Answer:
[tex](0,-2)[/tex]
Step-by-step explanation:
Let the coordinates of the desired point be [tex](a, -a^2-2)[/tex]. Let the distance of this point from [tex](0,1)[/tex] be [tex]f(a)[/tex].
By the distance formula, [tex]f(a)=\sqrt{a^2+(a^2+3)^2}[/tex].
Clearly, [tex]f(a)[/tex] is minimized when the radicand is minimized.
Clearly, the radicand is always increasing, so the minimum is achieved at the left endpoint of the maximal domain of [tex]f(a)[/tex], which is [tex]a=0[/tex].
So, the coordinates are [tex](0,-2)[/tex].
The point on the curve y = -x^2 - 2 that is closest to the point (0, 1) will be (0, -2)
How to calculate the value?From the information, we want to know the point on the curve y = -x^2 - 2 that is closest to the point (0, 1).
Let the coordinates of the desired point be illustrated as (a - a² - 2).
The distance of the point from (0, 1) is depicted as f(a).
When the radicand is minimized, f(a) is minimized.
In this case, the minimum will be achieved at the left endpoint of the maximal domain of f(a) which is a = 0.
Therefore, the coordinates will be (0, -2).
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A bank B is 8.6 km north and 12.5 km west of a school S. Calculate correct to 3 significant figures:
a the bearing of S from B [2] b the bearing of B from S.
The bearing of B from S = 63.8 + 180 = 243.8°
How to calculate the distance?To calculate the distance that the boys walked, you would need to know their speed and the duration of their walk.
Speed is typically measured in units such as miles per hour (mph) or kilometers per hour (kph). If you know the speed of the boys and the duration of their walk in hours, you can calculate the distance they walked using the formula: distance = speed x time.
To calculate the bearing of S from B, you can use the following steps:
Calculate the distance between S and B using the Pythagorean theorem. The distance is the hypotenuse of a right triangle, where one side is 8.6 km (the north-south distance) and the other side is 12.5 km (the east-west distance).
Calculate the angle formed by the distance between S and B and the north-south line. To do this, you can use the arctangent function (atan), which returns the angle in radians.
To convert radians to degrees, multiply by 180/π
The bearing of S from B = atan(12.5/8.6) x 180/π = 63.8°
To calculate the bearing of B from S, you just need to add 180 degrees to the bearing of S from B
The bearing of B from S = 63.8 + 180 = 243.8°
b. 243.8
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Complete question:
A bank B is 8.6 km north and 12.5 km west of a school S.
Calculate correct to 3 significant figures:
a the bearing of S from B
b the bearing of B from S.
Find the length of the midsegment of the trapezoid with the vertices A(0,3) ,B(2 , 5) ,C(6,4) ,D(2,0)
The length of the midsegment of the trapezoid with the vertices A(0,3) ,B(2 , 5) ,C(6,4) ,D(2,0) is; 3√2
How to find the distance between two coordinates?The length of the mid-segment of a trapezoid is half the sum of the lengths of the two parallel sides, AB and CD. T
The vertices are;
A(0,3) ,B(2 , 5) ,C(6,4) ,D(2,0)
Thus;
Length of sides AB and CD
length = √(x₂ - x₁)² + (y₂ - y₁)²
AB =√(2 - 0)² + (5 - 3)²
AB = 2√2
length = √(x₂ - x₁)² + (y₂ - y₁)²
CD = √(2 - 6)² + (0 - 4)²
CD = 4√2
Formula to use for the mid segment is;
Mid segment = (AB + CD)/2
= (2√2 + 4√2) / 2
= 3√2
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please help will mark BRAINLIEST
Please answer this question for me
The value of x and y in the parallel lines are 14 and 60 respectively.
How to find angles in parallel lines?When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate exterior angles, alternate interior angle, linear angles, vertically opposite angles etc.
Therefore, let's find the values of x and y in the parallel lines as follows:
4x + 12 = 68 (vertically opposite angles)
Vertically opposite angles are congruent.
Hence,
4x + 12 = 68
4x = 68 - 12
4x = 56
divide both sides by 4
x = 56 / 4
x = 14
Therefore, let's find the value of y.
68 + 2y - 8 = 180(same side interior angles)
Same side interior angles are supplementary
68 + 2y - 8 = 180
2y = 180 - 68 + 8
2y = 120
y = 120 / 2
y = 60
Therefore,
x = 14
y = 60 degrees
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which equation can be used to find the scale price, s,of an oil change?
If an oil change at city auto is regularly $30 Mr. Allen has a coupon for 15% off. The equation that can be used to find the sale price, S, of an oil change is: 3. s=0.85(30).
How to find the sales price?First step is to find the percentage left if he has a coupon for 15% off.
Percentage left = ( 1- 0.15)
Percentage left = 0.85 or 85%
Now let find the sales price
Sales price = 0.85(30)
Sales price = $25.50
Therefore the equation that can be used to find the sale price, S, of an oil change is: 3. s=0.85(30).
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The complete question is:
An oil change at city auto is regularly $30 Mr. Allen has a coupon for 15% off. Which equation can be used to find the sale price, S, of an oil change?
1. s=0.85 divided by 30
2. s=85 divided by 30
3. s=0.85(30)
4. s=85•30
Una granja tiene q
cerdos, 2 caballos.
y 4 vacas. ¿Cuantos
animales hay ahi?
animales
Answer: letra “q” no es un número
Step-by-step explanation:
answer the following
The slope of the line is -20
How to find the slope of the graph of a line?The slope of a line is a measure of how steep the line is. It is defined as the ratio of the change in the y-coordinate (rise) to the change in the x-coordinate (run) between two points on the line. The formula for the slope of a line is:
m = (y2 - y1) / (x2 - x1)
Where (x1, y1) and (x2, y2) are the coordinates of two distinct points on the line.
From the graph, you can pick any two points. That is:
x1 = 0, y1 = 120 and x2 = 4, y2 = 40
m = (y2 - y1) / (x2 - x1)
m = (40- 120) / (4 - 0)
m = -80/4
m = -20
Thus, the slope is -20
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a researcher wants to examine the effect of fertilizer and the effect of sunlight on the yield of tomatoes. she bought 60 tomato plants at a local garden store. she randomly assigned 30 tomato plants to be planted on the sunny side of the hill and 30 to be planted on the shady side. the 30 plants which are planted on the shady side are randomly assigned to one of three groups. the first group are grown with no fertilizer, the second group with a small amount of fertilizer, and the third group with a large amount of fertilizer. the 30 plants which are planted on the sunny side are likewise randomly assigned to one of three groups. the first group are grown with no fertilizer, the second group with a small amount of fertilizer, and the third group with a large amount of fertilizer. all tomato plants are planted at the same time and are all treated alike (in terms of how much they are watered, weeded, etc.), and the person who tends the plants does not know which group each is in. each plant is grown to maturity. the total weight of tomatoes obtained from each plant is recorded. Describe the design of the experiment (completely randomized or blocked).
Completely randomized over one factor (location), blocked by fertilizer
Blocked by fertilizer, blocked by location
Completely randomized over one factor (fertilizer)
Completely randomized over one factor (fertilizer), blocked by location
Completely randomized over two factors (fertilizer and location)
The design of the experiment is Completely randomized over two factors (fertilizer and location).
Randomization is a statistical technique used in experimental design to ensure that all possible combinations of the factors being studied are represented in the study groups. It is used to eliminate bias and control for confounding variables that may affect the outcome of an experiment.
The researcher randomly assigned the tomato plants to be planted on either the sunny or the shady side of the hill. This creates two groups or two levels of the factor "location". She also randomly assigned the tomato plants to one of three groups based on the amount of fertilizer given, creating three groups or three levels of the factor "fertilizer".
The random assignment of plants to the different groups for both factors helps to ensure that any differences in the yield of tomatoes is due to the independent variables (fertilizer and location) being tested, and not due to other extraneous factors.
Therefore, The design of the experiment is Completely randomized over two factors (fertilizer and location).
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complete the table by using your knowledge of the formula for simple interest. principle amount saved (dollars) 425, interest rate 7% time (years) 5 how many interest Earned (dollars)
Answer:
$ 148.75
Step-by-step explanation:
Simple interest:Principle = $ 425
Rate = 7%
Time = 5 yeats
[tex]\sf \boxed{Simple \ Interest = \dfrac{Principle*rate*time}{100}}[/tex]
[tex]= \dfrac{425*7*5}{100}\\\\=\dfrac{17*7*5}{4}\\\\\\=\dfrac{595}{4}\\\\=148.75[/tex]
Suppose that X and Y are integer valued random variables with joint probability mass function given by pX, Y(a, b) = {1/4a, for 1 > b > a > 4, otherwise. a. Show that this is indeed a joint probability mass function. b. Find the marginal probability mass function of X and Y. c. Find P(X = Y + 1).
The joint probability mass function given by PX, Y(a, b) = {1/4a, for 1≤ b≤a≤4, otherwise is indeed a joint probability mass function because the sum of all the joint probabilities is equal to 1.
To find the marginal probability mass function of X, we need to sum the joint probabilities over all possible values of Y:
PX(a) = ∑ PX, Y(a,b) = ∑ (1/4a) = 1/4
To find the marginal probability mass function of Y, we need to sum the joint probabilities over all possible values of X:
PY(b) = ∑ PX, Y(a,b) = ∑ (1/4a) = 1/4
To find P(X = Y + 1), we need to find the joint probability of X = a and Y = a-1, where a = 2,3.
P(X = Y + 1) = PX, Y(2,1) + PX, Y(3,2) = (1/42) + (1/43) = 1/4 + 3/12 = 5/12
So the probability that X is one more than Y is 5/12.
It's important to note that the given joint probability mass function is valid as it satisfies the non-negativity and the condition of summing to 1.
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-6z - 18z + 2z + 6z = 16
nvm don't answer
The value of z in the given linear equation in one variable is -1.
What is a single-variable linear equation?By equating it to zero, a linear polynomial over a field, from which the coefficients are extracted, can be converted into a linear equation.
The values that, when employed as stand-ins for the unknowns in such an equation, lead to the equality being true are the solutions.
When there is just one variable, there is just one solution. The term "linear equation" is generally understood to relate to this particular circumstance, when the variable is accurately referred to as the "unknown."
It is possible to interpret each solution as the Cartesian coordinates of a specific point on the Euclidean plane when there are only two variables.
-6z -18z + 2z +6z = 16
-16z = 16
z = -1
Hence, the value of z is -1
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The size of a pentagon are given as x, x+1,x+3,x-2 and 6.If the perimeter is less than 78cm and x is an interger.Find the largest value of x
The largest value of x is 13.
What is perimeter?A closed shape's perimeter is the sum of the lengths of its outside boundaries. The lengths of all the sides are added to determine the measurement.
Given:
The size of a pentagon are given as x, x+1,x+3,x-2 and 6.
The perimeter is less than 78 cm and x is an integer.
The perimeter of the pentagon = the sum of all the sides.
x + x+1 + x+3 + x-2 + 6 < 78
4x + 10 - 2 < 78
4x < 70
x < 14
The largest value of x is 13.
Therefore, the largest value of x is 13.
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please help me with math i’ll give you brainlist
Answer:
1. Funnel cakes- 12
2. Oreos- 21
Step-by-step explanation:
1. x= 42/3.50
x=12
2. y= 42/2
y= 21
Zach had been walking for
distance.
when both boys had walked exactly the same
Place the correct value to complete the sentence.
Two boys, Zach and Carlos, go for a walk. Zach begins walking 20 seconds earlier
than Carlos
Two boys, Zach and Carlos, go for a walk. Zach begins walking 20 seconds earlier than Carlos and they both walked the same distance.
How to calculate the distance?
To calculate the distance that the boys walked, you would need to know their speed and the duration of their walk.
Speed is typically measured in units such as miles per hour (mph) or kilometers per hour (kph). If you know the speed of the boys and the duration of their walk in hours, you can calculate the distance they walked using the formula: distance = speed x time.
The sentence is describing a scenario in which two boys, Zach and Carlos, go for a walk. It is stated that Zach begins walking 20 seconds earlier than Carlos. This means that Zach starts his walk 20 seconds before Carlos does. It is also stated that both boys had walked exactly the same distance. This means that despite Zach starting his walk 20 seconds earlier than Carlos, they both covered the same distance during their walk.
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two expressions that are equivalent to 3f
The two expressions are written as :
3f + 2f + 4s 5f + 4sHow to solve for the expressions that are equivalent to 3f+4s+2f3f+4s+2f this expression that we have here is a mathematical expression that we can combine by making use of the commutative addition.
We would have the first expression when we write the equation as:
3f+4s+2f = 3f + 2f + 4s
We would have the second expression when we write the equation as
5f + 4s
This is the solution of the expression.
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two expressions that are equivalent to 3f+4s+2f ?
5. To predict the performance of her first
period class on their next quiz, a teacher
randomly selects eight students from the
class and takes the mean of their scores on
the last quiz. Is this sample representative
of the class's performance on the quiz?
Explain your reasoning.
Yes this sample(straightforward random sample)representative of the class's performance on the quiz
What is average?In mathematics, the middle value—which is determined by dividing the sum of all the values by the total number of values—is the average value in a set of numbers. To calculate the average of a set of data, add up all the values and divide the result by the total number of values.
According to data:A teacher randomly selects eight students from the class and averages their test scores to forecast how well her first period class will fare on their upcoming quiz. Is this sample indicative of how the class performed on the test?
Yes, since it is a straightforward random sample.
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the lengtjs of the three sides of a traigle nor necessarlity a right trianglw are 2.92 m, 7.67 m, 8.82 m what is the cosine od the angle opposite the sidw of 8.82 m
The cosine of the angle opposite the side of length 5.64 meters is 0.4536.
In a triangle, the cosine of the angle opposite a side is given by the formula:
cos(angle) = (a^2 + b^2 - c^2)/(2ab) where a, b, and c are the lengths of the sides of the triangle and angle is the angle opposite the side of length c. Given the side lengths of the triangle as 3.18 meters, 7.82 meters and 5.64 meters, the side opposite angle we want to find is 5.64 meters.
so we can use the above formula and substitute the values,
cos(angle) = (3.18^2 + 7.82^2 - 5.64^2)/(23.187.82) = 0.4536
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at a school, 20 percent of the sixth-grade students said that jazz is their favorite kind of music. if 30 sixth-grade students prefer jazz music, how many sixth-grade students are at the school? explain your reasoning.
Answer:
150 students in total
Step-by-step explanation:
30 students is 20%
20% x 5 = 100%
30 x 5 = 150 students
convert the following unsigned binary numbers to hexadecimal. a. 1101 0001 1010 1111 b. 001 1111 c. 1 d. 1110 1101 1011 0010
Answer:
a. D1AF
b. 1F
c. 1
d. EDB2
Step-by-step explanation:
You want these unsigned binary numbers converted to hexadecimal.
a. 1101 0001 1010 1111
b. 0001 1111
c. 0001
d. 1110 1101 1011 0010
HexEach group of 4 bits can take on any of 16 different values. Conveniently, each of those corresponds to a hexadecimal digit, as shown in the attachment.
To do the conversion, we replace each group of 4 bits by its hexadecimal equivalent.
a. D1AF
b. 1F
c. 1
d. EDB2
__
Additional comment
A couple of the given numbers are one or more bits short of a group of 4 bits. You may want to check your actual problem statement to see if the numbers here are the same. The attached table applies in any event.
help pls A rational expression has been simplified below.
(x-2)(x+6)/7(x+6) = x-2/7
For what values of x are the two expressions equal?
O A. All real numbers except 2
OB. All real numbers
O C. All real numbers except -6
O D. All real numbers except -6 and 2
All real numbers, with the exception of -6 , are the solution to a rational equation. The quotient of two polynomials is the definition of a rational expression.
What do you meant by rational expression ?[tex]$\frac{(x-2)(x+6)}{7(x+6)}=\frac{x-2}{7} \quad: \quad x \neq-6$[/tex]
[tex]$\frac{(x-2)(x+6)}{7(x+6)}=\frac{x-2}{7}$[/tex]
Simplify
[tex]$\frac{(x-2)(x+6)}{7(x+6)}: \quad \frac{x-2}{7}$[/tex]
[tex]$\frac{x-2}{7}=\frac{x-2}{7}$[/tex]
Seven times both sides
[tex]$\frac{x-2}{7} \cdot 7=\frac{x-2}{7} \cdot 7$[/tex]
Simplify
[tex]$x-2=x-2$[/tex]
There is equality between the two sides.
For every x Verify Solutions, true
Search for ill-defined (singularity) points: [tex]$x=-6$[/tex]
Because -6, the equation is undefined.
[tex]x \neq -6[/tex]
Therefore the correct answer is option C ) All real numbers except -6 .
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Imagine a study that looks at nutrition and memory. Each subject is randomly assigned to one of three groups: high-protein diet; high-fiber diet; standard diet (control). After a month on this diet, each subject undergoes a memory test. The initial statistical analysis of this study would be conducted using __________ because __________.
A. Analysis of variance (ANOVA) / there are more than two levels of the independent variable
B. Analysis of variance (ANOVA) / there are more than two levels of the dependent variable
C. A t test / there are only two experimental conditions (plus a control condition)
D. A t test / the goal would be to compare high-protein with control and high-fiber with control
Options
For each value below, enter the number to four decimal places Suppose an arrow is shot upward on the moon with a velocity of 60m / s then its height in meters after seconds is given by h(t) = 60t - 0.83t ^ 2 Find the average velocity over the given time intervals [4, 4, 5]; (4,4,1) 2; [4,4,01]:; [4,4,001]:
Average speed is determined by dividing the total distance you traveled by the total time,
How fast is it moving on average?In order to calculate average velocity, divide the change in position or displacement (x) by the time intervals (t) during which the displacement takes place. Depending on the displacement's sign, the average velocity can either be positive or negative. The SI unit for average speed is meters per second (m/s or ms-1).
Average speed is determined by dividing the total distance you traveled by the total time, whereas average velocity is determined by dividing your displacement, which is a vector pointing from your initial location to your end position, by the whole time.
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a picture is enlarged by keeping its width the same and increasing its length. the scatter plot shows the perimeter of the picture (y) for different lengths (x):plot the ordered pairs 20, 60 and 30, 80 and 40, 100 and 50, 120 and 60, 140which function best represents the data in the scatter plot?
The function best represents the data in the scatter plot is y = 2x + 20.
The function of the straight line has the general formula: y = mx + c
where m is the slope of the line, and c is the y-intercept
So first, we will need to find the slope (m):
The slope can be calculated with the points (x₁, y₁) and (x₂, y₂) as follows:
m = (y₂ - y₁)/(x₂ - x₁)
= 120 - 60/50 - 20
= 60/30
= 2/1
So, now we have the slope of our equation y = 2x + b but we still need to find b (or where the y intersects.)
Now, consider the ordered pair (20, 60)
y = 2x + b
60 = 2 × 20 + b
b = 60 - 40
b = 20
Now, put the value of b in y = 2x + b, and we get
y = 2x + 20
Also, b can not be -20 because this is a positive y-intercept, and we know it has a slope of 2.
Therefore the function is y = 2x + 20
--The given question is incomplete; the complete question is
"A picture is enlarged by keeping its width the same and increasing its length. The scatter plot below shows the perimeter of the picture (y) for different lengths (x):
Plot the ordered pairs 20, 60 and 30, 80 and 40, 100 and 50, 120 and 60, 140
Which function best represents the data in the scatter plot?
y = 2x − 20
y = 2x + 20
y = x − 20
y = x + 20"--
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Solve the equation for all real values of x.
3 tan²x =√3 tanx
The trigonometric equation has the following roots: x₁ = ± i · π, x₂ = π / 6 ± i · π, where i are integers. (Correct choice: D)
How to solve a trigonometric equation
Trigonometric equations are equations that involve trigonometric functions. Trigonometric functions are periodic trascendent functions. In this problem we must determine the roots of a trigonometric equations by means of algebra properties and trigonometric formulas:
3 · tan² x = √3 · tan x
3 · tan² x - √3 · tan x = 0
tan x · (3 · tan x - √3) = 0
The roots of the equation are tan x = 0 or tan x = √3 / 3, whose angles are: x₁ = ± i · π, x₂ = π / 6 ± i · π, where i are integers.
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24(20) this is my question please answer
Answer:
480
Step-by-step explanation:
Lets break this down to make it even easier
(24x2)x10
=(48)x10
=480
Answer:
If you are looking for the simplest form of 24/20 it is basically 6/5.
because if you multiply 6/5 by 4/4 you could get the answer which is 24/20.
and the same thing if you divide
I hope that I helped
6. Write a polynomial function of the least degree that has the root x = (5+ i).
Factors:
Polynomial Function:
To much to right but have it in pic: \/ \/
solve for y2?
please
[tex]m = \frac {y2 - y1}{x2 - x1} [/tex]
how to Solve the following Systems of Linear Equations 4X + 3Y= 7
Answer:
4x−3y+4=0
⟹x=
4
−4+3y
Let, y=4, then x=
4
−4+3(4)
=2
Similarly, when y=0,x=−1
4x+3y−20=0
⟹x=
4
20−3y
Let, y=4, then x=
4
20−3(4)
=2
Similarly, when y=0,x=5
Rewrite this number in appropriate scientific notation:
459,000
Answer:
4.59 × 10^(5)
Step-by-step explanation:
Answer: 4.59 x 10^5
Step-by-step explanation:
If we move the decimal place over 5 times in the answer we get 459,000.
I hope this was able to help you :D
4 (2 points): consider the following linear transformation of a random variable: , where is the mean and is the standard deviation. find the expected value and standard deviation of .
The standard deviation of is equal to the standard deviation multiplied by, and the anticipated value of is equal to the mean.
The mean, which is the average of the random variable, is equal to the expected value of. It is determined by summing up all of the random variable's values and dividing the total number of values in the set. The result of multiplying the standard deviation by is the standard deviation of. By taking the square root of the variance, the standard deviation—a measurement of the range of data points from the mean—is created. By dividing the total of the squares of the deviations between each data point and the mean, the variance is computed.
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