The simplified form of the expression 5x³3y² ÷ 27x × 9xy ÷ 25x²y² is
[1/15(xy)³] and (x, y) ≠ 0.
What is a numerical expression?A mathematical statement expressed as a string of numbers and unknowable variables is known as a numerical expression. Statements can be used to create numerical expressions.
Given, An expression 5x³3y² ÷ 27x × 9xy ÷ 25x²y².
= 5x³3y² ÷ 243x⁴y³ ÷ 25x²y².
= 5x³3y² ÷ 25x²y² ÷ 243x⁴y³.
= (3/5)x ÷ 243x⁴y³.
= (3/5)x/(243x⁴y³).
= (3/5)/(243x³y³).
= 1/(81×5x³y³).
= [1/15(xy)³].
The restriction should be x and y can not be equal to zero as it would make the expression undefined.
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Evaluate this problem
Answer:
78
Step-by-step explanation:
a + 8b = 6 + 8 x 9 = 6 + 72 = 78
Answer: 78
Step-by-step explanation:
value of a=6
value of b=9
a+8b= 6+8*9
as the 8 will be multiplied by 9
6+8*9= 6+72
6+72 = 78
Miguel rode his bike to work which was 15 miles from home. However he was too tired to ride back so he got a ride in a
car from a co-worker. He spent a total of 2 hours traveling. The average speed of traveling by car was 3 times faster
than on his bike. What was Miguel's average speed on his bike and in the car?
Answer:
Bike: 10 miles per hour
Car: 30 miles per hour
Step-by-step explanation:
He spent: 2h/(1+3) = 0,5h by car and 0,5h x 3 = 1,5h by bike
The car is: 15 miles/ 0,5h = 30 miles/h
The bike is: 15 miles/ 1,5h = 10 miles/h
Raina has to give medicine to her cat every morning for the next days. How many weeks is this?
Answer:
(number of days)/7
Step-by-step explanation:
1 week = 7 days
Divide the number of days by 7 to find the number of weeks.
Two alien spaceships start traveling toward each other from space stations that are 710,000 km apart. The first spaceship started an hour before the second spaceship and is traveling at 110,000 km/hr. In how many hours will the two spaceships meet if the second spaceship is traveling at 90,000 km/hr?
The spaceship will meet in how many hours?
The time that it will take for the spaceships to meet is given as follows:
3 hours.
How to model the situation?Each of the spaceships is traveling at a constant rate, hence linear functions are used to model the situation.
The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which the parameters are given as follows:
The slope m represents the velocity.The intercept b represents the initial position.The positive direction is considered from the first spaceship towards the second spaceship.
The first spaceship started an hour before the second spaceship and is traveling at 110,000 km/hr, hence the difference when the second spaceship starts traveling is given as follows:
710,000 - 110,000 = 600,000 km.
Then the functions are given as follows:
x1(t) = 110t.x2(t) = 600 - 90t. (negative as they travel in opposite direction).They will meet when:
x1(t) = x2(t).
Hence:
110t = 600 - 90t
200t = 600
t = 600/200
t = 3 hours.
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The time that it will take for the spaceships to meet is given as follows:
3 hours.
How to model the situation?
Each of the spaceships is traveling at a constant rate, hence linear functions are used to model the situation.
The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which the parameters are given as follows:
The slope m represents the velocity.
The intercept b represents the initial position.
The positive direction is considered from the first spaceship towards the second spaceship.
The first spaceship started an hour before the second spaceship and is traveling at 110,000 km/hr, hence the difference when the second spaceship starts traveling is given as follows:
710,000 - 110,000 = 600,000 km.
Then the functions are given as follows:
x1(t) = 110t.
x2(t) = 600 - 90t. (negative as they travel in opposite direction).
They will meet when:
x1(t) = x2(t).
Hence:
110t = 600 - 90t
200t = 600
t = 600/200
t = 3 hours.
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which equation represents the lime that is parallel to y=3 and passes through (-2,-8)?
A. x=-2
B. x=3
C. y=-8
D. y=3x -2
The line that parallels y = 1/2 x + 8 and goes through the point (-2, 2) is represented by the equation y = 1/2 x + 3.
What do you meant by x=-2 and x=3?
The entire time, the x-coordinate -2 is shown. A function is NOT what this is. A number is multiplied three times by itself to form a cube. The symbol for the cube of a number is x. 3.
To increase an integer to the third power is to cube it. A function is an equation with just one solution for every value of y in the equation. A function pairs each input of a particular type with exactly one output. Instead of y, it is typical to name functions f(x) or g(x). f(2) instructs us to calculate the value of our function when x is equal to 2.
A function, in general, is a relationship between two variables. In other words, the relationship x = y2 is not a function.
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Find a quartic function
The quartic equation y = x⁴ - x³ - 5 · x² - x - 6 has x = - 2 and x = 3 as its only real zeros. (Correct choice: C)
What quartic equation contains a given set of zeros?
Quartic equations are polynomials of grade 4, whose standard form is described below:
y = a · x⁴ + b · x³ + c · x² + d · x + e
Where a, b, c, d, e are real coefficients. A value of x is a zero of a polynomial when the result is equal to zero. The quickest way to find the polynomial is by evaluating each expression at x = - 2 and x = 3:
x = - 2
y = (- 2)⁴ - (- 2)³ - 5 · (- 2)² - (- 2) - 6
y = 16 + 8 - 20 + 2 - 6
y = 0
x = 3
y = 3⁴ - 3³ - 5 · 3² - 3 - 6
y = 81 - 27 - 45 - 3 - 6
y = 0
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An octagon has a perimeter of 27 feet. If the sides of the octagon shrink by a scale factor of 8/9, what will the perimeter of the new octagon be
The perimeter of the new octagon be 24 feet.
What is the perimeter of octagon?A closed path that covers, encircles, or outlines a one-dimensional length or a two-dimensional shape is called a perimeter. A circle's or an ellipse's circumference is referred to as its perimeter.
There are numerous uses in real life for perimeter calculations. The measurement of the fence needed to completely enclose yard or garden is called the perimeter. How far a wheel or circle will roll in one revolution is determined by its circumference, or perimeter.
The length of each side of an octagon is the same. In order to calculate the perimeter of an octagon, multiply 8 by the length of its sides.
Given that the perimeter of an octagon is 27 feet
so the length of its side is 27/8 feet
if the side of the octagon shrink by a scale factor of 8/9
The side of new octagon is (27/8) * (8/9)
The side of new octagon is 3 feet.
So the perimeter of new octagon is 8 * side
⇒ the perimeter of new octagon = 8 * 3 feet
⇒ the perimeter of new octagon = 24 feet
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#2 Lauren draws a still life picture of a vase of flowers using a scale where 1 inch= 3 inches. In her drawing, the vase is 6.75 inches tall. What is the actual height?
Answer:
20.25
Step-by-step explanation:
6.75 times by 3 is 20.25
13. The line y = -2x +1 is reflected in the line y = 2. Write the equation of the image.
After reflecting the line in the y-axis, the slope of the line will be positive 2 and the y-intercept remain unchanged.
so the equation of the image is y = 2x + 1.
What is the line of reflection?A reflection over a line is a transformation in which each point of the initial figure (the pre-image) has an image that is on the opposite side of the reflection line from the original point and is situated at the same distance from the reflection line. The pre-size image's and shape are replicated in a reflection.
The line of reflection is typically expressed as y = m x + b y=mx+by, equals, m, x, plus, b. What need I do to draw the line of reflection? The starting points in the figure are all perpendicularly separated from the line of reflection by the same amount as the starting points in the image.
To reflect a line in the y-axis, we need to negate the slope of the line.
The line y = -2x +1 has a slope of -2 and y-intercept of 1.
After reflecting the line in the y-axis, the slope of the line will be positive 2 and the y-intercept remain unchanged.
so the equation of the image is y = 2x + 1.
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Using the collected data above what would be a reasonble rough estimate of a ratio of how many cubic inches per orange?
given the farmer's market wanted o use a box that had the dimensions, approximately how many oranges should fit?
The ratio is 17.14 cubic inch per orange and 168 oranges for given dimensions.
What is volume?In three dimensions, everything takes up some space. What is being measured here is the area's volume. The volume of an object is the area occupied inside its three-dimensional boundaries. It is referred to as the object's capability on occasion.
The amount required to fill an object can be determined by finding its volume, for example, how much water is required to fill a bottle, aquarium, or water tank.
Given
dimensions of box 20 x 13 x 12, 12 x 12 x 12 and 20 x 10 x 6
volume of box 1 = 20 x 13 x 12 = 3120 cubic inches
volume of box 2 = 1728 cubic inches
volume of box 3 = 20 x 10 x 6 = 1200 cubic inch
oranges in box 1 = 96
oranges in box 2 = 53
oranges in box 3 = 37
and radius of orange = 32./2 = 1.6 inches
volume of each orange = 4/3πr³
volume of each orange = 4/3(3.14)(1.6)³
volume of each orange = 4/3(3.14)(4.096)
volume of each orange = 17.14 cubic inches
here one orange will cover 17.14 cubic inches.
7. let the dimension of box is 15 x 12 x 16
volume of box is = 15 x 12 x 16 = 2880 cubic inches
the number of oranges in box will be 2880/17.14 = 168 oranges
Hence there will be 17.14 cubic inch per orange volume is covered, and 168 oranges will be in box for given dimensions.
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Question 7 is incomplete the missing dimensions are 15 x 12 x 16.
Sara is saving her money in a piggy bank
and counts it each month. The graph
shows her monthly savings. Choose any
two points and draw a slope triangle.
Dilate the slope triangle along the graph
to determine whether the amount Sara
saves each month is constant.
Answer: It is not possible for me to draw a slope triangle or dilate it along the graph without more information about Sara's monthly savings.
To determine whether the amount Sara saves each month is constant, you can choose any two points on the graph and use them to calculate the slope of the line connecting them. If the slope is constant for all pairs of points, then the amount Sara saves each month is constant. If the slope is not constant, then the amount Sara saves each month is not constant.
To calculate the slope of the line connecting two points, you can use the following formula:
slope = (y2 - y1)/(x2 - x1)
where (x1, y1) and (x2, y2) are the coordinates of the two points.
You can then use the slope triangle to visualize the slope of the line connecting the two points. If you dilate the slope triangle along the graph and the slope remains constant, then the amount Sara saves each month is also constant.
Step-by-step explanation:
-20 POINTS- Find the value of X
X=[?]
Answer:
x=1252x^2
I'm not sure if I'm 100% correct
Sorry.
Find the value of x.
Answer: x = 4
Step-by-step explanation:
Based on the given distances and angle measures, DE is congruent to XY, DF is congruent to ZX, and EF and ZY are congruent.
This means that:
[tex](4x-1)=15[/tex]
Simplify and solve for x.
[tex]4x-1=15\\4x=16\\x=4[/tex]
So, x = 4
what is the evaluation for 4-4y+y-3
Answer:
1-3 y
Step-by-step explanation:
Subtract the numbers 4 AND 3 WHICH WOULD EQUAL REWRITING THE ADDITON SO IT CHANGES THE MINUS SIGN TO A PLUS.
After 9 years in an account with a 3.9% annual interest rate compounded continuously, an investment is worth a total of $17,757.16. What is the value of the principal investment? Around the answer to the nearest penny.
The value of the principal investment would be = $12,500.75
What is a principal investment?A principal investment is defined as the capital amount of money that is being deposited into an account with the purpose of receiving interest for a particular period of time.
The years of investment (t) = 9 years
The annual interest rate (r) = 3.9% = 3.9/100= 0.039
The total worth of the investment (A) = $17,757.16
Then, solve the equation for P
P = A / ert
P = 17,757.16 / e(0.039*9)
P = $12,500.75
Therefore, the principal amount that is needed which can be compounded continuously to get the total amount given = $12,500.75
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Can y’all pls help me solve this!!
the mass liquid having a density of 1.40 g and a
volume of 3090 ml
The mass of the liquid is 4326 grams.
How to find the mass of a liquid?The liquid has a density of 1.40 g/ml and the volume of the liquid is 3090 ml. Therefore, the mass of the liquid can be calculated as follows:
The density of a liquid is a measure of how heavy it is for the amount measured. The liquid density is defined as its mass per unit volume.
Therefore,]
density = mass / volume
cross multiply
mass = density × volume
density = 1.40 g/ml
volume = 3090
Therefore,
mass of the liquid = 1.40 × 3090
mass of the liquid = 4326 grams.
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50 POINTS! PLEASE HELP TT
A bag contains 1 red marble, 2 blue marbles, 3 yellow marbles, and 4 black marbles. A marble is randomly chosen from the bag, returned, and then another marble is chosen. What is the probablility that both marbles are blue?
Answer:
The probability that both marbles are blue is 1/25------------------------------------
Number of marbles:
Red = 1, blue = 2, yellow = 3, black = 4Total number:
1 + 2 + 3 + 4 = 10Probability of getting a blue marble:
P(blue) = number of blue / total numberP(blue) = 2/10 = 1/5Since the second marble is selected with replacement, the probability of the second blue marble is same, so the probability of two blue marbles is:
P(blue, blue) = 1/5*1/5 = 1/25[tex] \sf \: Probability _{(Blue)}=2/10×2/10 \\ \\ \sf Probability _{(Blue)}= \frac{1}{25} [/tex]
Find the value of the lesser root of x squared -7x +12 =0
Answer:
3
Step-by-step explanation:
x² -7x + 12 =0
by factoring:
(x-4)(x-3) = 0
x = 4
x = 3
3<4
what is the slope for the equation?
Answer:
Slope: -1/2
Step-by-step explanation:
You can find the slope from this equation by adding 1/2 to each side of the equation since the way you find the slope of a line is by using: y = mx + b. The "m" must ALWAYS be on the right for it to be a valid slope equation, therefore, we have to use inverse operations for -1/2x to bring it to the right side.
Now, after we added 1/2x to each side, we get this equation:
-y = 1/2x + 3/4
We are not yet done since the y is accompanied by a negative 1, so, to isolate the variable, you use inverse operations once again and you get this equation:
y = -1/2x - 3/4
Therefore, the slope for this equation is -1/2.
Hope this helped! :D
Here are the two sums
2/7 + 1/4 and 5/6 - 1/4
A. B
Which of the two sums is closer in value to 1/2?
You must show your working and state clearly whether the answer is A or B.
Note: Please use the “/“ key of your keyboard to enter the fractions (e.g. 2/7 as 2/7)
On solving the provided question, we can say that - the value of the fraction will be 1/4
what is fraction?Any number of equal portions, or fractions, can be used to represent a whole. Fractions in standard English indicate how many units of a certain size there are. 8, 3/4. A whole includes fractions. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. True fractions have numerators that are less than their denominators. A fraction is a sum that constitutes a portion of a total. By breaking the entire up into smaller bits, you can evaluate it. Half of a full number or item, for instance, is represented as 12.
here,
x + x = 1/2
2x = 1/2
x = 1/4
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4. What is the slope-intercept form of 9x + 3y = 15?
Oy=-3x+5
Oy=3x+5
Oy = 3x - 5
Oy=-3x - 5
The slope-intercept form of the equation 9x + 3y = 15 is y = -3x + 5.
What is slope-intercept form?
The line with m as the slope, m and c as the y-intercept is the graph of the linear equation y = mx + c. The values of m and c are real integers in the slope-intercept form of the linear equation.
The given equation is 9x + 3y = 15.
Rearranging it to get in slope-intercept form -
⇒ 9x + 3y = 15
⇒ 3y = -9x + 15
Dividing LHS and RHS by 3 -
⇒ y = -3x + 5
Here, the equation is the slope-intercept form y = mx + c.
So, the slope is m = -3 in the equation.
Therefore, the slope-intercept form is y = -3x + 5.
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solue, giving all solutions between 0 and 360 degrees 8 (COS X)² - 10 COS X+3=0
Step-by-step explanation:
please refer to the sketch
Find the slope of the line that passes through (4, 10) and (1, 11).
Answer:
-1/3
Step-by-step explanation:
What is the vertex of the function?
f(x) = 3(r - 2)2 + 4
Answer:
(2,4)
Step-by-step explanation:
The vertex of a parabola in the form of [tex]y=a(x-h)^2+k[/tex] is [tex](h,k)[/tex]. In this function, we have [tex](2,4)[/tex] as our vertex.
The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room. Which equations can be used to solve for y, the length of the room? Select three options. y(y + 5) = 750 y2 – 5y = 750 750 – y(y – 5) = 0 y(y – 5) + 750 = 0 (y + 25)(y – 30) = 0
Answer:
B, C, E
Step-by-step explanation:
Let y = length.
Then, y - 5 = width.
area = length × width
area = y(y - 5)
area = 750
y(y - 5) = 750
y² - 5y = 750
A: y(y + 5) = 750
Since y = length, width must be y - 5, not y + 5, so A does not work.
B: y² - 5y = 750
This is what we got above, so this equation works.
C: 750 - y(y - 5) = 0
750 = y(y - 5)
750 = y² - 5y
This is the same as B and works.
D: y(y - 5) + 750 = 0
y(y - 5) = -750
The area cannot be -750, so this equation does not work.
E: (y + 25)(y - 30) = 0
y = -25 or y = 30
This also works.
Answer: B, C, E
What are the dimensions of this shape in terms of the dimensions of the circle?
The diameter or radius of the circle is the dimension of a circle.
What is a circle?The circular line is drawn equidistant from the center point of a circle, which is a two-dimensional geometry object on a plane.
A geometrical rule states that the dimension of an object with n dimensions is n+1. For instance, a square is made up of line segments that are 1d and a cube is built up of squares that are 2d. The circle is therefore 2d or two-dimensional space since it is made up of 1d diameters.
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Answer:
The length of the parallelogram is half of the circumference of the circle, and its height is equal to the radius of the circle.
Step-by-step explanation:
72 ounces and 6 steaks = what rate and unit rate
What is the equation of the line that passes through the point (-4,-4) and has a
slope of -3/4?
[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{-4})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{3}{4} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-4)}=\stackrel{m}{- \cfrac{3}{4}}(x-\stackrel{x_1}{(-4)}) \implies y +4= -\cfrac{3}{4} (x +4) \\\\\\ y+4=-\cfrac{3}{4}x-3\implies {\Large \begin{array}{llll} y=-\cfrac{3}{4}x-7 \end{array}}[/tex]
Answer:
y = -3/4x - 7
Step-by-step explanation:
Given: slope = m = -3/4
Plug this value into the standard slope-intercept equation of y = mx + b.
y = -3/4x + b
To find b, we want to plug in a value that we know is on this line: in this case, point (-4, -4). Plug in the x and y values into the x and y of the standard equation.
-4 = -3/4(-4) + b
To find b, multiply the slope and the input of x(-4)
-4 = 3 + b
Now, subtract 3 from both sides to isolate b.
-7 = b
Plug this into your standard equation.
y = -3/4x - 7
This is your equation.
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Ella has the same number of acorns as frank. Ella has 9 in one hand and 10 in the other hand. How many acorns does frank have in the other hand?
The number of acorns that Frank have in the other hand will be 14.
How to calculate the word problem?A word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real.life scenario given.
Since Ella has the same number of acorns as frank. Ella has 9 in one hand and 10 in the other hand.
When Frank has 5 on one hand, the number of acorns that Frank have in the other hand will be:
= 10 + 9 - 5
= 14
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Complete question
Ella has the same number of acorns as frank. Ella has 9 in one hand and 10 in the other hand. Frank has 5 on one hand. How many acorns does frank have in the other hand