These points are linear.
Find the slope.
x-3-2-1 0 1 2
y-8 0 8 16 24 32
slope = [?]
Enter

The monthly interest payment is 162

Interest, in its most simple form, is calculated as a percent of the principal.

First,

monthly interest rate,

= 0.24/12

= 0.02.

Now,

Average monthly interest,

=0.02×$675

= $13.50.

Thus, the annual interest payments,

= 12×$13.50

= $162

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Answer:

[tex]-6+5i[/tex]

Step-by-step explanation:

[tex]-6+\sqrt{-25}\\\\=-6+5i[/tex]

The area of the square of the leg 6 is 36 square units.

The area of the square of the leg 8 is 64 square units.

The area of the square of the hypotenuse square is 100 square units.

The length of the hypotenuse is 10 units.

Formula Used

Area of square, A = [tex](a)^{2}[/tex]

Here, [tex]a[/tex] is the length of the side of the square.

Pythagoras Theorem is given as,

[tex]h^{2} =p^{2} +b^{2}[/tex]

Here, [tex]h, p, b[/tex] are the hypotenuse, perpendicular, and the base of a right angle triangle respectively.

Area of the Square of the Leg 6

Length of the edge of the square = 6 units

Area of square = 6*6

= 36 square units

Area of the Square of the Leg 8

Length of the edge of the square = 8 units

Area of square = 8*8

= 64 square units

Area of the Hypotenuse Square and the Length of the Hypotenuse

Applying Pythagoras theorem,

[tex]h^{2} = (8)^{2} +(6)^{2}[/tex]

[tex]h^{2} = 64+36[/tex]

[tex]h = \sqrt{100}[/tex]

[tex]h = 10 units[/tex]

Therefore, the area of the hypotenuse square is 100 square units and the length of the hypotenuse comes out to be10 units.

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Answer: in the picture

Step-by-step explanation:

Answer:

  18x

Step-by-step explanation:

The HCF is the highest factor common to both expressions. We can find it by factoring both expressions and identifying common factors.

  36(x³+x²y-12xy²) = 18x·2·(x +4y)(x -3y)

  54(x³y+4x³y²-21xy) = 18x·3y·(x +7)(x -3)

The highest common factor is 18x.

The correct response that would be expected based on the probability information is 164

From the information, there were 352 trials that were made and we're correct 164 times.

Therefore, the correct response that would be expected is 164.

The success rate will be:

= 164/352

= 0.466

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Answer:

Step-by-step explanation:

The vertex and direction of opening can be read from the vertex-form equation of a quadratic.

Consider the "parent" quadratic function ...

  y = x²

For this function, the value of y cannot be negative. Larger positive values of x will give larger positive values of y. And, negative values of x that have greater magnitude (are farther from the y-axis) will also give larger positive values of y.

This means that the farther away from the y-axis an x-value is, the farther away from the x-axis is the corresponding y-value. The graph of this is said to "open upward." This will be the case for any positive coefficient of x². (Red graph in the first attachment.)

If the coefficient of x² is negative, then larger-magnitude x-values result in more negative y-values. This makes the graph "open downward." (Blue graph in the first attachment.)

The vertex form of a quadratic equation is ...

  y = a(x -h)² +k . . . . . . vertex (h, k); vertical scale factor 'a'

The value of 'a' is the coefficient of the x² term when this is simplified to standard form: y = ax² +bx +c. That is, the sign of 'a' tells you whether the graph opens upward (a > 0) or downward (a < 0).

The other constants in the vertex form equation tell you how the function has been translated. The value of k is a vertical translation quantity. Since it is added to each function value, it tells the number of units the function is translated upward.

The value h is a horizontal translation quantity. It seems slightly counter-intuitive that the function graph is translated to the right h units when h is subtracted from the x-value. That is the case.

As you may have noticed from the graphs in the first attachment, the vertex (turning point) of the parent function graph is at (x, y) = (0, 0). The vertex of the function ...

  y = a(x -h)² +k

is located at (x, y) = (h, k).

You want the opening direction of y = -2(x +3)² -1. You need look no further than the leading minus sign. It tells you the graph opens downward. (Red graph in the second attachment.)

Of course, the -1 at the end of the equation is the vertical translation of the vertex. That vertex is (-3, -1), as shown by the graph.

You want the vertex of y = -1/2(x +5)² +7. Writing this so the binomial term has a minus sign, we have ...

  y = -1/2(x -(-5))² +7

Comparing this to the vertex form ...

  y = a(x -h)² +k

we identify the parameters to be ...

  a = -1/2 . . . . opens downward

  h = -5

  k = 7 . . . . the vertex is (h, k) = (-5, 7)

The graph is the blue graph in the second attachment. It opens downward and has its vertex at (-5, 7).

__

Additional comment

A lot of math is about matching patterns. Here, you're asked to match the given equations to the "vertex form" pattern, and identify corresponding parts of the pattern: the leading coefficient (a), the horizontal translation (h), and the vertical translation (k). Once you know what the parts of the pattern mean, you can answer the questions easily.

Answer:

step-by-step explanation:

A 7/1 ARM is a mortgage that has a fixed interest rate in the beginning, then switches to an adjustable or variable one. The 7 in 7/1 indicates the initial fixed period of seven years. After that, the interest rate adjusts once yearly based on the index stated in the loan agreement, plus a margin set by the lender.

Answer:

[tex]f=-18a^2+3[/tex]

Step-by-step explanation:

Given equation:

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

[tex]\textsf{Apply exponent rule} \quad (ab)^n=a^n b^n:[/tex]

[tex]\implies f=3-2(3^2a^2)[/tex]

Rewrite 3² as 9:

[tex]\implies f=3-2(9a^2)[/tex]

Remove the parentheses:

[tex]\implies f=3-2 \cdot 9a^2[/tex]

Multiply the numbers 2 · 9 = 18 :

[tex]\implies f=3-18a^2[/tex]

Rearrange to make the variable the first term:

[tex]\implies f=-18a^2+3[/tex]

[tex]y = 2x {}^{2} + e {}^{ - x {}^{4} } [/tex]

[tex] \frac{dy}{dx} = 4x +( e {}^{ - x {}^{4} } )( - 4x {}^{3} )[/tex]

[tex] \frac{dy}{dx} = 4x - 4x {}^{3} e { }^{ - x {}^{4} } [/tex]

[tex] \frac{dy}{dx} = 4x(1 - x {}^{2} e {}^{ - x {}^{4} } )[/tex]

[tex] \frac{dy}{dx} = 0 \\ 4x = 0 \: \: \: \: \: 1 - x {}^{2} e {}^{ - x {}^{4} } = 0[/tex]

[tex]4x = 0 \\ x = 0 \: \: \: \: \: \: y(0) = 0 + e {}^{0} = 1[/tex]

Answer:

Anne has n

Fiona has 3n

3n=6

so n=2

so Anne have 2

Answer:

(x+10,y-3)

Step-by-step explanation:

The angle-bisector construction can be used to bisect any angle and this is proven by:

The angle-bisector construction means that a line is made that can divide an angle into two congruent angles.

This is shown by the fact that all the radii of a circle are congruent and that the corresponding parts of congruent triangles are also congruent (CPCTC) when an angle bisector is made on a circle or triangle respectively.

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For the given quadratic equation we only have a maximum at y = 18.

Here we have:

[tex]f(x) = -2x^2 - 4x + 16[/tex]

Notice that this is a quadratic equation of negative leading coefficient.

Then we have a maximum at the vertex, and both arms tend to negative infinity as x tends to infinity or negative infinity.

The vertex is at:

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

The maximum is:

[tex]f(-1) = -2*(-1)^2 - 4*(-1) + 16 = -2 + 4 + 16 = 18[/tex]

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Answer:

The perimeter of the garden is [tex]12a[/tex].

Step-by-step explanation:

[tex]3a+14+4(a-6)+10+5a=12a[/tex]

The function for the given situation is f(x)=35.0-0.7x.

Given that, Mark bought 10 pound of two types of candies, caramel candies for $2.80 per pound and chocolate candies for $3.50 a pound.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

Now, the function for the given situation is as follows:

If x is the weight of the less expensive candy, the 10-x is the weight of the high expensive candy.

So, f(x)=2.80x+3.50(10-x)

⇒ f(x)=2.80x+35.0-3.50x

⇒ f(x)=35.0-0.7x

Therefore, the function for the given situation is f(x)=35.0-0.7x.

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In a playing card there are 52 cards. (i) '2' of spades: Number of favourable outcomes i.e. '2' of spades is 1 out of 52 cards.

Solution: Check the picture I uploaded.

Answer:

same slope, different intercepts (parallel lines essentially)

Step-by-step explanation:

The required points of x where the slope of tangent and secant is equal at boundary points 4 and 9.

Slope is defined as the rate of change or angle at which curve is having inclination or declination.

Since, the curve of 1/2√x defined for interval [4,9]
The curve is of increasing order so the tangent and secant having equal slope only possible at the boundaries of the curve.

Boundary conditions = (4,1) and (9, 1.5)

Equation can be given as,
y = 0.1x + 0.5

Thus, the  required points of x where the slope of tangent and secant is equal at boundary points 4 and 9.

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Answer: y = 3x - 2

Step-by-step explanation:

gradient = (4 - 1)/(2 - 1) = 3/1 = 3

y = 3x + c needs to work for both points

Substitute (1,1) into equation

1 = 3 x 1 + c

c = 1 - 3 = -2

y = 3x - 2

Answer:

its D

Step-by-step explanation:

Answer:

4.12310562562, 4.23, 4.5

Answer:

D

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = - 2 , then

y = - 2x + c ← is the partial equation

to find c substitute (3, - 2 ) into the partial equation

- 2 = - 6 + c ⇒ c = - 2 + 6 = 4

y = - 2x + 4 ← equation of line in slope- intercept form

Answer:

p=10

Step-by-step explanation:

-7+p=3

+7-7+p=3+7

p=10

Answer:

Hello! The answer to this question is 10.

Step-by-step explanation:

You have to get p by itself so we will add 7 to both sides:

-7 + p = 3

+7        +7

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

p = 10

When doing so, we get p = 10.

You can check your work:

-7 + 10 ⇒ 10 - 7 = 3

Therefore, p = 10 is the correct answer.

The price of the washer and the dryer set is $720.

The commission earned by Alice is $36.

Percentage can be described as a fraction an amount expressed as a number out of hundred. Percentage is a measure of frequency.

Price after the mark up = ( + percentage mark up) x cost price

(1  + 0.20) x $600  = $720

Commission earned by Alice = 5% x 720 = $36

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The combinations of ordered triplets that are possible is equal to: A. 18.

Since the common difference (d) between the consecutive terms in an arithmetic progression (AP) is constant, we have:

d = y - x = z - y

Rearranging the terms, we have:

x = y - d

z = y + d

From the given equation:

x + y + z = 30

y - d + y + y + d = 30

3y = 30

y = 30/3

y = 10.

So the arithmetic progression (AP) is given by:

(10 - d), 10, (10 + d)....

Since the common difference (d) is a natural number which would be from 1 to 9, the combinations of ordered triplets that are possible is as follows:

Number of possibilities = 9 × 2

Number of possibilities = 18.

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Complete Question:

If x, y, z are three natural numbers in A.P. such that x + y + z = 30 then the possible number of ordered triplet (x, y, z) is?

A. 18

B. 19

C. 20

D. 21

Answer:

a = sqrt(c^2 - b^2)

see image.

Step-by-step explanation:

If you square both sides of the equation, you get the Pythagorean Theorem back again.

c = sqrt(a^2 + b^2)

c^2 = a^2 + b^2

Solve for a means to get a all by itself on one side of the equation. Subtract b^2 and then take the square root. See image.

The mistakes that were made regarding the transformation are:

It should be noted that a transformation simply means the changing of the position of an object

In this case, the transformation is incorrect as he applied the reflection to the pre-image first and used an incorrect angle of rotation around point P.

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Answer: I prefer to find the area of the base first and then multiply by the height