[tex]\bf \qquad \qquad \textit{combined proportional variation} \\\\ \begin{array}{llll} \textit{\underline{y} varies directly with \underline{x}}\\ \textit{and inversely with \underline{z}} \end{array}\implies y=\cfrac{kx}{z}\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]\bf \stackrel{\textit{"x" varies with}}{x}~~=~~k\stackrel{\textit{inverse of "r"}}{\cfrac{1}{r}}\cdot \stackrel{\stackrel{\textit{inverse of}~\hfill }{\textit{square of a sum}}}{\cfrac{1}{(y+z)^2}}~\hfill x=\cfrac{k}{r(y+z)^2}[/tex]
The variation: x varies jointly with the inverse of r and the inverse of the square of the sum of y and z is, [tex]x = \frac{1}{r + y^{2} + z^{2} }[/tex]
What is an Equation ?An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.
For example, 3x+2y=0.
Types of equation
1. Linear Equation
2. Quadratic Equation
3. Cubic Equation
Given that,
the variation,
x varies jointly with the inverse of r
And the inverse of the square of the sum of y and z
[tex]x = \frac{1}{r + y^{2} + z^{2} }[/tex]
Therefore, the general formula [tex]x = \frac{1}{r + y^{2} + z^{2} }[/tex]
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On a piece of paper, graph y+2>-3x - 3. Then determine which answer
choice matches the graph you drew.
Answer:
D.
Step-by-step explanation:
【Look at the image】
Answer:
option D
Step-by-step explanation:
[tex]y+2>-3x - 3[/tex]
Subtract 2 from both sides and solve for y
[tex]y>-3x - 5[/tex]
Now graph it using a table
Replace > symbol by == sign
[tex]y=-3x - 5[/tex]
make a table
x y=-3x-5
0 -5
-1 -2
-2 1
Graph the points (0,-5) and (-2,1)
WE have only > symbol so we use dotted line
For shading we use test point (0,0)
[tex]y>-3x - 5[/tex]
Plug in 0 for x and 0 for y
[tex]0>-3(0) - 5[/tex]
0>-5 True
So we shade the region that contains (0,0)
option D is correct
A small bat weighs about 2/5 of an ounce. A small hummingbird weighs about 14/25 of an ounce. Explain how to find the difference in the weights of these animals
Answer:
The difference is about [tex]\frac{4}{25}[/tex] of an ounce
Step-by-step explanation:
we know that
A small bat weighs about 2/5 of an ounce
A small hummingbird weighs about 14/25 of an ounce
step 1
Multiply 2/5 by 5/5
Remember that
5/5 is 1
so
[tex](\frac{2}{5})(\frac{5}{5})=\frac{10}{25}[/tex]
step 2
To find the difference in the weights of these animals, subtract the weight of the small bat from the weight of the small hummingbird
[tex](\frac{14}{25})-(\frac{10}{25})[/tex]
Remember that
When subtract fractions with the same denominators, subtract the top numbers and put the answer over the same denominator
so
[tex](\frac{14}{25})-(\frac{10}{25})=\frac{4}{25}[/tex]
therefore
The difference is about [tex]\frac{4}{25}[/tex] of an ounce
Janice ran mile. She walked mile. How far did she run and walk?
Answer:
two miles
Step-by-step explanation:
Answer:
if she ran one mile....and walked one mike.....that makes...2 miles altogether
Step-by-step explanation:
1 +1=2
If f(x)=-2x-3 find f(4)
Answer:
f(4) = -11
Step-by-step explanation:
Plug in 4 for x: Note that x = 4.
f(x) = -2x - 3
f(4) = -2(4) - 3
Remember to follow PEMDAS. First, solve the multiplication, then subtract:
f(4) = (-2 * 4) - 3
f(4) = (-8) - 3
f(4) = -11
f(4) = -11 is your answer.
~
QP contains the points Q(-6,10) and P(-12,-2). Find the slope of a line perpendicular to QP
Answer: -2
Step-by-step explanation: Find the slope of between the two points. P is the bottom point and Q is the top point. Both x and y numbers increase, meaning that the slope is positive. The x numbers increase by 6, and the y numbers increase by 12. This means that the rise is 12, and the run is 6. The slope is 12/6 but can be simplified to 2/1. The perpendicular slope is -1/2 because the perpendicular slope of a line is opposite reciprocal. This means to make the number negative and to flip it.
Answer:
-1/2
Step-by-step explanation:
So we are asked to find the slope of a line perpendicular to the line going through Q(-6,10) and P(-12,-2).
To do this we first need to find the slope of the line going through Q(-6,10) and P(-12,-2).
We can use the slope formula for a line given two points on that line which is (y2-y1)/(x2-x1).
I like to do something I consider easier to remember and is the same thing
It is:
A) line up the points
B) subtract vertically
C) put 2nd difference over first difference
D) done unless it needs reducing
So that is exactly what I'm going to do here:
(-6, 10)
-(-12,-2)
------------
6 12
So the slope is 12/6 or 2.
Now you might prefer to write 2 as a fraction now, because I'm about to tell you to find the slope of a line that is perpendicular, you just need to take the opposite reciprocal.
Opposite means to change the sign. I'm referring to negative or positive sign.
Reciprocal means to flip the number.
Let's put 2 through that process.
Opposite of 2: -2
Reciprocal of the opposite: -1/2
I got that reciprocal there by realizing -2 is just -2/1.
Anyways the slope of a line that is perpendicular to the one that goes through P and Q is -1/2 or -0.5.
Help me on this math question
Answer:
Step-by-step explanation:
The smallest number is 0.6. A fractional amount is always less that a whole number.
6.0 is the next smallest amount in some form. 6.009 The 0.009 is very tiny compared to the other numbers
then comes 6.08 That has only 2 decimal places, but those two places are bigger than 6.009
0.009 has 3 decimal places.
========
Finally 6.24 is larger than anything else. The 2 is in the tenths place.
Regular hexagon FGHIJK shares a common center with square ABCD on a coordinate plane. || . Across which lines can the combined figure reflect onto itself? A. any of the perpendicular bisectors of the sides of the hexagon B. either diagonal of the square C. any of the perpendicular bisectors of the sides of the square D. there are no lines across which this figure can reflect onto itself
Answer:
(C) Any of the perpendicular bisectors of the sides of the square
Step-by-step explanation:
In Regular Hexagon FGHIJK, we have 6 line of reflection across which the hexagon reflects onto itself. Those lines are:
3 perpendicular bisectors of sides i.e. perpendicular bisector of IJ , IH and GH
3 lines passing through vertices i.e. HK, IF and GJ.
While in Square, we have 4 line of reflection across which the square reflects onto itself. Those lines are:
2 perpendicular bisectors of sides AB and BC i.e. HK and perpendicular bisector of CD
2 digonals of square i.e. AC and BD
Also from figure we know that perpendicular bisector of CD and perpendicular bisector of IJ is the same line.
So, for combined figure we have to take common lines from both figures i.e. perpendicular of sides CD or IJ and line HK.
Answer:
Answer C
Step-by-step explanation:
Edmentum
Hook me up with a 5 star and a Thanks
A wall is 15 ft. high and 10 ft. from a house.
Find the length of the shortest ladder which
will just touch the top of the wall and reach a
window 20.35 ft. above the ground.
Answer:
=11.35 ft.
Step-by-step explanation:
The ladder, the flat surface the wall and the height up to the window form a trapezium.
The triangle that constitutes of the trapezium has the ladder as the hypotenuse, the distance between the two walls as base and the perpendicular distance from the base of the ladder to the window as height.
The height=20.35 ft-15 ft= 5.35 ft
Distance between the walls=10 ft
Hypotenuse²= base²+height²
H²=b²+h²
=10²+5.35²
=128.6225
H=√128.6225
=11.35 ft.
Answer:
11.41 ft
Step-by-step explanation:
Same steps as the other guy but, I have the correct answer(especially for Acellus)
Which statements are true regarding the prism? Check
all that apply.
The prism has no vertices.
The prism has 9 edges.
The bases of the prism are triangles.
The bases of the prism are rectangles.
The prism has 5 faces.
O
Answer:
1. The base is a triangle.
Step-by-step explanation: This one seems like it's the only corret one, You might have to wait and see the other answers roll in.
Answer:
2,3&5
Step-by-step explanation:
got it right on edg 2020
How to solve 3,4 and 6
Answer:
[tex]\large\boxed{3.\ V\approx130.88\ m^3}\\\boxed{4.\ V\approx35.21}\\\boxed{6.\ V\approx1.06\ in^3}[/tex]
Step-by-step explanation:
3.
The formula of a volume of a sphere:
[tex]V=\dfrac{4}{3}\pi R^3[/tex]
R - radius
We have R = 3.15 m. Substitute:
[tex]V=\dfrac{4}{3}\pi(3.15)^3\approx\dfrac{4}{3}\pi(31.26)\approx\dfrac{4}{3}(3.14)(31.26)\approx130.88\ m^3[/tex]
4.
The formula of a volume of a cone:
[tex]V=\dfrac{1}{3}\pi r^2H[/tex]
r - radius
H - height
We have 2r = 11.6 → r = 5.8 and H = x. Substitute:
[tex]V=\dfrac{1}{3}\pi(5.8)^2(x)=\dfrac{1}{3}\pi(33.64)x\approx\dfrac{1}{3}(3.14)(33.64)x\approx35.21[/tex]
6.
The formula of a volume of a cube:
[tex]V=s^3[/tex]
s - edge
We have s = 1.02 in. Substitute:
[tex]V=(1.02)^3\approx1.06\ in^3[/tex]
What is the y-value of the vertex of the function f(x)=-(x-3)(x+11)
so, this is a quadratic equation, meaning two solutions, and we have a factored form of it, meaning you can get the solutions by simply zeroing out the f(x).
[tex]\bf \stackrel{f(x)}{0}=-(x-3)(x+11)\implies 0=(x-3)(x+11)\implies x= \begin{cases} 3\\ -11 \end{cases} \\\\\\ \boxed{-11}\stackrel{\textit{\large 7 units}}{\rule[0.35em]{10em}{0.25pt}}-4\stackrel{\textit{\large 7 units}}{\rule[0.35em]{10em}{0.25pt}}\boxed{3}[/tex]
so the zeros/solutions are at x = 3 and x = -11, now, bearing in mind the vertex will be half-way between those two, checking the number line, that midpoint will be at x = -4, so the vertex is right there, well, what's f(x) when x = -4?
[tex]\bf f(-4)=-(-4-3)(-4+11)\implies f(-4)=7(7)\implies f(-4)=49 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \stackrel{vertex}{(-4~~,~~49)}~\hfill[/tex]
When price increases, quantity supplied:
stays the same
decreases
increases
becomes zero
The area of the regular hexagon is 10.4 in.2. What is the measure of the apothem, rounded to the nearest tenth of an inch? 1.3 in. 1.7 in. 2.0 in. 3.4 in.
Answer:
1.7
Step-by-step explanation:
Given:
Area of polygon=10.4
sides of polygon=2
Formula for area of a regular polygon= 1/2 (apothem x perimeter )
Putting value, we get
10.4= 1/2 ( a x 12 )
10.4=6a
a=10.4/6
a=1.73
the measure of the apothem, rounded to the nearest tenth of an inch=1.7!
Answer:
1.7 inches
Step-by-step explanation:
If the area of the regular hexagon is 10.4 in.2, the measure of the apothem, rounded to the nearest tenth of an inch is 1.7 inches
Given the following absolute value function find the range.
f(x) = |x+5| - 8
Answer:
{f ∈ R : f≥-8}
Step-by-step explanation:
The range is the output values
f(x) = |x+5| - 8
The smallest value the absolute value part can take is 0
f (min) = 0-8
The largest value is infinity
f(max) = infinity -8 = infinity
The range is -8 to infinity
Simplify (Y^2+7y+6)/(6y^2-6)
Answer:
[tex]\frac{y + 6}{6(y - 1)} [/tex]
Step-by-step explanation:
The given expression is
[tex] \frac{ {y}^{2} + 7y + 6}{6 {y}^{2} - 6} [/tex]
The numerator is a quadratic trinomial and the denominator is different of two squares when 6 is factored.
We factor both the numerator and the denominator to obtain;
[tex] \frac{ (y + 6)(y + 1) }{6(y - 1)(y + 1)} [/tex]
Cancel out the common factors to get:
[tex] \frac{y + 6}{6(y - 1)} [/tex]
This is the simplest form since, we cannot simplify this further.
For this case we must simplify the following expression:
[tex]\frac {y ^ 2 + 7y + 6} {6y ^ 2-6}[/tex]
We factor the numerator, looking for two numbers that when multiplied by 6 and when added together give 7. These numbers are +6 and +1.
Then, rewriting the expression:
[tex]\frac {(y + 6) (y + 1)} {6 (y ^ 2-1)} =[/tex]
We rewrite the denominator:
[tex]\frac {(y + 6) (y + 1)} {6 (y + 1) (y-1)} =[/tex]
We simplify similar terms:
[tex]\frac {(y + 6)} {6 (y-1)}[/tex]
Answer:
[tex]\frac {(y + 6)} {6 (y-1)}[/tex]
Given: AD = BC and
Prove: DE congruent to CE
Answer:
Step-by-step explanation:
the first two steps in determining the solution set of the system of equations y=x^2-6x
+12 and y=2x-4. Which represents the solution(s) of this system of equations?
For this case we have the following system of equations:
[tex]y = x ^ 2-6x + 12\\y = 2x-4[/tex]
Equating the equations:
[tex]x ^ 2-6x + 12 = 2x-4\\x ^ 2-6x-2x + 12 + 4 = 0\\x ^ 2-8x + 16 = 0[/tex]
We look for two numbers that when multiplied, get 16, and when added together, get -8.
These numbers are -4 and -4.
[tex](x-4) (x-4) = 0\\(x-4) ^ 2 = 0[/tex]
So, the solution is[tex]x = 4[/tex]
We look for the value of y:
[tex]y = 2x-4\\y = 2 (4) -4\\y = 8-4\\y = 4[/tex]
Finally, the solution is:[tex](4,4)[/tex]
ANswer:
[tex](4,4)[/tex]
If 47400 dollars is invested at an interest rate of 7 percent per year, find the value of the investment at the end of 5 years for the following compounding methods, to the nearest cent.
(a) Annual: $ _____.
(b) Semiannual: $ _____.
(c) Monthly: $ _____.
(d) Daily: $______.
Answer:
Part A) Annual [tex]\$66,480.95[/tex]
Part B) Semiannual [tex]\$66,862.38[/tex]
Part C) Monthly [tex]\$67,195.44[/tex]
Part D) Daily [tex]\$67,261.54[/tex]
Step-by-step explanation:
we know that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
Part A)
Annual
in this problem we have
[tex]t=5\ years\\ P=\$47,400\\ r=0.07\\n=1[/tex]
substitute in the formula above
[tex]A=47,400(1+\frac{0.07}{1})^{1*5}\\A=47,400(1.07)^{5}\\A=\$66,480.95[/tex]
Part B)
Semiannual
in this problem we have
[tex]t=5\ years\\ P=\$47,400\\ r=0.07\\n=2[/tex]
substitute in the formula above
[tex]A=47,400(1+\frac{0.07}{2})^{2*5}\\A=47,400(1.035)^{10}\\A=\$66,862.38[/tex]
Part C)
Monthly
in this problem we have
[tex]t=5\ years\\ P=\$47,400\\ r=0.07\\n=12[/tex]
substitute in the formula above
[tex]A=47,400(1+\frac{0.07}{12})^{12*5} \\A=47,400(1.0058)^{60}\\A=\$67,195.44[/tex]
Part D)
Daily
in this problem we have
[tex]t=5\ years\\ P=\$47,400\\ r=0.07\\n=365[/tex]
substitute in the formula above
[tex]A=47,400(1+\frac{0.07}{365})^{365*5}\\A=47,400(1.0002)^{1,825}\\A=\$67,261.54[/tex]
an app on your phone can estimate your time of arrival when given distance covered. You have travelled 4 1 2 kilometres. The app only accepts improper fractions.
Answer:
?
Step-by-step explanation:
wait is the kilometers number 412 or 41.2?
The mixed fraction 4 1/2 can be converted to the improper fraction 9/2 by multiplying the whole number by the denominator and then adding the numerator.
Explanation:The question is asking you to convert a mixed fraction (4 1/2) into an improper fraction. In your case of 4 1/2, an improper fraction is a fraction where the numerator (the top number) is greater than the denominator (the bottom number). To convert a mixed number into an improper fraction, you multiply the whole number (4) by the denominator of the fractional part (2) and add the numerator of the fractional part (1). This gives you the numerator of the improper fraction.
Here's how you do it: 4*2 = 8, then add 1, which gives you 9. Your improper fraction is thus 9/2.
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solutions to equation x^2 + x - 30 = 12 using zero product property
Answer:
Our solutions are x= -7 , x=6
Step-by-step explanation:
x²+x-30=12
First we calculate the constants:
x²+x-30-12=0
x²+x-42=0
Now split the middle term:
x²+7x-6x-42=0
x(x+7)-6(x+7)=0
(x+7)(x-6)=0
As we know that:
a.b=0
⇒either a=0 or b=0
(x+7)=0 , (x-6)=0
x=0-7 , x=0+6
x= -7 , x=6
So our solutions are x= -7 , x=6....
A teacher needs to choose seven students to hand out papers. The total number of ways he may choose the students can be found using a combination
Answer:
True
Step-by-step explanation:
Apex
SCIENCE--What is the connection between glaciers high in the Himalayan Mountains and hundreds of millions of people living in the lowlands of India, China and Bangladesh? Select one: a. The glaciers cool the region. b. There is no connection. c. The glaciers feed the great rivers of Asia and supply the lowlands with freshwater. d. The glaciers prevent people from being able to travel through the mountains.
C. Those glaciers cause large rivers and in turn large population centers to form.
Why are glaciers so important?Glaciers are the cornerstone of life on Earth. As vast freshwater reservoirs, they support the Earth's life system and affect our daily lives, including communities that live far away. But glaciers are disappearing. The disappearing glacier reveals the tallest glacier on Everest, which has lost ice for 2,000 years since the 1990s.
Even the highest mountains in the world are not safe from climate change. Even the glaciers of Everest are unsafe from climate change, new research suggests. Glacier ice turns blue because the red (long wavelength) part of white light is absorbed by the ice and the blue (short wavelength) part is transmitted and scattered. The longer the pass light travels through the ice, the bluer it looks.
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1,547.489 which digit is in the ten place
1,547.489
4 - Bold and underline one above is in the ten place.
Answer:
1,547.489
Step-by-step explanation:
Note that there is a decimal point in between 7 & 4, and the numbers to the left are whole numbers, while the numbers to the right is part of the decimal.
From the decimal point, count to the left two place value (to find the tens place):
1,547
1,547
4 is your digit in the ten's place, & is your answer.
~
how do you calculate the median and mean of X based on the table?
Answer:
The mean is all the #s added up and divided by 5, and median is the number in the middle which is 0.18
Step-by-step explanation:
PLZ vote me for BRAINILEST
3 sin^{2} x +cos 2x= (5/4)
answer in radians
Answer:
I believe it's 0.540717
Step-by-step explanation:
3(sin(2))x+(cos(2))(x)=5/4
Simplify: 2.311745x=5/4
Divide: 2.311745x/2.311735=5/4/2.311745
x=0.540717
The height of the parallelogram, h, can be found by dividing the area by the length of the base. If the area of the parallelogram is represented by 4x2 – 2x + 5 and the base is 2x – 6, which represents the height? 2x + 5 + 2x – 7 – 2x – 7 + 2x + 5 –
Answer:
[tex]\frac{4x^{2}-2x+5}{2x-6} =2x + 5 + \frac{35}{2x-6}[/tex]
Step-by-step explanation:
We know that the height of a parallelogram can be found by divind the area by the lenght of the base.
The area is 4x2 – 2x + 5 and the base is 2x – 6. To find the height, we need to divide both polynomials:
[tex]\frac{4x^{2}-2x+5}{2x-6} =2x + 5 + \frac{35}{2x-6}[/tex]
Answer:
[tex]2x+5+\frac{35}{2x-6}[/tex]
Step-by-step explanation:
Given,
The area of the parallelogram, A = [tex]4x^2-2x+5[/tex]
The length of its base, b = [tex]2x-6[/tex]
∵ The height of the parallelogram.
[tex]h=\frac{A}{b}[/tex]
[tex]\implies h=\frac{4x^2-2x+5}{2x-6}[/tex]
[tex]=2x+5+\frac{35}{2x-6}[/tex] ( by long division shown below )
Hence, the height of the given parallelogram is,
[tex]2x+5+\frac{35}{2x-6}[/tex]
Solve for x given the equation Vx+9 -4=1. Extraneous or not
Answer:
x=-4/V
Step-by-step explanation:
Add 4 to both sides to cancel out the 4.
So it now the equation is Vx+9=5
Subtract 9 from both sides to cancel out the 9.
Now the equation is Vx=-4
Divide V to both sides to get x alone.
The answer being x=-4/V
For this case we must find the value of "x" of the following equation:
[tex]\sqrt {x + 9} -4 = 1[/tex]
We add 4 to both sides of the equation:
[tex]\sqrt {x + 9} = 4 + 1\\\sqrt {x + 9} = 5[/tex]
We raise both sides of the equation to the square to eliminate the radical:
[tex]x + 9 = 5 ^ 2\\x + 9 = 25[/tex]
We subtract 9 from both sides of the equation:
[tex]x = 25-9\\x = 16[/tex]
Answer:
[tex]x = 16[/tex]
From the equation, find the axis of symmetry of the parabola. y=-3x^2+3x-13 a. x=1/2 b. x=3 c. x=-1/2 d. x=1
The axis of symmetry of the parabola [tex]y = -3x^2 + 3x - 13[/tex] is x = 1/2.
The axis of symmetry of a parabola in the form [tex]y = ax^2 + bx + c[/tex] is given by the formula x = -b/2a.
In the given equation [tex]y = -3x^2 + 3x - 13[/tex],
we can identify a = -3, b = 3, and c = -13.
The axis of symmetry is then calculated as x = -b/2a:
x = -3/(2*-3) = -3/-6 = 1/2
So, the correct answer is a. x = 1/2.
segment SW is the diameter of circle C. Point S is located at (6,-1) and point W is located at (10,-7). What are the coordinates of the center of this circle?
A. (8, -3)
B. (7, -5)
C. (9, -3)
D. (8, -4)
You put $280 in a one-year CD that will earn 4.5% a year, calculated semiannually. How much simple interest will you earn?
Answer:
25.77 dollars
Step-by-step explanation:
280 × .045 = y
y + 280 = z
z × .045 = c
z + c = d
d - c = the answer. $25.77