The two consecutive odd numbers such that the difference between their reciprocals is of 2/99 are given as follows:
9 and 11.
How to obtain the numbers?The two numbers are odd numbers and consecutive, hence they are symbolized as follows:
n and n + 2. (as n + 1 is even).
Their reciprocals are given as follows:
1/n.1/(n + 2).The difference of their reciprocals is obtained as follows:
1/n - 1/(n + 2) = 2/99.
The least common factor of n and n + 2 is of n x (n + 2), hence:
(n + 2 - n)/[n(n + 2)] = 2/99
2/[n(n + 2)] = 2/99.
As the numerators are equal, we take the denominators to solve for n as follows:
n(n + 2) = 99.
n² + 2n - 99 = 0.
(n - 9)(n + 11) = 0.
Applying the Factor Theorem, the solutions are given as follows:
n - 9 = 0 -> n = 9.n + 11 = 0 -> n = -11.We want the positive numbers, hence the numbers are:
n = 9 and n + 2 = 9 + 2 = 11.
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Simplify the expression 3a² + 1/4a + 3 + a² + 4 + 1/4a
The Correct answer while simplifying the given algebraic expression is: 4a²+1/2a+7
What are Algebraic Expressions?The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values. We learned how to express an unknown value using letters like x, y, and z in the fundamentals of algebra. Here, we refer to these letters as variables. Variables and constants can both be used in an algebraic expression. A coefficient is any value that is added before a variable and then multiplied by it.
Method to simplify any algebraic Expressions are :
By multiplying factors, remove any grouping symbols like brackets and parenthesis.If the words contain exponents, use the exponent rule to eliminate grouping.Add or subtract like terms to combine them.Add the constants togetherGiven:
=3a²+1/4a+3+a²+4+1/4a
=(3a²+a²)+(1/4a+1/4a)+(3+4)
=4a²+1/2a+7
So the Answer is
=4a²+1/2a+7
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Algebraic expressions
Delete the parentheses and reduce the similar terms
(2x -y² -2xy)-(xy -x -3y² -3x -8y²
Answer:
10y^2-3xy+6x
Step-by-step explanation:
Shirt Prices
$50, $35, $48,
$31, $34
What is the median price of the five shirts?
Answer: 35 would be the median
Step-by-step explanation: Put the numbers in order and whichever one is the middle value is the median
Answer:
35
Step-by-step explanation:
The median is the middle price when listed from smallest to largest
31, 34, 35, 48, 50
The middle price is 35
The median is 35
Using elimination, what is the solution to the following system?
2x+4y=16
-2x-3y=-13
Answer:
x=2, y=3. (2, 3).
Step-by-step explanation:
2x+4y=16
-2x-3y=-13
-----------------
y=3
2x+4(3)=16
2x+12=16
2x=16-12
2x=4
x=4/2
x=2
A line has a slope of 3/8 and passes through the point (15.2,-7)
The equation of the line in point-slope form is???
ANSWERS↓↓
The linear equation can be written in point-slope form as:
y + 7 = (3/8)*(x - 15.2)
So the correct option is A.
How to get the linear equation?A linear equation with a slope M and a known point (h, k), can be written in the point-slope form as:
y - k = m*(x - h)
Here we know that the slope of the line is 3/8, then we get:
y - k = (3/8)*(x - h)
And we also know that this line must pass through the point (15.2, -7), then we know that:
h = 15.2
k = -7
Replacing these values we get:
y + 7 = (3/8)*(x - 15.2)
Thus the correct option is the first one, A.
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Answer this please:
Look at the image and answer the question.
Answer:
hope it helps...........Two lines, A and B, are represented by equations given below:
Line A: y = x − 2
Line B: y = 3x + 4
Which of the following shows the solution to the system of equations and explains why?
Group of answer choices:
A) (−3, −5), because the point does not lie on any axis
B) (−3, −5), because the point satisfies both equations
C) (−4, −8), because the point satisfies one of the equations
D) (−4, −8), because the point lies between the two axes
a tee junction occurs when a connection meets an existing pipe of header at what angle? A 180 degree, B 30 degree, C. 90 degree, D.45 degree
Tee welding joints are formed when two members intersect at a 90-degree angle that makes the edges come together in the center of a plate or component
A 3kg cart moving with a speed of 4m/s collides with a 1 kg cart at rest
The speed of the carts after collision is 3 m/s.
What is the velocity after collision?We have to note that in this case, we would need to apply the principle of the conservation of linear momentum. This implies that the momentum before collision would have to be the same as the momentum after collision.
Then we have;
Momentum before collision = Momentum after collision thus;
(3 * 4) + ( 1 * 0) = (3 + 1) v
Note that the two carts are said to stick together and move with a common speed
Hence;
12 = 4v
v = 12/4
v = 3 m/s
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Suppose f is a function. If f(6) = -9, give an ordered pair of numbers that is a solution of the function.
The ordered pair solution to the function f(x) is (6, -9) because f(6) = -9,
What is an equation?An equation is an expression relating numbers and variables.
A function is a rule that defines the relationship between the dependent and independent variable. Dependent variables are variables that depends on others variable while independent variables are variables that does not depends on others variable
A solution to a function is the values of the variable that makes the equation true.
Given the function f(x) have solution of f(6) = -9. The ordered pair is (6, -9)
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A cake recipe calls for 2 1/3 cups of flour. If Gloria is planning on making 6 cakes for a bake sale, how many cups of flour will she need?
Answer: Gloria will need 14 cups of flour
Step-by-step explanation: 2 1/3 x 6 = 14
If ∠WOZ and ∠WOX are supplementary angles and ∠WOX and ∠XOY are complementary angles, then what is the value of x and m∠XOY?
Answer:
b.) x= 6, m∠XOY= 18
Step-by-step explanation:
comment if u need explanation :))
Only answer if you’re sure :) thank yew
Suppose a young couple deposits $1000 at the end of each quarter in an account that earns 7.6%, compounded quarterly, for a period of 8 years. After the 8 years, they start a family and find they can contribute only $200 per quarter. If they leave the money from the first 8 years in the account and continue to contribute $200 at the end of each quarter for the next 19 years, how much will they have in the account (to help with their child’s college expenses)?
If they leave the money from the first 8 years in the account and continue to contribute $200 at the end of each quarter for the next 19 years, the future value in the account to help with their child's college is $215,293.42.
How the future value is computed?The future value for this investment is computed in two separate solutions.
We have used an online finance calculator to facilitate the process.
The future value denotes the present deposits compounded at an interest rate.
Initial Deposits:
N (# of periods) = 32 quarters (8 years x 4)
I/Y (Interest per year) = 7.6%
PV (Present Value) = $0
PMT (Periodic Deposit) = $1,000
Results:
FV = $43,489.87
Sum of all periodic payments = $32,000.00
Total Interest = $11,489.87
Subsequent Deposits:
N (# of periods) = 76 quarters (19 years x 4)
I/Y (Interest per year) = 7.6%
PV (Present Value) = $43,489.87
PMT (Periodic Payment) = $200
Results:
Future Value (FV) = $215,293.42
Sum of all periodic payments = $15,200 ($200 x 76 quarters)
Total Interest = $156,603.55
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An Item costs $450 Before tax. and the sales tax is $31.50
Find the sales tax rate. Write your answer as a percentage
The tax rate of an Item that costs $450 Before tax. and the sales tax is $31.50 is 7%
What is tax rate?The tax rate is the percentage of an income or an amount of money that has to be paid as tax.
To find the tax rate of $31.50 from $450
The formula is
Amount taxed/Principal amount x 100
= $31.50/$450 x100
=$3150/450
=7%
Hence, the tax rate is 7%
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1+1+1+1=4
2+2+2+2=16
3+3+3+3=?
Answer:
12
Step-by-step explanation:
he average movie admission price for a recent year was $7.18. The population variance was 3.81. A random sample of 15 theater admission prices had a mean of $8.02 with a standard deviation of $2.08. At α = 0.05, is there sufficient evidence to conclude a difference from the population variance? Assume the variable is normally distributed.
Answer:
Since the calculated value of z= 1.6279 does not fall in the critical region Z ≥ ±1.96 we conclude that there is no difference between the population variance and the sample variance.
Step-by-step explanation:
The data given is
Population mean μ= $ 7.18
Population variance= σ²= 3.81
Population Standard Deviation = √σ²= √3.81= 1.952
Sample Mean= x`= $ 8.02
Sample Standard Deviation =s = $ 2.08
Sample Size = 15
Significance Level = ∝= 0.05
The null and alternate hypotheses are
H0: σ1=σ2 against the claim that Ha: σ1≠ σ2
where σ1 is the population variance and
σ2 is the sample variance
The rejection region is Z ≥ ±1.96 for two tailed test at ∝= 0.05
The test statistic z is used
z= x`- μ/ σ/√n
Putting the values
Z= 8.02-7.18/1.952/√15
z= 0.84/0.51599
z= 1.6279
Since the calculated value of z= 1.6279 does not fall in the critical region Z ≥ ±1.96 we conclude that there is no difference between the population variance and the sample variance.
The point (0,0) is located on a line with slope of 3/4. which point could also be located on the line?
Answer:
Below
Step-by-step explanation:
The equation of the line will be y = 3/4 x pick ANY value of 'x' to find the corresponding 'y' value
Say x = 8 then y = 6 8,6 is a point on the line
Answer:
(1 , 0.75)
(2 , 1.5)
(3 , 2.25)
(4 , 3)
(5 , 3.75)
(4 , 3)
(6 , 4.5)
(7 , 5.25)
(8 , 6)
(9 , 6.75)
(10 , 7.5)
(11 , 8.25)
(12 , 9)
Step-by-step explanation:
To find the other points we must put the given information into the slope-intercept form: [tex]y=mx+b[/tex] m = slope and b = y-intercept
[tex]y=\frac{3}{4} x+0[/tex] or [tex]y=\frac{3}{4} x[/tex]
Then just simply start inputting any numbers for x so you can solve for [tex]y=\frac{3}{4} x[/tex] to get the other points of the line.
graph f and h , write h in terms of f, describe the transformation from the graph of f to the graph of h .
the equation :
f(x) = 3x ; h(x) = 3x - 5
h(x) = f(x) + 5 represents a vertical shift of 5 units down from the graph of f(x) = 3x. The slope of the two lines is the same, but the y-intercept of h(x) is different from f(x).
What is the graph of the function?A graph of a function is a visual representation of the relationship between the input values (x-coordinates) and the output values (y-coordinates) of a function. It is a way to visualize the behavior of the function and its relation to the x and y axes.
Here,
We can draw the graph as
h(x) = 3x - 5 can be written in terms of f(x) by adding 5 to the output of f(x)
h(x) = f(x) + 5
The transformation from the graph of f(x) to the graph of h(x) is a vertical shift of 5 units down. This is because the original function f(x) is shifted down by 5 units to get h(x). The slope of the two lines is still the same, 3, but the y-intercept of f(x) is (0,0) and the y-intercept of h(x) is (-5/3,0). The transformation causes the graph of h(x) to be shifted down 5 units along the y-axis, while the slope and x-intercept of the graph remain the same.
Hence, h(x) = f(x) + 5 represents a vertical shift of 5 units down from the graph of f(x) = 3x. The slope of the two lines is the same, but the y-intercept of h(x) is different from f(x).
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Rewrite 12x4y3 − 48x3y4 using a common factor.
Answer: 12x^3 y^3 (x − 4y)
(GCF is: 12x^3 y^3)
Step-by-step explanation:
This is the best I can do, sorry that I don't have an explanation.
Can someone solve this?
Answer:
u=4
v=2√3
Step-by-step explanation:
The 30-60-90 triangle theorem states that the shortest side of a triangle is half of the hypotenuse, so 2*2=4. So, the hypotenuse, u, is 4.
The longest leg is √3 times greater than the shortest leg, so 2*√3=2√3. So, the longest leg, v, is 2√3.
Given m | n, find the value of x and y.
m
(2y+17) (4x-3)°
(7x+18)°
n
Answer:
the first one is scamer
Step-by-step explanation:
help me report that userdescribe the translation of the figure ABCD. Complete the sentence to explain your answer
Please please help!!!!
Answer:
280 inches
Step-by-step explanation:
8 x 8 = 64
9 × 24 = 216
64 + 216 = 280
The scatter plot shows the number of chin-ups and push-ups completed by a sample of fourth grade students.
What is the median number of chin-ups for all students?
Student Name
Label
Number of Chin-ups and Push-ups
10-
9
А
B
H
B
8
Jared
Tonya
Alex
Rishab
L
D
G
с
7-
F
D
K к
Gao
E
E
А
с
F
Riki
Anne
5-
4-
3
2-
G
Amira
H
12
/
Samuel
Lily
0
J
1
6
8
9
10
Abdu
K
2
Chin-ups
Mike
Answer:
9
Step-by-step explanation:
One did 10,one did 9, and 1 did 8 and 9 is the median number of those 3 numbers.
Answer:
Abdu, Tonya, Gao, Lily, Mike, Rishab
Step-by-step explanation:
HELP MEEEEEE 25 POINTS
Answer:
m arc 1 = 65°, m arc 3 = 129°, m ∠9 = 25.5°, m ∠ 10 = 57.5°
Step-by-step explanation:
m arc 1 => 180 - 115 = 65°
m arc 3 => 180 - 51 = 129°
m ∠9 => 51 ÷ 2 = 25.5°
m ∠ 10 => 115 ÷ 2 = 57.5°
pls help and give only correct answers
Answer:b
Step-by-step explanation:
i took that test
Length of insect is 23mm and length of drawing is 85mm. So what is Magnification
Answer:
The magnification is the ratio of the size of the image to the size of the object. In this case, the length of the insect is the size of the object, and the length of the drawing is the size of the image.
To find the magnification, we can divide the size of the image by the size of the object:
Magnification = size of image / size of object
Plugging in the values, we have:
Magnification = 85mm / 23mm
Calculating, we find that the magnification is approximately 3.7. This means that the length of the drawing is 3.7 times the length of the insect.
Step-by-step explanation:
a rectangular table is 5 1/4 feet by 3 3/4feet. what is the area of the table?
Answer:Area = Length times Width
5 1/4 times 3 3/4
5 x 4 + 1 = 21
21/4
3 x 4 +3 = 15
15/4
21/4 x 15/4 = 315 / 16 or 19 11/16 ft^2
Step-by-step explanation:
can someone please help me with this math question?
9514 1404 393
Answer:
D. 0, 1, or 2 solutions
Step-by-step explanation:
The line represented by g(x) may intersect the parabola represented by f(x) in 0, 1, or 2 places, as illustrated in the attachment. The curves are different shapes, so cannot overlap to give infinite solutions.
The system may have 0, 1, or 2 solutions.