Two water balloons were launched into the air at different moments and collided. The water balloons were modeled by the quadratic functions: y = −3x2 + 24x + 3 and y = −4x2 + 25x + 15, where y represents the height in meters and x represents the time in seconds after the launch. What is the time, in seconds, that the balloons collided at the highest point?

Answer/Step-by-step explanation:

Triangle PNM is an equilateral triangle, and angles in an equilateral triangle are all equal to 60.

y=60

Triangle PON is a different triangle, but all angles in a triangle add up to 180.

180-80=100

Because there are 2 angles, you do 100 divided by 2=50

x=50

Answer:

-4, 9, -1

Step-by-step explanation:

x³ - 4x² - 41x - 36

= x²(x + 4) - 8x² - 41x - 36

= x²(x + 4) - 8x(x + 4) - 9x - 36

= x²(x + 4) - 8x(x + 4) - 9(x + 4)

= (x + 4)(x² - 8x - 9)

= (x + 4) (x - 9)(x + 1)

so the zeros of f(x) are: -4, 9, -1

Answer is A

Hope this helps!

Answer:

Step-by-step explanation:

We know that angles BAD and DAE are supplementary, so the measure of angle DAE is 180-133=47 degrees.

Because of this, we can determine that angle ADE measures 180-82-47=51 degrees.

Now, since triangles ADE and BCE are similar, we can say that the measure of angle ABC is 47 degrees and the measure of angle BCE is 51 degrees.

Finally, to find the measure of angle ADC, we can notice that its the supplement of angle ADE, meaning ADC measures 180-51=129 degrees.

Answer:

4.5 kg

Step-by-step explanation:

Weight of the puppy last year - x

1) 150 % = 1.5

2) x * 1.5 = 6.75

   x = 6.75 / 1.5

   x = 4.5 (kg)

Answer:

A

Step-by-step explanation:

First i take every answer and multiply them by 0.150. When i do this i can find the answer quickly because only one will equal the 6.75.

A equals the 6.75.

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Answer:

x=-3 or x=-7/3

Step-by-step explanation:

Answer:

B is the linear relationship

Answer:

second option where y = 8, 16 and 24

Step-by-step explanation:

second option where y = 8, 16 and 24

This table shows a linear relationship because the y-values increase by the same amount each time (i.e. the difference between the y-values is the same).

Answer:

C. 150 degrees

Step-by-step explanation:

Angles 2 and 4 are opposite angles which means that they are congruent to each other

Answer:

150

Step-by-step explanation:

∠2 and ∠4 are vertically opposite angles and they are congruent.

Answer:

[tex]x=90\\y=-40[/tex]

Step-by-step explanation:

Let's set up a system of equations using the given information.

x+y=50

x-y=130

We can solve this system using elimination. In this case, we can eliminate x by subtracting the two equations.

[tex]x-x+y-(-y)=50-130\\x-x+y+y=50-130[/tex]

[tex]2y=-80[/tex]

Divide both sides by 2.

[tex]y=-40[/tex]

Then, plug -40 in for y to solve for x:

[tex]x+y=50\\x+(-40)=50\\x-40=50\\\text{Add 40 to both sides}\\x=90[/tex]

Therefore..

[tex]x=90\\y=-40[/tex]

Answer:

You have to give the number by which the 20% is increased in order to cross multiply and divide by a hundred to find the missing % of the decrease. Otherwise, you would simply subtract 20% from 100%, which seems unlikely to be the answer. We need more information.

Step-by-step explanation:

Answer:

36? I believe im right

Step-by-step explanation:

Twice the difference of a number and four:  2(x - 4)

three times the sum of the number and 2:  3(x + 2)

2(x - 4) = 3(x + 2)

2x - 8 = 3x + 6

-14 = x

to confirm

2[(-14) -4] = 2(-18) =-36

3 [(-14) +2] = 3 (-12) = -36

Answer: i believe in c but it could be any of em im super sorry if you get it wrong though like seriously sorry  

Step-by-step explanation:

If the ramp starts closer to the step then the angle would increase.

The angle of elevation is an angle that is formed between the horizontal line and the line of sight. If the line of sight is upward from the horizontal line, then the angle formed is an angle of elevation.

Given here the height of the step =6 inches and the distance of the ramp from the ground is 5 feet or 59.99 inches

let the angle be θ then  tanθ=6/x where x is the distance from the ramp to the ground thus with the decrease in the distance the value of tanθ increases and hence tan⁻¹(6/x) increases since the arctan function is the inverse of the tangent function.

Hence, If the ramp starts closer to the step then the angle would increase.

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Answer:

It will 26 weeks to save for the cruise starting from a balance of $140

(It will take 30 weeks in total, if you start saving from $0)

Step-by-step explanation:

let x = number of weeks

Given starting balance = $140

⇒ 140 + 35x = 1050

⇒ 35x = 1050 - 140

⇒ 35x = 910

⇒ x = 910 ÷ 35

⇒ x = 26

Answer:

Inconsistent

4x + 2y = 6   and   4y = -8x + 4

Step-by-step explanation:

Inconsistent: parallel lines, no solutions

Consistent dependent: same line, infinite solutions

Consistent independent: intersects at one point, one solution

Therefore, the pair of lines are INCONSISTENT.

Both lines have negative slopes.  As they are parallel, the slopes will be the same for both lines.

Therefore, solution is:

4x + 2y = 6   and   4y = -8x + 4

Because:

4x + 2y = 6  ⇒  y = -2x + 3

4y = -8x + 4  ⇒  y = -2x + 1

Both lines have same slope of -2

Answer:

2.8 + 2x = 0.6

______

   8

multiply by 8 to both sides

x8          x8

2.8 + 2x = 4.8

subtract 2.8 from both sides

-2.8        -2.8

2x = 2

divide by 2 from both sides

/2      /2

x = 1

Answer:

x = 1

Step-by-step explanation:

Step 1: Multiply both sides by 8.

Step 2: Subtract 2.8 from both sides.

Step 3: Divide both sides by 2.

Therefore, x = 1.

Answer:

No!

Step-by-step explanation:

no explanation!

b/c no equal sign this is no equation!

so,exactly no!

Answer:

You have a maximum when the parabola opens down (-x^2), and a minimum when it opens up (+x^2). In your case, it opens down because of the -. That is the special notation, the vertex of the parabola is already there.

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

Explanation:

Rule: If a set has n elements in it, then it will have 2^n subsets.

For example, there are n = 3 elements in the set {a,b,c}. This means there are 2^n = 2^3 = 8 subsets. The eight subsets are listed below.

Subsets 2 through 4 are subsets with exactly 2 elements.  Subsets 5 through 7 are singletons (aka sets with 1 element). The last subset is the empty set which is a subset of any set. You could use the special symbol [tex]\varnothing[/tex] to indicate the empty set.

For more information, check out concepts relating to the power set.

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

The problem is asking what value of n will make 2^n = 64 true.

You could guess-and-check your way to see that 2^n = 64 has the solution n = 6.

Another approach is to follow these steps.

[tex]2^n = 64\\\\2^n = 2^6\\\\n = 6[/tex]

Which is fairly trivial.

Or you can use logarithms to solve for the exponent.

[tex]2^n = 64\\\\\text{Log}\left(2^n\right)=\text{Log}\left(64\right)\\\\n*\text{Log}\left(2\right)=\text{Log}\left(64\right)\\\\n=\frac{\text{Log}\left(64\right)}{\text{Log}\left(2\right)}\\\\n\approx\frac{1.80617997398389} {0.30102999566399} \ \text{ ... using base 10 logs}\\\\n\approx5.99999999999983\\\\[/tex]

Due to rounding error, we don't land exactly on 6 even though we should.

Considering that it has an angle of 90º degrees, the triangle is classified as:

B. right

In this problem, two angles are 40º and 50º. Since the sum of the angles is of 180º, we have that:

x + 50 + 40 = 180

x = 90º.

Hence, it is a right triangle, and option B is correct.

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Answer:

C) 1.6 million

Step-by-step explanation:

Every two years it increases by 0.15

= 150,000

Therefore, previous year + 0.15

= 1.45 + 0.15

= 1.6

Answer:

396 in³

Step-by-step explanation:

You need to find the area of each side, then add them up.

Top and bottom sides: 12*7=84*2=168

Left and right sides: 6*7=42*2=84

Front and back sides: 12*6=72*2=144

168+84+144=396

Answer:

P-2D=N

Step-by-step explanation:

P=N+2/D

L.C.M

[tex] \binom{n + d}{1} [/tex]

The required value of the given sum is given as 4.8. Option B is correct.

Given that,
To estimate the sum of 3.62 + 1.16 by rounding each addend to the nearest tenth.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

The rounding of values is superseding a number with an inexact value that has a more ephemeral, more uncomplicated, or more direct representation.

Here,
Given expression,
= 3.62 + 1.16
Round the values to the nearest tenth,
= 3.6 + 1.2
= 4.8

Thus, the required value of the given sum is given as 4.8. Option B is correct.

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Answer:

2x+8b

Step-by-step explanation:

First since 1 and 8b are on the same side mutiply them:

1bx8=8b

So our new equation is 2x+8b

FG = 16

Step-by-step explanation:

Two pairs of consecutive are congruent so, its a kite,

Opposite sides are equal in kite so,

x + 11 = 3x + 1

or, 11 - 1 = 3x - x

or, 2x = 10

so, x = 5

FG = x + 11 = 5 + 11 = 16

Answer:

Step-by-step explanation:

a)h,q,r,y

b) p,x,z,h,q,r,y

Answer:The probability of spinning a 3 is also 2 / 8.

Answer:

2[7x(y – 2) – 6(3y – 4)]

Step-by-step explanation:

If you go down the answer choices and find the solution, this one matches.  Look at picture for better explaining.

The expression will be equal to 2[7x(y-2) - 6 (3y - 4)].

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.

The given expression will be solved as:-

=    2  [  7x(  y-2 ) -  6 ( 3y - 4 ) ].

=   14x ( y - 2 ) - 12 ( 3y - 4 ) ]

=   14xy  -  28x -  36y  -  48

Therefore expression will be equal to 2[7x(y-2) - 6 (3y - 4)].

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Answer:

y=2x+5

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(13-25)/(4-10)

m=-12/-6

m=2

y-y1=m(x-x1)

y-25=2(x-10)

y=2x-20+25

y=2x+5

Answer:

3x + x - 2x + 8 = 3x + x

2. 2 (2x + 4) - 2x = x + 18

3. If x = 5 , evaluate : 2 ( x + 3) + 3x

4. 3 (2x) - 3x + 4= 2x + 5

5. 3x +2x + x = x + 6

6. 2 ( x+ 4) + x = 16