complete the square with the following equation of a circle so that you can convert the equation into standard form.
Equation of a Circle
We are given the equation:
[tex]x^2+y^2+10x+12y+12=0[/tex]The equation of a circle of radius r and center (h,k) is:
[tex](x-h)^2+(y-k)^2=r^2[/tex]To convert the given equation into the standard form, we need to complete squares as follows.
First, rearrange terms:
[tex]x^2+10x+y^2+12y+12=0[/tex]The term 10x is divided by 2x to find the correct number to complete:
10x/(2x) = 5
Similarly, dividing 12y/(2y) = 6
Now we complete both squares by adding (and subtracting) 25 and 36:
[tex]x^2+10x+25+y^2+12y+36+12-25-36=0[/tex]Operating:
[tex](x+5)^2+(y+6)^2=49[/tex]Second choice
The function h is defined by h (x)=3x² - 4.Find h (3x).
When we have a function f(x) we can evaluate it for different arguments (the value of x) by replacing the argument in the definition of the function.
In this case, we know h(x) and we have to express h(3x). To do this, we replace x in the original function with 3x:
[tex]\begin{gathered} h(x)=3x^2-4 \\ h(3x)=3(3x)^2-4=3\cdot(3^2x^2)-4=3\cdot9x^2-4=27x^2-4 \end{gathered}[/tex]Answer: h(3x) = 27x²-4
- Graph the function f (x) = x - 4. Use the line tool and select two points to graph. Line * Move Undo Redo x Reset 10 9 8 7 6 5 4 3 N 1 1 2. 3 4 6 7 8 9 10 10 9 8 7 6 5 4 3 2 -19 -2
we have the function
f(x)=x-4
That is the equation of a line
to graph a line we need at least two points
so
Find out the intercepts
step 1
Find out the y-intercept (value of y when the value of x is zero)
For x=0
f(x)=0-4
f(x)=-4
the y-intercept is the point (0,-4)
step 2
Find out the x-intercept (value of x when the value of y is zero)
For y=0
0=x-4
x=4
the x-intercept is the point (4,0)
step 3
Plot the points (0,-4) and (4,0), join them, to graph the line
see the attached figure to better understand the problem
if you could please try to answer quickly my brainly keeps crashing
The lateral area of a cylinder is given by:
[tex]L=2\pi rh[/tex]where r represents the radius and h represents the height.
Then,
h=13m
In this case, we have the diameter. However, the radius is the half value of the diameter.
Then,
r=d/2=6m/2=3m
Replacing:
[tex]\begin{gathered} L=2\pi(3m)(13) \\ L=245m^2 \end{gathered}[/tex]Hence, the lateral area is 245m².
A sample of 26 customers was taken at a computer store. Each customer was asked the price of the computer she bought. Here is a summary Number of computers 7, 10,9 Price paid for each (in dollars) 900, 800, 1200 Find the mean price for this sample. Round your answer to the nearest dollar.
formula for the mean
[tex]\bar{x}=\frac{\sum ^{\infty}_{n\mathop=0}x_i}{n}[/tex]for this exercise n=26
replace data on the formula
[tex]\begin{gathered} \bar{x}=\frac{(7\cdot900)+(10\cdot800)+(9\cdot1200)}{26} \\ \bar{x}=965.385 \end{gathered}[/tex]Us a tree diagram to find the sample space and the total number of possible outcomesSo which choice is the answer.
In order to create the tree diagram, first, create the principal branches which is the type of item,
Then, divide the three colors for each of the items
.the, count the final branches to know the possible outcomes, meaning that the number of possible outcomes is 6.
i need help with math
∠1 and ∠2 are on same side exterior angles. FALSE
∠3 and ∠12 are alternate interior angles. FALSE
∠2 and ∠10 are corresponding angles. TRUE
∠6 and ∠11 are alternate exterior angles. TRUE
What are the different types of angles?Corresponding angles ; Angles that are present in similar locations are said to be in correspondence with one another. The dimensions of both angles are equal
Alternate Interior Angle: This term refers to the angles that are present on the opposing sides of the transversal. They can be found on the inside of the Z that the figure's Z has produced. The angles are both equal to one another.
Alternative Exterior Angle: The alternative exterior angles are those that are externally located and present on the opposing sides of the transversal. Both angles measure the same and they may be seen on the exterior.
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which functions are correctly graphed?
Solution
final answer is.
Choice A, C ,D
The 5 participants in a 200-meter dash had the following finishing times in seconds)24, 28, 26, 30, 32Send data to calculatorAssuming that these times constitute an entire population, find the standard deviation of the population. Round your answer to two decimal places,
Given:
Data x: 24, 28, 26, 30, 32
n = 5
Asked: What is the standard deviation of the population?
Formula:
[tex]\text{standard deviation = }\sqrt[]{\frac{\sum ^{}_{}(x-\bar{x})^2}{n}}[/tex]Solution:
Step 1: We will get the average of the data given.
NOTE: Bar x is also the mean or the average.
[tex]\begin{gathered} \bar{x}\text{ = }\frac{24+28+26+30+32}{5}\text{ } \\ \bar{x}=\text{ 28} \end{gathered}[/tex]Step 2: We will subtract the mean from each number.
Step 3: We will square the differences and get the summation.
Step 4: We will substitute the acquired values to find the standard deviation using the formula above.
[tex]\begin{gathered} \text{standard deviation = }\sqrt[]{\frac{\sum ^{}_{}(x-\bar{x})^2}{n}} \\ \text{standard deviation = }\sqrt[]{\frac{40^{}}{5}}\text{ } \\ \text{standard deviation = 2}\sqrt[]{2}\text{ = }2.828427125 \end{gathered}[/tex]ANSWER: standard deviation = 2.83 (Rounded off to 2 decimal places)
What is the value of the expression below? If entering the value as fraction or mixed number, give the answer in lowest term.-0.2 + (-¾) + 2.15 - (-⅖)
Explanation:
-0.2 + (-¾) + 2.15 - (-⅖)
let's convert the decimal to fractions:
-0.2 = -2/10 = -1/5
2.15 = 215/100 = 43/20
-0.2 + (-¾) + 2.15 - (-⅖) = -1/5 + (-¾) + 43/20 - (-⅖)
Expanading the bracket:
Multiplication of same sign gives positive number. Multiplication of opposite signs give negative number.
= -1/5 -3/4 + 43/20 + 2/5
[tex]\begin{gathered} \text{The LCM = 20} \\ =\frac{-1(4)-3(5)+43+2(4)}{20} \\ \end{gathered}[/tex][tex]\begin{gathered} =\frac{-4-15+43+8}{20}=\frac{32}{20} \\ =\frac{8}{5} \\ =1\frac{3}{5} \end{gathered}[/tex]Does the equation x = 1 represent a function?How do I know if it represents a function if it doesn't have y axis to show if it is.
A function is a relation between variables y and x,
where theres only a y value for every x value
In this case x=1 . For every value of x = 1 ,there are infinite values for y , it can take any value , negative or positive.
So this is NOT a function
Ignore the 58.I just need to find the m
The angles in the question are vertically opposite angles and Vertically opposite angles are equal.
Therefore,
[tex]\begin{gathered} (12x-37)^0=(9x+5)^0 \\ by\text{ collecting like terms we will have} \\ 12x^0-9x^0=5^0+37^0 \\ 3x^0=42^0 \\ \text{divide both sides by 3} \\ \frac{3x}{3}=\frac{42}{3} \\ x=14^0 \end{gathered}[/tex][tex]\begin{gathered} to\text{ measure }\angle y \\ 12x-37+y=180^0 \\ \text{substitute x=}14^0\text{ in the above equation to get y} \\ 12(14)-37^0+y^0=180^0 \\ 168^0-37^0+y=180^0 \\ 131^0+y=180^0 \\ y=180^0-131^0 \\ y=49^0 \end{gathered}[/tex]Therefore,
[tex]\angle y=49^0[/tex]Given the following expressions, you will identify the followingslope, y- intercept , x intercept, domain range , and is the function increasing or decreasing
Given the following function:
[tex]\text{ 3x - 2y = 16}[/tex]A.) SLOPE
Let's first transform the given equation into the standard slope-intercept form: y = mx + b
Because the m in the equation represents the value of the slope.
We get,
[tex]\begin{gathered} \text{ 3x - 2y = 16} \\ \text{ (3x - 2y = 16)( -}\frac{\text{ 1}}{\text{ 2}}) \\ \text{ -}\frac{3}{2}x\text{ + y = -}\frac{16}{2} \\ \text{ -}\frac{3}{2}x\text{ + y = -}8 \\ \text{ y = }\frac{3}{2}x\text{ - 8} \end{gathered}[/tex]The slope-intercept form of 3x - 2y = 16 is y = (3/2)x - 8. Where m = 3/2.
Therefore, the slope of the function is 3/2.
B.) Y - INTERCEPT
In the standard slope-intercept form : y = mx + b, b represents the y - intercept.
Therefore, in the converted form of the function y = (3/2)x - 8. b is equals to -8.
The y-intercept is 0, -8.
C.) X - INTERCEPT
The x - intercept is the point at y = 0.
We get,
[tex]\text{ 3x - 2y = 16}[/tex][tex]\text{ 3x - 2(0) = 16}[/tex][tex]\text{ 3x = 16}[/tex][tex]\text{ }\frac{\text{3x}}{3}\text{ = }\frac{\text{16}}{3}[/tex][tex]\text{ x = }\frac{\text{ 16}}{\text{ 3}}[/tex]Therefore, the x - intercept is 16/3, 0
D.) DOMAIN RANGE
The function has no undefined points nor domain constraints. Therefore, the domain is
[tex]-\infty\: We usually encounter undefined points when a given value of x will make the denominator equal to zero (0).Example: 2/(3 - x) at x = 3 is undefined.
E.) INCREASING OR DECREASING
The easiest way to determine if the function is decreasing or increasing is by looking at the slope (m). If the slope is greater than 0 (m > 0) or a positive, the function is increasing. If the slope is less than 0 (m < 0) or a negative, the function is decreasing.
Here, the slope is 3/2 which we first solved. Since the slope is greater than zero or a positive, the function is, therefore, increasing.
The answer is increasing.
11. The trigonometric ratio of cos B isPYTHAGOREAN TRIPLE PROBLEMB13590°A125/1212/135/1313/5
From the given right-angled triangle, we have the following:
Hypothenuse side = 13
Opposite side = 12
Adjacent side = 5
Solution
The trigonometric ratio of cos B can be found using the relationship:
[tex]\cos \text{ B = }\frac{Adjacent}{Hypothenus}[/tex]By substituting, we have:
[tex]cos\text{ B = }\frac{5}{13}[/tex]Hence, the answer is 5/13 (option C)
Question AA baseball is hit, following a path represented by x = 135t and y = 3.3 + 38t − 16t 2 for 0 ≤ t ≤ 3.Part A: Find the ordered pairs, (x, y) when t = 0.2, 1.2, and 2.2.Part B: The fence, which is 10 feet tall, lies 320 feet away from home plate. Does the baseball travel over the fence? Justify your answer mathematically.Part C: Write a rectangular equation to represent the plane curve.
Explanation
For the given question, we have the following
[tex]\begin{gathered} x=135t \\ y=3.3+38t-16t^2 \end{gathered}[/tex]Part A
find the ordered pairs (x,)
[tex]\begin{gathered} when \\ t=0.2 \\ \\ x=135(0.2)=27 \\ y=3.3+38(0.2)-16(0.2)^2=10.26 \\ \\ when\text{ t=0.2} \\ (x,y)=(27,10.26) \\ \end{gathered}[/tex][tex]\begin{gathered} when \\ t=1.2 \\ x=135(1.2)=162 \\ y=3.3+38(1.2)−16(1.2)^2=25.86 \\ \\ (x,y)=(162,25.86) \end{gathered}[/tex][tex]\begin{gathered} when \\ t=2.2 \\ x=135(2.2)=297 \\ y=3.3+38(2.2)−16(2.2)^2=9.46 \\ \\ (x,y)=(297,9.46) \end{gathered}[/tex]I just need to know the answer to question 11
Answer:
A number line a closed circle on 8, shading to the left, and a closed circle on 11, shading to the right.
Explanation:
Given the compound inequalities:
[tex]x-1\le7\text{ or }2x\ge22[/tex]First, solve both inequalities:
[tex]\begin{gathered} x-1\le7\implies x\le7+1\implies x\le8 \\ 2x\ge22\implies x\ge\frac{22}{2}\implies x\ge11 \end{gathered}[/tex]Thus, the number line should be the one that represents the solution:
[tex]x\le8\text{ or }x\ge11[/tex]• For x≤8, there is a ,closed circle on 8, and ,shading to the left.
,• For x≥11, there is a ,closed circle on 11, and ,shading to the right.
Therefore, the correct description will be:
A number line a closed circle on 8, shading to the left, and a closed circle on 11, shading to the right.
The last option is correct.
i need help with math
Answer:
x = 33
Step-by-step explanation:
Creating an equation
The angles shown are corresponding angles
Corresponding angles are angles that occupy the same position and are on the same side of the transversal. For a better sense of this, kindly review the attached image.
Corresponding angles are congruent ( equal to each other )
This means that 124 = 4x - 8
Solving for x
124 = 4x - 8
==> add 8 to both sides
132 = 4x
==> divide both sides by 4
33 = x
Linus leaves his house and walks 7 blocks West to avoid Lucy. He then walks 3 blocks North to visit Charlie Brown. What is the shortest distance between the houses? Round to the nearest tenth.
First, draw a schematic representation of that situation:
The shortest distance between the starting point (Linus's house) and the endpoint (Charlie's house) is a straight line. Since a right triangle is formed with the sides of length 7 blocks and 3 blocks, we can use the Pyhtagorean Theorem to find the length of the hypotenuse:
[tex]\begin{gathered} ?=\sqrt[]{3^2+7^2} \\ =\sqrt[]{9+49} \\ =\sqrt[]{58} \\ \approx7.6 \end{gathered}[/tex]Therefore, the shortest distance between those two points would be 7.6 blocks.
Can help me:coin is flipped 6 times. What is the probability that heads and tails occur an equal number times?
The probability that heads and tails occur an equal number times is 5/16.
From the question, we have
The number of permutations =HHHTTT
The total number of permutations = 6!=720.
Since, there are two groups comprising 3 identical objects, the number of permutations = 720/3!3!=20.
total number of possibilities in the event space= 2^6=64
the required probability = 20/64=5/16.
Probability:
Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution.
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Teresa is riding in a bike race that goes through a valley and a nearby mountain range.The table gives the altitude (in feet above sea level) for the five checkpoints in the race.Use the table to answer the questions.Checkpoint,Altitude(feet above sea level)1, -1152, 2,1663, 1,1854, -1685, -32(a)The top of a hill rises 530 feet above Checkpoint 4.What is the altitude of the top of the hill?(b)How much lower is Checkpoint 4 than Checkpoint 1?
a)
Checkpoint 4 = -168 ft
Add 530
-168 + 530 = 362 ft
b) Compare checkpoint 1 to checkpoint 4
1 = -115 ft
4 = -168
-168 -(-115) = -53
Checkpoint 4 is 53ft lower than checkpoint 1
4:58 PM 16 AA.18 Area of compound figures... < Surina Silva's prac... 38 What is the area of this figure? 3 mi 14 mi 5 mi 9 mi 10 mi 5 mi 4 mi 10 mi Write your answer using decimals, if necessary. square miles.
ANSWER
230 square miles
EXPLANATION
We can divide this figure as shown in the picture: 2 rectangles and a right triangle. We find the area of each figure and then we add them up.
One of the rectangles's length is 5 mi and its width is 14 mi. Its area is:
[tex]A_{\text{rectangle}1}=5mi\times14mi=70mi^2[/tex]The other rectangle's lenght is 10mi and its width is 5mi. Its area is:
[tex]A_{\text{rectangle}2}=10mi\times5mi=50mi^2[/tex]The triangle height is:
[tex]3mi+5mi+10mi+4mi=22mi[/tex]And its base is 10mi. Its area is:
[tex]A_{\text{triangle}}=\frac{22mi\times10mi}{2}=\frac{220mi^2}{2}=110mi^2[/tex]The area of the figure is:
[tex]\begin{gathered} A=A_{\text{rectangle}1}+A_{\text{rectangle}2}+A_{\text{triangle}} \\ A=70mi^2+50mi^2+110mi^2 \\ A=230mi^2 \end{gathered}[/tex]Simplify the Expression [tex]12g + 3 - g {}^{2} + 2[/tex] g=4
done
Find the surface area of a sphere with a radius of 1 cm to the nearest tenth. (Do NOTtypeinany units in your answer.)
The area of the sphere is 12.6
Here, we want to find the area of the sphere given the radius
Mathematically, we can calculate the area of the sphere using the formula below;
[tex]\begin{gathered} A\text{ = 4}\times\pi\times r^2 \\ r\text{ = 1 cm} \\ \pi\text{ = 3.142} \\ \text{Area of sphere = 4}\times3.142\times1^2=12.6cm^2 \end{gathered}[/tex]Ahmad is choosing between two exercise routines.In Routine #1, he burns 20 calories walking. He then runs at a rate that burns 10.5 calories per minute.In Routine #2, he burns 46 calories walking. He then runs at a rate that burns 5.3 calories per minute.For what amounts of time spent running will Routine #1 burn fewer calories than Routine #2?Use t for the number of minutes spent running, and solve your inequality for t.0ロロロメロOSDDADxХ5?ExplanationCheck
Solution:
Let t for the number of minutes spent running
In Routine #1, he burns 20 calories walking. He then runs at a rate that burns 10.5 calories per minute.
This can be represented as 20 + 10.5t
In Routine #2, he burns 46 calories walking. He then runs at a rate that burns 5.3 calories per minute.
This can be represented as 46 + 5.3t
The required inequality is
[tex]\begin{gathered} 20+10.5t<46+5.3t \\ 10.5t-5.3t+20<46+5.3t-5.3t \\ 5.2t+20<46 \\ 5.2t+20-20<46-20 \\ 5.2t<26 \\ \frac{5.2t}{5.2}<\frac{26}{5.2} \\ t<5 \end{gathered}[/tex]The answer is 5 minutes
Given the right triangle find the value of sec(90 degree - theta) when a= 12, b= 5, c= 13
Use the next trigonometric identities:
[tex]\begin{gathered} \sec (90º-\theta)=\frac{1}{\cos (90º-\theta)} \\ \\ \cos (90º-\theta)=\sin \theta \end{gathered}[/tex]Then, the sec(90º - θ) is:
[tex]\sec (90º-\theta)=\frac{1}{\sin \theta}[/tex]The sin(θ) is:
[tex]\sin \theta=\frac{opposite}{hypotenuse}=\frac{5}{13}[/tex]Then:
[tex]\sec (90º-\theta)=\frac{1}{\frac{5}{13}}=\frac{13}{5}[/tex]Then, the sec(90º - θ) is 13/5The following scatter plot represents the relationship between a person's weight and the number of calories the person burns in one minute of jump roping. What type of relationship is shown?
The scatter plot shows a positive correlation because the points show a linear-trend describing that when x-values (weight) increases then y-values (calories) also increases.
Hence, the relationship is a Positive correlation.
Turn into an inequality A speed limit of 65 mph
The question says we should turn into an inequality a speed limit of 65 miles per hour.
This means the speed should'nt be more than 65 miles per hour. In other words the speed shouldn't exceed 65 miles per hour.
Let represent the speed with a. Therefore,
a < 65 miles per hour
a < 65
write in algebraic expression1) quotient of a number b and 36 2) 45 divided into a number r3) sum of 21 and a number x4) a number z less 19 5) a number f divided by 6
Solution
For this case we can do the following:
1)
[tex]\frac{b}{36}[/tex]2)
[tex]\frac{45}{r}[/tex]3)
[tex]21+x[/tex]4)
[tex]z-19[/tex]5)
[tex]\frac{f}{6}[/tex]Totsakan enlarged the size of a photo to aheight of 18 in. What is the new width if itwas originally 2 in tall and 1 in wide?
Let's begin by identifying key information given to us:
New size: Height = 18 in, Width = ?
Old size: Height = 2 in, Width = 1 in
We will get the width of the new photo by following the explanation below:
[tex]\begin{gathered} 18\colon2=x\colon1 \\ \Rightarrow\frac{18}{2}=\frac{x}{1} \\ \text{Cross multiply, we have:} \\ 2\cdot x=18\cdot1\Rightarrow2x=18 \\ 2x=18 \\ \text{Divide both sides by ''2'', we have:} \\ x=\frac{18}{2}=9 \\ \therefore x=9in \end{gathered}[/tex]Therefore, the width of the enlarged photo is 9 inches
Solve the following equation for X 5x+7y=19 X= ?
1) We can solve this equation for x, by doing the following algebraic manipulation:
[tex]\begin{gathered} 5x+7y=19 \\ \\ 5x+7y-7y=19-7y \\ \\ 5x=19-7y \\ \\ \frac{5x}{5}=\frac{19}{5}-\frac{7y}{5} \\ \\ x=-\frac{7}{5}y+\frac{19}{5} \\ \\ x=\frac{19-7y}{5} \end{gathered}[/tex]2) In this problem, we can't go any further than that. So, that is the answer.