The 4th term of the expansion is 8z³.
How to expand in mathematics?The expression to be expanded is (y + 2z)³
To expand a bracket means to multiply each term in the bracket by the expression outside the bracket
Therefore,
(y + 2z)³ = (y + 2z)(y + 2z)(y + 2z)
Therefore,
(y + 2z)(y + 2z) = y² + 2yz + 2yz + 4z²
y² + 2yz + 2yz + 4z² = y² + 4yz + 4z²
Hence,
y² + 4yz + 4z² (y + 2z) = y³ + 2y²z + 4y²z + 8yz² + 4yz² + 8z³
Therefore,
(y + 2z)³ = y³ + 2y²z + 4y²z + 8yz² + 4yz² + 8z³
(y + 2z)³ = y³ + 6y²z + 12yz² + 8z³
Therefore, the 4th term is 8z³
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The function shown can be used to determine the amount of money, indollars, in a savings account after m months. If no money is added orwithdrawn, which of the following is closest to the amount of money inthe account after 30 months?f(m) = 1500(1.003)^m
Given data:
The given function of amount of mmoney after m months is f(m)=1500(1.003)^m.
Substitute 30 for m in the given expression.
f(30)=1500(1.003)^(30)
=1500(1.094)
=1641
Thus, the total amount of money after 30 monnths is 1641.
It takes a sheet metal worker 2/3 of an hour to fabricate a fitting, How many fittings can a sheet metal worker
make in an 8 hour day?
12 fittings can a sheet metal worker make in 8 hours.
What is ratio calculator?
Ratio Calculator is a formula used to solve ratio problems to express two or three numbers ratio to its simplest form.
2/3 hours taken to fabricate = 1 sheet
8 hours taken to fabricate = 8/2/3
= 4(3)
= 12
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Help pleasee i want it today
Answer:
Since polynomials are used to describe curves of various types, people use them in the real world to graph curves. For example, roller coaster designers may use polynomials to describe the curves in their rides. Combinations of polynomial functions are sometimes used in economics to do cost analyses, for example. Polynomials are used in engineering, computer and math based jobs, in management, business and even in farming. In all careers requiring knowledge of polynomials, variables and constants are used to create expressions defining quantities which are known and unknown.
Step-by-step explanation:
hope this helps you
How do i write 4/5inch per hour as a ratio
Answer:
4/5 to 1
Step-by-step explanation:
you just put the numbers next to each other
Answer:
4 : 5 are 8 : 10 and 12 : 15
Step-by-step explanation:
Therefore, the two equivalent ratios of 4 : 5 are 8 : 10 and 12 : 15. Note: In this question we can't apply division method to get the answer in integer form because the G.C.F. of 4 and 5 is 1. That means, 4 and 5 cannot be divisible by any other number except 1.
Hannah reads at a constant rate of
3pages every 8minutes.
Write an equation that shows the relationship between
p, the number of pages she reads, and
m
mm, the number of minutes she spends reading.
The relationship between p, the number of pages she reads, and m, the number of minutes she spends reading is 8p = 3m.
It is given in the question that Hannah reads at a constant rate of 3 pages every 8 minutes.
We have to write an equation that represents the relationship between p, the number of pages she reads, and m, the number of minutes she spends reading.
If she reads 3 pages every 8 minutes, then
She reads 1 page every 8/3 minutes.
If she reads p pages , she will take 8p/3 minutes
If m represents the number of minutes she she spends reading p pages.
Then, we can write,
8p/3 = m
8p = 3m
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Nathan is planning to ride his bike for 24 minutes. Write an equation that Nathan can use to find d, the distance he will travel in 24 minutes, if his rate in miles per hours is represented by r
Answer:
Step-by-step explanation:
We are required to find the distance Nathan will travel.
Total distance travelled of Nathan is 2 miles
speed = Total distance travelled ÷ Total time take
total distance travelled = Speed × Total time taken.
Speed = 5 miles per hour
Time = 24 minutes
Convert minutes to hour
60 minutes = 1 hour
24 minutes = 0.4 hour
total distance travelled = Speed × Total time taken
= 5 miles per hour × 0.4 hour
= 2 miles
Therefore, total distance travelled of Nathan is 2 miles
What type of correlation is shown in this scatterplot 1. Perfect positive 2. Perfect Negavite 3. Low positive 4.High Negavite
SOLUTION
A Scatter Plot has points that show the relationship between two sets of data.
When the line shows a negative slope, the correlation is a negative correlation
Consider the image below
This shows a perfect Negative correlation between the set of data.
Hence
The Second option is Right(2)
help me please
thank you
Answer:
Domain: [1, 7], Range: [-4, 2]
Step-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
Hana is organizing a 3/4 mile fun run. There will be a water station every 1/4 of a mile after the start. How many water station will there be?
There will be 3 water stations along the fun run using the mathematical operation of division.
What is a mathematical operation?A mathematical operation uses addition, subtraction, division, or multiplication to reach a result after combining variables, numbers, and mathematical operands.
In this situation, we only use division to get the quotient, which is the number of water stations along the fun run.
The total distance for a fun run = 3/5 miles (0.75 miles)
The spread of the water station along a mile = every 1/4 mile (0.25 miles)
The number of water stations along the run = 3 (0.75/0.25)
Thus, Hana needs to station 3 water stations along the run by dividing the total distance by the expected spread.
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Match the function to the table of values 2. 7. yurt 3 8. y=r-7 9. y=x+2 I 10. = 3+1
If you use the values of the table for each of the equations, you can find the answers
Try Again3Graph the line with slopepassing through the point (-4,5)
THE RECTANGLE BELOW IS DILATED BY A SCALE FACTOR OF 3.6 TO CREATE A NEW RECTANGLE. WHICH OF THE FOLLOWING COILD BE THE DIMENSIONS OF THE NEW RECTANGLE? A: 14.4 CM x 5.4 B: 5.4 cm x C: 7.2 cm x 1.8 cm D: 14.4 cm x 7.2 cm.
ANSWER:
A: 14.4 CM x 5.4
STEP-BY-STEP EXPLANATION:
We must multiply the value of the scale factor by the original measures of the rectangle, like this:
[tex]\begin{gathered} AB=3.6\cdot1\frac{1}{2}=5.4 \\ BC=3.6\cdot4=14.4 \end{gathered}[/tex]Find the solution(s) for x in the equation below. 12 + 10.1 + 21 = 0 O A. I = -3; I = -7 OB. I = -3; 1 -3; r = 7 O c. 3; 1 = -7 3; D = 7 OD..I
Answer:
Choice A: x = -3, x = -7
Explanation:
To solve the equation for x, we use the quadratic formula which says that if you have an equation
Which of the following represents a linear function? these are the options a, c or b How do you know?these are the options it creates a simple shapeit passes the vertical line testit is a straight line
We want to identify the linear function.
Of course,
a linear function is going to be a line
The vertical line test is for understanding whether it is a function or not.
By vertical line test,
Picture 1 [passes]
Picture 2 [passes]
Picture 3 [fails]
Now, we can clearly see that Option B is the a straight line, hence a linear function.
30 year term calculation
In 30 years, the total amount would be $1,259,430.95 if the principal value is $63,000.
What is a loan amortization schedule?It is defined as the systematic way of representing of loan payments according to the time in which the principal amount and interest are mentioned in a list manner
It is given that:
P = 63,000
i = 5.3%
t = 30 years
[tex]\rm Total \ amount = P\times\dfrac{(\dfrac{r}{n})(1 + r/n)^{tn}}{(1 + r/n)^{tn}-1}[/tex]
After putting the values in the formula we get:
Total amount = $1,259,430.95
Thus, in 30 years, the total amount would be $1,259,430.95 if the principal value is $63,000.
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solve the system of equations for each variable x, y, and z. please show your work 2xy=z 4x+z=4y y=x+1
The solution of the system of equations 2xy = z, 4x + z = 4y, y = x + 1 are:
x = 1, y = 2, z = 4 and;
x = - 2, y = - 1, z = 4.
Consider the system of equations,
2xy = z ------------(1)
4x + z = 4y ------------(2)
y = x + 1 -------------(3)
Substituting equation (3) in equation (2),
4x + z = 4y
4x + z = 4( x + 1)
4x + z = 4x + 4
z = 4
Substituting equation (3) in equation (1),
2xy = z
2x( x + 1 ) = z
2x² + 2x = 4
x² + x = 2
Hence, x = 1, - 2
Therefore,
When x = 1,
y = x + 1 = 2
When x = - 2, y = x + 1 = - 1
So, the solution for the system of the equations are x = 1, y = 2, x = 4 and x = - 2, y = - 1, z = 4.
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find the absolute value |97| =
Absolute value means take the non-negative number of what is between the bars
|97|
Since 97 is already positive, the absolute value of 97 is 97
What is 201 divided by 12
Answer: 16.75
Step-by-step explanation:
201/12
The value of c must be greater than 0 1 3 7
The true statement about the triangle is the value of c must be greater than 3.
How to complete the statementThe figure that completes the question is added as an attachment
From the figure, we have the following parameters
The length of segment AB is 12 units.The length of segment AC is 15 units.The length of segment of BC is represented by the variable c
By the triangle inequality theorem, we have:
The sum of any two sides length is greater than the third length
This means that
12 + 15 > c
c < 27
Also, we have
15 + c > 12
c >-3
Lastly, we have
12 + c > 15
c >3
Using the list of options as a guide, we have x > 3 to be true
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A bank tellers’ hourly wage will increase from $24 to $27.60. What percent increase does this represent? An employee’s salary for Alar Services is $37,500. Next year, she will get an 8% increase in salary. How much is her new salary?
(a).A bank tellers’ hourly wage will increase from $24 to $27.60.
The increament n wage is
[tex](27.60-24)=3.6[/tex]Therefore, the percent of increament is
[tex]\frac{3.6}{24}\times100=15[/tex]Therefore, it represents 15% increament.
(b). An employee’s salary for Alar Services is $37,500. Next year, she will get an 8% increase in salary.
So, new salary is
[tex]37500+(37500\times\frac{8}{100})=40500[/tex]Therefore, new salary is $40500.
state the value of as a 5/7 recurring decimal
Answer:
The value of 5/7 recurring numbers is 714285
Explanation:
The given fraction 5/7 is the equivalent of
0.7142857142857142857142857142857142857142857142857142857142857142...
Notice that the recurring numbers are:
714285
find the acute angle between the lines 2y+x=1 and x+3y=6
Given the equations of the lines:
[tex]\begin{gathered} 2y+x=1 \\ x+3y=6 \end{gathered}[/tex]the given equations written in standard form, we will rewrite in in the slope-intercept form
So,
[tex]\begin{gathered} y=-\frac{1}{2}x+\frac{1}{2} \\ y=-\frac{1}{3}x+\frac{6}{3} \end{gathered}[/tex]So, the slopes of the lines are { -1/2, -1/3 }
The acute angle between the lines of slopes m1 and m2 is given by the formula:
[tex]\text{tan}\theta=|\frac{m_{1_{}}-m_2}{1+m_1m_2}|[/tex]Substitute with slopes of the lines
So,
[tex]\tan \theta=|\frac{-\frac{1}{2}-(-\frac{1}{3})}{1+(-\frac{1}{2})(-\frac{1}{3})}|=|\frac{-\frac{1}{6}}{1+\frac{1}{6}}|=\frac{1}{7}[/tex]so, the angle will be:
[tex]\theta=\tan ^{-1}(\frac{1}{7})=8.13\degree[/tex]So, the answer will be the acute angle = 8.13°
Determine whether the coordinate plane shows a reflection in the x-axis, y-axis, or neither.O neitherO X-axisy-axis
1) To determine a reflection across the x-axis, the rule to be followed is
Pre-Image Image
(x,y) --------------------> (x, -y)
A reflection across the y-axis follows this one:
Pre-Image Image
(x,y) --------------------> (-x, y)
2) Let's pick one point from the pre-image and the image on the graph
Since A (-2,0) and F (1,-3) then we cannot state that there was a reflection across the x-axis or y-axis.
3) The answer is neither
Some people advise that in very cold weather, you should keep the gas tank in your car more than half full. Irene’s car had 6.5 gallons in the 15-gallon tank on the coldest day of the year. Irene filled the tank with gas that cos $3.70 per gallon.
How much did Irene spend on gas?
After doing some mathematical operations, we can conclude that Irene spends $24.05 on 6.5 gallons of gas.
What are mathematical operations?An operation is a mathematical function that converts zero or more input values into an output value with a known value.The number of operands affects how complex the operation is.The order of operations refers to the rules that define the sequence in which multiple operations should be performed to solve an expression.PEMDAS is an abbreviation for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction (from left to right).So, the amount Irene spends on gas:
The gas in the tank is 6.5 gallons.The gas amount per gallon is $3.70.Then, the amount of 6.5 gallons of gas:
6.5 × 3.70 = $24.05Therefore, after doing some mathematical operations, we can conclude that Irene spends $24.05 on 6.5 gallons of gas.
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help me decide wheter this is SSS, SAS, or AA problemsI choose SAS, am I right?
Yes, they are similar triangles.
The answer is SSS
Which set of numbers are integers but not whole numbers or natural numbers?{V1, –4, V=5}IO{*}O {V2, , V3}O {0,1,2,3}O {-2, -3, - 4}
The set of whole numbers or natural numbers are the ones that appear naturally, which would go from 0 and beyond. While the set of integers are the numbers that don't have any decimal point, which would include negative numbers. Therefore the correct answer is the last option.
Wesley has just been hired for a new job and wants to work out his budget for each month. The healthinsurance plan he selected has an average monthly premium of $294. The average monthly cost of hiselectric bill is $199 and the phone/internet/cable package he wants costs an average of $110 eachmonth. If his monthly salary is $1900, estimate the amount of money he will have after paying thesebills each month.
Answer:
$1297
Explanation:
First, let's add all the costs that Wesley has each month, so
$294 + $199 + $110 = $603
Because the health insurance cost $294, the electric bill is $199 and the phone/internet/cable cost $110.
Then, To find the amount of money that he will have after paying these bills, we need to subtract $603 from his salary, so
$1900 - $603 = $1297
Therefore, the answer is $1297
y = 2x + 1y = -x - 2Solve the following system by graphing. What isthe solution?1. (-1, -3)2. (-1, 3)3. (-1, -1)4. (3, -1)
Which equation represents the relationship shown in
the graph?
Answer:
[tex]y\le-\frac{1}{4}x^{2}+\frac{1}{2}x+12[/tex]
Step-by-step explanation:
It has to have a y-int of +12 so that eliminates the first 2.
It needs to be contained inside the parabola therefore the x^2 value needs to be negative.
It needs to be shifted 1/2 to the right, therefore it needs a pos x value.
Hope that helps
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The table of 3 × 3 such that the sum of any row, column, or even diagonal is 30.3 has been created below.
What is the arithmetic operator?Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,
Summation = addition of two or more numbers or variable
Subtraction = Minus of any two or more numbers.
The third grid in first raw will be → 39.3 - (14.9 + 10.7) = 13.7
The third grid in second raw will be→ 39.3 - (13.7 + 11.3) = 14.3
The 2nd grid of 2nd raw will be → 39.3 - (17.9 + 11.3) = 13.1
The 1st grid in 2nd column will be→ 39.3 - (13.1+14.3) = 11.9
The 1st grid of 3rd raw will be → 39.3 - (14.9+11.9) = 12.5
The 2nd grid of 3rd raw will be → 39.3 - (12.5 + 11.3) = 15.5
Hence "The table of 3 × 3 such that the sum of any row, column, or even diagonal is 30.3 has been created below".
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