On dividing both the numerator and the denominator of [tex]\frac{20a^2b}{5ab^2}[/tex] by 5b, the result is [tex]\frac{4a}{b}[/tex].
In order to evaluate and solve this expression, we would have to apply the PEMDAS rule, where mathematical operations within the parenthesis (grouping symbols) are first of all evaluated, followed by exponent, and then multiplication or division from the left side of the expression to the right.
Lastly, the mathematical operations of addition or subtraction would be performed from left to right.
Note: Let the variable x represent the unknown expression or missing term.
Based on the information provided, we can logically set up the following mathematical equation:
[tex]\frac{20a^2b}{5ab^2} \div \frac{x}{x} =\frac{4a}{b}[/tex]
Next, we would solve the equation in parts by using the numerators and denominators as follows;
[tex]20a^2b \div x = 4a\\\\\frac{20a^2b}{x} =4a\\\\x4a=20a^2b\\\\x=\frac{20a^2b}{4a} \\\\x=5a\\\\\\\\\frac{5ab^2}{x} =b\\\\xb=5ab^2\\\\x=\frac{5ab^2}{b} \\\\x=5a[/tex]
Complete Question:
Select the correct answer from the drop-down menu.
Find the missing term.
On dividing both the numerator and the denominator of [tex]\frac{20a^2b}{5ab^2}[/tex] by ___, the result is [tex]\frac{4a}{b}[/tex].
Find the values of x and y that fit both the equation 2x - 3y = 8 − = and 4x + 3y = -2.
Answer:
Step-by-step explanation:
In other words, solve the system
2x - 3y = 8
4x + 3y = -2
Let's use the method of elimination. Mult. the first equation by -2:
-4x + 6y = -16
4x + 3y = -2
----------------------
8y = -18, so y = -9/4. If y = -9/4, then 2x - 3(-9/4) = 8, and:
2x + 27/4 = 8, or
2x + 27/4 = 32/4, or
2x = 5/4, or
x = 5/8
Then the solution is (5/8, -9/4).
If this does not match any of the possible answer choices, please check to ensure that y ou have copied down this problem correctly. Where do the "- =" symbols following the '8' come from?
To find the values of x and y that fit both equations, we can solve the system of equations using the elimination method. The values of x and y that fit both equations are x = 1 and y = -2.
Explanation:To find the values of x and y that fit both the equations 2x - 3y = 8 and 4x + 3y = -2, we can solve the system of equations. This can be done using the elimination method or the substitution method. Let's use the elimination method:
Multiplying the first equation by 4 and the second equation by 2, we get:
8x - 12y = 32
8x + 6y = -4
Subtracting the second equation from the first, we get:
-18y = 36
Dividing both sides by -18, we find that y = -2. Substituting this value back into the first equation, we can solve for x:
2x - 3(-2) = 8
2x + 6 = 8
2x = 2
x = 1
Therefore, the values of x and y that fit both equations are x = 1 and y = -2.
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Carmen was hired as a salaried computer programmer for $42,000 per year. What is her bi-weekly (26 weeks) salary?
Question 1 options:
$1,615.38
$807.69
$1,000.00
$3,500.00
Answer:
$1,615.38
Step-by-step explanation:
Remember that
1 year=52 weeks
we know that
Carmen was hired as a salaried computer programmer for $42,000 per year
or
was hired as a salaried computer programmer for $42,000 per 52 weeks
using proportion
Find out how much is the salary per 2 weeks
[tex]\frac{42,000}{52}=\frac{x}{2}\\\\x=42,000*2/52\\\\x=\$1,615.38[/tex]
What is P(A or B)...?
P(A or B) = P(A) + P(B) - P(A and B)
P(A or B) = 0.5 + 0.4 - 0.15
P(A or B) = 0.75
g(x) = x^3 - x^2 - 4x + 4 what are the zeros, the y-intercept and the end behavior.
I think it's -2,0 1,0 2,0 for the zeros
y-intercept 0,4 but i'm not sure about them and have no clue about the end behavior
Answer:
See explanation
Step-by-step explanation:
Zeros of the function are those values of x, for which g(x)=0, so solve the equation g(x)=0:
[tex]x^3-x^2-4x+4=0\\ \\x^2(x-1)-4(x-1)=0\\ \\(x-1)(x^2-4)=0\\ \\(x-1)(x-2)(x+2)=0\\ \\x_1=-2,\ x_2=1,\ x_3=2[/tex]
Hence, the function has three zeros, x=-2, x=1 and x=2.
To find the y-intercept, substitute x=0:
[tex]y=g(0)=0^3-0^2-4\cdot 0+4=4,[/tex]
so y-intercept is at point (0,4).
The graph of the function shows that when x is infinitely small, then y is infinitely small too and if x is infinitely large, then y is infinitely large too.
Answer:
The zeros: x = 1, -2, 2
The y-intercept: (0, 4)
The end behavior :
x --> + ∞, f(x) --> + ∞
x --> - ∞, f(x) --> - ∞
Step-by-step explanation:
Zero function:
x^3 - x^2 - 4x + 4 = 0
(x^3 - x^2) - (4x - 4) = 0
x^2(x - 1) - 4(x - 1) = 0
(x^2 - 4)(x - 1) = 0
(x + 2)(x - 2)(x - 1) = 0
x + 2 = 0; x = -2
x - 2 = 0; x = 2
x - 1 = 0; x = 1
The zeros: x = 1, -2, 2
The y-intercept when x = 0 so y-intercept = 4 or (0, 4)
The end behavior of a function f(x) : the behavior of the graph of the function at the ends of the x-axis.
As x approaches + ∞, f(x) approaches + ∞
As x approaches - ∞, f(x) approaches - ∞
I need help asap please ?!
Answer:
B
Step-by-step explanation:
[tex]m+4\leq6[/tex]
We subtract 4 from each side to get [tex]m\leq2[/tex]
Let's plug in a random point such as 0.
[tex]0+4\leq6 \\ \\ 4\leq6[/tex]
Since this is true, the inequality we made is true.
Find the distance between the point (-3,-4) and the line 2y=-3x+6
A.sqr13
B.23
C.14
D.23sqr13/13
The distance between the point (-3, -4) and the line 2y = -3x + 6 is 23 ÷ 13.
The distance between the point (-3, -4) and the line given by the equation 2y = -3x + 6 can be found using the point-to-line distance formula:
D = |Ax + By + C| ÷ (A^2 + B^2)
Firstly, we want to put the line equation in the standard form of Ax + By + C = 0. Let us rearrange the given equation of the line to this form:
3x + 2y - 6 = 0
Where A = 3, B = 2, and C = -6. Using the point (-3, -4), we plug the values into the point-to-line distance formula:
D = |3(-3) + 2(-4) - 6| ÷(3^2 + 2^2)
D = |-9 - 8 - 6| ÷(9 + 4)
D = | -23 | ÷ 13
D = 23 /÷ 13
Since ÷ 13 is an irrational number, we can't simplify it further. Therefore, the distance is:
D = 23 ÷ 13
What is the answer for #4 ?
Answer:
[tex]x>5[/tex] or [tex]x<-5[/tex]
Step-by-step explanation:
Isolate the absolute value term.
[tex]7|\frac{x}{7}|>5 \\ \\ |\frac{x}{7}|>35[/tex]
Take about the absolute value sign.
[tex]\frac{x}{7}>5[/tex] or [tex]-\frac{x}{7}>5[/tex]
Solve for each inequality.
[tex]x>5[/tex] or [tex]x<-5[/tex]
your math class is going to test new digital clinometers by measuring the angle of elevation of a kite you will fly. the kite flies to an angle of 50.2° on 520 feet of string. Assuming the the string is taut, how high is the kite to the nearest foot?
A) 624 ft
B) 400 ft
C) 333 ft
D) 677 ft
Check the picture below.
make sure your calculator is in Degree mode.
Thus, the kite is height of 400 ft above the ground.
Hence, option B is correct.
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that,
Hypotenuse of tringle = 520 ft
And inclination angle = 50.2 degree
We know that if any one of interior angle is of 90 degree then the angle is said to be right angle triangle.
Since,
sinΘ = (opposite side of Θ)/Hypotenuse
Therefore,
⇒ sin50.2 = Height/520 (since opposite side is height of triangle as shown in figure)
⇒ 0.76 = Height/520
⇒ Height = 395.2 feet ≈ 400ft (in nearest foot)
Hence,
Height of kite is 400 ft.
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The vertices of ABC are A(-2. 2). B(8.2), and C(O. 8). The perimeter is 22.8 . What is the area in square units ?
Answer:
multiply 22.8 by 22.8
Step-by-step explanation:
A sequence is defined by the recursive function f(n + 1) = –10f(n).
If f(1) = 1, what is f(3)?
3
–30
100
–1,000
Answer:
100
Step-by-step explanation:
f(n+1) = -10f(n)
f(1) = 1
f(2) = -10f(1) => f(2) = -10·1 => f(2) = -10
f(3) = -10f(2) => f(3) = -10·(-10) => f(3) = 100
Answer:
100
Step-by-step explanation:
IS the slope ( -3, -3) ( 3, 1)
A=positive
B= negative
C= no slope
D = undefined
and find the slope
The correct answer is A - positive
Answer:
A and the slope is 8/12
Step-by-step explanation:
Complete the statements below using the 2 graphs
Answer:
unit pay 10
slope 10
Step-by-step explanation:
$40/4hr = $10/1hr =10
Select the correct answer from each drop-down menu.
m^2-5/2m=-11/2 , m=___±___.
1st options:
1/4
1
5/4
2nd options:
(3i square root 7)/4
(i square root 21)/2
(square root 113)/4
Answer:
correct option for first blank is 5/4 and for second blank is [tex]\frac{ 3i\sqrt{7}}{4}[/tex]
i.e m= [tex]\frac{5}{4}\pm\frac{ 3i\sqrt{7}}{4}[/tex]
Step-by-step explanation:
The given equation
[tex]m^2 - \frac {5m}{2} = \frac{-11}{2}[/tex]
and we have to find m= ______ ± ________
We can use quadratic formula to solve this question.
The above equation can be written as: [tex]m^2 - \frac {5m}{2} + \frac{11}{2} = 0[/tex]
and the formula used will be:
[tex]m= \frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Putting values of a= 1, b= -5/2 and c= 11/2 and solving we get:[tex]m=\frac{-\frac{-5}{2}\pm\sqrt{{(\frac{-5}{2})}^2-4(1)(\frac{11}{2})}}{2(1)}\\\\m=\frac{\frac{5}{2}\pm\sqrt{(\frac{25}{4})-22}}{2}\\m=\frac{\frac{5}{2}\pm\sqrt{(\frac{-63}{4})}}{2}\\m= \frac{\frac{5}{2}}{2}\pm\frac{\sqrt{(\frac{-63}{4})}}{2}\\m= \frac{5}{4}\pm\frac{\sqrt{-63}}{4}[/tex]
Since there is - sign inside the √ so [tex]\sqrt{-1}[/tex] is equal to i and we have to divide [tex]\sqrt{63}[/tex] into its multiples such that the square root of one multiple is whole no so,
[tex]\sqrt{63}[/tex] = [tex]\sqrt{9}* \sqrt{7}[/tex]=[tex]3* \sqrt{7}[/tex]
Putting value of [tex]\sqrt{63}[/tex] and [tex]\sqrt{-1}[/tex]
the value of m= [tex]\frac{5}{4}\pm\frac{ 3i\sqrt{7}}{4}[/tex]
so, correct option for first blank is 5/4 and for second blank is [tex]\frac{ 3i\sqrt{7}}{4}[/tex] .
1) Which of the following will give a negative correlation?
a) As time goes on, the number of endangered elephants decreases
b) As speed decreases, the number of accidents decreases
c) As time goes on, the height of a baby increases
d) As time goes on, the height of the plant remains the same
2) Brian made a scatter plot and drew in a line of best fit. The equation of his line was
y = -x + 120, where x represents the number of hours spent exercising in a week and y
represents weight. If someone were to spend 12 hours working out this week, use Brian's
line of best fit to predict a reasonable weight.
a) 120
b) 96
c) 114
d) 216
For number 1 the answer is A because negative correlation means something decrease as times goes on and for number 2 the answer is B because it is the best fit and is not really far away if you sustract.hope this helps. please add brainlist
Find the area of the balcony in square feet . Round to the nearest square foot.
A. 22
B. 85
C. 86
D. 96
16x6=96 square feet
Answer: The answer is D. 96
Step-by-step explanation: Why? well on the paper it shows the balcony 16*6 so the answer is 96 square feet.
Plz help me with this
Answer: C) 2
Step-by-step explanation:
The red curve is: y = eˣ
The blue line is: y = 2x + 3
The intersect at two coordinates: (-1.4, 0.2) & (2, 7)
The only x-value option provided in your answer choices is: x = 2
Use the figure below to determine the length of side x help plz
The right answer for this one is C.
The length of side x is 4√3
What is tan of an angle?The tangent of an angle in trigonometry is the ratio of the lengths of the adjacent side to the opposing side. In order for the value of the cosine function to not be 0, it is the ratio of the sine and cosine functions of an acute angle.
Given
Height = 12
θ = 60
tan θ = height/base
tan 60 = 12/base
√3 = 12/x
x = 12/√3 = 4√3
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6! = (4! x (6-4)!) =
Answer:
6! = 720(4! × (6 - 4)!) = 48Step-by-step explanation:
n! = 1 · 2 · 3 · 4 · ... · n
6! = 1 · 2 · 3 · 4 · 5 · 6 = 720
(4! × (6 - 4)!) = (1 · 2 · 3 · 4 × 2!) = 24 × 1 · 2 = 24 × 2 = 48
If you accept you are going to die at anytime, then you might not be as ambitious as you are.
Answer:
Nice quote!
Step-by-step explanation:
<:)
The discussion reflects on how accepting the inevitability of death might influence one's ambition, with perspectives ranging from it being a motivator to live more purposefully to a potential cause for nihilism or inaction.
The question delves into philosophical reflections on mortality and ambition, suggesting that acknowledging the inevitability of death might dampen one's drive to achieve. This idea taps into a broader discussion on how our perceptions of life and death can shape our motivations and actions. Ancient philosophies and modern thought leaders offer varying perspectives on this issue.
For instance, sources suggest that embracing the certainty of death can lead to a life lived with greater purpose and less fear, implying that the awareness of mortality can actually enhance one's ambition by instilling a sense of urgency and focus. This is supported by the notion that knowing each day could be our last encourages us to grow, reach out to others, and live authentically. Conversely, others argue that an excessive preoccupation with death may lead to nihilism or inaction, driven by the belief that all efforts are ultimately futile in the face of mortality. The balance between these viewpoints highlights the complex relationship between accepting death and pursuing ambition.
Which inequality can be represented by the graph below ?
Answer:
Option F. [tex]y\geq x+b[/tex]
Step-by-step explanation:
we know that
The solution of the inequality of the graph is the shaded area above the solid line
step 1
Find the equation of the solid line
The intercepts are
The y-intercept is the point (0,b)
The x-intercept is the point (-b,0)
Find the slope
[tex]m=\frac{b-0}{0+b} =1[/tex]
The equation of the solid line is
[tex]y=x+b[/tex]
step 2
The solution of the inequality is the shaded area above the solid line
therefore
the inequality is equal to
[tex]y\geq x+b[/tex]
A bag contains 5 red marbles, 4 blue marbles, 3 green marbles, and no other marbles. If a marble is chosen at random from the bag, what is the probability that the marble chosen will not be red?
Answer:
A = choosing a red marble
B = choosing a green marble
Probability of A happening = P(A) = 5/(3+5+4) = 5/12
Probability of B happening = P(B) = 4/(3+5+4) = 4/12
Probability of either happening = P(A) + P(B) = 5/12 + 4/12 = 7/12
The key word in their question is red OR green and that is why we add the two probabilities. If they ask the probability of them both happening (if they said red AND green), you would multiply P(A)*P(B).
The probability that the chosen marble is not red is [tex]\frac{7}{12}[/tex].
What is probability?A probability is a number that reflects the chance or likelihood that a particular event will occur.
What is the formula for the probability?The formula of the probability is
[tex]P(E) = \frac{Number\ of\ favorable\ outcomes}{Total\ number\ of\ outcomes }[/tex]
Where, P(E) is the probability of an event.
According to the given question.
Number of red marbles = 5
Number of blue marbles = 4
Number of green marbles = 3
So,
The total number of marbles in a bag = 5+4+3 = 12
And, the probability that chosen marble is red = [tex]\frac{5}{12}[/tex]
Therefore,
the probability that the chosen marble is not red
[tex]=1-\frac{5}{12} \\[/tex]
[tex]= \frac{12-5}{12}[/tex]
[tex]= \frac{7}{12}[/tex]
Hence, the probability that the chosen marble is not red is [tex]\frac{7}{12}[/tex].
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Gloria can knit one block of a quilt in 50 minutes. If she knits at the same rate for 5 hours, how many blocks can she knit ?
Answer:
The answer is 6.
Step-by-step explanation:
Remember, Gloria can knit one block in 50 minutes, and they want to know how many blocks she can knit in 5 whole hours.
Which means, that is 5 squares in 4 hours, but we still have the 10 minutes from each of the 50 minutes.
So, you add up the 5 ten minutes (50 minutes) Which gives you a whole square.
Therefore, Gloria can knit 6 squares in 50 minutes.
Gloria can knit 6 blocks in 5 hours if she maintains her knitting rate of one block every 50 minutes.
Gloria can knit one block of a quilt in 50 minutes. To find out how many blocks she can knit in 5 hours, one should first convert the knitting time from hours to minutes. Since there are 60 minutes in an hour, 5 hours is equal to 300 minutes. Next, divide the total available knitting time by the time it takes to knit one block.
300 minutes / 50 minutes per block = 6 blocks
So, if Gloria knits at the same rate, she can knit 6 blocks in 5 hours.
Which statement is true?
A.
The x-intercept of f(x) is equal to the x-intercept of g(x).
B.
The y-intercept of f(x) is equal to the y-intercept of g(x).
C.
The y-intercept of f(x) is greater than the y-intercept of g(x).
D.
The x-intercept of f(x) is greater than the x-intercept of g(x).
Answer:
D
Step-by-step explanation:
We can see in the graph f(x) that the x intercept is [tex](1,0)[/tex].
In the table of g(x), we can see that the x intercept is [tex](-1,0)[/tex].
Since [tex]1>-1[/tex], the x intercept of the graph f(x) is greater than the x intercept of graph g(x).
ANSWER
D. The x-intercept of f(x) is greater than the x-intercept of g(x).
EXPLANATION
From the graph, f(x) touches the y-axis at y=-1.
The y-intercept of -1
The graph touches the x-axis at x=1.
This is the x-intercept.
From the table, the y-intercept is the point with x-coordinate of zero.
From the table, x=0 when y=1.
The y-intercept of g(x) is 1.
The x-intercept is where y=0.
The x-intercept is -1.
The x-intercept of f(x), which is 1, is greater than the x-intercept of g(x), which is -1
The correct choice is D.
SUPER EASY/////
What is the midpoint of a line segment with the endpoints (8,-3) and (-5,-9)?
For this case we have that by definition, the coordinates of the midpoint are given by:
[tex]M = (\frac {x_ {1} + x_ {2}} {2}, \frac {y_ {1} + y_ {2}} {2})[/tex]
We have the following points:
[tex](x_ {1}, y_ {1}) :( 8, -3)\\(x_ {2}, y_ {2}): (- 5, -9)[/tex]
Substituting the values:
[tex]M = (\frac {8 + (- 5)} {2}, \frac {-3 + (- 9)} {2})\\M = (\frac {8-5} {2}, \frac {-3-9} {2})\\M = (\frac {3} {2}, \frac {-12} {2})\\M = (1.5; -6)[/tex]
Answer:
Option C
Answer:
(1.5, -6) ~apex
Step-by-step explanation:
If you substitute the value 22.5 for h into the equation
h = 11.25, does it make the statement true or false?
Answer:
Step-by-step explanation:
False, because plugging it in would imply that 22.5 = 11.25
False
its false
The answer is false ok. there
What is the measure of the angle
Answer:
is 235
Step-by-step explanation:
shown in the image attached
Hope this helps
For this case we have that by definition, a flat angle is one that measures 180 degrees. It is observed that a flat angle is formed from the first to the second quadrant.
Now, we must add 55 degrees of the third quadrant, then:
[tex]180 + 55 = 235[/tex]
Thus, the angle formed is 235 degrees.
Answer:
235 degrees
Option A
what is the factorization of the expression below 16x^2-25y2
For this case we must factor the following expression:
[tex]16x ^ 2-25y ^ 2[/tex]
By definition, the formula of square difference states that:
[tex]a ^ 2-b ^ 2 = (a + b) (a-b)[/tex]
In this case:
[tex]a = 4x\\b = 5y[/tex]
Then, we can factor the expression as:
[tex](4x + 5y) (4x-5y)[/tex]
Answer:
[tex](4x + 5y) (4x-5y)[/tex]
Final answer:
The expression [tex]16x^2-25y^2[/tex]is a difference of squares and factors into the product of two binomial conjugates, which is (4x + 5y)(4x - 5y).
Explanation:
The expression [tex]16x^2-25y^2[/tex] is a difference of squares, which is a special factoring case where you have two perfect squares separated by a subtraction sign. The difference of squares can be factored into the product of two binomials that are conjugates of each other. This means that they are identical except for the sign between their terms.
The factorization is:
Identify the square root of each term: [tex]\(4x\) and \(5y\)[/tex]Write the expression as the difference of squares: [tex]\((4x)^2 - (5y)^2\)[/tex]Factor into two binomials:[tex]\((4x + 5y)(4x - 5y)\)[/tex]Therefore, the factorization of the given expression is[tex]\((4x + 5y)(4x - 5y)\).[/tex]
which methods could you use to calculate the y-coordinate of the midpoint of a vertical line segment with endpoints at (0,0) and (0,15)?
A. Count by hand
B. Divide 15 by 2.
C. Add the endpoint.
D. Divide 1 by 15.
The y-coordinate of the midpoint of the vertical line segment is calculated by method B. Divide 15 by 2, which gives the midpoint's y-coordinate as 7.5.
Explanation:To calculate the y-coordinate of the midpoint of a vertical line segment with endpoints at (0,0) and (0,15), you can use the method of dividing the y-coordinates of the endpoints by 2. In this case, you would divide 15 by 2 to find the midpoint's y-coordinate, which is method B. Divide 15 by 2. This is because the midpoint of a line segment is found by averaging the coordinates of the endpoints, and for the y-coordinates you add them together and then divide by 2. So, the calculation is (0 + 15) / 2, which equals 7.5. Thus, the midpoint of the segment is at the point (0, 7.5).
Answers????? Very confused
Answer:
Step-by-step explanation:
12/7 cups of blueberries
Answer:
111 g
Hope this helps :)
Have a great day !
5INGH
Step-by-step explanation:
2 + 3 = 5
185 ÷ 5 = 37
2 : 3
( × 37 )
74 : 111
on a trip to the museum, Lance saw a replica of a circular shield used by ancient Greek soldiers if the circumference of the shield is 100.48 inches, ts radius is inches and the area of the front of the shield is aboutsquare inches
Answer:
If the circumference of the shield is 100.48 inches, its radius is 16 inches and the area of the front of the shield is about 803.84 square inches.
Explanation:
Circumference = 2x r x Pi implies r =Circumference / 2Pi=100.48/2x3.14=16
Area = Pi x r²=3.14 x 16²=804.84
Answer:
If the circumference of the shield is 100.48 inches, its radius is 16 inches and the area of the front of the shield is about 803.84 square inches.