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3 years ago

Type this equation in standard form.3x = 2y + 7

Mathematics

2 answers:

Svetach [21]3 years ago

8 0

3x-2y=7 Should be your answer

irinina [24]3 years ago

4 0

Y= 3/2x-7/2 ............

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Brainliest to correct quickly

Setler79 [48]

Answer:

1. -0.25

2. -11/25

3. 9 23/25

4 0

3 years ago

What is the sum of the geometric sequence −4, 24, −144, ... if there are 8 terms?

Helga [31]

Answer:

The sum of 8 geometric sequence is 959780

Step-by-step explanation:

We are given

this sequence is geometric

-4 , 24 , -144

First term is -4

so, $a_1=-4$

now, we can find common ratio

$r=\frac{24}{-4}=-6$

we can use formula

$S_n=a_1(\frac{1-r^n}{1-r} )$

n=8

now, we can plug values

$S_8=-4(\frac{1-(-6)^{8}}{1+6} )$

now, we can simplify it

and we get

$S_8=959780$

4 0

4 years ago

The hypotenuse of a right angled triangle is 2√13 cm . If the smaller side is increased by 2 cm and the larger side is increased

White raven [17]

Statement:

The hypotenuse of a right angled triangle is 2√13 cm. If the smaller side is increased by 2 cm and the larger side is increased by 3 cm, the new hypotenuse will be √117 cm.

To find out:

The length of the larger side of the right angled triangle.

Solution:

Let us consider x as the smaller side and y as the larger side.

Then, in the right angled triangle,

x² + y² = (2√13)² ...(I) [By Pythagoras Theorem]

Now, if the smaller side is increased by 2 cm, then the smaller side will be (x + 2).

And if the larger side is increased by 3 cm, then the larger side will be (y + 3).

Then, in the new right angled triangle,

(x + 2)² + (y + 3)² = (√117)² [By Pythagoras Theorem]

or, x² + 2 × 2 × x + 2² + y² + 2 × 3 × y + 3² = (√117)²

or, x² + 4x + 4 + y² + 6y + 9 = (√117)²

or, x² + y² + 4x + 6y + 13 = (√117)²

Now, put the value of x² + y² from equation (I),

or, (2√13)² + 4x + 6y + 13 = (√117)²

or, (2 × 2 × √13 × √13) + 4x + 6y + 13 = (√117 × √117)

or, 52 + 4x + 6y + 13 = 117

or, 4x + 6y = 117 - 52 - 13

or, 4x + 6y = 52

or, 4x = 52 - 6y

or, x = $\frac {(52 - 6y)}{4}$ ...(II)

Now, put the value of x of equation (II) in (I),

x² + y² = (2√13)²

or, $\frac {(2704-624y +36y²)}{16}$ + y² = 52

or, $\frac {(2704-624y +36y² + 16y²)}{16}$ = 52

or, 52y²-624y + 2704 = 52 × 16

or, 52y² - 624y + 2704 - 832 = 0

or, 52y² - 624y + 1872 = 0

or, 52(y² - 12y + 36) = 0

or, y²-12y +36 = 0 ÷ 52

or, y²-12y +36 = 0

or, (y)² - 2 × 6 × y + (6)² = 0

or, (y - 6)² = 0

or, y - 6=0

or, y = 6

We have taken y as the length of the larger side of the right angled triangle.

So, the length of the larger side is 6 cm.

Answer:

6 cm

Hope you could understand.

If you have any query, feel free to ask.

6 0

3 years ago

Help!!! Look at the image below.. X= 8? 9? 10?

Korolek [52]

I think it is 10 lol sorry I’m not sure

8 0

3 years ago

Find the minimum or maximum value of the function. What is the H? (Desmos)

beks73 [17]

Answer:

Minimum: (2,4)

Step-by-step explanation:

h(x)=3( $x^{2}$ -4x)+16

=3( $x^{2}$ -4x+4-4)+16 (- For the balance of equation, and attention 1)

=3 $(x-2)^{2}$ -3*4+16

=3 $(x-2)^{2}$ +4

<h3>Attention:</h3>

1. $(a-b)^{2}=a^{2} -2ab+b^{2}$

2. The formula for the vertex form is y = $a(x-h)^{2}+k$ , the vertex is (h,k)

4 0

3 years ago