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2 years ago

How do you factor 6x² +7x-3? Please show the steps!

Mathematics

1 answer:

Gnesinka [82]2 years ago

4 0

$6x^2+7x-3=\ \ \ \ | write\ 7x\ as\ -2x+9x\\\\ 6x^2-2x+9x-3=0\\\\ 2x(3x-1)+3(3x-1)=0\\\\\boxed{(2x+3)(3x-1)}=0$

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Can someone help me with 3 a and b?? Thank you

polet [3.4K]

M∠ADB + m∠BDC = m∠ADC [<span>angle addition postulate]

x + x + 10 = 60
2x + 10 = 60
2x = 60 - 10
2x = 50
x = 50/2
x = 25

a
m</span>∠ADB = x = 25°

b
m∠BDC = x + 10 = 25 + 10 = 35°

5 0

2 years ago

2.27 is a terminating decimal true or false??

IRINA_888 [86]

Answer:

true

Step-by-step explanation:

5 0

2 years ago

Read 2 more answers

Explain how to find the vertex of 2x^2+12x+16

Elina [12.6K]

The vertex form:

$y=a(x-h)^2+k\\\\(h,\ k)-vertex$

Use $(a+b)^2=a^2+2ab+b^2\qquad(*)$

$2x^2+12x+16=2(x^2+6x)+16=2(x^2+2(x)(3))+16\\\\=2(\underbrace{x^2+2(x)(3)+3^2}_{(*)}-3^2)+16=2((x+3)^2-9)+16\\\\=2(x+3)^2+(2)(-9)+16=2(x+3)^2-18+16\\\\=\boxed{2(x-(-3))^2-2}\to h=-3,\ k=-2$

<h3>Answer: (-3, -2).</h3>

Other method:

$f(x)=ax^2+bx+c\\\\vertex:(h,\ k)\\\\h=\dfrac{-b}{2a},\ k=f(h)$

We have

$f(x)=2x^2+12x+16\\\\a=2,\ b=12,\ c=16$

Substitute:

$h=\dfrac{-12}{(2)(2)}=\dfrac{-12}{4}=-3\\\\k=f(-3)=2(-3)^2+12(-3)+16=2(9)-36+16=18-36+16=-2$

<h3>Answer: (-3, -2).</h3>

5 0

2 years ago

Write an equation of the line that passes through the pair of points (5, 8) and<br> (9, 16).

SashulF [63]

Answer:

D: y = 2x - 2

Step-by-step explanation:

1. $\frac{16-8}{9-5}$ = 2

2. y = 2x + b

3. Insert the points into the equation: 8 = 10 + b

4. b = -2

5. y = 2x - 2

6 0

2 years ago

Read 2 more answers

1. You are standing on top of a ridge using a clinometer trying to figure out how far your dog has wandered off in

olga_2 [115]

<u>Given:</u>

It is given that the ridge is 360 inches tall.

<u>Assumptions:</u>

Assume you are 170.1 cm tall which equals 67 inches tall, the height from your eye to the floor is $360+67 = 427$ inches.

The distance from your eye level to the bottom of the ridge is 427 inches.

Assume the angle A is 60°.

<u>To find the distance from you to your dog.</u>

<u>Solution:</u>

A right-angled triangle can be formed where the angle is 60°, the distance between you and the dog is the hypotenuse of the triangle and your height from the floor is the adjacent side of the triangle.

Assume the hypotenuse of the triangle measures x inches.

To determine the length of the hypotenuse, we determine the cos of the angle.

$cos \theta = \frac{adjacent side}{hypotenuse} .$

$cos A = \frac{427}{x} , x = \frac{427}{cos60} , cos60=0.5.$

$x=\frac{427}{0.5} = 854.$

So if the ridge is 360 inches tall and you are 67 inches tall and the angle A is 60°, the distance between your dog and you is 854 inches.

3 0

2 years ago