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svlad2 [7]
2 years ago
6

Performance Matters

Mathematics
1 answer:
Yuliya22 [10]2 years ago
7 0

Answer: most likely be (7,7) not sure right or wrong but i tried so yeah

Step-by-step explanation:

You might be interested in
Question 3<br> 5 1<br> Divide 6 • 12
puteri [66]

Answer:

5/6 divided by 1/12 = 10.

Hope this helped!

Step-by-step explanation:

3 0
2 years ago
Read 2 more answers
A spring has natural length 24 cm. Compare the work W1 done in stretching the spring from 24 cm to 34 cm with the work W2 done i
Scilla [17]

Answer:

From the analysis W1=W2.

they are directly related

Step-by-step explanation:

the work-done in stretching a spring can be expressed as

W=\frac{1}{2}kx^2

where k= spring constant

           x= change on length of spring

Hence for W1

Given data

x= 34-24= 10 cm

solving in terms of k we have

W=\frac{1}{2}k*10^2\\\W=\frac{1}{2}k*100\\\W=50k

Hence for W2

Given data

x= 44-34= 10 cm

solving in terms of k we have

W=\frac{1}{2}k*10^2\\\ W=\frac{1}{2}k*100\\\ W=50k

4 0
3 years ago
Find the vertex of the graph of the function.
lapo4ka [179]

Answer: The correct options are  (1) (5,10), (2) (3,-3), (3) x = -1, (4) y=(x+2)^2+3, (5) 21s and (6) 0, -1, and 5.

Explanation:

Te standard form of the parabola is,

f(x)=a(x-h)^2+k        .....(1)

Where,  (h,k) is the vertex of the parabola.

(1)

The given equation is,

f(x)=(x-5)^2+10

Comparing this equation with equation (1),we get,

h=5 and k=10

Therefore, the vertex of the graph is (5,10) and the fourth option is correct.

(2)

The given equation is,

f(x)=3x^2-18x+24

f(x)=3(x^2-6x)+24

To make perfect square add (\frac{b}{2a})^2, i.e., 9. Since there is factor 3 outside the parentheses, so subtract three times of 9.

f(x)=3(x^2-6x+9)+24-3\times 9

f(x)=3(x-3)^2-3

Comparing this equation with equation (1),we get,

h=3 and k=-3

Therefore, the vertex of the graph is (3,-3) and the fourth option is correct.

(3)

The given equation is

f(x)=4x^2+8x+7

f(x)=4(x^2+2x)+7

To make perfect square add (\frac{b}{2a})^2, i.e., 1. Since there is factor 4 outside the parentheses, so subtract three times of 1.

f(x)=4(x^2+2x+1)+7-4

f(x)=4(x+1)^2+3

Comparing this equation with equation (1),we get,

h=-1 and k=3

The vertex of the equation is (-1,3) so the axis is x=-1 and the correct option is 2.

(4)

The given equation is,

y=x^2+4x+7

To make perfect square add (\frac{b}{2a})^2, i.e., 2^2.

f(x)=x^2+4x+4+7-4

f(x)=x^2+4x+4+7-4

f(x)=(x+2)^2+3

Therefore, the correct option is  4.

(5)

The given equation is,

h=-16t^2+672t

It can be written as,

h=-16(t^2-42t)

It is a downward parabola. so the maximum height of the function is on its vertex.

The x coordinate of the vertex is,

x=\frac{b}{2a}

x=\frac{42}{2}

x=21

Therefore,  after 21 seconds the projectile reach its maximum height and the correct option is first.

(6)

The given equation is,

f(x)=3x^3-12x^2-15x

f(x)=3x(x^2-4x-5)

Use factoring method to find the factors of the equation.

f(x)=3x(x^2-5x+x-5)

f(x)=3x(x(x-5)+1(x-5))

f(x)=3x(x-5)(x+1)

Equate each factor equal to 0.

x=0,-1,5

Therefore, the zeros of the given equation is 0, -1, 5 and the correct option is 2.

3 0
3 years ago
What is the completely factored form of this polynomial?<br> 18x^3– 120x^2-42x
Vlada [557]

Answer:

6×(3×+1)(×-7)

Step-by-step explanation:

18×^3-120×^2-42×

=6×(3×+1)(×-7)

4 0
2 years ago
Read 2 more answers
The number of bagels and coffee sold by a bagel shop yesterday can be modeled using the equation b+c=84. Their sales for the sam
Yakvenalex [24]

Answer:

There were 61 bagels and 23 coffee sold

Step-by-step explanation:

Let us solve the question

∵ The number of bagels and coffee sold by a bagel shop yesterday

   can be modeled using the equation b + c = 84

∴ b + c = 84 ⇒ (1)

∵ Their sales for the same day can be modeled using the equation

   2b + c = 145

∴ 2b + c = 145 ⇒ (2)

Let us solve the system of equations using substitution

→ Subtract the two sides of equation (1) by b to find c in terms of b

∵ b - b + c = 84 - b

∴ c = 84 - b ⇒ (3)

→ Substitute c in equation (2) by equation (3)

∵ 2b + 84 - b = 145

→ Add the like terms on the left side

∴ (2b - b) + 84 = 145

∴ b + 84 = 145

→ Subtract 84 from both sides

∵ b + 84 - 84 = 145 - 84

∴ b = 61

→ Substitute the value of b in equation (3) to find c

∵ c = 84 - 61

∴ c = 23

∴ There were 61 bagels and 23 coffee sold.

3 0
2 years ago
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