Marco needs to buy cat food. At the nearest store, 6 bags of cat food cost 19.50. How much would Marco spend on 3 bags of cat food. proportional relationships

Answer:

[tex]\rm 4k(2k+ h)[/tex]

Step-by-step explanation:

A expression is given to us and we need to factorise it . The given expression is ,

[tex]\rm\implies (h+2k)^2+4k^2-h^2[/tex]

Open the brackets using the identity, (a +b)² = a² + b² + 2ab , we have ;

[tex]\rm\implies h^2+4k^2+4hk + 4k^2 - h^2 [/tex]

Simplify ,

[tex]\rm\implies 8k^2+4hk [/tex]

In the above expression 4k is common in both the terms , so that ,

[tex]\rm\implies \boxed{\pink{\frak{ 4k(2k+h) }}}[/tex]

The expression factorized completely is (h +2k)[(h+2k) + (2k-h)]

From the question,

We are to factorize the expression (h+2k)²+4k²-h²​ completely

The expression can be factorized as shown below

(h+2k)²+4k²-h²​ becomes

(h+2k)² + 2²k²-h²​

(h+2k)² + (2k)²-h²​

Using difference of two squares

The expression (2k)²-h²​ = (2k+h)(2k-h)

Then,

(h+2k)² + (2k)²-h²​ becomes

(h+2k)² + (2k +h)(2k-h)

This can be written as

(h+2k)² + (h +2k)(2k-h)

Now,

Factorizing, we get

(h +2k)[(h+2k) + (2k-h)]

Hence, the expression factorized completely is (h +2k)[(h+2k) + (2k-h)]

Learn more here:https://brainly.com/question/12486387

Answer:

The initial speed of the ball is  98.22 ft/s

The maximum height of the ball is 75.02 ft.

Step-by-step explanation:

Hi there!

Step-by-step explanation:

The position and velocity vectors of the ball can be calcualted as follows:

r = (x0 + v0 · t · cos α, y0 + v0 · t · sin α + 1/2 · g · t²)

v = (v0 · cos α , v0 · sin α + g · t)

Where:

r = position vector at time t.

x0 = initial horizontal position.

v0 = initial velocity.

t = time.

α = launching angle.

y0 = initial vertical position.

g = acceleration due to gravity (-9.8 m/s² considering the upward direction as positive).

v = velocity vector at time t.

Let´s call r final to the position vector when the ball is caught (see attached figure). The components of r final are:

x = 300 feet

y = 0

Then, r final = (300 feet, 0)

Notice that the origin of the frame of reference is located at the launching point.

Then, when the ball is caught:

300 feet = x0 + v0 · t · cos α

0 = y0 + v0 · t · sin α + 1/2 · g · t²

We have a system of two equations with two unknowns (t and v0), so, let´s solve it.

Let´s solve the first eqation for v0:

300 feet = x0 + v0 · t · cos α

Since the frame of reference is located at the launching point (x0 = 0). Then:

300 feet = v0 · t · cos 45°

300 feet /( t · cos 45°) = v0

Now, let´s replace v0 in the secod equation of the system:

0 = y0 + v0 · t · sin α + 1/2 · g · t²    (y0 = 0)

0 = 300 feet/(t · cos 45°) · t · sin 45° - 1/2 · 9.8 m/s² · t²

0 = 300 feet · sin 45°/cos45° - 4.9 m/s² · t²       (sin45°/cos45° = 1)

0 = 300 feet - 4.9 m/s² · t²

-300 feet = -4.9 m/s² · t²

-300 feet / -16.08 ft/s²  = t²

t = 4.32 s

Now, we can calculate the initial velocity:

300 feet /( t · cos 45°) = v0

300 feet /( 4.32 s · cos 45°) = v0

v0 = 98.22 ft/s

The initial speed of the ball is  98.22 ft/s

To obtain the maximum height of the ball, we have to find at which time the ball is at its maximum height. We can do this in several ways, but we will use the equation of velocity. See in the figure that when the ball is at its maximum height, the y-component of the velocity is zero (because the vector is horizontal). Then, using the equation of the y-component of the velocity:

vy = v0 · sin α + g · t

0 = 98.22 · sin 45° - 32.15 ft/s² · t

(-98.22 · sin 45°) / - 32.15 ft/s² = t

t = 2.16 s

(Notice that this time is half the total time of flight calculated above (4.32 s). This is also the time at which the horizontal distance traveled by the ball is half the total horizontal traveled distance. This is so because the trajectory of the ball is a parabola).

Now that we have the time, we can calculate the y-component of the position vector (r1y in the figure).

r1y = v0 · t · sin α + 1/2 · g · t²

r1y = 98.22 ft/s · 2.16 s · sin 45° - 1/2 · 32.15 ft/s² · (2.16 s)²

r1y = 75.02 ft

The maximum height of the ball is 75.02 ft.

Answer:

42

Step-by-step explanation:

to find how many 0.25 there are in 10.5 we have to divide 10.5 by 0.25

10.5÷0.25

=42

Hope this helped you- have a good day bro cya)

Answer:

when in doubt choose c

Step-by-step explanation:

Answer: 11/48 cubic feet

Step-by-step explanation:

alright ill try my best to explain

so you use the formula V = 22/21r^2h

where V is volume

r is radius

and h is height of cone

you simply plug in the values given in the question, so

V=22/21*1/2^2*7/8

so the answer would be 11/48 cubic feet

Rewrite 1/2 as 4/8

Now add 5 3/8 + 2 4/8

Answer: 7 7/8

Answer:60

Step-by-step explanation:The measure of 1 is 60 because it's only half the size of 120

Answer:

4^-14

Step-by-step explanation:

4^-5 x 4^-4 x 4^-5 = 4^-14

1/4^14

reflection over y axis...........

Answer:A

Step-by-step explanation:A

Answer:

2

Step-by-step explanation:

Thats what I got im 99.9999% sure it's correct pls give brainy crown thing because I used real effort for this.

Adjoa’s gross salary for last month was Ghc4,687.24. If Ghc421.78 was deducted from Adjoa’s salary pay, the take-home pay that Adjoa earn in the past month is Ghc4,265.46

The gross salary is the amount received by an individual prior to the deduction of the taxes.

Given that:

Then, the take-home that Adjoa earned in the past month is calculated by removing the amount deducted from her gross salary.

i.e.

= Ghc4687.24 - Ghc421.78

= Ghc4,265.46

Learn more about gross salary here:

https://brainly.com/question/13582411?referrer=searchResults

https://brainly.com/question/16688602

Answer:

98.2

Step-by-step explanation:

100 x 0.982 = 98.2

98.2 / 100 = 0.982

Answer:

92%

Step-by-step explanation:

Answer:

if you noticed, it is reduces by 2

so the sequence would be

93, 91, 89, 87, 85, 83

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

Hope this helps!

Answer:

93,91,89,87,85,83

Answer: .013, .130, .301, .31

Step-by-step explanation:

Answer:

you didnt give the options .. but its going to be the one saying something like its staying the same speed.

Using the information given, it is found that the class width for this frequency distribution table is of 1.

In this problem, these following classes are given:

0 – 1 14

2 – 3 1

4 – 5 8

6 – 7 12

8 – 9 12

The classes not given, which are 1 - 2, 3 - 4 and 5 - 6, have values of 0.

The difference between the bounds of the classes is of 1, thus, the class width is of 1.

A similar problem is given at https://brainly.com/question/24701109

Answer:

Step-by-step explanation:

You can consider 78.50 as 78.5, cause we basically remove the 0 from it.  The whole point is, they are both the same.

Hello there!

Yes, 78.50 is the same as 78.5 because you can remove the 0 and the numbers will be identical.

Hope this helps!

~Just a joyful teen

[tex]SilentNature\\(GraceRosalia)[/tex]

Answer:

5

Step-by-step explanation:

f(-1) = -3(-1)^3 + 2(-1)^2

f(-1) = -3(-1) + 2(1)

f(-1) = 3 + 2

f(-1) = 5

Hope this helps! Pls give brainliest!

Answer:

5

Step-by-step explanation:

plug in -1 for x

so

[tex] -3 ({ - 1})^{3} + 2 ({ - 1})^{2} [/tex]

went we solve we get

[tex]3 + 2 \\ = 5[/tex]

so 5 is ur answer

pls give brainlist

if any questions ask

have a great day thanks :)

Answer:

In order: 7.5, 7.5061, 7.56, 9.213

Step-by-step explanation:

Step-by-step explanation:

x = 360°- (90°+36°+36°)

= 360 - (162°)

= 198°

___________

[tex] \: [/tex]

PQR = 360°

QR = 90°

PQ = 36°

RX = 36°

Soo :

x = 360° - (90° + 36° × 2)

x = 360° - (90° + 72°)

x = 360° - (162)

x = 198°✔

Answer:

[tex]y = 4x - 5[/tex]

Step-by-step explanation:

rewrite the equation

[tex]x + 4y - 8 = 0 \\ 4y = - x + 8 \\ y = - \frac{1}{4} x + 2[/tex]

perpendicular slope is a negative reciprocal. we will use the negative reciprocal to find the y-intercept

[tex]3 = 4(2) + b \\ 3 = 8 + b \\ b = - 5[/tex]

Answer:

3. 10

4. 6

5. 81,000

6. 36

7. x=-0.5

Step-by-step explanation:

3. 25-3(5)

4. 3 + 3

5. 81 x 1000

6. 4 x 9

Using the Empirical Rule, it is found that:

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

In this problem:

First, by the Empirical Rule, 95% of K-cups can be expected to fall within 2 Standard Deviations of the mean.

0.33 ounces is one standard deviation above the mean.

0.16 = 16% probability that a K-cup will have more than .33 ounces.

16% weigh less than 0.23 ounces. Out of 128:

[tex]0.16(128) = 20[/tex]

20 of them will weight less than 0.23 ounces.

5% of the measures are more than 2 SD from the mean. Due to the symmetry of the normal distribution, 2.5% are more than 2 SD below the mean, thus, 2.5% of K-cups are considered weak.

Thus, the proportion between 0.23 and 0.38 is:

[tex]p = 0.68(0.50) + 0.95(0.5) = 0.815[/tex]

Out of 44:

[tex]0.815(44) = 36[/tex]

36 will weigh between 0.23 and 0.38 ounces.

68% are within 1 standard deviation of the mean.

Out of 44:

[tex]0.68(44) = 30[/tex]

30 of the Sam's Club box of K-cups are ideal.

A similar problem is given at https://brainly.com/question/13503878

Answer:

Step-by-step explanation:

x ≥ 1

Hope this helps!

close circle = ≥ or ≤

open circle = > or <

positive number = going to the right

negative number = going to the left

Answer:

5 equation matches the table

Answer: Im 99.9% sure that its 4.48

Step-by-step explanation: 17 1/8 is 17.13 as a Decimal and that subtrcated by 12.65 is 4.48   :)

Answer:

7w

Step-by-step explanation:

Simplify the parenthesis first

(13-6)=7

Then multiply by the w

7*w=7w

(13-6)*w=7w

* Can be rewritten as (13-6)w or w(13-6) or w*(13-6).