a. Evaluate f(5) given that f(x) =
f(5) =
b. Evaluate g(x + 3) given that g(x) = 3x² - 6x + 9.
g(x + 3) =
c. Evaluate h(2x) given that h(y) =
x² + (17-4x)
9x
h(2x)=
Preview
y³ - 5
7y
Preview
Preview

Answer:

y= x +4

Step-by-step explanation:

The equation of a line can be written in the slope-intercept form, y= mx +c, where m is the slope and c is the y-intercept.

Overview of steps:

The slope can be found using the gradient formula below:

[tex]\boxed{\text{Gradient} = \frac{y_1 - y_2}{x_1 - x_2} }[/tex]

Given: (5, 9) and (0, 4)

Start by finding the slope, m:

m

[tex] = \frac{9 - 4}{5 - 0} [/tex]

[tex] = \frac{5}{5} [/tex]

= 1

Substitute m= 1 into y= mx +c:

y= x +c

In this case, the y-intercept is given by the point (0, 4). This is because y-intercepts occur at x= 0. This also means that c takes the value of 4.

Substitute c= 4:

y= x +4

Thus, the equation of the line is y= x +4.

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Answer: 3x+14

Step-by-step explanation:

Evaluate 4.2x+3−1.2x+11

Subtract the terms 3x+3+11

Solution 3x+14

Reflexive property of congruence CPCTC .

When two objects or figures have the same size and shape, the term "congruence" is used to describe it. Congruence has the transitive property, which states that if two sets of lines, angles, or triangles are congruent with a third pair of lines, angles, or triangles, then the first pair of lines, angles, or triangles are also congruent with the third pair of lines, angles, or triangles. As was previously mentioned, the transitive property creates an equivalence relationship between 3 lines, 3 angles, and 3 triangles. According to the definition of the transitive property of congruence in geometry, if any two angles, lines, or forms are, respectively, congruent with a third angle, line, or shape, then the first two angles, lines, or shapes are likewise congruent with the third angle, line, or shape.

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Answer:

The answer to the first box is SSS criterion, im not sure about the second box, i know it isnt ASA criterion, but i hope this helps!

Step-by-step explanation:

Answer:

Absolute value means taking the positive value, ie drop the negative sign.

Absolute value brackets are: | value |

|(4,-4)| = (4,4)

|(-3,-4)| = (3,4)

Hope that helps

Given: The equation of a line below

To Determine: The slope and the y intercept

Solution

The general form of slope-intercept form of a line is given as

Let us re-write the given equation in slope-intercept form

Let us compare the derived given equation to the general form

The graph is as shown below

Hence, the slope is 2 and the y intercept is -8

1) The fraction is given as,

c) The fraction is given as,

d) The fraction is given as,

ANSWER: y - 0 = 7/2(x - 6)

STEP-BY-STEP EXPLANATION:

The formula for point-slope form is y - y1 = m(x - x1).

From the two points given, y1 is 0 while x1 is 6.

m in the formula is the slope, so it needs to be found:

(y2 - y1)/(x2 - x1)

(7 - 0)/(8 - 6)

7/2

Answer:

Remember, when you are calculating the slope from two given points, you are finding the change in y over the change in x.

P1   =  ( x1,  y1 )

P2   =  ( x2,  y2 )

m = Δy  / Δx   --->      m = (y2 - y1) / (x2 - x1)

Now let's assign the given points:

(-8, -6)  -->   x1 = - 8   &   y1 = -6

(-4, 2)   -->    x2 = -4    &   y2 = 2

Now, let's plug these values into the slope formula:

m = (y2 - y1) / (x2 - x1)

= (2 - (-6)) / ((-4) - (-8))

Let's simplify:

(2 - (-6)) / ((-4) - (-8))

= (8) / (4)

= 2

Therefore, the slope, or m, is 2.

Now that we have found the slope, let's write out the final equation in point-slope form.

What is required for the equation is a slope, and any pair of points on the line. Since we were given two to choose from, I will use (-4, 2) in this case.

Remember, the point-slope formula is:  y - y1 = m (x - x1)

In terms of this formula:

m  =   2

y1  =   2  

x1  =  -4

Let's plug in these values into the point slope formula and simplify:

y - y1 = m (x - x1)

y - (2)  =  (2)(x - (-4))

y - 2  =  2(x + 4)

y - 2  = 2x + 8

y = 2x + 10

Therefore, our final answer is: y = 2x + 1

Step-by-step explanation:

i gat that from https://www.wyzant.com/resources/answers

Answer: 1.176 pounds of sugar per dollar.

Step-by-step explanation:

3 / 2.55 = 1.1764705

Answer:

Please see attachment for explanation and answer.

The number of batches of cookies that can be made with 4 pounds of flour is 6 batches.

In order to determine the number of batches of cookies that can be made, divide the amount of flour by the fraction that represents the amount of flour needed for a batch of cookies.

Division is the operation that is used in mathematics to determine the quotient of two or more numbers. It entails grouping a number into equal parts using another number.

Number of batches that can be made = amount of flour ÷ amount of flour needed for one batch

4 ÷ 2/3

4 x 3/2 = 6 batches

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During plantation sunflower was 15 inches tall , then grow at the rate of 2 inches per week , after 9 weeks sunflower would be 33 inches tall.

As given in the question,

During plantation sunflower was 15 inches tall

Rate of growth per week = 2 inches

Let x be the number of weeks and y be the height of the plant.

Required height :

y = 15 + 2x

Change in the height of sunflower after 9 weeks

y =15 +2x

 = 15 + 2(9)

 = 15 +18

  = 33 inches

Therefore, during plantation sunflower was 15 inches tall , then grow at the rate of 2 inches per week , after 9 weeks sunflower would be 33 inches tall.

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Answer: 24

Step-by-step explanation:

Factors of 96:  1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96

Factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60 , 120

Highest number between the two sets of factors which is common is 24

Answer:

155

Step-by-step explanation:

125 (1+24%) = 155

Answer: Neither Im prrtty sure but someone double check me

Considering the angle relations when two parallel lines are cut by a transversal, the measures of the angles are given as follows:

18. <4 = 56º.

19. <3 = 132º.

20. <2 = 55º.

21. <8 = 120º.

22. <6 = 129.5º.

23. <2 = 61.3º.

When two parallel lines are cut by a transversal, there are multiple relations among the angles, which are going to be used to solve this question.

In item 18, the angles 1 and 4 are consecutive interior angles, hence they are supplementary angles, meaning that the measure of angle 4 is found as follows:

<4 + <1 = 180º

<4 + 124º = 180º

<4 = 56º.

In item 19, angles 2 and 3 are also consecutive interior angles, hence:

<2 + <3 = 180º

48º + <3 = 180º

<3 = 132º.

For item 20, angles 2 and 4 are alternate interior angles, hence they are congruent and their measures are given by:

<2 = <4 = <55º.

For item 21, angles 6 and 8 are alternate exterior angles, also being congruent, hence their measures are given as follows:

<6 = <8 = 120º.

For item 22, angles 7 and 6 are same side exterior angles, meaning that they are supplementary, hence:

<6 + <7 = 180º

<6 + 50.5º = 180º

<6 = 129.5º.

For item 23, the relation is the same as item 19, hence:

<3 + <2 = 180º

<2 = 180 - 118.7

<2 = 61.3º.

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The rigid transformations of translation and reflection of the pentagon ABCDE to obtain A'B'C'D'E' gives;

First part;

[tex]AB \cong A'B'[/tex] True

[tex]\angle D \cong \angle D'[/tex] True

[tex] \overline{D'E'} \cong \overline{DE}[/tex] True

[tex] ABCDE \cong A'B'C'D'E'[/tex] True

Second part;

Their perimeters are equal; True

The area of the image is greater; False

They are congruent; True

Their orientations are the same; False

A rigid transformation is an Euclidean space one in which the distances between corresponding points on the figure and the image are preserved.

The vertices of the pentagonal figure are; A(-3, 4), B(0, 5), C(1, 4), D(1, 2,), and E(-2, 1)

The transformation are;

Translation transformation

Vertical translation transformation 2 units downwards

Horizontal translation of 5 units to the right

The coordinates of the vertices of the pentagon following the transformations are;

A(-3, 4) → (-3 + 5 + 4 - 2) → (2, 2)

B(0, 5) → (0 + 5 + 5 - 2) → (5, 3)

C(1, 4) → (1 + 5 + 4 - 2) → (6, 2)

D(1, 2) → (1 + 5 + 2 - 2) → (6 0)

E(-2, 1) → (-2 + 5 + 1 - 2) → (3 -1)

Reflection;

A reflection in the y–axis, which gives;

(2, 2) Reflection in y–axis gives A'(-2, 2)

(5, 3) Reflection in y–axis gives B'(-5, 3)

Similarly, we have;

(6, 2) → C'(-6, 2)

(6 0) → D'(-6, 0)

(3, -1) → E'(-3, -1)

AB = √((0-(-3))² + (5 - 4)²) = √(10)

A'B' = √(((-5)-(-2))² + (3 - 2)²) = √(10)

Therefore;

[tex]AB \cong A'B'[/tex]

Similarly, given that the specified transformations of translation and reflection are rigid transformations, we have;

[tex]\angle D \cong \angle D'[/tex]

[tex] \overline{DE} \cong \overline{D'E'}[/tex]

[tex] ABCDE \cong A'B'C'D'E'[/tex]

Second part;

Given that the transformation are rigid transformations, we have that the perimeter of the figure and the image have the following statements that are true

Their perimeter are equal

The areas of the image and figure are the same

They are congruent

The orientation are different following the reflection which reverses the order of the appearance of the vertices relative to the y–axis

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The part of speech of word 'rainstorm' is a noun in the sentence 'the campers were drenched by the rainstorm'.

There are eight parts of speech. They are noun, pronoun, adjective, verb, adverb, preposition, conjunction, and interjection. Further, these parts of speech are subdivided into different types.

A noun is the name of a person (for example, Ram, Neetu, John, etc.), place (for example, Delhi, Lucknow, Jaipur, America, etc.) or a thing (for example, table, desk, pen, rainstorm, etc.).

There are five types of noun: proper noun, common noun, abstract noun, material noun and collective noun.

Hence, the italicized word in the given sentence is a noun.

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Using proportions, we find that the hedgehog loses 3.45 ounces after 115 days of hibernation.

Here, we are given a table shows the proportional relationship between a​ hedgehog's weight loss and the number of days of hibernation

A proportional relationship is mathematically represented as-

y = kx

where k is the constant of proportionality.

Here x = days in hibernation and y = loss in weight

From the table we see that when x = 8, y = 0.24

⇒ 0.24 = 8k

8k = 0.24

k = 0.24/ 8

k = 24/ 800

k = 3/100

k = 0.03

Now, when x = 115, y will be-

y = 0.03*115

y = 3.45

Thus, using proportions, we have found that the hedgehog loses 3.45 ounces after 115 days of hibernation.

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Your question was incomplete. Check for full content below-

The table shows the proportional relationship between a​ hedgehog's weight loss and the number of days of hibernation. How much weight does the hedgehog lose during 115 days of​ hibernation? Use pencil and paper. Explain how you know that the relationship between the​ hedgehog's weight loss and the number of days of hibernation is proportional.

Weight Loss of Hedgehog

Days of Hibernation    8        28      75      93

Loss in Weight​ (oz)    0.24   0.84   2.25   2.79

If Emily wants to buy a 22 feet wire and Andy wants to buy a 14 yards wire then their total cost would be $23.04.

The length of a foot is 12 inches. A ruler can be used to calculate the length of a foot, which is usually one foot. The length of a piece of paper is about one foot.

3 feet make up one yard. A yardstick, which is equal to 1 yard, is typically used to measure yards. The length of a baseball bat is about one yard.

Using the conversion Rule we will convert feet into inches that is

22 feet = 264 inches

We will also convert yards into inches that is

14 yards = 504 inches

Total wire they need = 264 + 504 inches

                                   = 768  inches

We have given that

100 inches wires costs = $3

1 inch wire costs = 3/100

768 inch wire costs = (3/100) × 768

                                 = $23.04

Thus, If Emily wants to buy a 22 feet wire and Andy wants to buy a 14 yards wire then their total cost would be $23.04.

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Possible answer:

y = 2x + 60

Step-by-step explanation:

First, we will have to find the slope for the line that passes through those points, because parallel lines have the same slope but different y-intercepts. We only need the slope.

Let's use the formula for finding the slope from two points: [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]. My work is shown below:

[tex]\frac{9-1}{2-(-2)} \\\frac{8}{4} \\2[/tex]

The slope is 2, so this will be the slope for our parallel line. Parallel lines can have any y-intercepts, so let's just pick a random one - 60 (yours doesn't have to be this, I just picked one at random). So, one example of an answer to this question would be y = 2x + 60.

The common difference of the arithmetic sequence is found as -10.

For the given question;

The arithmetic sequence is given as;

28, 14,....

Where 28 is the first term; a₁ = 24.

14 is the second term; a₂ = 14.

Then the common difference 'd' is calculated as;

d =  a₂ - a₁

put the values.

d = 14 - 24

d = - 10

Thus, the common difference of the arithmetic sequence is found as -10.

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The length of the rectangle whose area is 7 units larger than its perimeter is 13 units.

The area of a rectangle is the product of its length and width.

The perimeter of a rectangle is the sum of the lengths of all the sides.

Given, Area of a rectangle is 7 units larger than its perimeter.

Assuming the length of the rectangle to be 'l' and the width to be 'w',

and the width is 3 units.

∴ (l×w) = 2(l + w) + 7.

(l×3) = 2(l + 3) + 7.

3l = 2l + 6 + 7.

l = 13 units.

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The most appropriate choice for equation of line in slope intercept form will be given by-

[tex]y = -4x-3[/tex] is the required equation of line

What is equation of line in slope intercept form?

The most general form of equation of line in slope intercept form is given by y = mx + c

Where m is the slope of the line and c is the y intercept of the line.

Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.

If [tex]\theta[/tex] is the angle that the line makes with the positive direction of x axis, then slope (m) is given by

m = [tex]tan\theta[/tex]

The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.

The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.

Here,

Slope of the line = -4

The line passes through (-2 , 5)

Equation of the required line =

[tex]y - 5 = -4(x - (-2))\\y - 5 =-4x - 8\\y = -4x - 8+5\\y = -4x-3[/tex]

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1. In a situation when a heat capacity is negative, it should instead be set to zero since it is not possible for an object to not be able to have internal energy.

2. A negative value mean that an object is continuously releasing or creating energy which violates the Law of Conservation of Energy.

An experiment is a technique that is carried out to support or deny a hypothesis, or to test the efficacy or likelihood of something that has never been tried before. Experiments shed light on cause-and-effect relationships by revealing what happens when a certain element is changed.

When a system loses energy, such as through radiating energy into space, the average kinetic energy increases. If temperature is defined by average kinetic energy, the system is said to have a negative heat capacity.

Heat transfer into a system is positive, whereas heat transfer out of a system is negative. It means that any heat transfer that raises a system's energy is positive, whereas any heat transfer that decreases a system's energy is negative.

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Answer:

Domain: (-5, ∞)

Range: [-4, 1]

Step-by-step explanation:

Domain is the set of all permissible values of x for the function. The smallest value of x is at x = -5. However note that there is an unfilled circle at x = -5 where y = -1. This means the point(-5, -1) is excluded in the function

The function flattens out at x = 3 and the arrow on the end of the function plot indicates that the x-value of the function goes up to ∞

The domain in interval form is (-5, ∞).
Be careful with the brackets. The regular parentheses ( and ) indicate that the extremes of the interval -5 and ∞ are not included in the interval. ∞ is never included. Such an interval is called an open interval.

The range is the set of y-values for the domain
Looking at the graph we can see that the lowest y value is -4 at x = -2 and it is a valid value for the function so included in the interval

The highest value of y is 1 and it becomes 1 at x =3 but since the plot after x = 2 is horizontal, that means the y value will be 1 for any value x >= 3

Therefore the range of the function is
[-4, 1]

Here note that we are using square brackets to indicate that -4 and 1 are included in the interval. Such an interval is called a closed interval.

The number of Nickle is 7 and number of dimes is 13.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

Michael has $1.65 worth of nickels and dimes.

He has 6 more nickels than dimes.

Let x be the number of nickels

then,  the number of dimes = x + 6

as, we know that nickel is worth 5 cents.  

A dime is worth 10 cents.

So, 0.05x + 0.10(x + 6) = 1.65

0.05x + 0.10x + 0.60 = 1.65

0.15x = 1.65- 0.60

0.15x = 1.05

x= 7

Hence, the number of Nickle is 7 and number of dimes is 13.

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Divide [tex]\frac{p^{3} - 13p +12 }{p +4}[/tex] by p+4  is [tex]p^{2} -4p +3\\[/tex]

One of the four fundamental mathematical operations, along with addition, subtraction, and multiplication, is division. Division is the process of dividing a larger group into smaller groups so that each group contains an equal number of things. It is a mathematical operation used for equal distribution and equal grouping. An equation that establishes a connection between all four components of the division is known as the division algorithm. The dividend value is always equal to the product of the divisor and the quotient added to the remainder in any division fact. Dividend = (Divisor Quotient) + Remainder is the general formula for division. The algorithm for division is used in this.

=[tex]\frac{p^{3} - 13p +12 }{p +4}[/tex]

= [tex]p^{2} -4p +3\\[/tex]

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Using the equation x - 7 = 12, we can apply it to find the number of students in Mrs. Jones' class, where the girls are 12 and the boys are 7.

An equation is a mathematical statement that two or more expressions share equality or are equivalent in value.

The equation sign (=) is used when two expressions or values are equal.

x - 7 = 12

Where the number of girls = 12

And the number of boys = 7

x = 12 + 7

x = 19

Thus, we can conclude from the equation x - 7 = 12 that x is the total number of students in Mrs. Jones' class.

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The inequality we want to find is:

$40 + $0.08*x ≤  $170

Where x is the number of miles Justin can drive, and the solution is:

x ≤ 1,625

We know that there is a fixed cost of $40 plus $0.08 for every mile driven. So if you rent the car and drive for x miles, the total cost is:

C(x) = $40 + $0.08*x

We know that Justin has at most $170 to spend, so we can write the inequality:

$40 + $0.08*x ≤  $170

Solving this for x, we get:

$0.08*x ≤  $170  - $40

$0.08*x ≤  $130

x ≤  $170 /$0.08  

x ≤ 1,625

So Justin can drive at most 1625 miles with the money he has.

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Answer:

Inequality: 40x+10≤170

Answer: x 4x≤4

Step-by-step explanation:

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