Answer:
no solution
Step-by-step explanation:
16x - 32y = 27 → (1)
8x - 16 = 16y ( subtract 16y from both sides )
8x - 16 - 16y = 0 ( add 16 to both sides )
8x - 16y = 16 → (2)
multiply (2) by - 2 and add to (1)
- 16x + 32y = - 32 → (3)
add (1) and (3) term by term
0 + 0 = - 5
0 = - 5 ← not possible
this indicates the system has no solution
(b)
the solution to a system is the point of intersection of the 2 lines
since there is no solution, no point of intersection, then
this indicates the lines are parallel and never intersect
Answer:
a) no solution
b) the two lines never intersect
Step-by-step explanation:
Given system of equations:
[tex]\begin{cases} 16x-32y=27\\8x-16=16y \end{cases}[/tex]
Part (a)To solve by linear combination (elimination):
Step 1
Write both equations in standard form: Ax + By = C
[tex]\implies 16x-32y=27[/tex]
[tex]\implies 8x-16y=16[/tex]
Step 2
Multiply one (or both) of the equations by a suitable number so that both equations have the same coefficient for one of the variables:
[tex]\implies 16x-32y=27[/tex]
[tex]\implies 2(8x-16y=16) \implies 16x-32y=32[/tex]
Step 3
Subtract one of the equations from the other to eliminate one of the variables:
[tex]\begin{array}{l r l}& 16x-32y & = 32\\- & 16x-32y & = 27\\\cline{1-3}& 0 & =\:\: 5\end{array}[/tex]
Therefore, as 0 ≠ 5, there is no solution to this system of equations.
Part (b)
The solution to a system of equations is the point(s) of intersection.
As there is no solution to the given system of equations, this tells us that the two lines never intersect.
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tammy smith deposits $5,000 in First Internet Bank's 5-year CD, which pays 5.22% compounded monthly.How much will she have in the account at the end of 5 Years? How much interest did she earn?
Answer: a) $ 6,487.47
b) $ 1,487.47
Step-by-step explanation:
How tall is a pole if a 40 ft guy wire reaches from the top of that pole
to a point on the ground 19 ft from the bottom of the pole?
– 30% OF THE CELL PHONE USERS TODAY USE A MOTOROLA
PHONE. DETERMINE THE PROBABILITY THAT IF SIX CELL PHONE USERS
ARE SELECTED AT RANDOM, EXACTLY FOUR OF THEM USE A MOTOROLA CELL
PHONE.
Using the binomial distribution, there is a 0.0595 = 5.95% probability that exactly four of them use a Motorola cell phone.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.For this problem, the values of the parameters are given by:
p = 0.3, n = 6.
The probability that exactly four of them use a Motorola cell phone is given by P(X = 4), hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
P(X = 4) = C(6,4) x (0.3)^4 x (0.7)² = 0.0595
0.0595 = 5.95% probability that exactly four of them use a Motorola cell phone.
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PLWASW HELP ALOT OF POINTS Charlie used construction paper, scissors and a ruler to construct an
isosceles triangle with a pair of sides each 3 inches long and an acute
angle on top. He drew an altitude from the acute angle to the base and
wrote down his observations. He then created another isosceles triangle
with a pair of sides of 7 inches long with an obtuse angle on top, drew a
altitude to the base, and recorded his observations.
Which of these is the best conjecture for Charlie to develop?
The best conjecture for Charlie to develop is that an altitude drawn to the base of the isosceles triangle creates the smaller congruent triangles by the HL postulate.
What is conjecture?It should be noted that conjecture simply means a conclusion that's proffered on a tentative basis without any proof.
From the information, Charlie used construction paper, scissors and a ruler to construct an isosceles triangle with a pair of sides each 3 inches long and an acute angle on top.
Here, the best conjecture for Charlie to develop is that an altitude drawn to the base of the isosceles triangle creates the smaller congruent triangles by the HL postulate.
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HELP ASAP WILL GIVE BRAINLIEDT IF CORRECT!!!!!!!
Find the equation to the line below
Answer:
y = 3/2x + 2
Step-by-step explanation:
y = mx + c
y = gradient(x intercept) + y intercept
y = 3/2x + 2
Answer:
[tex]\sf y =\dfrac{3}{2}x+2[/tex]
Step-by-step explanation:
Equation of line:Pick any two points on the line.
(0,2) and (2 , 5)
(0,2) ⇒ x₁ = 0 & y₁ = 2
(2,5) ; x₂ = 5 & y₂ = 5
[tex]\sf \boxed{\bf Slope =\dfrac{y_2-y_1}{x_2-x_1}}[/tex]
[tex]\sf =\dfrac{5-2}{2-0}\\\\=\dfrac{3}{2}[/tex]
Equation of line in point slope form:
[tex]\sf y - y_1 =m(x -x_1)[/tex]
Point(0 ,2) and m = 3/2
[tex]\sf y - 2 = \dfrac{3}{2}(x -0)\\\\ y - 2 = \dfrac{3}{2}x\\\\[/tex]
Equation of line in slope y-intercept form:
[tex]\sf y =\dfrac{3}{2}x+2[/tex]
irections: Simplify each expressio
25-(√16-1)-(3-9)²
Answer:
-14
Step-by-step explanation:
[tex]\sqrt{16} = 4\\\\(\sqrt{16} - 1) = (4 -1) =3\\\\(3-9) = (-6)\\\\(3-9) ^2 = (-6)^2 = 36\\\\25 - 3 - 36 = 25 - 39 = -14\\[/tex]
f(x)=4x+1 and g(x)=2x2+1, find (f∘g)(x) and (g∘f)(x)
The value of the composite functions (g∘f)(x) and (f∘g)(x) are 32x^2 + 16x + 3 and 8x^2 + 5 respectively
Composite functionsComposite function is also known as function of a function. They are determined by representing x with the other function.
Given the following functions
f(x)=4x+1
g(x)=2x^2+1
(f∘g)(x) = f(g(x))
(f∘g)(x) = f(2x^2+1)
(f∘g)(x) = 4(2x^2+1) + 1
(f∘g)(x) =8x^2 + 5
For the composite function (g∘f)(x)
(g∘f)(x) = g(f(x))
(g∘f)(x) = g(4x+1)
Replace x wit 4x+1 to have:
(g∘f)(x) = 2(4x+1)^2 + 1
(g∘f)(x)= 2(16x^2+8x+1) + 1
(g∘f)(x) = 32x^2 + 16x + 3
Hence the value of the composite functions (g∘f)(x) and (f∘g)(x) are 32x^2 + 16x + 3 and 8x^2 + 5 respectively
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Given the linear function of 3x-7y=14, determine the ordered pair where the line crosses the y axis. Remember to write your answer in form (x,y)
Answer:
(0, -2)
Step-by-step explanation:
The equation of y axis is x = 0. So, the y intercept is located at point (0, b). Therefore we can substitute 0 into x in the given equation to find b and hence the coordinates of the y intercept.
3x - 7y = 14
3*0 - 7y = 14
-7y = 14
y = -2
1 gallon of paint covers 300 ft how many gallons I needed for a room 30 ft long 20 ft wide by 12 ft high
Answer:
6 gallons
Step-by-step explanation:
the total area to be painted :
= The total surface area - area of the floor
= area of the walls + area of the ceiling
area of the walls :
= [perimeter of the room] ×height
= [2 × (30+20)] × 12
= 1 200
area of the ceiling :
= length × width
= 30 × 20
= 600
the total area to be painted :
= 1200 + 600
= 1800
The number of gallon of paint needed to cover the room :
= 1800 ÷ 300
= 6
Write an equation of the line that passes through (3,-2) and is parallel to the line y = 2x + 4.
Answer: [tex]y+2=2(x-3)[/tex]
Step-by-step explanation:
Parallel lines have the same slope, so substituting into point-slope form, the equation is
[tex]y+2=2(x-3)[/tex]
the number has 3 digits the number is less than 140 the number has 7 as a factor the number is even the sum of the digits is less than 9
Answer:
It could be 105, 112 or 133.
Step-by-step explanation:
Having 7 as a factor means it is a multiple of 7.
The first 3 digit multiple of 7: 100 ÷ 7 = 14 2/7 → first 3 digit multiple of 7 is 15 × 7 = 105
Last 3 digit multiple of 7 less than 140: 140 ÷ 7 = 20 → last 3 digit multiple of 7 less than 140 is 19 × 7 = 133
→ The possible multiples of 7 to consider are [15..19] × 7 which gives 105, 112, 119, 126 and 133.
The sum of the digits of these number is:
105 → 1 + 0 + 5 = 6
112 → 1 + 1 + 2 = 4
119 → 1 + 1 + 9 = 11
126 → 1 + 2 + 6 = 9
133 → 1 + 3 + 3 = 7
Of these sums only 6, 4 and 7 are less than 9, thus the possible numbers are 105, 112 or 113.
Sampson has been given the following budget guidelines. If his department’s budget is $50,000, how much can he spend in each budget category? Be sure to list dollars and cents (round to the nearest hundredth).
The amount he can spend on marketing is $8,333.33.
The amount he can spend on supplies is $16,666.67
The amount he can spend on trainings is $12,500
The amount he can spend on travel is $2,500
The amount he can spend on equipment is $10,000
How much can he spend on each category?The amount he can spend on each category can be determined by multiplying the fraction of that category by the total department's budget.
The amount he can spend on marketing : 1/6 x $50,000 = $8,333.33.
The amount he can spend on supplies: 1/3 x $50,000 = $16,666.67
The amount he can spend on trainings: 1/4 x 50,000 = $12,500
The amount he can spend on travel $2: 1/20 x 50,000 = 2,500
The amount he can spend on equipment $: 1/5 x 50,000 = 10,000
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Interpreting Slope in a Line of Best Fit
Use the scatterplot and equation to answer the question.
AY
180+
160+
140+
120+
100+
80+
Number of Customers Served
2
60+
40+ y= 17.9x+6.67
20+
3 4 5 6 7 8 9
Number of Hours
x
The data reflects the number of hours an employee
spends working a checkout line (x), paired with the
number of customers served (y). How can the slope of
the line be interpreted?
With each additional hour, between 6 and 7
customers are served.
With each additional hour, nearly 18 customers are
served.
Each additional customer requires 17.9 minutes to
check out.
O Each additional customer requires 6.67 minutes to
check out.
Done
Answer:
b
Step-by-step explanation:
b
Rock Solid Bank and Trust (RSB&T) offers only checking accounts. Customers can write checks and use a network of automated teller machines. RSB&T earns revenue by investing the money deposited; currently, it averages 7.00 percent annually on its investments of those deposits. To compete with larger banks, RSB&T pays depositors 0.50 percent on all deposits. A recent study classified the bank’s annual operating costs into four activities.
Activity Cost Driver Cost Driver Volume
Using ATM Number of uses $ 4,200,000 5,600,000 uses
Visiting branch Number of visits 2,520,000 420,000 visits
Processing transaction Number of transactions 18,480,000 224,000,000 transactions
Managing functions Total deposits 16,800,000 $ 1,050,000,000 in deposits
Total overhead $ 42,000,000
Data on two representative customers follow.
Customer A Customer B
ATM uses 100 200
Branch visits 5 20
Number of transactions 40 1,500
Average deposit $ 6,000 $ 6,000
Required:
a. Compute RSB&T's operating profits.
b. Compute the profit from Customer A and Customer B, assuming that customer costs are based only on deposits. Interest costs = 0.50 percent of deposits; operating costs are 4 percent (= $42,000,000/$1,050,000,000) of deposits.
c. Compute the profit from Customer A and Customer B, assuming that customer costs are computed using the information in the activity-based costing analysis.
A) RSB&T's operating profits are 2,625,000.
B) The profit from Customer A = 42 and Customer B=42.
C) The profit from Customer A=77.7 and Customer B=-207.75(loss)
What does mean by profit?Profit is the term used to describe the financial gain experienced when the revenue from a commercial activity outweighs the costs, costs, and taxes incurred to maintain the activity in question.A business's financial gain when revenue exceeds costs and expenses is frequently referred to as profit. One cup of lemonade, for instance, costs a child at a lemonade stand one quarter. She then charges $2 for the beverage. She made $1.75 in profit on the cup of lemonade.All costs are first deducted from sales, and the result is then divided by sales. This creates the profit formula, which is expressed as a percentage. (Sales - Expenses) Sales = Profit is the formula.Data on two representative customers follow.
[A] Compute RSB&T's operating profits.
Computation of Operating Profits:-
Revenue 19,500,000
Interest to Depositors (1,875,000)
Overheads (15,000,000)
Total operating Profit 2,625,000
[B] Costs are based only on Deposits
Particulars A B
Revenue 312 312
Interest Cost -30 -30
Operating Cost -240 -240
Profits 42 42
[C] As per Activity based costing
Particulars A B
Revenue 312 312
Interest Cost -30 -30
ATM Uses -75 -150
Branch Visit -30 -120
Processing Transaction -3.3 -123.75
Managing Function -96 -96
Profits/Loss 77.7 -207.75
Therefore,
A) RSB&T's operating profits are 2,625,000.
B) The profit from Customer A = 42 and Customer B=42.
C) The profit from Customer A=77.7 and Customer B=-207.75(loss)
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Hello please help asap!! i will mark brainliest and this is worth 20 points!!!!! tysm
The least number of colors you need to correct color in the sections of these pictures so that no two touching sections are the same color is 5 colors. This can be obtained by simply giving colors to the small shapes according to the criteria.
What is the least number of colors?From the question the figure, the number of colored sections with which are not colored with respect to a "touching" colored section, would not be half of the total colored sections since the sections are not alternating as they still meet at a common point.
After all, it notes no two touching sections, not adjacent sections.
There is no equation to calculate this requirement with respect to the total number of sections.
Taking one triangle or square as the starting we can give colors to each small units. This figure will be the start of sequence of other small figures.
If a square were to be this starting shape that have same color as that color of the square.
Now from the remaining given another color to the starting figure. We will get that shapes, that will have same color.
Like that the remaining figures are given colors.
Therefore, the least number of colored sections you can color in the sections meeting the given requirement, is 5 sections for this first figure.
Hence the least number of colors you need to correct color in the sections of these pictures so that no two touching sections are the same color is 5 colors.
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Do companies that provide mobile wifi hotspots see your history?
Yes, companies that provide mobile wifi hotspots can see your history.
What is a Wi-Fi hotspots?A Wi-Fi hotspots can be defined as the hotspots that makes it possible for other mobile user connected to a wifi hotspots to browse or to connect to the internet.
For a mobile user to connect to the internet through the mobile wifi hotspot, the mobile hotspot wifi owner must have giving access to mobile user to browse .
Hence, companies that provide mobile wifi hotspots can see your history of the site you visit.
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Instructions: Find the missing side of the triangle.
X= Answer
Answer: 15
Step-by-step explanation: Using the pythagorean theorem A^2 + B^2 = C^2 where C is the hypotenuse of the triangle and any A and B are any sides of the triangle that are not the hypotenuse; we can rewrite this as A^2 = C^2 - B^2 to find out the missing side. I picked A to be the unknown side but you could also choose B. We know the hypotenuse is 39, and side B is 36. 39^2 - 36^2, or 1521 - 1296, is 225.
Now we have A^2 = 225. To get rid of the square, we have to take the square root of both sides. The A^2 cancels to be A, and sqrt(225) is 15. Thus, side A, or the missing side is 15.
Hope this helped!
If A= {1,2,3,4,5},B= {1,3,5,7}and C= {2,4,6,8}
Step-by-step explanation:
Intersection of A and B={1,3,5}Intersection of B and C={ }B - A={1,3,5,7} - {1,2,3,4,5} ={1,7}solve the algebraic equation 7 x - 2 equals to 2x + 13
Answer:
x = − 6
Step-by-step explanation:
I have my work
if two vertical angles are 2x-10 and x+20 find the value of x
Answer:
x=70
Step-by-step explanation:
when added together, verticle angles equal 180 degrees.
2x-10+x+20=180
3x-10+20=180
3x-30=180
3x=210
x=70
Which equation can be simplified to find the inverse of y = 5x^2 + 10?
Answer:
Step-by-step explanation:
Here's the solution
f^(-1)(x)=(\sqrt(5(x-10)))/(5), -(\sqrt(5(x-10)))/(5)
PLEASE HELP ME !” ASAP?
Answer:
39°
Step-by-step explanation:
Opposite angles of a parallelogram are congruent.
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
" The opposite angles of a Parallelogram are always equal to one another "
[tex] \qquad \large \sf {Conclusion} : [/tex][tex] \qquad \large \sf {Conclusion} : [/tex]
Angle M = Angle N = 39°ill give brainliest
Directions: Factor the following trinomials containing negative numbers. Follow the rules for operations with signed numbers to identify the correct binomial factors.
1. x2 + 6x - 7
2. x2 - 5x + 6
3. x2 - 6x - 7
4. x2 + 5x - 6
5. x2 + x - 12
6. x2 - 2x - 8
7. x2 - 4x - 5
8. x2 + 2x - 3
9. x2 - 16
10. x2 - x - 12
11. x2 -9x + 18
12. x2 -5x - 14
13. x2 - 7x + 10
14. x2 -11x + 24
15. x2 - x - 30
The aim of factorization to obtain the common factors that are present in the expression.
What are factors?When we factorize an expression, the aim is to obtain the common factors that are present in the expression.
Now we have trinomials numbered 1 - 15. Trinomial is an expression that is made up of three terms. Quadratic expressions are mostly found to appear as trinomial
The binomial factors that are associated with each are shown in the factorized expressions below. The binomials contain two terms in each bracket.
Given the trinomials, the correct binomial factors are;
(x−1)(x+7) (x−2)(x−3)(x+1)(x−7) (x−1)(x+6)(x−3)(x+4)(x+2)(x−4)(x+1)(x−5)(x−1)(x+3) (x+4)(x−4)(x+3)(x−4)(x−3)(x−6)(x+2)(x−7)(x−2)(x−5) (x−3)(x−8) (x+5)(x−6)Learn more about factorization:https://brainly.com/question/19386208
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Lamar, an artist, plans to paint and sell some miniature paintings. He just bought some brushes for $10, and paint and canvas for each painting costs $45; he will sell each painting for $50. Once Lamar sells a certain number of his paintings, he will be breaking even. How many paintings will that be?
Answer:
2
Step-by-step explanation:
If he sells and makes x paintings, his expenses will he 10+45x and his revenue will be 50x.
50x = 45x + 105x = 10x = 2The break-even point is the point at which total cost and total income are equal. For breakeven, Lamar needs to sell 2 paintings.
What is breakeven?In economics, business, and especially cost accounting, the break-even point is the point at which total cost and total income are equal, i.e. "even."
Let the number of paintings that Lamar makes and sells at the break-even point be represented by x.
Given that Lamar bought some brushes for $10, and paint and canvas for each painting cost $45. Therefore, the total cost of making x number of paintings is,
Total cost of x painting = $10 + $45(x)
Also, the selling price of each painting is $50. Therefore, the revenue generated from x paintings is,
Revenue generated = $50(x)
Further, at the breakeven point, the total cost of production of any product is equal to the revenue generated by the product. Therefore, we can write,
Total cost of x painting = Revenue generated
$10 + $45(x) = $50(x)
10 + 45x = 50x
10 = 50x - 45x
10 = 5x
x = 10/5
x = 2
Hence, For breakeven Lamar needs to sell 2 paintings.
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Given that 3 is a root of a given polynomial, what can you say is a factor of that polynomial?
The factor of such equation described as having the number 3 as a root can be determined as; (x-3).
What is a possible factor of a given polynomial whose root is 3?It follows from the task content that; we are required to determine a possible factor of a polynomial in the event that such polynomial has a root of 3.
The implication of a polynomial having a root of 3 is that; such a polynomial has 3 to be one of it's zeros.
Hence, a linear equation which holds for such polynomial is that; x = 3 and when expressed as a linear factor, the linear factor is; (x-3).
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Which of the following proves these triangles are congruent
Answer:
SAA
Step-by-step explanation:
Identify the corresponding congruent parts as either sides or angles. Look at their order of appearance around the triangle.
Corresponding partsThe sides marked with a single hash mark are identified as corresponding and congruent.
The angles marked with a single arc are identified as corresponding and congruent.
The vertical angles where the lines cross are congruent.
SequenceWorking counterclockwise around the left triangle, we encounter ...
side marked congruentvertical angles (congruent)angle marked congruentThese same features appear in the same order working counterclockwise around the triangle on the right.
The "side," "angle," and "angle" are referenced in the congruence postulate as S, A, and A.
Congruence is proved by the SAA congruence postulate.
There are values of t so that the equation cos t = 5/3.
A. True
B. False
the statement is false, as there no exist a value of t such that cos(t) > 1.
Is the statement true or false?
Here we have the statement:
"There are values of t so that the equation cos(t) = 5/3"
Now, remember that the range of the sine and cosine equations is given by:
R: -1 ≤ y ≤ 1
And 5/3, the value in the statement, is larger than 1, which is the maximum in the range.
Then the statement is false, as there no exist a value of t such that cos(t) > 1.
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14. A photograph measures eight inches wide and ten inches long. The picture is enlarged to fit on a wall. If the new larger picture is 208 inches wide, how long is it?
Answer:
The file contains the solution to the question
Image is attached below, please help. Thank you so much!
The limit of f(x) as x goes to 1 will not exist for function III.
What is a limit?A limit is given by the value of function f(x) as x tends to a value. For a function with different lateral limits at a point x = a, the limit will not exist at the point x = a. Additionally, the limit may not exist at a point if there is a non-removeable discontinuity.
Factoring the function 1, the limit will be given as follows:
[tex]\lim_{x \rightarrow 1} \frac{1 - x^2}{x - 1} = \lim_{x \rightarrow 1} \frac{(1 - x)(1 + x)}{x - 1} = \lim_{x \rightarrow 1} -(1 +x) = -2[/tex]
Hence the limit exists.
Factoring the function 2, the limit will be given as follows:
[tex]\lim_{x \rightarrow 1} \frac{x^2 - x^3}{x^2 - 1} = \lim_{x \rightarrow 1} \frac{x^2(1 - x)}{(x - 1)(x + 1)} = \lim_{x \rightarrow 1} -\frac{x^2}{x + 1} = -\frac{1}{2}[/tex]
Hence the limit exists.
Factoring the function 3, the limit will be given as follows:
[tex]\lim_{x \rightarrow 1} \frac{x + 1}{x^2 - 1} = \lim_{x \rightarrow 1} \frac{x + 1}{(x - 1)(x + 1)} = \lim_{x \rightarrow 1} \frac{1}{x - 1}[/tex]
Non-revemoveable discontinuity, as we can't remove x - 1 for the denominator, ence the limit does not exist for function III.
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Match the matrix operations with the resulting matrices. Image Attached.
Answer:
1. 2A + 3A
2. 2A - B
3. 2A
4. 2(A-B)
Step-by-step explanation:
When multiplying matrix by a number you just multiply each number in the matrix by whatever you are multiplying. When adding 2 matrices you just add the corresponding number in each matrix. Ex: You add the top left number to the top left number. The same goes with subtraction.
Answer:
Behold!
Step-by-step explanation: