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sveta [45]
3 years ago
9

Brandy is trying to factor the quadratic $3x^2 - x - 10.$ She starts by assuming that the quadratic factors as \[3x^2 - x - 10 =

(x + B)(3x + D),\]for some integers $B$ and $D.$ After some work, Brandy successfully factors the quadratic. Find the ordered pair $(B,D).$
Mathematics
1 answer:
taurus [48]3 years ago
7 0

Answer:

(B , D) = (-2,5)

Step-by-step explanation:

The given quadratic expression is

3x^{2} -x-10

compare the given expression with ax^{2} +bx+c

so we have a = 3 , b = -1 ,c = -10

now ac=3 (-10)=- 30 and b= -1

we need to find two numbers such that their product is -30 and sum is -1

-6 and 5 are such numbers

so we have

3x^{2} -6x+5x-10

grouping first two terms and last two terms

(3x^{2} -6x)+(5x-10)

factor out 3x from first two terms and 5 from last two terms

3x(x-2) +5(x-2)          

(x-2)(3x+5)        ( factor out (x-2))

(x+(-2))(3x+5)

hence B =-2 and D= 5

(B,D)= (-2,5)

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A square has vertices J(–1, 4), U(5, 4), M(5, –2), P(–1, –2). After a dilation, square J U M P has vertices J(–0.5, 2), U(2.5, 2
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3 years ago
5. A car travels at a speed of 72 miles per hour. Write a direct variation equation for the distance, y, the car will travel in
astraxan [27]

Answer:

 y  = 72x

324miles

Step-by-step explanation:

Given parameters:

      Speed of the car = 72miles/hr

       distance  = y

        time  = xhrs

Unknown:

Write a direct variation equation for the distance=  ?

Distance covered in 4.5hrs =?

Solution:

A. Write a direct variation equation for the distance;

    A direct variation is a linear equation.

   It often takes the form y = kx

   

For this problem;

      Distance  = speed x time

input the parameters;

      y  = 72x

The direct variation equation is  y  = 72x

B. Distance traveled in 4.5hrs

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  x is the time taken;

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3 years ago
Janet, an experienced shipping clerk, can fill a certain order in 2 hours. Tom, a new clerk, needs 3 hours to do the same job.
Arte-miy333 [17]

Answer:

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Step-by-step explanation:

Since Janet, an experienced shipping clerk, can fill a certain order in 2 hours, while Tom, a new clerk, needs 3 hours to do the same job, to determine how long will it take them to fill the order by working together you must perform the following logical reasoning:

Each of them will do half the work, so in principle, Janet will do her work in 1 hour, while Tom will do it in 1 hour and a half. Now, the remaining half hour that Tom has more than Janet can in turn be divided in two, with which each one will do their work in 15 minutes. Thus, the order will be ready in 1 hour and 15 minutes.

8 0
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The formula can be used to find the velocity v in feet per second of an object that has fallen h feet. Find the velocity of an o
Mama L [17]
The formula for a falling object is
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where
u =  initial velocity (=0 for a falling object)
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Because h = 23 ft and u = 0, therefore
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Answer: 28.49 ft/s (nearest hundredth)
8 0
3 years ago
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