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2 years ago

2. US, SV and UV are the midsegments of triangle QRT. If the length of US is 22 cm, what is the length of QT?

Mathematics

1 answer:

Rufina [12.5K]2 years ago

4 0

Answer:

2nd option, 44 cm

Step-by-step explanation:

QT = 2×SU = 2×22 = 44 cm

Since it's the midsegment, US is the half of QT

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What is the exponential form of 100000

Yanka [14]

Answer:

10^4

Step-by-step explanation:

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3 years ago

The sum of a number 1/6 of that number 2 1/2 of that number and seven is 12 1/2 find the number

Zigmanuir [339]

Answer:

Step-by-step explanation:

x = the number

x + 1/6x + 2 1/2x + 7 = 12 1/2

3 + (1/6 + 1/2)x = 12 1/2 - 7

3 + (1/6 + 3/6)x = 5 1/2

3 2/3x = 5 1/2

x = (11/2) / (11/3)

x = 11 / 2 * 3 / 11

x = 3/2

x = 1 1/2

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3 years ago

For the graphed function f(x) = (4)x − 1 + 2, calculate the average rate of change from x = 1 to x = 2.

lorasvet [3.4K]

Average rate of the function: 3

Step-by-step explanation:

The function in this problem is

$f(x)=4^{x-1}+2$

The average rate of change of a function over an interval $(x_1,x_2)$ is given by

$r=\frac{f(x_2)-f(x_1)}{x_2-x_1}$

where

$f(x_1),f(x_2)$ are the values of the function calculated in $x_1,x_2$ respectively

For the function in this problem we have:

$x_1=1$ , so

$f(x_1)=f(1)=4^{1-1}+2=4^0+2=1+2=3$

$x_2=2$ , so

$f(x_2)=f(2)=4^{2-1}+2=4^1+2=4+2=6$

So, the average rate of change is

$r=\frac{6-3}{2-1}=\frac{3}{1}=3$

Learn more about rate of change:

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4 0

3 years ago

If x+ay =b and ax-by=c Then find out x , y . (with process)

n200080 [17]

Answer:

The solution of the given system of equations is,

$x=\frac{b^2+ac}{a^2+b};\; y=\frac{ab-c}{a^2+b}$

Step-by-step explanation:

The given equations are :

x + ay = b .......(1)

ax - by = c .......(2)

We will use 'Substitution Method' to solve the given system of equations.

In this method, we will find out the value of either of the two variables that is 'x' and 'y' from one of the two equations in terms of the another variable and then substitute that value in the other equation to find the value of the another variable.

Now, we will be finding out the value of 'x' in terms of 'y' from equation (1) and then substitute it in the equation (2).

Consider the equation (1), that is,

x + ay = b ⇒ x = b - ay ........(3)

Substitute the value of 'x' from (3) in (2), we get

a(b - ay) - by = c

⇒ab - a²y - by = c

⇒-a²y - by = c - ab

⇒-y(a²+b) = c - ab

⇒y(a²+b) = ab - c

$\implies y=\frac{ab-c}{a^{2}+b}$

Now, substituting the above value of 'y' in equation (3), we get

$x=b-a(\frac{ab-c}{a^2+b})$

$\implies x=\frac{b(a^2+b)-a(ab-c)}{a^2+b}$

$\implies x=\frac{a^2b+b^2-a^2b+ac}{a^2+b}$

$\implies x = \frac{b^2+ac}{a^2+b}$

Hence, the solution of the given system of equations is,

$x = \frac{b^2+ac}{a^2+b} ;\; y = \frac{ab-c}{a^2+b}$

5 0

3 years ago

Given that B is between A and C. If AB=x, BC =2x-3, and AC = 30. Find x and bc

Artemon [7]

Answer:

x=11

BC=19

Step-by-step explanation:

AB+AC=AC this is because B is in between A and C. So now we can substitute all of the line segments, so we have

x+2x-3=30 Now you add 2x and x

3x-3=30 Now you add 3 to both sides so you can get 3x alone on one side

3x=33 Now you divide both sides by 3 so you get the x alone on one side

x=11

The next step is to substitute x to find BC.

BC=2x-3 Substitute the x with 11

BC=2(11)-3 Then multiply 2 and 11 because that is the rule with parenthesis

BC=22-3 then subrtact the 3 from 22

BC=19

You can check your work by doing AB+BC=AC

11+19=30 substitute your answers and then add them together

30=30

3 0

3 years ago