Answer:
11*w=x
Step-by-step explanation:
x= the amount of money he will have after w weeks
so, 11 times the amount of weeks will give you the amount he has after any number of weeks
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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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
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
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:
3. What is the area of the figure below? O26 in. 27 in. 52 in.2 54 in.2
Answer:
26 in²
Step-by-step explanation:
area of triangle half base times height
gives you 20 and 6
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:
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)
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:
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
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
Given the geometric sequence where a1=3 and the common ratio is -1, what is the domain for n?
Answer:
natural numbers: integers n for n ≥ 1
Step-by-step explanation:
As it is for any sequence, the domain of term numbers (n) is the positive integers, the natural numbers.
__
In general, the domain of any "n' that represents something being counted will be the counting numbers. These are also referred to as "natural numbers" or "positive integers." For integer n, n ≥ 1.
__
Additional comment
The geometric sequence described in this problem statement is represented by the exponential function ...
a(n) = 3(-1)^n
This evaluates to a real number (3 or -3) for all integer values of n, and for some fractional values of n. In the complex numbers, the function is defined for all real and complex values of n.
Answer:
All integers where n ≥ 1
Step-by-step explanation:
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Explanation please how to do it
Answer:
I can't see the whole problem but if it says how many times per week does he practice it would be 13 times
Step-by-step explanation:
9 3/4 divided by 3/4.
39/4 times 4/3=13
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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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.
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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PLEASE HELP : A cylindrical fish tank has a base radius of 7 inches . The volume of the tank is approximately 3,080 cubic inches . What is the approximate height of the fish tank A) 62 in. B) 20 in C) 11in D) 10 in
Answer: B) 20 in
I plugged it into a calculator for this specific formula.
How much money has to be invested at 2.9% interest compounded continuosly to have 34,000 after 18 years
Answer:
[tex]\$20,173.31[/tex]
Step-by-step explanation:
we know that
The formula to calculate continuously compounded interest is equal to
[tex]A=P(e)^{rt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
e is the mathematical constant number
we have
[tex]t=18\ years\\ A=\$34,000\\ r=0.029[/tex]
substitute in the formula above
[tex]34,000=P(e)^{0.029*18}[/tex]
[tex]P=34,000/((e)^{0.029*18})=\$20,173.31[/tex]
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)
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).
Mike is renting a boat. The hourly rental fee is the same per hour for any boat. Mike paid $50 to rent a canoe, and then $25 to rent a kayak. which is the dependent variable in the situation!
Answer:
The dependent variable is the cost of renting a boat
Step-by-step explanation:
Let
x-----> the number of hours
y----> the cost of renting a boat
In this problem
The independent variable is the number of hours
The dependent variable is the cost of renting a boat
Answer:
cost
Step-by-step explanation:
I need to find the volume of the shapes. Can you help me on 5and6.
Answer:
5. 96 ft³
6. 108 cm³
Step-by-step explanation:
I will answer in spite.
5. To find the volume, seperate the figure into two separate rectangles (one long one along the bottom, and one small one sitting on top).
The volume of rectangle one is 4ft × 9 ft × 2ft = 72 ft³.
The volume of rectangle two is 4ft × 3ft × 2ft = 24 ft³.
72 ft³ + 24 ft³ = 96 ft³.
6. Patty treated the figure as two separate rectangles with the dimensions 2x3x11 and 2x3x10, not taking into account the space where the rectangles meet.
She should have calculated (2x3x11) + (2x3x7), which is 108 cm³.
You're welcome Mr. Harvard.
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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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:
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]
PLEASE HELP WITH MY MATH
1. What is thw width of a rectangular room with a area of 90 square feet and a length of 9ft?
2. What is the width of a rectangular swimming pool with a rea of 180 square feet and a width of 12 feet?
3. What is the perimeter of a rectangular rose garden that mesures 8 meters by 10meters
4. What is the width of a rectangular ping pong table that messures 8ft in length with a area of 32 square feet?
1. 10 ft
2. 15 ft
3. 36 meters
4. 4 ft
Hope this helps!
Write the equation that represents the line use exact numbers
Answer:
[tex]y=1.5x+3[/tex]
Step-by-step explanation:
Observing the graph
Let
[tex]A(0,3)[/tex] -----> this point is the y-intercept of the line
[tex]B(2,6)[/tex]
we know that
The equation of the line into slope intercept form is equal to
[tex]y=mx+b[/tex]
where
m is the slope
b is the y-coordinate of the y-intercept
In this problem
[tex]b=3[/tex]
Find the slope of the line m
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
substitute the values
[tex]m=\frac{6-3}{2-0}[/tex]
[tex]m=\frac{3}{2}[/tex]
[tex]m=1.5[/tex]
The equation of the line is
[tex]y=1.5x+3[/tex]
The equation of the line that passes through the points (0, 3) and (2, 6) is y = 1.5x + 3. The slope (m) is calculated as 1.5 and the y-intercept (b) is 3.
Explanation:To find the equation of a line that passes through two points, you'll first have to find the slope (m), and then find the y-intercept (b). Linear equations are typically represented in the form y = mx + b, where m is the slope and b is the y-intercept.
The line passes through points (0, 3) and (2, 6). To calculate the slope m, we use the formula (y2-y1)/(x2-x1). Plugging in our points, we get (6-3)/(2-0) = 1.5. This is our slope.
Next, we want to use the formula y = mx + b to calculate b. Since the line passes through the point (0,3), we know that when x = 0, y = 3. Plugging these values into the equation along with our determined slope, we get 3 = 1.5*0 + b. Solving for b reveals that our y-intercept is 3.
Therefore, the equation for this line appears as: y = 1.5x + 3.
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Janice bought her mother a bunch of 10 flowers two of the flowers are daisies one half of the remaining flowers are tulips write the fraction of the flowers that are daisies
Answer:
2/10 or 1/5 of the flowers are daises.
4/10 of the flowers are tulips.
Since there is 10 flowers, that will be your denominator. 2 out of the ten flowers, so 2 is your numerator. There is 8 flowers left over and half of that is 4.
Explain how to use multiplication to find 4÷1/5=
Final answer:
To find 4 divided by 1/5, multiply 4 by the reciprocal of 1/5, which is 5, resulting in an answer of 20.
Explanation:
To solve the division problem 4 ÷ 1/5, you can utilize multiplication by the reciprocal of the fraction. Recall that dividing by a fraction is equivalent to multiplying by its reciprocal. In this case, the reciprocal of 1/5 is 5/1, because when you flip the numerator and denominator of 1/5, you get 5.
Now, you can rewrite the original equation as a multiplication problem: 4 × 5/1. When you multiply fractions, you multiply the numerators with numerators and the denominators with denominators. Since the denominator of 5/1 is 1, multiplying by it doesn't change the value of the numerator. Thus, multiplying 4 by 5 gives you the answer 20.
A map has a scale of 1:25 000.
David walks 3.5 km in real life.
How far will this be on the map?
Answer:
250 m
Step-by-step explanation:
Final answer:
To find how far 3.5 km will be on a map with a scale of 1:25,000, convert the distance to meters (3,500 m) and then divide by the scale factor (25,000) to get the map distance, which is 14 centimeters.
Explanation:
When working with map scale, it's essential to understand how to convert distances on a map to actual distances in the real world. In this particular case, we have a map with a scale of 1:25,000, which means that 1 unit on the map is equivalent to 25,000 units in real life. David has walked a distance of 3.5 km in reality, and we need to calculate how far this would be represented on the map.
To convert David's actual walking distance to the map distance, we first need to express the 3.5 km in the same unit that is used in the map scale, which is meters. Since 1 km equals 1,000 meters, David walked 3,500 meters. Simply divide the actual distance walked by the scale factor to find the distance on the map:
Map distance = Actual distance / Scale
Map distance = 3,500 meters / 25,000
Map distance = 0.14 meters
Map distance = 14 centimeters
Thus, on the map, David's 3.5 km walk will be represented by a line that is 14 centimeters long.
Watts per square meter