The equation of the parabola that has zeros of x = - 6 and x = 6 and a y-intercept of (0, 4) would be Y=-1/9(x^2-36).
What is the equation of the parabola that has zeros?Since the zeros are symmetrical to the y axis, the equation can be written as;
y = a(x-b)(x+b),
where a is a scale factor and b is x-intercept.
From the given zeroes
y = A(x-6)(x+6).
Now we can plug in the y-intercept (0,4)
4 = A(0-6)(0+6)
4 = A(-36)
-36A=4
A = -1/9
Therefore the equation would be
Y = -1/9(x-6)(x+6),
or Y=-1/9(x^2-36)
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a man bought a motor at 400,000 Kenyan shillings in January 1999 it depreciated at a rate of 16% per annum if he value it six months determines its value in January 2003
The value of the car is January 2003 is $199,148.54.
What is the value of the car?Depreciation is the rate of decline in the value of an asset with the passage of time.
The exponential equation that can be used to determine the value of the car is:
Value of the car = purchase value(1 - rate of decline)^time
400,000 x (1 - 0.16)^(2003 - 1999)
400,000 x (0.84^4) = $199,148.54
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Find the product of (x − 5)2.
Group of answer choices
x2 + 10x + 25
x2 − 10x + 25
x2 − 25
x2 + 25
Answer:
x² - 10x + 25
Step-by-step explanation:
The formula for squaring any binomial (an expression with two terms) is:
(a ± b)² = a² ± 2ab + b²
Let a = x and b = 5.
∴ Substituting:
(x - 5)² = x² - 2(x)(5) + (-5)²
= x² - 10x + 25
Find the value of x.
Answer:
x=21°
Step-by-step explanation:
40°+5x+14°+x=180°
5x+x=180°-40°-14°
6x=126°
x=21°
Answer:
x = 21
Step-by-step explanation:
The sum of the angles of a triangle is 180 degrees
x + 40 + 5x+14 = 180
Combine like terms
6x+54 =180
Subtract 54 from each side
6x+54-54 = 180-54
6x =126
Divide each side by 6
6x/6 =126/6
x = 21
what is the value of sin(80°)cos(20°)-cos(80°)sin(20°)
Answer: sqrt 3 / 2
Step-by-step explanation: cos20°sin80°-cos80°sin20° is about 0.66 and sqrt(3)/2 is about 0.66.
Please mark as brainliest if my answer was correct and/or helpful.
The market value of a home is $180,000. The assessment rate is 55%. What is the assessed value of the home?
Answer:
$99 000
Step-by-step explanation:
[tex](180000)(\frac{55}{100} )=99000[/tex]
Hope this helps
For every 1 litre of water used to make a
medicine, 311ml of sucrose and 29ml of
saline solution are used. Express the amount
of water, sucrose and saline solution needed
as a ratio in its simplest form.
Step-by-step explanation:
hope you can understand
anwer this question with full method please
Step-by-step explanation:
Let simplify the identity
[tex] \frac{ \csc {}^{2} (x) - \sec {}^{2} (x) }{ \csc {}^{2} (x) + \sec {}^{2} (x) } [/tex]
[tex] \frac{ \frac{1}{ \sin {}^{2} (x) } - \frac{1}{ \cos {}^{2} (x) } }{ \frac{1}{ \sin {}^{2} (x) } + \frac{1}{ \cos {}^{2} (x) } } [/tex]
Combine Like Fractions
[tex] \frac{ \frac{ \cos {}^{2} (x) - \sin {}^{2} (x) }{ \sin {}^{2} (x) \cos {}^{2} (x) } }{ \frac{ \sin {}^{2} (x) + \cos {}^{2} (x) }{ \cos {}^{2} (x) \sin {}^{2} (x) } } [/tex]
Multiply by reciprocals.
[tex] \frac{ \cos {}^{2} (x) - \sin {}^{2} (x) }{ \sin {}^{2} (x) \cos {}^{2} (x) } \times \frac{ \cos {}^{2} (x) \sin {}^{2} (x) }{ \sin {}^{2} (x) + \cos {}^{2} (x) } [/tex]
Pythagorean Identity
[tex] \frac{ \cos {}^{2} (x) - \sin {}^{2} (x) }{1} [/tex]
Double Angle Identity
[tex] \frac{ \cos(2x) }{1} [/tex]
[tex] \cos(2x) [/tex]
Now, we need to find cos 2x. Given that we have tan x.
Note that
[tex] \cos {}^{2} (x) - \sin {}^{2} (x) = \cos(2x) [/tex]
So let find cos x and tan x.
We know that
[tex] \tan(x) = \frac{ \sin(x) }{ \cos(x) } [/tex]
We know that
[tex] \tan(x) = \frac{o}{a} [/tex]
[tex] \sin(x) = \frac{o}{h} [/tex]
[tex] \cos(x) = \frac{a}{h} [/tex]
So naturally,
[tex] \tan(x) = \frac{ \frac{o}{h} }{ \frac{a}{h} } = \frac{o}{a} [/tex]
So we need to find the hypotenuse,
remember Pythagorean theorem.
[tex]h {}^{2} = {o}^{2} + {a}^{2} [/tex]
Here o is 1
h is root of 5.
So
[tex] {h}^{2} = {1}^{2} + ( \sqrt{5} ) {}^{2} [/tex]
[tex] {h}^{2} = 1 + 5[/tex]
[tex] {h}^{2} = 6[/tex]
[tex]h = \sqrt{6} [/tex]
Now, we know h, let plug in to find sin x and cos x.
[tex] \sin(x) = \frac{1}{ \sqrt{6} } [/tex]
[tex] \cos(x) = \frac{ \sqrt{5} }{ \sqrt{6} } [/tex]
Let's find these values squared
[tex] \sin {}^{2} (x) = \frac{1}{6} [/tex]
[tex] \cos {}^{2} (x) = \frac{5}{6} [/tex]
Finally, use the trig identity
[tex] \frac{5}{6} - \frac{1}{6} = \frac{2}{3} [/tex]
So part I.= 2/3
ii. Use the definition of sine and cosine and Pythagorean theorem
Let sin x= o/h
Let cos x= a/h.
So
sin x squared is
[tex] \sin {}^{2} (x) = \frac{o {}^{2} }{h {}^{2} } [/tex]
[tex] \cos {}^{2} (x) = \frac{ {a}^{2} }{h {}^{2} } [/tex]
By definition,
[tex] \frac{ {o}^{2} }{ {h}^{2} } + \frac{ {a}^{2} }{h {}^{2} } = 1[/tex]
[tex] \frac{ {o}^{2} + a {}^{2} }{h {}^{2} } = 1[/tex]
Remember that
[tex]{ {o}^{2} + {a}^{2} } = {h}^{2} [/tex]
So
[tex] \frac{ {h}^{2} }{h {}^{2} } = 1[/tex]
[tex]1 = 1[/tex]
Kayla has just subscribed to a music streaming service. For a one-time fee of $12.99, she can download songs for $0.65 each, for an entire month. Kayla's budget will allow her to spend no more than a total of $27 on the streaming service this month. What is the maximum number of songs she can download while still remaining within her budget?
a) x <= 22
b) <= 41
c) x <= 21
d) X <= 42
The maximum number of songs she can download while still remaining within her budget is x <= 21
How to determine the maximum number of songs?The given parameters are:
One-time fee = $12.99
Rate = $0.65 per song
Budget = $27
The inequality is then represented as:
One-time fee + Rate * x <= Budget
So, we have:
12.99 + 0.65x <= 27
Subtract 12.99 from both sides
0.65x <= 14.01
Divide both sides by 0.65
x <= 21.55
Round down
x <= 21
Hence, the maximum number of songs she can download while still remaining within her budget is x <= 21
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The slope of the line below is -2. Write the equation of the line in point-slope
form, using the coordinates of the labeled point. Do not use parenthesis on
the y side.
(-2,1)
Answer:
y - 1 = -2(x + 2)
Step-by-step explanation:
The general structure of an equation in point-slope form is:
y - y₁ = m(x - x₁)
In this form, "x" and "y" stand for the values of one point and "x₁" and "y₁" stand for the values of another point. The variable "m" represents the value of the slope. You have been given the values of one point and the slope. When you plug them into the general form, you get this answer:
Point: (-2, 1)
m = -2
y - y₁ = m(x - x₁) <----- Point-slope form
y - y₁ = -2(x - x₁) <----- Plug -2 in "m"
y - 1 = -2(x - (-2)) <----- Plug in values from point
y - 1 = -2(x + 2) <----- Simplify
The directrix and vertex of a parabola are shown on the graph. What is the vertex form of the equation for the associated parabola?
Considering the directrix and vertex given in the graph, the equation of the parabola is:
B. [tex]x = -\frac{1}{4}(y + 2)^2 - 2[/tex]
What is the equation of a parabola given it’s vertex?The equation of a quadratic function, of vertex (h,k), is given by:
(y - k)² = 4p(x - h).
In which the directrix is the line x = h - p.
Looking at the graph, we have that:
The vertex is (-2,-2), hence h = k = -2.The directrix is x = -1, hence -1 = -2 - p -> p = -1.Thus the equation is:
(y + 2)² = -4(x + 2).
Writing x as a function of y:
B. [tex]x = -\frac{1}{4}(y + 2)^2 - 2[/tex]
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can someone help me?
Answer:
-6
30
22
8x² + 18x + 4
8x² - 2x - 6
Step-by-step explanation:
f(x) = 8x² + 2x - 6
f(0) = 8(0²) + 2(0) - 6 = -6
f(2) = 8(2²) + 2(2) - 6 = 32 + 4 - 6 = 30
f(-2) = 8 × (-2)² + 2(-2) - 6 = 32 - 4 - 6 = 22
f(x + 1) = 8(x + 1)² + 2(x + 1) - 6 = 8(x² + 2x + 1) + 2x + 2 - 6 = 8x² + 18x + 4
f(-x) = 8(-x)² + 2(-x) - 6 = 8x² - 2x - 6
(9x + 1) − (−7x² + 4x + 10)
Answer:
7x² + 5x - 9
Step-by-step explanation:
(9x + 1) - (- 7x² + 4x + 10) ← distribute parenthesis by - 1
= 9x + 1 + 7x² - 4x - 10 ← collect like terms
= 7x² + 5x - 9
A ship is stationary at sea.
A tugboat is 36 km away at a bearing of 130°, and a yacht is 27 km from the tugboat at a bearing of 260°.
Draw a scale diagram showing the positions of the three vessels.
Use a scale of 1 : 450,000.
Measure the distance from the ship to the yacht to the nearest km.
Bearing is a topic that deals with the distance and location of a given object with respect to a reference point. Thus in the given question, the ship is 57.23 km to the yacht.
Bearing is a topic that considers the distance and position of a given object with respect to a reference point. Thus the angles are usually measured with reference to the north pole.
Thus to solve the given question, let the required distance be represented by x.
Applying the cosine rule, we have;
[tex]c^{2}[/tex] = [tex]a^{2}[/tex] + [tex]b^{2}[/tex] - 2ab Cos C
The angle C between the line from ship to tugboat and from tugboat to yacht can be determined as;
C = [tex]10^{o}[/tex] + [tex]40^{o}[/tex]
C = [tex]50^{o}[/tex]
Thus,
[tex]c^{2}[/tex] = [tex]36^{2}[/tex] + [tex]27^{2}[/tex] + 2(36 x 27) Cos [tex]50^{o}[/tex]
= 1296 + 729 + 1944(0.6429)
= 2025 + 1249.8
[tex]c^{2}[/tex] = 3274.8
c = [tex]\sqrt{3274.8}[/tex]
= 57.2259
c = 57.23
Therefore, the distance from the ship to the yacht is 57.23 km.
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A cube has side length x. one side of the cube is increased by 4 inches, and another side is doubled. the volume of the new rectangular prism is 450 cubic inches. the equation 2 x cubed 8 x squared = 450 can be used to find x. what was the side length of the original cube? use a graphing calculator and a system of equations to find the answer.
The side length of the original cube is 1.95 inch.
Let each side length of each cube be 'x' inch.
Given : New side = (x+4 ) inch
Another new side = 2x inch
Since the sides are not equal, so it forms a cuboid in the case of new sides as given.
Also, according to question,
The volume of new rectangular prism is 450 cubic inches
= (x+4)*2x*x = 450
⇒ 2x cubed 8x squared =450
=16x5=450= 1.95 inch ( by taking out the cubic root of x3=7.5)
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What is the intersection of line CA a and line XA?
Answer:
point A is the intersection point between XA and AC
An automobile company is running a new television commercial in five cities with approximately the same population. the following table shows the number of times
the commercial is run on tv in each city and the number of car sales in hundreds). find the linear regression line for the data given in the table. round any intermediate
calculations to no less than six decimal places, and round the coefficients to two decimal places.
number of tv commercials, x
car sales, y (in hundreds)
13 6 12 14 17
3 28 97
The linear regression equation is y = 0.50x - 0.36
How to determine the linear regression equation?The proper format of the table of values is:
Number of tv commercials, x: 13 6 12 14 17
Car sales, y (in hundreds): 3 2 8 9 7
Next, we determine the linear regression equation using a graphing calculator.
From the graphing calculator, we have the following summary:
Sum of X = 62Sum of Y = 29Mean X = 12.4Mean Y = 5.8Sum of squares (SSX) = 65.2Sum of products (SP) = 32.4The regression equation is the calculated as:
y = bx + a
Where
b = SP/SSX = 32.4/65.2 = 0.49693
a = MY - bMX = 5.8 - (0.5*12.4) = -0.36196
Substitute these values in y = bx + a
y = 0.49693x - 0.36196
Approximate
y = 0.50x - 0.36
Hence, the linear regression equation is y = 0.50x - 0.36
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Which choice is the most efficient first step to solve this set of
equations?
y=3x-5
2x+6y=20
Answer:
b) Substitute (3x - 5) for y in the second equation.
Step-by-step explanation:
If using the substitution method, then the second choice is the most efficient first step.
What is the substitution method?
The substitution method can be used to solve a system of equations. It is when you isolate any of the variables from one of the equations and then substitute that value into the other equation.
Here, the first equation already has an isolated variable, y. We can then substitute its value into the second equation. Like so:
⇒ 2x + 6y = 20
⇒ 2x + 6(3x - 5) = 20
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Angle AMO is 50 degrees. If ray MB bisects angle AMO, what would be the measure of angle AMB?
In △BCD, BP=15 cm.
What the length of BX?
Answer:
10
Step-by-step explanation:
BX=2/3 (BP)
2/3 of 15 = 10
Which of the following is a factor of x^3-7x-6?
A. X+3
B. X+4
C. X-2
D. X+1
Can someone help me out with this problem
Answer:
[tex]\fbox {1) A}\\\fbox {2) A}[/tex]
Step-by-step explanation:
Q1
⇒ Graph A is most accurate as the situation is linear and the dots indicate per cup as you can't have any rational part (such as 0.5 cups, etc.)
Q2
⇒ A
⇒ The graph is discrete because the sellers have limited the purchaser to buy a distinct whole number of cups
A foam cylinder, with a diameter of 3 inches in height of 8 inches, is carved into the shape of a cone. What is the maximum volume of a cone that can be carved? Round your answer to the nearest hundredths place. One point
Answer:
volume of cone = 1/3 volume of cylinder
according to the question, volume of cylinder =
V =
[tex]\pi \times (r) {}^{2} h[/tex]
diameter = 3 inches
radius = 3/2 inches
height = 8 inches
V = 22.7 * (3/2)²* 8
V = 22.7 * 9/4 * 8
V = 22.7 * 18
maximum volume a cone can have = 1/3 of cylinder
Volume of cone = 1/3 * 22.7 * 18
= 22.7 * 6
= 132.6
Jared bought eighteen doughnuts to share with his coworkers. If each doughnut cost c cents, which expression represents his total cost?
I give you 12 points if you help me ;) it’s math
Answer:
y=23.6
Step-by-step explanation:
20+0.45×8
20+3.6
23.6
if the area of an isosceles triangle 56 units squared and the base is one third of the height what is the perimeter
The perimeter of the given isosceles triangle is; 725.77 units
How to find the area of a Triangle?We are given;
Area of Isosceles Triangle = 56 units squared
Base of Isosceles Triangle = ¹/₃h where h is height
Formula for area of triangle is;
A = ¹/₂bh
A = ¹/₂ * ¹/₃h * h
A = ¹/₆h²
Thus;
¹/₆h² = 56
h² = 56 * 6
h = √336 = 18.33
Thus, base = ¹/₃√336
Length of hypotenuse = √((√336)² + (¹/₃√336)²)
Length of hypotenuse = √(336 + (336/9))
Length of hypotenuse = 373.33
Thus, Perimeter of Triangle = 2(373.33) + ¹/₃(√336)
Perimeter = 725.77 units
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a recursive formula for the sequence 18,9,4.5,... is
Answer:
A1 = 18
A(n) = A (n-1) -2
Step-by-step explanation:
N represents the number in a sequence and the difference in the sequence is -2 since each time the number is listed in the sequence it is divide by 2.
Find the equation of the line of best fit and the correlation coefficient for the data shown.
(1, 88), (2, 75), (3, 71), (4, 69), (5,66), (6, 68), (7, 50)
Regression equation:
Using a calculator, we have that:
The regression equation is given by: y = -4.75x + 88.57143.The correlation coefficient is given by: -0.906.How to find the equation of linear regression using a calculator?To find the equation, we need to insert the points (x,y) in the calculator.
In this problem, we have that:
The values of x are: 1, 2, 3, 4, 5, 6, 7.The values of y are: 88, 75, 71, 69, 66, 68, 50.Hence the regression equation is:
y = -4.75x + 88.57143.
Also using a calculator, the correlation coefficient is of -0.906.
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which graph correctly represents 3x+y > 7
Answer:
What graph? add a photo?
Which graph shows the solution to the system of linear inequalities? Edge.
x + 3y > 6
y ≥ 2x + 4
A system of inequalities can be solved graphically.
See attachment for the required graph
The inequalities are given as
[tex]x + 3y > 6\\y \geq 2x + 4[/tex]
The options are not given.
So, I have attached the graph that illustrates the solution to the system of inequalities.
What is the inequality?An inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size.
From the graph, we have the solutions as
[tex]x > -0.857[/tex]
[tex]y\geq 2.276[/tex]
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What can be concluded if ÐABC and ÐCBD are a linear pair? Select all statements that you think are correct.
If ÐABC and ÐCBD are a linear pair, then it means that their sum is 180°.
What is Linear pair of angles?Linear pair of angles are angles formed when two lines intersect each other at a single point.
Now, the angles are also said to be linear if they are adjacent to each other after the intersection of the two lines and the sum of the linear pair of angles is always equal to 180°.
Looking at the definition above we can say that if ÐABC and ÐCBD are a linear pair, then it means that their sum is 180°.
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