MATHEMATICS MIDDLE SCHOOL

2 pointsFind the x-and y-intercepts of the following equation: 5x – 3y = 15
O (15,0) and (0, -15)
0 (-5,0) and (3,0)
0 (0.-5) and (3,0)
0 (0.3) and (-5,0)

Answers

Answer 1

Answer:

The x - intercept of 5x - 3y = 15 is (3, 0)

The y -intercept of 5x - 3y = 15 is (0, -5)

Solution:

Given equation is 5x - 3y = 15

To find: x - intercept and y -intercept

The x intercept is the point where the line crosses the x axis. At this point y = 0

The y intercept is the point where the line crosses the y axis. At this point x = 0.

Finding x - intercept:

To find the x intercept using the equation of the line, plug in 0 for the y variable and solve for x

So put y = 0 in given equation

5x - 3(0) = 15

5x = 15

x = 3

So the x - intercept is (3, 0)

Finding y - intercept:

To find the y intercept using the equation of the line, plug in 0 for the x variable and solve for y

So put x = 0 in given equation

5(0) - 3y = 15

-3y = 15

y = -5

So the y - intercept is (0, -5)

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Solve each equation by completing the square. If necessary, round to the nearest hundredth.19. X²-18x=19
20. 4 a²+8a-20=0

Answers

$x^2-18x=19\n\nx^2-2x\cdot9+9^2-9^2=19\n\n(x-9)^2-81=19\n\n(x-9)^2=19+81\n\n(x-9)^2=100\iff x-9=\pm√(100)\n\nx-9=-10\ \vee\ x-9=10\n\nx=-10+9\ \vee\ x=10+9\n\nx=-1\ \vee\ x=19$

$4a^2+8a-20=0\ \ \ \ /:4\n\na^2+2a-5=0\n\na^2+2a\cdot1+1^2-1^2=5\n\n(a+1)^2-1=5\n\n(a+1)^2=5+1\n\n(a+1)^2=6\iff a+1=\pm\sqrt6\n\na=-\sqrt6-1\ \vee\ a=\sqrt6-1\n\na\approx-3.45\ \vee\ a=\approx1.45$

Complete the pattern 5,10,30,60,180, ?

Answers

Let

$a1=5 \n a2=10\n a3=30\n a4=60\n a5=180$

we know that

$(a2)/(a1) = (10/5)=2 \n a2= a1*2$

$(a3)/(a2) = (30/10)=3 \n a3= a2*3$

$(a4)/(a3) = (60/30)=2 \n a4= a3*2$

$(a5)/(a4) = (180/60)=3 \n a5= a4*3$

The pattern is times two then times three then times two then times three

the sixth term will be

$a6=a5*2$

$a6=180*2=360$

therefore

the answer is

$360$

540 is the answer because the doubled the first number to get the second number and multiplyed that by 3 to get the third number

1.Find the exact solution to the equation.(2 points)

log base four of x equals two.

Answers

Answer:

x = 16

Step-by-step explanation:

The equation is $\log_(4) x = 2$

Now, converting this logarithmic equation into exponential equation, we get

$x = 4^(2) = 16$ (Answer)

Alternate solution:

Given, $\log_(4) x = 2$

⇒ $\log_(4)x = 2\log_(4)4$

{Since, we know that $\log_(a)a = 1$ }

⇒ $\log_(4)x = \log_(4)4^(2) = \log_(4)16$

{Since, $a\log b = \log b^(a)$ is a property of logarithm}

Cancelling log from both sides we get,

⇒ x = 16 (Answer)

Answer:

$x = 8^4$

Step-by-step explanation:

hey there,

< Here is what is given:

㏒ $_(8) x=4$

There's actually a lot of different ways you can remember this but the way I remember this is x is equal to 2nd to the power of last.

So 8 is the 2nd (since log is first), 4 is last (very last thing in the equation).

x = 8^4

You can use any of your own ways to remember this, but this is just my personal way. :) >

Hope this helped! Feel free to ask anything else.

Which equation is a point slope form equation for line AB ?y+2=2(x+3)
y−3=2(x−2)
y−5=2(x−6)
y−6=2(x−5)

A graph with a line running through point A, with coordinates (3, 2), and point B, with coordinates (5, 6)

Answers

Answer: $y-6=2(x-5)$

Step-by-step explanation:

The point-slope form of equation of s line that passes through two points (a,b) and (c,d) is given by :-

$(y-d)=(d-b)/(c-a)(x-c)$

Given : A graph with a line running through point A, with coordinates (3, 2), and point B, with coordinates (5, 6).

Then, the a point slope form equation for line AB will be :-

$(y-6)=(6-2)/(5-3)(x-5)$

$(y-6)=(4)/(2)(x-5)$

$y-6=2(x-5)$

Hence , equation is a point slope form equation for line AB will be :

$y-6=2(x-5)$

Answer:

Answer choice D:

y - 6 = 2(x - 5)

Step-by-step explanation:

This question is basically asking you to find the point-slope form equation for a line going through the points (3, 2) and (5, 6).

As you can tell by the name, point-slope form needs both a point that the line goes through and the slope of the line.

You can find the slope of the line by using the slope formula since you have two points that the line goes through.

Slope formula: $m=(y_2-y_1)/(x_2-x_1)$

Substitute in the points A and B into the formula.

$m=(6-2)/(5-3) \rightarrow(4)/(2) \rightarrow 2$

The slope of this line is 2.

Now since we have the slope and a point of the line, we can plug this into the point-slope form equation, which is y - y1 = m(x - x1).

We will be using one of the points (I will be using point A) to substitute the coordinates into y1 and x1, and using the slope to substitute into m.

Substitute point A's coordinates and the slope of the line into the point-slope form equation.

y - (2) = 2(x - (3))

I always put parentheses around the numbers I substitute into an equation to see exactly what is being plugged in, but now you can remove them to find your answer.

y - 2 = 2(x - 3)

Now, since none of the answer choices do not fit with the answer we have found, we can use the other point coordinate-- point B.

Substitute point B and the slope 2 into the equation.

y - (6) = 2(x - (5))

Remove the parentheses.

y - 6 = 2(x - 5)

There is an answer choice for this answer we have found, answer choice D.

By the way, both of the equations we found: y - 2 = 2(x - 3) and y - 6 = 2(x - 5) will yield the same answer in the end so don't worry if one of the points don't work if you have a multiple choice like this question.

you have $550 in a savings account that earns 3% simple interest each year . how much will be in your account in 10 years?