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2 years ago

The four digit numeral 3AA1 is divisible by 9. What digit does A represent

Mathematics

1 answer:

dexar [7]2 years ago

4 0

Answer:

A = 2, the number is 3221

Step-by-step explanation:

In order for the number to be divisible by 9, the sum of it's digit has to be divisible by 9.

In our case, $4+A+A+1= 9k$ where k is an integer. the easiest way happens when k=1

$5+2A= 9 \rightarrow 2A=4 \rightarrow A = 2$

Higher values of k will likely most work (with k=2 you get A to be a non-integer, which can't work since it's the digit of a number, and with higher values of K you're not getting a number in base 10.

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Form quadratic functions given the following information:

nignag [31]

Answer:

$f(x)=-\frac{4}{7}(x-\sqrt{2}-3)(x+\sqrt{2}-3)$

$f(x)=-\frac{4}{7}(x^2-6x+7)$

Step-by-step explanation:

we have

f(3+√2 )=f(3− √2 )=0

x1=3+√2 and x2=3−√2 are the roots or x-intercepts of the quadratic equation

The quadratic equation in factored form is equal to

$f(x)=a(x-x1)(x-x2)$

substitute

$f(x)=a(x-(3+\sqrt{2}))(x-(3-\sqrt{2}))$

Find the value of the coefficient a

Remember that

f(1)=−8

For x=-1 -----> f(x)=-8

substitute

$-8=a(-1-(3+\sqrt{2}))(-1-(3-\sqrt{2}))$

solve for a

$-8=a(-4-\sqrt{2}))(-4+\sqrt{2}))$

apply difference of squares

$-8=a(14)$

$a=-\frac{4}{7}$

therefore

$f(x)=-\frac{4}{7}(x-(3+\sqrt{2}))(x-(3-\sqrt{2}))$

$f(x)=-\frac{4}{7}(x-\sqrt{2}-3)(x+\sqrt{2}-3)$

simplify

Applying distributive property

$f(x)=-\frac{4}{7}(x^2+\sqrt{2}x-3x-\sqrt{2}x-2+3\sqrt{2}-3x-3\sqrt{2}+9)$

$f(x)=-\frac{4}{7}(x^2-6x+7)$

5 0

4 years ago

Transformation on y=-(x-2)

Kruka [31]

You can look it up on Socratic

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3 years ago

The price of an item was reduced by 10% and then by 20%. Is that the same as reducing the price by 30%? If not, then what percen

Natasha2012 [34]

Answer:

28%

Step-by-step explanation:

Hello,

When the item is reduced by 10%, this is like we multiply this price by 1-0.10=0.90

When the item is reduced by 20%, this is like we multiply this price by 1-0.20=0.80

When the item is reduced by 10% and then by 20%, this is like we multiply this price by 0.90*0.80=0.72

so this is equivalent that the item is reduced by 28% (as 1-0.28=0.72)

hope this helps

8 0

3 years ago

Given d = 1/2 at^2, solve for a.

Anastaziya [24]

Isolate the variable by dividing each side by factors that don't contain the variable.
The Answer is B
2d/t^2

8 0

3 years ago

What is the equation of a line that is perpendicular to -x+3y=9 and passes through point (-3,2)

Lynna [10]

Answer:

The perpendicular line would be y = -3x - 7

Step-by-step explanation:

To find the equation of the line, we first need to solve the original line for y.

-x + 3y = 9

3y = x + 9

y = 1/3x + 3

Now we know the slope of the original line to be 1/3. Since perpendicular lines have opposite and reciprocal slope, we know the new line to have a slope of -3. We can then use that along with the given point in point-slope form to find the equation.

y - y1 = m(x - x1)

y - 2 = -3(x + 3)

y - 2 = -3x - 9

y = -3x - 7

8 0

4 years ago