Question 5 of 10
What can you say about the y-values of the two functions f(x) = 32 - 3
and g(x) = 7x² - 3?
A. The minimum y-value of f(x) is -3.
B. The minimum y-value of g(x) is -3.
C. g(x) has the smallest possible y-value.
D. f(x) has the smallest possible y value.
SUBMIT

The value of y is 2 * √3.

In the second right triangle, we have a 60-degree angle and a leg opposite to that angle labeled y. The hypotenuse of the first right triangle is equal to the leg of the second right triangle.

Let's denote the hypotenuse of the first right triangle as h. From the first right triangle, we know that the vertical leg is equal to the square root of 2.

Using trigonometric ratios, we can relate the sides of a right triangle as follows:

sin(angle) = opposite/hypotenuse

In the first right triangle, the angle is 45 degrees, and the opposite side is the square root of 2. Therefore, we have:

sin(45 degrees) = √2 / h

By rearranging the equation, we can solve for h:

h = √2 / sin(45 degrees)

Using the value of sin(45 degrees) = 1/√2, we can simplify the equation:

h = √2 / (1/√2) = √2 * √2 = 2

Now, we can find the value of y in the second right triangle. Since the hypotenuse of the first right triangle is equal to the leg of the second right triangle, we have:

y = 2 * √3

Therefore, the value of y is 2 * √3.

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Answer:

ab(3a + 4b)

Step-by-step explanation:

Here are the steps on how to write the expression

3a^2 b + 4ab^2 as an equivalent algebraic expression:

1. Factor out the greatest common factor, which is ab.

2. The expression becomes ab(3a + 4b).

3. This is an equivalent algebraic expression to 3a^2 b + 4ab^2.

steps:

I hope this helps! Let me know if you have any other questions.

Answer:

Step-by-step explanation:

To simplify the expression 3a^2b + 4ab^2, [ we can factor out the common factor of ab from both terms: Step 1: Take out the common factor of ab. 3a^2b + 4ab^2 = ab(3a + 4b) Now the expression is in its factored form.

Option C is the table of values representing a proportional relationship in the context of this problem.

A proportional relationship is a relationship in which a constant ratio between the output variable and the input variable is present.

The equation that defines the proportional relationship is a linear function with slope k and intercept zero given as follows:

y = kx.

The slope k is the constant of proportionality, representing the increase or decrease in the output variable y when the constant variable x is increased by one.

For item c, we have that the output is equals to the input, hence the proportional relationship is given as follows:

y = x.

The problem asks for which table represents a proportional relationship.

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Answer:

please see answers below

Step-by-step explanation:

In a right-angled triangle, a ² + b ² = c ².

angles in a triangle add up to 180°.

Sine rule:   a/SIN A  =  b/SIN B  =   c/SIN C

angle C = 90° (little square means 90).

if angle A is 30, then angle B must be 180 - 90 - 30 = 60°.

using the Sine rule:

a/Sin A  =  c/Sin C

multiply both sides by Sin A:

a = (c Sin A) / Sin C

= (12 Sin 30) / Sin 90

= 6.

so a = 6.

Using Pythagoras (In a right-angled triangle, a ² + b ² = c ²),

c² = a² + b²

b² = c² - a²

= 12² - 6²

= 144 - 36

= 108

so b² = 108

b = √108

angle B is correct

floor plan => It is the scale drawing that show the relationship between rooms, spaces, and physical features viewed from the above

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The largest possible number of people attending the match is 31,249, and the smallest possible number is 31,100.

To determine the largest and smallest possible number of people attending the football match, given that the figure is stated as 31,200 with 3 significant figures, we need to consider the range of values that can be represented within that significant figures constraint.

For a number to be stated with 3 significant figures, the last significant figure is uncertain and can be either rounded up or down.

To find the largest and smallest possible numbers, we'll consider the cases where the last significant figure is rounded up and rounded down.

Rounding up:

If we round up the last significant figure, the possible range of values is from 31,150 to 31,249.

So the largest possible number of people attending the match would be 31,249.

Rounding down:

If we round down the last significant figure, the possible range of values is from 31,100 to 31,199.

So the smallest possible number of people attending the match would be 31,100.

Therefore, the largest possible number of people attending the match is 31,249, and the smallest possible number is 31,100.

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Answer:

100 cubic feet

Step-by-step explanation:

To find the volume of a rectangular prism, we need to multiply the area of the base by the height.

Given:

Area of the top face = 20 ft²

Height = 5 ft

The volume (V) can be calculated as follows:

V = Area of the top face * Height

V = 20 ft² * 5 ft

V = 100 ft³

Therefore, the volume of the rectangular prism is 100 cubic feet.

Answer:

k = - 9

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given equation of PQ is

3x - 2y = 12 ( subtract 3x from both sides )

- 2y = - 3x + 12 ( divide through by - 2 )

y = [tex]\frac{3}{2}[/tex] x - 6 ← in slope- intercept form

with slope m = [tex]\frac{3}{2}[/tex]

now calculate the slope of PQ using the slope formula and equate to [tex]\frac{3}{2}[/tex]

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

with (x₁, y₁ ) = P (6, 3 ) and (x₂, y₂ ) = Q (- 2, k )

m = [tex]\frac{k-3}{-2-6}[/tex] = [tex]\frac{k-3}{-8}[/tex]

equating the slopes of PQ

[tex]\frac{k-3}{-8}[/tex] = [tex]\frac{3}{2}[/tex] ( cross- multiply )

2(k - 3) = - 8 × 3 = - 24 ( divide both sides by 2 )

k - 3 = - 12 ( add 3 to both sides )

k = - 9

The nth roots of perfect nth powers evaluates to:

[tex]\sqrt[5]{-32}[/tex] = -2

[tex]-\sqrt[4]{256}[/tex] = -4

Perfect nth Power is an integer which is obtained from multiplying a single integer by itself n times.

The nth root of a Perfect nth Power is an integer which when multiplied by itself n times it will produce the original value under the radical.

To find the nth roots of perfect nth powers with signs, you can use the following steps:

1. Write the perfect nth power as a product of nth roots.

2. Find the nth root of each factor.

3. Combine the nth roots to get the final answer.

[tex]\sqrt[5]{-32}[/tex] = [tex]\sqrt[5]{-2^{5} }[/tex]

         = -2

-[tex]\sqrt[4]{256}[/tex] = -[tex]\sqrt[4]{4^{4} }[/tex]

           = -4

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Answer:

Step-by-step explanation:

According to the sources I found, cows consume an average of 3 to 30 gallons of water per day. One gallon is equivalent to 3.78541 liters. Therefore, a cow drinks between 11.35623 liters and 113.5623 liters per day.

If we assume that each cow drinks 30 gallons (113.5623 liters) per day, then a full trough would have enough water for 2.37 cows per day (226.8 liters / 113.5623 liters per cow). Therefore, Zipho’s statement is incorrect if we assume that each cow drinks 56 liters per day.

Answer:

64π

Step-by-step explanation:

To calculate the surface area (S.A) of the circle with a radius (r) of 4 inches and a height (h) of 6 inches, we need to consider both the curved surface area (lateral surface area) and the area of the circular base.

The curved surface area, also known as the lateral surface area, is calculated using the formula:

L.A = 2πrh

Substituting the given values, we have:

L.A = 2π(4)(6)

L.A = 48π square inches

The area of the circular base is calculated using the formula:

A = πr^2

Substituting the given radius, we have:

A = π(4^2)

A = 16π square inches

To find the total surface area (S.A), we need to sum the lateral surface area (L.A) and the area of the circular base (A):

S.A = L.A + A

S.A = 48π + 16π

S.A = 64π square inches

Therefore, the surface area (S.A) of the given circle is 64π square inches.

The total number of data values (games played) represented in the table is 14.

To determine the total number of data values (games played) represented in the frequency table, we need to sum up the frequencies for each category (number of goals scored).

The frequency represents the number of games in which a particular number of goals was scored.

Let's calculate the total number of games played by summing up the frequencies:

Total number of games played =

Frequency of 0 goals + Frequency of 1 goal + Frequency of 2 goals + Frequency of 3 goals + Frequency of 4 goals + Frequency of 7 goals + Frequency of 9 goals

Total number of games played = 1 + 3 + 2 + 4 + 2 + 1 + 1

Total number of games played = 14

We must add the frequencies for each category (number of goals scored) to get the total number of data values (games played) reflected in the frequency table.

The number of games with a specific amount of goals scored is the frequency.

Let's add up the frequencies to determine the total number of games played:

Total games played = Frequency of 0 goals, Frequency of 1, Frequency of 2, Frequency of 3, Frequency of 4, Frequency of 7, and Frequency of 9 goals.

Total games played: 1 plus 3 plus 2 plus 4 plus 2 plus 1 plus 1

14 games were played in total.

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The elements in the range that correspond to the elements 0 and 3 are y = 2 and y = 4 and the equations are solved.

Given data ,

To find the elements in the range that correspond to the elements 0 and 3 of the domain, we need to solve the equation 3y - 2x = 6 for the corresponding values of y when x = 0 and x = 3.

When x = 0:

Substituting x = 0 into the equation 3y - 2x = 6, we get:

3y - 2(0) = 6

3y = 6

y = 2

So, when x = 0, the corresponding value of y is 2.

When x = 3:

Substituting x = 3 into the equation 3y - 2x = 6, we get:

3y - 2(3) = 6

3y - 6 = 6

3y = 12

y = 4

So, when x = 3, the corresponding value of y is 4.

Hence , the elements in the range that correspond to the elements 0 and 3 of the domain are y = 2 and y = 4, respectively.

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The coordinates of midpoint P are P(-1/2, 3/2) and coordinates of midpoint Q are Q(-3/2, -4).

To find the coordinates of the midpoints P and Q of sides AB and AC, we can use the midpoint formula.

The midpoint formula states that the coordinates of the midpoint of a line segment between two points (x1, y1) and (x2, y2) are given by:

Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)

Using this formula, we can find the coordinates of P and Q as follows:

Coordinates of midpoint P:

P = ((2 + (-3)) / 2, (-1 + 4) / 2)

= (-1/2, 3/2)

Therefore, the coordinates of midpoint P are P(-1/2, 3/2).

Coordinates of midpoint Q:

Q = ((2 + (-5)) / 2, (-1 + (-7)) / 2)

= (-3/2, -4)

Therefore, the coordinates of midpoint Q are Q(-3/2, -4).

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Let the points A(2,-1), B(-3,4), and C(-5,-7) be the vertices of triangle A B C. Let P and Q be the midpoints of the sides AB and AC respectively. Find the coordinates of P and Q. (2 marks)

Answer:

–6x – 3

Step-by-step explanation:

To find the expression that is equivalent to 3(–2x – 1), we need to distribute the 3 to each term inside the parentheses.

When we distribute 3 to –2x, we get:

3 * –2x = –6x

When we distribute 3 to –1, we get:

3 * –1 = –3

Therefore, the expression equivalent to 3(–2x – 1) is:

–6x – 3.

Answer:

-6x - 3

Step-by-step explanation:

Distribute 3 through the parenthesis:

[tex]\sf{3(-2x-1)}[/tex]

[tex]\sf{3*(-2x)+3*(-1)}[/tex]

[tex]\sf{-6x-3}[/tex]

Hence, the expression that is equivalent  to 3(-2x - 1) is -6x - 3.

The own price elasticity of good X is -0.60, so we can conclude that good X is price inelastic.

The own price elasticity of good X is calculated using the formula:

Given the demand function for good X: Qxd = 6 - 2Px + 5Py, we can calculate the initial quantity demanded at a price of $3 per unit:

Qxd1 = 6 - 2(3) + 5(2)

= 6 - 6 + 10

= 10

The new quantity demanded when the price changes to $2.90 per unit:

[tex]Qxd_2[/tex] = 6 - 2(2.90) + 5(2)

[tex]Qxd_2[/tex] = 6 - 5.80 + 10

[tex]Qxd_2[/tex] = 10.20

Now, we can calculate the percentage change in quantity demanded:

% Change in Quantity Demanded = (Qxd2 - Qxd1) / Qxd1 * 100

% Change in Quantity Demanded = (10.20 - 10) / 10 * 100

% Change in Quantity Demanded = 0.20 / 10 * 100

% Change in Quantity Demanded = 2%

Next, we calculate the percentage change in price:

% Change in Price = (New Price - Old Price) / Old Price * 100

% Change in Price = (2.90 - 3) / 3 * 100

% Change in Price = -0.10 / 3 * 100

% Change in Price = -3.33%

The own price elasticity will be:

Elasticity = (% Change in Quantity Demanded) / (% Change in Price)

Elasticity = 2% / -3.33%

Elasticity ≈ -0.60

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Answer:

B. 33

Step-by-step explanation:

Step 1:  Find total measure of ∠R:

Step 2:  Find total measure, m, of ∠Q:

m∠P + m∠Q + m∠R = 180

m∠Q = 180 - (m∠P + m∠R)

m∠Q = 180 - (60 + 76)

m∠Q = 180 - 136

m∠Q = 44°

Since QA bisects ∠Q into two congruent angles, we divide 44 by 2 to find the measures of each angle made by the bisector:  44/2 = 22.

Step 3:  Find x by setting the sum of the 38° angle, the 22° angle, and angle C equal to 180:

38 + (3x + 21) + 22 = 180

60 + 3x + 21 = 180

81 + 3x = 180

3x = 99

x = 33

Thus, x equals 33.

Answer:

76b^2

Step-by-step explanation:

Basically you just multiply 4x19 which gives you 76, and the two b's equal b^2 (I'm not great at explaining i know)

Answer:

5446cm²

Step-by-step explanation:

the surface area = the 2 isosceles triangles + the 2 sides + the base

= 2 (24/2 X 35) + 2(37 X 47) + (47 X 24)

= 5446cm²

Answer: 5,446 cm²

Step-by-step explanation:

First, we will find the area of the two triangle sides.

       A = 2 * ([tex]\frac{bh}{2}[/tex])

       A = bh

       A = (35 cm)(24 cm)

       A = 840 cm²

Next, we will find the area of the three rectangular sides. We have two that are congruent and a third that is not.

       A = 2 * (LW)

       A = 2 * ((47 cm)(37 cm))

       A = 2 * 1,739 cm²

       A = 3,478 cm²

       A = LW

       A = (24 cm)(47 cm)

       A = 1,128 cm²

Lastly, we will add all of these faces together.

       840 cm² + 3,478 cm² + 1,128 cm² = 5,446 cm²

Answer:

664 Square yards

Step-by-step explanation:

Surface area= 2lw+2lh+2hw

=2(17×6)+2(17×10)+2(10×6)

=2(102)+2(340)+2(120)

=204+340+120

=664 Square yards

Julia's total cost for the car purchase, including the negotiated price, rebate coupon deduction, optional stereo and accessories, and financing, amounts to $16,531.05 + $380 = $16,911.05 (excluding title fees, license plate charges, and sales taxes).

Let's break down the information given and calculate the various costs and payments involved in Julia's car purchase:

1. Dealer's Cost:

The dealer's cost is 11.7% lower than the sticker price of $17,350.

Dealer's Cost = $17,350 - (11.7% * $17,350) = $15,320.95

2. Negotiated Price:

Julia negotiated a price that left the dealer with a 9.5% profit margin over the invoice price.

Negotiated Price = Dealer's Cost + (9.5% * Dealer's Cost) = $15,320.95 + (9.5% * $15,320.95) = $16,781.05

3. Rebate Coupon:

Julia has a rebate coupon of $250, which will be deducted from the negotiated price.

Negotiated Price after Rebate = Negotiated Price - $250 = $16,781.05 - $250 = $16,531.05

4. Optional Stereo and Accessories:

Julia ordered a $300 stereo unit and other accessories costing $80.

Total Additional Cost = $300 + $80 = $380

5. Financing:

Julia will finance 83% of the total cost at an APR of 9 ¼ % over 4 years.

Loan Amount = 83% * Negotiated Price after Rebate = 83% * $16,531.05 = $13,711.48

APR = 9.25%

Loan Term = 4 years

6. Title Fees, License Plate Charges, and Sales Taxes:

The costs for title fees, license plate charges, and sales taxes will be paid later at the Registry of Motor Vehicles and are not included in the calculations above.

In summary, Julia's total cost for the car purchase, including the negotiated price, rebate coupon deduction, optional stereo and accessories, and financing, amounts to $16,531.05 + $380 = $16,911.05 (excluding title fees, license plate charges, and sales taxes).

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Answer:

5.25 feet tall

Step-by-step explanation:

Doug's height / Doug's shadow = Statue's height / Statue's shadow

x / 3.5 = 12 / 8

Cross-multiplying:

8x = 3.5 * 12

8x = 42

Dividing both sides by 8:

x = 42 / 8

x ≈ 5.25

Answer:

It's the 3rd one down. 4,-12,6,42,18,0

Step-by-step explanation:

Answer:

[24  -12  6]

[42   18  0]

Step-by-step explanation:

Multiply each number in the brackets individually by 6.

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The walkway is 12 feet 9 inches long.

To find the total length of the walkway, we need to add the lengths of the three boards together.

The first board is 3 feet 7 inches long, which can be written as 3'7".

The second board is 5 feet 4 inches long, which can be written as 5'4".

The third board is 3 feet 10 inches long, which can be written as 3'10".

Now, let's add the lengths together:

3'7" + 5'4" + 3'10"

When adding feet and inches, we need to carry over any extra inches beyond 12 to the feet.

Adding the inches first:

7" + 4" + 10" = 21"

Now, let's add the feet:

3' + 5' + 3' = 11'

So, the total length of the walkway is 11 feet 21 inches.

We need to convert the inches to feet by dividing by 12:

11' + 21" ÷ 12 = 11' + 1'9" = 12'9"

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The graph of the function f(x) = x³- 2x² - 4x + 8​  is added as an attachment

From the question, we have the following parameters that can be used in our computation:

f(x) = x³- 2x² - 4x + 8​

The above function is a polynomial function that has undergone for several transformations

Next, we plot the graph using a graphing tool by taking note of the transformations rules

The graph of the function is added as an attachment

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The relationship between Calorie and weight is very weak and insignificant.

Comparing the relationship between Calorie and Weight using the correlation coefficient, the coefficient value obtained is 0.0086 which is very weak.

There is no obvious pattern linking an increase in calorie to Weight or decrease in association between the two variables.

Therefore, we can conclude that a very weak and insignificant relationship exists between Calorie and weight for the given data.

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Answer:

  0.90

Step-by-step explanation:

You want the probability of either event A or event B given the Venn diagram shown.

The probability of an event shown in the diagram is the ratio of counts for that event to the total of all counts in the diagram. That total is 50.

The number of counts that are not part of either event is shown as 5.

  P(A or B) = 1 - P(not (A or B)) = 1 - 5/50

  P(A or B) = 0.90

__

Additional comment

Using the given formula, ...

  P(A or B) = (25+5)/50 +(15 +5)/50 -5/50 = (25 +15 +5)/50 = 45/50

  P(A or B) = 0.90

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Answer:

19 - 42x

Step-by-step explanation:

To differentiate this, we must use the product rule
f'(x) = (7x+3)'(4-3x) + (4-3x)'(7x+3)
= (7)(4-3x) + (-3)(7x+3)
= 28 - 21x - 21x - 9
= 19 - 42x

Answer:

x = 1 or x = 7

Step-by-step explanation:

-x² + 8x - 7

= -(x² - 8x) - 7

= - [(x - 4)² - 16] - 7

= -(x - 4)² + 16 - 7

= -(x - 4)² + 9.

-(x - 4)² + 9 = 0

-(x - 4)² = -9

(x - 4)² = 9

x - 4 = ±√9

x - 4 = ±3

x = 3 + 4 or x = -3 + 4

x = 7 or x = 1