1.
Find a and b so that the graph of y = ax^2+bx+3 has a relative minimum at (2,1)

Answer:

Step-by-step explanation:

6*68=408

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

48/10=4.8

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

3.8=x/7.7

x=3.8*7.7x

x=29.26

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

x+5.1=13.4

x=13.4-5.1

x=8.3

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

8x=64

x=64/8

x=8

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

22=m+1

m=22-1

m=21

----------

45-4x for x=5

45-4(5)=45-20=25

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

256, 64, 16, 4

Answer:

6*68=408

Step-by-step explanation:

Answer:

8^5

Step-by-step explanation:

8^5

Answer:

C) Profit f(x) of the yogurt company after selling x units is given as :

    f(x)   = 1.03 x - 1850

Step-by-step explanation:

Here, the fixed cost spend by the company  = $1850

Also,cost per yogurt per unit = $0.22

Now, let us assume the total yogurt units sold  = x

So, the total cost for m units  = x ( cost per unit) = x ($0.22) = 0.22 x

SO, the total COST PRICE of company  = Cost of m units +  Fixed cost

                                                                    = $1850 + 0.22 x

Also,selling price of each unit = $1.25

So, the selling price of m units =  x ( per unit selling price) = x ($1.25)

                                                    =  1.25 x

PROFIT = SELLING PRICE - COST PRICE

or f(x)  = 1.25 x  -  $1850 + 0.22 x  

or, f(x)   = 1.03 x - 1850

Hence, the profit f(x) of the yogurt company after selling x units is given as :      f(x)   = 1.03 x - 1850

Answer:

the length of the room = 25 feet

Step-by-step explanation:

Area =W*L

Area = 17*L =425

Divide all by 17

L=25

17*25=425

The length of the room will be 25 feet.

What is mean by Rectangle?

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Given that;

A rectangular living room has an area of 425 square feet the width of the room is 17 feet.

Now,

Let the length of the room = x feet

Since, The area of rectangle = Width x Length

Substitute all the values, we get;

⇒ 425 = 17 × x

⇒ x = 425 / 17

⇒ x = 25

Thus, The length of the room will be 25 feet.

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Answer:

12+4y

Step-by-step explanation:

12+3y+y=12+4y

Answer:

The earning to James per year is $ 39,440

The earning of Lin per year is $ 42,540  .

Step-by-step explanation:

Given as :

The total earning of James and Lin together = $ 81,980 per year

The earning of Lin is $ 3100 more per year than James

Let The earning of James = $ J

And The earning of Lin = $ J + $ 3100

So, According to question

The total earning of James and Lin together = $ 81,980 per year

Or, The earning of Lin +  The earning of James  = $ 81,980 per year

Or,  $ J + $ 3100 + $ J  = $ 81,980 per year

or, 2 $ J = $ 81,980 - $ 3100

Or,  2 $ J = $ 78880

∴ J = [tex]\frac{78880}{2}[/tex]

I.e The earning to James per year = $ 39,440

And  The earning of Lin per year = $ 34,440 + $ 3100 = $ 42,540

Hence, The earning to James per year is $ 39,440

And The earning of Lin per year is $ 42,540  . answer

Answer:

D

Step-by-step explanation:

Straight line (straight angle) is always 180 degrees.

The angle adjacent to 115 and 115 degree angle would sum up to 180 (straight line).

So, that angle would be:

180 - 115 = 65

Now, we know the triangle's 2 angles: 85 (given) and 65 (found), thus we can find the third angle (leftmost):

85 + 65 + third angle = 180 [sum of 3 angles in a triangle is 180]

150 + third angle = 180

third angle = 180 - 150

third angle = 30

This third angle is adjacent to w and forms a straight line, so we can write:

third angle + w  = 180

30 + w = 180

w = 180 - 30

w = 150

Correct answer is D

Answer:

The  number of original students desk were there before the purchase is 980 .  

Step-by-step explanation:

Given as :

The total number of students and teachers new desks to be purchased = 295

The number of teacher's new desk to be purchased = 50

So , The number of student's new desk to be purchased = 295 - 50 = 245

The number of student's new desk to be replaced this year = [tex]\frac{1}{4}[/tex] of the original students desk

Let The number of original students desk were there before the purchase = x

Or, According to question

[tex]\frac{1}{4}[/tex] of x = 245

Or, x = 245 × 4

∴   x = 980

Hence The  number of original students desk were there before the purchase is 980 .  Answer

Answer:

the answer is 1/4 ^10

Step-by-step explanation:

Answer:

$15.40

Step-by-step explanation:

first, let's find the 3/4. to find this, just multiply the decimal form, .75 by the price per pound because then we get the amount for 3/4 pound. that number is $4.20. next, we need to find the 2 pounds by multiplying the price per pound by the 2 pounds, which gets us $11.20. add those together and you get $15.40.

Bella can cut 24 pieces of ribbon from this long strip

Solution:

Given that Bella has 85 feet of ribbons in total

She needs identical strips of ribbon measuring 3.5 feet each

To find: Number of peices of ribbon can she cut from long strip

Number of peices of ribbon can she cut from long strip can be calculated by dividing the total feet of ribbon she has by length of identical strips she needs

Mathematically written as:

[tex]\text { Number of Strip that can be cut }=\frac{\text { Total length of ribbon }}{\text { Length of each piece }}[/tex]

[tex]\begin{array}{l}{\text { Number of Strip that can be cut }=\frac{85}{3.5}} \\\\ {\text { Number of Strip that can be cut }=24.28 \approx 24}\end{array}[/tex]

Hence , the number of strip can be 24 each of size 3.5 feet

Answer:

Step-by-step explanation:

the answer is 14 i already took the test

The answer is A) 14.

Based on the information provided in the table, the number of girls on team B is 31.

The table shows the breakdown of boys and girls on two teams, Team A and Team B, along with the total for each category and the overall total.

Looking at the "Girls" row, we see that a total of 31 girls are represented in the data.

Since the table specifies that this is a "two-way table," implying no other teams or categories beyond Team A and Team B, we can conclude that all 31 girls must be distributed between these two teams.

The "Girls" column further shows that Team A has 17 girls.

Therefore, the remaining 31 girls - 17 girls (Team A) = 14 girls must be on Team B.

Question:

Subash created the two-way table below. Team A  and Team B. Total Boys are 33 and distributed in both the teams, where A has 15 and B has 18 boys. Total Girls are 31, where team A includes 17 girls. Both the teams have total 32 members. According to the table, how much girls were on team B?

A) 14

B) 15

C) 17

D) 18

Answer:

From figure A

The value of ∠ B = 75.74°   ,  ∠ C = 70.26° and  AB = 27.37

From figure B

The value of ∠ A = 42.8°   ,  ∠ B = 106.2° and  AC = 30.04

Step-by-step explanation:

Given first figure as :

AC = 28.2

BC = 16.5

∠ A = 34°

Let AB = c

From law of sines

[tex]\dfrac{a}{Sin A}[/tex] = [tex]\dfrac{b}{Sin B}[/tex] = [tex]\dfrac{c}{Sin C}[/tex]

Or, [tex]\dfrac{a}{Sin A}[/tex] = [tex]\dfrac{b}{Sin B}[/tex]

or, [tex]\dfrac{16.5}{Sin 34}[/tex] = [tex]\dfrac{28.2}{Sin B}[/tex]

Or,  29.506 =  [tex]\dfrac{28.2}{Sin B}[/tex]

Or, Sin B =  [tex]\dfrac{28.2}{29.5}[/tex]  

Or, Sin B = 0.955

∴  ∠B = [tex]Sin^{-1}[/tex] 0.955

I.e∠ B = 75.74

Now, ∠ C = 180° - ( ∠A + ∠B )

Or, ∠ C = 180° - ( 34° + 75.74° )

Or, ∠ C = 70.26°

Now, Again

[tex]\dfrac{b}{Sin B}[/tex] = [tex]\dfrac{c}{Sin C}[/tex]

so,  [tex]\dfrac{28.2}{Sin 75.74}[/tex] = [tex]\dfrac{c}{Sin 70.26}[/tex]

Or,   [tex]\dfrac{28.2}{0.9691}[/tex] = [tex]\dfrac{c}{0.9412}[/tex]

Or, c = 29.09 × 0.9412

∴    c = 27.37

I.e AB = 27.37

Hence,  The value of ∠ B = 75.74°   ,  ∠ C = 70.26° and  AB = 27.37

From figure second

Given as :

AB = c= 12

BC = a = 16

∠ C = 31°

let AC = b

From law of sines

[tex]\dfrac{a}{Sin A}[/tex] = [tex]\dfrac{b}{Sin B}[/tex] = [tex]\dfrac{c}{Sin C}[/tex]

Or, [tex]\dfrac{a}{SinA }[/tex] = [tex]\dfrac{c}{Sin C}[/tex]

or,  [tex]\dfrac{16}{Sin A}[/tex] = [tex]\dfrac{12}{Sin 31}[/tex]

or,  [tex]\dfrac{16}{Sin A}[/tex] = [tex]\dfrac{12}{0.51}[/tex]

Or, [tex]\dfrac{16}{Sin A}[/tex] = 23.52

∴ Sin A = [tex]\dfrac{16}{23.52}[/tex]

I.e Sin A = 0.68

Or,  ∠ A = [tex]Sin^{-1}[/tex] 0.68

or,  ∠ A = 42.8°

Now,  ∠ B = 180° - ( 31° + 42.8° )

Or,  ∠ B = 106.2°

Now,  [tex]\dfrac{b}{Sin B}[/tex] = [tex]\dfrac{c}{Sin C}[/tex]

or,  [tex]\dfrac{b}{Sin 106.2}[/tex] = [tex]\dfrac{16}{Sin 31}[/tex]

Or, [tex]\dfrac{b}{0.96}[/tex] = [tex]\dfrac{16}{0.51}[/tex]

or, b = 31.3×0.96

∴ b = 30.04

Hence The value of ∠ A = 42.8°   ,  ∠ B = 106.2° and  AC = 30.04

Answer

If the side lengths of rectangle B are proportional to the side lengths of rectangle A, the possible side lengths of rectangle B, with a ratio of 2, could be 12 cm and 7 cm.

If the side lengths of rectangle B are proportional to the side lengths of rectangle A, it means that the corresponding sides are in the same ratio. The ratio of the side lengths of rectangle B to rectangle A can be expressed as:

Ratio = Side length of B / Side length of A

In this case, you are given the side lengths of rectangle A as 6 cm and 3.5 cm. Let's find the ratio:

Ratio = Side length of B / Side length of A

Now, you can choose any common multiple to scale up the ratio. For example, you could multiply both sides by 2 to get a simpler ratio.

New Ratio = 2 * (Side length of B / Side length of A)

Now apply this ratio to the side lengths of rectangle A to find the corresponding side lengths of rectangle B:

Side length of B = 2 * Side length of A

Side length of B = 2 * 6 cm

Side length of B = 12 cm

Similarly, Side length of B = 2 * 3.5 cm

Side length of B = 7 cm

So, the possible side lengths of rectangle B, if they are proportional to rectangle A with a ratio of 2, could be 12 cm and 7 cm.

Answer:

2x^2-5x+13

Step-by-step explanation:

(4x^2-3x+8)-(2x^2+2x-5)

4x^2-2x^2-3x-2x+8-(-5)

2x^2-5x+8+5

2x^2-5x+13

A nationwide sample of people ages 18 to 25. This option provides a broader representation of the population, ensuring a more comprehensive understanding of young adults' opinions on video games. The correct choice of option is A.

Option A provides a broader representation of the population as it includes individuals from across the country, capturing a diverse range of demographics, backgrounds, and gaming habits. This sample is more likely to reflect the general attitudes and behaviors towards video games among young adults in the country.

Options B, C, and D are less likely to generalize to Matt's population of interest as they target specific subsets of individuals who may have a higher propensity for gaming or different gaming preferences, potentially biasing the survey results.

Option E, while focusing on the correct age range, is limited to Matt's hometown and may not represent the broader population's opinions and behaviors towards video games.

Therefore, option A, a nationwide sample of people ages 18 to 25, is the most likely to generalize to Matt's population of interest.

Question:-

Matt wants to investigate the opinions of young adults in the country, ages 18 years to 25 years, about time spent playing video games. He plans to administer a survey to a sample of people. Which of the following samples is most likely to generalize to his population of interest?

A)A nationwide sample of people ages 18 to 25.

B) A sample of attendees of a gaming convention

c) A sample of people who click on a link in an online gaming site

D) A sample of people who buy video games from an online store

E) A sample of people ages 18 to 25 in Matt's hometown

Based on the analysis above, the most likely sample to generalize to Matt's population of interest is: A nationwide sample of people ages 18 to 25

The correct option is (a).

To determine which sample is most likely to generalize to Matt's population of interest (young adults aged 18 to 25), let's analyze each option:

a. A nationwide sample of people ages 18 to 25:

  This option covers a broad range of young adults across the entire country, which increases the likelihood of representing Matt's population of interest. However, it may still include individuals who do not play video games, as well as those who play video games excessively. Overall, this sample is more likely to generalize to Matt's population compared to options c, d, and e.

b. A sample of attendees of a gaming convention:

  This option would likely include individuals who are particularly interested in gaming, which may not be representative of all young adults aged 18 to 25. Attendees of a gaming convention may have different gaming habits compared to the general population of young adults, making this sample less likely to generalize to Matt's population of interest.

c. A sample of people ages 18 to 25 in Matt’s hometown:

  While this sample may be convenient for Matt to access, it is limited to individuals in his hometown and may not be representative of young adults nationwide. Additionally, individuals in Matt's hometown may have different demographics and gaming habits compared to the entire population of young adults aged 18 to 25.

d. A sample of people who click on a link in an online gaming site:

  This sample is likely biased towards individuals who are already interested in gaming, as they are visiting an online gaming site. Therefore, it may not represent the entire population of young adults aged 18 to 25, especially those who do not regularly visit gaming sites.

e. A sample of people who buy video games from an online store:

  Similar to option d, this sample is biased towards individuals who are interested in video games, as they are purchasing video games from an online store. Therefore, it may not represent the entire population of young adults aged 18 to 25.

Based on the analysis above, the most likely sample to generalize to Matt's population of interest is:

a. A nationwide sample of people ages 18 to 25

complete question given below:

Matt wants to investigate the opinions of young adults in the country, ages 18 years to 25 years, about time spent playing video games. He plans to administer a survey to a sample of people. Which of the following samples is most likely to generalize to his population of interest?

a. A nationwide sample of people ages 18 to 25

b. A sample of attendees of a gaming convention

c. A sample of people ages 18 to 25 in Matt’s hometown

d. A sample of people who click on a link in an online gaming site

e. A sample of people who buy video games from an online store

Answer:

y = 2x-3

Step-by-step explanation:

y-17=2(x-10)

distribute 2 ---> y-17= 2x-20

add 17 to both sides ---> y=2x-3

The equation of the given line will be [tex]y =2x - 3[/tex]

If the slope of a line is m and the y-intercept is c, then the equation of that straight line is given as: [tex]y = mx+c[/tex]

Since given line has slope = 2, thus its equation will be: [tex]y = 2x + c[/tex]

The other data about the straight line will help us find the value of c.

Since the line passes through (10,17) coordinate, thus this must satisfy the equation. Putting x = 10, and y = 17 will give us:

[tex]y = 2x + c\\17 = 2 \times 10 + c\\17 = 20 + c\\c = 17 - 20 = -3[/tex]

Thus, the value o y-intercept = c = -3

Thus, the equation of considered straight line is  [tex]y =2x - 3[/tex]

The graph of this equation is given below.

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Answer:

Length = 17, Width = 6

Step-by-step explanation:

Let the length be L and width be W.

L = 3W - 1 , and,

2(L + W) = 46 => L+W = 23  => L = 23 - W, putting this into L = 3W - 1

23 - W = 3W - 1

24 = 4W

W = 6

therefore, L = 23 - W = 17

Answer:

55 degrees

Step-by-step explanation:

So to figure this out, you need to know what a complementary angle is. A complementary angle is a 90 degree angle.

Now you know what a complementary angle is, all you have to do is 90-35 to find the remaining angle.

90-35=55

The answer is 55 degrees

Answer:

x-int = 18

y-int = -9/2

Step-by-step explanation:

Use slope-intercept form y=mx + b

To find the slope, substitute the two points into the slope formula and solve.

[tex]m  = \frac{y2 - y1}{x1 - x1} \\m  = \frac{-4 - (-6)}{2 - (-6)} \\m = \frac{2}{8}\\m= \frac{1}{4}[/tex]

Substitute a random point (2,-4) and m=1/4 into slope-intercept form

y = mx+b

-4 = 1/4 (2) + b

-4 = 2/4 + b

-4 = 1/2 + b

Isolate b to solve

b = -4 - 1/2

b = -8/2 - 1/2

b = -9/2    <= this is the y-intercept

b is the y-intercept in slope-intercept form

Substitute b= -9/2 and m=1/4 to get the equation of the line.

y = 1/4 x - 9/2

Substitute y for 0 to find the x intercept

y = 1/4 x - 9/2

0 = 1/4 x - 9/2

9/2 = 1/4 x

x = (9/2) / (1/4)

x = (9/2) X (4/1)

x = 36/2

x = 18

Answer:

5×4=20

Step-by-step explanation:

5 blocks across multiplied by the 4 blocks down equals 20 blocks all together

Answer:

-15

Step-by-step explanation:

x-1/2(x+5)=-10

x-1/2x-5/2=-10

2/2x-1/2x-5/2=-10

1/2x-5/2=-10

1/2x=-10+5/2

1/2x=-20/2+5/2

1/2x=-15/2

x=(-15/2)/(1/2)

x=(-15/2)(2/1)

x=-15/1

x=-15

Answer:

-1 is the answer

Step-by-step explanation:

4+(-5)= -1

Britt will earn more interest after three years due to the compound interest on her account, totaling $788.13 compared to Adam's $750 from simple interest, resulting in a difference of $38.13. The key distinction lies in the interest calculation: Adam's remains constant, while Britt's increases each year due to the compounding effect.

The question involves calculating and comparing simple and compound interest earned on two separate $5,000 deposits over a period of three years at an annual interest rate of 5%.

Adam's account earns simple interest, meaning the interest each year is calculated using the original principal of $5,000, resulting in $250 of interest per year, totaling $750 after three years.

Britt's account, however, earns compound interest, with each year's interest calculated on the growing balance from the previous year.

As we can see from the tables, Britt's first year interest is the same as Adam's ($250), but it increases each subsequent year because it's calculated on the new principal (original plus accumulated interest).

After three years, Britt's total interest is $788.13, earning more interest than Adam's $750. The difference in the total interest earned after three years between Britt (compound interest) and Adam (simple interest) is $38.13.

The main difference in how interest is calculated between Britt and Adam's accounts is that Adam's interest is consistently $250 each year (calculated as $5,000 x 0.05),

while Britt's interest increases each year, demonstrating the effect of compound interest.

By Year 3, Britt earns $275.63 in interest compared to Adam's unchanged $250.

Average rate of temperature loss is 6.4 degrees per minute

Step-by-step explanation:

Given

Temperature =T =  80 degrees

Time = t = 12.5 min

In order to find the temperature decrease in one minute, Total decrease in temperature will be divided by time

[tex]Average\ rate\ of\ temp\ loss = \frac{80}{12.5}\\= 6.4\ degrees\ per\ minute[/tex]

Hence,

Average rate of temperature loss is 6.4 degrees per minute

Keywords: Rate of change, Average

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Answer:

A ) The selling price of radio is $ 81.64

B ) The selling price of microscope is $ 72.94

Step-by-step explanation:

Given as :

A ) Market price of radio = M.P = $ 125.60

Let The selling price of radio = S.P =  $ x

The discount = 35 %

So, Discount %  = [tex]\dfrac{M.P - S.P}{M.P}[/tex]

Or, [tex]\frac{35}{100}[/tex] = [tex]\dfrac{125.60 - x}{125.60}[/tex]

Or, [tex]\frac{x}{125.60}[/tex] = 1 - [tex]\frac{35}{100}[/tex]

Or,  [tex]\frac{x}{125.60}[/tex] =  [tex]\frac{100-35}{100}[/tex]

Or,  [tex]\frac{x}{125.60}[/tex] =  [tex]\frac{65}{100}[/tex]

∴  x = [tex]\frac{125.60\times 65}{100}[/tex]

I.e  x = $ 81.64

So, The selling price of radio is $ 81.64

B ) The market price of microscope = M.P = $ 96.25

    The discount = 20 %

    Tax percentage = 6 %

Let the selling price of microscope = $ y

Now, So, Discount %  = [tex]\dfrac{M.P - S.P}{M.P}[/tex]

Or, [tex]\frac{20}{100}[/tex] = [tex]\dfrac{96.25 - y}{96.25}[/tex]

Or, [tex]\frac{y}{96.25}[/tex] = 1 - [tex]\frac{20}{100}[/tex]

Or,  [tex]\frac{y}{96.25}[/tex] =  [tex]\frac{100-20}{100}[/tex]

Or,  [tex]\frac{y}{96.25}[/tex] =  [tex]\frac{80}{100}[/tex]

∴  y = [tex]\frac{96.25\times 80}{100}[/tex]

I,e y = $ 77

Again Tax of 6% is added

So , $ 77 - 6 % of $ 77

Or, $ 77 × 0.94 = $ 72.38

∴ The final cost of microscope after discount and tax is $ 72.94

Hence A ) The selling price of radio is $ 81.64

And     B ) The selling price of microscope is $ 72.94   Answer

Answer:

Negative

Step-by-step explanation:

Answer:

x=-2+sqrt(7)*i, -2-sqrt(7)*i

Step-by-step explanation:

x^2+4x=-11

x^2+4x-(-11)=0

x^2+4x+11=0

Apply the quadratic formula with a=1, b=4 and c=11.