Answer:
[tex] {3x}^{ - 1} - {4y}^{ - 1} = 5 \: ....(1) \\ \\ {2x}^{ - 1} + {3y}^{ - 1} = 7 \: ....(2) [/tex]
__o__o__
[tex] \frac{1}{3x} - \frac{1}{4y} = 5 \: ....(1) \\ \\ \\ \frac{1}{2x} + \frac{1}{3y} = 7 \: ....(2)[/tex]
From equation (1) ;
[tex] \frac{1}{3x} - \frac{1}{4y} = 5 \\ \\ \frac{1}{4y} = \frac{1}{3x} - 5 \\ \\ \frac{1}{4y} = \frac{1 - 15x}{3x} \\ \\ \\ 4y(1 - 15x) = 3x \\ \\ 4y = \frac{3x}{1 - 15x} \\ \\ y = \frac{3x}{4(1 - 15x)} \\ \\ \\ y = \frac{3x}{4 - 60x} [/tex]
[tex] \frac{1}{2x} + \frac{1}{3y} = 7 \\ \\ \\ \frac{1}{2x} + ( \frac{1}{3( \frac{3x}{4 - 60x} )} ) = 7 \\ \\ \\ \frac{1}{2x} + ( \frac{1}{ \frac{9x}{4 - 60x} } ) = 7 \\ \\ \\ \frac{1}{2x} + \frac{4 - 60x}{9x} = 7 \\ \\ \\ \frac{9}{18x} + \frac{2(4 - 60x)}{18x} = 7 \\ \\ \\ \frac{9}{18x} + \frac{8 - 120x}{18x} = 7 \\ \\ \\ \frac{9 + 8 - 120x}{18x} = 7 \\ \\ \frac{17 - 120x}{18x} = 7 \\ \\ 18x \times 7 = 17 - 120x \\ \\ 126x = 17 - 120x \\ \\ 126x + 120x = 17 \\ \\ 246x = 17 \\ \\ x = \frac{17}{246} [/tex]
[tex]y = \frac{3x}{4 - 60x} \\ \\ y = \frac{3( \frac{17}{246}) }{4 - 60( \frac{17}{246} )} \\ \\ y = - \frac{17}{12} [/tex]
An airplane flies into the wind for 5 hours, traveling 900 miles. The airplane then
turns around and flies with the wind, returning to its starting place in 4 hours.
This can be modeled by the following system of equations, where (s) is the speed
of the plane with no wind and (w) is the speed of the wind.
5(s-w)=900
4(s+w) = 900
What is the speed of the wind in miles per hour?
Answer:
22.5 miles per hour
Step-by-step explanation:
Given system of equations
5(s-w)=900
4(s+w)=900
Set equations equal to each other
5(s-w)=4(s+w)
5s-5w=4s+4w
s-5w=4w
s=9w
Solve for w using the substitution s=9w
4(s+w)=900
4(9w+w)=900
4(10w)=900
40w=900
w=22.5
Therefore, the speed of the wind is 22.5 miles per hour
Rearrange the fractions in order from least to greatest. Show your work
Answer:
A) 2/3, -3/4, 1/2, -1/3
Start by making all of them have the same denominator. They all multiply to 12 easily, so I will use that. Remember that whatever you do to the top you have to do to the bottom, and vice versa.
Multiply 2/3 by 4/4 to get 8/12
Multiply -3/4 by 3/3 to get -9/12
Multiply 1/2 by 6/6 to get 6/12
Multiply -1/3 by 4/4 to get -4/12
Least to greatest (new): -9/12, -4/12, 6/12, 8/12
Least to greatest (old): -3/4, -1/3, 1/2, 2/3 <-------- this is your answer
C) -9/10, -8/9, -4/5, -41/45
Make them have the same denominator. They all multiply to 90, so I'll use that.
Multiply -9/10 by 9/9 to get -81/90
Multiply -8/9 by 10/10 to get -80/90
Multiply -4/5 by 18/18 to get -72/90
Multiply -41/45 by 2/2 to get -82/90
Least to greatest (new): -82/90, -81/90, -80/90, -72/90
Least to greatest (old): -41/45, -9/10, -8/9, -4/5 <-------- this is your answer
E) -3, -2 2/3, -3 1/6, 2 3/4
Make the mixed numbers into improper fractions by multiplying the whole number with the denominator, and then adding the numerator:
-3 ---> -3/1 (this one's easy)
-2 2/3 ---> -8/3
-3 1/6 ---> -19/6
2 3/4 ---> 11/4 (this one is the only positive one, so it will be the greatest)
Same denominator. I'm using 12.
Multiply -3/1 by 12/12 to get -36/12
Multiply -8/3 by 4/4 to get -32/12
Multiply -19/6 by 2/2 to get -38/12
Multiply 11/4 by 3/3 to get 33/12
Least to greatest (new): -38/12, -36/12, -32/12, 33/12
Least to greatest (old): -3 1/6, -3, -2 2/3, 2 3/4 <-------- this is your answer
what is petrification???????????..
Answer:
the process by which organic matter exposed to minerals over a long period is turned into a stony substance.
Step-by-step explanation:
Picture example:
Which operation symbol could be placed in the circle so that B is a non linear function of T?
B= t___t
A. +
B. -
C. x
D. division sign
It can be deduced that a non linear function is a function where the graph isn't a line.
What is a non linear function?Your information is incomplete as the circle isn't given. Therefore, an overview of the non linear function will be given.
A non linear function simply means a function where the graph is not a line. In this case, they do not have a constant slope.
A non linear function is a function shows graph isn't a line or part of a line. In such a case, the graph isn't a straight line.
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please help me with rhis question
Answer:
He is correct!
Step-by-step explanation:
one quarter of 9 is 2.25 cause if u divide 9 by 2, you get 4.50 which is one half, so if you divide 4.50 by 2 you get 2.25 which is one quarter of 9
Which one of the following statements about the projected unit sales volumes per company in the table on p.6 of the Player's Guide is false?
A. The projected unit sales volumes of branded footwear per company in Europe-Africa in Years 11-13 are higher than in North America.
B. Branded footwear sales per company in North America in Years 11-13 are projected to exceed branded footwear sales per company in the other three geographic regions.
C. The unit sales volumes of private-label footwear per company in the Europe-Africa region in Years 11-13 are projected to be the same as in North America.
D. Unit sales volumes per company of branded footwear in Years 11-13 are projected to be higher in the Europe Africa region than in either the Asia-Pacific region or the Latin America region.
E. The unit sales volumes per company in Latin America in Year 13 are projected to be 1,997,000 pairs of branded footwear and 288,000 pairs of private-label footwear
There are factors that makes a statement to be true. The false statement is that the projected unit sales volumes of branded footwear per company in Europe-Africa in Years 11-13 are higher than in North America.
What are the factors in knowing a company's unit sales?The factors to consider in knowing a company's unit sales and market share of products such as branded footwear in a specific geographic region includes;
The expenditures made on advertising.The number of models/styles in the company's product lineThe delivery times to retailers (such as 1,2,3,or 4 weeks)From the study, the market for branded athletic footwear is projected to grow approximately 9-11% annually in Latin America and the Asia-Pacific and 5-7% annually in North America an Europe-Africa during the Year 11-15.
Therefore the above is false since their projected growth is the same percentage.
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Find the value of (8/125)^-2/3
Answer:
6.25
Step-by-step explanation:
Using the rules of exponents
[tex](\frac{a}{b}) ^{-\frac{m}{n} }[/tex] = [tex](\frac{b}{a}) ^{\frac{m}{n} }[/tex]
[tex]a^{\frac{m}{n} }[/tex] = [tex](\sqrt[n]{a} )^m[/tex]
Given
[tex](\frac{8}{125}) ^{-\frac{2}{3} }[/tex]
= [tex](\frac{125}{8}) ^{\frac{2}{3} }[/tex]
= [tex](\sqrt[3]{125} )^2[/tex] × [tex]\frac{1}{(\sqrt[3]{8})^2 }[/tex]
= 5² × [tex]\frac{1}{2^2}[/tex]
= 25 × [tex]\frac{1}{4}[/tex]
= [tex]\frac{25}{4}[/tex]
= 6.25
1)make x the subject of formula
Y = 6x + 11
2) make b and h the subject of formula
A =
[tex] \frac{1}{2} bh[/tex]
Answer:
o 1)
[tex]Y= 6x + 11 \\ \\ 6x = Y - 11 \\ \\ x = \frac{Y - 11}{6} \\ \\ x = \frac{Y}{6} - \frac{11}{6} [/tex]
___o__o__
o 2)
[tex]A = \frac{1}{2} bh \\ \\ bh = A \div \frac{1}{2} \\ \\ bh = A \times 2 \\ \\ bh = 2A[/tex]
[tex]b = \frac{2A}{h} [/tex]
[tex]h = \frac{2A}{b} [/tex]
21. The following dataset depicts the hypothetical test scores of students in a random college
statistics course: {92, 84, 53, 77, 81, 71, 62, 54, 67, 69, 88, 75, 96, 75, 78}
Based on the data, construct a five-class frequency distribution with a lower class limit of
50, an upper class limit of 99, and a class width of 10. Include the relative and cumulative
frequencies for each class.
Answer: answer 98 , 78
Step-by-step explanation:
the way you just flip then and your done
50 points!!!!
Type the correct answer in the box use numerals instead of words
Rebecca Hut a circular cake into six slices of equal size each cake slice has an area of 13 in.² what is the radius of Rebecca‘s cake to the nearest whole inch
The cakes radius is ______ inches
Answer:
5 inches
Step-by-step explanation:
Area of the cake:
1 slice = 13 in²6 slices = 13 in² * 6 = 78 in²Area circle: πr²
Solve for r:
78 = πr²r² ≈ 24.84 r ≈ 5-Chetan K
Answer:
The cakes radius is 5 inches.
Explanation:
cake has a circular area. Therefore we will use, area of circle: πr²Here given the cake is cut in six equal size.The area of the slice will be [tex]\frac{1}{6}[/tex](πr²)Steps:
→ [tex]\frac{1}{6}[/tex]πr² = 13
→ πr² = 13(6)
→ πr² = 78
→ r² = [tex]\frac{78}{\pi }[/tex]
→ r = [tex]\sqrt{\frac{78}{\pi }}[/tex]
→ r = 4.982787485
→ r = 5
Therefore the cake has a radius of 5 inches. Do not misunderstand that we are taking slice radius, its the radius of the cake all along.
An artist designs a sculpture in the shape of a rectangular prism.
The sculpture has a width of x feet. The depth of the sculpture is 6 feet more than the width. The length of the sculpture is 12 feet less than twice the width.
Given the sculpture's volume in cubic feet is 26 times its width in linear feet, what is the length of the sculpture?
Answer: 2
Step-by-step explanation:
took the quiz
The length of the sculpture is 2 feet.
Given information about the sculpture:
Width of the sculpture = x feet
Depth of the sculpture = x + 6 feet
Length of the sculpture = 2x - 12 feet
The volume of a rectangular prism is given by the formula:
Volume = length × width × depth
According to the given information, the volume of the sculpture is 26 times its width in linear feet. Therefore, write the equation as:
Volume = 26 × Width
Volume = 26x
Write the expression for the volume of the sculpture using the dimensions:
Volume = (2x - 12) × x × (x + 6)
Set up the equation:
26x = (2x - 12) × x × (x + 6)
26x = (2x² - 12x) × (x + 6)
26x = 2x³ + 12x² - 12x² - 72x
26x = 2x³ - 72x
Now, rearrange the equation to set it equal to zero:
2x³ - 72x - 26x = 0
2x³ - 98x = 0
2x(x² - 49) = 0
2x = 0
x = 0
And, the value of x is calculated as:
x² - 49 = 0
x² = 49
x = ±√49
x = ±7
Since dealing with dimensions, have a negative value for x.
Therefore, x = 7.
The value of x is 7, find the length of the sculpture:
Length = 2x - 12
Length = 2 × 7 - 12
Length = 14 - 12
Length = 2 feet
So, the length of the sculpture is 2 feet.
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What is 0.08 divided by 0.24
Please hurry and answer please
Review the graph
Thank you
Answer:
f : 8
Step-by-step explanation:
hope that helps sorry if im wrong
Find amount when principal is 7150 and rate is 5% time is 2.5 years
Answer:interest =p×r×t ÷100
Time = 21/2 -5/2
Interest = 7150×5×5/100×2
answer =1787.5
Amount = P-I
7150-17875/10
Answer = 5362.5
Step-by-step explanation:
40 POINTS!!!!
ANSWER ASAP PLEASE!
A six-sided number cube is rolled, and then a spinner with 5 equal sections labeled A through E is spun.
What is the probability of rolling a 6 and spinning a vowel?
1/15
1/10
1/3
17/30
Answer:
1/15
Step-by-step explanation:
K-12 quiz
The probability of rolling a 6 and spinning a vowel is 1/15.
What is Probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
We have,
A six-sided number cube is rolled, and then a spinner with 5 equal sections labeled A through E is spun.
Outcome for cube rolled = {1, 2, 3, 4, 5, 6}
Outcome spinner spun = {A, B, C, D, E}
So, the probability of rolling a 6 and spinning a vowel
= 1/6 x 2/5
= 1/15
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Of 250 seventh grade students, 130 walk to school. What percent of seventh graders do not walk to school? % of seventh graders do not walk to school.
Answer:
48%
Step-by-step explanation:
I like to look at percentages as test grades. If you got a 130/250 on a test, you would simply need to view the dash line as a 'divided by'. So you would figure 130 divided by 250 is .52, or 52%... Then, you would need to subtract 52 from 100 to get 48% to get the percentage of people who do not walk to school.
48%
48% of 250 is 120
120+130=250
Pls help i will provide picture
Answer:
A. 4
Step-by-step explanation:
First, we can try the first option. 2/4 is equivalent to 6/12 when you multiply the fraction by 3 to get a common denominator. Since 6/12 is larger than 4/12, and the question has 1 answer, 4 is the only value that satisfices the statement and is the answer.
4. A hiker covers in the first hour of his hike 6 km, in the second hour 9 km and in the third hour 7 km. What was his average speed during the hike
Answer: 7 km per hour
Step-by-step explanation:
shi i may be wrong but im pretty sure thats his average speed
A 6 inch by 10 inch rectangle is dilated by a factor of 3. What is the area of the dilated
rectangle?
Answer:
Step-by-step explanation:
Dilated by a factor of three means that the two dimensions needed for the are are multiplied by 3.
width = 6*3 = 18
Length = 10 * 3 = 30
Area of dilated rectangle = 18*30 = 540 inches ^2
3x + 5y = 4 2x + 3y = 4 solve in elimination
Answer:
y=-4, x=8
Step-by-step explanation:
1)3x+5y=4
2)2x+3y=4
Make 1 and 2 have the same co-efficient of x or y (i chose x as it is easier to get to 6 then 15)
Label the 2 new equations as 3 and 4
3)6x+10y=8
4)6x+9y=12
Now we can take away to give
y=-4
Now we substitute this into 1 or 2
I chose 2:
2x+3(-4)=4
2x=4+12
2x=16
x=8
Answer:
x = 8
y = -4
Step-by-step explanation:
Multiply the first equation by 2:
⇒ 3x + 5y = 4 ⇒ 6x + 10y = 8
(we will call this equation 3)
Multiply the second equation by 3:
⇒ 2x + 3y = 4 ⇒ 6x + 9y = 12
(we will call this equation 4)
Subtract equation 3 from equation 4 to eliminate the x variable:
6x + 9y = 12
- 6x + 10y = 8
-y = 4
Therefore, y = -4
Substitute y = -4 into one of the equations and solve for x:
3x + (5 x -4) = 4
⇒ 3x - 20 = 4
⇒ 3x = 24
⇒ x = 8
a room in a bank is shaped like the rectangular prism shown below. the room has a security system that is triggered by two laser beams which stretch from point a to d and point b to c. how many total feet of laser beams are there?
There are 8 laser beams.
What is Pythagoras theorem?The relationship between the three sides of a right-angled triangle is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem. The Pythagorean theorem states that the square of a triangle's hypotenuse is equal to the sum of its other two sides' squares.
The length of the laser beams is the addition of the segments AD to segment CB (which are equal).
Using Pythagoras theorem in ECD
ED² = EC² + CD²
ED= √(12² + 35²)
ED = √144 + 1225
ED = 37 unit
Again In Triangle AED
AD² = EA² + ED²
AD=√15² + 37²
AD = 40 unit
Then, there are total of 80 ft of laser beams.
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Eric uses 585 liters of water to water his lawn. How many milliliters of water does he use?
Answer: 585000mL
Step-by-step explanation:
We know that there are 1000 milliliters (mL) in a liter (L), hence the prefix milli meaning thousand (for future reference).
As a result, in order to find the amount of milliliters, we need to multiply the amount of liters by 1000.
585Lx1000 = 585000mL
Remember: 1L = 1000mL; mL = 1000L
Answer:
585 into milimiter is 585000000mm
Step-by-step explanation:
that is the answer thank you
Some one please me find the volume for this rectangular prism
Answer:
5/8
Step-by-step explanation:
Please make me the brainlest
Find the area of the composite figure.
Answer:
The Area of the composite figure would be 76.26 in^2
Step-by-step explanation:
According to the Figure Given:
Total Horizontal Distance = 14 in
Length = 6 in
To Find :
The Area of the composite figure
Solution:
Firstly we need to find the area of Rectangular part.
So We know that,
[tex]\boxed{ \rm \: Area \: of \: Rectangle = Length×Breadth}[/tex]
Here, Length is 6 in but the breadth is unknown.
To Find out the breadth, we’ll use this formula:
[tex] \boxed{\rm \: Breadth = total \: distance - Radius}[/tex]
According to the Figure, we can see one side of a rectangle and radius of the circle are common, hence,
[tex] \longrightarrow\rm \: Length \: of \: the \: circle = Radius[/tex]
Since Length = 6 in ;[tex]\longrightarrow \rm \: 6 \: in = radius[/tex]
Hence Radius is 6 in.
So Substitute the value of Total distance and Radius:
Total Horizontal Distance= 14 Radius = 6[tex] \longrightarrow\rm \: Breadth = 14-6[/tex]
[tex] \longrightarrow\rm \: Breadth = 8 \: in[/tex]
Hence, the Breadth is 8 in.
Then, Substitute the values of Length and Breadth in the formula of Rectangle :
Length = 6Breadth = 8[tex] \longrightarrow\rm \: Area \: of \: Rectangle = 6 \times 8[/tex]
[tex]\longrightarrow \rm \: Area \: of \: Rectangle = 48 \: in {}^{2} [/tex]
Then, We need to find the area of Quarter circle :
We know that,
[tex]\boxed{\rm Area_{(Quarter \; Circle) } = \cfrac{\pi{r} {}^{2} }{4}} [/tex]
Now Substitute their values:
r = radius = 6 π = 3.14[tex]\longrightarrow\rm Area_{(Quarter \; Circle) } = \cfrac{3.14 \times 6 {}^{2} }{4} [/tex]
Solve it.
[tex]\longrightarrow\rm Area_{(Quarter \; Circle) } = \cfrac{3.14 \times 36}{4} [/tex]
[tex]\longrightarrow\rm Area_{(Quarter \; Circle) } = \cfrac{3.14 \times \cancel{{36} } \: ^{9} }{ \cancel4} [/tex]
[tex]\longrightarrow\rm Area_{(Quarter \; Circle)} =3.14 \times 9[/tex]
[tex]\longrightarrow\rm Area_{(Quarter \; Circle) } = 28.26 \: {in}^{2} [/tex]
Now we can Find out the total Area of composite figure:
We know that,
[tex]\boxed{ \rm \: Area_{(Composite Figure)} =Area_{(rectangle)}+ Area_{ (Quarter Circle)}}[/tex]
So Substitute their values:
[tex]\rm Area_{(rectangle)}[/tex] = 48 [tex]\rm Area_{(Quarter Circle)}[/tex] = 28.26[tex]\longrightarrow \rm \: Area_{(Composite Figure)} =48 + 28 .26[/tex]
Solve it.
[tex]\longrightarrow \rm \: Area_{(Composite Figure)} =\boxed{\tt 76.26 \:\rm in {}^{2}} [/tex]
Hence, the area of the composite figure would be 76.26 in² or 76.26 sq. in.
[tex] \rule{225pt}{2pt}[/tex]
I hope this helps!
57 women make up an all female choir in a church.
Two women are chosen to sing together for a duet.
How many possible pairs could be chosen for the duet?
Answer:
there could be 28 possible pairs because 57/2=28.5
Step-by-step explanation:
Bill's chocolate bar is 69% cocoa. If the weight of the chocolate bar is 83 grams, how many grams of cocoa does it contain? Round your answer to the nearest tenth.
Answer:
Bill's bar has 57.3 grams of cocoa.
Step-by-step explanation:
The math part that your question is asking is: What is 69% of 83?
In order to use the percent 69% in a calculation, you need to change it to a decimal.
69% is 0.69
You move the decimal to the left, two places.
69% is 69.% If you don't see a decimal to start with and it is a whole number, then the decimal is starting on the right.
Move it two places to the left, you get
.69
Now MULTIPLY.
.69 × 83
= 57.27
ROUND your answer to the nearest tenth. That means only one digit to the right of the decimal.
57.27 rounds to 57.3
Bill's bar has 57.3 grams of cocoa.
A field is a rectangle with a perimeter of 960 feet. The length is 400 feet more than the width. Find the width and length of the rectangular field.
I'm almost absolutely positive the width is 40 and the length is 440
HELP PLEAS EI GIVE BRAINLISt
Answer:
D
Step-by-step explanation:
40 is in the same place for B and C, 83 is in the same place for A and C, and 57 is in the same place for A and B.
Triangle D is not similar to the other three triangle.
Similar triangle:Similar triangle may have different sizes but the shape. In similar triangles, corresponding sides are always in the same ratio. The corresponding angles are congruent.
Therefore, triangle A, B and C are similar triangle because the corresponding angles are equal. The angles are 40°, 83° and 57°.
The last triangle D has a different angles sizes which are 40°, 67° and 73°.
Therefore, triangle D is not similar to the other three triangle.
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PLEASE HELP!!!! Solve for the variable. Show all work.
x2 - 33 = -1
Answer:
x = 4√2
Step-by-step explanation:
x² - 33 = -1 [ change sides ]
x² = -1 + 33
x² = 32
x = √3 [changing sides, changes power of square, (²) turns square root,√ ]
x = √4 * 4 * 2
x = 4√2 .......final answer.
Answer:
x = 4√2 or x = −4√2
Step-by-step explanation:
Step 1: Add 33 to both sides.
x2 − 33 + 33 = −1 + 33
x2 = 32
Step 2: Take square root.
x = ±√32
x = 4√2 or x = −4√2
Mr.Nadsen buys 12 posters. each poster costs 15$. if mr.nadsen receives a 4$ discount on each poster, what is the total amount of money mr. nadsen spends? write an expression that matches the words.
Answer:
132
Step-by-step explanation:
1 poster = $15
12 poster = $180
$4 discount * 12 posters = $48
180 - 48 = 132
so the answer is 132!
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