If y= x+1/2-x , evaluate y given x= 5i .

There are 24 bouquets making by Rachel.

What is Factor?

A number which means to break it up into numbers that can be multiplied together to get the original number.

Now, To solve this problem,

Let us first lay out all the factors of each number.

72 : 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

48 : 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

So, The greatest number of bouquets that can be made would be equal to the greatest common factor of the two numbers 72 and 48 will 24.

Hence, There are 2 bouquets making by Rachel.

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Rachel can make 24 bouquets with 72 carnations and 48 roses.

To determine the greatest number of bouquets Rachel can make with 72 carnations and 48 roses, we need to find the greatest common divisor (GCD) of 72 and 48. The GCD is the largest number that divides both 72 and 48 without leaving a remainder.

Here are the steps to find the GCD:

Answer:

Step-by-step explanation:

Step 1 : 27-t*3

Now put the value  t=6

Step 2:

=27-6*3

According to the DMAS rule multiplication wll be solved first.

Step3:

=27-18

Step 4:

=9 ....

Answer:

[tex]\lim_{x \to 0} x^2-3=-3[/tex]

Step-by-step explanation:

This limit can be written as follows

[tex]\lim_{x \to 0} x^2-3[/tex]

Direct substitution means that we substitute in the value for x to get our limit

[tex]\lim_{x \to 0} x^2-3\\\\0^2-3\\\\-3[/tex]

[tex]\displaystyle\\\lim_{x\to 0}(x^2-3)=0^2-3=-3[/tex]

Answer:

F=0 or (7/3)

Step-by-step explanation:

When F is 0, the equation reads -0(3(0)-7)=0. The outside 0 will multiply by everything and make it equal 0. When F is 7/3, the inside of the parenthesis read 3(7/3)-7. This equals 7-7. It'll end up being (7/3)0, which equals 0.

Answer:

5=.25, 3=.30, 2=.50

Step-by-step explanation:

5×5=.25

Answer: 25%

Step-by-step explanation: A nickel is worth 5 cents. There are 5 nickels. Multiply 5 by 5. 5 x 5 = 25. You have 25 cents in nickels. There are 100 cents in a dollar, so divide 25 by 100. 25/100 = 0.25. To get the percent, multiply 0.25 by 100. 0.25 x 100 = 25%.

Answer:

Option A.) 16 m³. The volume of the new pyramid is the volume of the original pyramid times 1/64.

Step-by-step explanation:

step 1

Find the volume of the original pyramid

The volume of the pyramid is equal to

[tex]V=\frac{1}{3}Bh[/tex]

where

B is the area of the base

h is the height of the pyramid

we have

[tex]B=16^{2}=256\ m^{2}[/tex] ----> is the area of a square

[tex]h=12\ m[/tex]

substitute

[tex]V=\frac{1}{3}(256)(12)[/tex]

[tex]V=1,024\ m^{3}[/tex]

step 2

Find the volume of the new pyramid

we know that

If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube

so

Let

z -------> the scale factor

x ------> the volume of the new pyramid

y -----> the volume of the original pyramid

[tex]z^{3}=\frac{x}{y}[/tex]

we have

[tex]z=\frac{1}{4}[/tex]

[tex]y=1,024\ m^{3}[/tex]

substitute and solve for x

[tex](\frac{1}{4})^{3}=\frac{x}{1,024}[/tex]

[tex]x=(1,024)\frac{1}{64}=16\ m^{3}[/tex]

therefore

The volume of the new pyramid is the volume of the original pyramid times 1/64

Answer:

The answer is A

Step-by-step explanation:

Answer:

P(10)=0

Step-by-step explanation:

As per factor theorem:

If x-10 is factor of polynomial p(x), then the remainder after division by x-10 should be zero. i.e.  If we synthetic-divide a p(x) by x = 10 and get zero remainder as following

P(10)=0

it is reverse of remainder theorem!

Answer:

-4/5-(-1/5)

Step-by-step explanation:

-4/5-1/5 is equivalent to -4/5+-1/5 which equals -1

-(4/5+1/5) when you add the expression in the parenthesis you get 1 and when you multiply that by -1 you get -1

-4/5+ -1/5 this is like the first choice so it equals -1

-4/5-(-1/5) this expression is the equivalent to -4/5+1/5 which gives you -3/5

The last option is -3/5 while the others are -1 which it the one with the different value

All of the expressions have the same value except -4/5 - (-1/5).

In this case, all of the expressions have the same value except -4/5 - (-1/5).

To simplify each expression:

Therefore, the expression that has a different value is -4/5 - (-1/5).

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Answer:

8a.

Step-by-step explanation:

32 = 2*2*2*2*2

40 = 2*2*2* 5

Thus the GCF of 32 and 40 is 2*2*2 = 8.

The GCF of a and ab = a.

For this case we must find the GCF of the following expressions:

[tex]32ab ^ 3\\40a ^ 2[/tex]

By definition, the GCF is given by the largest factor that divides both numbers without leaving residue.

We look for the factors of 32 and 40:

32: 1,2,4,8,16

40: 1,2,4,5,8,10,20

Thus, the GCF is 8.

On the other hand, the GCF of [tex]ab ^ 3[/tex]and [tex]a ^ 2[/tex] is a.

Finally, the GFC of the expressions is:

[tex]8a[/tex]

Answer:

[tex]8a[/tex]

Answer:

p' = {2, 4, 6, 8}.

Step-by-step explanation:

The set p' has all the elements in the universal set U that are not in set p.

p' = {2, 4, 6, 8}.

Step-by-step answer:

U = universal set (all possible members)

P = given set

P' = complement of P, i.e. contains all members in U but NOT 1,3,5,7in P.

Thus, U=P or P'.

Here,

U={1,2,3,4,5,6,7,8}

P={1,3,5,7}

so P'={2,4,6,8}

Check: P or P' ={1,3,5,7} or {2,4,6,8} = {1,2,3,4,5,6,7,8} = U   good !

[tex]\bf \begin{array}{llll} term&\stackrel{a_{n-1}+8}{value}\\ \cline{1-2} a_1&4\\ a_2&\stackrel{4+8}{12}\\ a_3&\stackrel{12+8}{20}\\ a_4&\stackrel{20+8}{28}\\ a_5&\stackrel{28+8}{36}\\ a_6&\stackrel{36+8}{44} \end{array}[/tex]

Answer:

The first 6 terms are 4,12,20,28,36,44

Step-by-step explanation:

So we have the recursive sequence

[tex]a_n=a_{n-1}+8 \text{ with } a_1=4[/tex].

If you try to dissect what this really means, it becomes easy.  

Pretend [tex]a_n[/tex] is a term in your sequence.

Then [tex]a_{n-1}[/tex] is the term right before or something like [tex]a_{n+1}[/tex] means the term right after.

So it is telling us to find a term all we have to is add eight to the previous term.

So the second term [tex]a_2[/tex] is 4+8=12.

The third term is [tex]a_3[/tex] is 12+8=20.

The fourth term is [tex]a_4[/tex] is 20+8=28.

The fifth term is [tex]a_5[/tex] is 28+8=36

The sixth term is [tex]a_6[/tex] is 36+8=44.

Now sometimes it isn't that easy to see the pattern from the recursive definition of a relation. Sometimes the easiest way is to just plug in. Let's do a couple of rounds of that just to see what it looks like.

[tex]a_n=a_{n-1}+8 \text{ with } a_1=4[/tex].

[tex]a_2=a_1+8=4+8=12[/tex]

[tex]a_3=a_2+8=12+8=20[/tex]

[tex]a_4=a_3+8=20+8=28[/tex]

[tex]a_5=a_4+8=28+8=36[/tex]

[tex]a_6=a_5+8=36+8=44[/tex]

Answer:

True.

Step-by-step explanation:

This is  'less than' so the area below the line is shaded.

It is a dotted line  because the solution does not contain points on the line as the inequality sign is < NOT ≤.

Answer:

First option: True.

Step-by-step explanation:

The equation of the line in Slope-Intercept form is:

[tex]y=mx+b[/tex]

Where "m" is the slope of the line and "b" is the y-intercept.

Given this inequality:

[tex]y<2x -5[/tex]

We know that the line is:

[tex]y=2x -5[/tex]

Whose slope is 2 and the y-intercept is -5

The symbol "<" provided in the inequalty, indicates that the shaded region must be below the line and the line must be dotted. Therefore, the answer is: TRUE.

The domain is the X values.

There are two dots located at x = -4 and x = 9

The answer would be: D -4 < x < 9

The domain of the graphed function is - 4 ≤ x ≤ 9, that is option D. This can be obtained by finding all the x-values.

⇒Domain is all x-values of a function.

From the graph, we can say that the graph start from (-4,-4) to (8,9).

Thus x-values are from -4 to 9.

Since the endpoints are closed circles the points -4 and 9 are included.

∴The required domain is - 4 ≤ x ≤ 9

Hence the domain of the graphed function is - 4 ≤ x ≤ 9, that is option D.

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Answer:

AAS theorem

Step-by-step explanation:

Angle SUT = Angle TVS (given)

Angle SRY = Angle TRV (vertically opposite angles)

SU = TV (given)

So, Triangle SUR is congruent to triangle TVR by AAS theorem.

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Answer:

[tex]\large\boxed{\sqrt{-2}+\sqrt{-18}=4\sqrt2\ i}[/tex]

Step-by-step explanation:

[tex]\sqrt{-1}=i\\\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\===================\\\\\sqrt{-2}+\sqrt{-18}=\sqrt{(2)(-1)}+\sqrt{(9)(2)(-1)}\\\\=\sqrt2\cdot\sqrt{-1}+\sqrt9\cdot\sqrt2\cdot\sqrt{-1}\\\\=\sqrt2\cdot i+3\cdot\sqrt2\cdot i\\\\=i\sqrt2+3i\sqrt2=4i\sqrt2[/tex]

The sum of √-2 and √-18 is 4√2i.

The square root of -1 is an imaginary number which is represented by i.

√-1=i

Here we have to calculate √-2+√-18

√-2+√-18

=√(-1).2+√(-1).18

=√(-1).√2+√(-1).√18

=i√2+i√18             (as √-1=i where i is imaginary number)

But √18=√(9*2)=√9*√2=3√2    

(as √(ab)=√a.√b)

=i√2+i3√2

=√2(i+3i)

=√2*4i

=4√2i

Therefore the sum of √-2 and √-18 is 4√2i.  

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Answer:

70

Step-by-step explanation:

75-55=20

95-85=10

100-90=10

115-95=20

100-90=10

sum of the differences is 70

Answer:

A: 10

Step-by-step explanation:

Let's add the actual enrollments all together. 55 + 80 + 95 + 100 + 115 + 90 all added together is 535. The predicted enrollments, all added together, is: 75 + 80 + 85 +90 +95 + 100 = 525.

535 - 525 = 10 residuals.

Answer:

B. [3,5]

Step-by-step explanation:

The rate of change of a function is the same as the slope between two given points from that same function,

Hence,

all we need to do is use the slope's equation, that is

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

And eval it in every couple of ordered pairs given from the table we obtain the following>

x2 y2 x1 y1  m

0 4 -1 3,5  0,5

1 5 0 4  1

2 7 1 5  2

3 11 2 7  4

4 19 3 11  8

5 35 4 19  16

The rate of change from g(x) is 4 (its slope)

Hence, the interval when the rate of change of f(x) is greater than g(x) is from x=3 to x=5

Answer:

(x + 2)(4x^2 + 3)

Step-by-step explanation:

The first two terms factor as follows:  4x^2(x + 2).

The last two factor as follows:  3(x + 2).

Thus, (x + 2) is a factor of 4x3 + 8x2 + 3x+6:

4x^2(x + 2) + 3(x + 2), or:

(x + 2)(4x^2 + 3).

Note that 4x^2 + 3 can be factored further, but doing so yields two complex roots.

Answer: (x + 2)(4x^2 + 3)

Step-by-step explanation:

4x3 + 8x2 + 3x+6 becomes 4x^2(x + 2) + 3(x + 2) and can also be written as (x + 2)(4x^2 + 3).

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

Now you know the answer as well as the formula. Hope this helps, have a BLESSED AND WONDERFUL DAY!

- Cutiepatutie ☺❀❤

first off, let's check what's the slope of that line through those two points anyway

[tex]\bf (\stackrel{x_1}{5}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{2}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{2-(-2)}{7-5}\implies \cfrac{2+2}{7-5}\implies \cfrac{4}{2}\implies 2[/tex]

now, let's take a peek of what is the slope of that equation then

[tex]\bf -5y+kx=6-4x\implies -5y=6-4x-kx\implies -5y=6-x(4+k) \\\\\\ -5y=-x(4+k)+6\implies -5y=-(4+k)x+6\implies y=\cfrac{-(4+k)x+6}{-5}[/tex]

[tex]\bf y=\cfrac{(4+k)x-6}{5}\implies y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{(4+k)}{5}} x-\cfrac{6}{5}\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \stackrel{\textit{since both slopes are the same then}}{\cfrac{4+k}{5}=2\implies 4+k=10}\implies \blacktriangleright k=6 \blacktriangleleft[/tex]

Answer:

The number of toys that Kevin can make per hour is equal to [tex]60\frac{c}{m}\ toys[/tex]

Step-by-step explanation:

we know that

Kevin makes c toys in m minutes

Remember that

1 hour=60 minutes

so

Using proportion find out how many toys can be make in 60 minutes (one hour)

Let

x -----> the  number of toys that Kevin can make per hour

so

[tex]\frac{c}{m}=\frac{x}{60}\\ \\x=60\frac{c}{m}\ toys[/tex]

therefore

The number of toys that Kevin can make per hour is equal to [tex]60\frac{c}{m}\ toys[/tex]

Answer:

9.10 km to the nearest hundredth.

Step-by-step explanation:

We have a triangle whose adjacent side is 25 km and angle  20 degrees.

If h is the height we have the equation:

tan 20 = h / 25

h = 25 tan 20

= 9.099 km.

Answer:

The values of x are 0 and 4

Step-by-step explanation:

we have

[tex]f(x)=x^{2}-2x-4[/tex] ------> equation A

[tex]g(x)=2x-4[/tex] ----> equation B

To find the values of x when f(x) and g(x) intersect

equate f(x) and g(x)

[tex]f(x)=g(x)[/tex]

[tex]x^{2}-2x-4=2x-4[/tex]

[tex]x^{2}-2x-4-2x+4=0[/tex]

[tex]x^{2}-4x=0[/tex]

Factor x

[tex]x(x-4)=0[/tex]

The solutions are

x=0 and x=4

Final answer:

The functions f(x) = x²- 2x - 4 and g(x) = 2x - 4 intersect at x = 0 and x = 4, found by setting the equations equal to each other and solving for x.

Explanation:

To find the intersection points of the functions f(x) = x2 - 2x - 4 and g(x) = 2x - 4, we need to set the two functions equal to each other and solve for x.

Set f(x) equal to g(x): x ²- 2x - 4 = 2x - 4.

Move all terms to one side to set the equation to zero: x² - 4x = 0.

Factor the quadratic equation: x(x - 4) = 0.

Find the solutions for x by setting each factor equal to zero: x = 0 and x - 4 = 0, which gives us x = 0 and x = 4.

Therefore, the functions f(x) and g(x) intersect at the values x = 0 and x = 4.

Answer:

The discriminant of this quadratic equation is less than zero.

This means the quadratic equation will have no real solution(s) and two complex solution(s).

Step-by-step explanation:

The discriminant is found using the formula b^2 - 4ac.

Therefore, the discriminant is (3)^2 - 4(2)(5), which yields -31.

Since the discriminant is negative, there are no real solutions.

Answer: less then

No

Two distinct

Step-by-step explanation:

Answer: First and last option

The birds began 1320 miles from the equator.

The birds are flying toward the equator at a rate of 60 mph.

Step-by-step explanation:

Note that the function f(x) is a linear function.

[tex]f (x) = - 60x + 1320[/tex]

If x represents the number of hours and f(x) represents the distance from the equator, then x = 0 means that the first hour has not yet elapsed.

When x = 0 then:

[tex]f (0) = -60 * 0 +1320\\f (0) = 1320[/tex].

This means that the initial distance at which the birds of the equator are located is 1320 miles.

Then when x = 1 then:

[tex]f (x) = -60 * 1 + 1320\\f (x) = -60 +1320[/tex]

When x = 2 then:

[tex]f (x) = -60 * 2 + 1320\\f (x) = -120 +1320[/tex]

As x increases by one unit then the distance of the birds to the equator decreases by 60 miles. This means that birds travel at a speed of 60 miles per hour

Answer:

The birds began 1320 miles from the equator.

The birds are flying toward the equator at a rate of 60 mph.

Step-by-step explanation:

Answer:

1/40

Step-by-step explanation:

A bag contains 5 blue, 3 red, and 8 green marbles

You have (5+3+8=16) marbles

P(red 1) = red/total = 3/16

You do not replace it

A bag contains 5 blue, 2 red, and 8 green marbles

You have (5+2+8=15) marbles

P(red 2nd) = red/total = 2/15

P(red 1, red 2) = P (red 1)* P (red 2) = 3/16 * 2/15

                                                         =1/40

Answer:

fourth degree monomial

Step-by-step explanation:

-8x^4

There is one term so it is a monomial

The highest power is degree 4, so it would be a quartic

part A)

[tex]\bf \begin{array}{|c|cccccc|ll} \cline{1-7} x&8&27&64&125&&x\\ \cline{1-7} y&\stackrel{\sqrt[3]{8}}{2}&\stackrel{\sqrt[3]{27}}{3}&\stackrel{\sqrt[3]{64}}{4}&\stackrel{\sqrt[3]{125}}{5}&&\sqrt[3]{x} \\ \cline{1-7} \end{array}~\hspace{10em}y = \sqrt[3]{x}[/tex]

part B)

f(x) = 10 + 20x

so if you rent the bike for a few hours that is

1 hr.............................10 + 20(1)

2 hrs..........................10 + 20(2)

3 hrs..........................10 + 20(3)

so the cost is really some fixed 10 + 20 bucks per hour, usually the 10 bucks is for some paperwork fee, so you go to the bike shop, and they'd say, ok is 10 bucks to set up a membership and 20 bucks per hour for using it, thereabouts.

f(100) = 10 + 20(100) => f(100) = 2010.

f(100), the cost of renting the bike for 100 hours.

Answer:

F

Step-by-step explanation:

The equation of a line in slope-intercept form is

y = mx + b

where m = slope, and b = y-intercept.

This line has equation

y = 4x

When we compare y = 4x with y = mx + b, we see that m = 4, and b = 0.

This line intersects the y-axis (the y-intercept) at y = 0, which is the origin. The slope is positive, so it slopes up to the right.

Answer: F

The function f(x) = 4x is a linear function, and when graphed, it will produce a straight line with a slope of 4. The graph demonstrates the dependence of y on x and it's an example of a line graph.

The question asks for a description of the graph of the function f(x) = 4x.

The function f(x) = 4x is a linear function, which means it creates a straight line when graphed. The number 4 in the function is the slope of the line. This value indicates that for each increase by 1 in the x value, the y value will increase by 4.

This demonstrates the dependence of y on x. So, a graph of this function would be a straight line that slopes upward from left to right, starting at the origin (0,0) and increasing by 4 in the y direction for each step of 1 in the x direction. This is a typical representation of a linear function demonstrating the relationship between two variables on a line graph.

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Answer:

Range of this relation = -3, 2

Step-by-step explanation:

We are given the following relation and we are to find its range:

[tex](2,-3),(-4,2),(6,2),(-5,-3),(-3,0)[/tex]

The set of all the possible dependent values a relation can produce from its values of domain are called its range. In simple words, it is the list of all possible inputs (without repeating any numbers).

Therefore, the range of this relation is: -3, 2

Answer: [tex]Range:[/tex]{[tex]-3,0,2[/tex]}

Step-by-step explanation:

The range of a relation is the set of y-coordinates of the ordered pairs (These are the second numbers of each ordered pair).

In this case you have the following relation:

[tex](2,-3),(-4,2),(6,2),(-5,-3),(-3,0)[/tex]

Therefore, based on the explained bofore, you can conclude that the rsnge of the given relation is the following:

[tex]Range:[/tex]{[tex]-3,0,2[/tex]}

(Notice that you do not need to write the same number twice)

Answer:

Two times the difference of a number x and 7 plus 10.

Step-by-step explanation:

We are to write a phrase which matches the following algebraic expression below:

[tex] 2 ( x − 7 ) + 1 0 [/tex]

We can see that there is a bracket with a coefficient outside it so we can express it as:

'Two times the difference of a number x and 7'.

While + 10 can be added to it to complete the phrase:

Two times the difference of a number x and 7 plus 10.