The dimension of the rectangle will be 6 inches by 3 inches.
What is the area and perimeter of the rectangle?Assume L is the length and W is the width. Then the area is given as,
A = L × W
And the perimeter is given as,
P = 2(L + W)
A rectangular note card has an area of 18 square inches. Its perimeter is 18 inches. Then the equations are given as,
18 = 2(L + W)
9 = L + W ...1
L x W = 18 ...2
From equations 1 and 2, then we have
L x (9 - L) = 18
L² - 9L + 18 = 0
L² - 6L - 3L + 18 = 0
L(L - 6) - 3(L - 6) = 0
(L - 6)(L - 3) = 0
L = 3, 6
Then the width of the rectangle will be calculated as,
W = 9 - 3 = 6
W = 9 - 6 = 3
Then the dimension of the rectangle will be 6 inches by 3 inches.
More about the area and perimeter of the rectangle link is given below.
https://brainly.com/question/16572231
#SPJ2
Solve for x under the assumption that x > 0. Enter your answer in interval notation using grouping symbols.
x−24/x<10,
The solution for the set would be: x is (0,12).
What is the solution?
To arrive at the solution, we would first move the constant term to the right side as follows;
x - 24/x < 10
x < 10 + 24/x
We then multiply both sides by x to eliminate the fraction:
x² < 10x + 24
Collect all terms to one side;
x² - 10x - 24 < 0
Factorize
(x - 12)(x + 2) < 0
So, x - 12 is positive when x > 12 and negative when x < 12.
x + 2 is positive for all values of x > 0.
my sister needs help on this?can anyone give an explanation and answer/show work? you'll be brainliest if you do! thank you so much for taking the time :) v
Felicity recorded the number of laps she swam each month for 7 months.Her data is shown.
112,134,150,98,120,68,116
Which is the mean absolute deviation to the nearest whole number of Felicity's lap data?
A.16
B.18
C.20
D.36
Answer C
to calculate mean absolute deviation, we need to use the formula = (∑|x-mean|)/n
where x is each term given in data set
n is number of terms = 7
mean = sum of terms / n = (112+134+150+98+120+68+116)/7 = 114
now find (∑|x-mean|) = 138
MAD = (∑|x-mean|) / n = 138 /7 = 19.714 = 20
Which transformations are rotations?
Choose all answers that are correct.
ANSWER NOW PLEASE! EXTRA POINTS!
1) Martha is covering this trapezoid-shaped board with fabric. How many square feet of fabric does Martha need?
2) A garden in the shape of a regular hexagon has sides that are each 5 meters long. If the height of each of the congruent triangles within the hexagon is about 4.33 meters,what is the area of the garden?
part one: How do you solve a system of equations approximately using graphs and tables?
part 2: A lake has a native population of 1,000 frogs. The native frog population increases at a rate of 200 frogs per year. A new species of 10 frogs migrates to the lake. This new species’ population increases at a rate of 50% per year. When will the two populations equal each other? Select to reveal each frog population’s growth model.
the rest: A system of equations can be created with the two functions to determine when the populations will have the same population output value, y.
y = 200x + 1,000
y = 10(1.5x)
To determine when the populations will be equal, set the equations equal to each other, and solve for x.
200x + 1,000 = 10(1.5x)
This equation is a little more challenging to solve by algebraic methods. In this lesson, you will solve systems of equations like the one above approximately by effectively using technology and tables.
what is x in the equation
4(x+6)= 5(x+9)+4x?
If (3x + 17) is equivalent to (4x - 8) what is x
whats the answer to 8n−15=41
solve - 2 x 3 + 22 - 8 - 2 =
in a exponent 3 + 3 + 3 + 3 + 3
Read the word problem. Hershel buys 5 bags of cookies, 3 bags of granola, and several bags of fruit snacks from a bake sale. In total, he buys 10 bags from the bake sale. How many bags of fruit snacks did Hershel buy? Which type of word problem is shown? part-whole comparison multiplication division
Final answer:
Hershel bought 2 bags of fruit snacks in a part-whole comparison word problem, where the total (10 bags) minus the sum of known parts (5 bags of cookies and 3 bags of granola) equals the unknown part.
Explanation:
The word problem presented asks how many bags of fruit snacks Hershel bought if he bought a total of 10 bags, including 5 bags of cookies and 3 bags of granola. To solve this, we subtract the known quantities from the total: 10 total bags - 5 bags of cookies - 3 bags of granola = 2 bags of fruit snacks.
The type of word problem shown is a part-whole comparison because it involves figuring out a missing part of a whole based on the other known parts.
At the Roadside Restaurant, each milkshake comes with 2 straws.
Which equation shows the number of straws the restaurant will use if they serve m milkshakes?
Use t to represent the total number of straws used and m to represent the number of milkshakes served.
A.
t = 2m
B.
t = 2 + m
C.
t = 2 – m
D.
t =
How many triangles exist with the given angle measures? 32°, 51°, 97°
The correct answer is 1.
To determine if a set of three angles can form a triangle, we need to check if the sum of the three angles is equal to 180°. If the sum is 180°, then the angles can form a triangle; otherwise, they cannot form a triangle.
Given angles: 32°, 51°, 97°
we can represent the calculation as follows:
[tex]\text{Sum of the given angles} &= 32^\circ + 51^\circ + 97^\circ&= 180^\circ[/tex]
Since the sum of the three given angles is equal to 180°, these angles can form a triangle.
To determine the number of triangles that exist with these angle measures, we need to consider the permutations of the angles. Since the order of the angles does not matter in a triangle, we have:
[tex]\text{Number of triangles} = \frac{3!}{3} = 1[/tex]
Therefore, there exists only one triangle with the given angle measures of 32°, 51°, and 97°.
Please help! Picture included!!!
In the figure below, triangle ABC is similar to triangle PQR.
What is the length of PQ?
A)18
B)4
C)32
D)6
Which ordered pairs are solutions to the inequality 2x+3y≥−1?
Final answer:
To find the ordered pairs that are solutions to the inequality 2x+3y≥−1, we can solve the inequality and substitute different x-values to find corresponding y-values.
Explanation:
To find the ordered pairs that are solutions to the inequality 2x+3y≥−1, we can use a graph or a table of values.
Let's solve the inequality for y:
2x + 3y ≥ -1
3y ≥ -1 - 2x
3y ≥ -2x - 1
y ≥ (-2/3)x - 1/3
Now we can choose some x-values and substitute them into the inequality to find corresponding y-values:
Let's choose x = 0:
y ≥ (-2/3)(0) - 1/3
y ≥ 0 - 1/3
y ≥ -1/3
So one ordered pair that is a solution is (0, -1/3).
Let's choose x = 3:
y ≥ (-2/3)(3) - 1/3
y ≥ -2 - 1/3
y ≥ -7/3
So another ordered pair that is a solution is (3, -7/3).
In a 30-60-90 triangle, what is the length of the hypotenuse when the shorter leg is 5 cm?
Enter your answer in the box.
The length of the hypotenuse is 10cm
SOH CAH TOA identityGiven a 30-60-90 triangle where:
Length of the shorter leg = 5cm (adjacent)
The hypotenuse is what we need.
[tex]cos \theta = \frac{adj}{hyp} \\ [/tex]
Substitute the given parameters
[tex]cos 60 = \frac{5}{h}\\ h =\frac{5}{cos 60}\\ h = \frac{5}{0.5}\\ h = 10cm[/tex]
Hence the length of the hypotenuse is 10cm
Learn more on SOH CAH TOA here: https://brainly.com/question/20734777
0.135 written as a fraction is _____.
The decimal 0.135 can be written as 27/200 in fractions.
What is a Fraction?A fraction is a number that can be expressed as p/q, where q is not equal to zero.
It is defined as part of the whole.
0.135 is a decimal and to convert into a fraction it has to be written as
=135/1000
On simplifying the fraction
=27/200
Therefore, the decimal 0.135 can be written as 27/200 in fractions.
To know more about Fraction
https://brainly.com/question/10354322
#SPJ2
Calculate the altitude of a triangle corresponding to its shortest side of it's area is 720cm², perimeter is 180cm and two of its sides are 80cm and 18cm.
The graph of a linear function has a slope of 5, and it passes through the point (–7, 5). What is the value of the dependent variable when the independent variable is equal to 2?
Final answer:
To find the value of the dependent variable, we use the point-slope form of the linear equation. Using the given slope of 5 and point (-7, 5), we first find the y-intercept to be 40. We then calculate the dependent variable's value to be 50 when the independent variable is 2.
Explanation:
The student has asked about the value of the dependent variable when the independent variable is 2 for a given linear function that has a slope of 5, and passes through the point (–7, 5). To find this value, one should use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept.
First, using the given point (–7, 5), we can find the y-intercept by substituting the slope and point into the equation:
y = 5x + b
5 = 5(-7) + b
b = 5 + 35
b = 40
So the equation of the line is y = 5x + 40. Now, to find the value of y when x is 2:
y = 5(2) + 40
y = 10 + 40
y = 50
Therefore, the value of the dependent variable when the independent variable is 2 is 50.
Mrs. Cho has 24 students in her class. Some of her students are also in the play. Explain why it is not possible for exactly 24% of the students in Mrs. Cho’s class to be in the play.
which value is a solution of the equation 2-8x=-6 ? ( 1point )
A. 1
B. 1/2
c. -1
d. 8,
Factor completely 3x(x + 2) + 4(x + 2). (1 point)
(x + 2)(7x)ANSWER
[tex](x + 2)(3x + 4)[/tex]
EXPLANATION
The given expression is
[tex]3x(x + 2) + 4(x + 2)[/tex]
We can see that (x+2) is the greatest common factor.
We factor to obtain;
[tex](x + 2)( 3x + 4)[/tex]
The correct choice is C.
Answer:
(x + 2) (3x + 4)
Step-by-step explanation:
I got it correct on my test
You are an accountant doing an audit for a law firm. A paralegal worked for a client for 5 hours per day for 3 days. The client was billed $50 per hour, and the paralegal was paid $30 per hour. After the paralegal’s wages were paid, what was the amount made by the law firm?
The areas of two similar octagons are 112 in.² and 63 in.². What is the ratio (larger to smaller) of their perimeters?
16/3
4/9
16/9
4/3,
Domain -1,4,5,3,-5 Range n,w,y,n,w is this a function
please help me on this question
and explain.
At Devon's new job he spent $12.99, $10.50, $9.89, $6.90, and $7.58 on lunch the first week.
In the second week, he spent $2 more in total for the 5 lunches than the first week.
What is the increase in the mean for the second week compared to the first?
Round the answer to the nearest penny.
Enter your answer in the box.
$
The increase in the mean for the second week compared to the first with the given parameters is; $0.40
Let us first find the mean of the lunch costs for the first week;
Mean for first week = ($12.99 + $10.50 + $9.89 + $6.90 + $7.58)/5 = $9.572
We are told that he spends a total of $2 more on lunch in the second week.
Second week total = $12.99 + $10.50 + $9.89 + $6.90 + $7.58 + $2 = $49.86.
Mean of second week = 49.86/5 = $9.972
The increase in the mean for the second week compared to the first is;
9.972 - 9.572 = $0.40
Read more about average increase at; https://brainly.com/question/11360390
A ladder reaches a window 20 feet above the ground. The foot of the ladder is 4 feet from the wall. Which of the following measures correspond to the length to the laddder? Round to the nearest hundredth
Answer:
20.40
Step-by-step explanation:
Test Yourself
The area of a rectangle is 54 m^2 , and the length of the rectangle is 3m more than twice the width. find the dimensions of the rectangle.
Could I get the answer, all work and explanation for this problem?
[tex]y = - x + 10 \\ y = x + 2[/tex]