Answer:
[tex] \sqrt{32 \div 2 = } 82 \\ [/tex]
Find the values of the numbers m and n that will make (2x + m)2 = 4x2 + nx + 9 true, given
that both m and n are positive numbers.
The values of the numbers m and n that makes the given expression true are 3 and 12 respectively
Solving an equationFrom the question, we are to determine the values of the numbers m and n that will make the given expression true
The given expression is
(2x + m)² = 4x² + nx + 9
Opening the bracket on the left hand side,
(2x + m)²
(2x + m)(2x + m)
4x² + 2mx + 2mx + m²
4x² + 4mx + m²
∴ 4x² + 4mx + m² = 4x² + nx + 9
By comparing,
4mx = nx;
Then, 4m = n
and
m² = 9
∴ m = ±√9
m = ±3
Since we are given that both m and n are positive numbers,
∴ m = 3
Substitute the value of m into the equation, 4m = n
4×3 = n
∴ n = 12
Hence, the values of the numbers m and n that makes the given expression true are 3 and 12 respectively
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Select either relation (if the set is a relation but not a function), function (if the set is both a relation and a function), or
nelther (If the set is not a relation).
A={(1, 2) (2, 2) (3, 2) (4, 2)
A. Function
B. Relation
C. Neither
Answer:
C neither
the coordinates shows that only the x intercepts are moving not y the line of the graph will be horizontal and straight . it is not a function
I already answered one please answer the rest
Which would indicate the water in a lake is not safe for drinking
Answer:
The water in a lake is not safe for drinking, high turbidity levels in the lake Coliform bacteria occur innately in soil and in the intestines of humans and other organism.
CORRECT ANSWER: high turbidity levels in the lake.
Step-by-step explanation:
Bag contains fewer than 90 lollipops it is possible to evenly divide all of the lollipops among 2, or 6, or 7 children. how many lollipops are in the bag? list all possible answers
Find the area of a circle with an arc length of 4π and a central angle of 45 degrees. Leave the answer in terms of π.
[tex]~~~~~~\text{Arc length} = r \theta \\\\\implies 4\pi = r\left( 45 \times \dfrac{\pi}{180} \right)~~~~~~~~;[\theta ~ \text{is in radians.}]\\\\\implies 4 = \dfrac{45r}{180}\\\\\implies 45r = 180 \times 4 = 720\\\\\implies r = \dfrac{720}{45}\\\\\implies r = 16~ \text{units.}\\\\\text{Now,}\\\\\text{Area} = \pi r^2\\\\~~~~~~~=\pi \cdot 16^2\\\\~~~~~~~=256\pi~ \text{units}^2[/tex]
CAN SOMEONE HELP ME PLEASE
Answer:
13.9
Step-by-step explanation:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Find the difference between coordinates:
(x2 - x1) = (-5 - 0) = -5
(y2 - y1) = (-3 - 10) = -13
Square the results and sum them up:
(-5)^2 + (-13)^2 = 25 + 169 = 194
Now Find the square root and that's your result:
Exact solution: √194
Approximate solution: 13.9284
Can this please be worked out so I can have a better understanding?
Given the equation (picture 1)
and using the formula(picture 2)
find A, B, and C
Please if take your time to break it down for me so I can use it as a guide for the rest of the test!!! Thx <3 :)
Step-by-step explanation:
no, no, you use the equation to identify a, b and c.
then you use the formula with these values to get the solutions to the equation (the values of x for which the equation delivers 0).
always remember, a quadratic equation always has 2 solutions. sometimes at least one of them are not a real number, sometimes the 2 springs are equal, ...
x² - 4x - 2 = 0
a, b, c are the factors of the terms in x and the constant term.
so,
a = 1
b = -4
c = -2
x = (-b ± sqrt(b² - 4ac))/(2a)
x = (4 ± sqrt((-4)² - 4×1×-2))/(2×1) =
= (4 ± sqrt(16 + 8))/2 = (4 ± sqrt(24))/2 =
= (4 ± sqrt(4×6))/2 = (4 ± 2×sqrt(6)) / 2 =
= 2 ± sqrt(6)
x1 = 2 + sqrt(6)
x2 = 2 - sqrt(6)
Answer:
x = 4.45 and x=-0.45
Step-by-step explanation:
A = 1
B= -4
C = -2
= [tex]\frac{-(-4) \sqrt{ (-4)^{2} -4 (1)(-2) } }{2(1)}[/tex]
= [tex]\frac{4\sqrt{16+8} }{2}[/tex]
= [tex]\frac{4\sqrt{24} }{2}[/tex]
X = 4 + [tex]\sqrt{24}[/tex] / 2
x = 4.45
For x2
x= 4 - [tex]\sqrt{24}[/tex] / 2
x=-0.45
The volume of the prism is 275 cm³ the area of the base of the prism is 25 square centimeters what is the height of the prism
Answer:
11
Step-by-step explanation:
volume of a prism = area of base × height
plug in what we are given
volume = 275cm³area of base = 25cm²275 = 25 × height
==> divide both sides by 25
11 = height
Which situation can be represented by the inequality 150 ≤ 15x + 55 ?
a. Thomas has 15 baseball cards in his collection. He will buy 55 new ones every month. Thomas collects baseball cards for x months. For what values of x will Thomas have at most 150 baseball cards?
b. Thomas has 15 baseball cards in his collection. He will buy 55 new ones every month. Thomas collects baseball cards for x months. For what values of x will Thomas have at least
150 baseball cards?
c. Thomas has 55 baseball cards in his collection. He will buy 15 new ones every month. Thomas collects baseball cards for x months. For what values of x will Thomas have at most 150 baseball cards?
d. Thomas has 55 baseball cards in his collection. He will buy 15 new ones every month. Thomas collects baseball cards for x months. For what values of x will Thomas have at least 150 baseball cards?
Inequalities help us to compare two unequal expressions. The correct option is C.
What are inequalities?Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed.
It is mostly denoted by the symbol <, >, ≤, and ≥.
The situation that can be represented by the inequality 150 ≤ 15x + 55 is Thomas has 55 baseball cards in his collection. He will buy 15 new ones every month. Thomas collects baseball cards for x months. For what values of x will Thomas have at most 150 baseball cards?
Hence, the correct option is C.
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write 13/20 fraction to percent
On World Environment day, Class-9 students bought five plants of mango, silver oak, orange, banyan, and
Amla from the soil department. They plotted where to plant these trees and noted the locations as (x, y).
Then the group leader was then assigned to join these points in the given order.
(iv) Which of the following trees are planted exactly in the x - axis?
(a) Amla and Mango
(b) Orange and Amla
(c) Orange and mango
(d) Silver Oak and Banyan
Based on the points given about the locations these trees are planted, the trees that will be planted exactly on the x-axis are (a) Amla and Mango.
Which trees will be on the x-axis?When plotting a line on a graph, the points that will be found on the x-axis are those that will have a y coordinate of 0.
From the table given, both Mango and Amla have y coordinates of 0 which means that they will be planted exactly on the x-axis.
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Find the vertex. f(x) = 9x2 + 1
Answer:
vertex = (0, 1 )
Step-by-step explanation:
f(x) = 9x² + 1 ← has it's vertex on the y- axis
let x = 0 in f(x)
f(0) = 9(0)² + 1 = 0 + 1 = 1
vertex = (0, 1 )
Given zy = 4 and x² + y² = a, which expression is equal to (x + y)²?
The value of the given expression will be equal to ( x + y )² = a + 8.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.
Given that:-
xy = 4 and x² + y² = aThe expression will be calculated as:-
( x + y )² = x² + y² + 2 xy
( x + y )² = a + 2 x ( 4 )
( x + y )² = a + 8
Therefore the value of the given expression will be equal to ( x + y )² = a + 8.
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The volume of an aquarium is 4,000 cubic feet and has a height of 10 ft. if a similar aquarium has a height of 1 foot, how many cubic feet would the smaller aquarium hold
The volume that the similar aquarium will hold is 400 cubic feet
Similar figuresSimilar figures are figures that have similar angles and sides.
Given the following parameters
volume of aquarium = 4000 cubic feetheight of aquarium = 10feetheight of similar aquarium = 1 feetRequiredVolume of similar aquarium
Substitute into the formula
V/H = v/h
4000/10 = v/1
400 = v
v = 400 cubic feet
Hence the volume that the similar aquarium will hold is 400 cubic feet
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17. A glider lands 26 miles west and 12 miles south from where it took off. The result of the trip
can be described by the vector (-26, -12).
What is another description of this vector using distance (for magnitude) and direction?
about 29 miles at 25° south of west
about 25 miles at 29° south of east
about 29 miles at 25° south of east
about 25 miles at 29° south of west
By finding the magnitude and bearing, we conclude that the correct option is:
"about 29 miles at 25° south of west"
How to write the vector in polar coordinates?For a vector (x, y), the polar coordinates are the magnitude R and the bearing θ.
Such that:
[tex]R = \sqrt{x^2 + y^2} \\\\\theta = Atan(y/x)[/tex]
In this case, the original vector is (-26, -12), replacing that we get:
[tex]R = \sqrt{(-26)^2 + (-12)^2} = 28.6 \\\\\theta = Atan(-12/-26) = 24.7\°[/tex]
Where the angle is measured from the negative x-axis counterclockwise, so it is South of West.
Then we can describe this vector as:
"About 29 miles at 25° south of west".
The first option is the correct one.
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The midpoint of overline AB is M(-4, -3). If the coordinates of A are (-1, -2) what are the coordinates of B?
Answer:
(-2.5,-2.5)
Step-by-step explanation:
(-4+-1)÷2=-2.5
(-3+-2)÷2=-2.5
Answer:
(-7, -4)
Step-by-step explanation:
Equating A and B to the Midpoint (M) :
(-4, -3) = (-1 + x / 2, -2 + y / 2)Equations formed :
-1 + x / 2 = -4-1 + x = -8x = -72. -2 + y / 2 = -3
-2 + y = -6y = -4Coordinates of B :
(x, y)(-7, -4)The following data points represent the number of quesadillas each person at Toby's Tacos ate.
Sort the data from least to greatest.
0,0, 1/2, 1/2, 1/4, 1, 1, 1, 5/4, 2, 2.
What is the interquartile range of this data?β
The interquartile range for the given data is 1 quesadilla.
What is the interquartile range?The interquartile range is a measurement of a data set's "middle fifty." A range is a measurement of where a set's beginning and end are located.
To get the interquartile range, we must know the first and third quartiles. To find those, we need to know the median of the data.
There are 11 data points, so we can cross out 5 numbers on the left and cross out 5 numbers on the right. That leaves a median of 1.
Since we know the median is 1, we can find the first quartile by finding the median of the following numbers:
0, 0, 1/4, 1/2, 1/2 (any number less than 1).
There are five numbers, so cross out two numbers from the left and cross out two numbers from the right. We are left with the first quartile of 1/4.
Now that we have the first quartile, we need to find the third quartile. Since the median was actually the first "1" in the data set, the third quartile will be the median of the numbers to the right of that "
1: 1, 1, 5/4, 2, 2.
Cross out the leftmost two numbers, and cross out the rightmost two numbers. We are left with the third quartile of 5/4.
Now that we have both the third and first quartiles, we can find the interquartile range! The IQR is calculated by finding the third quartile minus the first quartile.
5/4 - 1/4 = 4/4 = 1.
Therefore, the interquartile range is 1 quesadilla.
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Which equation is the inverse of y = x2 – 36? y = plus-or-minus startroot x endroot 6 y = plus-or-minus startroot x 36 endroot y = plus-or-minus startroot x endroot 36 y = plus-or-minus startroot x squared 36 endroot
The inverse of the given function is expressed as y = ±√x + 38
Inverse of an equationGiven the equation below expressed as:
y = x² - 36
Replace y with x
x = y² - 38
Add 38 to both sides of the equation
x + 38 = y² - 38 + 38
y² = x + 38
Take the square root of both sides
√y² = ±√x + 38
y = ±√x + 38
Hence the inverse of the given function is expressed as y = ±√x + 38
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Answer:
B on edge 2022
Step-by-step explanation:
took the quiz
A ball is dropped from a height of 600 feet. The function describing the height of the ball at t seconds after it dropped is [tex]f(t)=-16t^2+600[/tex].
a) Find the average velocity of the object during the first 3 seconds.
b) Verify that at some time during the first 3 seconds the instantaneous velocity equals the average velocity. Find that time.
The average velocity: _ ft/sec
The instantaneous velocity equals to the average velocity at t = _ sec
The average velocity of the object after during the first three seconds is: 48m/s
The time at which the instantaneous velocity equals the average velocity within the first three seconds is 1.5 seconds.
What is instantaneous and average velocities?Instantaneous velocity is the speed of an object at a particular point in time.
Average velocity is the velocity of an object after covering a certain distance for a period of time
Analysis:
Given
initial height = 600 feet
Height with respect to time = f(t) = -16[tex]t^{2}[/tex] + 600
a) Height at t = 0 = 600 feet
Height at t = 3 seconds = f(3) = -16[tex](3)^{2}[/tex] + 600 = 456 feet
Distance travelled = 600 - 456 = 144 feet
Average velocity = distance travelled/time taken = 144/3 = 48 feet/seconds
b) instantaneous velocity at time t = [tex]\frac{df(t)}{dt}[/tex] = [tex]\frac{d(-16t^{2} + 600) }{dt}[/tex] = -32t
when instantaneous velocity equal average velocity
-32t = -48
t = 1.5 seconds
In conclusion, the Average velocity after 3 seconds is 48 feet per seconds and the time taken for the average velocity to equal the instantaneous velocity is 1.5 seconds.
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Find (a) arc length and (b) Area of a sector.
Answer:
a) 38.40 yd (2 dp)
b) 211.18 yd² (2 dp)
Step-by-step explanation:
Formula
[tex]\textsf{Arc length}=2 \pi r\left(\dfrac{\theta}{360^{\circ}}\right)[/tex]
[tex]\textsf{Area of a sector}=\left(\dfrac{\theta}{360^{\circ}}\right) \pi r^2[/tex]
[tex]\quad \textsf{(where r is the radius and}\:\theta\:{\textsf{is the angle in degrees)}[/tex]
Calculation
Given:
[tex]\theta[/tex] = 200°r = 11 yd[tex]\begin{aligned}\implies \textsf{Arc length} &=2 \pi (11)\left(\dfrac{200^{\circ}}{360^{\circ}}\right)\\ & = 22 \pi \left(\dfrac{5}{9}\right)\\ & = \dfrac{110}{9} \pi \\ & = 38.40\: \sf yd \:(2\:dp)\end{aligned}[/tex]
[tex]\begin{aligned} \implies \textsf{Area of a sector}& =\left(\dfrac{200^{\circ}}{360^{\circ}}\right) \pi (11)^2\\& = \left(\dfrac{5}{9}\right)\pi \cdot 121\\& = \dfrac{605}{9} \pi\\& = 211.18\: \sf yd^2 \:(2\:dp)\end{aligned}[/tex]
Please note: As you have not specified if π should be approximated, I have not used an approximation for π.
The nearest-known exoplanet from earth is 4.25 light-years away.
about how many miles is this?
give your answer in standard form.
Answer:
24 trillion miles. The nearest-known exoplanet is a small, probably rocky planet orbiting Proxima Centauri – the next star over from Earth. A little more than four light-years away, or 24 trillion miles.
The number of miles in 4.25 light-years will be 24.986 × 10¹² miles.
What is conversion?Conversion means to convert the same thing into different units.
The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.
The nearest-known exoplanet from the earth is 4.25 light-years away.
We know that 1 lightyear = 5.879 × 10¹² miles.
Then the number of miles in 4.25 light-years will be
⇒ 4.25 light-years
⇒ 4.25 × 5.879 × 10¹² miles
⇒ 24.986 × 10¹² miles
The number of miles in 4.25 light-years will be 24.986 × 10¹² miles.
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If the perimeter of a pool is 102ft, and the length is 6 more than twice the width, what are the dimensions?
Nick has a rope that is 3 1/4 yards long. He cuts off a piece of the rope so that it is now 5/9 as long as the original rope? What is the length of his rope now?
The length of the rope remaining after Nick cut off a piece of the rope is 1 29/36 yards
How to solve fractionsTotal length of Nick's rope = 3 1/4 yardsLength remaining = 5/9 of original length
5/9 of 3 1/4
= 5/9 × 13/4
= 65/36
= 1 29/36 yards
Therefore, the length of the rope remaining after Nick ncur off a piece of the rope is 1 29/36 yards
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There are 90 people going on this feild trip. The budget allows for $542.94 total for tickets to the Buccaneers game. There is a service fee of $45.82. How much does each ticket cost?
does someone know this answer
Help me with this question please
Answer:
∠A≅∠X AB≅XZ
∠B≅∠Z AC≅XY
∠C≅∠Y BC≅ZY
ΔABC≅ΔZYX
Step-by-step explanation:
congruent is identical in form so if the angle has one dash than look for the identical version on the other triangle
HELP IM STUCK ON THIS
Answer: Let's just say that each of the units are 1 inch in sides, and since it's an irregular shape you have to separate each shape. So, the rectangle I separated is 14 inches.
The semicircle is 12.56.
Adding those two answers together comes out to 26.56.
which represents possible choices for the third missing side of the triangles given the other two sides?
1st side 30ft
2nd side 21ft
answer choices
a 9ft<51ft
b 9ft
c 30ft
d 0ft
Based on the triangle inequality theorem, the possible length of the third side of the triangle is: 9 < x < 51
What is the Triangle Inequality Theorem?The triangle inequality theorem states if a and b are two sides of a triangle, the possible length of the third side would be: a + b < x < a - b.
Two given sides of the triangle are 30 ft and 21 ft. The possible length of the third side of the triangle would be:
30 - 21 < x < 30 + 21
9 < x < 51
Possible length of the third side would range between: 9 < x < 51
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-
X
o
1
2
3
4
5
6
Y
4.1 -0.9 -3.9 -5.1 -4.1
-4.1 -1.1 4.1
Use the data in the chart. Fill in the blanks to write a quadratic regression equation
that looks like y =
x² +
_xt
ટ
Use the Desmos graphing calculator and round each coefficient in the equation to
the nearest thousandth.
Enter your answers (numbers only) in the boxes. Do not use spaces. Be sure to type a
negative sign if needed on your coefficient.
The quadratic regression equation of the table of values is y = 0.71x² - 5.04x + 3.76
How to determine the regression equation?The table of values is given as:
x: 0 1 2 3 4 5 6
y: 4.1 -0.9 -3.9 -5.1 -4.1 -4.1 -1.1
To determine the quadratic regression equation, we make use of a graphing calculator
From the graphing calculator, we have the following calculation summary:
a = 0.7, b = -5.04 and c = 3.76
A quadratic regression equation is represented as:
y = ax² + bx + c
Hence, the quadratic regression equation of the table of values is y = 0.71x² - 5.04x + 3.76
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