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3 years ago

Witch expression represents the value of 5 nickels and x dimes

Mathematics

2 answers:

Kitty [74]3 years ago

7 0

Answer:

5(0.05) + 0.10x

Step-by-step explanation:

This would be correct because, first of all, you have 5 nickels. The value of a nickel is 0.05, and you would then multiply that by 5. That's how we would get 5(0.05)

Next, we know the value of a dime is 0.10 (10 cents), but we don't know how many dimes there are. So, the unknown amount of dimes would be represented by x. Then, we multiply 0.10 by x.

We also want to add the two expressions, because of the word "and."

So, altogether, we would get 5(0.05) + 0.10x

Setler [38]3 years ago

4 0

10x+25 (expressions don't have equal signs)

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If f(1) = 0, what are all the roots of the function f(x)=x^3+3x^2-x-3? Use the Remainder Theorem.

Sophie [7]

There's no if about it,

$f(x)=x^3+3x^2-x-3
$

has a zero $f(1)=0$ so $x-1$ is a factor. That's the special case of the Remainder Theorem; since $f(1)=0$ we'll get a remainder of zero when we divide $f(x)$ by $x-1.$

At this point we can just divide or we can try more little numbers in the function. It doesn't take too long to discover $f(-1)=0$ too, so $x+1$ is a factor too by the remainder theorem. I can find the third zero as well; but let's say that's out of range for most folks.

So far we have

$x^3+3x^2-x-3 = (x-1)(x+1)(x-r)$

where $r$ is the zero we haven't guessed yet. Again we could divide $f(x)$ by $(x-1)(x+1)=x^2-1$ but just looking at the constant term we must have

$-3 = -1 (1)(-r) = r$

so

$x^3+3x^2-x-3 = (x-1)(x+1)(x+3)$

We check $f(-3)=(-3)^3+3(-3)^2 -(-3)-3 = 0 \quad\checkmark$

We usually talk about the zeros of a function and the roots of an equation; here we have a function $f(x)$ whose zeros are

$x=1, x=-1, x=-3$

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2 years ago

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Four thousand students at a school were asked to name their favorite pizza topping. The results were 800 Pepperoni, 1,000 Sausag

4vir4ik [10]

Answer:

The pepperoni and peppers are mixed up

Step-by-step explanation:

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2 years ago

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What is the value of the expression 3y−zy+5z3y−zy+5z when y = 6 and z = 2?

WARRIOR [948]

The valve of the expression would be 184

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3 years ago

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Es 18 de junio de 1815, las tropas napoleónicas se encuentran justo adelante, tu eres el ingeniero en balística y el general Wel

Airida [17]

Answer:

89.1° or -1.4°

Step-by-step explanation:

1. Location:

You are on the Mont-Saint-Jean escarpment, near the Belgian town of Waterloo.

The French troops are about 50 m below you and 1.2 km distant.

2. Finding the firing angle

Data:

R = 1200 m

u = 600 m/s

h = -50 m (the height of the target)

a = 9.8 m/s²

We have two conditions.

Horizontal distance

(1) 1200 = 600t cosθ

Vertical distance

(2) -50 = 600t sinθ - 4.9t²

Divide each side of (1) by 600cosθ.

$(3) \, t =\dfrac{2}{\cos \theta}$

Substitute (3) into (2)

$-50 = 600t \sin \theta - 4.9t^{2} = 600 \left( \dfrac{2}{\cos \theta} \right ) \sin \theta - 4.9 \left( \dfrac{2}{\cos \theta} \right )^{2}\\\\(4) \, -50 = 1200 \tan \theta - \dfrac{19.6}{\cos^{2} \theta}$

Recall that

(5) sec²θ = 1/cos²θ = tan²θ + 1

Substitute (5) into (4)

$-50 = 1200 \tan \theta - 19.6 \left(\tan^{2} \theta}+ 1\right )$

Set up a quadratic equation

$\begin{array}{rcl}-50 & = & 1200 \tan \theta - 19.6\tan^{2} \theta -19.6 \\0 & = & 1200 \tan \theta - 19.6\tan^{2} \theta + 30.4\\0 & =&19.6\tan^{2} \theta - 1200 \tan \theta - 30.4\\0 & =&\tan^{2} \theta - 61.224 \tan \theta - 1.551\\\end{array}$

Solve for θ

Use the quadratic formula.

tanθ = 61.249 or -0.025

θ = arctan(61.249) = 89.1° or

θ = arctan(-0.025) = -1.4°

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2 years ago

A strawberry farm had 7,200 plants in total, one field had 18 rows of 200 plants ; the other field had 9. Rows of

Svetradugi [14.3K]

Answer:

We have a total of 7200 plants.

The plants are distributed in one field with 18 rows of 200 plants and another field with 9 rows of N plants.

Where we want to find the value of N.

The total number of plants in the rows is:

"number of rows times number of plants in each row."

Then the total number of plants is:

18*200 + 9*N

And we know that we have a total of 7200 plants, then:

18*200 + 9*N = 7200

9*N = 7200 - 18*200 = 3600

N = 3600/9 = 400

Then the plants are distributed in 18 rows of 200 plants for one field, and 9 rows of 400 plants in the other field.

8 0

2 years ago