Find the zeros

JUANITA WANTS TO PARTICIPATE IN A 20 KILOMETER BICYCLE RACE. SHE IS CONSIDERING TWO TRAINING PROGRAMS BELOW. PROGRAM A: RIDE 10

barxatty [35]

She would ride 17,343.75 kilometers in three days because the first day is 7,500 meters and the get the third day you multiply that by .75 which would be 5,625, and to get the third day you would multiply the 5,625 by .75 to get about 4,218. Lastly, you would add the three numbers together

4 0

3 years ago

The triangles are similar. What is the value of x? Enter your answer in the box. x = two right triangles. the larger triangle ha

grandymaker [24]

<h2>Answers:</h2>

These problems can be solved by the Thales’s Theorem, which states:

Two triangles are similar when they have equal angles and proportional sides

In addition, if two triangles are similar, their angles are similar as well. This means that the relation between two sides of the big triangle is equal to the relation between two sides of the small triangle, as follows:

$\frac{B}{A}=\frac{b}{a}$

Knowing this, lets’s begin with the answers:

1. For this first problem, see the first figure attached. There are shown the two triangles, and we are told both are similar, this means (according the prior explanation above) that we can use the Thale’s Theorem to find $x$ .

Therefore, we can establish a relation between two sides of the big triangle which is equal to the relation between two sides of the small triangle; in this case let’s use $B$ and $C$ for the first triangle and $b$ and $c$ for the second:

$\frac{C}{B}=\frac{c}{b}$

$\frac{6x+28}{96}=\frac{25}{24}$

Now we find $x$ :

$6x+28=\frac{(25)(96)}{24}$

$6x+28=100$

$6x=100-28$

$x=\frac{72}{6}$

$x=12$

Finally, the value of $x$ is 12 units.

2. For this problem, see the second figure attached. In order to find the values of the segments BE and EC, we will use two sides of each triangle (ABE and DCE) according to the Thale’s Theorem:

For the segment BE:

$\frac{BE}{10}=\frac{x+3}{4}$

$BE=\frac{(x+3)(10)}{4}$

Simplifying:

$BE=\frac{5}{2}(x+3)$ >>>>>This is the length of the segment BE

For the segment EC:

$\frac{EC}{4}=\frac{2x+10}{10}$

$EC=\frac{(2x+10)(4)}{10}$

Simplifying:

$EC=\frac{4}{5}(x+5)$ >>>>>This is the length of the segment EC

3. For this problem, see the third figure attached:

$\frac{12 inches}{8 inches}=\frac{x}{7 inches}$

Solving for $x$ :

$x=\frac{(12 inches)(7 inches)}{8 inches}$

Finally:

$x=10.5 inches$ >>>>>This is the height of the smaller sail

4. For this problem, see the fourth figure attached.

$\frac{80 inches}{45 inches}=\frac{x}{40 inches}$

Solving for $x$ :

$x=\frac{(80 inches)(40 inches)}{45 inches}$

$x=71.11 inches$ >>>>>This is the height from the floor to the son's hand

6 0

3 years ago

List all the sets that the number -6 belongs to.

liberstina [14]

Answer:

Integers

Step-by-step explanation:

4 0

4 years ago

If neither a nor b are equal to zero, which answer most accurately describes the product of (a + bi)(a - bi)?

Scrat [10]

Answer: the correct option is

(D) The imaginary part is zero.

Step-by-step explanation: Given that neither a nor b are equal to zero.

We are to select the correct statement that accurately describes the following product :

$P=(a+bi)(a-bi)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

We will be using the following formula :

$(x+y)(x-y)=x^2-y^2.$

From product (i), we get

$P\\\\=(a+bi)(a-bi)\\\\=a^2-(bi)^2\\\\=a^2-b^2i^2\\\\=a^2-b^2\times (-1)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~[\textup{since }i^2=-1]\\\\=a^2+b^2.$

So, there is no imaginary part in the given product.

Thus, the correct option is

(D) The imaginary part is zero.

3 0

3 years ago

Which expression is equivalent to 4^-5?

Basile [38]

Since there is a negative exponent, you need to first convert that into a positive exponent which is going to be 1/4^5
Then, we can find out the answer by simply breaking apart the exponents into 5 groups of 4.
1/(4)(4)(4)(4)(4)
Answer: B

7 0

4 years ago

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