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Final answer:

In a 45-45-90 triangle, with a hypotenuse of 2√14, both legs x and y are equal and their lengths can be found by dividing the hypotenuse by √2, which results in lengths of √14 for each leg.

Explanation:

In a 45-45-90 triangle, also known as an isosceles right triangle, the legs are of equal length and the hypotenuse is √2 times the length of one leg. If the hypotenuse is given as 2√14, we can use the fact that the hypotenuse is √2 times the length of a leg to find the length of the legs x and y.

Let x represent the length of one leg and y represent the length of the other leg. Since the triangle's legs are equal in this special triangle, x = y. The relationship between the legs and the hypotenuse in a 45-45-90 triangle can be expressed using the Pythagorean Theorem:

x² + y² = hypotenuse²

Solving for x and y, we get:

x = y = hypotenuse/√2 = (2√14)/√2 = √14

Therefore, in a 45-45-90 triangle with a hypotenuse of 2√14, both x and y, which are the lengths of the legs, are √14.

Mario says that the expression [tex]4+3n^2[/tex] has four terms: 4, 3, n, and 2. Mario is incorrect

Solution:

Given that the expression is:

[tex]4+3n^2[/tex]

Given that, Mario says that the above expression has four terms

But Mraio is incorrect

Because the given expression has two terms only

4 is one of the term

[tex]3n^2[/tex] is another term

So there are totally 2 terms only

A term can be a signed number, a variable, or a constant multiplied by a variable or variables

Here 3 is a constant multiplied by [tex]n^2[/tex]

So, [tex]3n^2[/tex] is one term

Each term in an algebraic expression is separated by a + sign or - sign

Thus there are two terms in mario expression

The value of 9 × 9 is 81.

Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number.

a × b means that a is added to itself b times or b is added to itself a times.

The question is to find the product of 9 × 9.

By the definition of multiplication, 9 × 9 is the addition of the number up to 9 times.

That is, 9 × 9 can also be written as,

9 × 9 = 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9

Adding number 9 to itself 9 times we get 81.

So 9 × 9 = 81

Hence the product after multiplying 9 with 9 is 81.

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For every 1 cup of blue paint, [tex]\frac{10}{4}[/tex] cups of red paint are needed

For every 1 cup of red paint, [tex]\frac{4}{10}[/tex] cup of blue paint is needed

For every 4 cups of red paint, [tex]\frac{16}{10}[/tex] cups of blue paint are needed

Solution:

Given that, there are 3 1/3 red cups of paint for every 1 1/3 cups of blue paint

Therefore, ratio is

[tex]Red : blue = 3\frac{1}{3} : 1\frac{1}{3}\\\\Red : blue = \frac{10}{3} : \frac{4}{3}[/tex]

Let "x" be the cups of red paint needed

Then we get,

[tex]\frac{10}{3} : \frac{4}{3}\\\\x : 1[/tex]

This forms a proportion

[tex]1 \times \frac{10}{3} = \frac{4}{3} \times x\\\\x = \frac{10}{4}[/tex]

Therefore, 10/4 cups of red are needed for 1 cup of blue

Let "x" be the cups of blue paint needed

Then, we get

[tex]\frac{10}{3} : \frac{4}{3}\\\\1 : x[/tex]

This forms a proportion

[tex]\frac{10}{3} \times x = \frac{4}{3} \times 1\\\\x = \frac{4}{10}[/tex]

Thus, 4/10 cups of blue are needed for 1 cup of red paint

Let "x" be the cups of blue paint needed

Then, we get

[tex]\frac{10}{3} : \frac{4}{3}\\\\4 : x[/tex]

This forms a proportion

[tex]\frac{10}{3} \times x = \frac{4}{3} \times 4\\\\x = \frac{16}{10}[/tex]

Thus 16/10 cups of blue paint are needed for every 4 cups of red paint

The ratio of red paint to blue paint is 5:2. Therefore, for every 1 cup of blue paint, 2.5 cups of red paint are needed, for every 1 cup of red paint, 0.4 cup of blue paint is needed and for every 4 cups of red paint, 1.6 cups of blue paint are needed.

The initial statement tells us that the ratio of red paint to blue paint needed is 3 1/3:1 1/3. Converting these mixed numbers into improper fractions, that ratio transforms to 10/3:4/3, which simplifies further to 5:2.

So, if you reduce it down:

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Option c : 9 is the answer.

Explanation:

The expression is [tex]1.2-(-7.8)[/tex]

We need to determine the subtracted value of the expression.

From the expression we can see that the expression contains two negative signs.

To simplify the expression, we know that, When we multiply two negative numbers then the product is always positive.

This means [tex](-) *(-) = +[/tex]

Thus, the expression can be written as

[tex]1.2+7.8[/tex]

Adding the two numbers, we get,

[tex]1.2+7.8=9[/tex]

Thus, the value of the expression is 9.

Hence, Option c is the correct answer.

Answer: People don't get confused by this guy the answer is basically clear its neither trust me guys.

The area of new circle is 5625π square inches.

Step-by-step explanation:

Given,

Area of circular plate = 625π square inches

Let,

Radius = r

Area of circular plate = πr²

[tex]\pi r^2=625\pi[/tex]

Dividing both sides by π

[tex]\frac{\pi r^2}{\pi}=\frac{625\pi}{\pi}\\\\r^2=625[/tex]

Taking square root on both sides

[tex]\sqrt{r^2}=\sqrt{625}\\r=25[/tex]

The radius of plate is 25 inches.

When the radius is tripled = 25*3 = 75 inches

New area of circle = πr²

New area of circle = [tex]\pi (75)^2\\[/tex]

New area of circle = [tex]5625\pi[/tex] square inches

The area of new circle is 5625π square inches.

Keywords: circle, area

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Answer:

Yes, it is.

Step-by-step explanation:

d(10 + 20) is equivalent to d * 10 + 20 * d. This can be proved with the distributive property, which states that a(b + c) = ab + ac.

Using the distributive property of multiplication over addition and the commutative property of multiplication, it is proven that d(10 + 20) is equivalent to d × 10 + 20 × d.

The question asks if the expression d(10 + 20) is equivalent to d × 10 + 20 × d, using properties of mathematics to explain.

First, let's simplify the expressions using the distributive property of multiplication over addition, which states that a(b + c) = ab + ac. Applying this property, d(10 + 20) becomes d × 10 + d × 20.

Comparing d × 10 + d × 20 with d × 10 + 20 × d, we see they are indeed the same because multiplication is commutative—meaning the order of the operands does not change the result. Therefore, d(10 + 20) is equivalent to d × 10 + 20 × d.

Answer:

The product of 1/2*32 is taking 32/2

Half of 32 is 16

Product of 1/2*32=16

Hope this helps ;)

Answer:

16

Step-by-step explanation:

when you multiply buy a fraction you will end up with half of the one of the things you were multiplying this means that half of 32 is 16 so 16 is your answer if you need help on understanding how to multiply fractions think of it like this

1/2 x 32=    32 divided by 2

both ways will give you the same answer

hope this helps better your understanding

Answer:

x<8

Step-by-step explanation:

4x+8>5x

8>5x-4x

8>x

Answer:

427 feet.

Step-by-step explanation:

Answer:

Triangle W X Z is congruent to triangle Z Y X

Step-by-step explanation:

Answer:

its acctually Triangle W X Z is congruent to triangle Y Z X

Step-by-step explanation:

Answer:

Equation for the area of a circle- π r²

The 2 radiuses are 6 and 9.

6 squared is 36 and 9 squared is 81.

The smaller one is 36π and the larger one is 81π.

The difference between them is the area of the shaded region.

81π - 36π = 45π

Use 3.14 for π.

45 x 3.14 = 141.3 u²

Hope this helps!

A circle is a curve sketched out by a point moving in a plane. The area of the shaded region is equal to 141.37 cm²

A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the centre.

The area of the shaded region can be found by subtracting the area of the larger circle from the area of the smaller circle. Therefore, the area of the shaded region is,

Area = π(9 cm)² - π(6 cm)²

        = 141.37 cm²

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Answer:

[tex](9x-5)\ units[/tex]

Step-by-step explanation:

The picture of the question in the attached figure

we know that

The perimeter of a triangle is the sum of the length of their three  sides

so

[tex]P=a+b+c[/tex]

where

a,b,c are the length sides of the triangle

In this problem we have

[tex]P=(16x-6)\ units\\a=(2x-5)\ units\\b=(5x+4)\ units[/tex]

substitute and solve for the missing length

[tex](16x-6)=(2x-5)+(5x+4)+c\\c=(16x-6)-(2x-5)-(5x+4)\\c=(9x-5)\ units[/tex]

Answer:

LCM= 360

Steps:

8=2*2*2

6=2*3

9=3*3

5=1*5

2*2*2*3*3*5

8*9=72*5=360

Answer:

Step-by-step explanation:

Answer:$49.00

Step-by-step explanation:

9x5-5=$49

Answer: P(A|B) = 0.40.

Step-by-step explanation: Since A and B are independent events, P(A|B) = P(A).

Therefore, P(A|B) = 0.40.

The probability of A given B is 0.40.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

Example:

The probability of getting a head in tossing a coin.

P(H) = 1/2

We have,

Since A and B are independent events, we know that:

P(A and B) = P(A) x P(B)

But since they are independent, we also know that:

P(A and B)

= P(A) x P(B|A)

= P(B) x P(A|B)

Thus:

P(A|B) = (P(A) x P(B|A)) / P(B)

We are given that P(A) = 0.40 and P(B) = 0.30.

We don't know P(B|A), but since A and B are independent, we know that:

P(B|A) = P(B)

So,

P(A|B) = (0.40 x 0.30) / 0.30 = 0.40

Thus,

The probability of A given B is 0.40.

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Answer:

We will need 50 feet of chain link fence to build a fence around the garden.

Step-by-step explanation:

Measurements of the garden = 10 * 15 feet

How many feet of chain link fence will you need to build a fence around the garden?

For answering the question, let's calculate the perimeter of the garden, this way:

Perimeter = 2 Width + 2 Length

Replacing with the values we have:

Perimeter = 2 * 10  + 2 * 15

Perimeter = 20 + 30

Perimeter = 50 feet

Final answer:

The solution to the polynomial equation x³ + 2x² - 4x - 8 = 0 can be found by factoring, which yields the solutions x = -2 and x = 2.

Explanation:

The solution to the polynomial equation x³ + 2x² - 4x - 8 = 0 can be found by factoring, using synthetic division, or by using numerical methods such as graphing or using a calculator. Let's use factoring to find the solution.

We can begin by factoring out the greatest common factor, which is 1:

x³ + 2x² - 4x - 8 = (x + 2)(x² - 4)

We can further factor the quadratic term using the difference of squares:

(x + 2)(x + 2)(x - 2) = 0

So, the solutions to the equation are x = -2 and x = 2.

Answer:

14 and 25

Step-by-step explanation:

x = smaller number

y = larger number

x + y = 39

x = y - 11

now we sub

y - 11 + y = 39

2y - 11 = 39

2y = 39 + 11

2y = 50

y = 50/2

y = 25 <=== larger number

x = y - 11

x = 25 - 11

x = 14 <==== smaller number

The problem can be solved by setting up and solving two algebraic equations. The two numbers in question are 25 and 14.

The subject of this problem is algebra. To solve it, we can set up two equations based on the problem's statements, and then solve those equations.

First, we know that the sum of two numbers is 39, so we can write that as: x + y = 39 (Equation 1).

Second, we know that the smaller number is 11 less than the larger number. Assuming x is the larger number and y is the smaller one, we can write this as: y = x - 11 (Equation 2).

To solve these equations in parallel, insert Equation 2 into Equation 1, that results in: x + (x - 11) = 39. Solving this equation simplifies to 2x = 50, so x = 25. Substitute x = 25 in Equation 2, we get: y = 25 - 11 = 14. So, the two numbers are 25 and 14.

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Step-by-step explanation:

look at the picture shown

Answer:

8x^2-18x-56

Step-by-step explanation:

(4x+7)*(2x-8)=

4x*2x+4x*(-8)+7*2x+7*(-8)=

8x^2-32x+14x-56=

8x^2-18x-56

Answer:

168 girls.

Step-by-step explanation:

There are a total of 6 + 7 = 13 'parts'.

So one part = 364 / 13 = 28.

So the number of girls = 6 * 28

= 168.

Answer:

0.45

Step-by-step explanation:

The ratio of apple trees to cherry tree is 14:1.

In the orchard, there are 14 apple trees and 1 cherry tree.

To find the ratio of apple trees to cherry trees, we simply divide the number of apple trees by the number of cherry trees, yielding 14:1.

This ratio indicates that for every cherry tree in the orchard, there are 14 apple trees.

Ratios express the relationship between different quantities, providing a comparative measure.

In this case, it illustrates the abundance of apple trees in relation to the singular cherry tree, highlighting the disparity in their numbers within the orchard.

Answer:

1:2, 2:4, 3:6

Step-by-step explanation:

If you times 1:2 by 2, you get 2:4. If you times 1:2 by 3, you get 3:6.

You have to multiply each individual number in the ratio.

Answer:1:3

2:6

4:12

Step-by-step explanation:

Answer:36

Step-by-step explanation: if 2 out of 9 or red and there are 8 red that means that divide 8 by to get 4 * 9 + 36

By using the theoretical probability formula, the total number of grapes in the bag is 36

From the question, we are to determine how many grapes are in the bag

Let the total number of grapes in the bag be x

From the probability formula,

[tex]P(A) = \frac{Number\ of\ favorable \ outcomes \ to \ A }{Total\ number\ of\ possible\ outcomes}[/tex]

Let R represent red grapes,

Then,

[tex]P(R) = \frac{Number\ of\ favorable \ outcomes \ to \ R }{Total\ number\ of\ possible\ outcomes}[/tex]

From the given information,

P(R) = 2/9

Number of favorable outcomes to R = 8

Therefore,

[tex]\frac{2}{9} = \frac{8}{x}[/tex]

2x = 9 × 8

2x = 72

x = 72 / 2

x = 36

Hence, the total number of grapes in the bag is 36.

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Answer:4.25 tons

Step-by-step explanation:

Answer:

Given a number N, print all numbers in range from 1 to N having exactly 3 divisors. Examples: Input : N = 16 Output : 4 9 4 and 9 have exactly three divisors. Divisor Input : N = 49 Output : 4 9 25 49 4, 9, 25 and 49 have exactly three divisors.

Step-by-step explanation: