find the range of the function below if the domain is {-1,0,2}
f(x)=x^2 -2x +3

For this case we have the following quadratic equation:

[tex]p = -5x ^ 2 + 70x-165[/tex]

To find the roots, we equal 0.

[tex]-5x ^ 2 + 70x-165 = 0[/tex]

Where:

[tex]a = -5\\b = 70\\c = -165[/tex]

The solution will be given by:

[tex]x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2a}[/tex]

Substituting we have:

[tex]x = \frac {-70 \pm \sqrt {70 ^ 2-4 (-5) (- 165)}} {2 (-5)}\\x = \frac {-70 \pm \sqrt {4900-3300}} {- 10}\\x = \frac {-70 \pm \sqrt {1600}} {- 10}\\x = \frac {-70 \pm40} {- 10}\\x = - (-7\pm4)[/tex]

We have two roots:

[tex]x_ {1} = 7-4 = 3\\x_ {2} = 7 + 4 = 11[/tex]

Answer:

[tex]x_ {1} = 3\\x_ {2} = 11[/tex]

Answer:

So here is the answer.

We represent h = hardwood and p = pine bark

Here is the equation: h + p = 176

2.75p + 3.50h = 520

Next, p = 176 -h (substitute)

2.75 (176-h) + 3.5h = 520

484 -2.75h + 3.5h = 520

3.5h-2.75h = 520 -484

0.75h = 36 (divide both by 0.75)

h = 48

Therefore, the number of hardwood sold is 48.

h + p = 176

p = 176-48

p= 128

The number of pine bark sold is 128.

Hope this helps :)

Step-by-step explanation:

The problem revolves around solving a system of linear equations to find out how many bags of hardwood and pine bark mulch were sold by the boys club, given the total number of bags and the total revenue generated from the sales.

The student is asking for help with solving a system of linear equations using the information provided about the sale of mulch bags. We'll define two variables: let x represent the number of hardwood mulch bags and y represent the number of pine bark mulch bags sold. To solve for x and y, we need to set up two equations based on the given information:

We solve this system of equations, possibly using the substitution or elimination method, to find the values of x and y that satisfy both equations, which will give us the number of bags of each type of mulch sold.

Answer:

Step-by-step explanation:

1) Sin² Ф = 1 - cos² Ф

So, 1 - Sin² Ф = 1 - (1 - cos² Ф)

                     = 1 - 1 + cos² Ф = cos² Ф

2) tan x = Sin x /Cos x

tan x * csc x = Sin x /Cos x  * 1/Sin x = Sinx  * 1 / cos x  * sin x

                        =1/cos x = Sec x

The elevator can carry the adults with average mass of 80 kg.

Step-by-step explanation:

Given

Capacity to weight that can be hold by elevator = 2500 pounds

Average mass of one adult = 80 kg

Average mass of 10 adults = 80*10 = 800kg

We need to have the weights in same unit in order to determine whether the elevator can carry the adults or not.

We will convert the weight of 10 adults into pounds.

1 kg = 2.205 pounds

800 kg = 800*2.205 = 1764 pounds

Therefore,

1764 pounds < 2500 pounds

The elevator can carry the adults with average mass of 80 kg.

Keywords: conversion, multiplication

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By converting the average mass from kilograms to pounds and multiplying by the number of adults, the total weight is calculated to be 1763.696 pounds, which is under the elevator's capacity of 2500 pounds, so the elevator can carry them safely.

The student is asking whether an elevator would be able to carry 10 adults with an average mass of 80 kg each without exceeding its maximum weight capacity of 2500 pounds. To answer this, we will first convert 80 kg to pounds and then multiply by the number of adults to find the total weight. After that, we can compare the total weight with the maximum capacity of the elevator.

First, let's convert the average mass of one adult from kilograms to pounds. Since 1 kg is equal to approximately 2.20462 pounds, we can calculate like this:

80 kg * 2.20462 lbs/kg = 176.3696 lbs per adult

Now, multiplying this by 10 adults:

176.3696 lbs/adult * 10 adults = 1763.696 lbs for 10 adults

When comparing this total weight of 1763.696 pounds to the elevator's maximum capacity of 2500 pounds, we see that the weight of 10 adults is less than the elevator's capacity.

Therefore, the elevator can safely carry 10 adults with an average mass of 80 kg each.

Answer:

Step-by-step explanation:

3+3+4+5+6+6+7+7+7+8+8=64

64÷11=5.81818181818

simplify to......5.82

Answer: 5.81818181818

Step-by-step explanation: The mean of a data set is equal to the sum of the set of numbers divided by how many numbers are in the set.

So to find the mean of the data set shown here, let's begin by adding the numbers.

So we have [tex]\frac{3 +3+4+5+6+6+7+7+7+8+8}{11}[/tex] and notice that I put an 11 on the bottom since there are 11 numbers.

Adding the numbers, we get 64. This will be divide by how many numbers are in the set or 11.

[tex]\frac{64}{11} = 5.81818181818[/tex]

Therefore, the mean of the data set is 5.81818181818.

Sid will pay $76.26 in total including ta and tip.

Step-by-step explanation:

Given,

Cost of Sid's bill = $62.00

Tax rate = 8%

Tip = 15%

Tax amount = 15% of bill

[tex]Tax\ amount=\frac{8}{100}*62.00\\Tax\ amount=0.08*62.00\\Tax\ amount=\$4.96[/tex]

As the tip will be on Pre-tax amount, therefore,

Tip amount = 15% of bill

[tex]Tip\ amount=\frac{15}{100}*62.00\\Tip\ amount=0.15*62.00\\Tip\ amount=\$9.30[/tex]

Total amount = Bill + Tax amount + Tip amount

Total amount = 62.00 + 4.96 + 9.30 = $76.26

Sid will pay $76.26 in total including ta and tip.

Keywords: addition, percent

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Answer:

76.26

Step-by-step explanation:

Answer:

The vertical columns on the periodic table are called groups or families because of their similar chemical behavior. All the members of a family of elements have the same number of valence electrons and similar chemical properties. The horizontal rows on the periodic table are called periods.

Step-by-step explanation:

Answer:

C.

Step-by-step explanation:

https://tex.z-dn.net/?f=24x%5E%7B5%7Dy%5E%7B4%7D%5Csqrt%7B7x%5E%7B2%7Dy%7D

this is correct

the simplified expression is [tex]\(24x^7 y^4 \sqrt{7y}\)[/tex], which corresponds to option A.

To simplify the expression [tex]\(8\sqrt{63x^{14}14y^9}\),[/tex] we can break down the radicand into its prime factors and then simplify:

[tex]\(8\sqrt{63x^{14}14y^9} = 8\sqrt{7 \cdot 9 \cdot 7 \cdot 2 \cdot (x^7)^2 \cdot (y^4)^2 \cdot (y^1)}\)[/tex]

Now, we can take the square root of perfect squares and pull them out of the square root:

[tex]\(8 \cdot 3 \cdot 7 \cdot x^7 \cdot y^4 \cdot \sqrt{y}\)[/tex]

Simplifying further:

[tex]\(24x^7 y^4 \sqrt{7y}\)[/tex]

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The 9 at the side on the fraction represents one full 6/6

So by taking one out, it will give the top number an extra 6.

Answer:

88 feet

Step-by-step explanation:

perimeter (P)=2πr

P= 2*22/7*14

P=88 feet

Answer:

2. B, 25.12 feet.

3. B, 88 feet.

P=2πr, r = radius or 1/2 diameter, replace [tex]\pi[/tex] with given value for each question and then simplify.

Answer:

0.53, 0.35, 0.05, 0.03, and 3.5

Step-by-step explanation:

Order Least to greatest

Answer: Yes, you put cm for the units of the missing side

Step-by-step explanation:

Answer:

domain: {x | x is a real number}

range: {y l y> -8}

Step-by-step explanation:

f(x) = 4x² – 8 is a parabola, a U shape.

Since the stretch factor, 4, is positive, it opens up, there it will have a minimum value, the lowest point in the parabola.

y > -8  because the minimum is -8.

Parabolas do not have restricted "x" values. "4" does not restrict x because it is the stretch factor, which determines how wide the parabola is.

Quadratic standard form:

f(x) = ax² + bx + c

"a" represents how wide the graph is. If it's negative it opens down, if it's positive it opens up.

"b", if written, tells you it is not centred on the y-axis. It is not written, so the vertex is on the y-axis.

"c" is the y-intercept. In this case, since b = 0, it is also the minimum value.

The domain of f(x) = 4x - 8 is all real numbers, as x can take any value without restriction. The range is all values greater than or equal -8 because this is the function's minimum value (occurs when x=0).

In mathematics, the domain and range of a function represent the set of input values (x-values) and output values (y-values) respectively. For the function f(x) = 4x - 8, the domain is all real numbers, represented as {x | x is a real number} because there's no restriction on the values that x can take. On the other hand, the range is all values greater than or equal to -8, which is represented as {y | y > -8}, since the function's minimum value occurs at y=-8 (when x=0).

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Answer:

540 seconds

Step-by-step explanation:

1 minute is equal to 60 second

so 90 min is equal to 90 multiplied by 60 which is equal to 540 seconds.

Answer:5400 seconds

Step-by-step explanation:

Multiply his pay rate by number of hours worked:

$10.50 x 275 hours = $2887.50

Now multiply his earnings by 40%:

2887.50 x 0.40 = 1155

He saved $1,155

Answer: B

Step-by-step explanation:

First off, choices A and D can be elimination because you are not subtracting. In choice C, we have 10 divided by 5 as opposed to z divided by 5. The answer is B.

The factors for given equation f(x)=[tex]x^{3} +3x^{2} -25x-75[/tex].

Step-by-step explanation:

The given equation is f(x)=[tex]x^{3} +3x^{2} -25x-75[/tex] .

Add 0 at the end of the equation.

[tex]x^{3} +3x^{2} -25x-75[/tex] = 0.

Let us group the given equation,

[tex](x^{3} +3x^{2}) -(25x-75)[/tex] =0.

⇒ Group 1: [tex]x^{3} +3x^{2}[/tex] .

Group 2: [tex]- 25x +75[/tex] .

Pull out factor from each group,

⇒ Group 1: [tex](x+3)(x^{2})[/tex].

Group 2: (x+3) (-25).

Join the two group since both (x+3) is common in both groups.

[tex](x+3)(x^{2} -25)[/tex] =0.

One of the factor is (x+3).

Other factors are solved by the formula, [tex]a^{2}-b^{2} = (a+b) (a-b)[/tex] .

[tex](x+3)(x^{2} -25)[/tex] = (x+5) (x-5) .

The other factors are (x+5) and (x-5).

Answer:

the sum of two numbers is multplication and its opposite is a negative version of it

Step-by-step explanation:

Answer:

See the attached figure.

Step by step solution:

Part (1):

When ΔABC is an isosceles triangle with AB = AC

The summing of the three of the triangle = 180°

∴ m∠ABC + m∠BAC + m∠ACB = 180°

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

Part (2):

When ΔABC is an isosceles triangle with AB = AC

So, m∠ABC = m∠ACB = x

if m∠BAC = 70

∵ m∠ABC  + m∠ACB + m∠BAC= 180°

∴ x + x + 70 = 180 ⇒ x = 55°

∴ m∠ABC = 55°

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

Part (3):

When m∠QRP = 30°, and ΔPQR is an isosceles triangle with PQ = QR

So, m∠QPR = m∠QRP = 30°

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

Part (4):

When m∠BAC = 45° and points D and E are the midpoints of AB and BC in ΔABC

∵ Points D and E are the midpoints of AB and BC in ΔABC

∴ DE // AC

∴ m∠BDE = m∠BAC ⇒ the corresponding angles are congruent

∴ m∠BDE = 45°

Answer:402.03

Step-by-step explanation:

Increasing by 5% is just multiplying by 1.05 then you repeat step for x amount of years

a. She pays $100 for 5 sheets

b. 25+15x dollars for x sheets

c. 8 sheets

Step-by-step explanation:

Given

Sitting cost = $25

Per sheet picture cost = $15

Let p be the number of sheets of pictures

Then the cost can be written as a function of p

[tex]c(p) = 25+15p[/tex]

Now,

a. How much does she pay for 5 sheets of pictures?!

Putting p = 5 in the function

[tex]c(5) = 25 + 15(5)\\= 25+75\\=100[/tex]

She will pay $100 for 5 sheets of pictures

b. How much does she pay for "x" sheets?

Putting x in place of p

[tex]c(x) = 25+15x[/tex]

c. How many sheets can she buy for $145?

We know the cost now, we have to find p so,

[tex]145 = 25+15p\\145-25 = 25+15p-25\\120 = 15p[/tex]

Dividing both sides by 15

[tex]\frac{15p}{15} = \frac{120}{15}\\p = 8[/tex]

Hence,

She can buy 8 sheets for $145

Keywords: Linear equation, Algebraic functions

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Answer:

[tex]\displaystyle y - 3 = -1\frac{1}{5}x\:OR\:y + 3 = -1\frac{1}{5}x - 5[/tex]

Step-by-step explanation:

First, find the rate of change [slope]:

[tex]\displaystyle \frac{-y_1 + y_2}{-x_1 + x_2} = m \\ \frac{3 + 3}{-5 ± 0} = -\frac{6}{5} = -\frac{1}{5}[/tex]

Then plug these coordinates into the Point-Slope Formula Remember, in this formula, all the negative symbols give the OPPOSITE terms of what they really, so be EXTREMELY CAREFUL inserting the coordinates into the formula with their CORRECT SIGNS. It does not matter which ordered pair you choose:

[tex]\displaystyle y - y_1 = m[x - x_1] \\ \\ y - 3 = -1\frac{1}{5}x\:OR\:y + 3 = -1\frac{1}{5}x - 5[/tex]

I am joyous to assist you anytime.

Answer:

the answer is

129

Step-by-step explanation:

cyclic

Answer:

-8/3

Step-by-step explanation:

-4 1/2=-9/2

(-8/9)(-2/3)=16/27

(16/27)(-9/2)=-144/54

-8/3

Answer:

Step-by-step explanation:

Has the form  y = kx :  

y = -0.05x

y =50x

Can be put in the form of y = kx:

y/7 = x

y/x = 6.5

other:

y = 1/5x - 1/5

2x + 1/2 = y

The equation y=kx is a form of a linear equation where there is a direct proportionality between the variables 'y' and 'x'. This equation reflects a direct variation scenario, where 'y' increases or decreases as 'x' does.

The question pertains to the understanding and categorization of linear equations, which are frequently used in Mathematics and Physics. You mention the equation y=kx, where 'k' is a number. It's a simplified version of the standard linear equation, y = mx + b, where 'm' is the slope (rate of change) and 'b' is the y-intercept (the value of 'y' when 'x' is zero). When 'b' is zero, we have the equation y=mx or in your context, y=kx, a direct proportionality.

For instance, if we see the equation y = 6x, it fits the category of y=kx where the 'k' value is 6. Such equations show a direct variation 'y' with 'x', meaning when 'x' increases or decreases, 'y' will also increase or decrease respectively.

Other forms of equations such as quadratic relationships or inverse relationships occur when the variables have a different kind of interaction, such as being squared or inversely proportional to each other.

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Answer:

D) translation 5 units up, then dilation with a factor of  1/4

Step-by-step explanation:

The Geometric Transformation over a triangle that produces a similar triangle an not a congruent one is, the one that makes its sides larger\smaller but maintain its angle measures. Namely, the Dilation.

1) In the example below, we have a pair of isosceles triangle ABC and DEF

2) Translating up 5 units adding 5 units to y in DEF

3) Check it out on the third graph how the triangle DEF is similar to ABC  share the same angle measure with different legs size.

4) So it's D

Answer:

The answer is d

Step-by-step explanation:

Answer:

$7.17

Step-by-step explanation:

(1 year) 4.45 x .01= .45    $4.45 + .45=$4.90

(2 year)4.90 x .01= .49 $4.90+.49=$5.39

(3 year)$5.39 x .01=.54 $5.39+.54=$5.93

(4 year) $5.93 x .01=.59 $5.93+.59=$6.52

(5 year) $6.52 x .01=.65 $6.52+.65=$7.17

Answer:

$7.17

Explination: $6.52 x .01=.65 $6.52+.65=$7.17

Answer: 8 sqrt7

Step-by-step explanation:

Answer:

$0.35 per minute

Step-by-step explanation:

Rate in terms of unit price is something made in 1 unit (seconds, cups, minutes etc.)

per minute refers to per 1 minute

Answer:

The answer is A 0.35 per minute

Step-by-step explanation: