f(x)=x² +16x-24 and
g(x)=x²-5x-17, find (ƒ + g)(x).

Triangle JKL is congruent to triangle MLK based on angle - angle - side congruency theorem

A triangle is a polygon that has three sides and three angles. Types of triangles are equilateral, isosceles, scalene, right angled triangle. In an equilateral triangle, two sides are equal.

Two triangles are said to be congruent, if all angles and all sides are congruent to each other.

From the diagram:

∠KJL = ∠LMK (Given)

∠JKL = ∠MLK (Given)

KL ≡ KL

PS = QS (Definition of equilateral triangle)

ΔJKL ≅ ΔMLK (angle - angle - side congruency theorem)

Triangle JKL is congruent to triangle MLK

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The standard form, of the expression 3x³+7x-1+4x³-9x²-11x+1 is 7x³-9x²-4x

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given is an expression, 3x³+7x-1+4x³-9x²-11x+1 we need to make it in a standard form,

To arrange this expression in a standard form, we will just have to perform operations in like terms and then arrange them in decreasing order of the power of the variables,

Therefore,

3x³+7x-1+4x³-9x²-11x+1

Adding the like terms

= 4x³+3x³+7x-11x-9x²+1-1

= 7x³-9x²-4x

Hence, the standard form, of the expression 3x³+7x-1+4x³-9x²-11x+1 is 7x³-9x²-4x

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The distance of 2√65 miles Joselyn is from where she started.

The formula of the distance between two points is P(x₁, y₁) and Q(x₂, y₂) is given by: d (P, Q) = √ (x₂ – x₁)² + (y₂ – y₁) ².

Her initial position is the origin (0, 0), and she ran 2 miles north to reach (0, 2). Then, she ran 10 miles east to reach (10, 2). After that, she ran 4 miles north to reach (10, 6). Then, she ran 4 miles east to reach (14, 6). Finally, she ran 2 miles north to reach (14, 8).

To find the magnitude of Joselyn's displacement, we can use the Pythagorean theorem.  

We can consider the displacement from the starting point to Joselyn's final position as the hypotenuse of a right triangle, and the north-south and east-west displacements as the two shorter sides.

Thus, the displacement (d) can be calculated as:

d = √((14 - 0)² + (8 - 0)²)

d = √(14² + 8²)

d = √(196 + 64)

d = √(260)

d = 2√65

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The solution is, the quadrilateral ABCD is a trapezium.

In geometry a quadrilateral is a four-sided polygon, having four edges and four corners. The word is derived from the Latin words quadri, a variant of four, and latus, meaning "side".

here, we have,

from the given figure we get,

the figure has four sides, which are not all equal, and, two of them are parallel to each other.

here we get,

angle A = angle C = 80

angle B = angle D = 100

and, two sides are parallel to each other.

Hence, The solution is, the quadrilateral ABCD is a trapezium.

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Answer:

2. x=16

4. x=18.75, y=11.2

Step-by-step explanation:

2. x/8=30/15 ⇒x=2x8=16

4. x/15=8/6.4 ⇒x=1.25x15=18.75

  y/14=6.4/8 ⇒y=0.8x14=11.2

The missing side lengths x = 16; y = 11.2 and x = 18.75

Similar figures (2)

Given that the triangles are similar, we make use of the following equivalent ratio

8 : 15 = x : 30

Multiply the first ratio by 2

So, we have

16 : 30 = x : 30

By comparison, we have

x = 16

Similar figures (4)

Given that the triangles are similar, we make use of the following equivalent fraction equation

y/6.4 = 14/8

So, we have

y = 6.4 * 14/8

Evaluate

y = 11.2

For x, we have

x/8 = 15/6.4

This gives

x = 8 * 15/6.4

So, we have

x = 18.75

Hence, the value of x is 18.75

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Answer:

the value of x is 12 as per my calculation it goes in equation

Answer:

[tex]-0.281250[/tex]

Step-by-step explanation:

The given number has [tex]5[/tex] after the decimal point, so add a trailing zero.

the mile-a-minute weed can grow up to 0.25 inches per hour.

A fraction is a mathematical expression that represents a part of a whole. It is written as a ratio of two numbers, the numerator and the denominator, separated by a horizontal line. The numerator represents the part of the whole that is being considered, while the denominator represents the whole.

Given by the question.

To convert 0.5 ft per day to inches per hour, we can use the following conversion factors:

1 ft = 12 inches (since there are 12 inches in a foot)

1 day = 24 hours (since there are 24 hours in a day)

So, to convert 0.5 ft per day to inches per hour, we can use the following steps: Convert feet to inches:

0.5 ft x 12 inches/ft = 6 inches

Convert days to hours:

1 day = 24 hours, so:

6 inches/24 hours = 0.25 inches per hour

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The arithmetic expressions are solved and answered below -

5 - 9 = - 4

8 - 8 = 0

- 1 + 12 = 11

- 12 + 12 = 0

- 2 + 4 + 3 = 5

- 4 + 3 + 2 - 1 = - 2 + 2 = 0

In mathematics, an expression or mathematical expression is a combination of terms both variables and constants. For example -

2x + 4y + 5z

4y + 2x

Given are the expressions as given in the questions.

{a} -

5 - 9 = - 4

{b} -

8 - 8 = 0

{c} -

- 1 + 12 = 11

{d} -

- 12 + 12 = 0

{e} -

- 2 + 4 + 3

5

{f} -

- 4 + 3 + 2 - 1 = - 2 + 2 = 0

Therefore, the arithmetic expressions are solved and answered below -

5 - 9 = - 4

8 - 8 = 0

- 1 + 12 = 11

- 12 + 12 = 0

- 2 + 4 + 3 = 5

- 4 + 3 + 2 - 1 = - 2 + 2 = 0

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{Complete question -

Calculate the following:

a) 5-9

b) 8-8

c) -1 + 12

d) -12 + 12

e) -2 +4+3

f) -4-3+2-1}

The range of the given piecewise function is -

-4 ≤ x ≤ 3.

A piecewise function is a function that is defined on a sequence of intervals. A common example is the absolute value function.

Given is the piecewise function as shown in the image.

Range is the set of values that exist for a specific value in the domain of the function. So, we can write the range as the set of {y} values for the function. From the graph, we can write the range as -

-4 ≤ x ≤ 3

Therefore, the range of the given piecewise function is -

-4 ≤ x ≤ 3.

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The common factors of 20 and 45 are 1 and 5, since these are the only factors that both numbers share.

To find the common factors of two numbers, we need to find the factors of each number and then identify the ones that they have in common. For example, if we want to find the common factors of 20 and 45, we first find the factors of 20 and 45:

The factors of 20 are: 1, 2, 4, 5, 10, 20

The factors of 45 are: 1, 3, 5, 9, 15, 45

The factor 1 is always a common factor of any two numbers, since every number is divisible by 1. The factor 5 is a common factor of 20 and 45 because both 20 and 45 are divisible by 5. It is important to note that the other factors of 20 and 45 are not common factors, since they are not shared by both numbers.

Therefore, the common factors of 20 and 45 are 1 and 5, since these are the only factors that both numbers share.

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The gallon is a unit of volume that represents the capacity of a liquid in both conventional and US imperial systems of measurement. 1 gallon is defined as 4.54609 liters.

Gallon:

The gallon is a common unit of volume in both English and US customary units. There are three types of gallons in use today: Imperial Gallon, US Gallon, and US Dry Gallon. There are 4 quarts in a gallon, for a total of 8 pints, and each system has a different volume.

Current use of the imperial gallon as of 2021 is still used as the standard unit of petrol in four British overseas territories. It is also the standard unit of measure for six countries: Antigua and Barbuda, Grenada and Saint Lucia.

Liter:

A liter is a metric unit of volume. A liter costs 1/1000 of a cubic meter. The liter was used as the base unit of the basic French metric system. 1 liter is the volume of a cube, i.e. 10 cm x 10 cm x 10 cm, so 1 liter = 1000 cm3 and 1 liter = 0. 2641720524 gallons.

This unit of volume can be used in the International System of Units even though it is not an SI unit. Current use of liters . The liters are primarily used for pourable items (these items can be solid or liquid). These items are measured by the size or capacity of the container. It is also used to measure non-liquid volumes such as backpacks, car trunks, etc.

Formula for Converting Gallons to liters

The formula for converting 1 gallon of water in liters is :

Liter = Gallon x 3.785411784

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The value of x in the given figure is 6.

Alternate angles are angles that occur on opposite sides of the transversal line and have the same size.

Given that, two lines are parallel, line U ║ line V, we need to find the value of x,

Using the concept of alternate interior angles between parallel lines,

Alternate angles between the parallel, line are equal,

Therefore,

16x-6 = 90

16x = 96

x = 6

Hence, the value of x in the given figure is 6.

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The SI (International System of Units) unit of pressure is the pascal (Pa), which is defined as one newton per square meter (N/m²).

To convert megapascals (MPa) to pounds per square inch (psi), you can use the following conversion factor:

1 MPa = 145.0377377 psi,

To convert, simply multiply the number of megapascals by 145.0377377 to get the equivalent pressure in psi.

For example, if you want to convert 20 MPa to psi, you can use the conversion factor as follows:

20 MPa × 145.0377377 psi/MPa = 2900.75515 psi (rounded to two decimal places)

Therefore, 20 MPa is approximately equal to 2900.76 psi.

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Answer:

The true statement on the profitability is c.

Step-by-step explanation:

The theoretical profitability of the swimming, P(swimming), is one-half, but the experimental probability is 23 over 50.

The theoretical probability of an occurrence indicates the propensity to occur. The theoretical probability of receiving heads is 1/2 since we know that flipping a coin has an equal chance of landing tails or heads. The frequency of an event actually occurring in an experiment is referred to as its experimental probability.

The theoretical probability of swimming is 1 / 2 because it is either heads or tails. However, the experimental probability of swimming is:

so,

= Number of swimmers / Total number of students

= 23 / 50

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The theoretical probability of swimming, P(swimming), is one half, but the experimental probability is 12 over 40. The correct statement is option B.

The theoretical probability of an event is the probability calculated based on the assumption of equally likely outcomes, while the experimental probability is the probability determined from actual data or outcomes observed in an experiment.

In this case, there are 40 students, and each camper flips a coin to decide between swimming and hiking. The outcome frequency shows that 12 students chose swimming, and 28 students chose hiking.

Let's compare the theoretical and experimental probabilities of swimming:

The theoretical probability of swimming, P(swimming), is one-half (1/2), as there are two equally likely outcomes (heads or tails) when flipping a fair coin.

The experimental probability of swimming is the number of students who chose swimming (12) divided by the total number of students (40), which is 12/40.

Now, let's analyze the options:

A. The theoretical probability of swimming, P(swimming), is one half, but the experimental probability is 28 over 40.

The theoretical probability is correct (1/2), but the experimental probability is incorrect (it should be 12/40, not 28/40).

B. The theoretical probability of swimming, P(swimming), is one half, but the experimental probability is 12 over 40.

This statement correctly represents both the theoretical probability (1/2) and the experimental probability (12/40).

C. The theoretical probability of swimming, P(swimming), is 12 over 28, but the experimental probability is one half.

This statement has incorrect values for both the theoretical and experimental probabilities.

D. The theoretical probability of swimming, P(swimming), is 28 over 40, but the experimental probability is one half.

The theoretical probability mentioned here (28/40) is not correct. The theoretical probability of swimming is 1/2 (one-half), not 28/40.

The correct statement is option B:

The theoretical probability of swimming, P(swimming), is one half, but the experimental probability is 12 over 40.

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Answer:

Step-by-step explanation:

a)C

b)D

c)B

d)A

ok so 5/10=0.5

and 5/50=0.1

and 5/100=0.05

and 5/20=0.25

Answer:

(4,0)

Step-by-step explanation:

I will assume the fiorst equation is missing an "x," so I'll assume it was meant to be:  y = -x + 4

See the attached graph.  The lines cross at (4,0).

The nth term of the sequence is a{n} = 35 + (-5)(n - 1) and the 100th term would be a{100} = - 460.

A sequence in which the difference of the consecutive terms remain constant is called a arithmetic sequence.

Given is the sequence as -

35, 30, 25, 20

We can write the nth term of the sequence as -

a{n} = a + (n - 1)d                                            ... { 1 }

a{n} = 35 + (-5)(n - 1)

For {n} = 100, we can write -

a{100} = 35 + (-5)(99)

a{100} = 35 - 495

a{100} = - 460

Therefore, the nth term of the sequence is a{n} = 35 + (-5)(n - 1) and the 100th term would be a{100} = - 460.

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The number of miles driven is 150

From the question, we have the following parameters that can be used in our computation:

Base fee = $15.99

Additional charge = $0.90

Using the above as a guide, we have the following:

Total charge = Base fee + Additional charge * Number of miles

Substitute the known values in the above equation, so, we have the following representation

15.99 + 0.9 * Number of miles = 150.99

Evaluate the like terms

0.9 * Number of miles = 135

Divide

Number of miles = 150

Hence, the Number of miles is 150

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Answer: 70.08

Step-by-step explanation:

0.96*73=

Answer:

The one you provided in your text: Yes, each input has exactly one output.

The second one: No. 3 has two outputs.

The third one: No, two outputs for each x>-4.

The fourth one: Yes, unique y for each x.

9 is the value of C.

A triangle is a three-sided polygon that consists of three edges and three vertices.

The three given angles are (3c)° 42° 111°

We need to find the value of C.

The figure might be a triangle because there are three angles.

From angle sum property , the sum of three angles of triangle is 180 degrees.

3c+42+111=180

3c+153=180

Substitute 153 from both sides

3c=27

Divide both sides by 3

c=9

Hence, the value of c is 9.

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Answer: The correct pair of functions that could have been used to create the graphs of q and w is:

q(x) = x² - 18 and w(x) = x²

The vertex of the graph of q is (0, -18) and the vertex of the graph of w is (0, 0). Since the vertex of the graph of q is 18 units below the vertex of the graph of w, this is the pair of functions that would produce the given information.

Step-by-step explanation:

The measure of angle ∠A will be 53.13.

The branch of mathematics that sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.

The trigonometric functions, also known as circular, angle, or goniometric functions in mathematics, are real functions that link the angle of a right-angled triangle to the ratios of its two side lengths.

The two sides are perpendicular = 9.2 and the base is 7.2. The angle ∠A will be calculated as:-

tan(A) = P / B

A = tan⁻¹ ( 9.2 / 7.2 )

A = 53.13°

Therefore, the measure of angle ∠A will be 53.13.

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Answer:

A : 0.9 B: 45.2 C:0.006 D:3/500 E:25% F: 1/4

Step-by-step explanation:

Percent error in Keiko's estimate is 6.25%

Percent error is the difference between estimated value and the actual value in comparison to the actual value and is expressed as a percentage.

[tex]Percent error=\frac{|observed value -true value|}{true value}*100[/tex]

Students estimate the distance a toy car will role down a ramp.

The car rolls 80cm.

Keiko estimate for the distance the car will role is 85cm.

Percent error in Keiko's estimate is calculated by,

[tex]Percent error=\frac{|observed value -true value|}{true value}*100[/tex]

                     = [tex]\frac{|85-80}{80} *100[/tex]

                     =6.25%

Hence, percent error in Keiko's estimate is 6.25%

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The slope of the segment [tex]\overline{DC}[/tex] of the line DA is equivalent to the slope of the segment [tex]\overline{BA}[/tex], which is 2/5. Therefore;

Slope of [tex]\overline{DC}[/tex] = [tex]\frac{2}{5}[/tex]

The slope, m, of a graph with points (x₁, y₁), and (x₂, y₂) can be found using the formula;

[tex]m = \frac{y_2 - y_1}{x_2-x_1}[/tex]

The colinear points are; D, C, B, and A

The slope of the each section of a straight line graph are equivalent, therefore;

The slope of the line DA using the segment [tex]\overline{BA}[/tex] is the same as the slope of the line DA found using the segment of the line [tex]\overline{DC}[/tex].

The slope of a line is the ratio of the rise to the run of the line

Slope = Rise/Run

The rise of a segment of a line is the vertical elevation of the line segment, while the run of the segment of a segment of the line is the horizontal distance between the boundaries of the segment of the line.

The rise of the line between points A and B is 2 unit while the run of the segment [tex]\overline{BA}[/tex] is 5 units.

The slope of [tex]\overline{BA}[/tex] = (2 units)/(5 units) = 2/5

The slope of [tex]\overline{DC}[/tex] = The slope of BA = 2/5

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The amount of square feet that will be needed is given as follows:

122 ft².

The amount of square feet needed is given by the total area of the figure, which is composed as follows:

The area of the rectangle is given by the multiplication of the dimensions, hence:

Ar = 6 x 15 = 90 ft².

The area of the trapezoid is given by half the multiplication of the sum of the bases and the height, hence:

At = 0.5 x 4 x (6 + 10) = 32 ft².

Hence the total area is given as follows:

A = Ar + At

A = 122 ft².

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The following table contains the appropriate values for A, B, and C:

White 13 52 91 130 Black 9 36 63 90

The definition of a proportionate relationship is as follows:

y = kx.

where k is the proportionality constant.

The following are the input and output variables for this issue:

Number of black keys to enter.

Number of white keys is the output.

The constant k is then obtained using the formula:

91 = 63k

k = 91/63

k = 13/9.

Hence the equation is:

y = 13x/9.

Hence the values are given as follows:

A: when x = 9, y = 13.

B: when x = 36, y = 13 x 36/9 = 52.

C: when x = 90, y = 13 x 90/9 = 130.

Hence the first table is correct.

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To reflect a point across the y-axis, you multiply the x-coordinate of the original point by -1 while keeping the y-coordinate the same. So, reflecting the point (-9, -5) across the y-axis results in the point (9, -5).

Answe

To reflect a point across the y-axis, you multiply the x-coordinate of the original point by -1 while keeping the y-coordinate the same. So, reflecting the point (-9, -5) across the y-axis results in the point (9, -5).

Step-by-step explanation: