FLED is definitely a parallelogram

Answer:

[tex]a_{n} =1.7n+(n-1)0.5[/tex]

Step-by-step explanation:

I hope this helps.

Answer:

an = .5n +1.2

Step-by-step explanation:

The formula for an arithmetic sequence is given by

an =a1 + d(n-1)  where a1 is the first term and d is the common difference

an = 1.7 + .5 (n-1)

Distribute

an = 1.7 + .5n - .5

Combine like terms

an = .5n +1.2

Answer: d

Step-by-step explanation:

However much more you pay over the minimum will be applied to the principle, which means it will take less time to pay the credit card bill off  

When paying a credit card bill, it is recommended to pay more than the minimum amount every month to reduce the principal balance faster and avoid accruing high interest. This practice leads to less overall cost and faster debt elimination.

The recommended practice when paying a credit card bill is D. Pay more than the minimum amount every month. This is crucial because paying only the minimum amount mostly covers the interest and only a small part of the principal balance. Interest accrues on the remaining balance, leading to higher overall costs.

By paying more than the minimum, you reduce the principal balance faster, thereby reducing the amount of interest that can accumulate. For instance, if two friends both have $2,000 in credit card debt but one pays just the minimum while the other adds an additional $10 each month, the latter will pay off their debt quicker and accrue less interest overall.

Managing credit effectively involves more than just timely payments; it's also about managing your credit utilization and striving to pay off the full balance as quickly as possible. This avoids the high-interest rates that can double the initial amount over time if only minimum payments are made.

Answer:

19) sin 48° ≅ 0.7431

20) sin 38° ≅ 0.6157

21) cos 61° ≅ 0.4848

22) cos 51° ≅ 0.6293

Step-by-step explanation:

* Lets explain the meaning of trigonometry ratio

- In any right angle triangle:

# The side opposite to the right angle is called the hypotenuse

# The other two sides are called the legs of the right angle

* If the name of the triangle is ABC, where B is the right angle

∴ The hypotenuse is AC

∴ AB and BC are the legs of the right angle

- ∠A and ∠C are two acute angles

- For angle A

# sin(A) = opposite/hypotenuse

∴ sin(A) is the ratio between the opposite side of ∠A and the hypotenuse

# cos(A) = adjacent/hypotenuse

∴ cos(A) is the ratio between the adjacent side of ∠A and the hypotenuse

# tan(A) = opposite/adjacent

∴ tan(A) is the ratio between the opposite side of ∠A and the

  adjacent side of A

# The approximation to the nearest ten-thousandth, means look to

  the fifth number before the decimal point if its 5 or greater than 5

  ignore it and add the fourth number (ten-thousandth) by 1 if it is

 smaller than 5 ignore it and keep the fourth number as it

* Now lets solve the problems

19) sin 48° is the ratio between the side opposite to the angle of

    measure 48° and the hypotenuse of the triangle

∴ sin 48° = 0.74314 ≅ 0.7431 ⇒ to the nearest ten-thousandth

20) sin 38° is the ratio between the side opposite to the angle of

    measure 38° and the hypotenuse of the triangle

∴ sin 38° = 0.61566 ≅ 0.6157 ⇒ to the nearest ten-thousandth

21) cos 61° is the ratio between the side adjacent to the angle of

    measure 61° and the hypotenuse of the triangle

∴ cos 61° = 0.48480 ≅ 0.4848 ⇒ to the nearest ten-thousandth

22) cos 51° is the ratio between the side adjacent to the angle of

    measure 51° and the hypotenuse of the triangle

∴ cos 51° = 0.62932 ≅ 0.6293 ⇒ to the nearest ten-thousandth

Answer:

Step-by-step explanation:

[tex]a^2+a-2=a^2+2a-a-2=a(a+2)-1(a+2)=(a+2)(a-1)[/tex]

The period of the trigonometric function, given the graph provided, is [tex]\( 9.4 \)[/tex]units.

To determine the period of the trigonometric function from the graph, we need to find the length of one complete cycle of the function.

The period of a trigonometric function is the horizontal length between two points where the function begins repeating its pattern. For sine and cosine functions, this is typically from peak to peak, from trough to trough, or between any two identical points on the graph that are one cycle apart.

Looking at the image, we can see that the function reaches a maximum at the point (-4.7, 3.8) and then again at (4.7, -3.8). However, the points given are not one full cycle apart because they represent a maximum and the function's intersection with its midline. Instead, we should look at the distance along the x-axis between two consecutive maximums or two consecutive midline crossings.

If we assume that the graph is symmetric and the pattern repeats in the positive direction of the x-axis, the period would be twice the distance from the given midline crossing to the next one. This is because the midline crossing at (4.7, -3.8) is halfway through a cycle. Therefore, we can double this x-value to find the period.

Since the crossing occurs at x = 4.7, and it's half the period, the full period [tex]\( P \)[/tex] would be:

[tex]\[ P = 4.7 \times 2 \][/tex]

Let's compute the exact value.

The period of the trigonometric function, given the graph provided, is [tex]\( 9.4 \)[/tex]units.

complete question given below:

Answer:

37.6 units

Step-by-step explanation:

khan Academy said so

Answer: 100mL

Step-by-step explanation:

A 15% alcohol solution contains 15mL alcohol in 100mL solution

In 400ml there will be 400mL·15/100 = 6,000mL/100 = 60mL alcohol

Let the volume of pure alcohol to be added V.

In the new solution there will be (60 + V)mL  alcohol

And the total volume will be (400 + V)mL

Concentration required 32% = 0.32

Concentration = (60 + V)mL/(400 + V)mL = 0.32

60mL + VmL = 0.32(400 + V)mL

60mL + VmL = 128mL + V·*0.32mL

VmL - V·0.32mL = 128mL - 60mL = 68mL

V(1 - 0.32)mL = 68mL

V·0.68mL = 68mL

VmL = 68mL/0.68 = 100mL ►  alcohol volume to be added

Answer : 100mL

Verification

New solution

There will be  400mL + 100mL = 500mL total volume

There will be 60mL alcohol + 100mL alcohol = 160mL alcohol

The concentration will be   160mL/500mL = 0.32 = 32%

[tex]\textit{\textbf{Spymore}}[/tex]

Answer:

c=0

Step-by-step explanation:

x² + 11x + 0 = y

x² + 11x + 0 = 0

U already know that y=0 by looking at the equations above,

But your worksheet never state "c", so we will take that c is 0   (look at the equations above.)

So c is just 0.

In a quadratic equation of the form ax^2 + bx + c=0, 'c' is the constant term. In your equation x^2 + 11x = 0, therefore the 'c' value is 0.

The equation you provided, x^2 + 11x = 0, is a quadratic equation of the form ax^2 + bx + c = 0. In this equation, 'a' is the coefficient of x^2, 'b' is the coefficient of x, and 'c' is the constant. Comparing your equation with this form, the values of 'a', 'b', and 'c' in your equation are 1, 11, and 0 respectively. Therefore, in your equation, the 'c' value is 0.

To find roots or solutions for the equation, we use the quadratic formula: -b ± √(b^2 - 4ac) / 2a. Substituting 'a', 'b' and 'c' values from your equation will help to find the value of 'x'.

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We have 220 students total.

140 like Chocolate.

120 like Vanilla.

140+120=260.

260 is 40 more than 220.

Therefore there are 40 students who said they like both.

I hope this helps! :)

Final answer:

By applying the principle of inclusion-exclusion, we found that 40 students like both chocolate and vanilla ice cream.

Explanation:

To determine how many students like both chocolate and vanilla ice cream, we need to use the principle of inclusion-exclusion. This principle is a fundamental counting technique in mathematics that considers the overlap of two sets.

According to the principle, if we have two overlapping sets, we can find the number of elements that are in both sets by adding the number of elements in each set (in this case, the number of students who like chocolate and the number of students who like vanilla) and then subtracting the number of elements that have been counted twice (the students who like both).

The formula we will use is: Number of students liking both = (Number of students liking chocolate) + (Number of students liking vanilla) - (Total number of students surveyed).

Applying the formula:

Number of students liking chocolate = 140

Number of students liking vanilla = 120

Total number of students surveyed = 220

Number of students liking both = 140 + 120 - 220 = 40.

Therefore, 40 students like both chocolate and vanilla ice cream.

Answer: The radius is 12 feet

Step-by-step explanation:

You know that the formula used to calculate the area the a sector of a circle is:

[tex]A=\frac{C\pi }{360}*r^2[/tex]

Where C is the central angle in degrees and r is the radius of the circle

Solve for "r" from this formula:

[tex]360*A=C\pi*r^2\\\\\frac{360*A}{C\pi}=r^2\\\\r=\sqrt{\frac{360*A}{C\pi}}[/tex]

You know the that the angle is 90 degrees and you know that the area of the sector is 36π ft², then substituting values you get that the radius of this circle is:

[tex]r=\sqrt{\frac{360(36\pi ft^2)}{90\°\pi}}=12ft[/tex]

Answer:

C. 17.3

Step-by-step explanation:

Using Pythagoras theorem

Divide the triangle into half

c^2=a^2+b^2

20^2=a^2+10^2

400=a^2+100

400-100=a^2

300=a^2

17.32=a^2

The height of the equilateral triangle to the nearest tenth is 17.3

Given that:

An equilateral triangle has sides of length 20.

Equilateral triangles are the type of triangles which has all the sides equal to each other.

That is, three sides will have equal length.

So all the side of the triangle is 20.

The height of the triangle is the perpendicular line drawn from any of these vertices.

Since this is an equilateral triangle, the height divides the base into equal lengths.

So each half will be 20/2 = 10.

Here, a right angle is formed.

Using Pythagoras theorem,

h = √(20² - 10²)

  = √(400 - 100)

  = √300

  = 17.3

Hence the correct option is C.

Learn more about Pythagoras' Theorem here :

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Answer:

39.9

Step-by-step explanation:

A good trick to remember is SOH CAH TOA.

Sine = Opposite / Hypotenuse

Cosine = Adjacent / Hypotenuse

Tangent = Opposite / Adjacent

Here, we're given an angle and the opposite side, and we want to find the adjacent side.  So we need to use tangent.

tan 31° = 24 / x

x = 24 / tan 31°

x ≈ 39.9

Answer:

Yes, (0,4) is a solution

Step-by-step explanation:

We have to plug in 0 in x and 4 in y IN BOTH THE INEQUALITIES.

IF BOTH ARE TRUE, then the system of inequalities is TRUE.

Let's check:

y ≤ -3x+4

4 ≤ -3(0)+4

4 ≤ 4

Is 4 less than OR equal to 4? Yes. THis is satisfied.

Now, checking 2nd one:

y > x^2 + 3x - 2

4 > (0)^2 + 3(0) - 2

4 > -2

Is 4 greater than -2? Yes, it is. So this is satisfied as well.

Hence, (0,4) is a solution to the system of inequalities shown.

Answer:

Yes, it is the solution

Step-by-step explanation:

You are given the system of two inequalities

[tex]\left\{\begin{array}{l}y\le -3x+4\\ \\y>x^2+3x-2\end{array}\right.[/tex]

To check whether point (0,4) is the solution to this system, substitute x=0 and y=4 into each inequality:

1.

[tex]4\le -3\cdot 0+4\\ \\4\le 4 \ [\text{true}][/tex]

2.

[tex]4>0^2+3\cdot 0-2\\ \\4>0+0-2\\ \\4>-2\ [\text{true}][/tex]

Since the coordinates of the point (0,4) satisfy both inequalities, the point (0,4) is the solution to the system

Answer:

7 to 50

Step-by-step explanation:

First, find the area of lot A.

To find the area, multiply the length by the width.

33*42=1,386

Now, subtract the area of lot a from the total area. This will give us the area of lot b.

1,848-1,386=462

The area of lot b is 462 square feet.

Finally, divide the area of lot b (462) by its length to find the width. Since they both share a side, we know that it’s length is 42 feet.

462/42=11

Lot b is 11 feet wide.

Hope this helps!

Answer:

y = 8.9

Step-by-step explanation:

Use Pythagoras Theorem a² = b² + c²

In this case a = 12 and c = 8 so,

12² = b² + 8²

( Simplify )

144 = b² + 64

( Minus 64 from both sides to isolate b² )

80 = b²

( Square root to isolate b )

8.94427191 = b

Answer:

8.9

Step-by-step explanation:

The triangle is a right triangle, so we can use the Pythagorean theorem, where a and b are the lengths of the legs (the sides forming the right angle), and c is the length of the hypotenuse (the angle opposite the right angle).

a^2 + b^2 = c^2

y^2 + 8^2 = 12^2

y^2 + 64 = 144

y^2 = 80

y = sqrt(80)

y = sqrt(16 * 5)

y = 4sqrt(5)

y = 8.9

Answer:

Tessa's mistake was to have multiplied each dimension by two instead of multiplying by a square root of two.

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its areas is equal to the scale factor squared

Let

z -----> the scale factor

x ----> the area of the enlarged garden

y ----> the area of the original garden

[tex]z^{2}=\frac{x}{y}[/tex]

we have that

If Tessa multiplies each dimension by 2, then the scale factor equals 2.

[tex]z=2[/tex]

substitute

[tex]2^{2}=\frac{x}{y}[/tex]

[tex]4=\frac{x}{y}[/tex]

[tex]x=4y[/tex]

The area of the enlarged garden will be equal 4 times the area of the original garden

so

If Tessa wanted to have twice as much surface, she must multiply each dimension by a square root of 2.

therefore

Tessa's mistake was to have multiplied each dimension by two instead of multiplying by a square root of two.

Answer:

1. B nearly 70%

2. C nearly 9%

Step-by-step explanation:

1. There are 26 people which agree with the question and 61 people which disagree with the question. In total, 26+61=87 people.

So,

[tex]\dfrac{61}{87}\cdot 100\%\approx 70\%[/tex]

disagree with question 1.

2. There are 87 people in total and only 8 females agree with question, so

[tex]\dfrac{8}{87}\cdot 100\%\approx 9\%[/tex]

of females agree with the question 1.

Answer:

Q1:  about 70%

Q2:  about 9%

Step-by-step explanation:

Question 1:

The grand total number of people is the right and bottom most cell, which is the addition of the column or the row. So grand total = 60 + 27 = 87 (or 61 + 26 = 87)

The number of people (BOTH MALE AND FEMALE) that disagreed with question 1 is 61.

As a percentage, that would be (61/87) * 100 = 70.11%, which is about 70%

Question 2:

Here, the total number of people is still the same, 87. We want the number of females that agreed. So we move in line with agree and in line with female is the table. We see that it is 8, so 8 females agreed with question 1.

As a percentage, (8/81) * 100 = about 9%

To find the y intercept replace the x in the equation with zero and solve

-2/9(0) + 1/3

0 + 1/3

The y-intercept is:

(0, 1/3)

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

y intercept is 1/3

Step-by-step explanation:

[tex]f(x)=-\frac{2}{9} x+ \frac{1}{3}[/tex]

To find y intercept we plug in 0 for x

Y intercept point is a point where the graph f(x) crosses y axis.

At y intercept, the value of x is 0

to find y intercept we plug in 0 for x

[tex]f(0)=-\frac{2}{9} (0)+ \frac{1}{3}[/tex]

[tex]f(0)=\frac{1}{3}[/tex]

Answer:

B. 14.7

Step-by-step explanation:

You would need to use the Pythagorean Theorem to find the length of the other leg. But you basically have to use it backwards. The theorem is a^2+b^2=c^2.

Substitute the values: a^2+12^2=19^2

Calculate the exponents: a^2+144=361

Subtract 144 from both sides: a^2=217

Find the square root of 217: 14.70309

Round to the nearest tenth: 14.7

Answer:

C

Step-by-step explanation:

Given

5x + 10y - 15 ← factor out 5 from each term

= 5(x + 2y - 3) → C

Final answer:

After factoring out the common factor of 5 from the expression 5x+10y-15, we obtain the equivalent expression, which is 5(x+2y-3). Option C is correct.

Explanation:

To find an expression equivalent to 5x+10y-15, we need to factor out the common factor in all three terms. The common factor here is 5. By dividing each term by 5, we get:

Putting these together within parentheses after factoring out the 5 gives us 5(x+2y-3).

Therefore, the answer is: C. 5(x+2y-3)

Answer:

Its diagonals are perpendicular, then it is a rhombus

Step-by-step explanation:

* Lets revise the properties of the parallelogram and the rhombus

- In the parallelogram each two opposite sides are parallel

- In the parallelogram each two opposite sides are equal in length

- In the parallelogram the diagonals bisect each other

- In the rhombus each two opposite sides are parallel

- In the rhombus all the sides are equal in length

- In The rhombus the diagonals are perpendicular to each other

- Parallelogram is a rhombus if two adjacent sides are equal in length

- Parallelogram is a rhombus if its two diagonals are perpendicular

* Now lets solve the problem

∵ The vertices of the parallelogram are

   A(-3 , 2) , B(-2 , 6) , C (2 , 7) , D (1 , 3)

- The slope of the line which passes through points (x1 , y1) and (x2 , y2)

  is m = (y2 - y1)/(x2 - x1)

* lets find the slopes of the sides and the diagonals

∵ The slope of AB = (6 - 2)/(-2 - -3) = 4/1 = 4

∵ The slope of BC = (7 - 6)/(2 - -2) = 1/4 = 1/4

∵ The slope of CD = (3 - 7)/(1 - 2) = -4/-1 = 4

∵ The slope of DA = (2 - 3)/(-3 - 1) = -1/-4 = 1/4

- The product of the slopes of the perpendicular line is -1

∵ AB and BC are two adjacent sides and the product of their slopes

  = 4 × 1/4 = 1 ≠ -1

∴ AB and BC are not perpendicular

∴ The parallelogram can not be a rectangle

- Lets check the slopes of the diagonals

∵ The diagonals of the parallelogram are AC and BD

∵ The slope of AC = (7 - 2)/(2 - -3) = 5/5 = 1

∵ The slope of BD = (3 - 6)/(1 - -2) = -3/3 = -1

∵ The product of the slopes of AC and BD = 1 × -1 = -1

∴ AC and BD are perpendicular

∴ ABCD is a rhombus

Answer:

a° = 80° , b° = 40° , c° = 40° , d° = 100°

Step-by-step explanation:

* Lets study the information in the question to solve it

- There is a circle and two chords of it are parallel

∵ The two chords are parallel

- The measure of b° is the same with the angle of measure 40°

   because they are alternate angles

∴ b° = 40°

- The vertex of the angle of measure 40° is on the circle

∴ This angle is inscribed angle subtended by the arc of measure a°

- There is a relation between the inscribed angle and its subtended arc,

 the measure of the arc is twice the measure of the angle

∵ The measure of the angle is 40°

∴ a = 40° × 2 = 80°

∴ a° = 80°

- In the circle any two inscribed angles subtended by the same arc

 are equal in measure

∵ The angle of measure 40° and the angle of measure c° are

  inscribed angles subtended by the same arc of measure a°

∴ c° = 40°

- The sum of the measures of the interior angles in any triangles is 180°

∴ b° + c° + d° = 180° ⇒ interior angles of a Δ

∵ b° = 40° , c° = 40°

∴ 40° + 40° + d° = 180° ⇒ add

∴ 80° + d° = 180° ⇒ subtract 80 from both sides

∴ d° = 100°

Answer:

x = -1.

Step-by-step explanation:

√(x + 10) - 4 = x

√(x + 10) = x + 4

Squaring both sides:

x + 10 = x^2 + 8x + 16

x^2 + 8x - x + 6 = 0

x^2 + 7x + 6 = 0

(x + 6)(x + 1) = 0

x = -6, -1.

Check for any extraneous roots:

√(x + 10) - 4 = x

Try x = -6:

√(-6 + 10) - 4 = 2 - 4 = -2.

but we found x = -6  , so -6 is not a root.

Try x = -1:

√(-1 + 10) - 4 = 3 - 4 = -1. So x = -1 is a root.

x=-1

Step-by-step explanation:

sqrt(x+10) -4= x

sqrt(x+10) = x+4

square each side

x+10=(x+4)^2

x+10= x^2+8x+16

subtract x+10 from each side

x^2+7x+6=0

(x+6)(x+1)=0

x=-6 x=-1

Then we plug both back into the equation.

sqrt(-1+10) -4= -1

sqrt(9) -4= -1

3-4 = -1

-1=-1. this works out.

sqrt(-6+10) -4 = -6

sqrt(4) -4= -6

2-4= -6

-2= -6. this does not work so the only solution is x=-1

Answer:

9. 1620°

10. 360°

11. 180°

Step-by-step explanation:

The answers of problems 10 and 11 give you the way to find the answer to problem 9.

__

10. The sum of exterior angles of any convex polygon is 360°.

__

11. An internal angle and an external angle are a linear pair, so always sum to 180°.

__

9. At every vertex, the sum of interior and exterior angles is 180°, so the total of those angles at all vertices is n·180°. Of that total, 360° is the sum of exterior angles, so the total of interior angles of an n-gon is ...

n·180° -360° = (n -2)·180°

For an 11-gon, the sum of interior angles is ...

(11 -2)·180° = 1620°

Answer:

Angle 3 and angle 4 are linear pair

Step-by-step explanation:

* Lets revise the types of angles

- If two line intersected at a point, there are two types of

pairs of angles

- Two vertically opposite angles equal in measure

- Linear pair of angles their sum is 180°

* Now lets solve the problem

- There are two lines intersect each other at a point

- They formed between them 4 angles

- Angle 2 and angle 4 are vertical opposite angles, equal in measure

- Angle 1 and angle 3 are vertical opposite angles, equal in measure

∴ m∠2 = m∠4

∴ m∠1 = m∠3

- Angle 1 and angle 2 formed a line

∴ They are linear pair of angles

- Angle 3 and angle 4 formed a line

∴ They are linear pair, of angles

∵ m∠1 + m∠2 = 180°

∴ m∠3 + m∠4 = 180°

* Angle 3 and angle 4 are linear pair

12a^2b^3 / 3ab

Factor 3 out of the numerator:

3(4a^2b^3) / 3ab

Cancel out the common factors:

4a^2b^3 / ab

Cancel out the common factors again to get the final answer:

4ab^2

____________________________________________________

Answer:

$203.5

____________________________________________________

Step-by-step explanation:

In order to find the answer to your question, we would need to find how much money she made when selling the collars.

Lets gather the important information:

$4.75 for small collar

$7.75 for large collar

With the information above, we can solve the problem.

What we would do is multiply the amount of collars that was sold to the right price.

Therefore, we would multiply 4.75 by 20, since small collars cost 4.75 and she sold 20 of them. We would also multiply 7.75 by 14, since large collars cost 7.75 and she sold 14 of them.

Lets calculate:

[tex]4.75*20=95\\\\7.75*14= 108.50[/tex]

Now, we would add the final prices together in order to find how much revenue she made off of the collars.

[tex]95+108.50=203.5[/tex]

When you're done soplving, you should get 203.5.

This means that her revenue last month was $203.5.

$203.5 should be your FINAL answer.

____________________________________________________

Answer:

205.50

Step-by-step explanation:

Answer:

Jenny would have to get a 99 on her next test to raise her average from a 94 to a 95.

Step-by-step explanation:

First you need to find her current average:

93 + 89 + 96 + 98 = 376/4 = 94

Now that you have the current average, all you need to do is find what would be the total of her grades if she had a average of 95. Since her average would be 95, and she would have completed 5 tests, it makes sense to multiply the average by the number of tests:

95 x 5 = 475

Now all you need to do is remove from this number the sum of the original 4 tests, and voila! There is her 5th test score:

475 - 376 = 99

Her 5th test score is 99%.

To raise her average to 95, Jenny needs to score a 99 on her next test.

To find out what score Jenny needs to get on her next test, we can use the average formula. We know that Jenny's average score is currently 94 (the average of 93, 89, 96, and 98). Let's call the score she needs to get on her next test 'x'. To raise her average to 95, the sum of all her test scores would be (93 + 89 + 96 + 98 + x) and the number of tests would be 5 (since she has taken 4 tests so far). We can set up the equation (93 + 89 + 96 + 98 + x)/5 = 95 and solve for x:

(93 + 89 + 96 + 98 + x)/5 = 95

Combine like terms and multiply both sides by 5:

376 + x = 475

Subtract 376 from both sides:

x = 99

Therefore, Jenny needs to score a 99 on her next test in order to raise her average to 95.

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Answer:

The cost is GHC 20.00

Step-by-step explanation:

We can write a proportion to solve this

3 bottles     10 bottles

-------------- = -----------

6.00             x

Using cross products

3x = 10 *6

3x = 60

Divide by 3

3x/3 = 60/3

x = 20

The cost is GHC 20.00

Answer:

B

Step-by-step explanation:

The domain is (- infinity, infinity) (or the set of all real numbers) bc the function goes never ending to the left and right

The range is f(x) is greater than or equal to 3 bc the y value 3 is the turning point. Also, it's "greater than or equal to" bc the graph opens upward

The domain and range of the function f(x)= |x-4|+3 are the set of real numbers and every real number greater than or equal to 3 respectively.

The domain of a function is the set of all possible inputs of the function. The range of a function is the set of all possible outputs of that function.

The function is given:

f(x)= |x-4|+3.

We can substitute any value of x to the given function. This means that the domain of the function is the set of all real numbers.

The lowest value that the given function can have is 3. This is possible only when the value of x = 4.

It cannot go lower than that as a modulus or absolute value is used in the function.

Thus, the range of the function can be defined as the set of all real numbers greater than or equal to 3.

Therefore, we have found that the domain and range of the function f(x)= |x-4|+3 are the set of real numbers and every real number that is greater than or equal to 3 respectively.

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