Answer:
The coordinates of point X that divides the line in 1:4 are: (3,8/5)
Step-by-step explanation:
When a point divides a line with coordinates (x1,y1) and (x2,y2) in ratio m:n,
the coordinates of point are given by:
\((x,y) = (\frac{mx_2+nx_1}{m+n} , \frac{my_2+ny_1}{m+n})\)
Given points are:
(x1,y1) = (5,1)
(x2,y2) = (-5,4)
Putting the values in the formula
\(X(x,y) = (\frac{(1)(-5)+(4)(5)}{1+4} , \frac{(1)(4)+(4)(1)}{1+4})\\= (\frac{-5+20}{5}, \frac{4+4}{5})\\=(\frac{15}{5}, \frac{8}{5})\\=(3,\frac{8}{5})\)
Hence,
The coordinates of point X that divides the line in 1:4 are: (3,8/5)
720 gallons/day = ______ gallons/hour
Answer:
30
Step-by-step explanation:
just divide 720 by 24 (Hours in a day)
mark as brainliest please.
1. Prove the following trig identity
tan(x/2)=sinx/1+cosx
Step-by-step explanation:
\( \tan( \frac{x}{2} ) = \frac{ \sin(x) }{1 + \cos(x) } \)
\( \tan( \frac{x}{2} ) = \frac{ \sqrt{1 - \cos(x) } }{ \sqrt{1 + \cos(x) } } \)
So we have
\( \frac{ \sqrt{1 - \cos(x) } }{ \sqrt{1 + \cos(x) } } = \frac{ \sin(x) }{ \sqrt{1 + \cos(x) } } \)
Next, we then rationalize the numerator so we get
\( \frac{ \sqrt{1 - \cos(x) } }{ \sqrt{1 + \cos(x) } } \frac{ \sqrt{1 + \cos(x) } }{1 + \cos(x) } = \frac{ \sin(x) }{ {1 + \cos(x) } } \)
The denominator should be square root so to let you know .
So know we ahev
\( \frac{ \sqrt{1 - \cos {}^{2} (x) } }{1 + \cos(x) } = \frac{ \sin(x) }{1 + \cos(x) } \)
\( \frac{ \sqrt{ \sin {}^{2} (x) } }{1 + \cos(x) } = \frac{ \sin(x) }{ {1 + \cos(x) } } \)
\( \frac{ \sin(x) }{1 + \cos(x) } = \frac{ \sin(x) ) }{1 + \cos(x) } \)
Multiply (-4)(-2)(-5)
Answer:
-40
Step-by-step explanation:
So what this question is basically saying is that you have to multiply -4 by -2 first to get 8 and then you multiply that by -5 hence getting the answer of -40
(-2) (4+6)+(-2) 6 / (-2) (4-1) simplified
The simplified form of the expression is \(-32\).
To simplify the expression, we can perform the calculations written below step by step:
\(\(\frac{{-2(4+6)+(-2)6}}{{-2(4-1)}}\)\)
We follow the order of operations (PEMDAS/BODMAS):
Step 1: Simplify within parentheses:
\(\(4+6 = 10\)\).
Step 2: Perform multiplications and divisions from left to right:
\(\(-2(10) = -20\) and \(-2(4-1) = -2(3) = -6\)\).
Step 3: Evaluate the remaining additions and subtractions:
\(\(-20 + (-2) \cdot 6 = -20 - 12 = -32\)\).
Therefore, the simplified form of the expression \(\(\frac{{-2(4+6)+(-2)6}}{{-2(4-1)}}\) is \(-32\).\)
When simplifying an expression, several factors need consideration. First, apply the order of operations correctly, respecting parentheses and exponents. Next, combine like terms by adding or subtracting them. Distribute and simplify within parentheses or brackets as needed. Pay attention to negative signs and ensure their proper placement.
Finally, review the simplified expression to ensure accuracy and validity within the given context.
Note: The complete question is:
\(\(\frac{{-2(4+6)+(-2)6}}{{-2(4-1)}}\)\), calculate the simplified form of this expression.
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When plotting points on the coordinate plane below, which point would lie on the x-axis?
(6, 0)
(0, 2)
(3, 8)
(5, 5)
Answer: (6,0)
Coordinate points are always written in pairs of the x- and y-coordinate: (x, y). Knowing this, the point would need to have a y-value of 0 in order to lie on the x-axis (otherwise, it would be on a random spot on the grid). The only coordinate point with a y-value of 0 is (6, 0). Therefore, the coordinate point (6, 0) lies on the x-axis.
Please refer to the attached graph below to see all the coordinate points.
I WILL GIVE EXTRA POINTS!!! HELPPPPP PLEASE!!!! SHOW ALL WORK!!!
Answer: 2x+52=2(x+26)
3x-35=-105
Step-by-step explanation:
Michal got a $50 gift card to an online music store. He bought an $10 album.He wants to buy songs that cost $1.25? Per song. Write and some solve an inequality to find the most songs he can.
Answer:
Step-by-step explanation:
Step-by-step explanation:
Given that:
Worth of gift card = $50
Cost of album purchased = $10.00
Cost per song to purchase = $1.25
Number of songs to purchase = n
Inequality to model the situation :
Cost of album + cost per song * (Number of songs) ≤ worth of gift card
$10.00 + ($1.25 * n) ≤ $50
$10.00 + $1.25n ≤ $50
Find the common difference of the sequence 4, 12, 20, ....
8
In this pattern, we have 4 12 then 20.
We can see that the difference 4 and 12 is 8.
Since the difference between 12 and 20 is also 8, the common difference of the sequence is 8.
Joe hasn't studied for the Pass/Fail final test in his statistics class, but he does have some background, so he's pretty sure he can get or guess the right answer about 60% of the time. Assuming there are 100 multiple choice questions, and the lowest passing score is 60%, what is the probability Joe will pass the test?
The probability that Joe will pass the test is 100%.
How to calculate the probabilityFrom the information, Joe hasn't studied for the final test in his statistics class, but he does have some background, so he's sure he can get the right answer about 60% of the time.
Therefore, if there are 100 multiple choice questions, and the lowest passing score is 60%, the probability that Joe will pass is 100%. This is because he usually has a 60% passing rate and this tallies with the lowest percentage needed to pass.
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In a manufacturing process, the assembly line speed (feet per minute) is believed to affect the number of defective parts found during the inspection process. Data (File 3) are collected on the number of defective parts for a variety of line speeds. Develop a linear regression equation that can be used to predict the number of defective parts given the line speed.
Line Speed Number of Defective Parts Found
20 21
20 19
40 15
30 16
60 14
40 17
Required:
a. Develop a scatter chart with line speed as the independent variable. What does the chart indicate about the relationship between line speed and the number of defective parts found?
b. Use the data to develop an estimated regression equation that could be used to predict the number of defective parts found, given the line speed. What is the estimated regression model?
c. Test whether each of the regression parameters βo and β1 is equal to zero at 0.01 level of significance. What are the correct interpretations of the estimated regression parameters?
d. How much of the variation in the number of defective parts found for the sample data does the model you estimated in part (b) explain?
Answer:
Jaime foxcgvxccvyyvytctvtvffddrgfgqvrctcrgctgtgtgygyg goku is the site
If possible factor. Find LCD. Multiply both sides by LCD. Solve show all work.
The lowest common denominator of the fraction is 6
What is LCDThe lowest common denominator (LCD) is the smallest common multiple of the denominators of a set of fractions. It is used to add or subtract fractions with different denominators.
The LCD of a set of fractions is the smallest number that is divisible by all the denominators in the set. When all the denominators are divided into the LCD, each fraction has an equivalent fraction with the same value and a denominator equal to the LCD.
In the fraction given;
x / 3 + x / 2 = 20
The lowest common denominator is 6
Using 6, we can divide through each of the fraction.
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Find the Value of Y.
The value of y in the triangle is 2√10 units.
How to find the side of similar triangle?Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .
The value of y can be found using the similar triangle ratios as follows:
Hence,
8 / y = y / 5
cross multiply
y² = 8 × 5
y²= 40
square root both sides of the equation
y = √40
Therefore,
y = 2√10 units
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Solve sin(5x)cos(8x) - cos(5x)sin(8x) = - 0.85 for the smallest positive solution
The solution to the equation is x ≈ 20°.
What are trigonometric functions?The periodic functions known as trigonometric functions indicate how a right-angled triangle's angle and sides relate to one another.
The given equation is sin(5x)cos(8x) - cos(5x)sin(8x) = - 0.85.
The formula for the sin(A-B) states that:
sin(A-B) = sinAcosB - cosAsinB.
Use this formula to solve the equation:
sin(5x)cos(8x) - cos(5x)sin(8x) = - 0.85
sin(5x - 8x) = -0.85
sin (-3x) = -0.85
Since sin(-A) = -sinA, it follows:
-sin(3x) = -0.85
sin(3x) = 0.85
3x = sin⁻¹(0.85)
3x ≈ 60°
x ≈ 20°
Hence, the solution to the equation is x ≈ 20°.
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. In a fort, there were provisions for 400 men for 23 weeks. 60 more men joined them. How long will the provisions
last?
The additional 60 men, the provisions will last for approximately 20 weeks.
To determine how long the provisions will last with the additional 60 men, we need to consider the total number of people and the original duration the provisions were meant to last.
Originally, the provisions were intended to sustain 400 men for 23 weeks. This means that the provisions were estimated to be sufficient for a total of 400 * 23 = 9200 person-weeks.
Now, with the additional 60 men, the total number of men becomes 400 + 60 = 460.
To calculate how long the provisions will last with the increased number of men, we divide the total person-weeks by the new number of men:
Provisions last = Total person-weeks / Number of men
= 9200 / 460
≈ 20 weeks (rounded to the nearest whole number)
The additional 60 men will extend the supply's shelf life to around 20 weeks.
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f(x)=3x2-15. find x if f(x)=-3
Step-by-step explanation:
Given
f(x) = - 3
Now
f(x) = 3x² - 15
-3 = 3x² - 15
3x² = 15 - 3
3x² = 12
x² = 12/ 3
x² = 4
x = + 2
Therefore x = + 2.
Two sides of a triangle have lengths 5 and 4. Which of the following can NOT be the length of the third side?
SOLUTION
From the triangle inequality theorem, the sum of the lengths any two sides must be greater than the length of the third side
So, looking at the options and looking at 4 and 5, it means that 5 is the longest side. So
\(\begin{gathered} 4+2=6>5 \\ 4+4=8>5 \\ 4+1=5=5 \\ 4+3=8>5 \end{gathered}\)So since 4 + 1 = 5 and 5 is not greater than 5, hence 1 cannot be the length of the 3rd side.
The answer is option C
Please answer this!!! WILL GIVE BRAINLIEST
Answer:
p > 9
Step-by-step explanation:
First let's note down-
George- has 23$
Total cost of m+p= more than $14
Second, let's subtract 23 and 14 to get what the glue costs.
23 - 14 = 9
So now we can cross out choice A and D.
Third, now earlier I said more than $14, this is the key part to find what we are going to choose.
more than = >
now we just plug in the variable,
p > 9
Hope this helps!
Please reach out to me if you still don't understand :)
Which transformation represents a reflection over the x-axis?
O (X,Y) - (-x, y)
O(x,y) → (X, -y)
O(x, y) (y,x)
(x, y) - (-y, x)
what does the mean absolute deviation tell you about the set?
a
The middle number if the data points are arranged in order
b
The most likely value of a data point
c
The average value of the data points
d
The variation of the data points
The correct answer is d i.e. The variation of the data points.
What is mean absolute deviation?
Mean absolute deviation (MAD) is a measure that describes the average distance between each data point in a set and the mean of that set. It is a way of measuring how spread out the data points are from the average or central value.
The correct answer is d. The mean absolute deviation tells you about the variation of the data points in a set. Specifically, it measures how much the data points deviate, on average, from the mean value of the set.
A higher mean absolute deviation indicates that the data points are more spread out from the mean, while a lower mean absolute deviation indicates that the data points are closer to the mean. The mean absolute deviation is useful for comparing the amount of variation between two or more sets of data, and can provide insight into the consistency or stability of the data.
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beinggreat78, you're looking for this
Answer:
z = 6
9 followed by a lowercase number, whether it's x, y, or z usually always means add 1 or multiply by an unknown number. In this case, we are multiplying.
\(9 * 45 = 405(wrong)\\\\9 * 63 = 567(wrong)\\\\9 * 7 = 63(wrong)\\\\9 * 6 = 54(correct)\)
That said, the answer is six.
What is x?
-2 + 3x = 5x - 8
Answer:
x = 3
Step-by-step explanation:
-2 + 3x = 5x - 8
add 8 to both sides:
-2 + 3x + 8 = 5x - 8 + 8
6 + 3x = 5x
subtract 3x from both sides:
6 + 3x - 3x = 5x - 3x
6 = 2x
divide both sides by 2:
6/2 = 2x/2
x = 3
check: when x = 3
-2 + 3(3) = 5(3) - 8
-2 + 9 = 15 - 8
7 = 7
Answer:
X = 3
Step-by-step explanation:
-2 + 3x = 5x - 8
+8 Because -8 is lower then -2 we start by doing the opposite and +8 to -2
6 + 3x = 5x
-3x Because now we have to do the opposite on the variable too.
6 = 2x
/2 Because you have to divide the integer by the variable
x = 3
What is 0.14 as a fraction
Answer:
7/50
Step-by-step explanation:
Here is an easy way of converting a decimal number to fraction.
Step 1:
Write it down as 0.14/1
Step 2:
Multiply bottom and top by 10 for every number after the decimal, since there is 2 numbers after the decimal you do 10*10 = 100
\(\frac{0.14(100)}{1(100)}\) = 14/100
Step 3:
You can simplify 14/100 to 7/50 and thats why 7/50 is the answer
Answer:
\(\frac{14}{100}\) or \(\frac{7}{50}\)
Step-by-step explanation:
To find 0.14 we have to see what place it's in, since it was in the hundredths place, we put 14 over 100, which is 14/100.
To simplify this fraction we have to find the GCM (Greatest Common Factor), the GCM of 14 and 100 is 2. Then we divide both the bottom and the top by 2 (whatever you do to the bottom, you do to the top), which gives us 7/50.
To conclude, 0.14 as a fraction is 14/100 or 7/50.
Which graph below represents the solution to the inequality 6 x − 12 − x ≤ 3
Answer:
The solution is:
\(6x-12-x\le \:3\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x\le \:3\:\\ \:\mathrm{Interval\:Notation:}&\:(-\infty \:,\:3]\end{bmatrix}\)
The graph of the solution is attached below.
Both the number line and graph is attached below.
Step-by-step explanation:
Note: you missed to add the graph options. Therefore, I am solving the inequality and adding the corresponding graph which would anyways clear your concept.
Given the inequality expression
\(6\:x\:-\:12\:-\:x\:\le \:3\)
Group like terms
\(6x-x-12\le \:3\)
Add similar elements: 6x-x=5x
\(5x-12\le \:3\)
Add 12 to both sides
\(5x-12+12\le \:3+12\)
simplify
\(5x\le \:15\)
Divide both sides by 5
\(\frac{5x}{5}\le \frac{15}{5}\)
simplify
\(x\le \:3\)
Therefore, the solution is:
\(6x-12-x\le \:3\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x\le \:3\:\\ \:\mathrm{Interval\:Notation:}&\:(-\infty \:,\:3]\end{bmatrix}\)
The graph of the solution is attached below.Both the number line and graph is attached below.
Please look at the graphs in the photo. Thank you!
(a). The graph of y = -f(x) is shown in the image below.
(b). The graph of y = g(-x) is shown in the image below.
How to draw the graph of the transformed functions?By reflecting the parent absolute value function g(x) = |x + 2| - 4 over the x-axis, the transformed absolute value function can be written as follows;
y = -f(x)
y = -|x + 2| - 4
Part b.
In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.First of all, we would determine the slope of this line;
Slope (m) = rise/run
Slope (m) = -2/4
Slope (m) = -1/2
At data point (0, 5) and a slope of -1/2, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 5 = -1/2(x - 0)
g(x) = -x/2 + 5, -4 ≤ x ≤ 4.
y = g(-x)
y = x/2 + 5, -4 ≤ x ≤ 4.
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Question 6 (5 points)
Which of the following pairs of triangles can be proven similar through SSS
similarity?
The pairs of triangles can be proven similar through SSS similarity is given by Third pair.
We know that the SSS similarity criteria will have the ratio of three corresponding sides of both triangles congruent.
1. KL / EG = HL / DG = HK / DE
3/6 = 6.5/13 ≠ 4/10
Thus, SSS similarity does not follow.
2. KL / EG = HL / DG = HK / DE
3/10 ≠ 6.5/13 ≠ 4/10
Thus, SSS similarity does not follow.
3. KL / EG = HL / DG = HK / DE
3/6 = 6.5/13 = 5/10
Thus, SSS similarity follow.
4. All three angles are congruent.
Thus, SSS similarity does not follow.
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Please help me with this proof.
Answer:
See below
Step-by-step explanation:
For the second step, \(\angle T\cong\angle R\) by Alternate Interior Angles. The rest of the steps appear to be correct.
How many feet are in a full minute, yes or no?
Answer:
2500 feet = 1 minute
Step-by-step explanation:
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
\(\frac{x/15000}{650}+\frac{y/15000}{1400} \leq 1\)
x/23.07 + y/10.71 ≤ 1
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Which of the following sets are continuous? Check all that apply.
A. {2, 4, 6, 8, ...)
B. (-0, +00)
C. (30, 45]
D. [60, 100)
E. {3,7)
Answer: The correct answer option is B.
Step-by-step explanation:
We are to determine whether which of the given data sets in the answer options are continuous.
For this, we need to know what a continuous data set is.
A data set that has no definite end to its value but keeps on continuing.
Here, the data sets are given in A, C, D, and E have definite starting and ending points.
While B is a continuous set as its values are continuing to infinity.
PLEASE SOMEONE HELP THIS IS THE LAST ANSWER ON MY TEST BUT I DONT KNOW MATH GOOD???
Answer:
x = 7
Step-by-step explanation: