What is the number of square units in the area of the triangle whose vertices are points (2,0), (6,0), (8,5)
Answers
you can pretty much just count how many units for the base, and height.
Answer: 10 square units.
Step-by-step explanation:
The area of triangle with vertices [tex](x_1,y_1),(x_2,y_2)\text{ and }(x_3,y_3)[/tex] is given by :-
[tex]A=\dfrac{1}{2}[x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)][/tex]
Given : The vertices of triangle : (2,0), (6,0), (8,5)
Then , the area of the triangle will be :_
[tex]A=\dfrac{1}{2}[(2)((0)-(5))+(6)((5)-(0))+(8)((0)-(0))\\\\\Rightarrow A=\dfrac{1}{2}[20]\\\\\Rightarrow A=10\text{ square units}[/tex]
Hence, the number of square units in the area of the triangle whose vertices are points (2,0), (6,0), (8,5) = 10
Related Questions
Let r(t)=⟨t2,1−t,4t⟩. calculate the derivative of r(t)⋅a(t) at t=5, assuming that a(5)=⟨−4,4,−5⟩ and a′(5)=⟨−5,9,3⟩
Answers
[tex]\implies\mathbf r'(t)=\langle 2t,-1,4\rangle[/tex]
[tex]\dfrac{\mathrm d(\mathbf r(t)\cdot\mathbf a(t))}{\mathrm dt}\bigg|_{t=5}=\mathbf r'(5)\cdot\mathbf a(5)+\mathbf r(5)\cdot\mathbf a'(5)[/tex]
[tex]=\langle10,-1,4\rangle\cdot\langle-4,4,-5\rangle+\langle25,-4,20\rangle\cdot\langle-5,9,3\rangle[/tex]
[tex]=(-40-4-20)+(-125-36+60)[/tex]
[tex]=-165[/tex]
A number N is multiplied by 3. The result is the same as when N is divided by 3. What is the value of N?
Answers
Answer:
[tex]N=0[/tex]
Step-by-step explanation:
We have been given that a number N is multiplied by 3. So our number would be [tex]3\cdot N[/tex].
We are also told that N is divided by 3. So our number would be [tex]\frac{N}{3}[/tex].
As we are told that the both results are same, so we can equate both expressions as:
[tex]3\cdot N=\frac{N}{3}[/tex]
[tex]3*3\cdot N=\frac{N}{3}*3[/tex]
[tex]9N=N[/tex]
[tex]9N-N=N-N[/tex]
[tex]8N=0[/tex]
[tex]\frac{8N}{N}=\frac{0}{N}[/tex]
[tex]N=0[/tex]
Therefore, the value of N is 0.
Jeremiah is asked to write the equation of an ellipse. He is given one vertex along the major axis and the location of the center. He realizes he does not have enough information to write the equation. He asks his teacher for one additional piece of information. What information could Jeremiah ask for to help him write the equation? Check all that apply.
-the location of the focus nearest the given vertex
-the location of the focus nearest the other vertex
-the location of the other vertex along the major axis
-the location of one covertex along the minor axis
-the location of the directrix nearest the given vertex
-the location of the directrix nearest the other vertex
-the length of the minor axis
Answers
Jeremiah needs additional information such as the location of the foci, the other vertex on the major axis, a covertex along the minor axis, or the length of the minor axis to write the equation of the ellipse that is options A, B, C, D and G are correct.
Jeremiah is asked to write the equation of an ellipse given one vertex along the major axis and the location of the center.
He realizes he does not have enough information. He could ask for the following additional pieces of information to help him write the equation:
The location of the focus nearest the given vertexThe location of the focus nearest the other vertexThe location of the other vertex along the major axisThe location of one covertex along the minor axisThe length of the minor axisWith any of these pieces of information, he could determine the necessary parameters to complete the equation of the ellipse.
Jeremiah could ask for the other information that is the location of the other vertex along the major axis, the location of one covertex along the minor axis, the length of the minor axis and the location of the focus nearest the given vertex.
To write the equation of an ellipse, Jeremiah needs more information. Given the center and one vertex along the major axis, he can ask for:
The location of the other vertex along the major axis: This will help determine the length of the major axis.The location of one covertex along the minor axis: This will help find the length of the minor axis.The length of the minor axis: Directly needed to formulate the equation.The location of the focus nearest the given vertex: This helps identify the distance from the center to the foci, which is necessary for finding the equation.With any of this additional information, Jeremiah can confidently determine the parameters required to write the equation of the ellipse.
What is 75% of the area of a circle with a circumference of 10 units? Round the solution to the nearest square unit.
Answers
area=pir^2
so if c=10units
10=2pir
5=pir
5/pi=r
sub for area
area=pir^2
area=pi(5/pi)^2
area=pi(25/pi^2)
area=25/pi
75% or 3/4 of that is
25/pi times 3/4=75/(4pi)
use calculator
5.9683103659460750913331411264693 square units
or rounded
6 square units
Answer: 6 sq. units
Step-by-step explanation:
The formula to find the circumference of a circle is given by :-
[tex]C=2\pi r[/tex], where r is the radius of the circle.
Given : Circumference = 10 units
Then , [tex]10=2\pi r[/tex]
[tex]\\\\\Rightarrow\ r=\dfrac{10}{2\pi}\approx1.59[/tex]
The area of a circle is given by :-
[tex]A=\pi r^2=\pi(1.59)^2=7.9422603875\approx7.94\text{ sq. units}[/tex]
Now, the 75 % of the area is given by :-
[tex]0.75\times7.94=5.955\approx6\text{ sq. units}[/tex]
Hence, 75% of the area of a circle with a circumference of 10 units = 6 sq. units
A cone shaped funnel has a radius of 3 inches and a height of 7 inches.
Betty closes the nozzle of the funnel and fills it completely with a liquid. She then opens the nozzle. If the liquid drips at the rate of 14 cubic inches per minute, how long will it take for all the liquid in the funnel to pass through the nozzle? (Use π = 3.14.)
A) 4.71 minutes
B) 3.14 minutes
C) 14.13 minutes
D) 9.42 minutes
Answers
= Pi(3*3)*7/3 = 4.71
Answer A
Hence, it will take 4.71 minutes for all the liquid in the funnel to pass through the nozzle.
Step-by-step explanation:A cone shaped funnel has a radius(r) of 3 inches and a height(h) of 7 inches.
Now, the volume(V) of the cone is given as:
[tex]V=\dfrac{1}{3}\times (\pi r^2h)[/tex]
Hence, on putting the value of r and h in the formula of volume we obtain the volume of cone funnel as:
[tex]V=\dfrac{1}{3}\times (3.14\times (3)^2\times 7)\\\\\\V=\dfrac{1}{3}\times (197.82)\\\\V=65.94 \ in^3[/tex]
If the liquid drips at the rate of 14 cubic inches per minute.
i.e. for 14 cubic inches it takes 1 minutes.
Now for 1 cubic inches it will take:
[tex]\dfrac{1}{14} \ min.[/tex]
Hence, for all the liquid ( i.e. 65.94 cubic inches) to pass the nozzle is the time taken is:
[tex]\dfrac{65.94}{14}\ min.\\\\=4.71\ min.[/tex]
Hence, it will take 4.71 minutes for all the liquid in the funnel to pass through the nozzle.
Henry Devine bought a new dishwasher for$320 he paid $20 down and made 10 monthly payments of $34 what actually yearly rate did Henry pay
Answers
Amount financed
320-20=300
Total payments
34×10=340
Total interest=total payments-amount financed
Total interest=340-300=40
Now to find the yearly interest rate use the formula of
I=(2yc)÷(m×(n+1))
I ?
Y number of months in a year 12
C total interest 40
M amount financed 300
N number of payments 10
I=(2×12×40)÷(300×(10+1))
I=0.2909×100=29.09%
What is 45 ones times 10?
Choices are:
45 hundreds
45 tenths
or 45 tens.
Answers
Answer:
Option 3 - 45 tens
Step-by-step explanation:
Given : Expression 45 ones times 10.
To find : What is the expression?
Solution :
We know that,
"one" means " 1
We have 45 ones means multiply 45 by 1.
[tex]45\text{ ones}=45\times 1=45[/tex]
Now, 45 ones times 10 means
[tex]45\times 10=450[/tex]
450 means 45 tens as tens is 10.
So, The correct choice is 45 tens.
Therefore, Option 3 is correct.
Expressions 4 tens + 6 tens in standard form
Answers
I hope this helps^^
What is the value of s in the equation 3r=10+5s when r=10
Answers
30 = 10+5s
20 = 5s
s = 4
Answer:
[tex]s=4[/tex].
Step-by-step explanation:
We have been given an equation [tex]3r=10+5s[/tex]. We are asked to find the value of 's', when [tex]r=10[/tex].
To find value of 's', we will substitute [tex]r=10[/tex] in our given equation as shown below:
[tex]3(10)=10+5s[/tex]
[tex]30=10+5s[/tex]
Upon subtracting 10 from both sides of our given equation, we will get:
[tex]30-10=10-10+5s[/tex]
[tex]20=5s[/tex]
Now, we will divide both sides of our equation by 5.
[tex]\frac{20}{5}=\frac{5s}{5}[/tex]
[tex]4=s[/tex]
Therefore, the value of 's' is 4, when [tex]r=10[/tex].
Simplify: (4a + 2b)(a - b)
A) 4a^2 - 6ab - 2b^2
B) 4a^2 - 2ab - 2b^2
C) 4a^2 - 8ab - 2b^2
D) 4a^2 + 2ab - 2b^2
Answers
If a squared + b -c÷m, if a=6 ,b = 8, c=5 and m =3
Answers
Pemdas dictates that exponents go first.
36+8-5/3
Then evaluate the division.
36+8-(5/3)
Then add and subtract going from left to right.
36+8=44
44-(5/3)= 42 1/3
f(x)=-x^2-2x-4
Does the function have a minimum or maximum value?
Where does the minimum or maximum value occur? x = ____
What is the function's minimum or maximum value?
Answers
Then, find the vertex:
x_vertex = 2/(-2)=-1, and the corresponding f(x) is
f(-1)=-1+2-4 = -3
Maximum at (-1,-3)
What is 2/15 in simplest form
Answers
Hope this helps : )
Convert: 6y + y² = x² from rectangular to polar form.
Answers
[tex]\bf 6y+y^2=x^2\implies \cfrac{6y}{x^2}+\cfrac{y^2}{x^2}=1\implies \cfrac{6rsin(\theta )}{[rcos(\theta )]^2}+\cfrac{[rsin(\theta )]^2}{[rcos(\theta )]^2}=1 \\\\\\ \cfrac{6rsin(\theta )}{r^2cos^2(\theta )}+\cfrac{r^2sin^2(\theta )}{r^2cos^2(\theta )}=1\implies \cfrac{6sin(\theta )}{rcos^2(\theta )}+\cfrac{sin^2(\theta )}{cos^2(\theta )}=1[/tex]
[tex]\bf \cfrac{6sin(\theta )}{rcos^2(\theta )}=1-\cfrac{sin^2(\theta )}{cos^2(\theta )}\implies \cfrac{6sin(\theta )}{1-\frac{sin^2(\theta )}{cos^2(\theta )}}=rcos^2(\theta ) \\\\\\ \cfrac{6sin(\theta )}{cos^2(\theta )\left[ 1-\frac{sin^2(\theta )}{cos^2(\theta )} \right]}=r\implies \cfrac{6sin(\theta )}{cos^2(\theta )-sin^2(\theta )}=r \\\\\\ \cfrac{6sin(\theta )}{cos(2\theta )}=r[/tex]
What is the value 6,035
Answers
0-hundreds
3-tens
5-ones
Good luck on your assignment!
~MeIsKaitlyn
Write an appropriate inverse variation equation if y = 9 when x = 3.
Answers
The front of an a frame cabin in a national park is the shape of a triangle, with an area of 189 ft.². If the height is 1 foot less than twice the base, find the base and the height of the front of the cabin.
Answers
it can't be a negative value, since it's a measurement unit, thus it can't be -27.
so, anyhow, base is "b", and the height is "2b - 1".
Final answer:
The student needs to solve a quadratic equation to find the base and height of a triangle using the area formula and the given relationship between height and base. The solution involves substitution, expansion, and application of the quadratic formula or factoring.
Explanation:
The problem involves finding the base and height of a triangular front of an A-frame cabin based on its given area and a relationship between the height and base. It's a typical quadratic equation problem found in the high school mathematics curriculum when dealing with geometry and algebra.
To find the base (b) and height (h) of the triangle, we first use the area formula of a triangle A = 1/2 × base × height. We know that the area (A) is 189 ft² and that the height (h) is 1 foot less than twice the base, so h = 2b - 1. Substituting h into the area formula, we get 189 = 1/2 × b × (2b - 1). Solving this quadratic equation, we find the values for the base (b) and substitute back to find the height (h).
The process entails expanding the equation, moving all terms to one side to set the equation to zero, and then using the quadratic formula or factoring to find the value of b. Once the base is found, we use the relationship h = 2b - 1 to determine the height.
,,,Help Please.. Question in the file.
Answers
now, in $6.10, there are 610 pennies
n = amount of nickels coins
d = amount of dime coins
q = amount of quarter coins
so... we know, there are 5*n or 5n pennies in the nickels, and 10*d or 10d pennies in the dimes and 25*q or 25q in the quarter coins, and we know their sum is 610 pennies total, thus
5n + 10d + 25q = 610
now, there are 4 more "n" then "d", so whatever "d" is, "n" is 4 more than that
n = d + 4
and twice as many "q" than "n", so, whatever "n" is, then
q = 2n
[tex]\bf 5n+10d+25q=610\implies n+2d+5q=122\qquad \begin{cases} n=d+4\\ q=2n\\ ------\\ q=2(d+4)\\ \qquad 2d+8 \end{cases} \\\\\\ \boxed{d+4}+2d+5\left( \boxed{2d+8} \right)=122[/tex]
solve for "d", to see how many dimes are there
what about the nickels? well, n = d + 4
what about the quarters? well, q = 2d + 8
which of the following is irrational? 7.51•(-4)
Answers
The irrational number among the options is root 3 + 8.486. option C.
An irrational number is a number that cannot be expressed as a fraction of two integers and has a non-repeating, non-terminating decimal expansion.
Let's examine each option:
A. [tex]\(7.51\ldots \times -4\)[/tex]
This is a rational number because it's the product of a rational number [tex](\(7.51\ldots\)) and \(-4\),[/tex] which is also rational. So, option A is not irrational.
B. [tex]\(\sqrt{16} + \frac{3}{4}\)[/tex]
[tex]\(\sqrt{16} = 4\)[/tex], so this expression simplifies to [tex]\(4 + \frac{3}{4}\)[/tex], which is a rational number. So, option B is not irrational.
C. [tex]\(\sqrt{3} + 8.486\)[/tex]
If [tex]\(\sqrt{3}\)[/tex] is not exactly equal to 8.486 , then this expression is irrational because it's the sum of an irrational number and a rational number. However, if [tex]\(\sqrt{3}\)[/tex] does happen to be exactly 8.486, then this expression would be rational. To determine if [tex]\(\sqrt{3}\)[/tex] is exactly 8.486, we need to compute [tex]\(\sqrt{3}\).[/tex] Since [tex]\(\sqrt{3}\)[/tex] is irrational (it's not a perfect square), 8.486 is not [tex]\(\sqrt{3}\)[/tex], so this expression is irrational. Therefore, option C is the correct answer.
D.[tex]\(8 \frac{2}{3} \times 17.75\)[/tex]
This is a rational number because it's the product of a rational number [tex](\(8 \frac{2}{3}\)) and \(17.75\),[/tex] which is also rational. So, option D is not irrational.
Complete question: Which of the following is irrational?
A. 7.51... x -4
B. root 16 + 3/4
C. root 3 + 8.486
D. 8 2/3 x 17.75
In a literal question what does f and c represent
Answers
Can the sum of two irrational numbers ever be a rational number?
Answers
If X is a irrational number, than the number Y=1-X is also irrational and the sum of these two irrational numbers is: X+Y=X+1-X=1 is rational number.
So, the sum of two irrational numbers can be a rational number.
You are dealt one card from a standard 52-card deck find the probability of being dealt an ace or an 8
Answers
there are 4 Aces and 4 8's for a total of 8 cards
52 cards in a deck
so probability of picking an Ace or 8 = 8/52
Final answer:
The probability of being dealt an ace or an 8 from a standard 52-card deck is 2/13, which is approximately 15.38%.
Explanation:
The question asks for the probability of being dealt an ace or an 8 from a standard 52-card deck. There are 4 aces and 4 eights in a 52-card deck. To calculate the probability of getting either an ace or an 8, we add the probability of getting an ace to the probability of getting an 8. The probability of drawing an ace (P(Ace)) is 4/52 and the probability of drawing an 8 (P(8)) is also 4/52. Since these are mutually exclusive events (you cannot draw an ace and an 8 simultaneously with one card), we can simply add these probabilities together:
P(Ace or 8) = P(Ace) + P(8)
= (4/52) + (4/52)
= 8/52
= 2/13
Therefore, the probability of being dealt an ace or an 8 is 2/13, which is approximately 0.1538 or 15.38%.
the sum of three numbers is 85. the second number is 5 times more than the first. the third number is 2 time the first. what are the numbers?
Answers
y = x + 5
z = 2x
x + (x + 5) + 2x = 85
4x + 5 = 85
4x = 85 - 5
4x = 80
x = 80/4
x = 20
x + 5 = 20 + 5 = 25
2x = 2(20) = 40
ur numbers are : 20,25,and 40
11 X 11= 4, 12x12=9,13x13=?
Answers
Based on the pattern observed in the given equations, 13 + 13 would equal 8.
The given equations seem to follow a pattern where the sum of two numbers is not their arithmetic sum but rather a result derived from some other relationship. Let's try to decipher the pattern:
For the equation 11 + 11 = 4:
The word "eleven" has 6 letters, so it becomes 6 + 6 = 4, which is true.
For the equation 12 + 12 = 9:
The word "twelve" has 6 letters, so it becomes 6 + 6 = 9, which is true.
Following the same pattern:
For 13 + 13:
The word "thirteen" has 8 letters, so it becomes 8 + 8 = ?
Thus, 13 + 13 = 8.
Therefore, based on the pattern observed in the given equations, 13 + 13 would equal 8.
The probable question maybe:
If 11 + 11 = 4 and 12 + 12 = 9 then what is 13 + 13 = ?
3. A carpenter is framing a window with wood trim where the length of the window is 6 and 2\3 feet. If the width of the window is 7 and3\4 feet, how many feet of the wood is needed to frame the window?
Answers
SO the length of rectangular window is [tex]= 6 \frac{2}{3} = \frac{20}{3} [/tex] feet.
Width of the rectangular window is = [tex]7 \frac{3}{4} = \frac{31}{4} [/tex] feet.
In general parameter of rectangle is = [tex]2(l+b)[/tex]
So the parameter of window is = [tex]2( \frac{20}{3} + \frac{31}{4}) = 2* \frac{(80+ 93)}{12} = 2* \frac{173}{12} = 28.834 [/tex]
So the required length of wood to frame window is = 28.834 feet
What is 16.35 written as a fraction
Answers
Improper fraction:
327⁄20
16.35 = 1635/100
Calculating the return on investment using financial leverage. suppose Dave invested only 20,000 of his own money and borrowed 180,000 interest-free from his rich father. what was his return on investment?
Answers
If the profit is x dollars, the ROI is x/20000. Here Dave levered 10:1 with the help of his father.
If he had invested totally with his own money, the ROI would be x/200000, a much less impressive number even though the profit is the same.
110 students are surveyed about their pets. The results are shown in the table. Which statement is true?
Answers
The only true statement is b. 40% of the boys surveyed have at least one pet.
To determine which statement is true, let's analyze the data provided in the table:
- Total number of boys surveyed: 45
- Total number of girls surveyed: 65
Now, let's break down the information based on the provided table:
1. **At least one pet:**
- Boys: 18
- Girls: 39
- Total: 57
2. **No pets:**
- Boys: 27
- Girls: 26
- Total: 53
Now, let's check each statement:
a. 27% of the boys surveyed have no pets.
- Percentage of boys with no pets = (Number of boys with no pets / Total number of boys surveyed) * 100%
- = (27 / 45) * 100% ≈ 60%
- This statement is false.
b. 40% of the boys surveyed have at least one pet.
- Percentage of boys with at least one pet = (Number of boys with at least one pet / Total number of boys surveyed) * 100%
- = (18 / 45) * 100% = 40%
- This statement is true.
c. 49% of the girls surveyed have no pets.
- Percentage of girls with no pets = (Number of girls with no pets / Total number of girls surveyed) * 100%
- = (26 / 65) * 100% ≈ 40%
- This statement is false.
d. 57% of the students surveyed have at least one pet.
- Percentage of students with at least one pet = (Total number of students with at least one pet / Total number of students surveyed) * 100%
- = (57 / 110) * 100% ≈ 52%
- This statement is false.
So, the only true statement is b. 40% of the boys surveyed have at least one pet.
The probable question may be:
110 students are surveyed about their pets. The results are shown in the table. Which statement is true?
Boys | Girls | Total
At least one pet | 18 | 39 | 57
No pets | 27 | 26 | 53
Total | 45 | 65 | 110
a. 27% of the boys surveyed have no pets.
b. 40% of the boys surveyed have at least one pet.
c. 49% of the girls surveyed have no pets.
d. 57% of the students surveyed have at least one pet.
The sum of the roots of 8x² - 2x = 1 is:
-1/4
1/4
-1/8
Answers
8x^2-4x+2x-1=0
4x(2x-1)+1(2x-1)=0
(4x+1)(2x-1)=0
x=1/2 and -1/4
So the sum is 1/2-1/4=1/4
1/4
8x^2 - 2x - 1 = 0
(2 +/-√(-2)^2 - 4(8)(-1))/ 2(8)
(2 +/-√4 + 32) / 16
(2 +/-√36) / 16
(2 +/- 6) / 16
2+6/16
1/2
2-6/16
-1/4
now since they want the sum of the roots
1/2 - 1/4
sum = 1/4
"what is the binary equivalent of the decimal value 97?"
Answers
very easy
8 bits
Bit 1 Value 128
Bit 2 value 64
Bit 3 value 32
Bit 4 value 16
Bit 5 value 8
Bit 6 value 4
Bit 7 value 2
Bit 8 value 1
Final answer:
To find the binary equivalent of the decimal number 97, one divides it by 2 repeatedly and records the remainders in reverse order, resulting in the binary number 1100001.
Explanation:
The binary equivalent of the decimal value 97 can be found using a process of dividing by 2 and keeping track of the remainders. Firstly, divide 97 by 2, which gives a quotient of 48 and a remainder of 1. We write down the remainder. Continuing this process:
48 divided by 2 equals 24 with 0 remainder.24 divided by 2 equals 12 with 0 remainder.12 divided by 2 equals 6 with 0 remainder.6 divided by 2 equals 3 with 0 remainder.3 divided by 2 equals 1 with 1 remainder.1 divided by 2 equals 0 with 1 remainder (as we have now reached a value less than 2).After collecting all the remainders in reverse order, the binary equivalent of decimal 97 is 1100001.