1. According to the affordability formulas given, Joe-Bob cannot afford to take out another loan.
2. Joe-Bob should follow the affordability formulas if he wants to live without financial stress caused by debts.
3. Joe-Bob may decide not to follow the affordability formula, if he can reduce his fixed monthly payments or increase his income.
4. Taking out the car loan will force Joe-Bob to increase his DTI and reduce his savings, investments, and discretionary spending.
What is affordability?Affordability refers to a person's financial ability to afford some fixed expenses without impacting negatively the variable expenses.
Affordability can be measured as a Debt To Income (DTI) ratio.
Data and Calculations:Current monthly income = $3,500
Monthly mortgage payment = $900
Monthly student loan payment = $350
Total monthly debt payment = $1,250
Debt To Income (DTI) = 35.7% ($1,250/$3,500 x 100)
Thus, with a DTI of 36%, Job Bob should not take out an additional car loan.
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The base of the following pyramid is a square. If the volume of the pyramid is 400 feet³, what is the missing length? Round the answer to the nearest hundredth. The S=11ft
The length of the missing side is 9.92 ft given that the base of the following pyramid is a square, base side length(s) is 11 ft and the volume of the square pyramid is 400 ft³. This can be obtained using the formula of finding the volume of the pyramid with base as square.
Calculate the length of the missing side:The formula of finding the volume of the pyramid with base as square is,
⇒ V = s²h/3
where V is the volume of the square pyramid, s is the side length of the base and h is the height of the square pyramid.
Here in the question it is given that,
it is a pyramid with base as squarethe side length of the base is 11 ftvolume of the square pyramid is 400 ft³that is, s = 11 ft, V = 400 ft³
By using the formula of finding the volume of the pyramid with base as square we get,
V = s²h/3
400 = (11)²h/3
By rearranging the equation we get,
h = 400 × 3/11²
h = 9.92 ft
Hence the length of the missing side is 9.92 ft given that the base of the following pyramid is a square, base side length(s) is 11 ft and the volume of the square pyramid is 400 ft³.
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Which function has the greatest y-intercept?
Answer:
Second one from the left
Answer:
b
Step-by-step explanation:
edg 22'
by selling an article for rs.144 a man loses 1÷7 of his outlay. If it is sold for rs. 189. What is the gain or loss percentage.
Answer:
5250%
Also, if you could label this brainliest that would be a great help!
Thanks xx
-Dante
Step-by-step explanation:
1) Formulate
2) Calculate
3) Transform expression
4) Calculate
5) Invert and multiply
6) Simplify
7) Calculate
8) Calculate
9) Rewrite the number
10) Calculate
11) Calculate
12) Convert the number
You’re done!
please solve this question asap
Step-by-step explanation:
[tex]y = \sqrt{4x + 6} [/tex]
[tex] {y}^{2} = 4x + 6[/tex]
[tex] {y}^{2} - 6 = 4x[/tex]
[tex] \frac{1}{4} ( {y}^{2} - 6) = x[/tex]
Swap x and y
[tex] \frac{ {x}^{2} - 6 }{4} = y[/tex]
If f(x)=√x^3 and (fog)(x)=√√x, then g(64) =
The value of g(x) is (x^3+5) and g(64) = 262149.
According to the statement
we have given that the
f(x)=√x^3 and (fog)(x)=√(x^3+5) and we have to find the value of the g(64).
So, For find the value of g(64), Firstly we have to find the g(x).
So,
We given that
f(x)=√x^3 and (fog)(x)=√(x^3+5)
And here the formula used is
(f o g)(x) = f (g(x))
here (fog)(x)=√(x^3+5) and f(x)=√x^3
From this we get g(x) is (x^3+5)
So,
g(x) = (x^3+5) and
g(64) = ((64)^3+5)
g(64) = 262149.
So, The value of g(x) is (x^3+5) and g(64) = 262149.
Disclaimer: This question was incomplete. Please find the full content below.
Question:
If f(x)=√x^3 and (fog)(x)=√(x^3+5). Then find the value of g(64).
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I take this to mean [tex]f(x) = \sqrt{x^3}[/tex] and [tex](f\circ g)(x) = \sqrt x[/tex].
Let's first find the inverse of [tex]f[/tex].
[tex]f\left(f^{-1}(x)\right) = \sqrt{\left(f^{-1}(x)\right)^3} = x \\\\ \implies \left(f^{-1}(x)\right)^3 = x^2 \\\\ \implies f^{-1}(x) = x^{2/3}[/tex]
(Note that [tex]f[/tex] is defined only if [tex]x^3\ge0[/tex], or [tex]x\ge0[/tex].)
Apply the inverse of [tex]f[/tex] to [tex]f\circ g[/tex].
[tex](f\circ g)(x) = f(g(x)) = \sqrt x \\\\ \implies f^{-1}\left(f(g(x))\right) = f^{-1}(\sqrt x) \\\\ \implies g(x) = \left(\sqrt x\right)^{2/3} = \left(x^{1/2}\right)^{2/3} = x^{1/3} = \sqrt[3]{x}[/tex]
Then
[tex]g(64) = \sqrt[3]{64} = \sqrt[3]{4^3} = \boxed{4}[/tex]
Define the linear programming problems. State the key terms in L.P.P.
Answer:
Step-by-step explanation:
Linear Programming Problems (LPP): Linear programming or linear optimization is a process which takes into consideration certain linear relationships to obtain the best possible solution to a mathematical model. It is also denoted as LPP. It includes problems dealing with maximizing profits, minimizing costs, minimal usage of resources, etc. These problems can be solved through the simplex method or graphical method.
Linear Programming For Class 12
Linear Programming
Linear Programming Worksheet
The Linear programming applications are present in broad disciplines such as commerce, industry, etc. In this section, we will discuss, how to do the mathematical formulation of the LPP.
Mathematical Formulation of Problem
Let x and y be the number of cabinets of types 1 and 2 respectively that he must manufacture. They are non-negative and known as non-negative constraints.
The company can invest a total of 540 hours of the labour force and is required to create up to 50 cabinets. Hence,
15x + 9y <= 540
x + y <= 50
The above two equations are known as linear constraints.
Let Z be the profit he earns from manufacturing x and y pieces of the cabinets of types 1 and 2. Thus,
Z = 5000x + 3000y
Our objective here is to maximize Z. Hence Z is known as the objective function. To find the answer to this question, we use graphs, which is known as the graphical method of solving LPP. We will cover this in the subsequent sections.
Graphical Method
The solution for problems based on linear programming is determined with the help of the feasible region, in case of graphical method. The feasible region is basically the common region determined by all constraints including non-negative constraints, say, x,y≥0, of an LPP. Each point in this feasible region represents the feasible solution of the constraints and therefore, is called the solution/feasible region for the problem. The region apart from (outside) the feasible region is called as the infeasible region.
The optimal value (maximum and minimum) obtained of an objective function in the feasible region at any point is called an optimal solution. To learn the graphical method to solve linear programming completely reach us.
Linear Programming Applications
Let us take a real-life problem to understand linear programming. A home décor company received an order to manufacture cabinets. The first consignment requires up to 50 cabinets. There are two types of cabinets. The first type requires 15 hours of the labour force (per piece) to be constructed and gives a profit of Rs 5000 per piece to the company. Whereas, the second type requires 9 hours of the labour force and makes a profit of Rs 3000 per piece. However, the company has only 540 hours of workforce available for the manufacture of the cabinets. With this information given, you are required to find a deal which gives the maximum profit to the décor company.
Linear Programming problem LPP
Given the situation, let us take up different scenarios to analyse how the profit can be maximized.
He decides to construct all the cabinets of the first type. In this case, he can create 540/15 = 36 cabinets. This would give him a profit of Rs 5000 × 36 = Rs 180,000.
He decides to construct all the cabinets of the second type. In this case, he can create 540/9 = 60 cabinets. But the first consignment requires only up to 50 cabinets. Hence, he can make profit of Rs 3000 × 50 = Rs 150,000.
He decides to make 15 cabinets of type 1 and 35 of type 2. In this case, his profit is (5000 × 15 + 3000 × 35) Rs 180,000.
Similarly, there can be many strategies which he can devise to maximize his profit by allocating the different amount of labour force to the two types of cabinets. We do a mathematical formulation of the discussed LPP to find out the strategy which would lead to maximum profit.
what is the area of the figure bellow?
Answer:
The area of the figure is C. 48.5 cm²
Calculate the following, and place the calculated solution on the appropriate line. In all cases, assume the companies that are the subject of the question are US companies using US GAAP.
a. Berful sells one product. It had one item in beginning inventory that cost $10,000, and purchased 4 more items during the accounting period. The cost changed with each purchase, as shown below:
Item Cost of Item
First $12,000
Second 14,000
Third 15,000
Fourth 16,000
If 3 items were sold during the year, calculate the cost of ending inventory using the following cost flow assumptions (Remember beginning inventory in your calculations!):
FIFO $_____________
LIFO $_____________
Weighted Average $_____________
b. Berful purchased a machine on the first day of the accounting period at a cost of $22,000. The machine is expected to have a life of 5 years or 20,000 units, and a salvage value of $2,000. Calculate the second year depreciation expense using the following depreciation methods (6,000 units produced in year 2):
Straight-line $_____________
Double-declining Balance $_____________
Units-of-production $_____________
c. Calculate the correct balance of cash to be included in the Cash account on the firm’s balance sheet by preparing a bank reconciliation of its checking account from the data given below:
Item Amount
Balance per Bank Statement $16,655.44
Balance per Books $12,091.94
Deposits in Transit $ 2,234.81
Outstanding Checks $ 6,808.16
Bank Service Charge $ 9.85
Correct balance of cash in this account $__________
d. Show the accounting entry required as a result of the above bank reconciliation in the space below:
e. If Berful uses the Allowance Method to determine its bad debt expenses, establishing its estimate as 1% of Net Sales, and Net Sales total $600,000, show the adjusting journal entry required if the Allowance for Bad Debts account has a debit balance of $2,000?
a) The calculation of the cost of ending inventory using the following cost flow assumptions are as follows:
FIFO $31,000 ($15,000 + $16,000)
LIFO $22,000 ($10,000 + $12,000)
Weighted Average $26,800 ($13,400 x 2)
b) The calculation of the second-year depreciation expense using these depreciation methods is as follows:
Straight-line $4,000
Double-declining Balance $5,280
Units-of-production $6,000.
c) The correct balance of cash to be included in the Cash account on the firm’s balance sheet based on the bank reconciliation is $12,082.09.
d) The accounting entry required for the bank reconciliation is as follows:
Debit Bank Service Charges $9.85
Credit Cash Account $9.85
To record the bank service charge for the period.e) The adjusting journal entry required is as follows:
Debit Bad Debt Expense $8,000
Credit Allowance for Bad Debts $8,000
To record the bad debt expense for the period.Data and Calculations:a) Berful Company:
Beginning inventory = $10,000
Purchases:
First $12,000
Second 14,000
Third 15,000
Fourth 16,000
The total cost of goods available for sale = $67,000
Weighted average cost = $13,400 ($67,000/5)
Total items available for sale = 5 items (1 + 4)
Sales = 3 items
Ending inventory = 2 items (5 - 3)
b) Cost of machine = $22,000
Estimated useful life = 5 years or 20,000 units
Salvage value = $2,000
Depreciable amount = $20,000 ($22,000 - $2,000)
Straight-line Method:Annual depreciation for second year = $4,000 ($20,000/5)
Double-declining balance:Depreciation rate = 40% (100/5 x 2)
For the first year = $8,800 ($22,000 x 40%)
Declined balance = $13,200 ($22,000 - $8,800)
For the second year = $5,280 ($13,200 x 40%)
Units-of-production Method:Depreciation per unit = $1 ($20,000/20,000)
For the second year, Depreciation = $6,000 ($1 x 6,000)
c) Bank Reconciliation Statement:Balance per Bank Statement $16,655.44
Add: Deposits in Transit $ 2,234.81
Less: Outstanding Checks $ 6,808.16
Balance as per Cash Book $12,082.09
Cash Book Adjustment:Balance per book $12,091.94
Bank Service Charge ($ 9.85)
The correct balance of cash in this account $12,082.09.
Bank Service Charges $9.85 Cash Account $9.85
e) Data and Calculations:Allowance for Bad Debts = $2,000 Debit
Net Sales = $600,000
Estimated allowance for bad debt expenses = 1% of Net Sales
= $6,000 ($600,000 x 1%)
Bad Debt Expense $8,000 Allowance for Bad Debts $8,000 ($2,000 + $6,000)
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Question 8
What is wrong with the following equation: 8 + (6/2) = 17-5
The loft
Answer:
11=12
they are not equal to each other
Step-by-step explanation:
8+(6/2)=17-5
8+3=12
11=12
hope this helps
A pack of soil weighs 43 lbs. Each plant pot requires just 12 lbs of soil.
Calculate how many plant pots can be filled.
cual es el valor de 15+b=23
(GIVING BRAINLYST)Which expression represents the following statement? Multiply 7 by the sum of 6 and 3, and then subtract the quotient of 4 and 2. 07x (6+3)-4+2 07+6 (3+4) x 2 - 07+6+3 (4+2) 7x (6+3)+4-2
The expression representing the given statement is 7×(6+3)-(4÷2). Option A is correct.
Given the statement is Multiply 7 by the sum of 6 and 3, and then subtract the quotient of 4 and 2.
Firstly, we will break the statement in two parts that is Multiply 7 by the sum of 6 and 3 and second part is subtract the quotient of 4 and 2.
Multiply 7 by the sum of 6 and 3 means there is addition sign between 6 and 3 and the addition of 6 and 3 is multiply with 7, we get
7×(6+3) ......(1)
subtract the quotient of 4 and 2 means 4 is divisible by 2 and this is subtract means there is a minus sign, we get
-(4÷2) .....(2)
Combine equation (1) and (2), we get
7×(6+3)-(4÷2)
Hence, the expression which represents the given statement Multiply 7 by the sum of 6 and 3, and then subtract the quotient of 4 and 2 is 7×(6+3)-(4÷2).
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Find the measures of x and y
Answer:
x = 159; y = 140
Step-by-step explanation:
a = 40
a + y = 180
y = 180 - 40
y = 140
b = 61
b = (180 - x) + a
61 = 180 - x + 40
x = 159
Answer:
m∠x = 159°
m∠y = 140°
Step-by-step explanation:
PART I: Find the measure of yGiven information
∠a = 40°
Given formula
∠a + ∠y = 180° (Supplementary angles)
Substitute values into the formula
40 + ∠y = 180
∠y = 180 - 40
[tex]\Large\boxed{\angle y=140^\circ}[/tex]
PART II: Find the measure of xGiven information
∠b = 61°
∠c = Supplementary angle of ∠b
Given formula
∠b + ∠c = 180°
Substitute values into the formula
61 + ∠c = 180
∠c = 180 - 61
∠c = 119°
Determine the value of ∠x
∠x = ∠a + ∠c (Exterior angle theorem)
∠x = (40) + (119)
[tex]\Large\boxed{\angle x=159^\circ}[/tex]
Hope this helps!! :)
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For the function given below, find a formula for the Riemann sum obtained by dividing the interval (0, 3) into n equal subintervals and us right-hand endpoint for each Then take a limit of this sum as c_{k}; n -> ∞ to calculate the area under the curve over [0, 3] . f(x) = 2x ^ 2 Write a formula for a Riemann sum for the function f(x) = 2x ^ 2 over the interval [0, 3]
Splitting up [0, 3] into [tex]n[/tex] equally-spaced subintervals of length [tex]\Delta x=\frac{3-0}n = \frac3n[/tex] gives the partition
[tex]\left[0, \dfrac3n\right] \cup \left[\dfrac3n, \dfrac6n\right] \cup \left[\dfrac6n, \dfrac9n\right] \cup \cdots \cup \left[\dfrac{3(n-1)}n, 3\right][/tex]
where the right endpoint of the [tex]i[/tex]-th subinterval is given by the sequence
[tex]r_i = \dfrac{3i}n[/tex]
for [tex]i\in\{1,2,3,\ldots,n\}[/tex].
Then the definite integral is given by the infinite Riemann sum
[tex]\displaystyle \int_0^3 2x^2 \, dx = \lim_{n\to\infty} \sum_{i=1}^n 2{r_i}^2 \Delta x \\\\ ~~~~~~~~ = \lim_{n\to\infty} \frac6n \sum_{i=1}^n \left(\frac{3i}n\right)^2 \\\\ ~~~~~~~~ = \lim_{n\to\infty} \frac{54}{n^3} \sum_{i=1}^n i^2 \\\\ ~~~~~~~~ = \lim_{n\to\infty} \frac{54}{n^3}\cdot\frac{n(n+1)(2n+1)}6 = \boxed{18}[/tex]
Solve for n:
(n+4)/10 = (n-8)/2
Answer:
n=11
Step-by-step explanation:
(n+4)/10 = (n-8)/2
We can solve using cross products
(n+4) * 2 = 10 * ( n-8)
Distribute
2n+8 = 10n -80
Subtract 2n from each side
2n+8-2n = 10n-80-2n
8 = 8n-80
Add 80 to each side
8+80= 8n-80+80
88 = 8n
Divide each side by 8
88/8 = 8n/8
11 = n
Answer: n=11
Step-by-step explanation:
(n+4)/10 = (n-8)/2
multiply both sides by 10
n+4 = (n-8)/2*10
cancel
n+4=(n-8)*5
n+4=5(n-8)
multiply
n+4=5n-40
subtract both sides by 5n
n-5n+4=-40
subtract both sides by 4
n-5n=-40-4
subtract the like terms
-4n=-44
cancel the negatives
4n=44
divide each side by 4
n=11
find the square roots by division method of 151,321
Answer: 389 is the square root.
Answer:
389 is the square root
Step-by-step explanation:
BRAINIEST PLS
Find the equation of the line that passes through point (6, 1) with the x-intercept of 2.
Answer:
○ [tex]y = \frac{1}{4}x - \frac{1}{2}[/tex]
Step-by-step explanation:
To find the equation of the line, let's first consider the points whose coordinates we have been given:
• (6, 1)
• (2, 0).
The point (2, 0) is what is called the x-intercept, which is the point where the line crosses the x-axis. This means that at this point, the y-coordinate of the line is 0.
Next, let's calculate the slope (gradient) of the line using the formula:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
where:
m = gradient,
[tex](x_2, y_2)[/tex] and [tex](x_1, x_2)[/tex] = points on the line.
Using the formula:
[tex]m = \frac{1 - 0}{6 - 2}[/tex]
⇒ [tex]m =\bf \frac{1}{4}[/tex]
Finally, now that we have two points on the line as well as the line's slope, we can use the following formula to find the equation of the line:
[tex]\boxed{y - y_1 = m(x - x_1)}[/tex]
You can use any of the points on the line as [tex]y_1[/tex] and [tex]x_1[/tex].
Using (2, 0):
[tex]y - 0 = \frac{1}{4}( x - 2)[/tex]
⇒ [tex]y = \frac{1}{4}x - \frac{1}{2}[/tex]
Therefore the equation of the line is [tex]y = \frac{1}{4}x - \frac{1}{2}[/tex].
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NO LINKS!! Please help me with this problem
Answer:
[tex]\frac{x^2}{784}+\frac{y^2}{400}=1[/tex]
Step-by-step explanation:
Horizontal Major Axis:
[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}[/tex]
Vertical Major Axis:
[tex]\frac{(y-k)^2}{a^2}+\frac{(x-h)^2}{b^2}+[/tex]
So these two expressions are essentially the same with the only difference being the location of "a" and "b". The length of the major axis will be "2a" and the length of the minor axis will be "2b". The way I remember this is because when you have the horizontal major axis the "a" value is in the denominator of the (x-h) and I think of "x" as a horizontal value, since it moves a point horizontally. When you have a vertical major axis the "a" value is in the denominator of (y-k) and I think of "x" as a vertical value, since it moves a point vertically.
So just by looking at the graph, you can easily determine that the eclipse has a horizontal major axis. This can be further proven, since the distance from the origin on the right side is 28, and the distance from the the top to the origin is only 20.
So you could set up an equation to solve for a, since 2a = length of major axis, but since we're given the two points, the "a" value is really just the length from the origin to the right/left side, and combining these together you get the value of 2a/major axis, but you don't have to do that. So by looking at the graph you'll see the distance from the origin to the right side is 28. This means "a=28"
You can do the same thing here for the "b" value, and since the top is 20 units away from the origin, "b = 20"
So now let's set up the equation:
[tex]\frac{x^2}{28^2} + \frac{y^2}{20^2}=1[/tex]
Square the values in the denominator
[tex]\frac{x^2}{784}+\frac{y^2}{400}=1[/tex]
Teresa bought a new desktop computer. One side of the desktop screen is 14 inches and the other side is 18 inches. What is the length of the diagonal of the desktop screen
Given the width and length of Teresa's new desktop computer, the length of the diagonal of the desktop screen is approximately 22.8 inches.
What is the length of the diagonal of the desktop screen?If a diagonal line cuts through a rectangle, it forms two equal right triangles. the side lengths of this triangle can be easily determined using Pythagoras theorem. Pythagoras theorem is expressed as;
c² = a² + b²
Where c is the hypotenuse or diagonal, a is base length and b is perpendicular height.
Given the data in the question;
Perpendicular height b = 14inBase length a = 18inHypotenuse or Diagonal c = ?We substitute into the equation above.
c² = a² + b²
c² = (18in)² + (14in)²
c² = 324in² + 196in²
c² = 520in²
c = √( 520in² )
c = 22.8in
Given the width and length of Teresa's new desktop computer, the length of the diagonal of the desktop screen is approximately 22.8 inches.
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Claim: Fewer than 94% of adults have a cell phone. In a reputable poll of 1057 adults, 89% said that they have a cell phone. Find the value of the test statistic. The value of the test statistic is nothing. (Round to two decimal places as needed.)
Answer:
suma todos los decimales
Step-by-step explanation:
empieza sumando 1059-94%eso te da 993,58 luego le sumas 89% lo que te da 884,2862 espero haberte ayudado
hey can anyone give me the answers to the questions that are blank
The value of the rate of change of the function is 14a + 7h
Rate of change of functionThe rate of change of function is also known as the slope expressed according to the equation shown below;
f'(x) = f(a+h)-f(a)/h
Given the function below expressed as:
f(x) =1 + 7x^2
Determine the function f(a)
To determine the function, simply replace x with 'a" to have:
f(a) =1 + 7a^2
Determine the function f(a+h)
f(a+h) = 1 + 7(a+h)^2
f(a + h) = 1 + 7(a^2+2ah+h^2)
f(a + h) = 1 + 7a^2 + 14ah + 7h^2
To determine the rate of change
f'(x) = f(a+h)-f(a)/h
f'(x) = 1 + 7a^2 + 14ah + 7h^2 - 1 - 7a^2/h
f'(x) = + 14ah + 7h^2/h
f'(x) = 14a + 7h
Hence the value of the rate of change of the function is 14a + 7h
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Set W consists of the even whole numbers from 2 to 20, inclusive. If a number is selected at random from set W, then what is the probability that the number is a
multiple of 4 and also a multiple of 6?
Answer:
1/19
Step-by-step explanation:
The number in the set that are a multiple of both 4 and 6 is 12.
This is one number out of the 19 numbers in the set, so the probability is 1/19.
Enter the correct answer in the box.
The function f(x) = 7x + 1 is transformed to function g through a horizontal compression by a factor of 1/3 What is the equation of function g?
Substitute a numerical value for k into the function equation.
Using translation concepts, the equation for function g is given by:
g(x) = 7x/3 + 1.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
Supposing that we have a function f(x), a horizontal compression by a factor of a is equivalent to finding f(ax).
In this problem, the function is:
f(x) = 7x + 1.
For the horizontal compression by a factor of 1/3, we have that:
g(x) = f(1/3x) = 7x/3 + 1.
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Find the slope of the line. On a coordinate plane, a line goes through (0, negative 6) and (2, 0). a. Negative one-third c. 3 b. One-third d. Negative 3 Please select the best answer from the choices provided A B C D
The slope of the line that passes through between (0, -6) and (2, 0) is: C. 3.
What is the Slope of a Line?The slope of a line can be defined as the measure of the ratio of the vertical distance to the horizontal distance that exists between two points on a coordinate plane.
How to Find the Slope of a Line?If we are given two points on a line, (x1, y1) and (x2, y2), the slope (m) is the rise/run = change in y / change in x = (y2 - y1)/(x2 - x1).
Given the following coordinates of two points as follows, (0, -6) and (2, 0), let:
(0, -6) = (x1, y1)
(2, 0) = (x2, y2)
Plug in the values into the slope formula to find the slope:
Slope (m) = (0 - (-6)) / (2 - 0)
Slope (m) = (0 + 6) / (2 - 0) [minus multiplied by minus is plus]
Slope (m) = (6) / (2)
Slope (m) = 3
Thus, the slope of the line that passes through between (0, negative 6) and (2, 0) is calculated as: C. 3.
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PLEASE HELP FAST (6 1/7 divided by x + 3 5/9) / 4 1/6 = 1 1/3 what is x
Answer:
0.524
Step-by-step explanation:
That is the answer not really sure tho
How do I this please
(i) The expanded form of (1 / 2 - 2 · x)⁵ in ascending form is 1 / 32 - (5 / 8) · x + 5 · x² - 20 · x³ + 40 · x⁴ - 32 · x⁵.
(ii) The coefficient of x³ from (1 + a · x + 3 · x²) · (1 / 2 - 2 · x)⁵ is - 265 / 8.
What is the value of a coefficient of the power of a binomial
In this problem we must apply the concept of Pascal's triangle to expand the power of a binomial of the form (x + y)ⁿ and further algebra properties.
(i) First, we proceed to expand the power binomial (1 / 2 - 2 · x)⁵ in ascending order:
(1 / 2 - 2 · x)⁵ = (1 / 2)⁵ + 5 · (1 / 2)⁴ · (- 2 · x) + 10 · (1 / 2)³ · (- 2 · x)² + 10 · (1 / 2)² · (- 2 · x)³ + 5 · (1 / 2) · (- 2 · x)⁴ + (- 2 · x)⁵
( 1 / 2 - 2 · x)⁵ = 1 / 32 - (5 / 8) · x + 5 · x² - 20 · x³ + 40 · x⁴ - 32 · x⁵
(ii) Second, we proceed to expand the following product of polynomials by algebra properties:
(1 + a · x + 3 · x²) · (1 / 2 - 2 · x)⁵ = (1 + a · x + 3 · x²) · [1 / 32 - (5 / 8) · x + 5 · x² - 20 · x³ + 40 · x⁴ - 32 · x⁵]
(1 + a · x + 3 · x²) · (1 / 2 - 2 · x)⁵ = 1 / 32 + (a / 32 - 5 / 8) · x + (- 5 · a / 8 + 163 / 32) · x² + (- 175 / 8 + 5 · a) · x³ + (65 - 20 · a) · x⁴ + (- 92 + 40 · a) · x⁵ + (120 - 32 · a) · x⁶ - 96 · x⁷
In accordance with the statement, we find that:
- 5 · a / 8 + 163 / 32 = 13 / 2
- 5 · a / 8 = 45 / 32
a = - 9 / 4
Thus, the coefficient of x³ is:
C = - 175 / 8 + 5 · (- 9 / 4)
C = - 265 / 8
The coefficient of x³ from (1 + a · x + 3 · x²) · (1 / 2 - 2 · x)⁵ is - 265 / 8.
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How do I write the following number in scientific notation?
788,000
Which of the following statements is equivalent to 10x – 30? 10(x – 30) 10(x – 3) 10 + (x – 20) 10(x – 20)
Answer:
10(x-3) is equivalent to 10x – 30
Step-by-step explanation:
First you have to take everything of out the parentheses and then simplify if needed.
10(x – 30) is not equivalent to 10x – 30 because, 10 times x is 10x, but 10 times 30 is 300. So, 10(x – 30) is not equivalent to 10x – 30.10(x – 3) is equivalent to 10x – 30 because, 10 times x is 10x, and 10 times 3 is 30. So, 10(x – 3) is equivalent to 10x – 30.10 + (x – 20) is not equivalent to 10x – 30 because, 10 minis 20 plus x are -10 + x. So, 10+(x – 20) is not equivalent to 10x – 30.10(x – 20) is not equivalent to 10x – 30 because, 10 times x is 10x, but 10 times 20 is 200. So, 10(x – 20) is not equivalent to 10x – 30.Answer: 10(x-3) is equivalent to 10x – 30
The graph of the function f(x) = –(x + 6)(x + 2) is shown below.
On a coordinate plane, a parabola opens down. It goes through (negative 6, 0), has a vertex at (negative 4, 4), and goes through (negative 2, 0).
Which statement about the function is true?
The function is increasing for all real values of x where
x < –4.
The function is increasing for all real values of x where
–6 < x < –2.
The function is decreasing for all real values of x where
x < –6 and where x > –2.
The function is decreasing for all real values of x where
x < –4.
Answer:
c,d
Step-by-step explanation:
PLEASE HELPPPPP PLEASE so confused
Answer:
105°
Step-by-step explanation:
EFGH is an isosceles trapezoid (a trapezoid with congruent legs is an isosceles trapezoid)
∠G=75° (base angles of an isosceles trapezoid are congruent)
∠F=105° (same-side interior angles theorem)
