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7th Grade Math Solving Equations

4. a-9=15
5. n-9=13
6. b-8=9
7. X-5=16
8. n-6=17​

The correct number line is: A number line going from negative 8 to positive 2. An open circle is at negative 3. Everything to the left of the circle is shaded.

The mathematical expression of a connection between two values, stating that one value is larger than, less than, or not equal to another value, is called an inequality. Common symbols for inequality include (less than), > (greater than), (less than or equal to), and (greater than or equal to). For instance, the inequality 2x + 3 > 7 denotes that the value of 2x + 3 is larger than 7. Depending on the circumstance, inequalities can be resolved algebraically or visually. A collection of values that meet the connection implied by the inequality is the answer to an inequality.

Here, the inequality is y - 2 < -5, which can be rewritten as y < -3.

Hence, the correct option is: A number line going from negative 8 to positive 2. An open circle is at negative 3. Everything to the left of the circle is shaded.

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Therefore, the quadratic function in standard form that represents the data in the table is: y = 1/2 x² - 5/2 x + 5.

A function is a mathematical concept that describes the relationship between two sets of numbers. It is a rule that assigns to each input (or element in the domain) exactly one output (or element in the range). In simpler terms, a function is like a machine that takes in a number and produces another number as output, according to some specific rules. The input is usually denoted by x, and the output by f(x), which is read as "f of x". Functions can take many forms, such as linear, quadratic, trigonometric, exponential, logarithmic, and more. They are widely used in mathematics, science, engineering, and many other fields to model and analyze various phenomena.

Here,

To write a quadratic function in standard form, we need to use the general form of the quadratic equation:

y = ax²+ bx + c

where a, b, and c are constants. We can use the values in the table to find these constants.

When x = 2, y = 3

When x = 4, y = 1

When x = 6, y = 3

When x = 8, y = 9

When x = 10, y = 19

Substituting these values into the quadratic equation, we get:

3 = 4a + 2b + c

1 = 16a + 4b + c

3 = 36a + 6b + c

9 = 64a + 8b + c

19 = 100a + 10b + c

We can now use these equations to solve for a, b, and c. One way to do this is to use a matrix equation:

|16 4 1| |a| |1|

|36 6 1| |b| = |3|

|64 8 1| |c| |9|

Using a calculator or matrix software, we can solve for a, b, and c:

a = 1/2

b = -5/2

c = 5

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1 + 2i in polar form is 5√2∠63.4°.

What is a polar form ?

In mathematics, the polar form is a way of representing complex numbers using their magnitude and angle. A complex number can be represented in the form r(cos θ + i sin θ), where r is the magnitude (or modulus) of the complex number, and θ is its argument (or phase angle). Alternatively, the polar form can be represented in terms of magnitude and angle as r ∠θ, where r is the magnitude and θ is the angle in radians. This form is also known as the exponential form of a complex number. The polar form is useful in calculations involving complex numbers, especially in multiplication and division, where it is often easier to work with the polar form rather than the rectangular form (a + bi).

D. 5√2∠63.4°

To convert a complex number from rectangular form to polar form, we use the following formulas:

r = √(a^2 + b^2)

θ = tan^-1 (b/a)

Where a and b are the real and imaginary parts of the complex number, respectively.

In this case, a = 1 and b = 2, so:

r = √(1^2 + 2^2) = √5

θ = tan^-1 (2/1) = 63.4°

Therefore, 1 + 2i in polar form is 5√2∠63.4°.

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Answer:

The midpoint of a line segment AB with endpoints A(x1, y1) and B(x2, y2) is given by the coordinates:

[(x1 + x2) / 2, (y1 + y2) / 2]

In this case, A is located at (1, 4) and B is located at (3, -6). So the midpoint M of AB is:

[(1 + 3) / 2, (4 + (-6)) / 2]

= [2, -1]

Therefore, the midpoint of AB is at the point (2, -1).

The coordinates of the midpoint of the line AB is [2, -1]

Section formula is used to find the ratio in which a line segment is divided by a point internally or externally.

It is used to find out the centroid, incenter and excenters of a triangle. In physics, it is used to find the center of mass of systems, equilibrium points, etc.

Given that, we need to find the midpoint of AB if A located at (1, 4) and B is located at (3, -6).​

The midpoint of a line segment AB with endpoints A(x1, y1) and B(x2, y2) is given by the coordinates:

[(x1 + x2) / 2, (y1 + y2) / 2]

In this case, A is located at (1, 4) and B is located at (3, -6).

So the midpoint M of AB is:

= [(1 + 3) / 2, (4 + (-6)) / 2]

= [2, -1]

Hence, the midpoint of AB is at the point (2, -1).

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Step-by-step explanation:

the perimeter of a rectangle is

2×length + 2×width

in our case

length = width + 3

and

2×length + 2×width = 30

using the first equation in the second :

2×(width + 3) + 2×width = 30

width + 3 + width = 15

2×width + 3 = 15

2×width = 12

width = 12/2 = 6 ft

length = width + 3 = 6 + 3 = 9 ft

Answer: 2.5 dm

Step-by-step explanation:

Divide 25.0 by 10

= 2.5

The maximum revenue is achieved when she sells 33 photos at a price of 25 per photo.

Using quadratic regression, [tex]y = ax^2 + bx + c[/tex]

where a, b and c are constants and x is the independent variable we can determine the equation of the curve that best fits the data. The equation will be in the form of[tex]y = ax^2 + bx + c[/tex], where y is the revenue, x is the number of photos sold, and a, b, and c are constants. The constants can be determined by solving the system of equations formed by the three data points.

After solving for the constants, we can determine the maximum revenue by finding the vertex of the curve. The vertex is located at x = -b/2a, and the corresponding revenue is[tex]y = ax^2 + bx + c[/tex]. Plugging in the values for a, b, and c, we can calculate that the maximum revenue is achieved when she sells 33 photos at a price of 25 per photo.

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Complete question

Darlena has started taking photos at amateur dog racing events, later offering the photos for sale to the dog owners by email. The prices she has charged per photo at each of her first three events, and the corresponding number of photos sold and total revenue raised, appear in the table below. Treating revenue as a function of the number of photos sold, a graph of the three data points is also shown. If she uses quadratic regression to fit a curve to the data, what number of photos sold and what price per photo will maximize her revenue?

Answer:

p=84

Step-by-step explanation:

p=6×14

p=84

answer: p=84

Answer:

18

Step-by-step explanation:

siz times three is eighteen

1. Calculating the output when using -6 as the input, we have:

Rule 1: subtract 7  = -13

Rule 2: square the input = 36.

Rule 3: divide by 3 = 12

Rule 4: divide the input into 3 = -2

Rule 5: write π = -2π

Rule 6: volume of a cube = -216cm³

A function rule is a mathematical expression that describes how to calculate the output value of a function based on its input value. It can be thought of as a set of instructions that tell you what to do with the input value to get the output value.

2. a. True. Speed is the ratio of distance traveled to the time taken to travel that distance. In this case, the distance is fixed at 100 meters, so speed is solely dependent on time. For each value of time, there is only one corresponding value of speed, making it a function.

b. False. While time and distance are related in the formula for speed, time is not a function of distance in this case. Each student's time is independent of the distance they cover, and the same distance is covered by all students (100 meters). Therefore, for any given distance, there are multiple possible values of time, making it not a function.

c. False. The number of students racing is not related to their speed. Each student's speed depends solely on their individual time, which is not affected by the number of other students racing.

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To subtract 6/7 from 2 1/4, we need to find a common denominator. The least common multiple of 7 and 4 is 28, so we can convert 2 1/4 to 9/4 and 6/7 to 24/28. Then we can subtract:

9/4 - 24/28

= 63/28 - 24/28

= 39/28

Therefore, 2 1/4 - 6/7 = 39/28.

To solve for the blank in 2 5/12 - blank = 2/3, we can start by converting 2 5/12 to an improper fraction:

2 5/12 = (2*12 + 5)/12 = 29/12

Then we can subtract 2/3 from both sides:

2 5/12 - 2/3 = blank

To subtract these fractions, we need to find a common denominator. The least common multiple of 3 and 12 is 12, so we can convert 2/3 to 8/12. Then we can subtract:

29/12 - 8/12

= 21/12

= 7/4

Therefore, the blank in 2 5/12 - blank = 2/3 is 7/4.

To subtract 5 3/8 from 7 1/12, we need to find a common denominator. The least common multiple of 8 and 12 is 24, so we can convert both mixed numbers to improper fractions:

7 1/12 = (712 + 1)/12 = 85/12

5 3/8 = (58 + 3)/8 = 43/8

Then we can subtract:

85/12 - 43/8

= 85/12 - (433)/(83)

= 85/12 - 129/24

= 5/24

Therefore, 7 1/12 - 5 3/8 = 5/24.

To solve for the blank in blank + 7/10 = 2 9/20, we can start by converting 2 9/20 to an improper fraction:

2 9/20 = (2*20 + 9)/20 = 49/20

Then we can subtract 7/10 from both sides:

blank + 7/10 - 7/10 = 49/20 - 7/10

Simplifying the right side:

49/20 - 7/10 = (492)/(202) - (74)/(104) = 98/40 - 28/40 = 70/40 = 7/4

Therefore, blank + 7/10 - 7/10 = 7/4, and solving for blank:

blank = 7/4

Therefore, the blank in blank + 7/10 = 2 9/20 is 7/4.

Answer:

a-no for the first triangle, because the total of the inner angles must be 180, the last angle must be 90.

b-yes- a triangle with angles 90, 50, and 40 is possible

c-yes. 65+45+70=180.

Step-by-step explanation:

According to the question the percent abundance of the medium nails in the sample is approximately 18.95%.

Whenever the set of data is presented from least to largest, the median is indeed the number in the middle. For instance, since 8 is in the middle, this would represent the median value here.

To find the percent abundance of the medium nails in the sample, we first need to calculate the total number of nails in the sample:

Total number of nails = 67 + 18 + 10 = 95

Next, we can calculate the percent abundance of the medium nails using the formula:

Percent abundance = (number of medium nails / total number of nails) x 100%

Using the values from of the table as inputs, we obtain:

Percent abundance of medium nails = (18 / 95) x 100% ≈ 18.95%

As a result, the sample's average percentage of medium nails is roughly 18.95%.

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Answer:

1. 57/16 or 3.5625 ounces of water

8 : 4.75

1 : 19/32  -----> divide both by 8

19/32x6=57/16 = 3.56 ounces

2. 2.4375 ounces of other ingredients

6-3.5625=2.4375

Answer:

(gof)(x) = 14x + 1

Step-by-step explanation:

We can think of (gof)(x) as g(f(x)).  Writing it in this form shows that we must start with the inner function and work our way to the outer function.

Essentially, the input of the inner function yields an output and the output becomes the input of the outer function.

f(x) means that the input is x and since we're given no value for x (e.g. x = so and so), the output is the original function or 2x - 1

Now, this output becomes the input for g(x):

g(2x-1) = 7(2x - 1) + 8

14x -7 + 8

(gof)(x) = 14x + 1

Answer:

I will not show you the process it is easy the answer is 4.5 or 6 ≈

The function that expresses f(x) is f(x) = 1.99x + 3, and its graph is continuous.

A continuous function is one that doesn't have any sudden or unexpected changes in value. It means that if we make small enough changes to its input, the output will also change by a small amount.

We can express the total cost of an order as a function of the number of books sold, x, using the formula:

f(x) = 1.99x + 3

This function takes the number of books sold, multiplies it by the cost per book ($1.99), and adds a fixed fee of $3.

For example, if we sold 3 books, we can use the function to find the total cost:

f(3) = 1.99(3) + 3 = 9.97

This means that selling 3 books would cost $9.97 in total.

The graph of this function is continuous, which means that as we move along the x-axis, the y-values change smoothly and without any sudden jumps.

The term "continuous" refers to a function that can take on any value between two given points and can be broken down into infinitely many fractions and decimals.

In contrast, a discrete function can only take on specific values, usually whole numbers or integers.

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To find the area of the total figure, we need to first find the areas of the rectangle and triangle, and then add them together.Therefore, the area of the total figure is 200 square feet.

Area is the measurement of the size of a two-dimensional surface enclosed by a closed figure

Area of rectangle = length x width

= 20 ft x 8 ft

= 160 sq. ft

Area of triangle = 1/2 xbase xheight

= 1/2 x 8 ft x 10 ft

= 40 sq. ft

To find the base of the triangle, we can use the Pythagorean theorem, which states that the square of the hypotenuse (slope) of a right triangle is equal to the sum of the squares of its two sides. In this case, the hypotenuse is 12 ft, one of the other sides is the height of the triangle (10 ft), and the other side is the base of the triangle (b).

Using the Pythagorean theorem, we have:

12² = 10² + b²

144 = 100 + b²

44 = b²

b = √44

b ≈ 6.63 ft

Now that we know the base of the triangle, we can find the area of the total figure by adding the area of the rectangle and the area of the triangle:

Area of total figure = area of rectangle + area of triangle

= 160 sq. ft + 40 sq. ft

= 200 sq. ft

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Answer:2

Step-by-step explanation:Because the 2 is closest to the middle line

Answer:

relationship describes angles 1 and 2 is supplementary angles. From the given figure

it is concluded that

the relation ship between angle 1 and 2 is supplementary angles

because its is  linear pair

and forms a line

therefore , the angles are supplementary angles

hence , relationship describes angles 1 and 2 is supplementary angle

Step-by-step explanation: Hope this helps !! Mark me brainliest!! :))

The sum of x and 2 is equal to x + 2.

Value in math is the numerical representation of a quantity or expression. It can also be defined as an amount or a numerical representation of a quantity that is assigned to a variable or a constant in a mathematical expression. Value can be expressed in various forms, such as decimal, fraction, and scientific notation. Value is also used to calculate the result of an equation or a problem. Value is a fundamental concept in mathematics, and it is used to measure and compare different quantities.

This equation can be used to calculate the sum of any two numbers, x and 2. For example, if x is equal to 5, then the sum of x and 2 is equal to 5 + 2, which is equal to 7. Similarly, if x is equal to 10, then the sum of x and 2 is equal to 10 + 2, which is equal to 12. Therefore, the sum of x and 2 depends on the value of x.

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The order of the matrix is 2 x 2.

What is a matrix and what is meant by its order?

In the field of mathematics, matrices are rectangular arrangements of numerical values, symbols, or algebraic expressions, organized in rows and columns. Matrices are used in many areas of mathematics and science, as well as in engineering, physics, and computer graphics.

The term 'order' in the context of matrices refers to the dimensions of the matrix, which are determined by the number of rows and columns it contains. It is denoted by m x n, where m is the number of rows and n is the number of columns. To find the order of a matrix, we simply count the number of rows and columns. The order is usually written as a pair of numbers in the form m x n.

Determine the order of the given matrix:

In the given problem, we are asked to find the order of the matrix:

[tex]\begin{pmatrix}9 &6 \\-4 & 8\end{pmatrix}[/tex]

we count the number of rows and columns.

This matrix has 2 rows and 2 columns, so its order is 2 x 2.

Therefore, the order of the matrix is 2 x 2.

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Answer:

A.=False

B.=True

C.=False

D.=True

Step-by-step explanation:

The original ration is 2 gallons of water for 4 players.

Each player requires 1/2 gallon of water.

To get the amount of water needed multiply 1/2 by the amount of players.

1*(1/2) does not equal 1

2*(1/2) equals 1

10*(1/2) does not equal 4

30*(1/2) equals 15

The volume of the cone is  2119. 5 cubic centimeters

The formula used for calculating the volume of a cone is expressed as;

V = πr² h/3

Given that the parameters are namely;

Now, substitute the values, we have;

Volume , V = 3.14 × 15² × 9/3

Divide the values, we have;

Volume = 3.14 × 225 × 3

Multiply the values, we get;

Volume, V = 2119. 5 cubic centimeters

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Answer: Sally will earn $4,830.00 in interest over 7 years.

Step-by-step explanation:

If the interest is not compounded, then Sally will earn simple interest, which can be calculated using the formula:

I = P * r * t

where:

I = the interest earned

P = the principal amount (initial investment)

r = the annual interest rate (as a decimal)

t = the time period, in years

In this case, we have:

P = $9,000 (the initial deposit)

r = 7% = 0.07 (the annual interest rate)

t = 7 (the number of years)

So, plugging in the values:

I = $9,000 * 0.07 * 7

I = $4,830.00

Therefore, Sally will earn $4,830.00 in interest over 7 years.

Answer:

162, 147 etc.

Step-by-step explanation:

we have to find

[tex]N = k^2 \cdot p[/tex]

we can iterate k = 1 to 10 to check all possible solutions,

[tex]N = 9^2 \cdot 2[/tex]

[tex]N = 7^2 \cdot 3[/tex]

N = 162, 147 etc.

Hopefully this answer helped you!!

Answer: Linear

Step-by-step explanation:

Since the difference between consecutive values of f(x) is constant, this suggests that the function could be linear. To confirm this, we can calculate the differences between consecutive values:f(1) - f(0) = -15 - (-18) = 3

f(2) - f(1) = -12 - (-15) = 3

f(3) - f(2) = -9 - (-12) = 3

f(4) - f(3) = -6 - (-9) = 3

Since the differences are constant and equal to 3, this confirms that the function is linear.

To find the equation of the linear function, we can use the slope-intercept form of a linear equation:

y = mx + bwhere m is the slope and b is the y-intercept.

We can use the first two points (0, -18) and (1, -15)  to find the slope:

m = (change in y) / (change in x) = (-15 - (-18)) / (1 - 0) = 3

Now we can use the slope and one of the points to find the y-intercept:

y = mx + b

-18 = 3(0) + b

b = -18

Therefore, the equation of the linear function is:

f(x) = 3x - 18

So the function type that could represent the values in the table is linear.

Answer:

4.88%

Step-by-step explanation:

All sides of a square are equal

let x = length of a side

Area = x·x = x²

Estimated area = (8.5)² = 72.25 in²

Actual area = (8.3)² = 68.89 in²

percent error  = (actual area - estimated area) / (estimated area) x 100

% error = (68.89 - 72.25) / (68.89) x 100 = -4.88%     the negative sign means the estimate was higher than the actual.  

Answer:

Experimental Procedure:

Materials:

Piece of wood

Electronic balance

Bunsen burner

Heat-resistant mat

Stopwatch or timer

Safety goggles

Lab coat

Safety Precautions:

Wear safety goggles and a lab coat to protect your eyes and clothing from any sparks or flames.

Place the heat-resistant mat under the Bunsen burner to prevent any accidental fires.

Use the Bunsen burner only under adult supervision.

Be cautious when handling hot objects, and allow them to cool before touching.

Procedure:

Measure the initial mass of the piece of wood using an electronic balance, and record it in a table.

Light the Bunsen burner, and place the piece of wood over the flame using tongs. Ensure that the wood is fully engulfed in the flame.

Use a stopwatch or timer to time how long the wood burns for (in this case, 15 minutes).

After 15 minutes, turn off the Bunsen burner and remove the piece of wood from the flame using tongs.

Allow the wood to cool, and then measure its final mass using the electronic balance, and record it in the table.

Calculate the difference between the initial and final mass of the wood, and record it in the table.

Repeat steps 1-6 three times to obtain three sets of data.

Calculate the average mass of the burned wood and compare it to the initial mass of the unburned wood to determine if the student's prediction was correct.

Conclusion:

If the average mass of the burned wood is less than the initial mass of the unburned wood, the student's prediction was correct, and he can conclude that the wood underwent a chemical change when it was burned. If the average mass is greater than or equal to the initial mass, the prediction was incorrect, and the student may need to revise his hypothesis or experimental design.

Answer:

1.986 x 10 to the tenth power

Step-by-step explanation:

The ratio between the perimeter of triangle ABC and the perimeter of triangle XYZ is given as follows:

1/3.

The perimeter of a triangle is the total length of its three sides. To find the perimeter of a triangle, you need to add up the lengths of all three sides.

The ratio between the side lengths of triangle ABC and triangle XYZ is given as follows:

5/15 = 1/3.

The perimeter of a triangle is measured in units, as area the side lengths, hence they have the same ratio, and thus the ratio between the perimeter of triangle ABC and the perimeter of triangle XYZ is given as follows:

1/3.

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