Which triangles are similar to ABE?

Solve the following system of equations by substitution. Show all steps.

Alinara [238K]

Answer:

Given system of equations:

$\begin{cases}f(x)=-x^2+2x+3\\g(x)=-2x+3\end{cases}$

To solve by substitution, equate the equations and solve for x:

$\begin{aligned}f(x) & = g(x)\\\implies -x^2+2x+3 & = -2x+3\\-x^2+4x & = 0\\x^2-4x & = 0\\x(x-4) & = 0\\\implies x & = 0\\\implies x-4 & = 0 \implies x=4\end{aligned}$

Therefore, the x-values of the solution are $x = 0$ and $x = 4$ .

To find the y-values of the solution, substitute the found values of x into the functions:

$f(0)=-(0)^2+2(0)+3=3$

$g(0)=-2(0)+3=3$

$f(4)=-(4)^2+2(4)+3=-5$

$g(4)=-2(4)+3=-5$

Therefore, the solutions to the given system of equations are:

$(0, 3)$ and $(4, -5)$

4 0

2 years ago

Please please help me please help please please help me please help please

AVprozaik [17]

Answer:

Perimeter is 17.07

Step-by-step explanation:

We know that DF = EF = 5 cm, since D and E are the midpoints of AC and AB, both of which are 10 cm in length.

We need to use the Pythagorean theorem to get the length of DE.

$DE = \sqrt{5^{2} +5^{2}}=\sqrt{50} = 7.07\\$

So the perimeter of DEF is 5 + 5 + 7.07 = 17.07

5 0

3 years ago

1.8 divided by 3 please.

lidiya [134]

Answer: 0.6 is the answer

8 0

2 years ago

A bank loaned out $19,000, part of it at the rate of 9 % per year and the rest at 19 % per year. If the interest received in o

VMariaS [17]

Answer: $11100 was loaned at 9%

Step-by-step explanation:

Let x represent the amount that the

bank loaned out at the annual rate of 9%.

Let y represent the amount that the

bank loaned out at the annual rate of 19%.

The bank loaned out $19,000, part of it at the rate of 9% per year and the rest at 19% per year. It means that

x + y = 19000

The interest on $x after 1 year would be

9/100 × x = 0.09x

The interest on $y after 1 year would be

19/100 × y = 0.19y

If the interest received in one year totaled $2500. It means that

0.09x + 0.19y = 2500- - - - - - - - - 1

Substituting x = 19000 - y into equation 1, it becomes

0.09(19000 - y) + 0.19y = 2500

1710 - 19000y + 0.19y = 2500

- 0.09y + 0.19y = 2500 - 1710

- 0.1y = - 790

y = - 790/- 0.1

y = $7900

x = 19000 - y = 19000 - 7900

x = $11100

7 0

3 years ago

Tan^2x+sec^2x=1 for all values of x. <br> true or false?

amid [387]

This is not true.

$\tan^2x+\sec^2x=\dfrac{\sin^2x}{\cos^2x}+\dfrac1{\cos^2x}=\dfrac{1-\cos^2x+1}{\cos^2x}=2\sec^2x-1$

$2\sec^2x-1=1\implies\sec^2x=1\implies\sec x=\pm1\implies x=n\pi$

where is $n$ is any integer. So suppose we pick some value of $x$ other than these, say $x=\dfrac\pi4$ . Then

$\tan^2\dfrac\pi4+\sec^2\dfrac\pi4=1+2=3\neq1$

5 0

3 years ago

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