1. Select all the conditions for which it is possible to construct a triangle.

A 60°, 80°, and 80°
B) 4cm, 5cm, and 6CM
C)4 cm, 5 cm, and 15 cm
D)4cm, 5 cm, and 50°
E)30°, 60°, and 3 cm

Present age of father is 48 years and that of son is 23 years.

Let the age of father be x years

And the son's age be y years

According to the question,

x - y = 25 -----------1

15 Years ago, x= 6( y - 15 )

x= 6y - 90 -------------2

Substituting value of x from equation 2 in equation 1, we get

6y - 90 - y = 25

5y -90 = 25

5y = 25+90

5y= 115

y= 23

Therefore son's age is 23 years and from equation 1 we get x= 25+y = 25+23 = 48 years. So father's age is 48 years.

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The augmented matrix for the system of equations is  [tex]\left[\begin{array}{ccc}\frac{6}{5} \\\frac{1}{10} \\\frac{23}{5} \end{array}\right][/tex]

A matrix is a rectangular array or table where data is organized into rows and columns, and "matrixes" is the plural version of matrix. It doesn't matter how many columns and rows they have. Matrices can be used for a variety of operations, including addition, multiplication, transposition, and scalar multiplication. When executing these matrix operations, certain guidelines must be followed. For example, matrices can be added to or subtracted from if only their rows and columns are the same, whereas they can be multiplied if only their first and second sets of columns are exactly the same.

A =[tex]\left[\begin{array}{ccc}1&-2&0\\-5&8&2\\0&4&1\end{array}\right] \left[\begin{array}{ccc}X\\Y\\Z\end{array}\right] =\left[\begin{array}{ccc}1\\4\\5\end{array}\right][/tex]

Ax = B

multiply by [tex]A^{-1}[/tex] to both side

 [tex]A^{-1}[/tex]Ax =  [tex]A^{-1}[/tex]B

x = [tex]A^{-1}[/tex]B

[tex]\left[\begin{array}{ccc}0&\frac{-1}{5} &\frac{2}{5} \\\frac{-1}{2} &\frac{-1}{10} &\frac{1}{5} \\\ 2&\frac{2}{5} &\frac{2}{5} \end{array}\right][/tex]= [tex]A^{-1}[/tex]

X = [tex]\left[\begin{array}{ccc}0&\frac{-1}{5} &\frac{2}{5} \\\frac{-1}{2} &\frac{-1}{10} &\frac{1}{5} \\\ 2&\frac{2}{5} &\frac{2}{5} \end{array}\right][/tex][tex]\left[\begin{array}{ccc}1\\4\\5\end{array}\right][/tex]

X = [tex]\left[\begin{array}{ccc}\frac{6}{5} \\\frac{1}{10} \\\frac{23}{5} \end{array}\right][/tex]

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Answer

Explanation

We can approximate the distribution to the normal distribution.

As we know the mean of the sample and standard deviation of the population

The solution of the equation −46x + 874 = 86 − x will be 17.51 which is that number.

The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.

−46 times a number minus 19 is equal to 86 less than the number.

Let the number be x. Then the equation is given as,

−46(x − 19) = 86 − x

Simplify the equation, then we have

−46x + 874 = 86 − x

45x = 788

x = 788 / 45

x = 17.51

The solution of the equation −46x + 874 = 86 − x will be 17.51 which is that number.

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Answer:

  2x +y = 1

Step-by-step explanation:

You want the equation of a line parallel to 2x+y=4 through point (-1, 3).

A parallel line will have the same slope, which is a function of the ratio of the x- and y-coefficients. Hence, the equation of the parallel line can use the same coefficients. It will have a constant suitable for the given point.

  given: 2x +y = 4

  parallel: 2x +y = c

  through point (-1, 3): 2x +y = 2(-1) +(3) = 1

The equation of the parallel line is 2x+y = 1.

Answer:

Step-by-step explanation:

Transversal or Corresponding angles

x=5

Answer:

a: alternate angle

Step-by-step explanation:

alternative relation

Answer:

Step-by-step explanation:

first u add them all up 949

1080-949=131 degrees for the first 1

second one is 36.5

tell me if the answers r wrong

The answer is x = 2

I have attached a picture with the work

6.

We know area of circle is

Radius increases at a rate of 4.

So, we can write:

We want rate of change of area. Thus,

We want dA/dt at r = 7, so substituting all that we know:

The correct answer: 56*pi m^2/min

Answer:

y = 90

Step-by-step explanation:

Given,

x and y vary directly

Also, when y = 120, x = 15

So,

x = 1, y = 120/15 = 8

Therefore, when x = 6, y = 90

Step-by-step explanation:

you can ask questions for clarification

Answer:

The graph depicting inequality y > -2x - 3 is C

The quadratic equation is of the form y = ax² + bx + c

In algebra, a polynomial function with one or more variables in which the highest-degree term is of the second degree is known as a quadratic function, a quadratic polynomial, a polynomial of degree just 2, or simply known as a quadratic.

Complete question: The table represents a quadratic function. Write an equation of the function in standard form.

[tex]$$\begin{array}{lllll}x & -9 & -7 & -5 & -3\end{array}$$$\begin{array}{lllll}y & 0 & 8 & 8 & 0\end{array}$[/tex]

y=

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Answer:

59.40

Step-by-step explanation:

Sheila's mapping diagram doesn't represent a function because it includes the points (3, 6) and (3, 6) and fails the vertical line test.

An illustration of two circles that depicts the relationship between input and output values is known as a mapping diagram. By drawing an arrow from one x-value to its corresponding y-value, the x-values (inputs) in the image are transferred to the y-values (outputs).

It does not represent a function because the same input value, 3, is mapped to more than one output value, 3 and 6. Her relation has the following ordered pairs: (1, 1), (2, 2), (3, 3), (3, 6), (4, 4), 5, 5), and (6, 6). Since both (3, 3) and (3, 6) have the same x-coordinate, the relation fails the vertical line test and is not a function.

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Sheila is playing a game with a 6-sided number cube. The number rolled determines the number of spaces moved. However, if a 3 is rolled, the player can choose to move 3 or 6 spaces. This mapping diagram shows the inputs and outputs for Sheila's game.

Does Sheila's mapping diagram represent a function? Why or why not?

Answer: (1, 4)

Use a grapher

In the picture, There is graph with a triangle SNZ. The reflected triangle of y=3 as (1,2),(5,3) and (5,5).

Given that,

In the picture, There is graph with a triangle.

The triangle is SNZ.

We have to find the reflection across y=3.

We have to draw a line on y=3.

On the line y=3,

Z point is there so it will be same that is (5,3).

Now, the point S is on (5,1)

Here, y is 1 that is 3+2=5

So, we take the reflected S point as (5,5)

Now, the point N is on (1,4)

Here, y is 4 that is 3-1=2

So, we take the reflected N point as (1,2).

Therefore, we get the reflected triangle of y=3 as (1,2),(5,3) and (5,5).

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The thing that is wrong with the bookkeeper’s entry assuming Karlin uses the allowance method is that the company uses allowance method and thus the write-off entry would not be to bad debt account.

How yo illustrate the information?

It should be noted that because the business is using the allowance approach in this instance, the write-off entry would not be to the account for bad debts. To write off an account, a debit must be made to a separate account that is kept as an allowance for dubious accounts.

Since the receivables would not be collected, the accounts receivable account would be credited. In this case,the write off isn't appropriately illustrated in the account.

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The new bookkeeper at Karlin Construction Company was asked to write off two accounts totaling $1,610 that had been determined to be uncollectible. Accordingly, he debited Accounts Receivable for $1,610 and credited Bad Debt Expense for the same amount.

Determine what was wrong with the bookkeeper’s entry assuming Karlin uses the allowance method.

Answer:

Negative 2, negative 3 + i StartRoot 3 EndRoot, negative 3 minus i StartRoot 3 EndRoot.

Step-by-step explanation:

So basically that whole last section you had your answer should look like this:

We have that the following two points lie on the line:

• (-2, 0) and (4, 6)

And we need to find the equation of the line that passes through both points.

To find the equation of the line, we can proceed as follows:

1. Apply the two-point equation of the line, which is given by:

2. We have to label both points as follows:

• (-2, 0) ---> x1 = -2, y1 = 0

• (4, 6) ---> x2 = 4, y2 = 6

3. Now, we can substitute the corresponding points into the two-point equation of the line:

Therefore, we have that the slope of the line is m = 1, and the equation of the line is y = x + 2.

Therefore, in summary, the equation of the line is y = x + 2 (Option D).

Answer:

815/99 (fraction); 8 23/99 (mixed number)

Step-by-step explanation:

the fraction for 0.23 repeating is 23/99

you add 8 in front of it

8 23/99 is the mixed number version

for the fraction version you must multiply 99 to 8 and then add it to 23

8 * 99 = 792

792 + 23 = 815

so

the fraction is 815/99

Answer:

[tex]{ \tt{volume = \frac{4}{3} \pi {r}^{3} }} \\ \\ { \tt{v = \frac{4}{3} \pi {r}^{3} }} \\ \\ { \tt{area = \frac{dv}{dr} = 4\pi {r}^{2} }} \\ \\ { \tt{area = \frac{d(3x + 1)}{dx} }} \\ \\ { \tt{area = 3 \: {cm}^{2} }}[/tex]

Answer: 3 x 3 x 5 x 5 x 7 x 11.

Step-by-step explanation:

Prime Factors of 17325 are 3, 5, 7, 11, and usually expressed as 3 x 3 x 5 x 5 x 7 x 11.

Step-by-step explanation:

[tex] \sqrt{8} x - \sqrt{2} x = 4[/tex]

[tex]x( \sqrt{8} - \sqrt{2} ) = 4[/tex]

[tex]x = \frac{4}{ \sqrt{8} - \sqrt{2} } [/tex]

the second term could be positive or negative

therefore

x=2.83 or

=-2.83

which is the square root of 8 - and positive

Answer:   Triangle

Reason:

A circle that goes through all three vertices of a triangle is known as the circumcircle. Every triangle has such a circle, which is why we can inscribe a triangle inside a circle.

The length of the actual schoolyard given the scale is 144 meters

A scale drawing is either an enlarged or reduced image of another image or object. A scale drawing is enlarged or reduced using a scale. The scale drawing is usually reduced at a constant dimension using a scale. A scale is the ratio of the dimensions of the scale drawing and the dimensions of the original image.

Length of the actual schoolyard = (length of the school yard x scale of the schoolyard) / scale of the drawing

(324 x 4) / 9 = 144 meters

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It should be noted that when multiplying powers you add rather than multiply the exponents in order to give an accurate value as multiplication do powers means the addition of the powers.

Exponentiation is a mathematical process that involves the base b and the exponent or power n. It is represented as bⁿ and is pronounced as "b to the n."

Algebra is the study of mathematical symbols, and logic is the manipulation of those symbols.

For example 3⁴ × 3² will be 3^6 rather than 3^8.

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Answer:

a=11

Step-by-step explanation:

If both triangles have two sides E and G the same then thethird side F and H must be equal

EF=EH

6a=55+a

5a=55

a=11

Since the area of the solution is below the x-axis, and includes the line.

y ≤ 0