Suppose that data collected from police reports of motor vehicle crashes show a moderate positive correlation between the speed of the motor vehicle at the time of the crash and the severity of injuries to the driver. Answer the following question based only on this information.
True or false: Traveling faster in a motor vehicle at the time of a crash causes more severe injuries to the driver.
A. True
B. False

Answer:

Following are the solution to the question:

Step-by-step explanation:

The objective is to find the orthogonal trajectory of the family curves:

[tex]x^2+2y^2=17k^2[/tex]

The family curves are: [tex]x^2 + 2y^2=17k^2[/tex]  

Differentiate the equation with the respect of x.

[tex]\to x^2+2y^2=17k^2 \\\\\to 2x+4y \frac{dy}{dx} =0\\\\\to \frac{dy}{dx} =- \frac{2x}{4y}\\\\\to \frac{dy}{dx} =- \frac{x}{2y}[/tex]

The negative reciprocal is:

[tex]\to \frac{dy}{dx} =-\frac{1}{-\frac{x}{2y}}\\\\\to \frac{dy}{dx} = \frac{2y}{x}[/tex]

Integration of the above equation:

[tex]\to \frac{dy}{dx} = \frac{2y}{x} \\\\\to \int \frac{dy}{2y} = \int \frac{dx}{x}\\\\\to \frac{1}{2} \log y = \log x + \log C\\\\\to \log y = 2 \log x + 2\log C \\\\\to \log y = \log x^2 +\log C^2 \\\\\to y = Ax^2 \ \ \ \ \ \ \ \ \ (A=C^2)[/tex]

Hence, the orthogonal trajectory of the family of the curves [tex]x^2 + 2y^2 =17k^2 \ \ is \ \ y=Ax^2[/tex]

Answer: It is B/Spinner 2

Answer:

11

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

g(x) = x³ - 4

h(x) = x² + 2

h(-2) is x = -2

g(-1) is x = -1

Step 2: Find h(-2) - g(-1)

Answer:

3.26 Euro I believe.

Step-by-step explanation:

Answer:

1080 boys

Step-by-step explanation:

2400 x 0.45 = 1080

Answer:

36  x 2 - 49 y 2

Step-by-step explanation:

6  x (6x) +6 x ( - 7 y ) + 7 y (6x) +7 y ( - 7 y)

Answer:

c)

Step-by-step explanation:

Answer:

the answer above is correct

Answer:

boxes

7

8

58.1

119.7

Step-by-step explanation:

look when u solve this it equals

8.3(7)+7.7(8)=119.7 but it tells u to add 61.6 so u go backwards subtract

119.7-61.6

58.1

just plug in

8.3(7)+7.7(8)=____+61.6

plug in

58.1+61.6

119.7

Answer:

Slope is -2

y intercept is -3

Equation :y=-2x-3

Step-by-step explanation:

answear is 7/17 hope its useful

[tex]f(x)=2x^2+6x-4[/tex]

Find the f(-5) by substituting x = -5 in the equation.

[tex]f(-5)=2(-5)^2+6(-5)-4\\f(-5)=2(25)-30-4\\f(-5)=50-34\\f(-5)=16[/tex]

Therefore, the answer is f(-5) = 16.

Answer:

i think it might be 15m

Step-by-step explanation:

Answer:

50xy

Step-by-step explanation:

(2x)(5y)(5y)

~Simplify

(2x)(25y)

~Multiply

50xy

Best of Luck!

Answer: A, B, C, and E

Step-by-step explanation:

If both sides are real numbers, then the product will be a real number.

If in at least one of the sides we have a complex number, then the product will be real if:

The other number is zero.

The other number is the conjugate of the first.

This is when:

Suppose we have a number:

z = a + b*i

The conjugate will be:

w = a - b*i

And the product between them is:

(a + b*i)*(a - b*i) = a^2 + a*b*i - a*b*i + b^2 = a^2 + b^2

Then the options that will have a real answer are:

A. (4+5i)(4-5i) = 4^2 + 5^2 = 16 + 25 = 41

B. (4 + 91)*(41 - 9) = 3040

C. (3 + 2*i)*(3 -2*i) = 3^2 + 2^2 = 9 + 4 = 13

E. (312 + 7i)*(312 - 7i) = 312^2 + 7^2 = 97,393

The grouped frequency distribution for the data with the given intervals is 2, 4, 2 and 2 respectively.

Given that, ten cyclists were each asked the distance in miles they biked last week. The distance travelled by 10 cyclists is 3, 20, 6, 3, 7, 8, 13, 10, 18 and 12.

We need to complete the grouped frequency distribution for the data.

In this type, the data is arranged and separated into groups called class intervals. The frequency of data belonging to each class interval is noted in a frequency distribution table. The grouped frequency table shows the distribution of frequencies in class intervals.

Now, the frequency distribution for the given intervals is as follows:

That is, for intervals 1 to 5 the frequency is 2.

For intervals 5 to 10 the frequency is 4.

For intervals 11 to 15 the frequency is 2.

For intervals 16 to 20 the frequency is 2.

Therefore, the grouped frequency distribution for the data with the given intervals is 2, 4, 2 and 2 respectively.

To learn more about the grouped frequency distribution visit:

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#SPJ2

9514 1404 393

Answer:

  see below

Step-by-step explanation:

When the intercepts are given, plot those and draw a line through them.

_____

Additional comment

The equation shown with the graph is the equation of a line in "intercept form." It is especially useful in a case like this where the intercepts are given.

Answer: 10 yards

Step-by-step explanation: 50% = 1/2

1/2 x 20 = 10

15 yeards mowed by Wednesday

Answer:

2x - 4

Step-by-step explanation:

f(x) = x - 7

= 2x + 3 - 7

= 2x - 4

Answer:

The equation of the polynomial in vertex form is [tex]y +8= (-2)\cdot (x-3)^{2}[/tex], its vertex is [tex](h,k) = (3, -8)[/tex].

The expression of the axis of symmetry is [tex]x = 3[/tex].

The y-intercept of the function is -26.

Step-by-step explanation:

The vertex form of the second order polynomial is defined by the following expression:

[tex]y-k = C\cdot (x-h)^{2}[/tex]  (1)

Where:

[tex]x[/tex] - Independent variable, dimensionless.

[tex]y[/tex] - Dependent variable, dimensionless.

[tex]h,k[/tex] - Coordinates of the vertex, dimensionless.

[tex]C[/tex] - Vertex constant, dimensionless.

Let [tex]y = -2\cdot x^{2}+12\cdot x - 26[/tex], then we proceed to present the produre for the determination of the vertex form:

1) [tex]y = -2\cdot x^{2}+12\cdot x - 26[/tex] Given

2) [tex]y = (-1)\cdot (2\cdot x^{2})+(-1)\cdot (-12\cdot x) + (-1)\cdot (26)[/tex] [tex](-a)\cdot (-b) = a\cdot b[/tex]/[tex](-a)\cdot b = -a\cdot b[/tex]

3) [tex]y = (-1)\cdot (2\cdot x^{2}-12\cdot x +26)[/tex] Distributive property

4) [tex]y = [(-1)\cdot (2)]\cdot (x^{2}-6\cdot x +13)[/tex] Associative and distributive properties

5) [tex]y = (-2)\cdot [(x^{2}-6\cdot x+9)+4][/tex] [tex](-a)\cdot b = -a\cdot b[/tex]

6) [tex]y = (-2) \cdot [(x-3)^{2}+4][/tex] Perfect square trinomial

7) [tex]y = (-2)\cdot (x-3)^{2}+4\cdot (-2)[/tex] Distributive property

8) [tex]y = (-2)\cdot (x-3)^{2}+(-8)[/tex] [tex](-a)\cdot b = -a\cdot b[/tex]

9) [tex]y +8= (-2)\cdot (x-3)^{2}[/tex] Compatibility of addition/Existence of the additive inverse/Modulative property/Result.

The equation of the polynomial in vertex form is [tex]y +8= (-2)\cdot (x-3)^{2}[/tex], its vertex is [tex](h,k) = (3, -8)[/tex].

The axis of symmetry is a line perpendicular to axis in which the square component of the vertex form is set. The expression of the axis of symmetry is [tex]x = 3[/tex].

The y-intercept is the value of the polynomial when [tex]x = 0[/tex], then, the value is:

[tex]y = -2\cdot (0)^{2}+12\cdot (0) -26[/tex]

[tex]y = -26[/tex]

The y-intercept of the function is -26.

Answer:

5/100

1/20

Step-by-step explanation:

Answer: 5/100

Step-by-step explanation:

Answer: Many people assume that because DNA is so small, we can't see it without powerful microscopes. But in fact, DNA can be easily seen with the naked eye when collected from thousands of cells.

Answer:

C) Reflection across the x-axis.

Step-by-step explanation:

From Linear Algebra we define the reflection across the x-axis is for [tex]P(x,y) =(x,y)[/tex]:

[tex]P'(x,y) = (x, -y)[/tex] (1)

If we know that [tex]A(x,y) = (-1, 2)[/tex], [tex]B(x,y) =(-1,5)[/tex], [tex]C(x,y) = (-3, 5)[/tex] and [tex]D(x,y) =(-3, 2)[/tex], then the reflected points are, respectively:

[tex]A'(x,y) = (-1, -2)[/tex]

[tex]B'(x,y) = (-1,-5)[/tex]

[tex]C'(x,y) = (-3,-5)[/tex]

[tex]D'(x,y) = (-3,-2)[/tex]

In consequence, Kim performed a reflection across the x-axis to create triangle A'B'C'D'. The correct answer is C.

This question is based on the reflection of x- axis. Hence the correct answer is C, reflection across the x-axis.

Given:

Transform  rectangle ABCD to rectangle A'B'C'D',

The vertices of rectangle ABCD is A(-1,2) B(-1,5) C(-3,5) D(-3,2).

The vertices of rectangle A'B'C'D is A'(-1,-2) B'(-1,-5) C'(-3,-5) D'(-3,-2).

We need to determined the transformation that Kim perform to create rectangle A'B'C'D.

From Linear Algebra we define the reflection across the x-axis is for,

P(x,y) = (x,y)

P(x,y) = (x,-y)                                .....(1)

It is given that  A(-1,2), B(-1,5), C(-3,5) and D(-3,2).

Therefore from equation (1)  above point becomes,

A'(x,y) = (-1,-2)

B'(x,y) =(-1,-5)

C'(x,y) =(-3,-5)

D'(x,y) =(-3,-2)

Therefore, It is observe that Kim performed a reflection across the x-axis to create triangle A'B'C'D'. Hence the correct answer is C, reflection across the x-axis.

For further details, please refer this link:

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