Answer:
Here are a few examples.
(30/2 + 1)/2
(26/2 + 3)/2
(28/2 + 2)/2
Two tablespoons of peanut butter contain 190 calories. Two tablespoons of grape jelly contain 122 calories. Which contains more calories, two tablespoons of peanut butter or two tablespoons of grape jelly?
Find x so that the points (x,x+1), (x+2,x+3) and (x+3,2x+4) form a right-angled triangle.
Let a, b, and c be vectors each starting at the origin and terminating at the points (x, x + 1), (x + 2, x + 3), and (x + 3, 2x + 4), respectively.
Then the vectors a - b, a - c, and b - c are vectors that point in directions parallel to each of the legs formed by the triangle with these points as its vertices.
If this triangle is to contain a right angle, then exactly one of these pairs of vectors must be orthogonal. In other words, one of the following must be true:
(a - b) • (a - c) = 0
or
(a - b) • (b - c) = 0
or
(a - c) • (b - c) = 0
We have
a - b = (x, x + 1) - (x + 2, x + 3) = (-2, -2)
a - c = (x, x + 1) - (x + 3, 2x + 4) = (-3, -x - 3)
b - c = (x + 2, x + 3) - (x + 3, 2x + 4) = (-1, -x - 1)
Case 1: If (a - b) • (a - c) = 0, then
(-2, -2) • (-3, -x - 3) = (-2)×(-3) + (-2)×(-x - 3) = 2x + 12 = 0 ==> x = -6
which would make a - c = (-3, 3) and b - c = (-1, 5), and their dot product is not zero. Then the triangles vertices are at the points (-6, -5), (-4, -3), and (-3, -8).
Case 2: If (a - b) • (b - c) = 0, then
(-2, -2) • (-1, -x - 1) = (-2)×(-1) + (-2)×(-x - 1) = 2x + 4 = 0 ==> x = -2
which would make a - c = (-3, -1) and b = (-1, 1), and their dot product is also not zero. The vertices are the points (-2, -1), (0, 1), and (1, 0).
Case 3: If (a - c) • (b - c) = 0, then
(-3, -x - 3) • (-1, -x - 1) = (-3)×(-1) + (-x - 3)×(-x - 1) = x ² + 4x + 6 = 0
but the solutions to x here are non-real, so we throw out this case.
So there are two possible values of x that make a right triangle, x = -6 and x = -2.
438 Friday night, 820 Saturday night and 636 Sunday afternoon. How many more people attended the play on Sunday than on Friday?
Answer:
198 more people attended the play on Sunday than on Friday
Step bye step explanation:
638 - 438 = 198.
(438 Friday night
(438 Friday night 636 Sunday night)
Christopher has $1947 in his savings account. This weekend he will deposit another $99 in the account. How much money will be in Christopher savings account after this weekend
Answer:
$2046
Step-by-step explanation:
Add 1947 and 99 because he is depositing, as in adding, 99 dollars
How much would you have to
deposit today to have an
accumulated amount of
$20,000 in 20 years if yearly
interest is 4.75% compounded
continuously?
Because the account is compounded continuously, Euler number is required
e = 2.7182818
Find the common factor of 75,00 and 60
The common factors of 60 and 75 are
1, 3, 5 and 15
And GCF is 15
Must click thanks and mark brainliest
What is the difference between the centroid and the center of mass?A: When (), ,, ,x y zc x y zthen the center of mass is the centroid.
The centroid and center of mass need not be the same point. They are the same only when a body's mass is uniformly distributed.
find the missing side. round your answer to the nearest tenth. PLEASE HURRY!
Answer:
44.8
Step-by-step explanation:
Using the Cosine formula, we first have Cos 48 = 30/x. So then we just solve for x and get 44.8342965, which rounds to 44.8
I hope this helped! :D
what is the lub and glb of the following sets, in the set of real numbe if exists E={ 0.2,0.23,0.234,0.2343,0.23434,0.23434,...}
Answer:
Hello,
Step-by-step explanation:
[tex]LUB(E)=0.2=\dfrac{1}{5} \\\\GUB(E)=0.2 34 34 34 ....=0.2+\dfrac{1}{10} *0.343434....\\\\=\dfrac{1}{5} +\dfrac{1}{10} *\dfrac{34}{99} \\\\=\dfrac{198+34}{990} \\\\=\dfrac{116}{495}[/tex]
Please help with step by step.
Make a substitution to express the integrand as a rational function and then evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.)
2 sec^2(t)/tan^2(t) + 14 tan(t) + 48 dt
Complete the square in the denominator to get
tan²(t ) + 14 tan(t ) + 48 = tan²(t ) + 14 tan(t ) + 49 - 1
… = (tan(t ) + 7)² - 1
Substitute u = tan(t ) + 7 and du = sec²(t ) dt. Then the integral becomes
[tex]\displaystyle \int \frac{2\sec^2(t)}{\tan^2(t)+14\tan(t)+48} \,\mathrm dt = 2 \int \frac{\mathrm du}{u^2-1}[/tex]
Separate the integrand into partial fractions:
[tex]\dfrac1{u^2-1} = \dfrac12 \left(\dfrac1{u-1}-\dfrac1{u+1}\right)[/tex]
Then we get
[tex]\displaystyle \int \frac{2\sec^2(t)}{\tan^2(t)+14\tan(t)+48} \,\mathrm dt = \int \left(\frac1{u-1}-\frac1{u+1}\right)\,\mathrm du \\\\ =\ln|u-1|-\ln|u+1| + C \\\\ = \ln\left|\frac{u-1}{u+1}\right|+C \\\\ = \boxed{\ln\left|\frac{\tan(t)+6}{\tan(t)+8}\right|+C}[/tex]
11. A surveyor at point S discovers that the angle between peaks A and B is 3 times as large as the angle
between peaks B and C. The surveyor knows that ZASC is a right angle. Find mzASs and m2BSC.
The measures of the angles between the peaks are;
m∠BSC = 22.5°
m∠ASB = 67.5°
The reason for arriving at the above angles is as follows:
The known values are;
The location of the surveyor = Point S
The angle between peaks A and B = m∠ASB = 3 times as large as the angle between peaks B and C = 3 × m∠BSC
The measure of angle m∠ASC = A right angle = 90°
Required:
To find m∠ASB and m∠BSC
From the given diagram, we have;
m∠ASC = 90°
m∠ASC = m∠ASB + m∠BSC (angle addition postulate)
m∠ASB = 3 × m∠BSC
∴ m∠ASC = 3 × m∠BSC + m∠BSC = 4 × m∠BSC
m∠ASC = 4 × m∠BSC = 90°
m∠BSC = 90°/4 = 22.5°
m∠BSC = 22.5°
m∠ASB = 3 × m∠BSC
∴ m∠ASB = 3 × 22.5° = 67.5°
m∠ASB = 67.5°
Learn more about angle addition postulate here:
https://brainly.com/question/4208193
find the area of the triangle
9514 1404 393
Answer:
108 cm²
Step-by-step explanation:
The area of a triangle is given by the formula ...
A = 1/2bh
where b represents the base length, and h represents the height--the perpendicular distance from the base to the opposite vertex. The area of this triangle is ...
A = 1/2(12 cm)(18 cm) = 108 cm²
You pick a marble from a bag containing 1 green marble, 4 red marbles, 2 yellow marbles, and 3 black marbles. You replace the first marble and then select a second ones find p(blue, then black).
If you do not replace the first marble in the previous question before you select the 2nd one, find p(red, then red)
Show your work!!
Answer:
First question:0
Second question:2/15
Step-by-step explanation:
First:
Total of marbles=10
since there is no blue the probability is 0, since black is 3. then prob= number of black/total number of marbles. =3/10
therefore 0*3/10 =0
second:
probability of red is 4/10
since the first marble wasn't returned,the total number of marbles=9
therefore probability if the second red marble is =3/9 =1/3
probability of first marble *probability of second marble
(4/10)*(1/3) =(4/30)= 2/15
lee is planning an event for 28 people, he wants to make a fruit drink and he thinks that each person will drink 3 glasses each. If he is correct , how many glasses of fruit should he make?
Answer:
84
Step-by-step explanation:
Since there will be 28 people, and each of them will drink 3 glasses, you just multiply the number of people times the number of glasses they will drink each, so 28*3. The result is 84.
I hope this helped! :D
Lee should need to make 84 glasses of fruit if is planning an event for 28 people.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
Let Lee needs to make x number of glasses of fruit.
From the question we can frame a linear equation in one variable:
x/3 = 28
As we know, the arithmetic operation can be defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
After cross multiplication:
x = 28×3
x = 84 glasses
Thus, Lee should need to make 84 glasses of fruit if is planning an event for 28 people.
Learn more about the linear equation here:
brainly.com/question/11897796
#SPJ2
Show that Reſiz) = -Im(z)
Step-by-step explanation:
[tex]re(i(x + yi) = - im(x + yi) \\ re(xi - y) = - im(x + yi) \\ - y = - (y) \\ - y = - y \\ proved \: is \: correct[/tex]
A fifth grade teacher calculates that 27% of her students are late for class. If the teacher is right, what is the probability that the proportion of late students in a sample of 724 students would differ from the population proportion by less than 4%? Round your answer to four decimal places.
Answer:
answer: 0.9479
hope I helped
Hurry quick i have more questions answer then all for a total of about 100 points
Answer:
1/5
Step-by-step explanation:
.7555555(repeating )
writing as a fraction
x = .755555555
10 x = 7.555555
Subtract the two
10x = 7.555555
-x = .75555555
--------------------------
9x =6.8
Divide each side by 9
x = 6.8/9
x = 68/90
Divide by 2
x = 34/45
We do the same for .555555 repeating
y = .5555 repeating
10 y = 5.5 repeating
10y = 5.5
-y = .555
-------------------
9y = 5
y = 5/9
Subtract x - y
34/45 - 5/9
Get a common denominator
34/45 - 25/45
9/45
1/5
find the surface area of the prism HURRY
Answer:
does the answer help you?
If the Miller's spend $1200 on housing each month, then what is their total monthly budget?
Answer:
2400$
Step-by-step explanation:
Miller's Family spends 50% of their budget on housing and we know that they spent 1200$ this month, so 1200$*2 = 2400$.
Have a nice day! :-)
A square has a side length of 520
meters. What is the perimeter of
the square in kilometers?
Answer: 2.08 km
Step-by-step explanation:
Side of Square = 520 m
Perimeter of Square = Side × 4
= 520 × 4
= 2080 m
1000 m = 1km
2080 m = 2080 ÷ 1000
= 2.08 km
how far from 0" is the green rectangle for both
Answer:
C. 3 3/4
Step-by-step explanation:
just is
id k how to explain
A segment bisector is a line, ray or segment that divides a line segment into two equal parts. in the triangle formed by points A(-1,7), B(1,2), C(7,6) what is the slope of the line that goes through point A and bisects BC?
In decimal form, this is equivalent to -0.6
=================================================
Explanation:
This segment bisector is cutting side BC in half. So we have a point D such that it is between B and C. Also, we can say BD = DC. Refer to the diagram below.
To find the location of D, we'll apply the midpoint formula to points B and C.
B(1,2) and C(7,6) have x coordinates of 1 and 7 respectively. Average those x values to get (1+7)/2 = 8/2 = 4. This is the x coordinate of point D.
Repeat this idea for the y coordinates. We'll get (2+6)/2 = 8/2 = 4 which is the y coordinate of D.
Point D is located at (4,4)
---------------------
The takeaway from that last section, if we were to summarize it in one sentence, is that D is located at (4,4).
Now focus on the points A(-1,7) and D(4,4)
We'll apply the slope formula
m = (y2-y1)/(x2-x1)
m = (4-7)/(4-(-1))
m = (4-7)/(4+1)
m = -3/5 is the slope
Notice that to go from A to D, we can drop down by 3 units and move to the right 5 units. We can say rise = -3 and run = 5; therefore, slope = rise/run = -3/5
in alska the colderst temprauter ever recorded is -80 that is much colder than in hawil where the coldest temperature is 15
Answer: What are we supposed to do ???
A cell phone company charges a monthly fee of $18 plus five cents for each call. A
customer's total cell phone bill this month is $50.50. Use n to represent the number of
calls.
Answer:
650 calls
Step-by-step explanation:
so since you have 18$ per month plus 5 cents per call you would do
18+0.5n(n represent the number of calls)= the total fee of $50.50 cents.
thus,now you need to figure out how much the phone calls were without the monthly fee so you would do:
50.50-18=32.50
so 32.50 is the price of all the phone calls
then you divide 32.50 by 0.05 which equals to 650
meaning that n=650
hope I helped!
find the length of leg x
x=
side a is 15
side b is 12
side x=
Answer:
x=9
Step-by-step explanation:
a=hyp=15
b=base=12
x=perp=?
using pathagorus theorem:
[tex] {hyp}^{2} = {base}^{2} + {perp}^{ 2} \\ {15}^{2} = {12}^{2} + {x}^{2} \\ 225 = 144 + x \\ 225 - 144 = {x}^{2} \\ 81 = {x}^{2} \\ x = 9[/tex]
1) Santhosh packed 240 oranges and 288 apples in boxes. He packed oranges and apples in separate boxes. He put equal number of fruits in each box. What is the maximum number of fruits that can be put in each box?
The maximum no of fruits that could be put in each box is 48
For determining the maximum no of fruits, we have to find out the highest common factor i.e. HCf between two numbers i.e. 240 and 288
So,
For 240 = [tex]2 \times 2 \times 2 \times 2 \times 3 \times 5[/tex]
And, for 288, it is = [tex]2 \times 2 \times 2 \times 2 \times 2 \times3 \times 3[/tex]
So, the highest common factor between two numbers is
= [tex]2\times 2\times 2\times 2\times 3[/tex]
= 48
So we can conclude that the maximum no of fruits that could be put in each box is 48
Learn more about numbers here: brainly.com/question/17429689?
Answer:
the maximum number of fruits that can be put in each box=48
Given :
Total number of oranges = 240
Total number of apples = 288
we find maximum number of fruits by finding highest common factor HCF
Step-by-step explanation:
Lets find out HCF of 240 and 288
Write the prime factors for 240 and 288
[tex]288=2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3\\240=2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 5[/tex]
Now write the common factor for both numbers
[tex]2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 =48[/tex]
So, GCF is 48
We have to put 48 fruits in each box.
Learn more :
brainly.in/question/8084599
Find the distance between the points (0, 10) and (–9, 1).
[tex]\\ \sf\longmapsto \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]\\ \sf\longmapsto \sqrt{(-9-0)^2+(1-10)^2}[/tex]
[tex]\\ \sf\longmapsto \sqrt{(-9)^2+(-9)^2}[/tex]
[tex]\\ \sf\longmapsto \sqrt{81+81}[/tex]
[tex]\\ \sf\longmapsto \sqrt{162}[/tex]
[tex]\\ \sf\longmapsto 12.42[/tex]
Help pls and thank you
PLEASE HELP!!
find the value of r
The two sides and two top angles are identical so the two bottom halves are the same
18 -2r = 4R
Add 2r to both sides
18 = 6r
Divide both sides by 6
R = 3
The answer is A. 3
