Answer:
This is called the independent variable.
Step-by-step explanation:
We know this because it is independent of all outside factors. Additionally, the horizontal axis (also known as the x axis), is the axis known for the independent variable.
Consider the line that passes through the point P(l,-3) and is parallel to the line -3x-4y=9. Write the point-slope equation of the line. Use exact values.
parallel slopes always has the same exact slope.
The equation of required line is [tex]y=-\frac{3}{4} x-\frac{9}{4}[/tex]
Slope-intercept equation :Equation of line which is given,
[tex]-3x-4y=9\\\\y=\frac{-3x+9}{4} =-\frac{3}{4}x+\frac{9}{4}[/tex]
Compare above equation with [tex]y=mx+c[/tex]
Where m is slope of line, [tex]m=-\frac{3}{4}[/tex]
The slope of parallel lines are always equal.
So that, slope of required line is also [tex]-\frac{3}{4}[/tex].
[tex]y=-\frac{3}{4} x+c[/tex]
the line that passes through the point [tex]P(1,-3)[/tex]
Substitute given point in required equation of line.
[tex]-3=-\frac{3}{4} *1+c\\\\c=-3+\frac{3}{4} \\\\c=-\frac{9}{4}[/tex]
The equation of required line is [tex]y=-\frac{3}{4} x-\frac{9}{4}[/tex]
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Five people will equally share 2 pizzas.How much pizza will each person will receive?
Answer:
⅖ pizza
Step-by-step explanation:
Divide each pizza into five slices.
Then there will be 10 slices, and each person will get two slices.
Two slices = ⅖ pizza
Each person will receive ⅖ pizza.
Each of the five people will receive 2/5 of a pizza when two pizzas are shared equally amongst them.
Explanation:The student asked how much pizza each person will receive if five people are sharing two pizzas equally. To answer this, we divide the total number of pizzas by the number of people. Since there are 2 pizzas and each pizza is usually considered to be 1 whole, when split among 5 people, each person will get 2/5 of a pizza.
A 190-pound man and a 130-pound woman went to Burger King for lunch. The man had a BK Big Fish sandwich (750 Cal), medium french fries (400 Cal), and a large Coke (225 Cal). The woman had a basic hamburger (370 Cal), medium french fries (400 Cal), and a diet Coke (0 Cal). After lunch, they start shoveling snow and burn calories at a rate of 420 Cal/h for the woman and 610 Cal/h for the man. Determine how long each one of them needs to shovel snow to burn off the lunch calories. The metabolizable energy contents of different foods are as given in the problem statement. Shoveling snow burns calories at a rate of 420 Cal/h for the woman and 610 Cal/h for the man.
Answer:
2.25 hours for the man and 1.83 hours for the woman.
Step-by-step explanation:
We first find the number of calories consumed by both the man and the woman.
The man's calories are:
750+400+225 = 1375
The woman's calories are:
370+400+0 = 770
The man burns 610 calories per hour. This means to find the number of hours, we divide the number of calories by the rate burned per hour:
1375/610 = 2.25 hours
The woman burns 770 calories per hour. This means to find the number of hours, we divide the number of calories by the rate burned per hour:
770/420 = 1.83 hours
A 190-pound man needs to shovel snow for approximately 2.25 hours, and a 130-pound woman needs to shovel for approximately 1.83 hours to burn off the calories from their Burger King meal.
The question involves calculating the time it takes for a 190-pound man and a 130-pound woman to burn off the calories consumed from a meal at Burger King through the physical activity of shoveling snow. The man consumed a total of 1375 Calories (750 Cal for BK Big Fish sandwich, 400 Cal for medium french fries, and 225 Cal for a large Coke). The woman consumed a total of 770 Calories (370 Cal for a basic hamburger, 400 Cal for medium french fries, and 0 Cal for a diet Coke).
To find out how long each person needs to shovel snow to burn off the lunch calories, we divide the total number of calories consumed by the rate at which they burn calories while shoveling snow.
For the man: 1375 Calories / 610 Cal/h = approximately 2.25 hours.
For the woman: 770 Calories / 420 Cal/h = approximately 1.83 hours.
A plumber charges $55 per hour plus a $50 service charge. Kevin hired the plumber to install a new hot water heater. What are the total charges if the plumber took 4 hours to complete the installation?
A.
$220
B.
$250
C.
$255
D.
$270
The correct answer is D.
$55 per hour x 4 hours = $220
$220 + $50 service charge = $270 total
Hope this help.
Answer:
D. $270
Step-by-step explanation:
$55 per hour for 4 hours = $55 * 4 = $220
$50 service fee
total = hourly amount + service fee
total = $220 + $50
total = $270
What transformations of the parent function f(x) = x| should be made to graph, f(x) = - |x| + 5
Reflection over the x-axis, shift down 5 units
Reflection over the x-axis, shift up 5 units
Reflection over the y-axis, shift down 5 units
Reflection over the y-axis, shift up 5 units
Reflection over x-axis, shift down 5 units.
Answer:
Option B is correct.
Step-by-step explanation:
Given Parent Function, f(x) = |x|
Transformed function, f(x) = - |x| + 5
In transformed function, f(x) = -|x|
Represent that parents function is first reflected ove x - axis.
then in transformed function, f(x) = -|x| + 5
represent that after reflection function is shifted 5 unit in upward direction.
Therefore, Option B is correct.
A company offers you a job with an annual salary of $70 000 for the first year and a 5% raise every year after. Approximately how much money in total would you earn in 5 years of working there?
$386794
$87500
$89340
$367500
Answer:
$386794
Step-by-step explanation:
To be able to find how much we get in 5 years, we need to base it off the initial salary value.
So in the first year we get.
$70,000
To get how much we get in the 2nd year we add the extra 5%.
2nd year salary = (1.05)70000
2nd year salary = 73500
Now we continue to do that until the 5th year
3rd year = (1.05)73500
3rd year = 77175
4th year = (1.05) + 77175
4th year = 81033.75
5th year = (1.05) + 81033.75
5th year = 85085.44
Now we add them all up to get the total.
70000 + 73500 + 77175 + 81033.75 + 85085.44 = $386794.19 or $386794
For the geometric series given by 5 + 10 + 20+ . . . , which of the following statements is FALSE?
None of the other 3 statements here are False.
S₅₀₀ > S₄₉₉
S₅₀₀ > a₅₀₀
S1 = a1
Answer:
All statements are true
Step-by-step explanation:
1. The statement [tex]S_{500}>S_{499}[/tex] is true, because [tex]S_{499}[/tex] is the sum of first 499 terms, [tex]S_{500}[/tex] is the sum of first 500 terms, and all these terms are positive, then the sum of smaller number of terms is less than the sum of larger number of terms.
2. The statement [tex]S_{500}>a_{500}[/tex] is true, because [tex]S_{500}[/tex] is the sum of first 500 terms, [tex]a_{500}[/tex] is 500th term and the sum of 500 terms is greater than the 500th term.
3. The statement [tex]S_1=a_1[/tex] is true, because [tex]S_1[/tex] is the sum of first 1 term that is exactly [tex]a_1.[/tex]
All statements are true.
Given: Circles k1(A) and k2(O)ext. tangent
KE- tangent to k1(A) and k2(O)
AK=5, OE=4 Find: KE
There is a visual
AO is a line segment containing the radii of both circles, which are AK and OE, so AO = AK + OE = 9.
Extend AO to a point P on the line KE. Then we get two similar triangles APK and OPE. Let [tex]x[/tex] be the length of KE, [tex]y[/tex] the length of EP, and [tex]z[/tex] the length of OP.
By similarity, we have
[tex]\dfrac{OE}{AK}=\dfrac{EP}{KP}=\dfrac{OP}{AP}\iff\dfrac45=\dfrac y{y+x}=\dfrac z{z+9}[/tex]
OPE is a right triangle, so
[tex]OP^2=OE^2+EP^2\implies z=\sqrt{16+y^2}[/tex]
Now,
[tex]\dfrac45=\dfrac y{y+x}\implies 4(y+x)=5y\implies 4x=y[/tex]
and we also have
[tex]z=\sqrt{16+(4x)^2}=\sqrt{16+16x^2}=4\sqrt{1+x^2}[/tex]
Substituting this into the expression containing [tex]z[/tex] gives us an equation that we can solve for [tex]x[/tex]:
[tex]\dfrac45=\dfrac z{z+9}=\dfrac{4\sqrt{1+x^2}}{4\sqrt{1+x^2}+9}[/tex]
[tex]16\sqrt{1+x^2}+36=20\sqrt{1+x^2}[/tex]
[tex]9=\sqrt{1+x^2}[/tex]
[tex]\implies KE=x=\sqrt{80}=3\sqrt{10}[/tex]
What is the length of the missing side of the triangle in simplest radical form? the figure is not drawn to scale.
Answer:
option (c)
4√34
Step-by-step explanation:
Given in the question is a right angle triangle
height of triangle = 20 cm
base of triangle = 12 cm
To find the length of missing side of the triangle we will use pythagorus theorem
hypotenuse² = height² + base²hypotenuse² = 20² + 12²
hypotenuse² = 400 + 144
hypotenuse² = 544
take square root on both sides
√hypotenuse² = √544
hypotenuse = 4√34 cm
Hence, the length of missing side of the triangle is4√34 cm
(6CQ) Evaluate the limit, or state that the limit does not exist. 2n+7n/13n
Answer:
option(b)
9/13
Step-by-step explanation:
Given the expression
[tex]\frac{2n+7n}{13n}[/tex]
=[tex]\frac{9n}{13n}[/tex]
n will cancel out on both sides
so,
9/13 will remain
As 9/13 is a constant so any value of n when approaches to a constant will not affect it. Hence limit = 9/13
It is one of the limit laws thatThe limit of a constant function is equal to the constant.
Answer:
B
Step-by-step explanation:
John picks 150 apples on the first day, 250 on the second day, 350 on the third day, and so on. How many apples does John pick on the 10th day?
1250
1150
1050
950
To determine the number of apples John picks on the 10th day, we use the formula for the nth term of an arithmetic sequence. Given the first day's pick at 150 apples and an increase of 100 apples each day, we find that John picks 1050 apples on the 10th day.
Explanation:An arithmetic sequence is a sequence of numbers in which each term after the first is obtained by adding a constant difference to the preceding term.
In this case, the first term (the number of apples picked on the first day) is 150, and the common difference (the increase each day) is 100 apples.
To find the number of apples picked on the 10th day, we use the formula for the nth term of an arithmetic sequence, which is:
an = a1 + (n - 1) × d
Where an is the nth term, a1 is the first term, n is the term number, and d is the common difference. For the 10th day:
a10 = 150 + (10 - 1) × 100
a10 = 150 + 9 × 100
a10 = 150 + 900
a10 = 1050
Therefore, John picks 1050 apples on the 10th day.
PLEASE HELP!!!!!!!
For f(x) = 4x + 3 and g(x) = 9x find the following composite functions and state the domain of each
(a) f o g (b) g o f (c) f o f (d) g o g
(a) (f o g)(x) =
Answer:
Step-by-step explanation:
For f(x) = 4x + 3 and g(x) = 9x
(a) (f o g) (x)
= f (g (x))
= f (9x)
= 4(9x) +3
= 36x + 3
Its domain is any real number.
(b) (g o f) (x)
= g (f (x))
= g (4x + 3)
= 9 (4x + 3)
= 36x + 27
Again its domain is any real number.
(c) (f o f) (x)
= f (f (x))
= f (4x + 3)
= 4(4x + 3) + 3
= 16x + 12 + 3
= 16x + 15
Again its domain is any real number.
(d) (g o g) (x)
= g ( g (x))
= g (9x)
= 9(9x)
= 81x
Again its domain is any real number.
Answer:
solution given:
f(x) = 4x + 3
g(x) = 9x
answer:
a.fog(x)=f(9x)=4×9x+3=36x+3
domain=real number
b.gof (x)=g(4x+3)=9(4x+3)=36x+26
domain=real number
c.fof(x)=f(4x+3)=4(4x+3)+3=16x+12+3
=16x+15
domain: real number
d.
gog(x)=g(9x)=9×9x=81x
domain: real number.
A school principal ordered 1,000 pencils .He gave equal number to each of 7 teachers until he had given out as many as possible . How many pencils were left?
Answer:6
Step-by-step explanation: 1,000 divided by 7 is 994 with a remainder of six. Which means the principal had six left
first to answer gets brainlyest
Answer: 60 degrees
Step-by-step explanation:
the line is 180 degrees so minus 50 equals 130 minus 10 120 divide my 2 60
A coin is tossed. The probability of getting tails is 1?2. What is the likelihood of getting tails?
It’s a 50/50 chance since there is only 2 sides. (1?2)
Place the circles in order from the circle with the largest area to the circle with the smallest area.
a circle with a diameter
of 8 metersa circle with a radius
of 7 metersa circle with a circumference
of 37.68 metersa circle with a diameter
of 16 meters
Answer:
Diameter 16, radius 7, circumference 37.68, diameter 8
Step-by-step explanation:
Largest area will be in a circle with the largest radius. So let's find all radii.
d = 8, so r = 4;
r = 7;
circumference = 2pi*r = 37. 68, so r = 6
diameter 18, so r = 8
A square and a rhombus have the same perimeter. What about their areas? Are they the same? If not then which is bigger?
The area of a square is always larger than the area of a rhombus when they have the same perimeter.
Explanation:The areas of a square and a rhombus with the same perimeter are not equal. The square will always have a larger area than the rhombus.
To understand why, let's compare the sides and angles of a square and a rhombus.
Therefore, the square will always have a bigger area than the rhombus when both shapes have the same perimeter.
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What is the measure of angle A?
Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth.
Answer:
20
Step-by-step explanation:
You multiply the 80 and the 18 and then you add 82
How many Cubes with the side length of 1/4 unit would it take to make a unit cube
Answer:
4
Step-by-step explanation:
1/4 is a quarter at up 1/4 4 time and it gives you a whole, 1/4+1/4+1/4+1/4=1
Find the angle of elevation, to the nearest degree, of the sun if a 54 foot flagpole casts a shadow 74 feet long.
Answer:
If the angle is in degrees, when taking the tangent, make sure your calculator is in Degree mode.
I hope this helps.
What is measure of angle A?
Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth.
Answer:
[tex]A=53.13\°[/tex]
Step-by-step explanation:
The figure shows a right triangle.
To calculate the measure of the angle A, you can use the inverse trigonometric function arctangent:
[tex]\alpha=arctan(\frac{opposite}{adjacent})[/tex]
Identify the angle [tex]\alpha[/tex], the opposite side and the adjacent side:
[tex]\alpha=A\\opposite=4cm\\adjacent=3cm[/tex]
Substitute into [tex]\alpha=arctan(\frac{opposite}{adjacent})[/tex].
The measure of the angle A is:
[tex]A=arctan(\frac{4}{3})\\\\A=53.130\°[/tex]
Rounded to the nerarest hundreth:
[tex]A=53.13\°[/tex]
The answer is m∠A = 53.13 °
Randy took out a subsidized student loan of $7,000 at a 3.6% APR, compounded monthly, to pay for his last semester of college. If he will begin paying off the loan in 10 months with monthly payments lasting for 20 years, what will be the total amount that he pays in interest on the loan?
A.) 10,128.00
B.) 9,830.40
C.) 2,830.40
D.) 3,128.00
Answer: 2830.40
Step-by-step explanation:
By using mathematical formulas for calculating compound interest and the total payment of an installment loan, and then subtracting the original loan principal, the total interest paid on the loan is identified as $9,830.40.
Explanation:To solve this problem, use the formula for the compound interest on a loan: A = P(1 + r/n)^(nt), where:
A is the total amount of money accumulated after n years, including interest. P is the principal amount (the initial amount of money). r is the annual interest rate (in decimal) (3.6% APR). t is the number of years the money is invested or borrowed for. n is the number of times that interest is compounded per unit t.
Since Randy is not going to start paying off his loan until 10 months later, the money will compound for 20 years and 10 months. Convert 10 months into years we get 10/12 = 0.833 years. Therefore, t = 20 + 0.833 = 20.833 years.
The loan was compounded monthly which means n = 12 and the rate is r = 3.6/100 = 0.036. Now you can substitute these values into the formula.
Next, find the total amount paid over the entire period of the loan by using the formula for the total payment of an installment loan: M = P*r*(1 + r)^n / [(1 + r)^n – 1], where M is monthly payment.
Subtract the principal from the total payment to find the total interest paid. From the given options, it appears that the answer is B.) $9,830.40
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You roll a number cube numbered from 1 to 6. What is the probability that the number is 2,6,3,4,or 1
[tex] \frac{5 \: = \: number \: of \: favorable \: outcomes}{6 \: = \: number \: of \: possible \: outcomes} [/tex]
Since there are 6 possible outcomes, that will become the denominator. In addition, since we are trying to find the probability of rolling 5 numbers out of that 6, 5 would be the numerator.
So the answer is,
[tex] \frac{5}{6} [/tex]
The probability that the number is 2,6,3,4, or 1 is 5/6.
What is probability?Probability is the ratio that shows the likelihood that an event will occur from a given set of events.
The probability of the given event can be found as shown below:A cube has six sides. Each side has a unique number.
We have to find the probability of getting 2,6,3,4, or 1.
The total number of favorable events = 5
The sample space has 6 events.
Therefore, the probability is given by 5/6.
Therefore, we have found the probability that the number is 2,6,3,4, or 1 to be 5/6.
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3x/5-0.5=1.9
a: 0.16
b: 16
c: 4
d: 2.3
Answer:
C. 4
Step-by-step explanation:
(3x/5) - 0.5 = 1.9
+ 0.5 +0.5
3x/5 = 2.4
*5 *5
3x = 12
— —
3 3
X = 4
Answer is C
I hope I helped!
Let me know if you need anything else!
~Zoe
Find the distance from point P to RQ
To find the distance from point P to line RQ, we first find the vectors for PQ and PR. Then we calculate the projection of PR onto PQ which gives us the vector from P to the point on line RQ nearest to P. The length of this vector gives us the shortest distance from point P to the line RQ. This explanation assumes we have coordinate data for points P, Q, and R.
Explanation:The distance from point P to RQ can be found utilizing mathematical principles of geometry and vectors. Let's assume that we know the coordinates of points P, R, and Q. Having these information, we can follow these steps:
First, find the vector RQ which is Q - R. Let's presume this gives us the vector a. Then, calculate the vector RP which is P - R and let's assume this gives us the vector b. The projection of vector b onto vector a is given by [(b.a)/|a|²]a (where . denotes the dot product and |a| is the magnitude of a). This will give us a vector from point R to the point on the line RQ that is nearest to point P, let's call this point M. Finally, find the vector PM by subtracting the projection from vector b. The length of this vector gives us the shortest distance from point P to the line RQ.
Remember, this is the process given that you know the coordinates of the points involved. If you only have a diagram, you might need to use tools like a ruler or a protractor to measure distances and angles.
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A winter jacket is marked down 75% from its original price. According to the new price tag, it now costs $52.50. What was the original price?
Answer:
x = 70
Step-by-step explanation:
70 % of x = 52.50
75 out of 100 X = £ 52.50
Answer:
The Original Price of the Winter Jacket is $70
Step-by-step explanation:
The Original Price is calculated by using the given information on a Simple Rule of Three formula, which looks like the following.
X --------> 100%
$52.50 --------> 75%
The Rule of Three simply asks if $52.50 is 75% then What is 100%? We solve the Rule of Three by multiplying $52.50 by 100 and then dividing the result by 75.
[tex]X = \frac{52.50*100}{75}[/tex]
[tex]X = 70[/tex]
According to the formula the Original Price of the Winter Jacket was $70
I hope this answered your question. If you have any more questions feel free to ask away at Brainly.
Please help me solve this as soon as possible.
Thanks!!
BRAINLIEST TO FIRST WHO ANSWERS
Answer:
x=-5
Step-by-step explanation:
Set up the rational expression with the same denominator over the entire equation.
2x-2/6=3x+3/6
Since the expression on each side of the equation has the same denominator, the numerators must be equal.
2x−2=3x+3
Move all terms containing x to the left side of the equation.
−x−2=3
Move all terms not containing x to the right side of the equation.
-x=5
Multiply each term in x=−5 by −1
x=−5
A zoo had 12 large aquariums with fish. The number of fish in each aquarium is shown 37, 58, 62,36,42,71,56,58,69,66,47,68 what is the range in the number of fish
Answer:
35
Step-by-step explanation:
First, we will define range.
The difference between the highest and lowest values in a data is called range. To find the range, first the highest and lowest values are found from data, then the lowest value is subtracted from the highest value.
In the above data,
Highest Value=71
Lowest Value=36
Range=Highest value-lowest value
=71-36
=35
The range in the number of fish across the 12 large aquariums is 35, calculated by subtracting the minimum number of fish, 36, from the maximum number, 71.
The question asks us to calculate the range in the number of fish across 12 large aquariums at a zoo. To find the range, we need to identify the largest and smallest numbers in the given data set and then subtract the smallest from the largest.
Here is the list of the numbers of fish in each aquarium: 37, 58, 62, 36, 42, 71, 56, 58, 69, 66, 47, 68.
First, we find the maximum and minimum values:
Maximum (the largest number of fish in an aquarium): 71
Minimum (the smallest number of fish in an aquarium): 36
Next, we calculate the range by subtracting the minimum value from the maximum value:
Range = Maximum - Minimum
Range = 71 - 36
Range = 35
Therefore, the range in the number of fish across the 12 aquariums is 35.
I need help with question 9
let's not forget that a function and its inverse have a domain <-> range relationship, namely, if the original function has a point of say (3 , 7 ), then its inverse function will have a point of (7 , 3 ), the same pair just flipped sideways.
[tex]\bf (g\circ f^{-1})(x)\implies g(~~~f^{-1}(x)~~~) \\\\\\ (g\circ f^{-1})(2)\implies g(~~~f^{-1}(2)~~~) \\\\[-0.35em] ~\dotfill\\\\ \textit{so let's firstly find out what is }f^{-1}(2)[/tex]
we don't have an f⁻¹(x), darn!! but but but, we do have an f(x) on the left-hand-side graph, and it has a pair where y = 2, namely ([ ] , 2), so then, f⁻¹(x) will have the same pair but sideways, let's inspect f(x).
hmmmmmm when y = 2, x = 0, notice the y-intercept on the graph, ( 0, 2 ).
so then, that means that f⁻¹(x) has a pair sideways of that, namely ( 2, 0), or f⁻¹(2) = 0.
so then, g( f⁻¹(2) ), is really the same as looking for g( 0 ), well then, what is "y" when x = 0 on g(x)? let's inspect the right-hand-side graph.
hmmmmmmmmmmm notice, the point is at ( 0 , 2 ), namely when x = 0, y = 2.
[tex]\bf (g\circ f^{-1})(2)\implies g(~~~f^{-1}(2)~~~)\implies g(0)\implies 2[/tex]
Find the minimum value of the function for the polygonal convex set determined by the given system of inequalities.
3x+2y≥14
-8x+3y≤10
f(x,y)=8x+8y
Answer:
Option b (4,1)
Step-by-step explanation:
The region given by the system of inequalities is shown in the graph. We must look within this region for the point that minimizes the objective function [tex]f(x, y) = 8x + 8y[/tex]
The minimum points are found in the lower vertices of the region.
These vertices are found by equating the equations of the lines::
[tex]3x+2y=14\\-5x +5y=10[/tex]
-------------------
[tex]x = 2\\y = 4[/tex]
[tex]-8x + 3y = -29\\3x + 2y = 14[/tex]
---------------------
[tex]x = 4\\y = 1[/tex]
The lower vertices are:
(4, 1) (2, 4)
Now we substitute both points in the objective function to see which of them we get the lowest value of [tex]f(x, y)[/tex]
[tex]f(4, 1) = 8(4) +8(1) = 40\\f(2, 4) = 8(2) + 8(4) = 48[/tex]
Then the value that minimizes f(x, y) is (4,1).
Option b