Find the equation of the axis of symmetry of the following parabola algebraically.
y=x^2-12x+34

Answer:

Hi there user! I'll help you!

96 should be the correct answer!

Step-by-step explanation:

4 x 3 = 12

4 x 7 = 28

5 x 7 = 35

3 x 7 = 21

12 + 28 + 35 + 21 = 96

Answer:

Distance of first boat = 8 meter

Distance of second boat = 13.87 meter (Approx.)

Step-by-step explanation:

Given:

Height of cliff = 8 meter

Angle of depression respectively = 45° and 30°

Find:

Distance of boats

Computation:

Tanθ = Perpendicular / Base

Tan45 = 8 / Distance of first boat

1 = 8 / Distance of first boat

Distance of first boat = 8 meter

Tan30 = 8 / Distance of second boat

0.577 = 8 / Distance of second boat

Distance of second boat = 8 / 0.577

Distance of second boat = 13.8648

Distance of second boat = 13.87 meter (Approx.)

Answer:

58

Step-by-step explanation:

The center line in a box plot represents the median

Answer:

the top is right 2/5

Step-by-step explanation:

The probability is 3 / 10.

The chance that a particular event (or set of events) will occur expressed on a linear scale from 0 (impossibility) to 1 (certainty), also expressed as a percentage between 0 and 100%.

Given:

7, 11, 12, 13, 14, 18, 21, 23, 27, and 29

So,

even numbers are = 12, 14, 18.

The probability of picking a card = 3 / 10

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Answer: I believe you mean x and y intercepts? They are (0, -1) and (-1/7, 0)

Step-by-step explanation:

Plug in 0 for x and y (one at a time) for each intercept. eg The x intercept is at y=0 and the y intercept is at x=0.

Answer:

So, after 6 months, they both have the same number of coins.  

Step-by-step explanation:

Jack has 56 coins

Jill has 80 coins

Jack collect 12 coins per month

Jill collect 8 coins per month

Let after m months, they both have the same coin.

56 + 12 m = 80 + 8 m

12 m - 8 m = 80  - 56

4 m = 24

m = 6

So, after 6 months, they both have the same number of coins.  

Answer:

12000 cubic meters

Step-by-step explanation:

v=(1/3)(900)(40)

Answer:

(4,1);(1,4)

Step-by-step explanation:

The point on the parabolic equation y = -x² + 4x + 1 and line y = -x + 5 intersect is P ( 4 , 1 ) and Q ( 6 , -1)

A Parabola, open curve, a conic section produced by the intersection of a right circular cone and a plane parallel to an element of the cone. A parabola is a plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed line

The equation of the parabola is given by

( x - h )² = 4p ( y - k )

y = a ( x - h )² + k

where ( h , k ) is the vertex and ( h , k + p ) is the focus

y is the directrix and y = k – p

The equation of the parabola is also given by the equation

y = ax² + bx + c

where a , b , and c are the three coefficients and the parabola is uniquely identified

Given data ,

Let the parabolic equation be y = -x² + 4x + 1

Let the equation of line be y = -x + 5

Now , To find the points of intersection between the parabola y = -x² + 4x + 1 and the line y = -x + 5, we need to set the two equations equal to each other and solve for x and y simultaneously.

Setting y = -x² + 4x + 1 equal to y = -x + 5, we get:

-x² + 4x + 1 = -x + 5

Rearranging the equation, we get a quadratic equation in standard form:

-x² + 4x + x - 1 - 5 = 0

-x² + 5x - 6 = 0

Factoring the quadratic equation, we get:

-(x - 1)(x - 6) = 0

Setting each factor equal to zero and solving for x, we get two potential values for x:

x - 1 = 0 or x - 6 = 0

x = 1 or x = 6

Now, substituting the values of x back into the equation y = -x + 5 to find the corresponding y-values, we get:

For x = 1:

y = -1 + 5

y = 4

So, one point of intersection is (1, 4)

For x = 6:

y = -6 + 5

y = -1

So, the other point of intersection is (6, -1).

Hence , the point of intersection is P ( 4 , 1 ) and Q ( 6 , -1)

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Answer:

y = 2x + 3

Step-by-step explanation:

The slope can be found by taking two points, for instance: (0,3) and (3,9) which lie on the graph.  Find the slope between the two, remember rise over run:

(9-3)/(3-0) = 6/3 = 2

The y-intercept is (0,3)

So b in the y= mx + b equation is 3.

m is the slope, so it is 2.

y = 2x + 3

Answer:

Step-by-step explanation:

surface area=(a+b+c)*h

=(5+5+6)*5

=16*5

=80 cm^2

Answer:

B. If an object is dropped from a height of 38 feet, the function h(t) = –16t2 + 38 gives the height of the object after t seconds.

Step-by-step explanation:

The equation that models the movement of the object is:

Where,

t: time

a: acceleration due to gravity

v0: initial speed

h0: initial height

Suppose that the object falls with zero initial velocity and from a height of 38 feet.

The equation that models the problem is:

Answer:

If an object is dropped from a height of 38 feet, the function h (t) = -16t2 + 38 gives the height of the object after seconds

Answer: If an object is dropped from a height of 38 feet, the function h (t) = -16t2 + 38 gives the height of the object after seconds

Step-by-step explanation:

Answer: Choice A)  

y = -4x+1

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

Explanation:

The general format of a linear equation can be written as y = mx+b

m = slope

b = y intercept

The steepest slope is the value of m that is furthest away from zero. If m > 0, then we're looking for the largest value of m or value to the right of 0. If m < 0, then we're trying to get as left as possible.

Of the choices we have, choice A has the m value furthest from 0. If you want, you can make each slope positive and then compare to see which slope is largest.

Answer:

The answer would be 20 mi

Step-by-step explanation:

a^2+b^2=c^2

a^2=144

b^2=256

C^2=400

Then you find the square root of ABC to find that C is 20

Answer: x=-3

Step-by-step explanation:

i don't really know if this is what I was supposed to do, but i did 6 divided by x=-2 and got x=-3

Answer:

$27-$15

= $12

$3 per hour

$12÷$3

=4 hours

Jessica rent the bike for 4 hours.

Answer:

11. 26

12. 111

Step-by-step explanation:

_______________

Answer:

11.since diagonal are equal of rectangle

QS=RT

4x+6=6x-4

6+4=6x-4x

2x=10

x=10/2

x=5

now

diagonal :4x+6=4*5+6=26

12.

again

QS=RT

9x+12=11x-10

12+10=11x-9x

2x=22

x=11

now

diagonal=9*11+12=99+12=111

Answer:

u need to provide the statement

Step-by-step explanation:

Answer:

x = 27.6907 units

Step-by-step explanation:

cos (62) = 13/x

x cos (62) =13

13 / cos(62)=x

x is 27.6907 units

Answer:

12

Step-by-step explanation:

Answer:

( x + 5 )² + ( y + 4 )² = 29

Step-by-step explanation:

Equation of the circle is

( x - h )² + ( y - k )² = r²

( h, k ) are coordinates of the center

~~~~~~~~~~~~~~~~~~~~~

Coordinates of the center of the circle are

( [tex]\frac{-3-7}{2}[/tex] , [tex]\frac{-9+1}{2}[/tex] ) = ( - 5 , - 4 )

d = 2√29 ⇒ r = √29

( x + 5 )² + ( y + 4 )² = 29

Answer:

theres no picture

Step-by-step explanation:

Answer:

41 ft

Step-by-step explanation:

Since that's the height the Robin flew to.

Answer:

its either 41 feet or 50 feet or neither cause im dum.b

Step-by-step explanation:

41 feet explanation = the bird was on the ground and was 9 feet away from the tree so the bird moved 9 feet ON THE GROUND and then flew up 41 feet

50 feet explanation = the bird was on a branch 9 feet up from the tree base and flew the rest of the 41 feet

Step-by-step explanation:

[tex]( \frac{2 \frac{3}{3} }{4} - \frac{3}{10} ) \times \frac{3}{17} \\ = ( \frac{ \frac{9}{3} }{4} - \frac{3}{10}) \times \frac{3}{17} \\ = ( \frac{9}{3 \times 4} - \frac{3}{10}) \times \frac{3}{17} \\ = ( \frac{9}{12} - \frac{3}{10} ) \times \frac{3}{17} \\ = ( \frac{9 \times 5}{12 \times 5} - \frac{3 \times 6}{10 \times 6} ) \times \frac{3}{17} \\ = ( \frac{45 - 18}{60} ) \times \frac{3}{17} \\ = \frac{27}{60} \times \frac{3}{17} \\ = \frac{81}{1020} \\ = \frac{27}{340} [/tex]

[tex]\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{Happy\:learning.}}}}}∘[/tex]

its A, C, and E

Good Luck

Answer:

I got A and C

Step-by-step explanation:

The variable in answer choice A would be when it says "An elephant eats 5 tons of food every day". In C the the number of min is reverse multiplies by the number of tests.

Answer:

11 hours

Step-by-step explanation:

Using an inequality, find how many additional hours must she work in order to reach this goal?

From the above question, the term at least means less than or equal to and it is represented by the inequality = ≤

Hence,

Let the number of additional hours = h

Last summer Myrtle, worked 45 hours and earned $443.70.

The amount she earned per hour = $443.70/45

= $9.86

Our inequality equation is written as;

She wanted to make at least $550 this summer.

$9.86 × h ≤ $550

= 9.86h ≤ 550

h = 550/9.86

h = 55.780933063 hours

Approximately the additional hours she has to work =

55.780933063 - 45 hours

= 10 .780933063 hours

Approximately = 11 hours

Answer:

it's 149.(54)=7

Step-by-step explanation:

that's the answer