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skad [1K]
3 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.
Mathematics
2 answers:
aleksandrvk [35]3 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]3 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).

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Given the following mAB = mBC= mCD in circle F what is the measure of angle AFB
Svetach [21]
50° <span>is the measure of angle AFB</span>

8 0
3 years ago
What is the phase shift of the graph of y=−sin(x+π/4)+2
butalik [34]

Answer:

π/4

Step-by-step explanation:

x is the variable

-1 inverts the curve

π/4 is the phase shift or x axis offset

2 is the y axis offset

5 0
3 years ago
Kiyo bought a pizza for $12.75 and four medium drinks at Paola’s pizza. Define a variable and write an expression to represent t
Travka [436]
Y = total amount of money spent
x = cost of one drink

So our expression is:
4x + 12.75

4x stands for 4 drinks times x price of one drink
The 12.75 is a one time fee for the pizza, since Kiyo isn't buying multiple pizzas.

The problem also asks us to find the total price, so we write an equation:

y = 4x + 12.75
We insert what x is which in this case is $3
y = 4(3) + 12.75
Order of Operations tells us to multiply first:
y = 12 + 12.75
Now add your values:
y = 24.75
Therefore, Kiyo spent a total amount of 24.75 at Paola's pizza.

Let's check our problem just in case:

24.75 = 4x + 12.75
Since we now know what y is equal to, we can plug that into our original equation and check just to verify

We should subtract 12. on both sides of the equation because of inverse operations:

24.75 - 12.75  = 12.75 - 12.75 + 4x
We are left with:

12 = 4x
We divide:
\frac{12}{4}  =  \frac{4x}{4}
Our result is:
3 = x
Which checks out because each drink was in fact, $3 dollars as stated in the word problem. Hope that was thorough enough.


4 0
3 years ago
Ali and Tibor get paid $9 per hour. This week, Tibor made an additional $27 in overtime.
Leviafan [203]
9a + (9t+27)=x

To write it another way you could flip the numbers around:

(9t+27)+9a=x

Or flip the variable to the other side.

x=9a + (9t+27)

Any way you put the numbers as long as x is on the either side, you will get the same answer.

Hope this helps!
4 0
3 years ago
14.36 rounded to the nearest tenth
Finger [1]

Answer:

14.4

Step-by-step explanation:

6 is closer to 40 than to 30

3 0
3 years ago
Read 2 more answers
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