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4 years ago

5

What non-zero rational number must be placed in the square so that the simplified product of these two binomials is a binomial:

(7t-10)(5t+Box )? Express your answer as a mixed number.

2 answers:

aleksandrvk [35]4 years ago

7 0

The product would expand to

$(7t-10)(5t+x)=35t^2+7tx-50t-10x=35t^2+(7x-50)t-10x$

This is a trinomial, and the only way to make it a binomial is to cancel out a coefficient using our variable $x$ .

So, we can cancel either the linear term or the constant term.

In the first case, we require

$7x-50=0 \iff 7x=50 \iff x=\dfrac{50}{7}=\dfrac{49}{7}+\dfrac{1}{7}=7\dfrac{1}{7}$

In the second case, we require

$-10x=0\iff 10x=0 \iff x=0$

But $x$ must be a non-zero rational number, so this solution is not feasible.

dimaraw [331]4 years ago

3 0

Answer:

7 1/7.

Step-by-step explanation:

The middle 2 numbers in the expansion will be cancelled out if one of them is + 50 t so the required rational number is 50/7:

(7t - 10)(5t + 50/7) = 35t^2 - 50t + 350/7 t - 500/7)

= 35t^2 - 50t + 50t - 500/7)

= 35t^2 - 500/7)

So 50 / 7 = 7 1/7 (answer).

You might be interested in

If 7/12 is multiplied by a fraction less than 1 what would be the product

olga55 [171]

Answer:

<em>Examples below</em>

Step-by-step explanation:

We have the fraction

$\frac{7}{12}$

It's required to multiply it by any fraction less than 1. Let's select the following fractions. All of them are less than 1 because the numerator is less than the denominator:

$\frac{1}{7}$

$\frac{4}{5}$

$\frac{6}{35}$

The required products are:

$\frac{7}{12}\cdot \frac{1}{7}=\frac{7}{7*12}=\frac{1}{12}$

$\frac{7}{12}\cdot \frac{4}{5}=\frac{4*7}{12*5}=\frac{7}{15}$

$\frac{7}{12}\cdot \frac{6}{35}=\frac{6*7}{12*35}=\frac{1}{10}$

4 0

3 years ago

Which is the inverse of the following statement?

sergiy2304 [10]

Yes if it’s less than 90 it’s an acute but yes 90 is a right angle

4 0

3 years ago

Which algebraic expression represents the difference of e squared and twenty-one? A. E2+21 b.21 times e2 c. E2 - 21 d. 21 divide

Digiron [165]

Answer: c. E2 - 21

Step-by-step explanation:

difference means to subtract

Now, e squared=E² and twenty-one=21

Therefore the difference of e squared and twenty-one is E2 - 21

6 0

3 years ago

schepotkina [342]

The area of the triangle ABC is 207.5 square units.

Explanation:

The measurements of the sides of the triangle are $AB=19$ , $AC=24$ and $m\angle A=65^{\circ}$

We need to determine the area of the triangle ABC.

<u>Area of the triangle:</u>

The area of the triangle can be determined using the formula,

${Area}=\frac{1}{2} b c \sin A$

where $b=19$ , $c=24$ and $m\angle A=65^{\circ}$

Substituting these values in the above formula, we get,

${Area}=\frac{1}{2}(19)(24) \sin 65^{\circ}$

Simplifying the values, we get,

${Area}=\frac{1}{2}(456) (0.91)$

${Area}=\frac{1}{2}(414.96)$

${Area}=207.48$

Rounding off to the nearest tenth, we get,

${Area}=207.5$

Thus, the area of the triangle ABC is 207.5 square units.

5 0

3 years ago

Read 2 more answers

Jim says that the output of the floor function is the number before the decimal point in the input. For what domain is Jim’s sta

sweet [91]

Answer:

integers ∪ [0, ∞)

Step-by-step explanation:

The floor function gives the largest integer not greater than the input value. For non-negative numbers, that is the integer portion of the number, as Jim says.

However, for negative numbers, the floor is one less than the integer portion of any number that has a non-zero fractional part.

floor(1.2) = 1

floor(0.2) = 0

floor(-0.2) = -1

floor(-1.2) = -2

For any integer, negative or otherwise, the floor function gives that integer value.

Jim is correct on the domain of all integers and positive non-integers.

6 0

3 years ago

Read 2 more answers