The ordered pair is [4k , 3k]
In first equation, 3x - 4y = 0
∴ 3x = 4y
x = 4y/3. ----1
Placing the value of x in second equation:
4x - 5y = k
4[4y/3] - 5y = k
16y/3 - 5y = k
[tex]\frac{16y - 15y}{3}[/tex] = k
16y - 15y = 3k
y = 3k
Replacing the value of y in eq. 1, we get
x = 4k
∴ The ordered pair is [4k , 3k]
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Help!! Which of the following is a true statement of the figure ?
Answer:
3rd option
Step-by-step explanation:
In the 3rd option, two sides from each triangle in the large triangle are compared.
30 points asap
The equation y = –117.5 x + 31,379.9 gives the population y of a city x years after 1975. What is the real-world meaning of the rate of change and the y-intercept?
Rate of Change: The city’s population decreases by about 118 people each year. Y-intercept: In 1975, the city’s population was about 31,380 people.
Rate of Change: The city’s population decreases by about 31,380 people each year. Y-intercept: In 1975, the city’s population was about 118 people.
Rate of Change: The city’s population decreases by about 1975 people each year. Y-intercept: In year 0, the city's population was about 118 people.
The equation y = –117.5 x + 31,379.9 gives the population y of a city in x years after 1975 , in real world ,
Rate of Change means The city’s population decreases by about 118 people each year , and Y-intercept means In 1975, the city’s population was about 31,380 people.
In the question ,
the equation that gives the population y of a city in x years is
y = –117.5 x + 31,379.9
let us find the population for 1976
So , x = 1 ,
we get , y = –117.5(1) + 31,379.9
y = –117.5 + 31,379.9
y = 31262.4
So, the population in the year 1976 is 31262.4
change in population = population in 1976 - population in 1975
= 31262.4 - 31,379.9
= -117.5
≈ -118
to find the population in the year 1977
x = 2 ,
we get , y = –117.5(2) + 31,379.9
= –235 + 31,379.9
= 31144.9
change in population = population in 1977 - population in 1976
= 31144.9 - 31262.4
= -117.5
≈ -118
From above , we can see that the population is decreasing in the year 1976 and 1977 , by 118 people,
hence , we can say that , the city’s population decreases by about 118 people each year
For population in 1975 , we put x=0 ,
So , y = –117.5(0) + 31,379.9
= 31379.9
≈ 31380
Therefore , the equation y = –117.5 x + 31,379.9 gives the population y of a city in x years after 1975 , in real world ,
Rate of Change means The city’s population decreases by about 118 people each year , and Y-intercept means In 1975, the city’s population was about 31,380 people .
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Please help me asap (20 points)
Answer:
1.7^28/1.6^21 the second option.
Step-by-step explanation:
The half-life of a radioactive kind of uranium is 2 years. How much will be left after 4 years, if you start with 776 grams of it?
ANSWER
194 grams
EXPLANATION
We have that the half life of the uranium is 2 years.
This means that it will take 2 years for the uranium to decay to half of its original value.
The formula for exponential decay is:
[tex]y=ab^t[/tex]where y = the value after the decay
a = initial value
b = rate of decay.
t = number of years
First, we have to find b.
We have that 776 grams of uranium will decay to half its amount (388 grams) in 2 years. This means that:
[tex]\begin{gathered} 388\text{ = 776 }\cdot b^2 \\ \Rightarrow b^2\text{ = 388 / 776} \\ b^2\text{ = 0.5} \\ b\text{ = }\sqrt[]{0.5} \\ b\text{ = 0.707} \end{gathered}[/tex]Therefore, after 4 years (t = 4), the amount of uranium left will be:
[tex]\begin{gathered} y\text{ = 776 }\cdot(0.707)^4 \\ y\text{ = 776 }\cdot\text{ 0.25} \\ y\text{ = 194 grams} \end{gathered}[/tex]That is the amount of uranium that will be left after 4 years.
Whats the answer? For a b c d
By evaluating the given linear equation, we will see that the missing values in the table are:
a = -3b = 1c = 3d = 5How to get the missing values?
Here we have a table that relates the inputs, x, with the outputs, y, of the linear equation:
y = 2x + 1
To find the missing values we need to evaluate the linear equation in the given inputs, a is the value that we get when x = -2, evaluating in that we get:
a = 2*(-2) + 1
a = -4 + 1
a = -3
The value of b is what we get when x = 0.
b = 2*0 + 1
b = 1
The value of c is what we get when x = 1.
c = 2*1 + 1
c = 3
The value of d is what we get when x = 2.
d = 2*2 + 1
d = 4 + 1
d = 5
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I need help on this question
Adam's school is 12 miles from his house. It takes his older brother
20 minutes to drive him to school.
If Adam's brother drives s mph faster than usual, how fast will
they reach the school?
(b) what are the quotient and remainder when −34 is divided by 6? remember that the remainder r has to satisfy 0≤r<6, and in particular cannot be negative.
The quotient and remainder when −34 is divided by 6 is -6 and 2 respectively.
What is termed as the division?Multiplication is the inverse of division. If 3 groups of 4 add up to 12, 12 divided into three equal groups adds up to 4 in each cluster in division.Each component of a division equation is given its own name.Dividend: The dividend is just the number divided during the division process.Divisor: The divisor is the number whereby the dividend is divided.Quotient: A quotient is an outcome of the division process.Remainder: We can't always divide things exactly. There could be an extra number. The leftover number is known as the remainder.Dividend = Divisor x Quotient + Remainder
For the given question,
The number -34 is to be divided by 6.
In this, dividend is -34 and divisor is 6.
Now while dividing the number comes should be less than -34.
Thus, -34 divided by 6 gives quotient as -36 and remainder as 2.
Where, the remainder r has to satisfy 0≤r<6, and in particular cannot be negative.
Therefore, the quotient and remainder when −34 is divided by 6 is -6 and 2 respectively.
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The length of a rectangle is three times its width.
If the perimeter of the rectangle is 48 in, find its length and width.
length: in
width: in
Length: 18 in.
Width: 6 in.
We can use “x” as the width in this scenario. If the width is x, then the length is 3x, since length is three times the width. The perimeter would be length + length + width + width. Since the perimeter is 48, we could say that:
x + x + 3x + 3x = 48
Which simplifies to 8x=48
If you divide by 8 on both sides, you get
X=6. Then you Can plug 6 back into your x width and 3x length.
(See attached image) hope this helped!
Hello!
Let's set up some variables:
L: length of the rectangleW: width of the rectangleLet's consider the relationship between the length and the width:
The length of a rectangle is three times its width[tex]\hookrightarrow L=3W[/tex]
The perimeter of the rectangle is equal to 48 and 2W + 2L
[tex]\hookrightarrow 2L + 2W = 48[/tex]
Let's replace the 'L' in terms of 'W' and solve:
[tex]2(3W) + 2W = 48\\6W + 2W=48\\8W = 48\\W = 6[/tex]
Since L = 3W
[tex]\hookrightarrow L = 3W = 3*6 = 18[/tex]
Answer:
Length = 18Width = 6Hope that helps!
Use the following equation to answer the questions:
−3x+y=9
Rewrite the equation in function notation:
Response area
What is the slope of the line? Response area
What is the y-intercept? (Response area, Response area)
What is the x-intercept?
The equation in function notation is: f(x) = 3x + 9.
Slope of the line = 3
Y-intercept = 9
X-intercept is: -3.
How to Write the Equation of a Line in Function Notation?In function notation, the equation can be written as .f(x) = mx + b, where:
m = slopeb = y-intercept of the line.Given the equation, -3x + y = 9, rewrite in function notation as:
-3x + y + 3x = 3x + 9
y = 3x + 9
f(x) = 3x + 9
Slope of the line is, m = 3.
The y-intercept of the equation is, b = 9.
To find the x-intercept, substitute y = 0 into y = 3x + 9:
0 = 3x + 9
-3x = 9 [subtraction property of equality]
-3x/-3 = 9/-3 [division property of equality]
x = -3
The x-intercept is: -3.
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I have a question about exponential functions I will submit a photo
The values are given as:
(a) Approximate the value of e^6 to 4 decimal places:
The value of
[tex]e^6=403.42879[/tex]The approximate value to 4 decimal places is 403.4288.
(b) Approximate the value of e^(-0.66) to 4 decimal places:
[tex]\text{The value of e}^{-0.66}=0.5168513344916[/tex]Approximated value to 4 decimal places is 0.5168..
whats the co-ordinates of the midpoint of (8,10) and (7,2)
Answer:
[tex](\frac{15}{2},6)[/tex]
Step-by-step explanation:
Hey, Grace! Pleasure to meet you.
To solve this problem, I would strongly suggest for you to use the midpoint formula.
I have attached an image below of the formula used for plugging in values.
Confused? Let me show you! :)
M means midpoint by the way...
M = [tex](\frac{8+7}{2},\frac{10+2}{2}) = (\frac{15}{2} ,6)[/tex]
There you go! Let me know if you have any questions, and best of luck with the rest of your assignment.
In a class, 2/5 of the students are less than 115 cm in height and 7/10 are less than 130 cm in height. what fraction are more than 115 cm but less than 130 cm?
Which table represents a linear function?
x y
1 3
2 7
3 11
4 15
x y
1 3
2 8
3 15
4 21
x y
1 3
2 9
3 3
4 9
x y
1 3
2 9
3 27
4 81
The first table represents a linear function.
What is a linear function?A linear function is one that changes at a constant rate. Any linear function has an increase or decrease that is constant. The slope of the line, denoted by the letter m in the equation y = mx + b, is this constant rate of change.
Given are the tables with values of x and y.
In a table of linear functions, the ratio of the difference in y values to the difference in x values is consistently constant.
The first table is given as:
x y
1 3
2 7
3 11
4 15
Only table 1 in the provided tables represents a linear function.
This is because the equivalent values of y change by 4 when the value of x changes by 1.
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PLEASE ANSWER AS QUICKLY AS POSSIBLE PLEASE. WILL GIVE BRAINlESt
A linear function with the same y-intercept as the one that is represented by the graph is: table 1.
How to calculate the slope of a linear function?In Mathematics, the slope of any linear function can be calculated by using this formula;
Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope, m = (y₂ - y₁)/(x₂ - x₁)
At points (-3, -4) and (-1, 2) from table 1, the slope of the line would be calculated as follows:
Slope, m = (2 + 4)/(-1 + 3)
Slope, m = 6/2
Slope, m = 3.
Note: The y-intercept of the line shown on the graph is equal to 5 because the x-value is zero (0) at this point.
By using point (-3, -4), the y-intercept of this line would be calculated by using the slope-intercept form:
y = mx + b
Where:
x and y are the points.b is the y-intercept.m represents the slope.Making y-intercept (b) the subject of formula, we have:
y-intercept, b = y - mx
y-intercept, b = -4 - 3(-3)
y-intercept, b = -4 - (-9)
y-intercept, b = -4 + 9
y-intercept, b = 5.
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Complete Question:
Which linear function has the same y-intercept as the one that is represented by the graph?
What is the length of side BC to one decimal place?
Answer:
BC ≈ 9.0
Step-by-step explanation:
using the tangent ratio in the right triangle
tan42° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{BC}{10}[/tex] ( multiply both sides by 10 )
10 × tan42° = BC , then
BC ≈ 9.0 ( to 1 dec. place )
In the space provided below, solve the inequality x/8 - 13 > -6 for x algebraically. Show all work.
Answer:
x > 56
Step-by-step explanation:
x/8 - 13 > -6
x/8 > 7
x > 56
What is the range for -|x+3|
The function is -|x+3|. The range is (-∞,0].
Given that,
The function is -|x+3|
We must determine the function's range.
A function's domain and range are its constituent parts. The domain of a function is the set of all possible input values, whereas the range of a function is its potential output. Range, Domain, and Function. A is the domain and B is the co-domain if a function f: A → B exists that maps every element of A to an element in B.
The function is -|x+3|
The domain is (-∞,∞)
The range is (-∞,0]
Therefore, the range is (-∞,0].
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Calculate the volume of liquid that would fill the bowl of the glass. SHOW ALL WORK!!
Answer:
49.7 cm³Step-by-step explanation:
We need to find the volume of the cone with:
Diameter = 5 cm andSlant height = 8 cmFirst, find the height, using Pythagorean, where hypotenuse of the triangle is 8 cm and base is the radius = 5 cm/2 = 2.5 cm:
[tex]h = \sqrt{8^2-2.5^2} =\sqrt{57.75} =7.6[/tex] (rounded)Find the volume of the cone:
[tex]V=\pi r^2h/3=3.14*2.5^2*7.6/3 = 49.7[/tex] (rounded)please help this worth half ny grade
Answer:
see image
Step-by-step explanation:
See attached image
the radius of a circular disk is given as 30 cm with a maximum error in measurement of cm. use differentials to estimate the maximum possible error in the calculated area of the disk.
The calculated area's maximum percentage relative error is approximately 1.33%.
we know that:
Area of the circular disc is given by A = πr²
consider A = πr²
Differentiate both sides with respect to r, we get
dA/dr = 2πr
⇒ dA = 2πr dr
calculate area:
A = πr²
A = π(30)²
A = 900π
A = 2826 cm²
Because of an error in measurement, the radius might actually be as big as 30+0.2 cm
= 30.2 cm
If r is increased from 30 by an amount Δr = dr = 0.2
Then the actual change in the calculated area would be :
ΔA = A(30+Δr)-A(30)
ΔA = A(30.2)-A(30)
ΔA = (30.2)²π - 900π
ΔA = 912.04π - 900π
= 12.04π cm²
So we estimated the maximum error in calculated area as 12.04π cm²
≅ 37.8 cm²
The maximum relative error in calculated area is:
ΔA/A= dA/A = 12.04π/900π
= 0.013
= 1.33 %
The maximum % relative error in calculated area is about 1.33%.
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What is the answer to the problem for sin, sec, tan. I don’t really need a detailed explanation just the answer. Thank you.
Answer:
[tex]\begin{gathered} \sin(\theta)=-0.35 \\ \\ sec(\theta)=-1.07 \\ \\ \tan(\theta)=0.38 \end{gathered}[/tex]Step-by-step explanation:
Remember that for a given terminal point of an angle, we define those trigonometric functions as following:
[tex]\begin{gathered} \sin(\theta)=\frac{y}{\sqrt{x^2+y^2}} \\ \\ sec(\theta)=\frac{\sqrt{x^2+y^2}}{x} \\ \\ \tan(\theta)=\frac{y}{x} \end{gathered}[/tex]This way, we'll have that:
[tex]\begin{gathered} \sin(\theta)=-0.35 \\ \\ sec(\theta)=-1.07 \\ \\ \tan(\theta)=0.38 \end{gathered}[/tex]determine whether the function has a minimum or maximum f(x)=-2/3x+5 if x<0 -x if 0 4 -x^2+4x+4 if x>4
The function has no minimum or maximum
How to determine the minimum or the maximum of the functionThe function is given as
f(x) = -2/3x + 5 if x < 0
f(x) = -x^2 + 4x + 5 if x > 4
The above function is a piecewise function
And the type of functions in the piecewise function are
Linear functionQuadratic functionA linear function does not have a minimum or a maximum
This means that the function would have no minimum or maximum
Hence, the minimum or the maximum value of the function does not exist
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Sid burrowed a single payment loan at $10,000 at an interest rate of 5.5%. The term of the loan is 120 days. What is the maturity value of his loan at exact interest?
For this case
P = 10 000
i=0.055
t=120
After you compute the formula you would get
A = 6 170 141
HELP ME
solve x^4-17x^2+16=0
select all of the solutions to the original equation
x=4
x=-16
x=-4
x=16
x=-8
x=-1
x=1
x=8
In the diagram, ABC is a straight line.
Work out the size of the angle marked x.
Answer:
See below
Step-by-step explanation:
1 note the other angle at d = 62 ( isosceles triangle)
2 x = 180 - 62 - 62 -25
Answer:
x = 31°
Step-by-step explanation:
since AB = BD then Δ ABD is isosceles with base angles congruent, so
∠ ADB = ∠ BAD = 62°
the sum of the 3 angle in Δ ABD = 180° , so
∠ ABD = 180° - 62° - 62° = 180° - 124° = 56°
∠ ABD and ∠ CBD are a linear pair and sum to 180° , so
56° + ∠ CBD = 180° ( subtract 56° from both sides )
∠ CBD = 124°
the 3 angles in Δ CBD sum to 180° , then
x + 124° + 25° = 180°
x + 149° = 180° ( subtract 149° from both sides )
x = 31°
Walter Slater sells appliances and earns 2.5% commission in addition to his salary. Last month he sold
$63,000 in appliances. How much was his commission check?
Answer:
1575
Step-by-step explanation:
Comment
You are just asked to figure out the commission. The rule is to place 100 underneath what is given as the %. In effect, % = x / 100 in decimal form. In this case x = 2.5
So the % is 2.5/100 = 0.025 as a decimal
So commission is 63000 * 0.025 = $1575 commission
Leah has a home-based business making and selling scented soaps. She initially spent $100 to purchase soap-making equipment, and the materials for each pound of soap cost $5. Leah sells the soap for $15 per pound. Eventually, she will sell enough soap to cover the cost of the equipment. What will be Leah's total sales and costs be? Write a system of equations, graph them, and type the solution.
Answer:
Equations:
Cost equation C(x) = 100 + 5x
Sales equation S(x) = 15x
Graph provided
Solution at breakeven point i.e. where sales = costs is at x = 10 lbs
Step-by-step explanation:
Total cost = $100 capital cost of equipment + production cost of $5 per pound of soap
Cost equation C(x) = 100 + 5x where x is the number of pounds of soaps produced
Sales Equation S(x) = 15x where x is the number of pounds of soap sold
The break-even quantity (in lbs) of soap to be sold to pay for equipment is when both equations are equal to each other
100 + 5x = 15x
==> 15x = 100 + 5x
==> 15x - 5x = 100 (subtract 5x on both sides)
==> 10x = 100
==> x = 10 lbs of soap
At this quantity, Sales and Costs are evened out
Please help thank you
The value of [x] in the figure given is 54.
What are Alternate interior angles?
Alternate interior angles are the angles formed when a transversal intersects two coplanar lines. They lie on the inner side of the parallel lines but on the opposite sides of the transversal.
Given are two parallel lines.
The two lines are parallel and are intersected by a transversal. Assume
that -
∠1 = (x +3)°
∠2 = (2x - 61)°
Now, the angle at the vertically opposite position with respect to ∠2 will have same measurements. Let's call this ∠3 = (2x - 61)°.
Now, ∠3 and ∠1 are alternate interior angles and their measures will be equal. So, we can write -
∠1 = ∠3
x + 3 = 2x - 61
3 + 61 = 2x - x
x = 64
The value of [x] is 54
Therefore, the value of [x] in the figure given is 54.
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What is the measure of m?n20m5= [?]?]Vm =Give your answer in simplest form.Enter
To answer this question, we need to remember the next theorem:The
We have that the hypotenuse is the largest side of a right triangle. In this case, it is equal to (5 + 20) = 25 units.
The leg of the right triangle we need to find is m, and we know that the projection of m on the hypotenuse is 5 units.
Theref
