Answer:
y - 5 = -2(x + 3)
Step-by-step explanation:
When you write an equation in point-slope form, you only need two things: a point and a slope.
Given:
point: (-3, 5)
slope (m): -2
The standard point-slope equation is
y - y₁ = m(x - x₁)
Plug in what you know.
y - (5) = -2(x - (-3))
Simplify.
y - 5 = -2(x + 3)
This is your equation.
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Solve the linear programming problem.
Minimize and maximize
P = 10x + 5y
Subject to
2x+3y 230
2x+y ≤ 26
-2x+3y ≤ 30
x, y 20
The minimized value is 50 and the maximized value is 130
How to minimize and maximize the function?The objective function is:
P = 10x + 5y
Subject to
2x+3y ≤30
2x+y ≤ 26
-2x+3y ≤ 30
x, y >0
Next, we plot the graph of the constraints (see attachment)
From the graph, the vertices of the feasible regions are:
(0, 10),(12, 2) and (6,14)
Substitute these values in P = 10x + 5y
P = 10(0) + 5(10) = 50
P = 10(12) + 5(2) = 130
P = 10(6) + 5(14) = 130
Hence, the minimized value is 50 and the maximized value is 130
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8
Diameter;
Radius:
B
(a) Find the perimeter of the square
(b) Find the area of the square Area =
(c) Find the circumference of the circle C = 2πr
(d) Find the area of the circle. Area = πr²
(e) Find the area of the region between the square and the circle
answer: A: 16
B: 16
C: 12.57
D: 12.57
E: 3.43 (do area of square-area of circle 16-12.57
If f(x) = 6x² - 4 and g(x) = 2x + 2, find (f- g)(x)
Step-by-step explanation:
[tex]f(x) = 6 {x}^{2} - 4[/tex]
[tex]g(x) = 2x + 2[/tex]
[tex] \: [/tex]
[tex] = (f - g)(x)[/tex]
[tex] = f(x) - g(x)[/tex]
[tex] = 6 {x}^{2} - 4 - (2x + 2)[/tex]
[tex] = 6 {x}^{2} - 4 - 2x - 2[/tex]
[tex] = 6 {x}^{2} - 2x - 4 - 2[/tex]
[tex] = 6 {x}^{2} - 2x - 6[/tex]
[tex](f - g)(x) = 6 {x}^{2} - 2x - 6[/tex]
The graph of a function is shown on the coordinate plane below.
Between which two values of x is the function nonlinear and increasing?
A -5 and -3
B -3 and 1
C 1 and 4
D 4 and 6
The answer to this question is choice B
What are the solutions to the quadratic equation below?
x²-2x-168 =0
Answer:
x= 14, –12
Step-by-step explanation:
The given question might make you believe that it's difficult due to it's frightening digit (168) but in fact in you use the following methods, it's going to be a pieces of cake.
the delta formula:
Δ=b²–4ac===> (–2)²–4(1)(–168)=676
[tex]x 1 = \frac{ - ( - 2) + \sqrt{676} }{2} = 14 [/tex]
[tex]x2 = \frac{ - ( - 2) - \sqrt{676} }{2} = - 12[/tex]
well this can be on of the methods and the other one is
The full square formula:
[tex]x ^{2} - 2x - 168 = 0 \\ {x}^{2} - 2x = 168[/tex]
[/tex]
now what you need to do is to put this on both side of the equation (½b)²=1
[tex] {x}^{2} - 2x + 1 = 168 + 1 \\ {(x - 1)}^{2} = 169 \\ x - 1 = 13 = = > x = 14 \\ x - 1 = - 13 = = = > x = - 12[/tex]
Complete the following table using the equation: y = -2x²
The parabola is a downward parabola which is passing through origin and leading coefficient of the negative 2.
What is the parabola?It's the locus of a moving point that keeps the same distance between a stationary point and a specified line. The focus is a non-movable point, while the directrix is a non-movable line.
The equation of a quadratic function, of vertex (h, k), is given by:
y = a(x – h)² + k
where a is the leading coefficient.
The equation of the parabola will be
y = -x²
The given parabola is a downward parabola which is passing through origin and leading coefficient of the negative 2.
The graph of the function is given below.
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file attached belowfile attached below
A $1,000.00 bond at 85 1/4 % pays 6.8 % annual interest. Calculate cost of bond.
Based on the par value of the bond and the percentage it was issued at, the cost of the bond is $852.50.
What is the cost of the bond?The current cost of the bond is the present value of the bond's cashflows and its par value.
This is taken into account when the bond is issued at a certain percentage which in this case is 85 ¹/₄%.
The cost of the bond is:
= 1,000 x 85 ¹/₄%
= $852.50
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2) Sarah takes a small business loan for
$25,000. The term for repayment is 60
months and the interest rate is 5.75%.
formula,
Use the loan amortization
what is the estimated monthly
payment?
Using it's formula, it is found that the estimate monthly payment is of $480.42.
What is the monthly payment formula?It is given by:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
In which:
P is the initial amount.r is the interest rate.n is the number of payments.The parameters are given as follows:
P = 25000, n = 60, r = 0.0575.
Hence:
r/12 = 0.0575/12 = 0.00479167.
Hence the payment will be of:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
[tex]A = 25000(0.00479167)\frac{(1+0.00479167)^{60}}{(1+0.00479167)^{60}-1}[/tex]
A = 480.42.
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paul asked to order snacks for an office meeting of 180 people. she decides to order desert squares which come in boxes of 24. she estimates she will need 3.5 snacks per person. how many boxes should she buy?
Answer:
27 boxses
Step-by-step explanation:
calculations is shown in the picture
Find the product write your answer in exponential form 7^-1•7^-7
Answer:
1/5764801
Step-by-step explanation:
7^-1 × 7^-7
= 1/7(7^-7)
= 1/7(1/823543)
= 1/5764801
Simplify this expression:
12a−8−5a+12
12a - 8 -5a + 12
arranging like terms
12a - 5a - 8 + 12
a ( 12-5) - 8 - 12
a(7) - 4(2 - 3)
a(7) -4(-1)
a(7) + 4
7a + 4
simplifing the expressions
Answer:
12a-5a-8+12
=(12-5)a+4
=7a+4
? Question
Select the graph of the transformation.
The graph f(x)=√√ is transformed to form
shows g(x).
Answer: The vertex of the graph of [tex]y=x^2[/tex] is shifted to the right 4 units and up 3 units.
Please help me answer this question
Answer:
Z = sin(xy)
[tex]\frac{1}{y} \times \frac{\partial Z}{\partial x} =\cos \left( xy\right) =\frac{1}{x} \times \frac{\partial Z}{\partial y}[/tex]
If x=3 y=4 z=6 then 4x+8yz+3y equals
Answer:
216
Step-by-step explanation:
4x+8yz+3y
Let x=3 y=4 z=6
Substitute the values into the expression
4(3)+8(4)(6)+3(4)
Multiply first
12+192+12
Then add
216
What's the solution to –9x + 4 < 40? Question 4 options: A) No solutions B) All real numbers C) x > –4 D) x < –6
Hey there!
-9x + 4 < 40
SUBTRACT 4 to BOTH SIDES
-9x + 4 - 4 < 40 - 4
SIMPLIFY IT!
-9x < 40 - 4
-9x < 36
DIVIDE -9 to BOTH SIDES
-9x/-9 < 36/-9
SIMPLIFY IT!
x < 36/-9
x < -4
Therefore, the answer should be:
x < -4
(The graph is down below)
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Samantha opened a savings account and deposited $8192. The account earns 10% in interest annually. She makes no further deposits and does not withdraw any money. In t years, she has $25,710 in this account. Write an equation in terms of t that models the situation.
The equation in terms of t that models the situation is given by
[tex]8192(1+\frac{0.01}{12} )^{12t} = 25710[/tex].
We know that the interest on a loan or deposit that is accrued on both the initial principal and the total interest from prior periods is known as compound interest and it can be calculated as
[tex]A = P(1+\frac{r}{n})^{nt}[/tex],
where P is the initial principal, r is the rate of interest, n is the number of times interest was charged for each time period, t is the amount of time that has passed and A is the final amount.
Here, P = 8192, r = 10% = 10/100 = 0.01, n = 12 and A = 25,710
So, we can write
[tex]8192(1+\frac{0.01}{12} )^{12t} = 25710[/tex]
Therefore the required equation is
[tex]8192(1+\frac{0.01}{12} )^{12t} = 25710[/tex]
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HELP ASAP!!!
At which values of x does the graph of the function F(x) have a vertical asymptote? Check all that apply. x = -8 x = 4 x = 3 x = -3 x = 8 x = -4
Answer:
A,E
Step-by-step explanation:
Answer:
x = 3
x = -8
Step-by-step explanation:
Maria expanded the following square as follows: (x+3)² =x²+9, is this correct?
Answer:
x² + 6x + 9
Explanation:
[tex]\sf = \left(x+3\right)^2[/tex]
Use perfect square formula: (a + b)² = a² + 2ab + b²
[tex]= \sf x^2 + 2(x) (3) + 3^2[/tex]
simplify the following
[tex]= \sf x^2 + 6x +9[/tex]
Hence Maria is not correct. The correct answer is x² + 6x + 9.
PLEASEEEEEEE PLEASEEEEEE HELPPPPPP ASAPPPP
Find the measure of angle A in degrees.
Answer:
Angles are 45, 45 and 90 degrees because
AB and BC are congruent so that means the angles eating the sides are also congruent.
So to find the congruent angles:
180-90=90/2=45 degrees
To find AC:
a²+b²=c²
x²+x²=h²
√18=√c²
3√2=c
(I don't know why it says 3√3, but I think the q is wrong)
Hope it helps!
Answer:
45 degrees
Step-by-step explanation:
This is a special right triangle with these lengths. Which leads us to find the angles of 45, 45, 90 and B is 90 so A and C are 45 degrees.
Prove: An odd number squared is
an odd number.
(2n + 1)² = [?]n² + [ ]n +
=
[](2n² + 2n) + [ ]
= an odd
Considering the result of the expression of the square of the sum, 2(2n² + 2) is always an even number, then when 1 is added it will always be an odd number.
What is the square of the sum notable product?It is given as follows:
(a + b)² = a² + 2ab + b².
In this problem, the expression is:
(2n + 1)² = (2n)² + 2(2n)(1) + 1²
= 4n² + 4n + 1
= 2(2n² + 2) + 1
The term 2(2n² + 2) will always be even(multiplication by 2), and when 1 is added to an even number it will always be odd, hence it is proved that an odd number squared is an odd number.
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I need all of these please
Answer:
second answer is 120
firsr answer is 25
Given the coordinate T(8, -4), find the location of T after a dilation using a scale factor of 0.4.
The new coordinate will be T'(3.2 , -1.6) .
What is the meaning of Dilation ?Dilation is the transformation that changes the size of the object without changing its shape .
If a coordinate point is (x,y) and a dilation of scale factor f is applied then the new coordinates will be (fx ,fy)
The coordinate given in the question is T(8, -4)
The scale factor is 0.4
The new coordinate is
T'( 0.4 * 8 , 0.4 * (-4))
T'(3.2 , -1.6)
Therefore the new coordinate will be T'(3.2 , -1.6)
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What is the value of x in the figure below? In this diagram, AABD ~ ACAD.
The value of x in the right angle triangle is 45 / 4 units
How to find the side of a right triangle?AB² = 20² - 15²
AB = √400 - 225
AB = √175
AB = √175 units
Hence, using similarity ratio,
x / 15 = 15 / 20
cross multiply
20x = 225
x = 225 / 20
x = 45 / 4
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5
The recursive formula for a geometric sequence is given below. What is the third term in the sequence?
f(1) = 2
f(n) = 3f(n − 1)
-
OA. 18
OB. 54
OC. 162
OD. 12
Reset
Submit
[tex]\Large{ \boxed{ \tt{ \blue{A}}}}\Large{ \boxed{ \tt{ \pink{N}}}}\Large{ \boxed{ \tt{ \green{S}}}}\Large{ \boxed{ \tt{ \purple{W}}}}\Large{ \boxed{ \tt{ \red{E}}}}\Large{ \boxed{ \tt{ \pink{R}}}}[/tex]
[tex] \: \: [/tex]
A. 18[tex] \: \: [/tex]
[tex]\Large{ \boxed{ \tt{ \blue{S}}}}\Large{ \boxed{ \tt{ \pink{O}}}}\Large{ \boxed{ \tt{ \green{L}}}}\Large{ \boxed{ \tt{ \purple{U}}}}\Large{ \boxed{ \tt{ \red{T}}}}\Large{ \boxed{ \tt{ \pink{I}}}}\Large{ \boxed{ \tt{ \blue{O}}}}\Large{ \boxed{ \tt{ \pink{N}}}}[/tex]
[tex] \: \: [/tex]
[tex] \mathtt{f(1) = 2}[/tex][tex] \tt{f(2) \: = \: 3f \: (1) \: = \: 3(2) \: = \: 6}[/tex][tex] \tt{f(3) \: = \: 3f(2) \: = \: 3(6) \: = \: 18}[/tex][tex]\color{pink}─────────────────────────────────────[/tex]
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If f(x)=x+2 and g(x)=x2+1 find:a. f(g(x)) b. g(f(x))
Answer:
Step-by-step explanation:
Answer:
x² + 3 and x² + 4x + 5
Step-by-step explanation:
(a)
to find f(g(x)) substitute x = g(x) into f(x)
f(g(x))
= f(x² + 1)
= x² + 1 + 2
= x² + 3
(b)
to find g(f(x)) substitute x = f(x) into g(x)
g(f(x))
= g(x + 2)
= (x + 2)² + 1 ← expand factor using FOIL
= x² + 4x + 4 + 1
= x² + 4x + 5
Factor the following expression. x² - 10x +9 2 Factor the following expression . x² - 10x +9 2
Answer:
x² - 10x + 9 = (x-9)(x-1)
the factored expression would be (x-9)(x-1)
Use the Factor Theorem to determine whether x−1 is a factor of 4x^3−6x^2+2x+1.
the data below shows the number of workers employed in the various section s of each a construction company in the Lagos
Carpenter 24
plumber 12
labourers 27
plasterers 15
painters 9
Messengers 3
bricklayers 18
if the Worker is retrenched, what is the probability that he is a plumber or a plasterer?
If the Worker is retrenched, the probability that he is a plumber or a plasterer will be 0.0152.
What is probability?The chances of an event occurring are defined by probability. Probability has several uses in games, in business to create probability-based forecasts,
The probability that the employee is a plumber;
[tex]\rm P(plumber)= \frac{No \ of \ plumber}{Total \ number \ of \ employ} \\\\ P(plumber)=\frac{12}{108} \\\\\ P(plumber)= 0.11[/tex]
The probability that the employee is a plasterer;
[tex]\rm P(plasterers )= \frac{No \ of \ plasterers }{Total \ number \ of \ employ} \\\\ P(plasterers )=\frac{15}{108} \\\\\ P(plasterers )= 0.13[/tex]
The probability that he is a plumber or a plasterer:
P = 0.13 × 0.11
P= 0.0152
Hence, if the worker is retrenched, the probability that he is a plumber or a plasterer will be 0.0152.
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Terick ran 2 3of a mile in 8 minutes. It took Chad 40 minutes to run 3 1 4miles. a. If Terick runs at that speed, how long will it take him to run one mile?
The time taken for Terick to run one complete mile is determined as 12 minutes
Speed of Chad
The speed of chad is calculated as follows;
s = distance/time
s = (3.25 miles)/(40)
s = 0.08125 miles/min
Total distance ran by Terick2/3 of a mile = 8 mins
1/3 of a mile = ?
1/3 of a mile = 4mins
1 mile = 8 mins + 4 mins = 12 mins
Thus, the time taken for Terick to run one complete mile is determined as 12 minutes.
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