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6. Solve for x

w=-1.5

w=2

Answer:

Solution given:

[tex]\sqrt{2w²-19w+31}+2=7-2w[/tex]

again

keep square root alone

[tex]\sqrt{2w²-19w+31}=7-2w-2[/tex]

solve subtraction of 7-2

[tex]\sqrt{2w²-19w+31}=5-2w[/tex]

Squaring on both side

[tex](\sqrt{2w²-19w+31})²=(5-2w)²[/tex]

2w²-19w+31=5²-2*5*2w+4w²

take terms one side

2w²-19w+31-25+20w-4w²=0

-2w²+w+6=0

2w²-w-6=0

doing middle term factorisation

2w²-(4-3)w-6=0

2w²-4w+3w-6=0

take common from each two term

2w(w-2)+3(w-2)=0

(w-2)(2w+3)=0

either

w=2

or

W=-3/2=-1.5

Answer:

0.6375 = 63.75% probability to select a pupil that uses the tennis courts.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

Total:

In total, there are 160 pupils.

Uses the tennis courts:

21 pupils use the swimming pool, the gym and the tennis courts.

48 pupils use the gym and the tennis courts, which adds 48 - 21 = 27 to the number of those who use the tennis courts.

40 pupils use the tennis courts and the swimming pool, which adds 40 - 21 = 19 to the number of those who use the tennis courts.

35 use the tennis courts only.

So

21 + 27 + 19 + 35 = 102 use the tennis courts.

Find the probability to select a pupil that uses the tennis courts.

102 out of 160, so:

[tex]p = \frac{102}{160} = 0.6375[/tex]

0.6375 = 63.75% probability to select a pupil that uses the tennis courts.

Answer:

Step-by-step explanation:

Answer:

3/(n + 3)

Step-by-step explanation:

The given probability that Sara wins a raffle draw, P = n/(n + 3)

Given that the sum of all probabilities is 1, we get

The probability that Sara does not win, Q = 1 - P

Therefore;

Q = 1 - n/(n + 3) = (n + 3) - n/((n + 3) = 3/(n + 3)

The probability that Sara does not win, Q = 3/(n + 3)

Answer:

20 degrees

Step-by-step explanation:

One angle is 70 degrees and the other is 90. Angles of a triangle add up to 180. 180 - 70 - 90 = 20. The final angle is 20 degrees.

Answer:

[tex]{ \tt{5a - 4b - 2{ (a - (2b + c))}}} \\ = { \tt{5a - 4b - 2a + 4b - 2c}} \\ { \tt{ = (5 - 2)a + ( - 4 + 4)b - 2c}} \\ { \tt{ = 3a - 2c}}[/tex]

Answer:

Step-by-step explanation:

5a - 4b -2[a - 2b + c] = 5a - 4b -2a + 4b - 2c     {Distributive property}

                                  = (5a - 2a) + (4b - 4b) - 2c   {Group like terms}

                                  = 3a - 2c

Total amount she wants to raise = $3200

Amount she'll get for each kilometer = $35

So, number of kilometers she need to run

= Total amount she wants to raise/Amount she'll get for each kilometer

= $3200/$35

= 91.42....

Since her sponser is will donate only for whole kilometers she'll have to run 92 km.

Answer: [tex]12\ ft[/tex]

Step-by-step explanation:

Given

Total height of utility pole is 18 ft

After breakage, only 5 foot tall portion is standing

The fallen part is [tex]18-5=13\ ft[/tex] in length

From the figure, apply the Pythagoras theorem

[tex]\Rightarrow 13^2=x^2+5^2\\\Rightarrow x^2=169-25\\\Rightarrow x=\sqrt{169-25}\\\Rightarrow x=\sqrt{144}\\\Rightarrow x=12\ ft[/tex]

Thus, the fallen part is [tex]12\ ft[/tex] away from the base of the pole.

Answer:

A

Step-by-step explanation:

f(x)+g(x)=-3x^2+4x+4+x(-7x-7)= -3x^2+4x+4 -7^2-7x

= -10x^2-3x+4

One of the ways to graph this is to use plug in a few x-values and get an idea of the shape. Since the x values keep getting squared, there is an exponential increase on either side of the y-axis. You can see this by plugging in a few values:

When

x=0,f(x)=0

x=1,f(x)=1^2=1

x=2,f(x)=2^2=4

x=3,f(x)=3^2=9

x=4,f(x)=4^2=16

The same holds true for negative x-values to the left of the y-axis since a negative value squared is positive. For example,

x=−1,f(x)=(−1)2=1*−1=1

x=2,f(x)=(−2)2=−2*−2=4

The graph of f(x)=x^2 is called a "Parabola." It looks like this:

Answer:

The answers are options A and C.

They are (-2,0) and (0,0).

Step-by-step explanation:

x-intercept

(-2,0) and (0,0)

Answer:

7/16 mile

Step-by-step explanation:

Distance of the loop = 7/8 mile

Distance of Water fountain = 1/2 of the Distance of the loop

= 1/2 of 7/8

Ibrahim stopped to get a drink of water at the water fountain. How far did Ibrahim run?

= 1/2 of 7/8

= 1/2 * 7/8

= (1 * 7) / (2 * 8)

= 7/16

Ibrahim ran 7/16 mile to drink water at the water fountain around the loop

Answer:

A

Step-by-step explanation:

The graph of h(x) = (x-3)^2. The (x-3) indicates that the graph is shifted horizontally right 3 units because the change takes place inside the parantheses. Because the units are being subtracted, the graph will shift to the right. I highly recommend using Desmos to find your answer next time.

Answer:

the second option : w should be 25 units

Step-by-step explanation:

the area of the rectangle is length×width = L×W

the perimeter of a rectangle = 2L + 2W

now, we know that the perimeter is 100 units.

and we have to find the best length of W, that will then define L (to keep the 100 units of perimeter) and maximizes the area of the rectangle.

in other words, what is the maximum area of a rectangle with perimeter of 100 (and what are the corresponding side lengths)?

now, w = 625 is impossible. that side alone would be bigger than the whole perimeter.

W = 0 would render the whole rectangle to a flat line with L = 50 because of

100 = 2L + 2W = 2L + 0 = 2L

L = 50

and A = L×W = 50×0 = 0

an area of 0 is for sure not the largest possible area.

w = 50 would cause L = 0

100 = 2L + 2W = 2L + 2×50 = 2L + 100

0 = 2L

L = 0

and with L = 0 the same thing happens as with W = 0 : a flat line with 0 area.

so, the only remaining useful answer is W = 25

100 = 2L + 2W = 2L + 2×25 = 2L + 50

50 = 2L

L = 25

A = L×W = 25×25 = 625 units²

and indeed, the maximum area for a given perimeter is achieved by arranging the sides to create a square.

Answer:

1. = 5 10 15 20 25

2. 2 4 6 8 10 12 14

X, y =10

Answer:

assuming that this is your question

[tex]log_{6} 36 = x[/tex]

[tex]6^{x} = 36[/tex]

x = 2

Note: your actual question log 636

is actually [tex]log_{10} 636 = x[/tex]

[tex]10^{x} = 636[/tex]

x = 2.803 (i am sure that tis not the question in your homework)

Step-by-step explanation:

Answer:

(-2,0)

Step-by-step explanation:

y < |x - 2|

Substitute the points in and check

(-2,0)

0 < |-2 - 2|

0 < |-4|

0 < 4  True

(2,1)

1 < |2 - 2|

1 < |0|

1 < 0  False

(2,0)

0 < |2 - 2|

0 < |0|

0 < 0 False

Answer:

Solution given:

7.<OYM=15°base angle of isosceles triangle

<OYL=50°base angle of isosceles triangle.

<OYL=<OYM+<MYL

50°=15°+<MYL

<MYL=50°-15°

<MYL=35°

again;

<MOL=35*2=70°central angle is double of a inscribed angle.

18.

Solution given:

<PQR+<PSR=180°sum of opposite angle of a cyclic quadrilateral is supplementary

<PQS+42°+78°=180°

<PQS=180°-120°=60°

<PQS=60°

<SPR=42°inscribed angle on a same arc is equal

:.<QPS=18°+42°=60°

<QSR=18°inscribed angle on a same arc is equal

again.

<PSR=78°

<QSR+<PSQ=78°

18°+<PSQ=78°

<PSQ=78°-18°

<PSQ=60°

In ∆ PQS

<PSQ=60°

<QPS=60°

<PQS=60°

In triangle ∆PQS all the angles are equal.

Answer:

5:4 or 1.25:1

Step-by-step explanation:

Answer:

The maximum  volume is 35316.4 in^3.

Step-by-step explanation:

Length + width + height is less than equal to 62 inches

Height = width = W

Let the length is L .

[tex]L + W + W = 62 \\\\L= 62 - 2 W\\\\Volume, V = L W H\\\\V = (62 - 2 W)\times W \times W\\\\V = 62 W^2 - 2 W^3\\\\\frac{dV}{dW}=124 W - 6 W^2\\\\So, \frac{dV}{dW} =0\\\\124 = 6 W\\\\W = 20.67 inches[/tex]

So, the maximum volume is

[tex]V =124\times 20.67\times 20.67 - 2 \times 20.67^3\\\\V =52978.86 - 17662.46 = 35316.4 inch^3[/tex]

Answer:

Below.

Step-by-step explanation:

4^(x+2)+4^(x+1)+4^x

= 4^x*4^2 + 4^x*4 + 4^4

= 4^x(16 + 4 + 1)

= 21*4^x.

As 21 is divisible by 7, 21*4^x is also divisible by 7  for all positive integers of x.

Thus the original expression must be also divisible by 7  for all positive integers of x.

Answer:

[tex]\angle ARU=40^{\circ}[/tex]

AU=20 units

[tex]m\angle QPA=35^{\circ}[/tex]

Step-by-step explanation:

We are given that

[tex]\angle ARQ=40^{\circ}[/tex]

AT=20 units

Point A is the incenter of triangle PQR.

Incenter is that point where three angle bisector of triangle meets.

AR is the bisector of angle R of triangle PQR.

Therefore, [tex]\angle ARQ=\angle ARU=40^{\circ}[/tex]

All right triangles are similar when two triangles are similar then the ratio of their corresponding sides are equal.

Right angled triangle ATP and Right triangle AUP are similar.

Therefore,

[tex]\frac{AT}{AU}=\frac{AP}{AP}=1[/tex]

[tex]\frac{20}{AU}=1[/tex]

[tex]AU=20[/tex]units

AP is the angle bisector  of angle P of triangle PQR

[tex]\angle APQ=\angle APU[/tex]

[tex]3x+2=4x-9[/tex]

[tex]2+9=4x-3x[/tex]

[tex]x=11[/tex]

Using the value of angle x

[tex]\angle APQ=3x+2=3(11)+2[/tex]

[tex]\angle APQ=35^{\circ}[/tex]

Hence, the measure of angle QPA=35 degree

The incenter of a triangle is the point of intersection of all the three interior angle bisectors of the triangle. This point is equidistant from the sides of a triangle.

Angle ARU = 40 degree

Length of AU = 20

Angle QPA = 35 degree

Here a figure is attached.

Since, AR is angle bisector of angle URK.

So,   ∠ARU = ∠ARK = 40 degree

Since, incenter point is equidistant from the sides of a triangle.

So, AT = AU = AK = 20

Since, PA is angle bisector of angle QPU.

So,  ∠QPA = ∠UPA

    3x + 2 = 4x - 9

    4x - 3x = 9 + 2

        x = 11

Substituting value of x in angle 3x + 2

We get,  ∠QPA = 3(11) + 2 = 35 degree

Learn more:

https://brainly.com/question/1620555

Answer:

[tex]f(t)=12(1.0139)^{12t}[/tex]

Step-by-step explanation:

Let the initial number of frogs = 12

And their population is growing with the annual growth rate = 16.68% per year

Function modeling the population after 't' years will be,

[tex]P(t)=12(1+r)^{t}[/tex]

Here, r = Annual growth rate

t = Number of years

If we convert the annual growth rate to monthly growth rate,

Expression modeling the population will be,

[tex]f(t)=12(1+\frac{r}{12})^{12t}[/tex]

       [tex]=12(1+\frac{16.68}{12})^{12t}[/tex]

       [tex]=12(1.0139)^{12t}[/tex]

Therefore, [tex]f(t)=12(1.0139)^{12t}[/tex] will be the answer.

[tex]\boxed{\large{\bold{\blue{ANSWER~:) }}}}[/tex]

[tex]\sf{ }[/tex]

Answer:

8/x-6

Step-by-step explanation:

When it says a number fewer, that means to put it behind rather than in the front.

Hope this helps!!:)

Answer:

The expression to represent the phrase is 8/x - 6.

Answer:

Volume=Area × height

=35×7

volume = {245} m³

OAmalOHopeO

Answer:

Since the area of the triangle(base) is known we now multiply it to the height so we can get the volume.

7 x 35 = 245 m3 is your answer

You can picture it too:

(sorry my drawing is bad with the marker)

THE answer is

10 hours

Answer:

QR=5.25 units

PR=5 units

PQ=6.25 units

Answer:

Sin ? = 4/7

? = arcSin (4/7)

? = 35° (rounded to the nearest degree)

So the answer is 35°

Answered by GAUTHMATH