Given the following formula, w=x-y/2 -z. The value of y is y = x - 2w + wz .
What is a simplification of an expression?Usually, simplification involves proceeding with the pending operations in the expression.
Like, 5 + 2 is an expression whose simplified form can be obtained by doing the pending addition, which results in 7 as its simplified form.
Simplification usually involves making the expression simple and easy to use later.
Given the following formula,
w=x-y/2 -z
We need to solve for y.
[tex]w = \dfrac{x-y}{2 -z}[/tex]
By cross multiplication
[tex]w\times (2 -z)= {x-y}\\\\2w - wz = x - y[/tex]
subtract x both side
2w - wz -x = x - y -x
y = x - 2w + wz
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A woman sprints at a rate of 19 ft/s. How many minutes will it
take her to sprint 600 feet ?
[tex]\begin{array}{ccll} feet&seconds\\ \cline{1-2} 19 & 1\\ 600& x \end{array} \implies \cfrac{19}{600}~~=~~\cfrac{1}{x} \\\\\\ 19x=600\implies x=\cfrac{600}{19}\implies \stackrel{\textit{about half a minute}}{x\approx 31.58~seconds}[/tex]
Answer:
10/19 min ≈ 0.5263 min
Step-by-step explanation:
The woman's sprinting speed is given in feet per second, and we are asked for it in minutes per 600 feet. To find the time, we can use the relation ...
time = distance / speed
Using the given numbers will give a time in seconds, so we need to do a units conversion to find the answer in minutes.
__
setuptime = distance/speed
time = (600 ft) / (19 ft/s) = (600/19) s
Converting the units gives ...
time = (600/19) s × (1 min)/(60 s) = (600·1)/(19·60) min
evaluationThe time it takes the woman to sprint 600 feet will be ...
time = 600/(19·60) min = 10/19 min ≈ 0.5263 min
Find the length of the curve.
x=3t² +5₁y = 2t³ +5,0 ≤t≤1
The length of the curve will be given by the definite integral
[tex]\displaystyle \int_0^1 \sqrt{\left(\frac{dx}{dt}\right)^2 + \left(\frac{dy}{dt}\right)^2} \, dt[/tex]
From the given parametric equations, we get derivatives
[tex]x(t) = 3t^2 + 5 \implies \dfrac{dx}{dt} = 6t[/tex]
[tex]y(t) = 2t^3 + 5 \implies \dfrac{dy}{dt} = 6t^2[/tex]
Then the arc length integral becomes
[tex]\displaystyle \int_0^1 \sqrt{\left(6t\right)^2 + \left(6t^2\right)^2} \, dt = \int_0^1 \sqrt{36t^2 + 36t^4} \, dt \\\\ = \int_0^1 6|t| \sqrt{1 + t^2} \, dt[/tex]
Since 0 ≤ t ≤ 1, we have |t| = t, so
[tex]\displaystyle \int_0^1 6|t| \sqrt{1 + t^2} \, dt = 6 \int_0^1 t \sqrt{1 + t^2} \, dt[/tex]
For the remaining integral, substitute [tex]u = 1 + t^2[/tex] and [tex]du = 2t \, dt[/tex]. Then
[tex]\displaystyle 6 \int_0^1 t \sqrt{1 + t^2} \, dt = 3 \int_1^2 \sqrt{u} \, du \\\\ = 3\times \frac23 u^{3/2} \bigg|_{u=1}^2 \\\\ = 2 \left(2^{3/2} - 1^{3/2}\right) = 2^{5/2} - 2 = \boxed{4\sqrt2-2}[/tex]
Match the average rates of change of f(x) to the corresponding intervals.
-3
-8
-7
[-5, -1]
[-4,-1]
[-3, 1]
[-2, 1]
The average rates of change of f(x) and their corresponding intervals are given as:
Interval Rate of Change
[-5, -1] -8
[-4, -1] -7
[-3, 1] -4
[-2, 1] -3.
What is the explanation for the above?Step 1 - See Table Attached
Step 2 - State the formula for rate of change
The formula for rate of change is given as:
= [change in f(x)] / [change in x]
a) For interval [5, -1] ⇒
Rate of Change - [ f(1) - f(-5) ] / [-1 - (-5)]
= [-1 - 35] / [-1+5]
= -36 / 4
= - 8
b) For interval [-4, -1] ⇒
rate of change = [ f(-1) - f(-4) ] / [ -1 - (-4) ]
= [3 - 24] / [-1 + 4]
= -21/3
= - 7
c) interval [-3,1] ⇒
rate of change = [ f(1) - f(-3) ] / [ 1 - (-3) ]
= [-1 - 15] / [1 + 3]
= -16/4
= - 4
d) interval [-2,1] ⇒
rate of change = [f (1) - f(-2)] / [1 - (-2)]
= [ -1 - 8] / [1 + 2]
= -9/3
= -3
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Put these numbers in order, starting with the largest.
Largest
293,000
545,417
779,500
459,300
273,481
Smallest
A bag has 9 blue cubes, 11 red cubes, and 5 green cubes. If you
draw a cube and replace it in the bag 250 times, which of the
following amounts would you expect to pull?
The numbers that can be pulled based on the probability of the calls will be 90, 110, and 50.
How to depict the probability?From the information given, the bag has 9 blue cubes, 11 red cubes, and 5 green cubes and when one draws a cube and replace it in the bag 250 times, the number of blue balls that can be gotten will be:
= 9/(9+ 11 + 5) × 250
= 9/25 × 250
= 90
The number of red balls that can be gotten will be:
= 11/25 × 250
= 110
The number of green balls that can be gotten will be:
= 5/25 × 250
= 50
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Determine the area, in square centimeters, of
this quarter circle with a radius of 8 cm. Use 3.14
for π and round your answer to the nearest
hundredth.
Step-by-step explanation:
quarter circle means that you just find the are and then divide it by 4.
hence,
(3.14 × 8²) ÷ 4 = answer
the answer is 50.24 cm²
hope this helps.
Answer: 6.28
Step-by-step explanation: In order to get your answer, the equation that you need to do is 8 X 3.14 / 4 to get your answer.
a rectangular mural measures 3.5ft by 5.5ft. Rosalie creates a new mural that is 1.5 ft longer. What is the perimeter of Rosalie's new mural?
The perimeter of Rosalie's new rectangular mural is given by P = 21 feet
What is the Perimeter of a Rectangle?The perimeter P of a rectangle is given by the formula, P=2 ( L + W) , where L is the length and W is the width of the rectangle.
Perimeter P of rectangle = 2 ( Length + Width )
Given data ,
Let the perimeter of the rectangular mural be represented as P
Now , the equation will be
Let the initial length of the rectangular mural be L = 3.5 feet
Let the initial width of the rectangular mural be W = 5.5 feet
Now , the new mural is having an extra length of 1.5 feet
So , the new length of the rectangular mural is L₁ = 3.5 + 1.5 = 5 feet
Now , Perimeter P of rectangle = 2 ( Length + Width )
Substituting the values in the equation , we get
Perimeter of rectangular mural = 2 ( 5 + 5.5 )
On simplifying the equation , we get
Perimeter of rectangular mural P = 2 x 10.5
Perimeter of rectangular mural P = 21 feet
Hence , the perimeter of rectangular mural is 21 feet
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Answer:
1400
Step-by-step explanation:
PLEASE HELP! YOU WILL GET 100 POINTS! SUPER CONFUSED NEED HELP AS SOON AS POSSIBLE THIS IS DUE SOON!!! QUESTION IN PICTURE BELOW!
Answer:
Q = 40.6°
Explanation:
Given three sides: 9.6, 8.1, 6.3
Use the cosine rule:
c² = a² + b² - 2ab cos(C)
Insert following variables:
6.3² = 9.6² + 8.1² - 2(9.6)(8.1) cos(Q)
39.69 = 157.77 - 155.52 cos(Q)
cos(Q) = -118.08/-155.52
cos(Q) = 41/54
Q = cos⁻¹(41/54) = 40.6°
[tex]-3/z+7/4z=5/z-25[/tex]
Answer:
z = 1/4
Step-by-step explanation:
See attached image
Answer:
z = 5
Step-by-step explanation:
simplify
5/(z-25) first
turning it into
((0 - 3/z) + 7/4z) - 5/(z - 25) = 0
then simplify 7/4z
((0 - 3/z) + 7/4z) - 5/(z-25) = 0
when the fractions denominator is 0 then the numerator must be 0
turning the equation into
-25 * (z - 5) = 0
solve
-25 = 0
something that is not zero cannot equal zero.
z - 5 = 0
5 - 5 = 0
z = 5
hope this helps:)
Construct a triangle with the given conditions. Questions are on the picture.
Answer + Step-by-step explanation:
Question 4 :
Construct the angle 0MN :
1) Draw a segment MO
2) Put the protractor so that it is in line with the segment MO
At the same time ,line up the points M with the little circle of the protractor.
3) Spot 40° on the protractor ,then draw a point.
4) Use the ruler to connect point M through that point
Construct the angle MON :
1) Put the protractor so that it is in line with the segment MO
At the same time ,line up the points O with the little circle of the protractor
2) Spot 70° on the protractor ,then draw a point.
3) Use the ruler to connect point O through that point.
Construct the point N :
N is the point of intersection of the lines that go (respectively) through M and O.
Question 6 :
1) Draw a segment XZ such that XZ = 2.
2) construct the angle ZXY = 25°. (follow the steps described in the Previous question).
NOTE : ∠Z = 180 - (∠X + ∠Y) = 180 - (25 + 45) = 110°
3) construct the angle XZY = 110° . (follow the steps described in the Previous question)
4) Y is the point of intersection of the lines that go (respectively) through X and Z.
The height of an arrow is shot upward at an initial velocity of 40 meters per second can be modeled by h=40t-5t^2 where h is the height in meters and t is the time in seconds. Find the time is take for the arrow to reach the ground. Can someone please explain this to me thanks
We are given the equation for the height of the arrow. If you graph it, you see that it's a parabola and that the arrow kinda peaks and then falls back down. Another way of thinking about this problem is that you're looking for the time when the height is 0. You can see on the graph that there are two times that h=0. The first is obviously at t=0, when the arrow hasn't left the ground yet. The second is what we're looking for, when the arrow reaches the ground.
To solve this, let's set h=0. So 0=40t-5t^2. If you factor this, you get 5t(8-t) = 0. Continuing that leads to 5t=0 where t=0 which we already knew, and 8-t=0 where t=8. So that second time is when the arrow is back on the ground. Therefore your answer is 8 sec.
The incorrect work of a student to solve an equation 2(y + 6) = 4y is shown below: Step 1: 2(y + 6) = 4y Step 2: 2y + 8 = 4y Step 3: 2y = 8 Step 4: y = 4 Which of the following explains how to correct Step 2 and shows the correct value of y? (5 points) a 2 should be distributed as 2y + 12; y = 6 b 2 should be distributed as 2y + 12; y = 3 c The equation should be y + 6 = 4y after division by 2; y = 2 d The equation should be y + 6 = 4y after division by 2; y = 1
Step-by-step explanation:
The wording is slightly confusing so I will just solve the equation.
2 (y + 6) = 4y
We expand the bracket
2y + 12 = 4y
We subtract 2y from both sides
12 = 2y
We divide both sides by 2
6 = y
It’s geometry… need help solving
Answer:
Angle 1 = 90 degree
Angle 2 = 55 degree
Angle 3 = 35 degree
Step-by-step explanation:
A rhombus has four equal sides. Since the intersection angle of a rhombus is always 90 degree, angle 1 is 90 degree
Angle 3 = 180 degree - 90 degree - 55 degree = 35 degree
Angle 2 = 180 degree - 90 degree - 35 degree = 55 degree
Solve the system of equations
−5x−3y=−28 and x+2y=0 by combining the equations
Answer: (8, -4)
Step-by-step explanation:
-5x - 3y = -28
x + 2y = 0
1. Multiply both sides of the bottom system by 5 to cancel the x out
5(x+2y=0)
5x + 10y = 0
2. rewrite
-5x - 3y = -28
5x + 10y = 0
3. add
0x + 7y = -28
4. divide by 7
7y = -28
5. y = -4
6. plug in -4 for y in one of the original equations
x + 2(-4) = 0
7. simplify
x = 8
9. solution is
(8, -4)
Joan has some dimes and quarters. If she has 19 coins worth a total of $2.35, how many of each type of coin does she have?
The number of each type of coin that Joan has are; 16 dimes and 3 quarters
How to convert currencies?
We are told that Joan has a total of 19 coins.
Now, the worth of the coins is $2.35
Let dimes be d and let quarters be q. Thus;
10d + 25q = 235
d + q = 19
Substitute d = 19 - q in the 1st equation to get;
10(19 - q) + 25q = 235
190 - 10q + 25q = 235
15q = 45
q = 45/15
q = 3
Thus;
d = 19 - 3
d = 16
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Question 4 of 10
If ƒ(x) = 3(x+5) +−, what is f(a+2)?
[tex]f(x) = 3(x+5)\\\\f(a+2) = 3(a+2 +5) \\\\~~~~~~~~~~~~=3(a+7)\\\\~~~~~~~~~~~~=3a+21[/tex]
can you help me with this question
Which item is the U.S. Treasury most known for issuing?
-CDs
-savings notes
-bonds
-investment notes
Answer:
Bonds
Step-by-step explanation:
A bond is a fixed-income instrument that represents a loan made by an investor to a borrower (typically corporate or governmental).
Every day sandra eats 1/8 pound of a blueberries. If she does this for 9 days, how many pounds of blueberries did she eat?
Answer: 1.125 pounds of blueberries or [tex]1 \frac{1}{8}[/tex] or [tex]\frac{9}{8}[/tex]
Step-by-step explanation:
Since she will eat it for 9 days, just multiply or add the pounds.
an angle measures 122 degrees more than the measure of a supplementary angle. What is the measure of each angle?
Answer:
the measure of each angle is 75degrees
The solution to an absolute value inequality is shown on the graph below.
-5-4-3-2-1 0 1 2 3 4 5
What is another way to show the solution?
O x>-3 or x < 2
O {x|x <-3 orx <2}
O [-3, 2]
O (-3,2)
The solution to the absolute value inequality is (-3,-2)
How to determine the absolute inequality?On the absolute value inequality, we have:
Interval = -3 to 2
The intervals are represented with open circles.
This means that -3 and 2 are exclusive of the values of the inequality.
So, we have:
-3 < x < 2
As an interval notation, we have:
(-3,-2)
Hence, the solution to the absolute value inequality is (-3,-2)
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Triangle
ABC
GHI
DEF
S
NU
H"
Dimensions
2, 4, 5
5,5,9
4,4,4
Classify by
Sides
E
Classify by
Angles
Answer:
See below ~
Step-by-step explanation:
Classifying the triangles by sides and angles :
Triangle ABC
⇒ By Sides : Scalene (All sides are unequal)
⇒ By Angles : Right (There is a right angle = 90°)
============================================================
Triangle GHI
⇒ By Sides : Isosceles (2 sides are equal)
⇒ By Angles : Obtuse (One angle is greater than 90°)
============================================================
Triangle DEF
⇒ By Sides : Equilateral (All sides are equal)
⇒ By Angles : Acute (All angles are less than 90°)
How many liters each of a 24% iodine solution in a 40% iodine solution must be used to produce a total make sure of 100 L of 28% iodine solution
By weighted average, we need 75 liters of 24 % iodine solution and 25 liters of 40 % iodine solution to obtain 100 liters of 28 % iodine solution.
How to determine the volume associated with a given concentrationPhysically speaking, concentration is equal to the amount of solute divided by the volume of solution. We have two solutions with same solute and different concentration and can find the right proportion between the 24 % solution and the 40 % solution by concept of weighted average:
x · 24 + (1 - x) · 40 = 28
40 - 16 · x = 28
16 · x = 40 - 28
16 · x = 12
x = 3/4
By weighted average, we need 75 liters of 24 % iodine solution and 25 liters of 40 % iodine solution to obtain 100 liters of 28 % iodine solution.
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(01.06 LC)
Which number is not in scientific notation?
Answer:
[tex]0.95*10^8[/tex]
Step-by-step explanation:
Hello!
Rules for scientific notation format:
Has to be multiplied to a power of 10One factor has to be greater than 1 but less than 10[tex]\bold{0.95*10^8}[/tex]
There is a multiplication to a power of 10, but the other factor is less than 1.
This is NOT in Scientific Notation.
All the other options have a multiplication operation to a power of 10, and all the other factors are above 1 and less than 10.
Use four unit multipliers to convert 120 square inches to square yards.
The conversion of 120 sq. inches is equivalent to 0.09264 sq. yd.
What is Conversion?Conversion is the process of changing the value of one form to another for example inches to millimeters, or liters to gallons.
Here, we know that,
1 square inches = 0.000772 sq yd
we have 120 sq. inches
so, 120 sq. inches = 120 X 0.000772 sq yd
= 0.09264 sq. yd.
Thus, the conversion of 120 sq. inches is equivalent to 0.09264 sq. yd.
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what is the sum of the exterior angles of 28-gon
Answer:
360 degrees
..............
Which of the following is equal to this expression?
(256·64)^1/4
A) 4·[tex]\sqrt[4]{4}[/tex]
B) 8·[tex]\sqrt[4]{4}[/tex]
C) 8·[tex]\sqrt[4]{2}[/tex]
D) 2·[tex]\sqrt[4]{2}[/tex]
Answer:
B) [tex]8\sqrt[4]{4}[/tex]
Step-by-step explanation:
[tex](2^{8} *2^{6} )^\frac{1}{4} = (2^{8+6} )^\frac{1}{4} =(2^{14} )^\frac{1}{4} =2^{\frac{7}{2} }=\sqrt{2^{7} } =2^{3} \sqrt{2} =8\sqrt{2} = 8\sqrt[4]{2^{2} } = 8\sqrt[4]{4}[/tex]
Based on the measures
provided in the diagram,
determine the measure of
BC.
(You may assume that point A is the
center of the circle.)
O 130⁰
O 25⁰
O 50⁰
O 100⁰
The measures of BC will be 100°. Option D is correct.
What exactly is a circle?It is a point locus drawn equidistant from the center. The radius of the circle is the distance from the center to the circumference.
The angle at the center is twice as large as the angle at the perimeter.
BC = 2 ×∠CDB
BC=2×50°
BC= 100°
Hence option D is correct.
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A boat heading out to sea starts out at Point A, at a horizontal distance of 1315 feet
from a lighthouse/the shore. From that point, the boat's crew measures the angle of
elevation to the lighthouse's beacon-light from that point to be 12°. At some later
time, the crew measures the angle of elevation from point B to be 8°. Find the
distance from point A to point B. Round your answer to the nearest foot if
necessary.
Answer: 674 ft
Step-by-step explanation:
[tex]\tan 12^{\circ}=\frac{y}{1315} \\ \\ 1315\tan 12^{\circ}=y[/tex]
[tex]\tan 8^{\circ}=\frac{y}{x+1315} \\ \\ (x+1315)\tan 8^{\circ}=y \\ \\ (x+1315)\tan 8^{\circ}=1315 \tan12^{\circ} \\ \\ x \tan 8^{\circ}+1315 \tan 8^{\circ}=1315 \tan 12^{\circ} \\ \\ x \tan 8^{\circ}=1315 \tan 12^{\circ}-1315 \tan 8^{\circ} \\ \\ x=\frac{1315 \tan 12^{\circ}-1315 \tan 8^{\circ}}{\tan 8^{\circ}} \approx \boxed{674 \text{ ft}}[/tex]
3/4(2x-3) = 2/3 x+5 with detailed explanation
Answer:
x = 11
Step-by-step explanation:
3/(3(2x-3)) = 2/(3x+5)
3(2x-3) = 6x - 9
3/(6x-9) = 2/(3x+5)
3(3x+5) = 2(6x-9)
9x + 15 = 12x - 18
12x - 9x = 15 + 18
3x = 33
x = 11
Answer:
[tex]\mathrm x= \dfrac{87}{10} \quad or \quad 8.7[/tex]
Explanation:
[tex]\longrightarrow \sf \dfrac{3}{4} (2x-3)=\:\dfrac{2}{3}\:x+5[/tex]
Distribute inside parenthesis[tex]\longrightarrow \sf \dfrac{3}{2} x-\dfrac{9}{4} =\:\dfrac{2}{3}\:x+5[/tex]
Group the variables[tex]\longrightarrow \sf \dfrac{3}{2} x-\dfrac{2}{3}x=5+\dfrac{9}{4}[/tex]
Add or Subtract[tex]\longrightarrow \sf \dfrac{5}{6} x=\dfrac{29}{4}[/tex]
Cross Multiply[tex]\longrightarrow \sf x=\dfrac{29(6)}{4(5)}[/tex]
Simplify the following[tex]\longrightarrow \sf x=\dfrac{87}{10} \quad or \quad 8.7[/tex]