All categories

3 years ago

an average ant is 1/4 of an inch long. an average aphid is 3/32 of an inch long. how many times longer is the ant than the aphid

1 answer:

3 0

First find the common denominator. In this case, you would want to use 32. So, 1/4 = 8/32. So, an ant is 8/32 of an inch and an aphid is 3/32 of an inch. Now to find the difference, you subract. 8/32 - 3/32 = 5/32. So the answer is, the ant is 5/32 of an inch longer.

You might be interested in

The areas of two similar triangles are 75m2 and 300m2. The length of one of the sides of the second triangles is 9m. What is the

Ymorist [56]

Answer:

4.5 m

Step-by-step explanation:

The area of two similar triangles are 75 m2 and 300 m2. This gives you the scale factor of the triangles:

$\dfrac{A_{small}}{A_{large}}=k^2\Rightarrow k^2 =\dfrac{75}{300}=\dfrac{3}{12}=\dfrac{1}{4}\Rightarrow k=\dfrac{1}{2}.$

Then you can find the length of the corresponding side:

$\dfrac{side_{small}}{side_{large}}=k\Rightarrow =\dfrac{side_{small}}{9}=\dfrac{1}{2},\ side_{small}=\dfrac{9}{2}=4.5\ m.$

4 0

3 years ago

The area of the triangle formed by x− and y− intercepts of the parabola y=0.5(x−3)(x+k) is equal to 1.5 square units. Find all p

Juliette [100K]

Check the picture below.

based on the equation, if we set y = 0, we'd end up with 0 = 0.5(x-3)(x-k).

and that will give us two x-intercepts, at x = 3 and x = k.

since the triangle is made by the x-intercepts and y-intercepts, then the parabola most likely has another x-intercept on the negative side of the x-axis, as you see in the picture, so chances are "k" is a negative value.

now, notice the picture, those intercepts make a triangle with a base = 3 + k, and height = y, where "y" is on the negative side.

let's find the y-intercept by setting x = 0 now,

$\bf y=0.5(x-3)(x+k)\implies y=\cfrac{1}{2}(x-3)(x+k)\implies \stackrel{\textit{setting x = 0}}{y=\cfrac{1}{2}(0-3)(0+k)} \\\\\\ y=\cfrac{1}{2}(-3)(k)\implies \boxed{y=-\cfrac{3k}{2}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{area of a triangle}}{A=\cfrac{1}{2}bh}~~ \begin{cases} b=3+k\\ h=y\\ \quad -\frac{3k}{2}\\ A=1.5\\ \qquad \frac{3}{2} \end{cases}\implies \cfrac{3}{2}=\cfrac{1}{2}(3+k)\left(-\cfrac{3k}{2} \right)$

$\bf \cfrac{3}{2}=\cfrac{3+k}{2}\left( -\cfrac{3k}{2} \right)\implies \stackrel{\textit{multiplying by }\stackrel{LCD}{2}}{3=\cfrac{(3+k)(-3k)}{2}}\implies 6=-9k-3k^2 \\\\\\ 6=-3(3k+k^2)\implies \cfrac{6}{-3}=3k+k^2\implies -2=3k+k^2 \\\\\\ 0=k^2+3k+2\implies 0=(k+2)(k+1)\implies k= \begin{cases} -2\\ -1 \end{cases}$

now, we can plug those values on A = (1/2)bh,

$\bf \stackrel{\textit{using k = -2}}{A=\cfrac{1}{2}(3+k)\left(-\cfrac{3k}{2} \right)}\implies A=\cfrac{1}{2}(3-2)\left(-\cfrac{3(-2)}{2} \right)\implies A=\cfrac{1}{2}(1)(3) \\\\\\ A=\cfrac{3}{2}\implies A=1.5 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \stackrel{\textit{using k = -1}}{A=\cfrac{1}{2}(3+k)\left(-\cfrac{3k}{2} \right)}\implies A=\cfrac{1}{2}(3-1)\left(-\cfrac{3(-1)}{2} \right) \\\\\\ A=\cfrac{1}{2}(2)\left( \cfrac{3}{2} \right)\implies A=\cfrac{3}{2}\implies A=1.5$

7 0

3 years ago

What fraction is equal to .66? A.1/3 B.1/5 C.2/3 D.2/4

photoshop1234 [79]

2/3 is the answer.

1/3 is equal to 33.33333333% 

so 2/3 is equal to 66.6666666%

8 0

3 years ago

Select the correct answer. One factor of the polynomial 213 3r2 – 3x + 2 is (t – 2), which expression represents the other facto

Darina [25.2K]

Answer:

(x - 2)(x + 1)(2x -1)

Step-by-step explanation:

We use synthetic division as a tool for factoring the given expression. The coefficients of the terms given are {2, -3, -3, 2}. If x - 2 is a factor of this expression, then 2 is a root. We perform synthetic division as follows:

2 / 2 -3 -3 2

4 2 -2

-------------------------------

2 1 -1 0

Next, we determine whether or not (2x - 1)(x + 1) represents the remaining factor(s). Using -1 as divisor, we get:

-1 / 2 1 -1

-2 1

---------------------

2 -1 0

Since the remainder is zero, x + 1 must be a factor and (2x - 1) the third factor. Answer D is correct.

4 0

2 years ago

Item 2

V125BC [204]

Answer:

its b

Step-by-step explanation:

justfollow the rules

8 0

2 years ago

Read 2 more answers