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fiasKO [112]
3 years ago
11

CANT GET WRONG What is the measure of ∠ADC? A) 42° B) 47° C) 121° D) 131°

Mathematics
2 answers:
creativ13 [48]3 years ago
8 0

Answer:

131

Step-by-step explanation:

The correct answer is D

Dafna1 [17]3 years ago
7 0
Add them
89+42=131


answer is D
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A line has a y intercept of 7 and a slope of 3/4, and goes DOWNHILL. What is the equation of this line?
Vladimir79 [104]

the answer is b, if not then try d:)

4 0
2 years ago
Read 2 more answers
The system of equations may have a unique solution, an infinite number of solutions, or no solution. Use matrices to find the ge
Leno4ka [110]

Answer:

Infinite number of solutions.

Step-by-step explanation:

We are given system of equations

5x+4y+5z=-1

x+y+2z=1

2x+y-z=-3

Firs we find determinant of system of equations

Let a matrix A=\left[\begin{array}{ccc}5&4&5\\1&1&2\\2&1&-1\end{array}\right] and B=\left[\begin{array}{ccc}-1\\1\\-3\end{array}\right]

\mid A\mid=\begin{vmatrix}5&4&5\\1&1&2\\2&1&-1\end{vmatrix}

\mid A\mid=5(-1-2)-4(-1-4)+5(1-2)=-15+20-5=0

Determinant of given system of equation is zero therefore, the general solution of system of equation is many solution or no solution.

We are finding rank of matrix

Apply R_1\rightarrow R_1-4R_2 and R_3\rightarrow R_3-2R_2

\left[\begin{array}{ccc}1&0&1\\1&1&2\\0&-1&-3\end{array}\right]:\left[\begin{array}{ccc}-5\\1\\-5\end{array}\right]

ApplyR_2\rightarrow R_2-R_1

\left[\begin{array}{ccc}1&0&1\\0&1&1\\0&-1&-3\end{array}\right]:\left[\begin{array}{ccc}-5\\6\\-5\end{array}\right]

Apply R_3\rightarrow R_3+R_2

\left[\begin{array}{ccc}1&0&1\\0&1&1\\0&0&-2\end{array}\right]:\left[\begin{array}{ccc}-5\\6\\1\end{array}\right]

Apply R_3\rightarrow- \frac{1}{2} and R_2\rightarrow R_2-R_3

\left[\begin{array}{ccc}1&0&1\\0&1&0\\0&0&1\end{array}\right]:\left[\begin{array}{ccc}-5\\\frac{13}{2}\\-\frac{1}{2}\end{array}\right]

Apply R_1\rightarrow R_1-R_3

\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right]:\left[\begin{array}{ccc}-\frac{9}{2}\\\frac{13}{2}\\-\frac{1}{2}\end{array}\right]

Rank of matrix A and B are equal.Therefore, matrix A has infinite number of solutions.

Therefore, rank of matrix is equal to rank of B.

4 0
3 years ago
Locate the points of discontinuity in the piecewise function shown below.
algol13

Answer:

Step-by-step explanation:

The given piecewise function i

From the given function it is clear that function is divided at x=-1 and x=2. It means we check the discontinuity at x=-1 and x=2.

For x=-1,

LHL:  

Since LHL ≠ f(-1), therefore the given function is discontinuous at x=-1.

For x=2,

LHL:  

Since LHL ≠ f(2), therefore the given function is discontinuous at x=2.

Therefore, the correct option is A.

8 0
3 years ago
10. 10. If AB bisects CAF, and m&lt;EAF = 72°,<br>then the m&lt;BAF =​
never [62]

The measure of ∠BAF is 54°.

Solution:

DF and CE are intersecting lines.

m∠EAF = 72° and AB bisects ∠CAF.

∠EAF and ∠DAC are vertically opposite angles.

Vertical angle theorem:

<em>If two lines are intersecting, then vertically opposite angles are congruent.</em>

∠DAC ≅ ∠EAF

m∠DAC = 72°

<em>Sum of the adjacent angles in a straight line = 180°</em>

m∠DAE + m∠EAF = 180°

m∠DAE + 72° = 180°

Subtract 72° from both sides.

m∠DAE = 108°

∠CAF and ∠DAE are vertically opposite angles.

⇒ m∠CAF = m∠DAE

⇒ m∠CAF = 108°

AB bisects ∠CAF means ∠CAB = ∠BAF

m∠CAB + m∠BAF = 108°

m∠BAF + m∠BAF = 108°

2 m∠BAF = 108°

Divide by 2 on both sides, we get

m∠BAF = 54°

Hence the measure of ∠BAF is 54°.

4 0
3 years ago
You need 660 mL of a 40% alcohol solution. On hand, you have 35% alcohol mixture. You also have a 95% alcohol mixture. How much
ozzi

Answer:

A. 605 mL of the 35% solution

B. 55 mL of the 95% solution

Step-by-step explanation:

It is given that, you need 660 mL of a 40% alcohol solution. On hand, you have 35% alcohol mixture. You also have a 95% alcohol mixture.

Let x and y be the amount of 35% alcohol solution and 95% alcohol solution (in mL) respectively.

So,

Amount equation: x+y=660        ...(1)

Alcohol equation : 0.35x+0.95y=0.40(660)\Rightarrow 0.35x+0.95y=264     ...(2)

On solving (1) and (2), we get

0.35(660-y)+0.95y=264

231-0.35y+0.95y=264

0.6y=264-231

y=\dfrac{33}{0.6}

y=55

Now, substitute y=55 in (1).

x+55=660  

x=660-55  

x=605  

Therefore, we need 605 mL of the 35% solution  and 55 mL of the 95% solution.

4 0
3 years ago
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