A car travels at 30 1/5 miles in 2/3 of an hour. What is the average speed in miles per hour of the car

Answer:

y=1/2x+5

Step-by-step explanation:

y=mx+b

The equation of the line that passes through the point (6,8) and has a slope of 1/2 will be y=1/2x+10.

A straight line is a combination of endless points joined on both sides of the point. A linear equation has the form y = mx + b in the slope-intercept format. X and Y are the variables in the equation. The values m and b represent the line's slope (m) and the value of y when x is 0.

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

It is given that the equation of the line that passes through the point (6,8) and has a slope of 1/2,

The standard equation of the line passes through the points (x₁,y₁) having slope m is,

y-y₁=m(x-x₁)

Substitute the given value as

y-8=-1/2(x-6)

2(y-8)=-1(x-6)

2y-16=x-6

2y=x-6+16

2y=x+10

y=1/2x+10

Thus, the equation of the line that passes through the point (6,8) and has a slope of 1/2 will be y=1/2x+10.

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Answer:

square so all sides are equal

bc^2+mc^2=bm^2

16x^2+4x^2=20x^2=2root5x

nd^2+dm^2=nm^2

x^2+4x^2=5x2=root5x

then:-

1/2*b*h=1/2*2root5x*root5x

=1/2*10x^2=5x^2

==================================

Work Shown:

ND = x

AN = 3x

MD = 2x

MC = 2x

BC = 4x

AB = 4x

-------

P = Area of square ABCD

P = (AB)^2

P = (4x)^2

P = 16x^2

-------

Q = Area of triangle ABN

Q = (1/2)*base*height

Q = (1/2)*AN*AB

Q = (1/2)*3x*4x

Q = 6x^2

-------

R = Area of triangle MBC

R = (1/2)*base*height

R = (1/2)*BC*MC

R = (1/2)*4x*2x

R = 4x^2

-------

S = Area of triangle MND

S = (1/2)*base*height

S = (1/2)*ND*MD

S = (1/2)*x*2x

S = x^2

-------

T = Area of triangle BMN

T = P - Q - R - S

T = 16x^2 - 6x^2 - 4x^2 - x^2

T = 5x^2

-------

An alternative method is to use the pythagorean theorem to find the lengths of BM and MN. Then you can directly compute the area of triangle BMN. You should find that BM = sqrt(20)*x and MN = sqrt(5)*x.

Answer:

10

Step-by-step explanation:

10^0=1

1*10=10

Answer:

C

Step-by-step explanation:

They're solid lines and overlap at that point

Good evening ,

Answer:

(x - 6 + i)(x - 6 - i) = x² - 12x + 37

Step-by-step explanation:

(x - 6 + i)(x - 6 - i) = [(x - 6) + i]×[(x - 6) - i] = (x-6)² - i² = (x-6)² + 1 = x² - 12x + 37 .

:)

Answer:

Option C

10%

Step-by-step explanation:

Given information

Cost of investment=$20000

Selling price=$22000

Profit=Selling price-Cost of investment=22000-20000=2000

Return on investment=profit/cost of investment

[tex]RoI=\frac {2000\times 100}{20000}=10%[/tex]

The amount of money on a property or good sold is known as ROI. Pete’s return on investment is 10%

The amount of money on a property or good sold is known as ROI.

Given the following

Cost price = $20000

Selling price = $22000

ROI = SP-CP/CP * 100

%ROI = 2000/20000 * 100

%ROI = 1/10 * 100
%ROI = 10%

Hence Pete’s return on investment is 10%

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The amount of sheet tin needed to make the roof of the farm silo is approximately 25132.74125 square feet.

The roof of the farm silo is in the shape of a hemisphere, which means it is like half of a sphere. The diameter of the silo is given as 126.5 feet. To find the amount of sheet tin needed to make the roof, we need to calculate the surface area of the hemisphere.

The surface area of a hemisphere can be calculated using the formula: SA = 2πr^2, where SA is the surface area and r is the radius of the hemisphere.

Since the diameter is given, we can find the radius by dividing the diameter by 2. So, the radius is 126.5/2 = 63.25 feet. Plugging this value into the formula, we get:

SA = 2π(63.25^2)

Using a calculator to find the surface area, we get:

SA ≈ 2π(4005.0625) ≈ 25132.74125 square feet

Therefore, approximately 25132.74125 square feet of sheet tin is needed to make the roof of the farm silo.

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The amount of sheet tin needed to make the roof of a farm silo, in the shape of a hemisphere, with a diameter of 126.5 feet is approximately 25,132.741 square feet.

To calculate the sheet tin needed to make the roof of a farm silo shaped like a hemisphere, we need to find the hemisphere's surface area. The surface area of a hemisphere is given by the formula 2πr2, where r is the radius of the hemisphere.

The diameter of the silo provided is 126.5 feet, meaning the radius, r, would be half of the diameter, or 63.25 feet.

Now, substitute 63.25 feet into the formula:

2 * π * (63.25)2 = 2 * π * 3996.0625.

The total sheet tin needed to make the roof is approximately 25,132.741 square feet.

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Answer:

Step-by-step explanation:

The domain on all x-squared parabolas is all real numbers.  

The range of an x-squared parabola is always found at the y coordinate of its vertex, and then is determined by whether it opens upwards or downwards. Our vertex has a y coordinate of -1 and opens downwards, so the range is all real numbers less than or equal to -1.

There are no x-intercepts (aka places on the graph that go through the x-axis), but the y-intercept is also the vertex, which is (0, -1).

Because this is an upside down parabola, it has a max point, again at the vertex.  It has no min point.

It increases from negative infinity to its max point and is notated as follows: (-∞, 0]

and decreases from its max point to negative infinity: [0, -∞)

Answer

Step-by-step explanation:

From the attached diagram below,

< ADC + <D = 180° (sum of linear angle) ------------(1)

<B + <C + <D = 180° (sum of interior angle in a triangle)---------(2)

Since the two equations are equal to 180°, We equate the two equation

i.e

(1) = (2)

< ADC + <D = <B + <C + <D

<D from the left hand side will cancel <D on the right hand side

We are now left with

<ADC = <B + <C

The Exterior Angle Theorem is proven by using the Triangle Sum Theorem, the Linear Pair Postulate, and the Subtraction Property of Equality to show that the sum of the interior opposite angles of a triangle equals the exterior angle.

To complete the proof of the Exterior Angle Theorem using the fact that angle ACD is an exterior angle of triangle BCD and prove that angle B + angle C = angle ACD, follow the steps below:

Answer:

x=9

Step-by-step explanation:

8(2x-6)=96

2x-6=96/8

2x-6=12

2x=12+6

2x=18

x=18/2

x=9

Hello, thanks for usin Brainly. :)

Let's solve by using distributive property.

8(2x-6)=96

16x-6=96

16x-48=96

     +48 +48

16x = 144

x = 9

First, what we did was do 8 x 2 & 6 x 8.

Then, we got 16x-6=96.

We want to get X by itself, therefore we need to get rid of -48, so we 48 to all of our terms.

Then our equation should look like 16x = 144.

Divide and get 9!

Therefore, x = 9.

Wait, how can we be sure?

Let's check our answer.

Let's allow our x value to be 9.

Now, our equation should look like:

8(2(9)-6=96

Follow the PEMDAS rule.

8(18-6)=96

8(12)=96

8 times 12 is 96.

96 = 96 Done!

Therefore, we know our answer is correct.

Answer:

Step-by-step explanation:

The solution for x in that equation is 3.

The solution to the equation 1/2 - x + 3/2 = x - 4 is x = 3. This solution was found by simplifying and solving the equation step-by-step.

You're trying to solve an equation for x. The equation given is 1/2 - x + 3/2 = x - 4.

First, combine similar terms on each side of the equation. So, this becomes -x + 2 = x - 4.

Next, add x to both sides to get 2 = 2x - 4.

Then, add 4 to both sides to isolate x on one side, you will get 2x = 6.

Finally, divide both sides by 2 to determine the value of x. So, x = 3.

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Answer:

7000

Step-by-step explanation:

nhi batunga

Final answer:

To find the total distance driven to and from work over 3 days, multiply the daily round-trip distance of 4310 miles by 3, resulting in 12,930 miles.

Explanation:

The question asks how many miles you would drive to and from work in 3 days if your round-trip to work is 4310 miles. To calculate this, you just need to multiply the daily round-trip distance by the number of days you travel. In this case, you travel to and from work for 3 days.

Determine the daily round-trip distance. (Already provided as 4310 miles)

Multiply the daily round-trip distance by the number of days traveled: 4310 miles × 3 days.

The calculation would be 4310 miles × 3 which equals 12,930 miles. This is the total distance driven to and from work over the 3 day period.

Answer:

16

Step-by-step explanation:

let "x" be the number of correct questions and 37-x be the wrong questions,

4x-1(37-x)=44

4x-37+x=44

5x=81

x=16.2

hence,16 is the answer

The minimum number of correct answers obtained is 17.

In this mathematics competition, each correct answer is awarded 4 marks, while a wrong answer incurs a deduction of 1 mark. If a question is not attempted, no marks are awarded or deducted.

Let's use "c" to represent the number of correct answers and "w" to represent the number of wrong answers. Since there are 30 multiple-choice questions in total, we can express the number of attempted questions as c + w = 30.

Now, we know that the student skipped 3 questions, so the number of attempted questions is 30 - 3 = 27. Since no marks are awarded or deducted for questions not attempted, the number of correct answers will be c = 27 - w.

Next, let's consider the score of the student. Each correct answer earns 4 marks, and each wrong answer incurs a deduction of 1 mark. So, the total score can be expressed as 4c - w.

The problem states that the score is more than 44. Therefore, we have the inequality 4c - w > 44.

Now, we need to find the minimum value of "c" that satisfies this inequality. To do this, let's substitute c = 27 - w into the inequality:

4(27 - w) - w > 44

Simplify the equation:

108 - 4w - w > 44

Combine like terms:

108 - 5w > 44

Now, isolate "w" by moving constants to the other side:

-5w > 44 - 108

-5w > -64

Finally, divide both sides by -5 (remember to reverse the inequality when dividing by a negative number):

w < 64/5

w < 12.8

Since "w" represents the number of wrong answers, it must be a whole number. The largest integer less than 12.8 is 12, so the minimum number of wrong answers is 12.

Now, let's find the corresponding value of "c":

c = 27 - w

c = 27 - 12

c = 15

So, the minimum number of correct answers obtained is 15. However, the question asks for the minimum number of correct answers to achieve a score *more than* 44. Let's check the score:

4c - w = 4 * 15 - 12 = 48 - 12 = 36

The student's score is 36, which is less than 44, meaning they need more correct answers to exceed 44.

Let's try c = 16:

4c - w = 4 * 16 - 12 = 64 - 12 = 52

Now, the student's score is 52, which is greater than 44. Thus, the minimum number of correct answers obtained is 16.

However, the question states that the student *skipped* 3 questions, meaning they did not attempt them. So, we need to subtract these skipped questions from the total:

Total attempted questions = c + w = 16 + 12 = 28

Skipped questions = 3

Total questions = Total attempted questions + Skipped questions = 28 + 3 = 31

Since there are only 30 questions in the competition, the maximum number of attempted questions should be 30. Therefore, the minimum number of correct answers obtained is 16 - 3 = 13.

But remember, the question asks for the minimum number of correct answers obtained, so we need to find the smallest possible number of correct answers. Since the student skipped 3 questions, the actual number of attempted questions must be 27.

Let's try c = 17:

4c - w = 4 * 17 - 12 = 68 - 12 = 56

The student's score is 56, which is greater than 44. Therefore, the minimum number of correct answers obtained is 17.

In conclusion, the minimum number of correct answers obtained is 17.

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Answer:

BC ≈ 11.9 cm

Step-by-step explanation:

Using the sine ratio in the right triangle

sin58° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{BC}{14}[/tex]

Multiply both sides by 14

14 × sin58° = BC, thus

BC ≈ 11.9 cm ( to 1 dec. place )

To find the length of side BC in a triangle, you would typically use the Pythagorean theorem if given a right triangle. Additional information or a diagram is required for a precise answer. The theorem can be rearranged to solve for any side of the triangle.

Finding the length of side BC requires you to use the principles of geometry, specifically the Pythagorean theorem if this is a right triangle context. However, without a provided diagram or additional information, it's impossible to give a specific answer. The Pythagorean theorem states that in a right-angle triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as a^2 + b^2 = c^2, where c represents the length of the hypotenuse, and a and b represent the lengths of the other two sides. You could rearrange this equation to solve for b if you knew the lengths of a and c.

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Answer:

More wins required = 59 wins

Step-by-step explanation:

Given:-

Total numbers of games played = 160.

Total games won = 50.

Total win percentage required = 68 %

Now,

Total percentage of games won = [tex]\frac{50}{160} \times 100[/tex]

Total percentage of games won = 0.312 [tex]\times[/tex]100

Total percentage of games won =31.25% ------------(equation 1)

Balance percentage of wins required = total win percentage required   - total percentage of games won

Balance percentage of wins required = 68 - 31.25 -----(from equation 1)

Balance percentage of wins required = 36.75%

More wins required = [tex]\frac{Balance\ percentage\ of\ win\ required}{100} \times 160[/tex]

More wins required =[tex]\frac{36.75}{100}\times 160[/tex]

More wins required = 0.368 [tex]\times[/tex] 160

More wins required =58.88

More wins required = 59 wins --------------(rounded value)

St. Louis Cardinals need to win 59 more games to achieve at least a 68% winning percentage for the season.

To determine how many more games the St. Louis Cardinals must win in order to achieve at least a 68% winning percentage for the season, let's go through the calculations step by step.

Total Games: The Cardinals play a total of 160 games in a season.

Current Wins: The Cardinals have currently won 50 games.

Winning Percentage Goal: We want the Cardinals to win at least 68% of their games.

The formula to calculate the winning percentage is:

[tex]\text{Winning Percentage} = \frac{\text{Wins}}{\text{Total Games}} \times 100\%[/tex]

Therefore, the number of wins needed to achieve at least a 68% winning percentage can be calculated as follows:

[tex]\text{Wins Needed} = 0.68 \times 160 = 108.8 \text{ (approximately 109 games)}[/tex]

Calculating Additional Wins Needed: To find out how many more games the Cardinals need to win, we'll subtract the current wins from the wins needed:

[tex]\text{Additional Wins Needed} = \text{Wins Needed} - \text{Current Wins}[/tex]

[tex]\text{Additional Wins Needed} = 109 - 50 = 59[/tex]

Answer:

You would know what people would say by saying that because they mean that you were to match up the letters into a shape in that order

Step-by-step explanation:

Hopefully this helps, give me a brainliest

Answer:

The given angles are

[tex]\angle BOA\\\angle AOC[/tex]

When we write down angles, we have different notations to do it.

In this case, we have angles with three letter, each one indicates a specific element.

The first letter indicate the initial point where the angle starts, for example, [tex]\angle BOA[/tex], beginas at point B, the middle letter indicates the vertex where the angle is at, so [tex]\angle BOA[/tex] indicates is at vertex O, at last, the third letter A indicates the final point where the angle goes.

Having said that, [tex]\angle BOA[/tex] is the opening from point B, then goes to vertex O and finally goes to point A, in the image attached you can see this angle highlighted.

Using the same reasoning, we have that [tex]\angle AOC[/tex] starts at points A, goes to vertex O, and ends at point C. Refer to the image attached.

Answer:

Hittites, Aryans, Portuguese.

Step-by-step explanation:

I just know for a fact. These are the correct answers.

Answer:

The larger angle is 52. 4

The smaller angle is 37. 6

Step-by-step explanation:

The equation is:

(x-14. 8)+x=90

x+x-14. 8=90

2x=90+14. 8

2x=104. 8

x=52. 4

The value for the larger angle is x

and x =52. 4

The value for the smaller angle is x-14. 8

and x-14. 8=52.4-14.8

=37.6

Verification

(x-14.8)+ x=90

(52.4-14.8)+52.4=90

37.6+52.4=90

90=90

The smaller angle measures 37.6° and its complementary angle measures 52.4°. These measures satisfy the condition that one angle is 14.8° less than the measure of its complementary angle, and both angles sum to 90°.

To determine the measure of each angle when one angle is 14.8° less than its complementary angle, we need to set up an equation.

Complementary angles add up to 90°.

Let's denote the smaller angle as x, so the complementary angle is x + 14.8°. The equation becomes:

x + (x + 14.8°) = 90°

Combining like terms, we have:

2x + 14.8° = 90°

Subtracting 14.8° from both sides:

2x = 90° - 14.8°

2x = 75.2°

Dividing both sides by 2 to solve for x:

x = 75.2° / 2

x = 37.6°

So the smaller angle measures 37.6° and the complementary angle measures x + 14.8° = 37.6° + 14.8° = 52.4°.

The situation that can be represented by the inequality x < 3 is that the backpack is heavier than 3 kg.

The situation that can be represented by the inequality x < 3 is: The backpack is heavier than 3 kg.

This means that if the weight of the backpack is represented by 'x', then 'x' is less than 3 kg.

For example, if the weight of the backpack is 2 kg, then 2 is less than 3, which satisfies the inequality x < 3.

The situation that can be represented by the inequality x<3 is "The ceiling is lower than 3 m." This inequality shows that the value of x is less than 3. In real-world terms, it could mean the height of a ceiling, length of an object, or the age of a child, among other things. However, in the given options, it corresponds to a ceiling's height being less than 3 meters.

Let's explore a couple of examples to understand inequalities better with metric measurements:

Answer:

There are 7 chairs in each row length.

Step-by-step explanation:

Let number of chairs in 1 row be 'x'.

Let total number of chairs be 'y'.

Given:

Hue can form 6 rows of a given length with 3 chairs left over.

It means that Total number of chairs is equal to chairs in 1 rows multiplied by number of rows which is 6 plus number of chairs which is left which is 3.

Framing in equation form we get.

[tex]y=6x+3 \ \ \ \ \ equation \ 1[/tex]

Also Given:

Hue can form 8 rows of that same length if she gets 11 more chairs.

It means that Total number of chairs is equal to chairs in 1 rows multiplied by number of rows which is 8 minus number of chairs which is required more which is 11.

Framing in equation form we get.

[tex]y=8x-11 \ \ \ \ \ equation \ 2[/tex]

From equation 1 and equation 2 we can say that L.H.S is same.

So according to law of transitivity we get;

[tex]6x+3=8x-11[/tex]

Combining like terms we get;

[tex]8x-6x=11+3[/tex]

Using Subtraction and Addition property we get;

[tex]2x=14[/tex]

Now Using Division Property we will divide both side by 2.

[tex]\frac{2x}{2}=\frac{14}{2}\\\\x=7[/tex]

Hence there are 7 chairs in each row length.

By setting up the equations as described, we find that each row has 7 chairs.

The subject of the question is a mathematical problem involving the concept of solving linear equations. Let's denote the number of chairs in a row as x. According to the problem, Hue can form 6 rows with 3 chairs leftover. So the total number of chairs she has is 6x + 3. Also, if she gets 11 more chairs, she can form 8 rows of the same length. So, in that case, the total number of chairs would be 8x. So we can write the equation 6x + 3 + 11 = 8x.

This equation simplifies to 14 = 2x. Therefore, x = 7. That is, each row has 7 chairs.

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Answer:

y = -3x + 6

Step-by-step explanation:

Distribute -

y + 6 = -3x + 12

Subtract 6 from both sides, final answer

y = -3x + 6

Final answer:

The equation y + 6 = -3(x - 4) in slope-intercept form is y = -3x + 6, where the slope is -3 and the y-intercept is 6.

Explanation:

To write the equation y + 6 = -3(x - 4) in slope-intercept form, which is y = mx + b, we need to solve the equation for y. First, distribute the -3 to both terms within the parentheses: y + 6 = -3x + 12. Next, subtract 6 from both sides to isolate y: y = -3x + (12 - 6). Simplifying the equation, we get y = -3x + 6. Thus, the slope-intercept form of the equation is y = -3x + 6, where the slope (m) is -3 and the y-intercept (b) is 6.

Answer:

35.2

Step-by-step explanation:

1/22=1.6/?

Cross multiply: 1.6*22=35.2

Answer:

(5) ∠ FEH ≅ ∠ GHE : CPCTC

(6) ∠ FEH and ∠ GHE are supplementary : Consecutive angles of a parallelogram are supplementary.

(7) m∠ FEH = 90° : Congruent supplementary angles are right angles.

(8) EFGH is a rectangle : Definition of a rectangle.

Step-by-step explanation:

Given:

Quadrilateral EFGH is a parallelogram.

[tex]\overline{EG}\cong \overline{HF}[/tex]

Statements                                                           Reasons

1. EFGH is a parallelogram.                                  Given

  [tex]\overline{EG}\cong \overline{HF}[/tex]

2. [tex]\overline{EF}\cong \overline{GH}[/tex]    If a quadrilateral is a parallelogram, then the opposite sides are congruent

3. [tex]\overline{EH}\cong \overline{EH}[/tex]    Reflexive property of Congruence.

4. Δ EFH ≅ Δ HGE                                SSS Triangle Congruence Postulate.

Now, when two triangles are congruent by SSS, their corresponding angles are also congruent by CPCTC.

(5) ∠ FEH ≅ ∠ GHE                                    CPCTC

Also, for a parallelogram, the same side angles sum is 180 degrees. ∠ FEH and ∠ GHE are supplementary as their sum is 180°.

(6) ∠ FEH and ∠ GHE are supplementary  Consecutive angles of a parallelogram are supplementary.

Now, from statement (5), ∠ FEH ≅ ∠ GHE, so the supplementary pair are congruent. Therefore, each angle is equal to 90°.

Let ∠ FEH = ∠ GHE = [tex]x[/tex]. Then,

[tex]x+x=180\\2x=180\\x=\frac{180}{2}=90\°[/tex]

Therefore, ∠ FEH = ∠ GHE = 90°

(7) m∠ FEH = 90°  Congruent supplementary angles are right angles.

Now, for a parallelogram with congruent diagonals, if any two consecutive angles are 90 degree each, then the remaining angles are also 90 degrees.

Now, if a parallelogram has all its angles equal to 90°, then the parallelogram is a rectangle from the definition of a rectangle.

(8) EFGH is a rectangle                        Definition of a rectangle.

The focus must be the point (0, 4), because it is equidistant from the vertex (0, 2) as the focus is from the directrix, y = 0, which indicates that the focus is twice the distance from the vertex to the directrix or (0, 4)

The evaluation that shows the reasons the focus must be the point (0, 4) are as follows;

The location of the vertex of the parabola at the point (0, 2), and the location of the directrix on the x-axis, we get;

The location of the focus is on the line passing through the vertex, which is the line x = 0

The definition of a parabola is the path of a point that moves such that the distance from the focus and the directrix are the same

The equation of the directrix is; y = 0

The shortest distance of the vertex from the directrix is 2 - 0 = 2 units

The distance from the focus to the vertex is therefore 2 units

Whereby the focus is 2 units above the x-axis, the focus, which is 2 units from the vertex on the remote side of the directrix is 2 + 2 = 4 units above the x-axis and the coordinates of the vertex must be (0, 4)

The definition of a parabola indicates that the location of the focus should be 2 units from the

The complete question found through search can be presented as follows;

A parabola is shown graphed on the grid below. Its directrix is the x-axis

(a) Explain why the focus must be the point (0, 4)

The coordinates of  the vertex of the parabola is (0, 2)

The coordinates of other points on the parabola are (-8, 8), (8, 8)

Answer:

2.25 miles of road they have to build this week

Step-by-step explanation:

Given:

Total distance of the road = 3 miles

Distance constructed on Tuesday = 1/4 mile of road.

To Find:

Miles of road still have to be built this week=?

Solution:

Let the Distance that have  to be built be X

Then,  

X= total distance of the Road – the distance built on Tuesday

X = 3  –  [tex]\frac{1}{4} \text{ of the 3}[/tex]

X = 3 - [tex]\frac{3}{4}[/tex]

X =[tex]\frac{12 -3}{4}[/tex]

X= [tex]\frac{ 9}{4}[/tex]

X= 2.25  miles

Answer:

The interest charged for this month is $7.5

Step-by-step explanation:

Given:

Principal = $300

Interest = 30%

Time =  1 month

To Find:  

The interest charged for this month = ?

Solution:

we know that the  interest charged = [tex]principal \times \text {Interest rate} \times time[/tex]

1 month can also be written as [tex]\frac{1}{12}[/tex]

Substituting the values,

interest charged:

=> [tex] 300 \times 30%  \times \frac{1}{12}[/tex]

=> [tex] 300 \times \frac{30}{100} \times \frac{1}{12}[/tex]

=> [tex] 300 \times \frac{3}{120}[/tex]

=>[tex] \frac{900}{120}[/tex]

=>[tex] \frac{30}{4}[/tex]

=>[tex] \frac{15}{2}[/tex]

=> 7.5

Answer:

shape and size

Step-by-step explanation:

we know that

If two figures are similar, then its corresponding sides are proportional and its corresponding angles are congruent

Similar figures have the same shape but not necessarily the same size

Answer:

E) [tex]f(x)=|x-8|+2[/tex]

Step-by-step explanation:

We will check each of the given choices by finding [tex]f(2)[/tex] of the given functions.

In order to find [tex]f(2)[/tex], we plugin [tex]x=2[/tex] in the function.

A) [tex]f(x)=2x+1[/tex]

[tex]f(2)=2(2)+1[/tex]

[tex]f(2)=4+1[/tex]

[tex]f(2)=5[/tex]

B) [tex]f(x)=3x-2[/tex]

[tex]f(2)=3(2)-2[/tex]

[tex]f(2)=6-2[/tex]

[tex]f(2)=4[/tex]

C) [tex]f(x)=x(5x-2)[/tex]

[tex]f(2)=2(5(2)-2)[/tex]

[tex]f(2)=2(10-2)[/tex]

[tex]f(2)=2(8)[/tex]

[tex]f(2)=16[/tex]

D) [tex]f(x)=3x-2x+4[/tex]

[tex]f(2)=3(2)-2(2)+4[/tex]

[tex]f(2)=6-4+4[/tex]

[tex]f(2)=6[/tex]

E) [tex]f(x)=|x-8|+2[/tex]

[tex]f(2)=|2-8|+2[/tex]

[tex]f(2)=|-6|+2[/tex]

[tex]f(2)=6+2[/tex]   [Since absolute value of any number is positive]

[tex]f(2)=8[/tex]

So, the function in E has value =8 for [tex]f(2)[/tex]

As the rate of change of function is negative from x=1 to x=2, the function decreases at this interval.

Step-by-step explanation:

We have to find the rate of change of the function

The rate of change of function is given by:

[tex]Rate\ of\ change = \frac{h(b)-h(a)}{b-a}[/tex]

Given function is:

[tex]h(x) = -2x+5[/tex]

Here

a =1

b = 2

So,

[tex]h(2) = -2(2) +5\\= -4+5\\= 1\\h(1) = -2(1) +5\\= -2+5\\= 3[/tex]

Putting the values in the formula

[tex]Rate\ of\ change = \frac{1-3}{2-1} = -2[/tex]

As the rate of change of function is negative from x=1 to x=2, the function decreases at this interval.

Keywords: Functions, rate of change

Learn more about functions at:

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