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Charra [1.4K]
3 years ago
12

What is the value of x? ​

Mathematics
1 answer:
neonofarm [45]3 years ago
7 0

Answer:

12

Step-by-step explanation:

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set the equation up for "Eight less than the square of a number is the same as adding the number and four"
TEA [102]
X^2-8 = x+4 is your answer!
5 0
3 years ago
a boy is standing on a pole of height 14.7m throws a stone upwards. it moves in a vertical line slightly away from the pole and
fomenos

Answer:

The time taken for the upward motion is 1 second. The same time is taken for the downward motion

It reaches a maximum height of 4.9 meters.

Step-by-step explanation:

The equation of motion is:

x(t) = -4.9t^{2} + 9.8t

Since the term which multiplies t squared is negative, the graph is concave down, that is, x increases until the vertex, where it reaches it's maximum height, then it decreases.

Vertex of a quadratic equation:

Quadratic equation in the format x(t) = at^{2} + bt + c

The vertex is the point (t_{v}, x(t_{v})), in which

t_{v} = -\frac{b}{2a}

In this question:

x(t) = -4.9t^{2} + 9.8t

So a = -4.9, b = 9.8

Vertex:

t_{v} = -\frac{9.8}{2*(-4.9)} = 1

The time taken for the upward motion is 1 second.

x(t_{v}) = x(1) = 9.8*1 - 4.9*(1)^{2} = 4.9

It reaches a maximum height of 4.9 meters.

Downward motion:

From the vertex to the ground.

The ground is t when x = 0. So

-4.9t^{2} + 9.8t = 0

4.9t^{2} - 9.8t = 0

4.9t(t - 2) = 0

4.9t = 0

t = 0

Or

t - 2 = 0

t = 2

It reaches the ground when t = 2 seconds.

The downward motion started at the vertex, when t = 1.

So the duration of the downward motion is 2 - 1 = 1 second.

5 0
3 years ago
You order the hardcover book shown from a website that offers free shipping on orders of $25 or more. Write and solve an inequal
jenyasd209 [6]

Answer:

If P= price of the hardcover book, then

We have to spend $25-P, if P<$25; or $0 if P>= $25

Step-by-step explanation:

Lets call P the price of the hardcover book, in $. We can suppose that P is less than 25, otherwise we shoudnt spend on anything else to get the free shipping. If X is the amount that we have to spend to reach 25, then we get that P+X = 25. If P is known, we can obtain X by substracting P in both sides, therefore

X = 25-P

We conclude that if the price of the book P is less than 25, then we have to spend $25-P. Otherwise we have to spend 0.

6 0
3 years ago
1. (2 points) Solve each equation and write the answer on the line
BARSIC [14]
Eighteen tens < 21 × (5+5)

Hope this helps!
7 0
3 years ago
Given a term and the common difference, find the explicit formula.<br> 8. a(19) = 135<br> d = 15
Rasek [7]

The explicit formula is a(n) = 15(n – 10)

<u>Solution:</u>

Given, a term a(19) = 135 and common difference d = 15

We have to find the explicit formula.

Now, we know that, a(n) = a + (n – 1)d where a(n) is nth term, a is first term, d is common difference,

So, for a(19)  

\begin{array}{l}{\rightarrow a(19)=a+(19-1) 15} \\\\ {\rightarrow 135=a+18 \times 15} \\\\ {\rightarrow a=135-270} \\\\ {\rightarrow a=-135}\end{array}

Now, we know that, an explicit formula is an expression for finding the nth term,  

So, in our problem, expression for finding nth term is a + (n – 1)d  

\begin{array}{l}{\rightarrow-135+(n-1) 15} \\\\ {\rightarrow-135+15 n-15} \\\\ {\rightarrow 15 n-150} \\\\ {\rightarrow 15(n-10)}\end{array}

Hence, the explicit formula is a(n) = 15(n – 10).

7 0
3 years ago
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