To solve for the length and width of the rectangle, equations were set up based on the given perimeter and the relation between length and width. The width was found to be 8 cm, and substituting this into the length formula gave a length of 19 cm.
The question concerns finding the length and width of a rectangle given that the length is 5 cm less than three times the width and the perimeter is 54 cm. To solve this, let's denote the width of the rectangle as 'w' and the length as 'l'. The relationship between the length and width can be expressed as 'l = 3w - 5 cm'. The perimeter (P) of a rectangle is given by P = 2l + 2w, and substituting our expressions in terms of 'w' into the formula gives us 2(3w - 5) + 2w = 54. Simplifying and solving for 'w' gives us the width. Subsequently, we can substitute this width into the equation for length to find 'l'.
So, let's start by setting up the equation:
2(3w - 5) + 2w = 54
6w - 10 + 2w = 54
8w - 10 = 54
8w = 64
w = 8 cm
Now we substitute w = 8 cm into the length formula:
l = 3(8) - 5
l = 24 - 5
l = 19 cm
Therefore, the width of the rectangle is 8 cm and the length is 19 cm.
Which of the following is a possible long-term health effect of stress?
A. heart disease
B. rapid breathing
C. heartburn
D. tense muscles
choose all that apply
The larger of two numbers is four more than the smaller number. If the sum of the numbers is 74, find the numbers
Your baseball team has a goal to collect at least 160 blankets for a shelter. Team members brought 42 blankets on monday and 65 on wednesday . Write and solve an inequality to find out how many blankets the team has to collect on friday?
Answer:
Atleast 53
Step-by-step explanation:
We are given that your basketball team has a goal to collect atleast 160 blanket for a shelter.
Team member bought blankets on Monday =42
Team member bought blankets on Wednesday=65
We have to write an inequality and find the number of blankets has to collect on Friday.
Let x be the number of blankets bought by team members on Friday
According to question
[tex]42+65+x \geq 160[/tex]
[tex]107+x \geq 160[/tex]
Subtract 107 on both sides
[tex]107-107+x\geq 160-107[/tex]
[tex]x\geq 53[/tex]
Hence, team members bought atleast 53 blankets on Friday .
Use a trigonometric ratio to find the length of side ST.
A sample is a sample that isn't representative of the entire population.
unbiased
systematic
biased
Answer: The answer is biased :)
Convert rational numbers into improper fraction-29
29/1
Improper fractions have a greater numerator.
29 > 1
what can be divided thit number 288
Can someone please help me and like show and explain how to get the answer?
Layla is on page 30 of her book and reads 3 pages every night. Sidney is on page 40 of the same book and reads 2 pages every night. How long will it take for Layla to be further in the book than Layla?
A) 3 nights
B) 11 nights
C) 15 nights
D) 71 nights
Please help with 12!!!!!
Hat is the equation in point-slope form of the line passing through (2, 5) and (−1, 8)?
What is the equation of a line that passes through the point (8, −2) and is parallel to the line whose equation is 3x + 4y = 15? Enter your answer in the box
Step 1
Find the slope of the given line
we have
[tex]3x+4y=15[/tex]
Isolate the variable y
Subtract [tex]3x[/tex] both sides
[tex]3x+4y-3x=15-3x[/tex]
[tex]4y=-3x+15[/tex]
Divide by [tex]4[/tex] both sides
[tex]y=-\frac{3}{4}x+ \frac{15}{4}[/tex]
the slope of the given line is
[tex]m=-\frac{3}{4}[/tex]
Step 2
Find the equation of the line that passes through the point [tex](8,-2)[/tex] and is parallel to the given line
we know that
if two lines are parallel, then their slopes are equal
The equation of the line into point-slope form is equal to
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=-\frac{3}{4}[/tex]
[tex](x1,y1)=(8,-2)[/tex]
substitute in the equation
[tex]y+2=-\frac{3}{4}(x-8)[/tex]
[tex]y=-\frac{3}{4}x+6-2[/tex]
[tex]y=-\frac{3}{4}x+4[/tex] or [tex]3x+4y=16[/tex]
therefore
the answer is
[tex]y=-\frac{3}{4}x+4[/tex]
or
[tex]3x+4y=16[/tex]
Answer:
3x+4y=16
Clarifying because other explanation was confusing
Just took review
Step-by-step explanation:
What's the answer to
4.5 divided by 1.8
3x-43=8 slove the equation
find the value of x and BC if B is between C and D CB=4x-9 BD=3x+5 and CD= 17
To find the value of x and BC, set up the equation CB + BD = CD and solve for x. The value of x is 3 and BC is 3.
Explanation:To find the value of x and BC, we can set up the equation CB + BD = CD and solve for x.
Substituting the given values CB = 4x - 9, BD = 3x + 5, and CD = 17, we get (4x - 9) + (3x + 5) = 17.
Combining like terms, we have 7x - 4 = 17. Solving for x, we find x = 3. Plugging this value back into CB = 4x - 9, we get BC = 4(3) - 9 = 12 - 9 = 3.
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Question 4 deon runs 7 miles in 50 minutes. at the same rate, how many miles would he run in 75 minutes?
Find the product and simplify your answer. -4k^2(-3k^3+5k-5)
A culture started with 3000 bacteria. After 4 hours, it grew to 3,600 bacteria. Predict how many bacteria will be present after 10 hours. Round your answer to the nearest whole number. Use exponential growth formula
Gina's number is 2 more than sara's. the sum of their numbers is 68. what are their numbers?
Answer:
Gina=35, Sara=33
Step-by-step explanation:
Gina's number is 2 more than Sara's.
Lets start by saying cookies as the number.
Sum = 2 numbers add together. The answer to the equation. Lik 5+5=10. 10 is the sum.
You only know that Gina has 2 more cookies than Sara.
If Sara has 3 cookies then Gina has 5 cookies. Whats the Sum? 8.
So, you figure out an random big number but, smaller than 68.
Lets do 68 to try now. So you do 68/2 = 34. You remember that Gina has 2 more than Sara. So, 35 cookies for Gina. So, you can guess that Sara has 33 cookies.
While catching fireflies, you and a friend decide to have a competition. after mm minutes, you have (3m+13)(3m+13) fireflies and your friend has (4m+6)(4m+6) fireflies.
a. write an expression in simplest form that represents the number of fireflies you and your friend caught together?
In the equation y = 2x -3 if x = 3, what is the ordered pair of the solution?
I’m stuck on 5-6. Please help if you could explain the answer also that would be awesome
The answer to the first question is "b. one," according to Euclid's First Postulate. The answer to the second question is "c. infinitely many," according to Euclid's Second Postulate. These principles form the foundation of Euclidean geometry.
In Euclidean geometry, there are fundamental postulates and theorems that govern the behavior of lines and angles in triangles. Let's address your questions:
1. How many lines can be drawn through point A perpendicular to segment BC?
Answer: There can be only one line drawn through point A that is perpendicular to segment BC. This follows from Euclid's First Postulate, which states that a straight line can be drawn between any two points. In this case, the straight line from point A to any point on segment BC is unique and perpendicular.
2. How many lines can be drawn through point C perpendicular to segment AB?
Answer: Infinitely many lines can be drawn through point C that are perpendicular to segment AB. This is based on Euclid's Second Postulate, which states that a straight line can be extended infinitely in both directions. So, you can draw as many lines as you like, all of which are perpendicular to segment AB, and they will extend infinitely in both directions.
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the product of three consecutive nonzero integers
Final answer:
To find the product of three consecutive nonzero integers, multiply the first number by the next two numbers in the sequence.
Explanation:
If the first integer is n, the next will be n+1 and the next to it will be n+2
The product of three consecutive nonzero integers can be calculated using the formula:
n * (n+1) * (n+2)= n(n^2 + 3n+ 2)=n^3 +3n^2 + 2n
where 'n' represents the first integer. For example, if we take 'n' as 2, the three consecutive nonzero integers would be 2, 3, and 4. So, the product would be 2 * 3 * 4 = 24= (2)^3+ 3*(2)^2+ 2*2
How many different types of cross sections of a cone are possible? A.3
B.5
C.6
D.10
Solve for a.
7a-2b=5a-b
Answer: a=-3b
2
Step-by-step explanation:
get all letters on the same side so:
7a-5a (because when you cross the = you do the opposite)=-b+2b
2a=b
you are solving for a so: 2a/2=b/2
so the 2 cancel out and you have a=1/2b
The united states has 12,383 miles of coastline. If 0.8% of the coastline is located in Georgia, about how many miles of coastline are in Georgia
Answer:
99.064 miles of coastline are in Georgia.
Step-by-step explanation:
Consider the provided information.
The united states has 12,383 miles of coastline and 0.8% of the coastline is located in Georgia.
Now we need to find about how many miles of coastline are in Georgia.
Thus solve this as shown:
0.8% of 12,383
[tex]\frac{0.8}{100} \times 12,383[/tex]
[tex]0.008 \times 12,383[/tex]
[tex]99.064[/tex]
Hence, 99.064 miles of coastline are in Georgia.
40% of the men and 30% of the women also belong to a cycling club.
Work out the percentage of the whole membership that belong to a cycling club.
completa cada enunciado y escribe la proporción correspondiente. si por cada 21.000 se compran tres agendas ¿ con cuanto se compran nueve?
Identify the coefficients and variables in each expression. 5j-9cd+2 ??
Find the 55th derivative of y = cos(3x).
Final answer:
The 55th derivative of y = cos(3x) is recognized by repeating the derivative patterns of cosine functions and is found to be -27cos(3x).
Explanation:
The 55th derivative of y = cos(3x) can be found by recognizing that the derivatives of sine and cosine functions repeat every four steps. Considering the pattern cos(x) -> -sin(x) -> -cos(x) -> sin(x) -> cos(x), and that the derivative of cos(3x) is -3sin(3x), we can determine that the pattern repeats every four derivatives with a factor of 3n, where n is the number of times the derivative is taken.
The 55th derivative will be the same as the third derivative in the cycle, but with an iteration count of 55/4, which leaves a remainder of 3, so the 55th derivative will be -27cos(3x).
Please help me on this question