a. Expressing y in terms of x, y = 20/(x + 3)
b. When x = 5, the value of y is 2.5
The question has to do with inverse variation.
What is inverse variation?Inverse variation is variation in which one quantity varies inversely as the other.
a. How to express y in terms of x?Given that y is inversely as x + 3 and that y = 4 when x = 2.
Since y varies inversely as x + 3, we have
y ∝ 1/(x + 3)
y = k/(x + 3)
When y = 4, x = 3. So
y = k/(x + 3)
4 = k/(2 + 3)
4 = k/5
k = 4 × 5
k = 20
So, y = k/(x + 3)
y = 20/(x + 3)
So, expressing y in terms of x, y = 20/(x + 3)
b. Find the value of y when x = 5.Since y = 20/(x + 3)
Substituting x = 5 into the equation, we have
y = 20/(x + 3)
y = 20/(5 + 3)
y = 20/8
y = 5/2
y = 2.5
So, when x = 5, the value of y is 2.5
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Algebra
x^3- 2x^2 + x
Answer:
x(x-1)^2
Step-by-step explanation:
x(x^2-2x+1)
x(x-1)(x-1)
(x-1)(x-1)=(x-1)^2
Does anyone know the answer? I want to make sure I did it right. Evaluate the expression using the given values type your answer in the open box
=======================================================
Explanation:
Replace x with 4 and y with 5.
Then use the order of operations (PEMDAS) to simplify until you get a single number.
Something like 9x means "9 times x", and a similar situation happens with the 8y term as well.
---------
Here's what the steps look like:
9x + 8y
9*4 + 8*5
36 + 40
76
Therefore, 9x+8y = 76 when x = 4 and y = 5.
The point (4,5) is located on the line 9x+8y = 76
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
In the given diagram, ∆ABC is a right triangle with . Segment AB is divided into four equal parts.
A right triangle A C B with A at (negative 3, negative 1), C at (negative 3, negative 3), and B at (6, negative 3). Side A B has 3 points D, E, and F, from the top to the bottom in equal increments. A line runs down from D to G on side C B.
The coordinates of point F are (
,
), and the coordinates of point G are (
,
).
The coordinates of point F are (15/4 , -5/2)
The coordinates of point G = (-3/4 , -3)What is the coordinates about?From the image attached:
AB divided into 4 similar parts, hence
E is the mid-point of AB D is the mid-point of AE F is the mid-point of EBNote that the rule of the mid-point states that:
When M (x , y) is the mid-point of the segment of AB, where A (x1 , y1) and B (x2 , y2), Then x = (x1 + x2)/2 and that of y = (y1 + y2)/2
Then lets solve for points E, F, D
Since A (-3 , -1) and B (6 , -3),
E is the mid-point of AB
Then E =[(-3 + 6)/2, (-1 + -3)/2]
= (3/2 , -2)
Since F is the mid-point of EB,
E (3/2 , -2) , B (6 , -3)
Then F = [(3/2 + 6)/2 , (-2 + -3)/2]
= (15/4 , -5/2)
Since D is the mid-point of AE, A (-3 , -1), E (3/2 , -2)
Then D = [(-3 + 3/2)/2 , (-1 + -2)/2]
= (-3/4 , -3/2)
Note also that:
BC is said to be an horizontal segment due to the fact that B and C have similar y - coordinate and G can be found on BC.
Since the y-coordinate of G is similar to y-coordinate of B and C
Then y-coordinate of G is = -3
Since DG ⊥ BC
Then DG = vertical segment
So G has similar x-coordinate of D
Then The x-coordinate of G = -3/4
The G = (-3/4 , -3)
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JDIDJRJDJF PLS HELP IM STUCK
Step-by-step explanation:
we have
B = J + 2
as the number of laps Bill ran.
to get the number of laps Jill ran we need to transform this equation, so that we get
J = ...
or
... = J
J has to be on one side, and the rest on the other (just as it is with B = ...).
so,
B = J + 2
B - 2 = J
or
J = B - 2
hey ! we are finished already !
find the solution of systems of equations
8x-5y=-8 -7x-5y=82
Answer:
x = -6, y = -8
Step-by-step explanation:
8x - 5y = -8
-7x - 5y = 82
minus them
15x = -90
x = -90 / 15
x = -6
8(-6) - 5y = -8
-48 - 5y = -8
-5y = -8 + 48
-5y = 40
5y = -40
y = -40 / 5
y = -8
PLEASE HELP I WILL GIVE 40 POINTS IF THE ANSWER IS RIGHT, AND BRAINLEST PLEASE HELP ASAP
Answer:
5/52 i think
Step-by-step explanation:
there are 52 cards in desk ,with26red and black cards.There 2red and 2 blackthree and. 1 six of hearts .
.
.
.
..
.
.
.
The types of transformations of geometric figures in the coordinate plane can be described as a slide, a flip, or a turn. What are the other names used to identify these transformations?
The other names used to identify the transformation of geometric figures is translation or reflection and rotation.
Given that the types of transformations of geometric figures in the coordinate plane can be described as a slide, a flip, or turn.
We are required to find the other names used to identify the above transformations.
The other names used to identify the transformation of geometric figures is translation or reflection and rotation.
Translation means the displacement of a figure from one place to another. In translation a figure can move upward, downward,right , Iift or anywhere in the coordinate system. In translation, the position of the object changes, its size remains the same.
Reflection is a type of transformation that flips a shape in a mirror line so that each point is the same distance from the mirror line as its reflected point.
Rotation is a motion of a space that preserves at least one point.
Hence the other names used to identify the transformation of geometric figures is translation or reflection and rotation.
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Type the missing number in this sequence: 4, , 144, 864, 5,184, 31,104
The missing number in the given series is 24.
What is missing number in the given sequence?Missing numbers are the numbers that have been missed in the given series of a number with similar differences among them. The method of writing the missing numbers is stated as finding similar changes between those numbers and filling the missing terms in the specific series and places.
Given the series,
4, ?, 144, 864, 5184, 31104
Multiplying with 6 in each term in the given sequence.
4×6 = 24
24×6 = 144
144×6 = 864
864×6 = 5184
5184×6 = 31104
Following the above sequence, we get the 2nd term is 24.
Hence the missing number is 24.
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19. Two hikers are wandering through heavy woods with walkie talkies. The walkie talkies have a range c
100 yards. From their starting point, they head off at an angle of 109°10' of each other. Hiker 1 walks 0.24
miles per hour, hiker 2 walks 0.17 miles per hour. If each continues to go straight, how long will it be before
they can no longer communicate?
The computation shows that the time before
they can no longer communicate will be 10 minutes
How to illustrate the information?From the information, it was stated that two hikerd are wandering through heavy woods with walkie talkies and that the walkie talkies have a range c of 100 yards.
It should be noted that after t hours, the distance between the hikers will be:
d² = (0.24t)² + (0.17t)² - 2(0.24t)(0.17t) cos 109.10°
d = 0.0568
Therefore, we will find the time when d = 0.0568. This will give a time of 10 minutes.
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How to find ‘x’ if 8.4 % of ‘x’ is 420.
I will mark the first answerer as brainliest
This is reverse percentage
8.4% = 420
÷8.4 both side
1% is now 50
1% =50
x100
100% is 5000
Check:
8.4/100 = 0.084 our decimal multiplier
5000 x 0.084 = 420
Thus, x is 5000
Hope this helps!
In what kind of an event does a choice made for one decision affect the choices available for
the other decisions?
Let's say you want to go on a vacation this summer because you finally saved enough money for it. While at the store to buy more hairbands (you just can't seem to figure out where they all went) you see something that you have been wanting for ages. The item is a bit on the more expensive side but you don't know when you will see it again. You decide to buy the item but you had to use some of the money planned for your trip to pay for it. But because you bought the item you now can't do all the activities you wanted on your trip.
The choice of buying the item affected your choices available on your trip.
Answer:
dependent events
Step-by-step explanation:
Triangle ABC is rotated to create the image A'B'C'.
Which rule describes the transformation?
Ty
O (x, y) - (x, -
O (x, y) - (v, x)
O (x, y) - (-x, -y)
B'AL
O (x, y) - (-Y, -x)
Answer-
Step-by-step explanation:
Pls Help!!!!! I will give brainliest!!!!!
Answer:
Step-by-step explanation:
The equation of a circle in standard form is (x - h)² + (y - k)² = r² ,
where (h, r) are coordinates of a center of a circle and "r" is a radius of a circle.
a² ± 2ab + b² = (a ± b)²
~~~~~~~~~~
x² + y² - 2x - 10y + 17 = 0
To rewrite the equation in standard form, need to group terms with the same variables, move the constant to the right side and complete the square for each grouping:
(x² - 2x) + ( y² - 10y) = - 17
( x² - 2x + 1 ) + ( y² - 10y + 25 ) = - 17 + 1 + 25
( x - 1 )² + ( y - 5 )² = 9
( x - 1 )² + ( y - 5 )² = 3²
The center of the given circle is
( 1 , 5 )
The radius of the given circle is
3 units
Calculate a four-day moving average for the price of the stock for the end of day 7. day 1 - 62.00; day 2 - 56.00; day 3 - 50.00; day 4 - 60.00; day 5 - 59.00; day 6 - 55.00; day 7 - 59.00; day 8 - 63.00
Answer:
58.25
Step-by-step explanation:
A "moving average" is a "boxcar average," the unweighted average over the specified number of days.
SolutionThe 4-day moving average ending on day 7 is ...
4-day average = (day 4 +day 5 +day 6 +day 7)/4
= (60 +59 +55 +59)/4 = 233/4
4-day average = 58.25
The four-day moving average for the price of the stock for the end of day 7 is 56.00
What is moving average?
The moving average on a particular day is the average of prices on the days prior to the pricing day.
In other words, four-day moving average on day 7 is the sum the prices of four days prior to day 7 divided by the number of days whose prices were considered.
In computing the four-day moving average for day 7, we would sum the prices for days 3-6, then divide the sum by 4 since prices of 4 days were made use of.
four-day moving average on day 7=(50.00+60.00+59.00+55.00)/4
four-day moving average on day 7= 56.00
Note, as the day of pricing changes, the input prices would also change
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My Uncle ordered 5 Pizzas, we were 20 people in all. I was just thinking how many pieces of
Pizza will each one of us will get if divided equally? (Each Pizza has 8-pieces)
Rhombus A B C D is shown. Lines are drawn from point A to point C and from point D to point B and intersect at point E. All sides are congruent.
The area of rhombus ABCD is 72 square units. EC = 8 units and DB = x – 1.
What is the value of x?
9
10
14
16
The rhombus ABCD has an area of 72 square units. Diagonals AC and BD intersect at E. Given EC = 8 units and DB = x - 1, the value of x is 10 units. The correct option is B).
We are given a rhombus ABCD with area 72 square units. The diagonals AC and BD intersect at point E.
Since all sides of the rhombus are congruent, we can assume that the length of each side is "s" units.
We are also given that EC (a part of diagonal AC) is 8 units long.
As diagonals of a rhombus bisect each other, we can deduce that the other half of diagonal AC is also 8 units. So, the full diagonal AC is 16 units (8 units + 8 units).
Now, we are told that DB (a part of diagonal BD) is x - 1 units long.
To find the value of x, we need to find the length of the other half of diagonal BD, which is also x - 1 units. So, the full diagonal BD is
(x - 1) units + (x - 1) units = 2x - 2 units.
The area of a rhombus is given by the formula:
Area = 1/2 × Product of Diagonals.
Substituting the given values, we have:
72 = 1/2 × 16 × (2x - 2).
Now, we can simplify the equation:
72 = 8x - 8.
Move the constant term to the right side:
8x = 72 + 8.
Combine the constants:
8x = 80.
Finally, solve for x by dividing both sides by 8:
x = 80 / 8 = 10.
So, the value of x is 10 units. The correct answer is B).
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--The given question is incomplete, the complete question is given below " Rhombus A B C D is shown. Lines are drawn from point A to point C and from point D to point B and intersect at point E. All sides are congruent.
The area of rhombus ABCD is 72 square units. EC = 8 units and DB = x – 1.
What is the value of x?
9
10
14
16 "--
Juliana is training to run a marathon. in her second week of training she ran 13 km more than she did during her first week of training. she ran a total of 145 km during the first two weeks of training. how far did she run during her first week of training?
1)give your answer in terms of π
2) give your answer using 3.14 for π
The volume of the composite solid in terms of pi and using 3.14 as pi are 1125π cubic inches and 3532.5 cubic inches respectively
Volume of a cylinderA cylinder has traditionally been a three-dimensional solid, one of the most basic of curvilinear geometric shapes
The volume of the composite cylinder is expressed as shown below;
V = πr²h
where
r is the radius
h is the height
According to the given diagram;
V = Vl - Vs
V = π(10)²*15 - π(5)²*15
V = 1500π - 375π
V = 1125π cubic inches
If the value of π is 3.14, hence;
V = 1125(3.14) cubic inches
V = 3532.5 cubic inches
The volume of the composite solid in terms of pi and using 3.14 as pi are 1125π cubic inches and 3532.5 cubic inches respectively
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Find the distance between (-6, -12) and (4,8) using the distance formula.
Answer:
The distance formula is 22.360679775
if you round it to the nearest tenth, then the answer is 22.4
Step-by-step explanation:
(-6, -12) and (4,8)
(x2 - x1)² + (y2 - y1)²
Place the x and y values
(4 - - 6)² + (8 - - 12)²
= 10² + 20²
= 100 + 400 = 500
√500 = 22.360679775
Round it to the nearest tenth, and you will get 22.4
Hope this helps!
Please mark me as the brainliest
Answer: Distance = 10√2
Step-by-step explanation:
Given formula
[tex]Distance~=~\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Given information
(x₁, y₁) = (-6, -12)
(x₂, y₂) = (4, 8)
Substitute given information into the formula
[tex]Distance~=~\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]Distance~=~\sqrt{((4)-(-6))^2+((8)-(-12))^2}[/tex]
Simplify values in the parenthesis
[tex]Distance~=~\sqrt{(4+6)^2+(8+12)^2}[/tex]
[tex]Distance~=~\sqrt{(10)^2+(20)^2}[/tex]
Simplify the exponents
[tex]Distance~=~\sqrt{100+400}[/tex]
Simplify the radical number
[tex]Distance~=~\sqrt{500}[/tex]
[tex]Distance~=~\Large\boxed{10\sqrt{5}}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Find the ratio of the areas of to squares whose sides are 3cm and 5cm, respectively
Answer: 9 cm² : 25 cm²
Step-by-step explanation:
The area of a square can be found with x² where x is the length of one side.
x² : x²
3² : 5²
9 : 25
9 cm² : 25 cm²
Does anyone know the answer to this question? I’ve been staring at this for a solid 20mins but can’t figure it out.
[tex]\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}[/tex]
A linear function is an equation of the form:
[tex]\sf{y=mx+b}[/tex]
▪ [tex]\sf{m= \: slope}[/tex]
▪ [tex] \sf{b= \: y-intercept}[/tex]
First, pick any two pairs of points from the table.
[tex]\small\longrightarrow \sf{(x_1,y_1)(-1.13)}[/tex]
[tex]\small\longrightarrow \sf{(x_2,y_2)=(0,10)}[/tex]
Using these points, find the slope.
[tex]\small\longrightarrow \sf{m= \dfrac{y _{2 } - y_1}{x_2-y_1} }[/tex]
When x=0, y=10, therefore, the y-intercept, b=10.
[tex]\leadsto[/tex] Substitute m=-3 and b=10 into the slope-intercept form given above:
[tex]\small\longrightarrow \sf{m=m = \dfrac{10 - 13 }{0 -( - 1) } = - \dfrac{3}{1} = - 3}[/tex]
▪ [tex]\small\longrightarrow \sf{y= -3x+10}[/tex]
[tex]\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}[/tex]
[tex]\large\boxed{\bm{y= -3x+10}}[/tex]
ÐA in cos A = 0.7715 in degrees? (not sure if the way I worded that makes sense but yea)
The value of A such that cos A = 0.7715 is 39.5 degrees
How to solve for A in the equation cos A = 0.7715?The equation is given as:
cos A = 0.7715
Where the angle is in degrees
There are several ways to solve this equation, some of which include:
Using a scientific calculatorUsing a graph or a graphing toolUsing the cosine tableIn this case, we make use of the first option; using a scientific calculator
Recall that the equation is represented as:
cos A = 0.7715
Next, we take the arccos (or anti cosine) of the above equation.
This is represented as
arccos(cos A) = arccos(0.7715)
Evaluate the expression on the left-hand side
A = arccos(0.7715)
Evaluate the expression on the left-hand side using the scientific calculator
A = 39.5112207183
Approximate the above expression
A = 39.5
Hence, the value of A such that cos A = 0.7715 is 39.5 degrees
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PLEASE HELP ASAP, I WILL GIVE 40 POINTS IF THE RIGHT ANSWER, AND BRAINLEST, ASAP
Answer:
We multiply by 2 and add 4
Step-by-step explanation:
To find the pattern, we find the slope
m = ( y2-y1)/(x2-x1)
m = ( 10-6)/(3-1)
m = 4/2
m =2
We are multiplying by 2
y = mx+b where m is the slope and b is the y intercept
y = 2x+b
Using the point (1,6)
6 = 2(1)+b
6 = 2+b
The y intercept is 4
y = 2x+4
We multiply by 2 and add 4
Why is proficiency in statistics an important skill for a data analyst?
Proficiency in statistics is an important skill for a data analyst because it is needed in identifying patterns and correlations in data.
What is Data analysis?Data analysis can be regarded as the process of collecting as well as modeling, and analyzing data so as to be able to extract insights that support decision-making.
Some Types of Data Analysis are:
Descriptive Analysis.Exploratory Analysis.Inferential Analysis.Predictive Analysis.Causal Analysis.Mechanistic Analysis.It should be noted that Proficiency in statistics is an important skill for a data analyst because it is needed in identifying patterns and correlations in data.
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Please Help me i will give brainlist !Which of the choices below show the pre-image quadrilateral ABCD, rotated 180° about the origin?
Answer:
The first choice.
Step-by-step explanation:
The second choice is a translation and the third choice is a reflection.
Two equations are shown Y equals four over X +3 and Y equals negative 2X subtract four which statement best describes the graph of the two equations
The graph for the given system of equations is shown below
Graph of System of Linear equationsFrom the question, we are to determine the graph that describes the given system equations
First, we will graph the given system of linear equations.
The given equations are
Y equals four over X +3
and
Y equals negative 2X subtract four
That is,
y = 4/(x+3)
y = -2x -4
The graph for the given system of equations is shown below
The statement that best describes the graph of the two equations is the statement that describes the graph of the system of equations as shown below
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Question 3
What's the height of a cone if the volume is 562 cubic inches and the radius is 5 inches.
O 72.05 units
O 120.62 units
O21.47 units
O38.90 units
Previous
[tex]\textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ V=562\\ r=5 \end{cases}\implies 562=\cfrac{\pi (5)^2 h}{3}\implies 1686=25\pi h \\\\\\ \cfrac{1686}{25\pi }=h\implies 21.47\approx h[/tex]
[tex]3y - 5x = 10[/tex]
Find the gradient of the linear relation
Isolate y
3y=5x+10y=5/3x+10/3Compare to slope intercept form y=mx+b
Slope=m=5/3
Answer:
[tex]\dfrac{5}{3}[/tex]
Step-by-step explanation:
To find the gradient (slope) of the given linear relation, use arithmetic operations to isolate y:
Given relation:
[tex]3y-5x=10[/tex]
Add 5x to both sides:
[tex]\implies 3y-5x+5x=10+5x[/tex]
[tex]\implies 3y=5x+10[/tex]
Divide both sides by 3:
[tex]\implies \dfrac{3y}{3}=\dfrac{5}{3}x+\dfrac{10}{3}[/tex]
[tex]\implies y=\dfrac{5}{3}x+\dfrac{10}{3}[/tex]
Slope-intercept form of a linear equation
[tex]y = mx+b[/tex]
where:
m is the slope (gradient)b is the y-interceptComparing the rewritten equation with the slope-intercept formula, the gradient (slope) of the given linear relation is ⁵/₃.
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“Eighteen is equal to the product of a number (n) and 9.”
Answer:
n=2
Step-by-step explanation:
Create an equation.
9n=18
Divide 9 from both sides.
9n/9=18/9
n=2
Hope this helps!
Find the length of the function over the given interval. x = 2y from y = −1 to y = 1
The length of the function x = 2y is 2√5 units
According to the given question.
We have a function
x = 2y
Since, we know that the length of the function in the interval [a, b] is given by
l = [tex]\int\limits^a_b\sqrt{1+(\frac{dx}{dy}) ^{2} } \,dy[/tex]
Where, l is the length of the function.
Now, differentiating the given function x = 2y w.r.t y.
Therefore,
dx/dy = 2
So, the length of the given function x = 2y from y = -1 to y = 1 is given by
l = [tex]\int\limits^1_{-1}{\sqrt{1+2^{2} } } \,dy[/tex]
⇒ l = [tex]\int\limits^1_{-1} {\sqrt{1+4} } \,dy[/tex]
⇒ l = [tex]\int\limits^1_{-1}{\sqrt{5} } \,dy[/tex]
⇒ l = √5[1 - (-1)]
⇒ l = √5(2)
⇒ l = 2√5
Hence, the length of the function x = 2y is 2√5 units.
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