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Alecsey [184]
3 years ago
6

Point T has coordinates (-1,3). Point M is symmetric to point T with respect to the line y=1

Mathematics
1 answer:
marin [14]3 years ago
6 0
T (-1, 3) is vertically 2 units away from the line y = 1.
When finding the ordered pair for the new point, M, it must also be 2 units from the line y = 1, but on the opposite of the line. The x-value will not change only the y-value.
Counting two units BELOW the line we get M(-1, -1)
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The linear function ƒ(x) = 5x − 8 has a slope of:
olga nikolaevna [1]

Answer:

5

The slope of y = 5x - 8 is 5.

Since this equation is already in slope-intercept form the slope of the graph is the coefficient of x, 5.

Step-by-step explanation:

5

The slope of y = 5x - 8 is 5.

Since this equation is already in slope-intercept form the slope of the graph is the coefficient of x, 5.

3 0
2 years ago
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Solve for equation √-5p=√24-p
blsea [12.9K]

Answer:


Step-by-step explanation:

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p2-5p-24=0  

Two solutions were found :

    p = 8

    p = -3  

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "p2"   was replaced by   "p^2".  

Step by step solution :

Step  1  :

Trying to factor by splitting the middle term

1.1     Factoring  p2-5p-24  

The first term is,  p2  its coefficient is  1 .

The middle term is,  -5p  its coefficient is  -5 .

The last term, "the constant", is  -24  

Step-1 : Multiply the coefficient of the first term by the constant   1 • -24 = -24  

Step-2 : Find two factors of  -24  whose sum equals the coefficient of the middle term, which is   -5 .

      -24     +     1     =     -23  

      -12     +     2     =     -10  

      -8     +     3     =     -5     That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -8  and  3  

                    p2 - 8p + 3p - 24

Step-4 : Add up the first 2 terms, pulling out like factors :

                   p • (p-8)

             Add up the last 2 terms, pulling out common factors :

                   3 • (p-8)

Step-5 : Add up the four terms of step 4 :

                   (p+3)  •  (p-8)

            Which is the desired factorization

Equation at the end of step  1  :

 (p + 3) • (p - 8)  = 0  

Step  2  :

Theory - Roots of a product :

2.1    A product of several terms equals zero.  

When a product of two or more terms equals zero, then at least one of the terms must be zero.  

We shall now solve each term = 0 separately  

In other words, we are going to solve as many equations as there are terms in the product  

Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation :

2.2      Solve  :    p+3 = 0  

Subtract  3  from both sides of the equation :  

                     p = -3

Solving a Single Variable Equation :

2.3      Solve  :    p-8 = 0  

Add  8  to both sides of the equation :  

                     p = 8

8 0
3 years ago
If f(x)=x2+1, then (f∘f)(x)=
PSYCHO15rus [73]

The resulting composite function (f∘f)(x) is x⁴+2x²+2

When a function is written inside another function, it is known as a composite function

Given the function f(x)=x²+1,

(f∘f)(x) = f(f(x))

f(f(x)) = f(x²+1)

This means we will need to replace x with x²+1 in f(x) as shown:

f(x²+1) = (x²+1)²+1

Expand

f(x²+1) = x⁴+2x²+1+1

f(x²+1) =  x⁴+2x²+2

Hence the resulting composite function (f∘f)(x) is x⁴+2x²+2

Learn more here: brainly.com/question/3256461

3 0
2 years ago
What is the arc length S what is shown below?
Solnce55 [7]

Answer:

  14 cm

Step-by-step explanation:

The applicable formula is ...

  s = rθ

  s = (7 cm)(2) = 14 cm

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2 years ago
Margaret used 12 gallons of gas to drive 252 miles. How many miles can Margaret drive with 16 gallons of gas?
nexus9112 [7]

Answer:

336

Step-by-step explanation:

if she can drive 252 miles with 12 gallons, you must divide 252 and 12 to figure out how many miles she can get per gallon. Once you find that answer, you multiply that by 16 gallons.

3 0
2 years ago
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