Solve 7x − 2(x + 1) = 6x + 14

A person standing 130 feet away from the foot of a tall building must look up at an angle of 30° to see the top of the building.

Vanyuwa [196]

Answer:

30 angels

Step-by-step explanation:

5 0

3 years ago

Find the point P on the line yequals=33x that is closest to the point (60 comma 0 )(60,0). What is the least distance between P

scoray [572]

Answer:

$18\sqrt{10}$ units$

Step-by-step explanation:

We are given the equation of the line y=3x and a point, say Q(60,0) outside of that line.

We want to find the point on the line y=3x which is closest to Q.

Let P(x,y) be the desired point. Since it is on the line y=3x, it must satisfy the line.

If x=a, y=3a, so the point P has the coordinates (a,3a).

Distance between point Q and P

$=\sqrt{(60-a)^2+(0-3a)^2}\\D =\sqrt{10a^2-120a+3600}$

To minimize D, we find its derivative

$\dfrac{dD}{da}=\dfrac{10a-60}{\sqrt{10a^2-120a+3600} }\\$Setting \dfrac{dD}{da}=0\\10a-60=0\\10a=60\\a=6$

Therefore, the y-coordinate for P is 3*6=18.

The point P=(6,18).

Next, we calculate the distance between P(6,18) and (60,0).

$D =\sqrt{10(6)^2-120(6)+3600}\\=\sqrt{3240}\\=18\sqrt{10}$ units$

8 0

4 years ago

What is the answer for 3\5=a+5\25

IceJOKER [234]

Answer:

a = 2/5 = 0.400

Step-by-step explanation:

Step 1 :

1

Simplify —

5

Equation at the end of step 1 :

3 1

— - (a + —) = 0

5 5

Step 2 :

Rewriting the whole as an Equivalent Fraction :

2.1 Adding a fraction to a whole

Rewrite the whole as a fraction using 5 as the denominator :

a a • 5

a = — = —————

1 5

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

2.2 Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

a • 5 + 1 5a + 1

————————— = ——————

5 5

Equation at the end of step 2 :

3 (5a + 1)

— - ———————— = 0

5 5

Step 3 :

3

Simplify —

5

Equation at the end of step 3 :

3 (5a + 1)

— - ———————— = 0

5 5

Step 4 :

Adding fractions which have a common denominator :

4.1 Adding fractions which have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

3 - ((5a+1)) 2 - 5a

———————————— = ——————

5 5

Equation at the end of step 4 :

2 - 5a

—————— = 0

5

Step 5 :

When a fraction equals zero :

5.1 When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

2-5a

———— • 5 = 0 • 5

5

Now, on the left hand side, the 5 cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

2-5a = 0

Solving a Single Variable Equation :

5.2 Solve : -5a+2 = 0

Subtract 2 from both sides of the equation :

-5a = -2

Multiply both sides of the equation by (-1) : 5a = 2

Divide both sides of the equation by 5:

a = 2/5 = 0.400

One solution was found :

a = 2/5 = 0.400

Processing ends successfully

plz mark me as brailiest :)

4 0

3 years ago

Read 2 more answers

You might need: 3 Calculator

Aleks04 [339]

Answer:

3.14 or pi

Step-by-step explanation:

the area of a circle = $pi * r^{2}$ where r is the radius of the circle

this is 1/4 of the circle, so it would be 1/4 (pi * r²)

it shows that the radius is 2, so you have

1/4 ( pi * 2²)

= 1/4 ( pi * 4 )

= 1/4 (3.14 * 4)

= 3.14 units²

8 0

3 years ago

Can anyone help I am doing really mad in math

Vadim26 [7]

For this problem, we are going to have to use our order of operations, which is: Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction (often abbreviated PEMDAS).

First, let's see if there are any parentheses. There is one set of parentheses which we will have to remove. To do this, we will simply multiply the -4 by the 6, given us a value of -24 to take the place of the -4(6). Now our problem is:

$\dfrac{12^2 - 24 + 1}{11^2}$

Next, we will check for exponents. There are exponents, so we will need to take care of those. $12^2$ is equal to 144, and $11^2$ is equal to 121. We can now substitute these values into the original expression to get:

$\dfrac{144 - 24 + 1}{121}$

Now, we will check for any multiplication or division. Besides the entire expression (which is a fraction), there is none, so we will move on to the next step: Addition and Subtraction. You can see there is addition and subtraction in the numerator. $144 - 24$ is equal to 120, and $120 + 1$ is equal to 121. Our problem is now:

$\dfrac{121}{121} = \boxed{1}$

Our answer is 1.

8 0

4 years ago