Answer:
x=-7/6, y=16/3. (-7/6, 16/3).
Step-by-step explanation:
y+2x=3
y-4x=10
-----------
y=4x+10
4x+10+2x=3
6x+10=3
6x=3-10
6x=-7
x=-7/6
y+2(-7/6)=3
y-14/6=3
y=3+14/6
y=18/6+14/6
y=32/6=16/3
3.25x10^-6 written in decimal notation
3.25 x 10^-6 written in decimal notation is 0.00000325
Solution:
Decimal notation is simply a form of a number using a decimal point
Given number : [tex]3.25 \times 10^{-6}[/tex]
Steps to follow:
In order to convert a number written in scientific notation to one written in standard or decinal notation, follow these steps:
Write the given scientific notation numberUse the sign and numerical value of the exponent (power) to determine the direction and number of places to move the decimal place.Move the decimal point to the right if the exponent is positive.Move the decimal point to the left if the exponent is negative.To convert to decimal notation:
Multiply the decimal number by 10 raised to the power indicated.
[tex]\rightarrow 3.25 \times 10^{-6}[/tex]
Here the exponent of 10 is -6
So the decimal point is moved 6 places to right
[tex]\rightarrow 3.25 \times 10^{-6} = 0.00000325[/tex]
Final answer:
To convert the scientific notation 3.25 x 10^-6 into decimal form, you move the decimal point six places to the left, resulting in 0.00000325.
Explanation:
To convert 3.25 x 10^-6 into decimal notation, you need to move the decimal point 6 places to the left because it is a negative exponent. Start with 3.25 and move the decimal:
0.3250.03250.003250.0003250.00003250.00000325The decimal notation of 3.25 x 10^-6 is 0.00000325.
Louisiana biologists tagged 250 fish in the oxbow lake False River on October 5. On a later date, they found 7 tagged fish in a sample of 350 fish. Estimate the total number of fish in False River to the nearest hundred.
At a school, the school population is 2/5 boys. There are 450 boys in the school. How many total students are in the school?
A bag contains quarter and dimes in a ratio of 3:5. If there is $6 in quarters in the bag, how many dimes are there?
1. Set up a ratio:
7 tagged / 350 fish = 250 tagged / x fish
Solve for x:
x = (350 * 250) / 7
x = 12,500 fish
2. Divide number of boys by the population ratio:
450 / 2/5 = (450 *5) /2 = 2250 / 2 = 1125 total students.
3. 4 quarters = $1, so they have 24 quarters total.
The ratio 3:5 means for every 3 quarters there are 5 dimes.
24 quarters / 3 = 8
8 x 5 = 40 dimes.
(1) The population of fish in the False river is 12500.
(2) There are 1125 total number of students in the school .
(3) There are 40 dimes in the bag.
(1) Number of fish tagged by Louisiana biologists = 250
On the next day a sample was collected from the False river
The number of fish in the sample = 350
Number of tagged fish in the sample = 7
Let the population of fish in the False river = P
Takin the ratio we can
[tex]\rm \dfrac{7}{350}= \dfrac{250}{P} \\\\P = (250)(350)/(7)\\P = 12500[/tex]
So the population of fish in the False river = 12500
(2) The number of boys in the school = 450
Let the total number of students in the school be B
According to the given condition
[tex]\rm \dfrac{2}{5}\times B = 450\\\\B = (450\times 5) /2 \\B = 2250/2 =1125[/tex]
So the total number of students in the school = 1125
(3) Let the number of dimes in the bag be x
According to the given condition we can write
[tex]\rm \dfrac{Number\; of\; quarters }{Number\; of\; dimes } = \dfrac{3}{5} ........(1)[/tex]
Also it is given that there are $6 in quarters in the bag.
$1 = 4 quarters
So $6 has [tex]\rm 4\times 6 = 24 \; quarters[/tex]
So we can put this value in equation (1)
[tex]\dfrac{24}{x} =\dfrac{3}{5} \\\\x = 40 dimes[/tex]
So we can conclude that there are 40 dimes in the bag.
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problem solving involving rational equation
1. The reciprocal of 5 plus the reciprocal of 7 is the reciprocal of what number?
2. The reciprocal of the product of two consecutive intergers is 1/72
1. The reciprocal of 5 plus the reciprocal of 7 is the reciprocal of what number?
Answer:The reciprocal of 5 plus the reciprocal of 7 is the reciprocal of [tex]\frac{12}{35}[/tex]
Solution:1. The reciprocal of 5 plus the reciprocal of 7 is the reciprocal of what number?
From given question,
[tex]\text{ reciprocal of 5} = \frac{1}{5}[/tex]
[tex]\text{ reciprocal of 7} = \frac{1}{7}[/tex]
Given that,
reciprocal of 5 + reciprocal of 7 = ?
[tex]\frac{1}{5} + \frac{1}{7} = x[/tex]
On cross-multiplying we get,
[tex]\frac{1}{5} + \frac{1}{7} = \frac{7+5}{5 \times 7} = \frac{12}{35}[/tex]
Thus reciprocal is [tex]\frac{35}{12}[/tex]
So the reciprocal of 5 plus the reciprocal of 7 is the reciprocal of [tex]\frac{12}{35}[/tex]
Question 22. The reciprocal of the product of two consecutive integers is 1/72
Answer:The value of two consecutive numbers are 8 and 9
Solution:Let the two consecutive integers be x and x + 1
Given that reciprocal of product of two consecutive integers is [tex]\frac{1}{72}[/tex]
product of two consecutive integers = x(x + 1) = [tex]x^2 + x[/tex]
reciprocal of the product of two consecutive integers = [tex]\frac{1}{72}[/tex]
[tex]\frac{1}{x^2 + x} = \frac{1}{72}\\\\x^2 + x = 72\\\\x^2 + x - 72 = 0[/tex]
Solve the above quadratic equation by grouping method
[tex]x^2 + x - 72 = 0\\\\x^2 -8x + 9x - 72 = 0\\\\x^2 + 9x + (-8x - 72) = 0\\\\x(x + 9) -8(x + 9) = 0\\\\(x + 9)(x - 8) = 0[/tex]
Thus x = -9 or 8
Ignoring negative value,
x = 8
Thus two consecutive integers are x = 8 and x + 1 = 8 + 1 = 9
8 and 9 are two consecutive integers
What is 4 and square root of 72
Answer:
square root of 72 is approximately 8.49
i hope that right!
Step-by-step explanation:
-6x+3y=-7−6x+3y=−7minus, 6, x, plus, 3, y, equals, minus, 7
x
Answer: none
Step-by-step explanation: since -6x+3y can't equal to -7−6x+3y
A shopper bought a 12-pound bag of oranges for 18.75. What is the unit price per ounce?
Answer:
About $0.10 per ounce
Step-by-step explanation:
12 pound costs $18.75. Lets find the cost per pound first:
Cost Per Pound = [tex]\frac{18.75}{12}=1.5625[/tex]
We know, there are 16 ounces in 1 pound.
We know 1 pound costs 1.5625
To find cost per ounce, we have to divide this by 16.
So,
Cost Per Ounce = [tex]\frac{1.5625}{16}=0.097[/tex]
Rounded to nearest cent, that would be 10 cents per ounce
Square root of 60 divided by square root of 5
Answer: 2√3
Step-by-step explanation: To divide √60 by √5, we simply divide the numbers that are inside the radicals.
Since the quotient of 60 divided by 5 is 12,
the square root of 60 divided by the square root of 5 is √12.
However, we can simplify the square root of 12.
The √12 breaks down into 4 · 3 and 4 breaks down into 2 · 2.
The 2's match up, so a 2 comes outside of the radical.
Since the 3 doesn't pair up, it stays inside.
So our answer is 2√3.
Final answer:
The simplification of [tex]\sqrt{60}/\sqrt{5[/tex] results in [tex]2\sqrt{3,[/tex] by combining the square roots into one and then simplifying the inner value.
Explanation:
The question asks for the simplification of the expression which is the square root of 60 divided by the square root of 5. To simplify this expression, one can utilize the property of square roots that allows the division within a single square root function. Here’s a step-by-step explanation:
Write the expression as [tex]\sqrt{60}/\sqrt{5[/tex]
Combine the square roots using the property[tex]\sqrt{(a)}/\sqrt{(b)} = \sqrt{(a/b),[/tex] giving[tex]\sqrt{60}/\sqrt{5[/tex]
Simplify 60/5 to get 12.
Now take the square root of 12, which is not a perfect square. However, we can express 12 as the product of 4 (which is a perfect square) and 3 (4 * 3 = 12).
Finally, we write the expression [tex]\sqrt{4} * \sqrt{3,[/tex] which simplifies to [tex]2\sqrt{3,[/tex]
Thus, the simplified form of [tex]\sqrt{60}/\sqrt{5[/tex] is [tex]2\sqrt{3,[/tex], which cannot be simplified any further as [tex]\sqrt{3[/tex] is an irrational number and does not have a precise decimal representation.
It is always important to remember that when rounding is necessary, you should round the result up if the digit following the last significant digit is 5 or greater, and round it down if it is less than 5.
An account earned interest of 3% per year. The beginning balance was $150. The equation t=log1.03 (E/150) represents the situation, where t is the time in years and E is the ending balance. If the account was open for 8 years, what was the ending balance?
Answer:
190.02
Step-by-step explanation:
Trust
The ending balance of the account after 8 years is approximately $184.16.
Explanation:To find the ending balance of the account after 8 years, we can use the equation t=log1.03(E/150), where t is the time in years and E is the ending balance. Since the account was open for 8 years, we can substitute t=8 into the equation.
8=log1.03(E/150)
To solve for E, we can isolate it by first multiplying both sides of the equation by 150 and then raising both sides to the power of 1.03.
E/150=1.03⁸
E=150*1.03⁸
Using a calculator, we can find that E is approximately $184.16.
The solution to the equation x? = 45 is between
Answer:
9
Step-by-step explanation:
9 times 5 =45
Answer:
9
Step-by-step explanation:
When you do the math, 9 multiplied by 5 will get you 45
The clock face in a famous clock tower has a radius of 4 meters. What is the area of the clock face to the nearest square meter
Final answer:
To find the area of the clock face with a 4-meter radius, use the area formula for a circle, which gives approximately 50.265482 m². Rounded to the nearest square meter, the clock face area is about 50 m².
Explanation:
The clock face in a famous clock tower has a radius of 4 meters, and we want to find the area of the clock face to the nearest square meter. To do this, we use the formula for the area of a circle, which is A = πr², where A is the area and r is the radius of the circle.
Plugging in the radius of the clock face:
A = π(4 m)² = π(16 m²) ≈ 50.265482 m²
However, since we want the answer to the nearest square meter, we round this to:
A ≈ 50 m²
Final answer:
The area of the clock face with a radius of 4 meters is approximately 50 square meters when rounded to the nearest square meter.
Explanation:
The area of a clock face in a famous clock tower, given its radius is 4 meters, can be calculated using the formula for the area of a circle, which is [tex]A = πr^2[/tex] where A is the area and r is the radius of the circle. In this case, substituting the radius of 4 meters into the formula gives us[tex]A = π(4m)^2 = π16πm^2.[/tex] To give an answer to the nearest square meter, we use the value π = 3.14, resulting in [tex]A = 16(3.14)m^2 = 50.24m^2[/tex], which rounds to 50 m².
Which expression can be used to find the surface area of the following rectangular prism?
Answer
30+30+15+15+18+18
Step-by-step explanation:
The expression to calculate the surface area of the prism is 2 * (3 * 5 + 3 * 6 + 5* 6)
How to determine the expression of the surface area?The given parameters are:
Length = 3Width = 5Height = 6The surface area of a rectangular prism is:
Area = 2 * (Length * Width + Length * Height + Width * Height)
Substitute known values
Area = 2 * (3 * 5 + 3 * 6 + 5* 6)
Hence, the expression to calculate the surface area of the prism is 2 * (3 * 5 + 3 * 6 + 5* 6)
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Victor buys some six-packs of soda for a party. He buys 42 cans in all. How many six-packs of soda did Victor buy?
Divide the total number of cans by 6.
42 / 6 = 7
He bought 7 six packs.
Final answer:
Victor bought 7 six-packs of soda.
Explanation:
To find the number of six-packs of soda Victor bought, divide the total number of cans by 6. In this case, Victor bought 42 cans in total, so dividing 42 by 6 gives us 7. This means Victor bought 7 six-packs of soda.
Solving a Real-World Problem
Brigid is picking strawberries at the Pick-Your-Own Farm. Her goal is to pick 5 bushels of strawberries. She has
already pick
ushels, and she picks at a rat
hel per hour. The scenario is represented as
ah+15 = 5, where h is the number of hours she picks. How many more hours will it take Brigid to fill 5 bushels o
strawberries?
hours
16
hours
10
hours
unu
hours
) Intro
Done
Answer: The answer is 5 and 3/5 hours
Step-by-step explanation:
Answer:
5 and 3/5 hours
Step-by-step explanation:
Factor completely. x^2-4
Answer:
(x - 2)(x + 2).
Step-by-step explanation:
This is the difference of 2 squares:
a^2 - b^2 = (a - b)(a + b)
So
x^2 - 4 = (x - 2)(x + 2).
refer to the graphic novel frame below. write and solve an equation to find how many movies they have time to show.
Answer:
Number of movies that can be shown = 2
Step-by-step explanation:
Given:
Movie night duration = 4 hours
Duration of each movie = 1.75 hours
Time given for eating popcorn = 0.5 hours
Time alloted for movies (excluding popcorn time) = 4 - 0.5 = 3.5 hours.
Number of movies that can be shown = [tex]\frac{Total\ time\ alloted\ for\ movie}{Time\ for\ 1\ movie}=\frac{3.5}{1.75}= 2[/tex]
To determine the number of movies that can be watched, an equation M*X <= T can be formulated where M is the length of the movie, X is the number of movies, and T is the total time available. To find X, divide T by M. This works when the time for each movie is the same.
Explanation:Without the actual graphic novel frame, it's hard to provide a specific equation. However, I can give you an example on how to approach this situation. Let's assume each movie is of length 'M' minutes and you have a total of 'T' minutes available for watching movies.
,
Let 'X' be the number of movies you can watch. You would write this as a mathematical equation like this: M*X <= T. This equation states that the total time spent watching movies should be less than or equal to the total time available.
,
To solve the equation, you would divide both sides of the equation by 'M'. The result will be X <= T/M. If you know the values of 'M' and 'T', you can plug them in here to get the maximum number of movies you can watch.
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let f = {(-2,4), (-1,2), (0,0), (1,-2), (2,-5)}
let g= {(-3,3), (-1,1), (0,-3), (1,-4), (3,-6)}
what is g(f(2))?
Answer:9
Step-by-step explanation:4
What is the slope of y=4-6x
Answer:
the slope, m, is -6
Step-by-step explanation:
One of the most commonly used equations for a straight line is y = mx + b, where m is the slope and b is the y-intercept.
Comparing y=4-6x to y = b + mx, we see that the slope, m, is -6 and the y-intercept, b, is 4.
The slope of the line y = 4 - 6x is -6, which shows that for every increase of 1 in the x-coordinate, the y-coordinate decreases by 6.
The equation is given as follows:
y = 4 - 6x
As we know that the equation is in slope-intercept form, y=mx+b.
Here, m is the slope and b is the y-intercept.
As per the question, the y-intercept is 4, which means the line crosses the y-axis at (0,4).
The slope, -6, tells us that for every increase of 1 in the x-coordinate, the y-coordinate decreases by 6.
Thus, the slope of the line y = 4 - 6x is -6.
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7. The cost of renting the party room for 10 people is $117.50. The cost of renting the room is $151.25 for 15 people. Write an equation that represents the cost of renting the party room in terms of the number of people attending the party .
Answer:
C = 6.75n + 50
Step-by-step explanation:
The equation for the cost of renting the party room can be written in the form;
C= mn+k ......i
Where C = cost
n = number of people
Substituting the 2 cases into the equation we have,
Case 1
117.5 = 10m + k ......1
Case 2
151.25 = 15m + k .....2
Subtracting eqn 1 from 2 we have
151.25 - 117.50 = 15m - 10m
5m = 33.75
m = 33.75/5 = 6.75
Substituting m = 6.75 into eqn 1, we have
117.50 = 10(6.75) + k
k = 117.5 - 67.50
k = 50
Therefore, rewriting the eqn i, we have
C = 6.75n + 50
3n-5=19
Plz give me a step by step explanation cause i already have an answer i just need to work
Answer:
n=8
Step-by-step explanation:
3n-5=19
3n=19+5
3n=24
n=24/3
n=8
In this equation 5Z=-3 (z+7) in which order would you solve the problem? Put the steps below in the correct order
A. Use distribute property to simplify the right side (multiply the Z in the seven by -3)
B. Add 3z to both sides
C. Divided by -8 on both sides
Answer:
Use distributive property, add 3z to both sides, divide by -8 on both sides
Step-by-step explanation:
You have to do parenthesis first, then equal both sides, then divide
Simplify the expression.
7x + 7 +5(x + 3) + 3
Answer:
12x+25
Step-by-step explanation:
7x+7+5x+15+3
12x+25
HELP PLS IM IN CLASS RN!!!
Answer:
48 inches
Step-by-step explanation:
Dagne can jump 13.2 inches that is 27.5% of her height. Let x inches be Dagne's height.
Then
x inches - 100%
13.2 inches - 27.5%
Write a proportion:
[tex]\dfrac{x}{13.2}=\dfrac{100}{27.5}[/tex]
Cross multiply:
[tex]27.5x=13.2\cdot 100\\ \\27.5x=1,320\\ \\x=\dfrac{1,320}{27.5}\\ \\x=48\ inches[/tex]
tanA / 1-tan^2 = √3 /2
Answer:
A = π/6 + kπ, or A = 2π/3 + kπ
Step-by-step explanation:
tan A / (1 − tan² A) = √3 / 2
Cross multiply and simplify:
√3 (1 − tan² A) = 2 tan A
√3 − √3 tan² A = 2 tan A
3 − 3 tan² A = 2√3 tan A
0 = 3 tan² A + 2√3 tan A − 3
Solve with quadratic formula:
tan A = [ -2√3 ± √((2√3)² − 4(3)(-3)) ] / 2(3)
tan A = [ -2√3 ± √(12 + 36) ] / 6
tan A = (-2√3 ± √48) / 6
tan A = (-2√3 ± 4√3) / 6
tan A = -√3 or √3/3
Solve for A:
A = 2π/3 + kπ, or A = π/6 + kπ
What is the value of the expression shown below?
2 over 3 to the power of 2 + 5 × 2 − 4
6 and 8 over 9
6 and 4 over 9
6 and 2 over 3
6 and 1 over 3
(2/3)²+5×2-4
(4/9)+5×2-4
(4/9)+10-4
10 4/9 - 4
6 4/9
answer: second choice
Identify the equivalent expression for each of the expressions below. (m^(1/3)*1/5
Answer: 1
Anything that goes to the 0 power is always going to be 1
The area of a circle is directly
proportional to the square of its
radius. A circle with a radius of 2
cm has an area of 12.566 cm^2.
What is the radius of a circle with
an area of 78.54 cm^2?
[?] cm
Round to the nearest whole number.
Answer:
[tex]radius=5\ cm[/tex]
Step-by-step explanation:
Let r be the radius of the circle and A be the area of the circle.
Given:
[tex]r_{1} = 2\ cm, A_{1}=12.566\ cm^{2}[/tex]
And [tex]r_{2} = ?, A_{2}=78.54\ cm^{2}[/tex]
The area of a circle is directly proportional to the square of its radius.
A ∝ [tex]r^{2}[/tex]
[tex]A = kr^{2}[/tex]-----------(1)
Where k is the constant of proportionality
Find constant value by substituting [tex]r_{1} = 2\ cm, A_{1}=12.566\ cm^{2}[/tex]
in equation 1.
[tex]A = kr^{2}[/tex]
[tex]A_{1}=k(r_{1})^{2}[/tex]
[tex]12.566=k\times 2^{2}[/tex]
[tex]12.566=k\times 4[/tex]
[tex]k=\frac{12.566}{4}[/tex]
[tex]k=3.141[/tex]
Find [tex]r_{2}[/tex] by substituting k and [tex]A_{2}[/tex] value in equation 1.
[tex]A = kr^{2}[/tex]
[tex]A_{2}=k(r_{2})^{2}[/tex]
[tex]12.566=3.141\times (r_{2})^{2}[/tex]
[tex](r_{2})^{2}=\frac{78.54}{3.141}[/tex]
[tex](r_{2})^{2}=25.004[/tex]
where: 25.004 ≅ 25
[tex](r_{2})^{2}=25[/tex]
[tex]r_{2}=\sqrt{25}[/tex]
[tex]r_{2}=5\ cm[/tex]
Therefore; the radius of the circle is 5 cm.
Final answer:
The radius of a circle with an area of 78.54 cm² is approximately 4 cm, after setting up a proportion with a known circle area and solving for the unknown radius.
Explanation:
The area of a circle is given by the formula A = πr², where A is the area and r is the radius of the circle. Given that a circle with a radius of 2 cm has an area of 12.566 cm², we set up a proportion to find the radius of a circle with an area of 78.54 cm²:
(12.566 cm²) / (2 cm)² = (78.54 cm²) / r².
Solving for r, we find r² = (78.54 cm²) × (2 cm)² / (12.566 cm²).
After calculation, we get r approximately equal to 4 cm, rounding to the nearest whole number.
How do you find the sum of cube ?
Answer:
[tex](2x+5)(4x^{2} -10x+25)=0[/tex]
Step-by-step explanation:
Given:
The given equation is.
[tex]8x^{3} +125=0[/tex]
Find the some of cube.
Solution:
[tex]8x^{3} +125=0[/tex]
[tex]2^{3}x^{3} +5^{3}=0[/tex]
[tex](2x)^{3} +5^{3}=0[/tex]----------(1)
The sum of the cube formula is given below.
[tex](a^{3} +b^{3})=(a+b)(a^{2} -ab+b^{2} )[/tex]-----------(2)
By comparing equation 1 and equation 2
[tex]a=2x, b=5[/tex]
substitute a and b value in equation 2
[tex]((2x)^{3} +5^{3})=(2x+5)((2x)^{2} -(2x)(5)+5^{2})[/tex]
[tex]((2x)^{3} +5^{3})=(2x+5)(4x^{2} -(10x)+25)[/tex]
[tex]((2x)^{3} +5^{3})=(2x+5)(4x^{2} -10x+25)[/tex]
Therefore the sum of the cube [tex](2x+5)(4x^{2} -10x+25)=0[/tex]
help me???????????????????
Answer:
To answer X and Y, all you need is a little common sense and a little bit of algebraic thinking. -x can equal: -x = 0? -6?, etc. Y could equal: 3?, 6?, 12?, etc. But the answer will always no matter what number will be 6.
There are 452 pictures of dogs in 4 equal groups. How many pictures are in each group? Explain how you can use place value to place the first digit in the quotient. Please show with working
By dividing 452 pictures of dogs by 4, we find that each of the 4 equal groups has 113 pictures. The division process involves using place value and the standard algorithm for long division.
Explanation:To find out how many pictures of dogs are in each group, we need to divide the total number of pictures by the number of groups. The question states there are 452 pictures of dogs and these are divided into 4 equal groups. We can use long division to solve this.
Step-by-Step Solution:
Write down the division: 452 ÷ 4.
Start by looking at the hundreds place in 452. There are 4 hundreds in 452. Since 4 divided by 4 is 1, we put 1 in the hundreds place of the quotient.
Multiply the divisor (4) by the quotient (100) to get 400.
Subtract 400 from 452 to get 52.
Now, look at the tens place in 52. There are 5 tens in 52, and since 5 divided by 4 is 1 with a remainder, we put 1 in the tens place of the quotient and have a remainder of 12 after subtracting 40 (1 x 4 tens) from 52.
Next, look at the ones place in 12. There are 12 ones, and since 12 divided by 4 is 3, we put 3 in the ones place of the quotient.
After placing 3 in the ones place, we have no remainder, which means the division is complete and the quotient is 113.
Therefore, each group has 113 pictures of dogs.
3. Last week Jean ran 2 fewer than 4m miles.
This week she ran 0.5 miles more than last
week. Write and simplify an expression for
the total number of miles Jean ran in the
two weeks.
The total number of miles Jean ran in the two weeks is 4.5 m.
Given that, last week Jean ran 2 fewer than 4m miles.
What is an expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
Here,
Number of weeks Jean ran last week = 4-2=2 m
Number of weeks Jean ran this week = 2+0.5
= 2.5 m
Total number miles = 2+2.5
= 4.5 m
Hence, the total number of miles Jean ran in the two weeks is 4.5 m.
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