If the sum of the length and width of rectangle is 60 and rectangle is having maximum area then the dimensions are 30 units each.
Given that the sum of length and breadth of rectangle is 60.
We are required to find the dimensions of the rectangle that will have the maximum area. Area is basically how much part of surface is being covered by that particular shape or substance.
Let the length of rectangle be x.
According to question the breadth will be (60-x).----2
Area of rectangle=Length *Breadth
A=x(60-x)
A=60x-[tex]x^{2}[/tex]
Differentiate A with respect to x.
dA/dx=60-2x
Again differentiate with respect to x.
[tex]d^{2} A/dA^{2}[/tex]=-2x
-2x<0
So the area is maximum because x cannot be less than or equal to 0.
Put dA/dx=0
60-2x=0
60=2x
x=30
Put the value of x in 2 to get the breadth.
Breadth=60-x
=60-30
=30
Hence if the sum of the length and width of rectangle is 60 and rectangle is having maximum area then the dimensions are 30 units each.
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P: 2,012
1) El volumen de un cubo de arista 1 es Vc = 1³ y el
Volumen de una esfera de radior es
JE
V₁ = πr ²³ Entonces si en un cubo de arista 4cm
3
y se introduce una pelota de diametro 4 cm, al Calcular
aproximación con cuatro cifras decimales, por exceso.
Calcular el volumen que queda entre la esfera y el cubo.
(toma π =
3,141592654)
El volumen remanente entre la esfera y el cubo es igual a 30.4897 centímetros cúbicos.
¿Cuál es el volumen remanente entre una caja cúbica vacía y una pelota?
En esta pregunta debemos encontrar el volumen remanente entre el espacio de una caja cúbica y una esfera introducida en el elemento anterior. El volumen remanente es igual a sustraer el volumen de la pelota del volumen de la caja.
Primero, se calcula los volúmenes del cubo y la esfera mediante las ecuaciones geométricas correspondientes:
Cubo
V = l³
V = (4 cm)³
V = 64 cm³
Esfera
V' = (4π / 3) · R³
V' = (4π / 3) · (2 cm)³
V' ≈ 33.5103 cm³
Segundo, determinamos la diferencia de volumen entre los dos elementos:
V'' = V - V'
V'' = 64 cm³ - 33.5103 cm³
V'' = 30.4897 cm³
El volumen remanente entre la esfera y el cubo es igual a 30.4897 centímetros cúbicos.
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Tami earned $20.64 in simple interest by investing a principal of $400 in a Treasury bill.
If the interest rate was 1.72%/a, for how many years did she have her investment?
The number of years she had her investment is after 3 years
How to determine the years of investment?From the question, the given parameters are:
Principal Amount, P = $400Interest Rate, r = 1.72%Simple Interest, I = $20.64The number of years (T) is calculated from the following simple interest formula
I = PRT
Substitute the given parameters in the above equation
20.64 = 400 * 1.72% * t
Express 1.72% as decimal without percentage
20.64 = 400 * 0.0172 * t
Evaluate the product
20.64 = 6.88 * t
Divide both sides by 6.88
20.64/6.88 = 6.88/6.88 * t
Evaluate the quotient
3 = t
Rewrite the equation as
t = 3
This means that she had her investment after 3 years
Hence, the number of years she had her investment is after 3 years
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George paid a total of $985 to rent a storage unit.
He initially paid $290 plus an extra amount for
each month that he rented the storage unit. Write
an equation to find the extra amount George paid
each month if he had the storage unit for 5 months.
[?] + 5m= [ ]
Answer:
290 + 5m = 985
Step-by-step explanation:
Given information:
Initial payment = $290Total payment = $985Extra amount each month = mLength of rental = 5 monthsFrom the given information, we can create the following equation:
Initial payment plus extra amount each month for 5 months equals total payment.
⇒ 290 + 5m = 985
To solve the equation:
Subtract 290 from both sides:
⇒ 290 + 5m - 290 = 985 - 290
⇒ 5m = 695
Divide both sides by 5:
⇒ 5m ÷ 5 = 695 ÷ 5
⇒ m = 139
Therefore, the extra amount George paid each month was $139.
Answer: [tex]\Large\boxed{290+5m=985}[/tex]
Step-by-step explanation:
Given information
Initial cost = $290
Total cost = $985
Number of months = 5 months
Cost each month = ?
Set variable
Let [ m ] be the cost each month
The equation in verble sense
Initial paid + Extra each month = Total cost
Convert verbal equation to mathematical sense
$290 + 5m = $290
Therefore, to find the extra amount paid each month, the equation is [tex]\Large\boxed{290+5m=985}[/tex]
---------------------------------------------------------------------------------------------------------
EXTRA The following will be solving the derived equation, please ignore this part if it is useless for you.
Given equation
290 + 5m = 985
Subtract 290 on both sides
290 + 5m - 290 = 985 - 290
5m = 695
Divide 5 on both sides
5m / 5 = 695 / 5
m = $139
Hope this helps!! :)
Please let me know if you have any questions
The formula =MID("ABCDEFGHI",3,4) would yield the result
If the formula, =MID("ABCDEFGHI",3,4) is used, the result yielded would be CDEF.
What would =MID("ABCDEFGHI",3,4) yield?When using the =MID function on a spreadsheet, the number after the text in the formula would show the position of the text from the left that the function would begin to count from.
The text in the third position from the left as shown in ABCDEFGHI is C so we need to start counting from letter C.
The second number in the function would then show the number of texts that needs to be counted and selected from the row of letters. That number is 4.
So from the letter C, you'll count 4 letters including the letter C itself.
The result you get would therefore be C, D, E, F which are the four letters from C.
In conclusion, the formula =MID("ABCDEFGHI",3,4) would yield the result, "C, D, E, F,."
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Suppose that you repeated questions 5 and 6 using two line segments of your choice. The line segments could be any length and in any
orientation as long as the midpoints were marked correctly and coincided with each other. Would you reach the same conclusion that you
reached in question 7? How does your conclusion relate to the diagonals of a parallelogram?
A line segment can be defined as the part of a line in a geometric figure such as a parallelogram, that is bounded by two (2) distinct points and it typically has a fixed length.
In Geometry, a line segment can be measured by using the following measuring instruments:
A scale (ruler).A divider.What is a parallelogram?A parallelogram refers to a geometrical figure (shape) and it can be defined as a type of quadrilateral and two-dimensional geometrical figure that has two (2) equal and parallel opposite sides.
Based on the previous experiment conducted in question 5, 6 and 7, we can logically conclude that the opposite sides of quadrilateral ABCD have the same (equal) slopes, which implies that the opposite sides are parallel. Hence, quadrilateral ABCD is simply a parallelogram by definition.
In this context, yes I would you reach the same conclusion that I reached in question 7 because the line segments that I drew represent the diagonals of a parallelogram.
Therefore, if the point of intersection of the diagonals divide each diagonal in half, then, the quadrilateral belonging to these diagonals forms a parallelogram.
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Let f= {(-5,-4),(6,-5),(2, -3)}.
Find f(-5).
Answer:
f(–5)=–4
Step-by-step explanation:
as it is defined
Katrina has the option of an 8-year nonsubsidized student loan of $29,000 at an annual interest rate of 2.5% or an 8-year subsidized loan of $29,000 at an annual interest rate of 4.5%. Determine for which loan Katrina will pay less interest over the term of the loan if she starts making payments 2 years after obtaining the loan. (Assume Katrina makes monthly payments for each loan. Round your answers to the nearest cent, as appropriate.) The total interest paid on the nonsubsidized loan is $
Katrina would pay less amount of interest on the nonsubsidized student loan
The total interest paid on the nonsubsidized loan is $3,860.80
What is monthly compounding?
Monthly compounding means that the interest is computed and added to existing outstanding loan balance at the end of each month.
In this case, the loan would be repaid monthly but the first monthly payment would occur after 2 years of taking out the loans.
In other words, for the first 2 years, the interest would increase the balances with no corresponding reductions by a way of loan repayment, note that interest to be added monthly, as a result, we can compute outstanding balance 2 years for both loans using the future value formula of a single cash flow shown below:
FV=PV*(1+r/n)^(n*t)
FV=balance after 2 years=unknown
PV=loan amount
r=annual interest rate
n=number of times interest is compounded annually=12
t=number of years before repayments commence=2
Non-subsidized loan:
FV=$29,000*(1+2.5%/12)^(12*2)
FV=$30,485.28
Subsidized loan:
FV=$29,000*(1+4.5%/12)^(12*2)
FV=$31,725.71
Having determined the loan balances after 2 years, we can now compute the monthly payments that would be made in the remaining 6 years using the present value formula of an ordinary annuity because monthly payments would occur at the end of each month:
PV=PMT*(1-(1+r)^-N/r
PV=balance of loan after 2 years
PMT=monthly payment=unknown
r=monthly interest rate=annual interest rate/12
N=number of monthly payments in 6 years=12*6=72
Non-subsidized loan:
$30,485.28=PMT*(1-(1+2.5%/12)^-72/(2.5%/12)
PMT=$456.40
total monthly payments=$456.40*72
total monthly payments=$32,860.80
Interest= total monthly payments-loan
interest=$32,860.80-$29,000
interest=$3,860.80
Subsidized loan:
$31,725.71 =PMT*(1-(1+4.5%/12)^-72/(4.5%/12)
PMT=$503.61
total monthly payments=$503.61 *72
total monthly payments=$36,259.92
Interest= total monthly payments-loan
interest=$36,259.92 -$29,000
interest=$7,259.92
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Please help me with this question <3 ASAP!
Answer:
54°
Step-by-step explanation:
Opposite angles of a parallelogram are congruent, so;
[tex]9x+9=8x+14 \\ \\ x=5 \\ \\ m\angle S=9(5)+9=54^{\circ}[/tex]
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
Angle S = 54°[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]
In a Parallelogram, opposite angles are equal, so we infer that :
[tex] \qquad❖ \: \sf \:9x + 9 = 8x + 14 [/tex]
[tex] \qquad❖ \: \sf \:9x - 8x = 14 - 9[/tex]
[tex] \qquad❖ \: \sf \:x = 5 \degree[/tex]
Next,
Measure of Angle S is :
[tex] \qquad❖ \: \sf \:9x + 9[/tex]
[tex] \qquad❖ \: \sf \:9(5) + 9[/tex]
[tex] \qquad❖ \: \sf \:45 + 9[/tex]
[tex] \qquad❖ \: \sf \:54 \degree[/tex]
[tex] \qquad \large \sf {Conclusion} : [/tex]
Angle S = 54°A satellite orbits the Earth at a height of 343 kilometers. If the satellite makes 8 revolutions around the Earth, how many kilometers does it travel? (Earth's diameter is 6371 kilometers.).
The number of kilometres travelled by the satellite in discuss in which case, the satellite makes 8 revolutions around the earth is; C = 177,271.8 km.
What is the distance in kilometres covered by the satellite after 8 revolutions?Given from the task content, the earth's diameter is; 6371 km and since, the height at which the satellite orbits the earth is; 343km, it follows that the diameter of orbit if the satellite in discuss is;
D = 6371 + (343)×2
Hence, we have; diameter, D = 7057 km.
Hence, the distance travelled after 8 revolutions is;
C = 8 × πd
C = 8 × 3.14 × 7057
C = 177,271.8 km.
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Please help! Help Will Give 100 PTS
Solve for x and show your steps. Is the solution extraneous? Check your work to show how you determined if the solution is extraneous or not.
Square Root 3x+12 = 9
Answer:
x = 23; not extraneous
Step-by-step explanation:
A solution is extraneous if it does not satisfy the original equation. Extraneous solutions can sometimes be introduced in the process of solving radical and rational function equations.
SolutionSquaring both sides of the given equation, we get ...
√(3x +12) = 9
3x +12 = 81 . . . . . . square both sides
x +4 = 27 . . . . . . . divide by 3
x = 23 . . . . . . . . . . subtract 4
CheckThere is only one solution, and it satisfies the equation:
√(3×23 +12) = √81 = 9
The solution x = 23 is not extraneous.
Answer: x = 23; not extraneous
Step-by-step explanation:
The following information is available for Brownstone Products Company for the month of July:
Actual Master Budget
Units 3,500 4,000
Sales revenue $ 54,300 $ 60,000
Variable manufacturing costs 10,000 16,000
Fixed manufacturing costs 13,000 14,000
Variable selling and administrative expenses 6,500 8,000
Fixed selling and administrative expenses 8,000 9,100
Required:
1. What was the master budget variance for July? Was this variance favorable or unfavorable?
2. Compute the July sales volume variance and the flexible-budget variance for the month, both in terms of contribution margin and in terms of operating income.
4. Prepare pro-forma budgets for activities within its relevant range of operations. Prepare a flexible budget for each of the following two output levels:
a. 3,560 units.
b. 3,980 units.
1. The master budget variance for July was $3,900, and this variance was favorable.
2. The July sales volume variances in terms of contribution margin and operating income are $2,800 F and $3,900 F, respectively.
3. The July flexible-budget variances in terms of contribution margin and operating income are $5,550 F and $6,650 F, respectively.
4. Flexible budgets for the following output levels are:
3,560 units 3,980 units
Sales revenue $53,400 $59,700
Variable manufacturing costs 14,240 15,920
Fixed manufacturing costs 12,460 13,930
Variable selling and
administrative expenses 7,120 7,960
Fixed selling and
administrative expenses 9,100 9,100
Operating Income $10,480 $12,790
Data and Calculations:Actual Master Budget Per Unit Variance
Units 3,500 4,000 500 U
Sales revenue $ 54,300 $ 60,000 $15.00 $ 5,700 U
Variable manufacturing costs 10,000 16,000 4.00 6,000 F
Fixed manufacturing costs 13,000 14,000 3.50 1,000 F
Variable selling and
administrative expenses 6,500 8,000 2.00 1,500 F
Contribution margin $24,800 $22,000 $2,800 F
Fixed selling and
administrative expenses 8,000 9,100 1,100 F
Total costs $37,500 $47,100
Operating income $16,800 $12,900 $3,900 F
Sales volume variance:
Revenue per unit $15.51 $15.00 $0.51 F
Flexible-budget:Actual Master Budget Variance
Units 3,500 3,500 U
Sales revenue $ 54,300 $ 52,500 $ 1,800 F
Variable manufacturing costs 10,000 14,000 4,000 F
Fixed manufacturing costs 13,000 12,250 750 U
Variable selling and
administrative expenses 6,500 7,000 500 F
Contribution margin $24,800 $19,250 $5,550 F
Fixed selling and
administrative expenses 8,000 9,100 1,100 F
Operating income $16,800 $10,150 $6,650 F
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Is the answer true or false?
Find the product of the complex numbers. Express your answer in trigonometry form. Z1= 7cos(15) + isin(15)) z2= 2(cos(110)+ isin(110))
Answer:
14(cos(125°) +i·sin(125°))
Step-by-step explanation:
The product of two complex numbers is the product of their magnitudes at an angle equal to the sum of their angles.
ApplicationFor A = a·cis(α) and B = b·cis(β), the product AB is ...
AB = (a·cis(α))·(b·cis(β)) = ab·cis(α+β)
where "cis(x)" stands for the sum (cos(x) +i·sin(x)).
The product of interest is ...
Z1·Z2 = (7cis(15°))·(2cis(110°)) = (7·2)cis(15°+110°)
Z1·Z2 = 14cis(125°) = 14(cos(125°) +i·sin(125°))
find the length of the semi-major axis of the ellipse x^2/49+y^2/36=1
The length of the semi-major axis of the ellipse is 7.
What is the semi-major axis of an ellipse?
The semi-major axis of an ellipse is the half of the longest diameter passing through its vertex and focus.
The general equation of an ellipse is :
⇒ x²/a²+y²/b²=1, where a is the semi-major axis and b, is the semi-minor axis
x²/49+y²/36=1
x²/(7²)+y²/(6²)=1
x²/a²+y²/b²=1
a=7
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A storage shed is to be built in the shape of a box with a square base. It is to have a volume of 729 cubic feet. The concrete for the base cost $8 per square foot, The material for the roof costs $3 Per square foot, and the material for the sides costs $5.50 Per square foot. Find the dimensions of the most economical shed.
The dimensions of the most economical shed are 9 ft in length, 9 ft in width, and 9 ft in height if the storage shed is to be built in the shape of a box with a square base.
What is volume?It is defined as a three-dimensional space enclosed by an object or thing.
It is given that:
A storage shed is to be built in the shape of a box with a square base.
It is to have a volume of 729 cubic feet.
Let x be the length of the base
Let y be the height of the box.
V = 729 cubic feet
The base is square:
l = w = x
V = x²y
y = 729/x²
Cost of the base = $8x²
Cost of the roof = 3x²
Cost of the sides = 4(5.50)xy
= 22xy
Total cost
C= 8x² + 3x² + 22xy
C = 11x² + 22x(729/x²)
C = 11x² + 16038/x
Find the first derivative:
dC/dx = 22x - 16038/x²
Equate; dC/dx = 0
22x - 16038/x² = 0
22x = 16038/x²
22x³ =16038
x³ = 729
x = 9
y = 729/(9)² = 9
Length of base = 9 ft
Width of base = 9 ft
Height of box = 9 ft
Thus, the dimensions of the most economical shed are 9 ft in length, 9 ft in width, and 9 ft in height.
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There are 2,900 students at our school. If 51% of them are female, how many female students are there at our school?
Answer:
Step-by-step explanation:
1479
Cross Multiply With Fractional Ratios.
5 (1/2)
=
8 x
cross multiply to find the awnser
Answer:
5/16
Step-by-step explanation:
assuming you mean 5(1/2) = 8x
5(1/2) is the same as 5/2
so, 5/2 = 8x
5 = 16x
x= 5/16
Copy the problems onto your paper, mark the given and prove the statements asked. Prove, triangle CAV is congruent to triangle CEV
Quadrilateral is a family of plane shapes that have four straight sides. Thus the sum of their internal angles is [tex]360^{o}[/tex]. Examples include rectangle, square, rhombus, trapezium, and kite.
A kite is a plane shape that has its adjacent sides to have equal measures.
The given diagram in the question is a kite that has its specific properties compared to other quadrilaterals.
Thus, the required proof is stated below:
Given: ΔCAV and ΔCEV
Prove that: ΔCAV ≅ ΔCEV
Then,
CE ≅ CA (length of side property of a kite)
EV ≅ AV (length of side property of a kite)
<ACV ≅ <ECV (bisected property of a given angle)
<AVC ≅ <EVC (bisected property of a given angle)
CV is a common side to ΔCAV and ΔCEV
Therefore it can be deduced that;
ΔCAV ≅ ΔCEV (Angle-Angle-Side congruent theorem)
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1.
Find a polynomial f(x) of degree 3 that has the following zeros.
4, 0, -7
Leave your answer in factored form.
Answer:
x³+3x²-28x
Step-by-step explanation:
(x-4)(x-0)(x+7)
(x-4)(x)(x+7)
(x-4)(x+7)=(x²+3x-28)
(x²+3x-28)(x)=x³+3x²-28x
−5y2−3y−2, when y=2.
y=2
-5(2)²-3(2)-2
-5(4)-3(2)-2
-20-6-2
=12
Dominique has been working at an regular rate of $14. He works 54 hours per week and is paid time and a half for overtime. What is Dominique's average hourly rate?
Based on the given task content about the average hourly rate, Dominique's average hourly rate is $0.26.
Average hourly rateRegular rate of Dominique payment = $14Number of hours worked = 54 hoursAverage hourly rate = Regular rate of Dominique's payment ÷ Number of hours worked
= $14 / 54 hours
= 0.25925925925925
Approximately,
Average hourly rate = $0.26
Therefore, Dominique's average hourly rate is $0.26
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Is 3 1/4 a rational or irrational number?
Answer:
It is a rational number.
Step-by-step explanation:
A number is only irrational if it has a decimal that never ends and doesn't have a pattern. So a number like Pi (3.141592653589...) is irrational while a number like 1/3 (0.33333333...) is rational.
Hi :)
Below is the difference between rational & irrational numbers
______________RATIONALA number that can be expressed in [tex]\sf{\dfrac{p}{q}}[/tex] form, where [tex]\large\boldsymbol{q\ne0}[/tex]Evidently,
An irrational number is a number that cannot be expressed in [tex]\sf{\dfrac{p}{q}}[/tex] formLet's test the given number, [tex]\boldsymbol{3\dfrac{1}{4}}[/tex]
Well isn't it already in [tex]\sf{\dfrac{p}{q}}[/tex] form? It is.
Thus
[tex]\longrightarrow\darkblue\boldsymbol{3\dfrac{1}{4}\:is\:rational}[/tex]
[tex]\tt{Learn\:More;Work\:Harder}[/tex]
:)
How many three-digit positive integers have three different digits and at least one prime digit?
Answer:
252
Step-by-step explanation:
using a brute force method in c++
#include <stdio.h>
int main(){
int a, b, c, n = 0;
for(a = 1; a <= 9; a++)
for(b = 0; b <= 9; b++)
for(c = 0; c <= 9; c++)
if((a==3 || b==3 || c==3)) n++;
printf("%d\n", n);
}
Any help with this greatly appreciated.
Put the equation in standard linear form.
[tex]x'(t) + \dfrac{x(t)}{t + 5} = 5e^{5t}[/tex]
Find the integrating factor.
[tex]\mu = \exp\left(\displaystyle \int \frac{dt}{t+5}\right) = e^{\ln|t+5|} = t+5[/tex]
Multiply both sides by [tex]\mu[/tex].
[tex](t+5) x'(t) + x(t) = 5(t+5)e^{5t}[/tex]
Now the left side the derivative of a product,
[tex]\bigg((t+5) x(t)\bigg)' = 5(t+5)e^{5t}[/tex]
Integrate both sides.
[tex](t+5) x(t) = \displaystyle 5 \int (t+5) e^{5t} \, dt[/tex]
On the right side, integrate by parts.
[tex](t+5) x(t) = \dfrac15 (5t+24) e^{5t} + C[/tex]
Solve for [tex]x(t)[/tex].
[tex]\boxed{x(t) = \dfrac{5t+24}{5t+25} e^{5t} + \dfrac C{t+5}}[/tex]
giving brainliest!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The given focal points and the lengths of the minor and major axis of 16 and 20 gives the equation of the ellipse as the option;
[tex] B. \: \frac{(x + 3)^{2}}{ 100} + \frac{(y - 2)^{2}}{ 64} = 1 [/tex]
Which method can be used to obtain the ellipse?The equation of an ellipse is presented as follows;
[tex] \mathbf{ \frac{(x - h)^{2}}{ {a}^{2} } + \frac{(y - k)^{2}}{ {b}^{2} } } = 1 [/tex]
Where;
(x, y) = Coordinates of the center of the ellipse
a = Semi major axis
b = Semi minor axis
Length of minor axis = 16 units
Length of major axis = 20 units
By observation of the coordinates of the focal point, we have;
y-value of the center of the ellipse, k = 2
x-value of the center, h = (-9 + (3 - (-9))/2 = -3
The equation of the ellipse is therefore;
[tex] \frac{(x - ( - 3))^{2}}{ {10}^{2} } + \frac{(y - 2)^{2}}{ {8}^{2} } = 1 [/tex]
[tex] \frac{(x + 3)^{2}}{ 100} + \frac{(y - 2)^{2}}{ 64} = 1 [/tex]
The equation that represents the ellipse is the option;
[tex] B. \: \frac{(x + 3)^{2}}{ 100} + \frac{(y - 2)^{2}}{ 64} = 1 [/tex]
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Two sides of a triangle are 5 and 55 cm. Complete the inequality to show the possible lengths of the third side. If the third side of the triangle is x then...
The third side of the triangle falls between (50, 60).
How to find the third side of a triangle?Inequality triangle theorem states that the sum of any two sides of a triangle is greater than or equal to the third side.
Therefore, the other two sides are 5 cm and 55 cm. The range of the third side x can be computed using inequality triangle theorem.
Hence,
x < 5 + 55
x < 60
And,
x > 55 - 5
x > 50
Therefore, 50 < x < 60.
Hence, the third side of the triangle falls between (50, 60).
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A rectangle has a width w that is 5units longer than its lenght/. Which equation expresses the rectangle's area, A?
Area equals Length times Width.
since the width of this equation is 5 units Longer then its Length
W = L + 5
To put this area in a equation we could say
L(L+5)=A
Simplify the equation, L^2 + 5L = A.
help urgently need help
Answer:
[tex]y=\dfrac{8}{7}x - \dfrac{23}{7}[/tex]
Step-by-step explanation:
Rearranging the terms, we get [tex]7y=8x-23[/tex]. Dividing both sides by 7, we get [tex]\dfrac{7y}{7} = \dfrac{8x-23}{7}[/tex], so [tex]\boxed{y=\dfrac{8}{7}x - \dfrac{23}{7}}[/tex]
Answer:
y = [tex]\frac{8}{7}[/tex]x -[tex]\frac{23}{7}[/tex]
Step-by-step explanation:
You are changing this to the slope-intercept form of a line.
y = mx + b
8x -7y = 23 Subtract 8x from both sides of the equation
-7y = -8x + 23 Divide both sides of the equation by -7
y = [tex]\frac{-8}{-7}[/tex] - [tex]\frac{23}{7}[/tex]
[tex]\frac{-8}{-7}[/tex] is the same as [tex]\frac{8}{7}[/tex]
y = [tex]\frac{8}{7}[/tex]x - [tex]\frac{23}{7}[/tex]
Can someone help on this?
Step-by-step explanation:
this just means that the first function with input value x = 0 is calculated. that result becomes the input value x for the second function. and that result becomes the input value x for the 3rd function. and that result is then our result.
to answer a and b we only need to look at the main operation of each function :
the first one uses only basic multiplication and subtraction.
the second one uses squaring.
the third one is a 1/x operation.
a.
since the final result is a negative number (-31), the second function with the square operation cannot be last.
because a square operation always delivers a positive result.
+a × +a = +a²
-a × -a = +a²
remember, for a square operation we multiply the same number by itself. therefore we cannot mix signs like -a × +a, because then they would not be the same numbers anymore.
b.
since the initial input value is 0, the third function (1/x) cannot be the first, because 1/0 is not defined.
c.
because of the "large" -32 term in the first function I guess that this will be the last one to create such a low negative result of -31.
since 1/x cannot be first, (x - 2)² is then first. that makes 1/x second, and (4x - 32) third, as mentioned.
let's try :
x = 0
(x - 2)² = (0 - 2)² = (-2)² = 4
x = 4
1/x = 1/4
x = 1/4
4x - 32 = 4×1/4 - 32 = 1 - 32 = -31
hurrah ! we are correct !
Find the measure of XY
Answer:
18
Step-by-step explanation:
For this problem, you have to look at the ratios of the corresponding sides.
Side DC and ZY correspond. It has a length of 10 and 15, respectively. So The ratio is 2:3. Same with BC and XY. If 12 is 2, than 3 must be 18 since 12x(2/3)=18
