It takes Brian 15 hours longer to build a model car than it takes John. If they work together, they can build the model car in 4 hours. Using complete sentences, explain each step in figuring out how to determine the time it would take Brian to build the car on his own. (10 points)

The x-intercepts of an equation are simply the zeros of the equation

The equation [tex]\mathbf{y = bx(x - a)(x -a)(x + b)(x - b)}[/tex] has 4 distinct x-intercepts

The equation is given as:

[tex]\mathbf{y = bx(x - a)(x -a)(x + b)(x - b)}[/tex]

Set the equation to 0; i.e. calculate the zeros

[tex]\mathbf{bx(x - a)(x -a)(x + b)(x - b) = 0}[/tex]

Divide both sides by constant b

[tex]\mathbf{x(x - a)(x -a)(x + b)(x - b) = 0}[/tex]

Split the above equation, as follows

[tex]\mathbf{x= 0\ or\ x - a = 0\ or\ x -a = 0\ or\ x + b = 0\ or\ x - b = 0}[/tex]

Solve for x in each of the equation

[tex]\mathbf{x= 0\ or\ x = a\ or\ x = a\ or\ x= -b\ or\ x = b}[/tex]

Remove repeated solutions

[tex]\mathbf{x= 0\ or\ x = a\ or\ x= -b\ or\ x = b}[/tex]

The count of solutions above is 4

Hence, the equation has 4 distinct x-intercepts

Read more about x-intercepts at:

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Answer:

not a function

Step-by-step explanation:

you can not have one-to-many

there is two 3 in the X column  

Answer:

1. -15

2. 3

3. -15 [tex]\times[/tex] 3

4. Kindly refer to the attached image.

5. -45, This change represents that achieving the goal will reduced the time by 45 seconds.

Step-by-step explanation:

Given that it is a 5 kilometre race.

Time to be reduced each month = 15 seconds

Total number of months left in the race = 3

1. Riley wants to achieve each month a decrease of 15 seconds.

Integer representing the change = -15

2. Change in time i.e. 3 months is represented by integer 3.

3. There are a total of 3 months and there is a decrease of 15 every month.

so, multiplication expression is: -15 [tex]\times[/tex] 3

4. Kindly refer to the attached image for the number line representation of the answer.

The arrow is from 0 to -45.

5. Total change in time is -45.

This change represents that achieving the goal will reduced the time by 45 seconds.

Answer:

(7, -6)

Step-by-step explanation:

You will graph it at this point because the point is basically the origin and when you rotate it clockwise 90° it will end up in Quadrant IV.

Explanation:

Let y=3x

To calculate the inverse, interchange

x and y,    

x =3 y

Answer:

24

Step-by-step explanation:

Answer:

Step-by-step explanation:

for 2.2 you would still have 5^2 in brackets still

same kind of error for 2.1

no idea

Step-by-step explanation:

u can use google for this if u r in hurry

Answer:

0

Step-by-step explanation:

-(-x) ^3-x^3

x^3-x^3

=0

Answer: 3.9737436e-13

Step-by-step explanation: pi/12= 0.26179938779 to the tenth power = 5.0738475e-11 x 6/5.32018=  3.9737436e-13.

Answer:

it will be (3)

Step-by-step explanation:

since DB is a median

then DB= half AC , AB=BC

then AB=BD

then the two triangles are isosceles

The required m∠BDC is 32° .

In geometry, a median of a triangle is a line segment joining a vertex to the midpoint of the opposite side, thus bisecting that side. Every triangle has exactly three medians, one from each vertex, and they all intersect each other at the triangle's centroid.

According to the given question ;

DB is a median;

By the symmetry ;

Then DB = half AC ,

        = AB = BC

Then= AB = BD

In a triangle, a line that connects one corner (or vertices ) to the middle point of the opposite side is called a median. A property of isosceles triangles, which is simple to prove using triangle congruence, is that in an isosceles triangle the median to the base is perpendicular to the base.

Then the two triangles are isosceles.

Means m∠DAB = m∠BDC = 32°

For the more information about the properties of isosceles triangle click the link given below.

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Answer:

x = 8

Is that what you wanted?

Angle GFJ = 56 degrees

Angle FGH = 124 degrees

Angle HFJ = 34 degrees

Angle HKJ = 101 degrees

Step-by-step explanation:

The measure of the angles are:

[tex]\mathbf{GFJ = 56}[/tex]

[tex]\mathbf{GFJ = 56}[/tex]

[tex]\mathbf{\angle HFJ = 34}[/tex]

[tex]\mathbf{\angle HKJ =101}[/tex]

The given parameters are:

∠GHF = 34°,

∠HJF = 124°,

∠FKJ = 79°.

(a) Angle ∠GFJ

This is calculated as:

[tex]\mathbf{GFJ = 180 - \angle HJF}[/tex] --- base angles of parallelogram add up to 180 degrees

So, we have:

[tex]\mathbf{GFJ = 180 - 124}[/tex]

[tex]\mathbf{GFJ = 56}[/tex]

(b) Angle ∠FGH

This is calculated as:

[tex]\mathbf{\angle FGH = \angle HJF}[/tex] --- opposite angles of parallelogram are equal

So, we have:

[tex]\mathbf{\angle FGH = 124}[/tex]

(c) Angle ∠HFJ

This is calculated as:

[tex]\mathbf{\angle HFJ = \angle GHF}[/tex] --- corresponding angles

So, we have:

[tex]\mathbf{\angle HFJ = 34}[/tex]

(d) Angle ∠HKJ

This is calculated as:

[tex]\mathbf{\angle HKJ =180 - \angle FKJ}[/tex] ---- supplementary angles

So, we have:

[tex]\mathbf{\angle HKJ =180 - 79}[/tex]

[tex]\mathbf{\angle HKJ =101}[/tex]

Read more about angles in a parallelogram at:

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Answer:

B. x = −3, x = −11

Step-by-step explanation:

−3|x + 7| = −12

-3x - 21 = -12 and -3x - 21 = 12

-3x - 21 = -12

      -3x = 9

          x = -3

-3x - 21 = 12

      -3x = 33

         x = -11

Answer:

hello

Step-by-step explanation:

Slope, sometimes referred to as gradient in mathematics, is a number that measures the steepness and direction of a line, or a section of a line connecting two points, and is usually denoted by m. Generally, a line's steepness is measured by the absolute value of its slope, m.

m = slope

Answer:

[tex]n = \frac{49}{2x}[/tex]

Step-by-step explanation:

1) Simplify [tex]\frac{4}{7}[/tex] xn to [tex]\frac{4xn}{7}[/tex]

[tex]\frac{4xn}{7}[/tex] = 14

2) Multiply both sides by 7.

4xn = 14 × 7

3) Simplify 14 × 7 to 98.

4xn=98

4) Divide both sides by 4.

[tex]xn = \frac{98}{4}[/tex]

5) Simplify [tex]\frac{98}{4}[/tex] to [tex]\frac{49}{2}[/tex]

[tex]xn = \frac{49 }{2}[/tex]

6) Divide both sides by x.

[tex]n = \frac{49}{2} / x[/tex]

7) Simplify [tex]\frac{49}{2} /x[/tex] into [tex]\frac{49}{2x}[/tex]

[tex]n = \frac{49}{2x}[/tex]

Answer:

50 dollars an hour

Step-by-step explanation:

Answer:

4x - 3 = y

Step-by-step explanation:

Here's why: 4 is your slope and -3 is your y intercept so the equation would look something like 4x - 3 = y.

Hope I helped

Answer:

y = 1x -1

Step-by-step explanation:

m is your slope which is 1 and -1 is you y intercept

the slope intercept form is y = mx + b

which means the equation will be y = 1x -1

Answer:

A, C, E, F

Step-by-step explanation:

Answer:

y = 0 , x = 1

Step-by-step explanation:

jdbdjdajhsbsbs

Answer:

Step-by-step explanation:

The graph has both a vertical and horizontal asymptote to which the value

of the function approaches as the y-values and x-values approaches

infinity respectively.

Reasons:

The horizontal asymptote is the horizontal line that the function's graph

tends towards as the value of the input variable approaches infinity.

The horizontal line that the graph of the function approaches is y = 0

Therefore;

Similarly, the vertical asymptote is the vertical line that the graph of the

function approaches but never meets.

Therefore;

The graph of the function on the bottom left approaches the line x = 1 from

the left, while the graph of the function with the domain 0 < x < ∞,

approaches the line x = 1 from the right.

Therefore;

Learn more here:

https://brainly.com/question/13939972

Answer:

ΔABD ≅ ΔCDB

Step-by-step explanation:

Since a = 3, we can sub 3 into the expressions and then get a value for each side length.

AB: 3 + 7 = 10

BC = 16

CD: 12 - 2 = 10

DA: 18 - 2 = 16

Hence:

AB = CD (both have sidelengths of 10)

AD = CB (both have sidelengths of 16)

BD = BD (common line)

Therefore: ΔABD ≅ ΔCDB      Q.E.D.

9514 1404 393

Answer:

  x = 4c-3d

Step-by-step explanation:

Cross multiply, separate variables terms and constant terms.

  [tex]3(x-d)=4(x-c)\\\\3x-3d=4x-4c\\\\4c-3d=x\qquad\text{add $4c-3x$}\\\\\boxed{x=4c-3d}[/tex]

Answer:

D.) y=-x-2

Step-by-step explanation:

Answer:

D.) y=-x-2

Step-by-step explanation:

Trust me I just know

Answer:

One

Step-by-step explanation:

Find the value of B

Applying the law of sines

[tex]\frac{a}{sin(A)}[/tex] = [tex]\frac{b}{sin(B)}[/tex]

substitute the given values

[tex]\frac{23}{sin(61)}[/tex] = [tex]\frac{24}{sin(B)}[/tex]

sin (B) = [tex]\frac{24}{23}[/tex]Sin(61)

step 2

Find the measure of angle C

Remember that the sum of the interior angles in any triangle must be equal to 180 degrees

so

61 + 65.87 + C = 180

C = 53.13

step 3

Find the value of c

Applying the law of sines

[tex]\frac{a}{sin(A)}[/tex] = [tex]\frac{c}{sin(C)}[/tex]

substitute the given values

[tex]\frac{23}{sin(61)}[/tex] = [tex]\frac{c}{sin(53.13)}[/tex]

c = [tex]\frac{23}{sin(61)}[/tex]SIN (53.13)

C=21.04 units

so

there can only be one value for each measurement, therefore there can only be one triangle

Answer:

The answer is 2 triangles

Step-by-step explanation:

I took the test.

Answer:

Step-by-step explanation:

BD divides CBA into two angles. The add to 90 degrees. Therefore they are complementary.

The key word is complementary. The angles are <CBA and <DBA are complementary.

Answer:

Right angle or adjacent angle. I'm not sure if there was a vocabulary bank.

Step-by-step explanation:

Step-by-step explanation:

perimeter = 2* ( length + width)

Length = 4 + Width = 4+x

Equation is,

2* (4+x+x) = 48

2* (4+2x) = 48

4+2x = 48/2 = 24

4+2x=24

2x = 24-4 = 20

2x = 20

x = 10

Answer:

m=56kx-6

Step-by-step explanation: