Show that 5x^2 + 2x - 3 < 0 can be written in the form | x + 1/5 | < 4/5

if possible with the explanation as well ​

Answer:

4.16 m/s

Step-by-step explanation:

Speed = Distance/Time

           = 10/2.4

           = 4.16 m/s

Hi

to solve you must transcrive every word in math terms correctly.

so let's first give a name to our mysterious number. As you know, in math we generally call unknown by letter. " X"

so let's now play the detective.

what do we know on " X" ?

we add 3 to X so we have : X+3

then we multiply by 5. so. ( X+3) *5 .

if we do that we have twice X , so 2X

so ( X+3) * 5 = 2 X

now that we have translatted our data in math term, let's unmask. " X"

( X+3) *5 = 2X

5*X +3*5 = 2X

5X +15 = 2X

5X-2X = -15

3X = -15

X = -15/3

X = -5

So is " -5" is our guy.

let's check it out to be sure .

-5 +3 = -2

-2*5 = -10

-10 is twice -5. so -5 is the correct answer.

Ps : some operation are commonly implied. if you do not. know how I could write some line in the calculus, dont hesitate to ask in comments.

There is no mysteries in math everything is done according to rules and can be explained. So don't hesitate !

Answer:

Length = 14 yd

Width = 5.5 yd

Step-by-step explanation:

Let width = x and length = 2x + 3

The formula for area is length x width.

(2x + 3) ( x ) = 77

2x² + 3x - 77 = 0

-77 x 2 = -154

What two numbers multiply to -154 and add to 3?

2x² + 14x - 11x - 77 = 0

2x (x + 7) - 11 (x + 7) = 0

(2x - 11) (x + 7) = 0

x = -7 (this isn't possible so ignore it)

x = 5.5 (width)

Now insert 5.5 into the initial equation.

2 (5.5) + 3 =

11 + 3 = 14

Answer:

Length is 3

width is 25•66

Step-by-step explanation:

Hope it helps!

Thanks.

Answer:

6 angles.

Step-by-step explanation:

This shape is a hexagon, since it has 6 sides. And because it has 6 sides, it has 6 vertexes, also known as angles.

Hope this helps!

Answer: 30, 45, 60, 75, 90

Step-by-step explanation: you will use multiples of 15 to find the answer. Detail given below:

1. if parking lot have 2 rows then 30 spaces

2. if parking lot have 3 rows then 45 spaces

3. if parking lot have 4 rows then 60 spaces

4. if parking lot have 5 rows then 75 spaces

5. if parking lot have 6 rows then 90 spaces

Answer:

the rational numbers is 3

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Answer:

32 cm²

Step-by-step explanation:

Area of rectangle

= length × breadth

= 8 cm × 4 cm

= 32 cm²

Answer:

-3x + 6

Step-by-step explanation:

-3(x - 2) to find the equivalent of this expression, we need to multiply inside the parenthesis with -3 (with both x and -2)

-3(x - 2 = -3x + 6 (two negative expressions multiplied results in positive)

Answer:

16 miles per hour (mph)

Step-by-step explanation:

Okay, so the beginning of the question states that Tamara rode her bicycle 8 miles in 0.5 hours.

0.5 is equivalent to 1/2 (one-half).

This means that she rode 8 miles in just half of an hour (30 minutes).

If she continues at this rate, she will have rode another 8 miles in the next 30 minutes.

And, 8 + 8 = 16.

Therefore, the average rate that she rode her bicycle is 16 miles per hour (mph).

Let me know if you have any questions.

Work Shown:

(f o g)(x) = f(g(x))

f(x) = x + 7

f( g(x) ) = g(x) + 7 ... replace every x with g(x)

f( g(x) ) = x^2-1 + 7 .... plug in g(x) = x^2-1

f( g(x) ) = x^2 + 6

(f o g)(x) = x^2 + 6

Answer:

answer is 2. thank you. have a nice day

Answer:

H-12=6

H−12+12=6+12

h=18

Answer:

h=18

Step-by-step explanation:

h-12=6

is the normal eqaution, you need to determine the value of h, on the left side of the eqaution you have negative twelve we must get the h on its own by moving the 12 to the right side using of basic math rules you must know that when you have a negative and want to move it to the right hand side it must become a positive

so in formula it wil look like this

h = 6 + 12

Add up 6 with 12 that wil give you 18

so the value of h is then 18

h = 18

Answer: x = 5

Step-by-step explanation:

Given information

The combined angle is a right angle meaning it is 90°

Angle 1 = 8x°

Angle 2 = 50°

Set equation

Angle 1 + Angle 2 = Total angle

Substitute values into the equation

8x + 50 = 90

Subtract 50 on both sides

8x + 50 - 50 = 90 - 50

8x = 40

Divide 8 on both sides

8x / 8 = 40 / 8

x = 5

Hope this helps!! :)

Please let me know if you have any questions

Answer:

x < -√3/2, x > √3/2, or -√1/2 < x < √1/2

Step-by-step explanation:

|1 - x^2| > 1/2

~Apply absolute value rule

​1 - x^2 < -1/2 or 1 - x^2 > 1/2

~Simplify

x < -√3/2, x > √3/2, or -√1/2 < x < √1/2

Best of Luck!

9514 1404 393

Answer:

  C.  60%

Step-by-step explanation:

Of the 5 bowls listed, bowls 2 and 4 are out of the allowed tolerance range. That leaves 3 of the 5 bowls that can be used.

  3/5 × 100% = 60% . . . fraction of bowls that can be included

Answer:

7

Step-by-step explanation:

Let's say our sum is s.

s = 10 right angles

a right angle is 90 degrees

s = 10 (90)

s= 900

Given the amount of sides in a polygon (n), the sum of the interior angles is equal to

(n-2) * 180

Therefore, the sum of the interior angles is equal to

(n-2) * 180 = 900

divide both sides by 180 to help isolate n

n-2 = 5

add 2 to both sides to isolate n

n = 7

Answer:

[tex]0.3[/tex]

Step-by-step explanation:

[tex]3 \div 10 = 0.3[/tex]

Answer: 0.3

Step-by-step explanation:

Answer:

what happened are you OK

Answer:

47.2

Step-by-step explanation:

Explanation:

Use the identity [tex]\sin{\theta} = 1 - \cos^2{\theta}[/tex] so we can write our equation as

[tex]6(1 - \cos^2{\theta}) - \cos{\theta} - 5 = 0[/tex]

or

[tex]6\cos^2{\theta} + \cos{\theta} - 1 = 0[/tex]

Let [tex]x = \cos{\theta}[/tex] so our equation becomes

[tex]6x^2 + x - 1 = 0[/tex]

Using the quadratic equation, we find that its roots are

[tex]x = \dfrac{-1 \pm \sqrt{(1)^2 - 4(6)(-1)}}{2(6)} = \dfrac{1}{3},\:-\dfrac{1}{2}[/tex]

which gives us

[tex]\cos{\theta} = \dfrac{1}{3} \Rightarrow \theta = 70.53°[/tex]

[tex]\cos{\theta} = -\dfrac{1}{2} \Rightarrow \theta = 120°[/tex]

Answer:

18360

Step-by-step explanation:

A = P (1 + r/n)^(nt)  where A is the amount in the account, P is the principle, r is the interest rate , n is the times compounded per year, t is the number of years

A = 17000 (1 + .08/1)^(1*1)

A = 17000( 1.08)^1

A = 18360

interest

[tex]\\ \rm\longmapsto 17000\times 8\%[/tex]

[tex]\\ \rm\longmapsto 17000\times \dfrac{8}{100}[/tex]

[tex]\\ \rm\longmapsto 170(8)[/tex]

[tex]\\ \rm\longmapsto 1360[/tex]

[tex]\\ \rm\longmapsto 17000+1360=18360[/tex]

Option C is correct

9514 1404 393

Answer:

  4 in 3492 is 100 times 4 in 704

Step-by-step explanation:

To find the value of a particular digit, set the other digits to zero.

  4 in 3492 = 400

  4 in 704 = 4

The first 4 is 100 times the value of the second 4.

Answer:

parallel: -1/2

perpendicular: 2

Step-by-step explanation:

lines that are parallel have the same slope because they never intersect

lines that perpendicular, have the opposite reciprocal slope.

y = mx + b

where m is the slope

y = -1/2x + 6

-1/2 is the slope.

the slope in the equation given: -1/2

the slope parallel to the line given : -1/2

the slope perpendicular : opposite reciprocal, so the opposite of -1/2 is 1/2 and the reciprocal of 1/2 is 2.

Answer:

7725

Step-by-step explanation:

h=75ft

b1=125ft

b2=81ft

A=75((125+81)/2)

Answer:

Step-by-step explanation:

Given data:

The 5-number summary is:

Answer:

6 tablespoons of baking soda

Step-by-step explanation:

There are 8 fluid ounces in 1 cup and shes going to use half a cup so that means shes going to use 4 fluid ounces of vinegar. To find how much baking soda she is going to use, we are going to multiply.

1.5 * 4 = 6

Best of Luck!

Answer:

3 Tablespoons, 6 teaspoons

Step-by-step explanation:

In order to find the right ratio of Baking Soda to Vinegar we have to find ratio given,... they tell us that for every 1.5 teaspoon of baking soda, you must add 1 fluid ounce or vinegar,... thus the ratio of Baking Soda to Vinegar is (1.5 teaspoon / 1 Fluid ounce)

There are:

3 teaspoons = 1 Tablespoons

8 fluid ounces = 1 cup

So if you use 0.5 cups of Vinegar as they tell us we do than that is the same thing as using 4 Fluid ounce, and because your problem say 1.5 teaspoon of baking soda for every Fluid ounce of vinegar all you have to do it multiply your 1.5t by your 4 to get how many teaspoons of Baking Soda you will need,...

1.5 * 4 = 6

You need 6 teaspoons or 3 Tablespoons,...

Hope that helps,... and I'll see you in life,... well not, literally, but you get what I mean,... Chow!

Answer:

the number of pink would be 112 because 224 divided by 2 is 112 then the red and white are 56 cuz 112 divided by 2 is 56

Step-by-step explanation:

the answer would be B.

2 + 4i  goodluck !! :))

Answer is B because it makes the most sense