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2 years ago

What is the factored form of 36x4 – 25?

Mathematics

2 answers:

gladu [14]2 years ago

8 0

$36x^4 - 25=(6x^2)^2-5^2=(6x^2-5)(6x^2+5)$

babunello [35]2 years ago

8 0

its A (6x2-5)6x2+5)

Step-by-step explanation:

That is the factored form if 36x4-25

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The vertices of ΔRST are R(–1,–1), S(–1,11) and T(4,11). Which could be the side lengths of a triangle that is similar but not c

Step2247 [10]

The side lengths could be 10, 24 and 26 units.

We must first find the side lengths. We use the distance formula to do this.

For RT:
$d=\sqrt{(11--1)^2+(-1--1)^2}
\\=\sqrt{(11+1)^2+(-1+1)^2}
\\=\sqrt{12^2+0^2}=\sqrt{144}=12$

For ST:
$d=\sqrt{(11-11)^2+(4--1)^2}
\\=\sqrt{0^2+(4+1)^2}=\sqrt{5^2}=\sqrt{25}=5$

For TR:
$d=\sqrt{(11--1)^2+(4--1)^2}
\\=\sqrt{(11+1)^2+(4+1)^2}=\sqrt{12^2+5^2}=\sqrt{144+25}=\sqrt{169}=13$

Our side lengths, from least to greatest, are 5, 12 and 13.

To be similar but not congruent, the side lengths must have the same ratio between corresponding sides but not be the same length. 10, 24 and 26 are all 2x the original side lengths, so this works.

5 0

2 years ago

A researcher is testing how bacterial cells react to different environments. She placed a petri dish that initially had 32,000 b

Nataly [62]

<u>Solution- </u>

A researcher placed a petri dish with 32,000 bacterial cells. One hour after being placed in the vacuum chamber, the number of cells in the petri dish had halved. Another hour later, the number of cells had again halved.

This can be represented as exponential decreasing function,

$y=a(1 - r)^x$

Where,

a = starting amount = 32000
r = rate = 50% = 0.5 as the sample becomes halved in each hour
x = hours

Putting the values,

$\Rightarrow y=32000(1 - 0.5)^x$

$\Rightarrow y=32000(0.5)^x$

y-intercept means, where x=0, so

$\Rightarrow y=32000(0.5)^0\\\\\Rightarrow y=32000\times 1=32000$

The coordinate of this poin will be (0, 32000)

This means when x=0 or at the starting of the research, the number of bacteria cells was 32000.

After 3 hours, number of bacteria cells will be,

$\Rightarrow y=32000(0.5)^3$

$\Rightarrow y=32000\times 0.125$

$\Rightarrow y=4000$

The coordinate of this point will be (3, 4000)

7 0

2 years ago

Stacey has a square piece of cloth. She cuts 3 inches off of the length of the square and 3 inches off of the width. The area of

ratelena [41]

Answer:

The side length of the original square was 6 inches

Step-by-step explanation:

we know that

The area of a square is

$A=b^2$

where

b is the length side of the square

Let

x ---> the length of the original square

The area of the original square is

$A=x^{2}\ in^2$

The length of the smaller square is

$b=(x-3)\ in$

The area of the smaller square is

$A=(x-3)^2\ in^2$

The area of the smaller square is 1/4 the area of the original square

$(x-3)^2=\frac{1}{4} x^{2}$

solve for x

$x^2-6x+9=\frac{1}{4} x^{2}$

Multiply by 4 both sides

$4x^2-24x+36=x^{2}$

$4x^2-x^2-24x+36=0\\3x^2-24x+36=0$

Solve the quadratic equation by graphing

using a graphing tool

x=2, x=6

see the attached figure

The solution is x=6 in

Remember that the solution must be greater than 3 inches (because Stacey cuts 3 inches off of the length of the square and 3 inches off of the width)

therefore

The side length of the original square was 6 inches

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2 years ago

A student raises her grade average from a 75 to a 90. What was the percent of increase

son4ous [18]

This can be solved algebraically. Before we start, as context, to find a percentage you multiply by the percentage/100.

$75*x=90 \\ x= \frac{90}{75} \\ \\ \boxed{x=1.2}$

This tells us that 90 is 120% of 75. However, your question wants us to find the <em>increase</em>, therefore we don't need that 100.
Therefore, the increase is 20%.

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Rufina [12.5K]

Answer:

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2 years ago

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