triangle shown to the right is 120 sq units. find the base and height

Answer: A.) Point.

Step-by-step explanation:

Final answer:

The average of three numbers that sum to 144 is 48, found by dividing 144 by 3.

Explanation:

The average of three numbers is the sum of those numbers divided by three. In this case, if the sum of three numbers is 144, then the average can be found by dividing 144 by 3. Calculating this, we get the average, which is 48 (144 ÷ 3 = 48). Hence, the average of the three numbers is 48.

Answer:

1)  Area of ΔABD = Area of ΔACD and

2)  Area of ΔABO = Area of ΔCDO

Step-by-step explanation:

1) In the given trapezoid ABCD,

AD || BC

Triangles ΔABD and ΔACD lie on the same base AD and lie between the parallel lines AD and BC.

Hence, they are equal in area.

Therefore, Area of ΔABD = Area of ΔACD.

2) From 1), we have

Ar (ΔABD) = Ar(ΔACD)

Subtract Ar (ΔAOD) from both sides,

Ar (ΔABD) - Ar (ΔAOD) = Ar(ΔACD) - Ar (ΔAOD)

Ar (ΔABO) = Ar (ΔCDO)

The probability of getting an odd number on a spinner with 5 equal parts numbered 1 to 5 is, 60%

The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

We have to given that;

To find the probability of getting an odd number on a spinner with 5 equal parts numbered 1 to 5.

Since, From 1 to 5, there are three numbers 1, 3, 5 are odd numbers.

Hence, the probability of getting an odd number on a spinner with 5 equal parts numbered 1 to 5 is,

P = 3/5

Change into percent as;

P = 3/5 x 100%

P = 60%

Thus, the probability of getting an odd number on a spinner with 5 equal parts numbered 1 to 5 is, 60%

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Answer: x = 17.5

Step-by-step explanation:

You're using interior angles

Use the law of cosine: c^2 = a^2 +b^2 - 2ab times cos (C)

h^2 = 8^2 + 10^2 - 2(8)(10) times cos (80) so h = 11.67

11.67 over sin (80) = 8 over sin (S) = 10 over sin (T)

sin -1 ((8 times sin (80)) over 11.67)  is equal to S

sin -1 ((10 times sin (80)0 over 11.67)) is equal to T

t over sin (T) = s over sin (S)

t = 10 + x

s = 8 + 18 = 22

10 + x over sin (57.54) = 22 over sin (42.45) 

x = 22 times sin (57.54) over sin (42.45) and next to this is -10

the answer of x = 17.50

Hope this helps, have a BLESSED and wonderful day! :-)

-Cutiepatutie <3

The height formed by this 25 foot ladder that leans against a wall is 24 feet.

Given the following data:

Pythagorean theorem can be defined as a fundamental mathematical expression in Euclidean geometry that can be used to determine any of the three (3) sides of a right-angled triangle.

Mathematically, Pythagorean's Theorem is given by this formula:

[tex]h^2 = a^2 + b^2[/tex]

Where:

Substituting the given parameters into the formula, we have;

[tex]h^2 = a^2 + b^2\\\\25^2 = 7^2 +b^2\\\\625=49+b^2\\\\b^2=625-49\\\\b=\sqrt{576}[/tex]

b = 24 feet.

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Answer:

A is rational, but B is irrational.

Step-by-step explanation:

Answer: (x+b) (a+2y)

Step-by-step explanation:

ax+ab+2by+2xy

split the equatuion in half

1.  ax+ab                    2.     2by+2xy

        gcf=a                          gcf=2y

        ax/a=x                        2by/2y= b  

        ab/a=b                        2xy/2y= x

a(x+b)                                 2y(x+b)

          Answer :(x+b)(a+2y)

Given a circle with a circumference of 21.4 inches, first calculate the radius using the circumference formula, then use the radius to calculate the circle's area, which results in approximately 36.29 square inches.

This question involves determining the area of a circle given its circumference. The formula to calculate the circumference of a circle is C = 2πr, where C is the circumference, r is the radius, and π is a constant (approximated to 3.14). Given that the circumference is 21.4 inches, we can rearrange this formula to find the radius (r = C/2π), giving us a radius of approximately 3.4 inches.

Now, knowing the radius, we can use it to find the area using the formula for the area of a circle, which is A = πr². Plugging in the values, we find that the area is approximately 36.29 square inches.

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The value of x is -3 and the solution to this system of equations is (-3 , 7).

When a number of variables are involved, the system of equation is generated. The system of equation has been the set of simultaneous equations as well.

Given :

[tex]y = -3x-2[/tex]   ----  (1)

[tex]y=7[/tex]  -----  (2)

Solution :

From, equation (1) and (2) we get the value of x to be:

[tex]7=-3x-2[/tex]

[tex]9=-3x[/tex]

[tex]x=-3[/tex]

Therefore, the value of x is -3.

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Final answer:

The expression that represents the sum of r and 7 is written simply as r + 7. This is a basic operation in algebra involving the addition of a variable and a constant.

Explanation:

To write an expression that represents the sum of r and 7, you simply add these two together. The mathematical expression for this is r + 7. This is a basic algebraic expression that demonstrates how to represent the addition of a variable, in this case r, with a constant number, which is 7.

A) This equation has only one solution. B) The solution would be x = 2.

For that ,we will try solving it first using the method of substitution in which we express one variable in other variable's form and then you can substitute this value in other equation to get linear equation in one variable.

If there comes a = a situation for any a, then there are infinite solutions.

Given equation is 5(2x − 3) = 5

By solving further,

10x -15 = 5

10x = 20

x = 2

A) This equation has only one solution.

B) The solution would be x = 2

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The other monomial must have the factors of 3x^2y, with the possibility of having higher powers of y, but not lower, as this would change the GCF. An example of a compatible monomial with 3x^4y is 3x^2y^2.

The question is asking for the other monomial given that the greatest common factor (GCF) of two monomials is 3x^2y and one of the monomials is 3x^4y. Since the GCF is the product of the lowest powers of common factors in the monomials, the other monomial must have at least the factors 3, x^2, and y to a certain power. It can have these factors to higher powers as well, but not to lower powers, since it would then alter the GCF.

An example of another monomial that could be paired with 3x^4y is 3x^2y^2, because it has the factors of the given GCF with potentially higher powers, without affecting the GCF. Therefore, any monomial of the form 3x^2y^n (where n is greater than or equal to 1) could be the other monomial.

Here, we need to calculate the expected number of students who are liberal arts major.

It is given that, 60 out of 65 students are liberal arts major.

So, we will calculate the percentage of liberal arts major from the total.

Percentage of liberal arts major = [tex] \frac{Number of liberal arts major}{Total students} [/tex] X 100

Percentage of liberal arts major = [tex] \frac{60}{65} [/tex] X 100

Percentage of liberal arts major = 92.31 %

Now, we will calculate for 8,943 liberal arts majors -

In total students of 8,943, liberal arts majors = 92.31 % X 8,943

In total students of 8,943, liberal arts majors =8,256 students (approximately)

Answer:

The answer is D) $897.12

Step-by-step explanation:

3 years = 36 months

173.33 * 36 = 6239.88

5 years = 60 months

118.95 * 60 = 7137.00

7137.00 - 6239.88 = 897.12