1 point
Calculate the rate of change for each function over the interval [0, 3], then tell which function is
growing faster.
f(x) = 2x + 3
g(x) = 2² +3
Of(x) has a rate of change of 2
g(x) has a rate of change of 2.33
So g(x) is growing faster
f(x) has a rate of change of 6
g(x) has a rate of change of 7
So g(x) is growing faster
f(x) has a rate of change of 6
g(x) has a rate of change of 7
So f(x) is growing faster
f(x) has a rate of change of 2
g(x) has a rate of change of 2.33
So f(x) is growing faster

The prove that segment MP is congruent to segment NO (MP ≅ NO) can be presented as follows;

Statement [tex]{}[/tex]                             Reasons

1. ∠LMN ≅ ∠LNM [tex]{}[/tex]                 1. Given

∠MPN ≅ ∠NOM

2. MN ≅ MN  [tex]{}[/tex]                        2. Reflexive property

3. ΔMNP ≅ ΔNMO [tex]{}[/tex]               3. SAA congruency postulate

4. MP ≅ NO  [tex]{}[/tex]                         4. CPCTC

Two segments are congruent if they have the same length

The known relationships between the measures of the angles are;

∠LMN ≅ ∠LNM

∠MPN ≅ ∠NOM

Required to prove that MP ≅ NO

The two column method can be used to prove the congruency of the sides MP and NO as follows;

Statement     [tex]{}[/tex]                                 Reasons

1. ∠LMN ≅ ∠LNM         [tex]{}[/tex]                1. Given            

∠MPN ≅ ∠NOM

2. MN ≅ MN     [tex]{}[/tex]                            2. Reflexive property of congruency

3. ΔMNP ≅ ΔNMO     [tex]{}[/tex]                  3. SAA congruency rule

4. MP ≅ NO     [tex]{}[/tex]                             4. CPCTC

Details of the above postulates and rules used to prove the congruency of the segments MP and NO are as follows;

SAA congruency postulate

The SAA (SAA is an acronym for Side-Angle-Angle) congruency postulate states that if two angles and a non included side of one triangle are congruent to two angles and a non included side of another triangle, then the two triangles are congruent.

CPCTC

CPCTC is an acronym for Corresponding Parts of Congruent Triangles are Congruent. It indicates that if two triangles are congruent, then, their corresponding sides are also congruent.

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−5.25  > −6.

There are two of them.

These two numbers need to be compared.

A number's square root is never greater than the number itself.

According to the question, we have -

A = −5.25

B =  −6.

Clearly, A > B

Hence,−5.25  > −6.

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The table represents a function. X y 0 6 2 8 4 10 6 12 complete the statement by selecting from the drop-down menu. The rate of change in the function y = x + 4 is  equal to the rate of change of the function represented in the table.

Consider the function shown in the table.

The table's coordinates are as follows:

(0,6) (2,8) (4,10) and (6,12) (6,12)

Take into account the first two coordinates (0, 6) and (2,8)

x₁=0, y₁=6, x₂=2, y₂=8

Linear equation is provided by (y-y₁) =m(x-x₁)

Where 'm' is the slope (rate of change), the following formula is used:

m = y₂ - y₁

      x₂ - x₁

So,

m = 8 - 6 = 1

      2 - 0

So, the line's equation is:

(y-6)= 1 (x-0) (x-0)

y-6=x

y=x+6

Putting it up against the common equation of the line y=mx+c with slope "m."

Thus, m(Rate of Change)=1 is obtained.

Now,

We will calculate the slope for the function y=x+4

Putting it up against the common equation of the line y=mx+c with slope "m."

Thus, m(Rate of Change)=1 is obtained.

The rate of change in the function y=x+4 is therefore equal to the rate of change of the function shown in the table.

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On solving the provided question, we can say that by permutation, 90  different 8-topping pizzas are possible

The permutation of a set in mathematics is essentially the rearranging of its elements if the set is already ordered, or the arrangement of its members in a linear or sequential order. The act of altering the linear order of an ordered set is referred to as a "permutation" in this context. The mathematical calculation of the number of possible arrangements for a given set is known as permutation. Permutation, in its simplest form, refers to the variety of possible arrangements or orders. The placement of the elements matters with permutations. The placement of items in a specific order is known as a permutation. Here, the set's components are sorted in either chronological order or linear order.

here,

by permutation

[tex]^{10}P_8[/tex] = 10!/2/1 = 10 X 9 / 1 = 90 ways

90  different 8-topping pizzas are possible

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The value of m∠5 = m∠4 + 10° or  m∠3 + 20°.

The exterior angle of a polygon is the angle formed by one side of the polygon and the extension of the adjacent side. The measure of each exterior angle of a polygon is equal to the sum of the interior angles of the polygon divided by the number of sides of the polygon.

Solution:

The given value of m∠4 = m∠3+ 10°

The value of m∠5 is increase in 10° of m∠4

The answer is m∠5 = m∠4 + 10°.

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Answer:

x=18/5, y=40. (18/5, 40).

Step-by-step explanation:

y=5x+22

y-4=10x

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

y=10x+4

10x+4=5x+22

10x-5x=22-4

5x=18

x=18/5

y-4=10(18/5)

y-4=36

y=36+4

y=40

The system of equations 2x + y = 40 and x - 2y = -20 has a solution of x = 12 and y = 16. We can solve this system by using the method of substitution or elimination.

One way to solve the system is to use the method of substitution. We can first solve one of the equations for one of the variables and substitute that expression into the other equation.

For example, we can solve the first equation for y by isolating y on one side: y = 40 - 2x. Then we can substitute that expression into the second equation and solve for x:

x - 2(40 - 2x) = -20

x - 80 + 4x = -20

5x = 60

x = 12

Then we can substitute x = 12 into the first equation, or either equation to find the value of y:

2(12) + y = 40

y = 16

So the solution to the system of equations is x = 12 and y = 16.

Another way to solve the system of equations is to use the method of elimination. This involves adding or subtracting the equations to eliminate one of the variables. For example, we can add the equations and get:

3x - y = 20

Then we can solve for x or y and substitute it back into either of the equation to find the other variable.

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The complete question is:

What is the solution to this system of equations 2x + y = 40 and x - 2y = -20?

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Answer:

35feet

Step-by-step explanation:

Since it's a scale, we can take the backsides of both buses. They read 2in and 10ft

12 inches are in one foot, so 120 inches are in 10ft

Next we'll divide 120/2 and we get 60.

That's means we can multiply 7 * 60, getting 420inches

To get it back to feet, we divide by 12

420/12 = 35 feet

Answer:

Below

Step-by-step explanation:

For the Quadratic Equation   - 16t^2+ 60t + 80

   the max value will occur at   t = - b/2a =  -60 / (2 * -16) = 1.875 s

     use this value f t in the equation to find max height = 136.25 ft

Answer:

36

Step-by-step explanation:

7/6 u=42

7u =42×6

u=252/7

u=36

In this quadrilateral, Dilation A will have largest scale factor.  Dilation B is smallest and will have smallest scale factor. Now for the given scale factors: 3/4 > 1/2 > 1/4

A quadrilateral is a four-sided polygon in geometry that has four edges and four corners. The word is a derivative of the Latin words quadri and latus (meaning "side"). Having four sides, four vertices, and four corners, a rectangle is a two-dimensional form. Concave and convex come in primarily two varieties. Additionally, there are several subclasses of convex quadrilaterals, including trapezoids, parallelograms, rectangles, rhombuses, and squares. Four straight sides make up a rectangle, which is a two-dimensional form. There are several different types of quadrilaterals, including parallelograms, trapezoids, rectangles, kites, squares, and rhombuses.

here,

in this quadrilateral

Dilation A will have largest scale factor.

Dilation B is smallest and will have smallest scale factor.

Now for the given scale factors:

3/4 > 1/2 > 1/4

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Answer:0.125% on all ingredients or go to the store and buy more

Step-by-step explanation:

what persent is 3 1/2 out of 4 is 87.5%

87.5% - 100% = 0.125%

Answer:

0.36

0.0068

0.043

0.00048

Step-by-step explanation:

trust me bro

The function that could represent Laura's charges is given by -

y = 5x + 12

Given is that bryan is starting a tutoring company that charges $10 as an initial fee and 7.50 dollars per hour of tutoring. Laura is starting her own company and she wants to charge less for the initial fee, but more per hour.

The function representing the amount charged by Brayan is -

{B} = 10 + 7.5x

Amount charged by Bryan per hour is -

$7.5

Amount charged by Bryan as an initial fee -

$10

The function which charge less for the initial fee, but more per hour is -

y = 5x + 12

Therefore, the function that could represent the amount charged by Laura is given by -

y = 5x + 12

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Answer: To solve this problem, we can use the law of cosines. The law of cosines is a useful tool for solving problems involving distances and angles between points in two-dimensional space. We can use the law of cosines to find the distance between the starting and ending point of the hike, and the bearing to get back to camp.

The law of cosines states that:

c^2 = a^2 + b^2 - 2ab * cos C

where c is the distance between the two points, a and b are the distances of the two legs of the hike, and C is the angle between them.

Using the given information, we can set a as the distance traveled at 3.5 miles per hour for 2 hours, which is 3.5 * 2 = 7 miles,

b as the distance traveled at 3.5 miles per hour for 4 hours which is 3.5 * 4 = 14 miles,

C as the angle between the two legs of the hike which is (72 + 23) = 95 degrees.

Now we can substitute this values into the law of cosines formula:

c^2 = 7^2 + 14^2 - 2(7)(14) * cos 95

Solving this equation will give us the square of the distance between the starting and ending point of the hike. To find the actual distance, we'll have to take the square root of that.

The distance directly back to camp is √(196 - 98*(√2/2)) = √(196 - 98*(√2/2)) ≈ 8.14 miles

To find the bearing to head back to camp, we must know that the bearing of a line is defined as the angle between the line and the North direction, measured clockwise.

We can use the bearing of N72°W and S23°W to find the back bearing to camp.

The back bearing is (180 + 72 + 23) = 275 degrees. The hikers should take a bearing of 275 degrees to head back to camp.

Step-by-step explanation:

The weight of the bag of pinto beans she bought is; 2.4 lbs

Algebraic word problems are defined as questions that require translating sentences to equations, after which we then solve those equations.

Now, we are told that;

Amount paid by Alicia for a bag of pinto = $1.32

Cost of beans = $0.55 per lb

Now, the weight of the bag of pinto beans that Alicia bought will be;

Weight = Amount paid/cost per lb

Weight = 1.32/0.55

Weight = 2.4 lbs

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A quadratic inequality is an inequality that can be written in the form of "ax² + bx + c < or > 0" where a, b and c are real numbers and x is a variable.

The solutions to a quadratic inequality are the values of x that make the inequality true. To solve a quadratic inequality, we first set the expression equal to zero and then find the roots (also known as the zeroes or solutions) of the equation. We then use these roots to divide the number line into three regions: the region where the expression is less than zero, the region where the expression is greater than zero, and the region where the expression is equal to zero.

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Yes, the given function y = g(x) in the attached graph is invertible as each input value of x has unique output y.

As given in the question,

Graph of the function y = g(x) is attached.

Invertible function are defined as when each input value of the function has unique output or for each input there is only one and only one output.

In the given graph of the function y = g(x)

Each input value of x there is only one and only one output.

Given graph y = g(x) is representing the straight line.

Therefore, the given graph of the function y = g(x) represent it is an invertible function as each input as one and only one output.

The above question is incomplete, the complete question is :

Does function g appear to be invertible? Use complete sentence to explain you reasoning?

Graph of the function g(x) is attached.

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[tex]\dfrac{2}{3} (n-6)=5n-43[/tex]

Distribute:

[tex](\dfrac{2}{3} )(n)+(\dfrac{2}{3} )(-6)=5n-43[/tex]

[tex]\dfrac{2}{3} n-4=5n-43[/tex]

Subtract 5n from both sides:

[tex]\dfrac{2}{3} n-4-5n=5n-43-5n[/tex]

[tex]-\dfrac{13}{3} n-4=-43[/tex]

Add 4 to both sides:

[tex]-\dfrac{13}{3} n-4+4=-43+4[/tex]

[tex]-\dfrac{13}{3} n=-39[/tex]

Multiply both sides by -3/13:

[tex]-\dfrac{3}{13} \times(-\dfrac{13}{3} n)=-\dfrac{3}{13} \times(-39)[/tex]

[tex]\fbox{n = 9}[/tex]

Two tiles will be left over. Jenny will have two square tiles left over after arranging her tiles into a rectangular array of four rows.

50 quare tiles divided by 4 rows = 12.5 quare tiles

12.5 quare tiles per row x 4 rows = 50 quare tiles

50 quare tiles used - 50 quare tiles = 0 quare tiles

Remaining tiles = 0 quare tiles

50 quare tiles - 0 quare tiles = 50 quare tiles

Left over tiles = 2 quare tiles

Jenny has 50 square tiles which she arranges into a rectangular array of four rows. To work out how many square tiles are left over, first divide 50 by 4. This gives us 12.5 tiles per row, however this is not possible so we need to round this number down to 12. Multiplying 12 by 4 gives us 48 tiles used in the rectangular array. Subtracting the 48 tiles used from the 50 tiles that Jenny had originally gives us a result of 2 square tiles left over. In conclusion, Jenny will have two square tiles left over after arranging her tiles into a rectangular array of four rows.

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Maryellen will have in her account at the end of 3 year? (Round to the nearet cent. ) is 1578.93 dollar of 5% interest

Why is it called compound interest?

Compound interest is the interest on a deposit calculated based on both the initial principal and the accumulated interest from previous periods. Or, more simply put, compound interest is interest you earn on interest

What are simultaneous equations?

When two or more algebraic equations are solved concurrently, we call them simultaneous equations.

We can solve simultaneous equations by graphing, elimination, or substitution methods.

deposit = 1500

interest = 5%

after one year = 1500+75= 1575

second year = 78.75+1500 = 1578.75

third year = 78.93+1500= 1578.93

Maryellen will have in her account at the end of 3 year? (Round to the nearet cent. ) is 1578.93 dollar of 5% interest

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The scatter plot shows the results of the survey and yes, there is an outlier in the data set which is the lowest time value of grade 11 and it is an outlier because it is an extremely low data point relative to the nearest data point.

This is referred to as an extremely high or extremely low data point relative to the nearest data point and the rest of the neighboring co-existing values in a data graph.

The outlier is at the lowest time value if grade 11 and it falls under such category because it is an extremely low data point relative to the nearest data point in the given graph.

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[tex]\frac{sqrt{5} }{3}[/tex]

Step-by-step explanation:

Its root 5 over 3

Answer:

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

If m° is one of the angles of a right triangle, the complementary angle is (90 - m)°.

We know that sine of the angle is same as the cosine of the complementary angle. It means:

Therefore the value of cos (90 - m)° is 2/3.

Answer: 0.2 cm/yr

Step-by-step explanation:

simply divide centimeters by years

25.0 cm ÷ 125 yr

0.2 cm/yr ... answer



The rate of uplift is 0.2 cm/yr

hope that helps...

Answer:

29,

Step-by-step explanation:

Answer: -12ab^3

Step-by-step explanation: (-3ab^3) 4 -12ab^3

The Fundamental Theorem of Algebra asserts that this 2 n d degree polynomial must have precisely two roots.

According to the Fundamental Theorem of Algebra, this 2 n d degree polynomial must have precisely two roots. Algebra is the branch of mathematics that aids in the representation of problems or situations using mathematical expressions. In algebra, we utilize integers with definite or fixed values such as 2, 7, 0.068, and so on. In algebra, we employ variables such as x, y, and z in addition to integers. Elementary algebra, advanced algebra, abstract algebra, linear algebra, and commutative algebra are all sub-branches of algebra. In algebra, an algebraic expression is composed of integer constants, variables, and the basic arithmetic operations of addition(+), subtraction(-), multiplication(), and division(/). 5x + 6 is an example of an algebraic expression.

Here,

According to the Fundamental Theorem of Algebra, this 2 n d degree polynomial must have precisely two roots.

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5=-7/2x+12

-7=-7/2x

x=2