Answers
Answer:
(x + 4)² + (y + 1)² = 4
Step-by-step explanation:
From the graph attached,
Extreme ends of the diameter of the circle,
(-4, 1) and (-4, -3)
Center of the circle = Midpoint of the diameter
Center = [tex](\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})[/tex]
= [tex](\frac{-4-4}{2},\frac{1-3}{2})[/tex]
= (-4, -1)
Radius of the circle = Distance between the center and extreme end
= 2 units
Since standard equation of the circle is,
(x - h)² + (y - k)² = r²
where (h, k) is the center and 'r' is the radius of the circle
By substituting the values in the standard equation,
(x + 4)² + (y + 1)² = 2²
(x + 4)² + (y + 1)² = 4
Related Questions
Use the drawing tools to form the correct answers on the graph. Plot the vertex and the axis of symmetry of this function: f(x) = (x – 3)2 + 5.
Answers
Answer:
Axis of Symmetry: x = 3
Vertex: (3, 5)
Step-by-step explanation:
Use a graphing calc.
Answer:
3
Step-by-step explanation:
Evaluate the function using the values.
Answers
Answer:
Blank 1: 3
Blank 2: 31
Step-by-step explanation:
f(x) = 2x + 7
Plug x as -2
2(-2) + 7
-4 + 7
= 3
Plug x as 12
2(12) + 7
24 + 7
= 31
Which situation best describes negative correlation? a. The amount of job experience and pay b. Salary and number of children c. Exercise and health d. Hours of TV viewing and test grades
Answers
Answer: D
Step-by-step explanation:
D makes a lot more sense because if you are someone who watches TV a lot then your more likely to score less on a given test.
Negative correlation means that as the x values increases the y value decrease.
So in this case hours will be on the x coordinate and y will be your test score.
This sequence represents the diameters of circles used to create an art project: 2.5 cm, 3.1 cm, 3.7 cm, 4.3 cm Let f(n) represent diameter in centimeters and n the term number in the sequence. Which equation represents the sequence of diameters? f(n) = 0.6n + 1.9 f(n) = 0.6n + 2.5 f(n + 1) = f(n) + 1.9 f(n + 1) = f(n) – 0.6
Answers
Answer:
f(n) = 1.9+0.6nStep-by-step explanation:
Given the sequence that represents the diameter of a circle
2.5 cm, 3.1 cm, 3.7 cm and 4.3 cm. This sequence forms an arithmetic progression with a common difference.
nth term of an arithmetic progression is expressed as [tex]T_n = a+(n-1)d[/tex]
a is the first term of the sequence
n is the number of terms
d is the common difference.
From the sequence above, the first term a = 2.5
common difference = 3.1-2.5 = 3.7-3.1 = 4.3-3.7 = 0.6
Substituting this given values into the formula above will give;
[tex]T_n = 2.5+(n-1)*0.6\\\\T_n = 2.5+0.6n-0.6\\\\T_n = 2.5-0.6+0.6n\\\\T_n = 1.9+0.6n[/tex]
If f(n) represent diameter in centimetres and n the term number in the sequence, the equation that represents the sequence of diameters is
f(n) = 1.9+0.6n
Answer:
f(n) = 0.6n + 1.9
Step-by-step explanation:
What is the mode for this set of data? 5,6,13,2,6,11,6,5,3,14
Answers
Answer:
6
Step-by-step explanation:
6 appears the most
Answer:
6
Step-by-step explanation:
Put the data in order from smallest to largest
5,6,13,2,6,11,6,5,3,14
2,3,5,5,6,6,6,11,13,14
The mode is the number that appears most often
6 appears most often so it is the mode
how would i simplify this?
Answers
Answer:
3^6-4x=3^3x-3
Step-by-step explanation:
9^3-2x = 27^x-1 ( 9 is 3² and 27 is 3³)
(3²)^3-2x= (3³)^x-1 in case of exponential between brackets , multiply the exponents.
3^6-4x=3^3x-3
Answer:
x = 9/7
Step-by-step explanation:
9^3-2x = 27^x-1
(3^2)^3-2x = (3^3)^x-1
3^2(3-2x) = 3^3(x-1)
2(3-2x) = 3(x-1)
2(-2x+3) = 3x - 3
-4x + 6 = 3x - 3
-4x = 3x - 9
-7x = -9
x = -9/-7
x = 9/7
if x to the power of 2 = 10 what is the value of x?
Answers
Answer:
x² = 10
x = ±√10 (Take the square root of both sides)
Y varies directly as cube root of
[tex]x[/tex]
And y=3 when
[tex]x = 27[/tex]
A. Find the value of the constant
B. Find the relationship
C. Find the value of y when
[tex]x = 8[/tex]
Answers
Step-by-step explanation:
Y varies directly as cube root of x is written as
y = k³√x
where k is the constant of proportionality
A).when y = 3
x = 27
We have
[tex]3 = k \sqrt[3]{27} [/tex]
But ³√27 = 3
That's
3 = 3k
Divide both sides by 3
k = 1
The value of the constant is 1B).The value of the relationship is
[tex]y = \sqrt[3]{x} [/tex]C).When x = 8
We have
[tex]y = \sqrt[3]{8} [/tex]y = 2Hope this helps you
Unit test Problem Becky tried to evaluate an expression step by step. \quad\begin{aligned} &\dfrac{4}{5} +7 -\dfrac{5}{4}\\\\ \\ =&\dfrac{4}{5} -\dfrac{5}{4}+7&\green{\text{Step } 1} \\\\ \\ \\ =&0+7&\blue{\text{Step } 2}\\\\ \\ \\ =&7&\purple{\text{Step } 3} \\\\ \\ \\ \end{aligned} = = = 5 4 +7− 4 5 5 4 − 4 5 +7 0+7 7 Step 1 Step 2 Step 3 Find Becky's mistake.
Answers
Answer:
Becky's mistake was that she said [tex]\frac{4}{5} - \frac{5}{4} = 0[/tex], while it's actually equal to [tex]-\frac{9}{4}[/tex].
Step-by-step explanation:
[tex]\quad\begin{aligned} &\dfrac{4}{5} +7 -\dfrac{5}{4}\\\\ \\ =&\dfrac{4}{5} -\dfrac{5}{4}+7&\green{\text{Step } 1} \\\\ \\ \\ =&0+7&\blue{\text{Step } 2}\\\\ \\ \\ =&7&\purple{\text{Step } 3} \\\\ \\ \\ \end{aligned}[/tex]
Step 1 looks fine as she just rearranged the equation, keeping the negatives and positives right.
Step 2 is where she said that [tex]\frac{4}{5} - \frac{5}{4} = 0[/tex]. This would only be true if we were multiplying one of the numbers by 0. So Step 2 was wrong.
Step 3 is right, as 0+7 = 7.
Hope this helped!
Answer:
step 2 is wrong
Step-by-step explanation:
How many more unit tiles must be added to the function
f(x)=x2-6x+1 in order to complete the square?
-X
--X
0 0
Answers
Answer:
8 more unit of tiles
Step-by-step explanation:
The function is given as;
f(x) = x² - 6x + 1
Now, we want to add more unit tiles to complete the square.
The given function(f(x)) is of the order 2 due to the highest power of 2 attached to x, but the side of the square will be of the order 1.
Now, Let's make a general order 1 expression ax + b to be the side of the square.
From the function forming the square after adding some p unit tiles, we have;
f(x) + p = (side of square)²
Thus;
x² - 6x + 1 + p = (ax + b)²
x² - 6x + 1 + p = a²x² + 2abx + b²
Comparing both sides of the equation, we have;
a² = 1
2ab = 6
b² = 1 + p
From a² = 1, a = 1
From 2ab = 6,putting 1 for a, we have;
2(1)b = 6
b = 6/2
b = 3
From b² = 1 + p
Putting 3 for b, we have;
3² = 1 + p
9 = 1 + p
9 - 1 = p
p = 8
Thus, 8 more unit of tiles are required to complete the square.
The slope of the line below is -3 which is the following is the point - slope from the line ?
Answers
Answer:
D. y + 6 = -3(x - 2)
Step-by-step explanation:
To find the equation in point-slope form, you need to use the slope and a point from that line. The slope is -3 and the point given is (2, -6).
Point-slope form is y - y₁ = m(x - x₁). Plug in the slope and point.
y - (-6) = -3(x - 2)
y + 6 = -3(x - 2)
Answer:
D. [tex]y - 2 = -3(x+6 )[/tex]
Step-by-step explanation:
Well point slope form is,
[tex]y - y_{1} = m(x-x_{1} )[/tex]
So we already have slope meaning we can plug that in for m.
[tex]y - y_{1} = -3(x-x_{1} )[/tex]
And with the given point (2,-6),
we can create point slope form.
[tex]y - 2 = -3(x+6 )[/tex]
Therefore,
the answer is d. [tex]y - 2 = -3(x+6 )[/tex].
Hope this helps :)
Food inspectors inspect samples of food products to see if they are safe. This can be thought of as a hypothesis test with the following hypotheses.
H0: The food is safe.
Ha: The food is not safe
Based on the hypotheses above, Is the following statement a Type I or Type II error?
The sample suggests that the food is not safe, but it actually is safe.
a) Type I
b) Type II
Answers
Answer:
Type I error
Step-by-step explanation:
Here, we are interested in knowing the type of error that stems from the hypotheses set up
in the question.
From the suggestion of the sample, we know that the food is actually safe but was wrongly labeled as being unsafe.
So in this case, the type of error committed is the type 1 error since the food is actually safe but there was a wrong suggestion of being generally unsafe by the sample
Molly is doing her math homework. To receive full credit, she must answer this question: What key features are necessary-and how are the features used-to create the sketch of a polynomial function? What is Molly's correct answer, so she receives full credit for the question? Explain in complete sentences. (10 points)
Answers
Answer:
The axis of symmetry, vertex, degree of polynomial and x and y intercepts
Step-by-step explanation:
When we talk of a polynomial function, we refer to a function that involves only non-negative integer(whole number) powers of the independent variable (x in most cases). Thus, popular examples of polynomial functions include quadratic, cubic and triatic functions.
Kindly note that once a function includes a non negative power, it is not a polynomial any longer. That is why although x^2 + 2x is a polynomial function, x^2 + 2x^-1 is not a polynomial function.
Now, there are some key features that are necessary in sketching a polynomial function.
These are the vertex, axis of symmetry, x and y intercepts and the degree of the polynomial
These properties are needed to successfully make a sketch of a polynomial function.
The vertex of a polynomial function refers to that point on the curve of the function where it changes direction. For example, quadratic polynomial functions are known to have a parabolic sketch. That point in which there is a change in direction of the parabolic curve is known as the vertex of the polynomial function. A knowledge of this would ensure a proper sketch of the polynomial function curve. It helps in showcasing the concavity of the function.
The axis of symmetry applies to polynomials with even degrees. A polynomial function with an axis of symmetry will have mirror images on each side of a line that directly cuts through the polynomial.
The x and y intercepts talks about the points at which the function touches the axes of the plot
The degree of the polynomial helps to find the end behavior of the polynomial. The degree of a polynomial refers to the highest power to which the independent variable is raised. It is an important factor in determining if a polynomial function sketch will possess an axis of symmetry.
Please can someone help me thank you loads
Answers
Answer:
[tex]\boxed{V = 3591.4 \ cm^3}[/tex]
Step-by-step explanation:
Diameter = 19 cm
Radius = 19/2 = 9.5 cm
Volume = [tex]\frac{4}{3} (3.14)(9.5)^3[/tex]
V = [tex]\frac{4}{3}(3.14)(857.375)[/tex]
V = [tex]\frac{10774}{3}[/tex]
V = 3591.4 cm³
Answer:
i just wanted to delete this sorry
Step-by-step explanation:
my answer that is
lol sorry
Dylan uses the expressions (x2 – 2x + 8) and (2x2 + 5x – 7) to represent the length and width of his bedroom. Which expression represents the area (lw) of Dylan's room?
Answers
Answer:
2x⁴+x³-x²+54x+56
Step-by-step explanation:
Given the expression length of dylan room = (x² – 2x + 8) and width = (2x² + 5x – 7), assuming the shap of the room is rectangular in nature, the formula for calculating area of a triangle is given as;
Area of rectangle = Length *Width
Area of the rectangle = (x² – 2x + 8)(2x² + 5x – 7)
Area of the rectangle = x²(2x² + 5x – 7) - 2x (2x² + 5x – 7) + 8(2x² + 5x – 7)
= (2x⁴+5x³-7x²)-(4x³+10x²-14x)+(16x²+40x-56)
expanding the bracket
= 2x⁴+5x³-7x²-4x³-10x²+14x+16x²+40x-56
Collecting the like terms;
= 2x⁴+5x³-4x³-7x²-10x²+16x²+40x+14x+56
= 2x⁴+x³-x²+54x+56
Hence, the expression that represents the area (lw) of Dylan's room is 2x⁴+x³-x²+54x+56
Answer:
2x^4+ x^3 - x^2 + 54x - 56 expression represents the area of Dylan’s room
Step-by-step explanation:
C on edge :)
im not sure wether to replace the minus signs with addition, so if you could help me that would be nice :) 1.2y+4.5-3.4y-6.3
Answers
Answer:
-2.2y - 1.8
Step-by-step explanation:
We are to simplify the expression:
1.2y + 4.5 - 3.4y - 6.3
Collect like terms:
1.2y - 3.4y + 4.5 - 6.3
Simplify:
-2.2y - 1.8
That is the answer.
Pleas answer this question now
Answers
Answer:
[tex]x = 17[/tex]
Step-by-step explanation:
According to the two tangent theory, tangent MN and tangent NP, which are both from point N, are congruent.
That is, [tex]x + 4 = 21[/tex]
Solve for x
[tex]x + 4 = 21[/tex]
Subtract 4 from both sides
[tex]x + 4 - 4 = 21 - 4[/tex]
[tex]x = 17[/tex]
Some pupils from your school participate in sports games; precisely 2/31 participate in athletics and 1/9 in volleyball games. Knowing that there are a total of 98 participants, calculate how many pupils are not participating in sports games.
Answers
Answer:
The pupils who are not participating in sports games are 82
Step-by-step explanation:
According to the given data we have the following:
2/31 participate in athletics
1/9 in volleyball games
Total participants=98
Therefore, pupils participate in athletics= 98*2/31
pupils participate in athletics=6
pupils participate in volleyball games=98*1/9
pupils participate in volleyball games=10
Therefore, pupils are not participating in sports games=98-16
pupils are not participating in sports games=82
The pupils who are not participating in sports games are 82
Which equation is represented by the graph below?
Answers
Answer: A. y-In x-3
explanation:
Find the missing side length of the right triangle shown. Round to the nearest tenth, if
necessary.
Answers
Answer: 15 cm
Step-by-step explanation:
For this problem, we can use the Pythagorean Theorem.
The legs of the triangle are 9 cm and 12 cm.
According to the theorem...
[tex]9^{2} +12^{2} =c^{2}[/tex], c being the hypotenuse.
[tex]81+144=225[/tex]
[tex]c^{2} =225\\\sqrt{225} =15[/tex]
Therefore c=15.
Answer:
15
Step-by-step explanation:
You need to find one of the other angle measures first, I will be solving for the top angle.
To find this you need to take the inverse tangent of the opposite length over the adjacent length, in this case it would be 12 over 9
tan^-1 (12/9)
=53.1. round to the nearest degree so 53
now that you have your angle measure you can take the sine of that angle
for sine you do opposite over hypotenuse, we dont know the length of the hypotenuse so use x
sin(53) = 12/x
0.79 = 12/x don't round the answer to sin(53) wait till the end to round and just use your calculator to remeber the exact number
0.79 = 12/x
•x •x multiply both sides by x
0.79x = 12
/0.79 /0.79 divide both sides by 0.79 this is when you would use the calculator to enter in the exact number not just 0.79
x = 15.02 now you can round to the nearest tenth or whole number for this one it would just be 15
x=15
Find the area and the perimeter of the shaded regions below. Give your answer as a completely simplified exact value in terms of π (no approximations). The figures below are based on semicircles or quarter circles and problems b), c), and d) are involving portions of a square. Need help quick Plz!!!
Answers
Answer:
The answer is below
Step-by-step explanation:
The shape of the figure attached is the shape of a sector with an angle of 90° (quarter of a circle).
From the sector, AB = AC = radius of the sector (r) = 12. Therefore:
[tex]Area\ of\ sector=\frac{\theta}{360}*\pi r^2 = \frac{90}{360}*\pi * (12)^2 = 0.25 * \pi * 144=36\pi\\\\Area\ of\ triangle\ ABC=\frac{1}{2}*base *height= \frac{1}{2}*AB*BC=\frac{1}{2}*12*12=72\\\\Area \of\ shaded\ region = Area\ of\ sector-Area\ of\ triangle=36\pi-72\\\\Area \of\ shaded\ region =36\pi-72[/tex]
From the triangle: AC² = AB² + BC²
AC² = 12² + 12² = 144 + 144
AC² = 288
AC=√288 = 12√2
[tex]Perimeter\ of\ sector=\frac{\theta}{360}*2\pi r = \frac{90}{360}*2\pi * (12) = 0.25 * 2\pi * 12=6\pi\\\\Perimeter \of\ shaded\ region = Perimeter\ of\ sector+AC=6\pi + 12\sqrt{2}[/tex]
if you help I will mark brainliest! Thank you
Answers
Answer: 8.94
Step-by-step explanation:
each side is the [tex]\sqrt{20}[/tex] so multiply that by 2 and you will have 8.94
The local ice cream shop offers 3 different types of cones and 15 different flavors of ice cream. How many possible ice cream cones (one scoop) can a customer order? a 40 b 18 c 45 d 35
Answers
Answer:
45
Step-by-step explanation:
There are 3 cones and 15 flavors
Multiply the number of cones by the number of flavors
3*15
45
There are 45 possible combinations
please answer fast. Alan is conducting an experiment to determine whether a new medication is effective in reducing coughing. He finds 2,000 volunteers with coughing issues and divides them into two groups. The control group does not receive any medication; the treatment group receives the medication. The patients in the treatment group show reduced signs of coughing. What can Alan conclude from this experiment? (10 points)
Answers
Alan can conclude that the medicine given out to the treatment group does indeed work and reduces the amount of coughing and the control group with no treatment never got any better so the medicine is far better than no treatment at all.
Please HELP me with this question! I am really struggling with this...
Answers
A) 22°
Step-by-step explanation:∡DBG = (360° - BD - BG)/2
= (360° - 170° - 146°)/2
= 44°/2
= 22°
N students joined the radio control club. Some had boats, some had airplanes, and some had cars. They divided into 3 equal groups according to what model each one had. Ten more students joined the radio-controlled airplane group. There are 15 students in this group now. How many students joined the radio control club in the beginning?
Answers
Answer:
36 people joined the radio control club.
Step-by-step explanation:
15-3= 12
12*3=36
(50000)^2×(0.00002)^3\(200)×(0.0000001)
Answers
Answer:
1
Step-by-step explanation:
concepts used is law of indices
where
(a^b)^c = a^bc
a^m/a^n = a^(m-n)
a^m *a^n = a^(m+n)
a^0 = 1
_______________________________________
50000)^2 = (5*10^4)^2 = 25*10^8
(0.00002)^3 = (2*10^-5)^3 = 8*10^-15
(0.0000001) = 10^-7
now
(50000)^2×(0.00002)^3\(200)×(0.0000001) = 25*10^8 * 8*10^-15/200*10^-7
= 200*10^8-15-(-7)/200 = 10^-7 +7 = 10^0 = 1
Thus,1 is the answer
Which of the following best classifies a quadrilateral with coordinates A(8, 4), B(6, 0), C(3, 2), and D(7, 10)? Trapezoid Parallelogram Kite Rectangle
Answers
Answer:
Trapezoid
Step-by-step explanation:
Got it right on quiz
The following that best classifies a quadrilateral with coordinates is :
A) Trapezoid
The following that best classifies a quadrilateral with coordinates is Trapezoid.A trapezoid could be a quadrilateral with one match of inverse sides parallel. In some cases individuals characterize trapezoids to have at slightest one match of opposite sides parallel, and some of the time say there's one and as it were one combine of inverse sides parallel.Thus, the correct answer is A.
Find out more information:
https://brainly.com/question/24200218referrer=searchResults
If the bases of an isosceles trapezoid have lengths of 11 and 26, what is the length of the median? A: 7.5 units B: 37 units C: 18.5 units D: 15 units
Answers
Answer:
C. 18.5
Step-by-step explanation:
1/2(11 + 26) = 18.5
Solve: [tex]cos^2(2x)-sin^2(2x)=0[/tex] Thanks
Answers
Answer:
x = pi/8 + pi/2 *n x = 3pi/8 + pi /2 *n
Step-by-step explanation:
cos ^2 ( 2x) - sin ^2 (2x) = 0
Substitute u = 2x
cos ^2 ( u) - sin ^2 (u) = 0
We know cos ^2(x)-sin ^2(x)=cos (2x)
cos ( 2u) =0
Replacing u with 2x
cos (2 *2x) =0
cos (4x) =0
cos u =0 when u = pi/2 + 2 pi n and 3pi/2 + 2 pi n where n is an integer
4x = pi/2+2 pi n 4x = 3pi/2+2pi n
x = pi/8 + pi/2 *n x = 3pi/8 + pi /2 *n