Answer:
[tex](x-1)^2+(y+6)^2=29[/tex][tex]\begin{gathered} h=1 \\ k=-6 \\ r=\sqrt{29} \end{gathered}[/tex]Explanation:
Given:
Endpoints of the diameter of a circle as (-4, -8) and (6, -4)
To find:
Equation of a circle in standard form
The equation of a circle in standard form is generally given as;
[tex](x-h)^2+(y-k)^2=r^2[/tex]where (h, k) is the coordinate of the center of the circle and r is the radius of the circle.
We'll go ahead and determine the coordinates of the midpoint of the endpoints of the diameter which will be the coordinates of the center of the circle as seen below wi;
[tex]h=\frac{x_1+x_2}{2}=\frac{-4+6}{2}=\frac{2}{2}=1[/tex][tex]k=\frac{-8+(-4)}{2}=\frac{-12}{2}=-6[/tex]So the center of the circle has coordinates (1, -6)
Since h = 1, and k = -6 and we have that x1 = -4 and y1 = -8, we can go ahead and solve for r as seen below;
[tex]\begin{gathered} (-4-1)^2+(-8-(-6))^2=r^2 \\ (-5)^2+(-2)^2=r^2 \\ 25+4=r^2 \\ 29=r^2 \\ \therefore r=\sqrt{29} \end{gathered}[/tex]We can now write the equation of the circle in standard form as;
[tex]\begin{gathered} (x-1)^2+(y-(-6))^2=29 \\ (x-1)^2+(y+6))^2=29 \end{gathered}[/tex]I would rlly appreciate if someone helped me out on this please!
Answer:
14.7
Step-by-step explanation:
Let's say the width is x
So volume would be 24 × 2x × x = 10368
24 × 2x² = 10368
2x² = 10368 / 24 = 432
x² = 216 , width can't be negative so
x = 14.6969... ~~ 14.7
a box is filled with 3 red cards, 6 Blue cards, and 6 green cards. A card is chosen at random from the box. what is the probability that it is a red or a green card? write your answer as a fraction in simplest form
Probability of red or green card = 3/5
Explanation:Number of red cards = 3
Number of blue cards = 6
Number of green cards = 6
Total number of cards = 6 + 6 + 3 = 15
Probability of red or green card = Probability of red card + Probability of green card
Probability of red card = number of red cards/total number of cards
Probability of red card = 3/15
Probability of green card = number of green cards/total number of cards
Probability of green card = 6/15
Probability of red or green card = 3/15 + 6/15
Probability of red or green card = 9/15
In simplest term:
Probability of red or green card = 3/5
Answer:
85% but in a fraction 17/20
Step-by-step explanation:
14. PR is the diameter of the circle with centre O. If mZPRQ = 65°. What will be the measure of
mZPOQ?
A. 65⁰
B. 90⁰
C. 130⁰
D. 150⁰
Given vectors a= (1, - 4) and b = (2, 5), find –2a+5b.Write your answer in component form.- 2a + 5b =?
We are given the following two vectors
[tex]\begin{gathered} a=<1,-4> \\ b=<2,5> \end{gathered}[/tex]We are asked to find the following
[tex]-2a+5b[/tex]First, multiply the vector a with the scaler -2 to get -2a
[tex]\begin{gathered} -2a=<-2\cdot_{}1,-2\cdot-4> \\ -2a=<-2,8> \end{gathered}[/tex]Now, multiply the vector b with the scaler 5 to get 5b
[tex]\begin{gathered} 5b=<5\cdot2,5\cdot5> \\ 5b=<10,25> \end{gathered}[/tex]Finally, add -2a and 5b to get -2a+5b
[tex]\begin{gathered} -2a+5b=<-2,8>+<10,25> \\ -2a+5b=<-2+10,8+25> \\ -2a+5b=<8,33> \end{gathered}[/tex]Therefore, the resultant vector in component form is
[tex]-2a+5b=<8,33>[/tex]C>0, |u|=c is equivalent to u=
|u|=c is equivalent to u = c or u = -c.
Given that c > 0.
i.e., c is a positive number.
Then |u| = c. That is, absolute value of u = c, a positive number.
An absolute value function is defined by,
|u| = { u ; if u ≥ 0
{ -u ; if u < 0
The absolute value of any number, Positive or negative, is always a positive number.
So here |u| = c, with c > 0.
Comparing with the definition of absolute value function, c is either u or -u.
More clearly, c = u, when u ≥ 0 or c = -u , when u < 0.
Hence the value of c depends on u.
Thus, |u|=c is equivalent to u = c or u = -c.
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which of the following is a function. then graph the function.
A relationship is a function if and only if for each input, there exists only one output i.e an input cannot have two or more outputs.
We can determine which of the relationship is a function by plotting a graph of the relationship.
The only correct option is the relationship:
[tex]y=x^2[/tex]The graph of the function is shown below:
the expression negative one eighth j plus two thirds minus the expression five thirds j plus nine twelfths
negative 37 over 24 times j minus 17 over 12
negative 37 over 24 times j plus 17 over 12
43 over 24 times j plus 1 over 12
negative 43 over 24 times j plus negative 1 over 12
Simplify the expression.
the expression negative one eighth j plus two thirds minus the expression five thirds j plus nine twelfths
negative 37 over 24 times j minus 17 over 12
negative 37 over 24 times j plus 17 over 12
43 over 24 times j plus 1 over 12
negative 43 over 24 times j plus negative 1 over 12
Which expression is equivalent to 3(−4.5b − 2.1) − (6b + 0.6)?
19.5b + 1.5
−19.5b − 1.5
−19.5b − 6.9
19.5b − 6.9
A) Simplification of the given Algebraic Expression is; [-⁴³/₂₄j + (-1)]/12
B) The equivalent expression to 3(−4.5b − 2.1) − (6b + 0.6) is - 19.5b - 6.9
How to simplify Algebraic Expressions?A) We want to simplify negative one eighth j plus two thirds minus the expression five thirds j plus nine twelfths. This would be expressed as;
-1/8j + 2/3 - (5/3j + 9/12)
= -1/8j + 2/3 - 5/3j - 9/12
= -1/8j - 5/3j + (2/3 - 9/12)
= (-3j-40j / 24 + (8-9) / 12
= [-⁴³/₂₄j + (-1)]/12
B) The expression equivalent to 3(−4.5b − 2.1) − (6b + 0.6)
Expand the brackets to get;
-13.5b - 6.3 - 6b - 0.6
= -13.5b - 6b - 6.3 - 0.6
= - 19.5b - 6.9
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Suppose that g(x) = f(x) + 5. Which statement best compares the graph ofg(x) with the graph of f(x)?
We are told that
[tex]g(x)=f(x)+5[/tex]If we were given the graph of f(x), note that in this equation we add 5 to the value of f(x) to find the value of g(x). So, in terms of the graph, as we are taking the final value of f and adding 5, this means that we are moving the graph of f 5 units up. That is the graph of g(x) is the graph of f(x) shifted 5 units up
I need help with this question but no one is helping me! Can someone please help me
Step-by-step explanation:
Chance to roll even number on one dice is 1/2 so
[tex] \frac{1}{2} \times \frac{1}{2} = \frac{1}{4} [/tex]
Could you please set it up in the form of "systems of equations" meaning, set to different equations with "x" and "y" ??
That is what they want me to do in class.
There are various types of equation systems, including linear, non-linear, and multiple or single-variable systems.
Explain the System of equations?A set of two linear equations with two variables is a system of linear equations.
ax + by = C
A set of two or more equations in two or more variables that includes at least one nonlinear equation is referred to as a system of nonlinear equations. A nonlinear equation can be written as ax+by+C≠0 or ax + b y + C ≠0.
The equation for a linear equation in one variable is written as ax+b = 0, where a and b are two integers, and x is a variable. This equation has only one solution.
Ex: ax+b = 0
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Rewrite the polynomial .22 – 52 + 6 as 2? + m2 + n2 +6, where m. n = 6 and m +n=-5. What are the values of m and n?
Answer:
m = -2 and n = -3
Explanation
Given the polynomial
x^2 - 5x + 6
Rewrite as x^2 +mx + nx + 6
x^2 - 2x - 3x + 6
Compare
mx = -2x
m = -2
Similarly;
nx = -3x
n = -3
Hence m = -2 and n = -3
SpongeBob spins the spinner to the left. What is the probability that the spinner lands on a number greater than 6?
SpongeBob spins the spinner to the left. What is the probability that the spinner lands on a number greater than 6?
we know that
The total numbers in the spinner are 10
The numbers that are greater than 6 are (7,8,9 and 10)------> 4 numbers
so
To find out the probability, divide the total numbers that are greater than 6 by the total number
therefore
P=4/10
Percent
P=4/10(100)
the answer is
P=40% o P=4/10 or P=0.4License plates in a particular state are to consist of 2 digits followed by 4 uppercase letters. a) How many different license plates can there be in this state if repetition of letters and numbers is permitted? b) How many different license plates can there be in this state if repetition of letters and numbers is not permitted? c) How many different license plates can there be in this state if the must be , and repetition of letters and numbers is not permitted? d) How many different license plates can there be in this state if the first digit cannot be , and repetition of letters and numbers is not permitted?
a)Total different number plates will be 45697600
b) Total different number plates will be 32292000
What is permutation and combination?
In a combination, the elements of the subset can be listed in any order. In a permutation, the elements of the subset are listed in a specific order.
Arranging people, digits, numbers, alphabets, letters, and colors are examples of permutations. Selection of menu, food, clothes, subjects, the team are examples of combinations
We are given that license plate allows 2 digits and 4 upper case letters
a) repetition is allowed
hence for 2 numbers we have 10*10=100 choices
Also letter are allowed 26*26*26*26=456976 choices
And Hence total choices are 456976*100=45697600 ways
b) Repetition is not allowed
hence for 2 numbers we have 10*9=90 choices
Also letter are not allowed 26*25*24*23= 358800 choices
And Hence total choices are 456976*100=32292000 ways
Hence
a)Total different number plates will be 45697600
b) Total different number plates will be 32292000
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a girl (who liked riddles) was asked how old she was, she responded "in 2 years I will be twice as old as I was 5 years ago". how old is she now?
Given data:
The expression for the age of the girl after two year is,
x+2
The age of girl 5 year ago is,
x-5
According to the given statement of the question.
x+2=2(x-5)
x+2=2x-10
x=12
Thus, the present age of the girls is 12 years old.
Find the y-intercept of the line graphed by the equation 1/2x + y = 7. (0, 14) (14, 0) (7, 0) (0, 7)
The y-intercept of the line graphed by the equation [tex]\frac{1}{2} x+y=7[/tex] is (0,7)
Option (D) is correct.
The x-intercept is the point where the line crosses the x-axis, and the y-intercept is the point where the line crosses the y-axis.
The given equation is [tex]\frac{1}{2} x+y=7[/tex]
Converting the equation in Slope-intercept form, we get
[tex]y=-\frac{1}{2} x+7[/tex] ...(1)
Now, to find the y-intercept, substitute x = 0 in the equation and solve for the value of y
Putting x = 0 in equation (1), we get
[tex]y=-\frac{1}{2} (0)+7[/tex]
[tex]y=7[/tex]
Therefore, the y-intercept of the line will be (0,y) i.e., (0,7)
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need help!! algebra 1
Answer:
f(1)= -3
Step-by-step explanation:
what f(1) means is when x is 1 what is y. I dont see the graph labeled so im just assuming that the graph is going by ones. So what i did was i found where x is one and then i checked at what point did the line match with the y axis which was 3 points below 0 on y axis ( disclaimer if the graph isnt going by ones then its going to be a different answer, but you can use the same process to find it.
Identify the vertex: y = (x+10)2+ 2 a. (10,2) b. (-10, -2) c. (-10,2) ) d. (10, -2)
Given a quadratic equation in vertex form
[tex]y=a(x-h)^2+k[/tex][tex]\begin{gathered} \text{ wh}ere\text{ a, h, and k are constants, } \\ \text{then the point (h, k) is the vertex of the function} \end{gathered}[/tex]In our case,
[tex]y=(x+10)^2+2[/tex]h = -10, and k= 2
Therefore the vertex is (-10, 2)
Car 1 leaves point A at 5:30 p.m., driving due south atan average speed of 35 mph. Car 2 leaves point A at6:30 p.m., driving due north at an average speed of 45mph. How far apart will the drivers be at 9:30 p.m.?
Answer:
Explanation:
• Car 1 leaves point A at 5:30 p.m., driving due south at an average speed of 35 mph.
,• Car 2 leaves point A at 6:30 p.m., driving due north at an average speed of 45 mph.
At 9:30 pm, the time taken by the cars is:
[tex]\begin{gathered} Car\;1:9:30-5:30=4\text{ hours} \\ Car\;2:9:30-6:30=3\text{ hours} \end{gathered}[/tex]The distance covered by each car is:
[tex]\begin{gathered} Distance=Speed\times Time \\ \text{Car 1's distance}=35\times4=140\text{ miles} \\ \text{Car 2's distance}=45\times3=135\text{ miles} \end{gathered}[/tex]Since car 1 drives due South and Car 2 due North of point A:
Therefore, the distance between the drivers at 9:30 p.m. will be:
[tex]Distance=140+135=275\text{ miles}[/tex]The two drivers are 275 miles apart at 9:30 pm.
1
-2-(-7) = ?
NEXT
BOOKMARK
Answer:
5
Step-by-step explanation:
negetive two minus negative seven equal to five
A diagram of the side of Robert's barn is shown. If he decides to paint one side of the barn, how many square feet will Robert paint?
1. 254.5 ft^2
2. 310.5 ft^2
3. 391 ft^2
4. 805 ft^2
Robert will paint 310.5 square ft
The side of Robert's barn contains a triangle and a rectangle of which the dimensions are given in the diagram.
If Robert paint one side of the barn, then he needs to paint the triangle as well as the rectangle. So we need to find the area of the triangle and rectangle first.
For the triangle, base = 23 ft
height = 7 ft
Area of the triangle = 1/2 bh
= 1/2 x 7 x 23
= 80.5 square ft.
For the rectangle, length = 23 ft
width = 10 ft
Area of the rectangle = length x width
= 23 x 10
= 230 square ft.
Area Robert needs to paint = Area of the triangle + Area of the rectangel
= 80.5 + 230
= 310.5 square ft.
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At the local food stand, the vendor sells small drinks for $1.25 each and large drinks for $2.50 each. They sold 155 drinks today and made $265. How many small drinks and how many large drinks did they sell?
Answer:
98 small drinks and 57 large drinks.
Explanation:
Let's call x the number of small drinks and y the number of large drinks.
If they sold 155 drinks, we can write the following equation:
x + y = 155
In the same way, they made $265, so
1.25x + 2.50y = 265
Because each small drink cost $1.25 and each large drink cost $2.50.
Now, we can have the following system of equations
x + y = 155
1.25x + 2.50y = 265
Solving the firs equation for y, we get:
x + y - x = 155 - x
y = 155 - x
Replacing this on the second equation:
1.25x + 2.50y = 265
1.25x + 2.50(155 - x) = 265
Then, solving for x, we ge:
1.25x + 2.50(155) - 2.50(x) = 265
1.25x + 387.5 - 2.50x = 265
-1.25x + 387.5 = 265
-1.25x + 387.5 - 387.5 = 265 - 387.5
-1.25x = -122.5
-1.25x/(-1.25) = -122.5/(-1.25)
x = 98
Finally, we can find the value of y replacing x = 98
y = 155 - x
y = 155 - 98
y = 57
Therefore, they sell 98 small drinks and 57 large drinks.
4. Describe the transformation from the parent graph of y - 4 = – 2(x – 3)?. Graphboth the parent graph and the transformed graph on the grid provided. Plot at leastthree distinct points for each.
Describe the transformation from the parent graph of y - 4 = – 2(x – 3)^2. Graph
both the parent graph and the transformed graph on the grid provided. Plot at least
three distinct points for each.
we have that
the parent function is
y=x^2
Is a vertical parabola open upward with the vertex at (0,0)
the transformed function
is
y-4=-2(x-3)^2
y=-2(x-3)^2+4
Is a vertical parabola open downward with vertex at (3,4)
so
The transformations are
1) Reflection over x-axis
Rule is
(x,y) ------> (x,-y)
y=x^2 ------------------> y=-x^2
2) Vertical Dilation with a scale factor of 2
Rule
(x,y) --------> (x,2y)
y=-x^2 ----------> y=-2x^2
3) Translation 3 units at right and 4 units up
Rule is
(x,y) --------> (x+3,y+4)
y=-2x^2 --------> y=-2(x-3)^2+4
see the graph to better understand the problem
7=1/4ax, solve for a
The given expression is
[tex]7=\frac{1}{4}ax[/tex]Solving for a means that we need to isolate that variable.
First, we need to multiply the equation by 4
[tex]7\cdot4=4\cdot\frac{1}{4}ax\rightarrow28=ax[/tex]Second, we divide the equation by x
[tex]\frac{28}{x}=\frac{ax}{x}[/tex]Therefore, the answer is
[tex]a=\frac{28}{x}[/tex]mario's school is also planning a smaller rectangular are as a sitting spot. A scale drawing of the sitting sot is shown. redraw the sitting spot on the grid at a scale of i grid unit/4 feet.
write and simplify the ratio of the new scale
The ratio of the new scale that we are to be having is going to be 1/2
How to simplify the new scale of the gridwe have the ratio to be 1 grid unit / 2 ft
the new scale ratio is given as 1 grid unit / 4 ft
We have to divide the ratio of the original scale to the new scale that we have here
This would be ( 1 grid unit / 4 ft ) / ( 1 grid unit / 2 ft)
This can be written as
1/4 * 2/1
when we rewrite it we would have 2/4
= 1/2
This is 1 unit 2 feet
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i need helpppp plsssssss
The one-time fling! Have you ever purchased an article of clothing (dress, sports jacket, etc.), worn the item once to a party, and then returned the purchase? This is called a one-time fling. About 5% of all adults deliberately do a one-time fling and feel no guilt about it! In a group of six adult friends, what is the probability of the following? (Round your answers to three decimal places.)
Using the binomial distribution, the probability of no one having done a one time fling is of 0.735 = 73.5%.
Binomial distributionThe mass density formula for the probability of x successes is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters of the formula are given as follows:
n is the number of trials of the experiment.p is the probability of a success on a single trial of the experiment.In the context of this problem, the values of the parameters are as follows:
p = 0.05, as about 5% of all adults deliberately do a one-time fling and feel no guilt about it.n = 6, as there are six adult friends in the group.The probability that no one has done a one time fling is P(X = 0), hence the probability is calculated as follows:
P(X = 0) = (0.95)^6 = 0.735 = 73.5%.
Missing informationThe problem asks for the probability that no one has done a one time fling.
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The cost of a Turkish cloth varies jointly as the length and width of the cloth. If the cost is TL3848 for an 8 ft by 13 ft cloth, then what is the cost of a 17 ft by 23 ft cloth?
The cost of the the 17 feet by 23 feet Turkish cloth given the constant of variation is TL14,467.
What is the cost?A variable varies jointly if the value of one variable depends on the value of two or more variables. In this question, if the length and width of the cloth increases, the cost of the cloth increases. Also, if the length and width of the cloth decreases, the cost of the cloth decreases.
The equation that represents joint variation is:
y = kab
Where:
y = dependent variable = cost of the Turkish cloth k = constant of variation a = dependent variable = length of the cloth b = dependent variable = widthTL3848 = k(13 x 8)
k = TL3848 / (13 x 8)
k = $37
The cost of 17 feet by 23 feet cloth :
37 x 17 x 23 = TL14,467
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I need whit math thats all(x-2) +(x+6)
To simplify the expression (x-2) +(x+6), you have to follow these steps:
1.Get rid of the parentheses:
(x-2) +(x+6)
x -2 + x + 6
2. Combine like terms:
x + x - 2 + 6
2x + 4
So the answer is 2x + 4
Solve this system of equations usingthe substitution method.y = x + 9y = -4x – 612] [UN
The given system of equations is
[tex]\begin{gathered} y=x+9\rightarrow(1) \\ y=-4x-6\rightarrow(2) \end{gathered}[/tex]We will substitute y in equation (2) by equation (1)
[tex]x+9=-4x-6[/tex]Now, add 4x to both sides
[tex]\begin{gathered} x+4x+9=-4x+4x-6 \\ 5x+9=-6 \end{gathered}[/tex]Subtract 9 from both sides
[tex]\begin{gathered} 5x+9-9=-6-9 \\ 5x=-15 \end{gathered}[/tex]Divide both sides by 5
[tex]\begin{gathered} \frac{5x}{5}=\frac{-15}{5} \\ x=-3 \end{gathered}[/tex]Substitute x by -3 in equation (1) to find y
[tex]\begin{gathered} y=-3+9 \\ y=6 \end{gathered}[/tex]The solution of the system is (-3, 6)
Suppose that IQ scores have a bell-shaped distribution with a mean of 101 and a standard deviation of 14. Using the empirical rule, what percentage of IQ scores are at least 73? Please do not round your answer.
Answer:
Explanation:
From the information given,
mean = 101
standard deviations = 14
We need to find the number of standard deviations between 73 and the mean.
Number of standard deviations = (73 - 101)/14 = - 28/14 = - 2
It is 2 standard deviations from the mean. According to the empirical rule, 95% of the population lies between 2 standard deviations of the mean. The required area is to the right of 2 standard deviations since we want to find the least score. Thus, the probability of having IQ scores are at least 73 is
We would convert to percentage by multiplying by 100