Answers
The value of x is 4 , 12 , - 1 resp. in eq 1 , 2 and 3 .
Finding values of unknown variable x .
Following are linear equations in one variable .
On solving them we get ,
1 ) 2 ( 3 x - 5 ) = - 4 x + 30
6 x - 10 = - 4 x + 30
10 x =40
x = 4
2 ) 5 x - 6 - 3 x = 18
2 x = 18 + 6
2 x = 24
x = 12
3 ) - 11 - 5 x = 6 ( 5 x + 4 )
- 11 - 5 x = 30 x + 24
- 35 x = 35
x = - 1
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Related Questions
Two cyclists, 54 miles apart, start riding toward each other at the same time. One cycles 2 times as fast as
the other. If they meet 3 hours later, what is the speed (in mi/h) of the faster cyclist?
a. Write an equation using the information as it is given above that can be solved to answer this problem.
Use the variable r to represent the speed of the slower cyclist.
b. What is the speed of the faster cyclist?
mi/hr
Answers
The equation that we need to solve is:
(S + 2*S)*3h = 54mi
The speed of the slower cyclist is 6 mi/h
The speed of the faster cyclist is 12 mi/h.
How to write an equation that models this situation?Let's define S as the speed of the slower cyclist, thus 2*S will be the speed of the other cyclist.
They travel in opposite directions, and after 3 hours the travel a combined distance of 54 miles, then we can write the equation:
(S + 2*S)*3h = 54mi
With that equation, we can determine the speeds of the cyclists.
Solving for S we get:
(S + 2*S)*3h = 54mi
3*S = 54mi/3h = 18 mi/h
S = (18 mi/h)/3 = 6 mi/h
Then the speed of the slower cyclist is 6 miles per hour, and the speed of the faster cyclist is twice that, so it is 2*6 mi/h = 12 miles per hour.
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A recent study of 50 U.S. chess players details such things as the number of years the players have been active and the chess ratings of the players. (A chess rating is a number, with a higher number indicating greater expertise.) The chess rating data for the sample of 50 players are summarized in the following
Answers
Using the given histogram, we have that 90% of the players in the sample have scores that are less than 2300.
What is the missing information?This problem is incomplete, but researching it on a search engine, we have that the histogram states as follows:
6 of these players have scores between 300 and 700.6 of these players have scores between 700 and 1100.13 of these players have scores between 1100 and 1500.14 of these players have scores between 1500 and 1900.6 of these players have scores between 1900 and 1300.5 of these players have scores between 2300 and 2700.The problem then asks the proportion of players in the sample with scores that are less than 2300.
What is an histogram?An histogram is a graph that shows the number of times each element of x was observed.
In the missing information section, we already gave the amounts presented by histogram, and we have that 45 out of 50 players have scores that are less than 2300, hence the proportion is given by:
p = 45/50 = 0.9.
Thus 90% of the players in the sample have scores that are less than 2300.
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reflection across the y-axis please I need help
Answers
W = (2,1)
X = (0,4)
Y = (-1,3)
Z = (-3,3)
The rule for a reflection over the y -axis is (x,y)→(−x,y) .
W (-2,1) ➡️ (2,1)
X (0,4) ➡️ (0,4)
Y (1,3) ➡️ (-1,3)
Z (3,3) ➡️ (-3,3)
Problem solved!
A student receives the following grades, with an A worth 4 points, a B worth 3 points, a C worth 2 points, and a D worth 1 point. What is the student's weighted mean grade point score? B in 2 two-credit classes D in 1 two-credit class A in 1 three-credit class C in 1 three-credit class
Answers
The student's GPA is of 2.33.
What is GPA?Grade Point Average (GPA) is the measure used to summaries your academic achievement at Griffith.
Given:
A worth 4 points,
B worth 3 points,
C worth 2 points,
D worth 1 point
The GPA is
= 3(3) + 1(3) + 2(4) + 2(2)/9+3+4+2
=9+3+8+4/18
=2.33
Hence, The student's GPA is of 2.33.
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Video on Converting from different bases to base 10 [+]
Convert the following base 2 numeral to a base 10 numeral and enter your answer in the box.
101011
(Remember, the above number is in Base 2!)
Base 10 numeral:
Note: Only enter your final result.
Question Help: Video Message instructor
Submit Question
Answers
101011 in base 2 is equal to 43 in base 10
1.2 A pyramid, with the base similar to an obtuse-angled triangle as indicated by the diagram below. A = 110°, B = 40° and BC = 6 meters. The perpendicular height of the pyramid is 8 meters
1.Calculate the length of AB
2.Calculate the area of the base.
3.Calculate the volume of the pyramid
Answers
a) The length of the side AB is approximately 11.276 meters.
b) The area of the base of the pyramid is approximately equal to 6.161 square meters.
c) The volume of the pyramid is equal to 16.429 cubic meters.
What are the length of a side, the surface area and the volume of a pyramid?a) The picture shows a pyramid with a triangular base, the triangle has one obtuse angle and the length of the side AB can be found by the law of the sine:
6 / sin 110° = AB / sin 30°
AB = 6 × (sin 30° / sin 110°)
AB ≈ 3.193 meters
The length of the side AB is approximately 11.276 meters.
b) First, find the length of the side AC:
6 / sin 110° = AC / sin 40°
AC = 6 × sin 40° / sin 110°
AC ≈ 4.104 meters
Second, determine the area of the triangular base by Heron's formula:
s = 0.5 · (AC + BC + AB)
s = 0.5 · (4.104 m + 6 m + 3.193 m)
s = 6.649 m
A = √[s · (s - AC) · (s - BC) · (s - AB)]
A = √[6.649 · (6.649 - 4.104) · (6.649 - 6) · (6.649 - 3.193)]
A ≈ 6.161 square meters
The area of the base of the pyramid is approximately equal to 6.161 square meters.
c) The volume of the pyramid can be found by using the following expression:
V = (1 / 3) · A · h
Where:
A - Area of the pyramid base, in square meters.h - Height, in meters.If we know that A ≈ 6.161 square meters and h = 8 meters, then the volume of the pyramid is:
V = (1 / 3) · (6.161 m²) · (8 m)
V = 16.429 m³
The volume of the pyramid is equal to 16.429 cubic meters.
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please help me I have mistake
Answers
Answer:
See below
Step-by-step explanation:
Here is one possible mistake:
Let y= u = ( 2ax^2 +c)^2 expand
4 a^2 x^4 + 4 a x^2 c + c^2
dy/ dx then becomes
16 a^2 x^3 + 8 a x c <====== you have 8 a^2x^3 + 8axc
MAYBE ??
[tex]y = (2ax^2 + c)^2 (bx^2 - cx)^{-1}[/tex]
By the product rule,
[tex]\dfrac{dy}{dx} = \dfrac{d(2ax^2+c)^2}{dx} (bx^2-cx)^{-1} + (2ax^2+c)^2 \dfrac{d(bx^2-cx)^{-1}}{dx}[/tex]
For the first derivative on the right side, let [tex]u=2ax^2+c[/tex]. Then by the chain rule,
[tex]\dfrac{d(2ax^2+c)^2}{dx} = \dfrac{du^2}{dx} \\\\ ~~~~~~~~~~~~~~~~~~ = \dfrac{du^2}{du}\dfrac{du}{dx} \\\\ ~~~~~~~~~~~~~~~~~~ = 2u \dfrac{du}{dx} \\\\ ~~~~~~~~~~~~~~~~~~ = 2(2ax^2+c) \dfrac{d(2ax^2+c)}{dx}[/tex]
and by the power rule, this reduces to
[tex]\dfrac{d(2ax^2+c)^2}{dx} = 2 (2ax^2+c) (4ax) \\\\ ~~~~~~~~~~~~~~~~~~ = 8ax (2ax^2 + c)[/tex]
For the other derivative, let [tex]v = bx^2-cx[/tex]. Then
[tex]\dfrac{d(bx^2-cx)^{-1}}{dx} = \dfrac{dv^{-1}}{dx} \\\\ ~~~~~~~~~~~~~~~~~~~~ = \dfrac{dv^{-1}}{dv}\dfrac{dv}{dx} \\\\ ~~~~~~~~~~~~~~~~~~~~ = -v^{-2} \dfrac{dv}{dx} \\\\ ~~~~~~~~~~~~~~~~~~~~ = -(bx^2-cx)^{-2}\dfrac{d(bx^2-cx)}{dx}[/tex]
which reduces to
[tex]\dfrac{d(bx^2-cx)^{-1}}{dx} = -(bx^2 - cx)^{-2} (2bx - c)[/tex]
So one expression for the derivative we want is
[tex]\dfrac{dy}{dx} = 8ax (2ax^2 + c) (bx^2-cx)^{-1} - (2ax^2+c)^2 (bx^2 - cx)^{-2} (2bx - c)[/tex]
There are 20 flowers in a bouquet, and 2 of them are roses. What percent of the flowers are roses?
Answers
Answer: 10%
Step-by-step explanation:
vertical compression by a factor of 1/3 and a reflection of why axis f(x)= 6x-2
Answers
Answer: f(x)=(-6x-2)/3
Step-by-step explanation:
f(x)= 6x-2
f(x)= (6x-2)*1/3 ==>Vertical compression
f(x)=(6x-2)/3
f(x)=(6(-x)-2)/3 ==> reflection over y-axis is when x is being negated
f(x)=(-6x-2)/3
Let U= {x | x is a whole number and 0 ≤ x ≤ 19) and C= {15, 16, 17, 18, 19). Write U U C using the listing method.
UUC=
Answers
set, in mathematics and logic, any collection of objects (elements), which may be mathematical (e.g., numbers and functions) or not. A set is commonly represented as a list of all its members enclosed in braces. The intuitive idea of a set is probably even older than that of number.
Let C=15, 16, 17, 18, and 19) and U=x | x is a full number and 0 x 19). Use the listing technique to write U U C.
UUC=
D U E = { 16, 18, 19, 20, 21 }
U stands for the union of sets.
We combine all of the components from the two groups.
16, 19, 21, and 16, 18, 19, 20 are the elements in sets D and E, respectively.
Therefore, we combine all of their components. The shared components of both sets are written just once.
As a result, there are 16, 18, 19, 20, and 21 elements in the set D U E.
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In Town A, homeowners pay a $25 monthly usage fee and $3 per hundred cubic feet for water. In Town B,
homeowners pay $2.00 per hundred cubic feet and a $50 monthly usage fee for water.
2.
1. Can these situations be represented by linear functions? Why? Why not?
Predict: If you graph both of these water costs on the same axes, will the graphs form the same line,
intersect at one point, or form two separate lines that never intersect? Explain your reasoning.
3. Write equations, in slope-intercept form, for a homeowner's monthly water cost in Town A and Town B,
where y is the total cost for x hundred cubic feet of water.
Answers
The homeowners pay a $25 monthly usage fee and $3 per hundred cubic feet for water number line is- 75,100
Given:
In Town A
$25 monthly usage fee
$3 per hundred cubic feet for water.
In Town B,
homeowners pay $2.00 per hundred cubic feet and a $50 monthly
For town A=25×3=75
For town B=50×2=100
When we write numbers on a number line, we can easily compare them and execute simple arithmetic operations on them. A number line's origin is defined as zero (0). The numbers to the left of 0 are all negative, whereas the numbers to the right of 0 are all positive. So, as we walk towards the right on a number line, the value of numbers increases.
A number line includes both positive and negative numbers. A negative number line is formed by the segment of the number line to the left of zero.
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Manu makes some money on the side by producing and selling customized drink glasses for family reunions. To make the glasses, it costs him a flat fee of $10 per order, plus $8 per glass. He sells the glasses for $13 per glass. How big must the order be in order to earn a profit of $100? Let x = the number of glasses and y = profit from selling x glasses. Set up the equation for this situation and solve it. You must show all calculation in order to earn any credit.
Answers
To earn $100 profit Manu should get the order of 22 glasses.
Given that, the cost price of a drinking glass=$8 and the selling price = $13.
What is profit?When, in a transaction, the selling price is greater than the cost price, it means we earn a profit. The basic formula used for calculating the profit is Profit = Selling Price - Cost Price.
Let x = the number of glasses and y = profit from selling x glasses.
Now, y=(13-8)x-10
Assumed that the order is x glasses to earn a profit of $100.
(13-8)x-10=100
⇒5x-10=100
⇒5x=110
⇒x=22
Therefore, to earn $100 profit Manu should get the order of 22 glasses.
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A shirt and a tie are 57 together if the shirt is $29 more than the tie how much money is the Tie worth
Answers
Answer:
$14
Step-by-step explanation:
The tie costs x.
The shirt costs x + 29
Together they cost $57.
x + x + 29 = 57
2x + 29 = 57
2x = 28
x = 14
Answer: $14
Answer:
14
Step-by-step explanation:
Tie is X
Shirt is x + 29
So,
X+X+29= 57
2x+29= 57
57-29= 2x
28=2x
X= 14
So tie is 14 bucks
graph the lines Slope -1 passing through point (2,2)
Answers
The graph of the equation (y = x ) is attached below and this can be determined by using the point-slope form of the line.
Given :
A line with a slope of 1 that passes through the point (2,2).
The following steps can be used in order to sketch the graph a line with a slope of 1 that passes through the point (2,2):
Step 1 - First, determine the equation of the line that passes through the point (2,2) and has a slope of 1
Step 2 - Point-slope form can be used in order to determine the equation of a line.
y-y1 = m(x- x1)
where m is the slope and (x1, y1) is the point on the line.
Step 3 - Substitute the known terms in the above formula.
y-2 = 1(x-2)
Step 4 - Simplify the above equation.
y-2=x-2
x=y
Step 5 - Now, graph the above equation. The graph of the equation
(y = x ) is attached below.
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Suppose that 14 inches of wire costs 84 cents.
At the same rate, how much (in cents) will 11 inches of wire cost?
Answers
Answer:
11 inches of wire will cost 66 cents
Step-by-step explanation:
14 inches - 84 cents
find unit rate by dividing 84 by 14
84/14=6
so is is 6 cents per inch
so multiply 6 by 11
11 inches of wire will cost 66 cents
I need help
What is x/10 = 4
Answers
Answer:
40
Step-by-step explanation:
another answer to something elsse it might help Solve for x x-4=10. x − 4 = 10 x - 4 = 10. Add 4 4 to both sides of the equation. x = 10+ 4 x = 10 + 4. Add 10 10 and 4 4. x = 14 x = 14.
Answer:X=40
Step-by-step explanation:
Find the area of AXYZ. (Hint: Draw a rectangle whose sides contain points X, Y, and Z.)
Ay
Y
-4
X
-2
Area: I
4
2
-2
N
2
square units
4 x
So
Answers
The area of triangle XYZ is of 13.3 units².
What is the missing information?The missing information are the vertices of the triangle, given as follows:
X(-3,2).Z(1,-1).Y(3,4).What is the area of a triangle?The area of a triangle is given by half the base multiplied by the height, that is:
A = 0.5bh
For this problem, the have that the base is the length of segment XZ, which is found applying the distance between two points as follows:
[tex]b = \sqrt{(1 + 3)^2+(-1 - 2)^2}[/tex]
b = sqrt(25)
b = 5.
The height is the distance between the midpoint of XZ and Y. The midpoint of XZ(mean of the coordinates) is (-1, 0.5), hence the height is:
[tex]h = \sqrt{(-1 - 3)^2+(4 - 0.5)^2}[/tex]
h = sqrt(4² + 3.5²)
h = 5.32.
Thus the area of the triangle is given by:
A = 0.5 x 5 x 5.32 = 13.3 units².
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as a contractor to make a hole 4 5/8 inches diameter. express the mixed number as an improper fraction.
Answers
The mixed number as an improper fraction is 37/8
How to express the mixed number as an improper fraction?The diameter is give as:
Diameter = 4 5/8
Next we convert the above number to an improper fraction
The numerator is calculated as
Numerator = 8 * 4 + 5
This gives
Numerator = 37
Hence, the mixed number as an improper fraction is 37/8
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I can't understand,
Answers
Answer:so dividing you add a extra zero behind the dot or point while multiplying you decrease the decimal to a whole number
if it is right pls give me brainliest
Step-by-step explanation:The relationship between 0.8 divided by 10^2 and 0.8x10^2 is that 0.8 divided by 10^2 means you add extra zero to the dot like this 0.008 so what it mean is that 10^2 is to add extra zeros in front of the point or dot in 0.8 while 0.8x10^2 decreases the zero like this 80 so we remove the 0 in 0.8 which mean 0.8 is no longer a decimal but a whole number now and then add a extra zero because 10^2 mean add two zeros so if you see a number infornt of 10^ like 2 is how many zeros you add. so you add to extra zeros to 0.8 which decreases
Convert 9.2495 to a percent
Answers
Answer:
924.95 %
Step-by-step explanation:
9.2495 x 100% = 924.95 %
A ball is thrown from an initial height of 6 feet with an initial upward velocity of 40 fVs. The ball's height h (in feet) after / seconds is given by the following.
h=6+401-16r²
Find all values off for which the ball's height is 28 feet.
Round your answer(s) to the nearest hundredth.
Answers
The value for which the ball's height is 28 feet are 0.817sec and 1.683sec using quadratic equations.
What is a quadratic equation?
In algebra, a quadratic equation( from Latin quadratus' forecourt') is any equation that can be rearranged in standard form asax^2 + bx + c = 0
where x represents an unknown, and a, b, and c represent known figures, where a ≠ 0. is still, not quadratic, as there's no ax^2 term,( If a = 0( and b ≠ 0) also the equation is direct.)
The figures a, b, and c are the portions of the equation and may be distinguished by calling them, independently, the quadratic measure, the direct measure, and the constant or free term.The values of x that satisfy the equation are called results of the equation, and the roots or bottoms of the expression on its left-hand side. A quadratic equation has at most two solutions.Given,
h(0)=6 ft (six)
v(0)=40 ft/sec (fourty)
h(t)=6+40t-16t2 (equation)
for h=28 ft(twenty eight)
28=6+40t-16t2 (equation)
or 16t2 - 40t + 22 = 0 (equation)
or 8t2 - 20t + 11= 0(equation)
on solving the quadratic equation
t=0.817sec and 1.683sec (answer)
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20 times 40 answer please
Answers
Answer: 800
Step-by-step explanation:
Answer:
800
Step-by-step explanation:
4/5 divided 1/10 math problem trying to figure out
Answers
Answer:
8
Step-by-step explanation:
(4/5)/(1/10)
oreja
take the top most number and bottom most number, multiply the two. Then multiply the two middle numbers.
(4*10)/(5*1)
Simplify and you get:
40/5
=8
I’ll give brainless to the right answer
Answers
Use the formula for simple interest, I=Prt, to find the indicated quantity. I=$28; r=8%; t=3 months; P=?
Answers
==================================================
Work Shown:
i = 28
r = 8% = 0.08
t = 3 months = (3/12) year = 0.25 year
-----------
i = P*r*t
28 = P*0.08*0.25
28 = P*0.02
P = 28/0.02
P = 1400
Side notes:
always use the decimal form of rThe value of t is in years because of the annual interest rateHELP I DONT UNDERSTAND MY MATH HOMEWORK AND I HAVE 3 PAGES OF IT
Answers
solve the brackets first - + = -
=-1-4
=-5
-1+(-4)=-1-
solve the left side
-1-4=-1-
-5=-1-
now think what will be -5 if we -1 from it
-5=-1-4
-5=-5
-1- =-5
-1 minus what will be -5
-1-4=-5
-5=-5
1-(-4)=1+4
dove brackets first - -=+
1+4=1+4
5=5
Jackson left his house and walked at a constant rate. After 20 minutes he was 2 miles from his house. Jackson then walked back towards his house at a constant rate. After another 30 minutes he arrived at his house. Why should Jackson not use an absolute value function to model the distance from his house d after t minutes? Multiple choice question. cross out A)
Answers
Answer:
B) The graph will not be symmetrical because the rates at which Jackson walks to and from his house are not equal.
Step-by-step explanation:
there you go I hope this help! :)
The graph will not be symmetrical because the rates at which Jackson walks to and from his house are not equal (option b).
Using an absolute value function to model the distance from his house would imply that the distances from his house are the same for both the outbound and return journeys, which is not the case in this scenario.
The rates at which Jackson walks to and from his house are not equal, as indicated by the different times taken for each leg of the journey (20 minutes to get away from his house and 30 minutes to return). This means the graph of the distance over time would not be symmetrical around a vertical line.
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The complete question is:
Jackson left his house and walked at a constant rate. After 20 minutes he was 2 miles from his house. Jackson then walked back towards his house at a constant rate. After another 30 minutes he arrived at his house.
Why should Jackson not use an absolute value function to model the distance from his house d after t minutes?
OA) The graph will be symmetrical because the rates at which Jackson walks to and from his house are equal.
OB) The graph will not be symmetrical because the rates at which Jackson walks to and from his house are not equal..
OC) The graph will be symmetrical because the rates at which Jackson walks to and from his house are not equal.
OD) The graph will not be symmetrical because the rates at which Jackson walks to and from his house are equal
5. Combien de paires de nombres naturels peut-on former dont : a) la somme est 23? b) la différence est 100?
Answers
Answer: a) 24 b) infini
Step-by-step explanation: a) parce que tu peut faire que 24 somme pour faire 23. B) infini car tout plus haut 100 fonctione
3x + 2 = 5x-8 how do I solve this
Answers
Answer:
x = 5
Step-by-step explanation:
Do children weigh 160 pounds together the oldest weighs 120lbs more how much do they each weigh
Answers
Answer:
One child weighs 120lbs, and the other weighs 40lbs.
Step-by-step explanation:
Assuming that you meant "Two" instead of "Do", there are two children that weigh 160 pounds together. If we know that one child weighs 120lbs more, we know that the other child has to weigh 40lbs using the equation below where x represents the weight of the second child:
120 + x = 160
Subtract 120 from both sides
x = 40
FINAL ANSWER: One child weighs 120lbs, and the other weighs 40lbs.