A coach needs both small and large cones to set up an obstacle course. The coach knows that there are fewer than 30 cones in the storage room. The coach needs at least a dozen large cones.

Let x represent the number of small cones and y represent the number of large cones.

Which inequalities model the situation? Select each correct answer.
x+y≤30
x>0
x+y<30
y≥12
y>12

Answer:- D shows the triangle pairs which can be mapped to each other using a single translation.

Explanation:-

Translation is a rigid transformation which creates a congruent image as that of the original figure such that the distance between the each point of the original figure and the image is fixed and same.

The translation mapping is given by (x,y)→(x+h,y+k) ,where h is the distance of the x coordinate of the each point of the original figure to the image and  k is the distance of the y coordinate of the each point of the original figure to the image.

In figure D we can see that the distance between each point of ΔCED is equal to the distance between each point of ΔMPN. Thus it shows  the triangle pairs which can be mapped to each other using a single translation.

The Figure 4 is correct as the triangle MNP and CDE can be mapped to each other using a translation.

Further  explanation:

Translation can be defined as to move the function to a certain displacement. If the points of a line or any objects are moved in the same direction it is a translation.

Explanation:

The angle MNP is equal to the angle CDE.

The side PN is equal to the side ED.

The side MN is equal to the side CD.

The translation mapping of a single translation can be expressed as follows,

[tex]\left( {x,y}\right) \Rightarrow \left({x + h,y + k} \right)[/tex]

Here, h represents the distance of translation in x-axis and k represents the distance of translation in y-axis.

In Figure 1 the triangle MNP and CDE cannot be mapped to each other using a single translation.

In Figure 2 the triangle MNP and CDE cannot be mapped to each other using a single translation.

In Figure 3 the triangle MNP and CDE cannot be mapped to each other using a single translation.

In Figure 4 the triangle MNP and CDE can be mapped to each other using a translation.

Hence, the Figure 4 is correct as the triangle MNP and CDE can be mapped to each other using a translation.

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Answer details:

Grade: Middle School

Subject: Mathematics

Chapter: Triangles

Keywords: rotation, translation, triangle, rotation about point A, mapped, triangle pair, mapping, equal angles, sides.

When n=3, the value of the expression is 54.

To find the value of the expression when n=3, we substitute n=3 into the expression: –2n(5 + n – 8 – 3n).

First, we simplify the expression:

–2n(5 + n – 8 – 3n) = –2(3)(5 + 3 – 8 – 3(3))

= –2(3)(5 + 3 – 8 – 9)

= –2(3)(-9)

= –2(-27)

= 54.

Therefore, when n=3, the value of the expression is 54.

The number of bacteria's in petri dish 'A' are 30 times more than the bacteria's in petri dish 'B'.

Bacteria are small single-celled organisms. Bacteria are found almost everywhere on Earth and are vital to the planet's ecosystems.

Given is a culture of 2.4 × 10¹¹ bacteria is in petri dish 'A' and a culture of

8 × 10⁹ bacteria is in petri dish B.

Number of bacteria's in petri dish A = n[A] = 2.4 × 10¹¹ bacteria

Number of bacteria's in petri dish B = n[B] = 8 × 10⁹ bacteria

For comparison, lets assume that -

k = n[A]/n[B]

k = 2.4 × 10¹¹ / 8 × 10⁹

k = 240 / 8

k = 30

n[A] = 30 n[B]

Therefore, the number of bacteria's in petri dish 'A' are 30 times more than the bacteria's in petri dish 'B'.

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There are a total of 8! different orders in which a skier can finish the race.

What are Permutations and Combinations?

Objects from a set may be chosen in a variety of ways, usually without replacement, to create subsets. These methods are known as permutations and combinations. When the order of selection is a consideration, this process of choosing subsets is known as a permutation; when it is not, it is known as a combination.

In the given question, we have 8 people, who compete in a downhill ski race.

Also, It is also given that there are no ties in the race.

So, There will be only one person among 8 people, who will rank 1,

Similarly, There will be only one person who will rank 2, and so on till rank 8.

So, The total number of orders a skier can finish the race will be:

Total number of ways = [tex]1 \times 2 \times 3 \times 4 \times 5 \times 6 \times7 \times 8[/tex]

The total number of ways is 8!

Hence, The total number of different orders that a skier can finish will be 8!.

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Answer:

DE≅MN

Step-by-step explanation:

We know that corresponding parts of congruent triangles are congruent (CPCTC). Using the congruence statement we can match up the corresponding sides.

From the statement, ∠D matches ∠M, ∠E matches ∠N, and ∠F matches ∠O.

We also see that DE matches MN, EF matches NO, and DF matches MO.

Thus we have that DE≅MN.

scale of 1:20 means for every 1 inch on the drawing it is 20 inches in real life

5 inches * 20 = 100 inches = 8.33 feet

4 inches *20 = 80 inches = 6.67 feet

8.33 * 6.67 = 55.56 square feet

To find the values of x where f ''(x) equals 0, solve the quadratic equation 12x + 6 = 0 by setting it equal to zero and solving for x: x = -1/2.

To find the values of x where f ''(x) equals 0, we need to solve the quadratic equation 12x + 6 = 0. To do this, we set the equation equal to zero and solve for x:

12x + 6 = 0

12x = -6

x = -6/12

Simplifying, we find that x = -1/2.

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Answer:

9.29 x 10^-2 it's wrong. It's 9.29 x 10^2 (positive)

Step-by-step explanation:

You can "move" or change the measure of everything using some scales based on specific boards.

There's a way to move from the imperial system (yards, feet, inches) to the metric system ( centimeters, meters, kilometers)

1 square foot = 929.03 square centimetre

929.03 can be written with the scientific notation, taking care of the significant figures like [tex]9.29x10^{2}[/tex]

3 [tex]feet^{2}[/tex] = 2787.09 [tex]cm^{2}[/tex] or [tex]27.87x10^{2}[/tex] [tex]cm^{2}[/tex]

The greatest integer is t/5 + 4 in terms of t.

Integers are numbers which includes the set of natural numbers, o and the negatives of all those natural numbers.

Set of integers are usually denoted as Z.

Let the first even integer be x.

Then the consecutive even integer is x + 2.

Integers are x, x + 2, x + 4, x + 6 and x + 8.

Given, sum of five consecutive even integers is t.

x + x + 2 + x + 4 + x + 6 + x + 8 = t

5x + 20 = t

5 (x + 4) = t

x + 4 = t / 5

Greatest integer is x + 8.

x + 8 = (x + 4) + 4 = t/5 + 4

Hence the greatest integer is t/5 + 4.

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When the slope is undefined, write the equation as x = c, where c is the constant value of the x-coordinate for all points on the vertical line.

When the slope of a line is undefined, it means that the line is vertical. In the slope-intercept form of a linear equation, y = mx + b, m represents the slope of the line. However, when the slope is undefined (infinite), you cannot express it as a finite value m.

For a vertical line passing through a point (a, b), the equation can be written as: x = a.

In this case, there is no slope term, because the line is vertical and does not have a slope in the traditional sense. Instead, the equation simply states that for all points on the line, the x coordinate remains constant at a.

Thus, when the slope is undefined, write the equation as x = c, where c is the constant value of the x-coordinate for all points on the vertical line.

product means multiply

-2 1/4 times 2 1/2:

-2 1/4 = -9/4

2 1/2 = 5/2

-9/4 x 5/2 = -45/8 = -5 5/8

Answer:

Because of change in conversion rates, the value in Carrie's account decreases by $39.85.

Step-by-step explanation:

Total money in Carrie's bank account = 45000 pesos.

If exchange rate is 1 USD = 12.94 pesos, then in dollars the money in account is :

[tex]\frac{45000}{12.94}[/tex] = $3477.588 ≈ $3477.59

If exchange rate is 1 USD = 13.09 pesos, then in dollars the money in account is :

[tex]\frac{45000}{13.09}[/tex] = $3437.738 ≈ $3437.74

Now, if the conversion rate is 12.94 pesos then the amount in dollars is more, than when the conversion rate is 13.09 pesos.

The difference is [tex]3477.59-3437.74=39.85[/tex] dollars.

So, because of change in conversion rates, the value in Carrie's account decreases by $39.85.

Answer:

Robyn will get the greater quotient

Step-by-step explanation:

Prediction: Since 1/16 >1/32

So, it will prove the smaller quotient

Susan divides the fraction 5/8 by 1/16 .

Calculation : [tex]\frac{5}{8} \div \frac{1}{16}[/tex]

                     [tex]\frac{\frac{5}{8}}{\frac{1}{16}}[/tex]    

                     [tex]\frac{5}{8} \times 16[/tex]    

                     [tex]10[/tex]    

Robyn divides 5/8 by 1/32

Calculation : [tex]\frac{5}{8} \div \frac{1}{32}[/tex]

                     [tex]\frac{\frac{5}{8}}{\frac{1}{32}}[/tex]    

                     [tex]\frac{5}{8} \times 32[/tex]    

                     [tex]20[/tex]    

So, The prediction is true.

Robyn will get the greater quotient

Answer:

=(3g-5)(2g+7)

Step-by-step explanation:

In order for Mr. Gonzalez to reach his goal of $60,000, if his base salary is $18,000 and he earns a 4% commission on sales, he would need to make about $87,500 in sales per month.

In this question, Mr. Gonzalez has a base salary of $18,000 and wishes to earn a total of $60,000 for the year. This means he needs to earn an additional $42,000 ($60,000 - $18,000) from sales commission.

The commission rate is 4%, which means for every $100 he sells, he earns $4. Therefore, to find out how much he needs to sell to make the required commission, we require to divide the target commission by the commission percentage.

Therefore, he will need to sell $42,000 / 0.04 = $1,050,000 for the whole year. If this is divided evenly over the year for monthly targets, then it would be $1,050,000 / 12 (months), which results in approximately $87,500 per month.

So, the correct answer option should be b. $87,500 per month.

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Given

The equation in the form

[tex]x^{4}+95x^{2}-500 =0[/tex]

Find the factor of the above equation

To proof

factoring the above equation

we get

[tex]x^{4}+100x^{2}-5x^{2}-500 =0\\\\x^{2}(x^{2}+100)-5(x^{2}+100)=0\\\\(x^{2}-5)(x^{2}+100)=0[/tex]

now sloving the equation we get the value

x² = 5

x² = -100

[tex]x =\pm \sqrt{5}\\\\ x=\sqrt{-100}[/tex]

The factor of the equation is

[tex]x=\pm \sqrt{5}\\\\ x= \pm 10i[/tex]

Hence proved

Final answer:

Using the properties of congruent triangles and the fact that the sum of the angles in a triangle is 180°, the measure of angle C (mC) is found to be 60°.

Explanation:

Given that triangle ABC is congruent to triangle XYZ, we know that corresponding angles of congruent triangles are equal. Since the measure of angle A (mA) is given as 50°, and in triangle XYZ, the measure of angle Y (mY) is 70°, we can use the fact that the sum of the angles in a triangle is 180° to find the measure of angle C (mC).

The sum of the angles in triangle ABC would be:

mA + mB + mC = 180°

50° + mB + mC = 180°

Since triangle ABC is congruent to triangle XYZ, mB will be equal to mX, which is the same as mY, that is 70°:

50° + 70° + mC = 180°

Now, we just need to subtract the sum of mA and mB from 180° to find mC:

mC = 180° - (50° + 70°)

mC = 180° - 120°

mC = 60°

The equation, in slope-intercept form, of the perpendicular bisector is: y = 1/3x.

The slope-intercept form is given as, y = mx + b.

b is y-intercept, and m is the slope.

Slope = change in y/change in x.

The slopes of two lines that are perpendicular to each other are negative reciprocal of each other.

Thus, let's find the slope of the blue line:

Slope = (-2 - 4)/(4 - 2) = -3

Therefore, the slope of the line perpendicular to it would be, 1/3.

Equation of the perpendicular bisector that passes through (3, 1):

Since slope (m) is 1/3, find b by substituting m = 1/3 and (x, y) = (3, 1) into y = mx + b.

Thus:

1 = 1/3(3) + b

1 = 1 + b

1 - 1 = b

b = 0.

Substitute b = 0, and m = 1/3 into y = mx + b:

y = 1/3x + 0

y = 1/3x

Therefore, the equation, in slope-intercept form, of the perpendicular bisector is: y = 1/3x.

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