Answer:
I don't actually have an image but i think the coordinate point is (-6,1)
I hope this helps
how do i solve 2k^2-5k-18=0
Answer:
factor left the side of the equation
(2k_9)(k+2)=0
set factors equal to 0
2k_9=0 or k+2=0
the answer is K= 9/2 or K =-2
2k^2 - 5k - 18 = 0 can be solved by splitting the middle term to get k = -2 and k = -4.5.
How to solve an equation?An equation can be solved by many methods which include using the quadratic formula, splitting the middle term, etc. When an equation is solved, it means we are finding the value of the variable in the equation.
We can solve the given equation as folows:Given : 2k^2 - 5k - 18 = 0
2k^2 - 5k - 18 = 0
⇒ 2k^2 +4k - 9k - (9*2) = 0
⇒ 2k( k + 2 ) -9( k + 2 ) = 0
⇒ ( 2k - 9 )( k+2 ) = 0
⇒ k = 4.5, k = -2
Therefore, we have solved 2k^2 - 5k - 18 = 0 to get k = 4.5 and k = -2.
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Solve the following system of equations below x-2y=3 2x-3y=9
Answer:
(9, 3)
Step-by-step explanation:
I'd strongly suggest that you write these two equations one above the other:
x-2y=3
2x-3y=9
Let's eliminate x by addition / subtraction: Multiply the first equation by -2 to obtain -2x in the first row over +2x in the second row:
-2x + 4y = -6
2x - 3y = 9
--------------------
y = 3
Now subst. 3 for y in the first equation: x - 2y = 3 becomes:
x - 2(3) = 3, or
x = 6 + 3 = 9
The solution is (9, 3).
URGENT!! Solve the following for θ, in radians, where 0≤θ<2π.
−4sin2(θ)−3sin(θ)+5=0
Select all that apply:
2.21
1.19
1.92
0.93
0.31
2.63
Answer: 0.93 radians & 2.21 radians
Step-by-step explanation:
[tex]-4sin^2\theta-3sin\theta+5=0\\\\\text{Since this is not factorable, use the quadratic formula to find the roots:}\\\\sin\theta=\dfrac{-(-3)\pm \sqrt{(-3)^2-4(-4)(5)}}{2(-4)}\\\\\\.\quad=\dfrac{3\pm \sqrt{9+80}}{-8}\\\\\\.\quad=\dfrac{3\pm\sqrt{89}}{-8}\\\\\\.\quad=\dfrac{3\pm9.43}{-8}\\\\\\.\quad=\dfrac{12.43}{-8}\quad and\quad \dfrac{-6.43}{-8}\\\\\\.\quad=-1.55\quad and\quad 0.80\\\\\\\theta=sin^{-1}(-1.55)\quad and\quad \theta=sin^{-1}(0.80)[/tex]
[tex]\theta=not\ valid\qquad and\quad \theta=0.927[/tex]
[tex]\theta = 0.927\ radians\text{\ in the 1st quadrant and}\\\pi-0.927=2.21\ radians\text{\ in the 2nd quadrant}[/tex]
Answer:
2.21
0.93
Step-by-step explanation:
Given that; [tex]-4\sin^2\theta-3\sin \theta+5=0[/tex]
This is a quadratic equation is [tex]\sin \theta[/tex], where [tex]a=-4,b=-3,c=5[/tex]
We want to solve for [tex]\theta[/tex] in radians, where 0≤θ<2π.
We apply the quadratic formula given by;
[tex]\sin \theta=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]
We substitute the given values to obtain;
[tex]\sin \theta=\frac{--3\pm\sqrt{(-3)^2-4(-4)(5)}}{2(-4)}[/tex]
Simplify;
[tex]\sin \theta=\frac{3\pm\sqrt{9+80}}{-8}[/tex]
[tex]\sin \theta=\frac{3\pm\sqrt{89}}{-8}[/tex]
[tex]\sin \theta=0.804[/tex] or [tex]\sin \theta=-1.55[/tex]
When [tex]\sin \theta=0.804[/tex] , [tex]\theta=\sin^{-1}(0.804)[/tex]
[tex]\Rightarrow \theta=0.93[/tex] --In the first quadrant.
In the second quadrant;
[tex]\theta=\pi-0.93=2.21[/tex]
When [tex]\sin \theta=-1.55[/tex] , [tex]\theta[/tex] is not defined.
What is the result when you convert 7/8 to a percent?
Answer:
the answer is 87.5%
Step-by-step explanation:
first, we have to turn 7/8 into a fraction with a denominator of 100. to do that, we can divide 100 by 8 to get 12.5. now, we multiply 7/8 x 12.5 which equals 87.5/100 which is equal to 87.5%
Answer: the answer would be 90%
Step-by-step explanation:
Graph f(x)=x and g(x) = 1/2x -5. Then describe the transformation from the graph of f(x)=x to the graph of g(x) - 1/2x -5
Answer:
Vertical Shrink by 1/2 and down 5
Answer:
The transformations are a rotation and a translation.
Create a system of equations that includes:
A linear equation
And a quadratic equation
Part 1: Show all work to solving your system of equations algebraically.
Graph your systems of equations, and show the solution graphically to verify solution.
Answer:For a system of equations, we'll use something fairly simple:
y = 2x (linear)
y = x^2 (quadratic)
Now to solve, we can set them equal to each other since they are both equal to y.
x^2 = 2x
Now to solve for the appropriate values of x, set equal to zero and factor.
x^2 = 2x ---> subtract 2x from both sides
x^2 - 2x = 0 ----> now factor out an x.
x(x - 2) = 0
Now to get the values of x, set each factored part equal to 0 on their own.
x = 0
x - 2 = 0
x = 2
A system of equations that includes a linear equation (y = 2x + 4) and a quadratic equation (y = x^2 - x - 6) can be solved algebraically by equating the two equations and solving the resultant quadratic equation. The solutions to this system are (5,14) and (-2,0). These solutions are the intersection points of the line and the parabolic curve on a coordinate plane.
Explanation:To create a system of equations that includes both a linear and a quadratic equation we might choose for example:
Linear equation: y = 2x + 4
Quadratic equation: y = x^2 - x - 6
Part 1: The algebraic solution is found by setting the two equations equal to each other and solving for x:
2x + 4 = x^2 - x - 6
This simplifies to: 0 = x^2 - 3x - 10
Then, we factor to find: (x - 5)(x + 2) = 0
Setting each factor equal to zero gives us: x = 5 and x = -2
Substitute back into the linear equation to find y: y1= 2(5) + 4 = 14 and y2= 2(-2) +4 = 0
Hence, the solution to the system of equations are (5,14) and (-2,0).
The solutions would be graphically represented by the intersection points of the line and the parabola on the coordinate plane.
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Which inequality is equivalent to -6x
30?
1.X greater than or equal to 5
2.X greater than or less than -5
3.X less than or equal to 5
4. X less than or equal to -5
Step-by-step explanation:
How to simplify
-6x (some sign, it didn't show in the question)30
Divide by -6 on both sides to isolate the variable.
30 divided by -6 is -5, so x=-5.
Answer:
,
Step-by-step explanation:
Garth has x books which is 20 more books than Henrietta has. If Garth gives Henrietta 7 books how many books does Henrietta now have
Answer:
she should have x-27 books left
Step-by-step explanation:
The number of books Henrietta has is x-13.
Given that, Garth has x books which are 20 more books than Henrietta has.
We need to find out how many books Henrietta now has.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Now, the number of books with Garth has =x
The number of books with Henrietta has =x-20
Garth gave Henrietta 7 books =x-20+7
=x-13
Therefore, the number of books Henrietta has is x-13.
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What value of x makes this equation true? 7x -14=35
Answer:
7x -14=35 add 14 on both sides
7x= 49 then, divide 7 on the whole equation
x=7
Which translation maps the vertex of the graph of the function f(x) = x2 onto the vertex of the function g(x) = -8 + x^2 + 7 ?
Answer:
The function translated 4 units right and 9 units down
The third answer
Step-by-step explanation:
* To solve the problem you must know how to find the vertex
of the quadratic function
- In the quadratic function f(x) = ax² + bx + c, the vertex will
be (h , k)
- h = -b/2a and k = f(-b/2a)
* in our problem
∵ f(x) = x²
∴ a = 1 , b = 0 , c = 0
∵ h = -b/2a
∴ h = 0/2(1) = 0
∵ k = f(h)
∴ k = f(0) = (0)² = 0
* The vertex of f(x) is (0 , 0)
∵ g(x) = -8x + x² + 7 ⇒ arrange the terms
∴ g(x) = x² - 8x + 7
∵ a = 1 , b = -8 , c = 7
∴ h = -(-8)/2(1) = 8/2 = 4
∵ k = g(h)
∴ k = g(4) = (4²) - 8(4) + 7 = 16 - 32 + 7 = -9
∴ The vertex of g(x) = (4 , -9)
* the x-coordinate moves from 0 to 4
∴ The function translated 4 units to the right
* The y-coordinate moves from 0 to -9
∴ The function translated 9 units down
* The function translated 4 units right and 9 units down
Final answer:
The question seeks the translation moving the vertex of f(x) = x^2 to match the vertex of g(x) = -8x + x² + 7. To achieve this, the function f(x) needs to be translated right by 4 units and down by 9 units, resulting in the translation (x, y) -> (x+4, y-9).
Explanation:
The student's question is asking for the translation that would move the vertex of a quadratic function f(x) to match the vertex of another quadratic function g(x). We are given two functions: f(x) = x2 and g(x) = -8x + x² + 7. To find the translation, we need to determine the vertices of both parabolas.
In the standard form of a quadratic function, y = a x² + bx + c, the vertex can be found using the formula h = -b/2a for the x-coordinate of the vertex. For f(x), the vertex is at (0, 0) since there is no b or c value, and it's just x² . For g(x), we can calculate the vertex by finding the x-coordinate: h = -(-8)/2(1) = 4. The y-coordinate can be found by substituting x = 4 into g(x) to get g(4) = -8(4) + 4² + 7 = -32 + 16 + 7 = -9. Therefore, the vertex of g(x) is at (4, -9).
To translate the vertex of f(x) to the vertex of g(x), we need to shift it right by 4 units and down by 9 units. The translation that does this is (x, y) -> (x+4, y-9).
what is the probability of spinning b
Answer:
45%
Step-by-step explanation:
It is 45% because is 1/4 of the circle
Answer:
37.5%
Step-by-step explanation:
The probability is 3/8, which is 37.5%.
Jack mows the lawns to earn money. he charges a flat fee of $20 for showing up plus $15 for each hour it takes him to mow the lawn. Write an equation that models this situation for the money Jack makes Y in terms of the hours he works X
Answer:
y = 15x + 20
Step-by-step explanation:
He charges a flat rate of $20, so any total for hours worked will have an additional $20 added to it.
The 15x represents his earnings per hour. He makes 15 per every hour worked, x represents the number of hours worked
A car travels 55.9 in an hour. If the car continues at the same speed, for 12 hours how many will it travel?
Can someone help me please
Answer:
670.8
Step-by-step explanation:
55.9x12=670.8
how do I simplify: 5p^3 - 2p^2 ?
Answer:
p²(5p - 2)
Step-by-step explanation:
p² is a factor common to both terms, and thus should be factored out:
p²(5p - 2)
Angie is x years old. Her sister is 12 years older than her while their mother is twice as old as her sister. Betty is 3 years younger than angie while Betty's mother is 4 times as old as Betty. Express Angie's mother's age in terms of x. express Betty's mother's age in terms of x. if Angie's mother is 6 years older than Betty's mother, find Angie's age
Step-by-step explanation:
Parking lot:
Angie=x
Sister=x+12
Amom=2•(sister) or 2(x+12)=2x+24
Betty=x-3
Bmom=4•(betty) or 4(x-3)=4x-12
--------
Part A: Amom=2x+24
Part B: Bmom=4x-12
PartC:
x=angie
Amom=Bmom+6
2x+24=4x-12+6
2x+24=4x-6
24-6=4x-2x
18=2x
9=x
Angie is 9 years old.
Find the solution of the equation from the given numbers. x + 14 = 23; 9, 55, 37, or 30 55 9 37 30
The equation is X + 14 = 23.
To solve for X subtract 14 from each side:
x+14 = 23
x = 23 - 14
x = 9
x+14=23
x=23-14
x=9
9+14=23
The first term of a Geometric progression is 16 and the fifth term is 9. what is the values of the seventh term?
Answer:
18
Step-by-step explanation:
Find the missing coefficient
Answer:
The missing coefficient is -8
Step-by-step explanation:
Let
a------> the missing coefficient
we have
[tex]ay^{2}-[-5y-y(-7y-9)]-[-y(15y+4)]=0[/tex]
[tex]ay^{2}-[-5y+7y^{2}+9y]-[-15y^{2}-4y]=0\\ \\ ay^{2}+5y-7y^{2}-9y+15y^{2}+4y=0\\\\ay^{2}-7y^{2}+15y^{2}=0\\\\ay^{2}+8y^{2}=0\\ \\a=-8[/tex]
i hate word problems...if i roll a regular 6 faced die 1200 times, about how many times would you expect to get a 4?
Answer:
200
Step-by-step explanation:
1/6 because the die has 6 sides so if you were to roll it 1200 times you would do 1/6*1200=200 , hope this helps!
Need help please help me
Answer:
Exterior Angle Theorem states the exterior angle is the sum of the interior angles opposite it.
Angle 4 = 75
Step-by-step explanation:
The exterior angle theorem states that the two interior angles across from the exterior angle add to the degree of the exterior angle.
Angle 4 = 20 + 55 = 75
A red die is tossed and then a green die is tossed. What is the probability that the red die shows an even number or the green die shows an even number? Make sure your answer is reduced
Final answer:
To find the probability that the red die shows an even number or the green die shows an even number, we can use the concept of probability of a union of two events. The probability is 3/4.
Explanation:
To find the probability that the red die shows an even number or the green die shows an even number, we can use the concept of probability of a union of two events. Let's denote the event that the red die shows an even number as E and the event that the green die shows an even number as F.
Since each die has 6 equally likely outcomes, the probability of rolling an even number on the red die is P(E) = 3/6 = 1/2, and the probability of rolling an even number on the green die is P(F) = 3/6 = 1/2.
To find the probability of the union of two events (E or F), we add the probabilities of E and F and subtract the probability of their intersection (E and F) to avoid double-counting. In this case, the intersection is the event that both dice roll an even number, which has a probability of P(E and F) = (1/2) × (1/2) = 1/4.
Therefore, the probability that the red die shows an even number or the green die shows an even number is P(E or F) = P(E) + P(F) - P(E and F) = 1/2 + 1/2 - 1/4 = 3/4.
Revenge of the mangled angles
Answer:
show me the other picture and closer up
Step-by-step explanation:
Triangle ABC with vertices A(4, −6), B(2, −8), and C(−10, 4) is dilated by a scale factor of 2 to obtain triangle A′B′C′. Which statement best describes triangle A′B′C′?
It is similar to triangle ABC and has coordinates A′(2, −3), B′(1, −4), and C′(−5, 2).
It is similar to triangle ABC and has coordinates A′(8, −12), B′(4, −16), and C′(−20, 8).
It is congruent to triangle ABC and has coordinates A′(2, −3), B′(1, −4), and C′(−5, 2).
It is congruent to triangle ABC and has coordinates A′(8, −12), B′(4, −16), and C′(−20, 8).
(Please answer asap ;-;)
Answer:
It is similar to triangle ABC and has coordinates A'(2, -3), B'(1, -4), and C'(-5, 2)
How many lines of symmetry does this regular polygon have
A.0
B.1
C.2
D.5
Answer:
c
Step-by-step explanation:
the top pair and the middle pair
The number of lines of symmetry that this regular polygon have is: D. 5.
What is the order of rotational symmetry?In Mathematics and Geometry, the order of rotational symmetry of any geometrical shape can be defined as the number of times in which the geometrical shape can be rotated around a full (complete) circle and still look the same.
As a general rule in geometry, a geometrical shape with number of sides (n) has "n" lines of symmetry and its order of rotational symmetry is equal to "n."
Based on the above rule, we can reasonably infer and logically deduce that the order of rotational symmetry for this geometrical figure is equal to 5 because a pentagon has five sides.
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18x__=504 plz help quickly
Answer:
28 times
Step-by-step explanation:
18 x 28 = 504
One tossed coin landing heads and the next landing tails
Answer:
1/4 or 0.25
Step-by-step explanation:
*I'm assuming you're asking about the probability of this happening...
There are 4 different results you can get when flipping a coin twice...
First Flip: heads
Second Flip: tails
First Flip: heads
Second Flip: heads
First Flip: tails
Second Flip: heads
First Flip: tails
Second Flip: tails
only one of these is heads, then tails, so our probability is
1/4, or 0.25
Determine the measures of the angles. 25 points!
A 35
B 70
C 75
D 100
E 105
F 110
Match the tiles to the numbers in the image.
Answer:
1: f; 110
2: b; 70
3: e; 105
4: c; 75
5: a; 35
Step-by-step explanation:
Start with one that is easy to find, like 5, 4, or 3.
5. We know that 5 is on a 180 degree line with the angle of 145. Subtract 145 from 180 to find 5. This angle is 35.
4. We also know that 4 is a vertical angle to 75, which means 4 will also be 75.
3. Solve like you did for 5. 180 - 75 = 105.
2. First, find another angle inside the triangle shape. Look at the angle for 5 for this one. We know it is 35. That means the vertical angle inside is also 35. Subtract both interior angles to find 2. 180 - 75 - 35 = 70.
1. Finally, take the angle you got for 2, 70, and subtract it from the straight line, 180. 180 - 70 = 110.
Answer:
1: f; 110
2: b; 70
3: e; 105
4: c; 75
5: a; 35
Step-by-step explanation:
Watts per square meter
What is the attribute being measured?
A)
inches
B)
height
C)
overweight males
D)
number of adult males
Answer:
What is the attribute being measured?
A) inches
B) height
C) overweight males
D) number of adult males
Step-by-step explanation:
Answer:It´s B, just did the assessment.
Step-by-step explanation:
The ratio of the areas of two triangles is 5:2. the area of the larger triangle 60 cm² what is the area of the smaller triangle
Answer:
24 cm²
Step-by-step explanation:
Using proportion to solve
let the area of the smaller triangle be x, then
[tex]\frac{5}{2}[/tex] = [tex]\frac{60}{x}[/tex] ( cross- multiply )
5x = 120 ( divide both sides by 5 )
x = 24
Area of smaller triangle = 24 cm²
Answer:
24 cm²Step-by-step explanation:
[tex]Let\\A_1,\ A_2-areas\ of\ triangles\ (A_1>A_2)\\\\A_1=60\ cm^2\\\\A_1:A_2=5:2\\\\\text{Substitute:}\\\\\dfrac{60}{A_2}=\dfrac{5}{2}\qquad\text{cross multiply}\\\\5A_2=(60)(2)\\\\5A_2=120\qquad\text{divide both sides by 5}\\\\A_2=24\ cm^2[/tex]