which equation can be used to find the measure of angle fge?

Answer:

Slope: [tex]\bf \boxed{-\dfrac{1}{3}}[/tex]

y-intercept: [tex]\boxed{-1}[/tex]

Equation: [tex]\boxed{\bf{y=-\dfrac{1}{3}x - 1}}[/tex]

The two boxes at the bottom are asking you to repeat the above information:

the slope is [tex]\bf \boxed{-\dfrac{1}{3}}[/tex]   the y-intercept is [tex]\boxed{-1}[/tex]

Step-by-step explanation:

Actually, you don't have to graph the equation since the graph is already provided

You have to answer the questions based on the provided graph

To find slope

1. Take any two well=defined points on the graph:

2. Find the difference in y-values between P2 - P1. This called rise

3. Find the corresponding difference in x-values: P2 - P. This is called run

4. The slope is computed as rise/run = - 1/3

To find y-intercept

Just note where the line crosses the y-axis and the y-value corresponding to that would be the y-intercept

This is also the y-value at which x = 0

Looking at the graph we see that the line crosses(intercepts) the y-axis at y = - 1
So y-intercept = - 1

To write the equation

The equation of the line is
y = mx + b

where

m = slope

b = y-intercept

So the equation of this particular line is

[tex]\bf{-\dfrac{1}{3}x - 1}[/tex]

Answer:

122

Step-by-step explanation:

the question is asking for the area of the whole shape

however, it's split into a trapezoid and rectangle, so all you have to do is find the area of the respective shapes and then add them

the formula for area of a rectangle is [tex]A = L(W)[/tex]

if you substitue, A = 15(6)

so the area of the rectangle is 90

then, you have the trapezoid

area of a trapezoid = [tex]\frac{1}{2} (h)(b_{1} +b_{2})[/tex]

you might assume that you don't have the second base, but it's in the rectangle - 6

A = 1/2(4)(6+10)

A=32

90+32 = 122

Option C is correct, the expression 24x⁷y² is equivalent to 3x³. 2x²y. 4x²y.

An expression is combination of variables, numbers and operators.

The given expression is 3x³. 2x²y. 4x²y.

We need to find the equivalent expression of the given expression.

Equivalent expressions are expressions that work the same even though they look different.

(3×2×4)x³. x²y. x²y.

24x³. x²y. x²y.

When bases are same then the powers will be added.

24x⁷y²

Hence, option C is correct, the expression 24x⁷y² is equivalent to 3x³. 2x²y. 4x²y.

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Answer:

B. 2/3

Step-by-step explanation:

If y directly varies with x, then y = kx where k is a constant

Given that when y = 20 when x = 30 we get the equation: 20 = k x 30

or

20 = 30k

Dividing by 30 both sides and switching sides gives

k = 20/30 = 2/3

The equation becomes
y = 2/3 x

Therefore if x = 1 we get

y = 2/3 x 1 = 2/3

Choice B

The solution to the division 3x³ - 2x² + 4x - 3 divided by x² + 3x + 3 is: 3x - 11  ( 28x  +  30) / (x² + 3x + 3).

The division of the polynomial 3x³ - 2x² + 4x - 3 by the polynomial x² + 3x + 3 can be performed using polynomial long division.

Here's the steps for long division:

                     3x - 11    

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

x² + 3x + 3 √ (3x³ - 2x² + 4x - 3 )

                  -  (3x³ + 9x² + 9x )

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

                                -11x² - 5x - 3

                           -  ( -11x² - 33x - 33 )

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

                                          28x  +  30

Thus, the solution to the division 3x³ - 2x² + 4x - 3 divided by x² + 3x + 3 is: 3x - 11  ( 28x  +  30) / (x² + 3x + 3)

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The required equation model the situation total amount of money, m, remaining on the gift card after playing g arcade games as m = $15 - 0.75g.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,
Let's start by representing the total amount of money spent on playing arcade games as 0.75g.

Since the gift card has a value of $15, the total amount of money remaining on the gift card after playing g games can be represented as:

m = $15 - 0.75g

This equation represents the total amount of money remaining on the gift card after playing g games, where m is the remaining amount and g is the number of games played.

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Answer: j/11 = 367

Step-by-step explanation:

Keywords: QUOTIENT. Quotient indicates a division answer. The quotient, in this case, is 367.

It also makes sense that j is the dividend and 11 is the divisor.

---
For the SOLVED version: j = 4037.
Multiply 11 on both sides, canceling the 11 on one side and getting 4037 when you multiply 11 by 367.

Answer:

J/11 = 367; this is the equation as When J is divided by 11 it answers to 367

Step-by-step explanation:

total answer;

J = 367(11)

J= 4037

The simplification of the expression gives 40x + 4y

Simplification is a way of determining an answer for a complex calculation that may involve numbers on division, multiplication, square roots, cube roots, plus and minus, etc.

The expression 2y + 3x +42x+5y-3y - 5x can be simplified by adding or subtracting like terms. That is:

2y + 3x +42x+5y-3y - 5x = 3x +42x- 5x + 5y-3y + 2y

                                         = 40x + 4y

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The required two other expression are d + 49d/100 and 149d/100.

In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).

We have;

An art teacher enlarged the area of a copy of a painting by 49%. and d represent the area of the original painting.

Given expression is d+ 0.49d

New expressions are

1) d+ 0.49d

= d + 49d/100

2) d+ 0.49d

= d + 49d/100

= 149d/100

Thus, required two other expression are d + 49d/100 and 149d/100.

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The factored form of the given trinomial as required in the task content is; (2x - 1) (x + 5).

It follows from the task content that the factored form of the trinomial 2x² + 9x - 5 is to be determined.

Therefore, the factorisation is as follows;

2x² + 10x - x - 5

2x (x + 5) -1 (x + 5)

(2x - 1) (x + 5)

Ultimately, the factored form of the trinomial is; (2x - 1) (x + 5).

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The number of minutes that you watch TV to get a 70% in math will be 77.14 minutes.

A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.

The grade you earn in math varies inversely with the number of minutes per night you watch TV.

We know that in inverse proportionality, the product of grade and number of minutes remains constant.

Let 'N' be the number of minutes. Then the equation is given as,

70N = 90 × 60

70N = 5,400

N = 77.14 minutes

The number of minutes that you watch TV to get a 70% in math will be 77.14 minutes.

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Answer: To graph the system of linear equations, you can plot the two lines on the same coordinate plane and look for the point where they intersect. If they intersect, that point represents the solution to the system.

The equation y = x - 6 can be written in slope-intercept form, y = mx + b, where m = 1 and b = -6. The equation of the line will be y = x - 6.

The equation y = -x - 2 can be written in slope-intercept form, y = mx + b, where m = -1 and b = -2. The equation of the line will be y = -x - 2.

Plotting these two lines on the same coordinate plane, we can see that they intersect at the point (2, -4). This means that there is one solution to the system of equations: (2, -4).

Step-by-step explanation:

Answer:7/12

Step-by-step explanation:

1/3 = 4/12

1/4=3/12

3/12+4/12 = 7/12

7/12 is the answer

Answer:

To write the radical ³√32m³ using rational exponents:

1. Rewrite the radical using exponential notation: 32m^3 ≈ 8m^3.

2. Convert the exponent into its equivalent fractional form: 8m^3 ≈ 2^3m^3/2^3.

3. Apply a rational exponent to the numerator: (2^3m^3)^(1/3)/2^3 = 2m.

4. The radical can now be written using rational exponents: (2m)^3/2^3.

Answer:

E) 19

Step-by-step explanation:

To find the value of -3Δ5, we need to substitute -3 and 5 into the equation: aΔb = a² + ab + b².

So, we have:

-3Δ5 = (-3)² + (-3)(5) + (5)²

= 9 - 15 + 25

= 19

Therefore, the answer is E) 19.

Answer 15489 Rupees

Step-by-step explanation:

Total parts= 7+2=9 parts

total salary= 9x
taken salary for car repair= 2x/7
remaining salary= 15000 rupees

9x-2x/7= 15000
(63x-2x)/7=15000
61x/7=15000

61x=105000
x= 105000/61
x= 1721(approx)

Total salary= 9x
                   = 9*1721
                   =15489 rupees


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The height of the cylinder having a volume of 471 cubic centimetres will be 6 cm. The correct option is D.

The volume of the cylinder is defined as the three-dimensional space occupied by the cylinder.

We can use the formula for the volume of a cylinder, which is given:

V = πr²h

Where V is the volume, r is the radius, and h is the height of the cylinder.

We are given that the cylinder is full at 471 cubic centimetres and that the radius is 5 centimetres. Therefore, we can plug in these values into the formula and solve for h:

471 = π(5²)h

471 = 25πh

h = 471 / (25π)

h ≈ 6 centimeters

Therefore, the height of the cylinder is approximately 6 centimetres.

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The values are written in commas as x², 6x  and 9

It is important to note that algebraic expressions are expressions that are made of terms, variables, coefficients, factors and constants.

From the information given, we have the quadratic expression as:

(x + 3)^2

Now, take the following steps to determine the values

(x + 3)(x +3)

expand the bracket, we get;

x² + 3x + 3x + 9

Now, collect the like terms and add the values

x² + 6x + 9

Hence, the value is x² + 6x + 9

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The dimensions of the box are given as follows:

The volume of a rectangular prism, with dimensions length, width and height, is given by the multiplication of these dimensions, as follows:

Volume = length x width x height.

The parameters for this problem are given as follows:

Hence the height of the cardboard is given as follows:

3 x 0.75 x h = 336

h = 336/(3 x 0.75)

h = 149.3 inches.

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Answer:

Step-by-step explanation:53/10

-2 is to be multiplied in the second equation to make the y-values additive inverses.

Additive inverse simply means changing the sign of the number and adding it to the original number to get an answer equal to 0.

Given are two equations,

3x-4y = -5.....(i)

5x-2y = -6.....(ii)

We need to find the additive inverse of y variable,

The coefficients of y variables in the both equations are ;-

-4 and -2

The additive inverse of -4 is 4,

If we multiply -2 by -2 it becomes 4,

Hence, -2 is to be multiplied in the second equation to make the y-values additive inverses.

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There are 10 terms in the equation

The variables are x, y, z

The constants in this equation are -6, 10

The coefficients of the variables of the equation are; 8, 7 and -3

2x + 3y - 6 - 3z + 4y - 6x = 4x + 2y - 4z + 10

The left side of the equation is;

2x + 3y - 6 - 3z + 4y - 6x

= 2x - 6x + 3y + 4y - 3z - 6

= 8x + 7y - 3z - 6

Therefore, the coefficients of the variables on the left side of the equation are; 8, 7 and -3

Variables are unknown numbers usually represented by letters or symbols.

The constant are numbers that cannot change its value

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A monomial is an algebraic expression that consists of a single term. A monomial can contain constants and/or variables, which are multiplied together.

The expression 3x²y is a monomial. It contains the constant 3, the variable x squared, and the variable y. The variables can be raised to an exponent, as in this example; however, the exponent must be a whole number.A monomial can also contain coefficients, which are the numbers that are multiplied with a variable. In the example above, the coefficient is 3. If there is no coefficient stated, then the coefficient is assumed to be 1. Therefore, the expression x²y is also a monomial, with the coefficient being 1.Additionally, a monomial can contain a product of numbers and variables, such as the expression 2xyz. This is also considered a single term, since all of the numbers and variables are multiplied together.

Monomials can be used to calculate polynomials, which are algebraic expressions consisting of multiple terms. By adding, subtracting, and multiplying monomials together, you can create a polynomial. For example, the expression (3x²y) + (2xyz) is a polynomial, since it consists of two terms. The first term is the monomial 3x²y, and the second term is the monomial 2xyz.

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The proof is not correct.

The given information that segments AB and BD are congruent does not imply that triangles ABE and DBE are congruent. Congruency of triangles requires more information, such as additional side lengths or angle measures.

While it is true that point C is the circumcenter of triangle ABD and that segment BE is a median, it is not necessarily true that BE is also a perpendicular bisector. In fact, this would only be true if triangle ABD were also an equilateral triangle.

The statement that triangles ABE and DEB share side BE is incorrect. Triangles ABE and DEB do not share any sides, but rather have segment BE as a common hypotenuse.

Therefore, the conclusion that triangles ABE and DBE are congruent by HL (hypotenuse-leg) is not valid since the previous steps in the proof are flawed.

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Answer:

1/4

Step-by-step explanation:

0.25 * 4 = 1

so, 1/4 = 0.25

Camden purchased 4 cans of soup and 3 frozen dinners.

We can solve this problem by using a system of two linear equations.

Let x be the number of cans of soup purchased and y be the number of frozen dinners purchased.

Then, based on the information given, we can set up two equations as follows:

150x + 300y = 1500 (the total amount of sodium consumed is 1500 mg)

x + y = 7 (Camden purchased 7 cans of soup and frozen dinners)

Now, we can use either substitution or elimination to find the values of x and y.

Using substitution:

Solve the second equation for y: y = 7 - x

Substitute the expression for y into the first equation: 150x + 300(7 - x) = 1500

Simplify the expression: 150x + 2100 - 300x = 1500

Combine like terms: -150x + 2100 = 1500

Solve for x: -150x = -600

Divide both sides by -150: x = 4

Use the second equation to find y: y = 7 - x = 7 - 4 = 3

So, Camden purchased 4 cans of soup and 3 frozen dinners.

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The required domain and range of the function are (-∞, ∞) and  (2, ∞).

The domain of a function is the set of all possible values of the input variable (x) for which the function is defined. In this case, the function is an exponential function with base 4, which means it is defined for all real numbers.

Therefore, the domain of f(x) is all real numbers, or (-∞, ∞).

The range of a function is the set of all possible values of the output variable (f(x)) for all possible values of the input variable (x).

Since 4^x is always positive (for all x), the value of the function f(x) will always be greater than 2 (the constant added to 5(4)^x), no matter what the value of x is.

As x approaches negative infinity, 5(4)^x approaches zero, so the minimum value of f(x) is 2.

As x approaches positive infinity, 5(4)^x increases without bound, so the range of f(x) is (2, ∞).

Thus, required domain and range of the function are (-∞, ∞) and  (2, ∞).

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The bearing are as follows:

(a) W from O = 70 degree south by east

(b) O from CA = 17 degree south by west

(c) CA from W = 21 degree west by north

What is angle ?

In geometry, an angle is the measure of the amount of rotation between two intersecting lines or surfaces, typically measured in degrees or radians.

An angle is formed when two lines or surfaces intersect at a point, which is called the vertex of the angle. The two lines or surfaces that form the angle are called the arms or sides of the angle. Angles are usually denoted using the vertex point, with a small angle symbol (such as ∠ABC).

Corresponding angles are a pair of angles that are in the same relative position at two different intersections of a line and a pair of parallel lines. In other words, if two parallel lines are intersected by a third line (called a transversal), then any pair of angles that are in the same position relative to the parallel lines are corresponding angles.

a. 70 degree south by east

b. 17 degree south by west

c. 21 degree west by north

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AThe bearing are as follows:

(a) W from O = 70 degree south by east

(b) O from CA = 17 degree south by west

(c) CA from W = 21 degree west by north

What is angle ?

In geometry, an angle is the measure of the amount of rotation between two intersecting lines or surfaces, typically measured in degrees or radians.

An angle is formed when two lines or surfaces intersect at a point, which is called the vertex of the angle. The two lines or surfaces that form the angle are called the arms or sides of the angle. Angles are usually denoted using the vertex point, with a small angle symbol (such as ∠ABC).

What is corresponding angle ?

Corresponding angles are a pair of angles that are in the same relative position at two different intersections of a line and a pair of parallel lines. In other words, if two parallel lines are intersected by a third line (called a transversal), then any pair of angles that are in the same position relative to the parallel lines are corresponding angles.

According to given conditions :

a. 70 degree south by east

b. 17 degree south by west

c. 21 degree west by north

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