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3 years ago

What is the value of x?

Mathematics

1 answer:

Rufina [12.5K]3 years ago

6 0

Answer:

X=23

Step-by-step explanation:

You should know that a triangle =180 degrees

Add all your angles together and =180

66+2x+3+3x-4=180

add similar terms

5x+65=180

Move your 65 to the other side

5x=115

x=23

(Optional)

to check if your answer is right substitute your x and add all angles together you should get 180 degrees.

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Christian’s Gym charges a one-time fee of $50 plus $30 per session for a personal trainer.

nydimaria [60]

Answer: For 10 sessions, the cost of the two plans the same.

Step-by-step explanation:

Let x= Number of sessions.

Given: Christian’s Gym charges a one-time fee of $50 plus $30 per session for a personal trainer.

Total charge for x sessions = 50+30x

Nicole's fitness center charges a yearly fee of $250 plus $10 for each session with a trainer.

Total charge for x sessions = 250+10x

When both plan charges the same, then

$50+30x=250+10x\\\\\Rightarrow\ 30x-10x=250-50\\\\\Rightarrow\ 20x=200\\\\\Rightarrow\ x=10$

i.e. For 10 sessions, the cost of the two plans the same.

3 0

3 years ago

Which is more valuable a pile of pennies equaling your weight or a stack of quarters equaling your height?

11Alexandr11 [23.1K]

Answer:

A pile of pennies

Step-by-step explanation:

7 0

3 years ago

The function below is written in vertex form or intercept form. Rewrite them in standard form and show your work.

lora16 [44]

Answer:

The standard form as $y=5x^2+30x+41$

Step-by-step explanation:

Given: A function which is written in vertex form or intercept form.

We have to re-write it in standard form that in terms of

Given $y = 5(x+3)^2-4$

Squaring using $(a+b)^2=a^2+b^2+2ab$ , we get,

$y=5(x^2+9+6x)-4$

Multiply 5 inside , we get,

$y=5x^2+45+30x-4$

Solving further , we get,

$y=5x^2+30x+41$

Thus , we have obtained the standard form as $y=5x^2+30x+41$

8 0

3 years ago

Read 2 more answers

30+ Points!!!<br> 5. Solve the following inequalities.<br> a) 2 log3x – 2 logx3 -3 <0

Ilya [14]

Answer:

I answered your last question also

2 log3x – 2 logx3 -3 <0

$\mathrm{Subtract\:}2\log ^3\left(x\right)\mathrm{\:from\:both\:sides}$

$2\log ^3\left(x\right)-2logx^3-3-2\log ^3\left(x\right)$

$\mathrm{Simplify}$

$-2logx^3-3$

$\mathrm{Add\:}3\mathrm{\:to\:both\:sides}$

$-2logx^3-3+3$

$\mathrm{Simplify}$

$-2logx^3$

$Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)$

$\left(-2logx^3\right)\left(-1\right)>-2\log ^3\left(x\right)\left(-1\right)+3\left(-1\right)$

$\mathrm{Simplify}$

$2lx^3og>2\log ^3\left(x\right)-3$

$\mathrm{Divide\:both\:sides\:by\:}2lx^3o;\quad \:l>0$

$\frac{2lx^3og}{2lx^3o}>\frac{2\log ^3\left(x\right)}{2lx^3o}-\frac{3}{2lx^3o};\quad \:l>0\\$

$\mathrm{Simplify}$

$g>\frac{2\log ^3\left(x\right)-3}{2lx^3o};\quad \:l>0$

Step-by-step explanation:

6 0

3 years ago

Find the rate of change of f(x, y, z) = xyz in the direction normal to the surface yx2 + xy2 + yz2 = 3 at (1, 1, 2).

Paladinen [302]

Answer:

Rate of change = 18/√74

Step-by-step explanation:

The rate of change of f at x_o in the direction of the unit vector v is given by: ∇f(x_o) × v

Now, for us to get the direction of the unit vector, since we are told that f(x, y, z) = xyz in the direction normal to the surface yx² + xy² + yz² = 3, we will use; g(x, y, z) = yx² + xy² + yz² = 3 and k =3 to give;

∇g(x,y,z) = (2xy + y², (x² + 2xy + z²), 2yz)

So;

∇g(1, 1, 2) = (2(1 × 1) + 1²) , (1² + 2(1 × 1) + 2²), 2(1 × 2))

This gives;

∇g(1, 1, 2) = (3, 7, 4)

Now,

||∇g(1, 1, 2)|| = √(3² + 7² + 4²)

||∇g(1, 1, 2)|| = √74

Normal vector would be given by the formula;

v = [∇g(1, 1, 2)]/[||∇g(1, 1, 2)||]

Thus;

v = (3, 7, 4)/√74

Let's not forget that our ∇f(1, 1, 2) = (1, 1, 2)

Thus, rate of change is given by;

∇f(1, 1, 2) × v = (1, 1, 2) × (3, 7, 4)/√74

This gives;

Rate of change = [(1 × 3) + (1 × 7) + (2 × 4)]/√74 = 18/√74

7 0

3 years ago