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denis23 [38]
4 years ago
5

Solve by completing the square w^2-10w+21=0

Mathematics
1 answer:
sergejj [24]4 years ago
5 0

Answer:

The solutions are w=7, w=3

Step-by-step explanation:

we have

w^2-10w+21=0

Group terms that contain the same variable and move the constant term to the right side

w^2-10w=-21

Complete the square

w^2-10w+5^2=-21+5^2

w^2-10w+25=-21+25

w^2-10w+25=4

Rewrite as perfect squares

(w-5)^2=4

take square root both sides

w-5=(+/-)2

w=5(+/-)2

w_1=5(+)2=7

w_2=5(-)2=3

therefore

The solutions are w=7, w=3

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∠1 and ​ ∠2 ​ are a linear pair, and ​ ∠2 ​ and ​ ∠3 ​ are vertical angles. m∠2=(5+4y)∘ and ​ m∠3=(6y−25)∘
Leni [432]

Answer:

The measure of angle 1 is 115°

Step-by-step explanation:

we know that

If ∠1 and ​ ∠2 ​ are a linear pair

then

∠1 +∠2 =180°​ -----> supplementary angles

If ∠2 and ​ ∠3 ​ are vertical angles

then

∠2 =∠3

step 1

Find the value of y

we know that

∠2 =∠3

substitute values

(5+4y)°=(6y-25)°

6y-4y=(5+25)°

2y=(30)°

y=15°

step 2

Find the measure of angle 2

∠2=(5+4y)°

substitute the value of y

∠2=(5+4(15))°

∠2=65°

step 3

Find the measure of angle 1

we know that

∠1 +∠2 =180°

we have

∠2=65°

substitute

∠1 +65°=180°

∠1 =180°-65°=115°

3 0
4 years ago
What is quadratic equations by factoring
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The concept of factoring quadratic equations simply is one of the ways to solve for the zeroes of the quadratic equation.

<h3>What is quadratic equations by factoring?</h3>

The concept of factoring quadratics is a technique which is characterized by expressing the quadratic equation ax2 + bx + c = 0 as a product of its associated linear factors as (x - f)(x - g), in which case, f and g are the roots of the quadratic equation ax2 + bx + c = 0.

Factoring is an important concept that helps express equations of any type in simpler forms The mode of operation of the factoring works such that, the polynomial is rewritten in a simpler form and consequently, expressed as a product of it's linear factors.

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brainly.com/question/472337

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2 years ago
A car travels from A to B at a speed of 40 mph then returns, using the same road, from B to A at a speed of 60 mph. What is the
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Hope this helps!
7 0
4 years ago
The probability that a person likes ice cream is .80. Assume each person is independent. Suppose 1000 people are selected. Use t
jenyasd209 [6]

Answer: 0.9591

Step-by-step explanation:

Given : The probability that a person likes ice cream is p=0.80.

Sample size : n= 1000

Using the normal approximation to the binomial ,

\mu=np=1000(0.80)=800\\\\\sigma=\sqrt{np(1-p)}\\\\=\sqrt{1000(0.80)(0.20)}\approx12.65

Let x be the random variable that represents the number of  people like ice cream.

Now, the probability that 822 or fewer people selected like ice cream will be :-

P(x\leq882)=P(z\leq\dfrac{822-800}{12.65})\\\\=P(z\leq1.74)

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=0.9591  [using p-value table for z]

Hence, the required probability = 0.9591

8 0
3 years ago
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