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3 years ago

Please help with this

Mathematics

1 answer:

N76 [4]3 years ago

8 0

$VWX\cong KLJ$ means that the triangles are congruent, that is exactly identical.

The order of letters is very important. Form the given congruence we can write the following ratio:

$\frac{VW}{KL} = \frac{WX}{LJ} = \frac{VX}{KJ} =1$

(notice that we do not mix the order: the first 2 letters of VWX are compared to the first 2 letters of KLJ and so on)

the ratio is one because the corresponding sides are equal.

$\frac{VW}{KL}=1\\\\ \frac{2z-1}{z+2}=1\\\\2z-1=z+2\\\\2z-z=2+1\\\\z=3$

$|VW|=2z-1=2.3-1=6-1=5$

Answer: 5 units

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What are the zeros of the quadratic function f(x) = 2x2 – 10x – 3?

Natasha2012 [34]

Answer:

$x=\frac{50+\sqrt{31}}{2},\frac{50-\sqrt{31}}{2}$ are zeroes of given quadratic equation.

Step-by-step explanation:

We have been a quadratic equation:

$2x^2-10x-3$

We need to find the zeroes of quadratic equation

We have a formula to find zeroes of a quadratic equation:

$x=\frac{b^2\pm\sqrt{D}}{2a}\text{where}D=\sqrt{b^2-4ac}$

General form of quadratic equation is $ax^2+bx+c$

On comparing general equation with b given equation we get

a=2,b=-10,c=-3

On substituting the values in formula we get

$D=\sqrt{(-10)^2-4(2)(-3)}$

$\Rightarrow D=\sqrt{100+24}=\sqrt{124}$

Now substituting D in $x=\frac{b^2\pm\sqrt{D}}{2a}$ we get

$x=\frac{(-10)^2\pm\sqrt{124}}{2\cdot 2}$

$x=\frac{100\pm\sqrt{124}}{4}$

$x=\frac{100\pm2\sqrt{31}}{4}$

$x=\frac{50\pm\sqrt{31}}{2}$

Therefore, $x=\frac{50+\sqrt{31}}{2},\frac{50-\sqrt{31}}{2}$

5 0

3 years ago

Read 2 more answers

Population Growth The population P (in thousands) of Oriando,Florida from 1980 through 2009 can be modeled by p = 130e0.0205t,wh

svetoff [14.1K]

Answer: a) 236,000.

b) 2021

Step-by-step explanation:

Given : Population Growth The population P (in thousands) of Oriando,Florida from 1980 through 2009 can be modeled by $p = 130e^{0.0205t}$ (1)

where t = 0 corresponds to 1980.

Then , for 2009

t= 2009-1980=29

a. ⇒The population of Phoenix in 2009 = $p = 130e^{0.0205(29)}$

$p = 130e^{0.5945}$

$p =130(1.81212465608)=235.57620529\approx236$

Hence, the population of Orlando in 2009 was about 236,000.

b) Substitute p= 300 in (1) , we get

$300 = 130e^{0.0205t}$

$2.3077= e^{0.0205t}$ (Divide both sides by 130)

Taking Natural log on both sides,

$\ln(2.3077) = 0.0205t\\\\\Rightarrow\ t=\dfrac{\ln(2.3077)}{0.0205}$

$t=\dfrac{0.836251357528}{0.0205}=40.7927491477\approx41$

Hence, The year Orlando will have a population of 300,000 =1980+41 =2021

6 0

3 years ago

Ivan has cut 19 pieces of reinforcing bar (rebar) that are each 1.14 meters long. What is the total length of the rebar used fo

madreJ [45]

Answer:

The total length of rebar used is 21.66 meters.

Step-by-step explanation:

Given:

Ivan had cut a reinforcing bar in 19 pieces and length of each bar is 1.14 meters.

Number of pieces = 19

Length of each piece = 1.14

We need to find the total length of reinforcing bar.

To calculate the total length we will multiply number of pieces with length of each piece.

Hence,

Total length of rebar = Number of pieces × Length of each piece = $19\times1.14 = 21..66 m$

Rounding to nearest hundred = 21.66 m

Hence the total length of reinforcing bar is 21.66 meters.

4 0

3 years ago

Results for: Timothy owns a t shirt printing buisnesses the expenses are $4 per t shirt Timothy sales each shirt for $10 he sold

topjm [15]

You have to do subtract 10 from 4 because 6 is how much we will profit from each shirt. Now, 6 times 327 is $1,962. That's how much Timothy earned of profit.

8 0

3 years ago

Using the numbers 3, 2, and 4, which of these problems would have a solution of 4?

Alexeev081 [22]

Pemdas

ok if we look at the first one
exponents first
2^3=8
2^3=8
we have
4*8/8
4*8=32
32/8=4
das is answer

the first one is the answer

7 0

3 years ago