Please help, I'm taking the semester test.

Drag and drop an answer to each box to correctly explain the derivation of the formula for the volume of a pyramid.

Consider a prism and a pyramid with the same base and height.
The volume of the prism is blank, the volume of the pyramid.
The formula for the volume of a prism is V=Bh ,
where B is the area of the base and h is the height, so the formula for the volume of a pyramid is blank


Picture shown below

Answer:

Karen spent $ 10 , Jasmine spent $20 , Maggie spent $30

When x disappears from the equation and the two sides of the equation not equal each other , then the equation has no solution

When x disappears from the equation and the two sides of the equation equal each other , then the equation has infinite solutions

Step-by-step explanation:

* Lets read the problem and solve it

- There are three sisters ⇒ Maggie , Karen , Jasmine

- Each sister bought a gift for their mom

- Maggie spent 3 times as much as Karen

- Karen spent half as much as Jasmine

- Altogether, they spent $60

- Let Jasmine spent x

∵ Karen spent half as much as Jasmine

∴ Karen spent 1/2 x

∵ Maggie spent 3 times as much as Karen

∴ Maggie spent 3 × 1/2 x = 3/2 x

∵ Altogether, they spent $60

∴ x + 1/2 x + 3/2 x = 60

∴ 3x = 60 ⇒ divide both sides by 3

∴ x = 20

* Lets find the share of each one

∵ Jasmine spent x

∴ Jasmine spent $20

∵ Karen spent 1/2 x

∴ Karen spent 1/2 × 20 = $10

∵ Maggie spent 3/2 x

∴ Maggie spent 3/2 x 20 = $30

* Karen spent $ 10 , Jasmine spent $20 , Maggie spent $30

* Lets describe what happens when an equation has no solution

- "No solution" means that there are no values of x satisfy the equation

- When x disappears from the equation and the two sides of the

 equation not equal each other , then the equation has no solution

- Ex: solve the equation 2 + 2x – 8 = 7x + 5 – 5x

∵ 12 + 2x – 8 = 7x + 5 – 5x ⇒ add the like terms

∴ 4 + 2x = 2x + 5 ⇒ subtract 2x from both sides

∴ 4 = 5 ⇒ the two sides not equal

∴ There is no value of x satisfy this equation

∴ There is no solution

* Lets describe what happens when an equation has infinite solutions

- "Infinite solutions" means all numbers are solutions.

- When x disappears from the equation and the two sides of the

 equation equal each other , then the equation has infinite solutions

- Ex: solve the equation 2x + 3 = x + x + 3

∵ 2x + 3 = x + x + 3 ⇒ add the like terms

∴ 2x + 3 = 2x + 3 ⇒ subtract 2x from both sides

∴ 3 = 3 ⇒ the two sides are equal

∴ All values of x satisfy the equation

∴ There are infinite solutions

Step-by-step explanation:

-4(27)+100

-108+100

=-8

To find the 27th term in the sequence defined by the formula an = -4n + 100, you substitute 27 for 'n' in the equation. The yielded result is -8, which is the 27th term in the sequence.

In Mathematics, a sequence can be defined by an equation, where each term an is defined in terms of its place in the sequence ('n'). In the given equation, an = -4n + 100,  the nth term is determined by multiplying 'n' by -4 and then adding 100. If we want to find the 27th term of the sequence, we substitute n with 27 in the equation.

So, a27 = -4(27) + 100 = -108 + 100 = -8.

Therefore, the 27th term of the sequence is -8.

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Answer:

55 small boxes, 65 large boxes.

Step-by-step explanation:

First, we let x = the amount of big boxes and let y = the amount small boxes. Then, we know that any combination of such will equal 120 so we say

x + y = 120

We also know that we have to fill 4900 pounds, so we can say

50x + 30y = 4900

Then, we can use either substitution or elimination. I'll do substitution. we make the first equation

x = 120 - y

And now we can plug this into our second equation

50(120 - y) + 30y = 4900

Then we distrubute

6000 - 50y + 30y = 4900

Then simplify

6000 - 20y = 4900

Subtract 6000 from both sides

-20y = -1100

then divide both sides by -20

y = 55

so there are 55 small boxes, which means we can subtract 55 from 120 to get 65 large boxes.

The truck is carrying 65 large boxes and 55 small boxes,

x + y = 120 (total number of boxes)

50x + 30y = 4900 (total weight of the boxes in pounds)

First, we can solve one of the equations for one variable and then substitute that into the other equation. Starting with the first equation:

x = 120 - y

Now substitute x in the second equation:

50(120 - y) + 30y = 4900

6000 - 50y + 30y = 4900

-20y = -1100

y = 55

Now we know there are 55 small boxes, we can go back to the first equation to find x:

x + 55 = 120

x = 120 - 55

x = 65

Therefore, the truck is carrying 65 large boxes and 55 small boxes.

Step-by-step explanation:

By the fundamental theorem of algebra, the degree of the polynomial equals the number of roots (including complex and multiplicities, i.e. multiple roots).

Since n=4, we expect to find 4 roots, although we are only given three, namely -1,3,2+4i.

Fortunately, if the polynomial has real coefficients (which we will ASSUME), for any complex root to exist, its conjugate is also a root to the equation.

Since the conjugate of 2+4i is 2-4i, we now have all four roots, -1, 3, 2+4i, 2-4i.

An n-degree polynomial may be construct by the product of (x-ri) where ri are the roots.  This means

P(x) = (x-(-1))(x-3)(x-2-4i)(x-2+4i), which is

P(x) = (x+1)(x-3)(x-2-4i)(x-2+4i)

When expanded, P(x) = x^4-6x^3+25x^2-28x-60

Check:

sum of roots = (-1+3+2+4i+2-4i) = 6  (same as negative of coefficient of term x^3)  ok

product of roots = (-1)(3)(2+4i)(2-4i)=-3*20 = -60  = constant term,  ok.

Note: kP(x) is also a polynomial with the same four roots, where k=any real number.  P(x) is a particular case where k=1.

The 4th degree polynomial with given zeros -1, 3, and 2+4i, can be derived from these roots and is of the form f(x) = a(x+1)(x-3)(x-2-4i)(x-2+4i). Complex roots always appear in conjugate pairs if the coefficients of the polynomial are real numbers.

The subject of the question is related to the Mathematics of polynomials. Specifically, the question requests the equation of an nth degree polynomial function with n=4 where the zeros include -1, 3, and 2+4i. Given that we have a 4th degree polynomial and we already have 3 roots, we are missing one more. In mathematics, complex roots always come in pairs, so if 2+4i is one of the roots, then its conjugate 2-4i must also be a root.

So, the four roots are: -1, 3, and 2±4i. The polynomial can then be constructed by setting these roots as factors of the polynomial which would then be of the form:

f(x) = a(x+1)(x-3)(x-2-4i)(x-2+4i)

Where 'a' is a constant that will be 1 if the leading coefficient is not specified in the problem.

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Answer:

1/8

Step-by-step explanation:

There's two ways you can solve this.

Method 1: Let's say you grab the socks one at a time.  The first sock you grab has a 6/16 probability of being red.  If the sock is red, then the second sock you grab has a 5/15 probability of being red, because there's one less red sock and one less sock total.  So the overall probability is:

P = 6/16 × 5/15 = 1/8

Method 2: There are ₆C₂ ways to choose 2 red socks from 6 red socks.  There are ₁₆C₂ ways to choose any 2 socks from all 16 socks.  So the probability that both socks you choose are red is:

P = ₆C₂ / ₁₆C₂ = 15 / 120 = 1/8

The probability that both socks are red is 1/8 if the drawer contains 6 red socks and 10 blue socks

It is defined as the ratio of the number of favourable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

We have:

Total number of socks= 6+10 = 16

Total ways of selecting = C(16, 2) = 120

Ways of selecting 2 red socks from 6 = C(6, 2) = 15

The probability = 15/120 = 1/8

Thus, the probability that both socks are red is 1/8 if the drawer contains 6 red socks and 10 blue socks

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Possible number of permutaions that the sum is 4 on two fair dice:

1 & 3

2 & 2

3 & 1

There are only 3 ways to make a sum of 4. Each cube has 6 digits. So, 6 x 6 is 36.

Answer: 3/36 or 1/12

Answer:

An estimate of a population parameter that provides an interval of values

believed to contain the value of the parameter is known as the inveral estimate.

Step-by-step explanation:

Therefore, the correct answer C.

* Hopefully this helps:)) Mark me the brainliest :))

OK, f is the graph and g is the table.

f(-2) > g(-2)

f(-2) means the y coordinate of the graph when x=-2.  That's y=2, so f(-2)=2

g(-2) we look up in the table, g(-2)=1

So it's true that f(-2) > g(-2)

Answer: f(-2) > g(-2)   TRUE

-----

The characteristic of an absolute value function, possibly shifted and scaled, is the distinct V shape.   Clearly f is an absolute value function; the slopes are -1 and 1 and the vertex is at (-3,1) so f(x) = |x+3|+1

g kinda also has the characteristic V shape, but it has a slope of -3  in one place and -1 in the other, so it isn't a straight line.

Answer: f(x) and g(x) are absolute value functions.   FALSE

-----

For all x, f(x) > g(x)

Presumably this means for all x in g's domain, which is only five points.  We already checked x=-2; let's do the rest.

f(-5) = 3, g(-5) = 4

So at x=-5 it's not true

For all x, f(x) > g(x)   FALSE

-----

f(x) and g(x) intersect at exactly two points.

We already know they don't at x=-5 and x=-2.  Let's check the other three.

f(-5) = 3, g(-5) = 4

f(-4) = 2,  g(-4)=1

f(-3) = 1, g(-3) = 0

f(-2) = 2, g(-2) = 1

f(-1) = 3, g(-1) = 4

This one's tricky.   All we really know about g is the points listed.   g may be a parabola where the function is continuous between the table points.   If that's true the functions intersect at exactly two points.  We don't really know that for sure so I'll go with:

Answer: f(x) and g(x) intersect at exactly two points.  FALSE

I may be marked wrong on this last one but I'm sticking with my answer.

Answer:

A and D are both true.

Step-by-step explanation:

f(x) is a quadratic. It is the graph in red. Its equation is y = (x + 3)^2

g(x) is an absolute value formula. It is the graph in blue. Its equation is y=abs(x + 3) + 1

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

The last statement is correct. The two figures cross at (-1.382,2.618) and (-4.618, 2.618) so D is true. But don't stop reading. You'll learn much from this question.

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

From the right intersect point to the left intersect point, the blue graph is greater than the red one. C is false. Remember the red graph is f(x)

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

B is false. g(x) is a quadratic

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

Unfortunately I'm getting that A is true

f(-2) = 2 and

g(-2) = 1

Answer:

Option B

Step-by-step explanation:

Plot points A, B, C and line y=x on the coordinate plane (see attached diagram, blue points)

1. The reflection across the line y=x has the rule

(x,y)→(y,x)

So,

Points A', B', C' are marked in red on the diagram

2. The rotation by 90° clockwise about the origin has the rule

(x,y)→(-y,x)

So,

Answer:

A (−7, −13) → A ′(−13, −7) → A ″(7, −13);

B (12, −8) → B ′(−8, 12) → B ″(−12, −8);

C (−17, 19) → C ′(19, −17) → C ″(17, 19)

Step-by-step explanation

The coordinates of the vertices of the preimage are given.

To find the image as it reflected from the preimage across the y=x line, use the transformation rule: (x,y)→(y,x).

Apply the transformation rule to vertices A(−7,−13), B(12,−8), and C(−17,19).

A(−7,−13)→A'(−13,−7).

B(12,−8)→B'(−8,12).

C(−17,19)→C'(19,−17).

To determine the vertices of the image after the rotation of 90∘ about the origin, use the rule: (x,y)→(−y,x).

Apply the rotation rule to the vertices of △A'B'C'.

A'(−13,−7)→A''(7,−13).

B'(−8,12)→B''(−12,−8).

C'(19,−17)→C''(17,19).

Therefore,

A(−7,−13)→A'(−13,−7)→A''(7,−13)

B(12,−8)→B'(−8,12)→B''(−12,−8)

C(−17,19)→C'(19,−17)→C''(17,19)

represents the reflection of △ABC across the line y=x and its rotation of 90∘ about the origin.

Answer:

  D)  0.08

Step-by-step explanation:

The pie chart shows that of the 6000 fish in the hatchery, 1/4 of them, or 1500 fish are salmon. A 5% sample of that population will be ...

  0.05 × 1500 fish = 75 fish

If 6 of these have dangerous levels of mercury, the probability of randomly choosing a contaminated fish from the test group is ...

  6/75 = 8/100 = 0.08

The probability of selecting a salmon with dangerous mercury levels can be determined using the given data.

To determine the probability of a randomly selected fish having a dangerous mercury level, we need to find the proportion of tested fish that had dangerous mercury levels. From the table, we can see that out of 120 tested salmon, 3 had dangerous mercury levels. So the probability is 3/120, which simplifies to 1/40 or 0.025. Therefore, the correct answer is option C) 0.02.

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Answer:

D.

Step-by-step explanation:

A function, by the easy-to-understand definition, is a relation where no x values are shared.  The only set where each x value is different is in D.  All the other sets share the same x value.  Example:  Set C has coordinates (-2, 1) and (-2, 2).  The x coordinates are the same, so this isn't a function.  It is only a relation.

Answer:

  D.  25%

Step-by-step explanation:

Each day, Julia's sales are 1.25 times the previous day's sales. That is, 25% more than the day before. Julia's sales are increasing 25% per day.

ANSWER:

The correct answer is D.25%

STEP-BY-STEP EXPLANATION:

f(x) = 2 * (1.25)^x

This is in the form

y = a b^x

where b is 1 plus the growth rate

b = 1.25 = 1+growth rate

1.25 = 1 + growth rate

.25 = growth rate

25% = growth rate

Answer:

x>56

Step-by-step explanation:

Ebony waited more than 56 minutes in the doctor's office. The first step is to recognize the inequality symbols.

"≥" Can be read as more than or equal to

"≤" Can be read as less than or equal to

">" Can be read as more tha

"<" Can be read as less than

In this case, Ebony waited MORE THAN which means that the correct symbol to be used is ">".

The second step is to define a variable. In this case, we're going to say that 'x' represents the time (in minutes) that Ebony waited.

Finally, let's write the inequality.

x > 56 ✔️

Answer:

x>25

Step-by-step explanation:

Answer:

  4n^3 -10n^2 +16n -10

Step-by-step explanation:

Use the distributive property to eliminate parentheses, then combine like terms.

  = 2n(2n^2 -3n +5) -2(2n^2 -3n +5)

  = 4n^3 -6n^2 +10n -4n^2 +6n -10

  = 4n^3 +n^2(-6-4) +n(10+6) -10

  = 4n^3 -10n^2 +16n -10

Answer:

C) -9.6

Step-by-step explanation:

1) The answer will be negative because a negative divided my a positive will always be negative and visa-versa.

2) 5 goes into 48 9 times; 5(9) = 45

3) 5 cannot go into 3 so add a 0 to make 30 and place a decimal after -9

4) 5 can go into 30 6 times; 5(6) = 30

5) The remainder is 0 and your answer is C. -9.6

Answer:

p ≥ 5.5 hrs

Step-by-step explanation:

Let p represent the number of hours Brandon spends practicing per week.

So he practices for atleast 5.5 hrs.

i.e p ≥ 5.5 hrs

The inequality to represent the number of hours Brandon will spend practicing this week is p ≥ 5.5 hrs.

Mathematical expressions with inequalities are those in which the two sides are not equal. Unlike to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

We have,

Brandon wants to practice his trombone for at least 5.5 hours this week.

Let p represent the number of hours Brandon spends practicing per week.

We know the sign for at least is "≥".

So, the inequality is p ≥ 5.5 hrs.

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Answer:

Step-by-step explanation:

Answer:

k =(2/3)

Step-by-step explanation:

25 ^ (3k) = 625

Replace 25 with 5^2   and 625 with 5^4

5^2^3k = 5^4

We know that a^b^c = a^(b*c)

5^(2*3k) = 5^4

5^ (6k) = 5^4

The bases are the same, so the exponents must be the same

6k = 4

Divide each side by 6

6k/6 = 4/6

k = 2/3

Answer:

  ASA

Step-by-step explanation:

Angles E/R and O and the sides EO/RO between them are indicated as congruent. Hence the Angle-Side-Angle (ASA) postulate will be the one that is applicable.

Answer:

18.1 cm

Step-by-step explanation:

Work out CD

[tex]\sqrt{16^{2}-7^{2}  } = 14.38749457[/tex] ⇒ Pythagoras Theorem

Use CD and AD to work out AC

[tex]\sqrt{14.38749457^{2}+11^{2}  } = 18.11077028[/tex] ⇒ Pythagoras Theorem

Answer:

B.

Step-by-step explanation:

The first number minus the 2nd number will close off the distance.

Answer:

Q'(0.4,-1.7),R'(2.4,9.3), S'(-10.6,7.3)

Step-by-step explanation:

we know that

The rule of the translation is equal to

(x,y) -----> (x-7.6,y+4.3)

That means---> the translation is 7.6 units left and 4.3 units up

Find the coordinates of the vertices of the image

Q(8,-6) -----> Q'(8-7.6,-6+4.3)

Q(8,-6) -----> Q'(0.4,-1.7)

R(10,5) -----> R'(10-7.6,5+4.3)

R(10,5) -----> R'(2.4,9.3)

S(-3,3) -----> S'(-3-7.6,3+4.3)

S(-3,3) -----> S'(-10.6,7.3)

The coordinates of the vertices Q, R, and S of the image of the triangle after a translation are (0.4, -1.7), (2.4, 9.3), and (-10.6, 7.3)

Translation is a way of changing the location of an object on the xy plane.

Given the vertices of the triangle QRS as

Q(8, –6)

R(10, 5)

S(–3, 3)

If the coordinate of the vertices is translated under the rule (x–7.6, y+4.3)

For Q'

Q' = (8-7.6, -6+4.3)

Q' = (0.4, -1.7)

For R':

Q' = (10-7.6, 5+4.3)

Q' = (2.4, 9.3)

For the coordinate S'

S' = (-3-7.6, 3+4.3)

S' = (-10.6, 7.3)

Hence the coordinates of the vertices Q, R, and S of the image of the triangle after a translation are (0.4, -1.7), (2.4, 9.3), and (-10.6, 7.3)

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Answer: The Answer is (4,-6)

Step-by-step explanation:

Answer:

14.18 units  &  4.88 units

Step-by-step explanation:

The right triangle in this problem is shown in the attached image.

Using trigonometry, the adjacent leg would be 15 Cos 19°

and the opposite leg would be 15 Sin 19°

Thus,

one leg is 15 Cos 19 = 14.18 units, and

another leg is 15 Sin 19 = 4.88 units

Answer:

For plato users the correct option is D.

Step-by-step explanation:

D. 4.9 units, 14.2 units

Answer:

for every 1000 there is 1  kilogram so therefore there are 5 kilograms to equal 5000 grams

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

Answer:

x+y=45, (5,40) and ( 25,20)

Step-by-step explanation:

Here we are given the information that Gian was given 45 mins to spend on computer after dinner. Out of those 45 mins , he can either play games of watch videos.

Therefore If the time for which he watches videos is x and that of the time he spend playing game is y , there sum must be equal to 45 mins.

Hence our equation in terms of x andy will be

[tex]x+y=45[/tex]

Now let us see the graph part.

Here we see that the graph is plot on xy plane where x is taken as time taken in watching videos and y as playing games

i) on Monday , he watch 5 minutes in watching videos

Hence x=5 , we put x=5 in x+y=45 and solve it for y

5+y=45

subtracting 5 from both sides

5+y-5=45-5

y=40

Hence he spend 40 mins on playing games.

So we plot Point (5,40) for monday.

i) on Tuesday , he watch 25 minutes in watching videos

Hence x=25 , we put x=25 in x+y=45 and solve it for y

25+y=45

subtracting 25 from both sides

25+y-25=45-25

y=20

Hence he spend 20 mins on playing games.

So we plot Point (25,20) for Tuesday.

Answer:

  {12, 13}

Step-by-step explanation:

Whole numbers that round to 50 will be in the range 45 to 54. Multiples of 4 in that range are 48 and 52.

  48 = 4·12

  52 = 4·13

Dev's number could be either 12 or 13.

Answer:

x^(7/5)

Step-by-step explanation:

Root goes on bottom of fraction

Power goes on top

x^(7/5)

Answer:

[tex]x^{\frac{7}{5}}[/tex]

Step-by-step explanation:

Rewrite the radical expression as an expression with rational exponents.

fifth root of x to the power of 7

[tex]\sqrt[5]{x^7}[/tex]

To write the given expression with radical exponent we use the rule

[tex]\sqrt[n]{a^m}=a^{\frac{m}{n}}[/tex]

Move the index n to the denominator of exponent

[tex]\sqrt[5]{x^7}=x^{\frac{7}{5}}[/tex]

Expression with rational exponent is [tex]x^{\frac{7}{5}}[/tex]

Answer:

The correct option is 2.

Step-by-step explanation:

The given inequalities are

[tex]50<2x+10[/tex]             .... (1)

[tex]2x+10<110[/tex]            .... (2)

Solve each inequality.

Subtract 10 from each side of inequality (1).

[tex]50-10<2x+10-10[/tex]

[tex]40<2x[/tex]

Divide both the sides by 2.

[tex]20<x[/tex]

The value of x is more than 20.

Subtract 10 from each side of inequality (2).

[tex]2x+10-10<110-10[/tex]

[tex]2x<100[/tex]

Divide both the sides by 2.

[tex]x<50[/tex]

The value of x is less than 50.

Since x > 20 and x < 50, therefore Malcolm needs to consume more than 20 grams of carbohydrates, but less than 50 grams of carbohydrates.

Hence the correct option is 2.

Answer:

its number 2

Step-by-step explanation:

The translation could result in:

Translation--

It is  a transformation which changes the location of the figure but the shape and size of the figures remains the same i.e. the shape and size of the figure is retained after the transformation.

It either moves the figure up or down by some units.

i.e. f(x) → f(x)+k

then the graph of the function f(x) is shifted k units up is k>0

and k units down if k<0

Similarly it may shift the figure k units to the left or to the right.

i.e. if f(x) → f(x+k)

if k<0 then the function f(x) is shifted k units to the right.

and if k>0 then the function is shifted k units to the left.

Options B, D, and E are correct. A translation could result in a figure moving up, down, and left or right.

Translation in geometry refers to moving a figure from one location to another without changing its shape, size, or orientation. It involves sliding the figure over a plane.

Let's analyze each option:

A. "A figure getting smaller" suggests a transformation involving a reduction in size or being scaled down.

B. "A figure moving up" implies a vertical translation, where the figure is shifting in the upward direction.

C. "A figure flipping upside down" suggests a reflection transformation rather than a translation. It involves a change in orientation rather than a shift in position.

D. "A figure moving left" indicates a horizontal translation, where the figure is shifting to the left.

E. "A figure moving down" signifies a vertical translation, where the figure is shifting in the downward direction.

Based on the given options, a translation can result in:

B. a figure moving up

D. a figure moving left

E. a figure moving down

Translations do not result in a figure getting smaller (Option A) or flipping upside down (Option C).

Complete question:

Which could a translation result in? Select all that apply.

A. a figure getting smaller

B. a figure moving up

C. a figure flipping upside down

D. a figure moving left

E. a figure moving down