What is the solution set of √
x + 7 − 1 = x?

Answer:

Step-by-step explanation:

Let x be the original price of the television set.

The sale price is 28% off the original price, which means that the sale price is equal to 100% - 28% = 72% of the original price.

So we can write an equation based on this information:

0.72x = 435.60

Solving for x, we get:

x = 435.60 / 0.72

x ≈ $605

Therefore, the original price of the television set was approximately $605.

Andrew needs to choose a captain creature and a partner creature for his expedition to a mysterious dungeon. Each creature belongs to the grass, fire, or water group, and each group has 6 creatures, hence there are 216 ways

If the captain and partner creatures cannot be from the same group, how many ways can Andrew choose a captain creature and a partner creature?" by using combinatorial techniques.

Since Andrew cannot choose a captain and partner creature from the same group, there are 3 choices for the captain creature and 2 choices for the partner creature.

Therefore, the number of ways that Andrew can choose a captain and partner creature is: 3 * 2 * 6 * 6 = 216

Therefore, there are 216 ways that Andrew can choose a captain creature and a partner creature for his expedition to the mysterious dungeon

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Answer: i think its A and B

Step-by-step explanation: 33 divided by 2 is 16.5

                                             50 divided by 3 is 16.6667

                                             72 divided by 4 is 18 so that would be to much

                                             89 divided by 5 is 17.8 which is also to much

The area of the sector formed by angle DFE is approximately 3.29 square feet.

What is area of the sector?

To find the area of a sector of a circle, we need to know the central angle that defines the sector and the radius of the circle. We can then use the formula:

Area of sector = (central angle / 360 degrees) x π x (radius)²

In this case, we are given that the radius of the circle is 4 feet and the central angle that defines the sector is 75 degrees. Therefore, the area of the sector can be calculated as:

Area of sector = (75 / 360) x π x (4)²

= (0.2083) x π x 16

= 3.29 square feet (rounded to the nearest hundredth)

Therefore, the area of the sector formed by angle DFE is approximately 3.29 square feet.

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Answer:

It depends on the context of the problem and the interpretation of the ratio represented by the point (7, 8).

If we interpret the point (7, 8) as representing the ratio 7:8, then Adela's claim is incorrect. Adding the same number to both coordinates of the point would change the value of the ratio. For example, adding 1 to both coordinates would give the point (8, 9), which represents the ratio 8:9, which is not equivalent to 7:8.

However, if we interpret the point (7, 8) as representing a different type of ratio, such as the ratio of the distances from the point to two fixed points or the ratio of the areas of two shapes, then it may be possible to find an equivalent ratio by adding the same number to both coordinates of the point. In this case, Adela's claim could be correct.

Without more information about the context and interpretation of the ratio represented by the point (7, 8), it is difficult to determine the correctness of Adela's claim.

Answer:

It’s the same

Step-by-step explanation:

There equal

7 liters = 7000 milliliters

Answer:

To simplify the inequality x - 10 > 3, we can isolate x by adding 10 to both sides:

x - 10 + 10 > 3 + 10

Simplifying, we get:

x > 13

Therefore, the simplified inequality is x > 13.

The area of the shaded region under normal distribution is: 3.51

The standard normal distribution is defined as the normal distribution with a mean of 0 and a standard deviation of 1.

The z-table or the  standard normal table is one that provides the area under the standard normal curve to the left of a specified value, or "z-value". The value for the area is also the probability that the variable is less than the specified z-value.

To the right of -2.25 and to the left of -0.35

From standard normal table, we have the p-values as:

Area to the left of -0.35 = 0.3632

Area to the left of -2.25 = 0.0122

Area of the shaded region = 0.3632 - 0.0122 = 0.351

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a.The equation of Lizzy's budget line can be written as:

4M + 8B + 20(20)S + 20(40)J = I.

b.To sketch the budget line, we can plot the points (0, I/8), (I/4, 0), and (5I/16, 3I/16) on a graph.

c.The lowest price of books that Lizzy will substitute for Milo is $6.

A budget line is a graphical representation of all possible combinations of two goods that can be purchased with a limited amount of income or resources. It shows the various combinations of two goods that a consumer can afford to buy with a given income and the prices of the two goods.

In the given question,

a. The equation of Lizzy's budget line can be written as:

4M + 8B + 20(20)S + 20(40)J = I

where M is the number of tins of Milo, B is the number of books, S is the number of pairs of shoes, J is the number of pairs of jeans, and I is the total income or budget.

Interpretation: This equation represents all the possible combinations of Milo, books, shoes, and jeans that Lizzy can buy with her given income. It shows that she has to choose between buying more of one good and less of the other goods depending on their prices and her budget.

b. To sketch the budget line, we need to solve the equation for one of the variables. Let's solve for B:

4M + 8B = I - 20(20)S - 20(40)J

B = (1/2)I - 40S - 40J - 2M

c. Let's assume that the lowest price of books that Lizzy will substitute for Milo is P dollars. Then, the new budget line can be written as:

4M + P(2/3)B + 20(20)S + 20(40)J = I

To find the lowest price of books that Lizzy will substitute for Milo, we need to solve for P. We can do this by setting the coefficients of M and B in the new budget line equal to those in the original budget line:

4 = (2/3)P

P = (3/2) * 4

P = 6

Therefore, the lowest price of books that Lizzy will substitute for Milo is $6.

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A.The equation of Lizzy's budget line can be written as:

4M + 8B + 20(20)S + 20(40)J = I.

B.To sketch the budget line, we can plot the points (0, I/8), (I/4, 0), and (5I/16, 3I/16) on a graph.

C.The lowest price of books that Lizzy will substitute for Milo is $6.

What is budget line?

A budget line is a graphical representation of the limits of a consumer's purchasing power, given their income and the prices of goods and services. It shows all the possible combinations of two goods that a consumer can purchase with a given income, while spending all of their available resources.

a. The equation of Lizzy's budget line can be written as:

4M + 8B + 20(20)S + 20(40)J = I

where M is the number of tins of Milo, B is the number of books, S is the number of pairs of shoes, J is the number of pairs of jeans, and I is the total income or budget.

Interpretation: This equation represents all the possible combinations of Milo, books, shoes, and jeans that Lizzy can buy with her given income. It shows that she has to choose between buying more of one good and less of the other goods depending on their prices and her budget.

b. To sketch the budget line, we need to solve the equation for one of the variables. Let's solve for B:

4M + 8B = I - 20(20)S - 20(40)J

B = (1/2)I - 40S - 40J - 2M

This equation shows that the maximum number of books that Lizzy can buy depends on her income (I), the prices of shoes (S) and jeans (J), and the number of tins of Milo (M) she buys. The slope of the budget line is -4, which means that for every 1 unit increase in the number of books, Lizzy has to give up 4 units of Milo.

To sketch the budget line, we can plot the points (0, I/8), (I/4, 0), and (5I/16, 3I/16) on a graph, where the x-axis represents the number of tins of Milo (M) and the y-axis represents the number of books (B). Then, we can draw a straight line connecting these points to represent Lizzy's budget line.

c. Let's assume that the lowest price of books that Lizzy will substitute for Milo is P dollars. Then, the new budget line can be written as:

4M + P(2/3)B + 20(20)S + 20(40)J = I

To find the lowest price of books that Lizzy will substitute for Milo, we need to solve for P. We can do this by setting the coefficients of M and B in the new budget line equal to those in the original budget line:

4 = (2/3)P

P = (3/2) * 4

P = 6

Therefore, the lowest price of books that Lizzy will substitute for Milo is $6.

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Answer:

28 units

Step-by-step explanation:

The perimeter of a rectangle is given by the formula P = 2(l + w), where l is the length and w is the width.

Substituting l = 9 and w = 5, we get:

P = 2(9 + 5) = 2(14) = 28

Therefore, the perimeter of the rectangle is 28 units.

The ranking from greatest to least goes on Nick, Olivia, Grace, and Brandon.

So in this, we have to rank the person who got most of the candy bars first and that is Nick.

After Nick Olivia has 94 candy bars so she is second in order.

Then on the third Grace had 75 candy bars.

And at the least Brandon is there with 53 candy bars.

Nick sold 100 candy bars

Olivia sold 94 candy bars

Grace sold 75 candy bars

Brandon sold 53 candy bars

Therefore, the ranking from greatest to least is Nick, Olivia, Grace, and Brandon.

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Answer:

75%

Step-by-step explanation:

3/4 =75%

If you divide 3 by 4 you get 0.75

1=100%

0.75=75%

Answer:

.75

Step-by-step explanation:

think of 3 quarters

Comparing the numerator 9 < 15 thus, 9/10 is less than 3/2.

A multiple of the denominators of two or more fractions can be used as a common denominator to add, subtract, or compare the fractions. As fractions with dissimilar denominators cannot be added together or directly compared, they must be changed into comparable fractions with the same denominator. We must determine the least common multiple (LCM) of the fraction denominators in order to determine a common denominator. The lowest number that is a multiple of both denominators is known as the LCM. Once we have the common denominator, we may multiply the numerator and denominator by the same factor to change each fraction to an equal fraction with the same denominator.

The two values are 9/10 and 3/2.

Taking the LCM we have:

9/ 10 and 15/10

Now comparing the numerator 9 < 15 thus, 9/10 is less than 3/2.

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On number line we can compare 9/10 and 3/2 as 9/10 < 3/2.

What is number line?

A number line is a visual representation of numbers in order, usually shown horizontally. It is a line with a starting point and an endpoint that represent the smallest and largest numbers, respectively.

To compare 9/10 and 3/2 on a number line, we need to first convert them to the same denominator. The least common multiple of 10 and 2 is 10, so we can convert 3/2 to 15/10:

9/10 = 0.9

3/2 = 15/10 = 1.5

Now, we can plot these two numbers on a number line:

We can see that 9/10 is to the left of 3/2 on the number line.

Therefore we can compare 9/10 and 3/2 as 9/10 < 3/2.

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Answer:

Step-by-step explanation:

However, we need to choose the positive value for t, since time cannot equation be negative in this case. Therefore, the rocket will be 20 feet from the ground approximately 1.411 seconds after it is launched.

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x Plus 3" equals the value "9." The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. The variable x is raised to the second power in the equation "x2 + 2x - 3 = 0." Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.

So we have:

[tex]-16t^2 + 170t + 30 = 20\\-16t^2 + 170t + 10 = 0\\8t^2 - 85t - 5 = 0\\t = (-b + \sqrt(b^2 - 4ac)) / 2a\\t = (-(-85) + \sqrt((-85)^2 - 4(8)(-5))) / 2(8)\\t = (85 + \sqrt(7225 + 160)) / 16\\t = (85 + \sqrt(7385)) / 16[/tex]

However, we need to choose the positive value for t, since time cannot be negative in this case. Therefore, the rocket will be 20 feet from the ground approximately 1.411 seconds after it is launched.

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Answer:

4/8 in lowest terms is 1/2.

Step-by-step explanation:

Answer: 1/2

4/8 is equivalent to 1/2

Answer:

7, 12, 17 which is the second choice

Step-by-step explanation:

The given sequence is expressed by the equation

[tex]a_n = 7 + (n - 1)5\\\\(n - 1)5 = 5n - 5\\\\a_n = 7 + (n - 1)5= 7 + 5n - 5\\\\= 2 + 5n\\\\a_n = 5 + 2n\\\\a_1 = 2 + 5(1) = 2 + 5 = 7\\\\a_2 = 2 + 5(2) = 2 + 10 = 12\\\\a_3 = 2 + 5(3) = 2 + 15 = 17\\\\[/tex]

So the first three terms are
7, 12, 17 which is the second choice

Step-by-step explanation:

No, the ratio in a 30-60-90 triangle is

::

[tex]1:1:\sqrt{2} [/tex]

not

1:1:2

Answer:

3/10 = 0.3

19/50 = 0.38

5/10 = 0.5

1/5 = 0.2

14/25 = 0.56

3/25 = 0.12

If triangle ABC has points A(2, -4) B(-3, 1) C(-2, -6) and you perform the following transformations, B' would be located at B' (3, -4).

In Mathematics, a translation is a type of rigid transformation which is used in moving every point of an object in the same direction, as well as for the same distance.

By applying a reflection over the y-axis to the coordinate of the given point B (-3, 1), we have the following coordinates:

Coordinate B = (-3, 1)   →  Coordinate B' = (-(-3), 1) = (3, 1).

Next, we would apply a rotation of 90° clockwise as follows;

(x, y)                               →            (y, -x)

Coordinate B' = (3, 1) → Coordinate B' = (1, (-3)) = (1, -3)

Lastly, we would apply a translation (x + 2, y - 1) as follows:

Coordinate B' = (1, -3) → (1 + 2, -3 - 1) = B' (3, -4).

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For the first equation, we can complete the square to find its vertex form. Here's how we do it:

0 = x^2 - 18x + 1

0 = (x - 9)^2 - 80

So we have (x - 9)^2 = 80. This is in the form (x - p)^2 = q, where p = 9 and q = 80.

For the second equation, we can complete the square in a similar way:

x^2 + 26x + 167.5 = 0

x^2 + 26x = -167.5

x^2 + 26x + (26/2)^2 = -167.5 + (26/2)^2

(x + 13)^2 = 9.25

So we have (x + 13)^2 = 9.25. This is in the form (x - p)^2 = q, where p = -13 and q = 9.25.

I hope that helps!

On the graph we have to ensure that the data points are seen, the text and design on the graph are meaningful along with keeping the alignment on a common scale.

The graph only presents the facts in an organised manner. It facilitates our understanding of the facts. The numerical information gleaned via observation is referred to as data.

For the given question,

In a graph the data should be shown clearly.

Now, displaying the data clearly entails making sure the data points are visible while also including relevant language on the graph itself.

Designing of the graph should be in a simple manner.

The alignment to be used has to be on a common scale.

The visual encoding has to be transparent.

Use of standard-forms are welcomed.

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Answer:

-2 and 3 is the required answer

Answer: The answer is: -2 or 3

Step-by-step explanation:

x^2 -x -6 = 0

x^2 -3x +2x -6 = 0

x(x-3) + 2(x-3) = 0

(x-3)(x+2) = 0

So x-3 = 0 :: x = 3

or x+2 = 0 ::  x=-2

Answer:

Below

Step-by-step explanation:

Pick two convenient integer coordinate sets on the line

 like 0,0 and 10,4

find slope, m  = ( y1-y2) / (x1-x) = ( 4-0) / ( 10-0) =  4/10  = 2/5

b = y axis intercept = 0

Slope - intercept equation of a line is of the form : y = mx + b

  substitute in the m and b values found above to get

     y = 2/5 x + 0

or just   y = 2/5 x

The right triangle BCD have the following solution:

a). The opposite side to the angle D is BC and the adjacent side is DC

b). sin D = 0.55

c). D = 33°

d). B = 57°

Considering the angle D for right triangle BCD, the side opposite the angle D is BD which is also equal to 11 cm, and the side adjacent to the angle D is DC.

sin D = 11/20 {opposite/hypotenuse}

sin D = 0.55 to the nearest tenth

D = sin⁻¹(0.55)

D = 33.3670

D = 33 to the nearest degree

angle B = 180 - (90 + 33) {sum of interior angles of a triangle}

angle B = 57°.

Therefore, the right triangle BCD have the following solution:

a). The opposite side to the angle D is BC and the adjacent side is DC

b). sin D = 0.55

c). D = 33°

d). B = 57°

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the answer is m + n = 24 + 55 = 79.

What is probability?

By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1.

There are two ways this can happen: either he selects an apple first and then an orange, or he selects an orange first and then an apple. We can compute the probability of each of these events separately and then add them together.

First, let's consider the probability that Preston selects an apple first and then an orange. The probability of selecting an apple first is 4/11, and then the probability of selecting an orange from the remaining 10 fruits (which includes 3 apples and 6 oranges) is 6/10. So the probability of this event is (4/11) * (6/10) = 24/110.

This can be simplified by dividing the numerator and denominator by 2:

48/110 = 24/55

So the probability that Preston selects an apple and an orange is 24/55. Therefore, the answer is m + n = 24 + 55 = 79.

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Answer:

Step-by-step explanation:

Let the amount invested by A, B, and C be denoted by a, b, and c respectively.

From the given information,

a + b + c = 60000 ---(1)

a + c = 2b ---(2)

a + b = 3c ---(3)

Multiplying equation (2) by 3 and equation (3) by 2, we get:

3a + 3c = 6b

2a + 2b = 6c

Adding these two equations, we get:

5a + 5b + 5c = 0

a + b + c = 0

This is not possible as the sum of the investments cannot be zero. Therefore, there must be an error in the problem statement.

Without further information or correction, it is not possible to find the share of B in the profit.

Answer:

2301 / 100

Step-by-step explanation:

We take

23.01 time 100 which makes 2301/100 fraction.

Answer:

height = 12 m

Step-by-step explanation:

We can assume from the problem that the movie screen is rectangular and the formula for perimeter (P) of a rectangle is

P = 2h + 2w, where l is the length and w is the width.

Thus, we can plug in 70 for P and 23 for w and solve for h:

[tex]70=2h+(2*23)\\70=2h+46\\24=2h\\12=h[/tex]