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Ket [755]
3 years ago
12

If RT bisects SU, find each measure ST, RU, SV, SU,

Mathematics
1 answer:
FinnZ [79.3K]3 years ago
6 0

Answer:

ST = 23

RU = 8

SV = 5

SV = 10

Step-by-step explanation:

Use the knowledge of the properties of a kite to find the measure of ST, RU, SV, and SU as shown below:

✍️Recall: Each pair of adjacent sides of a kite are congruent/equal.

ST and TU are a pair of adjacent sides.

TU = 23

✅Therefore, ST = 23.

RU and RS are a pair of adjacent sides.

RS = 8

✅Therefore, RU = 8.

✍️ Recall: the longer diagonal of a kite bisects the shorter one. This means RT divides SU into two equal parts, namely SV and UV.

Since UV = 5, therefore,

✅SV = 5

SU = UV + SV

✅SV = 5 + 5 = 10

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Solve for equation √-5p=√24-p
blsea [12.9K]

Answer:


Step-by-step explanation:

Algebra Calculator | Latest | Discuss | About | Help | Translation

25,219,829 solved | 850 online

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

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3 years ago
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marishachu [46]
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3 years ago
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algol [13]

Answer:

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Step-by-step explanation:

Given that:

Liters of punch purchased = 25 liters

Liters of punch left over = 6 liters

Liters of punch used = 25 - 6 = 19 liters

According to the given statement;

1 liter = 0.26 gallons

19 liters = 0.26*19 gallons

19 liters = 4.94 gallons

Hence,

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F(x)= 3x - 4x2 +6x and g(x)= 5x +2x2 – 3x. What is f(x) g(x)?
goldenfox [79]

f(x)g(x) = 9x² + 10x - 16

<u>Step-by-step explanation:</u>

Step 1:

Given f(x) = 3x - 4 × 2 + 6x and g(x) = 5x + 2 × 2 - 3x

f(x) = 9x - 8

g(x) = 2x + 4

f(x)g(x) = (9x - 8)(2x + 4)

= 18x² + 36x - 16x -32

= 18x² + 20x - 32

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