A triangle with an area of 60 square inches has a height that is 16 less than 6 times its base.
Find the base and height, in inches, of the triangle

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Explanation:

Let's use an example to see why this is

A = {1,2,3,4,5,6,7}

B = {x,y,z}

A U B = {1,2,3,4,5,6,7, x,y,z}

We simply glue the two sets together to form one single big set. Because sets A and B have no overlap, this means we dont have to worry about tossing out duplicates (since there aren't any).

There are 7 items in set A, and 3 items in set B.

Therefore, we have 7+3 = 10 items in set A U B

The symbol U refers to the set union operator.

If you wanted to make a Venn Diagram, then you'd have two circles overlapping. In circle A will be the numbers 1 through 7. These values are not in the overlapped region. For circle B, the letters x,y,z are inside but not in the overlapped region. The overlapped region remains empty.

The set A U B talks about the collection of everything mentioned. It's the set of stuff in set A or in set B or in both sets.

-----------------

If you want a formula to write down on a notecard or reference sheet, then it would be

n(A U B) = n(A)+n(B)

where A and B are mutually exclusive, aka disjoint. This means they have nothing in the overlapped region

Work Shown:

[tex]V = (4/3)*\pi*r^3\\\\V \approx (4/3)*3.14*18^3\\\\V \approx 24416.64\\\\[/tex]

Answer:

[tex]x =\pm\sqrt{\dfrac{y-c}a}[/tex]

Step-by-step explanation:

[tex]~~~~~~y= ax^2 +c\\\\\implies ax^2 = y-c\\\\\implies x^2 =\dfrac{y-c}{a}\\\\\implies x =\pm\sqrt{\dfrac{y-c}a}[/tex]

Based on Neena's qualifications and desire for the highest pay scale, she would be best suited for a supply chain manager career.

A supply chain manager ensures the movement of goods, from manufacturers and suppliers to the ultimate customer.

A supply chain manager oversees and manages the production flow:

A supply chain manager requires the following skills:

Thus, based on Neena's qualifications and desire for the highest pay scale, she would be best suited for a supply chain manager career.

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The volume of the box with a height of 10 inches and perimeter of 72 inches and width of w is 360w - 10w²

An equation is an expression that shows the relationship between two or more numbers and variables.

Let w represent the width of the box and v represents the volume, hence:

2(w + length) = 72

Length = 36 - w

Volume = w(36 - w) * 10

Volume = 360w - 10w²

The volume of the box with a height of 10 inches and perimeter of 72 inches and width of w is 360w - 10w²

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Answer:

see the attachment photo!

Answer:

vertex = -4, -26

Step-by-step explanation:

The standard form of a quadratic function is : [tex]y=ax^{2} +bx+c[/tex]
The function here : y = [tex]x^{2}[/tex] + 8x - 10
is in this form with a=1, b=8 and c = -10
x-coord of vertex = [tex]\frac{-b}{2a}[/tex]
[tex]x_{vertex} =\frac{-8}{2} = -4[/tex]
To find corresponding value of y-coord of vertex , substitute

x = -4 into the function.
x=-4  : [tex]y=(-4)^{2} +(8*(-4))-10 = 16 +(-32)-10=-26[/tex]

Answer:

2 * 21

3 * 14

6 * 7

Step-by-step explanation:

7 * 2 = 14

56 - 14 = 42

Multiples of 42 = 2,3,6,7, 14, 21

The possible dimensions of the larger rectangle are:

21 centimeters by 2 centimeters

14 centimeters by 3 centimeters

7 centimeters by 6 centimeters

Let the dimensions of the larger rectangle be length L and width W.

We know that the total area of the two rectangles is 56 square centimeters.

Area of the smaller rectangle = 2 cm * 7 cm = 14 square centimeters

Area of the larger rectangle = Total area - Area of the smaller rectangle

Area of the larger rectangle = 56 square centimeters - 14 square centimeters

Area of the larger rectangle = 42 square centimeters

Now, we need to find the possible dimensions of the larger rectangle with an area of 42 square centimeters.

To find the possible dimensions, we can list all the pairs of whole numbers (L, W) whose product is 42.

7 * 2 = 14

56 - 14 = 42

Multiples of 42 = 2,3,6,7, 14, 21

Remember that the length (L) should be greater than or equal to the width (W) to avoid counting duplicates.

The possible dimensions are:

L = 42, W = 1 (42 cm * 1 cm = 42 square centimeters)

L = 21, W = 2 (21 cm * 2 cm = 42 square centimeters)

L = 14, W = 3 (14 cm * 3 cm = 42 square centimeters)

L = 7, W = 6 (7 cm * 6 cm = 42 square centimeters)

So, the possible dimensions of the larger rectangle are:

42 centimeters by 1 centimeter

21 centimeters by 2 centimeters

14 centimeters by 3 centimeters

7 centimeters by 6 centimeters

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Answer:

1st answer supplementary angles

2nd answer complementary angles

3rd answer neither

4th ananswe complementary angles

5th answer complementary angles

6th answer supplementary angles

hope you find this helpful

Answer:

11.   g

12.  f

13.  e    (add all the frequencies)

14.  d

15.  c    (eg. 17.5 -8.5 = 9)

16.  b

17.  a

Let me know if you have any questions.

Hope this helps!

hat is the answer to a math problem I had it on khan academy but the problem I

1 2/7 divided by (-2 1/4)

Answer:

-4/7

Step-by-step explanation:

1 2/7 divided by (-2 1/4)

1 2/7 = 9/7

-2 1/4 = -9/4

9/7 divided by -9/4 =

9/7 multiplied by -4/9 =

9's cancel out

1/7 multiplied by -4/1 =

-4/7

Answer:

20 units²  

Step-by-step explanation:

The number of boxes will weigh 18 ounces or less will be 138. Then the correct option is A.

The z-score is a statistical evaluation of a value's correlation to the mean of a collection of values, expressed in terms of standard deviation.

The z-score is given as

z = (x - μ) / σ

Where μ is the mean, σ is the standard deviation, and x is the sample.

The weights of boxes of rice produced at a factory are normally distributed with a mean of 20 ounces and a standard deviation of 1.5 ounces.

Consider a shipment of 1500 boxes of rice.

Then the number of the boxes will weigh 18 ounces or less will be

z = (18 - 20) / 1.5

z = -1.33

Then the probability will be

P(x ≤ 18) = P(z ≤ -1.33)

P(x ≤ 18) = 1 - P(z > -1.33)

P(x ≤ 18) = 1 - [1 - P(z < -1.33)]

P(x ≤ 18) = P(z < -1.33)

P(x ≤ 18) = 0.091211

Then the number of the boxes will weigh 18 ounces or less will be

⇒ 0.091211 x 1500

⇒ 136.8

approximately 138 boxes.

Then the correct option is A.

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Answer:

3(4 + n) = n + 18

n = 3

Step-by-step explanation:

because the sum of 4 and a number is multiplied by three. That equals the number plus 18. N = 3. in the image below are the steps you can take to solve the equation.

Free trade is defined as "a system of buying and selling between countries that is. carried out with no government involvement Based on what you've learned about international trade,

The term "lobby" here refers to that action which seeks to influence or affect a certain issue most specifically those that are business and politically related. And based on the scenarios above, the one that would most likely motivate an autoworker union to lobby congress would be the first option.  

The World Bank is a financial institution created after World War II by developed countries to promote economic development around the world through loans to developing countries. To get a loan, a developing nation must submit a project that is evaluated by World Bank secretaries. Some focus areas of the bank finances are human development, agriculture, environmental protection, industrial projects, infrastructure, and corporate governance.

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Answer:

θ = 53.1°  (to the nearest tenth)

Step-by-step explanation:

FORMULA :

Let θ be the measure of the angle between U and V :

[tex]\cos \theta =\frac{\overrightarrow{U} .\overrightarrow{V} }{\left\Vert \overrightarrow{U} \right\Vert \times \left\Vert \overrightarrow{V} \right\Vert }[/tex]

========================

[tex]\overrightarrow{U} \times \overrightarrow{V} =6\times 2+\left( -3\right) \times 1=9[/tex]

[tex]\left\Vert \overrightarrow{U} \right\Vert =\sqrt{6^{2}+\left( -3\right)^{2} } =\sqrt{45} =3\sqrt{5}[/tex]

[tex]\left\Vert \overrightarrow{U} \right\Vert =\sqrt{2^{2}+\left( 1\right)^{2} } =\sqrt{5}[/tex]

[tex]\left\Vert \overrightarrow{U} \right\Vert \times \left\Vert \overrightarrow{V} \right\Vert =3\sqrt{5} \times \sqrt{5} = 15[/tex]

…………………………………………………

Then

[tex]\cos \theta =\frac{9}{15} =\frac{3}{5}[/tex]

[tex]\theta =\cos^{-1} \left( \frac{3}{5} \right) =53.130102354156[/tex]

Volume is a three-dimensional scalar quantity. The volume of the cube with side length of 4 inches is 64 inches³.

A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.

Given the volume of a cube is the cube of the length of a side. If a side is S, the volume is S^3. Therefore, the volume of cube with side 4 inches will be,

Volume of the cube = (4 in)³ = 64 in³

Hence, the volume of the cube with side length of 4 inches is 64 inches³.

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The geometric rule for the nth term of the geometric sequence for which a1 =−6 and a5=−486 is -6 × 3^(n - 1)

First term, a1 = -6

Fifth term, a5 = -486

a5 = ar^(n - 1)

-486 = -6 × r^(5-1)

-486 = -6r⁴

r⁴ = -486 / 6

r⁴ = 81

r = 4√81

r = 3

Geometric rule:

nth term = ar^(n-1)

nth term = -6 × 3^(n - 1)

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Answer:

theUse the Distance and Midpoint Formulas to find the length and midpoint of the segments with indicated endpoints. Show your solution and answer inside the box.

Endpoints

Distance

Midpoint

1. (-5,8) and (9,4)

2. (6 ,- 3) and (10,11)

3. (2,1) and (-16,13)

4. (3,0) and (9 ,- 13)

5. (-3 ,- 10) & (-7 ,- 2)

Answer:

the value of c is 13.

Step-by-step explanation:

See the picture attached below for a step by step explanation

The polynomic function that contains the points (0, 6), (3, 15.8) and (9.5, 0) is a quadratic function, whose model is y = -0.600 · x² + 5.066 · x + 6.

To determine the coefficients of a polynomic function we must know a set of distinct points, whose number is the same number of coefficients. In this case, we can derive a quadratic function, as quadratic functions have three coefficients:

y = a · x² + b · x + c     (1)

Now we substitute x and y in (1) and solve the resulting system of linear equations:

c = 6

9 · a + 3 · b + c = 15.8

90.25 · a + 9.5 · b + c = 0

Whose solution is a ≈ -0.600, b ≈ 5.066 and c = 6.

The statement is incomplete. The complete form is shown below:

There is a polynomial function. Find the function of (0, 6), (3, 15.8) and (9.5, 0).

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For boys, it's between the ages of 12-16

And for girls, it's between the ages of 10-14

Answer:

boys between ages 12 and 16 girls between ages 10 and 14

Answer:

2(x + 5) = x - 2

⟹ x = -12

Step-by-step explanation:

Doubling the sum of 5 and a number is equal to the same number decreased by 2. What is the equation?

This word problem can be written as:

⟹ 2(x + 5) = x - 2

1. Distribute:

2(x) + 2(5) = x - 2

⟹ 2x + 10 = x - 2

2. Subtract x from both sides:

2x - x + 10 = x - x - 2

⟹ x + 10 = -2

3. Subtract 10 from both sides:

x + 10 - 10 = -2 - 10

⟹ x = -12

4. Check your work:

2(x + 5) = x - 2

2(-12 + 5) = -12 - 2

2(-7) = -20

⟹ -14 = -14 ✔

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Answer:

Seconds:  2    ||  3     || 5     || 10     ||

---------------------||-------||--------||--------||

Gallons:   312  || 486 || 780 || 1560 ||

you have to use intercept theorem, also known as Thales's theorem to slove this problem

Answer:

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

it is because the hours spent by training will determine the pay at the end of the month.

therefore it's independent that's y it is the domain.

Step-by-step explanation:

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