Select all of the segments that must be 9 centimeters long.

x² + 7x + 12 = 0

Using the factorisation method

Find two numbers such that its product gives 12 and its sum gives 7

The two numbers are 3 and 4

Replace 7 in the equation by those two numbers and then factorise

That is;

x² + 3x + 4x + 12 = 0

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

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

Either x+3 = 0 or x+4 =0

Either x = -3 or x= -4

Explanation:

A proportional relationship means that the two variables are related by a constant called constant of proportionality:

k is the constant of proportionality.

To find k we have to use the values of a and b from the table:

Answers:

• equation: ,a = 8/3 b

• constant of proportionality:, 8/3

We can solve the given expression for [tex]a=\frac{1}{3m}[/tex] by using the division method.

The given expression is [tex]12am=4[/tex].

We have to solve the given expression for [tex]a=\frac{1}{3m}[/tex].

Now we solving the expression.

[tex]12am=4[/tex]

We can easily solve the expression by seeing the value that we have to solve.

We using the division method to solve the given expression.

In the division method we divide the both side by same variable to find to value of particular variable.

For solving the expression for [tex]a[/tex] we eliminate [tex]12m[/tex].

We divide the given expression by [tex]12m[/tex] on both side

[tex]\frac{12am}{12m}=\frac{4}{12m}\\a=\frac{4}{3\times4m}\\a=\frac{1}{3m}[/tex]

Now we solve the given expression for [tex]a=\frac{1}{3m}[/tex].

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image has the answers

Given data:

The given triangle in which AD is on perpendicular bisector on BC.

In triangle ABD and ACD.

Simmilary triangle BED and triangle CED.

The fisr expression can be written as,

Substitute CED in place of BED.

Thus, the triangle ABE is congruent to trriangle ACE.

Answer:

Equation of line is given as y = mx + c, where m is the gradient and c is the y-intercept.

Parallel lines have the same gradient so equation of line d is y = -5x + c.

Substitute (2,-6) into the equation to find c.

-6 = -5(2) + c

c = 4

Hence equation of line d is y = -5x + 4.

Answer: 2

Step-by-step explanation:

The constant of proportionality is the same as the slope of the line. Using the slope formula with the points (0, 0) and (2, 4), [tex]\frac{4-0}{2-0}=2[/tex].

To get the product we multiply.

[tex] = 5 \times y \\ = 5y[/tex]

If angle 5= 42° and angle 1 = 117°

angle CDF = angle 5 + angle 1

=42° + 117°

=159°

Solution:

Given the graph;

If a vertical line intersects a curve on an xy-plane more than once then for one value of x the curve has more than one value of y, and so, the curve does not represent a function.

ANSWER: B

The rule of the slope of a line has 2 points is

A = (1, -2), B = (3, 4), C = (-2, 6)

We will take the altitude from A to the opposite side of BC

Then we will find the slope of BC first

x1 = 3 and y1 = 4. point B

x2 = -2 and y2 = 6. point C

We will substitute them in the rule above

The slope of BC = -2/5

Since the product of the slopes of the perpendicular line is -1, then if the slope of one is m, then the slope of the other will be -1/m, we reciprocal it and change its sign, then the slope of the altitude of BC should be 5/2

The form of the equation in point-slope is

y - y1 = m(x - x1)

m = 5/2

Since point A is lying on the altitude from A to BC, then

x1 = 1 and y1 = -2 point A

Substitute m and coordinates of point A in the form of the equation above

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

The equation of the altitude from A to BC is

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

Answer:

-3

Step-by-step explanation:

im assuming u want to find x

1. move all the numbers with x to the left side to make life easier

2. 5x-2x= 3x

3. 3-12= -9

4. you want the x to be solo

5. -9/3 = -3

The next nice year will be 2 nice.

The nice year that will be the first one after it is 4 nice.

It should be noted that an exponent is used to express the numbers that are either too big or too small. This is usually expressed in their powers.

Fron the information, it as stated that a year is called "nice" if its number can be represented as the difference of two powers of two.

The next nice year will be the difference which will be

= (2² - 2) × nice

= (4 - 2) × nice

= 2 nice.

The one after it will be:

= 2 × 2 nice

= 4 nice.

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Answer:

I read it's south Dakota but not sure of it.

I found it from this picture

Answer

Options A, D and E are correct.

The two functions are increasing.

The function for plan II has a greater unit rate.

The function for plan I has a greater y-intercept.

Explanation

The slope and y-intercept form of the equation of a straight line is given as

y = mx + b

where

y = y-coordinate of a point on the line.

m = slope of the line.

x = x-coordinate of the point on the line whose y-coordinate is y.

b = y-intercept of the line.

For the first plan, there's a one time investment of 15,000 dollars and subsequent monthly payments of 500 dollars.

y = 15,000 + 500x

y = 500x + 15,000

Slope = unit rate of increase = 500

y-intercept = 15,000

For the second plan, the function is just given as

y = 12,000 + 520x

y = 520x + 12,000

Slope = unit rate of increase = 520

y-intercept = 12,000

We can see that

The two functions are increasing.

The function for plan II has a greater unit rate.

The function for plan I has a greater y-intercept.

Hope this Helps!!!

Considering the definition of a line, the equation in slope-intercept of the line that passes through the point (1, 10) and has a slope of 1 is y=x+9.

A linear equation o line can be expressed in the form y = mx + b

where

In this case, you know:

Substituting the value of the slope m, the line has a form: y=1x + b or what is the same y=x +b.

Replacing the value of the point in the expression of a linear equation, the value of the ordinate to the origin b can be obtained:

10= 1×1 + b

10= 1 + b

10 -1 = b

9= b

Finally, the equation of the line is y=x +9.

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Answer:

[tex]\frac{9}{10}[/tex]

Step-by-step explanation:

multiplies of 9, 18,27,36, and 45.  Every number has a change to be selected, but these 5.  There are 50 numbers

[tex]\frac{50-5}{50}[/tex]

[tex]\frac{45}{50\\}[/tex]

[tex]\frac{9}{10}[/tex]

The first compound inequality 4x+3>15 or -6x≥12 matches the third graph, i.e x>3 or x≥-2.

The second compound inequality -8x>-24 and -10≤2x-6 matches the second graph, i.e x>3 or x≥-2.

The third compound inequality -29≤9x-2<16 matches the first graph, i.e -3≤x<2.

Given the expressions are:

a. 4x+3>15 or -6x≥12

simplify.

4x+3>15  or  -6x≥12

4x>15-3   or  x≥12/-6

4x>12      or     x≥-2

x>3          or     x≥-2

hence the graph is third.

b. -8x>-24 and -10≤2x-6

simplify.

-8x>-24 and -10≤2x-6

x>-24/-8  and  -10+6≤2x

x>3  and  -4≤2x

x>3  and  -4/2≤x

x>3  and  -2≤x

x>3 and x≥-2

hence the second graph matches.

c. -29≤9x-2<16

first take -29≤9x-2

simplify

-29+2≤9x

-27≤9x

-27/9≤x

-3≤x

now take 9x-2<16

simplify.

9x<16+2

9x<18

x<18/9

x<2

hence we get -3≤x<2

hence the first graph matches the given inequality.

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Use ''compound inequality'' in the main answer and ''graph'' in the explanation.

The diagram which best represents the hiking track of the hiker is attached below.

As time increases, speed is constant, i.e., 214 miles per hour

So, the distance increases with an increase in time.

Speed = Distance/Time

Let, Distance = D and Time = T,

214 = D / T

D = 214T

Let, D = Y coordinate, Time = X coordinate

y = 214 x→→Equation of the line passing through the origin and slope 214.

For the given situation, the equation is a linear equation and the equation will be on the y-axis.

Hence, a diagram that represents this information is:  

Correct question :

A hiker began hiking from the 0-mile mark of a trail. The hiker walked at a steady rate of 214 miles per hour. Draw the diagram which best represents this information?

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Answer the point-slope form of the equation below that represents the line that passes through the point (6, -3) and has a slope of 1/2

A linear equation can have the form

y = mx + b

The slope is m

The point-slope form is

(y- y1) = m(x -x1) (1)

the point (x1, y1) = (6, -3)

______________

Replacing in (1) the slope and the point (x1, y1)

(y- y1) = m(x -x1)

(y- (-3)) = 1/2(x -6)

y+3 = 1/2(x-6)

__________________

So, checking the options the correct answer is C

A.) y-6 = 1/2(x+3)

B.) y = 1/2x - 6

C.) y+3 = 1/2(x-6)

D.) y-2y = 12

A Linear expression is an algebraic expression that contains a variable to the power of one. 3 + y is an example.

A Coefficient is a rational number multiplied by a variable. A Rational Number is a number that can be written as the ratio, or fraction or intgers.

4 in the expresson 4x is an example of a coefficient.

Like Terms are terms whose variables and their exponent are the same. One example is 9y and -7y

Answer:

(a) 31 years

(b) 59 years

(c) 56 years

Step-by-step explanation:

In general, when reading a stem and leaf plot, we read firstly the number in the steam (middle) and then in the leaf.

Now, let's move on to the question:

(a) As we can see in the graph, the youngest actor has 31 years.

(b) The youngest actress is 21 years old and the oldest is 80.

So, the difference is 80 - 21 = 59 years.

(c) In this exercise, we have to look for actors who had the same age. That means, when evaluating the steam, we will have to find similar values in the leaf. The oldest age shared is 56 years.

The estimate (to one decimal place) of the average rate of change f is 2.3

The interval is given as

[-1, 2]

This can be rewritten as

x = -1 to x = 2

This can also be represented as

(a, b) = (-1, 2)

From the attached graph, we have

f(-1) = -5

f(2) = 2

The estimate (to one decimal place) of the average rate of change f is

Rate = [f(b) - f(a)]/[b - a]

This gives

Rate = [f(2) - f(-1)]/[2 + 1]

So, we have

Rate = [2 + 5]/[2 + 1]

Evaluate

Rate = 2.3

Hence, the average rate of change f is 2.3

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A) The second graph gives the best representation of the daily amount of calories consumed by the rat.

B)The fourth graph gives the best representation of Jane's journey.

The first slope of the graph represents the steady increase in the consumption of calories by the rat until the age of 3. The horizontal line represents the level off until the age of 6. The slopes after the horizontal line represent the increase in consumption of calories after age 6.

The first slope of the graph represents the steady increase in the distance from her home as she is traveling away from her home. The horizontal line that comes after the slope represents the time she rested at the lemonade stand. And the negative slope that comes after the horizontal line represents the decreasing distance to her home as she travels back to her home.

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This problem is an application of the Geometric mean theorem. It says that

Comment: In other words, it says that the length of BC (x) is the geometric mean between the lengths of AC and DC.

Then,

................................................................................................................................................................

Let's talk a little about the simplest radical form of a square root

The first step to finding it is to write the number within the root as a product of prime powers, such product is called its integer factorization. Let's do that for 24:

Then, the integer factorization of 24 is

Thus,

The idea now is to take out of the root all we can. The rule is that we can only take out powers of 2 (for our root is a square root). In the expression

There is only one power of 2, within 2^3. We can write it as

How are we going to take out it? We are going to take out the base of the power, which is 2 in this case. Then,

In simple terms, the simplest radical form of a root is what results after taking out the root all that can be taken out.

The percentage increase or decrease can be calculated by :

7. New = 13, Orig = 10

% change = [(13 - 10)/10] x 100 = 30% (Increase)

8. New = 3, Orig = 5

% change = [(3 - 5)/5] x 100 = -40% or 40% (decrease)

Slope intercept form:

y = mx + b

m = (y2 - y1)/(x2 - 1) = (-8 - 1)/(2 - (-1)) = -9/(2 + 1) = -9/3 = -3

m = -3

If we take one of the point, for example (2, -8) and use it on the equation with the slope we already found:

y = -3x + b

-8 = -3(2) + b

Solving for b:

-8 = -6 + b

b = -8 + 6 = -2

b = -2

Therefore, the equation is: y = -3x -2

Answer:

y = -3x -2

The coordinates of the other endpoint Q.=(2,0)

How to calculate the coordinates of the other endpoint Q ?

Given:

Midpoint = PQ = M(4,0)

One endpoint = P = [tex](x_1,y_1)[/tex]  = (6,0)

Other endpoint Q= [tex](x_2,y_2)[/tex]

We know that,

[tex]\text{Midpoint PQ}=(\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )\\\\=(\frac{6+x_2}{2} ,\frac{0+y_2}{2} )=(4,0)\\\\= > \frac{6+x_2}{2} =4\\\\= > 6+x_2= 8\\\\= > x_2=2[/tex]

[tex]\text{Similarly},\\\\\frac{0+y_2}{2} =0\\\\= > y_2=0[/tex]

So, the Other endpoint Q=(2,0)

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Let the number x.

Then the number divided by 2 gives

Subtract 3.8 from the quotient gives

Hence,

x = 21.6