a machine that originally cost 15 600 has a value of 7500 at the end of 3 years the same machine has a value of 2800 at the end of 8 years



A) FIND the average rate of change in value (depreciation) of the machine between its purchase and the end of 3 years

B) find the average tare of change in value of the machine between the end of 3 years and the end of 8 years

C) interpret the sing of your answers

[tex]n,\ n+1-\text{ two consecutive whole numbers}\\57-\text{the sum}\\\\n+n+1=57\qquad\text{subtract 1 from both sides}\\2n=56\qquad\text{divide both sides by 2}\\n=28\\\\n+1=28+1=29\\\\Answer:\ \boxed{\text{The greater of the two numbers is 29}}[/tex]

The two consecutive whole numbers that sum to 57 are 28 and 29. The solution was achieved by setting up an equation and solving for x which represents the smaller number. The greater number is 29.

The sum of two consecutive whole numbers is 57 pertains to a simple arithmetic problem. If two consecutive numbers sum to 57, we can set up an equation to solve for the numbers. Let's call the smaller number 'x'. This means the next number would be 'x + 1' since it's consecutive, or next in line. The equation for your problem would then be x + (x + 1) = 57. Simplifying the equation gives us 2x + 1 = 57, and then subtracts 1 from both sides to get 2x = 56.

The last step is to divide both sides by 2, which gives us: x = 28. So, the smaller number is 28 and the greater number is 29.

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Answer:

value of QZ = 8 units and QM =  12 units.

Step-by-step explanation:

Given: In triangle PQR has medians QM and PN that intersect at Z.

If ZM = 4 units.

In the figure given below;  second median divided the two triangles formed by the first median in the ratio 2:1.

We have to find the value of QZ and QM;

QZ:ZM = 2: 1

⇒ [tex]\frac{QZ}{ZM} = \frac{2}{1}[/tex]

Substitute the value of ZM =4 units and solve for QZ;

[tex]\frac{QZ}{4} = \frac{2}{1}[/tex]

Multiply both sides by 4 we get;

[tex]QZ = 2 \times 4 = 8 units[/tex]

Now, calculate QM;

QM = QZ+ZM = 8 + 4 = 12 units.

Therefore, the value of QZ and QM are; 8 units and 12 units

Answer: 7/16 or .4375

Step-by-step explanation: 1/4 of 1 is 1/4. 1/4 of 3/4 is .1875 which also equals 3/16. Add 1/4 and 3/16 to get 7/16 cups of sugar or 0.4375. Hope this helps!

Triangles NPM and ABC are similar by SAS, establishing that angle ABC corresponds to angle NPM. Thus, <ABC = <MNP.

In triangles NPM and ABC, the given information suggests that these triangles are similar by the Side-Angle-Side (SAS) criterion. Specifically, MP = AC, AB = NM, and BC = PN, along with the corresponding equal angles A = M, B = N, and C = P.

The Angle-Angle Similarity Postulate asserts that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. Therefore, triangles NPM and ABC are similar.

The corresponding angles in similar triangles are equal. Hence, angle ABC is equal to angle NPM. Therefore, the correct answer is:

<MNP

This is because angle ABC in triangle ABC corresponds to angle NPM in triangle NPM.

Answer:

(21,5)

Step-by-step explanation:

To find the slope that passes through the points (7,5) and (21,15) , we use the formula

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

   = (15-5)/(21-7)

   = 10/14

  =5/7

We want a slope that is 1/3 this slope so we will multiply by 1/3

5/7 * 1/3= 5/21

We know the slope and one point (0,0)  we can use the same formula to figure out x and y

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

5/21 = (y2-0)/ (x2-0)

Let the tops be equal and the bottoms be equal

5 = y2-0

5 =y2

and the bottoms

21 = x2-0

21= x2

We have the point

(21,5)

Answer:

here you go

View the picture for your answer!

have a wonderful day :))

Answer:

the probability of getting the exact coins that make $0.15 is 33.3% (1/3)

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

given y = 3(x + 2)(x - 2) = 3(x² - 4) = 3x² - 12

for the y- intercept let x = 0

f(0) = - 12 → y-intercept is the point (0, - 12) → True

for x-intercepts let y = 0

3(x + 2)(x - 2) = 0

x + 2 = 0 ⇒ x = - 2

x - 2 = 0 ⇒ x = 2

x- intercepts are (- 2, 0) and (2, 0) → not (0, - 12)

since f(x) = 3x² - 12 is symmetric about the y-axis

the vertex is at (0, - 12 ) → not (- 2, 2)

The domain is the set of all numbers. The range is also the set of all real numbers.

Why is this the case? Because the line extends forever in both directions along the x and y axis. We can plug in any x value and solve for y, or vice versa, and we don't have any restrictions for the input or output.

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

To write "the set of all real numbers" in interval notation, you would write [tex](-\infty, \infty)[/tex]

This is the interval from negative infinity to positive infinity, spanning the entire real number line.

Answer:

(3 + 5i) – (2 + i)

Step-by-step explanation:

(–2 + 6i) – (1 – 2i)

The real parts  -2-1 = -3

The imaginary parts 6i--2i = 6i+2i = 8i

(–2 + 6i) – (–1 – 2i)

The real parts -2 +1 = -1

The imaginary parts 6i --2i = 6i+2i =8i

(3 + 5i) – (2 – i)

The real parts 3-2 =1

The imaginary parts = 5i --i = 5i+i = 6i

(3 + 5i) – (2 + i)

The real parts 3-2 =1

The imaginary parts 5i -i = 4i

Answer:

d.(3 + 5i) – (2 + i)

Step-by-step explanation:

Answer:

16(3x - 1)

Step-by-step explanation:

the greatest common factor of 48 and 16 is 16, hence

48x - 16 = 16(3x - 1)

Final answer:

After factoring out the greatest common factor of 16 from the expression 48x-16, the correct factored form is 16(3x - 1). The friend's factorization is correct if this result was obtained, demonstrating the universal application of mathematical rules.

Explanation:

To evaluate if your friend factored the expression 48x-16 correctly, we look for the greatest common factor that both terms in the expression share. Both 48x and 16 are divisible by 16. Factoring out the greatest common factor of 16, we get:

16(3x - 1)

This is the factored form of the expression 48x-16, which shows that your friend is correct if they arrived at this result. This method is an application of the distributive property, which states that a(b + c) = ab + ac. In this case, we take out a '16' from both terms, which is the inverse process - factoring.

Moreover, the principles that apply to factoring expressions are the same regardless of location or time, demonstrating the universality of mathematical rules. Whether we are factoring polynomials or checking arithmetic, using the correct rule and applying it properly is essential.

Answer:

changing by one

Step-by-step explanation:

Answer:

2A /b = h

Step-by-step explanation:

A=1/2 bh

We want to isolate h

First we multiply by 2

2A = 2 * 1/2 bh

2A = bh

Then we divide by b to isolate h

2A /b = bh/b

2A /b = h

Answer:

60 pounds

-hope this helps

Answer:

£60

Step-by-step explanation:

100% represents the original price of the shoes

then (100 - 10) = 90% of the original price

Divide the cost by 90% to find 1% then multiply by 100 for the original price

original price = [tex]\frac{54}{90}[/tex] × 100 = £60

The vertex of the parabola y = (x – 5)² + 8 with a vertical axis of symmetry is the point (5, 8).

The question is asking for the vertex of the parabola y = (x − 5)² + 8 which has a vertical axis of symmetry. In the general equation for a parabola, y - k = a(x - h)², the vertex is denoted by the (h, k). So, comparing this with the given parabola equation, we can determine that the h value corresponds to the value inside the brackets in the (x – h)² part of the equation, and the k value corresponds to the term added or subtracted outside the squared term.

For the given equation, y = (x – 5)² + 8, we can see that h = 5 and k = 8. Therefore, the vertex of the parabola is at the point (5, 8).

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Answer:

300 dollars of interest

Step-by-step explanation:

5000 (0.06)

300

Answer:

$30

Step-by-step explanation:

You are being asked to figure out simple interest, I think.

Givens

Formula

i = P*r*t

Solution

Edit

You want this to be done using a % proportion. Is that correct from what I read in the comments after the question (which I didn't see -- sorry).

So it comes to the same thing.

Answer:

a/b =6

Step-by-step explanation:

We want to evaluate a/b

a=24, b=4

Substitute these values into the expression

a/b =24/4

    = 6

Final answer:

When evaluating the expression a/b with a=24 and b=4, the result is 6, as you simply divide 24 by 4.

Explanation:

The expression to evaluate is a/b, where a=24 and b=4.

To calculate this, simply divide the value of a by the value of b:

Step-by-step calculation:

Insert the known values into the expression: a/b = 24/4.

Divide 24 by 4 to get the result.

24 divided by 4 equals 6.

Therefore, if a=24 and b=4, the value of a/b is 6.

Final answer:

To calculate the total distance traveled by the ball in the first four seconds, we sum the distances for each second, yielding 13k feet.

Explanation:

The student has provided a sequence of distances that a ball rolls down an inclined plane, with distances increasing each second. The distances in successive seconds are given by k feet, 2.5k feet, 4k feet, and so on. To calculate the total distance traveled by the ball in the first four seconds, we use the arithmetic sequence formula.

Let's calculate the distance for each second:

1st second: k feet

2nd second: 2.5k feet

3rd second: 4k feet

4th second: By the same pattern it follows that the 4th second should cover 5.5k feet.

To find the total distance, we sum these values:

Total distance = k + 2.5k + 4k + 5.5k = 13k feet.

This is the total distance traveled by the ball in the first four seconds.

Answer:

C

Step-by-step explanation:

$4.50 x 4 = $18.00          $6.00 x 2 = $12.00          $18 + $12  = $30

$4.50 + $6.00 = $10.50

Answer:

38.94

Step-by-step explanation:

To find the area, multiply the length times the width. In this case 9.5 times 4.1.

Answer:

[tex]y=\frac{3w}{10\left(2w-1\right)}[/tex]

Step-by-step explanation:

We are given

Miss Teng normal walk:

speed =0.5 m/s

distance traveled =y km =y*1000

now, we can find time

we know

time = distance / speed

[tex]t_1=\frac{1000y}{0.5}[/tex]

[tex]t_1=2000y[/tex]

Miss Teng  walk on cloudy day:

speed =w m/s

distance traveled =y km =y*1000

now, we can find time

we know

time = distance / speed

[tex]t_2=\frac{1000y}{w}[/tex]

If she reached her school 5 minutes earlier than usual

so,

[tex]t_1-t_2=5\times 60 sec[/tex]

[tex]t_1-t_2=300[/tex]

now, we can plug values

[tex]2000y-\frac{1000y}{w}=300[/tex]

now, we can solve for y

we can multiply both sides by w

[tex]2000yw-\frac{1000y}{w}w=300w[/tex]

[tex]2000wy-1000y=300w[/tex]

[tex]1000y\left(2w-1\right)=300w[/tex]

[tex]y=\frac{3w}{10\left(2w-1\right)}[/tex]

Answer:

The area is 1/2×3×3= 4.5

Step-by-step explanation:

Answer:363

Step-by-step explanation:

We have to find partial sum for the sequence 243 , 81 , 27 ..... up to 5 terms(S5 given)

The sequence actually is 3^5,3^4.,3^3.....

Therefore first 5 terms are 1) 3^5 I.e. 243

2) 3^4 I.e. 81

3) 3^3 I.e. 27

4)) 3^2 I.e. 9

5) 3^1 I.e. 3

Adding all those no. we get partial sum of first 5 no. of the sequence

So, 243 + 81 + 27 + 9 + 3

= 363

Hope it helps!!!

Answer:

D. 363 is the one

Answer:

5 years.

Step-by-step explanation:

She earns $339.3 per year on interest rate. So I divided 1,696.50 by 339.3 to get the amount of ears.

Lina invested for 5 years.

According to the problem,

So, we can say $ 1,696.50 is the interest

∴ Prt = 1696.50

⇒ (7800)(4.35/100)t = 1696.50

⇒ t = 5

∴ Line invested for 5 years.

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Answer:

640 bacteria.

Step-by-step explanation:

Make a chart.

Bacteria    Weeks

40                  0

80                  1

160                  2

320                 3

640                 4

It starts off with 40 bacteria, which means no weeks have passed so far. That is why 40 pairs with 0 rather than 1.

The x-intercept is for y = 0.

substitute y = 0 to the equation of the function:

[tex]\dfrac{1}{3}x+y=-15\\\\\dfrac{1}{3}x+0=-15\\\\\dfrac{1}{3}x=-15\qquad\text{multiply both sides by 3}\\\\\boxed{x=-45}[/tex]

Answer:

(-45,0)

Step-by-step explanation:

I took the test

Let the costs of shoes, t-shirt, and glasses be represented by s, t, g, respectively. The problem statement tells us these relationships:

... s = 2t

... g = t/2

... s +t +g +9 = 65 . . . . . the $9 cost of the hat is added into the total

_____

Solution

Substituting for s and g, we have ...

... 2t +t +t/2 +9 = 65

... (3 1/2)t = 56 . . . . . collect terms

... t = 56/3.5 = 16 . . . . divide by the coefficient of t

The shoes are 2t, so $32.

The t-shirt is t, so $16.

The sunglasses are t/2, so $8.

The hat is $9.

Answer:

1. ∠LOQ = 80°

2. ∠LRQ = 40°

3. ∠LBQ = 40°

Step-by-step explanation:

It is given that ARC QL has a measure of 80.

1.

m∠LOQ: ∠LOQ is the central angle from ARC QL so it has SAME MEASURE.

∠LOQ = 80°

2.

m∠LRQ: ∠LRQ is the opposite angle from ARC QL so it is HALF of ARC QL.

∠LRQ = [tex]\frac{1}{2}(80)=40[/tex]

∠LRQ = 40°

3.

m∠LBQ: ∠LBQ is also another opposite angle from ARC QL so it is HALF of ARC QL as well.

∠LBQ = [tex]\frac{1}{2}(80)=40[/tex]

∠LBQ = 40°

Answer:

t > - 27

Step-by-step explanation:

t + 4 > 31.  Next, solve for t:  t > -27

Answer:

t+4 > 31

t > 27

Step-by-step explanation:

(t + 4) exceeds 31

t+4 > 31

Subtract 4 from each side

t+4-4 > 31-4

t > 27

Answer:

Step-by-step explanation:

We can set up an equation:

4(3x+4)=76

We can distribute the left side and get:

12x+16=76

Subtract 16 from both sides:

12x=60

Divide 12 from both sides:

x=5

Check:

4(3*5+4)

4(15+4)

4(18)

76

So x=5

Answer:

tn = a*2^(n - 1)

Step-by-step explanation:

a = 4

r = 2

tn= a*2^(n-1)

Try it

t3 = 4*2^(3 -1)        Combine the power

t3 = 4 * 2^2            Find 2^2

t3 = 4 * 4                Multiply

t3 = 16                     Answer for t3

Answer:

2^(n+1)

Step-by-step explanation:

You don't even need to use algebraic methods or the formula for this; it's just common sense. 4=2^2, 8=2^3, 16=2^4.

4 is the term 1

8 is term 2

2=term # (1) + 1 for 4

3 = term # (2) + 1 for 8

And so on

So it is 2 to the power of (term # + 1)