Given,
The statement is "The height of a person and his weight".
Required/
Identify the statement is inverse or direct variation.
As the height of the person increase then its their weight is also increased.
Similarly,
The height of the person decrease then its their weight is also decreased.
Hence, it is direct variation.
Which is the equation of a line that is perpendicular to the line represented by ?
Answer:
It will be
.. y = -4/3x +c . . . . . for some value of c
_____
The slope of the perpendicular line will be the negative reciprocal of the slope of the given line, which is 3/4.
P(3,-3) Q(8,7) R(5,-2)
Given S(11,1) is a point which lies on the extended line PR where QS is a perpendicular line to PRS. Find the area of triangle PQR.
Answer: the area of triangle PQR is 7.5 square units
Step-by-step explanation:
[tex]\displaystyle\\A_{PQR}=\frac{PR*QS}{2} \\\\1.\ (3,-3)\ \ \ \ \ (5,-2)\\\\PR=\sqrt{(5-3)^2+(-2-(-3))^2}\\\\PR=\sqrt{2^2+(-2+3)^2} \\\\PR=\sqrt{4+1^2} \\\\PR=\sqrt{4+1}\\\\ PR=\sqrt{5} \ units[/tex]
[tex]\diplaystyle\\2.\ (8,7)\ \ \ \ \ (11,1)\\\\QS=\sqrt{(11-8)^2+(1-7)^2} \\\\QS=\sqrt{3^2+(-6)^2} \\\\QS=\sqrt{9+36} \\\\QS=\sqrt{45}\\\\QS=\sqrt{9*5} \\\\QS=\sqrt{3^2*5} \\\\QS=3\sqrt{5}[/tex]
[tex]\displaystyle\\Hence,\\A_{PQR}=\frac{\sqrt{5}*3\sqrt{5} }{2} \\\\A_{PQR}=\frac{(\sqrt{5}*\sqrt{5}) *3 }{2} \\\\A_{PQR}= \frac{5*3}{2}\\\\A_{PQR}=\frac{15}{2}\\\\A_{PQR}=7.5 \ units^2[/tex]
What is the speed of a vehicle when it covers a distance of 6Om in 3seconds?
The speed is calculated as distance over time, so:
[tex]\text{speed}=\frac{\text{distance}}{\text{time}}[/tex]Replacing distance by 60 m and time by 3 seconds, we get:
[tex]\text{ speed=}\frac{60\text{ m}}{3\text{ seconds}}=20\text{ m/second}[/tex]The speed of the vehicle is 20 m/second
Triangles FAD and DCE are translations of triangle ABC.
Select all the statements that must be true. (Lesson 1-21)
A. Points B, A, and F are collinear.
PERIOD
E
(B.) The measure of angle BCA is the same as the measure of angle CED.
C. Line AD is parallel to line BC.
D. The measure of angle CED is the same as the measure of angle FAD.
(E.) The measure of angle DAC is the same as the measure of angle BCA.
F. Triangle ADC is a reflection of triangle FAD.
The statements about triangles FAD and DCE which are translations of triangle ABC include the following:
A. Points B, A, and F are collinear.
(B.) The measure of angle BCA is the same as the measure of angle CED.
C. Line AD is parallel to line BC.
(E.) The measure of angle DAC is the same as the measure of angle BCA.
The types of transformation.Generally, there are four (4) main types of transformation and these include the following:
ReflectionDilationRotationTranslationWhat is a translation?In Geometry, a translation can be defined as a type of transformation which moves every point of a geometric figure (object) in the same direction, as well as for the same distance.
Since triangles FAD and DCE both represent the translations of triangle ABC (see attachment), we can logically deduce the following information:
Points B, A, and F all lie on the same line BF, which makes point B, A, and F collinear.All of the sides and angles of triangle ABC (ΔABC) are equal to triangle DCE (ΔDCE), which makes angle BCA (m∠BCA) equal to angle CED (m∠CED).Line AD and line BC are parallel lines because they can never meet.The measure of angle DAC (m∠DAC) is the same as the measure of angle BCA (m∠BCA).Read more on translation here: https://brainly.com/question/19880883
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Kaye Blanchard is 50 years old . She has $ 40,000 of adjusted gross income and $ 10,000 of qualified medical expenses . She will be itemizing her tax deductions this year . How much of a tax deduction will Kaye be able to deduct ( assume 10 % floor for deduction ) ?
Answer: 70
Step-by-step explanation:
easy addition
The following graph shows a proportional relationship.
What is the constant of proportionality between y and x in the graph?
The constant of proportionality between x and y in the given graph above is determined as: 2.
What is the Constant of Proportionality?The constant of proportionality of a proportional relationship between two variables, x and y, can be defined as the ratio of y to x, which is expressed as, k = y/x, where x and y are the coordinates of one point one the line that represents the proportional relationship.
Using the coordinates of a point on the graph, (2, 4), find the constant of proportionality, k:
Constant of proportionality (k) = y/x = 4/2
Constant of proportionality (k) = 2
Therefore, the constant of proportionality that represents the proportional relationship between the variables, x and y, is calculated as, 2.
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What is the smallest integer greater than 800 that is relatively prime to 10!
The smallest integer greater than 800 that is relatively prime to 10! is 801
How to determine the number greater than 800 that is relatively prime to 10!The term relatively prime refers to numbers who has a greatest common factor of 1. If two numbers have a greatest common factor of 1 the two numbers are said to be relatively prime
solving for 10!
10! = 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1
= 362880
prime factorization of 10!
= 2^7 * 3^4 * 5 * 7
prime factorization of 801
= 3^2 * 89
The greatest common factor of both numbers is 1, this is not included to the factors in the prime factorization but 1 is a known common factor already.
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write a phrase for each expression
X - 6
The phrase of the expression x - 6 is 6 less than a number.
Expression:
The expression refer the sentence with a minimum of two numbers/variables and at least one math operation in it.
Given,
Here we have the expression x -6.
And we need to convert this expression in order to get the phrase form.
In order to get the phrase form, we have to translate the given expression into word.
While we looking into the given expression we have identified the following three terms.
They are, x , (-) and 6.
Here x represents the unknown number.
(-) represents that we have to less the unknown number by the given number.
And 6 is the given number.
So, the phrase for this situation is 6 less than a number.
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Omar went shopping for a new video game because of a sale. The price on the tag was $37, but Omar paid $25.90 before tax. Find the percent discount.
Answer:
30%
Step-by-step explanation:
Omar went shopping for a new video game because of a sale. The price on the tag was $37, but Omar paid $25.90 before tax. Find the percent discount.
(37 - 25.9)/37 = 0.3 or 30% discount
check:
70% of $37 = $25.90
A cylindrical oil tank 8 ft deep holds 580 gallons when filled to capacity. How many gallons remain in the tank when the depth of oil is 3 1/2 ft.
Solution
[tex]\begin{gathered} 8ft=580\text{ gallons} \\ 3\frac{1}{2}ft=x \end{gathered}[/tex]Solution
[tex]\begin{gathered} \frac{8}{3.5}=\frac{580}{x} \\ cross\text{ multiply} \\ 8x=3.5\times580 \\ 8x=2030 \\ divide\text{ both sides by 8} \\ \frac{8x}{8}=\frac{2030}{8} \\ x=253.75 \end{gathered}[/tex]The final answer
253.75 gallons remain in the tank when the depth of oil is 3.5 ft
Find the area.
a.1604 ft
b.2600 ft
c.2160 ft
d.2180 ft
Answer:
d.2180
Step-by-step explanation:
add the two sides and subtract that one number on top I believe
Which answer is equivalent to
OA.
B. √
(4
OB.
C.
16
49
D.
16
49
3/16
349
√16
(49
? Please helpppp
Answer:
C [tex]\sqrt \frac{16}{49}[/tex]Step-by-step explanation:
looking at all the stress you're in I knew I had to help so all your lists are bunched up, so I went of the picture C is correct because B 4 and 7 aren't even a part of the question itself and A has 16 and 49 but it doesn't have sqrt so it's not = to the question and D is not correct either because it doesn't have one sqrt it has two on top of each other. HOPE THIS HELPED!
(7g - 6) - (-3n - 4) find the difference and show your work. Please this is due tomorrow
Answer:
7g + 3n - 2
Step-by-step explanation:
(7g - 6) - (-3n - 4)
7g - 6 + 3n + 4
7g + 3n - 2
I hope this helps!
1) the owner of a video store has determined that the cost c, in dollars, of operating the store is approximately given by where x is the number of videos rented daily. find the lowest cost to the nearest dollar. a) $400 b) $500 c) $650 d) $550
The lower cost will occur at the extreme point, that is if the number of videos rented daily is 8 pieces and the cost will be $550.
The cost function is given by:
C(x) = 2x² - 32x + 678
The lowest cost happens at the extreme point. In this point the derivative of C(x) is equal to zero.
Take the derivative:
C'(x) = 4x - 32 = 0
4x = 32
x = 32/4 = 8
Hence, the lowest cost will occur if the number of video rented daily is 8 pcs.
Substitute x = 8 into the cost function:
C(8) = 2(8)² - 32.(8) + 678 = 550
Complete question:
The owner of a video store has determined that the cost c, C(x) = 2x² - 32x + 678 in dollars, of operating the store is approximately given by where x is the number of videos rented daily. find the lowest cost to the nearest dollar
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For the following relation, complete the table of values and sketch the graph.
y=3x^2-10
x. y?
-3.
-2.
-1.
0
1
2
3
The table of values for the given equation is presented below:
x y
-3 17
-2 2
-1 -7
0 -10
1 -7
2 2
3 17
Quadratic FunctionThe Standard form for a quadratic equation is ax²+ bx + c=0, where: a, b and c are your respective coefficients. In the quadratic function, the coefficient "a" must be different than zero (a≠0) and the degree of the function must be equal to 2.
To solve a quadratic function, you should find the discriminant: D=b²-4ac and then use this variable in the formula: [tex]x=\frac{-b \±\sqrt{\Delta} }{2a}[/tex].
The given equation is a quadratic function because have a degree equal to 2. Then, when you plot the graph, you obtain a parabola.
First, you should replace the given values for x in the equation y=3x²-10
x y
-3 y=3*(-3)²-10= 3*9-10=27-10=17
-2 y=3*(-2)²-10= 3*4-10=12-10=2
-1 y=3*(-1)²-10= 3*1-10=3-10= -7
0 y=3*(0)²-10= 3*0-10=-10= -10
1 y=3*(1)²-10= 3*1-10=3-10= -7
2 y=3*(2)²-10= 3*4-10=12-10= 2
3 y=3*(3)²-10= 3*3-10=27-10= 17
Now, you have the points to draw the graph, show the attached image.
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x-3/5=x+3/15 pls help
Answer: The answer is no solution because the x cancels out
eamonn has just taken a statistics exam, and he wants to calculate a confidence interval to represent the exam scores in his class. the test mean was 75, with a standard deviation of 5. there are 30 students in the class. the 90% confidence interval for the class is:
The 90% confidence interval for the class is [73.49, 76.51].
Confidence interval is defined as the range of values where a parameter might fall at a given confidence level. It can be calculated using the formula below.
CI = μ ± z x SD/√n
where CI = confidence interval
μ = sample mean = 75
z = found by using a z-score table
SD = sample standard deviation = 5
n = sample size = 30
At 90% confidence level, the area in each tail of the standard normal curve is 5, and the cumulative area up to the second tail is 95.
(100 - 90) / 2 = 5
100 - 5 = 95
Find 0.95 in the z-table to get the value of z.
At p = 0.95, z = 1.65
Plug in the values to the formula for confidence interval, CI.
CI = μ ± z x SD/√n
CI = 75 ± 1.65 x 5/√30
CI = 75 ± 1.51
CI = [73.49, 76.51]
Hence, for every 100 samples, at 90% confidence level, the mean will be between 73.49 and 76.51.
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On Saturday mornings, Emmet volunteers at the hospital where his mother works. One Saturday, he answers phone calls at the information desk while the receptionist is away. Then he spends 25 minutes delivering flowers to patients' rooms. In all, Emmet volunteers at the hospital for 45 minutes that day.
Which equation can you use to find the amount of time t that Emmet answers phone calls?
The equation used to find the amount of time Emmet answers phone calls is t +25= 45
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The amount of time Emmet answers phone calls = 20
She spends delivering flowers to patient's room= 25 minutes
She spends meetings volunteering at the hospital= 45
Let t be the amount of time Emmet answers phone calls in the hospital
Hence the equation used to calculate the amount of time spent on calls;
t + 25= 45
Now collect the like terms;
t= 45-25
t= 20
Hence, The equation used to find the amount of time Emmet answers phone calls is t +25= 45
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Which subatomic particles are located in the nucleus of an He-4 atom?
The sub-atomic particles located in the nucleus of an He^4 atom are 2 protons and 2 neutrons.
Helium belongs to double-electronic species, unlike alpha-particles which are devoid of electrons. The two electrons of Helium are accommodated in the 1s orbital, outside the nucleus.
Nucleons are always present in the nucleus of various elements. Nucleons collectively refer to protons and neutrons. In this case, 2 protons and 2 neutrons reside in the nucleus.
The number of protons is always equal to the atomic number of the element. The number of neutrons is always equal to the difference between the mass number and the atomic number of the element.
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I need some help with my math.
Recall that the formula for the area of a rectangle is, A = l×w where l represents the length of the rectangle and w represents its width.
Find the area of a rectangle that has a length of 3.5 centimeters and a width of 2.2 centimeters. The answer is 7.7
Using the formula for the area of a rectangle is, A = l×w where l represents the length of the rectangle and w represents its width, the area of a rectangle with the length of 3.5 centimeters and a width of 2.2 centimeters will be 7.7 cm^2.
What is the area of a rectangle?The area of the rectangle can be calculated using the formula,
(A = l×w )
and the l = the length of the rectangle
w = represents the width of the rectangle
Then to calculate the area of the rectangle, we can substitute the values that is been given as :
(A = l×w )
A = (2.2 * 3.5) = 7.7 cm^2
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Answer:
7.7
Step-by-step explanation:
The answer was already in the question... He must've edited it or somethin'
Juanita has a part-time job that pays $12/hour and works about 50 hours every month. Her
withholdings are Social Security. (6.2%), Medicare (1.45%) and federal income tax (10%). What
is her approximate net pay?
a. $120
b. $500
c. $600
d. $700
The approximate net pay of Juanita is $500. Therefore, option B is the correct answer.
Given that, Juanita has a part-time job that pays $12/hour and works about 50 hours every month.
What is the net pay?Net pay means take-home pay or the amount employees earn after all payroll deductions are subtracted from their gross pay.
Now, total money earned in a month
= 12 × 50 = 600
Now
6.2% of 600 = $37.2
= 600 - 37.2 = $562.8
1.45% of 562.8 = $8.1606
= 562.8 - 8.1606 = $554.6394
10% of 554.6394 = $55.46394
= 554.6394 - 55.46394 = $499.17546
Total deductions = $499.17546
So, net pay = grass pay - deductions
= 600 - 105.9
= $499.17546
The approximate net pay of Juanita is $500. Therefore, option B is the correct answer.
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Find the distance between A(5,-4) and B(5,-5)
Answer:
1
Step-by-step explanation:
(5−5)^2+(−5−(−4))^2
0^2+-1^2
1
Two cities A and B are shown on diagram. every 1 cm = 4 km.
1) Find scale
2) Find distance between A and B
3) "C" city is in west 12km from A, 20km from B. Locate "C" on diagram.
1. The scale is of 1:400,000.
2. The distance between A and B is of 36 km.
3. The diagram with city C is given at the end of the answer.
What is a scale?The scale of a drawing is how much each unit in the drawing represents in actual distance.
In the context of this problem, the scale is given as follows:
1 cm = 4 km
Meaning that each cm drawn represents 4 km of actual distance.
Using the same unit, we have that:
4 km = 4 x 100,000 cm = 400,000 cm.
Hence the scale is given by:
1:400,000.
Measuring on the drawing, the distance between A and B is of 9 cm, hence, applying the scale, the real distance is of:
9 x 4 km = 36 km.
In the diagram, considering the given scale, we want to position city C 3 cm from City A, to the west = to the left.
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suppose that the miles per gallon (mpg) rating of passenger cars is a normally distributed random variable with mean of 33.8 mpg and standard deviation of 3.5mpg. what is the probability that a randomly selected car gets less than 40 mpg?
The probability that a randomly selected car gets more than 40 mpg is equal to 0.771.
Let us assume that the miles-per-gallon rating of passenger cars be represented by random variable X. According to the question we know that X ≈ N (μ = 33.8 mpg and σ² = 3.5² mpg). Now, to compute the probability that a randomly selected passenger will gets less than 40 mpg will be given as
P(X < 40) = P(X - μ/σ > 40 - 33.8/3.5)
= P(Z < 1)
= P(Z > 1) - 1
= 1.771 - 1
= 0.771 which is the required probability.
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Need help with writing a rule to describe each transformation
Explanation
By observation, we can see that the transformation from the original to the image, is a rotation of 90 degrees counterclockwise about the origin.
Answer: Option D
I need help with the question below please:A painter must thin some paint for use in a sprayer. If the recommended rate is 1/9 pint of water per gallon of paint, how many total gallons will there be after thinning 36 gallons of paint?
geometry topic 2 test
Answer:
what is the question?
Step-by-step explanation:
Petra must write a report with more than 1,000 words forher history class. So far, she has written 684 words. Writeand solve an inequality to find how many more wordsPetra needs to write for her report.
Step 1: Let the remaining number of words be X.
The inequality equation becomes:
[tex]\begin{gathered} X+684>1000 \\ X>1000-684 \\ X>316 \end{gathered}[/tex]Hence, the number of words Petra has to write to have more than 1000 words should be greater than 316 words.
Find sides AM and side AR
AR-9x-2 RM-2x+6 AM-5x-3
Using the segment addition postulate, the lengths of the sides are given as follows:
AM: 4.5625.AR: -0.8125.Segment Addition PostulateThe segment addition postulate is a geometry axiom that states that a line segment, divided into a number of smaller segments, has the length given by the sum of the lengths of the smaller segments.
In this problem, the line AM is divided into two segments by point R, as follows:
AR = 9x + 2.RM = 2x + 6.The total length of the line is given by:
AM = -5x + 3.
Hence the solution for x is given as follows:
AR + RM = AM
9x + 2 + 2x + 6 = -5x + 3
11x + 8 = -5x + 3
16x = -5.
x = -5/16
x = -0.3125.
Hence the lengths are:
AM = 5x - 3 = -5(-0.3125) + 3 = 4.5625.AR = 9x - 2 = 9(-0.3125) + 2 = -0.8125.There is a typo in the signals as we have a negative length, which is not possible, but the procedure is as shown in this problem.
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