Answer:
225Pi (in terms of Pi)
Or
706.5cm
Step-by-step explanation:
Area = Pi * radius^2
Radius is half of the diameter, so it is 15.
Area = Pi*15^2
Which is:
225Pi
Or
706.5
Answer:
The area of the circle is
[tex]225\pi[/tex]
Step-by-step explanation:
The diameter equals 30 cm, so the radio equals 15 cm.
The formula of the circle area is
[tex]\pi \times {r}^{2} [/tex]
Then,
[tex]\pi \times {15}^{2} = 225\pi[/tex]
Help please!!!!!!!!!!!!!!!!!!!!
9514 1404 393
Answer:
(c) The solution -6 is an extraneous solution
Step-by-step explanation:
If you solve the equation graphically, you can avoid extraneous solutions. The true solution is x = -1.
You can tell from the equation that the domain will be restricted to values of x that make the radical non-negative:
x+4 ≥ 0 ⇒ x ≥ -4
Then x=-6 must be an extraneous solution. It arises when the negative square root is used.
__
The conventional solution method has you square both sides and solve the resulting quadratic.
(x +4)² = x +10
x² +7x +6 = 0
(x +6)(x +1) = 0 ⇒ x = -6 or -1
The solution x=-6 is not in the domain, so is extraneous.
__
Additional comment
Graphical solution is often easier if the equation is in the form f(x) = 0. That form can be had by subtracting one side of the equation from both sides. In the attached, we subtracted √(x+10) from both sides. (We added the negative branch of the square root function to show where the extraneous root comes from.)
what number can be add to
[tex] {9x}^{2} + 24x[/tex]
to make it a perfect square
•∆•
The required number will be 16
the expression will be like :
[tex]9 {x}^{2} + 24x + 16[/tex][tex](3x) {}^{2} + (2 \times 3x \times 4) + (4) {}^{2} [/tex][tex](3x + 4) {}^{2} [/tex]hope it helps you cap !!
Anti - Venom
Which expression is represented by the model?
Answer:
X+3
Step-by-step explanation:
I did the test
Question 7 of 27
Which of the following is an element in the sample space for first rolling a
number cube and then tossing a coin?
Answer:
TH is an element on the sample space for first rolling a die and then tossing a coin. A coin has both heads and tails.
The sample space for rolling a number cube and then tossing a coin is:
{(1, H), (1, T), (2, H), (2, T), (3, H), (3, T), (4, H), (4, T), (5, H), (5, T), (6, H), (6, T)}
The elements can be any of the elements in the sample space.
What is sample space?It is the total number of possible outcomes from a given set.
We have,
The sample space for rolling a number cube and then tossing a coin consists of all possible outcomes from rolling the number cube and tossing the coin.
Each outcome is a pair consisting of a number from 1 to 6 (the possible outcome from rolling the number cube) and a head or tail (the possible outcome from tossing the coin).
Therefore, an element in the sample space can be represented as an ordered pair (n, h/t), where n is the number rolled on the number cube and h/t is the outcome of the coin toss (either head or tail).
So,
The sample space for rolling a number cube and then tossing a coin is:
{(1, H), (1, T), (2, H), (2, T), (3, H), (3, T), (4, H), (4, T), (5, H), (5, T), (6, H), (6, T)}
For example, (3, H), (6, T), (1, H), and (4, T) are all elements in the sample space.
Thus,
The sample space for rolling a number cube and then tossing a coin is:
{(1, H), (1, T), (2, H), (2, T), (3, H), (3, T), (4, H), (4, T), (5, H), (5, T), (6, H), (6, T)}
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Có 10 bạn mua cùng một loại vở hết tất ả 60 000 tính giá tiền của mỗi quyển vở biết rằng mỗi bạn mua 2 quyển vở
Answer:
Giá một cuốn sách là $ 1000
Step-by-step explanation:
Được
Tổng chi phí sách = 60000
Tổng số bạn bè = 10
Sách do mỗi người bạn mua = 2
Như vậy, tổng số sách mua của cả 10 bạn = 10 * 2 = 20
Giá của một cuốn sách = Tổng giá / tổng số sách đã mua
Giá một cuốn sách = 20000/20 = 1000
Giá một cuốn sách là $ 1000
what is the vertex of x^2
Answer:
The vertex is (0,0)
Step-by-step explanation:
To find the x coordinate of the vertex
x = -b/2a where ax^2 +bx +c
a=1 b=0 c=0
x = -0/2(1) = 0
The y value is found by substituting into the equation
y = (0)^2 =0
The vertex is (0,0)
Can someone help I don’t understand the question
Answer:
36x
Step-by-step explanation:
OF= 6x (given radius of circle)
OB=OF+FB
= 6x +6x(given OF=FB)
= 12x
Angle D= angle B and angle O= 60°( given arc EF is 60°)
D + B + O= 180° ( sum of angles in a triangle)
x + x + 60= 180° ( let the value of remaining angles be x and D= B)
2x= 180 -60
x = 120/2
x= 60°
now, triangle DOB is a equilateral triangle because all angles are equal.
so, OB=DB=OD= 12x ( all sides are equal in equilateral triangle)
so,
perimeter of DOB= OB+DB+OD
= 12x+12x+12x
= 36x
follow me if this was helpful
2020 people formed a line. In one move, you are allowed to exchange the positions of two people, separated by one other person. Can you always sort the people form tallest to shortest using these moves?
Answer:
yes you CAN you can use the descending to ascending formular but on people in which they might be a mixup of tallest and shortest
No, it is not always possible to sort the people from tallest to shortest using these moves.
Suppose there are four people in the line with heights A, B, C, and D, where A is the tallest and D is the shortest.
The initial order is A-B-C-D.
In each move, we can only exchange the positions of two people separated by one other person.
However, no matter how many moves we make, we cannot change the relative order of A and D since they are separated by two other people.
Thus, it is not possible to sort the people from tallest to shortest using these moves.
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For the given functions f(x) and g(x), find (f + g)(x) or (f – g)(x) as
indicated.
f(x) = 8x – 7,8(x) = 6x – 4
Find (f + g) (x)
Answer:
(f + g) (x) = 14x-11
Step-by-step explanation:
From the question, what we have to do is to add the two given polynomials
We have this as;
(8x-7) + (6x-4) = 8x + 6x -7-4 = 14x -11
By writing each number correct to 1 significant figure, estimate the value of
37.8 x 13.2
28,5 + 22.1
You must show all your working.
Answer:
37.8 x 13.2 =4988.6
28,5 + 22.1 = 50.6
find the value of x and y
Answer:
x = 58
y = 39
Step-by-step explanation:
x = 58 (Vertically opposite angles)
x + 2y + (x-14) = 180 (Angles in a straight line)
=> x + 2y + x - 14 = 180
=> 2x + 2y = 180 + 14
=> 2(58) + 2y = 194
=> 116 + 2y = 194
=> 2y = 194 - 116
=> 2y = 78
=> y = 78/2
=> y = 39
Trong mặt phẳng tọa độ Oxy , cho vectơ a = ( -3;4) . Độ dài vectơ a bằng bao nhiêu
Answer:
Step-by-step explanation:
Độ dài vecto a= căn bậc hai của (-3)*(-3)+4*4=5
Answer:
5
Step-by-step explanation:
If f(x) is discontinuous, determine the reason.
f of x equals the quantity x squared plus 4 for x less than or equal to 1 and equals x plus 4 for x greater than 1 (5 points)
A. f(x) is continuous for all real numbers
B. The limit as x approaches 1 does not exist
C. f(1) does not equal the limit as x approaches 1
D. f(1) is not defined
Answer: Choice A
f(x) is continuous for all real numbers
=============================================================
Explanation:
The piecewise function given to us basically breaks down into these two cases:
If x = 1 or smaller, then f(x) = x^2+4If x > 1, then f(x) = x+4So if we plug in x = 1, then we go for the top line and say
f(x) = x^2+4
f(1) = 1^2+4
f(1) = 5
Showing that f(1) is indeed defined. We rule out choice D because of this.
----------------
Let's see what happens when we plug x = 1 into the bottom equation
f(x) = x+4
f(1) = 1+4
f(1) = 5
Both pieces produce the same output. This tells us that as x approaches 1 from either the left or right sides, the y value approaches y = 5. Therefore, the limit at x = 1 exists. We rule out choice B because of this.
We rule out choice C as well because f(1) does equal the limiting value mentioned earlier.
----------------
The answer is choice A because no matter what x value we plug in, it's not only defined but also it's connected to the rest of the function curve as shown below.
Answer: A; f(x) is continuous for all real numbers
If the cos of an angle is .75, what is the csc?
A. 1/√(5)
B. 9/√(6)
C. 6/√(2)
D. 3/√(9)
E. 4/√(7)
F. 2/√(3)
Answer: Choice E. 4/sqrt(7)
This is the same as writing [tex]\frac{4}{\sqrt{7}}[/tex]
=================================================
Explanation:
0.75 = 3/4
Recall that cosine is the ratio of adjacent over hypotenuse.
That means if cos(theta) = 3/4, then the adjacent is 3 units and the hypotenuse is 4 units.
Through the pythagorean theorem, we would then find that
a^2+b^2 = c^2
a = sqrt(c^2 - b^2)
a = sqrt(4^2 - 3^2)
a = sqrt(7)
This is the opposite side of reference angle theta.
From here, we can say
csc(angle) = hypotenuse/opposite
csc(theta) = 4/sqrt(7)
which points to choice E as the final answer.
can someone help me I don't understand
Answer:
(a) 165 m/min
(b) 107.14m/min
Step-by-step explanation:
The slope of the distance time graph gives speed.
Here, the speed of the segment A is
[tex]v_A= \frac{900-0}{4-0}=225 m/min[/tex]
The speed of segment B is
[tex]v_B= \frac{1500- 900}{14-4}= 60 m/min[/tex]
(a) The change in speed is
= 225 - 60 = 165 m/min
(b) The average speed is defined as the ratio of total distance to the total time.
So, the average speed is
[tex]= \frac{1500}{14}= 107.14 m/min[/tex]
(2-3 t)^2 QUICK PLEASEEEEEEEEEEEEEEEE
Answer:
The answer is = 4 - 12t + 9t^2
Step-by-step explanation:
(2-3t)^2
= 2^2 - 2*2*3t + (3t)^2
= 4 - 12t + 9t^2
Using the net below, find the surface area of the pyramid. 6 cm 7 cm Surface Area - [?] cm2
Answer:
120 cm²
Step-by-step explanation:
Surface area of the pyramid = area of the 4 triangles + area of the square
✔️Area of the 4 triangles = 4(½*b*h)
b = 6 cm
h = 7 cm
Area = 4(½*6*7)
= 4(3*7)
= 4(21)
= 84 cm²
✔️Area of the square = s²
s = 6 cm
Area = 6² = 36 cm²
✅Surface area of the pyramid = 84 + 36 = 120 cm²
Use the three steps to solve the problem.
Betty has 10 more dimes than quarters. If she has $3.45, how many quarters and dimes does she have?
Answer:
17
Step-by-step explanation:
Let d be dimes
q represent quarters
d = q + 10
10d + 25q = 345 cents
Substitute for "d" and solve for "q";
10(q+10) + 25q = 345
35q + 100 = 345
35q = 245
q = 7
Since d = q+10, d = 17
he tables represent two linear functions in a system.
A 2 column table with 5 rows. The first column, x, has the entries, negative 6, negative 3, 0, 3. The second column, y, has the entries, negative 22, negative 10, 2, 14. A 2 column table with 5 rows. The first column, x, has the entries, negative 6, negative 3, 0, 3. The second column, y, has the entries, negative 30, negative 21, negative 12, negative 3.
What is the solution to this system?
(negative StartFraction 13 over 3 EndFraction, negative 25)
(negative StartFraction 14 over 3 EndFraction, negative 54)
(–13, –50)
(–14, –54)
Answer:
8-22 is the answer ok thanks
Can i get some help with this!
I think you've got it, I don't know man.
What am I doing wrong? I've tried every conceivable answer, I thought I knew this type of math well, but this program keeps telling me I'm wrong.
Answer:
15.0 units
Step-by-step explanation:
Here, we want to get the distance between the two points as follows;
CD = √(x2-x1)^2 + (y2-y1)^2
So we have;
CD = √(7+8)^2 + (-5+4)^2
CD = √225+ 1 =
CD = √(226
CD = 15.0 units
Anyone know the answer to this question ?
Answer:
4.35
Step-by-step explanation:
(1 * 0.35) + (2 * 0.2) + (5 * 0.1) + (8 * 0.2) + (10 * 0.15) = 4.35
Please help me ASAP
Answer:
no
Step-by-step explanation:
no
3a+5b+2c=?
a+b=15
b+c=14
5b=3b,2b
Step-by-step explanation:
please check you typing 5b = 3b, 2b
?????
Answer:
73
Step-by-step explanation:
3a + 5b + 2c = ?
Given:
a + b = 15
b + c = 14
now express in terms of b
a = 15 - b equation (i)
c = 14 - b equation (ii)
3a + 5b + 2c
substitute the values
3(15 - b) + 5b + 2(14 - b)
45 - 3b + 5b + 28 - 2b
add or subtract like terms
73 + 5b - 5b
plus 5b and minus 5b gets cancel
73
if cos A= 9\13 find csc A
Answer:
13[tex]\sqrt{22}[/tex] / 44
Step-by-step explanation:
cos A = 9/13
here adjacent = 9 and hypotenuse = 13 opposite = ?
using pythagoras theorem to find opposite
a^2 + b^2 = c^2
9^2 + b^2 = 13^2
81 + b^2 = 169
b^2 = 169 - 81
b^2 = 88
b = [tex]\sqrt{88}[/tex]
b = [tex]2\sqrt{22}[/tex]
therefore opposite = [tex]2\sqrt{22}[/tex]
cosec A = hypotenuse/opposite
= 13/[tex]2\sqrt{22}[/tex]
rationalizing the denominator
=13/ [tex]2\sqrt{22}[/tex] * [tex]2\sqrt{22}[/tex] / [tex]2\sqrt{22}[/tex]
=13 *[tex]2\sqrt{22}[/tex] /( [tex]2\sqrt{22}[/tex] )^2
=26 [tex]\sqrt{22}[/tex] / 4*22
=26 [tex]\sqrt{22}[/tex] / 88
=13[tex]\sqrt{22}[/tex] / 44
Answer:
[tex]cosec A = \frac{13}{\sqrt{88}}[/tex]
OR
[tex]cosec A = \frac{13 \sqrt{22}}{44}[/tex]
Step-by-step explanation:
Formulas used:
[tex]cos^2 A = 1 - sin^2 A\\\\cosec A = \frac{1}{sin A}[/tex]
Given :
[tex]cos A = \frac{9}{13}[/tex]
Find cosec A
[tex]sin ^2 A = 1 - cos^2 A[/tex]
[tex]= 1 - (\frac{9}{13})^2\\\\= 1 - \frac{81}{169}\\\\=\frac{169 - 81}{169}\\\\=\frac{88}{169}[/tex]
[tex]sin A = \sqrt{\frac{88}{169}} = \frac{\sqrt{88}}{13}[/tex]
Therefore,
[tex]cosec A = \frac{1}{sin A} = \frac{1}{ \frac{\sqrt{88}}{13}} = \frac{13}{ \sqrt{88}}[/tex]
OR In a simplified form :
[tex]cosec A = \frac{13}{\sqrt{88}} \times \frac{\sqrt{88}}{\sqrt{88}} = \frac {13 \times \sqrt{4 \times 22}}{88} = \frac{13 \times 2 \sqrt{22}} {88} = \frac{13 \sqrt{22}}{44}[/tex]
Write an equation of a line that passes through (3, -1) and is perpendicular to y = 6x - 4. Show work.
I NEED THIS FAST
Answer:
y = -1/6x - 1/2
Step-by-step explanation:
y = -1/6x + b
-1 = -1/6(3) + b
-1 = -1/2 + b
-1/2 = b
Q.No.1: A subset of {2, b} is:
Answer:
{2}
or
{b}
a subset is a part of the whole set.
Answer:
hope it helps...
In the diagram below, ΔPQR ≅ ΔSTR. Complete the statement ∠Q ≅ ___
Answer: Choice A. [tex]\angle T[/tex]
Explanation:
Notice how letters Q and T are in the middle of the sequences of PQR and STR respectively. This means the angles correspond.
Because the triangles are congruent, this means the corresponding pieces are congruent. Therefore, angle Q and angle T are the same measure.
As you can see, the order matters when it comes to forming congruence statements. Something like [tex]\triangle PQR \cong \triangle STR[/tex] is slightly different from [tex]\triangle PQR \cong \triangle SRT[/tex]
Congruent triangles have all corresponding measurements like angles and side lengths congruent. The completed statement would be ∠Q ≅ ∠T (Option A: ∠T)
What are congruent triangles?Suppose it is given that two triangles ΔABC ≅ ΔDEF
Then that means ΔABC and ΔDEF are congruent. Congruent triangles are exact same triangles, but they might be placed at different positions.
The order in which the congruency is written matters.
For ΔABC ≅ ΔDEF, we have all of their corresponding elements like angle and sides congruent.
Thus, we get:
[tex]\rm m\angle A = m\angle D \: or \: \: \angle A \cong \angle D[/tex] (small m shows we're taking about measurement) (both the statements are equivalent)[tex]\rm m\angle B = m\angle E \: or \: \: \angle B \cong \angle E[/tex][tex]\rm m\angle C = m\angle F \: or \: \: \angle C \cong \angle F[/tex][tex]\rm |AB| = |DE| \: \: or \: \: AB \cong DE[/tex][tex]\rm |AC| = |DF| \: \: or \: \: AC \cong DF[/tex][tex]\rm |BC| = |EF| \: \: or \: \: BC \cong EF[/tex](|AB| denotes length of line segment AB, and so on for others).
For this case, we have: ΔPQR ≅ ΔSTR
Thus, we have:
[tex]\angle Q = \angle T[/tex]
Thus, the completed statement would be ∠Q ≅ ∠T. (Option A: ∠T)
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The ages of five children in a family are 6, 1, 3, 10, and 17. Which statement is true for this group of data?
mode>mean
median>mean
median=mode
mean>median
Answer:D - mean>median
Step-by-step explanation:
There are no repeating variables to have a mode so median and mean are the only options. The mean of this data set is 7.4 and the median is 6. Therefore mean greater than median
Find the value of x in the triangle .Please show work
Answer:
x=4
Step-by-step explanation:
So basically first we see the angles of this triangle, and we learn that all the angles are congruent. Only a equilateral triangle can have all angles congruent, so this must be equilateral triangle. In equilateral triangles all the sides are congruent. So we just put 5x-12=3x-4. We then solve for x and get 4.