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3 years ago

Twice the difference of a number and 7 equals 5

Mathematics

1 answer:

RideAnS [48]3 years ago

4 0

Hey there!

Let's write an equation given this information. We will use x to represent the number.

2(x-7)=5

Now, we use the distributive property to remove the parentheses.

2x-14=5

Now, we add 14 to both sides.

2x=19

We divide both sides by 2.

x=9.5

Therefore, our number is 9.5

I hope this helps!

You might be interested in

Solve 3x2 + 5x − 8 = 0 by using an appropriate method. Show the steps of your work, and explain why you chose the method used.

IrinaK [193]

Answer:

Step-by-step explanation:

Hello,

<u>We need to solve the following equation:</u>

$3x^2 + 5x-8 = 0 \\ \\\text{*** divide by 3 ***}\\\\x^2+\dfrac{5}{3}x-\dfrac{8}{3}=0$

It means that the sum of the zeros is $-\dfrac{5}{3}$ and the product is $-\dfrac{8}{3}$ .

We can easily see that 1 and $-\dfrac{8}{3}$ does the job.

So the solutions are 1 and $-\dfrac{8}{3}$ .

Another way to see it is to notice that 1 is a trivial solution as 3+5-8=0, so (x-1) is a factor and (we match the terms)

$3x^2 + 5x-8 = (x-1)(3x+8)=0$

And we find again the same solutions.

Or we use the discriminant.

$x_1=\dfrac{-b-\sqrt{b^2-4ac}}{2a}=\dfrac{-5-11}{6}=-\dfrac{8}{3}\\\\x_2=\dfrac{-b-\sqrt{b^2-4ac}}{2a}=\dfrac{-5+11}{6}=1$

The discriminant method works in all cases, so you cannot be wrong using it.

The first method based on the sum and the product usually works well for integer solution which is not the case here.

Finding a trivial solution to be able to factorise could be used here as 1 is really a trivial solution.

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

7 0

3 years ago

Find the volume of the square pyramid with base area 49in^2 and a height of 8 inches. Round your answer to two decimal places

RideAnS [48]

Answer:

130.67

Step-by-step explanation:

4 0

3 years ago

It is very confusing with negatives so what do I do

Kamila [148]

A lot of people find it easier to visualize what the least to greatest would look like. So imagine a number line that starts (in the middle) at 0. All numbers to the right get GREATER and GREATER. Going for 0 to 1 to 2.... and higher. Going to the left it gets LOWER and LOWER. So, -1 to -2 to -3 and onward. Basically what I'm trying to say is the farther you are to the left the smaller you are.

Another way you can think of it is you could remove the negative, and put them in order from least to greatest. Then when you add the negative back you would flip the order. So let's do that with our current problem: (Keep in mind that if you do this with sequences that are not all negative numbers you need to make the positive numbers negative. Or you can write out a number line and put all the numbers on it)

Our Numbers:
-1.639, -7.06, -7.6, -0.6299, -7.0699, -7.399

Remove the Negative Temporarily:
1.639, 7.06, 7.6, 0.6299, 7.0699, 7.399

Put the numbers in order from least to greatest:
0.6299, 1.639, 7.06, 7.0699, 7.399, 7.6

Now add the negative sign back:
-0.6299, -1.639, -7.06, -7.0699, -7.399, -7.6

Now reverse the order to get the correct answer:
-7.6, -7.399, -7.0699, -7.06, -1.639, -0.6299

4 0

3 years ago

If f(x) is defined as follows,

Phantasy [73]

Answer: The required values are

f(-2) = 120, f(0) = 64 and f(1) = 84.

Step-by-step explanation: We are given the following function f(x) :

$f(x)=16x^2+4x+64~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$