Can someone please solve 10n - 3 = 7n + 21

Answers

Answer 1

Answer: $10 n-3 = 7n+21$

Add 3 to both sides :

$10n-3+3=7n+21+3$

$10n=7n+24$

Subtract 7 n from both sides:

$10n-7n=7n+24-7n$

$3n=24$

Divide both sides by 3 :

$(3n)/(3) = (24)/(3)$

$n = 8$

hope this helps!

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If f(x) = 2x + 3 and g(x) = (x - 3)/2, what is the value of f[g(-5)]?

Answers

If f(x) = 2x + 3 and g(x) = (x - 3)/2,what is the value of f[g(-5)]?f[g(-5)] means substitute -5 for x in the right side of g(x),simplify, then substitute what you get for x in the rightside of f(x), then simplify.It's a "double substitution".To find f[g(-5)], work it from the inside out.In f[g(-5)], do only the inside part first.In this case the inside part if the red part g(-5)g(-5) means to substitute -5 for x ing(x) = (x - 3)/2So we take out the x's and we haveg( ) = ( - 3)/2Now we put -5's where we took out the x's, and we nowhaveg(-5) = (-5 - 3)/2Then we simplify:g(-5) = (-8)/2g(-5) = -4Now we have the g(-5)]f[g(-5)]means to substitute g(-5) for x inf[x] = 2x + 3So we take out the x's and we havef[ ] = 2[ ] + 3Now we put g(-5)'s where we took out the x's, and wenow havef[g(-5)] = 2[g(-5)] + 3But we have now found that g(-5) = -4, we can putthat in place of the g(-5)'s and we getf[g(-5)] = f[-4]But thenf(-4) means to substitute -4 for x inf(x) = 2x + 3sof(-4) = 2(-4) + 3then we simplifyf(-4) = -8 + 3f(-4) = -5Sof[g(-5)] = f(-4) = -5

Leena consumes 400 calories at breakfast and 350 calories at lunch. She consumes of her daily calories at dinner. If x represents the calories consumed at dinner, which statements describe the situation? Check all that apply.a. Leena consumed 1,500 calories at dinner.
b. The equation 2/3(x + 400 + 350) = x can be used to model the situation.
c. Leena consumed 500 calories at dinner.
d. The equation 2/3(x) = x(400 + 300) can be used to model the situation.
e. Leena consumed 1,000 calories at dinner.
f. The equation 2/3x(400 + 300) = x can be used to model the situation.

Answers

Only Option 'A' and 'B' are correct.

a) Leena consumed 1,500 calories at dinner.

b) The equation 2/3(x + 400 + 350) = x can be used to model the situation.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Since, we have given that

Number of calories she consumed at breakfast = 400

Number of calories she consumed at lunch = 350

Now, Let number of calories she consumed at dinner be x

According to question,

She consumes 2/3 of her daily calories at dinner,

So, it becomes,

1/3 x total = 400 + 350

total = 2250

so, Number of calories she consumed at dinner is given by

2/3 of total = x

2/3 x 2250 = x

x = 1500

And by option 'B' we get,

2/3 (x + 400 + 350) = x

2 (x + 750) = 3x

2x + 1500 = 3x

x = 1500

So, only Option 'A' and 'B' are correct.

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Answer:

the answers are A and B

Step-by-step explanation:

hope i helped

Subtract 3x^2 - 2x + 1 from 5x^2 + 3x -7

Answers

$(5x^2 + 3x -7) - (3x^2 - 2x + 1)$

$5x^2 + 3x -7 - 3x^2 + 2x - 1$

$5x^2 - 3x^2 + 3x +2x - 7 - 1$

$2x^2 + 5x - 8$

$5x^2 + 3x -7-(3x^2 - 2x + 1)=\n 5x^2+3x-7-3x^2+2x-1=\n 2x^2+5x-8$

Which two temperatures have a sum of 0 degrees Celsius?4 degrees Celsius and 4 degrees Celsius
4 degrees Celsius and −4 degrees Celsius
−4 degrees Celsius and −4 degrees Celsius
4 degrees Celsius and 0 degrees Celsius

Answers

4 and -4 degrees Celsius

How many solutions does this system of equations have???
2x+3y=6
y=-2/3x-1

Answers

$2x+3y=6\n \n 3y=-2x+6\n \n y=-(-2x)/(3)+2\n$

System has no solution.

Check all that apply. cotθ is undefined for θ = _____. A. 3π/2 B. π/2 C. 0 D. π

Answers

The undefined value of $cot \theta = 0, \pi$ .

What are trigonometric ratios ?

"The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec). In geometry, trigonometry is a branch of mathematics that deals with the sides and angles of a right-angled triangle. Therefore, trig ratios are evaluated with respect to sides and angles.

The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec). In geometry, trigonometry is a branch of mathematics that deals with the sides and angles of a right-angled triangle. Therefore, trig ratios are evaluated with respect to sides and angles. "

The values of cot theta is undefined for $n\pi$ .

So, 0 , pi , 2pi , 3pi .....npi.

Hence C and D are correct option.

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cot theta is undefined for 0 but is a periodic function so it will be again undefined for n $\pi$

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A rocket is launched from the ground. The function h(t)= -4.9t^2 +180t models the height of a rocket launcher from the ground t seconds after it is launched. If all other factors remain the same, which of the following function models the height of a rocket above the ground after t seconds if it is launched from a platform 100 feet in the air? (1) h(t) = -4.9t^2 +280t (2) h(t) = -4.9t^2 +180t -100 (3) h(t) = -4.9t^2 +180t +100(4) h(t) = -4.9t^2 +180 (t+100)