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3 years ago

Identify the property that justifies the statement: If 4x - 3 = 7, then 4x = 10. -----> Is this substitution property?

2 answers:

8 0

The equation shown above does not show the substitution property. Instead, it shows the Addition Property of Equation where 3 is added to both of its sides. This is shown below,
4x - 3 = 7
4x - 3 + 3 = 7 + 3
4x = 10

Zigmanuir [339]3 years ago

3 0

Answer:

No, it is not substitution property. Addition property of equality justifies the statement.

Step-by-step explanation:

The given statement: If

$4x-3=7$ .... (1)

them

$4x=10$ ... (2)

According to the Addition property of equality, if a,b and c are real number, then

$a=b\Leftrightarrow a+c=b+c$

Using Addition property of equality, add 3 on both sides in equation (1).

$4x-3+3=7+3$

$4x=10$

This equation is same as equation (2).

Therefore Addition property of equality justifies the statement.

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The image shows a geometric representation of the function f(x) = x^2 + 2x + 3 written in standard form. What is this function w

AlekseyPX

Answer:

f(x) = (x + 1)² + 2 in vertex form ⇒ 3rd answer

Step-by-step explanation:

* Lets revise how to find the vertex form the standard form

- Standard form ⇒ x² + bx + c, where a , b , c are constant

- Vertex form ⇒(x - h)² + k, where h , k are constant and (h , k) is the

vertex point (minimum or maximum) of the function

- At first we must find h and k

- By equating the two forms we can find the value of h and k

* Lets solve the problem

∵ f(x) = x² + 2x + 3 ⇒ standard form

∵ f(x) = (x - h)² + k ⇒ vertex form

- Put them equal each other

∴ x² + 2x + 3 = (x - h)² + k ⇒ open the bracket power 2

∴ x² + 2x + 3 = x² - 2hx + h² + k

- Now compare the like terms in both sides

∵ 2x = -2hx ⇒ cancel x from both sides

∴ 2 = -2h ⇒ divide both sides by -2

∴ -1 = h

∴ The value of h is -1

∵ 3 = h² + k

- Substitute the value of h

∴ 3 = (-1)² + k

∴ 3 = 1 + k ⇒ subtract 1 from both sides

∴ 2 = k

∴ The value of k = 2

- Lets substitute the value of h and k in the vertex form

∴ f(x) = (x - -1)² + 2

∴ f(x) = (x + 1)² + 2

* f(x) = (x + 1)² + 2 in vertex form

5 0

4 years ago

Terry is filling spherical water balloons with a faucet that puts out 100cm^3 of water per second. At that rate, it takes Terry

ioda

Answer:

To the nearest centimeter

Radius= 5 cm

Step-by-step explanation:

Rate of filling balloon= 100cm³/s

Time to feel the balloon= 6 s

Volume of the filed balloon

= Rate*time

= 100*6

= 600 cm³

Volume of balloon= 4/3πr³

Volume of balloon=600cm³

600= 4/3πr³

(600*3)/4π= r³

1800/4π= r³

450/π= r³

143.239 = r³

5.232= r

To the nearest centimeter

Radius= 5 cm

6 0

3 years ago

Y * x = 20<br><br> y + x = 9 <br><br> what numbers are y and x equal to?

Ksivusya [100]

$y = 9 - x$
Substitute into
$y \times x = 20 \\ (9 - x) \times x = 20 \\ { - x}^{2} + 9x = 20 \\ {x}^{2} - 9x + 20 = 0 \\ (x - 5)(x -4) = 0 \\ x = 5 \: or \: x = 4$
When x = 5,
$y = 9 - 5 \\ y = 4$
When x = 4,
$y = 9 - 4 \\ y = 5$

x = 5, y = 4
x = 4, y = 5

Hope this helps. - M

4 0

3 years ago

What is the distance between the points (4.10) and (-3,-14) on the coordinates plane?

jeyben [28]

Answer:

25 units

Step-by-step explanation:

use the distance formula to get the square root of 24² + 7²

this will give you the square root of 625, which is 25

8 0

3 years ago

8. The endpoints of ST are s(-3, 2) and t(5,8). Find the coordinates of the midpoint of ST. Then find ST. OA midpoint: (1,5); ST

Naya [18.7K]

Answer:

The mid point of ST is (1,5) and ST = 10 units

Step-by-step explanation:

It is given that,

S(-3,2) and T(5,8). We need to find the coordinates of the midpoint of ST and also ST.

Let (x,y) be the mid point of ST. Using mid-point formula we get :

$(x,y)=(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2})$

We have, x₁ = -3, x₂ = 5, y₁ = 2 and y₂ = 8

So,

$(x,y)=(\dfrac{-3+5}{2},\dfrac{2+8}{2})\\\\(x,y)=(1,5)$

(1,5) is the midpoint of ST.

Using distance formula to find ST as follows :

$ST=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\\\ST=\sqrt{(5-(-3))^2+(8-2)^2} \\\\ST=10\ \text{units}$

Hence, the mid point of ST is (1,5) and ST = 10 units.

7 0

3 years ago