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3 years ago

Need help with middle two questions... I’ll give points

Mathematics

1 answer:

nignag [31]3 years ago

7 0

Answer:

ok sorry i could not put this into a formula im have to go but i will show you a really easy way.

Step-by-step explanation:

for number 1 i got (7,-1)

This is because there is a slope of 1/1 between these two points. so i plotted the two points on the graph. The distance between the two points is 4. so i followed the slope 4 times and thats what i got.

The correct way for doing number 1 is using the distance formula i believe but im running out of time

for the second one i got (3, -1/2)

we do this by using the midpoint formula.

The first picture is for number one and the second for number 2

if you have any questions feel free to ask in the comments

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Please help me with this surds question.

noname [10]

the answer is 0.2 or one fifths

3 0

3 years ago

Write an equation for a quadratic function that has x intercepts (-3, 0) and (5, 0)

Blizzard [7]

Answer:

One possible equation is $f(x) = (x + 3)\, (x - 5)$ , which is equivalent to $f(x) = x^{2} - 2\, x - 15$ .

Step-by-step explanation:

The factor theorem states that if $x = x_{0}$ (where $x_{0}$ is a constant) is a root of a function, $(x - x_{0})$ would be a factor of that function.

The question states that $(-3,\, 0)$ and $(5,\, 0)$ are $x$ -intercepts of this function. In other words, $x = -3$ and $x = 5$ would both set the value of this quadratic function to $0$ . Thus, $x = -3\!$ and $x = 5\!$ would be two roots of this function.

By the factor theorem, $(x - (-3))$ and $(x - 5)$ would be two factors of this function.

Because the function in this question is quadratic, $(x - (-3))$ and $(x - 5)$ would be the only two factors of this function. In other words, for some constant $a$ ( $a \ne 0$ ):

$f(x) = a\, (x - (-3))\, (x - 5)$ .

Simplify to obtain:

$f(x) = a\, (x + 3)\, (x - 5)$ .

Expand this expression to obtain:

$f(x) = a\, (x^{2} - 2\, x - 15)$ .

(Quadratic functions are polynomials of degree two. If this function has any factor other than $(x - (-3))$ and $(x - 5)$ , expanding the expression would give a polynomial of degree at least three- not quadratic.)

Every non-zero value of $a$ corresponds to a distinct quadratic function with $x$ -intercepts $(-3,\, 0)$ and $(5,\, 0)$ . For example, with $a = 1$ :

$f(x) = (x + 3)\, (x - 5)$ , or equivalently,

$f(x) = x^{2} - 2\, x - 15$ .

6 0

2 years ago

Simplify by expressing fractional exponents instead of radicals

igomit [66]

Answer:

$a^{\frac{1}{2}}b^{\frac{1}{2}}$

Step-by-step explanation:

Given:

The expression in radical form is given as:

$\sqrt{ab}$

We need to express this in fractional exponent form.

We know that,

$\sqrt a=a^{\frac{1}{2}}$

Also, $\sqrt{ab}=\sqrt a\times \sqrt b$

Now, clubbing both the properties of square root function, we can rewrite the given expression as:

$\sqrt{ab}=\sqrt a \times \sqrt b\\\\\sqrt{ab}=a^{\frac{1}{2}}\times b^{\frac{1}{2}}\\\\\therefore \sqrt{ab}=a^{\frac{1}{2}}b^{\frac{1}{2}}$

So, the given expression in fractional exponents form is $a^{\frac{1}{2}}b^{\frac{1}{2}}$ .

3 0

3 years ago

What is the GCF of 81 and 36?<br> What is the LCM of 4 and 9?

Mila [183]

The question "What is the LCM and GCF of 36 and 81?" can be split into two questions: "What is the LCM of 36 and 81?" and "What is the GCF of 36 and 81?"

In the question "What is the LCM and GCF of 36 and 81?", LCM is the abbreviation of Least Common Multiple and GCF is the abbreviation of Greatest Common Factor.

To find the LCM, we first list the multiples of 36 and 81 and then we find the smallest multiple they have in common. To find the multiples of any number, you simply multiply the number by 1, then by 2, then by 3 and so on. Here is the beginning list of multiples of 36 and 81:

Multiples of 36: 36, 72, 108, 144, 180, 216, etc.

Multiples of 81: 81, 162, 243, 324, 405, 486, etc.

The least multiple on the two lists that they have in common is the LCM of 36 and 81. Therefore, the LCM of 36 and 81 is 324.

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3 years ago

Please help! Read the question below!

Sunny_sXe [5.5K]

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Step-by-step explanation:

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3 years ago

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