the maximum walking speed S, in feet per second of an animal can be modeled by the equation S=the square root gL where g=32ft/sec and L is the length ,in feet, of the animal's leg.To the nearest hundredth how many greater is the maximum walking speed of giraffe with a leg length of 6 feet than a hipppotamus with a leg length of 3 feet.

Answer:

x = -5

Step-by-step explanation:

If one draws a perfect verticle line at x = -5, one will have exactly 1/2 the parabola on each side. Then is one where to fold the parabola on that line, then there would be no overhang. Hence x = -5 is the axis of symmetry.

Step-by-step explanation:

Hey there!

See explanation in picture!

Hope it helps...

The speed of plane in still air will be 550 miles / hour and speed of wind will be 50 miles / hour.

It is given that a plane traveled 3900 miles in 6.5 hours with wind and 3250 miles in 6.5 hours against wind.

We have to find out the speed of plane in still air and speed of wind.

What is algebra ?

Algebra is the branch that deals with various symbols and the arithmetic operations such as addition , division , etc.

As per the question ;

Distance travelled with wind in 6.5 hours = 3900 miles

Distance travelled against wind in 6.5 hours = 3250 miles

Let's assume speed of plane in still air be P and speed of wind be W.

So;

The total rate with the wind is the plane speed plus the wind speed and against the wind is speed of plane minus speed of wind.

i.e.,

d = rt

⇒ 6.5 ( P + W ) = 3900 miles  --- ---- --- --- -- ------- ----- --- Equation 1

and

⇒ 6.5 ( P - W ) = 3250 miles  --- ---- --- --- -- ------- ----- --- Equation 2

Let's solve the equations to get value of P and W ;

i.e.,

P + W = 3900 / 6.5

or

P + W = 600

and

P - W = 3250 / 6.5

or

P - W = 500

adding both equations ; we get ;

2P = 1100

or

P = 550 miles / hour

And

W = 50 miles / hour

Thus , the speed of plane in still air will be 550 miles / hour and speed of wind will be 50 miles / hour.

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Answer:

The numbers are:

{-1, 0, 1, 2, 3}

Step-by-step explanation:

Note: I am assuming "between" does not include the endpoints.

Given the statement

'Four times a number, increased by one, is between negative seven and seventeen'

Let us break down the word statement into small pieces and then combine them to write it into an algebraic expression.

Let x be the number.

4 times a number = 4x

Increase by 1 = 4x+1

between negative seven and seventeen ⇒   -7 < 4x+1  < 17

Thus, the combined statement can be written in an algebraic expression.

-7 < 4x+1  < 17

solving the inequality expression

[tex]-7 < 4x+1 < 17[/tex]

Add -1 to all parts

[tex]-7+-1<4x+1+-1<17+-1[/tex]

[tex]-8<4x<16[/tex]

Divide all parts by 4

[tex]\frac{-8}{4}<\frac{4x}{4}<\frac{16}{4}[/tex]

[tex]-2<x<4[/tex]

Thus, the numbers are:

{-1, 0, 1, 2, 3}

i.e

[tex]-7<4x+1<17\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-2<x<4\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-2,\:4\right)\end{bmatrix}[/tex]

The graph is also attached below.

Answer:

it is an answer if you are using a coordinate plane

Step-by-step explanation:

Answer: D=[185]^1/2 or 13.6

(I think but idk... sorry if not correct)

Step-by-step explanation:

D=[(12-8)^2+(4-17)^2]^1/2

D=[(4)^2+(-13)^2]^1/2

D=[16+169]^1/2

D=[185]^1/2

Answer:

Step-by-step explanation:

[tex]d=\sqrt{(4-17)^2+(4-8)^2} =\sqrt{169+16} =\sqrt{185}[/tex]

Answer:

∠EFA

Step-by-step explanation:

The diagram shows several rays starting at point F. There are 2 sets of rays that are opposite to each other ie their angles add up to 180°

These are
FD and FA
FB and FE

You can ignore the other two rays since they do not have any opposite rays and therefore do not figure in a linear relationship

Ignoring FG and FC we get the equivalent of two lines crossing each other at point F

We can eliminate any angles that contain C and G
So we can eliminate ∠BFC, ∠CFG and ∠GFD

Which leaves the last choice as the only option

So answer is ∠EFA

∠EFA is linearly paired with ∠BFD since they lie on the same straight line and the measure of sum of their angles is 180°

∠EFA also is vertically paired with ∠BFD since these angles are opposite each other

Answer:

the amount after 5 years using compound continuously is $135.03

Step-by-step explanation:

The computation of the amount after 5 years using compound continuously is as follows

= Principal × e^(rate × time period)

= $110 × e^(4.2% × 5)

= $110 × 1.227525065

= $135.03

Hence, the amount after 5 years using compound continuously is $135.03

We simply applied the above formula so that the correct value could come

And, the same is to be considered  

Answer:

$12.00

Step-by-step explanation:

Divide 504.00 by 42 hours

504/42 = 12

He earned $12 per hour

The required answers for the given questions is question are 1) x = -4,  2)  x = 6 - √15,   3) x = 3 + 3√3,   4) x = -3,  and  5)x = -9 - √21  / 5

The quadratic Equation formula is x = -b ± √(b² - 4ac) / 2a

1. x² + 7x + 12 = 0

By using the above formula

Here a = 1, b = 7, c = 12

x = -7 ± √(7² - 4*1*12) / 2*1

x = -7 ± √(49 - 48) / 2

x = -7 ± √1 / 2

x = -7 ±1 /2

x = -7+1 /2           x = -7 - 1 / 2

x = - 6 / 2            x = -8 / 2

x = -3                   x = -4

2) x²-12x+21=0

By using the above formula

Here a = 1,  b = -12, c = 21

x = -(-12) ± √((-12)² - 4*1*21) / 2*1

x = 12 ± √(144 - 84) / 2

x = 12 ± √60 / 2

x = 12 ±2√15  /2

x = 12 + 2√15 /2           x = 12 - 2√15  / 2

x = 6 + √15          x = 6 - √15

3. 18+6y-y²=0

By using the above formula

Here a = -1, b = 6, c = 18

x = -6 ± √((6² - 4*(-1)*18) / 2*(-1)

x = -6 ± √(36 + 72) / -2

x = -6 ± √108 / -2

x = -6 ± 6√3 / -2

x = -6+6√3 /-2           x = -6 - 6√3 / -2

x = 3-3√3            x = 3 + 3√3

4. 3x²+14×+15=0

By using the above formula

Here a = 3, b = 14, c = 15

x = -14 ± √((14² - 4*(3)*15) / 2*(3)

x = -14 ± √(196 - 180) / 6

x = -14 ± √16 / 6

x = -14 ± 4 / 6

x = -14 + 4 /6           x = -14 - 4  / 6

x = -10 / 6                x = -18 / 6

x = -5/3                   x = -3

5.5x²-18x+12=0 ​

By using the above formula

Here a = 5, b = -18, c = 12

x = -18 ± √((18² - 4*(5)*12) / 2*(5)

x = -18 ± √(324 - 240) / 10

x = -18 ± √84 / 10

x = -18 ± 2√21 / 10

x = -18 + 2√21 /10           x = -18 - 2√21  / 10

x = -9 + √21 / 5                x = -9 - √21  / 5

Hence, the values of the given question are 1) x = -4,  2)  x = 6 - √15,   3) x = 3 + 3√3,   4) x = -3,  and  5)x = -9 - √21  / 5

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Answer:

2.5198421

Step-by-step explanation:

Answer:

The answer is B, sorry if I'm wrong.

Step-by-step explanation:

Answer:B=17.3 in2

Step-by-step explanation:

41 dollarsStep-by-step explanation:

Answer:

x=17. I think.....

Step-by-step explanation:

Answer:

x = 17

Step-by-step explanation:

Since the two angles are vertical to each other they have the same measure.

x + 35 = 3x + 1 (subtract 1 on both sides)

x + 34 = 3x (subtract x on both sides)

34 = 2x (divide by 2 on both sides)

17 = x

Hope this helps ya!!

Answer:

71 degrees

Step-by-step explanation:

Use tangent to find x.

tantheta = opposite/adjacent

tan(x) = 130/45

x = tan^-1 (130/45)

x = 70.9

Round to nearest degree = 71 degrees

Answer:

a = 10 and b = 6

Step-by-step explanation:

I am having a little trouble reading the numbers, but I think that I see

[tex]\frac{7^{2} 7^{8} }{7^{4} }[/tex]

If we wrote this in expanded form, it would look like:

[tex]\frac{7x7x7x7x7x7x7x7x7x7}{7x7x7x7}[/tex]  How many 7s are on the top?  10  That is the answer to a.  The product of powers principle tells us that if we are multiplying powers with the same bases we add the exponents 2 + 8 = 10

[tex]\frac{^{10} }{7^{4} }[/tex]

Now it looks like

[tex]\frac{7x7x7x7x7x7x7x7x7x7}{7x7x7x7}[/tex]  if we cross the 7's out in the top and the bottom, we are left with 6 7's on the top.  That is the answer to b.

The quotient of powers principle tells us that if we are dividing powers with the same bases, we can subtract the exponents (10 -4 = 6)

Answer:

b

Step-by-step explanation:

n

Answer:

67.8 is the mean

81 is the median.

There is no mode in this set.

Step-by-step explanation:

Mean is the average.

Median is the middle number.

Mode is the number that appears the most.

I hope this helped and if it did I would appreciate it if you marked me Brainliest. Thank you and have a nice day!

around 44 or above

88+85+84+84+44= 385

385/5= 77

Answer:

false the answer is 1 1/9

Answer:

-4

Step-by-step explanation:

Answer:

the answer is -4. it's the same as dividing by a positive, except the number will be negative now :)

The length and midpoint of segment PQ, where the coordinate of P is (8, -15), and Q is (13, -10) are;

The given points are;

P(8, -15) and Q(13, -10),

Part A:

The distance between the points P and Q, which may be expressed as d(P, Q), is found as follows;

d(P, Q) = √((13-8)²+(-10-(-15))²) = √(50) = 5•√2

The length of PQ is therefore;

Second part;

The midpoint of segment PQ is obtained from the midpoint formula as follows;

[tex](x_m, y_m) = \left(\frac{x_1 + x_2}{2}, (\frac{y_1 + y_2}{2} \right)[/tex]

The midpoint, [tex](x_m, y_m) [/tex] of PQ is therefore;

[tex](x_m, y_m) = \left(\frac{8+13}{2}, \frac{(-15) + (-10)}{2} \right) = \left(11.5, -12.5\right) [/tex]

The coordinates of the midpoint of segment PQ is (11.5, -12.5)

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Answer:

0.25(7x-6y)

Step-by-step explanation:

Answer:

x = 20/3 or x = -12/5

Step-by-step explanation:

Solve for x over the real numbers:

2 abs(x - 1) = x/2 + 8

Divide both sides by 2:

abs(x - 1) = 1/2 (x/2 + 8)

Split the equation into two possible cases:

x - 1 = 1/2 (x/2 + 8) or x - 1 = 1/2 (-x/2 - 8)

Expand out terms of the right-hand side:

x - 1 = x/4 + 4 or x - 1 = 1/2 (-x/2 - 8)

Subtract x/4 - 1 from both sides:

(3 x)/4 = 5 or x - 1 = 1/2 (-x/2 - 8)

Multiply both sides by 4/3:

x = 20/3 or x - 1 = 1/2 (-x/2 - 8)

Expand out terms of the right-hand side:

x = 20/3 or x - 1 = -x/4 - 4

Add x/4 + 1 to both sides:

x = 20/3 or (5 x)/4 = -3

Multiply both sides by 4/5:

Answer: x = 20/3 or x = -12/5

Answer:

1 and 3/5

Step-by-step explanation:

Answer:

360 tablespoons.

Answer:

Step 1     z(c) = 2,323

CI = (  25 ;  30,2 )

Step-by-step explanation:

Normal Distribution:

Sample size  n = 25

Sample mean   μ  = 27,6

Sample standard deviation  s = 5,69

CI = 98 %   then  α  = 1 - 0,98     α = 0,02    α/2  = 0,01

From z-table we don´t  find z (score) for 0,01   directly, we need to interpolate between z = 2,32   and z = 2,33

For   0,0099           z score   is    2,33

for    0,0102            z score   is    2,32

Δ      0,0003                                  0,01

Then   by rule of three

for Δ        0,0003                ⇒      0,01

for Δ   (0,01- 0,0102)          ⇒        x

0,0003    0,01

0,0002      x

x = 0,0067

then  z (score for 0,01)   =  2,33 - 0,0067     z(c) = 2,3233

round to three decimal places z(c) = 2,323

Step 2:

CI =   μ  ±  z(c) * s/√n    ⇒   27,6  ± (2,323 * 5,69)/5

CI =  27,6 ± 2,6436

round to one decimal place

CI = 27,6 ± 2,6

CI = (  25 ;  30,2 )