Ramon wants to make a rectangular prism with 5 cubes. Can he do this? Explain. Draw cubes to show your answer.

Answers

Answer 1

Answer:

Place them in a line.

Step-by-step explanation:

Take the First cube and place it on the paper

Then place another cube behind that cube

Repeat with remaining cubes

Should end up with a line of cubes that create a rectangular prism.

Answer 2
Final answer:

Ramon cannot form a rectangular prism using exactly 5 cubes because a rectangular prism has 6 faces, which would each be formed by a cube. To create even the smallest possible rectangular prism, he would need at least 6 cubes.

Explanation:

No, Ramon cannot make a rectangular prism using exactly 5 cubes. A rectangular prism is a three-dimensional figure with six faces that are rectangles. It would not be possible to form a rectangular prism using only 5 cubes because to form a rectangular prism you need at least 6 cubes.

Each cube would represent one face of the rectangular prism.

This is because a rectangular prism has 3 dimensions: length, width, and height. Even if you make the smallest possible rectangular prism, you would need a minimum of 6 cubes (1 cube length, 1 cube width, and 6 cubes high). If he has only 5 cubes, at least one dimension (length, width, or height) would be incomplete.

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Related Questions

Help me please.................

Answers

Answer:

  $4140

Step-by-step explanation:

For each of the amounts, the final balance is ...

  A = P(1 +rt)

Filling in the given numbers, we can add the final balances:

  900(1 + 0.06·4) + 900(1 + 0.06·3) + 900(1 + 0.06·2) + 900(1 + 0.06·1)

  = 900(4 + 0.06(4 +3 +2 +1)) = 900·4.60

  = 4140

The amount withdrawn is $4140.

Two number cubes, each with the numbers 1 through 6, are rolled. What is the probability that the sum of the rolled numbers is 2? PLEASE HELP ANYONE IN LIKE @20 min

Answers

Final answer:

The probability of rolling a sum of 2 with two dice is 1/36. This is calculated by determining the independent probabilities of rolling 1 on each die and multiplying these probabilities together.

Explanation:

The subject of this question is probability in mathematics, specifically involving the numbers on two rolled dice. The only way two dice (number cubes) can add up to 2 is if both rolled dice shows 1. Each die has 6 sides, so the probability for each dies rolling 1 is 1/6.

The probability of two independent events both occurring is founding by multiplying the probability of each event. As the two dice is rolled independently, the probability of both are showing 1 (and hence their sum is being 2) is (1/6) x (1/6), which simplifies to 1/36. Therefore, the probability that the sum of the numbers rolled on two dice is 2 1/36.

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Use the drop-down menus to complete each equation so the statement about its solution is true.
The drop down menus consist of numbers 0-9

Answers

Answer with explanation:

    A)

No solution--

No solution is obtained when there is a condition such that the equation gives a absurd condition.

Hence we write our equation as:

        2x+9+3x+x=6x+1

 Hence, we have:

          6x+9=6x+1

i.e. we have:   9=1

which is a contradiction.

Hence, we get no solution.

B)

         One solution--

One solution or unique solution is obtained when we obtain a unique value for our given variable.

i.e. if we write our equation as:

             2x+9+3x+x=5x+1

i.e. 6x+9=5x+1

i.e. x= -8

Hence, we get a unique value for x.

C)

            Infinite many solution--

The infinite many solution is where we get a condition such that we could not get a unique value for x but the equation is true.

Hence, we have:

                     2x+9+3x+x=6x+9

i.e.   6x+9=6x+9

as left hand side of equation is equal to right hand side of the equation for every ''x'' Hence, we get infinite many solution.

                 

Answer:

1. 6x+1

2. 5x+1

3. 6x+9

consider the sequence -3,7,17,27...
which function (with domain all integers n>=1) could be used to define and continue the sequence.

A f(n)= 10n-13
B f(n)=-3n+10
C f(n)=10n-3
D f(n)=-3(n-1)+10

Answers

Answer:

The function is f(n) = 10n - 13 ⇒ answer A

Step-by-step explanation:

* Lets revise the arithmetic sequence

- There is a constant difference between each two consecutive

  numbers

- Ex:

# 2  ,  5  ,  8  ,  11  ,  ……………………….

# 5  ,  10  ,  15  ,  20  ,  …………………………

# 12  ,  10  ,  8  ,  6  ,  ……………………………

* General term (nth term) of an Arithmetic sequence:

# U1 = a  ,  U2  = a + d  ,  U3  = a + 2d  ,  U4 = a + 3d  ,  U5 = a + 4d

# Un = a + (n – 1)d, where a is the first term , d is the difference

  between each two consecutive terms, n is the position of the

  term in the sequence

* Now lets solve the problem

- The sequence is -3 , 7 , 17 , 27 , .........

∵ 7 - (-3) = 7 + 3 = 10

∵ 17 - 7 = 10

∵ 27 - 17 = 10

∴ The sequence is arithmetic with constant difference 10

∴ f(n) = a + (n - 1)d

∵ a = -3

∵ d = 10

∴ f(n) = -3 + (n - 1)(10) ⇒ lets simplify it

∴ f(n) = -3 + n(10) + (-1)(10) = -3 + 10n - 10 ⇒ add like terms

∴ f(n) = 10n - 13

* The function is f(n) = 10n - 13

Option A is the correct function to define the sequence. It starts at -3 when n=1 and increases by 10 as n increases, consistently matching the given sequence.

To determine which function could be used to define and continue the given sequence (-3, 7, 17, 27...), we need to analyze the pattern of differences between consecutive terms and see which option best represents this pattern. The sequence increases by 10 each time, as can be seen from the differences (7 - (-3) = 10, 17 - 7 = 10, 27 - 17 = 10).

Looking at the functions provided:

Option A: f(n) = 10n - 13If we put n=1, f(1) = 10*1 - 13 = -3; If we put n=2, f(2) = 10*2 - 13 = 7; and so on. The pattern matches.Option B: f(n) = -3n + 10 If we put n=1, f(1) = -3*1 + 10 = 7, which does not match the first term of our sequence.Option C: f(n) = 10n - 3 If we put n=1, f(1) = 10*1 - 3 = 7, which does not match the first term of our sequence.Option D: f(n) = -3(n - 1) + 10 If we put n=1, f(1) = -3*(1 - 1) + 10 = 10, which does not match the first term of our sequence.

Therefore, Option A is the correct function to define the sequence. It starts at -3 when n=1 and increases by 10 as n increases, consistently matching the given sequence.

What is the solution to the equation below?

[tex]\frac{\sqrt{3-2x} }{\sqrt{4x} } =2[/tex]

A. x = 5/6
B. x = 9/10
C. x = 1/6
D. x = 3/10

Answers

Answer: OPTION C

Step-by-step explanation:

 Given the equation [tex]\frac{\sqrt{3-2x} }{\sqrt{4x} } =2[/tex], you need to solve for  the variable "x".

First, you need to multiply both sides of the equation by [tex]\sqrt{4x}[/tex]:

[tex](\frac{\sqrt{3-2x}}{\sqrt{4x}})(\sqrt{4x} })=2(\sqrt{4x} })\\\\\sqrt{3-2x}=2\sqrt{4x}[/tex]

Now you need to square both sides of the equation:

[tex](\sqrt{3-2x})^2=(2\sqrt{4x})^2\\\\3-2x=4(4x)\\\\3-2x=16x[/tex]

Subtrac 3 and 16x from both sides:

[tex]3-2x-(3)-(16x)=16x-(3)-(16x)\\\\-18x=-3\\[/tex]

Divide both sides by -18:

[tex]\frac{-18x}{-18}=\frac{-3}{-18}\\\\x=\frac{1}{6}[/tex]

Find an equation of a line that comes close to the points listed in below. Then use a graphing calculator to check that your line comes close to the points.

x (2,4,5,6,8)

y (12,10,6,6,1)


A.

y = 2 x + 2

B.

y = negative 2 x + 17

C.

y = negative 2 x + 18

D.

y = negative 1.3 x + 15

Answers

Answer:

Option B: y = -2x + 17.

Step-by-step explanation:

Lets calculate values for option B:

x = 2 , y = -4+17 = 13   ( B gives the value 12)

x = 4, y = -8+17 = 9   (10)

x = 5, y = -10+17 = 7  (6)

x = 6, y = -12+17 = 5 (6)

x = 8, y = -16+17 =- 1  (1)

Sum of the differences =  1 + 1 + 1 + 1 = 4.

These values are close to the ones given in the question.

Option A  y = 6, 10, 12, 14, 18 -  some of the values of y are  a lot different than the given values.

Option C:

Working them out we get y =  14, 10, 8, 6, 2. which are not quite as good as Option B values The total difference is 5 compared with 4 for option B.

Option D.

y =  12.4,  9.8, 8.5, 7.2, 4.6 where some of  the differences are large.

Samantha is making special edition hazelnut and almond chocolate boxes to give to her friends. It costs Samantha $15 to make one hazelnut chocolate box and $30 to make one almond chocolate box. It takes her 20 minutes to make either box of chocolates. She wants to spend no more than $210 and 200 minutes making the chocolate boxes to give to her friends.

Answers

Answer:

6 hazelnut

4 almond

Step-by-step explanation:

Answer:

Samantha should make six hazelnut chocolate boxes and four almond chocolate boxes in order to maximize the number of chocolates she gives to her friends.

Step-by-step explanation: This is the right answer

simplify the number using the imaginary unit i √-75

Answers

[tex] \sqrt{ - 75} = \sqrt{ - 1 \times 75} = \sqrt{ {i}^{2} \times 75 } = 5i \sqrt{3} \\(therefore \: {i}^{2} = - 1)[/tex]

Answer:

[tex]\large\boxed{\sqrt{-75}=5\sqrt3\ i}[/tex]

Step-by-step explanation:

[tex]i=\sqrt{-1}\\\\\sqrt{-75}=\sqrt{(25)(3)(-1)}\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\=\sqrt{25}\cdot\sqrt3\cdot\sqrt{-1}=5\cdot\sqrt3\cdot i=5\sqrt3\ i[/tex]

A middle school has 490 students. Mae surveys a random sample of 60 students and finds that 24 of them have pet dogs. How many students are likely to have pet dogs?

Answers

Answer:

196

Step-by-step explanation:

New Question, I'll offer 40 points again. Please help me if you can. Thank you!!! Which statement best describes the association between variable X and variable Y?

A) moderate positive association

B) weak positive association

C) weak negative association

D) moderate negative association

Answers

Answer:

C) weak negative association

Step-by-step explanation:

As X increases, Y generally decreases.  So this is a negative association.  Because the points are widely scattered, it is also a weak association.  So the answer is C.

the answer is c because the graph is going down

PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!

Suppose the dial on the spinner is spun 2 times in a row.

X is the number of times the dial lands on region A.

Which table represents the probability distribution for the variable X?

Answers

Answer:

2nd table

Step-by-step explanation:

Because it’s split into 3 equal sections so each region is one third

Answer:  d) 4/9, 4/9, 1/9

Step-by-step explanation:

Let's look at all of the possible combinations of 1st spin & 2nd spin:

AA        BA         CA

AB        BB         CB

AC        BC         CC

P (X=0): how many times is A not in the combination? 4 out of 9

P (X=1): how many times is A in the combination once? 4 out of 9

P (X=2): how many times is A in the combination twice? 1 out of 9

Find the value of tan(sin^-1(1/2))

Answers

If you know that [tex]\sin\dfrac\pi3=\dfrac12[/tex], then you know right away

[tex]\tan\left(\sin^{-1}\dfrac12\right)=\tan\dfrac\pi3=\dfrac1{\sqrt}3=\dfrac{\sqrt3}3[/tex]

###

Otherwise, you can derive the same result. Let [tex]\theta=\sin^{-1}\dfrac12[/tex], so that [tex]\sin\theta=\dfrac12[/tex]. [tex]\sin^{-1}[/tex] is bounded, so we know [tex]-\dfrac\pi2\le\theta\le\dfrac\pi2[/tex]. For these values of [tex]\theta[/tex], we always have [tex]\cos\theta\ge0[/tex].

So, recalling the Pythagorean theorem, we find

[tex]\cos^2\theta+\sin^2\theta=1\implies\cos\theta=\sqrt{1-\sin^2\theta}=\sqrt{1-\left(\dfrac12\right)^2}=\dfrac{\sqrt3}2[/tex]

Then

[tex]\tan\theta=\tan\left(\sin^{-1}\dfrac12\right)=\dfrac{\sin\theta}{\cos\theta}=\dfrac{\frac12}{\frac{\sqrt3}2}=\dfrac1{\sqrt3}=\dfrac{\sqrt3}3[/tex]

as expected.

Answer:

c. square root 3/3

Step-by-step explanation:

just did it on edg

WILL GIVE BRAINLIEST

Answers

Answer: try A I took the same test earlier

Step-by-step explanation:

If you're any good at inequalities, please help!
The gas tank in Lou’s car holds 13 gallons of gasoline. There are already 7 gallons of gasoline in the tank. He is putting gasoline that costs $2.50 per gallon in his car. Lou spends x dollars putting gasoline in his car. Model a compound inequality for this situation.

Answers

Answer:

So the maximum amount of gasoline the tank can contain is 13 gallons and there are already 7 gallons of gasoline in the tank. Therefore, we want to make sure that the amount of gasoline put in the tank doesn't reach any higher than 13 gallon.

The amount of gasoline that Lou bought with x dollars is x/2.50 gallons.

We have the inequality:

x/2.50 + 7 ≤ 13

*If you solve it, x should be smaller or equal to $15.

Final answer:

The math problem can be solved by setting up a compound inequality expressing the range that Lou can spend on gasoline. This factors in the total capacity of his tank, the current amount of gas, and the price per gallon. The result is 0 <= x <= $15.

Explanation:

For this problem, Lou needs to fill the remainder of his gas tank, which is 13 gallons total but already has 7 gallons. That means he needs to fill 13 - 7 = 6 gallons more. Gasoline costs $2.50 per gallon, so the total amount of money he spends, represented by x, can be calculated using the inequality $2.50 * number of gallons <= x.

But because Lou can add anywhere from 0 to 6 gallons, we will have a compound inequality. So, the inequality will be: $2.50 * 0 <= x <= $2.50 * 6.

This simplifies to 0 <= x <= $15, meaning Lou can spend anywhere from $0 to $15 on gasoline, depending on how much more he wants to put in his tank.

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If BC = 6 and AD = 5, find DC. 4 4.5 7.2

Answers

Answer:

4

Step-by-step explanation:

The value of Side DC is 4.

What are similar triangles?

Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent.

We have three similar triangles because each has a right angle and shares an angle.   Let's write the angles in order: opposite to the short leg, long leg, and the hypotenuse.

CAB ≡ BAD ≡ CBD

Or as ratios,

CA:AB:CB = BA:AD:BD = CB:BD:CD

We also know

AC = AD + CD

(AD+CD):AB:CB = BA:AD:BD = CB:BD:CD

(AD+CD)/CB=CB/CD

Let CD = x

(5 +x )/6 = 6/x

(5+x)*x = 6*6

5x + x² = 36

x² + 5x - 36 = 0

x² + 9x -4x -36 = 0

x(x+9 ) -4 (x +9 ) = 0

(x-4)(x+9) = 0

x= 4, -9

We reject the negative root and conclude x=4

Therefore, Side DC is 4.

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What Is The Circumference Of This Circle? Use 3.14 For Pi. There Is A Line Down The Middle Saying "12 cm"

Answers

12 is the diameter. We need the circumference which you get by multiplying 12x2 sides which = 24 which is the circumference

In the straightedge and compass construction of the parallel line below, which of the following reasons can you use to prove that CD and EG are parallel?

A. ∠FCD ≅ ∠FDC by construction
B. ∠FEG≅ ∠FGE by construction
C. ∠FCD ≅ ∠GEC by construction
D. ∠FEG ≅ ∠FCD by construction

Answers

Answer:

D.

Step-by-step explanation:

Lines EG and CD are cut by transversal CF.

By construction, ∠FEG=∠FCD. These two angles are corresponding angles.

Since two corresponding angles are congruent, then lines EG and CD are parallel (by  converse of the corresponding angles postulate).

Converse of the Corresponding Angles Postulate: If the corresponding angles formed by two lines and a transversal are congruent, then lines are parallel.

Antoine stands on a balcony and throws a ball to his dog, who is at ground level. The ball's height (in meters above the ground), xx seconds after Antoine threw it, is modeled by: h(x)=-2x^2+4x+16h(x)=−2x 2 +4x+16 What is the height of the ball at the time it is thrown?

Answers

Answer:

[tex]\boxed{\text{16 ft}}[/tex]

Step-by-step explanation:

h(x) = -2x² + 4x + 16

At the time the ball is thrown,

x = 0

h(0) = -2 × 0² + 4 × 0 + 16 = [tex]\boxed{ \textbf{16 ft}}[/tex]

Answer:

The height of the ball at the time it is thrown is 16 meters.

Step-by-step explanation:

To find the height of the ball at the time it is thrown, we have that we set the time accordingly. So the height of the ball at the time it is thrown is given by h(0) since the ball was thrown at second 0.

Now that we know the time, which is our x, we set all of our x's to 0.

[tex]h(0)=-2(0)^{2} +4(0)+16[/tex]

Next we solve,

      [tex]=0+0+16[/tex]

      [tex]=16[/tex]

In conclusion, the height of the ball at the time it is thrown is 16 meters.

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The area of a rectangle is (81x^2 − 4y^2) square units. Determine the dimensions of the rectangle by factoring the area expression completely. Show your work.

Answers

Answer 81x^2 - 4y^2     Note this is the difference of 2 perfect squares

a^2 - b^2 = (a + b)(a - b)

so here we have a = 9x and b = 2y

and our factors are

(9x + 2y)(9x - 2y)

the dimensions are 9x + 2y and 9x - 2y

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Show Work

81x^2 - 4y^2     Note this is the difference of 2 perfect squares

a^2 - b^2 = (a + b)(a - b)

so here we have a = 9x and b = 2y

and our factors are

(9x + 2y)(9x - 2y)

The dimensions of the rectangle with an area of (81x² - 4y²) square units are (9x + 2y) and (9x - 2y) units, as the area expression is a difference of squares that has been factored accordingly.

The area of a rectangle is given by the expression (81x² − 4y²) square units. To determine the dimensions of the rectangle, we need to factor this expression completely.

This expression is a difference of squares and can be factored as follows:Use the difference of squares formula, which is a²- b² = (a - b)(a + b).Apply the formula: (81x² − 4y²) = (9x)² - (2y)² = (9x + 2y)(9x - 2y).

Therefore, the dimensions of the rectangle can be 9x + 2y and 9x - 2y units.

Which function f (x) , graphed below, or g (x) , whose equation is g (x) = 3 cos 1/4 (x + x/3) + 2, has the largest maximum and what is the value of this maximum?

f(x), and the maximum is 3.

g(x), and the maximum is 5.’

f(x), and the maximum is 2.

g(x), and the maximum is 2.

Answers

Answer:

Second option

g(x), and the maximum is 5.’

Step-by-step explanation:

In the graph it can easily be seen that the maximum value reached by the function f(x) is y = 3.

Then, the function g (x) is:

[tex]g(x) = 3cos(\frac{1}{4}(x + \frac{1}{3}x)) + 2[/tex]

By definition the function

[tex]y = cos(x)[/tex] reaches its maximum value when x = 0,  [tex]2\pi[/tex],  [tex]4\pi[/tex], ..., [tex]2k\pi[/tex]

So

When [tex](\frac{1}{4}(x + \frac{1}{3}x)) = 0[/tex]  entonces [tex]cos((\frac{1}{4}(x + \frac{1}{3}x)) = 1[/tex].

Thus:

[tex]g(0) = 3(1) + 2\\\\g(0) = 5[/tex].

Therefore the function that has the greatest maximum is g(x) when [tex]g(x) = 5[/tex]

The answer is the second option

6 libras de café y 5 de azúcar costaron 227 pesos y 5 libras de café y 4 libras de azúcar (a los mismos precios) costaron 188 pesos hallar el precio de una libra de café y una libra de azúcar

Answers

Answer:

The price of one pound of coffee is 32 pesos

The price of one pound of sugar is 7 pesos

Step-by-step explanation:

The question in English is

6 pounds of coffee and 5 pounds of sugar cost 227 pesos and 5 pounds of coffee and 4 pounds of sugar (at the same prices) cost 188 pesos Find the price of one pound of coffee and one pound of sugar.

Let

x-----> the price of one pound of coffee

y-----> the price of one pound of sugar

we know that

6x+5y=227 -----> equation A

5x+4y=188 ----> equation B

Solve the system of equations by graphing

Remember that the solution of the system of equations is the intersection point both graphs

The solution is the point (32,7)

see the attached figure

therefore

The price of one pound of coffee is 32 pesos

The price of one pound of sugar is 7 pesos

An office supply store has five different packages of black ink pens which is the best deal available on black ink pens at this office supply

Answers

Answer:

12 pack for $15.00

Step-by-step explanation:

4 pack for $7.00:  7 ÷4  = 1.75

6 pack for $10.25:  10.25 ÷6 ≈ 1.71

10 pack for $13.00:  13 ÷10  = 1.30

12 pack for $15.00:  15.00 ÷12 = 1.25

25 pack for $32.50:  32.50 ÷25 = 1.30

Given: PRST is a square
PMKD is a square
PR = a, PD = a
Find the area of PMCT.

Answers

Answer:

[tex](1-\sqrt{2})a^2[/tex]

Step-by-step explanation:

Consider irght triangle PRS. By the Pythagorean theorem,

[tex]PS^2=PR^2+RS^2\\ \\PS^2=a^2+a^2\\ \\PS^2=2a^2\\ \\PS=\sqrt{2}a[/tex]

Thus,

[tex]MS=PS-PM=\sqrt{2}a-a=(\sqrt{2}-1)a[/tex]

Consider isosceles triangle MSC. In this triangle

[tex]MS=MC=(\sqrt{2}-1)a.[/tex]

The area of this triangle is

[tex]A_{MSC}=\dfrac{1}{2}MS\cdot MC=\dfrac{1}{2}\cdot (\sqrt{2}-1)a\cdot (\sqrt{2}-1)a=\dfrac{(\sqrt{2}-1)^2a^2}{2}=\dfrac{(3-2\sqrt{2})a^2}{2}[/tex]

Consider right triangle PTS. The area of this triangle is

[tex]A_{PTS}=\dfrac{1}{2}PT\cdot TS=\dfrac{1}{2}a\cdot a=\dfrac{a^2}{2}[/tex]

The area of the quadrilateral PMCT is the difference in area of triangles PTS and MSC:

[tex]A_{PMCT}=\dfrac{(3-2\sqrt{2})a^2}{2}-\dfrac{a^2}{2}=\dfrac{(2-2\sqrt{2})a^2}{2}=(1-\sqrt{2})a^2[/tex]

Line CD passes through (0, 1) and is parallel to x + y = 3. Write the standard form of the equation of line CD. x + y = 1 x – y = 1 x + 1 = y x + y = 11

Answers

ANSWER

x+y=1

EXPLANATION

We want to find the equation of line CD which passes through (0, 1) and is parallel to x + y = 3.

In slope intercept form, the given line is

y=-x+3

The slope of this line is m=-1

Line CD also has the same slope

The equation is given by:

y=mx+b

The given point (0,1) means the y-intercept;is b=1

Hence the equation is

y=-x+1

In standard form the equation is:

x+y=1

Answer:

The answer is x + y = 1

Step-by-step explanation:

Given: Line CD passes through (0, 1) and is parallel to x + y = 3.

We know that if two line are parallel then they have equal slopes.

Thus, the slope of line = slope of line x + y = 3

 x + y = 3  when we compare this to the standard linear equation

= 3 - x

y = m x + c  .we get m = -1 .

The slope of CD (m)= -1

Now, the equation of line CD passing through (0,1) is given by :-

( y - 1 ) = m ( x - 0 )

⇒ ( y - 1 ) = ( -1 ) x

⇒ x + y = 1

The equation of line CD = x + y = 1

What is the average rate of change from x = −3 to x = −4?

Answers

Answer:

-2

Step-by-step explanation:

Since it would be immensely helpful to know the equation of this parabola, we need to figure it out before we can continue.  We have the work form of a positive upwards-opening parabola as

[tex]y=a(x-h)^2+k[/tex]

where a is the leading coefficient that determines the steepness of lack thereof of the parabola, x and y are coordinates of a point on the graph, and h and k are the coordinates of the vertex.  We know the vertex: V(-3, -3), and it looks like the graph goes through the point P(-2, -1).  Now we will fill in the work form equation and solve for a:

[tex]-1=a(-2-(-3))^2-3[/tex]

which simplifies a bit to

[tex]-1=a(1)^2-3[/tex]

and

-1 = a(1) - 3.  Therefore, a = 2 and our parabola is

[tex]y=2(x+3)^2-3[/tex]

Now that know the equation, we can find the value of y when x = -3 (which is already given in the vertex) and the value of y when x = -4.  Do this by subbing in the values of x one at a time to find y.  When x = -3, y = -3 so the coordinate of that point (aka the vertex) is (-3, -3).  When x = -4, y = -1 so the coordinate of that point is (-4, -1).  The average rate of change between those 2 points is also the slope of the line between those 2 points, so we will use the slope formula to find it:

[tex]m=\frac{-1-(-3)}{-4-(-3)} =\frac{2}{-1}=-2[/tex]

And there you have it!  I'm very surprised that this question sat unanswered for so very long!  I'm sorry I didn't see it earlier!

HELP ASAP PLZ
the function ​f(x)​ is the height of a model rocket x seconds after launch. The rocket reaches its maximum height in 2 seconds and hits the ground at 4 seconds. What is the practical domain for the function f(x)?

Answers

Final answer:

The practical domain of the function f(x), representing the height of a model rocket after launch, is [0,4], including the launch at time x=0, reaching the maximum height at x=2 seconds, and landing at x=4 seconds.

Explanation:

The practical domain for the function f(x), which represents the height of a model rocket x seconds after launch, refers to the interval of time during which the rocket is in flight. Since the rocket is launched at time x=0, reaches its maximum height at x=2 seconds, and hits the ground at x=4 seconds, the practical domain of f(x) is [0,4].

This domain includes all times from the launch to when the rocket lands, as the function's values will only be meaningful or defined within this interval.

Cathy has a nickel, a dime, and a quarter in her purse. She randomly picks a coin, replaces it, and then picks another coin. The probability that the two coins are of different denominations is .
SOMEONE HELP PLEASE THIS IS FOR PLATO.

Answers

Answer:

Hence, the probability that the two coins are of different denomination is:

                            2/3

Step-by-step explanation:

Let N denote nickel, D denotes dime and Q denotes Quarter.

Now when two coins are drawn one after the other with replacement then the outcomes is given by:

         (N,N)     (N,D)      (N,Q)

         (D,N)     (D,D)      (D,Q)

         (Q,N)     (Q,D)      (Q,Q)  

This means that there are a total of  9 outcomes.

The outcomes such that both the denominations are different i.e. the number of favorable outcomes are:  6

{ (N,D) (N,Q) (D,N) (D,Q) (Q,N) (Q,D) }

The probability that the two coins are of different denomination is:

                             6/9=2/3

What is the amplitude and period of f(t)=2.5 tan t?

Answers

Answer:

Option d.

Amplitude: None

Period: π

Step-by-step explanation:

To quickly solve this problem, we can use a graphing tool or a calculator to plot the equation.

Please see the attached image below, to find more information about the graph

The equation is:

f(t) = 2.5 tan (t)

We can see from the graph that the amplitude goes up to infinity, and the period is equal to π.

Option d.

Amplitude: None

Period: π

Final answer:

The amplitude of the function f(t)=2.5 tan t is 2.5, as it's the coefficient of the tangent function. The period is π, as it's obtained by dividing π by the number multiplying 't', which in this case, is 1.

Explanation:

The function given, f(t)=2.5 tan t, is a trigonometric function, which represents a wave. In the context of a wave represented by a trigonometric function such as this, there are several key components. The two most important for this question are:

Amplitude: The amplitude of a wave is the peak value of the wave. In the given equation, the amplitude is the coefficient of the trigonometric function, which is 2.5.Period: The period of a wave is the length of one cycle of the wave. The period of a tan function is (π/b), where 'b' is the number multiplying t. In this case, as 't' doesn't have any multiplier, the period is π.

Learn more about Amplitude and Period here:

https://brainly.com/question/15930409

#SPJ3

The measurement from the base of a tree to the tip of its shadow is 100ft.

Answers

the answer is200ftbecause cos(60)=100/the hight of the treethe hight of the tree=100/cos(60)=200ft

Answer: it’s 200ft

Step-by-step explanation:

Which of the following expressions is equal to sin⁡(-150°)?

A. sin(30°)
B. -sin(-30°)
C. -sin(30°)
D. sin(150°)

Answers

Check the picture below.

let's notice that the angle -150° has a reference angle of 30°, so any trigonometric function for either angle will be the same value, however, let's recall that the sine or y-coordinate is negative on the III Quadrant, so sin(-150°) is the same as sin(30°) BUT negative, -sin(30°).

Answer:

C. -sin(30°)

Step-by-step explanation:

180-150=30

-sin(30) = -.5 on calculator j like sin(-150) is

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