Answers
Answer:
1. Area = 113.1 square units
2. Area = 28.27 square units
3. Area of Shaded = 22.27 square units
Step-by-step explanation:
1.
Area of the circle is given by the formula [tex]A=\pi r^2[/tex]
where A is the area and r is the radius
In our case the radius is 6 units, thus we have:
[tex]A=\pi r^2\\A=\pi (6)^2\\A=\pi *36\\A=113.1[/tex]
Area = 113.1 square units
2.
When we have the angle given in radians, the area of sector is given by the formula [tex]A=\frac{1}{2}r^2\theta[/tex]
Where [tex]\theta[/tex] is the central angle ( in our case [tex]\theta = \frac{\pi}{2}[/tex] and r is the radius (it is 6)
Plugging in these info into the formula we have area of sector:
[tex]A=\frac{1}{2}r^2\theta\\A=\frac{1}{2}(6)^2(\frac{\pi}{2})\\A=\frac{1}{2}*36*\frac{\pi}{2}\\A=28.27[/tex]
Area = 28.27 square units
3.
Area of shaded region = Area of Sector - Area of Triangle
We know area of sector is 28.27
Since the angle is 90 degrees, we have a right triangle, we can use the pythagorean theorem to find the height of the triangle, CE.
Thus
[tex]DC^2+CE^2=DE^2\\3^2+CE^2=5^2\\9+CE^2=25\\CE^2=25-9\\CE^2=16\\CE=4[/tex]
The area of triangle is [tex]A=\frac{1}{2}bh[/tex]
where b is the base (in our case it is DC = 3 ) and h is the height (in our case it is CE, which is 4). Plugging into the formula we have the area of triangle as:
[tex]A=\frac{1}{2}bh\\A=\frac{1}{2}(3)(4)\\A=6[/tex]
Area of Shaded = 28.27 - 6 = 22.27 square units
Related Questions
Jacintas teacher asks her to find the tangent of angle y. what is her error
Answers
Answer:
what is her error?
Step-by-step explanation:
Answer:
Do you have a picture?
What is the image of ( 1 , 5 ) (1,5) after a reflection over the line y = − x y=−x?
Answers
The image would be (-1, 5)
Item 1 A bag contains 7 blue cards, 4 green cards, 6 red cards, and 8 yellow cards. You randomly choose a card. a. How many possible outcomes are there?
Answers
Answer:
4 possible outcomes
Step-by-step explanation:
we know that
The probability of an event is the ratio of the size of the event space to the size of the sample space.
The size of the sample space is the total number of possible outcomes
The event space is the number of outcomes in the event you are interested in.
so
Let
x------> size of the event space
y-----> size of the sample space
so
[tex]P=\frac{x}{y}[/tex]
In this problem
The probability of choose a blue card is
[tex]x=7[/tex]
[tex]y=7+4+6+8=25[/tex]
substitute
[tex]P=\frac{7}{25}[/tex]
The probability of choose a green card is
[tex]x=4[/tex]
[tex]y=7+4+6+8=25[/tex]
substitute
[tex]P=\frac{4}{25}[/tex]
The probability of choose a red card is
[tex]x=6[/tex]
[tex]y=7+4+6+8=25[/tex]
substitute
[tex]P=\frac{6}{25}[/tex]
The probability of choose a yellow card is
[tex]x=8[/tex]
[tex]y=7+4+6+8=25[/tex]
substitute
[tex]P=\frac{8}{25}[/tex]
The sum of the probabilities of the 4 possible outcomes is equal to
[tex]\frac{7}{25}+\frac{4}{25}+\frac{6}{25}+\frac{8}{25}=\frac{25}{25}[/tex] ----> represent the 100%
Can you guys help!! Have 8 more mins two finish
Answers
Answer:
60 / 120 is terminating, the rest are repeating.
Answer:
56/72 is repeating, 21/22 is repeating, 11/121 is repeating, and 60/120 is terminating
Step-by-step explanation:
Please help me,Asap
Answers
Answer:
2. y = 25 km
Step-by-step explanation:
To find the dimensions, write a proportion. A proportion is an equation of ratios.
[tex]\frac{scale}{factor} = \frac{Actual}{Model}[/tex]
Then solve for the unknown value by cross multiplying.
2. [tex]\frac{2}{5} = \frac{10}{y}[/tex]
2y = 5*10
2y = 50
y = 25
find the area of the shaded circle.give your answer in 3 significant numbers
Answers
Answer:
116 cm²
Step-by-step explanation:
The area of a circle = πr² ← r is the radius
shaded area = external area - internal area
= π × 6.5² - π × 2.3²
= π( 42.25 - 5.29)
= π × 36.96 ≈ 116 cm²
Answer:
116.113 cm²Step-by-step explanation:
Area of a circle = πr²
Shaded area = External area - Internal area
= π × 6.5² - π × 2.3²
= π × (42.25 - 5.29)
= π × 36.96 = 116.113 cm²
Suppose you had d dollars in your checking account. You spent $20 but have at least $55 left. How much money did you have initially? Write, solve, and graph an inequality that represents this situation.
Answers
Answer:
Step-by-step explanation:
55-20 is less than or equal to (d)
i think...
Answer:
The solution would be d ≥ 75
Step-by-step explanation:
To find this we know that we have at least 55, which can be modeled as:
d ≥ 55
And then we need to add 20
d ≥ 55 + 20
d ≥ 75
Find the inverse of y=2x^2+2
Answers
Answer:
Step-by-step explanation:
Plug x for y and y for x.
y = 2x^2 + 2
x = 2y^2 + 2
Then isolate the y variable.
x - 2 = 2y^2
sqrt(x - 2) = 2y
(sqrt(x - 2))/2 = y
Michelle collected data on the weight of 200 apples at the farmer's market. Most weighed 0.30 –.40 pounds, but three weighed over a p
ound each. Michelle identified this as a striking deviation. What should she do with it?
A) Ignore the data.
B) Do not include the striking deviation in the data display.
C) Ignore the striking deviation because it is so far from the average.
D) Include the striking deviation because it may explain an unusual occurrence.
Answers
Answer:
Step-by-step explanation:
include the striking deviation because it may explain an unusual occurrence is correct. Striking deviations or outliers can be useful in describing data set.
What is the characteristics of a line
Answers
• They're 180°
• Short, thin, or thick
• Could be curved, zig-zag, straight, bent etc.
• Perpendicular
A line is characterized by its length exceeding its width and the path it takes. Its qualities can express emotions and control the viewer's attention, with variations such as curved or angular, smooth or staccato, and different thicknesses. Lines play a crucial role in defining shapes and in expressive forms of writing such as calligraphy.
The characteristics of a line in design are defined by its length being greater than its width and by the paths it takes. A line is essentially a point in motion and is characterized by how it is used in art to determine motion, direction, and energy. When speaking of the qualities of a line, we refer to its character which can animate a surface. Lines can be curved or angular, and can progress smoothly or with a staccato rhythm, and they can be thick or thin, pale or bold.<\/p>
Lines have an emotional and expressive content that is understood both rationally and emotionally; they can control the viewer's attention and direction. Different types of lines like outline or contour line define shapes. Moreover, lines are integral to objects and writing symbols, where they denote meaning and can be expressive in themselves, illustrating their significance in calligraphy and other forms of art.<\/p>
Gestures are also related to lines, where a line produced by the artist's movement can be interpreted in various ways, like conveying calm with evenly drawn horizontal lines or rigidity with straight lines, which can be impactful depending on the context.<\/p>
How can i do this one ☝️
Answers
Hey there!
Let's start by adding 5 to both sides. This eliminates the -5.
1 = r/20
Now to solve for r we can multiply both sides by 20.
20 = r
Check
-4 = 20/20 - 5
-4 = 1 - 5
-4 = -4
Your answer is r = 20.
Hope this helps!
Answer:
20Step-by-step explanation:
-4 = [tex]\frac{r}{20}[/tex] - 5
⇒ -4 + 5 = [tex]\frac{r}{20}[/tex]
⇒ 1 = [tex]\frac{r}{20}[/tex]
⇒ 1 × 20 = r
⇒ 20 = r
August is making dinner for 8 people. She opens 7 cans of soup, how much soup will each person get? Use numbers and words to explain your awnser
Answers
Answer:7/8
Step-by-step explanation:
7 divided by 8 = 7/8
if you split that with 8 people, you multiply 7/8 and 8, and you'll get 7, which is the number of soup cans you started with.
How do I find the Axis of Symmetry for a parabola
Answers
Answer:
Explanation given below.
Step-by-step explanation:
The first step is to put the parabola in the form [tex]ax^2+bx+c[/tex] , which is the standard form of a parabola
Note: a is the coefficient before x^2 term, b is the coefficient before x term, and c is the independent constant term
The axis of symmetry divides the parabola symmetrically. The axis of symmetry has the equation [tex]x=-\frac{b}{2a}[/tex]
Where a and b are the respective values shown above
So, that is how you get the axis of symmetry of any parabola.
Answer:
The equation of the axis of symmetry of the parabola is x = h,
where h is the x-coordinate of the vertex point
Step-by-step explanation:
* The axis of symmetry is the line which divides the
shape into two congruent parts
* The general form of the quadratic equation is:
ax² + bx + c = 0
* The quadratic equation is represented graphically by parabola
∵ The parabola has minimum point or maximum point
∴ The axis of symmetry of the parabola is passing through this point
This point is called the vertex point or the turning point
- Lets find this point:
* the x-coordinate of this point calculated from the equation
x- coordinate of the vertex point h = -b/2a
- where b is the coefficient of x and a is the coefficient of x²
∴ The equation of the axis of symmetry of the parabola is x = -b/2a
EX:
- If ⇒ x² - 4x + 4 = 0
∵ a = 1 , b = -4
∴ h = -(-4)/2(1) = 2
∴ The equation of the axis of symmetry of the parabola is x = 2
The graph show you the axis of symmetry
The bar graph and line plot show the same temperatures. Where should you look to find the least common temperature?
Answers
Answer:
Step-by-step explanation:
AThe shortest column of the line plot
BThe shortest bar of the bar graph
CThe column farthest to the left on the line plot
DThe average bar height of the bar graph
Answer:
The shortest column of the line plot
Two geometric means are inserted between 4 and 864 so the four numbers form a geometric sequence. What are these two numbers ?
Answers
Answer:
24 and 144
Step-by-step explanation:
a = 4
t4 = 864
864 = 4*r^(4 - 1) divide by 4
216 = r^3 Take the cube root of 216
6 = r
Note you can find the cube root of any number by using your calculator.
216y^x or x^y or ^0.333333333333 = 5.99999999 which rounded is 6t2 = a * r^(2 - 1)
t2 = 4 * 6^1
t2 = 24
=================
t3 = a*r^(3 -1)
t3 = 4 * 6^2
t3 = 4 * 36
t3 = 144
Answer
24 and 144
Factor completely. x2−5x−24 Enter your answer in the box.
Answers
Answer:
(x-8)(x+3)
Step-by-step explanation:
Final answer:
To factor the quadratic expression x² - 5x - 24, we find the factors that multiply to -24 and add to -5, which are -8 and 3. Therefore, the factored form of the expression is (x - 8)(x + 3).
Explanation:
To factor the quadratic expression x² - 5x - 24 completely, we need to find two numbers that multiply to -24 (the constant term) and add to -5 (the coefficient of the x term). The numbers that fit this criteria are -8 and 3. So, our expression factors into:
(x - 8)(x + 3)
We can check our factoring by expanding these factors to see if we get the original expression:
(x - 8)(x + 3)
= x² + 3x - 8x - 24
= x² - 5x - 24
Thus, the original expression is correctly factored as (x - 8)(x + 3).
Solve this quadratic equation using the quadratic formula.
3x2 + 4x = 6
Answers
Answer: [tex]\bold{\dfrac{-2\pm \sqrt{22}}{3}}[/tex]
Step-by-step explanation:
[tex]3x^2+4x-6=0\quad \rightarrow \quad a=3,\ b=4,\ c=-6\\\\\\\text{Quadratic formula is: }x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\\\x=\dfrac{-(4)\pm \sqrt{(4)^2-4(3)(-6)}}{2(3)}\\\\\\.\ =\dfrac{-4\pm \sqrt{16+72}}{2(3)}\\\\\\\\.\ =\dfrac{-4\pm \sqrt{88}}{2(3)}\\\\\\\\.\ =\dfrac{-4\pm 2\sqrt{22}}{2(3)}\\\\\\\\.\ =\dfrac{-2\pm \sqrt{22}}{3}[/tex]
Is it possible for two numbers to have a difference of 6, and also a sum of 6?
Answers
Answer:
yes
Step-by-step explanation:
sum:
• `x+y=6`
• `y=6-x`
Difference:
• `y-x=6`
• `y=x+6`
Answer:
yes 12-6 has a difference of 6 and a sum of 6
Step-by-step explanation:
solve this equation
156=2b+5(-8-6b)
Answers
Answer:the answer is -7
Step-by-step explanation:
156=2b+5(-8-6b)
2b+5(-8-6b)
expand 2b+5(-8-6b) ---> -28b-40
-28b-40=156
add 40 to both sides
-28b-40+40=156+40
simplify
-28b=196
divide both sides by -28
(-28b/-28b) = (196/-28b)
simplify
b=-7
Solve the inequality
7x + 3 > 10
A x>1
B x<1
C x>=1
D x> 13/7
Solve the inequality
-3 + 5x < 7x - 5
A x>4
B x<4
C x>1
D x<1
Solve the inequality
-2x + >= 3x + 20
A x=<15
B x=<3
C x>= 3
D x=< -3
Answers
Answer:
[tex]\large\boxed{Q1.\ x>1}\\\boxed{Q2.\ x>1}\\\boxed{Q3.\ x\leq-3}[/tex]
Step-by-step explanation:
[tex]Q1.\\7x+3>10\qquad\text{subtract 3 from both sides}\\\\7x+3-3>10-3\\\\7x>7\qquad\text{divide both sides by 7}\\\\\dfrac{7x}{7}>\dfrac{7}{7}\\\\\boxed{x>1}\\\\Q2.\\-3+5x<7x-5\qquad\text{add 3 to both sides}\\\\-3+3+5x<7x-5+3\\\\5x<7x-2\qquad\text{subtract 7x from both sides}\\\\5x-7x<7x-7x-2\\\\-2x<-2\qquad\text{change the signs}\\\\2x>2\qquad\text{divide both sides by 2}\\\\\dfrac{2x}{2}>\dfrac{2}{2}\\\\\boxed{x>1}[/tex]
[tex]Q3.\\-2x+5\geq3x+20\qquad\text{subtract 5 from both sides}\\\\-2x+5-5\geq3x+20-5\\\\-2x\geq3x+15\qquad\text{subtract 3x from both sides}\\\\-2x-3x\geq3x-3x+15\\\\-5x\geq15\qquad\text{change the signs}\\\\5x\leq-15\qquad\text{divide both sides by 5}\\\\\boxed{x\leq-3}[/tex]
x>1
x>1
X>-3
Step-by-step explanation:
How many 3 letter words can be made from 4 letters “FGHI” if repetition is allowed and if repetition isn’t alllowed ?
Answers
When repetition is allowed, there can be 64 different 3-letter words made from the letters 'FGHI'. When repetition is not allowed, there can be 24 different 3-letter words made from those letters.
Explanation:In this question, we are asked to find the number of 3-letter words that can be made from the letters 'FGHI' with and without repetition. When repetition is allowed, each letter can be chosen independently for each position, so we have 4 choices for each position. Therefore, the total number of words is 4*4*4 = 64. When repetition is not allowed, each letter can only be used once, so we have 4 choices for the first position, then 3 choices for the second position, and finally 2 choices for the third position. Therefore, the total number of words is 4*3*2 = 24.
Learn more about Counting principles here:https://brainly.com/question/29594564
#SPJ12
Rewrite the quadratic function in vertex form.
Y=3x^2-12x+4
Answers
Answer:
[tex]\large\boxed{y=3(x-2)^2-8}[/tex]
Step-by-step explanation:
The vertex form of an equation of a parabola y = ax² + bx + c:
[tex]f(x)=a(x-h)^2+k[/tex]
(h, k) - vertex
[tex]h=\dfrac{-b}{2a},\ k=f(h)[/tex]
We have the equation:
[tex]y=3x^2-12x+4\\\\a=3,\ b=-12,\ c=4[/tex]
Substitute:
[tex]h=\dfrac{-(-12)}{2(3)}=\dfrac{12}{6}=2\\\\k=f(2)=3(2^2)-12(2)+4=3(4)-24+4=12-24+4=-8[/tex]
Finally:
[tex]y=3(x-2)^2+(-8)=3(x-2)^2-8[/tex]
Find y and x values please
Answers
What is the volume of the water contained in the cylinder?
Answers
Answer:
Vf = 118.365 m3
Step-by-step explanation:
Vcil = Pi*[(20)^2]*(100=
Vcil = 125.600 m3
Vesf = (4/3)*Pi*(12)^3
Vesf = 7235 m3
Then
Vf = Vci - Vesf
Vf = 125.600 - 7235
Vf = 118365 m3
Best regards
BASIC MATH PLEASE HELP
Answers
Answer:
8
Step-by-step explanation:
6 / .75(3/4)
6 divided by 3/4 is equivalent to 8
there are 60 girls and 45 boys who want to participate in a co-ed basketball tournament. if each team must have the same number of girls and boys, what is the greatest number of team that csn enter? how many girls and.boys would be on each of those teams?
Answer 1 the greatest of team that can enter are—— teams
Answer 2, there would be—- girls and —-boys on each team.
Answers
Answer:
15 teams, 4 girls and 3 boys on each team.
Step-by-step explanation:
What's the greatest common multiple of 60 and 45? It's 15.
This is the greatest number of teams that can be formed.
60/15 = 4; thus, there will be 4 girls on each team.
45/15 = 3; thus, 3 boys on each team
The greatest number of co-ed basketball teams that can be formed with an equal number of girls and boys is 3, with each team consisting of 4 girls and 3 boys.
To determine the greatest number of co-ed basketball teams that can enter the tournament with an equal number of girls and boys, you need to find the greatest common divisor (GCD) of the number of girls and boys. In this case, we have 60 girls and 45 boys. The GCD of 60 and 45 is 15, which means the largest number of teams that can be formed where each team has the same number of girls and boys is 15 (since 60 \/ 15 = 4 girls per team and 45 \/ 15 = 3 boys per team).
Answer 1: The greatest number of teams that can enter are 3 teams.
Answer 2: There would be 4 girls and 3 boys on each team.
Through: (-4,-3), slope= 3/2
Answers
Answer:
[tex]\large\boxed{y+3=\dfrac{3}{2}(x+4)}[/tex]
Step-by-step explanation:
The point-slope form of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
We have
[tex]m=\dfrac{3}{2},\ (-4,\ -3)[/tex]
Substitute:
[tex]y-(-3)=\dfrac{3}{2}(x-(-4))\\\\y+3=\dfrac{3}{2}(x+4)[/tex]
If you could please show all your steps that would be great.
Answers
a. Angles ABC and CBD are supplementary, so you know that [tex]m\angle ABC=180^\circ-24^\circ=156^\circ[/tex]
The interior angles of any triangle sum to 180 degrees in measure, so that [tex]m\angle ACB=180^\circ-156^\circ-16^\circ=8^\circ[/tex].
By the law of sines, we then have
[tex]\dfrac{\sin8^\circ}{7600\,\mathrm{ft}}=\dfrac{\sin16^\circ}{BC}\implies BC=\dfrac{(7600\,\mathrm{ft})\sin16^\circ}{\sin156^\circ}\approx15052\,\mathrm{ft}[/tex]
b. In triangle BCD, we have
[tex]\sin24^\circ=\dfrac{CD}{BC}[/tex]
and so
[tex]CD=\sin24^\circ\dfrac{(7600\,\mathrm{ft})\sin16^\circ}{\sin8^\circ}\approx6122\,\mathrm{ft}[/tex]
Choose the graph that shows the solution set for -2 ≥ x.
Answers
Explanation:
When looking at x on number lines, x is represented by the bold line. The x value can be anything on the bold line and therefore the line must respect the restrictions of x.
This question says -2 ≥ x which means "-2 is greater than or equal to x". Inversely, this also means that x is less than or equal to -2 because the original question can also be written as x ≤ -2. So, we are looking on the number line for the bold line that starts at -2 and continues to the left of -2, where the numbers that are less than -2 will be found.
The correct answer would be B.
Hope this helps!
Do I multiply all together, please
Answers
Answer:
40 m
Step-by-step explanation:
A= b(h)
A= 8(5)
A= 40 m
Answer:
It is a parallelogram and the area is 40.
Step-by-step explanation:
The area of a parallelogram is a=bh.
The base is 8 and the height is 5. All you do is times 8 and 5 to get 40.