Irina rode her bike to work at an average speed of 16 miles per hour. It started to rain, so she got a ride home along the same route in her coworker’s car at an average speed of 27 miles per hour. If Irina’s ride home in the car took 24 minutes (0.4 of an hour), how many hours was her bike ride to work, to the nearest tenth of an hour?

Final answer:

The equation of the line in slope-intercept form, given the points (-2, 8) and (1, 2), is y = -2x + 4, which is option D.

Explanation:

The question asks for the equation of a line in slope-intercept form given two points on the line (-2, 8) and (1, 2). To find the equation, we first calculate the slope (m) which is the change in y-values divided by the change in x-values. Using the given points,

m = (2 - 8) / (1 - (-2))

= -6 / 3

= -2.

With the slope known, we use one point to solve for the y-intercept (b) in the equation,

y = mx + b.

Let's use the point (1, 2):

2 = (-2)(1) + b, which simplifies to,

2 = -2 + b, so,

b = 4. Therefore, the equation in slope-intercept form is y = -2x + 4, which corresponds to option D.

Answer: the 3 one is the answer

Answer:

Given the system of equations, what is the value of the system determinant?  x + y = 8  

x - y = 10  

C. -2

Given the system of equations, what is the value of the y-determinant?

3x + y - 10 = 0

4x - y - 4 = 0

A. -28

Step-by-step explanation:

The determinant of the system is the determinant of the matrix formed with the coefficients of the system, usually, this matrix is called A.

[tex]A=\left[\begin{array}{cc}1&1\\1&-1\end{array}\right][/tex]

In the 2x2 matrix, the determinant is calculated by obtaining the difference between the diagonally down product and the diagonally up product.

[tex]det(A)=\left|\begin{array}{cc}1&1\\1&-1\end{array}\right|=(1)(-1)-(1)(1)=-1-1=-2[/tex]

The y-determinant is the determinant of the matrix [tex]A_y[/tex], this matrix is formed substituting in the matrix A the coefficients of y with the constant terms.

[tex]A_y=\left[\begin{array}{cc}3&10\\4&4\end{array}\right][/tex]

[tex]det(A_y)=\left|\begin{array}{cc}3&10\\4&4\end{array}\right|=(3)(4)-(4)(10)=12-40=-28[/tex]

The price of the service that was charged before the tip was:

                            $ 35

Let the price of the service be $ x.

Now it is given that:

Talia gave her hairdresser a 20 percent tip, which amounted to $7.

This means that the 20% of total service charge=7

i.e.  20% ×x =7

i.e. 0.20×x=7

i.e. x=7/0.20

i.e. x=35

Hence, the price of the service that was paid before the tip is: $ 35

If there was a piece of rope from the top of the building to Joel, how long would it be approx 222.01 feet. The angle of elevation from Joel to the top of the building is approx [tex]31.18 ^ \circ[/tex]

You look straight parallel to ground. But when you have to watch something high, then you take your sight up by moving your head up. The angle from horizontal to the point where you stopped your head is called angle of elevation.

Similarly, there is angle of depression, when you look horizontal, then down, the angle between both positions is the angle of depression.

Remember that we assume that buildings are usually vertical to the ground. This means, there is 90° formation. The length of the rope can be taken as length of hypotenuse.

If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:

[tex]|AC|^2 = |AB|^2 + |BC|^2[/tex]

where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).

Referring to the figure attached below, we get:
Length of the rope = Length of the line segment AC = |AC|

Using the fact that the triangle ABC is right angled triangle, we can use Pythagoras theorem.

We get the length of AC as:

[tex]|AC|^2 = |AB|^2 + |BC|^2\\|AC| = \sqrt{|AB|^2 + |BC|^2} \\\text{positive square root since length is non-negative quantity}\\\\|AC| = \sqrt{115^2 + 190^2} = \sqrt{51325} \approx 222.01 \: \rm ft[/tex]

Thus, if there was a piece of rope from the top of the building to Joel, how long would it be approx 222.01 feet.

The angle of elevation is calculated as:

[tex]\tan(\angle ABC) = \dfrac{\text{Length of perpendicular}}{\text{Length of base}} = \dfrac{|AB|}{|BC|}\\\theta = tan^{-1}(\dfrac{115}{190}) \approx 31.18^\circ[/tex]

The angle of depression is actually equal to angle of depression because they are pair of alternate interior angles (made by traversing line AC between two parallel lines).

Thus, Margaret statement is false.

Therefore, we get the answers as:

Learn more about Pythagoras theorem here:

https://brainly.com/question/12105522

Answer: its horizontal

see attached sketch with the coordinates the line passes

 the picture is upside down for some reason, rotate it 180 degrees

The factor of quadratic function 2x²-2x-40 is 2 (x-5) (x+4).

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. In other terms, a "polynomial function of degree 2" is a quadratic function.

Given:

The quadratic function 2x²-2x-40.

To find the factors;

Take common term out,

2(x²-x-20)

= 2 (x²-5x + 4x -20)

= 2 {x (x-5) + 4(x -5)}

= 2 (x-5) (x+4)

Therefore, the factors are 2 (x-5) (x+4).

To learn more about the quadratic function;

https://brainly.com/question/11485644

#SPJ5

Answer:

[tex]2x-3y+21=0[/tex]

Step-by-step explanation:

We are given that an equation

[tex]y=-\frac{3}{2}x+4[/tex]

We have to find an equation of line which is perpendicular to given line and passing through the point (3,9).

We know that when two lines of slope [tex]m_1\;and\;m_2[/tex] are perpendicular then

[tex]m_1=-\frac{1}{m_2}[/tex]

By comparing with

[tex]y=mx+b[/tex]

Where m=Slope of line

Slope of given line=[tex]=m_1=\frac{-3}{2}[/tex]

Slope of the line=[tex]-\frac{1}{m_1}=-\frac{1}{\frac{-3}{2}}=\frac{2}{3}[/tex]

Slope of the line=[tex]\frac{2}{3}[/tex]

The equation of line passing through the point (3,9) is given by

[tex]y-y_0=m(x-x_0)[/tex]

Substitute the values

The equation of line which passing through the point (3,9) is given by

[tex]y-9=\frac{2}{3}(x-3)[/tex]

[tex]3y-27=2(x-3)[/tex]

[tex]3y-27=2x-6[/tex]

[tex]3y=2x-6+27[/tex]

[tex]2x-3y+21=0[/tex]

To find the smallest possible ages for Jose and Robert, set up a system of equations based on the given information. Robert's age is X, and Jose's age is 3X. The sum of their ages is more than 40, so the smallest possible age for Robert is 11, and Jose would be three times that, which is 33.

To find the smallest possible ages for Jose and Robert, we need to set up a system of equations based on the given information.

Let's assume Robert's age is x. Since Jose is three times as old as Robert, his age would be 3x.

The sum of their ages is more than 40, so we can write the equation: x + 3x > 40.

Simplifying the equation: 4x > 40.

Dividing both sides of the equation by 4, we get x > 10.

Therefore, the smallest possible age for Robert is 11, and Jose would be three times that, which is 33.

To simplify 2^4\*2^7, you add the exponents because the bases are the same, resulting in 2^11 which equals 2048.

When simplifying the expression 2^4\*2^7, we use the property of exponents that states when multiplying two exponential terms with the same base, you add the exponents. So, the simplified form of the expression would be 2^(4+7) which is 2^11. Since we are adding the exponents, this process is known as the sum of exponents and is a fundamental concept in the squaring of exponentials.

To calculate 2^11, you would multiply 2 by itself 11 times, but for the sake of simplicity, the answer is 2048.

Answer:

It's all below...

Step-by-step explanation:

Part 1.

quadratic poynomial function:   f(x)=x2−5x+6

linear binomial:   x−2

x−3x−2x2−5x+6x2−2x−−−−−−−−−−3x+6−3x+6−−−−−−−−0

Part 2.  

f(2)=22−5(2)+6=4−10+6=−6+6=0

Part 3.  

The remainder theorem says that if f(x) is divided by x-a, then f(a) will be the remainder. When we divided f(x) by x - 2 , we got a remainder of 0, which by the remainder theorem implies f(2) = 0.  That means x-2 is a factor of f(x).

Answer:

The Answer is 4

Step-by-step explanation:

2x² - 16x + 32 = 0

we would multiply 2x² and 32

= 64x²

then factorise 64x² such that the sum of the two nos = -16 AND the product of the nos = 64

the only value that satisfies this condition is -8 (-8 + -8 = -16, and -8 * -8 = 64)

0 = 2x² - 8x -8x + 32

0 = (2x² - 8x) (-8x +32)

2x(x - 4) -8(x - 4)

0 = (2x - 8) (x - 4)

0 = 2x - 8 or 0 = x - 4

8 = 2x or 4 = x

x = 8/2 or 4

x = 4 or 4

x = 4

hope it was clear

Answer:

fourth degree trinomial

Step-by-step explanation: