Solve the radical equation. Be sure to check all solutions to eliminate extraneous solutions. 7t+5−−−−−√=7 Enter the exact answers.

The average cost per minute which the shop runs is $1.50

To find the shop's cost per minute, we can write down equations and proceed to solve.

In the given question, 3 cupcakes cost $6.75 and 5 cupcakes cost $9.75.

But we were not given the average cost per cupcake.

To do that, let's write an equation for this.

[tex]y = mx + c[/tex]

Let's find the slope to this equation which determines the average cost per minute.

[tex]m = \frac{y_2-y_1}{x_2-x_1} \\m = \frac{9.75 - 6.75}{5 - 3} \\m = 1.50[/tex]

The shop's cost per minute was calculated to be $1.50.

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The degree of the power function represented in the table f(x) is 2.

In order to find the degree of the power function represented in the given table, you must find the difference of the y-values.

The second difference is illustrated as:

2 - 6 = -4.

-2 - 2 = -4

-6 - (-2) = -4

This illustrates that the second differences are constant.

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What is the degree of the power function represented in the table?

1

2

3

4

x h(x)

−2 −8

−1 −2

0 0

1 −2

2 −8

Select all expressions that are equivalent to (2n + 6)(n + 3)

we have

(2n + 6)(n + 3)

apply distributive property

2n^2+6n+6n+18

2n^2+12n+18

Verify each option

option A

2(n^2 + 6n +9)=2n^2+12n+18 -------> is ok

option B

is not correct

option C

is correct

option D

is not correct

option E

2(n + 3)(n + 3)= (2n + 6)(n + 3) ------> is correct

option F

2(n + 3)^2=2(n^2+6n+9)=2n^2+12n+18 -----> is ok

therefore

From the frequency bar graph, we can read the following information.

15 students got an A

6 students got a B

5 students got a C

10 students got a D

14 students got an F

a) As described above, 5 students got a C

b) Adding up the frequencies of the students who got C or higher:

5 + 6 + 15 = 26

26 students passed the course

c) Assuming the students who did not pass got any credits, then we add up the students with D and F: 10 + 14 = 24

24 students received no credit for the course

d) Total students in the course: 15 + 6 + 5 + 10 + 14 = 50

e) The mode is the letter grade that got the highest frequency:

Mode = A

A got 15

The coat of the dress based on the percentage is $66.

From the information, it was stated that Tonya spends 55% of her savings on a new dress and that she saved $120.

Let the cost of the dress be represented as x

Therefore, the appropriate information given I'll be expressed as:

= 55% × 120 = x

0.55 × 120 = x

Multiply

x = 66

The amount spent is $66.

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(4x -2) yd, 2x yd, 2(x + 7) yd, 2.5x yd. The triangle's perimeter is the same as the square's perimeter. The value of x=6

Given that,

The graphic displays the yards-long sides of a triangle and a square. The triangle's perimeter is the same as the square's perimeter.

We have to find the value of x in the given side.

In the picture we can see the triangle and square.

The perimeter of the triangle is sum of the three sides of the triangle.

The perimeter of the square is 4 times the side of the square.

4x-2+2x+2(x+7)=4×2.5x

4x-2+2x+2x+14=10x

8x+12=10x

10x-8x=12

2x=12

x=12/2

x=6

Therefore, the value of x=6

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The mass of 21,000 molecules of oxygen in scientific notation is expressed as 1.1151 x [tex]10^{-28}[/tex] grams in the proper significant digits.

The number that is provided as digits is tried and established using significant figures. A meaningful representation of numbers is carried by these digits.

The crucial or important digits that can accurately represent the exact meaning of a certain number are known as the significant figures of that number.

Frequently, significant digits are employed in place of figures. By counting out each of the values beginning with the first non-zero digit on the left, we can use it to determine the number of significant digits.

The molecular mass of Oxygen is seen as 32 grams.

So, 6.023 x [tex]10^{23}[/tex] molecules of oxygen have mass as 32 grams

So, one molecule of oxygen has mass = [tex]\frac{32}{6.023 * 10^{23}}[/tex] grams

= 5.31 x [tex]10^{-23}\\[/tex] grams

So, 21,000 molecules will have mass = 21,000 x 5.31 x [tex]10^{-23}\\[/tex] grams

= 111510 x [tex]10^{-23}\\[/tex] grams

= 1.1151 x [tex]10^{-28}[/tex] grams

Thus 21000 molecules of oxygen have a mass of 1.1151 x [tex]10^{-28}[/tex] grams.

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If we start with the parent function f(x) = cot(x), the transformation needed to go from this function to cot(x + π/6) is expressed as:

That is, we need to make a shift of π/6 units to the left, beginning with the cot(x) graph. The graph of cot(x + π/6) is:

Given -

Money deposited in an account = $3,100

Interest rate = 2.5% compounded quarterly

Time = 5 years

To Find -

The final amount of money =?

Step-by-Step Explanation -

As we know there are 4 quarters in a year.

So,

In five years, there are 20 quarters.

On applying the formula:

Final Amount =

Final Answer -

The final amount of money = $3511.4

The expected value of the proposition is $22.6

The given parameters are

Represent the proportion as a fraction

So, we have

p = 359/449

The expected value is then calculated as

E(x) = p * Amount paid for making a throw - (1 - p) * Amount collected for losing a throw

Where p represents the proportion defined above

So, we have

E(x) = 359/449 * 39 - (1 - 359/449) * 43

Evaluate the difference

E(x) = 359/449 * 39 - 90/449 * 43

So, we have

E(x) = 22.6

Hence, the proposition has an expected value of $22.6

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Answer:

-1.09

The problem requires one to calculate the win payoff and win probability as well as the lose payoff and probability. You would then do a calculation like this:

[(Win Payoff) x (Win Probability)] + [(Lose Payoff) x (Lose Probability)]

Formula for the trigonometry is y = b sin ( πx/2 - π/2) + 4

y = A sin( ωx + δ) + b

period: t = 4

ω = 2π/t = 2π/4 = π/2

A = 10 -(-2)/ 2

  = 6

b = (10-2)/2

  = 4

y = b sin (πx/2 + δ) + 4

x = 0, y = bsinδ + 4 = -2

sinδ = -1   => δ = -π/2

y = b sin( πx/2 - π/2) + 4

Therefore the formula for the trigonometry function is y = b sin(πx/2 - π/2) + 4.

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Jenna bought a coat on sale for $120

The price of the coat is the 2/3of the original price

Let the original price is $x

So, the equation will be :

2/3 of x =120

So, The original price of the coat is $180

The factor by which the current changes if the resistance increases 10% is; 90.9% reduction

Ohm's law states that the electrical current (I) flowing in a circuit is directly proportional to the voltage (V) and inversely proportional to the resistance(R). Therefore, if the voltage is increased, the current will increase provided the resistance of the circuit does not change. Thus;

I = V/R

Now, we are told that the resistance increases by 10%.

Thus, New value of resistance = 1.1R

Thus, new current/old current = 1/1.1 = 0.909 = 90.9%

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The measure of the fourth angle that is x and the value is 133°

A regular octagon will have all its sides equal in length. Each interior angle of a regular octagon is equal to 135°. Therefore, the measure of exterior angle becomes 180° – 135° = 45°. The sum of the interior angles of the octagon is 135 × 8 = 1080°.

Let the 8 interior angles of the octagon be:

x-12, x-8, x-4, x, x+4, x+8, x+12, x+16.

Their sum = 8x+16 = 1080, or

this implies 8x = 1080–16 = 1064  

thus on further solving we get x = 133

Hence the sixth angle = x+8 =141 degrees.

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given: 100 cm = 1 meters

We need to convert 4 m to cm

so,

Solution

- To divide by a fraction, you simply invert the fraction and instead multiply by the inverted fraction.

- Thus, we have:

Answer: y = -2x + 5

Step-by-step explanation:

y = _x + 5

(5,0) (3,4)

(y2 - y1) / (x2 - x1)

(4 - 0 ) / (3 -5)

4 / -2

-2

y = -2x + 5

Answer:

26 centilitres.

Explanation:

First, we start by recalling the standard conversion between millilitres and centilitres.

Let 260 milliliters = x centiliters

We express it as a ratio:

Cross multiply to solve for x:

Therefore, 260 millilitres is 26 centiliters.

Every line through the center of a circle forms a line of reflection symmetry, and every angle has rotational symmetry around the center. The areas are 123.83 [tex]m^{2}[/tex] and[tex]209.07m^{2}[/tex]

The form having the greatest surface area for a given perimeter is a circle.

Every line through the center of a circle forms a line of reflection symmetry, and every angle has rotational symmetry around the center. The orthogonal group O is the symmetry group of it (2,R). Circle group T is the collection of rotations alone.

A distinct circle can be found through any three locations that are not all on the same line. It is feasible to express explicitly equations for the coordinates of the circle's center and radius in terms of the coordinates of the three specified points in Cartesian coordinates.

Circumference= [tex]2\pi r[/tex]= 220 and 286

[tex]2\pi r[/tex]= 220

2*3.14*r=220

r= 220/35.03= 6.28

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

     = 3.14*6.28*6.28

     = 123.83[tex]m^{2}[/tex]

[tex]2\pi r[/tex]= 286

2*3.14*r= 286

r= 286/35.03 = 8.16

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

      = 209.07[tex]m^{2}[/tex]

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The general form of a quadratic equation is given by the expression:

A quadratic equation having a maximum value or point is one that has its value of a to be lesser than zero

(a < 0). Such a graph opens downwards

Therefore, any quadratic equation that has the a-value to be lesser than zero has a maximum point

Mathematically expressed as:

Mina must have planned to read 8 pages everyday.

To accomodate reading in her everyday life, without spending extra time and not disturbing other activities, Mina should read particular number of pages everyday. These pages should be enough to be completed in 7 days.

So, relating the number of pages and days -

Number of pages to be read each day = total number of pages ÷ number of days

Keep the values in relation -

Number of pages to be read each day = 56 ÷ 7

Performing division

Number of pages to be read each day = 8

Thus, to return the book on time Mina should have planned to read 8 pages everyday.

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The level of water decreases would be 21 inches in 6 weeks if the water level of a lake decreases by 3 inches every week.

The addition, subtraction, division, and multiplication of built-in functions can also be used to specify arithmetic operations. The term "arithmetic operator" refers to the operator that executes the calculation.

We have been given that a lake's water level decreases 3 inches every week when there is a drought.

We have to determine the lake's water level looks like after a seven-week drought.

As per the given condition,

Level of water decreases a week = 3 inches.

Level of water decreases in 6 weeks = 7 × 3 = 21 inches

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Hello!

First, let's rewrite the expression here:

We will have to find the coefficients a, b and c:

• a ,= -2;

• b ,= 12;

• c ,= -15;

As we can see, coefficient a is negative. It means that the parabola will face downwards and have a maximum value.

We can obtain this point by using the two formulas below to calculate the coordinates (x, y) of this point, look:

As we know the coefficients, let's replace the values in the formulas:

Xv:

Now let's find Yv:

Doing this, we obtained the coordinate of the maximum point (x, y) = (3, 3).

As it doesn't have any restrictions, the domain will be: [-∞, +∞].

The maximum value will be when y = 3, so the range is [-∞, 3].

Look at the graph of this function below:

Answer: y = -3/2x - 1

Step-by-step explanation:

y = mx + b

1. m is the slope so substitute -3/2 for m. ( y = -3/2x + b)

2. b is the y intercept so substitute -1 in for b. ( y = -3/2x - 1)

There are two shiftments, 1 to the side along the x-axis and 1 vertical along the y-axis

Horizontal shifts:

Vertical shifts

Since the x is substracted 4 units, it means that the graph is translated 4 units to the right.

Since the function is completely added 1 unit its means that all the graph is shifted 1 unit up.

If Montraie is going to invest in an account paying an interest rate of 4.6% compounded annually, then she has to invest $820.06 for the value of the account to reach $1610 in 15 years

The interest rate = 4.6%

The final amount = $1610

The time period = 15 years

The compound interest

A = [tex]P(1+\frac{r}{100})^{t}[/tex]

Where A is the final amount

P is the principal amount

r = interest rate

t is the time period

Substitute the values in the equation

1610 = [tex]P(1+\frac{4.6}{100})^{15}[/tex]

1610 = P×1.96

P = 1610/1.96

P = $820.06

Hence, if Montraie is going to invest in an account paying an interest rate of 4.6% compounded annually, then she has to invest $820.06 for the value of the account to reach $1610 in 15 years

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The area of the given figure ABCDEFG is 28 units².

So, the area of the given figure:

Now, calculate areas separately and as as follows:

Area of square ECBD:

The area of square ECBD is 16 units².

Area of triangle ACB:

The area of triangle ACB is 6 units².

Area of triangle CEG:

The area of triangle CEG is 4 units².

Area of triangle BDF:

The area of triangle BDF is 2 units².

Area of the given figure: 16 + 6 + 4 + 2 = 28 units²

Therefore, the area of the given figure ABCDEFG is 28 units².

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Given the graph, we cam find f(-3)+g(-2) below.

Explanation

Answer: -2