The current value of a car is given by y = -2000x + 25000, where x represents the number of years after the car was first purchased and y represents the current market value of the car. Explain the significance of the slope and y-intercept of this equation.

Answer:

The new line is steeper than the original, but still crossing the y=axis at 7 .

Step-by-step explanation:

Since what has changed from y = 2 x + 7 going into y = 5 x + 7 is the slope of the linear function, (from 2 to 5) what one would notice is that the new line is steeper - raising 5 units every one unit ste to the right- but would still be intersecting the y-axis at the point (0, 7), since the y-intercept has not changed.

Answer:

Option (D)

Step-by-step explanation:

Sum of interior angles of a polygon is represented by the expression,

Sum of interior angles = n(n - 1)×180°

Here n is the number of sides of a polygon

If n = 18,

Sum of 18 sided polygon = (18 - 1) × 180°

                                         = 7 × 180°

                                         = 3060°

Therefore, sum of interior angles of a 18 sided polygon will be 3060°.

Option (D) will be the answer.

Answer:

2880

Step-by-step explanation:

SUM=_-2=

18-2=16

16*180 = 2880 OR

18*160 = 2880 degrees

Answer:

AB║CD and AD║BC

Step-by-step explanation:

By the property of a parallelogram,

" Consecutive angles of a parallelogram are supplementary"

In the figure attached,

∠DCB and ∠CDA are the supplementary angles. Therefore ABCD will be a parallelogram.

[Given: m(∠DCB) + m(∠CDA) = 180°]

And the pair of opposite sides of the parallelogram ABCD will be parallel.

AD║BC and AB║CD

Answer:

(2, f(2))

Step-by-step explanation:

f(x) = -3x^2

For point B, the y-coordinate is f(2).

Point B is (2, f(2))

Answer:

Hey there!

25(10+50)-25

25(60)-25

1500-25

1475

Hope this helps :)

Answer:

The answer is

Step-by-step explanation:

25 (10 + 50) - 25

Expand

250 + 1250 - 25

Simplify

We have the final answer as

1475

Hope this helps you

Answer:

10

Step-by-step explanation:

This is an arithmetic sequence.  The common difference is -6, and the first term is 52.

a = 52 − 6(n − 1)

When n = 8:

a = 52 − 6(8 − 1)

a = 52 − 42

a = 10

Step-by-step explanation:

68$53++83(-$(7(3($++$

Answer:

Of the 5000​ surveys, 14​% were returned. This response rate APPEARS to be low.

Step-by-step explanation:

Given:

Total sample collected = 5000

Survey returned = 700

i) What percentage of the 5000 surveys were​ returned?

To find percentage returned, we have:

[tex] = \frac{700}{5000} * 100 = 14 percent [/tex]

Percentage returned = 14%

ii) Does that response rate appear to be​ low?

Yes, the response is significantly low as only 14% is returned out of expected 100%

iii) In​ general, what is a problem with a very low response​ rate?

The problem with in low response rate in general is that it causes the result to be biased as biased samples of those interested in a particular aspect may have been gotten.

Therefore, of the 5000​ surveys, 14​% were returned. This response rate APPEARS to be low.

Answer:

The equation of the function in vertex form is f(x) = -2·(x - 8)² + 6

Step-by-step explanation:

The given values are

x,            f(x)

6,             -2

7,              4

8,              6

9,              4

10,            -2

The equation of the function in vertex form is given as follows;

f(x) = a × (x - h)² + k

To find the values of a, h, and k, we proceed as follows;

When x = 6, f(x) = -2

We have;

-2 = a × (6 - h)² + k = (h²-12·h+36)·a + k.............(1)

When x = 7, f(x) = 4

We have;

4 = a × ( 7- h)² + k = (h²-14·h+49)·a + k...........(2)

When x = 8, f(x) = 6...........(3)

We have;

6 = a × ( 8- h)² + k

When x = 9, f(x) = 4.

We have;

4 = a × ( 9- h)² + k ..........(4)

When x = 10, f(x) = -2...........(5)

We have;

-2 = a × ( 10- h)² + k

Subtract equation (1) from (2)

4-2 =  a × ( 7- h)² + k - (a × (6 - h)² + k ) = 13·a - 2·a·h........(6)

Subtract equation (4) from (2)

a × ( 9- h)² + k - a × ( 7- h)² + k

32a -4ah = 0

4h = 32

h = 32/4 = 8

From equation (6) we have;

13·a - 2·a·8 = 6

-3a = 6

a = -2

From equation (1), we have;

-2 = -2 × ( 10- 8)² + k

-2 = -8 + k

k = 6

The equation of the function in vertex form is f(x) = -2·(x - 8)² + 6

Answer:

f(x) = -2(x - 8)² + 6

Step-by-step explanation:

I did the test.

Answer: £2.4

Step-by-step explanation:

From the question, Erin buys 3 packs of potatoes costing £2 each, 4 packs of carrots for £2 per pack, and 4 turnips costing 90p each.

Total cost of potatoes = 3 × £2 = £6

Total cost of carrots = 4 × £2 = £8

Total cost of turnips = 4 × 90p = £360p = £3.6

The total cost of things bought by Erin will now be:

= £6 + £8 + £3.6

= £17.6

If she pays with a £20 note, she will collect a change of:

= £20 - £17.6

= £2.4

= 2 pounds, 40 pennies.

Answer:

t = 63.897 years

Step-by-step explanation:

Simple interest rate formula: A = P(1 + r)^t

Simply plug in what we know and solve:

12502 = 1020(1 + 0.04)^t

6251/510 = 1.04^t

log base 1.04 of (6251.510) = 63.897

To reflect a function across the x axis, we just stick a negative in front. This will make all point's y coordinates to go from positive to negative or vice versa. If the original function already has a negative out front, then remove it.

Answer:

B

Step-by-step explanation:

Here, we want to know at what values of b does the equation becomes not solvable

Now looking at the left hand side, we have;

2/(3-5bx) and also the right hand side bx + 1/3

For this expression if we insert b = 0, then automatically x cancels out on both sides of the equation and we shall be left with nothing to solve

Answer:

−5

Step-by-step explanation:

First, we observe that this is a linear equation.

A linear equation in one variable will have no solutions if the equation reduces to an equation of the form:

\blue a x+\red b=\blue c x + \red dax+b=cx+dstart color #6495ed, a, end color #6495ed, x, plus, start color #df0030, b, end color #df0030, equals, start color #6495ed, c, end color #6495ed, x, plus, start color #df0030, d, end color #df0030

where \blue a=\blue ca=cstart color #6495ed, a, end color #6495ed, equals, start color #6495ed, c, end color #6495ed and \red b\neq \red db



​

=dstart color #df0030, b, end color #df0030, does not equal, start color #df0030, d, end color #df0030.

In this case, the equation will reduce to the statement \red b=\red db=dstart color #df0030, b, end color #df0030, equals, start color #df0030, d, end color #df0030, which is not true for any value of xxx.

Hint #2

Since \red {\dfrac23}\neq \red {\dfrac13}

3

2

​



​

=

3

1

​

start color #df0030, start fraction, 2, divided by, 3, end fraction, end color #df0030, does not equal, start color #df0030, start fraction, 1, divided by, 3, end fraction, end color #df0030 , the equation will have no solutions if \blue b=\blue {-5}b=−5start color #6495ed, b, end color #6495ed, equals, start color #6495ed, minus, 5, end color #6495ed.

Let's check that this is the case. If we add \blue {5}{x}5xstart color #6495ed, 5, end color #6495ed, x to both sides, we get

\begin{aligned} \red{\dfrac23}\blue{-5}x&= \blue{-5} x+\red{\dfrac13}\\\\ \red{\dfrac23}\blue{-5}x+\blue5x&= \blue{-5}x+\blue{-5}x+\red{\dfrac13} \\\\ \red{\dfrac23}&=\red{\dfrac13} \end{aligned}

3

2

​

−5x

3

2

​

−5x+5x

3

2

​

​

=−5x+

3

1

​

=−5x+−5x+

3

1

​

=

3

1

​

​

which is not true for any value of xxx, so there are no solutions.

For all other values of b,b,b, comma there will be one solution.

Hint #3

If b=-5b=−5b, equals, minus, 5, the equation will have no solutions.

Answer:

Solution,

[tex]5 \frac{3}{4} \div 1 \frac{1}{2} [/tex]

Convert the mixed number to an improper fraction

[tex] \frac{23}{4} \div \frac{3}{2} [/tex]

To divide by a fraction, multiply by the reciprocal of that fraction

[tex] \frac{23}{4} \times \frac{2}{3} [/tex]

Reduce the numbers with the GCF 2

[tex] \frac{23}{2} \times \frac{1}{3} [/tex]

Multiply the fraction

[tex] \frac{23}{6} [/tex]

Hope this helps...

Good luck on your assignment...

Answer:

8%

Step-by-step explanation:

4/50 = 0.08, which is 8%

If 500 is not a typo, then 4/500 = 0.008, which would be 0.8%

Answer: 8%

Step-by-step explanation: 4/50 = 0.08 Convert the decimal to a percentage. 0.08 = 8%

Answer: subtract 85 with a hundred because you are trying to see how many students out of 100% are good students after that you should get your answer

Step-by-step explanation:

Answer:

77% (rounded)

Step-by-step explanation:

1. Find 85% of 100

           100 x 0.85 = 85

     SO 85 students out of 100 students are good students.

2. Add the 10 more students to the total number.

             100 + 10 = 110 total students

3. Find the percent of good students in the total number of current students.

          85/110 = 0.77 * 100 (to convert to percent) = 77%

Answer:

2310cm³

Step-by-step explanation:

volume= πr²h

22/7× radius of circle × height

circumference= πd

44cm=22/7×d, diameter= 7 cm, radius= 3.5cm

v= 22/7× 3.5× 21 = 2310cm³

Answer:

6-3/0-(-4)

=3/4

Step-by-step explanation:

Given two points of a line to find the slope, we use the formula.y2-y1/x2-x1 hence the answer above. Our xs are x2=0 x=-4 y2=6 y1=3

Answer:

0.5

Step-by-step explanation:

Let D be the event of selecting a marble with dots.

Let P be the event of selecting a purple marble.

The probability of selecting a marble with dots, P(D)=0.2

The probability of selecting a marble that is both purple and has dots, [tex]P(D \cap P)=0.1[/tex]

We want to determine the probability of selecting a purple marble given that the marble has dots on it, P(P|D)

By the definition of conditional probability:

[tex]P(P|D)= \dfrac{P(P \cap D)}{P(D)} \\= \dfrac{0.1}{0.2}\\ =0.5[/tex]

The probability of selecting a purple marble given that the marble has dots on it is 0.5.

Answer:

[tex]3\sqrt{17}$ or \approx 12.37$ Units[/tex]

Step-by-step explanation:

In the attached diagram

CA=CO+OA

CO=DB

Therefore:

5=2+OA

OA=3 Units

The angle between a tangent line and a radius is 90 degrees. therefore triangle OAB is a right triangle with:

OB=12 units

OA=3 units

Using Pythagoras theorem

[tex]AB=\sqrt{3^2+12^2}\\ =\sqrt{153}\\=3\sqrt{17}$ or \approx 12.37$ Units[/tex]

The equation to a line parallel to the line on the graph that passes through (4,15) is y = 3x + 3

The equation of a line can be represented as follows;

y = mx + b

where

Therefore,

parallel line have the same slope

(5, 35)(10, 50)

m = 50 - 35 / 10 - 5 = 15 / 5 = 3

Hence,

(4, 15)

y = 3x + b

15 = 3(4) + b

15 - 12 = b

b = 3

Therefore, the equation to a line parallel to the line on the graph that passes through (4,15) is y = 3x + 3

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Answer:

the slope of the perpendicular bisector is -2/3

Step-by-step explanation:

The slope of the line joining the two points P1(0,3), P2(6,12) is given by

m1 = (y2-y1) / (x2-x1) = (12-3) / (6-0) = 9/6 = 1.5

The slope m2 of a line perpendicular to the previous line is given by

m1*m2 = -1

solving

m2 = -1/m1 = -1/ (3/2) = -2/3

THerefore the slope of the perpendicular bisector is -2/3

Answer:

  B.  x = a(y - v)^2 + h

Step-by-step explanation:

The basic equation is ...

  x = f(y)

  x = y^2

To translate the vertex from (0, 0) to (h, v), we replace x with (x-h) and y with (y-v). Now, we have ...

  x -h = (y -v)^2

To scale the graph horizontally by a factor of "a", we multiply the right side by "a":

  x -h = a(y -v)^2

Adding h gives the form you want to compare to the answer list:

  x = a(y -v)^2 +h

_____

The attachment shows an example for (h, v) = (4, 3).

Answer:

B

Step-by-step explanation:

Hopefully this helps :)

Answer:

Step-by-step explanation:

Let's call hens h and ducks d. The first algebraic equation says that 6 hens (6h) plus (+) 1 duck (1d) cost (=) 40.

The second algebraic equations says that 4 hens (4h) plus (+) 3 ducks (3d) cost (=) 36.

The system is

6h + 1d = 40

4h + 3d = 36

The best way to go about this is to solve it by substitution since we have a 1d in the first equation. We will solve that equation for d since that makes the most sense algebraically. Doing that,

1d = 40 - 6h.

Now that we know what d equals, we can sub it into the second equation where we see a d. In order,

4h + 3d = 36 becomes

4h + 3(40 - 6h) = 36 and then simplify. By substituting into the second equation we eliminated one of the variables. You can only have 1 unknown in a single equation, and now we do!

4h + 120 - 18h = 36 and

-14h = -84 so

h = 6.

That means that each hen costs $6. Since the cost of a duck is found in the bold print equation above, we will sub in a 6 for h to solve for d:

1d = 40 - 6(6) and

d = 40 - 36 so

d = 4.

That means that each duck costs $4.

Answer:

C. 12,000≤715m+645

Step-by-step explanation:

You want to have either equal to or more than 12,000

Answecr:

C

Step-by-step explanation:

Answer:

d) 405 = 15 times 4.5 times h

The height of the prism 'h' = 6 inches

Step-by-step explanation:

Explanation:-

Given Volume of prism

                            V = 405 cubic inches

Given length of the prism

                         L = 15 inches

Given width of the prism

                       W = 4.5 inches

The volume of the prism

                        V = l w h

                       405 = 15 ×4.5× h

                       405 = 67.5 h

Dividing '67.5' on both sides , we get

                      h = 6 inches

Final answer:-

The height of the prism 'h' = 6 inches

Answer: V = l w h. 405 = 15 times 4.5 times h

Step-by-step explanation:

Given the following :

Volume of prism = 405 in^3

Length = 15 inches

Height = h

Width = 4.5 inches

Recall :

The volume of a prism is the product of the Base and the height.

That is;

Volume = Base × height

However, Base of prism is given by the area of the base shape of the prism.

From our parameters Base shape of the prism is a rectangle.

Therefore, Area of rectangle = Length × width

= 15 inches × 4.5 inches = 67.5 inch^2 = Base of prism

Therefore, Volume of prism equals ;

Volume = 15 × 4.5 × h

Volume = 405in^3

Volume = Base × height

405 = 15 × 4.5 × h

The solution is ΔFHE ≅ ΔGEH. [SAS], i.e. triangle FHE is similar to triangle GEH, by SAS rule.

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.

here, we have,

Given: An Isosceles trapezoid EFGH in which EF =GH

To prove: ΔFHE ≅ ΔGEH

Proof: In Isosceles trapezoid EFGH, Considering two triangles ΔFHE and ΔGEH

 1. FE ≅ G H   → [ Given]

 2. ∠H = ∠E

→ Draw GM⊥HE and FN ⊥EH, and In Δ GMH and ΔFNE,

                         GH=FE [Given]

         ∠M+∠N=180°

so, GM║FN and GF║EH, So GFMN is a rectangle.]

∴ GM =FN [opposite sides of rectangle]

∠GMH = ∠FNE [ Each being 90°]

Δ GMH ≅ ΔFNE  [ Right hand side congruency]

→∠H =∠E [CPCT]

→ Side EH is common i.e  EH ≅ EH .

→ΔFHE ≅ ΔGEH. [SAS]

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Answer: k = 4

Step-by-step explanation:

For this division, to determine the value of k, use the Remainder Theorem, which states that:

polynomial p(x) = dividend (x-a) * quotient Q(x) + remainder R(x)

Knowing the degree of quotient is

degree of Q = degree of p(x) - degree of (x-a)

For this case, Q(x) is a third degree polynomial.

Using the theorem:

[tex]x^{4}-3x^{2}+kx-2 = (x-2)(ax^{3}+bx^{2}+cx+d) + 10[/tex]

[tex]x^{4}-3x^{2}+kx-2 = ax^{4} + x^{3}(b-2a)+x^{2}(c-2a)+x(d-2c)-2d+10[/tex]

a = 1

b - 2a = 0 ⇒ b = 2

c - 2b = -3 ⇒ c = 1

-2d + 10 = -2 ⇒ d = 6

d - 2c = k ⇒ k = 4

Therefore, k = 4 and Q(x) = [tex]x^{4} -2x^{2} + 4x + 2[/tex]

the correct answer is:

A. 9/-6