Which two equations would be most appropriately solved by using the quadratic formula? Select each correct answer.
3x² = 9
0.25x2+0.8x−8=0
−2x2+5x=7
−(x−3)(x+9)=0

Answer:

Drama club 82 students

yearbook club 100 students

Answer:

you can go on a maximum of 11 rides

Step-by-step explanation:

you first have to subtract 30 from 100 since that is the admissons fee.

So now you are left with 70 dollars.

You divide 70 by 6 since you need 6 dollars to go on each ride.

and 70 divided by 6 is 11.6666666667 but round it to 11 since that the whole number you're left with.

hope this helped :)

Answer:

( 2 − 3 ) ( − 1 )

Step-by-step explanation:

Solution

For this case we can do the following:

Part 2

17/50 represent the conditional probability of being vegetarian given that the person selected is female

Part 3

17% of students surveyed were female vegetarians

Is a joint relative since represent the % of vegetarians and female in all the sample

The time it would take the teacher and aide are respectively;

Teacher: 25 minutes

Aide: 100 minutes

Algebraic word problems are defined as questions that require translating sentences to equations and thereafter, solving those equations.

Let x represent the time required by teacher

Let 4x represent the time required by aid

The Teacher works at the rate of 1/x of the newsletter per minute

Aide works at the rate of (1/4)x of the newsletter per minute

We are told that together they work at the rate of 1/20 of the newsletter per minute

Thus;

1/x + 1/4x = 1/20

multiply each term by 20x to get;

20 + 5 = x

x = 25 minutes which is the time required by the teacher

4x = 4*25

= 100 minutes which is the time required by aide

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Answer:

The answer is $35

Answer:

it's a square number

Step-by-step explanation:

Answer:

His total commission was: $2,960

Step-by-step explanation:

The commissions that Michael Fenton earns by selling plumbing supplies to contractors has three levels:

On the first $15,000 in sales, he earns 3%

On the next $15,000 in sales, he earns 5%

Over $30,000 in sales, he earns 8%.

Last month he sold $52,000 worth of plumbing supplies. His commissions will be calculated according to the levels reached:

The first $15,000 gave him 3%*15,000=0.03*15,000=$450

From the $52,000 sales, there remains $52,000 - $15,000 = $37,000 for the next levels.

The next $15,000 gave him 5%*15,000=0.05*15,000=$750

Now $37,000 - $15,000 = $22,000 remain for the last level.

Michael earned 8% of $22,000 = 0.08*22,000 = $1,760

His total commission was: $450 + $750 + $1,760 = $2,960

Answer:

Answer:

k=135

Step-by-step explanation:

180=45+k

-45 -45

_________

135=k

Answer:

C

Step-by-step explanation:

srslly its easy just look at it

Answer:

a S(-3) = 2(-3)(-3)+5(-3)-12

=18-15-12

=-9

b 2x2+5x-12=0

2x2+8x-3x-12=0

2x(x-4)-3(x+4)=0

(2x-3)(x+4)=0

2x-3=0

x=3/2

x=-4

sorry I couldn't answer the other question

Answer:

c=42

Step-by-step explanation:

To find the volume of the solid, we need to integrate the area of each square section perpendicular to the x-axis over the range of x values that correspond to the base of the solid.

The base of the solid is the region enclosed by the parabola y = 4x^2, the line x=1, and the x-axis in the first quadrant. To find the bounds of integration, we need to find the x values where the parabola intersects the line x=1.

Setting y = 4x^2 equal to x=1, we get:

4x^2 = 1

x^2 = 1/4

x = ±1/2

Since we are only interested in the first quadrant, we take x=0 to x=1/2 as the bounds of integration.

For each value of x, the plane section perpendicular to the x-axis is a square with side length equal to the y-value of the point on the parabola at that x-value. Thus, the area of the square section is (4x^2)^2 = 16x^4.

To find the volume of the solid, we integrate the area of each square section over the range of x values:

V = ∫(0 to 1/2) 16x^4 dx

V = [16/5 x^5] (0 to 1/2)

V = (16/5)(1/2)^5

V = 1/20

Therefore, the volume of the solid is 1/20 cubic units.

The volume of the solid is  8 cubic units.

Integrate the area of each square cross-section perpendicular to the x-axis to determine the solid's volume.

Find the parabolic region's equation in terms of y first. We get to x = ±√(y/4).  after solving y = 4x^2 for x. Since only the area in the first quadrant is of interest to us, we take the positive square root:  = √(y/4) = (1/2)√y.

Consider a square cross-section now, except this time it's y height above the x-axis. The area of the cross-section, which is a square, is equal to the square of the length of its side. Let s represent the square's side length. Next, we have

s is the length of the square's side projection onto the x-axis,

= 2x

= √y

As a result, s2 = y is the area of the square cross-section at height y.

We must establish the bounds of integration for y in order to build up the integral for the solid's volume. The limits of integration for y are 0 to 4 since the parabolic area intersects the line x = 1 at y = 4. As a result, the solid's volume is:

V = ∫[0,4] y dy

= (1/2)y^2 |_0^4

= (1/2)(4^2 - 0^2)

= 8

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Answer:

28 ; 76 ; 38

Step-by-step explanation:

KL = \(\frac{XY}{2}\) = \(\frac{56}{2}\) = 28 units

YZ = 2 × JK = 38 × 2 = 76 units

LZ = 76/2 = 38 units

The lengths are: KL =  28 units, YZ = 76 units and LZ= 38 units.

The line segment in a triangle connecting the midpoint of two sides of the triangle is said to be parallel to its third side and is also half the length of the third side, according to the midpoint theorem.

Given:

J, K, and L are the midpoints of the sides of ΔXYZ.

JK=38, X2=96, and YX=56.

Now, using Mid point theorem

JK= 1/2 YZ

38 = 1/2 YZ

YZ= 2 x 38

YZ = 76 units.

and, KL= 1/2 YX

KL = 1/2(56)

KL= 28

LZ = 1/2 (YZ)

LZ = 1/2(76)

LZ = 38 units

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Answer: 254.34

Step-by-step explanation:

The equation for area is: \(r^{2} * \pi\)

So you find  9 squared which is 81. Then, you multiply it by pi(using 3.14). This equals 254.34

Answer:

If 5 is zero then (x - 5) is a factor.

Only 4. has this factor.

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

Let x be that missing number

One third of it is x/3

One-ninth of it is x/9

Multiply x/3 and x/9

● (x/3)*(x/9) = (x^2/27)

● (x^2/27) = 108

Multiply both sides by 27

● (x^2/27)*27 = 108*27

● x^2 = 2916

● x = √(2,916) or x = -√(2,916)

● x = 54 or x = -54

So there are two possibilities 54 and -54.

a1/3×1/9=!08

if you multiply you should get 1/27a=108

in order to let a alone multiply both sides by 27

and now your a which is unknown will equal 2916.

a. The unemployment rate is 20%.

b. The labor-force participation rate is 60%.

According to the question,

Working age population- 100,000

Labour force - 60,000

Unemployed - 12000 instructions

a) The unemployment rate is the percentage of the labor force that is unemployed and it is calculated as follows:

Unemployment Rate = \(\frac{Number of unemployed People}{Labor force}\) × 100

When an unemployed population is 12,000 and the labor force is 60,000,

the unemployment rate is  = \(\frac{12000}{60000}\) × 100 = 20%

b) labor force participation rate is the percentage of working adult population that participates in labor either by actively looking for a job, or working. It is calculated as follows:

Labor Force Participation Rate = \(\frac{Labor force}{working age population}\) × 100

When the labor force is 60,000 and the working-age population is 100,000

Labor Force Participation Rate = \(\frac{60000}{100000}\) × 100 = 60%

So, a. The unemployment rate is 20%.

b. The labor-force participation rate is 60 %.

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ALGOL 68 is a language that prioritized orthogonality as a key design requirement. ALGOL 68's primary objectives and design tenets are as follows:

1. a thorough and clear design;

2. an orthogonal design

3. Safety

4. Efficiency: Mode-independent parsing, independent compilation, loop optimization, representations in small and big character sets, static mode verification, etc.

As a programming language, Algol 68 offers certain unique and practical concepts that were ground-breaking at the time and have appeared, in varying degrees, in various languages afterwards.

Orthogonal design, which means that core concepts stated in the language can be used anyplace that usage can be said to "make sense." Completeness and clarity of explanation (as facilitated by the adoption of two-level grammar, which sparked many critical reactions).

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Answer:

These triangles are congruent by AAS.

A firm should record an impairment in the value of property, plant, or equipment by reducing the carrying amount of the asset and recognizing the impairment loss as an expense in the financial statements.

When the value of property, plant, or equipment is impaired, meaning its recoverable amount is lower than its carrying amount, a firm should recognize this impairment in its financial statements. The impairment is recorded by reducing the carrying amount of the asset to its recoverable amount, which is the higher of its fair value less costs to sell or its value in use. The difference between the carrying amount and the recoverable amount is recognized as an impairment loss and recorded as an expense in the income statement. This adjustment reflects the decrease in the value of the asset and allows the firm to accurately report its financial position and performance.

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Answer:

(x+5)(2x^2 +8)

Multiply (x+5) in both sides

(x+5)(2x^2) × (x+5)(8)

Answer is a

To prove the given trigonometric identity:

cot A · cos (30° - A) - sin (30° - A) = √3/2 · cosec A

We'll start by simplifying each side of the equation separately using trigonometric identities:

Left-hand side (LHS):

cot A · cos (30° - A) - sin (30° - A)

Using the identity cot A = cos A / sin A, we can rewrite cot A as cos A / sin A:

(cos A / sin A) · cos (30° - A) - sin (30° - A)

Expanding the cos (30° - A) using the cosine difference formula cos (x - y) = cos x · cos y + sin x · sin y:

(cos A / sin A) · (cos 30° · cos A + sin 30° · sin A) - sin (30° - A)

cos 30° = √3/2 and sin 30° = 1/2:

(cos A / sin A) · (√3/2 · cos A + 1/2 · sin A) - sin (30° - A)

Multiply through by (2 / 2) to simplify:

(2cos A / 2sin A) · (√3/2 · cos A + 1/2 · sin A) - sin (30° - A)

Cancel out the 2's:

(cos A / sin A) · (√3/2 · cos A + 1/2 · sin A) - sin (30° - A)

Apply the quotient identity for sine and cosine: cos x / sin x = cot x:

cot A · (√3/2 · cos A + 1/2 · sin A) - sin (30° - A)

Right-hand side (RHS):

√3/2 · cosec A

Since cosec A = 1 / sin A, we can rewrite the RHS:

√3/2 · (1 / sin A)

Multiply the √3/2 into the parentheses:

(√3/2) · (1 / sin A)

Multiply √3/2 by 1:

(√3/2) / (sin A)

Now, we need to simplify the expression further to match the LHS:

To combine the terms on the LHS, we'll multiply (√3/2) by (cos A / cos A) to get a common denominator with sin A:

(√3/2) · (cos A / cos A) / (sin A)

Simplifying the numerator:

(√3cos A) / (2cos A) / (sin A)

Cancel out the common factor of cos A in the numerator and denominator:

(√3) / 2 / (sin A)

Since (√3) / 2 = sin 60°:

sin 60° / (sin A)

Using the identity sin 60° = √3/2, we have:

(√3/2) / (sin A)

which matches the RHS.

Therefore, the left-hand side (LHS) is equal to the right-hand side (RHS), proving the given trigonometric identity:

cot A · cos (30° - A) - sin (30° - A) = √3/2 · cosec A

To prove the given trigonometric identity:

cot A · cos (30° - A) - sin (30° - A) = √3/2 · cosec A

We'll start by simplifying each side of the equation separately using trigonometric identities:

Left-hand side (LHS):

cot A · cos (30° - A) - sin (30° - A)

Using the identity cot A = cos A / sin A, we can rewrite cot A as cos A / sin A:

(cos A / sin A) · cos (30° - A) - sin (30° - A)

Expanding the cos (30° - A) using the cosine difference formula cos (x - y) = cos x · cos y + sin x · sin y:

(cos A / sin A) · (cos 30° · cos A + sin 30° · sin A) - sin (30° - A)

cos 30° = √3/2 and sin 30° = 1/2:

(cos A / sin A) · (√3/2 · cos A + 1/2 · sin A) - sin (30° - A)

Multiply through by (2 / 2) to simplify:

(2cos A / 2sin A) · (√3/2 · cos A + 1/2 · sin A) - sin (30° - A)

Cancel out the 2's:

(cos A / sin A) · (√3/2 · cos A + 1/2 · sin A) - sin (30° - A)

Apply the quotient identity for sine and cosine: cos x / sin x = cot x:

cot A · (√3/2 · cos A + 1/2 · sin A) - sin (30° - A)

Right-hand side (RHS):

√3/2 · cosec A

Since cosec A = 1 / sin A, we can rewrite the RHS:

√3/2 · (1 / sin A)

Multiply the √3/2 into the parentheses:

(√3/2) · (1 / sin A)

Multiply √3/2 by 1:

(√3/2) / (sin A)

Now, we need to simplify the expression further to match the LHS:

To combine the terms on the LHS, we'll multiply (√3/2) by (cos A / cos A) to get a common denominator with sin A:

(√3/2) · (cos A / cos A) / (sin A)

Simplifying the numerator:

(√3cos A) / (2cos A) / (sin A)

Cancel out the common factor of cos A in the numerator and denominator:

(√3) / 2 / (sin A)

Since (√3) / 2 = sin 60°:

sin 60° / (sin A)

Using the identity sin 60° = √3/2, we have:

(√3/2) / (sin A)

which matches the RHS.

Therefore, the left-hand side (LHS) is equal to the right-hand side (RHS), proving the given trigonometric identity:

cot A · cos (30° - A) - sin (30° - A) = √3/2 · cosec A

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The vision statement of Mpumi Bottle Manufacturers is to be the largest distributor of bottles in the area.

Mpumi Bottle Manufacturers aims to establish itself as the premier distributor of bottles in the region by focusing on superior quality, innovative designs, and excellent customer service. Our vision is to meet the diverse bottle needs of our customers and become their trusted partner for all their packaging requirements.

Through continuous improvement, strategic partnerships and a relentless commitment to customer satisfaction, they hoped to strive to exceed expectations and maintain position as the industry leader in bottle distribution.

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The constant percent rate of change of the function is option (a) 45% growth

The equation of the function is given as

f(x) = 33(1.45)^x

The above function is an exponential function

An exponential function is represented as

y = ab^x

Where b represents the growth or decay factor

So, we have

b = 1.45

We can see that the value of b is greater than 1

This means that the graph would represent a growth

The percent rate of change is then calculated as

Rate = b - 1

This gives

Rate = 1.45 - 1

Evaluate

Rate = 0.45

Rewrite as

Rate = 45%

Hence, the rate of change is 45% growth

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Answer:

A) 45% growth !!!

Step-by-step explanation:

i took the test

Answer:

12100

Step-by-step explanation:

If the number B of federally insured banks could be approximated by B ( t ) = − 329.4 t + 13747 from 1985 to 2007 where t = 0 correspond to year 1985

In order to determine the amount of federally insured banks that were there in 1990, we will first calculate the year range from initial time 1985 till 1990

The amount of time during this period is 5years. Substituting t = 5 into the modeled equation will give;

B ( t ) = − 329.4 t + 13747

B(5) = -329.4(5) + 13747

B(5) = -1647+13747

B(5) = 12100

This shows that there will be 12100 federally insured banks are there in the year 1990.

So, an exponential function with a growth factor of 5 is of the form y = a * 5^x, where a is a constant coefficient.

An exponential function of the form y = a * b^x has a growth factor of b. Therefore, an exponential function with a growth factor of 5 is of the form y = a * 5^x, where a is a constant coefficient.

For example, if a = 2, then the function y = 2 * 5^x has a growth factor of 5.

Here is a table showing the values of y for some values of x:

x       y

0        2

1        10

2        50

3        250

4        1250

As x increases, the values of y increase exponentially at a rate determined by the growth factor of 5.

Therefore, an exponential function with a growth factor of 5 is of the form y = a * 5^x, where a is a constant coefficient.

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For example, if a = 2, then the function y = 2 * 5^x has a growth factor of 5.

Here is a table showing the values of y for some values of x:

x       y

0        2

1        10

2        50

3        250

4        1250

As x increases, the values of y increase exponentially at a rate determined by the growth factor of 5.

Therefore, an exponential function with a growth factor of 5 is of the form y = a * 5^x, where a is a constant coefficient.

They suffer loss by selling bananas at 65c.

To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. With the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.

Given:

Cost of one box = R75

Then, cost of three boxes = R75 x 3

                                            = R225

Now, one box has 12 bunches of 12 bananas each.

Then, one box contain = 12 x 12 = 144 bananas

and, 3 box contain = 144 x 3 = 432 Bananas

If managed to sell 80 % of the bananas then they sold

= 432 x 0.8 = 346 Bananas

So, they earned by selling those bananas

= 346 x 0.65

= R224.9

Thus, they suffer loss.

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If in one week, a printing center made 1,222 copies of a 46 page article. The printing center also printed 485 copies of a 16 page essay. The number pages that the printing center print during the week is: 63,972 pages.

First step is to calculate first sets printed

Number of pages=(1222 copies×46 page article)

Number of pages=56,212

Second step is to calculate the second set printed

Number of pages=(485 copies×16 page article)

Number of pages=7,760

Third step is to calculate the total pages

Total pages=56,212+7,760

Total pages=63,972 pages

Therefore If in one week, a printing center made 1,222 copies of a 46 page article. The printing center also printed 485 copies of a 16 page essay. The number pages that the printing center print during the week is: 63,972 pages.

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Respuesta:

1,4 kilometros

Explicación paso a paso:

Dado que :

Distancia que separa a Sandra y José en el mapa = 7cm

Dibujo a escala = 1: 20.000; Esto se puede interpretar en el sentido de que 1 cm en el mapa equivale a 20.000 cm en el suelo.

Por tanto, una distancia de 7 cm en el mapa será:

20.000 * 7 = 140.000 cm en el suelo = distancia real

Por lo tanto, la distancia real = 140.000 cm.

Recordar :

1 cm = 10 ^ -5 km

140000 cm = 1.4 kilometros

Por lo tanto, la distancia real entre Sandra y José es de 1,4 km.