Answers
Answer:
[tex]\large\boxed{A==\dfrac{3-\sqrt6}{12}\ cm^2}[/tex]
Step-by-step explanation:
The shaded region is the triangle with base b and height h.
[tex]b=BD-CD\to b=\dfrac{\sqrt2}{2}-\dfrac{\sqrt3}{3}=\dfrac{3\sqrt2}{(2)(3)}-\dfrac{2\sqrt3}{(2)(3)}=\dfrac{3\sqrt2-2\sqrt3}{6}\\\\h=AD\to h=\dfrac{\sqrt2}{2}[/tex]
The formula of an area of a triangle:
[tex]A=\dfrac{bh}{2}[/tex]
Substitute:
[tex]A=\dfrac{\frac{3\sqrt2-2\sqrt3}{6}\cdot\frac{\sqrt2}{2}}{2}=\left(\dfrac{3\sqrt2-2\sqrt3}{6}\right)\left(\dfrac{\sqrt2}{2}\right)\left(\dfrac{1}{2}\right)\\\\\text{use the distributive property}\ a(b+c)=ab+ac\\\\=\dfrac{(3\sqrt2-2\sqrt3)(\sqrt2)}{(6)(2)(2)}=\dfrac{(3\sqrt2)(\sqrt2)-(2\sqrt3)(\sqrt2)}{24}\\\\\text{use}\ \sqrt{a}\cdot\sqrt{a}=a\ \text{and}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\=\dfrac{(3)(2)-2\sqrt6}{24}=\dfrac{2(3-\sqrt6)}{24}=\dfrac{3-\sqrt6}{12}[/tex]
Answer:
see explanation
Step-by-step explanation:
The area of the shaded triangle = area of ΔABD - area of ΔADC
A of ΔABD = [tex]\frac{1}{2}[/tex] × AD × BD
A = [tex]\frac{1}{2}[/tex] × [tex]\frac{\sqrt{2} }{2}[/tex] × [tex]\frac{\sqrt{2} }{2}[/tex]
= [tex]\frac{2}{8}[/tex] = [tex]\frac{1}{4}[/tex]
--------------------------------------------------------------------------
A of ΔACD = [tex]\frac{1}{2}[/tex] × AD × DC
A = [tex]\frac{1}{2}[/tex] × [tex]\frac{\sqrt{2} }{2}[/tex] × [tex]\frac{\sqrt{3} }{3}[/tex]
A = [tex]\frac{\sqrt{6} }{12}[/tex]
-------------------------------------------------------------------------
shaded area = [tex]\frac{1}{4}[/tex] - [tex]\frac{\sqrt{6} }{12}[/tex]
= [tex]\frac{3}{12}[/tex] - [tex]\frac{\sqrt{6} }{12}[/tex] = [tex]\frac{3-\sqrt{6} }{12}[/tex]
Related Questions
help!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
π units^2.
Step-by-step explanation:
The area = π r^2 where r = the radius and the radius = 1/2 * the diameter.
So the radius of this circle = 1/2 * 2 = 1.
The required area = π * 1^2
= π units^2.
ANSWER
Exact form: π units square.
Or 3.14 square units.
EXPLANATION
The area of a circle is calculated using the formula:
[tex]Area = \pi \times {r}^{2} [/tex]
From the diagram, the diameter of the circle is d=2 units.
The radius is half of the diameter which is 1 unit.
We substitute r =1 into the formula to obtain;
[tex]Area = \pi \times {1}^{2} [/tex]
[tex]Area = \pi \: [/tex]
In decimal form, the area is
[tex]Area =3.14 \: square \: units[/tex]
Simplify 4!
A.24
B.10
C.9
D.4
Answers
Answer:
A. 24
Step-by-step explanation:
! = 2 multiplied by the maximum
So, 4! = 2 × 3 × 4 [24]
This is what is known as Factorials.
I am joyous to assist you anytime.
Answer:
[tex]\Huge\boxed{24}[/tex]
Step-by-step explanation:
Apply by the factorial rule.
[tex]\displaystyle 4!=1*2*3*4[/tex]
Then multiply to find the answer.
[tex]\displaystyle 1*2*3*4=4*3=12*2=24*1=24[/tex]
24, which is our answer.
The choices for the first one is
1/4
1
5/4
Choice for the second one is
(3i square root 7)/4
(i square root 21)/2
(square root 112)/4
Answers
Answer:
[tex]\large\boxed{\dfrac{5\pm3\sqrt7}{4}}[/tex]
Step-by-step explanation:
[tex]m^2-\dfrac{5}{2}m=-\dfrac{11}{2}\qquad\text{add}\ \dfrac{11}{2}\ \text{to both sides}\\\\m^2-\dfrac{5}{2}m+\dfrac{11}{2}=0\qquad\text{multiply both sides by 2}\\\\2m^2-5m+11=0[/tex]
[tex]\text{Use the quadratic formula:}[/tex]
[tex]ax^2+bx+c=0\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
[tex]\text{We have}[/tex]
[tex]a=2,\ b=-5,\ c=11[/tex]
[tex]\text{substitute:}[/tex]
[tex]\sqrt{b^2-4ac}=\sqrt{(-5)^2-4(2)(11)}=\sqrt{25-88}=\sqrt{63}=\sqrt{9\cdot7}=\sqrt9\cdot\sqrt7=3\sqrt7\\\\m=\dfrac{-(-5)\pm3\sqrt7}{2(2)}=\dfrac{5\pm3\sqrt7}{4}[/tex]
a biology class has a total of 34 students the number of males is 14 more than the number of females how many males and how many females are in the class
Answers
x: females
x+14: males
so 34=x+x+14
To find the number of males and females in the biology class, we can create a system of equations based on the given information and then solve for the variables. After solving the equation, we find that there are 10 females and 24 males in the biology class.
Explanation:To find the number of males and females in the biology class, we can create a system of equations based on the given information:
Let's assume the number of females in the class is 'x'.
The number of males in the class is then 'x + 14'.
Since the total number of students in the class is 34, we can write the equation:
x + (x + 14) = 34
Simplifying the equation, we have 2x + 14 = 34.
Subtracting 14 from both sides, we get 2x = 20.
Dividing both sides by 2, we find x = 10.
Therefore, there are 10 females and 24 males in the biology class.
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Please help answer this geometry
Answers
Answer:
a. [tex](8x+12y)^{2} +(6x+9y)^{2} = (10x+15y)^{2}[/tex]
b. [tex]100x+225y=100x+225[/tex] Which means it is an identity
Step-by-step explanation:
The Pythagorean Theorem states that in every right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the respective lengths of the legs. It is the best-known proposition among those that have their own name in mathematics.
If in a right triangle there are legs of length a, and b, and the measure of the hypotenuse is c, then The following relationship is fulfilled:
[tex]a^{2} +b^{2}=c^{2}[/tex]
a. Write an equation using the Pythagorean Theorem and the measurements provided in the diagram
From the exercise shown in the image, we can get the values of a, b, and c.
a = 8x+12y, b = 6x+9y, and c = 10x+15y
Write an equation using the Pythagorean Theorem
We obtain:
[tex](8x+12y)^{2} +(6x+9y)^{2} = (10x+15y)^{2}[/tex]
b. Transform each side of the equation to determine if it is an identity.
In mathematics, an identity is the realization that two objects that are mathematically written differently, are in fact the same object. In particular, an identity is an equality between two expressions, which is true whatever the values of the different ones are.
So, we transform each side of the equation
[tex](8x+12y)^{2} +(6x+9y)^{2} = (10x+15y)^{2}[/tex]
[tex](8x)^{2} +(12y)^{2} +(6x)^{2} +(9y)^{2}= (10x)^{2}+(15y)^{2}\\64x+144y+36x+81y=100x+225y\\(64x+36x)+(144y+81y)=100x+225y\\100x+225y=100x+225[/tex] Which means it is an identity
.
Answer:
a). (10x + 15y)² = (8x + 12y)² + (6x + 9y)²
b). It's an identity
Step-by-step explanation:
a). Pythagoras theorem says
(Hypotenuse)² = Height² + Base²
Therefore, form the given picture
(10x + 15y)² = (8x + 12y)² + (6x + 9y)² will be the equation.
b). For an identity we have to prove Right hand side of the equation(R.H.S.) = Left hand side of the equation(L.H.S.)
Now we solve the L.H.S. of the equation
(10x + 15y)²
= 100x² + 225y² + 300xy [ (a + b)² = a²+ b² + 2ab
Now we solve R.H.S. of the equation
(8x + 12y)² + (6x + 9y)²
= 64x²+ 144y² + 36x² + 81y² + 108y + 192xy + 108xy
= 100x² + 225y²+ 300xy
Therefore, L.H.S. = R.H.S.
The given equation is an identity.
Nita needs at least $85 to buy a skateboard. She already has $61 Which graph best represents all the possible dollar amounts that it can save to buy a
Skateboard?
Answers
I believe the answer would be B. Hope this helps!
Graph B. best represents all the possible dollar amounts that it can save to buy a Skateboard.
What is a number line?calculation:-
amount Nita needed to buy a skateboard=$85
amount had=$61
∴ amount Nita needed more= $85-$61
=$24
A number line is a horizontal line that has numbers in equal intervals.The numbers included on the line can be negative or positive taking zero as a reference point at the center called the origin.The horizontal straight lines in which the integers are placed in equal intervals increase as we go right.The horizontal straight lines in which the integers are placed in equal intervals decreases as we go left.Learn more about the number line here:https://brainly.com/question/24644930
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Unit 4 Lesson 10 MODIFIED Inequalities:
You are working a summer job as a retail salesperson at Macy’s. You earn $230 per week plus a commission of 8% of your sales. This week, you need to earn $510. You will write and solve an INEQUALITY to determine how to meet your goal.
1): Give the decimal form of 8%. __________________________
2): If you make $945 in sales, how much will you make from your 8% commission?
Show your work and circle your solution.
3): Create an expression representing how much you will make in one week if you sell
x amount of sales.
4): Create an inequality using the expression in problem 3 to find how much you need
to sell at a MINIMUM to make your goal.
Answers
Answer:
Part 1) 0.08
Part 2) $75.6
Part 3) y=230+0.08x
Part 4) The minimum amount to sell is $3,500
Step-by-step explanation:
Part 1) Give the decimal form of 8%
we know that
To convert percentage number to decimal number, divide by 100
8%=8/100=0.08 ----> decimal form
Part 2) If you make $945 in sales, how much will you make from your 8% commission?
Multiply the percentage of commission in decimal number by the total amount in sales
so
0.08*($945)=$75.6
Part 3) Create an expression representing how much you will make in one week if you sell
x amount of sales.
Let
x-----> amount of sales in a week
y ----> total earned in a week
we know that
The linear equation that represent this situation is
y=230+0.08x
Part 4) Create an inequality using the expression in problem 3 to find how much you need to sell at a MINIMUM to make your goal
we know that
The inequality that represent the situation is
[tex]230+0.08x \geq 510[/tex]
Solve for x
Remember that x is the amount of sales in a week
[tex]0.08x \geq 510-230[/tex]
[tex]0.08x \geq 280[/tex]
[tex]x \geq 280/0.08[/tex]
[tex]x \geq 3,500[/tex]
The minimum amount to sell is $3,500
How is the graph of y= 1/3x related to its parent function y=1/x
A)It is horizontally stretched by a factor of 3 and reflected over the x-axis.
B)It is horizontally stretched by a factor of 3 and reflected over the y-axis.
C)It is horizontally compressed by a factor of 3 and reflected over the x-axis.
D)It is horizontally compressed by a factor of 3 and reflected over the y-axis.
Answers
B it is horizontally stretched by a factor of of 3 and reflected over the y
Answer:
itś C on edge :)
Step-by-step explanation:
What are the solutions for x to the equation (x-3)(x+8)=0
Answers
For this case we have a factored expression, of a second degree equation:
([tex](x-3) (x + 8) = 0[/tex]
To find the solutions:
[tex]x-3 = 0[/tex]we add 3 to both sides of the equation:
[tex]x=3[/tex]
[tex]x+8=0[/tex]We subtract 8 on both sides of the equation:
[tex]x = -8[/tex]
Thus, the solutions of the equation are:
[tex]x_ {1} = 3\\x_ {2} = - 8[/tex]
Answer:
[tex]x_ {1} = 3\\x_ {2} = - 8[/tex]
Find x when F(x)=10
f(x)=2x-6
Answers
just substitute 10 into the equation
10=2x-6
add 6 to both sides
16=2x
divide both sides by 2
x=8
Which of the following is the solution to the quadratic equation -x2-5x-6=0 using the quadratic formula
Answers
Answer:
x = -2; x = -3
Step-by-step explanation:
(-x - 3)(x + 2) = 0
(-x - 3) = 0
x = -3
(x + 2) = 0
x = -2
Use the vertical line test to determine if the relation is a function!! HELP NEEDED!!
Answers
Below is an image of the vertical line test.
The vertical line test is passed only when a vertical line only intersects the graph once. As you can see this graph intersects the graph twice, and therefore is not a function.
The answer you selected was correct!
Hope this helped!
Monica runs on a treadmill at an average speed of 7.5 miles per hour for 15 minutes. If, the next day, she runs the same distance at a speed of 8 miles per hour, what is the average time taken?
Answers
Answer:
Option 2: 14.06 minutes
Step-by-step explanation:
For the first scenario, we will convert the minutes into hours first to get all the quantities in same unit
So,
15 minutes = 1/4 hours = 0.25 hours
Speed = 7.5 miles per hour
Now using the speed, distance and time formula
Speed = distance/time
[tex]Speed = \frac{distance}{time}[/tex]
[tex]7.5 = \frac{distance}{0.25}[/tex]
[tex]7.5 * 0.25 = Distance[/tex]
Distance = 1.875 miles
So the distance for 1st day is 1.875 miles.
For next day
Speed = 8 miles per hour
Distance = 1.875
So,
[tex]speed = \frac{distance}{time}[/tex]
[tex]8 = \frac{1.875}{time}[/tex]
[tex]time = \frac{1.875}{8}[/tex]
[tex]time = 0.234375 hours[/tex]
Converting the hours into minutes will give
0.234375 * 60 min = 14.0625 minutes
Rounding off to two decimals = 14.06 min
So 2nd option is correct..
I need help please. Very plz correct answer plz.
Answers
Answer:
Step-by-step explanation:
The 9 is in the tens place in 75, 293 so rounding to the tens place means we need to round to the place the 9 is in, and we can sort of disregard the number after that, which is a 3. It will eventually round to a 0, but if that number is 5 or greater, it rounds the 9 up. It's a 3, so the 9 stays a 9: 75, 290.
The 2 is in the hundreds place, so just like above, we can change everything after the 2 to a 0, after we use the 9 for rounding. 9 is greater than 5, so the 2 rounds up to a 3: 75, 300.
The 5 is in the thousands place, so everything after that will become 0's, but use the 2 for rounding first. 2 is less than 5, so the 5 stays a 5: 75, 000.
Would an experience downhill skier want the slope of the hill to be 1/10 or 9/10? Why?
Answers
Answer:
9/10
Step-by-step explanation:
step 1
Compare the slopes
[tex]1/10=0.10[/tex]
[tex]9/10=0.9[/tex]
[tex]0.9 > 0.10[/tex]
therefore
An experienced skier would like the 9/10 hill slope because it is steeper, while the 1/10 is a softer slope.
What actual floor number do each student live on? Show your work also.
Answers
Heathe lives halfway up: 42 / 2 = 21st floor.
Raveen = 42 x 4/7 = 168/7 = 24th floor.
Alveera = 42 x 3/14 = 126/14 = 9th floor.
Rafi = 42 x 4/6 = 168/6 = 28th floor.
Suha = 28-24 = 4 /2 = 2 = 24+2 = 26th floor.
Arabi = 42 x 2/3 = 84/3 = 28th floor
Another Urgent one!! you know the drill. HEEEEEEEEEEELP
Answers
Answer:
Step-by-step explanation:
It is a right angle triangle with height and base = 3. The 4.24, for area, is not relevant.
Area = h * b / 2
Area = 3 * 3/2
Area = 9/2
Area = 4.5
Answer:
4.5 units
Step-by-step explanation:
A=1/2(b×h)
b=base
h=height
plug in what we know ...
A=1/2 (3×3)
A=1/2 (9)
A=4.5
In last night’s baseball game, there were 4 walks and 15 hits. Express the ratio of walks to hits, written in three different ways.
Answers
Word form: 4 to 15
Fraction form: 4/15
Ratio form: 4:15
The ratio has been written in three different forms as 4:15, 0.266:1 or 1:3.75.
What is a Ratio?When a number is divisible by another number then it can be written in the form of p:q, if two ratios are equal then they are said to be in proportion.
The number of walks in the baseball game is 4
The number of hits in the baseball game is 15
The ratio of walks to hits is 4 :15
The ratio of walks to hits is 0.2666 : 1
The ratio of walks to hits is 1 : 3.75
Therefore, the ratio has been written in three different forms as 4:15, 0.266:1 or 1:3.75.
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Whitney needs to borrow $200 for school supplies. If she borrows the same amount from 5 friends, which equation will show now much she owes each friend? $200 ÷ 5 -$200 ÷ 5 $200 ÷ (-5) -$200 ÷ (-5)
Answers
Answer:
She'll owe each friend $40.
Step-by-step explanation:
That's a total of $200 borrowed from 5 friends, which comes to:
$200
------------- = $40/friend
5 friends
Answer: A. $200 ÷ 5
Step-by-step explanation:
Sorry about the answer above mine.. that's kinda embarrassing considering how easy this question is. Anyways, the correct answer is A because the outcome will be 40 which is what we want because if you did the math for any other answer, the outcome will be negative.
solve the proportional equation below 6/2=(v-8)/(v-3)
Answers
½ = v; multiply the divisor to remove the variable from the denominator.
What is the range of the function? f(x) = -2^x + 1
Answers
{y|1 > y}, (-∞, 1); you did not specifically mention what notation you needed, so I wrote both [Internal Notation and Set Notation].
Answer:
all real numbers less than or equal to 0
Step-by-step explanation:
EDGE 2020
10+13h-6-4h+9+12h simplified
Answers
Answer:
[tex]\boxed{\bold{21h+13}}[/tex]
Explanation:
Group Like Terms
= [tex]\bold{13h-4h+12h+10-6+9}[/tex]
Combine Similar Elements: [tex]\bold{13h-4h+12h=21h}[/tex]
= [tex]\bold{21h+10-6+9}[/tex]
Subtract: [tex]\bold{10-6+9=13}[/tex]
= [tex]\bold{21h+13}[/tex]
Mordancy.
A scientist enlarged a circular portion of a microscope slide to make it easier to count the number of bacteria present in the sample.He divided the circle into 5 sectors as shown below and plans to count bacteria only in the shaded sector. What is the area of the shaded sector to the nearest tenth of a square centimeter
A.141.4
B.212.1
C.377.0
D.424.1
Answers
Answer:
Option B. [tex]212.1\ cm^{2}[/tex]
Step-by-step explanation:
step 1
Find the central angle of the shaded sector
Remember that the diameter divide the circle into two equal parts ( 180 degrees each part)
so
Let
x -----> the measure of the central angle of the shaded sector
∠x+72°=180°
∠x=180°-72°=108°
step 2
Find the area of the circle
The area of the circle is
[tex]A=\pi r^{2}[/tex]
we have
[tex]r=15\ cm[/tex]
assume
[tex]\pi=3.1416[/tex]
substitute
[tex]A=(3.1416)(15)^{2}[/tex]
[tex]A=706.86\ cm^{2}[/tex]
step 3
Find the area of the shaded sector
Remember that the area of the complete circle subtends a central angle of 360 degrees
so
by proportion find the area of a sector by a central angle of 108 degrees
[tex]\frac{706.86}{360}=\frac{x}{108}\\ \\x=706.86*108/360\\ \\x=212.1\ cm^{2}[/tex]
Show all work to multiply (3+ V16)(6-
64).
Answers
Regroup terms
(3 + 16V)(6 - 64)
Simplify 6 - 64 to -58
(3 + 16V) * -58
Simplify
= -58(3 + 16V)
how many solutions exist for the givien equation 3(x+10)+6=3(x+12)
Answers
For this case we solve the following equation:
[tex]3 (x + 10) + 6 = 3 (x + 12)[/tex]
We apply distributive property to the terms within parentheses:
[tex]3x + 30 + 6 = 3x + 36[/tex]
We add similar terms:
[tex]3x + 36 = 3x + 36\\36 = 36[/tex]
Since 36 equals 36, then the equation will always be true for any value of x.
ANswer:
Infinite solutions
A basketball has a rebound ratio of 0.8. If you drop the basketball from a heigh of 10cm, what will the height of the 5th bounce be?
Answers
[tex]\bf n^{th}\textit{ term of a geometric sequence} \\\\ a_n=a_1\cdot r^{n-1}\qquad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ r=\textit{common ratio}\\ \cline{1-1} r=0.8\\ a_1=10\\ n=5 \end{cases} \\\\\\ a_5=10(0.8)^{5-1}\implies a_5=10(0.8)^4\implies a_5=4.096[/tex]
- |-9| x |7| =
whats the answer? help please!!
Answers
Answer:
Final answer is -63.
Step-by-step explanation:
Given expression is [tex]-|-9| \times |7|[/tex].
Now question says to simplify that expression [tex]-|-9| \times |7|[/tex]
| | indicates absolute function which results only in positive output so |-9| gives 9 only
and |7| gives 7.
then we can rewrite the expression as :
[tex]-|-9| \times |7|[/tex]
[tex]=-(9) \times (7)[/tex]
[tex]=-9 \times 7[/tex]
[tex]=-63[/tex]
Hence final answer is -63.
A strong foundation in mathematics is most necessary for which career?
Education
Engineering
Graphic design
Medicine
Answers
Answer:
b
Step-by-step explanation:
Solve the equation 8-6z=26
Answers
8-6z=26
8-8-6z=26-8
-6z=18
divide by -6 for -6z and 18
-6z/-6=18/-6
z=-3
Check answer by using substitution method
8-6(-3)=26
8+18= 26
26=26
Answer is z=-3
Answer:
answer - 3
Step-by-step explanation:
8 - 6z = 26 Subtract 8 from both sides.
8-8 - 6z = 26 - 8
- 6z = 18 Divide by - 6
-6z/-6 = 18/-6 Do the division. Note: you must leave the letter with 1 in front of it.
z = - 3
8-102.
The graph at right represents this situation: Cara jogs every
morning, and after 30 minutes, she has run 3.5 miles.
a. How is Cara's speed represented on the graph?
b. Write a rule for Cara's distance if t represents
the number of hours.
Distance (miles)
c.
If Cara continues to run at this rate, predict
how far she will run in 4 hours.
Answers
a. The speed is represented by 7 miles an hour
b. f(t)=7t
c. 28 miles