Answer:
B: 3/4a + 1/2b - 3
Step-by-step explanation:
Solve for x (12x-7)/4=(5x+18)/3
Answer:
x = 5.81
Step-by-step explanation:
3(12x-7) = 4(5x+18)
36x-21 = 20x +72
16x = 93
x = 5.81
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 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
Find the equation of a circle with a center at (1, 4) where a point on the circle is (4, 8). ( x - 1) 2 + ( y - 4) 2 = 25 ( x - 4) 2 + ( y - 1) 2 = 25 ( x - 1) 2 + ( y - 4) 2 = 5
Answer:
(x-1)^4 + (y-4)^2 = 25
Step-by-step explanation:
Center at 1,4 means the circle is of the form:
(x-1)^4 + (y-4)^2 = r^2
Find r^2 using distance formula from center to the given point
r ^2 = ( 8-4)^2 + (4-1)^2
r^2 = 16 +9 = 25
so you answer is (x-4)^4 + (y-8)^2 = 25
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
What is the answer?????
Answer:
36.7075 Hz is the answer
Which graph represents the function h(x) = |x| + 0.5?
On a coordinate plane, an absolute value graph has a vertex at (0, 1.5).
On a coordinate plane, an absolute value graph has a vertex at (negative 0.5, 0).
On a coordinate plane, an absolute value graph has a vertex at (0, 0.5).
On a coordinate plane, an absolute value graph has a vertex at (negative 1.5, 0).
Answer:
On a coordinate plane, an absolute value graph has a vertex at (0, 0.5).
Step-by-step explanation:
properties of the given function
domain=X€Rrange=[1/2,+♾️)minimum (0,1/2)Answer: it's the second option
Step-by-step explanation:
If side c measures 32.3 units long, how long is side a?
Answer:
16.15
Step-by-step explanation:
sin(30) = a / c
a = c * sin(30)
a = 32.3 * 0.5
a = 16.15
Consider the function given below. f(x)=x Plot the x- and y- intercepts of the function.
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
___________is a relation in which each element of the domain is paired with exactly one element of the range.
Answer:
A function
Step-by-step explanation:
A function is a relation in which each element of the domain is paired with exactly one element of the range.
When Manny goes on vacation, he boards his dog at a kennel. The kennel charges a flat fee
of $25, plus $15.50 per night.
Write an equation that shows how the cost of a kennel stay, y, depends on the number of
nights, x.
Step-by-step explanation:
y = 25 + 15.5x
it's $25 plus the number of nights times $15.5 per night
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 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.
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R is the midpoint of QS. If QR = 7x and QS = 15x − 7, what is QR?
Answer: 49
Step-by-step explanation:
If R is the midpoint of QS, QS=2(QR)=2(RS).
[tex]15x-7=2(7x)\\15x-7=14x\\-7=-x\\\\x=7\\\\QR=7(7)=\boxed{49}[/tex]
Josh and Bella picked apples from a tree. Josh had 3 less than 2/3 of Bellas apples. If Josh had 7 apples, how many apples did Bella have?
Answer:
Bella had 15 apples
Step-by-step explanation:
First, you see that Josh has 3 less than 2/3 of Bellas apples. If Josh has 7 apples you would add 3 to 7 which = 10. Assuming that 10 = 2/3 of Bellas apples, then you would subtract half of 10 and get 5. 1/3 = 5 apples. Lastly, you should do 5 * 3 which = 15. Bella had 15 apples.
Question 7 of 25
If f(x)=6x²,-4 and g(x)=2x+2, find (f- g)(x).
OA. 2x-5x2-2
OB. 6x²-2x-6
OC. 4x²-6
O D. 6x²2-2x-2
Answer:
x2
Step-by-step explanation:
x2
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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(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
The graph of F(x), shown below, resembles the graph of G(x)= x², but it has
been changed somewhat. Which of the following could be the equation of
F(x)?
A. F(x) = 3(x+4)2 +4
B. F(x)=3(x-4)2 - 4
C. F(x)=-3(x+4)² +4
D. F(x) = -3(x-4)² +4
The equation of the function is F(x) = -3(x-4)² +4 , the correct answer is Option D
The missing graph is attached with the answer
What is a function ?A function is a law that relate the independent variable and the dependent variable.
It is given that
The graph of F(x), shown below, resembles the graph of G(x)= x², but it has been changed
From the graph, it is seen that,
G(x) when shifted by -4 on the negative x axis.
and graph shifted by +4 on the positive y axis.
F(x) is scaled by a factor of -⅓ of G(x)
it is reflected across the x-axis.
So the equation of the function is
F(x) = -3(x-4)² +4
Therefore , the correct answer is Option D.
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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
In 20 years charlie will be three times as old as he is now.how old is charlie is he now
Answer:
10 years old
Step-by-step explanation:
let his age be x , then in 20 years
x + 20 = 3x ( subtract x from both sides )
20 = 2x ( divide both sides by 2 )
10 = x
Charlie is 10 years old
Angle AMO is 50 degrees. If ray MB bisects angle AMO, what would be the measure of angle AMB?
what are the pair of intergers whose product is -12
Answer:
The answer is -4×3 or -3×4 or -6×2 or -2×6 or -1×12 or -12×1
Step-by-step explanation:
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]
Need help simple explanation if possible
Answer: 21 sqrt(43)/43
Step-by-step explanation: The tangent identity states that tanx = sinx/cosx. Thus, we get 21/22 / sqrt(43)/22. We can simplify this to 21 sqrt(43)/43
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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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Question 10(Multiple Choice Worth 1 points)
(04.02 LC)
Solve the system of equations using substitution.
y = -2x + 1
4x + 2y = -3
Answer:
no solutions
Step-by-step explanation:
[tex]4x + 2(-2x+1) = -3\\4x-4x+2 = -3\\2 = -3\\[/tex]
this means there are no solutions.
what is the value of k such that x-2y=5 and 4x+ky=3 are perpendicular?
Answer:
k= -4/3
Step-by-step explanation:
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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