Answer:
4 units to the left and 2 units up.
Step-by-step explanation:
Norman makes $15 commission for selling $200 in merchandise. he makes $37.50 commission for selling $500 in merchandise. assuming that the variables are directly related and norman wants to make $150 in commission, what is the total value of merchandise he needs to sell?
So he needs to sell $2,000 in merchandise.
what is the total value of merchandise he needs to sell?
We can assume that we have a proportional relation:
y = k*x
Where y is the commission and x is what Norman sells, then:
$15 = k*$200
k = $200/$15 = 0.075
$37.50 = k*$500
k = $500/$37.50 = 0.075
Then the relation is:
y = 0.075*x
If he wants a commission of $150, then:
$150 = 0.075*x
$150/0.075 = x = $2,000
So he needs to sell $2,000 in merchandise.
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Consider the line y=3x-3.
Find the equation of the line that is perpendicular to this line and passes through the point (4, 5)
Find the equation of the line that is parallel to this line and passes through the point (4, 5).
Answer:
Perpendicular: [tex]y=-\frac{1}{3}x+\frac{19}{3}[/tex]
Parallel: [tex]y=3x-7[/tex]
Step-by-step explanation:
So when two lines are perpendicular, that means the the slope is the reciprocal with the opposite sign so: [tex]\frac{a}{b} \text{ has a slope perpendicular to } -\frac{b}{a}[/tex]. In this case we have the equation in slope-intercept form, so it's easy to determine the slope, it's 3. So that means the perpendicular line will have a slope of: [tex]-\frac{1}{3}[/tex]. Since you have a slope of 3/1 which becomes 1/3 and also an opposite sign. This gives you the equation: [tex]y=-\frac{1}{3}x+b[/tex]. We can solve for b, by plugging in a coordinate it passes through. This is given in the problem, with it being (4, 5) = (x, y). So plugging these values in as (x, y) gives you the equation: [tex]5=-\frac{1}{3}(4)+b\implies\frac{15}{3}=-\frac{4}{3}+b\implies\frac{19}{3}=b[/tex]. This gives you the complete equation: [tex]y=-\frac{1}{3}x+\frac{19}{3}[/tex]
So when two lines are parallel, that means they have the slope, and a different y-intercept. This is because if they had the same y-intercept, then the two lines would be the same exact line. We already know the slope, it's 3. So we have the general equation: [tex]y=3x+b\text{ where b}\ne-3[/tex]. The restriction on b, was explained on the previous sentence, if b=-3, then we have the same equation, which is not parallel, they would be the same line, meaning they would intersect at infinite points, which is completely different than two lines that never intersect. So now we can plug in the given point (4, 5) to solve for b. Plugging these coordinates in gives you: [tex]5=3(4)+b\implies5=12+b\implies-7=b[/tex]. This gives you the complete equation: [tex]y=3x-7[/tex]
The price of an emergency light is $375 and it decreased by
2% each year. Find the exponential model representing
this situation.
The price of the light as a function of x is given by the exponential function:
[tex]p(x) = \$375*(0.98)^x[/tex]
Which exponential model represents this situation?
We know that the original price of the light is $375.
This value decreases a 2% each year, so each year we need to multiply the above price by (1 - 2%/100%) = (1 - 0.02) = 0.98
Then, if x represents the number of years, the price of the light as a function of x is given by the exponential function:
[tex]p(x) = \$375*(0.98)^x[/tex]
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helppp!!!
Lynn is putting tiles on her bathroom floor. Each tile measures 1 square foot each. The floor measures 4 1/2 ft by 3 3/4 ft. How many tiles will she need to cover the floor?
Considering the area of the rectangle, it is found that she will need 17 tiles to cover the floor.
What is the area of a rectangle?The area of a rectangle of length l and width w is given by the multiplication of dimensions, that is:
A = lw
The dimensions in feet are given as follows:
l = 4 1/2 ft = 4.5 ft.w = 3 3/4 ft = 3.75 ft.Hence the area in square feet is given by:
A = 4.5 x 3.75 = 16.875 ft².
Each tile has 1 square foot, hence, rounding, she will need 17 tiles to cover the floor.
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Write a polynomial function with the real
zeros -3, 0, and 3.
[tex]f(x)=x(x-3)(x+3)[/tex]
Write a polynomial function of least degree with integral coefficients that has the given zeros. -1/3, 2/3, -1/4
Step-by-step explanation:
"integral" means here that the factors in the polynomial are integers.
we have 3 zeros.
the least degree of a polynomial with 3 zeros is 3.
and yes, that works also for 2 zeros (the degree must be at least 2, it must be at least a quadratic equation).
or 4 zeros (at least 4th degree).
it in general n zeros (at least nth degree).
constructing this out of the given zeros is easy.
what happens, when I multiply something by 0 ? the total result will be 0.
and so, we simply multiply 3 short terms with each other, where each term turns 0 for one of the given zeros.
what expression in x turns 0, when x = -1/3 ?
well : x + 1/3 or with integers 3x + 1 (multiplied by 3)
and for x = 2/3 ?
x - 2/3 or with integers 3x - 2
and for x = -1/4 ?
x + 1/4 or with integers 4x + 1
so, our polynomial function (of at least 3rd degree) is then
(3x + 1)(3x - 2)(4x + 1)
basically this could be already the result, depending on what your teacher wants.
for the fully extended form we need to do the multiplications :
(3x + 1)(3x - 2) = 9x² - 6x + 3x - 2 = 9x²- 3x - 2
(9x²- 3x - 2)(4x + 1) = 36x³ + 9x² - 12x² - 3x - 8x - 2 =
= 36x³ - 3x² - 11x - 2
the requested polynomial function is
f(x) = 36x³ - 3x² - 11x - 2
A ratio is...
O where two numbers are written as a fraction in lowest terms.
O where two or more values are compared in lowest terms.
O when two numbers are written as a division problem.
O all of these.
Answer:
All of these definitions are correct.
look at the pic below and please help.
Answer:
1) Equation's:
y = 500 + 15x y = 350 + 18x2) Number of guest and the charge:
Cost is same for both at 50 meals. The cost is $1250.Part 1
Turn sentences into equation's (Let 'y' be total cost and x per meal) :
(i) charges $500 and $15 per meal
y = 500 + 15x(ii) charges $350 and $18 per meal
y = 350 + 18xPart 2
y = y
500 + 15x = 350 + 18x
18x - 15x = 500 - 350
3x = 150
x = 150/3
x = 50
Charge at guest's 50 meal:
y = 500 + 15(50)
y = $1250
Point : (50, 1250)
At what meter mark will Ario be when Miguel starts the race? Round to the nearest tenth.
x = (StartFraction m Over m + n EndFraction) (x 2 minus x 1) + x 1
A number line goes from 0 to 25. A line is drawn from 3 to 25. The point at 3 is labeled Start and the point at 25 is labeled End.
Miguel and his brother Ario are both standing 3 meters from one side of a 25-meter pool when they decide to race. Miguel offers Ario a head start. Miguel says he will start when the ratio of Ario’s completed meters to Ario’s remaining meters is 1:4.
4.4 meters
7.4 meters
17.6 meters
20.6 meters
The meter mark at which Ario wil be when Miguel starts the race is; 7.4 meters
How to calculate the distance?A ratio such as the ratio 1:4 shows the proportion of two factors. In this case, it shows the ratio between the completed meters vs the remaining meters.
To find the distance, we will have to determine how much 1:4 represents in the total distance.
Total distance = 25 meters - 3 metes = 22 meters
Thus; 22 * 1/ 5 = 22/5 = 4.4
However, we also know they are three meters behind the start.
Thus, the meter mark at which Ario will be when Miguel starts the race
4.4 + 3 =7.4 meters
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According to the rational root theorem, the numbers below are some of the potential roots of f(x) = 10x3 29x2 – 66x 27. select all that are actual roots.
The actual roots of the function [tex]f(x)=10x^{3}+29x^{2} -66x+27[/tex] are -9/2, 3/5 and 1.
Given function [tex]f(x)=10x^{3}+29x^{2} -66x+27[/tex].
Function is a relationship between two or more variables expressed in equal to form.
The roots of a polynomial function are the zeroes of the polynomial function. A polynomial function is a function that involves only non negative integer powers in an equation.
The polynomial function is given as:
[tex]f(x)=10x^{3}+29x^{2} -66x+27[/tex]
factorize the above function
[tex]f(x)=(2x+9)(5x-3)(x-1)[/tex]
Now put the function f(x) equal to zero.
f(x)=(2x+9)(5x-3)(x-1)
split the function means put all the expressions equal to zero as under:
(2x+9)(5x-3)(x-1)=0
solve each for the value of x
x=-9/2,x=3/5,x=1
Hence the roots of the function [tex]f(x)=10x^{3} +29x^{2} -66x+27[/tex] are which are also the values of x are -9/2,3/5,1.
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Answer:
Step-by-step explanation:
-x+4y=9
pls find ordered pair
We can write the ordered pairs that meet this condition as:
(x, y) = (x, (9 + x)/4 )
How to find the ordered pair?An ordered pair on the X-Y plane is written as (x, y).
Here we also have the relation:
-x + 4y = 9
If we isolate y, we get:
4y = 9 + x
y = (9 + x)/4
Now, we can write the ordered pairs that meet this condition as:
(x, y) = (x, (9 + x)/4 )
To get the particular ones you can replace the value of x, for example, if x = 0, then:
(x, (9 + x)/4 ) = (0, 9/4)
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Which type of parent function is f(x) = 1/x
Since it has a variable in the denominator, the function f(x) is a parent function classified as rational.
What are rational functions?Rational functions are functions that have the input variable, be it x, t, or any other, in the denominator.
The most simple example is given by:
[tex]f(x) = \frac{1}{x}[/tex].
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Answer: Reciprocal
Step-by-step explanation:
Reciprocal functions are functions that contain a constant numerator and x as its denominator. Its parent function is y = 1/x.
P l e a s e h e l p~!!!!!!~!!~~~!
Answer:
A. 100
Step-by-step explanation:
Angle 1 = 40
Angles 1 and 2 are equal. Add the angles 1 and 2 together.
40+40=80
The last step is to subtract 80 from 180.
180-80=100.
∠3=100
Hope this helps!
If not, I am sorry.
Create a list of steps, in order, that will solve the following equation. (x-5)^2=25(x−5) 2 =25left parenthesis, x, minus, 5, right parenthesis, squared, equals, 25 Solution steps:
The value of x in the equation (x - 5)² = 25 is 10.
How to solve an equation?(x - 5)² = 25
Take the square root of both sides
Therefore,
√(x - 5)² = √25
x - 5 = 5
add 5 to both sides
x - 5 + 5 = 5 + 5
x = 10
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Find the distance between the two points in simplest radical form.
(−5,−4) and (−2,−6)
Answer: [tex]\sqrt{13}[/tex] units
Work Shown:
[tex](x_1,y_1) = (-5,-4) \text{ and } (x_2, y_2) = (-2,-6)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(-5-(-2))^2 + (-4-(-6))^2}\\\\d = \sqrt{(-5+2)^2 + (-4+6)^2}\\\\d = \sqrt{(-3)^2 + (2)^2}\\\\d = \sqrt{9 + 4}\\\\d = \sqrt{13}\\\\d \approx 3.6056\\\\[/tex]
I used the distance formula.
A slightly alternate method is to form a right triangle and use the pythagorean theorem. The hypotenuse will have the endpoints (-5,-4) and (-2,-6).
A diagonal of a cube measures StartRoot 150 EndRoot cm. The diagonal of a face measures 10 cm.
What is the length, in centimeters, of an edge of the cube? Round the answer to the nearest tenth.
The side of the edge of the cube is 7. 07cm
How to determine the lengthGiven that a diagonal of a cube measures the square root of 150 cm and the diagonal of a face measures 10 cm.
Let's find the edge of the face
Note that the face of the cube is in the shape of square .
The diagonal of the face is 10 cm.
The formula for diagonal of square = [tex]\sqrt{2a}[/tex]
a is the side of the square face
We have that,
[tex]\sqrt{2a} = 10[/tex]
Make 'a' subject of formula
a = [tex]\frac{10}{\sqrt{2} }[/tex]
Find the surd of the equation, we have
a = [tex]\frac{10}{\sqrt{2} }[/tex] × [tex]\frac{\sqrt{2} }{\sqrt{2} }[/tex]
a = [tex]\frac{10\sqrt{2} }{2}[/tex]
a = [tex]5\sqrt{2}[/tex]
a = [tex]7. 07cm[/tex]
Thus, the side of the edge of the cube is 7. 07cm
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A company produces candy bags that each hold about 528 cubic inches of candy. Each bag is filled with any mixture of lollipop candies and gummy bear candies. When a bag contains only lollipop candies, then it has about 361 candies. When a bag contains only gummy bear candies, then it has about 697 candies. Given any candy bag produced by this company, which of the following equations could relate the approximate number of lollipop candies, 7, in the bag and the approximate number of gummy bear candies, g, in the bag? A company produces candy bags that each hold about 528 cubic inches of candy . Each bag is filled with any mixture of lollipop candies and gummy bear candies . When a bag contains only lollipop candies , then it has about 361 candies . When a bag contains only gummy bear candies , then it has about 697 candies . Given any candy bag produced by this company , which of the following equations could relate the approximate number of lollipop candies , 7 , in the bag and the approximate number of gummy bear candies , g , in the bag ?
361 lollipop candies or 697 gummy bear candies fills the bag of volume 528 in.³, which gives the following possible equation;
1.46•l + 0.76•g = 528How can the correct equation be found?Volume of candy bag = 528 in.³
Number of lollipop candies the bag can hold = 361 candies
Number of gummy bear candies the bag can hold = 697 candies
Therefore;
[tex]1 \: lollipop = \frac{528}{361} = 1.46[/tex]
[tex]1 \: gummy \: bear = \frac{528}{697} = 0.76[/tex]
Which gives the following equation;
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Answer:
l/361 + g/697= 1
Khan Academy Sat Practice
find the value of x
A. √30
B. 16
C. 2√2
D. 20
Answer:
A. √30
=================
Use the intersecting chords theorem, according to which, the products of the lengths of the line segments on each chord are equal,
or
TW × WU = CW × WVSubstitute the lengths and solve for x:
x*2x = 6*102x² = 60x² = 30x = √30The matching answer choice is A.
The table gives the scores of 6 students from a class of 25 in a competitive exam. the point estimate of the mean score for the students is
The mean of the scores if 6 students in a competitive exam is 25 marks.
Given scores of 6 students are: 10,30,50,40,20 in a competitive exam.
We have to find out the mean of the mark of 6 students in a competitive exam.
Mean is the sum of all the values in a set of data, such as numbers, measurements, divided by the number of values. It is also known as average.
Mean=∑X/n
∑X=10+30+50+40+20
=150
N=6
Now to calculate the mean we have to divide 150 by number of students which is 6.
Mean=150/6
=25 marks.
Hence the mean of the scores of 6 students is 25 marks.
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Question is incomplete as it should include :
Marks of students =10,30,50,40,20.
Write and simplify an expression to represent the area. Then determine the area when x = 3
Answer:
5*8 = 40
Step-by-step explanation:
2(3) -1 = 5
3 +5 = 8
area = 5*8 = 40
Answer:
formula-Area=l×b
Step-by-step explanation:
Length (l)=2x-1
Breadth(b)=x+5
We know that,
Area(A)=l×b
=(2x-1)×(x+1)
=(2×3-1)×(3+1)
=5×4
=20cm*2*
In the figure, POG is a diameter of the circle with centre O.
Find x° + y°.
The value of x° + y° is 216°
How to determine the angles
Note that the shape is a regular pentagon
Sum of angle in a pentagon = 540
Angle on each side = 108°
x = 108°
y = 108°
x° + y° = 108 + 108
x° + y° = 216°
Thus, the value of x° + y° is 216°
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D
Distance
ST
Speed
Time
A bus is moving at an average speed of 70 mph on the
motorway.
The journey takes 3 hours 30 minutes.
How far did the bus travel?
miles
The distance would be 231 miles.
What is speed?Speed can be calculated as the ratio of distance traveled to the time taken
Given information;
Time taken = 3 hours 30 minutes
Speed = 70 mph
We know that,
Distance = speed x time
Distance = 70 x 3.30
Distance = 231 miles
Thus, the distance would be 231 miles.
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which number produced a rational number when added to 1/5
The number that produced a rational number when added to 1/5 is D. -2/3.
What is a rational number?A rational number is a number that can be written as a ratio (or fraction) of two integers.
For example, when 1/5 is added to -2/3, it produces a rational number, -7/15, that remains as a fractional value.
Thus, the number that produced a rational number when added to 1/5 is D. -2/3.
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4. A juice bottling company makes a variety pack
with 24 orange juices, 12 apple juices, and 8
grape juices. Describe the ratio of the juices to
one another (orange: apple: grape).
(A) 2:1:1
(B) 3:1:2
(C) 4:2:2
(D) 6:3:2
The ratio of orange juice to apple juice to grape juice is 6: 3 : 2
What is ratio?A ratio says how much of one thing there is compared to another thing.
Therefore, we are comparing the numbers of juice produce by a bottling company.
Hence,
number of orange juice = 24
number of apple juice = 12
number of grape juice = 8
Therefore, the ratio of orange juice to apple juice to grape juice is as follows:
ratio = 24 : 12 : 8
divide through by 4
ratio = 6: 3 : 2
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f(x) = 4^ x / 8
can you Graph this ?
Answer:
Graph is below
Brainliest, please :)
3y > 2x + 12
2x + y ≤ -5
The solution for the inequalities 3y>2x+12, 2x+y<=-5 is the value of x<-27/8 and y<7/4.
Given 3y>2x+12 and 2x+y<=-5.
We are given two inequalities 3y>2x+12 and 2x+y<=-5. Inequality are like equations but in greater than ,less than or in combination with equal to. To solve them we need to first write them properly.
2x-3y<-12
2x+y<=-5
Now assume these are equalities
2x-3y=-12
2x+y=-5
now subtract 2 from 1
2x-3y-2x-y=-12+5
-4y=-7
y=7/4
put the value of y in 2x-3y=-12
2x-3(7/4)=-12
2x-21/4=-12
2x=-12+21/4
2x=(-48+21)/4
2x=-27/4
x=-27/8
Now put the signs between the values
x<-27/8
y<7/4.
Hence the solution of the inequalities 3y > 2x + 12
2x + y ≤ -5 is the value of x<-27/8 and y<7/4.
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Determine whether the geometric series 27 + 18 + 12 + 8 + ... converges or diverges, and identify the sum if it exists.
The given geometric series as shown in the question is seen to; Be converging with its' sum as 81
How to identify a converging or diverging series?We are given the geometric series;
27 + 18 + 12 + 8 + ...
Now, we see that;
First term; a₀ = 27
Second Term; a₁ = 2(27/3)
Third term; a₂ = 2²(27/3²)
Fourth term; a₃ = 2³(27/3³)
Thus, the formula is;
2ⁿ(27/3ⁿ)
Applying limits at infinity gives;
2^(∞) * (27/3^(∞)) = 0
Since the terms of the series tend to zero, we can affirm that the series converges.
The sum of an infinite converging series is:
S_n = a/(1 - r)
S_n = 27/(1 - (2/3)
S_n = 81
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Given that f(x)=x2−4 and g(x)=x+3 , what are all the values of x for which f(g(x))=0 ?
Answer:
the answer is (x )
math way helps
Step-by-step explanation:
The requried function of function f(g(x)) is given as x² + 6x +5.
What are functions?Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
here,
Given functions,
f(x)=x²−4 and g(x)=x+3
In order to form a function of function we have to function g(x) in function f(x)
Now,
f(g(x)) = f(x)=(g(x))²−4
f(g(x)) = f(x)=(x+3)²−4
f(g(x)) = x² + 6x + 9 -4
f(g(x)) = x² + 6x +5
Thus, the requried function of function f(g(x)) is given as x² + 6x +5.
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help me with the fonction please im stuck U_U
Answer:
It is NOT a function
Step-by-step explanation:
No it is NOT a function.....each value of x can only have one y value....
this has two y values for x = 2 : y = 2 and 4 therefore not a function
Find a cubic polynomial whose zeros are 1/2,1 and -3.
Answer:
2x³+3x²-8x+3
Step-by-step explanation:
So we know x=½,x=1 and x=-3
Then (2x-1)(x-1)(x+3) are the factors
(2x-1)[(x²+3x-x-3)]
(2x-1)[(x²+2x-3)]
2x³+4x²-6x-x²-2x+3
2x³+3x²-8x+3