Sara needs to pack 108 stalks of roses, 81 stalks of lilies, and 54 stalks of orchids into identical baskets so that each type of flower is equally distributed among the baskets. Find the largest number of the basket that can be packed

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

- 3y + 4x = 9

3y = 4x - 9

Divide both sides by 3

y = 4/3x - 3

Comparing with the above formula

Slope / m = 4/3

Since the lines are parallel their slope are also the same

So slope of the parallel line l is also 4/3

Equation of the line using point (-12 , 6) is

y - 6 = 4/3(x + 12)

Multiply through by 3

That's

3y - 18 = 4(x + 12)

3y - 18 = 4x + 48

We have the final answer as

Hope this helps you

Answer:

D) Van: 7, Bus: 20

Step-by-step explanation:

Add the amount of students together (455 students in total)

Then I added the amount of buses and vans together (5 Vans and 21 Buses)

Then I plugged in each answer

5 x 7 = 35

455 - 35 = 420

420 / 21 = 20

Answer:

11 minutes. 1/4 of 44 is 11

Answer:

D.The distance you drive

Step-by-step explanation:

If you describe this situation as function, then it will look as:

The range of the function is the set of output values

In this case the range is the distance you drive

Correct option is D.

Answer:

The distance you drive

Step-by-step explanation:

i just took the test

Answer:

x = [ -b +- sqr root (b^2 - 4ac)] / 2a

a = 1

b = -5

c = -2

x = [- - 5 +- sqr root (-5^2 -4 * 1 * -2)] / 2 * 1

x = [5 +- sqr root (25 + 8)] / 2

x1 =  5.3723

x2 =-0.37228

Step-by-step explanation:

Exact solution for the give quadratic equation are

[tex]x=\frac{5+\sqrt{33}}{2},\:x=\frac{5-\sqrt{33}}{2}[/tex]

Quadratic equation of the form [tex]ax^2+bx+c=0[/tex]

For any quadratic equation we get two values for x. we can find the values for x by applying quadratic formula .

Quadratic formula

[tex]x=\frac{-b+-\sqrt{b^2-4ac} }{2a}[/tex]

Given equation is [tex]x^2-5x-2=0[/tex]

The value of a=1, b= -5  and c=-2

Substitute all the values in the formula.

To find out exact solutions , we need to simplify the final answer.

Exact solutions are without any decimals.

[tex]x=\frac{-\left(-5\right)\pm \sqrt{\left(-5\right)^2-4\cdot \:1\cdot \left(-2\right)}}{2\cdot \:1}\\x=\frac{-\left(-5\right)\pm \sqrt{33}}{2\cdot \:1}\\x=\frac{-\left(-5\right)\p+ \sqrt{33}}{2\cdot \:1}\\\\x=\frac{5+\sqrt{33}}{2}\\\\x=\frac{-\left(-5\right)- \sqrt{33}}{2\cdot \:1}\\\\x=\frac{5-\sqrt{33}}{2}\\[/tex]

Exact solutions are

[tex]x=\frac{5+\sqrt{33}}{2},\:x=\frac{5-\sqrt{33}}{2}[/tex]

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Answer:

A) it increases the mean value of the prizes.

Step-by-step explanation:

The median is resistant to large outliers, so it does not change if there is an especially large or small value. So, we can eliminate choices C and D.

I am actually not sure whether the data in the table count $100 as a large prize or a small one, but I am assuming it is a large prize. So, an extremely large prize would increase the mean value of the prizes.

Hope this helps!

The $100 gift card affect the measure of center of the data by increases the mean value of the prizes.

Option A is the correct answer.

It is the middles value of the given set of numbers after arranging the given set of numbers in an order.

We have,

The $100 gift card has a much larger value compared to the other prizes, and it is only given to one person.

Therefore, adding the $100 gift card to the prizes will significantly increase the total value of the prizes, which will affect the measures of center of the data.

The mean and median are two common measures of center in statistics. The mean is the sum of all the values divided by the number of values, while the median is the middle value when the data is arranged in order.

Adding the $100 gift card will increase the mean value of the prizes, but it will not affect the median value, since the median only depends on the order of the data, not the values themselves.

Therefore,

It increases the mean value of the prizes.

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Answer:

The answer to your question is given in the attached photo.

Step-by-step explanation:

To determine the answer to the question,

First, we shall determine the value 3A.

This is obtained by multiplying matrix A by 3 as shown in the attached photo.

Next, we shall carry out the operation 3A – B as shown in the attached photo.

Answer:

[tex]f(x) =\sqrt[3]{x}[/tex]

Step-by-step explanation:

Hello!

Considering the parent function, as the most simple function that preserves the definition. Let's take the function given:

[tex]g(x) = \sqrt[3]{x-5}+7[/tex]

To have the the parent function, we must find the parent one, let's call it by f(x).

[tex]f(x) =\sqrt[3]{x}[/tex]

This function satisfies the Domain of the given one, because the Domain is still [tex](-\infty, \infty)[/tex] and the range as well.

Check below a graphical approach of those. The upper one is g(x) and the lower f(x), its parent one.

Answer:

5 units to the right and 7 units up (B on edge)

Step-by-step explanation:

Answer:

The answer is below

Step-by-step explanation:

The Royal Fruit Company produces two types of fruit drinks. The first type is 65% pure fruit juice, and the second type is 90% pure fruit juice. The company is attempting to produce a fruit drink that contains 85% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 80 pints of a mixture that is 85% pure fruit juice?

Answer: Let x be the number of pints of the first fruit juice (i.e 65%) and y be the number of pints of the second fruit juice (i.e 90%).

Since the total number of pints to make the 85% pure fruit juice is 80, it can be represented using the equation:

x + y = 80                              .                  .                 .    1)

Also, x pints of the first juice = 0.65x, y pints of the second juice = 0.9y and 80 pints of the mixture to be produced = 80(0.85) = 68. Therefore:

0.65x + 0.9y = 68               .                 .                  .        2)

We have to solve equation 1 and 2 simultaneously, first multiply equation 1 by 0.65 to get equation 3:

0.65x + 0.65y = 52            .                  .               .        3)

Subtract equation 3 from 2 and solve for y:

0.25y = 16

y = 16/0.25 = 64

y = 64 pints

Put y = 64 in equation 1:

x + 64 = 80

x = 80 - 64 = 16

x = 16 pints

Therefore 16 pints of the 65% pure fruit juice, and 64 pints of the 90% pure fruit juice is required to make 80 pints of 80% fruit juice.

Answer:

i do not know either so please help me because this is not my level

Answer:

8=x

Step-by-step explanation:

can u give me a 5 star plz ty :)

Answer:

39 units²

Step-by-step explanation:

The figure is composed of a rectangle VEDR and Δ RMV

Area of rectangle = VE × ED = 5 × 6 = 30 units²

Area of Δ = 0.5 × RV × perpendicular from M to RV

                = 0.5 × 6 × 3 = 9 units²

Thus

Area of polygon = 30 + 9 = 39 units²

Answer:

ill help!

Step-by-step explanation:

find angle CBD

once you find that angle subtract it from 90 because that is the measure of ABC which is a right angle. Because all right angles are 90 degrees you can prove that it is the difference from angle CBD and 90.

hope it helped have good one!

Answer:

see below

Step-by-step explanation:

We need to write it on vertex form (f(x) = a(x - c)² + d where (c, d) is the vertex) and to do that we will complete the square.

f(x) = x² + 3x - 2

= (x² + 3x + 9/4) - 9/4 - 2

= (x + 1.5)² - 4.25

The vertex is (-1.5, -4.25).

Answer:

The carpenter can maximize profits by making  20 dining chairs and 10 rocking chairs . His total profit for all the chairs will be $2100

Step-by-step explanation:

Let x be the no. of dining chairs and y be the no. of rocking chair

Time taken by carpenter to make 1 dining chair = 1 hour

Time taken by carpenter to make x dining chairs = x hours

Time taken by carpenter to make 1 rocking chair = 2 hour

Time taken by carpenter to make y rocking chairs = 2y hours

He only has 40 hours available to work on the chairs.

[tex]\Rightarrow x+2y \leq 40[/tex]

He has enough wood to make 30 chairs.

[tex]\Rightarrow x+y\leq30[/tex]

He makes $60 profit on a dining chair and $90 profit on a rocking chair.

So, profit =60x+90y

Plot the equations on graph

Refer the attached figure

Coordinates of feasible region

(0,20),(20,10) and (30,0)

Profit =60x+90y

At(0,20)

Profit = 1800

At(20,10)

Profit = 1200+900=2100

At(30,0)

Profit=900

So,the carpenter can maximize profits by making  20 dining chairs and 10 rocking chairs . His total profit for all the chairs will be $2100

Answer:

Approximately 11.5 units.

Step-by-step explanation:

We need to find the side opposite to ∠W. We are given the two angles ∠W and ∠X. We are also given that Side X is equal to 7. Therefore, we can use the Law of Sines.

Now, like last time, use the Law of Sines:

[tex]\frac{\sin(V)}{v}=\frac{\sin(W)}{w}=\frac{\sin(X)}{x}[/tex]

We can ignore the first term. Plug in 144 for ∠W, 21 for ∠X, and 7 for x.

[tex]\frac{\sin(144)}{w}=\frac{\sin(21)}{7}[/tex]

Cross multiply:

[tex]7\sin(144)=w\sin(21)\\w=\frac{7\sin(144)}{\sin(21)} \\v\approx11.4812\approx11.5[/tex]

Answer:

greater than

Step-by-step explanation:

To compare 3/4 to 1/2, let's convert 1/2 so that it has a denominator of 4. This would then be 2/4. Because 3 > 2, 3/4 > 2/4 which means 3/4 > 1/2.

Answer:

Greater

Step-by-step explanation:

It is greater than 1/2 because when you divide the fractions you get- 1/2 = 0.5, 3/4 = 0.75 And this makes it greater.

The correct answer is Maxine

Explanation:

One of the easiest ways for knowing if a fraction is greater than another is by converting fractions to decimal numbers. This implies dividing the numerator (top number) by the denominator (bottom number). In the case of fraction, [tex]\frac{1}{2}[/tex] the decimal number is 0.5 considering 1 divided into 2 is equal to 0.5. Now to know if other fractions are greater or smaller, this process needs to be repeated.

Gina: [tex]\frac{3}{8} = 0.375[/tex]  

Maxine: [tex]\frac{2}{3} = 0.666[/tex]

Shari: [tex]\frac{2}{4} = 0.5[/tex]

Vanessa: [tex]\frac{3}{12} = 0.25[/tex]

According to this, the girl with a heigh increased greater than 1/2 inch is Maxine because 0.666 (Maxine heigh increase) is greater than 0.5 (1/2 inch).

Answer:

Step-by-step explanation:

Given the expression

[tex]40=\frac{90^2}{16} sinxcosx\\\\Cross\ multiplying;\\\\16*40 = 90^2 sinxcosx\\\\640 = 90^2 sinxcosx\\\\\frac{640}{8100} = sinxcosx\\ from\ trig\ identity, sin2x = 2sinxcosx\\sinxcosx = sin2x/2\\[/tex]

[tex]Hence, \ \frac{640}{8100} = \frac{sin2x}{2} \\\\\frac{2*640}{8100} = sin2x\\ \\\frac{1280}{8100}=sin2x\\ \\0.158 = sin2x\\\\2x = sin^{-1} 0.158\\\\2x = 9.09\\x = 9.09/2\\x =4.545[/tex]

Answer:

The amount in 2001 is 8400

Step-by-step explanation:

Let x be the amount in 2001

There is an increase of 25% to get to the amount in 2002

x+ .25x = 1.25 x

1.25x = 10500

Divide each side by 1.25

1.25x / 1.25 = 10500/1.25

x =8400

The amount in 2001 is 8400

We need to know the rules of congruence of triangles to solve the given problem. The required condition that is sufficient to prove that the triangles are congruent is option (C) AB≅JK.

There are three rules of congruence of triangles, if two triangles satisfy any one of these rules then we can say that the triangles are congruent.  The three rules are, SSS which means three sides are equal, ASA which means two angles and their corresponding sides are equal and SAS which means that two sides and the angle between them is equal. When two angles are said to be congruent it means they have the same measure that is they are equal. In this question we know that ∠A≅∠J and ∠B≅∠K , we can see that two angles are equal, if we can have the corresponding side of these two angles to be equal then we can say that the two triangles are congruent. The corresponding side of these angles are AB and JK.

Therefore we can see that the required condition to prove that the triangles are congruent is option (C) AB≅JK.

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Answer:

A. Volume: 819, Surface Area: 598

B. Surface area

C. Volume

Step-by-step explanation:

Sorry I'm late, but here I go.

The volume of a rectangular prism is [tex]lwh[/tex] or [tex]bh[/tex]. (l being length, w being width, and h being height.)

So if we multiply the 3 values of 13, 9, and 7, we get 819. This is the volume.

To find the surface area, we can take note that 4 sides are the exact same, and the remaining two are the same. Let's find the area of the top/bottom of the prism.

[tex]13\cdot9=117[/tex]

Since there are two, bottom and top:

[tex]117\cdot2 = 234[/tex].

Now, there are the remaining 4 sides. Let's find the area of one then multiply it by 4.

[tex]13\cdot7=91\\91\cdot4=364[/tex]

Adding 364 and 234 gets up 598, so this is the surface area.

If we are painting something, the surface area is being painted, as we can't paint inside the box. However if we fill up the box with something (concrete in this case), it will be the volume.

Hope this helped!  

Answer:

a.

v= 819 cm3

sa= 542 cm2

b. surface area

c. volume

Step-by-step explanation:

Volume of a rectangular prism: Length x width x height

Replacing with the values given:

V = 13 x 9 x 7 = 819 cm3

Surface area = S = 2 × (W × L + L × H + H × W)

S = 2 ( [9x13]+ [13 x7] +[7x9]) = 2 ( 117+91+63)= 542 cm2

b . Surface area, because we only have to paint the exterior of the brick.

c. Volume, because is the amount of concrete that the brick has.

Answer:

T1he values for x and y of the equations is y = 11, and x = -19/5.

Step-by-step explanation:

To solve this question, we need to rearrange the expression:

5x+4y=25 - (5x+2y=3)

Look, if we subtract one equation to the other, then:

5x+4y=25 [1]

-(5x+2y=3) [2]

Which is the same as:

5x+4y=25

-5x-2y=-3

Subtract them:

5x+4y=25

-5x-2y=-3

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

      2y =22

y = 22/2 = 11

Then, y = 11.

To find x, we can substitute y in either equation [1] or [2].

Let us use [1]

5x+4y=25

5x+4(11)=25

5x+44=25

5x=25-44

5x=-19

x = -19/5

Then, the values for x and y of the equations is y = 11, and x = -19/5.

Answer:

No amplitude

Period is pi

Step-by-step explanation:

Answer:

c. translation (x,y) -> (x-4, y-1) followed by reflection about y=0

Step-by-step explanation:

The strategy is to translate B to E then reflect about the x-axis (y=0)

From B to E, the process is

(x,y) -> (x-4, y-1)

Therefore it is a translation (x,y) -> (x-4, y-1) followed by reflection about y=0

Answer:

Step-by-step explanation:

-y = -3x - 12

y = 3x + 12

y - 5 = 3(x - 2)

y - 5 = 3x - 6

y = 3x - 1

Answer:

  0.20, 0.36 seconds

Step-by-step explanation:

We have already seen that the equation for y(t) can be written as ...

  y(t) = √29·sin(4πt +arctan(5/2))

The sine function will have a value of -1/2 for the angles 7π/6 and 11π/6. Then the weight will be halfway from its equilibrium position to the maximum negative position when ...

  4πt +arctan(5/2) = 7π/6 or 11π/6

  t = (7π/6 -arctan(5/2))/(4π) ≈ 0.196946 . . . seconds

and

  t = (11π/6 -arctan(5/2))/(4π) ≈ 0.363613 . . . seconds

The weight will be halfway from equilibrium to the maximum negative position at approximately 0.20 seconds and 0.36 seconds and every half-second thereafter.

Answer:

The table D represents the function that will have the greatest y-values for very large values of x.

Step-by-step explanation:

The table A represents a linear function, for which each one unit increment in the "x" variable produces a three unit increment in the "y" variable. This means that the growth rate of this function is 3.

The table B also represents a linear function, for which each one unit increment in the x variable produces a 100 unit increment in the y variable. This means that the growth rate of this function is 100.

The table C also represents a linear function, for which each one unit increment in the x variable produces a 10 unit increment in the y variable. This means that the growth rate of this function is 10.

The table D on the other hand does not represent a linear function, since the growth rate is variable and increases for greater values of x. This means that as x grows larger, the growth rate of the function also grows larger, resulting in a much greater y value for very large x values if we compare it to a linear function, like the other options.

Answer:

D

Step-by-step explanation:

BIGBRAIN

Answer:

Measure of arc TSU = 201°

Step-by-step explanation:

For the inscribed circle of  triangle XYZ, we have;

∠XZY = 21°

Segment TZ and segment  UZ are tangent to circle R

Therefore, ∠ZUR = ∠ZTR = 90° (angle formed by a tangent)

Length UR = Length TR = Radius of circle R

∴ ΔZTR ≅ ΔZUR Side Angle Side (SAS) rule of Congruency

∴ ∠RZT ≅ ∠RZU, (Congruent Parts of Congruent Triangles are Congruent, CPCTC)

∠XZY = ∠RZT + ∠RZU (Angle summation)

21° = ∠RZT + ∠RZU  = 2×∠RZU (Transitive property)

∠RZU = 21°/2 = 10.5° = ∠RZT

∴ ∠URZ = 180- 90 - 10.5 = 79.5° = ∠TRZ (CPCTC)

arc TU = ∠URT = ∠URZ + ∠TRZ = 79.5 + 79.5 = 159° (angle addition)

∴ Measure of arc TSU = 360° - 159° = 201° (Sum of angles at the center of the circle R)

Measure of arc TSU = 201°.

Answer:

a. See Attachment 1

b. [tex]PT = 12.3\ m[/tex]

c. [tex]HT = 31.1\ m[/tex]

d. [tex]OH = 28.4\ m[/tex]

Step-by-step explanation:

Calculating PT

To calculate PT, we need to get distance OT and OP

Calculating OT;

We have to consider angle 50, distance OH and distance OT

The relationship between these parameters is;

[tex]tan50 = \frac{OT}{20}[/tex]

Multiply both sides by 20

[tex]20 * tan50 = \frac{OT}{20} * 20[/tex]

[tex]20 * tan50 = OT[/tex]

[tex]20 * 1.1918 = OT[/tex]

[tex]23.836 = OT[/tex]

[tex]OT = 23.836[/tex]

Calculating OP;

We have to consider angle 30, distance OH and distance OP

The relationship between these parameters is;

[tex]tan30 = \frac{OP}{20}[/tex]

Multiply both sides by 20

[tex]20 * tan30 = \frac{OP}{20} * 20[/tex]

[tex]20 * tan30 = OP[/tex]

[tex]20 * 0.5774= OP[/tex]

[tex]11.548 = OP[/tex]

[tex]OP = 11.548[/tex]

[tex]PT = OT - OP[/tex]

[tex]PT = 23.836 - 11.548[/tex]

[tex]PT = 12.288[/tex]

[tex]PT = 12.3\ m[/tex] (Approximated)

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

Calculating the distance between H and the top of the tower

This is represented by HT

HT can be calculated using Pythagoras theorem

[tex]HT^2 = OT^2 + OH^2[/tex]

Substitute 20 for OH and [tex]OT = 23.836[/tex]

[tex]HT^2 = 20^2 + 23.836^2[/tex]

[tex]HT^2 = 400 + 568.154896[/tex]

[tex]HT^2 = 968.154896[/tex]

Take Square Root of both sides

[tex]HT = \sqrt{968.154896}[/tex]

[tex]HT = 31.1\ m[/tex] (Approximated)

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

Calculating the position of H

This is represented by OH

See Attachment 2

We have to consider angle 50, distance OH and distance OT

The relationship between these parameters is;

[tex]tan50 = \frac{OH}{OT}[/tex]

Multiply both sides by OT

[tex]OT * tan50 = \frac{OH}{OT} * OT[/tex]

[tex]OT * tan50 = {OH[/tex]

[tex]OT * 1.1918 = OH[/tex]

Substitute [tex]OT = 23.836[/tex]

[tex]23.836 * 1.1918 = OH[/tex]

[tex]28.4= OH[/tex]

[tex]OH = 28.4\ m[/tex] (Approximated)

angle HDG = angle HFE

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

Explanation:

We have the statement [tex]\triangle DHG \cong \triangle FHE[/tex] given to us. Note that "H" is in the middle for both sequences of three letters. For DHG, start at H and move back one space to get to D. Move back another unit to wrap around to G. So the new sequence is HDG which forms the first angle.

Follow the same pattern but for FHE now. Start at H, move backward one spot to F, then move back again to wrap around to E. We have HFE

This shows angle HDG pairs up with angle HFE. The corresponding angles are congruent due to CPCTC

CPCTC = corresponding parts of congruent triangles are congruent

Notice how angles HDG and HFE are alternate interior angles, which lead to showing DG is parallel to EF.