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Anastaziya [24]

2 years ago

13

Graph a line that contains the point (-5,-3)(−5,−3)left parenthesis, minus, 5, comma, minus, 3, right parenthesis and has a slop

e of -2−2minus, 2.
Graph a line that contains the point (-5,-3)(−5,−3)left parenthesis, minus, 5, comma, minus, 3, right parenthesis and has a slope of -2−2minus, 2.

1 answer:

dmitriy555 [2]2 years ago

3 0

Point (-5,-3) Slope -2
Y - y1 = m (x - x1)
y + 3 = -2 (x + 5)
y + 3 = -2x - 10
y = -2x -13

The line will also go through the point (0, -13)

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Six teachers and 12 students volunteer for a committee to discuss extra-curricular activities. How many committees of 5 people c

Alex17521 [72]

Answer:

a) $X=3300$

b) $Y=7770$

Step-by-step explanation:

From the question we are told that:

Number Teachers $T=6$

Number Student $S=12$

Number in committee $n=5$

a) Generally the equation for exactly 3 students on the committee is mathematically given by

$X=^{S}C_3*^{T}C_3$

$X=^{12}C_3*^{6}C_3$

$X=3300$

b) Generally the equation for at least one teacher and at least one student on the committee is mathematically given by

Total Ways-(no of ways of selection no teacher or student)

Where total Ways

$T=^{(6+12)}C_5$

$T=8568$

Therefore

$Y=8568-^{6}C_0*^{12}C_5+^{12}C_0*^{6}C_5$

$Y=8568-798$

$Y=7770$

8 0

2 years ago

In the figure below, \overline{AD} AD start overline, A, D, end overline and \overline{BE} BE start overline, B, E, end overline

VLD [36.1K]

Answer:

<u>The measure of the arc CD = 64°</u>

Step-by-step explanation:

It is required to find the measure of the arc CD in degrees.

So, as shown at the graph

BE and AD are are diameters of circle P

And ∠APE is a right angle ⇒ ∠APE = 90°

So, BE⊥AD

And so, ∠BPE = 90° ⇒(1)

But it is given: ∠BPE = (33k-9)° ⇒(2)

From (1) and (2)

∴ 33k - 9 = 90

∴ 33k = 90 + 9 = 99

∴ k = 99/33 = 3

The measure of the arc CD = ∠CPD = 20k + 4

By substitution with k

<u>∴ The measure of the arc CD = 20*3 + 4 = 60 + 4 = 64°</u>

6 0

2 years ago

The 8th term of a GP is -7/32 find its common ratio if its first term is 28

Ugo [173]

<h2>Common ratio = -1/2</h2>

Step-by-step explanation:

$\text{8}^{th}$ term of a Geometric progression is given as $\dfrac{-7}{32}$ . The first term is given as $28$ .

Any general Geometric progression can be represented using the series $a,ar,ar^{2},ar^{3},ar^{4}...\text{ }ar^{n-1}$ .

The first term in such a GP is given by $a$ , common ratio by $r$ , and the $n^{th}$ term is given by $ar^{n-1}$ .

In the given GP, $a=28;t_{8}=ar^{7}=\dfrac{-7}{32}\\\\28r^{7}=\dfrac{-7}{32}\\\\r^{7}=\dfrac{-1}{128}\\\\r=\dfrac{-1}{2}$

∴ Common ratio is $\dfrac{-1}{2}$ .

5 0

2 years ago

Charlie is watching hot air balloons. Balloon A has risen at a 60° angle. Balloon B has risen at an 82° angle. If the distance f

babymother [125]

Answer:

(B)1005 feet

Step-by-step explanation:

In the attached diagram

$\angle y =82^\circ\\\angle x =60^\circ$

|AG|=1400 feet

Distance from point C to point G=|CG|

Using Trigonometry in Triangle ACG

$\tan 60^\circ=\dfrac{1400}{CG}\\ CG=\dfrac{1400}{\tan 60^\circ}\\\approx 808$ feet$

Using Trigonometry in Triangle BCG'

$\tan 82^\circ=\dfrac{1400}{CG'}\\ CG'=\dfrac{1400}{\tan 82^\circ}\\\approx 197$ feet$

Therefore, the distance from balloon B from balloon A

=CG+CG'

=808+197

=1005 feet

4 0

2 years ago

Mr. Brent uses 1/4 cup of blue paint and 1/4 cup of yellow paint to make each patch of green paint. How many batches of green pa

harina [27]

12 batches of green paint

6 0

2 years ago

Read 2 more answers