If there are g girls and b-boys in a room, write an expression for the total number of children in the room.

Equaling both equations, it is found that the correct option that states the number of solutions you will have for the system is:

The equations are:

[tex]4y + x = 16 \rightarrow x = 16 - 4y[/tex]

[tex]y = 4 - x \rightarrow x = 4 - y[/tex]

Equaling both equations for x, we have that:

[tex]16 - 4y = 4 - y[/tex]

[tex]3y = 12[/tex]

[tex]y = \frac{12}{3}[/tex]

[tex]y = 4[/tex]

[tex]x = 4 - y = 4 - y = 0[/tex]

Hence, the system has one solution, which is (0,4), and option d is correct.

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Answer:

$5.84

Step-by-step explanation:

Part 1) Computing (p °q) (5)

[tex]p(x) = x-3\\\\p(q(x)) = q(x)-3\\\\(p \circ q)(x) = 2x-5-3\\\\(p \circ q)(x) = 2x-8\\\\(p \circ q)(5) = 2(5)-8\\\\(p \circ q)(5) = 2\\\\[/tex]

===========================================================

Part 2) Computing   (q °p) (5)

[tex]q(x) = 2x-5\\\\q(p(x)) = 2(p(x))-5\\\\q(p(x)) = 2(x-3)-5\\\\(q \circ p)(x) = 2x-6-5\\\\(q \circ p)(x) = 2x-11\\\\(q \circ p)(5) = 2(5)-11\\\\(q \circ p)(5) = -1\\\\[/tex]

Answer: -30

Step-by-step explanation:

-2 X -5 = 10

10 X -3 = -30

Therefore, -2(-5)(-3) = -30

The multiplication of −2(−5)(−3) is -30

The multiplication of numbers in brackets with negative signs takes a method whereby the signs are taken into account when performing the arithmetic operation.

From the given question, we are to multiply:

= - 2 × (-5) × (-3)

= +10 × (-3)

= -30

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Answer:

m=-7/15

Step-by-step explanation:

Answer:

Step-by-step explanation:

7/15

Answer:

d four

Step-by-step explanation:

How many solutions does the nonlinear system of equations graphed below have?  

Look at the number of points where the graphs intersect each other...the points where the graphs of the functions cross each other are the solutions to the system.  

Upon looking, you should see 4 points where the graphs intersect, so there are 4 solutions to the non-linear system of equations.

Answer:

6/8 and 12/16

Step-by-step explanation:

Important: 3/4 looks like a fraction, but it is actually an improper fraction.

There is an infinity number of equivalent fractions to 3/4. To find an equivalent fraction to 3/4 , or to any other fraction, you just need to multiply (or divide, if the fraction is not yet reduced), both the numerator and the denominator of the given fraction by any non-zero natural number. For example:

By multiplying the original fraction by 2, we get:

3x2/3x2=6/8

List of Equivalent Fractions of 3/4:

3/4, 6/8, 9/12, 12/16, 15/20, 18/24, 21/28, 24/32, 27/36, 30/40, 33/44, 36/48, 39/52, 42/56, 45/60, 48/64, 51/68, 54/72, 57/76, 60/80 ...

Answer:

See below

Step-by-step explanation:

(-4,0) is the solution to x+4=0

(0,0) is the solution to x=0

(2,0) is the solution to x-2=0

Therefore, (x+4)(x-2)(x) = (x²-2x+4x-8)(x) = (x²+2x-8)(x) = x³+2x²-8x is the function that has the given zeroes

Answer:

I believe that it would take 5 hours for 8 people to paint 8 fences.

Step-by-step explanation:

If 2 people are painting 2 fences in 5 hours, then 8 people can also paint 8 fences in the same time because each person is painting one fence. It take 5 hours to paint 1 fence if 1 person is painting it. The same goes for 2 or 8 people painting the same amount of fences as there are people. Im not 100% sure if this is accurate but I hope it helps.

Answer:

25 kilograms

Step-by-step explanation:

The plane flies a distance of approximately 10.536 kilometers in straight line and with a bearing of approximately 035°.

A plane that travels a distance [tex]r[/tex], in kilometers, with a bearing of [tex]\theta[/tex] sexagesimal degrees can be represented in standard position by means of the following expression:

[tex]\vec r = r\cdot (\sin\theta, \cos \theta)[/tex] (1)

We can obtain the resulting vector ([tex]\vec R[/tex]) by the principle of superposition:

[tex]\vec R = \Sigma_{i=1}^{n} [r_{i}\cdot (\sin \theta_{i}, \cos \theta_{i})][/tex] (2)

If we know that [tex]r_{1} = 5\,km[/tex], [tex]\theta_{1} = 0^{\circ}[/tex], [tex]r_{2} = 6\,km[/tex], [tex]\theta_{2} = 60^{\circ}[/tex], [tex]r_{3} = 4\,km[/tex] and [tex]\theta_{3} = 120^{\circ}[/tex], then the resulting vector is:

[tex]\vec R = 5\cdot (\sin 0^{\circ}, \cos 0^{\circ}) + 6\cdot (\sin 60^{\circ}, \cos 60^{\circ}) + 4\cdot (\sin 120^{\circ}, \cos 120^{\circ})[/tex]

[tex]\vec R = (5\sqrt{3}, 6) \,[km][/tex]

The magnitude of the resultant is found by Pythagorean theorem:

[tex]\|\vec R\| = \sqrt{R_{x}^{2}+R_{y}^{2}}[/tex]

And the bearing is determined by the following inverse trigonometric relationship:

[tex]\theta_{R} = \tan^{-1} \left(\frac{R_{y}}{R_{x}}\right)[/tex] (3)

If we know that [tex]R_{x} = 5\sqrt{3}\,km[/tex] and [tex]R_{y} = 6\,km[/tex], then the magnitude and the bearing of the resultant is:

[tex]\|\vec R\| = \sqrt{(5\sqrt{3})^{2}+6^{2}}[/tex]

[tex]\|\vec R\| \approx 10.536\,km[/tex]

[tex]\theta_{R} = \tan^{-1} \left(\frac{6}{5\sqrt{3}} \right)[/tex]

[tex]\theta_{R} \approx 34.715^{\circ}[/tex]

The plane flies a distance of approximately 10.536 kilometers in straight line and with a bearing of approximately 035°.

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Answer:

cylinder has greatest volume

Step-by-step explanation:

solution

given,

radius of cylinder(r)=6cm

height of cylinder (h)=6cm

we know,

volume of cylinder=πr^2h

=22÷7×6×6×6

=4752÷7

=678.857cm^3

radius of cone(r)=6cm

height of cone(h)=12cm

we know,

volume of cone=1÷3πr^3

= 1÷3×22÷7×6×6×6

= 4752÷21

=226.2857cm^3

as a result,cylinder has greatest volume

Applying the inscribed angle theorem, the missing measures are:

measure of arc TR = 106°

measure of arc TL = 74°

m∠L = 50°

m∠R = 37°

m∠RTV = 37°

Measure of an inscribed angle = half the measure of the arc it intercepts

Central angle = measure of intercepted arc

We are given the following:

LR and TV are diameters of the circle O.

m∠TOR = 106° (central angle)

Find measure of arc TR:

measure of arc TR = m∠TOR

measure of arc TR = 106°

Find measure of arc TL:

measure of arc TL = 180° - m∠TOR

measure of arc TL = 180° - 106°

measure of arc TL = 74°

Find m∠L:

m∠L = ½(measure of arc TR)

m∠L = ½(106°)

m∠L = 50°

Find m∠R:

m∠R = ½(measure of arc TL)

m∠R = ½(74°)

m∠R = 37°

Find m∠RTV:

m∠RTV = ½(measure of arc RV)

m∠RTV = ½(180 - 106)

m∠RTV = ½(74)

m∠RTV = 37°

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1. Assuming OP || NM, considering the triangle proportionality theorem possible measurements for the segments are: ON = 3 units, LO = 1 unit, PM = 6 units, LP = 2 units

2. The possible values are decided by assuming  [tex]\frac{ON}{LO} = \frac{PM}{LP} = 3[/tex] using the triangle proportionality theorem.

3. Another method is applying the AA Similarity Theorem to compare corresponding side lengths of the triangles that are proportional to each other.

Triangle proportionality theorem states that if a line is parallel to one of the sides of a triangle intersects two of the other two sides, it divides the two sides into proportional corresponding segments.

1. Assuming that OP || NM, we would apply the triangle proportionality theorem to have the following ratio:

[tex]\frac{ON}{LO} = \frac{PM}{LP}[/tex]

Using the above ratio, we can choose the following possible lengths for the segments:

ON = 3 units

LO = 1 unit

PM = 6 units

LP = 2 units

2. The values are decided assuming that the ratio, [tex]\frac{ON}{LO} = \frac{PM}{LP} = 3[/tex]

This means that the ratio of the proportional segments, irrespective of the their measurement should give you an assumed equal ratio of 3:1.

Therefore, since:

[tex]\frac{3}{1} = 3\\\\\frac{6}{2} = 3[/tex]

The measurements, ON = 3 units, LO = 1 unit, PM = 6 units, LP = 2 units are therefore possible measurements.

3. Using the AA Similarity Theorem to prove that ΔLPO ≅ ΔLMN, the corresponding sides of both triangles will be proportional.

LP/LM = LO/LN = PO/MN

We can use this to choose possible measurements while assuming a ratio between the proportional sides of both triangles.

Let's assume that: LP/LM = LO/LN = PO/MN = 1/4

Let,

LO = 1 unit

LN = 4 units

Therefore, ON = LN - LO = 4 - 1 = 3 units.

Same way the other possible measures can be gotten provided a ratio is assumed.

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Answer:

what are your options ??

Step-by-step explanation:

Answer: your answer is A) & D)

Step-by-step explanation:     Hope this helps :)

Answer:

A) (-5,10), (0,15), (5,10)

Step-by-step explanation:

In order for an ordered pair to be a function, no pair of coordinates can have the same x variable.

no why? cause the guy bought 2 shirts for 19 dollors each where was he at nikes?  on average a shirt cost 15 bucks but 19? yeah no

Answer:

Step-by-step explanation:

no why? cause the guy bought 2 shirts for 19 dollors each where was he at nikes?  on average a shirt cost 15 bucks but 19? yeah no

Answer:

Second and fourth

Step-by-step explanation:

A line is in point-slope form when you write down as [tex]y-y_0=m(x-x_0)[/tex] - do not be distracted by the signs, +1 and +5 can both be written as -(-1) or -(-5) rispectively.

Answer:

t = 11/21

Step-by-step explanation:

Hope this helps!!

Answer: 23,364

Step-by-step explanation:6 x 3000 + 6 x 800 + 6 x 90 + 6 x 4

Answer:

$0.44

Step-by-step explanation:

lmk if you want an explanation

Answer:

$88

Step-by-step explanation:

442.70 rounded to the nearest 10 dollars is 440.

20%= .2.

440 times .2 =

88

Answer:

Step-by-step explanation:

(x + 2y²)(2x - 2y²)

FOIL

First

x(2x) = 2x²

Outside

x(-2y²) = - 2xy²

Inside

2y²(2x) = 4xy²

Last

2y²(-2y²) = - 4y⁴

combine like terms

2x² + 2xy² - 4y⁴

Answer:

-4y^4 + 2xy^2 + 2x^2

Step-by-step explanation:

(x + 2y^2) (2x - 2y^2)

x(2x) + x(-2y^2) = 2x^2 - 2xy^2

2y^2(2x) + 2y^2(2y^2) = 2xy^2 + 4y^4

2x^2 - 2xy^2 + 4xy^2 - 4y^4

2x^2 + 2xy^2 - 4y^2

or

-4y^4 + 2xy^2 + 2x^2

[tex]\text{Given that,}\\\\(x+2y)^2 - (x-2y)^2\\\\=(x+2y +x -2y)(x+2y -x+2y)~~~~;[a^2 - b^2 = (a+b)(a-b)]\\\\=(2x)(4y)\\\\=8xy[/tex]

Explanation:

Start by calculating the first derivative of f(x) - use the quotient rule

ddx(f(x))=[ddx(x2)]⋅(x2+3)−x2⋅ddx(x2+3)(x2+3)2

f′=2x⋅(x2+3)−x2⋅2x(x2+3)2

f′=2x3+6x−2x3(x2+3)2=6x(x2+3)2❤