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2 years ago

5

Jorge gives an equal number of marbles to 6 friends. Which could be the total number of marbles he gave to his friends? (Answer

choices 15,33,56,60)

2 answers:

ladessa [460]2 years ago

6 0

Answer:

D. 60

Step-by-step explanation:

Since the question stated that the number of marbles given out to his 6 friends were equal, we are certain that the total number of marbles is a factor or multiple of 6.

The only other assumption here is the number of marbles given has to be whole number. This means we just have to go through the answer choices and pick the one that is a multiple of 6.

A. 15 - This is wrong as 15 is not a multiple of 6.

B. 33 - This is wrong as 33 is not a multiple of 6.

C. 56 - This is wrong as 56 is not a multiple of 6.

D. 60 - This is CORRECT as 60 is a multiple of 6.

If Jorge gives each of his friends 10 marbles each, it would bring the total number of marbles to be 60.

elena55 [62]2 years ago

5 0

Answer:

15

Step-by-step explanation:

5x3=15

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Kevin is 4 times as old as Daniel and is also 6 years older than Daniel

MAXImum [283]

Answer:

Part a) Daniel's age is 2 years

Part b) Kevin's age is 8 years

Step-by-step explanation:

<u><em>The question is </em></u>

Part a) How old is Daniel?

Part b) How old is Kevin?

Let

x ----> Kevin's age

y ----> Daniel's age

we know that

$x=4y$ -----> equation A

$x=y+6$ ----> equation B

Equate equation A and equation B

$4y=y+6$

solve for y

$4y-y=6$

$3y=6$

$y=2$

therefore

Daniel's age is 2 years

<em>Find the value of x</em>

substitute the value of y in any of the two equations

$x=4(2)=8\ years$

$x=2+6=8\ years$

therefore

Kevin's age is 8 years

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2 years ago

The formula for finding the volume of a triangular prism is V = 1/2(bh)l

saw5 [17]

False, true, & false

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3 years ago

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Solve the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to three decimal plac

valentinak56 [21]

Answer:

tan(θ) = 0, 0.577, -0.577

Step-by-step explanation:

3tan³(θ) - tan(θ) = 0

tan(θ)(3tan²(θ) - 1) = 0

tan(θ) = 0

tan²(θ) = ⅓ tan(θ) = +/- sqrt(⅓)

tan(θ) = 0, sqrt(⅓), -sqrt(⅓)

tan(θ) = 0, 0.577, -0.577

To find θ values, domain is required

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3 years ago

g Use this to find the equation of the tangent line to the parabola y = 2 x 2 − 7 x + 6 at the point ( 4 , 10 ) . The equation o

natali 33 [55]

Answer:

The tangent line to the given curve at the given point is $y=9x-26$ .

Step-by-step explanation:

To find the slope of the tangent line we to compute the derivative of $y=2x^2-7x+6$ and then evaluate it for $x=4$ .

$(y=2x^2-7x+6)'$ Differentiate the equation.

$(y)'=(2x^2-7x+6)'$ Differentiate both sides.

$y'=(2x^2)'-(7x)'+(6)'$ Sum/Difference rule applied: $(f(x)\pmg(x))'=f'(x)\pm g'(x)$

$y'=2(x^2)'-7(x)'+(6)'$ Constant multiple rule applied: $(cf)'=c(f)'$

$y'2(2x)-7(1)+(6)'$ Applied power rule: $(x^n)'=nx^{n-1}$

$y'=4x-7+0$ Simplifying and apply constant rule: $(c)'=0$

$y'=4x-7$ Simplify.

Evaluate y' for x=4:

$y'=4(4)-7$

$y'=16-7$

$y'=9$ is the slope of the tangent line.

Point slope form of a line is:

$y-y_1=m(x-x_1)$

where $m$ is the slope and $(x_1,y_1)$ is a point on the line.

Insert 9 for $m$ and (4,10) for $(x_1,y_1)$ :

$y-10=9(x-4)$

The intended form is $y=mx+b$ which means we are going need to distribute and solve for $y$ .

Distribute:

$y-10=9x-36$

Add 10 on both sides:

$y=9x-26$

The tangent line to the given curve at the given point is $y=9x-26$ .

------------Formal Definition of Derivative----------------

The following limit will give us the derivative of the function $f(x)=2x^2-7x+6$ at $x=4$ (the slope of the tangent line at $x=4$ ):

$\lim_{x \rightarrow 4}\frac{f(x)-f(4)}{x-4}$

$\lim_{x \rightarrow 4}\frac{2x^2-7x+6-10}{x-4}$ We are given f(4)=10.

$\lim_{x \rightarrow 4}\frac{2x^2-7x-4}{x-4}$

Let's see if we can factor the top so we can cancel a pair of common factors from top and bottom to get rid of the x-4 on bottom:

$2x^2-7x-4=(x-4)(2x+1)$

Let's check this with FOIL:

First: $x(2x)=2x^2$

Outer: $x(1)=x$

Inner: $(-4)(2x)=-8x$

Last: $-4(1)=-4$

---------------------------------Add!

$2x^2-7x-4$

So the numerator and the denominator do contain a common factor.

This means we have this so far in the simplifying of the above limit:

$\lim_{x \rightarrow 4}\frac{2x^2-7x-4}{x-4}$

$\lim_{x \rightarrow 4}\frac{(x-4)(2x+1)}{x-4}$

$\lim_{x \rightarrow 4}(2x+1)$

Now we get to replace x with 4 since we have no division by 0 to worry about:

2(4)+1=8+1=9.

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3 years ago

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Romashka [77]

This is how the whole equation goes:
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2 years ago

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