Answer:
The length of the rectangle is[tex](4+7y^3)[/tex] and its width is[tex]3y^2[/tex]
Step-by-step explanation:
Given:
The Area of the rectangle =[tex]12y^2+21y^5[/tex].
Width is the greatest common factor of [tex]12y^2[/tex] and[tex]21y^5[/tex]
To Find:
The length and width of the rectangle = ?
Solution:
Step 1: Finding the greatest common factor of [tex]12y^2[/tex]and[tex]21y^5[/tex]
[tex]12 y^2[/tex]= 2 x 3 x 3 x y x y
[tex]21y^5[/tex] = 3 x 7 x y x y x y x y x y
Thus the greatest common factor is [tex]3y^2[/tex] which is the width
Step 2: Finding the length and width
The area of the rectangle = length x breath
width x length= [tex]12y^2+21y^5.[/tex]
Taking[tex]3y^2[/tex] commonly from each term, we get
width x length= [tex](3y^2)(4 + 7y^3)[/tex]
A group of friends went to the movies. Movie tickets cost $8.50 each. One of the group bought some food for $6.50. The group spent a total of $57.50. Write and solve an equation to determine how many tickets were bought. Let t represent the number of tickets.
Answer:
they bought 6 tickets
Step-by-step explanation:
8.50t+6.50= 57.50 subtract 6.50
8.50t=51 divide 8.50
t=6
place the numbers 0 to 8, in the magic square so that sum of the numbers in each row, column,and diagonal is the same number, 12
Answer:
[tex]\begin{array}{ccc}1&6&5\\8&4&0\\3&2&7\end{array}[/tex]
Step-by-step explanation:
A magic square can be made by putting the average number in the middle spot. Here, there are 3 numbers in each row, column, or diagonal that total 12, so their average is 12/3 = 4.
There are only 2 pairs of numbers that total 12: (8+4) and (7+5). These must be in the same row and column as the digit 0. If 0 were on a diagonal, we would need three pairs of numbers that total 12, so 0 cannot be on a diagonal.
Our square has 4 in the middle and 0 in a side spot, so it could look like ...
[tex]\begin{array}{ccc}1&6&5\\8&4&0\\3&2&7\end{array}[/tex]
Final answer:
To solve the 3x3 magic square with numbers 0 through 8 adding up to 12, place the numbers strategically so that each row, column, and diagonal sum to the magic constant. One solution involves putting the number 4 in the center and arranging opposite pairs that add to 8 around it.
Explanation:
To place the numbers 0 to 8 in the magic square so that the sum of the numbers in each row, column, and diagonal is the same number, 12, you have to carefully choose where to place each number. A 3x3 magic square using the numbers 0 through 8 is indeed possible with each line adding up to 12. Here's one solution:
2 7 3
6 4 2
4 1 7
Following this pattern ensures that the sum of each row, column, and diagonal line equals 12. Here's the step-by-step process:
Start by placing the number 4 in the middle of the grid, because in a 3x3 magic square, the center is always one-third of the magic constant (12 in this case).
Next, remember that opposite numbers around the center number must be pairs that add up to 8 (since 4 + 8 = 12 which is the magic constant).
Arrange the pairs strategically across the square so that they add up to 12 in each line.
For instance, placing 2 opposite to 6 and 7 opposite to 1 makes sure that rows, columns, and diagonals all sum to 12.
Zach has above ground pool that has a radius of 5.5 feet. He wants to put a new wall liner around his pool and need to know the circumference of the pool. Find the circumference of the pool to the nearest hundredth
The circumference of above ground pool is 34.54 feet.
Step-by-step explanation:
Given,
Radius of above ground pool = 5.5 feet
Circumference of a circle is given by 2πr
Circumference of above ground pool = 2πr
r = 5.5, π = 3.14
Circumference of above ground pool = 2*3.14*5.5
Circumference of above ground pool = 34.54 feet
The circumference of above ground pool is 34.54 feet.
Keywords: radius, circumference
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Mr.Changs class has 28 students 4/7 of whom are girls. Which equation shows how to determine the number of girls in Mr. Chang’s class
I think 7 of them are girls and the rest are boys and how i got this answer is I took the 28 and divided it by 4 and got 7.
There are 16 girls in Mr. Chang's class.
the correct equation to determine the number of girls in Mr. Chang's class is [tex]\( 28 \times \frac{4}{7} = 16 \)[/tex]
The correct option is (b).
let's break down the problem step by step.
Given:
Total number of students = 28
Proportion of girls = 4/7
To find the number of girls in Mr. Chang's class, we need to multiply the total number of students by the fraction representing the proportion of girls.
So, we calculate:
[tex]\[ \text{Number of girls} = 28 \times \frac{4}{7} \][/tex]
Now, let's multiply:
[tex]\[ 28 \times \frac{4}{7} = \frac{28 \times 4}{7} \][/tex]
[tex]\[ = \frac{112}{7} \][/tex]
Now, we can simplify this fraction:
[tex]\[ \frac{112}{7} = 16 \][/tex]
So, there are 16 girls in Mr. Chang's class.
Therefore, the correct equation to determine the number of girls in Mr. Chang's class is:b.[tex]\( 28 \times \frac{4}{7} = 16 \)[/tex]
complete question given below:
Mr. Chang's class has 28 students, 4/7 of whom are girls. Which equation shows how to determine the number of girls i Mr. Chang's class?
a.28+ 4/7 =49
b.28* 4/7 =16
c.4/7 / 28= 1/49
d.7/4 -28= 1/16
Are two triangles always congruent if they have the following corresponding parts congruent?
a
Two sides and an angle. Explain your response.
Not necessarily.
Step-by-step explanation:
The two triangles can be always congruent if the given parts i.e two sides and an angle are congruent provided that the angle is between the two congruent sides, otherwise the two triangles may not be congruent.
This is known as Side Angle Side condition for congruency.
Other congruency conditions inclue SSS - Side side side i.e all three sides of both triangles are congruent and ASA - Angle Side Angle i.e two angles and their including side of the two triangles are congruent.
How can u get hundred as a denominator as 209 over 25
Hundred as a denominator as 209 over 25 is obtained by mulyiplying numerator and denominator by 4
[tex]\frac{209}{25} = \frac{836}{100}[/tex]
Solution:
Given that we have to get hundred as a denominator as 209 over 25
Thus the given fraction is:
[tex]\rightarrow \frac{209}{25}[/tex]
Now we have to get 100 as denominator
If you multiply both the numerator and denominator of a fraction by the same non-zero number, the fraction remains unchanged in value.
Therefore, equivalent fractions can be created by multiplying or dividing the numerator and denominator by the same number
Muliply and divide by 4, so that 25 muliplied by 4 gives 100
[tex]\rightarrow \frac{209}{25} = \frac{209 \times 4}{25 \times 4} = \frac{836}{100}[/tex]
Thus the denominator is 100
BN. What additional given information is needed to prove
Triangle BUN is isosceles with BU
A BUG ZA BNA by ASA?
LOOK AT PICTURE:::
Answer:
To me it looks to be A: UBA/NBG because I can see two right isosceles. Hope this helps!!
To prove Triangle BUN is isosceles with BU = BN using ASA, additional given information is needed to show that UN = NA.
Explanation:In order to prove that Triangle BUN is isosceles with BU = BN, we need additional given information. To use the ASA (Angle-Side-Angle) congruence criterion, we already have BUN = BNA, but we also need to know that UN = NA. Without this information, we cannot conclude that the triangles are congruent.
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m=0 passing through p(-2,-2)
Answer:
The equation of line is y+2=0
Step-by-step explanation:
The equation of line passing through the point [tex](x_{1},y_{1} )[/tex]and having slope m is
[tex]y-y_{1} = m (x-x_{1}[/tex]
Given slope m=0 and given point is is (-2,-2)
[tex]y-(-2)=0(x-(-2))[/tex]
[tex]y+2=0[/tex]
therefore equation of the straight line is [tex]y+2=0[/tex]
Therefore the straight is parallel to negative x-axis(y=-2)
What is the quotient?
StartFraction 2 y squared minus 6 y minus 20 Over 4 y + 12 EndFraction divided by StartFraction y squared + 5 y + 6 Over 3 y squared + 18 y + 27 EndFraction
StartFraction 2 Over 3 (y minus 5) EndFraction
StartFraction 3 (y minus 5) Over 2 EndFraction
StartFraction (y minus 5) (y + 2) squared Over 6 (y + 3) squared EndFraction
StartFraction 3 (y + 5) (y minus 2) Over 2 (y + 2) EndFraction
Answer:
StartFraction 3 (y minus 5) Over 2 EndFraction
Step-by-step explanation:
First we need to factor all the polynomials here using quadratic equation (-b +/- √(b^2 - 4ac)) / 2a :
* 2y^2 - 6y - 20 = 2(y^2 -3y - 10)
From quadratic equation, solutions are 5 and -2, which means that we can factor this to;
2(y+2)(y-5)
* y^2 + 5y + 6, in the same manner, is found to have solutions -3 and -2, so it can be factored to:
(y+3)(y+2)
* 3y^2 + 18y + 27 = 3(y^2 + 6y + 9)
Again, solving quadratic equation, we find solution to be -3, so we factor this to:
3(y+3)(y+3)
* 4y + 12 equals to 4(y+3)
Now, let's rewrite our polynomials:
2(y+2)(y-5) • 3(y+3)(y+3) / 4(y+3) • (y+3)(y+2)
We see that we can cancel out some factors here (x+3) and (x+2), so we are left with 6(y-5) / 4 which is 3(y-5)/2.
Answer:
Option B, 3(y-5)/2
Step-by-step explanation:
A nature center displayed 224 insects in 7 equal groups. How many insects were in each group
Answer:
32
Step-by-step explanation:
you have to divide 224 by 7
[tex]224 \div 7 = 32 \\ [/tex]
If you know the diameter of a circle, how do you find its circumference?
Group of answer choices
Answer:
circumference of a circle [tex]C = 2\pi r=\pi (d)[/tex]
Step-by-step explanation:
Explanation:-
Circumference of a circle having radius is [tex]C = 2\pi r[/tex]
we know that the radius of circle is 'r'
The diameter of a circle is passing through the center of the given circle.
there fore the diameter of circle is equal to the two times of radius of given circle so d= 2 r
Circumference of a circle having diameter is
[tex]C= 2\pi r = 2r(\pi )[/tex]........(1)
we know that d = 2 r
now the equation (1) is [tex]C= d\pi[/tex]
Therefore The circumference of circle by using diameter is
[tex]C = \pi d[/tex]
This is a copy of the worksheet my son was given from school, can anybody look at this and tell if this is being done correctly, because it doesn’t look right to me....
It looks good to me!
sorry for all the pictures just help me pls
Answer:
The yellow table
Step-by-step explanation:
Because when 9+12=21 or 2+6+2+6+5=21
Its most likely going to show the results of the spinner when spun 20 times.
factorise the following question2xsaquare-8x
Answer:
2x(x - 4)
Step-by-step explanation:
Given
2x² - 8x ← factor out 2x from each term
= 2x(x - 4) ← in factored form
Randy has two 28-pound blocks of ice for his snow cone stand. 1). How many pounds of ice does randy have at his snow cone stand? 2). How many tons of ice is there? Write your answer from number 2 as a fraction and a decimal.
Randy has 56 pound blocks of ice for his snow cone stand
Tons of ice is 0.028 tons or [tex]\frac{7}{250} \text{ tons }[/tex]
Solution:
Randy has two 28-pound blocks of ice for his snow cone stand
1). How many pounds of ice does randy have at his snow cone stand?
Calculate the total pounds that Randy has
Total pounds = 2 x 28 = 56
Thus Randy has 56 pound blocks of ice for his snow cone stand
2) How many tons of ice is there?
Total pounds of ice = 56 pounds
So we have to convert 56 pounds to tons
Use the conversion factor
1 pound = 0.0005 ton
Therefore, 56 pounds is equal to,
56 pound = 0.0005 x 56 tons = 0.028 tons
Thus in decimal we got, 0.028 tons
Convert to fraction form,
[tex]0.028 = \frac{0.028}{1000} \times 1000 = \frac{28}{1000} = \frac{7}{250}[/tex]
Thus tons of ice is 0.028 tons or [tex]\frac{7}{250} \text{ tons }[/tex]
One angle of a triangle measures 140°. The other two angles are in a ratio of 3:5. What are the measures of those two angles?
Answer:
15 and 25
Step-by-step explanation:
the interior angles of a triangle, when added, = 180...so if one angle equals 140, then the other 2 angles have to measure a combined total of 40.
the other 2 angles are in a ratio of 3:5....added = 8
so one angle is 3/8 of 40......3/8 * 40 = 120/8 = 15 <===
the other angle is 5/8 of 40....5/8 * 40 = 200/8 = 25 <==
Final answer:
To find the measures of the other two angles in the triangle, set up a ratio between them: angle 1 is 3x and angle 2 is 5x. Solve the equation and find that the measures of angle 1 and angle 2 are 15° and 25°, respectively.
Explanation:
To find the measures of the other two angles in the triangle, we can set up a ratio between them. Let's call one angle 3x and the other angle 5x. We know that the sum of all three angles in a triangle is 180°. So we can write the equation: 140° + 3x + 5x = 180°.
Simplify the equation: 140° + 8x = 180°.
Subtract 140° from both sides: 8x = 40°.
Divide both sides by 8: x = 5°.
Now we can find the measures of the other two angles: Angle 1 = 3x = 3(5°) = 15°. Angle 2 = 5x = 5(5°) = 25°.
Which graph represents a reflection of f(x) = 6(0.5)x across the x-axis?
On a coorindate plane, an exponential function starts in quadrant 3 and increases and approaches y = 0 in quadrant 4. It crosses the y-axis at (0, 6) and goes through (1, negative 3).
On a coordinate plane, an exponential function approaches y = 0 in quadrant 2 and increases into quadrant 1. It goes through (1, 3) and crosses the y-axis at (0, 6).
On a coordinate plane, an exponential function approaches y = 0 in quadrant 3 and decreases into quadrant 4. It goes through (negative 1, negative 3) and crosses the y-axis at (0, negative 6).
On a coordinate plane, an exponential function decreases from quadrant 2 to quadrant 1 and approaches y = 0 in the first qudrant. It goes through the y-axis at (0, 6) and goes through (1, 3).
The correct graph representing a reflection of the function f(x) = 6(0.5)^x across the x-axis is one that shows the function decreasing into quadrant 4, crosses the y-axis at (0, -6), and approaches y=0 in quadrant 3, precisely matching the expected transformations due to reflection.
Explanation:To find the graph that represents a reflection of f(x) = 6(0.5)^x across the x-axis, it's important to understand what reflection across the x-axis entails. Reflecting a function across the x-axis means taking every point (x, y) on the graph of the function and transforming it into a point (x, -y). Thus, for the function f(x) = 6(0.5)^x, this transformation results in a new function g(x) = -6(0.5)^x. This produces a graph where all y-values are the negatives of the original function's y-values.
Among the provided options, the correct representation of this reflection would be: "On a coordinate plane, an exponential function approaches y = 0 in quadrant 3 and decreases into quadrant 4. It goes through (negative 1, negative 3) and crosses the y-axis at (0, negative 6)." This description matches the characteristics of the reflected function by correctly indicating the new y-intercept at (0, -6) and demonstrating the behavior of the function decreasing into quadrant 4 while approaching y=0 in quadrant 3.
find the constant m and b in the linear function f(x)=mx+b so that f(6)=9 and the straight line represents by f has slope -4
Answer:
The constant m=-4, and b=33
Step-by-step explanation:
F(x)= MX+b
If f(6)=9 then x=6, m= -4
9= -4(6) + b
9= -24 + b
b= 9 + 24
b= 33
Therefore the constant m, which is the slope is -4 and b which is the intercept is 33
Given the linear function f(x) = mx + b, we see the slope m as -4. Using the point (6,9), we find the y-intercept b to be 33.
Explanation:In the linear function 'f(x) = mx + b', 'm' represents the slope of the line and 'b' is the y-intercept. As it's given that the slope is -4, we replace 'm' in the equation with -4 to get 'f(x) = -4x + b'. Now, we use the point (6,9) which lies on the line, allowing us to find the value of 'b'. Substituting x = 6 and f(x) = 9 into the equation, we get 9 = -4*6 + b. After solving this equation, we find that b = 33. Therefore, the constants are m = -4 and b = 33.
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14 - r < 9 ; r = 6 is the given value a solution of the inequality?
Answer:
YESStep-by-step explanation:
14 - r < 9
Put r = 6 and check inequality:
14 - 6 < 9
8 < 9 TRUE
By substituting r = 6 into the inequality 14 - r < 9, we find that the inequality holds true, indicating that r = 6 is a solution to the inequality.
Explanation:To determine if r = 6 is a solution to the inequality 14 - r < 9, we simply substitute the value of r into the inequality and check the result.
Substituting r = 6 into the inequality gives us:
14 - 6 < 9
Which simplifies to:
8 < 9
Since 8 is less than 9, the inequality holds true,
which means that r = 6 is indeed a solution to the inequality 14 - r < 9.
I NEED THE ANSWER ASAP PLEASE
Answer:
7
Step-by-step explanation:
the answer would be 7 because if there is 2 in per hour just go 2,4,6,8,10,12
and then count all the numbers i did and that will be your answer (7)
What is the square root of -16?
Answer:
-4
Step-by-step explanation:
-4*-4= 16
How many solutions are there to the following system of equations? 3x-9y=0 , -x+3y=-3
Answer:
no solution
Step-by-step explanation:
if you graph these two equations the line would be parallel.
parallel = no solution
intersect = one solution
overlap = infinite amount of solution
The perimeter of a rectangle is 40 inches. If the length of the rectangle is 12 inches, which equation could be used to find the width, x?
A. x+2(12)=40
B. 12( x+2)=40
C. x+12 =40
D. 2(x+12) =40
Answer:
C. x + 12 = 40
Answer: D. 2(x+12) =40
Step-by-step explanation:
The Perimeter of a rectangle is calculated by the formula :
P = 2 ( length + width )
Let the width of the rectangle be x , then the perimeter becomes
40 = 2 ( 12 + x )
i dont understand this help pls
Answer:3/5
Step-by-step explanation:
Write an equation of the line parallel to y=3x+2 that passes through (-1, -2)
Answer:
[tex]y=3x+1[/tex]
Step-by-step explanation:
From the question, we are given;
The equation y = 3x + 2A point (-1, -2)We are required to determine the equation of a line parallel to the given line and passing through the point (-1, -2)
We are going to determine the gradient of the line first; when an equation is written in the form of y = mx + c, where m is the gradient.y = 3x + 2, m₁ = 3
But, m₁ = m₂ for parallel lines Therefore, the gradient of the line in question, m₂ is 3With the gradient, m₂=3 , and a point (-1, -2) we can get its equation;Taking another point (x, y)...
Then;
[tex]\frac{y+2}{x+1}=3[/tex]
[tex]y+2=3(x+1)\\y+2=3x+3\\y=3x+1[/tex]
Therefore; the equation of the line is [tex]y=3x+1[/tex]
-7×-3×=-8×-8
[tex] [/tex]
Answer:
x = 4Step-by-step explanation:
[tex]-7x-3x=-8x-8\\\\-10x=-8x-8\qquad\text{add}\ 8x\ \text{to both sides}\\\\-10x+8x=-8x+8x-8\\\\-2x=-8\qquad\text{divide both sides by (-2)}\\\\\dfrac{-2x}{-2}=\dfrac{-8}{-2}\\\\x=4[/tex]
What is (5x+5)-(8x-9) subtract
[tex]\text{Simplify:}\\\\(5x+5)-(8x-9)\\\\\text{Distribute the negative to the variables in the parenthesis}\\\\5x+5-8x+9\\\\\text{Combine like terms}\\\\-3x+5+9\\\\\boxed{-3x+14}[/tex]
what do you think about when you get sick? Check any that apply
Answer:
What are the answer choices? I'd be happy to help!
What is (x+7)3y equal to
Answer:
(x + 7)3y = 3xy + 21y
Step-by-step explanation:
Expand the expression in the question by using the distributive property. This means you multiply the term (number) outside the bracket with each of the terms (numbers) inside the bracket.
(x + 7)3y Expand this
= (x)(3y) + (7)(3y) Multiply 3y with x and 7
= 3xy + 21y Simplified, final answer
Find the value of the variable
Do not answer if you are unsure!
Answer as many as you can please!
1. −4x−3=−6x+9
x = ___
(type your answer as a number)
2.
41−2n=2+n
n = ___
(type your answer as a number)
3.
5x−7=−10x+8
x = ___
(type your answer as a number)
4.
7y+3=4y−18
y = ___
(type your answer as a number)
Answer:
6
13
1
-7
Step-by-step explanation: