Answer:
See below
Step-by-step explanation:
Present Value = 400
Period = 1 month 8 years is n = 96 periods
Interest per period in decimal form i = .076 / 12 = .0063333
Fv = PV ( 1 + i)^n
Fv = 400 ( 1 + .076/12)^96 = 733.29 dollars
solve. help fast!! alots of points
x + y=10
x-y=-1
Answer:
∴ x = 4.5, y = 5.5
Step-by-step explanation:
x + y = 10 ------ equation (1)
x - y = -1 ------ equation (2)
Add equations (1) and (2):
(x + y) + (x - y) = 10 + (-1)
x + y + x - y = 10 - 1
2x = 9
∴ x = 4.5
Substitute x = 4.5 into equation (1):
4.5 + y = 10
∴ y = 5.5
Write the equation of the parabola that has the same shape as f(x)=-3 x² but with vertex (5,9) in the form f(x)=a(x-h)²+k.
f(x)=
A supply company manufactures copy machines. The unit cost C (the cost in dollars to make each copy machine) depends on the number of machines made.
If x machines are made, then the unit cost is given by the function C(x)=0.7x²-392x+60,983. How many machines must be made to minimize the unit
cost?
Do not round your answer.
The number of machines must be made to minimize the unit cost is 280
What is second order derivative test?
A real-valued function formed on a closed or bounded interval can have its absolute maximum and lowest values determined systematically using the second derivative test. In physics, economics, and engineering, the second derivative test can be used to solve optimization problems.
We are given a function
C(x)=0.7x²-392x+60,983.
We first find the first derivative of the function we get
C'(x) = 1.4x-392
We now equate the first derivative to zero
we get
1.4x= 392
x= 280
Now we derivate the function again we get
C"(x)= 1.4
Now this value is greater than zero hence here is the greatest minimum
Hence the company must produce 280 units to minimize the cost
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For the following exercises, find the x -or t -intercepts of the polynomial functions.11. C(t)=4t4+12t3−40t2
Answer: (0,0),(−5,0),(2,0)
Answer: (0,0), (-5,0), (2,0)
Step-by-step explanation:
c(t)=4t⁴+12t³-40t²
1) t=0
c(t)= 4(0⁴)+12(0³)-40(0²)
c(t)=4(0)+12(0)-40(0²)
c(t)=0+0+0
c(t)=0
Thus (0,0)
2) c(t)=0
4t⁴+12t³-40t²=0
Divide both parts of the equation by 4:
t⁴+3t³-10t²=0
t²(t²+3t-10)=0
t²=0
t=0
Thus (0,0)
t²+3t-10=0
t²+(5t-2t)-10=0
(t²+5t)-(2t+10)=0
t(t+5)-2(t+5)=0
(t+5)(t-2)=0
t+5=0
t=-5
Thus (-5,0)
t-2=0
t=2
Thus (2,0)
Where is the blue point on the number line?
Step-by-step explanation:
every marker marks obviously a unit of 6.
so, the values go up and down from 0 in multiples of 6.
for the blue dot we count down from 0 :
5 markers
each marker is worth 6. and we are going down into the negative realm.
so, the blue dot is
- 5×6 = -30
A boat travels north at a speed of 20 mph and a bearing of N 32 degrees E. Another boat travels at a speed of 28 mph and a bearing of S 42 degrees E. After 2 hours, how far apart are the boats
Answer:
78.23 miles----------------------------------
It is assumed boats leave from the same point.
Boats travel after 2 hours:
20*2 = 40 miles and 28*2 = 56 miles.The angle formed between the two directions:
90° - 32° + 90° - 42° = 108°The line between the endpoints is opposite to this angle.
Use the law of cosines and find the distance:
[tex]d=\sqrt{40^2+56^2-2*40*56*cos 108} \approx 78.23 \ miles[/tex]Answer:
77.3 miles apart (nearest tenth)
Step-by-step explanation:
Given information:
Boat A travels north at a speed of 20 mph and a bearing of N32°E. Boat B travels at a speed of 28 mph and a bearing of S42°E.After 2 hours, Boat A will have travelled 40 miles.After 2 hours, Boat B will have travelled 56 miles.Draw a diagram using the given information (see attached).
To find how far apart the boats are, model as a triangle and find the length of the missing side by using the cosine rule.
[tex]\boxed{\begin{minipage}{6 cm}\underline{Cosine Rule} \\\\$c^2=a^2+b^2-2ab \cos C$\\\\where:\\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides.\\ \phantom{ww}$\bullet$ $C$ is the angle opposite side $c$. \\\end{minipage}}[/tex]
From inspection of the drawn diagram:
a = 40 milesb = 56 milesc = distance between the boatsC = 180° - 32° - 42° = 106°Substitute the values into the cosine rule and solve for c:
[tex]\implies c^2=40^2+56^2-2(40)(56) \cos 106^{\circ}[/tex]
[tex]\implies c^2=1600+3136-4480 \cos 106^{\circ}[/tex]
[tex]\implies c^2=4736-4480 \cos 106^{\circ}[/tex]
[tex]\implies c=\sqrt{4736-4480 \cos 106^{\circ}}[/tex]
[tex]\implies c=77.27131004[/tex]
Therefore, the boats are 77.3 miles apart (nearest tenth) after 2 hours.
Help on perimeter please!
Manuel builds and sells wooden crates. He made this table to show how much his crates cost in dollars.
ill give brainlist if you answer is correct
Number of crates 2 4 6 8
Cost ($) $25 $45 $65 $85
Which equation represents this situation, where x is the number of crates and y is the cost?
Responses
y=−10x+252y
y=10x+5y
y=−10x+125y
y=10x−446
From the given details of Manuel wooden crates , where x represents the number of crates and y represents the cost then equation represents the given situation is given by y = 10x + 5.
As given in the question,
Given details of Manuel wooden crates :
Number of crates : 2 4 6 8
Cost in dollars : 25 45 65 85
From the given table where x represents the number of crates and y represents the cost :
(x₁ , y₁) = ( 2, 25)
(x₂ , y₂) = ( 4, 45)
For the given situation equation is given by :
( y - y₁) / (x- x₁) = (y₂ - y₁) / (x₂ - x₁)
⇒( y - 25) / (x -2) = (45 -25)/ (4 -2)
⇒(y -25) / (x -2) = 10
⇒y - 25 = 10(x-2)
⇒ y = 10x +5
Therefore, from the given details of Manuel wooden crates , where x represents the number of crates and y represents the cost then equation represents the given situation is given by y = 10x + 5.
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use the distributive property to rewite the expression 6x (y - z)
By the use of the distributive property, we have the result obtained as 6xy - 6xz.
What is the distributive property?The term distributive property has to do with the process by which we can remove the brackets that may sometimes occur in a mathematical expression. It is the way by which we can be able to rewrite the mathematical expression without adding the brackets thereby making mathematical operations much easier.
We have the expression; 6x (y - z)
Multiplying through by 6x we have;
6xy - 6xz
Using the distributive property, we obtain; 6xy - 6xz
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-40 -2 (3m + 1/2) = 7m -2
Please solve this linear equations to one variable
Guyton bought 13 plants to arrange along the border of his garden. How many distinct arrangements can he make if the plants are comprised of 5 tulips, 5 roses, and 3 daisies?
Guyton can make the 72,072 distinct arrangements of the flowers.
Given, that Guyton bought 13 plants to arrange along the border of his garden.
Now, we are asked that how many distinct arrangements he can make.
As, we know that to arrange 13 plants comprised of 5 tulips, 5 roses, and 3 daisies,
we need to apply Permutations over 13 objects among which 5 are tulips, 5 are roses and 3 are daisies.
Now, on applying the permutations, we get
13 plants can be arranged in 13! ways,
but as among them 5 are tulips, 5 are roses and 3 are daisies.
So, Guyton can arrange the flowers in 13!/(5!×5!×3!).
= (6,22,70,20,800)/(120×120×6)
= 72,072
So, the arrangement can be done in 72,072 ways.
Hence, he can make the 72,072 distinct arrangements.
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A rental car company charges $63.25 per day to rent a car and $0.07 for every mile driven. Ella wants to rent a car, knowing that: She plans to drive 50 miles. She has at most $130 to spend.
Find the measure of angle a
a =
Answer:
a = 48°
Step-by-step explanation:
Forming the equation,
→ 42° + a = 90°
Now the value of a will be,
→ 42° + a = 90°
→ a = 90° - 42°
→ [ a = 48° ]
Hence, the value of a is 48°.
The table below gives selected values for the differentiable and increasing function ff and its derivative. If g(x) = f^-1(x), what is the value of g'(-2)?
The derivative of the inverse function of the differentiable and increasing function f(x), g(x) = f⁻¹(x), at x = -2, g'(-2) is [tex]\dfrac{1}{7}[/tex]
What is the inverse of a function?An inverse function reverse the effect of the operations of a function, such that when the output of a function is the argument of its inverse function, the input of the function is obtained.
The derivative of an inverse function is found using the formula;
[tex]\dfrac{d}{dx} f^{-1}(x) = \dfrac{1}{f'[f^{-1}(x)]}[/tex]
When x = -2, we get, from the table included in the question;
g(-2) = f⁻¹(-2) = 1
Therefore;
[tex]\dfrac{d}{dx} f^{-1}(-2) = \dfrac{1}{f'[f^{-1}(-2)]} = \dfrac{1}{f'[1]}[/tex]
[tex]g'(-2) = \dfrac{d}{dx} f^{-1}(-2) = \dfrac{1}{f'[1]}[/tex]
In the included table, f'(1) = 7, from which we get;
[tex]g'(-2) = \dfrac{1}{f'[1]}=\dfrac{1}{7}[/tex]
[tex]g'(-2) = \dfrac{1}{7}[/tex]
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Show all work and please circle your final answer.
The simplest radical numbers according algebra properties are listed below:
5√7 √15 / 6How to simplify radical expressions
In this question we find two cases of radical numbers that must be simplified in accordance with algebra properties, especially those related to square roots, and factor decomposition. Now we proceed to simplify each expression:
Case A: √175
Step 1 - Use factor decomposition
√175 = √(5² × 7)
Step 2 - Apply algebra properties to simplify the expression
√175 = √5² × √7
√175 = 5 × √7
√175 = 5√7
Case B: √(5 / 12)
Step 1 - Use factor decomposition
√(5 / 12) = √[5 / (3 × 2²)]
Step 2 - Apply algebra properties to simplify the expression
√(5 / 12) = √5 / √(3 × 2²)
√(5 / 12) = √5 / [√3 × √2²]
√(5 / 12) = √5 / (2√3)
Step 3 - Rationalize the resulting expression
√(5 / 12) = (√5 × √3) / 6
√(5 / 12) = √15 / 6
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Martha had 12 2/3 yards of drapery material. She used 34 of it to make the drapes for her
family room. How much does she have left to make matching throw pillows?
The fraction that Martha has left to make matching throw pillows is 3 1/6 yards.
How to calculate the fraction?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers. On the other hand, a fraction appears in the numerator or the denominator of a complex fraction.
From the information given, Martha had 12 2/3 yards of drapery material. She used 3/4 of it to make the drapes for her family room.
Since 3/4 has been used, the fraction left will be gotten by subtracting the fraction that had already been used from the total fraction that she has. In this case, it should be noted that this will be illustrated as:
Total fraction that Martha has - The fraction that has been used
= 1 - 3/4
= 1/4
Therefore, the fraction will be the fraction that is left multiplied by the yards of drapery material that Martha had at the beginning. This will be:
= Fraction unused × Total yards of material
= 1/4 × 12 2/3
= 1/4 × 38/3
= 19/6
= 3 1/6
The fraction is 3 1/6 yards.
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how to rewrite 13/10 as a decimal
The decimal equivalent of 13/10 is 1.3
Decimal:
Decimal is referred as the numbers, which consist of two parts namely, a whole number part and a fractional part separated by a decimal point. For example, 12.5 is a decimal number.
Give,
Here we have the fraction 13/10
And we need to find the decimal equivalent to the fraction.
In the given fraction, we have to use the long division method in order to get the decimal for,
The steps for the long division is as follows:
1) Set up the problem with long division bracket. Put dividend inside bracket and divisor on outside left.
2) 10 goes into 13 (1-times). Put a 1 in the next place of quotient and multiply 10 by 1 to get 10.
Subtract 10 from 13 to get remainder (13-10=3).
3) Now, bring down 0 from the dividend, to make 30. 10 goes into 30 (3-times). Put a 3 in the next place of quotient and multiply 10 by 3 to get 30.
Subtract 30 from 30 to get remainder (30-30=0).
Therefore, the decimal equivalent to 13/10 is 1.3
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Question 1 Part A:
Select and use the most direct method to solve
3x(x - 3) = 12
X=___ Or X=____
The solution of the equation 3x(x - 3) = 12 will be 4 and negative 1.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The equation is given below.
3x(x - 3) = 12
Simplify the equation, then we have
3x(x - 3) = 12
x(x - 3) = 4
x² - 3x - 4 = 0
Factorize the equation, then we have
x² - 3x - 4 = 0
x² - 4x + x - 4 = 0
x(x - 4) + 1(x - 4) = 0
(x - 4)(x + 1) = 0
x = 4, -1
The solution of the equation 3x(x - 3) = 12 will be 4 and negative 1.
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Please help asap! Need this done for assignment done for tomorrow!
Answer:
Step-by-step explanation:
On average a clothing store gets 120 customers per day. What is the probability of getting 150 customers in one day?
Answer:
0.001.
Step-by-step explanation:
So, P (X=150) = P (X>150) - P (X>151) So, P (X>151) = (151-120)/sqrt (120) = P (Z>2.8299) = 0.5- 0.4977 = 0.0023 So, the probability of getting 150 customers in a day = 0.0033- 0.0023 which is equal to 0.001.
Part 1. Find the perimeter.
3x + 8
5x+2
4x -1
Answer:
12x + 9
Step-by-step explanation:
Combine the line terms
3x + 5x + 4x = 12x
8+ 2 -1 = 9
12x + 9
URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100 POINTS!!!!!
Answer:
x=66 degrees so b
Step-by-step explanation:
132 and 2x are corresponding angles so 132=2x and x=66 degrees
Answer:
x = 66
Step-by-step explanation:
2x = 132
Divide by 2 on both sides
x = 66
True or false
Wages have decreased because competition from foreign companies has increased the demand for low-skilled workers.
This just isn’t making any sense to me please help before 11pm
8 AB has endpoints A(-5, 0) and B(4, 3). CD has endpoints C(-3, 9) and
D(1, -3). The equations of the lines containing AB and CD are x - 3y = -5
and 3x + y = 0, respectively.
a. How could you quickly check that these equations are correct?
b. Verify that the lines are perpendicular.
c. Find the point of intersection of AB and CD by solving the system
of equations.
d. Find the midpoints of AB and CD. Compare your results with Part c.
e. What kind of quadrilateral is ACBD? Explain your reasoning.
Part (a)
To verify a point is on the line, we plug the coordinates into that equation. If we get a true result at the end, then we've confirmed the point is on that line.
For point A(-5,0) we have x = -5 and y = 0 pair up together. Let's plug these coordinates into x - 3y = -5 to get the following steps shown below.
x - 3y = -5
-5 - 3(0) = -5
-5 - 0 = -5
-5 = -5
We get a true statement at the end, which confirms x-3y = -5 is true when x = -5 and y = 0. Therefore, point A is definitely on the line x - 3y = -5
Repeat similar steps for B(4,3) to show that this point is also on x - 3y = -5
x - 3y = -5
4 - 3(3) = -5
4 - 9 = -5
-5 = -5
This confirms point B is also on this line.
We have confirmed line AB is x-3y = -5
I'll let you check to see if C(-3,9) and D(1,-3) are on the line 3x+y = 0. The steps will follow the same outline as shown above.
=========================================================
Part (b)
The standard form equation Ax+By = C has the slope m = -A/B, where B cannot be zero.
The equation x-3y = -5 has A = 1 and B = -3 to give us a slope of m = A/B = -1/(-3) = 1/3
Meanwhile the equation 3x+y = 0 gives the slope of A/B = -3/1 = -3
Notice that slopes 1/3 and -3 multiply to -1. This is one useful property of perpendicular lines. Their slopes always multiply to -1; this is assuming neither line is vertical, nor horizontal.
Put another way, the slopes are negative reciprocals of one another. We flip the fraction and flip the sign to go from 1/3 to -3, or vice versa.
I recommend using GeoGebra to plot out the points mentioned, and forming the lines AB and CD. This helps give a quick visual confirmation the lines are perpendicular.
----------
To summarize: We found the slopes of line AB and CD to be 1/3 and -3 respectively. The slopes multiply to -1 which is sufficient to conclude the lines are perpendicular.
=========================================================
Part (c)
We have this system of equations
x - 3y = -5
3x + y = 0
To represent lines AB and CD respectively.
Let's triple everything in line CD to go from 3x+y = 0 to 9x+3y = 0
Therefore, an equivalent system is this
x - 3y = -5
9x + 3y = 0
The first equation hasn't changed. After this point, we can see the y terms add to 0 since -3y+3y = 0y = 0. Therefore, the y terms cancel which lets us solve for x.
10x = -5
x = -5/10
x = -0.5
Then we use this to find y
x-3y = -5
-0.5-3y = -5
-3y = -5+0.5
-3y = -4.5
y = -4.5/(-3)
y = 1.5
The point of intersection is (-0.5, 1.5)
Notes:
-0.5 = -1/2
1.5 = 3/2
=========================================================
Part (d)
The x coordinates of points A and B are -5 and 4 in that order.
Add them up: -5+4 = -1
Divide the result in half: -1/2 = -0.5
This is the x coordinate of the midpoint of segment AB.
Repeat for the y coordinates
Add: 0+3 = 3
Divide in half: 3/2 = 1.5
The midpoint of segment AB is (-0.5, 1.5) which is exactly the result of part (c).
You should find that the midpoint of segment CD is also (-0.5, 1.5)
I'll let you do those steps.
=========================================================
Part (e)
Quadrilateral ACBD is a kite because of the perpendicular diagonals. This was confirmed in part (b).
The sides aren't all the same length (which you can confirm with the distance formula), which means we don't have a rhombus.
Answer:
a) See below.
b) See below.
[tex]\textsf{c)} \quad \left(-\dfrac{1}{2},\dfrac{3}{2}\right)[/tex]
[tex]\begin{aligned}\textsf{d)} \quad \textsf{Midpoint of $\overline{AB}$}&=\left(-\dfrac{1}{2},\dfrac{3}{2}\right)\\ \textsf{Midpoint of $\overline{CD}$}&=(-1,3)\end{aligned}[/tex]
e) Kite
Step-by-step explanation:
Given endpoints:
A = (-5, 0)B = (4, 3)C = (-3, 9)D = (1, -3)Given equations of the lines:
AB: x - 3y = -5CD: 3x + y = 0Part aTo quickly check that the given equations are correct, input the x-value of a point on the line into the given equation of the line containing that point. If the y-value corresponds with the y-value of the point, the equation is correct.
Using point A to check equation AB:
[tex]\begin{aligned}x=-5 \implies -5-3y&=-5\\-3y&=0\\y&=0\end{aligned}[/tex]
As point A is (-5, 0), the equation is correct.
Using point C to check equation CD:
[tex]\begin{aligned}x=-3 \implies 3(-3)+y&=0\\-9+y&=0\\y&=9\end{aligned}[/tex]
As point C is (-3, 9), the equation is correct.
Part bIf two lines are perpendicular, their slopes are negative reciprocals.
The negative reciprocal of a number is -1 divided by the number.
Rearrange each equation to slope-intercept form, then compare slopes.
[tex]\begin{aligned}\textsf{Line}\;AB: \quad x-3y&=-5\\-3y&=-x-5\\3y&=x+5\\y&=\dfrac{1}{3}x+\dfrac{5}{3}\end{aligned}[/tex]
Therefore, the slope of line AB is ¹/₃.
[tex]\begin{aligned}\textsf{Line}\;CD: \quad 3x + y &= 0\\y&=-3x\end{aligned}[/tex]
Therefore, the slope of line CD is -3.
[tex]\textsf{As} \;\dfrac{-1}{-3}=\dfrac{1}{3}, \textsf{ the slopes are negative reciprocals}.[/tex]
Hence, the lines are perpendicular.
Part cTo find the point of intersection of AB and CD, solve the system of equations.
[tex]\begin{cases}x - 3y = -5\\3x + y = 0\end{cases}[/tex]
Rearrange the second equation to isolate y:
[tex]\implies y=-3x[/tex]
Substitute the found expression for y into the first equation and solve for x:
[tex]\implies x-3(-3x)=-5[/tex]
[tex]\implies x+9x=-5[/tex]
[tex]\implies 10x=-5[/tex]
[tex]\implies x=-\dfrac{5}{10}[/tex]
[tex]\implies x=-\dfrac{1}{2}[/tex]
Substitute the found value of x into the expression for y and solve for y:
[tex]\implies y=-3\left(-\dfrac{1}{2}\right)[/tex]
[tex]\implies y=\dfrac{3}{2}[/tex]
Therefore, the solution to the system of equations is:
[tex]\left(-\dfrac{1}{2},\dfrac{3}{2}\right)[/tex]
Part d[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Midpoint between two points}\\\\Midpoint $=\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)$\\\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the endpoints.\\\end{minipage}}[/tex]
[tex]\begin{aligned}\textsf{Midpoint of $\overline{AB}$}&=\left(\dfrac{x_B+x_A}{2},\dfrac{y_B+y_A}{2}\right)\\&=\left(\dfrac{4+(-5)}{2},\dfrac{3+0}{2}\right)\\&=\left(-\dfrac{1}{2},\dfrac{3}{2}\right)\end{aligned}[/tex]
[tex]\begin{aligned}\textsf{Midpoint of $\overline{CD}$}&=\left(\dfrac{x_D+x_C}{2},\dfrac{y_D+y_C}{2}\right)\\&=\left(\dfrac{1+(-3)}{2},\dfrac{-3+9}{2}\right)\\&=\left(-1,3\right)\end{aligned}[/tex]
The midpoint of line segment AB is the solution to the system of equations.
Part eQuadrilateral ABCD is a kite:
The diagonals of a kite are perpendicular to each other, as proven in part b.The longer diagonal of a kite bisects the shorter diagonal. As the midpoint of line segment AB is the same as the solution to the system of equations, this proves that the longer diagonal (CD) bisects the shorter diagonal (AB).The two diagonals of a kite are not of the same length. As the longer diagonal bisects the shorter diagonal, and the midpoints of line segments AB and CD are not the same, this proves that the diagonals are not the same length.The probability that a particular region in Mexico will be hit by a hurricane in any given year is 0.07. Find the probability that the region will be hit by a hurricane in 3 consecutive years.
The probability that the region will be hit by a hurricane in 3 consecutive years is; 0.000343
How to solve binomial probability distribution?The binomial probability is defined as the probability of exactly x successes on n repeated trials, with p probability. The general formula for binomial probability distribution is;
P(X = x) = ⁿCₓ * pˣ * (1 - p)^(n - x)
where;
P(X = x) is binomial probability
x is number of times for a specific outcome within n trials
ⁿCₓ is number of combinations
p is probability of success on a single trial
n is number of trials
Now, we are given that the probability of success for a particular region in Mexico being hit by hurricane is 0.07. Thus;
P(three consecutive years hurricane) = 0.07 * 0.07 * 0.07 = 0.000343
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The graph below is a polynomial function in the form f(x)=(x−a)2(x−b)(x−c). Find suitable unique real numbers a, b, and c that describe the graph.
The required suitable unique real numbers a, b, and C that represents the given graph are a = -1, b = 1, and c = 3.
What is a graph?A graph can be defined as a pictorial representation or a diagram that represents data or values.
The polynomial function of the graph which is given in the question:
f(x) = (x - a)²(x - b)(x - c)
This means that the polynomial's factors are as follows:
(x - a)², (x - b) and (x - c).
The polynomial solution will now be the values of x when the components equal zero.
This shows that a, b, and c are polynomial function solutions. This indicates that the x-intercepts are a, b, and C.
The x-intercepts on the graph are;
-1, 1, and 3.
Hence;
a = -1
b = 1
c = 3
Thus, the required suitable unique real numbers a, b, and C that represents the given graph are a = -1, b = 1, and c = 3.
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Write the equation of the parabola that has the same shape as f(x)=-3 x² but with vertex (5,9) in the form f(x)=a(x-h)²+k.
f(x)=
The equation of the parabola from the vertex is f(x) = -3(x - 5)² + 9
How to determine the equation of the parabola?The equation of the function is given as
f(x) = 3x²
Also, we have
Vertex = (5, 9)
The form of the equation is given as
f(x) = a(x - h)² + k
Where
Vertex = (h, k)
This means that
Vertex = (h, k) = (5, 9)
Substitute (h, k) = (5, 9) in the equation f(x) = a(x - h)² + k
So, we have
f(x) = a(x - 5)² + 9
This also means that
f(x) = -3(x - 5)² + 9
The -3 is gotten from f(x) = -3x²
Hence, the equation of the parabola is f(x) = -3(x - 5)² + 9
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f(x)=2x^2+4x+9
F(0)=
F(-1)=
ANSWER NOW
In a game that you are playing, your friend says that she has -6 points "give or take" 4 points . You currently have -3 in the game . Can you say who is winning? why or why not .
Use a number line to explain if u want
Answer: The correct answer is No, you cannot determine who is winning.
Step-by-step explanation:
Why you cannot determine who is winning:
Your Score is -3
Your friend is -6 (plus or minus 4 points)
Therefore, the deviation in your friend's score is:
(-6+4) to (-6-4)
Your friend's score is between -2 to -10
Whether the highest or lowest score wins:
Since your score is -3, your friend would win with -2 or tie with -3 (or lose with less). Therefore, you cannot determine who would win based on your friend's score being in a range between -2 to -10.
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The temperature of a solution increases by 1.7° F each minute for 2 minutes. The solution is then placed in an ice bath, and its
temperature decreases by 11°F over the next minute. What is the current temperature?
The temperature of the solution is -7.6°F.
What is temperature?Temperature simply means the degree of hotness and coldness in a body.
In this case, the temperature of a solution increases by 1.7° F each minute for 2 minutes and the solution is then placed in an ice bath, and its temperature decreases by 11°F over the next minute.
The current temperature will be:
= (1.7 × 2) - 11
= 3.4° - 11°
= 7.6°F
The temperature is -7.6°F.
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