Let's organize what the problem gives us:
Mr. Smith had 4 daughters.Each daughter had 4 brothers.We want to find how many kids Mr. Smith has.Step 2: WorkWe can already tell that the initial amount of kids Mr. Smith has before we factor in the brother count is equal to 4, for the 4 daughters that were stated as a given in the problem.
Now, the tricky part comes in the form of "each daughter had 4 brothers." Remember that within a family, everyone has the same siblings. It doesn't matter which family member's perspective you are looking from, but your siblings will always stay the same. We can show this with an example:
Suppose I had a family of 4 kids total. I had 2 daughters and 2 sons. Their names were Rose, Sakura, David, and Andrew. Rose would then have 3 siblings: Sakura, David, and Andrew. Sakura would also have 3 siblings: Rose, David, and Andrew, so on and so forth.
Applying this example and knowledge to our current problem, if Mr. Smith's daughters each had 4 brothers, then the total number of kids Mr. Smith has is 8 total kids (4 daughters + 4 sons) since each daughter's brother would be the same sibling.
This would be called double-counting if you counted that each daughter would have 4 different siblings, resulting in a false answer of 16 kids (4 daughters multiplied by 4 brothers for each daughter).
Answer∴ Mr. Smith has 8 kids.
___
Topic: Math
Unit: ?
Find the area of the regular polygon. Round your answer to the nearest tenth.
Answer:
43.30 km^2
Step-by-step explanation:
Since the shape is a regular polygon, the sides of the triangle are equal (10km) now find the area on the triangle using herons formula
Working:
Side is 10
Perimeter= 30km
Semiperimeter (s) = 15km
Formula= √s(s-a)(s-b)(s-c)
= √15(15-10)(15-10)(15-10)
= √15*5*5*5
=5√5*15
=5√75
= 5*8.66
= 43.3 km^2
Answer:
43.3
Step-by-step explanation:
since it is a regular polygon thus it is a equilateral triangle where all sides are the same and all angles are 60
use formula 1/2 x a x b x sin C where a and b are sides and C is the angle
1/2 x 10 x 10 x sin 60 = 43.30
or method 2 is using Pythagoras theorem by drawing a perpendicular height to length 10km
h = [tex]\sqrt{10^{2} - (10/2)^{2} } = \sqrt{75} \\[/tex]
area of triangle = 1/2 x 10 x [tex]\sqrt{75}[/tex] = 43.30
Harry is installing a surveillance camera at the entrance of a Deli. He mounts the camera
8ft above the ground and 16 ft horizontally from the entrance. The camera is meant to
monitor every customer who enters and exits the store. At want angle of depression should
Harry set the camera to capture the faces of all customers? Use a diagram and
mathematical calculations to help you explain your answer.
Answer: The angle of depression would be 26.57°
Step-by-step explanation: Please refer to the attached picture for further details.
What harry has done has effectively led to the formation of a right angled triangle. As shown in the diagram, the camera has been mounted at a height of 8 feet above the ground. Also he mounts the camera at a horizontal from the entrance, which puts the camera at 16 feet away from the entrance (not from the ground). In order to capture every movement at the entrance, the camera range would be determined by an angle which covers everything from top to bottom of the entrance. That gives you the angle of depression which is at the point labelled CAMERA in the triangle.
Having determined two sides and an angle (unknown) in a right angled triangle, we shall use the trigonometric ratios as follows;
Tan ∅ = Opposite/Adjacent
Where the opposite is 8 (side facing the reference angle) and the adjacent is 16 (side that lies between the reference angle and the 90 degree angle)
Tan ∅ = 8/16
Tan ∅ = 0.5
By use of a calculator,
∅ = 26.5650
∅ ≈ 26.57
Therefore the angle of depression of the surveillance camera should be 26.57°
It is said that about 60% of the human body is made up of water. Adam weighs 78 kg. How much of his body weight is made up of water?
Answer:
46.8 kg
Step-by-step explanation:
78 * 0.6 = 46.8
Answer 5, 6 , and 7 by today please.
Answer:
Step-by-step explanation:
5. a) ∠1 and ∠2 are remote interior angles of ∠ACD so that means that ∠ACD = ∠1 + ∠2
b) Because an exterior angle is the sum of its two remote interior angles it makes sense that an exterior angle is greater in measure than either of its remote interior angles.
6. BD = DB Reflexive property
∠3 = ∠5, ∠4 = ∠6 Alt. int. angles
ΔADB = ΔCDB ASA
7. AB = BC Def. of midpoint
∠1 = ∠2 Given
∠BAE = ∠CBD Corresponding angles
ΔBAE = ΔCBD ASA
∠D = ∠E CPCTC
4. A triangle plotted in the coordinate plane has vertices at (2, 3), (sqrt15,3) and (4,8). Which of the following
is closest to its area?
(1) 4.68
(3) 7.12
(2) 5.93
(4) 8.76
Answer:
Option(1) is the correct answer to the given question .
Step-by-step explanation:
let [tex]x1, y1=\ (2, 3)[/tex]
[tex](x2,y2)=(\sqrt{15,3} \ )[/tex]
[tex](x3,y3)=\ (4,8)[/tex]
Now we know that
[tex]Area=\ \frac{1}{2} |x1(y2-y3)\ + \ x2(y3-y1)\ + x3(y1-y2)[/tex]
Now putting this value in the formula we get
[tex]\frac{1}{2}|2(3-8)\ +\sqrt{15}(8-3)\ * 4(5-3)|[/tex]
[tex]=\ \frac{1}{2}\ *9.3649[/tex]
=4.6824
Therefore option(1) is the correct answer .
Answer:
Option(1) is the correct answer to the given question .
Step-by-step explanation:
5 times a number is 14 less than the square of that number. find the negative solution.
Answer: The negative solution is -2
Step-by-step explanation:
[tex]5x+14=x^2\\x^2-5x-14=0\\\\(x-7)(x+2)=0\\x_1=7\\x_2=-2[/tex]
what is the volume of the cone using pi/3.14 using the numbers 2and 3
Answer:
V=π*r^(2)*h/3
Step-by-step explanation:
What is the range of the function below?
Answer:
C
Step-by-step explanation:
f(x)=72-4x
72-4x=0
4x=72
x=18
f(x)<=18
Five times one number minus two times a second number is 11. Three times the first number minus two times the second number is 1. what are the numbers?
Answer:
first number is 5
second number is 7
Step-by-step explanation:
let x and y represent the first and second number
5x - 2y = 11 ........ equation 1
3x - 2y = 11.......... equation 2
so by elimination, equation 1 minus equation 2
5x - 3x - 2y - 2y = 11 - 1
2x = 10
x = 5
therefore the first number is 5
put x = 5 into equation 1
5x - 2y = 11
5(5) - 2y = 11
25 - 2y = 11
-2y = 11 - 25
-2y = - 14
y = 7
therefore the second number is 7
hope it helps .
what is equivalent to 5 x a
1. 5a
2. a^5
3. a x a x a x a x a
4. 5^a
Answer:
5a
Step-by-step explanation:
[tex]5\cdot \:a\\\\[/tex]
5 multiply a
5a
Solve.
a + 1 = Vb + 1 for b.
Answer:
b = a² + 2a
Step-by-step explanation:
a + 1 = √(b + 1)
(a + 1)² = b + 1 (Square both sides)
a² + 2a + 1 = b + 1 (Expand left side)
a² + 2a = b (Subtract 1)
can someone help please
Answer:
C
Step-by-step explanation:
-3(x+ 2y) + 5(3x - y) + y2 for x = 6 and y= 2.
Answer:
54
Step-by-step explanation:
What is the value of [2/3]-4
Answer:
option 4
Step-by-step explanation:
[tex]a^{-m}=(\frac{1}{a})^{m}\\\\\\(\frac{2}{3})^{-4}=(\frac{1}{\frac{2}{3}})^{4}\\\\=(\frac{3}{2})^{4}\\\\=\frac{3^{4}}{2^{4}}\\\\=\frac{81}{16}[/tex]
D(t)D, left parenthesis, t, right parenthesis models the distance (in thousands of \text{km}kmstart text, k, m, end text) from the earth to the Moon ttt days after the moon's perigee (when it's closest to the earth). Here, ttt is entered in radians. D(t) = -21\cos\left(\dfrac{2\pi}{29.5}t\right) + 384D(t)=−21cos( 29.5 2π t)+384D, left parenthesis, t, right parenthesis, equals, minus, 21, cosine, left parenthesis, start fraction, 2, pi, divided by, 29, point, 5, end fraction, t, right parenthesis, plus, 384 How many days after its perigee does the moon first reach 380380380 thousands of \text{ km} kmstart text, space, k, m, end text from the Earth?
Answer:
6.48 days
Step-by-step explanation:
[tex]D(t) = -21\cos\left(\dfrac{2\pi}{29.5}t\right) + 384\\\\380=-21\cos\left(\dfrac{2\pi}{29.5}t\right)+384\\\\\dfrac{4}{21}=\cos\left(\dfrac{2\pi}{29.5}t\right)\qquad\text{subtract 384, divide by -21}\\\\\dfrac{2\pi}{29.5}t=\arccos{\dfrac{4}{21}}\qquad\text{use the inverse cosine function}\\\\t=\dfrac{29.5}{2\pi}\arccos{\dfrac{4}{21}}\approx 6.4752\quad\text{days}[/tex]
About 6.48 days after perigee, the moon reaches a distance of 380,000 km from Earth.
The hard-cover edition of a book cost 3 times as much as the paperback edition. Both editions together cost $26.60. Find the cost of each.
Answer:
the hardcover is 19.95, and the parback is 6.65. enjoy.
what is the product of 4/5 × 2/5
Answer:
8/25
Step-by-step explanation:
4/5 *2/5
Multiply the numerators
4*2 = 8
Multiply the denominators
5*5 = 25
8/25
Answer:
The answer would be 8/25 or 0.32
What is 34×60 Brainliest Answer Wins
Answer:
2040
Step-by-step explanation:
34x60=2040
Answer:
2040
Step-by-step explanation:
So we multiply them on a calculator.
7,10) and (7,20). Slope or no slope
Answer: No slope
Step-by-step explanation: The line is going straight down.
Write the explicit formula for the following sequence.
3, 30, 300, 3000
Answer:
common ratio(r) = 10
place of the term = n
a = 3
now
sequence of 1 term = ar^(n-1)
= 3×10^(1-1)
= 3× 10^0
= 3×1
= 3
sequence of 2 term = ar^(n-1)
= 3×10¹
= 30
and so on
A car costs £15000. Work out the price after a 13% discount.
Answer:
13, 050
Step-by-step explanation:
15,000 by 13% = 1,950
15,000-1,950= 13, 050
Mike built a sand castle that measured 484 centimetres by 386 centimetres, and dug a moat around it.Afterward, he decided to change the castle size, making it 725 centimetres by 314 centimetres.How much longer will the newer moat be than the older one?
Answer:
the newer moat is 169 cm longer than the older one
Step-by-step explanation:
in order to find the difference in length of the two castles, we will first find the perimeters of the two castles then calculate the difference in the perimeters:
old castle:
dimension = 484cm by 386cm
perimeter = 484 + 386 = 870 cm
new castle:
dimension = 725cm by 314cm
perimeter = 725 + 314 = 1039 cm
difference = 1039 - 870 = 169 cm
The total length of the moats used is equals to the perimeter of the sand castles, therefore, the newer moat is 169 cm longer than the older one.
Answer:
Look I know I'm about 2 1/2 years late but the answer is not 169 or whatever the person above me said, it's 660 I answered this before.
What is the value of x if:
-0.1x + 3/10 = 4/10
Solve as linear equation.
NEED HELP ASAP
Answer:
x= -1
Step-by-step explanation:
Solving through linear equation,
-0.1x + 3/10= 4/10
Bring 3/10 to the other side making it minus
-0.1x = 4/10 - 3/10
-0.1x = (4-3)/10
-0.1x= 1/10
Bring -0.1 to the other side n divide
x= 1/10 ÷ -0.1
( Note that -0.1 is the same as -1/10)
x = 1/10 ÷ -1/10
= 1/10*-10/1
= -10/10
= -1
What is the average rate of change from x = 0 to x = −2?
How I got that answer:
The graph shows the two points (0,-4) and (-2,2) are on the parabola. The x coordinates of both points are from x = 0 and x = -2 as given in the instructions. Compute the slope of the line through those points. The slope of this line is the exact same as the average rate of change from x = -2 to x = 0.
m = (y2 - y1)/(x2 - x1)
m = (2 - (-4))/(-2-0)
m = (2 + 4)/(-2-0)
m = 6/(-2)
m = -3
A negative slope means the line slopes downhill as you move from left to right. This is a negative average rate of change.
Please help me with this question
Answer:
P = (2, 3)
Step-by-step explanation:
P is a local minimum, so can be found from the upper zero of the derivative.
y' = 0 = 3x^2 -8x +4
0 = (3x -2)(x -2)
x = 2/3, x = 2
So, the x-coordinate of P is 2. The y-coordinate is found by evaluating the function:
y = ((x -4)x +4)x +3 = ((2 -4)2 +4)2 +3 = 3
The coordinates of P are (2, 3).
__
A graphing calculator confirms this result.
please help me w dis!! marking brainiest!!!
Answer:
D
Step-by-step explanation:
Distributing the factors we get
-8x^2 -6x +35
-7 written as a fraction is _____
Evaluate and simplify 2ab-1/3e-3d
Answer: 2ab - e/3 - 3d
Step-by-step explanation:
2ab - 1/3e - 3d
= 2ab - 1e/3 - 3d
= 2ab - e/3 - 3d
5.
Solve the equation.
(4x+10)^1/4 = (9+7x)^1/4
Answer:
1/3
Step-by-step explanation:
[tex]\sqrt[4]{4x+10}[/tex] = 4x+10 ^1/4
[tex]\sqrt[4]{9+7x}[/tex]= 9+7x^1/4
Since they are under the same root, you can combine them under the root.
Then you change the +/- sign of one side of the equation to move to the other side of the equation.
To get....[tex]\sqrt[4]{-3x+1}[/tex]=0
^4 both sides to get..
-3x+1=0
Move 1 to the other side...
-3x=-1
divide both sides by -3
x=1/3
In the last draw, the grand prize was won. If there are three winners, each would have received $ 720,000; if there are four winners, each of the winners would receive $ 540,000. How many winners are there if everyone has $ 144,000?
a) 12 winners
b) 15 winners
c) 16 winners
d) 18 winners
( if your doing this can you please do it step by step )
Answer:
b) 15 winners
Step-by-step explanation
if 3 winners get $720,000 each that means there is $2,160,000 total. So if each winner gets $144,000 each that means there are 15 winners.
(2,160,000/ 144,000)
