Answer:
B
Step-by-step explanation:
So, for this problem, it is only asking for vertex A, so you only have to apply the transformations to one point (unless you want to find out where the other points are at).
Vertex A is at (-4,2).
The triangle is first translated 2 units right and 5 units down.
So to find the coordinate of that you have to understand that is you translate something right or left, the x value will change. And if it's up or down, the y value will change. If you are going right or up, the amount it's moved will be added. And left or down will be subtracted.
-4+2=-2 (so the new x-value will be -2)
2-5=-3 (so the new y-value will be -3)
Thus vertex A' is (-2,-3).
Now for the next transformation.
(-2,-3) is moved 5 units right and 4 units up.
-2+5=3 (so x-value will be 3)
-3+4=1 (so the y-value will be 1)
SO, the new coordinate of vertex A" is...
(3,1)! aka B
(Also, you can just illustrate this on a graph but i'm showing it to you this way because when you get more advanced the amount it is being translated will be much higher.)
Answer: The answer is B
Which statement best explains the relationship between lines FG an HJ?
Answer:
the answer is B. They are perpendicular because their slopes are negative reciprocals.
Step-by-step explanation:
Which linear function represents the line given by the point-slope equation y + 1 = –3(x – 5)?
Answer:
[tex]y=-3x+14[/tex] or [tex]3x+y=14[/tex]
Step-by-step explanation:
we have
[tex]y+1=-3(x-5)[/tex] ----> equation of the line into point-slope form
step 1
Convert to slope intercept form
The equation of the line into slope intercept form is equal to
[tex]y=mx+b[/tex]
so
[tex]y+1=-3(x-5)[/tex]
[tex]y+1=-3x+15[/tex]
[tex]y=-3x+15-1[/tex]
[tex]y=-3x+14[/tex] ----> equation of the line into slope intercept form
step 2
Convert to standard form
The equation of the line into standard form is equal to
[tex]Ax+By=C[/tex]
so
we have
[tex]y=-3x+14[/tex]
Adds 3x both sides
[tex]3x+y=14[/tex] ----> equation of the line in standard form
What is the slope of a line that is parallel to the line y=-1/5?
Answer:
-1/5
Step-by-step explanation:
Which of the following lines is parallel to x = 7? (2 points) a 3y = 7 b y = 7 c x = y d x = 4
Answer:
Choice d. [tex]l:x = 7[/tex] is parallel to the line [tex]x = 4[/tex].
Step-by-step explanation:
Refer to the diagram attached. (Created with GeoGebra)
The line [tex]x = 7[/tex] is made of all the points on a cartesian plane that meet the requirement [tex]x = 7[/tex]. In other words, this line consists of points with x-coordinate [tex]7[/tex]. That includes:
[tex](7, -1)[/tex],[tex](7,0)[/tex], and[tex](7,1)[/tex].That line is perpendicular to the x-axis (the horizontal axis) and intersects the x-axis at the point [tex](7,0)[/tex].
Now, consider the lines in the choices.
The first line [tex]3y =7[/tex] requires only that the y-coordinates of its points be 7/3. This line accepts any x-values. Points on this line include:
[tex]\displaystyle \left(-1, \frac{7}{3}\right)[/tex],[tex]\displaystyle \left(0, \frac{7}{3}\right)[/tex], and[tex]\displaystyle \left(-1, \frac{7}{3}\right)[/tex].As a result, this line is parallel to the y-axis and is perpendicular to the line [tex]x = 7[/tex].
Similar to the first, the second line [tex]y = 7[/tex] is also parallel to the y-axis and is perpendicular to the line [tex]x = 7[/tex].
The third line [tex]x = y[/tex] requires that the x- and y- coordinates of all its points be equal. Points may include:
[tex](-1, -1)[/tex],[tex](0,0)[/tex], and[tex](1,1)[/tex].This line is slant.
The last line [tex]x = 4[/tex] is similar to the given line [tex]x = 7[/tex]. This line is also perpendicular to the x-axis. The difference is that this line is three units to the left of the line [tex]x = 7[/tex].
Find the sample Standard deviation and the population standard deviation of the data set 17,37,56,16,12,16,19,45,14,37,21,26,43,46,42
Answer:
1. 13.98
2. 14.47
Step-by-step explanation:
The question is on sample standard deviation and population standard deviation
Arrange the data in increasing order
12,14, 16,16,17,19,21,26,35,37,42,43,45,46,56
n=15
Find the mean of the data set
[tex]mean = (12+14+ 16+16+17+19+21+26+35+37+42+43+45+46+56)/15[/tex]
mean= 29.67 ⇒30
Find the deviations
You subtract the value of mean from each of the data set given
Deviations= -18, -16, -14, -14, -13,-11, -9,-4,5,7,12,13,15,16,26
Find squares of deviations
= 324, 256, 196, 196, 169, 121, 81, 16, 25, 49, 144, 196, 225, 256, 676
Find sum of squares of deviations
[tex]324+ 256+ 196+ 196+ 169+ 121+ 81+ 16+ 25+ 49+ 144+ 196+ 225+ 256+ 676 = 2930[/tex]
1. Treating the data set to represent an entire population then;
Variance= sum of squares of deviation/number of data set
Variance= 2930/15 = 195.33
Population standard deviation = √195.33 = 13.98
2. Treating the data set as a sample , the number of data set is reduced by one.i.e n= 15-1= 14
Sample Variance=2930/14 =209.29
sample standard deviation= √209.29 = 14.47
The estimator for a heating, ventilation, and air conditioning (HVAC) contractor estimated that the new hospital would require 5,840 feet of sheet metal ductwork. The order is too large for a single fabricator, so it was decided to split the order among four fabricators. Fabricator 1 received an order for 2,500 feet; Fabricator 2 obtained an order for 1,200 feet; and Fabricator 3 was awarded a contract for 1,150 feet. How many feet of ductwork would be required of Fabricator 4?
Answer:
990 feet
Step-by-step explanation:
Fabricator 4 recieved what's left after the rest were distributed
= 5,840 - 2,500 - 1,200 - 1,150 = 990
Answer:
990 feet.
Step-by-step explanation:
To calculate the feet of metal that the last fabricator will sell, you just have to substract from the total feet needed the amount of metal that have been already ordered to the other fabricators.
Total metal duct work= Fabricator 1+ Fabricator 2+ Fabricator 3+ Fabricator 4
If you clear the equation it would be:
F4= Total- F1- F2- F3
F4= 5840- 2,500- 1,200- 1150
F4= 990 ft.
The population P of a bacteria culture is modeled by P = 4100e^kt where t is the time in
hours. If the population of the culture was 5800 after 40 hours, how long does it take for
the population to double? Round to the nearest tenth of an hour.
Show work please
A LOT OF POINTS
Enter the given values into the equation and solve.
5800 = 4100e^(k*40)
Divide both sides by 4100 and simplify:
58 / 41 = e^(k*40)
Remove e by taking the logarithm of both sides:
ln(58/41) = k *40
Divide both sides by 40:
k = ln(58/41)/40
k = 0.00867
Now for the population to double set up the equation:
2*4100 = 4100e^kt
The 4100 cancels out on both sides:
2 = e^kt
Take the logarithm of both sides:
ln(2) = k*t
Divide both sides by k
t = ln(2) /k
replace k with the value from above:
t = ln(2) / 0.00867
t = 79.95
Rounded to the nearest tenth = 80.0 hours to double.
Answer:
It would take around 122 hours to double the population.Step-by-step explanation:
To answer the question, we first need to find the constant k, using the given information and the expression.
[tex]P=4100e^{kt} \\5800=4100e^{k(40)} \\\frac{5800}{4100}=e^{40k}\\e^{40k}=1.41\\lne^{40k}=ln1.41\\40k=0.34\\k=\frac{0.34}{40}\approx 0.0085[/tex]
Now that we have the constant. We can find the time it would take to double the population which would be 11600:
[tex]P=4100e^{kt}\\11600=4100e^{0.0085t}\\\frac{11600}{4100}= e^{0.0085t}\\e^{0.0085t}=2.83\\lne^{0.0085t}=ln2.83\\0.0085t=1.04\\t=\frac{1.04}{0.0085}\approx 122.35[/tex]
Therefore, it would take around 122 hours to double the population.
What’s is sherry error?
Answer:
the answer is B.
Step-by-step explanation:
It makes the problem solve smoother.
For what value of C will y = sin1/2(x - C) be an even function?
a. 2pi
b. pi
c. pi/2
Answer:
c. pi/2
Step-by-step explanation:
The answer is the option c. pi/2.
You must know that y = sin(x) is an odd function and also that y = cos(x) is an even function.
Also, you should know that sin(x + pi/2) = cos(x).
You can show it using the definition of the functions sine and cosine in the unit circle or using the formula of the sine of a sum: sin(A + B) = sin(A)*cos(B) + cos(A)*sin(B).
When you substitute B with pi/2 you get sin (A + pi/2) = sin(A)*0 + cos(A)*1 = cos(A).
Then, given that cos(A) is even sin(A+pi/2) is even.
Answer:
option b
Step-by-step explanation:
We are given that [tex]y=sin \frac{1}{2}(x-C)[/tex] be an even function
We have to find the value of C for which given function is even function
We know that sin x is odd function and cos is even function
Odd function : when f(x)[tex]\neqf(-x) [/tex] then the function is called an odd function.
Even function : When f(x)=f(-x) then the function is called an even function.
Sin(-x)=-Sin x
Cos (-x)= Cos x
When we take C=[tex]2\pi[/tex]
Then , y=Sin[tex]\frac{x}{2}-\frac{2\pi}{2}[/tex]
y=[tex]sin(\frac{x}{2}-\pi)[/tex]
[tex]y=-sin\frac{x}{2}[/tex] ( [tex]sin (x-\pi)=-sin x[/tex])
When x is replace by -x
Then, we get [tex]y=-sin(-\frac{x}{2})=sin\frac{x}{2}[/tex]
[tex]f(-x)\neq f( x)[/tex]
Hence, option a is false.
b.C=[tex]\pi[/tex]
[tex]y= sin (\frac{x}{2}-\frac{\pi}{2})[/tex]
[tex] y=-sin(\frac{\pi}{2}-\frac{x}{2})[/tex]
[tex]y=-cos \frac{x}{2}[/tex]
When x is replaced by -x then we get
[tex] y=-cos (-\frac{x}{2})=- cos \frac{x}{2}[/tex]
f(x)=f(-x) , Therefore, function is even,hence option b is true.
c.C=[tex]\frac{\pi}{2}[/tex]
[tex]y=sin (\frac{x}{2}-\frac{\pi}{4})[/tex]
[tex]Sin (A-B)=Sin A Cos B- Sin B Cos A[/tex]
[tex][y= sin \frac{x}{2} cos {\frac{\pi}{4}-cos\frac{x}{2} sin\frac{\pi}{4}[/tex]
[tex] sin\frac{\pi}{4}= cos \frac{\pi}{4}=\frac{1}{\sqrt2}[/tex]
[tex]y=\frac{1}{\sqrt2}(sin \frac{x}{2}- cos \frac{x}{2})[/tex]
When x is replaced by -x then we get
[tex]y=\frac{1}{\sqrt2}(-sin\frac{x}{2}-cos \frac{x}{2})[/tex]
[tex]f(x)\neq f(-x)[/tex]
Hence, function is odd .Therefore, option c is false.
The value of the expression 16-^3/4 is___
8
1/8
-6
6
1/40
1/64
Answer:
[tex]\frac{1}{8}[/tex]
Step-by-step explanation:
Using the rules of exponents
• [tex]a^{-m}[/tex] ⇔ [tex]\frac{1}{a^{m} }[/tex]
• [tex]a^{\frac{m}{n} }[/tex] ⇔ [tex]\sqrt[n]{a^{m} }[/tex]
Hence
[tex]16^{-\frac{3}{4} }[/tex] = [tex]\frac{1}{16^{\frac{3}{4} } }[/tex]
= [tex]\frac{1}{\sqrt[4]{16^{3} } }[/tex] = [tex]\frac{1}{2^{3} }[/tex] = [tex]\frac{1}{8}[/tex]
Which statement is true about the geometric figure that can contain these points?
No line can be drawn through any pair of the points.
One line can be drawn through all three points.
One plane can be drawn so it contains all three points.
Two planes can be drawn so that each one contains all three points.
The simplest basic geometric object is a point. It is named with a capital letter and symbolized by a dot. The correct option is C.
What is the point?The simplest basic geometric object is a point. It is named with a capital letter and symbolized by a dot. A point has no size and solely represents the position (that is, zero length, zero width, and zero height).
Since a plane is a flat, endlessly long two-dimensional surface. A plane is a two-dimensional analog that can incorporate three dimensions of space, a line, and a point.
Now, the statement that will be true about the three points given is that only one plane can be drawn so it contains all three points.
Hence, the correct option is C.
The complete question is mentioned in the image below.
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Which is the graph of y=3x+1-2?
To graph the equation y = 3x + 1 - 2, find the slope and y-intercept. Plot the y-intercept and use the slope to find additional points. Connect the points to get the graph.
Explanation:To graph the equation y = 3x + 1 - 2, we need to find the slope and the y-intercept. The slope, represented by m, is 3 in this equation. The y-intercept, represented by b, is -1. We can plot the y-intercept on the graph first, which is the point (0, -1). From there, we can use the slope to plot additional points and draw a line through them. Since the slope is 3, we can move up 3 units on the y-axis and 1 unit to the right on the x-axis to find another point. By connecting these points, we will have the graph of y = 3x + 1 - 2.
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What is the extended ratio relating the side lengths of a 30-60-90 triangle?
A. x:x2–√:3x
B. x:x3–√:2x
C. x:x:x3–√
D. x:x:x2–√
Answer:
x:2x:√3x.
Step-by-step explanation:
I would write it as x:2x:√3x.
The hypotenuse is twice the length of the shorter leg and the longer leg is the square root of 3 times the shorter leg.
Answer:
The correct option is A) x : 2x : x√3
Step-by-step explanation:
Consider the provided information.
For a 30-60-90 triangle.
The side opposite to the 30° angle is x.
The side opposite the 60° angle is √3 x.
The side opposite the 90° angle is 2 x.
Side opposite to the 30° angle is the smallest side as 30° is the smallest angle among 30-60-90. Similarly the side opposite of 60° is the second largest side as 60° is the second largest angle and for the side opposite of 90° is the largest side as 90° is the largest angle.
Hence, the correct option is A) x : 2x : x√3
Which equation can be used to calculate the surface area of the triangular prism net show below?
10 cm
13 cm
12 cm
5 cm
5 cm
[Not drawn to scale]
Answer:
(10 x 13) + (10 x 12) + (12 x 5 / 2) + (12 x 5 / 2) + (10 x 5)
360
Solve formula C=pied for pie
Answer:
yea its pi not pie, but he is right
Step-by-step explanation:
Question 8/Multiple Choice Worth 5 points)
(06.02 MC)
The masses, in kg, of some bags on an airplane are shown below:
7,6.2, 6.1,6.8, 6.1,6.2, 6.8, 5.8, 6.2, 6.3
Jack made the following box plot to represent the masses: its the pic i uploaded
Which of the following did Jack show incorrectly on his box plot?
1. Median
2. Minimum
3. First quartile
4. Third quartile
Answer:
1. The median.
Step-by-step explanation:
First arrange in ascending order:
5.8 6.1 6.1 6.2 6.2 6.2 6.3 6.8 6.8 7
The median = 6.2. On the box plot the median is marked at 6.3 so that is incorrect. All the others are correct
help plz I dont understand
Look at the equations and see if the statements are true.
Company 1 and 4 do not charge the same rate per mile, company one charges 0.5 per mile and company 4 charges 0.06 per mile.
Company 2 and 3 do not charge the same.
Company 2 has an x in the equation so is not just a flat fee.
Company 3 does not have an x in the equation, so only charges a flat fee.
The correct answer is the last one.
which of the following has a slope of -3 and a y-intercept of -4 ?
(A) y = -3x + 4
(B) y = 3x + 4
(C) y = 3x - 4
(D) y = -3x - 4
Answer:
Letter (D), or y = -3x - 4
Step-by-step explanation:
A slope of -3 should be self explanatory, and y intercept is determined by the b value in the form y = mx + b. Since b is negative, we are looking for -4. Therefore, your answer is (D).
Hope this helps!
Which equation represents a line that passes through (-9, -3) and has a slope of -6?
Oy-9= -6(x - 3)
Oy+9= -6(x + 3)
Oy-3 = -6(x -9)
Oy+3=-6(x +9)
Answer:
y+3=-6(x +9)
Step-by-step explanation:
equation represents a line that passes through (-9, -3) and has a slope of -6is:
y+3=-6(x +9)
because : The equation of a linear function in point-slope form is: y – y1 = m(x – x1) ....m : the slope
The point is A (x1 , y1)
you have m = - 6 x1 = -9 y1 = -3
The equation represents a line that passes through (-9, -3) and has a slope of -6 is y+3 = -6(x+9).
What is an equation?An equation is a mathematical statement that shows that two mathematical expressions are equal.
Given that, a line is passing through the point (-9, -3) and the slope of -6,
We need to determine the equation of the line,
The general formula of a line passing through a point (x', y') and have slope m is given by,
y-y' = m(x-x')
Here, (x', y') = (-9, -3), m = -6,
Therefore, the equation of the asked will be =
y-(-3) = -6(x-(-9))
y+3 = -6(x+9)
Hence, the equation represents a line that passes through (-9, -3) and has a slope of -6 is y+3 = -6(x+9)
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What is the least common multiple of 6 and 15? A) 3 B) 9 C) 21 D) 30
Answer:
D
Step-by-step explanation:
multiples of 6 : 6, 12, 18, 24, 30, 36, ....
multiples of 15 : 15, 30, 45, ......
From the lists the least common multiple is 30
[tex]6=2\cdot3\\15=3\cdot5\\\\\text{lcm}(6,15)=2\cdot3\cdot5=30[/tex]
What does the y-intercept mean
Answer:
50Step-by-step explanation:
The slope-intercept form of an equation of a line:
y = mx + b
m - slope
b - y-intercept
We have the equation y = 75x + 50.
Therefore
slope: m = 75
y-intercept: b = 50
List all the composite factors of 96
Answer:
96 is a composite number. 96 = 1 x 96, 2 x 48, 3 x 32, 4 x 24, 6 x 16, or 8 x 12
Step-by-step explanation:
what is .838383... as a fraction in simplest form?
Answer:
4/5
Step-by-step explanation:
start with putting the decimal over ten
8/10
than divide numerator and denominator with the common denominator 2
8÷2=4 10÷2=5
4/5
Which expression is equivalent to ?
algebra II
Answer:
Third option
Step-by-step explanation:
Given expression is:
[tex]\sqrt[3]{32x^8y^{10}}[/tex]
Making the exponents multiples of 3
[tex]=\sqrt[3]{8*4*x^6*x^2*y^{9}*y}\\=\sqrt[3]{2^3*4*x^6*x^2*y^{9}*y}\\Applying\ radical\\=2^{(3*\frac{1}{3})} *4^{\frac{1}{3} }*x^{(6*\frac{1}{3})}*x^{(2*\frac{1}{3})}*y^{(9*\frac{1}{3})}*y^{\frac{1}{3}}\\=2x^2y^3\sqrt[3]{4x^2y}[/tex]
Hence,
Option No 3 is correct ..
Can someone please help me ?
Answer:
it should be (based on the instructions we don't have) [tex]\frac{-3}{2}[/tex]
Step-by-step explanation:
because the "D" in the parenthesis has 2 negative signs, it inverts itself making it just what D equals, which on the number line is [tex]\frac{-3}{2}[/tex]
Jace wrote a sentence as an equation.
56 is 14 more than a number.
14+ = 56
Which statement best describes Jace's work?
Jace is not correct. The phrase more than suggests using the symbol > and Jace did not use that symbol.
Jace is not correct. He was correct to use addition, but the equation should be 56+ p = 14
Jace is not correct. The first number in the sentence is 56, so the equation should start with 56.
Jace is correct. The phrase more than suggests addition, so Jace showed that 14 plus a variable equals 56.
O
Answer: Fourth option is correct.
Step-by-step explanation:
Since we have given that
56 is 14 more than a number.
Let the number be 'p'.
So, the equation would be
[tex]14+p=56\\\\p=56-14\\\\p=42[/tex]
Jace is correct. The phrase more than suggests addition, so Jace showed that 14 plus a variable equals 56.
Hence, Fourth option is correct.
Answer: Jace is correct. The phrase more than suggests addition, so Jace showed that 14 plus a variable equals 56
__________________________________________________________
Hence, (d) is correct.
Step-by-step explanation:
edge2023
Anna is no more than 3 years older than 2 times Jamie’s age. Jamie is at least 14 and Anna is at most 35. Which system of linear inequalities can be used to find the possible ages of Anna, a, and Jamie, j?
Answer:
B
Step-by-step explanation:
A) a ≥ 3 + 2j; j ≥ 14, a ≤ 35
B) a ≤ 3 + 2j; j ≥ 14, a ≤ 35
C) a ≥ 3 + 2j; j ≤ 14, a ≤ 35
D) a ≤ 3 + 2j; j ≤ 14, a ≤ 35
All the system of linear inequalities which can be used to find the possible ages of Anna, a, and Jamie, j are,
a < 3 + 3j
j ≥ 14
a ≤ 35
We have to given that,
Anna is no more than 3 years older than 2 times Jamie’s age.
Jamie is at least 14 and Anna is at most 35.
Let us assume that,
Age of Anna = a
Age of Jamie's = j
Hence, system of linear inequalities which can be used to find the possible ages of Anna, a, and Jamie, j are,
For Anna is no more than 3 years older than 2 times Jamie’s age.
a < 3 + 3j
And, Jamie is at least 14 and Anna is at most 35.
j ≥ 14
a ≤ 35
Thus, All the system of linear inequalities which can be used to find the possible ages of Anna, a, and Jamie, j are,
a < 3 + 3j
j ≥ 14
a ≤ 35
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If value of cos330° is √3/2 then find tan165°.
Answer:
-2+sqrt(3)
Step-by-step explanation:
When cos(angle)=sqrt(3)/2
then sin(of that angle)= + or - 1/2 depending on the quadrant
Anyways 330 degrees is in the 4 quadrant. Cosine is positive there while sine is negative.
so sin(330)=-1/2
Formula for tan(x/2)=(1-cos(x))/sin(x)
Therefore tan(165)=tan(330/2)=(1-cos(330))/sin(330)=(1-sqrt(3)/2)/(-1/2)
Multiply top and bottom by 2 to get
tan(165)=(2-sqrt(3))/-1
tan(165)=-2+sqrt(3)
Question 4 (5 points)
The points obtained by students of a class in a test are normally distributed with a mean of 60 points and a standard
deviation of 5 points
About what percent of students have scored between 55 and 65 points?
a. 2.5
b. 47.5
c. 68
d. 34
Answer:
Option C
Step-by-step explanation:
Given
Mean= μ=60
and
Standard Deviation= σ=5
In order to calculate the percentage of students between 55 and 65, we have to calculate z-score for both
z-score for 55=(55-60)/5
=(-5)/5
=-1
The area to the left of z-score -1 is 0.1587
z-score for 65=(65-60)/5
=5/5
=1
The area to the left of z-score 1 is 0.8413
Area between z-scores of 55 and 65=0.8413-0.1587
=0.6826
Converting into percentage
=0.6826*100
=68.26%
Option C is the correct answer ..
Answer:
c. 68
Step-by-step explanation:
The empirical rule states that, if a population is approximately normal then 68% of the observations will fall within 1 standard deviation of the mean.
Going by this definition, 65 is one standard deviation to the right of the mean while 55 is one standard deviation to the left of the mean. Therefore, the percent of students who have scored between 55 and 65 points will be about 68%.
The question requires an approximation, About what percent, not exact computation. Thanks
for which of the following sample sizes(n)and sample proportions(p) can a normal curve be used to approximate the binomial probability
histogram
Answer:
The answer isc
Step-by-step explanation:
C
Answer:
B. n = 65; p = 0.8
Step-by-step explanation: