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3 years ago

What is the length of Line segment B C? 9 units 11 units 15 units 16 units

Mathematics

2 answers:

Ivahew [28]3 years ago

8 0

Answer:

its 15

Step-by-step explanation:

denpristay [2]3 years ago

3 0

Answer:

15 units

Step-by-step explanation:

The picture of the question in the attached figure

we know that

In the right triangle ABC

Applying the Pythagorean Theorem

$AB^2=AC^2+BC^2$

we have

$AB=17\ units\\AC=8\ units$

substitute the given values

$17^2=8^2+BC^2$

solve for BC

$289=64+BC^2\\BC^2=289-64\\BC^2=225\\BC=15\ units$

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Find the numbers a, b and c if the polynomial x3−18x2+24xb−c is the cube of the binomial x+2a.

mojhsa [17]

Answer:

$a=-3\\ \\b=\dfrac{9}{2}\\ \\c=216$

Step-by-step explanation:

Use formula

$(u+v)^3=u^3+3u^2v+3uv^2+v^3.$

Hence,

$(x+2a)^3=x^3+3x^2\cdot 2a+3x\cdot (2a)^2+(2a)^3=x^3+6ax^2+12a^2x+8a^3.$

This expression is equal to

$x^3-18x^2+24bx-c,$

so we can equate the coefficients at powers of x:

$x^3:\ 1=1\\ \\x^2:\ 6a=-18\Rightarrow a=-3\\ \\x:\ 12a^2=24b\Rightarrow b=\dfrac{9}{2}\\ \\1=x^0:\ 8a^3=-c\Rightarrow c=-8\cdot (-3)^3=216.$

6 0

3 years ago

What is the slope of the line?

erik [133]

Down 3 over 1
aka -3 is the slope
Your first point is (1,4) The second is (2,1). Use the formula
y-y
x-x = slope
4-1
1-2 = slope
3
-1
3/-1 equal to -3

4 0

2 years ago

Read 2 more answers

Write -1/16, 5/3, and -5/6 in order least to greatest

antoniya [11.8K]

in order least to greatest
-5/6, -1/16, 5/3

hope it helps

7 0

3 years ago

Worth 48 points!!!! plz help me.

Mrac [35]

Answer:

see below

Step-by-step explanation:

1. The inverse means take the not of both sides

If it is Saturday, then there is no school.

Inverse If it is not Saturday, then there is school.

The converse flips the then and the if

If there is no school, then it is Saturday.

2.) The first given part is the if, what will happen is the then part

If you are a freshman, then you are required to attend orientation.

3.)

Given: 3x+1=-14 Prove: x=-5

Statements Reasons

1. 3x+1=-14 Given

2. 3x=-15 Subtraction Property of equality ( since we subtract 1 from each side)

3. X=-5 Division Property ( since we divide each side by 3)

3 0

3 years ago

Read 2 more answers

2. Solve the system of equations. Write your answer in parametric vector notation. X, +5x2 + 4x3 + 3x4 +9xs = 18 2x, +6x2 + 4x3

ratelena [41]

Answer:

The system is inconsistent.

Step-by-step explanation:

The system is

$x_1+5x_2+4x_3+3x_4+9x_5=18\\2x_1+6x_2+4x_3+6x_4+6x_5=28\\3x_1+7x_2+4x_3+10x_4+x_5=41\\4x_1+6x_2+2x_3+7x_4+4x_5=29$

The associated matrix to the system is

$\left[\begin{array}{cccccc}1&5&4&3&9&18\\2&6&4&6&6&28\\3&7&4&10&1&41\\4&6&2&7&4&29\end{array}\right]$

Now we use row operations to find the echelon form of the matrix:

1. We substract to row 2, two times the row 1.

We substract to row 3, three times the row 1.

We substract to row 4, four times the row 1 and obtain the matrix

$\left[\begin{array}{cccccc}1&5&4&3&9&18\\0&-4&-4&0&-12&-8\\0&-8&-8&1&-26&-13\\0&-14&-14&-5&-32&-43\end{array}\right]$

2. We multiply the second row of the preview step by -1/4. We obtain the matrix

$\left[\begin{array}{cccccc}1&5&4&3&9&18\\0&1&1&0&3&2\\0&-8&-8&1&-26&-13\\0&-14&-14&-5&-32&-43\end{array}\right]$

We add to row 3, eight times the row 2.

We add to row 4, fourtheen times the row 2 and obtain the matrix

$\left[\begin{array}{cccccc}1&5&4&3&9&18\\0&1&1&0&3&2\\0&0&0&1&-2&3\\0&0&0&-5&10&-155\end{array}\right]$

4. We add to row 4 of the preview step, five times the row 3 and obtain the matrix

$\left[\begin{array}{cccccc}1&5&4&3&9&18\\0&1&1&0&3&2\\0&0&0&1&-2&3\\0&0&0&0&0&-140\end{array}\right]$

Using backward substitution we have that

$0x_5=-140$ , then $0=-140$ and this is absurd. Then The system is inconsistent.

4 0

3 years ago