The width of the rectangle with area 70y⁸+ 30y⁶ is; 10y⁶.
Then the length of the rectangle with area 70y⁸+ 30y⁶ is; (7y² + 3).
What are the dimensions of the rectangle?
The area of a rectangle is given by;
Area = Length× width
Given that;
The area of the rectangle = 70y⁸ + 30y⁶
Now, 70y⁸ can be broken down to; 7×5×2×y×y×y×y×y×y×y×y
And 30y⁶ can be broken down to; 5×3×2×y×y×y×y×y×y
The common factors of 70y⁸ and 30y⁶ are = 5,2,y,y,y,y,y,y
Thus, the greatest common factor of 70y⁸ and 30y⁶ is;
5×2×y×y×y×y×y×y = 10y⁶
Therefore our area 70y⁸+ 30y⁶ can be factorized to get;
A = 10y⁶(7y² + 3)
The greatest common monomial of 70y⁸+ 30y⁶ is 10y⁶ which is the width of the rectangle.
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A soap company wants to use a cylindrical container to hold their new liquid soap
A. solve the formula for h
B. what is the height of a container if the volume is 56.52 cubic inches and the radius is 1.5 inches? Round to the nearest tenth
A. The formula for h is h = V / πr².
B. The height of a container if the volume is 56.52 cubic inches and the radius is 1.5 inches is 8 inches.
How to calculate the value?The volume of a cylinder is calculated thus:
= πr²h.
where π = 3.142
r = radius
h = height
Therefore, the height will be:
V = πr²h
We have to make h the subject of the formula. This will be:
h = V / πr²
The height of a container if the volume is 56.52 cubic inches and the radius is 1.5 inches will be:
h = V / πr²
h = 56.52 / (3.142 × 1.5²)
h = 56.52 / 7.0695
h = 8
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write the equation of the line in a fully simplified slope-intercept form.
Slope intercept form: [tex]y=mx+b[/tex]
m = slopeb = y-interceptWe can identify two points on the given graph and solve for the slope and the y-intercept.
Solving the QuestionTwo clear points on the graph are (6,0) and (0,6).
First, we can solve for the slope by using the slope equation:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex] where two points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
⇒ Plug in the points (6,0) and (0,6):
[tex]m=\dfrac{0-6}{6-0}\\\\m=\dfrac{-6}{6}\\\\m=-1[/tex]
Therefore. the slope of the line is -1. Plug this into [tex]y=mx+b[/tex]:
[tex]y=-x+b[/tex]
Now, we can find the y-intercept. It is the value of y when the line crosses the y-axis.
In this case, we can see on the graph that this is 6.
[tex]y=-x+6[/tex]
Answer[tex]y=-x+6[/tex]
Which of these shapes are a trapezoid?
Answer: The Pink one
Step-by-step explanation: Trapezoids have 2 parallel sides and 2 non-parallel sides.
A bear cub weighs 8,800 grams in
March. After three months, it weighs
68.2 kg. How much weight did the cub
gain during the three months?
Answer:33 oz in march
Step-by-step explanation:
5
8
of the staff are male. 5
12
of the staff works part time at
the aquarium. What fraction of the staff is female?
The fraction that are female in the company is 227/256
How to determine the fraction that are female?The given parameters are
Male staff = 58
Total number of staff = 512
Start by calculating the number of female staffs
So, we have
Female staff = Total number of staff - Male staff
Substitute the known values in the above equation
So, we have
Female staff = 512 - 58
Evaluate the like terms
Female staff = 454
The fraction that are female is
Fraction = Female staff/Total number of staff
This gives
Fraction = 454/512
Simplify
Fraction = 227/256
Hence, the fraction is 227/256
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-2
-3
S
y = -2|x|
2
X
The function is positive when
The function is negative when
The function is increasing when
The function is decreasing when
Answer: Never, All real numbers, x<0, x>0
Step-by-step explanation:
The function is positive when it is above the x-axis.
The function is negative when it is below the x-axis.
The function is increasing when the graph is going up.
The function is decreasing when the graph is going down.
Solve the equation for the given variable. (type "no solution" if the equation has no solution and type "all
real numbers" if the equation is valid for all possible x-values)
4(4x + 2) + 2(9x + 4) + 3 = 34x + 19
Answer:
all real numbers
Step-by-step explanation:
4(4x+2)+2(9x+4)+3=34x+19
16x+8+18x+8+3=34x+19
34x+19=34x+19
all real numbers
:]
60 cents as percent of $3
60 cents is 20% of $3.
What is the percentage?In essence, percentages are fractions with 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100). The value of a number out of 100 is the percentage of that number. The terms "percent" and "cent" combine to make the word "percentage." Having Latin and French roots, the term "cent" means "hundred," while the word "percent" means "per hundred."
Given Data
60 cents as a percent of $3
1 dollar = 100 cents
$3 dollar = 300 cents
Percentage:
[tex]\frac{Value}{Total value}[/tex] × 100
[tex]\frac{60}{300}[/tex] ×100
20%
60 cents in 20% of $3.
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The complete question is:
"60 cents is what percent of $3."
What is the explination to the answer if I factor out the coefficient of 3/8d+3/4?
The fraction of coefficient factor out is 3/8.
What is Fraction?
A fraction is a portion of a whole or, more broadly, any number of equal parts. In everyday English, a fraction represents the number of pieces of a specific size, such as one-half, eight-fifths, or three-quarters. Numerators and denominators are also employed in uncommon fractions such as compound fractions, complex fractions, and mixed numerals. The numerator and denominator of positive common fractions are natural numbers.
The given expression is , 3/8d+3/4
From this, we have to eliminate the fraction for that we have to make common denominators like that,3/8 d + (3 * 2) / (4 * 2)=> 3/8 d + 6/8
Next, take out the common value i.e, 3/8=> 3/8 ( d + 2)
Therefore, the coefficient factor out is 3/8.
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HELP ME PLEASE! THIS IS URGENT!!
For what value of x will the line passing through the following pairs of points be veritcal? F(3-2x, 12) and G(x+9, 7)
By solving a linear equation, we will see that the points are vertical only if the value of x is -2.
For which value of x are the points vertical?
We say that two points (x₁, y₁) and (x₂, y₂) are vertical if the points have the same x-component and different y-component, so we must have:
x₁ = x₂
y₁ ≠ y₂
In this case, the two points are:
F(3-2x, 12) and G(x+9, 7)
The y-component is different, so we only need to have:
3 - 2x = x + 9
This is a linear equation, below I will solve it:
3 - 2x = x + 9
3 - 9 = x + 2x
-6 = 3x
-6/3 = x
-2 =x
The points are vertical if x = -2.
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What is the
domain?
Help me plssss
help me with this please!!
y -intercept #4 the starting value
(1 , 7.5) #3 the value after 1 year
because the x axis is the time (in years). When x = 0 (at the y-intercept) time = 0 or beginning time. When x = 1 one year has passed.
Solve the system of linear equations using the substitution method.
4x + 7y = 19 and y = x + 9
A. (-4, 5)
B. (-6, 4)
C. (-1, 2)
D. (-4, 3)
Answer:D
Step-by-step explanation:
A string measures 30 cm about how many lnches long is the string
Find the quotient of.(4.617 × 10 ^3 ) ÷ (5,700 ÷ 10^ 2 )
The quotient of the expression (4.617 × 10³ ) ÷ (5,700 ÷ 10² ) is 81.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Given that;
The expression is;
(4.617 × 10³ ) ÷ (5,700 ÷ 10² )
Now, Solve the expression by using BODMAS rule;
= (4.617 × 10³ ) ÷ (5,700 ÷ 10² )
= 4,617 ÷ 57
= 81
Thus, The quotient of the expression (4.617 × 10³ ) ÷ (5,700 ÷ 10² ) is 81.
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What is the lowest common multiple of six and nine
Answer: 18
Step-by-step explanation: it is the smallest one in both tables.
1x6=6 2x6=12 3x6=18
1x9=9 2x9=18
hope this helped
Answer the 3 question in the photo for EASY points ( 20 points )
-5w/9 = 30 solve for w and simplify your answer as much as possible
After simplification of the given expression -5w /9 =30 , value of w is equal to -54.
As given in the question,
Given expression is equal to :
-5w / 9 = 30
Simplification of the given expression to get the value of w is :
-5w / 9 = 30
Multiply both the side of the given expression by 9 we get ,
-5w = 30 × 9
Divide both the side of the given expression by -5 we get,
-5w /-5 = ( 30 × 9 ) / -5
⇒ w = -(6 × 9 )
⇒ w = -54
Therefore, after simplification of the given expression -5w /9 =30 , value of w is equal to -54.
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What is the value of p will the function be continuous?
The value of p that will guarantee the continuity of the function is given as follows:
p = 6.5.
What is the continuity concept?A function defined by f(x) is continuous at a point x = a if it is defined at x = a, and the lateral limits are equal, that is:
[tex]\lim_{x \rightarrow a^-} f(x) = \lim_{x \rightarrow a^+} f(x) = f(a)[/tex]
In the context of this problem, the continuity of the function will be guaranteed if the lateral limits at x = -1 are equal.
To the left of x = -1, the function is less than -1, hence the lateral limit is:
lim x -> -1^- f(x) = lim x -> -1 (-2x² - 8x + 3) = -2(-1)² - 8(-1) + 3 = 9.
To the right of -1, the function is greater than -1, hence the lateram limit is:
lim x -> -1^+ f(x) = lim x -> -1 (4x + 2p) = 4(-1) + 2p = -4 + 2p.
The lateral limits have to be equal for the function to be continuous, hence:
-4 + 2p = 9
2p = 13
p = 13/2
p = 6.5.
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k (x)=6x-12 ; k(x)=15
The input value x in the function k( x ) = 6x - 12 when k( x ) = 15 is 9/2.
What is the input value (x) in the given function?A function is simply a relationship that maps one input to one output, that is, each x-value can only have one y-value.
Given the data in the question;
k( x ) = 6x - 12k( x ) = 15x = ?To determine the value of x, equate the function to 15 and solve for x.
k( x ) = 6x - 12
k( x ) = 15
15 = 6x - 12
Rearrange the equation
6x - 12 = 15
Collect like terms
6x = 15 + 12
6x = 27
Divide but sides by 6
6x/6 = 27/6
x = 27/6
x = 9/2
Therefore, the input value (x) is 9/2, this forms an ordered pair of ( 9/2, 15 ).
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I need helping finding out the answers … I’m confused.
To solve this problem, we will use the following formula for the area of a trapezoid:
[tex]A=\frac{a+b}{2}h,[/tex]where a, and b are the lengths of the bases and h is the height.
Now, we are given that ( we will omit the units to simplify the calculations):
[tex]\begin{gathered} h=\frac{1}{4}(a+b), \\ h=2\frac{1}{2}. \end{gathered}[/tex]Therefore:
[tex]\frac{(a+b)}{2}=2(\frac{a+b}{4})=2h=2(2+\frac{1}{2})=4+1=5.[/tex]Substituting in the above formula, we get:
[tex]A=\frac{5}{2}\times(2\frac{1}{2}).[/tex]Simplifying the above result, we get:
[tex]A=\frac{25}{4}ft^2.[/tex]Answer:
[tex]\begin{gathered} A=\frac{1}{2}(2\frac{1}{2})(2\frac{1}{2}\cdot2) \\ =\frac{1}{2}(\frac{5}{2})(\frac{5}{2}\cdot2) \\ =\frac{50}{8}=\frac{25}{4}=6.25ft^2. \end{gathered}[/tex]The start of an arithmetic sequence is
17, 21, 25, 29,
21,
The rule for the sequence can be written in the form
In
= en + d, where c and d are numbers.
a) By first calculating the values of c and d, work out the rule
for the sequence.
b) What is the value of 211?
The equation of the sequence is xₙ = 4n + 17 and the 11th term is 61
The equation of the sequenceFrom the question, we have the sequence to be
17, 21, 25, 29, 21
The form of the sequence is given as
xₙ = cn + d
From the question, we have the first term to be 17
This means that
d = 17
So, we have
xₙ = cn + 17
When n = 1, we have x = 21
So, we have
21 = c + 17
Evaluate
c = 4
Substitute c = 4 in xₙ = cn + 17
xₙ = 4n + 17
The value of x₁₁This means that
n = 11
So, we have
x₁₁ = 4 * 11 + 17
Evaluate
x₁₁ = 61
Hence, the value is 61
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Standard form 10x-7y=-3
Answer:
x= −3/10
y= 3/7
Step-by-step explanation:
Which of the following is the best estimate of the slope of the best -fit line for the graph at the right?
The best estimate of the slope of the best-fit line for the graph at the right will be 7/4.
What is the slope?The ratio of the increase in elevation between two points to the run in elevation between those same two points is referred to as the slope. A line that is moving up will have a positive slope, and a line that is moving down will have a negative slope if you view the line from left to right. A line's slope often indicates the steepness and direction of the line. By calculating the difference between the coordinates of the two points, (x₁,y₁) and (x₂,y₂), it is simple to calculate the slope of a straight line between them. The letter "m" is frequently used to denote slope.
Given Data
x coordinate = 4
y coordinate = 7
Slope = y-coordinate/ x-coordinate
Slope = 7/4
The best estimate of the slope of the best-fit line for the graph at the right will be 7/4.
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Sandra is using the point-slope form y - y₁ = m(x-x₁) to graph the equation y+2=(x-3). She completed the following steps.
Step 1: Plot a point at (3, 2).
Step 2: Plot a point 5 units up and 4 units left from (3, 2), at (-1, 3).
Step 3: Connect the points with a line.
In which step did Sandra make her first mistake?
What mistake did Sandra make?
She make mistake in her first step. She plot a point at (3,2) instead of (3,−2).
Sandra is using the point-slope form [tex]y - y_{1} = m(x-x_{1})[/tex] to graph the equation [tex]y+2=(x-3)[/tex].
She completed the following steps.
1) Firstly she plot a point at (3,2)
2) Then she plot a point 5 units up and 4 units left from (3,2), at (−1,3).
3) Then she connect the points with a line.
She using the point slope for to graph the equation.
The point slope form is [tex]y - y_{1} = m(x-x_{1})[/tex].
The equation is [tex]y+2=(x-3)[/tex].
Now we compare the given equation to the point slope form.
After comparing we get
[tex]y_{1}[/tex] = -2 and [tex]x_{1}[/tex] = 3
So we have to plot a point at (3,-2) but she plot point at (3,2).
She make mistake in her first step.
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(Inv. 1)*30. Multiple Choice Tika's math class began 18 minutes ago. Theclass will end in 37 minutes. Which equation can be used to find thelength in minutes of Tika's math class?A 18 + m = 37Bm – 37 = 18C 37 - m = 18D 18 – m = 37
Step 1
Let the length in minutes of Tika's class be m
His class had lasted already for 18 minutes
His class had 37 more minutes to end.
Step 2
Get the equation
[tex]\begin{gathered} 18\text{ + 37 = m} \\ To\text{ suit the options} \\ 18\text{ = m-37} \\ \text{Therefore,} \\ m-37\text{ = 18} \end{gathered}[/tex]Hence the answer is option B ------ ( m - 37 = 18)
Ryan has a deck that measures 3 feet by 8 feet. He wants to increase each dimension
by equal lengths so that its area is increased by 50%. By how much should he increase each dimension?
The dimensions of the deck would be increased by 1 feet.
How much should he increase each dimension?Area of a rectangle = length x width
Initial area of the deck = 3 x 8 = 24 feet²
Area of the deck when it is increased = (1 + 0.50) x 24 = 36 feet²
Length of the deck after it is increased = 3 + x
Width of the deck after it is increased = 8+ x
Area of the new deck : (3 + x) + (8 + x) = 36
24 + 3x + 8x + x² = 36
x² + 8x + 3x + 24 - 36 = 0
x² + 11x - 12 = 0
The solutions of the quadratic equation are -1 and 12
-1 + x = 0
x = 1
or
12 + x = 0
x = -12
Thus, the dimension of the deck would be increase by 1 feet.
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Find the vertex of the function given below.
y = 2x² + 4x+1
A. (3,-4)
B. (-1,-1)
C. (1,7)
D. (-4,9)
The function has the vertex value of (-1, -1)
How to calculate the vertex of the function?From the question, the definition of the functuion is given as
y = 2x² + 4x + 1
Start by differentiating the function
This is done as follows
y' = 4x + 4
Next, we set the differentiated equation to 0
So, we have the following equation
4x + 4 = 0
This gives
4x = -4
Divide by 4
x = -1
Next, we substitute x = -1 in the given equation y = 2x² + 4x + 1
So, we have the following equation
y = 2(-1)² + 4(-1) + 1
Evaluate
y = -1
Recall that
x = -1 and y = -1
So, we have
(-1, -1)
Hence, the vertex of the function is (-1, -1)
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The vertex of the given function y = 2x² + 4x+1 is (-1, -1) which is the correct answer would be an option (B).
The function is below given by,
y = 2x² + 4x + 1
Differentiate with respect to x to get the derivative of the above function,
y' = dy/dx = d/dx (2x² + 4x + 1)
y' = 4x + 4
Equating the derivative of the function to zero
y' = 0
4x + 4 = 0
4x = -4
Divide by 4 into both sides of the equation,
x = -1
Substitute x = -1 in the given function y = 2x² + 4x + 1
y = 2(-1)² + 4(-1) + 1
y = 2(1) - 4 + 1
y = -1
Therefore, the vertex of the given function is (-1, -1).
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Write the slope-intercept form of the equation of the line through the given point with the given
slope.
through: (4, -1), slope = -1/2
Answer: y=-1/2x+1
Step-by-step explanation: plug in numbers to find y intercept (b).
-1=-1/2(4)+b
-1=-2+b
b=1
y=-1/2x+1
Two quarters of the basketball game are complete. Now it is half time. Explain how this could be
Using proportions, the explanation for this is that a basketball game has four quarters, hence half-time is at the end of the second quarter.
What is a proportion?A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using the basic arithmetic operations, especially multiplication and division with the unit rates in the problem.
The entirety of a basketball game is composed by:
4 quarters.
Hence the mid-point of the game is calculated as follows:
0.5 x 4 quarters = 2 quarters.
This means that the end of the second quarter is the mid-point of the game, which is why the halftime is positioned at the end of the second quarter.
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