The greatest whole possible whole number length of the unknown side is 9 inches.
How to identify if a triangle is acute?Let us have:
H = biggest side of the triangle
And let we get A and B as rest of the two sides.
Then we get:
If
[tex]A^2 + B^2 < C^2[/tex]
then the triangle is acute
Two sides of an acute triangle measure as 5 inches and 8 inches
The length of the longest side is unknown.
We have to find the length of the unknown side
WE know that the longest side of any triangle is a hypotenuse
For an acute triangle we know:
[tex]A^2 + B^2 < C^2[/tex]
Here in this sum,
a = 5 inches
b = 8 inches
c = ?
Substituting we get,
[tex]A^2 + B^2 < C^2\\\\5^2 + 8^2 < C^2\\\\25 + 64= C^2[/tex]
c < 9
Hence, The greatest whole possible whole number length of the unknown side is 9 inches.
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Please help me with my math
200 people are asked about three brands of beverages Coffee, Tea and Chocolate. 36 like
Coffee only, 46 like Coffee but not Tea, 52 like Coffee, 16 like Tea and Chocolate, 96 like
Chocolate, 16 like Coffee and Chocolate while a total of 108 like one and only one of the
beverages.
Required
i) Calculate the number of people like black coffee?
ii) How many people don’t like any of the drinks?
Answer:
32
Step-by-step explanation:
Answer:
i) 52
ii) 66
Step-by-step explanation:
This sort of problem is usually solved using some sort of table or Venn diagram. We have used a table in the attachment such that each of the cells in the grid represents one of the 8 possible combinations of coffee, tea, or chocolate.
The numbers in black are given directly by the problem statement. The numbers in blue are calculated from the numbers in black and one of the other given numbers in the problem statement. The numbers in red are calculated so the totals work out correctly.
The cells shaded blue-gray are "one and only one" of the drinks. The cell shaded purple-gray is "don't like any".
__
i) black coffeeWe assume that any form of "coffee" is "black coffee." The problem statement tells us 52 people like coffee.
__
ii) noneThe last number we calculated is the number who like none of the drinks: 66. This brings the total of non-coffee drinkers to 148.
_____
Additional comment
As noted above, the colors more or less indicate the order of the calculations. We started with 36 who like coffee only, and 46 who like coffee and not tea. That means 46-36=10 like coffee and chocolate, but not tea.
Since 16 like coffee and chocolate, that leaves 16-10=6 who like coffee and tea and chocolate (all three).
96 like chocolate, but 16 of those like chocolate and tea. The other 80 like chocolate, but not tea.
46+16=52, so there must be 0 who like coffee and tea, but not chocolate.
The number who like only one is 108. We already have 36 that are coffee only, 80-10 = 70 that are chocolate only, so there must be 108 -70 -36 = 2 who like tea only.
Now, we can finish filling the top row of the table and the totals in the bottom row.
please I need the answer
Answer:
The answer is c
Step-by-step explanation:
one add the numbers 108 & 96=204
then add the numbers from c which is 30+30=60 43+43=86 29+29=58
then add 60+86+58 which will be 204 so c is the answer your welcome
come
Two lines are intersecting. What is the value of x?
Answer:
The correct answer is x = 51.
Step-by-step explanation:
We have been given an image of two intersecting lines. We are asked to find the value of x.
We can see that both angles are supplementary (adding up to 180 degrees), so we can set an equation as:
x + 23 + 2x + 4 = 180
x + 2x + 4 + 23 = 180
3x + 27 = 180
3x + 27 - 27 + 180 - 27
3x = 153
3x/3 = 153/3
x = 51
Therefore, the value of x is 51.
Hope this helps:) Goodluck!
Answer:
Step-by-step explanation:
2x + 4 + x + 23 = 180
3x + 27 = 180
3x = 153
x = 51
Just a little help :,(
Find the volume of the cone. Round your answer to the nearest tenth. Use 3.14 for T.
9 in.
in³.
3 in.
The volume is about
A recipe for trail mix calls for 234
2
3
4
cups of peanuts, 123
1
2
3
cups of cashews, and 116
1
1
6
cups of almonds.
How many cups of nuts are used in all?
Please please help please please help me please please help please please help me please please help please please help me please please help please please help me please please help please please help me please
Answer: 2+2= DA ROCK
Step-by-step explanation:
SCAM..... ITS ABOUT DRIVE ITS ABOUT POWER WE STAY HUNGRY WE DEVOURE PUT IN THE WORK PUT IN THE HOUR AND TAKE WHATS OURSSSSSSSSSSSSSSSSSSSSS
YEHHHHHHHH
The product of two numbers is 5, if their sum is 9/2. What are the numbers? with detail explaniation
Answer: The numbers are 2 and 2.5
Explanation:
Let one number be "x" and another "y", Note: 9/2 = 4.5 [in decimal form]
[tex]\rule{185}{2}[/tex]
Their product :
[tex]\hookrightarrow \sf x \ \cdot \ y = 5[/tex]
[tex]\hookrightarrow \sf x = \dfrac{5}{y} \quad \ \ \leftarrow \quad equation _1[/tex]
Their sum :
[tex]\hookrightarrow \sf x + y = 4.5[/tex]
[tex]\hookrightarrow \sf x = 4.5-y \quad \ \ \leftarrow \ equation_2[/tex]
Solve them simultaneously:
[tex]\rightarrow \sf 4.5 - y = \dfrac{5}{y}[/tex]
cross multiply
[tex]\rightarrow \sf y(4.5 - y) = 5[/tex]
distribute inside parenthesis
[tex]\rightarrow \sf -y^2 +4.5y - 5 = 0[/tex]
multiply by -1
[tex]\rightarrow \sf y^2 -4.5y + 5 = 0[/tex]
factor them out
[tex]\rightarrow \sf ( y - 2.5)(y - 2)= 0[/tex]
set to 0
[tex]\rightarrow \sf y = 2.5, \ 2[/tex]
Another number:
When one number is 2.5, then another: 4.5 - 2.5 = 2
When one number is 2, then another: 4.5 - 2 = 2.5
Hence, the numbers are 2.5 and 2
Check:
Product: 2 × 2.5 = 5Sum: 2 + 2.5 = 4.5 or 9/2The numbers obtained by the given condition that the product of two numbers is 5 if their sum is 9/2 will be x =( 2 or 5/2) and y = ( 2 or 5/2).
How to form an equation?Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.
In other words, an equation is a set of variables that are constrained through a situation or case.
Let's say the first number is x and the second is y then
Product xy = 5
Sum x + y = 9/2
substitute y = 9/2 - x into first
x( 9/2 - x) = 5
2x² - 9x + 10 = 0
2x² -5x -4x + 10 = 0
x( 2x - 5 ) -2( 2x -5 ) = 0
(x -2)(2x -5) = 0
x =2 and x = 5/2
Corresponding to x y will be y = 2 and y = 5/2.
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Ms. Lui earned an annual income of 775,000, what is the weekly salary?
Answer:
$14,903.85
Step-by-step explanation:
So, Ms. Lui earns $775,000 each year. To find the weekly salary, we have to divide the annual income by the amount of weeks in a year. There are about 52 weeks in one year. Let's find the weekly salary:
[tex]\frac{775000}{52} = 14,903.85[/tex]
Therefore, Ms. Lui earns $14,903.85 a week.
Hope this helps! If you have questions about my work, please leave them in the comments!
Design an instructional activity that could help learners recognise that decimal
fractions can be applied across environmental situations (relating to activities
in real life).
Fraction refers to a part of a whole; e.g when cup is not completely filled, it covers only a part of the cup
What is fraction?The term fraction refers to a part of a whole. To design an instructional activity that could help learners recognize that decimal fractions can be applied across environmental situations, we could look at certain things in the house.
For instance, when cup is not completely filled, it contains water that covers only an fraction of the cup. Also, we could boil a part and not a whole cup of rice. These are all examples of fractions.
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Which of the following equations is equivalent to S=pi r^2 h
The equation that is equivalent to S=pi r^2 h is h = S/pir^2
Subject of formulaThis is a way of representing a variable with another. Given the equation
S=pi r^2 h
We are to make 'h" the subject of the formula.
Divide both sides by pir^2
S/pir^2 =pi r^2 h/pir^2
h = S/pir^2
Hence the equation that is equivalent to S=pi r^2 h is h = S/pir^2
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Help please with me math!!
Answer:
17.3
Step-by-step explanation:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Find the difference between coordinates:
(x2 - x1) = (-9 - 8) = -17
(y2 - y1) = (-6 - -3) = -3
Square the results and sum them up:
(-17)^2 + (-3)^2 = 289 + 9 = 298
Now Find the square root and that's your result:
Exact solution: √298 = √298
Approximate solution: 17.2627
He was, without a doubt, the most prolific writer of mathematics of all time. Euler is credited as being the first mathematician to define function in the way we currently think of functions. In his book, Introductio in analysin infinitoriumin, he stated, “A function of a variable quantity is an analytic expression composed in any way whatsoever of the variable quantity and numbers or constant quantities.”
Based on what we know a function to be today, what did Euler mean by an analytic expression?
an expression formed with many variables and no numbers
an expression formed with many numbers and no variables
an expression formed from operations such as addition, multiplication, powers, and roots
an expression formed using only multiplication of a variable and a number
Based on what we know a function to be today, Euler mean an analytic expression "an expression formed from operations such as addition, multiplication, powers, and roots"
Euler's definition of a functionAccording to Euler, a function of a variable quantity is an analytic expression composed in any way whatsoever of the variable quantity and numbers or constant quantities.”
The function is. combination of expression which includes variables and constants using various operations such as roots, power and multiplication.
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11 12 13
18
A local charity holds a carnival to raise money. In one
activity, participants make a $3 donation for a chance
to spin a wheel that has 10 spaces with the values, 0,
1, 2, 5, and 10. Whatever space it lands on, the
participant wins that value. Let X represent the value of
a random spin. The distribution is given in the table.
Value of a Spin
0
1
2
5
10
Probability
0.4 0.2
0.2
0.1
0.1
20
Which of the following is the correct interpretation of
P(X<5)?
The correct interpretation of the probability P(X < 5) is; 0.8
How to Solve Probability?We are given the probability of the spin values are;
Probability of Spin Value of 0 = 0.4
Probability of Spin Value of 1 = 0.2
Probability of Spin Value of 2 = 0.2
Probability of Spin Value of 5 = 0.1
Probability of Spin Value of 10 = 0.1
P(X < 5) simply means the probability of getting a spin value less than 5. Thus;
P(X < 5) = P(0) + P(1) + P(2)
P(X < 5) = 0.4 + 0.2 + 0.2
P(X < 5) = 0.8
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A company boss is planning on ordering a gift for each of his employees. He takes a sample of 30 employees in the company and asks them what gift they would like. The table shows the information about his results. Gift Number of employees iPad 12 phone 5 watch 9 voucher 4 There are 110 employees in the company. Work out how many watches should be ordered.
Answer:
I think the answer is 33
Step-by-step explanation:
Extremely sorry if it's wrong
There are 5 new books and 6 used books on a shelf. (a) What is the ratio of used books to all books on the shelf?
What is the surface area of the rectangular prism
represented by the net shown?
6 in.
1.5 in.
1.5.in.
#2
The shape can be cut into four rectangles and two squares.
Total surface area:
⇒ four rectangles + two squares
⇒ 4(Length × Width) + 2(side × side)
⇒ 4(6 × 1.5) + 2(1.5 × 1.5)
⇒ 36 + 4.5
⇒ 40.5 inch²
Therefore, the surface area of the rectangular prism is 40.5 inch²
#3
The polygons that would be used in this net surface area are:
✔ rectangle
✔ square
Answer:
40.5 in²
Step-by-step explanation:
Formula applied :
Surface Area (rectangular prism)
⇒ 2(Length × Width + Width × Height + Length × Height)
=============================================================
Given :
⇒ Length = 6 inches
⇒ Width = 1.5 inches
⇒ Height = 1.5 inches
============================================================
Solving :
⇒ Surface Area = 2(6 × 1.5 + 1.5 × 1.5 + 6 × 1.5)
⇒ Surface Area = 2(9 + 2.25 + 9)
⇒ Surface Area = 2 × 20.25
⇒ Surface Area = 40.5 in²
Given that the line y=ax+b passes through the points A(0; 3) and B(-2;7), how do I find the values of a and b?
9 cm
6 cm
8 cm
12. Some high school students made a rectangular prism-shaped box, shown in the figure, to
will be available. Find the volume of the rectangular prism.
OA. 432 cm³
O B. 348 cm³
O C. 729 cm³
O D. 512 cm³
O Mark for review (Will be highlighted on the review page)
Answer:
A
Step-by-step explanation:
the answer is A because I said its C :)
What is the length of a diagonal of a square with a side length of 8?
A. 4
B. 42
C. 4√3
D. 8√√2
Will give 50 points for answer to this question
Determine the value of y.
135°
27°
24°
45°
A candidate for office plans to visit 6 cities before the state primary.
How many different ways can the campaign staff arrange her travel route?
Enter your answer as a whole number, like this: 42
Question 2
A candidate for office plans to visit 6 cities before the state primary.
How many different ways can the campaign staff arrange her travel route?
Enter your answer as a whole number, like this: 42
There are 720 different ways the campaign staff can arrange her travel route
How to determine the number of route?The given parameter is:
Cities = 6
The candidate cannot be at all 6 cities at the same time.
This means that we make use of factorial.
So, we have:
Ways = 6!
Evaluate the factorial expression
Ways = 720
Hence, there are 720 different ways the campaign staff can arrange her travel route
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What is the future value of a 5-year annuity due with annual payments of $ 2,535 , evaluated at a 14.18 percent interest rate? Enter your answer to the nearest $.01. Do not use $ or , signs in your answer. Enter your answer as a positive number.
Answer:
$19,201.09
Step-by-step explanation:
The future value of the annuity due can be found using any of a number of apps, calculators, or spreadsheets. It can also be found using the formula ...
A = P(1 +r)((1 +r)^n -1)/r
where P is the annual payment, r is the annual interest rate, and compounding is yearly for n years.
A = 2535(1.1418)(1.1418^5 -1)/0.1418 ≈ 19,201.09
The value will be $19,201.09.
Jasmine played in a basketball tournament. The ratio of the number of baskets she missed during the tournament to the number of baskets she made is 3:8. If Jasmine missed 9 baskets during the tournament, how many baskets did she make? Draw a diagram to demonstrate how you found your answer.
By using the given ratio, we will conclude that she made 24 baskets.
how many baskets did she make?
We know that the ratio of the number of baskets she missed to the number of baskets she made is 3:8.
This means, for each 3 missed baskets, she made 8.
Here we know that she missed 9. If we divide that by 3, we get:
9/3 = 3.
This means that she missed 3 baskets 3 times. And for each one of these 3 times she makes 8 baskets (for the given ratio).
Then we conclude that she makes 8*3 = 24 baskets.
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the perpendicular distance of a point from the x-axis is 4 units and the perpendicular distance from the y axis is 5 units write the coordinates of such a point if it lies in the first quadrant second quadrant third quadrant and fourth quadrant
Step-by-step explanation:
let p be the point which is at a distance of 4 units from the x-axis and at a distance of 5 units from the y axis
(i) When P lies in the first quadrant then the coordinates of P are (5,4).
(ii) When of P lies in the second quadrant then the coordinates of P are (-5,4).
(iii) When P lies in the third quadrant then the coordinates of P are (-5,-4).
(iv) When P lies in the fourth quadrant then the coordinates of P are (5,-4).
Hope it helps you!!Known as periodic reports, interim reports or interim statements, these updates provide important company information between annual reporting periods. To help protect investors and keep the public informed, regulations typically require public companies to submit company performance reports more than once a year.Known as periodic reports, interim reports or interim statements, these updates provide important company information between annual reporting periods. To help protect investors and keep the public informed, regulations typically require public companies to submit company performance reports more than once a year.
Which represents the inverse of the
function f(x) = 4x?
• h(x) = X + 4
O h(x) = x - 4
O h(x) = 3/4x
O h(x) = 1/4X
Answer:
Step-by-step explanation:
Find the value of x.
33°
107°
x
Answer:
140
Step-by-step explanation:
Angles in a triangle add up 180 :
180 = 107 + 33 + y
y = 180 - (107+33)
y = 180 - 140
y = 40
Angles on a straight line add up to 180 so :
180 = x + y
180 = x + 40
x= 180 - 40
x = 140
Hope this helped and have a good day
Answer:
x = 140°
Step-by-step explanation:
Concepts
The Exterior Angle Theorem states that the two remote angles in a triangle is equal to the exterior angle.
Application
In this case, the two remotes angles are 107 and 33°, and the exterior angle is x. Now, all we have to do is just add 107 and 33 to get our answer.
Solution
107 + 33140°Find the area of a regular polygon with 7 sides that has a perimeter of 63 inches and an apothem of 8 inches.
Area = [?]in2
Answer:
see the attachment photo!
If a multiple-choice test consists of 5 questions, each with 4 possible answers of which only 1 is correct, (a) in how many different ways can a student check off one answer to each question?
(b) in how many ways can a student check off one answer to each question and get all the answers wrong?
Answer:
(a) 1024 ways
(b) 243 ways
Step-by-step explanation:
When answers are independent, the total number of ways all questions can be answered is the product of the number of ways each question can be answered.
__
(a)The first question can have one answer 4 ways. The second question can be answered 4 ways for each of the ways the first question was answered. That is, the two questions can be answered 4×4 = 16 ways. Similarly, each additional question multiplies the number of ways the questions can be answered by 4.
The 5 questions can be answered 4×4×4×4×4 = 4^5 = 1024 ways.
__
(b)There are 3 ways to answer the first question incorrectly. Each additional question can be answered incorrectly 3 ways for each of the ways previous questions were answered. The total number of ways all questions can be answered incorrectly is ...
3^5 = 243
A student can answer all questions wrong in 243 different ways.