Carol wants to make a square garden with 81 plants. Each row and column will have the same number of plants. How many plants will be in each row and column?

By using algebra properties, the quadratic equation y = x² - 4 contains the roots x = - 2 and x = 2.

In this problem we need to derive the quadratic equation that contains two roots: r₁ = - 2, r₂ = 2. We need to replace all roots in the factor form of the quadratic equation and expand it by algebra properties. First, replace the roots of the factor form of the quadratic equation:

y = (x - r₁) · (x - r₂)

y = (x + 2) · (x - 2)

Second, expand the expression derived in the previous step by algebra properties:

y = (x + 2) · x - (x + 2) · 2

y = x² + 2 · x - 2 · x - 4

y = x² - 4

Third, write the resulting expression:

y = x² - 4

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Answer:

Is this an arithmetic sequence?

Yes.

Is there a common difference and if so, what is it?

Yes, there is a common difference : 1

The common difference is 1

Option B, x = -5 is correct answer, x = -5 is the counter example to the student's conjecture.

What is inequality?

A mathematical phrase in which the sides are not equal is referred to as being inequal. In essence, a comparison of any two values reveals whether one is less than, larger than, or equal to the value on the opposite side of the equation.

Given inequality in the question is:

x +5 < x²

We will check each option given I question by putting value of x,

putting x = -1/5

x + 5 < x²

-1/5 + 5 < (-1/5)²

24/5 < 1/25

4.8 < 0.04

This is wrong inequality , Therefore, x is not equal to -1/5

putting x = -5

x + 5 < x²

-5 + 5 < (-5)²

0 < 25

This is satisfying the inequality ,

Therefore, x is equal to -5

Hence, correct answer is x = -5

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Answer:

I can use the given (algebraic expression) 24c+12 to find the total cost of the order

The expression has two (terms). They are 24c and 12

In 24c the number 24 is the (coefficient) and the letter c is the (variable).

The term 24c represents a (product)

To find the total cost of the order I can (evaluate) the given expression

I have to (substitute) the given value for the variable then I can follow the (order of operations) to simplify the expression

24c+12

24(6)+12

144+12

156

The total cost is 156

Hope this helps :)

Answer:

Q1 = 6.45f/s

Q2 = 0.633 times

Q3 = 0.107 miles

Step-by-step explanation:

Q1: Since

4.4 miles = 1 hour

and

1 mile = 5,280 feet

1 hour = 3600 seconds

Then 4.4 miles

= 5,280 feet × 4.4

= 23,232 feet / 3600 seconds

= 6.453f/s

= 6.45f/s

Q2: Wing beat per minute

= 38 ÷ 60

= 0.633 times

Q3: Miles per minute

Since 6.4 miles = 1 hour,

6.4 miles = 1 × 60

6.4 miles = 60 minutes

x miles = 1 minute

= 6.4/60

= 0.107 miles

Answer:

The number to the ration

Step-by-step explanation:

After being painted red on all six faces, a hardwood cube with nn units on each side is chopped into n3n 3-unit cubes. The unit cubes have exactly one-fourth of their faces be red, therefore nn equals 4.

On each face of the large wooden cube, there are tiny faces that have been painted red.

There are few faces overall because each unit cube has faces.

Given that one-fourth of the little faces are red,

[tex]6n^2/6n^3[/tex] [tex]= 1/4[/tex]

[tex]1/n = 1/4[/tex]

[tex]N=4[/tex]

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Answer:

82 and 2/4 (if it was 30 days)

Step-by-step explanation:

you turn the fraction into a decimal and multiply it by the certain number of what you need to figure out.

The value of y is 11.

That quadrilateral in which opposite sides are parallel is called a parallelogram.

Thus, a parallelogram is always a quadrilateral but a quadrilateral can or cannot be a parallelogram.

Given that Parallelogram ABCD is a rectangle.

Consider that AC and BD are opposite sides. In a parallelogram, we know that opposite sides are congruent which means:

AC = BD

2y + 7 = 3y - 4

Solving;

2y - 3y = -4 - 7

-y = -11

y = 11

Hence, the value of y is 11.

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We have an absolute value function that opens upwards. The interval where it is decreasing only is:

(-∞, 2)

All absolute value equations of the form:

y = |x - a| + b

have graphs that open upwards, and a vertex in the point (a, b).

While ones of the form:

y = -|x - a| + b

have graphs that open downwards, and again, a vertex in the point (a, b).

In this case we have one that open upwards:

h(x)=|x-2|+6

With a vertex at (2, 6)

The function will be decreasing on the left side of the vertex, so the interval where the function is only decreasing is:

(-∞, 2)

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Part A

The equation that shows the statement is

2N + 20 = 4N - 40

Part B

The value of N = 30

The number that he is thinking = N

Twice (N+10) = 2(N+10)

= 2N + 20

Four times (N-10) = 4(N - 10)

= 4N - 40

Twice (N+10) is the same as four times (N-10)

The equation that represent the given statement is

2N + 20 = 4N - 40

Part B

Solve the equation

2N + 20 = 4N - 40

4N - 2N = 20 + 40

2N =  60

N = 60/2

Divide the terms

N =30

Hence,

Part A

The equation that shows the statement is

2N + 20 = 4N - 40

Part B

The value of N = 30

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If sum of the measures of the angles in the triangle is 180 degrees then

measures of each angle is 60 degrees.

A triangle is a three-sided polygon that consists of three edges and three vertices.

Given,

The sum of the measures of the angles in the triangle is 180 degrees

By angle sum property,  sum of the measures of the angles in the triangle is 180 degrees

Let the measure of angle be x

x+x+x= 180 degrees

3x=180

Divide both sides by 3

x=180/3

x=60

Hence each angle measures 60 degrees.

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With the help of angles we can say that ∠HJI=∠FJG.

Acc to our question-

Hence, ∠HJI≅∠FJG are equal and congruent.

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Answer:

- 0.5 ≤ x ≤ 3.5

Step-by-step explanation:

since both ends of the interval are closed circles. This indicates that x can equal both - 0.5 and 3.5 and the values between , then

- 0.5 ≤ x ≤ 3.5

The inequality shown on the number line is -0.5 ≤ x ≤ 3.5.

Given is a number line where a value starts from -0.5 and end at 3.5, we need to write down the inequality shown on the number line,

To write down the inequality shown on the number line starting from -0.5 and ending at 3.5, we need to determine the range of values represented by the line segment.

The left endpoint of the line segment is -0.5, which means the value represented by that point is greater than or equal to -0.5.

We can express this as:

x ≥ -0.5

The right endpoint of the line segment is 3.5, which means the value represented by that point is less than or equal to 3.5.

We can express this as:

x ≤ 3.5

Combining these two inequalities, we have:

-0.5 ≤ x ≤ 3.5

This inequality represents all the values on the number line between -0.5 and 3.5, inclusive.

Hence the required inequality is -0.5 ≤ x ≤ 3.5.

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The ratio of gallons of blue paint to gallons of yellow paint will NOT make the same shade of green paint 4:9.

A ratio is a comparison between two amounts that is calculated by dividing one amount by the other. The quotient a/b is referred to as the ratio between a and b if a and b are two values of the same kind and with the same units, such that b is not equal to 0. Ratios are represented by the colon symbol (:). As a result, the ratio a/b has no units and is represented by the notation a: b.

Given:

A housepainter mixed 5 gal of blue paint with every 9 gal of yellow paint.

So, the ratio of gallons of blue paint to gallons of yellow paint is

= 5 to 9  or 5:9

Now, ratio of gallons of blue paint to gallons of yellow paint will NOT make the same shade of green paint

= 1- 5/9

=4/9

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The equation of line k is y = 1/2x - 1.

The equation y = mx + c is the general equation of any straight line, where m is the gradient of the line and c is the y -intercept.

Given that, the equation for line j can be written as y=1/2x-4. Parallel to line j is line k which passes through the point (-8, -5)

When two lines are parallel their slope are equal, so solving for c,

-5 = 1/2*-8 + c

c = -1

The equation will be,

y = 1/2x - 1

Hence, The equation of line k is y = 1/2x - 1.

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the figure for m3 in the above question is 50

Answer:

15 weeks.

Step-by-step explanation:

The radical form of each of the given expressions are;

1) 2^(2/3) =  ∛(2²)

2) 3^(1/3) = ∛3

3) 3^(3/2) = √3³

4) 2^(1/2) = √2

The radical form of the expression [tex]a^{\frac{x}{y} }[/tex] is; [tex]\sqrt[y]{a^{x} }[/tex]

Thus, we can solve each of the given expressions;

1) We are given the expression as 2^(2/3).

Thus;

x = 2 and y = 3 and we have; ∛(2²)

2) We are given the expression as 3^(1/3).

Thus, x = 1 and y = 3 and so we have;

∛3

3) We are given the expression as 3^(3/2). Thus;

x = 3 and y = 2 and so we now have; √3³

4) We are given the expression as 2^(1/2). Thus;

x = 1 and y = 2 and so we now have; √2

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As per the reference attachment attached thereby along with the question statement, to prove the triangles ABC and ADC are congruent by SAS property, proving either of (AB ≅ CD), (AB ≅ DC) or (AD ≅ BC) will suffice.

In the reference attachment attached thereby along with the question statement, we are provided with two triangles, (ADC and ABC),

And as per the question statement, we are required to determine the relation between the corresponding sides or angles of the concerned triangles which we will need to prove over the information already provided in the figure, to ascertain that triangles ABC and ADC are congruent by SAS property.

Now, for two triangles to be congruent by SAS property, they will need to have two pairs of equal corresponding sides, and one set of equal corresponding angles.

Among our concerned triangles, ΔABC and ΔADC, already given that,

(∠DAC = ∠BCA), i.e., one set of equal corresponding angles,

And, (AC) is a common side to both ΔABC and ΔADC, i.e., one set of equal corresponding sides.

At this point, for ΔABC and ΔADC to be congruent, we will need to prove another set of corresponding sides to be equal, to complete SAS property.

Therefore, proving either of (AB ≅ CD), (AB ≅ DC) or (AD ≅ BC) will complete the second set of corresponding sides being equal, and  (ΔABC and ΔADC) can be proved to be congruent triangles.

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If the total cost to rent 2 chairs and 12 tables is $107 and the total cost to rent 5 chairs and 3 tables is $38, then the costs to rent each chair and table are $2.5 and $8.5 respectively. We can solve this question using elimination and substitution methods.

Elimination and substitution methods are involved in solving this problem. We're going to use the variables x for the cost of a chair and y for the cost of a table. The total cost to to rent 2 chairs and 12 tables is $107, so the equation can be written as 2x + 12y = 107. The total cost to rent 5 chairs and 3 tables is $38, so the equation can be written as 5x + 3y = 38.

To find the value for x, we need to eliminate the variable y first. Start by multiplying each term in the second equation by 4.

5x · 4 + 3y · 4 = 38 · 4

20x + 12y = 152

Then, subtract the terms in the second equation from their counterparts in the first equation.

2x   + 12y = 107

20x + 12y = 152 -

-18x  + 0   = -45

Finally, with a little bit of algebraic manipulation, we've got x = 2.5, hence $2.5 is the cost in to rent a chair.

-18x = -45

x = -45/-18

x = 2.5

What about the cost to rent a table? Well, we can substitute 2.5 for x in either of the equations to get the value for y. For instance, we can pick the equation 2x  + 12y = 107 and substitute x with 2.5 to isolate the variable y, like this:

2(2.5) + 12y = 107

5 + 12y = 107

12y = 107 - 5 = 102

y = 8.5

The value for y turns out to be 8.5. So the cost to rent a table is $8.5.

Your question is incomplete, but it was most probably "A party rental company has chairs and tables for rent. The total cost to rent 2 chairs and 12 tables is $107. The total cost to rent 5 chairs and 3 tables is $38. What is the cost to rent each chair and each table?"

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The equation to represent the expression is C ( b ) = 2.25b , where C ( b ) is the cost of b number of chocolate bars

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the cost of b chocolate bars be = C

Let the cost of 1 bar of chocolate bar be = $ 2.25

Let the number of chocolate bar be = b

Now , the equation to find the cost of b number of chocolate bars is ,

The cost of b number of chocolate bar =
cost of 1 bar of chocolate bar x number of chocolate bar

So , the equation is

The cost of b number of chocolate bar = 2.25b

So , the equation to find the cost of b number of chocolate bars is ,

Cost of b chocolate bars C = cost of b number of chocolate bar

C ( b ) = 2.25b

Therefore , the expression is C ( b ) = 2.25b

Hence , The equation to represent the expression is C ( b ) = 2.25b , where C ( b ) is the cost of b number of chocolate bars

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Answer:

I hope this is right

TG = 34 TG=34  inches

From the figure

            PQR is a triangle

            PS, QT are medians of the triangle  

            G is the centroid

Step 1: Calculate the segment of the median (TG = ? )

              We know that

              Each median is divided into segments with a 2:1 ratio by the triangle centroid.

                    \therefore \frac{TG}{GQ} = \frac{2}{1} ∴

GQ/TG = 1/2

​

                          TG = 2 GQ TG=2GQ

                          TG = 2 * 17 TG=2∗17

                          TG = 34 TG=34

               Hence, segment of the median  TG = 34  inches

Answer:

x=10

Step-by-step explanation:

-3+x=7

Add 3 to both sides.

7+3=10

x=10

Answer:

x=10

Step-by-step explanation:

-3+x=7

You have to add 3 to both sides to cancel out the -3

x=10

That leaves you with x=10

The domain of the inequality is from zero to negative infinity

The domain refers to the values in the input of a function, these values are in the x direction.

The domain says the extents the values of the input is therefore no all the input values must be in the domain

Examining the graph shows that the graph reached the point x = 0 and returned with an arrow.

The arrow means that the values continued limitlessly, such limitless values are represented by infinity with symbol ∞.

The infinity is in the negative direction

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Answer:

the answer is 9/14

Step-by-step explanation:

2/7× 2 1/4 = 2/7× 9/4

= 2 × 9 / 7 × 4

= 18/28

= 9/14

The change in the amount of seed in the feeder after 7 days is 78.75 ounces.

A unit rate means a rate for one of something. We write this as a ratio with a denominator of one.

For example, if you ran 80 meters in 10 seconds, you ran on average 8 meters in 1 second

To find the rate at which the amount of seed decreases.

11 1/4 ounces = 5 days

Dividing both sides of the equation by 5.

11 1/4 ounces = 1 day

Multiplying 7 on both sides to get the number for 7 days

7 x 11.25 ounces = 7 days

78.75 ounces  = 7 days

If the amount of seed in a bird feeder decreases by 11 1/4 ounces in 5 days, the amount of seed decreases by 78.75 ounces.

The change in the amount of seed in the feeder in 7 days is 78.75 ounces.

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The perimeter of this semi-circle with diameter, d = 84cm the expression in terms of π are as follows:

= 48π + 42

The area of a circle, A, is calculated using the formula A = pi * r2, where r is the circle's radius. Since we already know that a semicircle is half of a circle, we can easily divide that equation by two to determine the area of a semicircle. As a result, A = pi * r2/2 is the formula for calculating the area of a semicircle.

With the aid of the following formula, we can determine a semicircle's perimeter: The semicircle's perimeter is equal to r + 2r units, where r is the radius of the semicircle.

Diameter of the semi-circle = 84cm

Now,

the circumference of the semi-circle  =  πr + 2r

Substituting the value of r in the given formula:

the circumference of the semi-circle  =  πr + 2r

                                                              = πr + 2r

                                                               = 48π + 42

The perimeter of this semi-circle with diameter, d = 84cm the expression in terms of π are as follows:

= 48π + 42

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Last year, Maria earned $54,000

In this question, we have been given  Maria earns a $50,000 salary plus a 10% commission on any sales over $20,000.

Last year Maria made $40,000 in sales.

This means, she got 10% commission

We find the 10 percent of 40000.

40000 * (10/100) = 4000

Her total earning would be,

$50,000 + $4000(commission) = $54,000

Therefore, Maria earned $54,000

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The value of x in the equation is $55 and this represents the cost of the expensive book

The variable x is not defined in the question

So, we represent x as the more expensive book and y to represent the less expensive book

Also, from the question we understand that

The above statements can be interpreted to the following equations

x = 4 + 3y

x + y = 72

Substitute x = 4 + 3y in the equation x + y = 72

So, the equation x + y = 72 is represented as

4 + 3y + y = 72

Evaluate the like terms in the above equation

4 + 4y = 72

Collect the like terms in the above equation

4y = 72 - 4

Evaluate

4y = 68

Divide both sides by 4

So, we have

y = 17

Substitute 17 for y in the equation x = 4 + 3y to solve for x

x = 4 + 3 * 17

Evaluate the products

x = 4 + 51

Evaluate the sum

This gives

x = 55

Hence, the cost of the more expensive book is $55

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