solve the following system of equations below 4x+y=16 2x+3y=-2​

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

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:

Step-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]

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:

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: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 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:

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:

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:

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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Answer:

670.8

Step-by-step explanation:

55.9x12=670.8

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:

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:

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

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

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:

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!

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:

p²(5p - 2)

Step-by-step explanation:

p² is a factor common to both terms, and thus should be factored out:

p²(5p - 2)

Answer:

show me the other picture and closer up

Step-by-step explanation:

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:

7x -14=35        add 14 on both sides

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

x=7

Answer:

26 in²

Step-by-step explanation:

area of triangle half base times height

gives you 20 and 6

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 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:

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:

18

Step-by-step explanation:

Answer:

Vertical Shrink by 1/2 and down 5

Answer:

The transformations are a rotation and a translation.

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%.

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