A triangular window pane has a base of 30 inches and a height of 24 inches what is the area of the window pane

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:

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:

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:

Answer: B) 20 in

I plugged it into a calculator for this specific formula.

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.

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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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.

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.

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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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.

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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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.

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]  

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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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.

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.

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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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

Answer:

670.8

Step-by-step explanation:

55.9x12=670.8

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]

Answer:

18

Step-by-step explanation:

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

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:

Answer:

It is similar to triangle ABC and has coordinates A'(2, -3), B'(1, -4), and C'(-5, 2)

1. 10 ft

2. 15 ft

3. 36 meters

4. 4 ft

Hope this helps!

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.

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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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).

Answer:

26 in²

Step-by-step explanation:

area of triangle half base times height

gives you 20 and 6

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.

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.

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.

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).

Answer:

7x -14=35        add 14 on both sides

7x= 49        then, divide 7 on the whole equation

x=7

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)