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3 years ago

If a triangle has a side that is 5 and a side that is 12, what is the third side

Mathematics

1 answer:

8090 [49]3 years ago

7 0

Is this multiple chose? if so I would like to see the answers. But just using my brain, I would say, 5, or 7.

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Tom determines that the system of equations below has two solutions, one of which is located at the vertex of the parabola.

xxTIMURxx [149]

Answer:

Option A: b must equal 7 and a second solution to the system must be located at the point (2, 5)

Step-by-step explanation:

The complete question is

Tom determines that the system of equations below has two solutions, one of which is located at the vertex of the parabola.

Equation 1: (x – 3)2 = y – 4

Equation 2: y = -x + b

In order for Tom’s thinking to be correct, which qualifications must be met?

A: b must equal 7 and a second solution to the system must be located at the point (2, 5).

B: b must equal 1 and a second solution to the system must be located at the point (4, 5).

C: b must equal 7 and a second solution to the system must be located at the point (1, 8).

D: b must equal 1 and a second solution to the system must be located at the point (3, 4).

step 1

Find the vertex of the quadratic equation

The general equation of a vertical parabola in vertex form is

$y=a(x-h)^2+k$

where

(h,k) is the vertex

we have

$(x-3)^{2}=y-4$

$y=(x-3)^{2}+4$

The vertex is the point (3,4)

step 2

Find out the value of b in the linear equation

we know that

If the vertex is a solution of the system of equations, then the vertex must satisfy both equations

substitute the value of x and the value of y of the vertex in the linear equation

$y=-x+b$

For x=3, y=4

$4=-3+b\\b=7$

$y=-x+7$

step 3

Find out the second solution of the system of equations

we have

$y=(x-3)^{2}+4$ -----> equation A

$y=-x+7$ ----> equation B

solve the system of equations by graphing

Remember that the solutions are the intersection points both graphs

The second solution of the system of equations is (2,5)

see the attached figure

therefore

b must equal 7 and a second solution to the system must be located at the point (2, 5)

5 0

3 years ago

Read 2 more answers

#1. 10, 13, 16, 19, ... O y = 3 + 10x y = 10 + 3x O y = 3 + 7x O y = 7+ 3x it's algebra

Gelneren [198K]

5=7

Step-by-step explanation:

6 0

3 years ago

The function y = 8.5(1.1)x models the population in thousands of a town where x is the number of years after 2000. What will be

nikdorinn [45]

Answer:

The population will be at 65.45 in 2007.

Step-by-step explanation:

I graphed the equation below to find the answer.

If this answer is correct, please make me Brainliest!

6 0

3 years ago

Sadie simplified the expression √54a^7b^3, where a>=0, as shown: √54a^7b^3= √3^2•6•a^2•a^5•b^2•b=3ab √6a^5b

Tamiku [17]

Answer:

We are to find the error made by Sadie and then find the correct simplification.

The error Sadie made is that she wrote $a^7$ as $a^2 * a^5$ instead of $a^6 * a$ .

The square root of $a^6$ is $a^3$ and so she could have further simplified.

The correct simplification is shown below:

$\sqrt{54a^7b^3} = \sqrt{2 * 3 * 3 * 3 * a^6 * a * b^2 * b} \\ \\= \sqrt{3^2 * a^6 * b^2 * 6 * a * b} \\\\= 3a^3b\sqrt{6ab}$

4 0

3 years ago

What is the simplified value of the exponential expression 64 1/4

katrin [286]

$\bf a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} 
\qquad \qquad
\sqrt[ m]{a^ n}\implies a^{\frac{ n}{ m}}\\\\
-------------------------------\\\\
64^{\frac{1}{4}}\qquad \boxed{64=2^6}\qquad (2^6)^{\frac{1}{4}}\implies 2^{6\cdot \frac{1}{4}}\implies 2^{\frac{6}{4}}\implies 2^{\frac{3}{2}}
\\\\\\
\sqrt[2]{2^3}\implies \sqrt{2^{2+1}}\implies \sqrt{2^2\cdot 2^1}\implies 2\sqrt{2}$

3 0

3 years ago