A right triangle has an acute angle measure of 22°. Which two numbers represent the lengths of the legs of this triangle?

1 and 5
2 and 5
3 and 5
4 and 5

1) There are no prime numbers whose sum is divisible by 7 and is a perfect square.

2) 1 pipe will take 2 hours to fill 1 pool, as it fills at the same rate as all 5 pipes combined.

3) Ron's score is 20%.

4) There are 20 students in the class.

5) Katie is 14 years old.

Let's evaluate each of the statements you provided:

1) The sum of 2 prime numbers is ALWAYS even, so if x and y are prime numbers, then (x+y)/7 = z².

In this case either x = 2 or y = 5 (or vice versa). This is the only possibility to be divisible by 7.

Then (5+2)/7 = 1² = 1.

The first part is correct; the sum of two prime numbers is always even. However, the statement about (x+y)/7 = z² doesn't hold true for all prime numbers. It might work for the specific values of x and y you mentioned, but it's not a general rule.

5 pipes → 2 hours → 2 pools, then 1 pipe takes (5x2) 10 hours to fill 2 pools, or 1 pipe takes (10/2) 5 hours to fill 1 pool.

This is a correct interpretation of the information provided. If 5 pipes can fill 2 pools in 2 hours, then each pipe alone takes 10 hours to fill 2 pools, or 5 hours to fill 1 pool.

It's 6/30 = 0.2 or 20%.

Correct, 6/30 simplifies to 0.2, which is equivalent to 20%.

35% represents 7 students, and 100% of the class represents x students. Therefore, 35%/7 = 100%/x. Cross-multiplying, we get 0.35x = 7, and x = 7/0.35, which simplifies to x = 20 students.

Let K be the age of Katie, and B her brother's age. K + 2 = B (Today). In 12 years, B+12 will be twice K (remember K = B-2):

B+12 = 2(K) OR B+12 = 2(B-2)

B+12 = 2(B-2)

B+12 = 2B - 4

12 + 4 = B, and B = 16. If the brother is 16, then Kate is 14.

The calculations and logic are correct. If Katie's brother is 16, then Katie is indeed 14 years old.

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In this case, we are simply asked to find for the value of:

xbya or abxy

Since we know that given values of ab and xy, therefore abxy is:

abxy = 37 * (1 / 37)

abxy = 37 / 37

abxy = 1

The value of x is the quantity x−9 negative would be negative for all values of x less than 9.

Algebra is the analysis of mathematical representations, while logic is the manipulation of those symbols.

What is inequality?

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

To determine the values of x is the quantity x−9 negative

As per the given condition, translate the phrase into an algebraic expression:

⇒ x - 9 < 0

Add 9 to both sides of the inequality,

⇒ x - 9 + 9   < 9

⇒ x < 9

So x - 9 is negative for all values of x less than 9.

Hence, the value of x is the quantity x−9 negative would be negative for all values of x less than 9.

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The perimeter of the rectangle ABCD is 14 units after using the distance formula.

It is defined as the two-dimensional geometry in which the angle between the adjacent sides is 90 degrees. It is a type of quadrilateral.

The area of a rectangle can be calculated using the following formula:

Rectangle area = length x width

The missing figure is in the picture, please attached to the picture.

We have:

Rectangle ABCD is graphed in the coordinate plane.

As we know,

The distance formula: it can be defined as the formula for finding the distance between two points. It has given the shortest path distance between two points.

The distance formula can be given as:

[tex]\rm d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

After using the distance formula:

The perimeter of the rectangle = AB + BC + CD + DA

The perimeter of the rectangle = 2 + 5 + 2 + 5

The perimeter of the rectangle = 14 units

Thus, the perimeter of the rectangle ABCD is 14 units after using the distance formula.

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Answer:  12

Step-by-step explanation:

Given : You are making identical gift bags using 24 candles and 36 bottles of lotion .

Then, the greatest number of gift bags you can make with no items left over= greatest common factor of 24 and 36

Prime factorization of 24 and 36 :_

[tex]24=2\times2\times2\times3\\\\ 36=2\times2\times3\times3[/tex]

GCF(24 , 36)= [tex]2\times2\times3=12[/tex]

Hence, the greatest number of gift bags you can make with no items left over =12

Answer:

cbd is 23 degrees

Step-by-step explanation:

The mathematical equation 'Twice the number n is no less than 10 units from -1' can be solved as two inequalities, yielding a solution of n ≤ -5.5 or n >= 4.5.

This is a math problem asking about the absolute value inequality of an equation. The question states 'Twice the number n is no less than 10 units from -1'. This can be written as |2n + 1| >= 10. To solve it, we'll divide it into two inequalities: 2n + 1 >= 10 and -2n - 1 >= 10. Solving the first inequality yields n >= 4.5, and solving the second inequality yields n <= -5.5. Thus, the solution to the equation is n ≤ -5.5 or n >= 4.5.

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132 + 56 + 79 = 267

360 - 267 = 93

answer is 93 degrees

To convert between meters and gigameters, use the equation 1 Gm = 10^9 m. This relationship is important for converting units in scientific and mathematical contexts.

To show the equivalency between meters and gigameters, we can use the following equation:

1 gigameter (Gm) = 10⁹ meters (m).

This equation means that one gigameter is equal to one billion meters. We can use this equivalency for converting measurements from meters to gigameters or vice versa. For example, to convert 2 gigameters to meters, simply multiply 2 by 10⁹ to get 2 x 10⁹ meters.

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The y-intercept of the function g(x) = (1/4)^x is (0,1), and the horizontal asymptote is at y=0.

The correct option is (c).

Given the function g(x) = (1/4)^x, we need to find the y-intercept and the equation of the horizontal asymptote.

The y-intercept occurs where x = 0. Substituting 0 for x in g(x), we get:

g(0) = (1/4)^0 = 1

So the y-intercept is at the point (0,1).

For horizontal asymptotes, we look at the behavior of the function as x goes to positive or negative infinity. In this case, as x goes to infinity, (1/4)^x approaches 0. Therefore, the horizontal asymptote of g(x) is at y = 0.

The correct answer is c. The y-intercept is (0,1) and the asymptote is at y=0.

Midpoint, as the word suggests, means the point which lies in the middle of something. If m is the midpoint of PQ then PM will be half of PQ.

Midpoint, as the word suggests, means the point which lies in the middle of something. The midpoint of a line segment means a point that lies in the mid of the given line segment.

Given that m is the midpoint of PQ. Therefore, it will divide PQ into two equal parts. Therefore,  we can write,

PQ = PM + MQ

But since PM = MQ,

PQ = PM + PM

PQ = 2 PM

PM = PQ/2

Hence, if m is the midpoint of PQ then the relationship between PM and PQ will be half of PQ.

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An equation with all real numbers as solutions is one that, regardless of what value a variable might have, both sides will always be equal, such as 2x+3 = 2x+3. An equation with no real solutions is a statement where the two sides cannot ever be equal, like 2x+5 = 2x+7.

An example of an equation with variables on both sides that has all real numbers as the solution is a statement where both sides are identical. For instance, 2x+3 = 2x+3. All real numbers can satisfy this equation for x because both sides are always equal, regardless of what your value of x is.

On the other hand, an equation with no real solutions is one where it's impossible to find any real number that satisfies the equation. An example can be 2x+5 = 2x+7. No matter what value you put in place of x, the two sides of the equation will never be equal. Hence, this equation has no real solution.

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Answer:

y= -2x-2

Step-by-step explanation:

point slope- y=mx+b

y-y1=m(x-x1)

you have the point   (-1,0) and you have to use (x1, y1)

your slope is -2      

Substitute

y-0= -2(x +1)        

Distribute

y-0=-2x-2

+0         +0

y= -2x-2

its actually y=>3x-1 because it's shaded below the line.

below the line: < or <=

above the line: > or>=

1. The algebraic property of equality that is represented is the multiplication property. The answer is letter P.

2. The algebraic property of equality that is represented is the subtraction property. The answer is letter E.


3. The algebraic property of equality that is represented is the substitution property. The answer is letter M.


4. The algebraic property of equality that is represented is the division property. The answer is letter A.


5. The algebraic property of equality that is represented is the addition property. The answer is letter A.


6. The algebraic property of equality that is represented is the distributive property. The answer is Letter E.


7. The algebraic property of equality that are represented is the transitive property. The answer is letter is E.


8. The algebraic property of equality that are represented is the symmetric property. The answer is Letter A.


9. The algebraic property of equality that are represented is the reflexive property. The answer is letter C.


10. The algebraic property of equality that are represented by is the multiplication property. The answer is letter P.


11. The algebraic property of equality that are represented is the subtraction property. The answer is letter L.

12. The algebraic property of equality that are represented is the reflexive property. The answer is letter S.

13. The algebraic property of equality that are represented is the transitive property. The answer is letter U.


14. The algebraic property of equality that are represented is the symmetric property. The answer is letter K.

The given is 3 5 14 2  4 1 10 11 6 12 8 13 9 7

Plugging in the letters we got for each number, gives us MAKE APPLESAUCE.

As the number of apples is less than the total number of friends among which the apples need to be distributed so, no one will get a complete piece of apple so, 5 apples can be shared in between 7 friends as [tex]\frac{5}{7}[/tex].

According to the question, the total number of apples are 5 and the total number of friends are 7.

So, each friend will get (bu unitary method)-

[tex]\rm{Each\;friend\;will\;get}=\dfrac{5}{7}\;\rm apples[/tex]

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Equations may be true or false, just as word sentences may be true or false. The equation:

3 + x = 7

will be false if any number except 4 is substituted for the variable. The value of the variable for which the equation is true (4 in this example) is called the solution of the equation. We can determine whether or not a given number is a solution of a given equation by substituting the number in place of the variable and determining the truth or falsity of the result.

Example 1 Determine if the value 3 is a solution of the equation

4x - 2 = 3x + 1

Solution We substitute the value 3 for x in the equation and see if the left-hand member equals the right-hand member.

4(3) - 2 = 3(3) + 1

12 - 2 = 9 + 1

10 = 10

Ans. 3 is a solution.

The first-degree equations that we consider in this chapter have at most one solution. The solutions to many such equations can be determined by inspection.

Example 2 Find the solution of each equation by inspection.

a. x + 5 = 12
b. 4 · x = -20

Solutions a. 7 is the solution since 7 + 5 = 12.
b. -5 is the solution since 4(-5) = -20.