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Dvinal [7]
3 years ago
9

Type you awsner Simplify |7 - 10|

Mathematics
1 answer:
erma4kov [3.2K]3 years ago
4 0

The answer is 3, do the problem in the absolute value marks, then apply the absolute value.

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the ratio of dogs to cats at the pet store is 2:5. if there are 14 total pets how many dogs and cats are there
anygoal [31]

Hi ;-)

2x ⇒ dogs

5x ⇒ cats

2x + 5x = 14

7x = 14  / : 7

x = 2

2 · 2 = <u>4 dogs</u>

5 · 2 = <u>10 cats</u>

6 0
2 years ago
Let f(x)=x²+kx+4 and g(x)=x³+x²+kx+2k, where k is a real constant.
antoniya [11.8K]

The value of k such that the graph of f and the graph of g only intersect one is equal to 2.

The value of k such that the graph of f and the graph of g only intersect one is equal to 2. According to the image attached below, functions f(x) and g(x) intersect at point (x, y) = (0, 4) for k = 2.

<h3>How to find the value of the constant k of a system of two polynomic equations</h3>

Herein we have a system formed by two <em>nonlinear</em> equations, a <em>quadratic</em> equation and a <em>cubic</em> equation. Given the constraint that both function must only intersect once, we have the following expression:

f(x) - x² - k · x = 4       (1)

g(x) - x² - k · x = x³ + 2 · k        (2)

x³ + 2 · k = 4

x³ + 2 · (k - 2) = 0

If f and g must intersect once, then the roots must of the form:

(x - r)³ = x³ + 2 · (k - 2)

x³ - 3 · r · x² + 3 · r² · x - r³ = x³ + 2 · (k - 2)

Then, the following conditions must be met: - 3 · r · x² = 0, 3 · r² · x = 0. If x may be any real number, then r must be zero and the value of k must be:

2 · (k - 2) = 0

k - 2 = 0

k = 2

Therefore, the value of k such that the graph of f and the graph of g only intersect one is equal to 2. According to the image attached below, functions f(x) and g(x) intersect at point (x, y) = (0, 4) for k = 2.

To learn more on polynomic functions: brainly.com/question/24252137

#SPJ1

7 0
1 year ago
A basket contains eight pieces of fruit: three apples three oranges and two bananas. Jonah takes a piece of fruit at random from
oksian1 [2.3K]
The answer is 3/8 because there is 3 oranges out of eight fruit.
8 0
3 years ago
Harry and Gwen ride in a bicycle race. Harry clocks 102.62 meters per minute, and Gwen clocks 101.94 meters per minute. What is
viva [34]
The difference in their cycling speeds is 0.68 meters per minute.
8 0
3 years ago
Help all of these are confusing me
swat32

Answer:

  • b
  • b
  • a
  • b

Step-by-step explanation:

There are a few algebraic, geometric, and trig relations you are expected to remember. These come into play in this set of questions.

  • vertex form for equation of a parabola: y = a(x -h)² +k, has vertex at (h, k)
  • Sine Law relates triangle sides and their opposite angles: a/sin(A) = b/sin(B)
  • Cosine Law relates triangle sides and the angle between two of them: c² = a² +b² -2ab·cos(C)
  • SOH CAH TOA reminds you of trig relations in a right triangle
  • relationships of corresponding sides and angles in congruent and similar triangles: angles are congruent; sides are congruent or proportional.

When solving any problem, the first step is to understand what is being asked. The second step is to identify the relevant information and relationships that can help you answer.

<h3>1)</h3>

You are asked for the equation of a parabola with a given vertex. The vertex form equation will be useful. We can assume a scale factor ('a') of 1.

For vertex (h, k) = (1, -4) and a=1, the vertex form equation is ...

  y = a(x -h)² +k

  y = 1(x -1)² +(-4)

  y = (x -1)² -4

<h3>2)</h3>

You are given 3 sides and want to find an angle. The useful relation in this case is the Cosine Law. (If you wanted to use the Sine Law, you would already need to know an angle.)

<h3>3) </h3>

The mnemonic SOA CAH TOA reminds you that the cosine relation is ...

  Cos = Adjacent/Hypotenuse

The side adjacent to angle C is marked 4; the hypotenuse is marked 5. The desired ratio is ...

  cos(C) = 4/5

<h3>4)</h3>

The measure x is also the measure of side AB. The similarity statement lists those letters as the first two. It also lists the letters DE as the first two. The other given side in ΔABC is BC, corresponding to side EF in the smaller triangle. Corresponding sides are proportional, so we have ...

  AB/DE = BC/EF

  x/6 = 10/4

We can find the value of x by multiplying this equation by 6:

  x = 6(10/4) = 60/4

  x = 15

Please note that BC is the shortest side in ΔABC. This means x > 10. There is only one such answer choice. (No math necessary.)

3 0
1 year ago
Read 2 more answers
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