Answer:
(x – 4)^2 + (y + 7)^2 = 16
Step-by-step explanation:
The formula of a circle is:
(x – h)^2 + (y – k)^2 = r^2
(h, k) represents the coordinates of the center of the circle
r represents the radius of the circle
If you plug in the given information, you get:
(x – 4)^2 + (y – (-7))^2 = 4^2
which simplifies into:
(x – 4)^2 + (y + 7)^2 = 16
In △ABC, m∠A=19°, a=13, and b=14. Find c to the nearest tenth.
Answer:
c is either 25.4 or 1.1
Step-by-step explanation:
The Law of Sines is used to find sides and angles when you have a side and its opposite angle. Since the given angle is not opposite the longest given side, there are two possible solutions.
a) sin(B)/b = sin(A)/a
sin(B) = (b/a)sin(A) = 14/13·sin(19°) ≈ 0.350612
B = arcsin(0.350612) or 180° -arcsin(0.350612)
B = 20.525° or 159.475°
Then angle C is ...
C = 180° -A -B = 161° -B = 140.475° or 1.525°
__
Side c can be found from ...
c = sin(C)·a/sin(A)
For C = 140.475°, ...
c = sin(140.475°)·39.9302 ≈ 25.4
For C = 1.525°, ...
c = sin(1.525°)·39.9302 ≈ 1.1
The length of side c could be 25.4 or 1.1.
Enter a range of values of x
Answer:
[tex]-5<x<26[/tex].
Step-by-step explanation:
We know that if two corresponding sides of two triangles are equal, then third sides of the triangles depend on angle between equal sides.
Angle opposite to larger side is larger.
Since, 14 < 15, therefore
[tex]2x+10<62[/tex]
[tex]2x<62-10[/tex]
[tex]2x<52[/tex]
[tex]x<26[/tex] ...(1)
We know that, angle can not not negative.
[tex]2x+10>0[/tex]
[tex]2x>-10[/tex]
[tex]x>-5[/tex] ...(2)
From (1) and (2), we get
[tex]-5<x<26[/tex]
Therefore, the range of values of x is [tex]-5<x<26[/tex].
Alexandria ate at most two hundred fifty calories more than twice the number of calories her infant sister ate. Alexandria ate eighteen hundred calories. If i represents the number of calories eaten by the infant, which inequality represents the situation? A. 1,800 less-than-or-equal-to 250 + 2 i B. 1,800 less-than 250 + 2 i C. 1,800 + 250 greater-than 2 i D. 1,800 + 250 greater-than-or-equal-to 2 i
Hey there! I'm happy to help!
The words at most means that there is a maximum point that is included as a probability. This means that we will use the less than or equal sign (≤) in our inequality.
Let's write this all out as an inequality now. We will use i to represent how much the baby ate.
1,800≤2i+250
This inequality shows that Alexandria's 1,800 calories is at most 250 more than twice those of her baby sister. Therefore, the correct option is A. 1,800≤250+2i .
Have a wonderful day!
Answer:
The correct option is A. 1,800≤250+2i.
How many different isosceles triangles have integer side lengths and perimeter 23?
Answer:
6 different isosceles triangles.
Step-by-step explanation:
This is a AMC 8 2005 question. (You can search up their solution)
There are 6 triangles:
6, 6, 11
7, 7, 9
8, 8, 7
9, 9, 5
10, 10, 3
11, 11, 1
There are only 6 because if there was an isosceles triangle with side lengths such as 5, 5, 13 the triangle would be impossible since the two smaller side lengths must sum up to be greater than the longest side length.
The number of isosceles triangles has integer side lengths and a perimeter of 23 is 6.
What is the isosceles triangle?In an isosceles triangle, two sides and angles are equal. The sum of the angle of the triangle is 180 degrees.
Given
Isosceles triangles have integer side lengths and a perimeter of 23.
Let x be the isosceles side and y be the other side. Then
[tex]\rm 2x + y = 23[/tex] ...1
And we know that the sum of the two sides of the triangle must be greater than the third side. Then
[tex]\rm 2x >y[/tex] ...2
From equations 1 and 2, we have
x > 5.75
But the value of x is an integer then x will be 6. Then
All possibilities are
[tex]6 + 6 > 11\\\\7 + 7 > 9\\\\8+8>7\\\\9+9>5\\\\10+10>3\\\\11+11>1[/tex]
Thus, the number of isosceles triangles has integer side lengths and a perimeter of 23 is 6.
More about the Isosceles triangle link is given below.
https://brainly.com/question/7915845
Pleased help with this
Answer:
A
Step-by-step explanation:
Help!! It’s much appreciated in this time
Answer: D. y = (x - 3)² + 2
Step-by-step explanation:
Inverse is when you swap the x's and y's and solve for y.
y = [tex]\sqrt{x-2}[/tex] + 3
Swap: x = [tex]\sqrt{y-2}[/tex] + 3
Solve: x - 3 = [tex]\sqrt{y-2}[/tex]
(x - 3)² = [tex](\sqrt{y-2})^2[/tex]
(x - 3)² = y - 2
(x - 3)² + 2 = y
24=3(n-5) solve for n
Answer:
n = 13
Step-by-step explanation:
24 = 3 (n-5)
3n - 15 = 24
3n = 24 +15
3n = 39
n = 39/3
n = 13
Answer:
[tex]\boxed{\sf n=13}[/tex]
Step-by-step explanation:
[tex]\sf 24=3(n-5)[/tex]
[tex]\sf Expand \ brackets.[/tex]
[tex]\sf 24=3n-15[/tex]
[tex]\sf Add \ 15 \ to \ both \ sides.[/tex]
[tex]\sf 24+15=3n-15+15[/tex]
[tex]\sf 39=3n[/tex]
[tex]\sf Divide \ both \ sides \ by \ 3.[/tex]
[tex]\sf \frac{39}{3} =\frac{3n}{3}[/tex]
[tex]\sf 13=n[/tex]
Is this strong positive correlation or weak positive or strong negative or weak negative?
Answer:
Weak negative correlation
Step-by-step explanation:
The scatter plot shown in the graph above indicates a negative correlation between the x-variables and the y-variables, because, as the variables on the x-axis increases, the variables on the y-axis decreases.
Also, the if we are to draw a line of best fit to connect some of the data points on a straight line, we would see that a number of the data points would be far apart from each other away from the line. The data points are not much clustered around the line of best fit, therefore, this shows that the negative correlation between the variables is a weak one.
The data represented on the scatter plot show a weak negative correlation.
What is the vertex of the graph of the function f(x) = x2+8x-2?
Answer:
the answer is (-4,-18)
Answer:
The vertex is at (-4, -18).
Step-by-step explanation:
f(x) = x^2 + 8x - 2
Covert to vertex form:
f(x) = (x + 4)^2 - 16 - 2
f(x) = (x + 4)^2 - 18.
So the
vertex is (-4,18
a small business had a total revenue of $51600. If this is 29% more than their total revenue the previous year, what was their total revenue the previous year?
I need help asap please
Answer:
I think the answer is B, tell me if it is wrong.
Find the smallest positive integer that is greater than $1$ and relatively prime to the product of the first 20 positive integers. Reminder: two numbers are relatively prime if their greatest common divisor is 1.
Answer:
23
Step-by-step explanation:
since the number is relatively prime to the product of the first 20 positive numbers
It number must not have factor of (1-20)
Therefore the smallest possible number is the next prime after 20
Answer is 23
The smallest positive integer that is greater than 1 and relatively prime to the product of the first 20 positive integers is,
⇒ 23
What is Greatest common factors?The highest number that divides exactly into two more numbers, is called Greatest common factors.
Since, The number is relatively prime to the product of the first 20 positive numbers means a number which must not have factor of (1 - 20).
Hence, The smallest possible number is the next prime after 20 is, 23
Therefore, The smallest positive integer that is greater than 1 and relatively prime to the product of the first 20 positive integers is,
⇒ 23
Learn more about the Greatest common factors visit:
https://brainly.com/question/219464
#SPJ2
Please help asap.
A pizza is cut into six unequal slices (each cut starts at the center). The largest slice measures $90$ degrees If Larry eats the slices in order from the largest to the smallest, then the number of degrees spanned by a slice decreases at a constant rate. (So the second slice is smaller than the first by a certain number of degrees, then the third slice is smaller than the second slice by that same number of degrees, and so on.) What is the degree measure of the fifth slice Larry eats?
Answer:
The answer is 5th angle = [tex]\bold{42^\circ}[/tex]
Step-by-step explanation:
Given that pizza is divided into six unequal slices.
Largest slice has an angle of [tex]90^\circ[/tex].
He eats the pizza from largest to smallest.
Let the difference in angles in each slice = [tex]d^\circ[/tex]
1st angle = [tex]90^\circ[/tex]
2nd angle = 90-d
3rd angle = 90-d-d = 90 - 2d
4th angle = 90-2d-d = 90 - 3d
5th angle = 90-3d-d = 90 - 4d
6th angle = 90-4d -d = 90 - 5d
We know that the sum of all the angles will be equal to [tex]360^\circ[/tex] (The sum of all the angles subtended at the center).
i.e.
[tex]90+90-d+90-2d+90-3d+90-4d+90-5d=360\\\Rightarrow 540 - 15d = 360\\\Rightarrow 15d = 540 -360\\\Rightarrow 15d = 180\\\Rightarrow d = 12^\circ[/tex]
So, the angles will be:
1st angle = [tex]90^\circ[/tex]
2nd angle = 90- 12 = 78
3rd angle = 78-12 = 66
4th angle = 66-12 = 54
5th angle = 54-12 = 42
6th angle = 42 -12 = 30
So, the answer is 5th angle = [tex]\bold{42^\circ}[/tex]
Assume that two marbles are drawn without replacement from a box with 1 blue, 3 white, 2 green and 2 red marbles. Find probability that both marbles are white. Round to nearest thousandth
An unbiased coin is tossed 14 times. In how many ways can the coin land tails either exactly 9 times or exactly 3 times?
Answer
[tex]P= 0.144[/tex] ways
the coin can land tails either exactly 8 times or exactly 5 times in
[tex]0.144[/tex] ways
Step by step explanation:
THis is a binomial distribution
Binomial distribution gives summary of the number of trials as well as observations as each trial has the same probability of attaining one particular value.
P(9)=(14,9).(0.5)⁹.(0.5)¹⁴⁻⁹
p(3)=(14,3).(0.5)⁹.(0.5)¹⁴⁻³
p=(9)+p(3)
p=C(14,9)(0.5)¹⁴ + C(14,3). (0.5)¹⁴
P= (0.5)¹⁴ [C(14,9) + C(14,3)]
P= (0.5)¹⁴ [2002 * 364]
P= 1/16384 * (2002 +364)
P= 91091/2048
P= 0.144
Hence,the coin can land tails either exactly 8 times or exactly 5 times in
[tex] 0.144[/tex] ways
Which of the following points is a solution of y > Ixl + 5?
A. (0, 5)
B. (1, 7)
C. (7, 1)
Answer:
B. (1,7)
Step-by-step explanation:
We can substitute the x and y values of each coordinate into the inequality and test if they work.
Let's start with A, 5 being y and 0 being x .
[tex]5 > |0|+5\\5> 0+5\\5 > 5[/tex]
5 IS NOT greater than 5, they are the exact same, so A is out.
Let's try B, 1 being x and 7 being y.
[tex]7 > |1| + 5\\7 > 1 + 5\\7 > 6[/tex]
7 IS greater than 6, so B. (1,7) does work for this inequality!
Let's do C for fun, when 7 is x and 1 is y.
[tex]1 > |7| + 5\\1>7+5\\1>12[/tex]
1 IS NOT greater than 12, it is quite less than 12, so C doesn't work.
Therefore B. (1,7) works for the inequality of [tex]y > |x|+5[/tex].
Hope this helped!
A movie theater has a seating capacity of 179. The theater charges $5.00 for children, $7.00 for students, and $12.00 of adults. There are half as many adults as there are children. If the total ticket sales was $ 1284, How many children, students, and adults attended?
Answer:
31 adults, 62 children, and 86 students.
Step-by-step explanation:
The seating capacity of the movie theatre = 179
c+s+a=179Children's(c) Ticket = $5.00
Student's(s) Tickets = $7.00
Adult's(a) Tickets = $12.00
There are half as many adults as there are children.
[tex]a=c/2 \implies c=2a[/tex]The total ticket sales was $1284
5c+7s+12a=1284We then solve the three resulting equations simultaneously.
c+s+a=179
c=2a
5c+7s+12a=1284
We substitute c=2a into the first and third equation
[tex]2a+s+a=179 \implies s=179-3a\\5(2a)+7s+12a=1284 \implies 22a+7s=1284[/tex]
Substitute s=179-3a into 22a+7s=1284
[tex]22a+7(179-3a)=1284\\22a+1253-21a=1284\\a=1284-1253\\a=31[/tex]
Recall:
c=2a
c=2*31
c=62
Finally:
c+s+a=179
62+s+31=179
s=179-62-31
s=86.
Therefore:
31 adults, 62 children, and 86 students attended the movie theatre.
A coin is tossed and -sided die numbered 1 through is rolled. Find the probability of tossing a and then rolling a number greater than . The probability of tossing a and then rolling a number greater than is nothing.
Answer:
hello your question has some missing parts here is the complete question
A coin is tossed and an eight-sided die numbered 1 through 8 is rolled. Find the probability of tossing tail and then rolling a number greater than 6. The probability of tossing a tail and then rolling a number greater than 6 is? Round to three decimal places as needed
Answer : 0.5, 0.25, 0.125
Step-by-step explanation:
A coin when tossed has only two outcomes which are ( Head or tail )
a)Therefore the probability of tossing a tail = 1/2 = 0.5
A die having eight sides when tossed will have 8 outcomes
B) Therefore the probability of rolling a number greater than 6
p( x > 6) = p(7) + p(8) = 1/8 + 1/8 = 0.25
C) The probability of tossing a tail and then rolling a number greater than 6 is
= p( x > 6 ) * p( tail )
= 0.25 * 0.5 = 0.125
If $y^2= 36$, what is the greatest possible value of $y^3$?
Answer:
The greatest possible value of [tex]y^3=216[/tex]
Step-by-step explanation:
We have the statement [tex]y^2=36[/tex], and we have to find the greatest possible value of [tex]y^3[/tex], first we need to find the value of y.
[tex]y^2=36[/tex], to get the y by itself on the left side, we need to take the square root of both sides. [tex]\sqrt{y^2} =\sqrt{36}[/tex] The square root of [tex]y^2[/tex] is y, because y*y = [tex]y^2[/tex], and the square root of 36 is 6 or -6.
We now need to find the greatest value of [tex]y^3[/tex]. When we plug in 6 to [tex]y^3[/tex], we get positive 216, and when we plug in -6, we get -216. We need to find the greatest possible value, so in this case we compare 216 and -216, 216 is greater than -216, so the answer would be positive 216.
Answer:
216
Step-by-step explanation:
If y² = 36, then y is 6 or -6. When y = 6, we have y³ = 6³ = 216. When y = -6, we have y³ = (-6)³ = -216. The greatest possible value of y³ is 216.
If 5e^x=300, x
I need help fast
Answer:
ln(60)
Step-by-step explanation:
We have the equation [tex]5e^x=300[/tex]. We can divide both sides of the equation by 5, getting [tex]e^x=60[/tex]. Finally, we can take the natural log of both sides, getting that x is equal to [tex]\ln(60)[/tex].
Someone help me please
Answer:
31Option D is the correct option.
Step-by-step explanation:
Given: 3 boxes with volumes 1331 , 1331 , 729
To find : Height of stacked boxes
[tex]h {1}^{3} = 1331 = h1 = \sqrt[3]{1331} = 11[/tex]
[tex]h {2}^{3} = 1331 = h2 = \sqrt[3]{1331} = 11[/tex]
[tex]h {3}^{3} = 729 = h3 = \sqrt[3]{729} = 9[/tex]
Now,
[tex]h = h1 + h2 + h3[/tex]
[tex] = 11 + 11 + 9[/tex]
[tex] = 31[/tex]
Hope this helps...
Good luck on your assignment...
Solve the initial value problem y′+y=f(t),y(0)=0 where f(t)={1,−1, if t<4 if t≥4 Use h(t−a) for the Heaviside function shifted a units horizontally.
Looks like the function on the right hand side is
[tex]f(t)=\begin{cases}1&\text{for }t<4\\-1&\text{for }t\ge4\end{cases}[/tex]
We can write it in terms of the Heaviside function,
[tex]h(t-a)=\begin{cases}1&\text{for }t\ge a\\0&\text{for }t>a\end{cases}[/tex]
as
[tex]f(t)=h(t)-2h(t-4)[/tex]
Now for the ODE: take the Laplace transform of both sides:
[tex]y'(t)+y(t)=f(t)[/tex]
[tex]\implies s Y(s)-y(0)+Y(s)=\dfrac{1-2e^{-4s}}s[/tex]
Solve for Y(s), then take the inverse transform to solve for y(t):
[tex](s+1)Y(s)=\dfrac{1-e^{-4s}}s[/tex]
[tex]Y(s)=\dfrac{1-e^{-4s}}{s(s+1)}[/tex]
[tex]Y(s)=(1-e^{-4s})\left(\dfrac1s-\dfrac1{s+1}\right)[/tex]
[tex]Y(s)=\dfrac1s-\dfrac{e^{-4s}}s-\dfrac1{s+1}+\dfrac{e^{-4s}}{s+1}[/tex]
[tex]\implies y(t)=1-h(t-4)-e^{-t}+e^{-(t-4)}h(t-4)[/tex]
[tex]\boxed{y(t)=1-e^{-t}-h(t-4)(1-e^{-(t-4)})}[/tex]
A food concession owner in a mall sold 120 beef, vegetable, and pork sliders in 7 days. 20% of the sliders sold were beef and 15% were vegetable. How many pork sliders were sold?
Answer:
78 pork sliders
Step-by-step explanation:
The food concession owner sold 120 beef, vegetable and pork sliders.
20% were beef.
15% were vegetable.
The percentage of pork sliders sold is:
100 - (20 + 15) = 100 - 35 = 65%
The number of pork sliders sold is therefore:
65/100 * 120 = 78
78 pork sliders were sold.
In the figure, find the value of x that makes a ∥ b. A. 50° B. 65° C. 75° D. 95°
Answer:
B
Step-by-step explanation:
Because alternate interior angles are congruent in parallel lines, the angle next to the 25° in the right triangle is 85 - 25 = 60° which makes the other angle in the right triangle 180 - 90 - 60 = 30°. Since they form a straight angle, we can write x + 30 + 85 = 180 → x + 115 = 180 → x = 65°.
Transformation of exponential functions
Answer:
left, 4 units
Step-by-step explanation:
This indicates a shift to the left of 4 units. We know that it's left because the +4 is in the exponent and, it's a +4 not -4.
use the substitution method to solve the system of equation.s choose the correct ordered pair y=6x-4 y=x -7
Answer:
x=-3/5 and y=-38/5
Step-by-step explanation:
y=6x-4
y= x -7 substitute y=6x-4
6x-4=x-7
6x-x=-7+4
5x=-3
x=-3/5 ( substitute for x in y=6x-4)
y=6(-3/5)-4
y=-18/5-4
y=(-18-20)/5= -38/5
The area of a circle is found using the formula A=\pi r^(2) , where r is the radius. If the area of a circle is 36π square feet, what is the radius, in feet? A. 6 B. 6π C. 18 D. 9π
Answer:
A. 6 feetStep-by-step explanation:
[tex]A=\pi r^2\\Area = 36\pi\\r = ?\\36\pi = \pi r^2\\Divide \:both \:sides \:of\: the \:equation\: by\: \pi\\\frac{36\pi}{\pi} = \frac{\pi r^2}{\pi} \\r^2 = 36\\Find\: the\: square\: root\: of\: both\: sides\: \\\sqrt{r^2} =\sqrt{36} \\\\r = 6\: feet\\[/tex]
How can you fit data into a pictogram?
Answer:
Step-by-step explanation:
In a pictogram, data can be arranged as follows:
The organization is given in a Cartesian plane, with a vertical and a horizontal axis, images can be introduced. An independent variable is placed on the horizontal axis, usually small numbers. The dependent variable can be placed on the vertical axis, they are usually larger numbers.
The temperature is 58° F. It gets warmer by h degrees and reaches to 65° F. Find h.
Answer:
h = 7 degrees
Step-by-step explanation:
To find h, we know that it is positive because it increases in value, not decreases:
h = 65 - 58
h = 7
Answer:
h = 7°F
Step-by-step explanation:
58 + h = 65
h = 65 - 58
h = 7
Check:
68 + 7 = 65
URGENT
What is the length of?
Answer:
option (c) 4
Step-by-step explanation:
sides opposite to equal angles are equal
so ML = MN
that is 4x = x+3
4x - x = 3
3x = 3
x= 1
ML= 4x = 4*1 = 4 units
MN = x+3= 1+3= 4 units
so answer is option (c) 4
hope this answer help you