Answer:
centre = (- 1, - 3 ) , radius = 6
Step-by-step explanation:
the equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k ) are the coordinates of the centre and r is the radius
given
x² + y² + 2x + 6y = 26 ( collect x and y terms )
x² + 2x + y² + 6y = 26
using the method of completing the square
add ( half the coefficient of the x/ y terms )² to both sides
x² + 2(1)x + 1 + y² + 2(3)y + 9 = 26 + 1 + 9
(x + 1)² + (y + 3)² = 36 ← in standard form
with centre = (- 1, - 3 ) and r = [tex]\sqrt{36}[/tex] = 6
[tex](x {}^{2} + 2x + 1) - 1 = (x + 1) {}^{2} - 1[/tex]
[tex](y {}^{2} + 6y + 9) - 9 = (y + 3) {}^{2} - 9[/tex]
[tex](x + 1) {}^{2} - 1 + (y + 3) {}^{2} - 9 = 26[/tex]
[tex](x + 1) {}^{2} + (y + 3) {}^{2} = 26 + 10[/tex]
[tex](x + 1) {}^{2} + (y + 3) {}^{2} = 36[/tex]
General form:[tex](x - a) {}^{2} + (y - b) {}^{2} = r {}^{2} [/tex]
Center coordinates: I ( a , b ) I ( -1 , -3 )Radius:[tex]r {}^{2} = 36[/tex]
[tex]r = \sqrt{36} = 6[/tex]
Male and female high school students reported how many hours they worked each week in summer jobs. The data is represented in the following box plots.
Identify any values of data that may affect the statistical measures of center and spread. (1 point)
A)The males worked less than the females, and the male median is close to Q1.
B)There are significant outliers at the high ends of both the males and females.
C)Both graphs are symmetrical, so IQR and median are appropriate measures of spread and center for both males and females.
D)There is a high data value that causes the data set for the or females to be asymmetrical.
Answer:
Males have a significantly high outlier
Step-by-step explanation:
what is the area of a square whose diagonal is 8?
Answer:
A=32
Step-by-step explanation:
A=[tex]a^{2}[/tex]
d=[tex]\sqrt{2[/tex] a
A= [tex]\frac{1}{2}[/tex] [tex]d^{2}[/tex] = [tex]\frac{1}{2}[/tex]=·[tex]8^{2}[/tex]=32
Answer:
Step-by-step explanation:
Write the equation of a line in the slope-intercept form that has a slope of 4 and contains the point (4, 12).
Answer:
y=4x-4
Step-by-step explanation:
Hi there!
we are given that a line has a slope of 4 and it contains the point (4, 12)
We want to write the equation of this line in slope-intercept form
Slope-intercept form is given as y=mx+b, where m is the slope and b is the y intercept
As we are already given the slope, we can immediately substitute it into the formula.
Replace m with 4 in y=mx+b:
y=4x+b
Now we need to find b
As the equation passes through the point (4, 12), we can use it to help solve for b
Substitute 4 as x and 12 as y:
12 = 4(4) + b
Multiply
12 = 16 + b
Subtract 16 from both sides
-4 = b
Substitute -4 as b
y = 4x - 4
Hope this helps!
Topic: Finding the equation of the line
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Зл
Given that tan a=-1, what is the value of
sece, for
2
- 2
O2
0 0
O 1
Answer:I think i remember this i think is A.
Step-by-step explanation:
The value of sec θ is -√2 in the interval 3π/2 < θ < 2π, where θ is the angle whose tangent is -1.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
We are given that tan θ = -1, and we need to find the value of sec θ in the interval 3π/2 < θ < 2π.
Since tan θ = -1, we know that θ is in the third quadrant, where both x and y coordinates are negative. In the third quadrant, the reference angle for θ is π - θ, so we have:
tan θ = -1 = tan(-π/4)
π/4 = π - θ
θ = 3π/4
Now, we can use the fact that sec θ is the reciprocal of cos θ, and find cos θ in the third quadrant.
In the third quadrant, cos θ is negative. We can use the Pythagorean identity to find cos θ:
sin²θ + cos²θ = 1
Since sin θ is positive and we know that θ is in the third quadrant, we have:
sin θ = -√(1 - cos²θ)
tan θ = sin θ/cos θ = -1
Substituting sin θ and simplifying, we get:
-√(1 - cos² θ)/cos θ = -1
√(1 - cos² θ) = cos θ
Squaring both sides:
1 - cos²θ = cos²θ
2cos²θ = 1
cos²θ = 1/2
cos θ = -√2/2 (since θ is in the third quadrant)
Finally, we can find sec θ:
sec θ = 1/cos θ = -√2
Therefore, the value of sec θ is -√2 in the interval 3π/2 < θ < 2π, where θ is the angle whose tangent is -1.
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A paper weight is in the shape of a square pyramid. The dimensions are shown in the net.
Square pyramid net consisting of a square and four triangles. The square has length and width of ten centimeters. Each triangle has a base of ten centimeters and a height of fourteen centimeters.
What is the surface area of the paper weight, including the base?
Enter your answer in the box.
cm²
The surface area of the square pyramid net consisting of a square and four triangles is 380 sq. cm
How to find the surface area of a figure?The surface area of a square pyramid is equal to the sum of the ara of the base square and the four triangle.
Find the area of the square baseArea of the base = 10cm * 10cm
Base area = 100 sq,cm
Find the area of a triangle
Area of triangle = 0.5 * 10 * 14
Area of a triangle = 70 square cm
Area of 4 triangles = 4(70) = 280 sq.cm
Determine the surface areaSA = 100 + 280
SA = 380 sq. cm
Hence the surface area of the square pyramid net consisting of a square and four triangles is 380 sq. cm
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What is 6x divided by 5x
Answer:
1 1/5 or 1.2
Step-by-step explanation:
6x / 5x the x's cancel and you are left with 6/5 or 1 1/5
Study results indicate that the mean length of time people spend on a bus in a city is between 23.4 minutes and 29.5 minutes.
What is the study's margin of error?
6.1 min
4.75 min
3.05 min
0.5 min
Answer:
[tex]+/-3.05[/tex]
Step-by-step explanation:
The margin of error will be the difference divided by two with a plus and minus sign
So we have;
[tex]29.5-23.4=6.1[/tex]
Divide by [tex]2[/tex]
[tex]6.1[/tex] ÷ [tex]2=3.05[/tex]
[tex]=3.05[/tex]
Therefore, The margin error is therefore
[tex]+/-3.05[/tex]
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I The following data set represents
the shoe size of a group of
kindergarteners.
12, 12, 9.5, 10.5, 11.5, 12
Answer:
12 because it is repeat which means multiple kindergarteners have a size 12 shoe
Step-by-step explanation:
Which of the following is a solution of the inequality?
-3 < 2x + 1 < 5
Answer:
-2<x<2
Step-by-step explanation:
Which line is a line of symmetry for the figure attached?
A.
Line B
B.
Line A
C.
Line C
D.
Line D
Answer:
The correct Answer is D.Line D.
Hope it helps you Czn.
Please Mark me Brainleast!!!!!!!!!
39-42 Differentiate [tex]f[/tex] and find the domain of [tex]f\text{.}[/tex]
40. [tex]f(x)=\ln \left(x^{2}-2 x\right)[/tex]
[tex]\text{Given that,}\\\\f(x) = \ln (x^2 - 2x)\\\\f'(x) = \dfrac 1{x^2 -2x} \cdot (2x - 2) = \dfrac{2(x-1)}{x(x-2)}\\\\\\\text{domain f(x): } \{x| x < 0, x > 2 \}[/tex]
answer asap!
A bag of chips weighs 8 ounces. How many pounds do 20 bags of chips weigh?
How many bags would you need to equal a ton?
Answer:
160 ounces
Which is 10 pounds
And 4410 chip packets will equal about a ton
Step-by-step explanation:
because 20 x 8 =160
35274/8 = 4409.25
*note 35274 ounces is equal to a ton
Answer:
4000 bags
Step-by-step explanation:
8 x 20 = 160 oz = 10 lb
2,000 lb = 1 ton
16 oz = 1b
2,000 x 16 = 32,000 oz = 1 ton
32,000/8 = 4,000 bags
The Staff family pays a rate of 31 mills in property tax.
The assessed value of the
home is $48,000. What is their property tax?
Using proportions, it is found that the rate of 31 mills means that their property tax is of 3.1%.
What is a proportion?A proportion is a fraction of a total amount.
The Staff family pays a rate of 31 mills in property tax, which means that for each $1000, $31 is paid in tax. Hence the rate is given by:
r = 31/1000 = 3.1/100 = 3.1%.
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What is the answer? 15 points
Answer:
The third option.
what conclusoin can be drawn based on the expirement
Answer:
Drawing a conclusion means making a state- ment summing up what you have learned from an experiment.
Step-by-step explanation:
this makes you understand the context or concept better and you may recall that a hypothesis is a possible explanation for a set of observations or answer to a scientific question.
Answer:
Drawing a conclusion means making a state- ment summing up what you have learned from an experiment. The conclusion of an experiment is usually related to the hypothesis. You may recall that a hypothesis is a possible explanation for a set of observations or answer to a scientific question.
Step-by-step explanation:
please consider as brainlest if useful
The half-life of Radium-226 is 1590 years. If a sample contains 300 mg, how many mg will remain after 1000 years?
Answerc
Step-by-step explanation:
simple
Solve for x:
AD bisects ZBAC
A
Answer: 3
Step-by-step explanation:
HOOK is a word that has horizontal line symmetry since it is made up of letters that each have horizontal line symmetry. Can you think of another word that has horizontal line symmetry? Is it possible to form a word that has vertical line symmetry? Explain your reasoning.
Another word that has horizontal line symmetry is "book" and it is possible to form words with vertical line symmetry.
What is horizontal line symmetry in letters?This implies that by dividing the letter in half using a horizontal line both sides would be the same. Lettters with horizontal line symmetry include:
HKOEBCWhat are some words with these symmetry?HoodBookCookBeeAre words with vertical line symmetry possible?Yes, they are because there are many letters that have this symmetry such as V, T, A, O, M, I, H. For example you can create the words:
HiMumHitLearn more about letters in: https://brainly.com/question/10361926
Now, you will consider Option 1, setting a maximum shower time of 10 minutes.
rer
Assume all students who showered longer than 10 minutes will now shower for
exactly 10 minutes. Assume the rest of the students will shower for the same amount
of time as they did yesterday.
Blake claims Option 1 would result in the class mean going below 8 minutes, but the
class median would not change.
Explain whether you agree or disagree with Blake's claim. Include the class mean and
median that would result from Option 1 in your explanation.
BI
The maximum shower time is an illustration of mean and median, and the conclusion is to disagree with Blake's claim
How to interpret the shower time?The question is incomplete, as the dataset (and the data elements) are not given.
So, I will answer this question using the following (assumed) dataset:
Shower time (in minutes): 6, 7, 7, 8, 8, 9, 9, 9, 12, 12, 12, 13, 15,
Calculate the mean:
Mean = Sum/Count
So, we have:
Mean = (6+ 7+ 7+ 8+ 8+ 9+ 9+ 9+ 12+ 12+ 12+ 13+ 15)/13
Mean = 9.8
The median is the middle element.
So, we have:
Median = 9
From the question, we have the following assumptions:
The shower time of students whose shower times are above 10 minutes, is 10 minutesOther shower time remains unchanged.So, the dataset becomes: 6, 7, 7, 8, 8, 9, 9, 9, 10, 10, 10, 10, 10
The mean is:
Mean = (6+ 7+ 7+ 8+ 8+ 9+ 9+ 9+ 10+ 10+ 10+ 10+ 10)/13
Mean = 8.7
The median is the middle element.
So, we have:
Median = 9
From the above computation, we have the following table:
Initial Final
Mean 9.8 8.7
Median 9 9
Notice that the mean value changed, but it did not go below 8 as claimed by Blake; while the median remains unchanged.
Hence, the conclusion is to disagree with Blake's claim
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which is the independent variable and which is the dependent variable
Answer:
2nd one dependent
1st one is independent
hope it will help u
Solve the system of equations:
4x+5y=18
2x+3y=10
i need the answer thank you<3
Answer:
The area is 15 units^2
Step-by-step explanation:
Area = ((a+b)/2) x h
= ((4+6)/2) x 3
= ((10)/2) x 3
= (5) x 3
= 15 units^2
Simone is four years older than her sister Olivia. Their combined ages is 28. What are their ages
Answer:
Simone is 16 and Olivia is 12
Step-by-step explanation:
Melissa is building
a skateboarding ramp by propping the end of a piece of wood on a cinder
block. If the ramp begins 24 inches from the block and the block is 7 inches tall, how long is
the piece of wood?
inches
Which of these is an equation?
O A 2x+5 = 13
O
B 3p+1
C 5b+1>4
Dy²2²-1
Answer:
answer is A
Step-by-step explanation:
it is because an equation simply means it has an equal sign in it, doesn’t matter which variable you use. Since A has an equal sign, it is an equation.
(x-7y)(2x+7y)
use FOIL method!
I need help on this please
Answer:
84x¹⁰
Step-by-step explanation:
Simplify the radicals by them by 2:
7x²√2x² × 6√2x⁶
When a sqaure root of an expression is multiplied by itself, the result is that expression:
7x² × 2x² × 6x⁶
Now multiply to get: 84x¹⁰
Hope this helps!
The hypotenuse of a right triangle measures 15 cm and one of its legs measures 13 cm. Find the measure of the other leg
Hi!
We can solve this using the Pythagorean Theorem.
[tex]a^2+b^2=c^2[/tex] where [tex]a[/tex] and [tex]b[/tex] are the legs and [tex]c[/tex] is the hypotenuse.
Given:
1 leg = 13
2 leg = ???
hypotenuse = 15
Plug the values into the equation above:
[tex]13^2+b^2=15^2[/tex]
Multiply using exponents:
[tex]169+b^2=225[/tex]
Subtract 169 from both sides:
[tex]b^2=56[/tex]
Take the square root of both sides:
[tex]b=[/tex][tex]\sqrt{56}[/tex]
A__ has cross-sectional shapes, taken parallel to a base, that are similar but not congruent to one another.
A.pyramid
B.polygon
C.cube
D.prism
A) pyramid
Explanation:
When you take the cross-section of a pyramid parallel to the base, the cross-section will be in the shape of the base.
As you take cross-sections further up the pyramid, you will still get a cross-section that is in the shape of the base, but it will be smaller. This is because as you go further up the pyramid, the distance between vertices is shorter because it comes to a point.
Answer:
pyramidStep-by-step explanation:
A__pyramid has cross-sectional shapes, taken parallel to a base, that are similar but not congruent to one another.
Find the volume of the cone. Either enter an exact answer in terms of π or use 3.14 for π. radius is 10 height is 6