Select the correct answer.

Which expression is equivalent to the given expression?

Answer:

45.27 miles

Step-by-step explanation:

Pythagorean theorem

23^2 + 39^2 = d ^ 2

d = 45.27 miles

If  a person drives 23 miles south and make a turn to east and drive 39 miles then the distance between starting point and person is 45.27 miles.

Pythagoras theorem applies in a right angled triangle. It says that in a right angled triangle the square of hypotenuse is equal to sum of squares of perpendicular and base of that triangle.

[tex]H^{2} =P^{2} +B^{2}[/tex]

When person drives towards south and then east , it forms a right angled triangle. We have to find the distance of person from the starting point. If we see the figure then we will come to know that we are require to find hypotenuse of triangle.

H=[tex]\sqrt{P^{2} +B^{2} }[/tex]

Distance=[tex]\sqrt{23^{2} +39^{2} }[/tex]

=[tex]\sqrt{1521+529}[/tex]

=[tex]\sqrt{2050}[/tex]

=45.27

Hence the distance of person from starting point is 45.27 miles.

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Step-by-step explanation:

|7x+4|≤18

7x+4≤ 18. 7x+4≥-18

x≤2. x≥-22/7

2≤x≤-22/7

Answer:

  9.  3x² +x -2y +5 = 0

  10.  4x² +x -y +4 = 0

  11.  9x² -6x -3y -12 = 0

Step-by-step explanation:

"General form" of a polynomial equation is ...

  f(x, y) = 0

where the terms are arranged in lexicographical order and decreasing degree. That is, for terms of the same degree, x-terms are listed before y-terms, and xy terms are listed before y-only terms.

The leading coefficient can be positive or negative, your choice. (Positive is generally preferred.) For linear equations, "standard form" has the coefficients mutually prime. Making that happen for a general form polynomial would be your choice.

__

The highest-degree term is 3x². If we keep the leading coefficient positive, we can get general form by subtracting the expression on the left side of the equal sign.

  3x² +x -2y +5 = 0

__

Subtracting the right side gives ...

  4x² +x -y +4 = 0

__

Subtracting the left side gives ...

  9x² -6x -3y -12 = 0

or

  3x² -2x -y -4 = 0 . . . . . . remove a common factor of 3

Answer:

parallelogram

Step-by-step explanation:

sr/pq=sp/rq

ab/dc=ad/bc

Answer:

Proven.

Step-by-step explanation:

So, fasten your seatbelts, we're about to go on a long ride(◠‿・)—☆

» In a parallelogram, opposite sides are equal in length.

This can be represented (in the vector way) by

'QR = '-SP = 'PS and 'RS = 'QS (let “'” represent a vector)

'QR + 'SP= 0 and 'RS-'QS = 0

Note the signs. The signs are determined by the arrows in the diagram. [A reminder: If you walk from a point A to a point B, your displacement vector is 'AB. If you walk back, that is, from B to A; your displacement vector is 'BA which is also equal to '-AB.]

This means: to prove that PQRS is a parallelogram, we must prove that

'QR + 'SP= 0 and/or 'RS-'QS = 0.

In this solution, we will only work on the first equation.

Permit me to remove this ' sign.

QR = QC+CR ...1

QR= QB+BA+AD+DR...2

ADD 1 TO 2

2QR= QC+CR+QB+BA+AD+DR

[LOOK CLOSELY, QC+QB=0 ; CR+DR=0. This is because BQ+QC = BC

BUT, BQ=QC= (BC)/2

QC-BQ= 0

AND, -BQ= QB

QC+QB= 0 ;)]

2QR= BA+AD...3

★

SP = SA+AP...4

SP= SD+DC+CB+BP...5

ADD 4 TO 5

2SP = SA+AP+SD+DC+CB+BP

[AGAIN, SA+ SD = 0 ; AP+ BP = 0]

2SP= DC+CB...6

3+6

2QR+2SP= BA+AD+DC+CB

[ BA+AD+DC+CB, IN A SIMPLE WAY, MEANS:

you start from B, and move to A (BA); from A to D (AD); from D to C (DC); and from C to B (CB). Therefore, you have gone from B to B (from your starting point and back). Hence, your total DISPLACEMENT is zero (you haven't changed your position).

2(QR+SP) = 0

'QR+'SP= 0

PROVEN

You can work out the other equation, but it is evident that PQRS is a parallelogram.

[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]

Let's solve ~

First we have to calculate g (-5) :

[tex]\qquad \tt \dashrightarrow \:x - 8[/tex]

[tex]\qquad \tt \dashrightarrow \: - 5 - 8[/tex]

[tex]\qquad \tt \dashrightarrow \: - 13[/tex]

Now, let's find f (g (-5)) :

[tex]\qquad \tt \dashrightarrow \: {x}^{2} + 6x[/tex]

[tex]\qquad \tt \dashrightarrow \:( - 13) {}^{2} + (6 \times - 13)[/tex]

[tex]\qquad \tt \dashrightarrow \:169 + ( - 78)[/tex]

[tex]\qquad \tt \dashrightarrow \:169 - 78[/tex]

[tex]\qquad \tt \dashrightarrow \:91[/tex]

The angle at which the ball takes off, distance the ball in the air, the ball's speed is mathematically given as

Generally, the equation for the verticle component   is mathematically given as

[tex]y=xtan\theta-\frac{16x^2}{v0cos^2\theta}\\\\Therefore\\\\\theta=tan^{-1}(1.8)[/tex]

theta=60

b)

hmax=vo^2sin^2\theta/2g

vo=116.486

Therefore, distance the ball in the air

[tex]d=\frac{2*114.486*0.874*2}{32}[/tex]

d=6.3658

c)

The ball's speed when it hits the ground will be vo

vo=116.486

Read more about Angle

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Answer:

$121,683.79

Step-by-step explanation:

A= P(1+ r)^t

A= Amount, P = Principal, r = Rate (decimal form), t= time

A = 47000(1+0.0825)^12

A = 47000(1.0825)^12

A = 47000(2.589016751)

A = 121683.7873

Rounded Answer = $121,683.79

(If there is meant to be no cents then $121,684). Good luck :)

well because he did not do it

Notice how

2x-5 = 2x - 2*2.5 = 2(x-2.5)

This means we can replace x with x-2.5 in the second step, in the "wrong way" column.

So,

y = ln(2x)

y = ln( 2(x-2.5) )

y = ln( 2x - 2*2.5 )

y = ln( 2x - 5 )

In the second step, the x-2.5 tells the reader to shift the curve 2.5 units to the right. Therefore, the 1/2 = 0.5 would shift to 0.5+2.5 = 3 as indicated by the correct graph.

Answer:

$ 200

Step-by-step explanation:

$ per ticket   =   $ 120 / 3 tix

Price for 5     $120 / 3 tix  * 5 tix = $ 200

Answer: 10

Step-by-step explanation:

Answer:

  245 ft

Step-by-step explanation:

The geometry of the problem can be modeled by a right triangle in which Meena's height is the side opposite the angle of depression, and the distance to the boat is the side adjacent to the angle of depression. The mnemonic SOH CAH TOA reminds us of the relation ...

  Tan = Oppsite/Adjacent

__

The more useful trig function for this problem is the inverse of the tangent function, the cotangent. Using that function, we have ...

  cot(angle) = (distance to boat)/(Meena's height)

Then the distance to the boat is ...

  distance to boat = (Meena's height)×cot(angle)

The change in distance from A to B is then ...

  A -B = (120 ft)(cot(18°) -cot(44°))

  = (120 ft)(3.0777 -1.0355) ≈ 245.06 ft

The distance from point A to point B is about 245 feet.

Answer:

92

Step-by-step explanation:

Add 95, 90, and 83 all together

add 92 to that total

divide by 4

Answer:

Cost for person is not always the same

For 80 dollars predicted would be 10 people

Step-by-step explanation:

4 people 36 dollars = 9 each

8 people 64 dollars = 8 each  

9 people 72 dollars = 8 each       seems to flatten at 8 dollars each

The motions for the calculation -5+ (-37) is given as a small movement to the left followed by a large movement to the left.

An equation is an expression used to show the relationship between two or more numbers and variables.

The expression -5+ (-37) can be solved using a number line. The motions for the calculation -5+ (-37) is given as a small movement to the left followed by a large movement to the left.

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Answer:

small movement to the left followed by a large movement to the left.

Step-by-step explanation:

Answer:

3x+21=57

Step-by-step explanation:

When we use distributive property we do

[tex]3*x[/tex] and [tex]3*7[/tex] which will like this when rewritten [tex]3x+21=57[/tex]

Check answer:

[tex]3x+21=57\\-21=-21\\3x=36[/tex]      [tex]\frac{3x}{3} =\frac{36}{3}[/tex]

x=12    3(12)+21=57

36+21=57

Answer:

The correct answer is 12/37

our number is x

we add seven (+7) to x

x+7

Answer:

Triangular prism

Step-by-step explanation:

There is one rectangular prism at the bottom and one triangular prism at the top.

Answer:

It is a square pyramid

Step-by-step explanation:

[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]

Let's solve ~

[tex]\qquad \tt \dashrightarrow \:(3 {x}^{5} \times 2xy) - ( {x}^{2} y \times 4 {x}^{4} )[/tex]

[tex]\qquad \tt \dashrightarrow \:6 {x}^{6} y - 4 {x}^{6} y[/tex]

[tex]\qquad \tt \dashrightarrow \:2 {x}^{6} y[/tex]

= (3x^5× 2xy) — (x^2y × 4x^4)

= 6x^6y - 4x^6y

= 2x^6y

Answer:

-Dilate circle A by scale factor of 2

Got it right on the test (see picture)

Circle A is translated using the rule (x + 1, y - 1). Then the correct option is B.

It is a locus of a point drawn an equidistant from the center. The distance from the center to the circumference is called the radius of the circle.

Circle A has a center of (2,3) and a radius of 5, and circle B has a center of (1,4) and a radius of 10.

Circle B is translated as 1 unit leftward in the x-direction and 1 unit upward in the y-direction.

Then circle B is dilated by a factor of 2.

More about the circle link is given below.

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Answer:

∠s = 158

Step-by-step explanation:

Since lines a and b are parallel,

∠s and 158 are alternate exterior angles.

Alternate exterior angles are equal if two lines are parallel.

So,

∠s = 158

Answer: 22°.

Step-by-step explanation: We're given the angle 158°, which is all we need. Angle u and 158°, have to add up to 180°.  180° - 158° = 22°, which is the angle measure of u.  You're probably wondering how this will help us.  The answer to that is it gives us the measurement of angle t, which is 158°.  Now, we'll do the same thing we did with angle u, which was to make angle u add up with 158° to make 180°.  We'll apply this to angle t and angle s.  We already know that angle t is 158°, so angle s has to be 22° in order to add up to 180°.  Therefore, your answer is 22° for angle s.

Let me know if this is right! :)

coat cost= $60.

the fraction of amount she needs to save.

saved/ actual cost

= $42/ $60 ÷ 2/2

= 21/30

answer= option a) 21/30

Answer:

Correct ones A and F

------------------------------------------

Correct ones H and K

Answer:

  350 adult tickets

Step-by-step explanation:

If x is the number of adult tickets sold, then x-57 is the number of student tickets sold (57 fewer). The total number sold is ...

  x +(x -57) = 643

  2x = 700 . . . . . . . . collect terms, add 57

  x = 350 . . . . . . . divide by 2

There were 350 adult tickets sold.

Answer:

I think 4000000000

Answer: 4,321,109,432 rounded to the nearest billion is 4,000,000,000

Step-by-step explanation:

First, you find the billions place which is right here:

4,321,109,432

Look to the number to the right of it. Is it greater or less than 5? Since it's less, you round down to 0, leaving a 4 and 3 sets of 3 zeroes.

Answer:

its B- 6 sq. cm.

Step-by-step explanation:

1/2 times base times height

1/2 x 4 x 3

6

Answer:

The answer is given below

Step-by-step explanation:

[tex]area = \frac{1}{2} \times base \times perpendicular[/tex]

[tex]area = \frac{1}{2} \times 3 \times 4[/tex]

Area = 1/2 * 12

Area = 6