The smallest distance between the origin and a point on the graph of y = 1/2(x² - 8) is √7 units.
Given, a function
y = 1/2(x² - 8)
We have to find the smallest distance between origin and a point on the graph of y = 1/2(x² - 8).
Now, the point on the graph be,
( x , 1/2(x² - 8) ) and origin be (0 , 0)
Let the function of the distance between both the points be,
D = √(x - 0)² + (1/2(x² - 8) - 0)²
D = √x² + 1/4(x² - 8)²
D² = x² + 1/4(x² - 8)²
On differentiating, we get
2DD' = 2x + x(x² - 8)
x³ + 2x - 8x = 0
x³ - 6x = 0
x(x² - 6) = 0
So, x = 0 , √6 , -√6
and the distance is minimum for x = √6
Therefore, using distance formula, we get
Distance = √(x1 - x2)² + (y1 - y2)²
Distance = √(0 - √6)² + (0 - (-1))²
Distance = √6 + 1
So, the smallest distance between the origin and a point on the graph of y = 1/2(x² - 8) is √7 units.
Hence, the smallest distance between the origin and a point on the graph of y = 1/2(x² - 8) is √7 units.
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Please help me Thank you :)
Answer:
3
Step-by-step explanation:
y difference is 9 and x difference is 3 so 9/3 = 3
Answer:
slope = 3
Step-by-step explanation:
(2, 7), (5, 16)
(x₁, y₁) (x₂, y₂)
m = slope
y₂ - y₁ 16 - 7 9
m = ------------ = ----------- = ------- = 3
x₂ - x₁ 5 - 2 3
I hope this helps!
13. Is the function y = 2x a one-to-one function? Justify your answer.
ation becaus
Answer:
yes
Step-by-step explanation:
every x value will have at lest one y value
Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options. x2 + (y – 3)2 = 36 x2 + (y – 5)2 = 6 (x – 4)² + y² = 36 (x + 6)² + y² = 144 x2 + (y + 8)2 = 36
The equations that represent the circle having a diameter of 12 units and a center lying on y-axis are; x² + (y – 3)² = 36, and x² + (y + 8)² = 36.
What is the standard form of the equation of a circle?The standard form of the equation of a circle is (x - h)² + (y - k)² + r², where (h, k) is the center of the circle, and r is its radius.
We have given that circle having a diameter of 12 units, will have a radius of 12/2 = 6 units. Thus, r = 6.
Since we know that circle having the center on the y-axis will have a center as (0, k) as all points on the y-axis have x-coordinate 0.
Thus, the equation of the circle, with a diameter of 12 units is;
x² + (y - k)² = 6², or,
x² + (y - k)² = 36.
From the given options, the equations x² + (y – 3)² = 36, and x² + (y + 8)² = 36, are correct.
Thus, the equations that represent the circle having a diameter of 12 units and a center lying on y-axis are; x² + (y – 3)² = 36, and x² + (y + 8)² = 36.
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A survey of 25 people was conducted to determine their favorite color. 13 people like Red, 8 people like blue and 13 people like yellow. 5 people like both Red & Blue, 4 people like both Blue & yellow, 7 people like both Red & yellow and 2 people like all three colors.
Question: How many did not like any of the three colors?
The number of people who do not like any of the three colour is 5, using the set theory.
What is Set theory?
A subfield of mathematics called set theory studies sets and their characteristics. Set theory's fundamental ideas are straightforward and seem to stand on their own. The set theory appears to be straightforward, but it is actually a very complex topic. Mathematicians have specifically demonstrated how almost all mathematical ideas and conclusions may be formalized within the theory of sets. This is regarded as one of the pinnacles of contemporary mathematics. Given this accomplishment, it is possible to assert that set theory serves as the foundation for mathematics.
In the given question, we have:
Total number of people in the survey = 25;
Number of people like red = 13;
The number of people who like blue = 8;
The number of people who like yellow = 13;
5 people like both Red & Blue,
4 people like both Blue & yellow,
7 people like both Red & Yellow
2 people like all three colors.
Let n be the number of people who do not like any of the three colour.
Using the concept of set theory, we can write it as:
3 + 4 + 1 + 5 + 2 + 3 + 2 + n = 25;
⇒20 + n = 25;
n = 25 - 20
n = 5;
Hence, The number of people who do not like any of the three colour is 5;
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what is the greatest comman facter of 2 and 3
helppp pls <233 i’ll make brainliest !!!
The congruent angle of Q is T
A right triangle has a leg length of square root of 6 and a hypotenuse length of 7. Determine the length of the other leg of the right triangle.
3
36
square root of 39
square root of 43
The length of the other leg of the right triangle is square root of 43
How to find the length of the other leg of the right triangle?
Given:
A leg length = square root of 6
Hypotenuse length = 7
Let the length of the other leg of the right triangle be y
The diagram of the triangle is as shown in the image attached
Using Pythagoras' theorem:
7² = (√6)² + y²
y² = 7² - (√6)²
y² = 49-6
y² = 43
y = √43
Therefore, the other leg is square root of 43. The 4th option is the angle
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Answer:
D = 43
Step-by-step explanation:
I got it right on my test!
Have a great day everyone:)
In the past, Jessica got paid $197,980 annually. Since switching to a new career, she has been making 35% more. How much does Jessica make now?
$
pwease
Answer:
$267,273
Step-by-step explanation:
197980 + .35(197980)
197980 + 69293
267273
2. Janet earns money making candles. From every candle she sells, she earns $4.18. How
much money would she earn if she sold 57 candles?
Answer:
$238.26
Step-by-step explanation:
Answer any of these two! If you can answer both I could possibly give you brain^^ THANK YOU
Answer:
12. [tex]\frac{1}{z^{2} }[/tex]
13. x⁶
Step-by-step explanation:
*Note: When multiplying two of the same variables you add the exponents. When dividing two of the same variables you subtract the exponents. When a variable to a power is raised to another power you multiply the exponents.
[tex](z^{6} z^{-5} )^{-2}[/tex]= [tex](z^{6+(-5)} )^{-2}[/tex]= [tex](z^{6-5} )^{-2}[/tex]= [tex](z^{1}) ^{-2}[/tex]= [tex]z^{1*-2}[/tex]= [tex]z^{-2}[/tex]= [tex]\frac{1}{z^{2} }[/tex]*Note: When there is a negative exponent the whole term is flipped (the reciprocal of the term).[tex]\frac{1}{x^{-6} }[/tex]= x⁶Mara's age is 5 less than four times Brandy's age. Let x represent Brandy's age, and let y represent Mara's age. Which ordered pair (x, y) makes the equation y = 4x − 5 true?
The ordered pair that made the equation, y = 4x - 5 correct is (5, 15).
How to find ordered pair from a linear equation?Mara's age is 5 less than four times Brandy's age. Let x represent Brandy's age, and let y represent Mara's age.
Therefore, the ages can be represented linearly as follows:
y = 4x - 5
where
x = Brandy's agey = Mara's ageTherefore, the ordered pair (x, y) that makes the equation correct can be computed as follows:
y = 4x - 5
y = 4(5) - 5
y = 20 - 5
y = 15
The ordered pair is (5, 15)
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Yellow and red dye are mixed in a 9 : 2 ratio
to make 44 litres of an orange-coloured dye.
A further 8 litres of red dye are added to the
mixture. What is the new ratio of yellow to red
dye in its simplest form?
Answer:
9 : 4
Step-by-step explanation:
Ratio:
Find the quantity of yellow and red dye in the mixture.
Yellow : Red = 9 : 2
Total share = 9 + 2 = 11
[tex]\sf \text{Quantiy of yellow} = \dfrac{9}{11}*44[/tex]
= 9 * 4
= 36 litres
[tex]\sf \text{Quantity of Red}= \dfrac{2}{11}*44[/tex]
= 2 * 4
= 8 litres.
Now, 8 litres of red dye is added.
New quantity of red dye = 8 + 8 = 16 liters.
New ratio of Yellow to red = 36 : 16
= (36÷4) : (16÷4)
= 9 : 4
Write equations for a pair of perpendicular lines that intersect at the point at (-3, -7)
Equation for the given pair of lines which are perpendicular to each other and intersect at the point (-3 , -7 ) are :
( y + 7 ) = m₁ ( x + 3) and ( y + 7 ) = (-1 / m₁ )( x + 3 )
As given in the question,
Pair of equations that are perpendicular to each other and intersect at point ( -3 , -7 ) are as follow:
let us consider slope of perpendicular lines are m₁ and m₂.
Product of the slope of perpendicular lines = -1
⇒ m₁ × m₂ = -1
⇒ m₂ = -1 / m₁
Pair of perpendicular intersect at point ( -3 , -7 ) .
Required equation of perpendicular lines is given by :
For line 1:
( y - (-7)) / ( x - (-3) ) = m₁
⇒ y + 7 = m₁ (x+3)
For line 2:
( y - (-7)) / ( x - (-3) ) = m₂
⇒ y + 7 = m₂( x+ 3)
⇒ y + 7 = -1 / m₁ ( x+ 3)
Therefore, equation for the given pair of lines which are perpendicular to each other and intersect at the point (-3 , -7 ) are :
( y + 7 ) = m₁ ( x + 3) and ( y + 7 ) = (-1 / m₁ )( x + 3 )
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Carlos is making goodie bags for a party. Every goodie bag has exactly the same treats in it. Carlos has 96 granola bars and 48 small popcorn balls. What is the greatest umber of identical goodie bags Carlos can make? How many of each kind of treat is in each goodie bag?
The greatest number of identical goodie bags Carlos can make is 48.
Therefore will be 2 granola bars and 1 popcorn balls in each bag.
How to calculate the value?From the information, Carlos is making goodie bags for a party and every goodie bag has exactly the same treats in it.
Carlos has 96 granola bars and 48 small popcorn balls. It should be noted that the greatest common factor between 96 and 48 is 48.
Therefore, granola bars will be:
= 96/48
= 2 in each bag
Popcorn will be:
= 48/48
= 1 in each bag.
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What number is halfway between 8.34 and 8.35?
Answer:
The correct answer is 8.345
Step-by-step explanation:
To find the midpoint of any two numbers, add the two numbers together and then divide the sum by two.
Addition:
8.34 + 8.35 = ?
= 16.69
Divide sum by 2:
16.69 ÷ 2 = ?
= 8.345
Hope this helps! Have an amazing rest of your day! Brainliest welcome! :)
What’s the correct answer answer asap for brainlist
Answer:
B
Step-by-step explanation:
Answer:
A.
Step-by-step explanation:
A commuter plane can carry 50 people per trip. At least How many times does the plane have to fly in order to carry 25,000 people? Identify the variable and answer the question. Please give details on how to set up problem. Thanks
Answer:
Step-by-step explanation:
First, since 50 people can go per trip and the plane wants to fly a lot of times to carry 25,000 people.
Second, then you have to do 25,000/50
Thirdly, you have to find the awnser
AWNSER=500
PLEASE HELP ASAP I ONLY HAVE 2 ATEMPTS LEFT
Make sure your answers are in slope intercept form (y=mx+b). NO SPACES, negatives are ALWAYS displayed in for of your number (ex: -1/2). ALWAYS SIMPLIFY!
You have made 8 of 10 attempts. You have 2 attempts remaining.
Answer:
y=-3/5x+1
Step-by-step explanation:
we use slope formula y2-y1/x2-x1
4-1/-5-0
3/-5
-3/5
Is the slope
The y intercept is 1
So we write like this
y=-3/5x+1
Hopes this helps please mark brainliest
The vet says that Lena's puppy will grow to be at most 20 inches tall. Lena's puppy Is currently 1 foot tall.
How many more inches will the puppy grow?
Answer:
8 inches
Step-by-step explanation:
1 foot is 12 inches
20 - 12 = n
n = 8
Answer: The correct answer is 8 more inches.
Step-by-step explanation:
The puppys' current height is 12 inches (1 foot)
The vet's advised maximum height is 20 inches
Difference in height = 20 - 12 = 8 inches
A chemist weighs samples obtained from a production run. The weights of the samples are 13 g, 14 g, 23 g, 11 g, 15 g, 14 g, 14 g, 12 g, 13 g, 15 g, 14 g, and 12 g. Are there any outliers?
The outlier of the data is 14.16 gram
What is Outlier?An outlier is a data point in statistics that dramatically deviates from other observations. An outlier may reflect measurement variability or it may point to an experimental error; the latter is occasionally removed from the data set. In statistical analyses, an outlier can result in significant issues.
Given:
Weights of the samples are 13 g, 14 g, 23 g, 11 g, 15 g, 14 g, 14 g, 12 g, 13 g, 15 g, 14 g, and 12 g.
So, the outlier is
= 13 x 2 + 14 x 4 + 12 x 2 + 11 + 15 x 2+ 13 / 12
= 170 gram /12
= 14.16 gram.
Hence, the outlier of the data is 14.16 gram
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You are playing a game in which a single die is rolled. If a 2 or a 5 comes up, you win $36, otherwise, you lose $30. What is your expected value for the game?
Find the value of Z such that 0.13 of the area lies to the right of Z
Answer:
the answer will be : 1.13
Solve for x: 5x + one third(3x + 6) > 14
The value of x for 5x + 1/3(3x+6) > 14 is x > 2
What are inequality equations in algebra ?
When you first begin learning algebra, the equals sign is used to denote that two items are, in fact, equal to one another. As an illustration, consider the equations 3 = 3, 5 = 3 + 2, apple = apple, pear = pear, etc. When compared, an inequality reveals two things: first, that the objects being compared are not equal, or at the very least, they are not always equal; and second, how they are uneven.
Consider the provided inequality.
5x + 1/3(3x+6) > 14
Distributive property:
a (b +c)= ab + ac
By the distributive property.
5x + 1/3 * 3x + 1/3 * 6 > 14
5x + x + 2 > 14
Add the like terms
6x + 2 > 14
Subtract 2 from both sides.
6x > 12
Divide both sides by 6.
6x/6 > 12/6
x > 2
Hence, value of x for the given inequality equation will be greater than 2 i.e, x > 2.
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Answer:
Nikita Knight
Nikita Knight
Step-by-step explanation:
Nikita Knight
Nikita Knight
Nikita Knight
Nikita Knight
69420
t is the solution to the linear equation?
x – StartFraction 2 Over 3 EndFraction x minus StartFraction one-half EndFraction equals StartFraction 1 Over 3 EndFraction plus StartFraction 5 Over 6 EndFraction x. = + x
The solution for the linear equation:
x - (2/3)*x - (1/2) = (1/3) + (5/6)*x
Is x = -5/3
How to solve the linear equation?Is hard to understand what you wanted to write, but I assume that the linear equation that we need to solve is:
x - (2/3)*x - (1/2) = (1/3) + (5/6)*x
To solve this linear equation, we need to isolate the variable x in one of the sides of the equation
To do so, we move all the terms with "x" to the left side and the terms without to the right side:
x - (2/3)*x - (5/6)*x = 1/3 + 1/2
Now we solve this:
x - (4/6)x - (5/6)x = 2/6 + 3/6
x - (9/6)*x = 5/6
We can write the "1" in the first term as 6/6
(6/6)*x - (9/6)*x = 5/6
(-3/6)*x = 5/6
-3x = 5
x = 5/-3
x = -5/3
That is the solution of the linear equation.
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The black graph is the graph of
= f(x). Choose the equation for the
red graph.
a.
y = f(2x)
b. y=f(2)
C.
2y = f(x)
d.
½ = f(x)
Enter
The equation for the red graph is y = f(x/2).
We are given a graph. The graph shows two functions. A function connects an input to an output. It is similar to a machine with input and output. And the result is somehow connected to the input in some way. One of the functions is depicted by black lines. We need to find the equation of the function represented by the red lines.
We can see that the function represented by the red lines can be formed if the black lines are stretched horizontally. The black lines can be stretched horizontally by a factor of 2 to form the red lines. A function y = f(x) can be stretched horizontally by a factor of "k" as given below.
y = f(x/k)
Hence, the equation for the red graph is y = f(x/2).
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Can you help on 7-9
Please this is due tomorrow
Answer:
The answer for no 7 is A. 24 in, for no 8 is C. 10 in, for no 9 is D. similar
Step-by-step explanation:
The answer for no 7 can be calculation as follows
Since both rectangles are similar, then the corresponding side are proportional, and it follows
[tex]\frac{\overline{KJ}}{\overline{AB}}=\frac{x}{\overline{AD}}[/tex]
[tex]\frac{48}{144}=\frac{x}{72}[/tex]
Where [tex]x[/tex] is the line segment [tex]\overline{MJ}[/tex]
Multiply both sides by [tex]72[/tex] to isolate [tex]x[/tex]
[tex]\frac{48}{144}\times 72=\frac{x}{72}\times 72[/tex]
[tex]\frac{48\times 72}{144}=x[/tex]
[tex]\frac{3456}{144}=x[/tex]
[tex]24=x[/tex]
Since the value of [tex]x[/tex] is [tex]24[/tex], then the length of [tex]\overline{MJ}[/tex] is [tex]24[/tex] in
The answer for no 8 can be calculation as follows
Since both rectangular frames are similar, then the corresponding side are proportional, and it follows
[tex]\frac{w_2}{w_1}=\frac{x}{h_1}[/tex]
Where [tex]w_2[/tex] is the width of frame [tex]2[/tex], [tex]w_1[/tex] is the width of frame [tex]1[/tex], [tex]x[/tex] is the height of frame [tex]2[/tex], [tex]h_1[/tex] is the height of frame 1
Substitute [tex]8[/tex] for [tex]w_2[/tex], [tex]12[/tex] for [tex]w_1[/tex], [tex]15[/tex] for [tex]h_1[/tex]
[tex]\frac{8}{12}=\frac{x}{15}[/tex]
Multiply both sides by [tex]15[/tex] to isolate [tex]x[/tex]
[tex]\frac{8}{12}\times 15=\frac{x}{15}\times 15[/tex]
[tex]\frac{8\times 15}{12}=x[/tex]
[tex]\frac{120}{12}=x[/tex]
[tex]10=x[/tex]
Since the value of [tex]x[/tex] is [tex]10[/tex], then the height of the second rectangular frame is [tex]10[/tex] in
The answer for no 9 can be evaluated as follows
Since two polygons are similar if and only if two conditions are satisfied
All pairs of corresponding angles are congruentAll pairs of corresponding side are proportionalThen the two polygons are similar
Model−−−−−: P=2,320(1.2)x
The model is used to estimate the deer population in a region, where x is the number of years after the year 2009. Using the model, estimate the deer population in the year 2018
The population of the deer in year 2018 would be 11971.
Given,
In the question:
The model is used to estimate the deer population in a region, where x is the number of years after the year 2009. Using the model, estimate the deer population in the year 2018
Model is given as:
P = 2,3201 [tex](1.2)^x[/tex]
Now, According to the question:
The number of years from 2009 to 2018 = 9
Here, the equation that shows the deer population after x years since 2009,
P = 2,3201 [tex](1.2)^x[/tex]
Substitute x=9 in the above equation,
P = 2,3201[tex](1.2)^9[/tex]
P = 2320(5.15978)
P ≈ 11971
Hence, the population of the deer in year 2018 would be 11971.
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Find the area of this parallelogram
Answer:
84unit square
Step-by-step explanation:
how many years do I need the 3
The answer is: " 84 cm² " ; or, write as: " 84 square centimeters."
____
Step-by-step explanation:
Note the formula for the area; "A" ; of a parallelogram—as follows:
A = b * h ;
in which:
A = the Area of this parallelogram given in the attached image;
for which we shall solve; in units of: cm² ;
or, write as: " square centimeters "
→ {since all the measurements shown in the image are in units of:
"cm" ["centimeters"].}
____
b = " base length " = 12 cm {as shown in the image};
____
h = " perpendicular height " = 7 cm {as shown in the image} .
____
To find the area; A :
We plug our given values into the equation/formula:
→ A = b * h ;
= (12 cm) * (7 cm) ;
= 12 * 7 * cm * cm ;
A = 84 cm² .
_____________
Note of interest: The following quadrilaterals are also parallelograms:
squares, rectangles, and rhombuses [or, "rhombi"].
_____________
The answer is: " 84 cm² " ; or, write as: " 84 square centimeters."
___
Hope this is helpful to you.
Wishing you well in your academic endeavors!
___
Please help!!! Will give Brainliest to the first person that answers!
Answer:
Below
Step-by-step explanation:
m = motorcylce speed
c = car speed = 2m-30
difference in speeds = 2m-30 - m = m-30
in two hours this speed accumulates 20 miles (rate * time = distance)
2 (m-30) = 20
2m - 60 = 20
m = 40 then c = 2m-30 = 50 mph
Given m||n, find the value of x.
Answer:
x = 17
Step-by-step explanation:
(5x - 23) and (7x - 1) are same- side interior angles and sum to 180° , so
5x - 23 + 7x - 1 = 180
12x - 24 = 180 ( add 24 to both sides )
12x = 204 ( divide both sides by 12 )
x = 17