The member equation which passes through the point (-2,-36) is y = 4 ( x-1)(x+5) .
What is a Parabola ?Parabola is a U shaped figure , whose all points are at a fixed distanced from a point called as focus and a line called as Directrix.
It is given that
The zeroes of the parabola is 1,-5.
The equation of the parabola is given by
y = a( x - x')(x-x'')
y = a( x-1)( x+5)
This is the equation for the parent function for the parabola
The parabola passes through the point ( -2 , -36 )
-36 = a( -2 -1)(-2+5)
-36 = (-3) * (3) a
-36 = -9 a
a = 4
y = 4 ( x-1)(x+5)
The member equation which passes through the point (-2,-36) is y = 4 ( x-1)(x+5) .
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100 POINTS!!! To find the distance AB across a river, a distance BC of 319 m is laid off on one side of the river. It is found that B = 104.6° and C = 14.4°. Find AB.
Answer: AB = 90.7 meter
Given following:
BC = 319 meterangle B = 104.6°angle C = 14.4°Find angle A :
⇒ 180° - (104.6° + 14.4°)
⇒ 61°
Now, use sine rule:
[tex]\sf \dfrac{AB}{BC} = \dfrac{sin(C^{\circ })}{sin(A^{\circ \:})}[/tex]
[tex]\sf \dfrac{AB}{319} = \dfrac{sin(14.4) } {sin(61)}[/tex]
[tex]\sf AB = \dfrac{319 \ sin(14.4) } {sin(61)}[/tex]
[tex]\sf AB = 90.70464953 \quad \approx \quad 90.7 \ m \ (rounded \: to \: nearest \ tenth)[/tex]
find the difference or type impossible [9 -1] [4 3] [2 -3] [5 0]
The difference based on the numbers given is -80.
How to compute the difference?The information given illustrates that the difference will be:
= (9 - 1) - (43) - (2 - 3) - 50
= 8 - 43 - (-1) - 50
= 8 - 43 + 1 - 50
= -80
Therefore, the difference or subtraction among the numbers given is -80.
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The concentration C of a chemical in the bloodstream t hours after injection into the muscle tissue is given by c=3t^2+t/t^3+50
The maximum concentration is greatest at; t = 4.926 hours
How to find the time at maximum concentration?We are given the equation that represents the concentration as;
C = (3t² + t)/(50 + t³)
The maximum value of C is obtained when the slope of C' is zero (can be a local maxima too). So we are going to find solutions of C'.
C' = (-3t⁴ - 2t³ + 300t + 50)/(50 + t³)
At C' = 0, we have;
-3t⁴ - 2t³ + 300t + 50 = 0
Using online polynomial root calculator, the only valid root of this is;
t = 4.926 hours
Thus, the maximum concentration is greatest at t = 4.926 hours
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Number sense is an important concept for young for young children to know because it provides a foundation for understanding arithmetic.
a. true
b. false
What is the degree of the polynomial f(x) = (x − 1)(x + 1)(x + 3)
Step-by-step explanation:
Multiply the factors
[tex](x - 1)(x + 1)(x + 3)[/tex]
[tex]( {x}^{2} - 1)(x + 3)[/tex]
[tex]{x}^{3} + 3 {x}^{2} - x - 3[/tex]
The highest exponent is 3, so the degree is 3
Describe how you could represent the fraction 4/10 using a model or number line
Answer:
Not going to give answer, but let you solve
Step-by-step explanation:
You first have to start by drawing a number line and mark two integers between the fraction lines. Then you have to divide the section between the two integers in an equal number of parts which is equal to the denominator.
Hope I helped
How many solutions does the system contain?
Answer: 2
Step-by-step explanation:
This system has 2 solutions because there are two points of intersection. See attached for where I pointed them out.
Sk+1=Sk+ak+1=(6+12+18+24+...+6k)+ak+1. ak+1=
I'm guessing you mean
[tex]S_{k+1} = S_k + a_{k+1}[/tex]
and that [tex]S_k[/tex] is the sum
[tex]S_k = 6 + 12 + 18 + \ldots + 6k = 6 (1 + 2 + 3 + \ldots + k) = 3 k (k+1)[/tex]
using the well-known formula
[tex]\displaystyle \sum_{i=1}^n i = 1 + 2 + 3 + \cdots + n = \frac{n(n+1)}2[/tex]
Then by substitution,
[tex]S_{k+1} = 6 (1 + 2 + 3 + \cdots + k + (k+1)) = 3 (k+1) (k+2)[/tex]
and hence
[tex]a_{k+1} = S_{k+1} - S_k[/tex]
[tex]a_{k+1} = 3 (k+1) (k+2) - 3k (k+1)[/tex]
[tex]a_{k+1} = 3 (k+1) \bigg((k+2) - k\bigg)[/tex]
[tex]\implies \boxed{a_{k+1} = 6 (k + 1)}[/tex]
Question 10 of 15
What is the solution to the system of equations graphed below?
Answer:
(1,5)
Step-by-step explanation:
The solution to the system of equations is where the two graphs intersect.
The two lines intersect at x=1 and y =5
The point of intersection is (1,5)
Answer: (1, 5)
Step-by-step explanation: Over to the right one, up five; I hope this helps!
Key: (xGraph, yGraph) If a number is positive on the x axis, go right, if negative, go left. The same applies to the y graph, if the number is positve, go up, if negative go down. Your solution is where the two lines meet.
whats the slope for (-17,12) (-8,3)
Answer:
-9/11
Step-by-step explanation:
slope is change in y/change in x
change in y is 9 (12-3)
change in x is -11 (-17--8)
slope is -9/11
A nurse opens a case that has a total of 160 ounces of med. If each vial in the case holds 1 1/3oz of medication how many vials are in the case
Answer:
120 Vials
Step-by-step explanation:
160/1and1/3
160/4over3
Multiply top by 3
480/4
120
The number of vials in the case is given by the equation A = 120 vials
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the number of vials in the case be represented as A
Now , the equation will be
The total amount of med = 160 ounces
The amount of med in each vial = 1 1/3 ounces
The amount of med in each vial = 4/3 ounces
So , the number of vials in the case A = total amount of med / amount of med in each vial
Substituting the values in the equation , we get
The number of vials in the case A = 160 / ( 4/3 )
The number of vials in the case A = ( 160 x 3 ) / 4
The number of vials in the case A = 40 x 3
The number of vials in the case A = 120 vials
Therefore , the value of A is 120
Hence , the number of vials is 120
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Lisa has 3 quarts of milk. Sanjay has 12 pints of milk. Who has more?
Answer:
Pints
Step-by-step explanation:
Answer:
Sanjay has more milk (12 pints)
Step-by-step explanation:
A quarter equals two pints
3 quarts = 3(2) = 6 pints
Lisa has 6 pints
Sanjay has 12 pints
Hope this helps
I need to know the slope and why intersect of Y = -32 x + 5
Answer:
slope = - 32 , y- intercept = 5
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - 32x + 5 ← is in slope- intercept form
with slope m = - 32 and y- intercept c = 5
[tex]\frak{Hi!}[/tex]
[tex]\orange\hspace{300pt}\above2[/tex]
We have the equation [tex]\boldsymbol{\sf y=-32x+5}[/tex].
We need to know its slope and y-intercept.
If an equation has the y=mx+c form, the slope is always
multiplied by x, the x co-ordinate. Such is the case here,
thereupon we note that the slope is [tex]\boldsymbol{\sf{-32}}[/tex].
As for the y-intercept, that's a constant. Do you remember
that constants have no variables attached to them?
Since the only number that has no variables attached to it is
5, we note that this is the desired value, the y-intercept.
done!!
[tex]\orange\hspace{300pt}\above3[/tex]
[tex]\large\boldsymbol{\sf{calligraphy}}[/tex]
i'm so confused! what answer am i missing???
(the first picture is the question)
(the second picture is the answers)
you might need to zoom in to see the picture
The point P could be located in quadrant I, quadrant IV and the x-axis
How to determine the quadrant?The coordinate of point P is given as:
P = (a, b)
Where a is positive
When a is positive, then the likely locations of P are:
On the x-axis, when b = 0In quadrant I, when b is positiveIn quadrant IV, when b is negativeHence, point P could be located in quadrant I, quadrant IV and the x-axis
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Please help I am behind on this questions!!
Answer:
$83,802
Step-by-step explanation:
The description is of an annuity due. Payments at the beginning of the period earn interest for the period, unlike those made at the end of the period.
FormulaThe future value of an annuity due is given by the formula ...
FV = P(1 +r)((1 +r)^t -1)/r
where P is the annual payment, r is the annual interest rate, and t is the number of years.
This is essentially the sum of t terms of a geometric series with first term P(1+r) and common ratio (1+r).
ApplicationFor P=$1000, r = 0.06, and t = 30, the future value is ...
FV = $1000(1.06)(1.06^30 -1)/0.06 ≈ $83,801.68
To the nearest dollar, the account value will be $83,802.
__
Additional comment
Spreadsheets and many graphing calculators have time-value-of-money (TVM) formulas built in. You need to make sure to choose the option that gives an annuity due, rather than an ordinary annuity. In the attached TVM picture, this setting is accomplished by PmtMode=1.
If A and B are vectors such as A+3b=-3i+j and A-B=i-2j find A and B
Solve by elimination.
[tex](\vec A + 3\, \vec B) - (\vec A - \vec B) = (-3\,\vec\imath + \vec\jmath) - (\vec\imath - 2\,\vec\jmath)[/tex]
[tex]\implies 4\,\vec B = -4\,\vec\imath + 3\,\vec\jmath \implies \boxed{\vec B = -\vec\imath + \dfrac34\,\vec\jmath}[/tex]
[tex]\implies \vec A = \vec\imath - 2\,\vec\jmath + \vec B[/tex]
[tex]\implies \boxed{\vec A = -\dfrac54 \,\vec\jmath}[/tex]
What is the common denominator of x+5/x+8 =1+6/x+1
Help QUICKLY!!
The value of a company’s stock is represented by the expression x2 – 2y and the company’s purchases are modeled by 2x + 5y. The company’s goal is to maintain a stock value of at least $7,000, while keeping the purchases below $1,000. Which system of inequalities represents this scenario?
1. x2 – 2y > 7000 2x + 5y < 1000
2. x2 – 2y ≥ 7000 2x + 5y < 1000
3. x2 – 2y > 7000 2x + 5y ≤ 1000
4. x2 – 2y ≤ 7000 2x + 5y ≤ 1000
Answer:
2
Step-by-step explanation:
2.is best possible answer as it.says below 1000...
Answer:
the answer is
x^2 – 2y ≥ 7000
2x + 5y < 1000
so it would be the second option
Step-by-step explanation:
just took the test:)
Use implicit differentiation to find an equation of the tangent line to the curve at the given point.
x^2+ 2xy - y^2 + x = 20, (3, 4) (hyperbola)
Differentiating both sides of
[tex]x^2 + 2xy - y^2 + x = 20[/tex]
with respect to [tex]x[/tex] yields
[tex]2x + 2y + 2x \dfrac{dy}{dx} - 2y \dfrac{dy}{dx} + 1 = 0 \\\\ \implies (2x-2y) \dfrac{dy}{dx} = -1 - 2x - 2y \\\\ \implies \dfrac{dy}{dx} = \dfrac{1 + 2x + 2y}{2(y-x)}[/tex]
At the point (3, 4) (so [tex]x=3[/tex] and [tex]y=4[/tex]), the tangent line has slope
[tex]\dfrac{dy}{dx} = \dfrac{1 + 2\times3 + 2\times4}{2(4-3)} = \dfrac{15}2[/tex]
Then the tangent line to (3, 4) has equation
[tex]y - 4 = \dfrac{15}2 (x - 3) \implies \boxed{y = \dfrac{15}2 x - \dfrac{37}2}[/tex]
So 488 is divided into 4 equal groups of
Answer:
Each group will have 122
Step-by-step explanation:
It technically means divide 488 by 4
f(x)= x³ + x² and g is a vertically scaled version of f. The functions are graphed where f is solid and g is
dashed.
-2
9
Y
5 ₹
4+
2+
-4
-2+
-6+
9
2
x
(06.02 LC)
Line AB contains points A (-2, 3) and B (4, 5). Line AB has a slope that is
How can i simplify this one, please someone help me!
Combine the fractions and factorize.
[tex]\dfrac{3a^2b}{a-b} + \dfrac{3ab^2}{b-a} = \dfrac{3a^2b}{a - b} - \dfrac{3ab^2}{a - b} \\\\ ~~~~~~~~ = \dfrac{3a^2b - 3ab^2}{a - b} \\\\ ~~~~~~~~ = \dfrac{3ab (a - b)}{a - b} \\\\ ~~~~~~~~ = 3ab[/tex]
Describe the relationship between the temperature and the coffee sales.
The relationship between temperature and the coffee sales is a negative exponential of temperature
relation is subject of order between to sets or how the connected to each other.
The temperature of liquid is essential in the process of brewing because its affects the rate of evaporation or extraction. it refers to the test and matters that are dissolved from the coffee beans. The hot is the water, the quick it is to extract. At a high temperature, it’s tougher to control the rate of extraction. This can lead to over-evaporation of liquid, making your coffee taste too bitter since the heat strips away a lot of oxygen.
since the temperature varies over the year, which implies the taste of coffee also vary in a manner that in cold days people love coffees and in hotter days the people love to drink cold drinks instead of coffees
so in cold days the sales of coffees is grater in comparison with hot days
Thus the relationship between the sales of coffees and temperature is negative exponential of temperature.
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A rectangular prism has a length of 3 1/2 inches, a width of 5inches, and a height of 1 1/2
PLEASE HELP!!!!
Question 7(Multiple Choice Worth 1 points)
(06.05 LC)
Given the functions m(x) = 4x - 11 and n(x) = x - 10, solve m[n(x)].
m[n(x)] = 4x - 51
m[n(x)] = 4x - 29
m[n(x)] = 4x²- 51
m[n(x)] = 4x² - 29
Answer:
4x -51
Step-by-step explanation:
m(n(x)) = m(x - 10) = 4(x-10) - 11 = 4x -40 -11 = 4x -51
Answer:
m[n(x)] = 4x - 51
Given following:
m(x) = 4x - 11n(x) = x - 10Solving steps:
m[n(x)]m[x - 10]4(x - 10) - 114x - 40 - 114x - 51On this route, she will pay a toll every 3 1⁄2 miles, and the cost of each toll is $1.35.1. How many tolls will Stephanie pay? 2.
The equation which can be used to represent the total tolls Stephanie will pay is y = 1.35x
Equationlet
Number of 3 1⁄2 miles = xCost of each toll = $1.35Total tolls paid = yy = 1.35x
If the number of 3½ miles on the route is 5
Then, the total toll paid is
y = 1.35x
= 1.35(5)
= $6.75
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Three men and eight women are waiting to be interviewed for jobs. If they are all selected in random order, find the probability that all will be interviewed first.
The probability that all men will be interviewed first is; 1/55
How to find probability combination?To solve this question we will make use of the probability combination formula which is;
nCr = n!/(r! * (n - r)!)
Thus, since we want to find the probability that all men will be interviewed first, then we will use the formula;
3(3!)/((11C1) * (10C1) * (9C1)) = 18/990
Simplifying that fraction gives us; 1/55
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You are buying mouthwash at your local store. The price of
the mouthwash is $4.39. It is currently on sale for 20% off.
You also have a store coupon for $1.00 off and a
manufacturer's
coupon for $1.25 off. What is your
subtotal?
Answer:
$1.26
Step-by-step explanation:
A 20% off means multiplying by 1-0.2=0.8
4.39*0.8=3.512
3.512-1=2.512
2.512-1.25=1.262
1.262 rounded to the nearest cent is $1.26
Find x.
Do not round your answer
12 cm
6 cm
5 cm
The value of x from the given diagram is 16.6
Secant-secant theoremIn order to determine the value of x from the given figure, we will use the secant-secant theorem shown by the equation.
(6 +12) * 6 = (5 + x) * 5
Expand
36+72 = 25 + 5x
108 = 25 + 5x
5x = 108 - 25
5x = 83
x = 83/5
x = 16.6
Hence the value of x from the given diagram is 16.6
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