If RSTW is a rhombus,what is the area of WXT
Since RSTW is a rhombus, the area of ∆WXT is equal to 18√3 square units.
In Mathematics and Geometry, the length of the hypotenuse (longest side) of a 30°-60°-90° triangle is double (twice) the length of the shorter leg (adjacent side), and the length of the longer leg (opposite side) of a 30°-60°-90° triangle is √3 times the length of the shorter leg (adjacent side):
Hypotenuse = 12 units.
Adjacent side = 12/2 = 6 units.
For the value of x, we have;
Opposite side = √3 × adjacent side
x = √3 × 6
x = 6√3 units.
Now, we can determine the area of triangle WXT;
Area of triangle = 1/2 × base × height
Area of ∆WXT = 1/2 × XT × WX
Area of ∆WXT = 1/2 × 6 × 6√3
Area of ∆WXT = 18√3 square units.
Complete Question:
If RSTW is a rhombus, what is the area of ∆WXT?
how to memorize my timetables
To memorize your timetables, you can use mnemonic techniques, break down the tables into smaller chunks, and practice regularly.
Explanation:Multiplication tables, also known as timetables, can be challenging to memorize. However, there are several strategies that you can use to make the process easier. One effective method is to create mnemonics, which are memory aids that help you associate numbers with images or phrases. For example, you can associate the number 9 with the shape of a cat's tail, and whenever you see the number 9 in a multiplication problem, you can visualize a cat's tail to help you remember the answer.
Another useful strategy is to break down the tables into smaller, more manageable chunks. Start by memorizing the tables for numbers 0-5, and once you feel comfortable with them, move on to the tables for numbers 6-10. By tackling smaller chunks, you can avoid overwhelming yourself and improve your retention.
Finally, practice regularly and consistently. The more you review the timetables, the more familiar they will become. Consider using online resources, flashcards, or interactive games to make the practice sessions more engaging and enjoyable. Over time, with practice and perseverance, you will gradually memorize your timetables.
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Which proportion would you use to set up to change 6 cups to pints?
Answer:
A) is the answer
Step-by-step explanation:
it worked
A soup recipe calls for 23/4 quarts of broth. An open can of broth contains 1/2 quart of broth. How much more broth do you need to make the soup?
What is (5/8) multiplied by (2/3)
Elevators have safety limits for how much weight they can lift. The elevator at the Terrace Hotel can hold up to 2,100 pounds. write an equation or inequality that represents the allowable weight on the elevator at the Terrace Hotel. Graph the solution to the equation or inequality you wrote on the number line. Explain your answer.
A triangle can be formed with side lengths 3 in, 5 in, and 9 in. (5 points) True False
Answer:
its false, i did the test
Step-by-step explanation:
5/8 of votes were blue,5/9 of remaining were for green and the remaining 48 votes were for red
There were [tex]\(38\)[/tex] votes for blue and [tex]\(13\)[/tex] votes for green.
Let's break it down step by step:
1. Votes for Blue:
Initially, [tex]\(5/8\)[/tex] of the votes were for blue. Let's denote the total number of votes as [tex]\(T\).[/tex]
So, the number of votes for blue initially is [tex]\(5/8\) of \(T\)[/tex], which is [tex]\((5/8) \times T\)[/tex].
2. Remaining votes after blue:
After blue votes are accounted for, the remaining votes are [tex]\(T - (5/8) \times T = (3/8) \times T\).[/tex]
3. Votes for Green:
[tex]\(5/9\)[/tex] of the remaining votes are for green. So, the number of votes for green is [tex]\((5/9) \times (3/8) \times T\)[/tex].
4. Votes for Red:
The remaining votes after blue and green are accounted for are 48 votes.
To find the solution, we need to set up equations based on the information given:
Equation 1: Votes for blue + Votes for green + Votes for red = Total votes
Equation 2: Votes for green = \(5/9\) of remaining votes
Equation 3: Votes for red = 48
Let's solve these equations:
Equation 1:
[tex]\[\frac{5}{8}T + \frac{5}{9} \times \frac{3}{8}T + 48 = T\][/tex]
Equation 2:
[tex]\[\frac{5}{9} \times \frac{3}{8}T = \frac{15}{72}T = \frac{5}{24}T\][/tex]
Now, let's substitute the value of [tex]\(T\)[/tex] from Equation 3 into Equation 1:
[tex]\[\frac{5}{8} \times \frac{48}{5} + \frac{5}{9} \times \frac{3}{8} \times \frac{48}{5} + 48 = \frac{48}{8} + \frac{15}{24} \times \frac{48}{5} + 48 = 6 + 3 \times 2 + 48 = 60\][/tex]
So, we have [tex]\(T = 60\).[/tex]
Now, let's find the number of votes for blue and green:
Votes for blue:
[tex]\[\frac{5}{8} \times 60 = 37.5\][/tex]
Votes for green:
[tex]\[\frac{5}{24} \times 60 = 12.5\][/tex]
Since we can't have half votes, we round 37.5 to 38 and 12.5 to 13.
So, there were [tex]\(38\)[/tex] votes for blue and [tex]\(13\)[/tex] votes for green.
The correct question is:
5/8 of the votes were for blue. 5/9 of the remaining votes were for green and the remaining 48 votes were for red. How many votes were for blue? How many votes were for green?
Grace saw 16 bird habitats at the zoo's aviary. The sign said each habitat had 12 birds.How many birds were in all?
Kateri draws a square. She wants to draw one line to draw one line to divide the square into 2 triangles. Is it possible for her to divide the square into 2 obtuse triangles? Explain
A square can be divided into two right-angled triangles with one line, but it can't be divided into two obtuse triangles because none of the angles in a square is more than 90 degrees.
Explanation:
No, it is not possible for Kateri to divide the square into two obtuse triangles by drawing just one line. An obtuse triangle is a triangle that has an angle greater than 90 degrees. However, a square is made up of four 90-degree angles. Therefore, when a square is divided into two triangles with one line, the maximum degrees any angle in resulting triangles would get is 90, hence they would be right-angled triangles and not obtuse triangles.
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The bases of an isosceles trapezoid are represented by 4x and 2x. The height of the trapezoid is represented by (x − 6). Which polynomial expression BEST represents the area of the trapezoid?
A) 3x2 − 18x
B) 3x2 + 18x
C) 3x − 18
D) 6x2 + 36x
Molly says that 4/8 is always the same as 1/2. Andrew says that 4/8 and 1/2 are equivalent fractions, but they could be different amounts. Use the models below to determine which student is correct. Explain.
how to simplify -7+(-7)
When 27x^2z/-3x^2z^6 is completely simplified, the exponent on the variable z is _____.
Final answer:
The expression 27x^2z/-3x^2z^6 simplifies to -9/z^5, so the simplified exponent on the variable z is -5.
Explanation:
When simplifying the expression 27x^2z/-3x^2z^6, we divide the coefficients and apply the laws of exponents. This means we divide 27 by -3 and subtract the exponents of like terms with variables of the same base.
27/-3 equals -9, and for the variables we subtract the exponents, for x^2 we have x^2/x^2 which simplifies to x^0 and for z we have z^1/z^6, simplifying to z^(1-6) which is z^-5. However, because negative exponents denote division by that variable to the positive exponent, z^-5 represents 1/z^5.
The final simplified expression is -9/z^5. Thus, the exponent on the variable z when the expression 27x^2z/-3x^2z^6 is completely simplified is -5.
If you buy 20 tickets for $6.00, how much are you paying per ticket?
Question 1 options:
.10
.20
.30
.40
Two friends work at different companies, P and S. Both companies use the number of hours that an employee works to calculate that employee’s vacation hours. In Company P if you work 10 hours you get 0.4 vacation hours, while in Company S if you work 100 hours you get 7 vacation hours. What is the difference in each friend’s vacation hours if both work 2,080 hours?
Answer:
62.4 hours
Step-by-step explanation:
For P:
Number of hours off on 10 hours of working=0.4
Number of hours on 2080 hours of working=2080/10*0.4
=83.2 hours
For S:
Number of hours off on 100 hours of working=7
Number of hours on 2080 hours of working=2080/100*7
=145.6 hours
The difference between the vacation hours of P and S is of 62.4 hours. S will get more hours of vacation.
the difference in vacation hours between the two friends is 62.4 vacation hours.
For company P:
We know that 10 working hours give 0.4 vacation hours. So, to find vacation hours for 2080 hours, we can set up the following proportion:
[tex]\frac{10}{0.4} = \frac{2080}{vacation\ hours\ of 2080\ working\ hours}[/tex]
Solving this we get:
[tex]vacation\ hours\ of\ 2080\ working\ hours = \frac{0.4 \times 2080}{10} = 0.04 \times 2080 = 83.2\ days[/tex]
Now for company S:
We know that 100 working hours give 7 vacation hours. So, to find vacation hours for 2080 hours, we can set up the following proportion:
[tex]\frac{100}{7} = \frac{2080}{vacation\ hours\ of 2080\ working\ hours}[/tex]
Solving this we get:
[tex]vacation\ hours\ of\ 2080\ working\ hours = \frac{7 \times 2080}{100} = 0.07 \times 2080 = 145.6\ days[/tex]
Finally, find the difference in vacation hours:
[tex]Difference = 145.6 - 83.2 = 62.4\ vacation\ hours[/tex]
Therefore, the difference in vacation hours between the two friends is 62.4 vacation hours.
Write the expression using only positive exponents. Assume no denominator equals zero. I will give brainliest!
By what percent will a fraction decrease if its numerator is decreased by 50% and its denominator is decreased by 25%? Quick I need an answer!!!!
Write a function rule for the table
Find the volume for a sphere with a radius of 7 cm. ROUND TO THE NEAREST WHOLE NUMBER
A.)307cm^3
B.)1,436 cm^3
C.)1,020cm^3
D.)615cm^3
Find the radius of a sphere with a surface area of 804 cm^2
A.) 9cm
B.)8cm
C.)64cm
D.)204cm
Answer:
im sorry i dont get it
Step-by-step explanation:
since y+y=y^2 also they following
A rectangular prism has a length of 114 centimeters, a width of 4 centimeters, and a height of 314 centimeters.
What is the volume of the prism?
Enter your answer in the box as a simplified mixed number or a decimal.
________m³
Answer:
Volume of rectangular prism = [tex]\frac{65}{4}=16\frac{1}{4}=16.25[/tex]
Step-by-step explanation:
Given : A rectangular prism has a length of [tex]1\frac{1}{4}[/tex] centimeters, a width of 4 centimeters, and a height of [tex]3\frac{1}{4}[/tex] centimeters.
We have to find the volume of prism.
We know,
Volume of rectangular prism = length × width × height
Given : Length = [tex]1\frac{1}{4}[/tex] centimeters = [tex]\frac{5}{4}[/tex]
Width = 4 centimeters, and
height = [tex]3\frac{1}{4}[/tex] centimeters = [tex]\frac{13}{4}[/tex]
Thus, Volume of rectangular prism = [tex]\frac{5}{4}\times 4\times \frac{13}{4}[/tex]
Simplify, we have,
Volume of rectangular prism = [tex]\frac{65}{4}=16\frac{1}{4}=16.25[/tex]
The volume of the given rectangular prism is 0.143184 cubic meters (m³).
The formula of the volume of a rectangular prism is:
Volume = Length × Width × Height
Given the dimensions:
Length = 114 cm
Width = 4 cm
Height = 314 cm
First, multiply the length and the width:
Length × Width = 114 cm × 4 cm = 456 cm²
Next, multiply this result by the height:
456 cm² × 314 cm = 143,184 cm³
Therefore, the volume of the rectangular prism is:
143,184 cm³
Now, to convert this into cubic meters (m³), note that 1 m³ = 1,000,000 cm³:
Volume in m³ = 143,184 cm³ ÷ 1,000,000 = 0.143184 m³
So, the volume of the prism is 0.143184 m³.
Evaluate 42 ÷ (5 − 3). 2 8 16 32
What fraction of this model,in simplest form,is shaded?u
Answer:2/10 is equal to
any even number has to have a half like 2 4 6 8
2 is half of 4 1 is half of 2 4 is half of 8 and so on
the fractiom is shaded into 2/10
5/10
your wecs :0 ;)
What is the missing number 200,188,152,80,8
Claire and Marisa are both waiting to get a rebound during a basketball game. If the height of the basketball hoop is 10 feet, the angle of elevation between Claire and the goal is 35°, and the angle of elevation between Marisa and the goal is 25°, how far apart are they standing?
Using trigonometry, Claire is approximately 19.42 feet away from Marisa, given their angles of elevation and the hoop's height.
Using trigonometry, we can find the distance between Claire and Marisa:
[tex]\[ \text{Let } h \text{ be the height of the basketball hoop.} \][/tex]
[tex]\[ \text{Distance}_{\text{Claire}} = \frac{h}{\tan(35°)} \][/tex]
[tex]\[ \text{Distance}_{\text{Marisa}} = \frac{h}{\tan(25°)} \][/tex]
[tex]\[ \text{Distance}_{\text{Claire-Marisa}} = \text{Distance}_{\text{Claire}} - \text{Distance}_{\text{Marisa}} \][/tex]
[tex]\[ \text{Distance}_{\text{Claire-Marisa}} = \frac{h}{\tan(35°)} - \frac{h}{\tan(25°)} \][/tex]
[tex]\[ \text{Distance}_{\text{Claire-Marisa}} = h \times \left( \frac{1}{\tan(35°)} - \frac{1}{\tan(25°)} \right) \][/tex]
Given [tex]\( h = 10 \)[/tex] feet:
[tex]\[ \text{Distance}_{\text{Claire-Marisa}} = 10 \times \left( \frac{1}{\tan(35°)} - \frac{1}{\tan(25°)} \right) \][/tex]
[tex]\[ \text{Distance}_{\text{Claire-Marisa}} \approx 19.42 \text{ feet} \][/tex]
So, Claire and Marisa are standing approximately 19.42 feet apart.
Ki’von has a sink that is shaped like a half-sphere. The sink has a diameter of 20 inches. One day, his sink clogged. He has to use one of two different cups to scoop the water out of the sink. The sink is completely full when Ki’von begins scooping.
(a) What is the exact volume of the sink? Show your work.
(b) One conical cup has a diameter of 8 in. and a height of 6 in. How many cups of water must Ki’von scoop out of the sink with this cup to empty it? Round the number of scoops to the nearest whole number. Show your work.
(c) One cylindrical cup has a diameter of 4 in. and a height of 6 in. How many cups of water must he scoop out of the sink with this cup to empty it? Round the number of scoops to the nearest whole number. Show your work.
What is 10 meters increased by 25%
Need help on this one
Jessica has 5 members in the sewing club that she started. In order to get school sponsorship she must have at least 30 members. How many more members does she need? Write an inequality that models this situation.
A) 5 + x ≥ 30
B) 5 + x ≤ 30
C) 30 + x ≥ 5
D) 30 + x ≤ 5
a local hamburger shop sold a combined total of 757 hamburgers and cheeseburgers on Sunday. There were 57 more cheeseburger sold than hamburgers. How many hamburgers were sold on Sunday?