The midpoint of the segment joining points (a,b) and (j,k) is, (a+j)/2, (b+k)/2)
The midpoint of the segment joining two points (x1, y1) and (x2, y2) is given by the point ((x1 + x2)/2, (y1 + y2)/2).
So, to find the midpoint of the segment joining the points (a, b) and (j, k), we need to take the average of the x-coordinates and the average of the y-coordinates:
((a + j)/2, (b + k)/2)
So the midpoint of the segment joining points (a,b) and (j,k) is (a+j)/2, (b+k)/2).
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A roller coaster’s height is given by the equation h = –.025t2 + 4t + 50, where t represents the time in seconds. How long will it take riders to pass over the hill and reach ground level? Hint: Set h = 0.
11.65 seconds
50.00 seconds
171.65 seconds
210.00 seconds
The time it will take the roller coaster to reach the ground is 171.65 seconds
Function and valuesGiven the roller coaster’s height given by the following parameters
h = –0.025t² + 4t + 50
On the ground level, the height will be zero. Substitute h = 0 and determine the value of t
–0.025t² + 4t + 50 = 0
0.025t² - 4t - 50 = 0
Factorize
On factorizing the time it will take the roller coaster to reach the ground is 171.65 seconds
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m∠ __ +m∠BPD=180∘
what is the blank for Linear Pairs
The blank space to form a linear pair with m∠BPD is m∠APD.
What are linear pair angles?Linear pair of angles are formed when two lines intersect each other at a single point.
Linear pair angles are adjacent to each other.
Therefore, the sum of a linear pair angles is equals to 180 degrees.
This means linear pair angles are supplementary.
Hence,
m∠APD + m∠BPD = 180°
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Find the slope between the two points given. Then, use the slope and one of the points to write the
equation of the line in Slope-Intercept form. State the slope and y-intercept.
Answer:
The slope is -2
y =-2x - 1
Step-by-step explanation:
The slope is -2 or -2/1.
The slope is the change in y over the change in x. The ordered pair is written in the form (x,y) The first number is the x coordinate and the second number is the y coordinate.
(1, -3) (0, -1) The -1 and the -3 are the y coordinates. We subtract these.
-1 -(-3) is the same as
- 1 + 3 which is 2.
(1, -3) (0, 1,) the 1 and the 0 are the x coordinates. We subtract these
0 - 1 is -1
The change in y is 2 and the change in x is -1, so our slope is -2/1 which is the same as -2.
To write the equation we need the slope and the y intercept. We have the slope now. We need to find the y-intercept. We will use the slope and one of the points to find the y-intercept. It does not matter which of the two points (1,-3) or (0,-1). I will use (0,-1)
y = mx + b The b is the y-intercept which is what we are looking for
-1 = -2(0) + b
-1 = 0 + b
-1 = b
y = -2x -1
please solve this
Solve by completing the square. 4x2+8x−3=0
Step-by-step explanation:
4x2+8x−3=0
For this equation: a=4, b=8, c=-3
4x2+8x+−3=0
Step 1: Use quadratic formula with a=4, b=8, c=-3.
x=
−b±√b2−4ac
2a
x= −(8)±√(8)2−4(4)(−3)
2(4)
x= −8±√112
8 x=−1+
1 2 √7 or x=−1+
−1 2 √7
Answer: x=−1+
1 2√7 or x=−1+
−1 2 √7
What’s the volume of a rectangle solid with the given dimensions: length 20, width 23, height 26
The volume of the rectangular solid is: 11,960 units³.
How to Find the Volume of a Rectangular Solid?The formula to find the volume of a rectangular solid is: (length)(width)(height).
Given the dimensions as:
Length = 20 unitsWidth = 23 unitsHeight = 26 unitsVolume = (20)(23)(26)
Volume of the rectangular solid = 11,960 units³.
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Educators should ensure math instruction is only taught through structured activities rather than through everyday situations and routines.
A- True
B- False
The statement ' educators should ensure math instruction is only taught through structured activities rather than through everyday situations and routines is True. Option A
Ways to improve mathematics education
They include;
Using hands-on learning methodsUsing visualsIntegration of mathematics gameConnecting math concepts to everyday lifeAllow students to explain their reasoningRewarding students progressThus, the statement ' educators should ensure math instruction is only taught through structured activities rather than through everyday situations and routines is True. Option A
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Answer:
Step-by-step explanation:
false
explain me the formula for a point that forms a partiton of a ratio on a segment in the 2nd grade real numbers.
Let’s say the ratio a:b, our formula those becomes
{(bx1 + ax2)/(a + b) ,( by1+ay2)/a+b}
From the question, we can identify that
(x1,y1) = (-6,-1)
(x2,y2) = (4,8)
a = 1 and b = 3
The partition point is (-7/2, 23/4)
How to determine the partition point?The given parameters are:
(x1,y1) = (-6,-1)
(x2,y2) = (4,8)
a = 1 and b = 3
The partition point is calculated as:
(x, y) = ((bx1 + ax2)/(a + b) ,( by1+ay2)/a+b)
So, we have:
(x, y) = ((3 * -6 + 1 * 4)/(1 + 3) ,(3 * 8 + 1 * -1)/1+3)
Evaluate
(x, y) = (-14/4, 23/4)
Simplify
(x, y) = (-7/2, 23/4)
Hence, the partition point is (-7/2, 23/4)
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90% of the flights that left a certain airport yesterday departed on time. If there were 150 flights from the airport yesterday, how many flights DID depart on time
giving brainliest!!!!!!!!!!!!!!!!!!!!!
Answer:
The function has 4 roots.
Step-by-step explanation:
Since the degree of the polynomial has is 4, there are a total of 4 roots (both real and complex).
Answer:
4 roots, two real and two complex.
Step-by-step explanation:
The degree of the polynomial indicates the number of solutions
Hope this helps
Answer to the question on the image attached to this thread. Thank you!
The solution of the system of equation of the matrix is as follows:
x = - 8
y = 3
How to find the solution of matrix?3x + 10y = 6
x + 3y = 1
multiply equation(ii) by 3
3x + 10y = 6
3x + 9y = 3
Therefore,
y = 3
Hence,
x + 3y = 1
x + 3(3) = 1
x + 9 = 1
x = 1 - 9
x = -8
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1. Determine the
square units of the
figure below.
Answer:
10
Step-by-step explanation:
In the diagram the origin is at the center of a cube that has edges 6 units long. The x-,y-, and z-axes are perpendicular to the faces of the cube give the coordinates of the corner at point A.
Answer:
the third answer (-3, -3, 3)
Step-by-step explanation:
the dotted lines indicate that these lines (or part of lines) are invisible due to being inside or behind the cube.
so, we know that A is the left-back-upper corner of the cube.
the x-axis goes front-back. front is positive.
the y-axis goes left-right. right is positive.
the z-axis goes up-down. up is positive.
since the origin (0, 0, 0) is the center of the cube, and the sides are all 6 units long, the corners can have only -3 or +3 coordinates (half of a side length on either side of the origin) in each direction.
as we said : left-back-upper corner.
left means negative y.
back means negative x.
upper means positive z.
so, the coordinates of A are
(-3, -3, 3)
If HK and GJ are congruent, what is the measure of GOJ?
125 ° 80°
Answer:
80°
Step-by-step explanation:
Congruent means the same size, so we know that the angle of the shapes made by the lines HK and GJ are the same, meaning that the angle of GOJ is simply 80°.
Find the root of the function f(x)=−4x+1.
Answer: A
Step-by-step explanation:
[tex]-\frac{4}{x}+1=0\\\\1=\frac{4}{x}\\\\x=4[/tex]
IM IN A HURRY PLEASE HELP ME QUESTION IS DOWN BELOW WORTH 15 POINTS each
Answer:
a: Angle EBD
b: Can't really phrase this well, a semicircle that is to the left or right of diameter BD
c: Arc EDC
d: 80 degrees
e: 180
Step-by-step explanation:
An inscribed angle is an angle with all 3 points on the circumference of a circle.
A semicircle is half a circle
A major arc is an arc greater than 180 degrees
The inner angle is 80 degrees
Arc BCD is half a circle so its 360/2=180 degrees
What are the domain and range of the function f of x equals the quantity of x squared minus 3 x minus 28, all over x plus 4?
domain is x is all real numbers where x does not equal 4 comma range is y is all real numbers where y does not equal 11
domain is x is all real numbers where x does not equal 7 comma range is y is all real numbers where y does not equal negative 4
domain is x is all real numbers where x does not equal negative 4 comma range is y is all real numbers where y does not equal negative 11
domain is x is all real numbers where x does not equal negative 7 comma range is y is all real numbers where y does not equal 4
The domain is x is all real numbers where x does not equal negative 4 comma range is y is all real numbers where y does not equal negative 11. Option C
What is the domain of a function?The domain of a function refers to the entire area for which the function returns a value. The function in this case is; f(x) = x^2 - 3x - 28/x + 4. The domain of the function will be real numbers except -4.
Hence, we can say that domain is x is all real numbers where x does not equal negative 4 comma range is y is all real numbers where y does not equal negative 11.
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Answer:
The answer is C.
A bacteria culture grows with constant relative growth rate. The bacteria count was 1,920 after 4 hours and 1,966,080 after 12 hours.
(a) What is the relative growth rate? Express your answer as a percentage. (Round your answer to two decimal places.)
(b) What was the initial size of the culture?
(c)Find an expression for the exact number of bacteria after t hours, y(t).
(d) Find the number of bacteria after 9.5 hours. (Round your answer to the nearest whole number.)
(e) Find the rate of growth (in bacteria per hour) after 9.5 hours. (Round your answer to the nearest whole number.)
(f) How many hours did it take for the population to reach 72,000? (Round your answer to two decimal places.)
From the calculation, the growth rate is 0.88.
What is the growth rate?To find the relative growth rate
P1 = Poe^rt
P2 = Poe^rt
Thus;
1920 = Poe^4r ------ (1)
1966080 =Poe^12r -------(2)
P2/P1 gives;
1966080/1920 = Poe^12r/Poe^4r
1024 = e^12r/e^4r
1024 =e^8r
1024 = (e^r)^8
2^10 = (e^r)^8
e^r = 2^1.25
e^r = 2.38
r = ln(2.38)
r = 0.88
The initial size of the culture is;
1920 = Poe^(0.88 * 4)
Po = 1920/e^(0.88 * 4)
Po = 57
The expression for the exact number of bacteria after t hours is
P(t) = 57e^0.08t
The growth (in bacteria per hour) after 9.5 hours is
P(t) = 57e^(0.88 * 9.5)
P(t) = 243544
For the number to reach 72,000;
72,000 = 57e^0.88t
72,000/57 = e^0.88t
ln 126 = ln[e^0.88t]
4.8 = 0.88t
t = 4.8/0.88
t = 5.5 hours
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Assume that the average healthy body temperature is 98.249 degrees and the standard deviation is 0.733 degrees. How many standard deviations below the mean would I be if my body temp is 97.2 degrees,
The standard deviation is 1.43 below the mean
How to determine the number of standard deviation?The given parameters are:
Mean = 98.249
Standard deviation = 0.733
x = 97.2
To calculate the number of standard deviation below the mean, we use
[tex]x = \bar x - n\sigma[/tex]
So, we have:
[tex]97.2 = 98.249 - n * 0.7333[/tex]
Evaluate the like terms
[tex]-1.049 =- n * 0.7333[/tex]
Divide both sides by -0.733
n =1.43
Hence, the standard deviation is 1.43 below the mean
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look at the pictures
Answer:
A
Step-by-step explanation:
9|x-8|<36
|x-8|<4
-4<x-8<4
add 8
-4+8<x-8+8<4+8
4<x<12
Write out the sum. Do not evaluate.
∑∑k=1 (k^2-5k-3)[tex]4\\E(K^2-5k-3)\\k=1[/tex]
Series are sum of a given sequence.. The sum of the given expression is -33
Sequence and seriesSeries are sum of a given sequence. According to the given expression
∑∑k=1 (k^2-5k-3)
Taking the sum from k = 1 to k = 4
Sum = (1-5-3) + (4-10-3) +(9-15-3)+(15-20-3)
Sum = (-7) + (-9) + (-9) + (-8)
Sum = -33
Hence the sum of the given expression is -33
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A clothing business finds there is a linear relationship between the number of shirts, n , it can sell and the price, p , it can charge per shirt. In particular, historical data shows that 1,000 shirts can be sold at a price of $30 , while 3,000 shirts can be sold at a price of $14 . Find a linear equation in the form p(n)=mn+b that gives the price p they can charge for n shirts.
Because this answer involves an expression that is more complex than a whole number times n , remember to type in multiplication symbols *. For example, if you wanted to enter 12n , type this in as (1/2)*n.
The value P price they charges for shirts is (-0.008n) + 38
According to the statement
we have given that the 1,000 shirts can be sold at a price of $30 , while 3,000 shirts can be sold at a price of $14 .
And we have to find the linear equation.So,
Let p = price
n = number of shirts
m = slope of the line (note, the more shirts, the lower the price, so we know it's going to be negative)
b = y intercept
And they gives us the two points like here (1000, $30) and (3000, $14) which have to be on our line.
To find the slope m, you use m = (p₁-p₂)/(n₁-n₂)
Filling in from our points m = (30-14)/(1000-3000)
m = 16/-2000
m = -0.008
Now that we have the slope and a point, we can find our equation
p-p₁=m(n-n₁)
p-30=(-.008)(n-1000)
p-30= (-.008n) + 8
p=(-.008n) + 38
So, The value P price they charges for shirts is (-0.008n) + 38
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Find the unit rate for each brand. Round to the nearest cent (hundredth).
The unit rate of each of the brands are:
Brand A's unit rate = 37 cents per ounce.
Brand B's unit rate = 31 cents per ounce.
How to Find the Unit Rate?The unit rate of each brand is simply how much a brand of tomatoes will cost per ounce.
To find the unit rate of each brand, do the following:
Brand A's unit rate = 2.99/8 = $0.37 per ounce = 37 cents per ounce.
Brand B's unit rate = 4.99/16 = $0.31 per ounce = 31 cents per ounce.
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A group of researchers wants to develop an experiment to determine whether a new drug effectively treats high blood pressure. The researchers want to inject the drug in monkeys first to determine whether there are any potential serious side effects.
Part A: What are some possible ethical issues to this type of testing? (5 points)
Part B: While conducting the experiment, the researchers find that blood pressure levels return to normal, and they declare the drug is the cause of the change. Is this a good assumption? Explain. (5 points)
The ethical issues about testing with animals is it resulting in suffering and they have the right to live without human interference.
What is Experiment?This is defined as a procedure which is carried in order to support or refute a hypothesis.
The blood pressure returning to normal when the drugs were used on the animals is a good assumption as most parts of the animal and human body work similarly.
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half a number is 21 less than double the number find the number.
Answer:
14
Step-by-step explanation:
let the number be x
2x is larger than half of x by 21: 2x = 0.5+21
Solve:
2x = 0.5+21
1.5x = 21
x = 14
One serving of vegetables is 1/2 cup. You want to make 2 1/2 servings of vegetables. How many cups of vegetables is that? Make a math drawing and write and annotate an equation for this problem.
Answer: 1 1/4 cups
Step-by-step explanation:
1 serving is half a cup so 2 servings would be 1 cup
and half of a serving would be 1/4 of a cup
for a drawing you could do something like this
Please please Help!
Need Answer to Multiple Choice! Brainliest!
The scores on the ACT exam are normally distributed with a mean of 21 and a standard
deviation of 5. If we selected a random sample of 37 test takers, what is the probability that the
sample mean of those test takers who would be less than a 19.8?
a) .0721
b) .5000
c) .0808
d) .0582
Answer:
a) 0.0721
Step-by-step explanation:
Let the random variable X be the score on the ACT exam.
Given:
mean (μ) = 21standard deviation (σ) = 5Therefore, the random variable X is normally distributed:
[tex]X \sim\textsf{N}(21,5^2)[/tex]
Z-score for a sample mean
[tex]\textsf{If }\: X \sim\textsf{N}(\mu,\sigma^2)\:\textsf{ then }\: \overline{X} \sim \left(\mu,\dfrac{\sigma^2}{n}\right) \implies Z=\dfrac{\overline{X}-\mu}{\sigma / \sqrt{n}} \sim \textsf{N}(0,1)[/tex]
[tex]\textsf{then the test statistic is}: \quad z=\dfrac{\overline{x}-\mu}{\sigma / \sqrt{n}}[/tex]
Given:
[tex]\overline{x}[/tex] = 19.8μ = 21σ = 5n = 37Therefore, the test statistic is:
[tex]\implies z=\dfrac{19.8-21}{5/ \sqrt{37}}=-\dfrac{6\sqrt{37}}{25}=-1.459863007=-1.46\:\: \sf (3\:s.f.)[/tex]
Using the Z-tables to find the probability:
[tex]\implies \text{P}(Z \leq -1.46)=0.0721[/tex]
8 to the second power to the -4 power is equivalent to
Answer:
1.138789 is equivalent to 8 to the second power to the -4 power.
Hope this helps :)
. Which of the following is parallel to
5x + 2y = 1?
Answer:
when the question is rearranged so that y is by itself, any of the options that say - 2.5x will be parallel.
Step-by-step explanation:
5x + 2y = 1
to get y by itself, simple algebra rules must be applied.
1. subtract 5x from both sides.
5x - 5x + 2y = 1 - 5x
2y = 1 - 5x
divide both sides by 2
2y / 2 = 1 / 2 - 5x / 2
twos cancel out on the left1/2 = 0.5- 5x /2 = - 2.5xtherefore the new equation is:
y = 0.5 - 2.5x
this is very close to standard form for a line which is y = mx + b
rearrange the right side of the equals sign:
y = -2.5x + 0.5
in a standard linear equation, the x value determines the gradient of the line. therefore, anything with the same gradient (in this case -2.5x) will be parallel to the given equation.
Hope this makes sense :)
A ball is thrown downward from the top of a 120-foot building with an initial velocity of 20 feet per second. The
height of the ball h in feet after t seconds is given by the equation h= - 16t²-20t+120. How long after the
ball is thrown will it strike the ground?
Answer:
[tex]t=\frac{-5+\sqrt{505}}{8}[/tex]
Step-by-step explanation:
The ball strikes the ground when h = 0.
[tex]-16t^2 - 20t + 120 = 0 \\ \\ 4t^2 + 5t - 30=0 \\ \\ t=\frac{-5 \pm \sqrt{5^{2}-4(4)(-30)}}{4(2)} \\ \\ t=\frac{-5 \pm \sqrt{505}}{8}[/tex]
However, as time most be positive, we only consider the positive case.
So,
[tex]t=\frac{-5+\sqrt{505}}{8}[/tex]
On a piece of graph paper, plot the following points: A (0, 0), B (5, 0), and C (2, 4). These coordinates will be the vertices of a triangle. How would you use the distance formula to determine what kind of triangle this is? Is the triangle equilateral, right, or scalene? Now use the midpoint formula to determine the midpoints of the triangle's sides: segments AB, BC, and CA. Connect the midpoints to make four triangles within the first triangle. Are these four triangles similar?
The triangle is an isosceles triangle and the four triangles are similar
How to determine the triangle type?
The coordinates are given as:
A (0, 0), B (5, 0), and C (2, 4).
Calculate the distance between the coordinates using:
[tex]d = \sqrt{(x_2 -x_1)^2 +(y_2 -y_1)^2[/tex]
So, we have:
[tex]AB = \sqrt{(0 -5)^2 +(0-0)^2} =5[/tex]
[tex]AC = \sqrt{(0 -2)^2 +(0-4)^2} =4.5[/tex]
[tex]BC = \sqrt{(5 -2)^2 +(0-4)^2} =5[/tex]
The above shows that two sides are congruent.
Hence, the triangle is an isosceles triangle
The midpoints of the sidesThis is calculated using:
(x, y) = 0.5 * (x1 + x2, y1 + y2)
So, we have:
AB = 0.5 * (0 + 5, 0 + 0) = (2.5, 0)
AC = 0.5 * (0 + 2, 0 + 4) = (1, 2)
BC = 0.5 * (5 + 2, 0 + 4) = (3.5, 2)
From the attached graph, we can see that the triangles are similar
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