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The function h(x) is vertically stretched by a factor of [tex]\frac{1}{2}[/tex] and is shifted 3 units to the left and shifted 2 units up.

Explanation:

The parent function is [tex]f(x)=x^{2}[/tex]

The translated function is [tex]h(x)=\frac{1}{2}(x+3)^{2}+2[/tex]

By using the function transformation rules, the translated function h(x) is stretched vertically by a factor of [tex]\frac{1}{2}[/tex]

Also, from the function transformation rules, we know that,  [tex]$f(x+b)$[/tex] shifts the function b units to the left.

Thus, the translated function h(x) is shifted 3 units to the left.

By using the function transformation rules, we know that,  [tex]$f(x)+b$[/tex] shifts the function b units upward.

Thus, the translated function h(x) is shifted 2 units upwards.

Thus, the translated function h(x) is vertically stretched by a factor of [tex]\frac{1}{2}[/tex] and is shifted 3 units to the left and shifted 2 units up.

Final answer:

To find the new temperature of the soup after cooling for 25 minutes, multiply the rate of decrease, 2.3 F/min, by 25 minutes to find the total decrease in temperature, which is 57.5 F. Then subtract this from the initial temperature of 192.7 F to get the final temperature of 135.2 F.

Explanation:

The question is about calculating the new temperature of chicken soup after it cools for a certain period. The initial temperature of the soup is 192.7 F, and it's stated that the soup temperature decreases by 2.3 degrees per minute. Since it's asking for the temperature after 25 minutes, we need to multiply the rate of cooling by the number of minutes.

To calculate the new temperature:
Decrease in temperature = 2.3 F/min × 25 min = 57.5 F

The new temperature would then be:
Initial temperature - Decrease in temperature = 192.7 F - 57.5 F = 135.2 F.

Problem Solving Strategies for the Effects of Heat Transfer

Although the question does not require complex problem-solving strategies involving specific heat capacity or mass of the substance, it does simulate a simplified version of heat transfer where we only consider the overall change in temperature over time.

Answer:

4%

Step-by-step explanation:

To solve this problem we can use a modified version of the simple interest formula which is shown below:

[tex]r=\frac{I}{Pt}[/tex]

I = interest amount

P = principal amount

t = time (years)

Lets plug in the values:

[tex]r=\frac{480}{(6,000)(2)}[/tex]

[tex]r=0.04[/tex]

The last step is to convert 0.04 into a percent:

0.04(100) = 4

The interest rate is 4%.

Answer:

{x| x < 10 and x > 14} is an empty set.

there cannot be any intersection between the two ranges that is , x< 10 and x>14.

Step-by-step explanation:

x < 10 and x > 14 will lead to an empty set.

there cannot be any intersection between the two ranges that is , x< 10 and x>14.

Final answer:

The set with condition { | < 10 and > 14} is the empty set, as no elements can satisfy being both less than 10 and greater than 14 simultaneously.

Explanation:

The set being asked about is defined as { | < 10 and > 14}.

To determine if this set is the empty set, interpret the conditions placed upon the members of the set.

The description says that an element must be both less than 10 and greater than 14 at the same time, which is an impossible condition. Since no number can satisfy both conditions simultaneously, no elements can exist within this set, making it the empty set, often denoted by Ø.

Answer:

Height = 16.4 inches

Step-by-step explanation:

V = Length*Width*Height, so solving for the Height by dividing the Volume with the product of the Length and Width gives:

Height = Volume/Length*Width = 7193.45/(30.25*14.5) = 16.4 inches

Answer:

a = 58

b = 34

Step-by-step explanation:

a + b = 92

a - b = 24

add

a + b + a - b = 92 + 24

2a = 116

a = 116 : 2

a = 58

b = 92 - 58

b = 34

Answer:

Step-by-step explanation:

Let the numbers be x and y

x + y = 92..........(1)

x - y = 24..........(2)

Adding (1) and (2)

2x = 116

x = 116/2

x = 58

From (1)... x + y = 92

58 + y = 92

y = 92 - 58

y = 34

Answer:

The cross section would be a square.

Step-by-step explanation:

The 2 ends of the rectangular prism are squares while the other 4 sides are rectangles. A cross section would be perpendicular to the rectangles, making the cross section a square. The cross section would be parallel to the end squares.

[tex]A = 100\pi cm^{2}[/tex]

Step-by-step explanation:

Given that an engineer is planning to install a new water pipe.

The diameter of the circular pipe is

d = 20 cm

Let us find the radius (r)

radius = diameter / 2

r = 20 / 2 = 10 cm

The area of circle (A) is given as:

[tex]A = \pi r^{2}[/tex]

[tex]A = \pi 10^{2}[/tex]

[tex]A = 100\pi cm^{2}[/tex]

Answer 4.6

Step-by-step explanation:

1. How much interest will Sara owe?

She will owe 5,966 dollars

2. How much will the payments be with a seven year agreement?

Sara will pay 21,666 dollars

The simple interest formula is as follows:

[tex]A=P(1+rt) \\ \\ \\ Where: \\ \\ A: \ is \ the \ Final \ Investment \Value \\ \\ P: \ is \ the \ Principal \ amount \ of \ money \ to \ be \ invested \\ \\ r: \ is \ the \ rate \ of \ interest \\ \\ t: \ is \ \ Number \ of \ Time \ Periods[/tex]

First, converting r percent to r a decimal

[tex]r = (5 \frac{3}{7})\%=(5+\frac{3}{7}))\%=\frac{38}{7}\% \\ \\ r=\frac{38/7}{100}=\frac{19}{350} \ per \ year[/tex]

Solving our equation:

[tex]A=15700 (1+\frac{19}{350}\times 7) \\ \\ A=15700(\frac{69}{50}) \\ \\ \boxed{A=\$21,666}[/tex]

So Sara will owe in interest the following amount of money:

[tex]I:Interest \\ \\ \\ I=21,666-15,700 \\ \\ \boxed{I=\$5,966}[/tex]

Finally, answering the questions:

1. How much interest will Sara owe?

She will owe 5,966 dollars

2. How much will the payments be with a seven year agreement?

Sara will pay 21,666 dollars

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The value of expression is 63 when e = 4 and g = 6

Solution:

Given expression is:

[tex]5e^2-4g+7[/tex]

We have to solve the expression

Given that e = 4 and g = 6

Substitute e = 4 and g = 6 in given expression

[tex]\rightarrow 5(4)^2 -4(6) + 7\\\\Simplify\ the\ above\ equation\\\\\rightarrow 5(16) -24 + 7\\\\\rightarrow 80-24+7\\\\Simplify\\\\\rightarrow 56+7=63[/tex]

Thus value of expression is 63

Answer:

A 2-column table has 4 rows. The first column is labeled x with entries 1, 2, 3, 4. The second column is labeled y with entries 2, 4, 8, 16.

Step-by-step explanation:

Let an exponential growth function is given by [tex]f(x) = a(b)^{x}[/tex]

So, [tex]f(1) = a(b)^{1}[/tex], [tex]f(2) = a(b)^{2}[/tex], [tex]f(x) = a(b)^{3}[/tex] and [tex]f(4) = a(b)^{4}[/tex]

Therefore, this series of values corresponding to the x-value 1, 2, 3, and 4 are in G.P. and the common ratio is b.

Now, from the given tables in the options only the second option i.e. a 2-column table has 4 rows. The first column is labeled x with entries 1, 2, 3, 4. The second column is labeled y with entries 2, 4, 8, 16 satisfies an exponential function.

Since, f(1) = 2, f(2) = 4, f(3) = 8 and f(4) = 16 are in G.P.(Answer)

Answer:

2

Step-by-step explanation:

Answer:

3.6

Step-by-step explanation:

3y+2/5=-1/5

3y=-1/5-2/5

3y=-0.6

0.6/3=y

-3.6=y

y=-3.6

Answer:

i) number of transactions for the month of January = 4

 number of transactions for the month of February = 4

 number of transactions for the month of March = 4

 number of transactions for the month of April = 4

ii) Mean of four months  = -495.7 /4 = -123.93

Step-by-step explanation:

i) number of transactions for the month of January = 4

 number of transactions for the month of February = 4

 number of transactions for the month of March = 4

 number of transactions for the month of April = 4

ii)     January              February              March            April

         -38.50                 250.00               -14.00           -86.80

         126.30                -135.20                 99.00          -570.00

         429.40                  35.50                -82.70           100.00

        -265.00                 -62.30                 -1.50           -280.10

Total  252.20                  88.20                 0.80            -836.9

Total of four months  = 252.2 + 88.20 + 0.80 - 836.9  =  -495.7

Mean of four months  = -495.7 /4 = -123.93

Answer:

1) number of transactions for the month of January = 252.20

number of transactions for the month of February = 88.00

number of transactions for the month of March = 1.70

number of transactions for the month of April = -836.90

2. mean total of the four months -123.93

Step-by-step explanation:

Step-by-step explanation:

Answer:

Step-by-step explanation:

6 ×12=72 rounded to the nearest tenth 5 or more add one more 4 or less let it rest

72 it would be 70 because 2 is not more than 5

_

Answer:

35

Step-by-step explanation:

7 x 7 = 35

Answer:

6

Step-by-step explanation:

27/4= 6 3/4

That doesn't work because we need whole numbers.

24/4=6

That is the solution. For $24 we buy 6 tubes for $4 each and we have $3 left over.

Answer:

6

Step-by-step explanation:

each tube of paint(one) = $ 4

(x) tube of paint = $ 27

Therefore,

x= (27/4)

 = 6.75 tubes ; which is equivalent to 6 whole tube of paint

The commission would be $2095.

Step-by-step explanation:

Given,

Commission on first $1000 = 7%

Amount of commission = 0.07*1000 = $70

Worth of sold items = $14,500

We will subtract $1000 from it.

Balance = 14500-1000 = $13500

Commission on balance = 15% = 0.15

Amount of commission = 0.15*13500

Amount of commission = $2025

Total commission = 70+2025 = $2095

The commission would be $2095.

Keywords: percentage, subtraction

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McKenzie would earn $2,095 in commission if her sales for the month were $14,500.

To calculate McKenzie's commission, we need to determine the amount of sales that fall under the 7% rate and the amount that falls under the 15% rate. First, we calculate the commission on the first $1,000 in sales: 7% of $1,000 = $70. Next, we calculate the commission on the remaining sales: $14,500 - $1,000 = $13,500. 15% of $13,500 = $2,025.

Finally, we add the two commissions together to get the total commission: $70 + $2,025 = $2,095. So McKenzie would earn $2,095 in commission if her sales for the month were $14,500.

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Answer:

(4x3-6x) + (8x-12)= 2x

(4x3+8x) + (-6x2-12)= 2(2x-3) (x^2+2)

Step-by-step explanation:

All you have to do is simplify.

Answer:

A,B,E

Step-by-step explanation:

Did on edgen

Answer:

1.5

Step-by-step explanation:

divide 1/2 and add 1

Vertex is calculated by -b/2a

So we have -(-5)/2(2)=5/4

The root is determined through the quadratic formula:

x=(-b+sqrt(b^2-4ac))/2a

x=(-(-5)+sqrt(-5^2-4(2)(-604)))/2(2)

x=(5+sqrt(25-4832))/4

x=(5+sqrt(-4807))/4

So the root is some imaginary number

Hope this helped!

Answer:

1 = 2 - 3. is this what you mean?

Answer:

21

Step-by-step explanation:

7x3=21

Answer:21

Step-by-step explanation:

You can get it srry if that was mean

Answer:

404 tickets to adults have been sold .

325 tickets to students have been sold .

Step-by-step explanation:

A system of linear equations is a set of two or more first degree equations, in which two or more variables are related.

In this case, a system of two linear equations with two unknowns is solved.

To assemble the system of equations you must first define the variables, which in this case will be:

On the one hand, you know that 729 tickets were sold, that is to say that tickets sold for students and adults must add 729. Expressed in an equation this is: x+y=729 equation (A)

On the other hand, you know that during a game, $ 2995 was raised for the sale of those 729 tickets. And you also know that tickets for a high school football game cost $ 3 for students and $ 5 for adults.

Then the proceeds from the sale of tickets for students is 3*x and for adults it is 5*y. And your sum must be $ 2995. Expressed in an equation this is:

3*x + 5*y=2995 Equation (B)

So the system of equations is:

[tex]\left \{ {{x+y=729} \atop {3*x+5*y=2995}} \right.[/tex]

There are several methods of solving a system of equations. In that case, the substitution method will be used, which consists of isolating an unknown element in one of the equations, which will be a function of the other unknown. In the other equation that has not been used, the same unknown is replaced by the expression previously obtained. In this case, the value of variable x in equation (A) will be isolated:

x+y=729 ⇒ x=729-y Equation (C)

Replacing this expression in equation (B) you get:

3*(729-y)+5*y=2995

Solving this equation:

3*729-3*y+5*y=2995

2187+2*y=2995

2*y=2995-2187

2*y=808

y=808÷2

y=404

Remembering that "y" is tickets for admission to a high school football game for adults. this indicates that 404 tickets to adults have been sold .

Replacing this value in equation (C), which is the previously isolated equation, you get:

x=729-y

x=729-404

x=325

Remembering that "x" is tickets for admission to a high school football game for students. this indicates that 325 tickets to students have been sold .

By setting up a system of linear equations, it's found that 325 student and 404 adult tickets were sold.

The subject of this question is a linear system, specifically related to the ticket sales at a high school football game. Let's denote 's' as the number of student tickets sold, and 'a' as the number of adult tickets sold. We'll use the following two equations to reflect the given information:

To solve the system of equations, one method is substitution or elimination. Using the elimination method, you could multiply the first equation by 3, getting 3s + 3a = 2187. Then, subtracting this from the second equation gives 2a = 808. Dividing by 2, we find that a = 404. Plugging this value into the first equation gives s = 729 - 404 = 325. Therefore, 325 student tickets and 404 adult tickets were sold.

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Answer:

infinite solutions

Step-by-step explanation:

Answer:

The required equation to the given slope m=-5 and a point (-1,3) is 5x+y+2=0

Step-by-step explanation:

Given that the slope  m=-5 and a point (-1,3)

Now we have to find an equation with the given slope and point :

Let [tex](x_1,y_1)[/tex] be the given point (-1,3)

The slope point formula is [tex]y-y_1=m(x-x_1)[/tex]

y-3=-5(x-(-1))

y-3=-5(x+1)

y-3=-5(x)-5(1) ( by using the distributive property a(x+y)=ax+ay here a=-5,x=x and y=1 )

y-3=-5x-5

y-3-(-5x-5)=-5x-5-(-5x-5) ( by using the distributive property a(x+y)=ax+ay  here a=-1,x=-5x and y=-5)

y-3+5x+5=-5x-5+5x+5

y+2+5x=0

5x+y+2=0 which is the required equation

Answer:

The measure of side AC is 6 cm.

Step-by-step explanation:

The information for the triangle ABC are:

AB = 6 cm

m∠A = 80°

m∠B = 50°

The sum of all angles of a triangle is 180°.

Compute the value of m∠C as follows:

m∠A  + m∠B + m∠C = 180°

m∠C = 180° - 80° - 50°

        = 50°

Thus, the angles, m∠C = m∠B.

Consider the triangle below.

If two angles of a triangle are equal or similar then that triangle is known as an isosceles triangle.

And in an isosceles triangle the sides corresponding to the equal angles are equal.

Then in this case as m∠C = m∠B then sides AC = AB.

The measure of the side AC is 6 cm.

you add them then divide ur answer by 2

Answer: v = 2

Step-by-step explanation:

30-48v+12 = -54

-48v = -54-30-12

[tex]\frac{-48v}{-48}[/tex] = [tex]\frac{-96}{-48}[/tex]

v = 2

Answer:

2

Step-by-step explanation:

6(5−8v)+12=−54

Divide through by 6, we have

5 — 8v + 2 = — 9

Collect like terms

— 8v = —9 — 2 — 5

—8v = — 16

Divide both side by the coefficient of v i.e —8

v = — 16/ —8

v = 2