Step-by-step explanation:
to eliminate the always positive absolute value at the end let's set y = -3x
that makes the absolute value term = 0 in all cases.
then we have
sqrt((x - 8)² + (-3x + 4)²)
the x-value that makes this a minimum result also makes
(x - 8)² + (-3x + 4)²
a minimum.
x² - 16x + 64 + 9x² - 24x + 16
10x² - 40x + 80
the x that makes this a minimum, also makes
x² - 4x + 8
a minimum.
we get the extreme value as zero of the first derivative :
0 = 2x - 4
4 = 2x
x = 2
so, we get the minimum of all these expressions for x = 2.
as y = -3x, we get y = -3×2 = -6.
the minimum value for the expression is with
x = 2
y = -6
so, the minimum value is
sqrt((2 - 8)² + (-6 + 4)²) + |-6 + 3×2| =
= sqrt((-6)² + (-2)²) + |-6 + 6| =
= sqrt(36 + 4) + 0 =
= sqrt(40) = 6.32455532...
Simplify quantity 15 x squared minus 18 end quantity over 6. 15x + 3 x + 3 quantity 5 x squared minus 18 end quantity over 2 quantity 5 x squared minus 6 end quantity over 2
The expressions are:
(5x² - 6)/ 2 5x² - 18/2 5x² -6 /2What is expression?A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:
An absolute numerical number is referred to as a constant.Variable: A symbol without a set value is referred to as a variable.Term: A term can be made up of a single constant, a single variable, or a mix of variables and constants multiplied or divided.Coefficient: In an expression, a coefficient is a number that is multiplied by a variable.Given:
15 x squared minus 18 end quantity over 6.
= 15x² - 18 / 6
= 3(5x² - 6)/ 6
= (5x² - 6)/ 2
and, 5 x squared minus 18 end quantity over 2
= 5x² - 18/2
and, 5 x squared minus 6 end quantity over 2
= 5x² -6 /2
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Which of the following (x,y) coordinates are solutions to the inequality 2x+5y<1?
The solution to the inequality given as 2x+5y<1 has the coordinates of (-10, 4)
How to determine the coordinates of the solution of the inequality?From the question, we have the following inequality that can be used in our computation:
2x+5y<1
Solving further, we need to collect the like terms
Since there are no like terms in the expression, it remains unchanged
So, the inequality becomes
2x + 5y < 1
Subtract 5y from both sides of the inequality
This gives
2x < 1 - 5y
Divide both sides by 2
The expression becomes
x < 1/2 - 5/2y
Evaluate
x < 0.5 - 2.5y
At this point, we assume any value for y and then solve for x
Assume that the value of y is 4
So, we have the following representation
x < 0.5 - 2.5 * 4
Evaluate the products
x < -9.5
This means that x is less than -9.5 when y is 4
-10 is less than -9.5
So, we have
x = -10 and y = 4
Express as ordered pairs (i.e. coordinates)
(x, y) = (-10, 4)
Hence, the coordinates of the solution is (-10, 4)
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Desmond is training for a bike race and is attempting to improve his average speed. With his old trainer, Desmond averaged a pace of 24 MPH. With his new trainer, he rode at an average speed of 30 MPH. By what percent did his average speed increase? %
The percent that Desmond average speed increase is 25%.
How to calculate the percentage?From the information, with his old trainer, Desmond averaged a pace of 24 MPH and with his new trainer, he rode at an average speed of 30 MPH.
It should be noted that the percentage increase in speed will be:
= Change in speed / Initial speed × 100
= (30 - 24) / 24 × 100
= 6/24 × 100
= 25%
The percentage is 25%.
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At 2 hours before sunset, the temperature is 0°F. At 2 hours after sunset, the temperature is −4°F. Identify the equation representing the temperature y, in degrees Fahrenheit, at x hours after sunset
The correct equation to representing the temperature y, in degrees Fahrenheit, at x hours after sunset will be;
⇒ y = - 4°x + 0°
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
At 2 hours before sunset, the temperature is 0°F.
And, At 2 hours after sunset, the temperature is −4°F.
Now,
Let the temperature in degrees Fahrenheit = y
So, We can formulate;
⇒ y = - 4°x + 0°
Thus, The correct equation to representing the temperature y, in degrees Fahrenheit, at x hours after sunset will be;
⇒ y = - 4°x + 0°
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10 = 6/5 W
Solve the missing variable, W
[tex]\framebox{w=$\dfrac{25}{3}$}[/tex]
Flip the equation:
[tex]\frac{6}{5} w=10[/tex]
Multiply both sides by [tex]\frac{5}{6}[/tex]:
[tex](\frac{5}{6} )\times(\frac{6}{5} w)=(\frac{5}{6} )\times(10)[/tex]
[tex]w=\frac{25}{3}[/tex]
Two integers are separated by 24 units on a number line. The sum of the integers is -12 and the quotient is -3. What are the two integers?
Answer:
6 and - 18
Step-by-step explanation:
let the 2 integers be a and b , then
a + b = - 12 → (1)
[tex]\frac{a}{b}[/tex] = - 3 → (2)
multiply both sides by b ( b ≠ 0 )
a = - 3b
substitute a = - 3b into (1)
- 3b + b = - 12
- 2b = - 12 ( divide both sides by - 2 )
b = 6
substitute b = 6 into (1) and solve for a
a + 6 = - 12 ( subtract 6 from both sides )
a = - 18
the two integers are - 18 and 6
Please help me I’ll mark your answer brainly
The measure of angle B is x, while the measure of angle A is 2·x. The 70° measure of angle C and the angle sum property of the interior angles of a triangle indicates that angle B is [tex]36.\overline 6^{\circ}[/tex] and angle A is [tex]73.\overline 3^{\circ}[/tex]
What are the interior angles of a triangle?The interior angles of a triangle are the angles formed by the sides sides of the triangle.
The question can be solved by making use of the known properties of a triangle.
The angle sum property of the interior angles in a triangle gives;
The sum of the interior angles of a triangle is 180°
Therefore; x + 2·x + 70 = 180
3·x = 180° - 70° = 110°
[tex]x = \dfrac{110^{\circ}}{3} = 36\frac{2}{3} ^{\circ}[/tex]
The measure of angle A is 2·x
Which gives;
[tex]A = 2 \times 36\frac{2}{3} ^{\circ} = 73\frac{1}{3} ^{\circ} = 73.\overline 3^{\circ}[/tex]
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Natalie has a budget of $15,000 dollars to spend on tracking devices to study bison. A radio tracker costs $650 and a GPS tracker costs $1400. Natalie wants to buy at least 9 radio trackers and more than 3 GPS trackers. The following system of inequalities represents this situation, where x is the number of radio trackers and y is the number of GPS trackers. x ≥ 9 y > 3 650x + 1400y ≤ 15000
The inequality as per the question is x ≥ 9 and y > 3 and the diagram according to this is attached below.
What is an equality?Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare the two values. Less than (or less than and equal to), larger than (or greater or equal to), or not similar to signs are used in place of the equal sign in between.
As per the given information in the question.,
x ≥ 9 and,
y > 3
The equation is,
650 x + 1400 y ≤ 1
[tex]\frac{x/15000}{650}+\frac{y/15000}{1400} \leq 1[/tex]
x/23.07 + y/10.71 ≤ 1
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what is (x+5)……………
……….:…………
Answer:
x+5
Step-by-step explanation:
there are no like terms
What is/are the effects when you perform the following transformations on your figure?
a. Reflections –
b. Translations –
c. Rotations –
d. Dilations –
Answer:
A. REFLECTION
Please guys do some research i know you're not that stu p id-_-
m∠M = 6x – 6 and m∠P = 4x + 10, what is m∠M?
a) Find the circumference of a circle whose radius is 4 inches. Round to the nearest tenth.
b) Find the length of if mACB = 60º and the radius of the circle is 4 inches. Round to the nearest tenth.
Complete your work in the space provided.
The circumference of the circle is 25.1 inches.
The length of the arc ACB is 4.2 inches.
How to find circumference of a circle?The circumference of a circle is the perimeter of the circle.
Therefore,
circumference of a circle = 2πr
where
r = radiusHence,
circumference of a circle = 2 × 3.14 × 4
circumference of a circle = 8 × 3.14
circumference of a circle = 25.1 inches
The length of the arc ACB can be found as follows:
length of arc = ∅/ 360 × 2πr
length of the arc = 60 / 360 × 2 × 3.14 × 4
length of the arc = 60 / 360 × 25.12
length of the arc = 1507.2 / 360
length of the arc = 4.18666666667
length of the arc = 4.2 inches
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What is the y-intercept of the graph shown?
Responses
b=2b
b=−2b
b=−3b
b=3b
The y-intercept of the graph as shown is 2.
How to find the y-intercept of a line?The equation of a line can be represented as follows:
y = mx + b
where
m = slopeb = y-interceptThe y-intercept is the point where the graph intersects the y-axis. In other words, it is the value of y when x = 0 .
Therefore, let's trace the value of y when x = 0 on the graph.
Hence, when x = 0, y = 2
Therefore,
b = y-intercept = 2
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Answer:b=2b
b=−2b
b=−3b
b=3b
Step-by-step explanation: because I tought myself i know
What is the image point of (2,0)(2,0) after the transformation D_{\frac{1}{2}}\circ R_{270^{\circ}}D
2
1
∘R
270
∘
The image of point (2,0) after the transformation involving the dilation and the rotation is given as follows:
(0, -1).
What are the transformations applied to the point?The first transformation applied to the point is a dilation, which multiplies the coordinates of the point by the scale factor.
The point has these following coordinates:
(2,0).
The scale factor of the dilation is:
k = 1/2 = 0.5.
Then each coordinate of the point is multiplied by 0.5, hence:
2 x 0.5 = 1.0 x 0.5 = 0.Hence the coordinates are:
(1,0).
The rule for a rotation of 270º clockwise around the origin is:
(x,y) -> (y,-x).
Then:
x = 1, -x = -1.y = 0.Thus the coordinates of the image are given as follows:
(0, -1).
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what percent is 25 of 100
if we take 25 to be the 100%, what is 100 off of it in percentage?
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 25 & 100\\ 100& x \end{array} \implies \cfrac{25}{100}~~=~~\cfrac{100}{x} \\\\\\ \cfrac{1}{4}=\cfrac{100}{x}\implies x=400[/tex]
Answer:
25
Step-by-step explanation:
25/100=.25x100=25
The statement 4 less than a number is given w
The equation representing the statement - "4 less than a number is given w" as -
[w] = x where x ∈ (- ∞, 4)
What is Equation Modelling?
Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
We have the following statement - "4 less than a number is given w".
Assume the number to be [x].
We can write the equation representing the statement -
"4 less than a number is given w" as a mathematical expression as -
[w] = x where x ∈ (- ∞, 4)
Therefore, the equation representing the statement - "4 less than a number is given w" as -
[w] = x where x ∈ (- ∞, 4)
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Simple random sampling uses a sample size of n from a population of size N to obtain data that can be sued to make inferences about the characteristics of a population. Suppose that, from a population of 50 bank accounts, we want to take a random sample of four accounts in order to learn about the population. How many different random samples of four accounts are possible?
If from a population of 50 bank accounts, we want to take a random sample of four accounts in order to learn about the population. The number of different random samples of four accounts that are possible is 230,300.
How to find the different random samples?Given data:
Number of population of bank account = 50
Random sample = 4 accounts
Now let find the different random samples of four account that are possible
Different random sample = 50! / (50 -4)! × 4!
Different random sample = 50! / 46! × 4!
Different random sample = 230,300
Therefore the different random samples is 230,300.
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Simon uses 121 one-inch tiles to make his square mosaic. What is the length of one side of his mosaic?
The graph below shows the daily low temperatures for one week in New Orleans, Louisiana. The shape of the temperature graph can be modeled by the quadratic function f (x) = 3x² 18x + 56, where 2 is the number of days starting Sunday, and f (2) is the temperature in Fahrenheit. Degrees Fahrenheit 60 50 40 30 20 10 0 - Sun. Mon. Tues Wed. Thu. Fri. Sat. a. Use the given quadratic function to approximate the temperature on Thursday. How does this approximation agree with the graph? b. Use the function and the quadratic formula to find when the temperature is 35 degrees Fahrenhait. (Hint: Set f (x) = 35 and solve.) Round the answer to one decimal place and interpret the decimal in terms of weekday and military time.
a. The numeric value at Thursday -> x = 4 is of 32 degrees, which agrees with the graph.
b. A numeric value of 35 degrees Fahrenheit is obtained on Monday and on Thursday, also agreeing with the graph.
How to obtain the numeric value of a function or of an expression?To obtain the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.
In this problem, the function is defined as follows:
f(x) = 3x² - 18x + 56.
Giving the temperature in degrees Fahrenheit in x days after Sunday.
The day that represents Thursday is given by:
x = 4.
Hence the temperature is the numeric value of the function at x = 4, replacing both instances of x on the function by 4, hence:
f(4) = 3(4)² - 18(4) + 56 = 32 ºF.
Which agrees with the graph, as the Thursday's bar is a value slightly above 30, which can be interpreted as 32.
The numeric value is of 35 when:
3x² - 18x + 56 = 35
The solutions to the quadratic equation are:
x = 1.6, x = 4.4.
Hence the days are:
Monday and Thursday.
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Please Help
Find (f+g)(x)if f(x)=4x2-5x+8 and g(x)=2x2+x-2
Answer: (f+g)(x) = 6x²- 4x + 6
Step-by-step explanation:
We add f(x) and g(x) together, (4x²-5x+8) + (2x²+x-2)
Add like terms together, (4x²+2x²) + (-5x+x) +(8-2)
We are left with (f+g)(x) = 6x²- 4x + 6
If V is the midpoint of WY, VY=29-4x, and WY=5x+19, find WV.
The value of WV is 9x - 10
What is line segment?A line segment can be defined as the part of a straight line which is bound by two distinct end points, and is known to be made up of every point on the line that between its endpoints.
From the information given, we can say that WY is a line with V as its midpoint with segments WV and VY.
We have;
VY=29-4x WY=5x+19This is represented as;
WV + VY = WY
Then;
WV = WY - VY
substitute the values
WV = 5x + 19 - (29 - 4x)
expand the bracket
WV = 5x + 19 - 29 + 4x
collect like terms
WV = 9x - 10
Hence, the value is 9x - 10
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A standard deck of playing cards has 4 different suits (hearts, spades, clubs and diamonds) and 13 different ranks for the cards (ace, 2-10, jack, queen, king). In a poker game you are dealt a hand of 5 cards.
How many ways are there to get dealt exactly a single pair? A pair is a hand with two cards of the same rank. (so two pairs, three of a kind, four of a kind, full house etc. aren't included)
The number of ways that there are to get dealt exactly a single pair is; 6,589,440 ways
What is the probability of Selection?The combination in probability selection is defined as a method where we count the number of ways a certain number of objects can be arranged in "n" different ways. If the number of different objects are "n", then it means that the number of ways that we can select "r" number of different objects is expressed as:
nCr = n!/(r!(n - r)!)
The total number of cards that we have in a deck of cards = 52.
There total number of different cards are 13 in number and this tells us that we can possibly have a pair of any one of the 13 cards. There are also 4 cards of the same rank and this means that the number of ways of selecting two cards of the same rank is; 4C2 = 6 ways
After selecting a card for the pair, we have 48 different cards as an option for the third card. Thereafter, we will have a total of 44 cards as an option for the fourth card and then 40 cards will be an option for the fifth card (due to the fact that none of the cards can be of same rank except for the pair of cards).
Therefore, the total number of ways that we can deal with exactly a single pair can be expressed as:
Number of ways = number of ways for the pair × number of ways for the third card × number of ways for the fourth card × number of ways for the fifth card
Plugging in the relevant values gives;
Number of ways = (13 × 6) × 48 × 44 × 40
= 6,589,440 ways
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Need help with question 2b please
Answer:
20 mph
Step-by-step explanation:
If it took the car originally 12 minutes to travel the road with an average speed of 60 mph. Than you would just divide the average speed by three because it is taking 3 times the amount of time than it would originally.
36/12=3
60/3=20
20 mph
Ms. Jones washed
2
7
of her laundry. Her son washed
1
3
of it. Who washed most of the laundry? How much of the laundry still needs to be washed?
What is the sum of −12, 5, and −10?
(A) −27
(B) −17
(C) 17
(D) 27
If P= (2, 7) and Q= (2, -3), which could be the coordinates of R if triangle PQR is isosceles?
If P= (2, 7) and Q= (2, -3), then for triangle to be isosceles coordinate of R must be 2
Let coordinates
P = (2, 7) and Q = (2, -3)
PR = QR
(X-2)^2 +(Y-7)^2 = (X-2)^2 + {Y-(-3)}^2
(Y-7) = {Y - (-3)}^2. or y - 7 = ±(Y
or Y^2 - 14Y + 49 = Y^2 + 6Y + 9
20Y = 40
Y=2
coordinates of R if triangle PQR is isosceles ;
Hence any point R on the line Y = 2 will make PQR a isosceles triangle
with PR = QR.
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Arianys runs a farm stand that sells grapes
and apples. Each pound of grapes sells for
$3.75 and each pound of apples sells for
$4. Arianys made $251.75 from selling a
total of 64 pounds of grapes and apples.
Determine the number of pounds of
grapes sold and the number of pounds of
apples sold.
The number of pounds of grapes sold is 17 pounds and the number of pounds of apples sold is 47 pounds.
According to the question,
We have the following information:
Cost of 1 pound of grapes = $3.75
Cost of 1 pound of apples = $4
Total cost made by selling = $251.75
And the weight of the apples and grapes sold = 64
Now, let's take the weight of grapes to be x pounds and the weight of apples to be y pounds.
So, we have:
x+y = 64
x = 64-y ....(1)
3.75x+4y = 251.75
Putting the value of x in this equation:
3.75(64-y)+4y = 251.75
3.75*64-3.75y+4y = 251.75
240+0.25y = 251.75
0.25y = 251.75-240
0.25y = 11.75
y = 11.75/0.25
y = 47 pounds
Now, putting this value of y in equation 1:
x = 64-y
x = 64-47
x = 17 pounds
Hence, the number of pounds of grapes sold is 17 pounds and the number of pounds of apples sold is 47 pounds.
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No one bothers to help, plsssssssssss!!!!!!!!!!!!!!!!!!!!!!!
slope-related question image pasted below!!!
Answer:
I'm not sure if its right but I got
6/9
Step-by-step explanation:
What I did was:
I took the 2 points:
(-4,4) and (5,-2)
Then did rise over run
Which left me with 6/9
reduce 12/16 to simplest terms
Answer: 3/4
Step-by-step explanation:
Find the GCD (or HCF) of numerator and denominator
GCD of 12 and 16 is 4
Divide both the numerator and denominator by the GCD
12 ÷ 4
16 ÷ 4
Reduced fraction: 3/4
Therefore, 12/16 simplified to lowest terms is 3/4.
Answer:.
Step-by-step explanation:
the table shows the number of pounds that 10 students in gary langs weight training class could bench press and squat. make a scatterplot to display the relationship between the bench press and squat weights for this sample. (use squat as the explanatory variable). describe the relationship shown in the scatterplot
The scatter plot that displays the relationship between the bench press and squat weights for this sample is given by the second image at the end of the answer.
From the scatter plot, it can be taken that the relationship is that the variables have a positive association, as when the bench press weight increases, so does the squat weight. The relationship, however, is not strong, as the scatter plot is not 100% increasing.
How to built the scatter plot?The scatter plot is built inserting all the points of the table in a graph, which are in the following input-output format:
(bench press weight, squat weight).
From the table given by the first image at the end of the answer, the points are listed as follows:
(95, 141), (111, 208), (113, 100), (125, 218), (135, 284), (145, 275), (165, 338), (180, 338), (140, 420), (196, 420), (95, 141), (111, 208).
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