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3 years ago

-20 + 5p-7 what is the terms and coefficients

Mathematics

1 answer:

Umnica [9.8K]3 years ago

6 0

Terms: -20, 5p, 7

Coefficient: 5

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Homework Progress<br> 0<br> Find the nth term of the following sequence: 4 7 12 19 28

just olya [345]

<em>Answer:</em>

n²+3

<em>Explanation:</em>

The differences between the terms are not the same, so this is not "linear". Knowing that the sequence may have started with a 1, you can try subtracting the first number with a number to get 1, and use that number to subtract the rest.

4 - 3 = 1
7 - 3 = 4
12 - 3 = 9
19 - 3 = 16
28 - 3 = 25

In this case, subtracting 3 to all the numbers gave us perfect squares! So this means the nth term has to do with squaring the number and adding three afterward! This can be checked.

√1 = 1
√4 = 2
√9 = 3
√16 = 4
√25 = 5

As we found the values of these terms by subtracting three first and then finding its square root, the nth term will be the opposite; squaring and then adding three! Again, this can be checked!

1² + 3 = 4
2² + 3 = 7
3² + 3 = 12
4² + 3 = 19
5² + 3 = 28

Hope this helps !! :D

5 0

2 years ago

Please help! Thank you!!!!!

katrin2010 [14]

9514 1404 393

Answer:

f(x) = x² -3
g(x) = 6x +7
h(x) = 3^x

Step-by-step explanation:

f(x) is copied from the problem statement.

g(x) is a symbolic representation of the English wording, using x to represent "a number."

h(x) is the exponential function that corresponds to the geometric sequence in the table. It has a common ratio of 3, and a multiplier of 1 at x=0.

8 0

3 years ago

A science museum makes gift bags for students using 168 magnets, 48 robot figurines, and 24 packs of freeze-dried ice cream. How

skelet666 [1.2K]

Answer:

7 magnets
2 robot figurines
1 pack of freeze-dried ice cream

Step-by-step explanation:

The greatest common factor of 24, 48, and 168 is 24, so 24 gift bags can be made. Each will have 1/24 of the number of gift items of each type that are available.

In each bag are ...

1/24 × 168 magnets = 7 magnets
1/24 × 48 robot figurines = 2 robot figurines
1/24 × 24 packs of ice cream = 1 pack of ice cream

_____

One way to find the greatest common factor (GCF) is to consider whether the smallest number divides all the numbers. If so (as here), then that is the GCF. If not, then consider the smallest difference between any pair of numbers, to see if it divides all of the numbers. If not, then test the smallest positive remainder from any of those divisions. Repeat until you have found a common divisor (which may be 1).

5 0

3 years ago

I don’t know any of these lol

neonofarm [45]

In this exercise, we want to know the x-intercepts of each item. To find the x-intercepts, set y = 0 as indicated in each item and solve for x. So:

<h2>1. Answer:</h2>

B. x=-1; x=-1.75

<h3>Step by step explanation:</h3>

we have the equation:

$4x^2+11x+7=0$

We can say that this equation comes from the function $f(x)=4x^2+11x+7$ so we have set $y=0$ to find the x-intercepts. By using the quadratic formula we have:

$x=\frac{-b \pm \sqrt{b^2-4ac}}{2a} \\ \\ where: \\ \\ a=4, \ b=11, \ c=7 \\ \\ x=\frac{-11 \pm \sqrt{11^2-4(4)(7)}}{2(4)} \\ \\ x=\frac{-11 \pm \sqrt{121-112}}{8} \\ \\ \boxed{x_{1}=-1 \ and \ x_{2}=-1.75}$

<h2>2. Answer:</h2>

B. x=-1; x=-1.75

<h3>Step by step explanation:</h3>

we have the equation:

$3x^2-4x+1=0$

We can establish a function $g(x)=3x^2-4x+1$ and say that we want to find the x-intercepts of this function by setting y = 0. Therefore, by using the quadratic formula we have:

$a=3, \ b=-4, \ c=1 \\ \\ x=\frac{-(-4) \pm \sqrt{(-4)^2-4(3)(1)}}{2(3)} \\ \\ x=\frac{4 \pm \sqrt{16-12}}{6} \\ \\ \boxed{x_{1}=1 \ and \ x_{2}=\frac{1}{3}}$

<h2>3. Answer:</h2>

H. No Solution

<h3>Step by step explanation:</h3>

we have the equation:

$3x^2-4x+2=0$

We can establish a function $h(x)=3x^2-4x+2$ and say that we want to find the x-intercepts of this function by setting y = 0. Therefore, by using the quadratic formula we have:

$a=3, \ b=-4, \ c=2 \\ \\ x=\frac{-(-4) \pm \sqrt{(-4)^2-4(3)(2)}}{2(3)} \\ \\ x=\frac{4 \pm \sqrt{16-24}}{6}$

Since 16 - 24 = -8, that is, a number less than zero which is within a square root, we say that the equation $3x^2-4x+2=0$ has no any real solution.

<h2>4. Answer:</h2>

E. x=1

<h3>Step by step explanation:</h3>

we have the equation:

$x^2-2x+1=0$

We can establish a function $c(x)=x^2-2x+1$ . By setting y = 0 we'll find the x-intercepts. Let's solve this problem using other method. You can find some binomial products having a special form. So it's easier to find a solution by using distributive. The form of this polynomial is a Square of a Binomial in the form:

$(x-1)^2=0 \\ \\ Because: \\ \\ (x-1)^2=(x-1)(x-1)=x^2-x-x+1= x^2-2x+1$

Therefore, the value that satisfies this equation is $\boxed{x=1}$

<h2>5. Answer:</h2>

K. x = -1

<h3>Step by step explanation:</h3>

we have the equation:

$x^2+2x+1=0$

We can establish a function $a(x)=x^2+2x+1$ . By setting y = 0 we'll find the x-intercepts. We are going to solve this problem by using the previous method. The form of this Square of a Binomial is:

$(x+1)^2=0 \\ \\ Because: \\ \\ (x+1)^2=(x+1)(x+1)=x^2+x+x+1= x^2+2x+1$

Therefore, the value that satisfies this equation is $\boxed{x=-1}$

<h2>6. Answer:</h2>

N) x = 1/2

<h3>Step by step explanation:</h3>

we have the equation:

$4x^2-4x+1=0$

We can establish a function $b(x)=4x^2-4x+1$ and say that we want to find the x-intercepts of this function by setting y = 0. Here we will use the quadratic formula, so:

$a=4, \ b=-4, \ c=1 \\ \\ x=\frac{-(-4) \pm \sqrt{(-4)^2-4(4)(1)}}{2(4)} \\ \\ x=\frac{4 \pm \sqrt{16-16}}{8} \\ \\ \boxed{x=\frac{1}{2}}$

So we have just one solution.

<h2>7. Answer:</h2>

M) x = -1/2

<h3>Step by step explanation:</h3>

we have the equation:

$4x^2+4x+1=0$

We can establish a function $b(x)=4x^2+4x+1$ and say that we want to find the x-intercepts of this function by setting y = 0. As in the previous exercise, we will use the quadratic formula, so:

$a=4, \ b=4, \ c=1 \\ \\ x=\frac{-4 \pm \sqrt{(4)^2-4(4)(1)}}{2(4)} \\ \\ x=\frac{-4 \pm \sqrt{16-16}}{8} \\ \\ \boxed{x=-\frac{1}{2}}$

So we have just one solution.

<h2>8. Answer:</h2>

D) x = -1.45; x=1.25

<h3>Step by step explanation:</h3>

we have the equation:

$5x^2+x-9=0$

We can establish a function $D(x)=5x^2+x-9$ and say that we want to find the x-intercepts of this function by setting y = 0. By using the quadratic formula we can solve this problem, so:

$a=5, \ b=1, \ c=-9 \\ \\ x=\frac{-1 \pm \sqrt{(1)^2-4(5)(-9)}}{2(5)} \\ \\ x=\frac{-1 \pm \sqrt{1+180}}{10} \\ \\ \boxed{x_{1}=-1.45 \ and \ x_{2}=1.25}$

<h2>9. Answer:</h2>

J) x = 4; x=-3

<h3>Step by step explanation:</h3>

we have the equation:

$-x^2+x+12=0$

We can establish a function $k(x)=-(x^2-x-12)$ and say that we want to find the x-intercepts of this function by setting y = 0. In this exercise we'll use other method. Since this is a non-perfect square trinomial, we know that: