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3 years ago

7

Kallisto built a rectangular sign that measured 2 and 3/4. The width is 1 and 1/4 shorter than the length. To find the area, mul

tiply the length and width. What is the area in square feet write an equation to solve it

1 answer:

prisoha [69]3 years ago

8 0

Answer:

<em>l</em> = 1 5/16

w = 1/16

A = 21/16 x 1/16 = 21/256

Step-by-step explanation:

Perimeter = 11/4

<em>l</em> = length

w = <em>l</em> - 5/4

2<em>l</em> + 2(<em>l</em> - 5/4) = 11/4

2<em>l</em> + 2<em>l</em> - -5/2 = 1/4

multiply each side by 4

8<em>l</em> + 8<em>l </em>- 10 = 11<em> </em>

16<em>l</em> = 21

<em>l</em> = 21/16 or 1 5/16

width = 21/16 - 20/16 = 1/16

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What are the coefficients for the binomial expansion of (p+q)^6

seropon [69]

Answer:

1 6 15 20 15 6 1

Step-by-step explanation:

To figure this out, we need to look at Pascal's Triangle, which is a tricky little way to find the coefficients for any binomial expression like this! Check the attached photo.

Because this is to the sixth, we need the 6th row, which is <u>1 6 15 20 15 6 1.</u> From this, we know that those numbers are the coefficients!

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3 years ago

Read 2 more answers

Factor the polynomial, x2 + 5x + 6

patriot [66]

Answer:

Choice b.

$x^{2} + 5\, x + 6 = (x + 3)\, (x + 2)$ .

Step-by-step explanation:

The highest power of the variable $x$ in this polynomial is $2$ . In other words, this polynomial is quadratic.

It is thus possible to apply the quadratic formula to find the "roots" of this polynomial. (A root of a polynomial is a value of the variable that would set the polynomial to $0$ .)

After finding these roots, it would be possible to factorize this polynomial using the Factor Theorem.

Apply the quadratic formula to find the two roots that would set this quadratic polynomial to $0$ . The discriminant of this polynomial is $(5^{2} - 4 \times 1 \times 6) = 1$ .

$\begin{aligned}x_{1} &= \frac{-5 + \sqrt{1}}{2\times 1} \\ &= \frac{-5 + 1}{2} \\ &= -2\end{aligned}$ .

Similarly:

$\begin{aligned}x_{2} &= \frac{-5 - \sqrt{1}}{2\times 1} \\ &= \frac{-5 - 1}{2} \\ &= -3\end{aligned}$ .

By the Factor Theorem, if $x = x_{0}$ is a root of a polynomial, then $(x - x_0)$ would be a factor of that polynomial. Note the minus sign between $x$ and $x_{0}$ .

The root $x = -2$ corresponds to the factor $(x - (-2))$ , which simplifies to $(x + 2)$ .
The root $x = -3$ corresponds to the factor $(x - (-3))$ , which simplifies to $(x + 3)$ .

Verify that $(x + 2)\, (x + 3)$ indeed expands to the original polynomial:

$\begin{aligned}& (x + 2)\, (x + 3) \\ =\; & x^{2} + 2\, x + 3\, x + 6 \\ =\; & x^{2} + 5\, x + 6\end{aligned}$ .

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2 years ago

A fair survey question is one that does not encourage biased responses.

laiz [17]

B because it's not putting the blame on anyone. It is completely unbiased and objective.

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3 years ago

a train travels 288km at a uniform speed.if the speed has been 4km per hour more it would have taken one hour less for the same

Lostsunrise [7]

Given:

A train travels 288 km at a uniform speed.

If the speed has been 4 km per hour more it would have taken one hour less for the same journey.

To find:

The initial speed of the train.

Solution:

Let x km/h be the initial speed on the train.

New speed of train = (x+4) km/h

We know that,

$Time=\dfrac{Distance}{Speed}$

Time taken by the train initially to cover 288 km is $\dfrac{288}{x}$ hours.

New time taken by the train to cover 288 km is $\dfrac{288}{x+4}$ hours.

It is given that If the speed has been 4 km per hour more it would have taken one hour less for the same journey.

$\dfrac{288}{x}-\dfrac{288}{x+4}=1$

$\dfrac{288(x+4)-288x}{x(x+4)}=1$

$288x+1152-288x=x^2+4x$

$1152=x^2+4x$

$0=x^2+4x-1152$

Splitting the middle term, we get

$x^2+36x-32x-1152=0$

$x(x+36)-32(x+36)=0$

$(x+36)(x-32)=0$

$x=-36,32$

We know that the speed cannot be negative. So, the only possible value of x is 32.

Therefore, the speed of the train is 32 km/h.

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2 years ago

List these numbers from least to greatest:<br><br> -1 2/5, 0, -2.3, 3/4, and<br> -1 9/10

kap26 [50]

Answer:

-2.3, -1 9/10, -1 2/5, 0, 3/4.

Step-by-step explanation:

First thing we need to do is express all of the fractions and the decimal in the same unit.

Let's turn the decimal into a fraction.

-2.3 = -2 3/10. The 3 is in the tenths place, so that means 3 over 10 or 3/10. The 2 is in the ones place so we get the 2 as a whole number.

Okay, now we need to express the fractions with the same denominator. You MUST do this if you are going to compare fractions.

First,

let's turn all the mixed numbers into improper fractions.

-1 2/5 = -7/5

-2 3/10 = -23/10

-1 9/10 = -19/10.

The last 2 already have the same denominator of 10, so we'll just change the -7/5 to have a denominator of 10. 5 x 2 equals 10, so we MUST also multiply by the numerator by 2. Whatever is done to the denominator has to be done to the numerator as well.

5 x 2 = 10

7 x 2 = 14.

Now, here is what we have.

-14/10, 0, -23/10, 3/4, -19/10.

First, know that negative numbers are ALWAYS SMALLER than zero and ANY positive number.

And, with negative numbers, the number that looks "greater" is actually lesser. For example, -5 is greater than -3 because -3 is closer to 0.

So, let's compare the negative fractions.

-14/10, -23/10, -19/10.

Ignoring the (-) the one that *looks* greatest is 23 because it has the greatest number in the numerator, however, because this is negative numbers, it's actually the smallest.

Second "biggest" is -19/10 but again, this is negatives, so its actually second smallest.

The only number now is -14/10 so that's the next smallest.

0 is obviously less than 3/4 so 0 comes next. And lastly, 3/4 is the only number we have left! so, 3/4 is the greatest!

LEAST TO GREATEST:

-2.3, -1 9/10, -1 2/5, 0, 3/4.

6 0

3 years ago