algebra ?The area of mathematics known as algebra is used to portray situations or problems using mathematical expressions. In algebra, we utilize integers with fixed or definite values, such as 2, 7, 0.068, etc. In algebra, we combine integers with variables like x, y, and z.One-step equations can be solved in four different ways: by adding, subtracting, multiplying, and dividing. In an equation, both sides will stay equal if we add the same amount to either side.The sequence in which you perform operations in arithmetic and algebra is governed by a number of rules. The Commutative, Associative, and Distributive Laws are the three that receive the most attention.Given data :
Difference = Huskies - Bobcats
Hence,
( 5x - 3 ) - ( 2x - 7 )
= 5x - 3 - 2x + 7
= 3x + 4
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just the linked questions, thanks . 8.4 similar triangles unit 8 practice a
The evaluation of the segment formed by the parallel lines using Thales Theorem also known as the triangle proportionality theorem are;
8. [tex]\overline {ST}[/tex] is parallel to [tex]\overline{PR}[/tex]
9. [tex]\overline{ST}[/tex] is parallel to [tex]\overline{PR}[/tex]
10. [tex]\overline{ST}[/tex] is not parallel to [tex]\overline{PR}[/tex]
11. x = 57.6
12. x = 25.8
13. x = 11
14. x = 10
15. x = 5
16. x = 17
What is Thales theorem?Thales Theorem also known as the triangle proportionality theorem states that a parallel line to a side of a triangle that intersects the other two sides of the triangle, divides the two sides in the same proportion.
8. The ratio of the sides the segment [tex]\overline{ST}[/tex] divides the sides QR and QP of the triangle ΔPQR into are; 7/11.2 = 10/16 = 0.625
Therefore; according to the Thales theorem, [tex]\overline{ST}[/tex] ║ [tex]\overline{PR}[/tex]
9. The ratio of the sides the parallel side to the base divides the other two sides are;
33/41.8 = 15/19
45/(102 - 45) = 45/57 = 15/19
Therefore, [tex]\overline{ST}[/tex] and [tex]\overline{PR}[/tex] bisects [tex]\overline{QP}[/tex] and [tex]\overline{QR}[/tex] into equal proportions and therefore, [tex]\overline{ST}[/tex] ║ [tex]\overline{PR}[/tex]
10. The ratio of the sides the segment [tex]\overline{ST}[/tex] bisects the other two sides are;
24/57 and 19/38
24/57 ≠ 19/38, therefore [tex]\overline{ST}[/tex] ∦ [tex]\overline{PR}[/tex]
Second part; To solve for x
11. x/30 = 48/25
x = (48/25) × 30 = 57.6
x = 57.6
12. x/34.4 = (49 - 28)/28
x = 34.4 × (49 - 28)/28 = 25.8
x = 25.8
13. (2·x + 6)/52.5 = 32/60
(2·x + 6) = 52.5 × (32/60)
x = (52.5 × (32/60)) - 6)/2 = 11
x = 11
14. (x - 3)/21 = (x - 1)/27
27·x - 27 × 3 = 21·x - 21
27·x - 81 = 21·x - 21
6·x = 60
x = 60 ÷ 6 = 10
x = 10
15. (35 - 20)/20 = (4·x - 2)/(7·x - 11)
15/20 = (4·x - 2)/(7·x - 11)
15 × (7·x - 11) = 20 × (4·x - 2)
105·x - 165 = 80·x - 40
105·x - 80·x = 165 - 40 = 125
25·x = 125
x = 125/25 = 5
x = 5
16. (x - 3)/35 = 4/(x - 7)
(x - 3) × (x - 7) = 35 × 4 = 140
x² - 10·x + 21 = 140
x² - 10·x - 119 = 0
(x - 17) × (x + 7) = 0
x = 17 or x = -7
Therefore, the possible value of x is 17
x = 17
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If Winston left a 15 percent tip on his orders every day, how much money in tips alone did he leave in total on Monday, Tuesday, and Wednesday?
The total amount that will be paid of there's a 15% tip is $57.50.
How to calculate the percentage?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100. The percentage therefore refers to a component per hundred. Per 100 is what the word percent means. It is represented by %.
Let's assume that the cost of the good bought is $50. A 15% tip will give a value of:
= 15% × $50
= $7.50
The total amount to be paid will be:
= $50 + $7.50
= $57.50
Note that an overview was given as the information is incomplete.
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Given f(x) = x² - 1 and g(x) = x + 5, find h(x) = (f. g)(x).
The function h(x) = (f.g)(x) would be x² + 10x + 24.
What are composite functions?
A composite function is generally a function that is written inside another function. The composition of a function is done by substituting one function into another function. For example, f [g (x)] is the composite function of f (x) and g (x). The composite function f [g (x)] is read as “f of g of x”.
To find h(x) = (f.g)(x), we need to find the composition of the functions f(x) and g(x).
The composition of two functions f(x) and g(x) is denoted by (f.g)(x) and is defined as (f.g)(x) = f(g(x)).
In this case, we have:
h(x) = (f.g)(x) = f(g(x)) = f(x + 5)
Substituting x + 5 for g(x) in the equation for f(x), we get:
h(x) = (f.g)(x) = f(x + 5) = (x + 5)² - 1
Simplifying this expression, we get:
h(x) = (f.g)(x) = x² + 10x + 24
Hence, the function h(x) = (f.g)(x) would be x² + 10x + 24.
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Find the perimeter and total area of the composite shape shown below. All measurements are given in inches. Use = 3.14 in
any formulas used.
The area of the composite shape is 292.96 in² and the perimeter of the composite shape is 65.12 inches
Area of Half circle:The quantity of surface contained within a semicircle's perimeter is known to as its area.
The formula for the Area of a half circle with a Radius (r) is given by
Area of Half circle = πr²/2
The formula for the perimeter of a half circle with a radius (r) is given by
Perimeter of Half circle = πr
Here we have
A picture of a Rectangle with a half circle
Dimensions of Rectangle = 16 in × 12 in
=> Area of rectangle = 16 in × 12 in = 192 in²
=> Perimeter of rectangle shape = 12 + 16 + 12 = 40 inches
[ Here we only take one side of the rectangle since one of the sides is connected with a Half circle ]
The radius of half circle = 8 inch
=> Area of Half circle = π(8)² = (3.14)(64)/2 = 100.96 in²
=> Perimeter of Half circle = πr =(3.14)(8) = 25.12 in
Area of the composite shape
= Ractangle's Area + Half circle's Area
= 192 in² + 100.96 in²
= 292.96 in²
The perimeter of the composite shape
= Ractangle perimeter + Half circle perimeter
= 40 inches + 25.12 inches
= 65.12 inches
Therefore,
The area of the composite shape is 292.96 in² and the perimeter of the composite shape is 65.12 inches
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∠A and \angle B∠B are complementary angles. If \text{m}\angle A=(2x-13)^{\circ}m∠A=(2x−13)
∘
and \text{m}\angle B=(2x+7)^{\circ}m∠B=(2x+7)
∘
, then find the measure of \angle A∠A.
The measure of ∠A is 29.
What is an angle?
An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The Latin word "angulus," which meaning "corner," is the source of the English term "angle." The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle.
Given that,
m∠A = (2x−13)° and m∠B = (2x+ 7)° and ∠A and ∠B are complementary angles.
Therefore
m∠A + m∠B = 90°
(2x−13)° + (2x+ 7)° = 90°
4x + 6 =90
Subtract 6 from both sides:
4x = 84
Divide both sides by 4:
x = 21
Putting x = 21 in m∠A = (2x−13)°:
m∠A = (2 × 21−13)°
m∠A = 29°
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find the least commmon multiple (LCM) for each pair of numbers.To solve the riddle the letters to the numberd lines below 2,5 3,15 6,12 2,15 2,3 8,24 4,10 6,9 7,9
The LCM of the given pairs are 10, 15,12,30,6,24,20,18, and 63 respectively.
What is LCM?The least common multiple (LCM) of two numbers is the lowest possible number that can be divisible by both numbers.
There are 9 pairs, so let's name them using the letters A to I.
The LCM of the first pair A (2, 5) is 10.
The LCM of the pair B (3, 15) is 1*3*5 = 15.
The LCM of the pair C (6, 12) is 3*2*1*2 = 12.
The LCM of the pair D (3, 15) is 2*3*1*5 = 30.
The LCM of the pair E (2, 3) is 1*3*2 = 6.
The LCM of the pair F (8, 24) is 2*2*2*1*3 = 24.
The LCM of the pair G (4, 10) is 2*2*5 = 20.
The LCM of the pair H (6, 9) is 3*2*3 = 18.
The LCM of the pair I (7, 9) is 7*9 = 63.
Hence, 10,15,12,30,6,24,20,18,63 are the LCM of the given pairs.
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