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netineya [11]
3 years ago
5

What is the measure of angle B in degrees?

Mathematics
2 answers:
natta225 [31]3 years ago
6 0

Answer: how do I delete my answer?

Step-by-step explanation.

yulyashka [42]3 years ago
3 0

Here's the solution,

=》 C + 112° = 180°

( they form linear pair )

=》 C = 180° - 112°

=》C = 68°

And we know, measure of exterior angle if a triangle is equal to the sum of measures of the opposite interior angles,

So,

=》B = C + 51°

=》B = 68° + 51°

=》B = 119°

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A jumping spider's movement is modeled by a parabola. The spider makes a single jump from the origin and reaches a maximum heigh
aleksklad [387]

The spider's movement is an illustration of a parabola.

  • The equation of a parabola is: \mathbf{y = -\frac{1}{160}(x - 40) + 10}
  • The focus of a parabola is: (40,-30)
  • The axis of symmetry is: \mathbf{x = 40}
  • The directrix is:\mathbf{y = 50}

<u>(a) The equation</u>

The spider passes through the origin.

So, we have:

\mathbf{(x,y) = (0,0)}

The spider jumps to a maximum height of 10mm, midway 80mm.

So, the vertex is:

\mathbf{(h,k) =  (40,10)}

The equation of a parabola is:

\mathbf{y = a(x - h)^2 + k}

So, we have:

\mathbf{0 = a(0 - 40)^2 + 10}

Subtract 10 from both sides

\mathbf{a(0 - 40)^2 =- 10}

\mathbf{1600a =- 10}

Solve for a

\mathbf{a =- \frac{1}{160}}

Substitute \mathbf{a =- \frac{1}{160}} and \mathbf{(h,k) =  (40,10)} in \mathbf{(h,k) =  (40,10)}

\mathbf{y = -\frac{1}{160}(x - 40) + 10}

<u>(b) The focus, directrix and the axis of symmetry</u>

The focus of a parabola is:

\mathbf{Focus= (h, k + p)}

Where:

\mathbf{p = \frac{1}{4a}}

So, we have:

\mathbf{p = \frac{1}{4 \times -1/160}}

\mathbf{p = -\frac{160}{4}}

\mathbf{p = -40}

So, we have:

\mathbf{Focus = (40,10-40)}

\mathbf{Focus = (40,-30)}

The axis of symmetry is:

\mathbf{x = h}

So, we have:

\mathbf{x = 40}

The directrix is:

\mathbf{y = k - p}

\mathbf{y = 10 + 40}

\mathbf{y = 50}

Read more about parabolas at:

brainly.com/question/25237745

4 0
2 years ago
Solve x(−2)3=−2(5). The solution is x=
Solnce55 [7]
Exact form : 5/3
decimal form : 1.6 repeating
mixed number form : 1 2/3
6 0
2 years ago
Find the product of 543.1187 and 100.
Natasha_Volkova [10]
A 54,311.87
It moves the decimal places to the left by two.
3 0
3 years ago
Solve the question: (-4)+(-1)+2+5+...+x=437
Alex Ar [27]
The sequence is an arithmetic sequence with
a₁ = -4

d = a₂ - a₁
d = -1 - (-4)
d = -1 + 4
d = 3

an = x

Sn = 437


General formula in arithmetic sequence
Formula to find nth term
an = a₁ + d(n - 1)
Formula to find sum of sequence (sn)
Sn = n/2 (a₁ + an)

We have to make an equation system based on the problem
plug the numbers into the formula
First equation
an = a₁ + d(n - 1)
x = -4 + 3(n - 1)
x = -4 + 3n - 3
x = 3n - 7

Second equation
Sn = n/2 (a₁ + an)
n/2 (a₁ + an) = 437
n/2 (-4 + x) = 437
n(x -  4) = 874
xn - 4n = 874

Solve the equation system by subtitution method
Subtitute x with 3n - 7 in the second equation
xn - 4n = 874
(3n - 7)n - 4n = 874
3n² - 7n - 4n = 874
3n² - 11n - 874 = 0
(3n + 46)(n - 19) = 0
n = -46/3 or n = 19
Because the number of terms shouldn't be negative, -46/3 isn't required, so the value of n is 19.

Solve for x, back to the first equatin
x = 3n - 7
x = 3(19) - 7
x = 57 - 7
x = 50

The solution is 50
6 0
3 years ago
Hi im Elizabeth and im new what do i do
Gwar [14]

Answer:

You ask and answer questions to get help and help others.

3 0
2 years ago
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