Solve the prime factorization of these numbers using the factor tree method


1. 48 2. 356 3. 1 240

Step-by-step explanation:

tan a = 9.6/7.2=4/3

a = 53.13

Answer:

  (x, y) = (-6, -10)

Step-by-step explanation:

Pick a variable whose coefficient you want to be zero in the sum. Note the two coefficients of that variable in the two equations. Write the second coefficient in the first box, and the opposite of the first coefficient in the second box.

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If you want to eliminate x-terms, the x-coefficients are -2 and -3. Write -3 in the first box and +2 in the second box.

  -3(-2x +2y = -8)   ⇒   6x -6y = 24

  +2(-3x +y = 8)      ⇒   -6x +2y = 16

Added together, the resulting equation is ...

  0x -4y = 40

  y = -10 . . . . . . . divide by -4

__

If you want to eliminate y-terms, the y-coefficients are 2 and 1. Write 1 in the first box, and -2 in the second box.

  1(-2x +2y = -8)   ⇒   -2x +2y = -8

  -2(-3x +y = 8)    ⇒   6x -2y = -16

Added together, the resulting equation is ...

  4x +0y = -24

  x = -6 . . . . . . . . divide by 4

__

Now, you know the solution is (x, y) = (-6, -10).

_____

Additional comment

It does not matter which is the first equation. You can swap the two equations and still achieve the desired results. Also, if the coefficients have a common factor, you can divide that out. As you may have noticed, the arithmetic is a little easier if one of the chosen coefficients is 1 or -1.

If you're combining the equations using addition, as we have done here, then one of the coefficient multipliers must be negated, as we have described. If you're combining the equations using subtraction, then you can preserve the original signs of the coefficients (or change them both).

Answer:

b=3.5

Step-by-step explanation:

Answer:

3.5x-1

Step-by-step explanation:

Solving:

4bx = 14

Solving for variable 'b'.

Move all terms containing b to the left, all other terms to the right.

Divide each side by '4x'.

b = 3.5x-1

Simplifying

b = 3.5x-1

Answer: 2/3 is the smallest ratio.

Step-by-step explanation:

Answer:

20$ is the answer of your question

Answer:

y = -5/2x - 4

Step-by-step explanation:

When given a point and a slope, we use slope-intercept formula:

y - y1 = m (x - x1)

m = slope  point: (-2,1)

y - y1 = m (x - x1)

y - 1 = -5/2 (x - (-2))

y -1 = -5/2x - 5

 + 1          + 1

y = -5/2x - 4

To check our answer, I attached the graph.

Hope this helps!

Step-by-step explanation:

For example, to find the probability that a prime is selected from 1 to 10 requires us to divide the number of primes from 1 to 10 by 10. The numbers 2, 3, 5, 7 are prime,

hope this helps you

please mark me brainliest

Answer:

multiply both sides by 4

Step-by-step explanation:

Answer:

- 3/2 is the answer:)

Step-by-step explanation:

Move the constant to the right

Calculate

Divide by both sides

Hope this helps!

Answer:

3

Step-by-step explanation:

[tex]x=\sqrt{2x+3}[/tex]

square both sides:   [tex]x^2=2x+3[/tex]

subtract [tex]2x + 3[/tex] from both sides:  [tex]x^2-2x-3=0[/tex]

factorize:  [tex](x-3)(x+1)[/tex]

Therefore, [tex]x=3 \ and \ -1[/tex]

Substitute found values of [tex]x[/tex] back into original equation:

[tex]3=\sqrt{2\times3+3}=3 \ \ \checkmark[/tex]

[tex]-1=\sqrt{2\times-1+3}=1[/tex]  incorrect!

So answer is [tex]x = 3[/tex] only

Answer:

I think standard form would be best because it is simplest.

Step-by-step explanation:

hope this helps

Answer: Intercept Form

Step-by-step explanation:

There are three methods for determining the minimum value of a quadratic equation. Each of them can be useful in determining the minimum. The first way is by using a graph. You can find the minimum value visually by graphing the equation and finding the minimum point on the graph. The y-value of the vertex of the graph will be the minimum. This is especially easy when you have a graphing calculator that can do most of the work  for you.

Step-by-step explanation:

the general point-slope form is

y - y1 = m(x - x1)

with (x1, y1) being a point on the line, and m being the slope (the incline of the line).

we have the point. we can pick one from the 2 choices, I typical go for the one with smaller values. so, I will use (-3, 1).

now we need to calculate the slope.

the slope is the ratio "y coordinate change / x coordinate change" when going from one point on the line to another.

so, for our 2 points we see

x changes by +1 (from -4 to -3).

y changes by +2 (from -1 to +1).

and the slope is +2/+1 = 2

therefore our equation is

y - 1 = 2(x - -3)

or simplified

y - 1 = 2(x + 3)

Answer:

2

Step-by-step explanation:

A fraction is undefined when the denominator is 0 because division by 0 is undefined.

When x=2, we have 3x-6=0 and the denominator is undefined.

Answer:

[tex]y = 3x + 12[/tex]

Step-by-step explanation:

The rate of change is represented as the slope.

The problem is asking for a slope that is equal to 3.

y=6x-3 is incorrect, the equation is simplified and the slope is 6.

3y=2x+5 is incorrect, the slope is 2 and the equation isn't simplified.

y=3x+12 is correct, the equation is simplified and it's showing the correct slope.

3) 60

Step-by-step explanation:

718 ÷ 9 = 79.78

So, if you round to the nearest whole number its about 80, the closest answer from your options is 60 so I think the best estimate is number three: 60.

Answer:

Step-by-step explanation:

1) find slope

y2-y1/x2-x1

10-9 divided by 8 - 4

1/4 = slope

1/4 = y

b = y-int

Answer:

49x²+126x+81

Step-by-step explanation:

Area of any square is length²

If the length given is 7x+9, we can square this to find out what represents the area:

[tex](7x+9)^{2}[/tex]

[tex](7x+9)(7x+9)[/tex]

[tex]49x^{2} +63x+63x+81[/tex]

[tex]49x^{2} +126x+81[/tex]

Answer:

49x² + 126x + 81

Step-by-step explanation:

A = a²

Since a = 7x + 9

=> A = (7x+9)²

= 49x² + 126x + 81

Note: (a+b)² = a² + 2ab + b²

Answer:

2:3 or 2/3

this is a ratio problem

Answer:

2:3?

Step-by-step explanation:

I'm kinda guessing from the question u gave cuz it doesn't really have a lot of information

-0.1

Explanation:

-3/3(a+c[b+5]-[-6+a])

-3/3(1-4[-6+5]-[-6+1])

-3/3(1-4[-1]-[-5])

-3/3(1 + 4 + 5)

-3/3(10)

-3/30

-0.1

Hope this helps!

Answer:

x=30

Step-by-step explanation:

i actually dont know but thnks for the points BTW

Answer:

  x = 4

Step-by-step explanation:

In this geometry, all of the right triangles are similar. That means the ratio of short side to long side is the same for all of the right triangles:

  x/10 = 10/25

  x = 100/25 = 4 . . . . . multiply by 10

_____

Additional comment

You may notice that the two segments of the hypotenuse, x and 25, have a product that is the square of the altitude. Another way to say this is that the altitude is the geometric mean of the segments x and 25.

There are two other geometric mean relations in this geometry:

  the short side at the right is the geometric mean of x and (x+25).

  the long side at the bottom is the geometric mean of 25 and (25+x).

That is, the segments that intersect the hypotenuse are the geometric mean of the two segments of the hypotenuse that they meet.

  geometric mean of A and B is √(AB)

Answer:

42 ft minimum.

Step-by-step explanation:

you need to place the ladder 12ft from the house and it is 30 ft above the ground.

Answer:

IVE BEEN LOCKED OUT OF MY HOUSE BEFORE.

Step-by-step explanation:

42 ft

Answer:

Compound interest

$34633.25

Step-by-step explanation:

Everything starts of at 100% and the rate of interest is 9.5% so we add them on=109.5%

Now we want this percentage as a decimal so we divide by 100 = 1.095 this our multiplier

Then get the original amount that you borrowed = 6000 times by the multipler=1.095 to the power of number of years so

6000 multipled by 1.095 to the power of 5

Giving me $34633.25

Answer:

The numbers are 4 and 6

Step-by-step explanation:

Let:

we know that

[tex]x^{2} =(x+2)+10[/tex]

solve for x

[tex]x^{2} -x-12=0[/tex]

We can use the quadratic formula for quadratics in the form [tex]ax^{2} +bx+c=0[/tex]

[tex]x= \frac{-b(+/-)\sqrt{b^{2} -4ac}}{2a}[/tex]

to give us an answer of 4 and -3

Since the question states positive and even we use 4 and that gives us 6 as the other answer
4 and 6

Answer:

4 and 6

Step-by-step explanation:

x = smaller integer

x+2 = larger integer

x² = 10 + (x + 2)

x² = x + 12

x² - x - 12 = 0

factors are:

(x-4)(x+3) = 0

x-4=0;  x = 4

x+3=0;  x = -3

Since the question states the numbers are even and positive we use only the 4 and the next consecutive even integer is 6

Answer

Its already in order: 1/7 4/14 2/3

Step-by-step explanation:

Because the common denominator for all three is 42, which turns the fractions to 6/42, 12/42, and 28/42 making it easier to place in order

ANSWER:

1/7,4/14,2/3.......................

Answer:

x=20

Step-by-step explanation:

These these angles are adjacent

because they share a vertex and side. They also form a linear pair meaning they add up to 180 degrees...

x+20+7x=180

Combine like terms

8x+20=180

Subtract 20 from both sides

8x=160

Divide both sides by 8

x=20

A translation 4 units right and 2 units up is done followed by a dilation of 3/2.

Transformation is the movement of  point from its initial location to a new location. Types are rotation, translation, reflection and dilation

Translation is the movement of point up, down, left or right. Dilation is the increase or decrease in the size.

To map circle B onto circle A, first a translation 4 units right and 2 units up is done followed by a dilation of 3/2.

Find out more on Transformation at: https://brainly.com/question/1462871

Answer: All 3 Parts

Part A :

Part B : A translation 4 units right and 2 units up is done followed by a dilation of 3/2

Part C : the two circles are equation congruent

Step-by-step explanation:

Answer:

25%

Step-by-step explanation:

Multiply:

3 × 5 = 25%

Hope this helps!! <3

Answer:

[tex]g(-3)=-2[/tex]

Step-by-step explanation:

Substitute g(-3) into the function:

[tex]g(-3)=2(-3)+4[/tex]

Multiply:

[tex]g(-3)=-6+4[/tex]

Add:

[tex]g(-3)=-2[/tex]

Answer: -2

Step-by-step explanation:

plug g(x) with -3 so it would be 2(-3) + 4 and then simply and add so 2(-3) equals -6 + 4 is -2

Trigonometric functions are the ratio of the different sides of a right-angled triangle. We can say that the coordinates of the point are (-77, 36).

Trigonometric functions are the ratio of the different sides of a right-angled triangle.

[tex]\rm Sin \theta=\dfrac{Perpendicular}{Hypotenuse}\\\\\\Cos \theta=\dfrac{Base}{Hypotenuse}\\\\\\Tan \theta=\dfrac{Perpendicular}{Base}[/tex]

where perpendicular is the side of the triangle which is opposite to the angle, and the hypotenuse is the longest side of the triangle which is opposite to the 90° angle.

Given to us

[tex]Sin(\theta) = \dfrac{-77}{85}[/tex]

[tex]Cos(\theta) = \dfrac{36}{85}[/tex]

[tex]Tan(\theta) = \dfrac{-77}{36}[/tex]

As we know that the Tangent(Tan) is the ratio of perpendicular and base. therefore, we can write the function as,

[tex]\rm Tan(\theta) = \dfrac{Perpendicular}{Base} = \dfrac{-77}{36}[/tex]

therefore, the length of the perpendicular is 77, while the length of the base is 36.

As given to us that the value of sin is negative, therefore, the perpendicular will be on the negative side of the y-axis. While the value of cos is positive, therefore, the base will be on the positive side of the x-axis.

Thus, we can say that the coordinates of the point are (-77, 36).

Learn more about Trigonometric functions:

https://brainly.com/question/6904750

Answer:

B

Step-by-step explanation: just did it gang 100%

Answer:

  CD = 3 -√3

Step-by-step explanation:

The ratio of leg lengths in a 30°-60°-90° triangle is ...

  1 : √3 : 2

The longest leg of ΔABD is 2√3, so we must multiply all of these ratio values by √3 to see the actual lengths of the triangle sides.

  AB : BD : AD = 1 : √3 : 2 = √3 : 3 : 2√3

That is ...

  AB = √3

  BD = 3

__

The lengths of the legs in isosceles right triangle ABC are the same, so ...

  BC = AB = √3

Then the length of interest is ...

  CD = BD -BC

  CD = 3 -√3 . . . . . . . a=3, b=-1

Answer:

y = −x + 1

y = −3/5x + 3