The graph of y = 2x2 - 4x + 2 opens downward.true or false

Answer

a. (4, 3)

Step-by-step explanation

The translation of a point (x, y) a units to the right and b units up transforms the point into (x + a, y + b).

Considering point B(2, 5), translating it 4 units to the right and 3 units up, we get:

B(2, 5) → (2+4, 5+3) → B'(6, 8)

The translation of a point (x, y) c units to the left and d units down transforms the point into (x - c, y - d).

Considering point B'(6, 8), translating it 2 units to the left and 5 units down, we get:

B'(6, 8) → (6 - 2, 8 - 5) → B''(4, 3)

Answer: The answer would be (4,3)

Step-by-step explanation: because if you started with (2,5), which would be (x,y) x goes left and right, and y goes up and down, and the questions says that you have to go 4 to the right and 3 up, then add 4 to 2, which is 6, and 3 to 5, which is 8, so now you have the point (6,8), then the second translation would be 2 to the left, and down 5, this is negative so you subtract this time, so subtract 2 from 6, which is 4, and 5 from 8, which is 3, so your final answer is (4,3).

we know that

L=KW(h^2)/l

we have that

W=5 in

h=8 in

l=216 in

L=7670 pounds

step 1

Find the value of K (constant of proportionality)

substitute the given values in the equation

7670=K(5)(8^2)/216

7670=k(1.4815)

k=5,177.25

step 2

we have the equation

L=(5,177.25)W(h^2)/l

for

W=3 in

h=5 in

l=240 in

substitute in the equation and solve for L

L=(5,177.25)(3)(5^2)/240

L=1,617.89 pounds

Round your answer to the nearest integer

so

L=1,618 pounds

Given:

The point which describes the relationship between the months and total amount is, (6, 47.94).

a) To find the constant proportionality:

6 months =47.94

Then, for 1 month,

Hence, the constant proportionality is $7.99.

b) The constant proportionality tells that, if the month is increased then the cost is also increased by $7.99.

c) To find the three more points and label it:

For the month, m=1, then the cost c=$7.99

For the month, m=2, then the cost c=$15.98

For the month m=3, then the cost c=$23.97

Therefore, the three points are (1, 7.99), (2,15.98) and (3, 23.97).

The graph is,

d) The relationship between the months and the cost is,

C=7.99 m

1) Solving that absolute value equation:

|2x+5|=13 Applying the absolute value eq. property

2x +5 = 13 subtracting 5 from both sides

2x = 13-5

2x= 8 Dividing by 2

x =4

2x +5=-13 subtracting 5 from both sides

2x = -13-5

2x = -18 Dividing by 2

x= -9

Then x=4 or x =-9

2) The equations 2x +5 =13 and 2x +15= -13

Resulting in x=4 or x =-9

The value of x = 16 + 4[tex]\sqrt{15}[/tex]

Given,

To solve the equations :

[tex]\sqrt{x+3} - \sqrt{x -1}[/tex] = -2

Solve by the given steps :

Now, According to the question:

Step 1: Simplify to obtain the radical form on one side of the equation:

[tex]\sqrt{x+3} - \sqrt{x -1}[/tex] = -2

Step 2: Raise both sides of the equation to the power of 2

[tex](\sqrt{x+3} - \sqrt{x -1})^2 = (-2)^2[/tex]

x + 3 + 2x - 1 -2 [tex]\sqrt{(x+3)(2x -1)}[/tex] = 4

3x - 2 = 2 [tex]\sqrt{(x+3)(2x -1)}[/tex]

[tex](3x - 2)^2 = [2\sqrt{(x+3)(2x -1)}]^2[/tex]

9[tex]x^{2}[/tex] - 12x + 4 = 4 (2[tex]x^{2}[/tex] + 5x -3)

Step 3: Apply the zero product rule, Simplify to get a quadratic equation :

[tex]x^{2}[/tex] - 32x +16 = 0

Step 4: Use the quadratic formula to find the values of x :

[tex]x^{2}[/tex] - 32x + 16 =0

x = 16 + 4[tex]\sqrt{15}[/tex] and x = 16 - 4[tex]\sqrt{15}[/tex]

x = 16 - 4[tex]\sqrt{15}[/tex]  (It is rejected)

So, the value of x = 16 + 4[tex]\sqrt{15}[/tex]

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Answer: Raise both sides of the equation to the power of 2

simplify to obtain the final radical term on one side of the equation

raise both sides of the equation to the power of 2 again

simplify to get a quadratic equation

use the quadratic formula to find the xvalues

Step-by-step explanation:

The number of ways that the planning committee can be formed if there are 3 members from each group is 6545 ways.

Combinations are also referred to as selections. Combinations imply the selection of things from a given set of things. In this case, we intend to select the objects. This can be illustrated by ⁿCr

The combination formula is illustrated thus:

ⁿCr = n! / ((n – r)! r!)

n = the number of items.

r = how many items are taken at a time

The number of people will be:

= 10 + 16 + 9

= 35

The number of ways will be:

= ³⁵C₃

= 35! / (35 - 3)! 3!

= 35! / 32! 3!

= 35 × 34 × 33 / 3 × 2

= 6545 ways

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6545 ways can a planning committee be formed if there are 3 members from each group.

Combination is a way of selecting items from a collection where the order of selection does not matter.

The formula for combination is ⁿCr = n! / ((n – r)! r!)

Where n is total number of objects and r is number of objects we have to choose.

The committee has 10 administrators, 16 faculty members, and 9 staff members.

The total number of persons

10+16+9

35

Now we need to select 3 persons from 35 persons

n=35 and r=3

³⁵C3 = 35! / ((35 – 3)! 3!)

=35! / ((32)! 3!)

=35×34×33×32! / (32! 3!)

=35×34×33 /6

=6545 ways

Hence in 6545 ways can a planning committee be formed if there are 3 members from each group.

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SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Define Prime factorization.

Prime factorization is a way of expressing a number as a product of its prime factors. A prime number is a number that has exactly two factors, 1 and the number itself. Examples of prime numbers are 2,3,5,7...etc.

STEP 2: Find the prime factors of the given number

Prime factorization of any number means to represent that number as a product of prime numbers.

We start by dividing the number by the lowest possible prime numbers.

STEP 3: Express 350 as a product of its prime factors

Hence, the prime factorization of 350 is given as:

From the graph, we are to determine the following:

(a) We are to find the option that costs less if Abdul drives 300 miles of the rental car and also how much less is it from the other option.

Option A: when x = 300, y = 140

Option B: when x = 300, y = 120

So the difference is:

140 - 120 = 20

So the option that costs less is B

And it costs $20 lesser than option A

(b) For what number of miles does the option costs the same and if Abdul drives less than that amount, what option cost more.

Option A: when x = 100, y = 60

Option B: when x = 100, y = 60

Therefore, the number of miles where the options cost the same is 100 miles.

If Abdul drives less than the amount:

That is x < 100, the B > A,

Which means, if Abdul drives less than 100 miles, Option B, costs more.

Line Segments and Rays

A line segment has two endpoints. It contains these endpoints and all the points of the line between them,

A ray is a part of a line that has one endpoint and goes on infinitely in only one direction. You cannot measure the length of a ray.

The figure shows a line that starts in B and goes infinitely to the left side, passing through A, thus the correct choice is B. Ray BA

Given the following equation:

You can solve for the variable "x" as following:

1. You need to apply the Division property of equality by dividing both sides of the equation by "p":

2. Remember that:

Then:

3. Now you have to apply the Subtraction property of equality by subtracting "q" from both sides of the equation:

The answer is:

The price/volume option that will allow the firm to avoid losing money on this project is C. 2,300 units at $34.00 each.

To determine the correct option, we use the cost-volume-profit analysis tool.

The cost-volume-profit (CVP) analysis involves determining how the volume of sales drives profitability.

The CVP technique classifies costs into their variable and fixed cost elements for the purpose of this analysis.

Variable cost per unit = $16

Fixed cost = $40,000

                        Option A    Option B   Option C  Option D   Option E

Sales units        3,000         1,900        2,300        2,500        1,700

Unit selling price $29       $36.50        $34          $31.50        $39

Sales revenue $87,000   $69,350   $78,200    $78,750    $66,300

Variable costs   48,000     30,400     36,800      40,000      27,200

Fixed cost         40,000     40,000     40,000      40,000     40,000

Total costs        88,000     70,400     76,800      80,000     67,200

Thus, the price/volume option that meets the firm's goal is Option C because the sales revenue exceeds the total costs.

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A. 3,000 units at $29.00 each.

B. 1,900 units at $36.50 each.

C. 2,300 units at $34.00 each.

D. 2,500 units at $31.50 each.

E. 1,700 units at $39.00 each.

Let's analyze each sentence to check if it is true or false:

First:

This sentence is true, the confidence interval is an interval where the true mean is likely to be.

Second:

This sentence is true, with a sample size smaller than 30, it is better to use the t-distribution instead of the normal distribution.

Third:

This sentence is true, the confidence interval is not a 100% guarantee that the true mean will be inside it.

Fourth:

Ti s sentence is true, this theorem states that when getting a large enough sample of a distribution with mean and standard deviation, the sample will be approximately normally distributed.

Fifth:

This sentence is false, because the number of degrees of freedom is 1 less than the sample size, so it would be 10.

Therefore the answer is:

True, True, True, True, False.

The expression 2x⁷· y⁴ would be equivalent to the given polynomial expression.

A polynomial is defined as a mathematical expression that has a minimum of two terms containing variables or numbers. A polynomial can have more than one term.

The given polynomial expression below is:

⇒ 10x⁵y⁷/5x⁵y · 3x⁴y⁸/3x⁻³y¹⁰

Apply the division operation in the constant terms

⇒ 2x⁵y⁷/x⁵y · x⁴y⁸/x⁻³y¹⁰

Apply the arithmetic operation in the Exponents of the same base variables

⇒ 2y⁶ · x⁷y⁻²

⇒ 2y⁶⁻² · x⁷

⇒ 2y⁴ · x⁷

⇒ 2x⁷· y⁴

Therefore, the expression 2x⁷· y⁴ would be equivalent to the given polynomial expression.

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1) Since we have a Rational Equation let's proceed with that, isolating the x on one side and then we can get rid of that fraction. This way:

Notice that now, we're going to get rid of that fraction on the left side, multiplying it by 7 (both sides) :

Thus, the answer is -14

Jessica bought 4 gallons of paint. Of that, she used 3/4 to paint. So the ammount she used was

So she used 3 gallons of paint.

If the domain is all real numbers greater than or equal to 4, the interval will be

Answer:

possible

Step-by-step explanation:

Answer:

Step-by-step explanation:

14x2=28

50 divided by 2 = 25 pages

14pages=28mins

page=2mins

so

pages =50/2

=25

We can model the cost and number of tickets by a linear equation of the form

Where c is the cost, t is the number of tickets.

m is the slope of the equation and b is the y-intercept.

First, let us find the slope which is given by

You can take any two pairs of values from the table.

The slope is 9.75 and the equation becomes

Now we need to find the y-intercept (b)

Choose any one pair of values from the table and substitute them into the above equation and solve for b.

Let's choose (12, 117)

The y-intercept is 0 so the equation is

Now to find the cost of 7 tickets, simply substitute t = 7 into the above equation

Therefore, the cost of 7 tickets is $68.25

1) Considering that the amount of lumber in this Data Set has been normally distributed, then we can start by finding this Percentage (or probability in this interval, writing out the following expressions:

Then:

Note that 0.1587 is the same as 15.87%. Multiplying that by the total number of trees we have:

Rounding it off to the nearest whole.

3) Thus, The answers are:

i.84%

ii. 2857 trees

Take the total number of oranges and divide by the number of crates

150 orange

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

10 crates

15 oranges per crate

The Solution to Question 24:

Given the function below:

We are asked to find the value of h(g(5)).

Step 1:

We shall find g(5) by substituting 5 for x in g(x).

So that:

Similarly, we shall find h(-25) by substituting -25 for x in h(x).

Therefore, the correct answer is

What integer represents the airplanes changes in altitude to avoid the storm ?

changes = 35000 - 30000

= 5000 ft

the integer 5000 represents the change in altitude to feet to avoid the storm.

the integer -5000 represents the change in altitude in feet immediately after passing the storm.



The subsets of E is all the above .

If every component present in Set A is also present in Set B, then Set A is said to be a subset of Set B. To put it another way, Set B contains Set A. As an illustration, if set A has the elements X, Y, and set B contains the elements X, Y, and Z, then set A is the subset of set B.

If every element in a set A is also an element in a set B, then the set A is a subset of the set B. The set A is therefore contained within the set B. AB is used to represent the subset connection. For instance, if the sets A and B are equal, AB but BB, respectively.

Let the event E =  {english, math, french, art}

The subsets of E is all the above .

null set is also subset of E

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At t = 1.5 sec the tool is at the height of 119 feet.

Given, A window washer drops a tool from their platform 155 ft high.

The polynomial -16r² + 155 tells us the height, in feet, of the tool / seconds after it was dropped.

we are asked to determine the height, in feet, after t = 1.5 seconds.

we know that h(t) = -16r² + 155

hence at t=1.5 sec, height is = ?

⇒ h(1.5) = -16t² + 155

⇒ h(1.5) = -16(1.5)² + 155

⇒ h(1.5) = -16(2.25) + 155

⇒ h(1.5) = -36 + 155

⇒ h(1.5) = 119

at t=1.5 sec the tool is at the height of 119 feet.

Hence we get the height as 119 feet.

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Let's call FC the fixed cost for production and VC the variable cost per item.

The company believes they can sell 2,500 items at $245 each.

Production costs:

For producing 2,500 items, the company has to spend (total cost, TC):

Sells:

Now, company sells eacho of the 2,500 items at $245, so, the company income (I) is:

where x is the number of items sold.

Break-even point:

This point is reached when company can recover the money they spend (TC). So, we have the following eaquation to solve:

Since company can not sell fractions of items, they have to sell 2,164 items to take back the money they invested.

So, "None of these choices are correct".

The radius of the circumference would be

x2 = 4.5

x1 = 2

r = x2 - x1

r = 4.5 - 2.0

r = 2.5

The radius would be 2.5

Answer:

a) Using the formula for the discriminant we get:

The discriminant is 64.

b) Based on the above result we know that the f(x)=0 has 2 real solutions,

Slope-intercept equation:

y=mx+b

Where:

m= slope

b=y- intercept

Point 1 = (x1,y1) = (-2,1)

Point 2 = (x2,y2)= (4,2)

First, find the slope by applying the formula:

Now we have:

y=1/6x+b

Replace x,y by a point ( for example point 1 (-2,1)) and solve for b:

1 = 1/6 (-2) +b

1= -1/3 +b

1+1/3 = b

b= 4/3

Final equation:

y= 1/6x+4/3

After solving the given polynomial (7x³ + 21x² - 63x = 0), the value of x are (x = 0) and {x = [(-3 ± 3√5)/2]}

So, 7x³ + 21x² - 63x = 0:

Now, solve for x as follows:

Zero factor principal, if ab = 0, then a = 0 and b = 0.

Now, x² + 3x - 9 = 0:

Therefore, after solving the given polynomial (7x³ + 21x² - 63x = 0), the value of x are (x = 0) and {x = [(-3 ± 3√5)/2]}

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