Which form of equation models the data if a is a negative integer and b is a positive integer?

A.) b =  ax/y
B.) y = ab^x
C.) y = ax+b
D.) y = ab^-x

* ^ = exponent *

The value of two figures that are similar to the 2 by 6 figure are shown in figure 2 and figure 4.

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

The figure is type of 2 by 6.

Now,

Since, The figure is type of 2 by 6.

Which is equal to 1 by 3.

Clearly, In figure 1;

The size is 2 by 4.

It is equal to 1 by 2.

In figure 2;

The size is 1 by 3.

It is equal to 1 by 3.

In figure 3;

The size is 1 by 6.

It is equal to 1 by 6.

In figure 4;

The size is 3 by 9.

It is equal to 1 by 3.

Thus, The figure 2 and figure 4 is equal to the figure 2 by 6.

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Answer:

[tex]4x^2+72x+259=0[/tex]

Step-by-step explanation:

If [tex]x_1[/tex] and [tex]x_2[/tex] are the solutions to the quadratic equation, then this equation can be written as

[tex](x-x_1)(x-x_2)=0[/tex]

In your case,

[tex]x_1=-9+\dfrac{\sqrt{65}}{2}\\ \\x_1=-9-\dfrac{\sqrt{65}}{2}[/tex]

Then the equation is

[tex]\left(x-\left(-9+\dfrac{\sqrt{65}}{2}\right)\right) \left(x-\left(-9-\dfrac{\sqrt{65}}{2}\right)\right)=0\\ \\\left(x+9-\dfrac{\sqrt{65}}{2}\right)\left(x+9+\dfrac{\sqrt{65}}{2}\right)=0\\ \\x^2+9x+\dfrac{\sqrt{65}}{2}x+9x+81+\dfrac{9\sqrt{65}}{2}-\dfrac{\sqrt{65}}{2}x-\dfrac{9\sqrt{65}}{2}-\dfrac{65}{4}=0\\ \\x^2+18x+\dfrac{259}{4}=0\\ \\4x^2+72x+259=0[/tex]

Answer:

A man drove x miles per hour for 3 hours and (2x-60) miles per hour for the next 4.75 hours.Express the total distance traveled in terms of x.

Total distance covered by the man in terms of 'x' = (12.5x-285)miles

Step-by-step explanation:

Given:

Speed of  a man = 'x' miles/hour

Time taken = [tex]3[/tex] hour

So, distance = product of speed and time.

Distance covered in term of 'x' [tex]=(d_1=3x)[/tex]

Now,

Speed = [tex](2x-60)[/tex] miles/hour

Time taken= [tex]4.75[/tex] hours

Distance [tex](d_2)[/tex]  = [tex](2x-60)\times 4.75[/tex]

                      = [tex](2x\times 4.75) -(60\times 4.75)[/tex]

                      = [tex](9.5x - 285)[/tex] miles

Total distance covered by the man = Summation of  [tex]d_1[/tex] and [tex]d_2[/tex]

                                                           = [tex](9.5x-285+3x)[/tex]

                                                           = [tex](12.5x-285)[/tex] miles

So the total distance covered by the man in terms of 'x' = (12.5x-285) miles.

For, "x" greater than 34, the perimeter of the picture frame greater than 152 inches

Solution:

Let "x" be the width of the frame

Given that, The length of a picture frame is 8 inches more than the width

Therefore,

Length = width + 8

Length = x + 8

The perimeter of rectangle is given by formula:

Perimeter = 2(length + width)

Substituting the values we get,

Perimeter = 2(x + 8 + x)

Perimeter = 2(2x + 8)

Perimeter = 4x + 16

The perimeter of the picture frame greater than 152 inches

Perimeter > 152

[tex]4x + 16>152\\\\\text{Subtract 16 from both sides of inequality}\\\\4x + 16 - 16 > 152 - 16\\\\4x>136\\\\\text{Divide both sides by 4}\\\\x>34[/tex]

Therefore, for, "x" greater than 34, the perimeter of the picture frame greater than 152 inches

Answer:

x>35

Step-by-step explanation:

Step-by-step explanation:

100%=245

x%=40

Let's see what part 40 is of 245. 40/245=0.16. so 0.16×245=40. Therefore 0.16×100%=x=16% roughly.

Answer:

-17

Step-by-step explanation:

f(n)=-5n-2

f(3)=-5(3)-2

f(3)=-15-2

f(3)=-17

Step-by-step explanation:

We have,

[tex]\dfrac{4}{5}[/tex] ÷ [tex]\dfrac{7}{6}[/tex] + [tex]\dfrac{2}{7}.2\dfrac{1}{5}[/tex]

To find, the value of [tex]\dfrac{4}{5}[/tex] ÷ [tex]\dfrac{7}{6}[/tex] + [tex]\dfrac{2}{7}.2\dfrac{1}{5}[/tex] = ?

∴ [tex]\dfrac{4}{5}[/tex] ÷ [tex]\dfrac{7}{6}[/tex] + [tex]\dfrac{2}{7}.2\dfrac{1}{5}[/tex]

[tex]=\dfrac{4}{5}\times \dfrac{6}{7} +\dfrac{2}{7}.\dfrac{8}{5}[/tex]

[tex]=\dfrac{24}{35} +\dfrac{16}{35}[/tex]

Taking LCM of denominator, we get

[tex]=\dfrac{24+16}{35}[/tex]

[tex]=\dfrac{40}{35}[/tex]

Dividing numerator and denominator by 5, we get

[tex]=\dfrac{8}{7}[/tex]

∴ The value of [tex]\dfrac{4}{5}[/tex] ÷ [tex]\dfrac{7}{6}[/tex] + [tex]\dfrac{2}{7}.2\dfrac{1}{5}[/tex] [tex]=\dfrac{8}{7}[/tex]

Hence, the value of [tex]\dfrac{4}{5}[/tex] ÷ [tex]\dfrac{7}{6}[/tex] + [tex]\dfrac{2}{7}.2\dfrac{1}{5}[/tex] is equal to [tex]\dfrac{8}{7} .[/tex]

The statement is true. The rational roots of a polynomial can be written in the form p/q. The rational root theorem is used to determine these potential roots.

The statement in the question is true.

The rational roots of a polynomial function can indeed be written in the form p/q, where p is a factor of the leading coefficient and q is a factor of the constant term. This is known as the Rational Root Theorem.

For example, if we have the polynomial function f(x) = 3x^3 - 7x^2 + 4x - 2, the leading coefficient is 3 and the constant term is -2. The potential rational roots would be of the form p/q, where p is a factor of -2 and q is a factor of 3. The factors of -2 are -1, 1, -2, and 2, while the factors of 3 are -1 and 3. Therefore, the potential rational roots would be:

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C = circumference of circle with radius r

C = 2*pi*r

C = 2*3.14*3500

C = 21,980

C = 22,000 rounding to 2 significant figures (3500 is also 2 sig figs)

Final answer:

To find an equivalent length for a wooden board that is 3 yards and 1 foot long, you convert yards to feet, using the fact that 1 yard equals 3 feet, and then add any remaining feet. The board is therefore 10 feet long in total.

Explanation:

Converting Yards to Feet:

A wooden board is 3 yards and 1 foot long. To find an equivalent length, we need to convert yards to feet because there are 3 feet in 1 yard. The calculation goes as follows:

 First, we know that 1 yard equals 3 feet.

 To convert 3 yards to feet, we multiply by 3: 3 yards × 3 feet/yard = 9 feet.

 Next, we add the extra foot: 9 feet + 1 foot = 10 feet.

 Therefore, the board is 10 feet long in total.

This process involves using equalities and conversion factors to change one unit of measurement to another while maintaining the same quantity.

Answer:

[tex] \frac{4}{15} [/tex]

Step-by-step explanation:

[tex] 3 \frac{1}{10} - 2 \ \frac{5}{6} [/tex]

Convert the above mixed numbers to improper fractions through this simple approach: 3 × 10 + 1 /10 = 31/10. Similarly, 2 × 6 + 5 /6 = 17/6

[tex] \frac{31}{10} - \frac{17}{6} [/tex]

Take the LCM of the denominators and simplify. LCM = 60. Thus, 60/10 = 6; 6 × 31 = 186. Also, 60/6 =10; 10×17 =170 all divide by 60:

[tex] = \frac{186 - 170}{60} [/tex]

Common factors between the numerator and denominator is 4, therefore 16/4 = 4 and 60/4 = 15.

[tex] = \frac{16}{60} = \frac{4}{15} [/tex]

Therefore the answer is 4/15 in simplest form.

Answer:

When solving equations the goal is to get the variable by itself so

4.5+1.5k=18-3k (first step is to subtract 4.5 from each side)

1.5k=13.5-3k (4.5-4.5=0, 18-4.5=13.5) (Next is to add 3k to each side)

4.5k=13.5 (1.5k+3k=4.5k, -3k+3k=0) (Last you divide both sides by 4.5)

k=3 (4.5/4.5=1, 13.5/4.5=3)

k=3

Hope this helps ;)

Answer:

For the first scatter plot, the variables have a negative association, which matches the option D. X is the amount of time in the mall and Y is the remaining money.

For the second scatter plot, it is a positive association. This plot could match A, B, or E.

The third scatter plot shows no correlation whatsoever, which represents C. Tomika's friends' heights did not associate with how much time they watched TV.

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Brainliest would be appreciated! I'd be Expert by now, but I never get brainliest. You don't have to though, but it would make me happy. Thanks!

Answer:

No solution.

Step-by-step explanation:

1/4x-3/4x=3-1/2x

-2/4x=3-1/2x

-1/2x+1/2x=3

0=3

no solution

Hope it will help u..............

The equation of a line is y = mx + b  [m is the slope, b is the y-intercept or the y value when x = 0  ---->  (0, y) or the point where the line goes through the y-axis]

To find the slope, you use the slope formula (m):

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]           and plug in 2 points

I will use the points (0, 0) and (1, 8)

(0, 0)  ---->  (x₁, y₁)

(1, 8) ---->   (x₂, y₂)

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

[tex]m=\frac{8-0}{1-0}[/tex]

m = 8

Since you know m, plug it into the equation.

y = 8x + b

The graph shows that the y-intercept is 0, so plug it into the equation

y = 8x    

Answer:

Divide 2 by 1/6 and you should get the value of x.

Step-by-step explanation:

simple 2 step equation.

Answer: x = 12

Step-by-step explanation: In this equation, notice that x is being multiplied by a fraction. In this situation, in order to get x by itself, we must multiply both sides of the equation by the reciprocal of that fraction. The reciprocal of a fraction is just that fraction flipped so the reciprocal of 1/6 is just 6/1.

So here, in order to get x by itself, we multiply both sides of the equation by 6/1. On the left our 6's cancel and our 1's cancel and we're left with x. On the right we have 2 x 6 which simplifies to 12 so x = 12.

Answer:the answer  is a

Step-by-step explanation:

Answer:

[tex]1\frac{1}{2}x + 4[/tex]

Step-by-step explanation:

We are given the Perimeter: P = Perimeter[tex]3\frac{1}{2}x + 18[/tex]    in decimal 3.5x+18

we know that a Perimeter is equal to all sides added up: S1+S2+S3+S4=P

we know that this is a rectangle so that means that it has 4 sides and two sides are the same and the other 2 are the same.

We are given the the height on the image

Height: H = [tex]\frac{1}{4}x + 5[/tex]  in decimal 0.25x + 5

That height is one side so we know another of the sides is the same.

Perimeter is equal to all sides added up. So we have to subtract the sides to find out each ones measurements.

(Height x 2) + (Width x 2) = Perimeter

Therefore we know the height which is given on the image is 0.25x+5 so that times 2 = 0.5x+10    (height x 2)

so now we can subtract the heights from the perimeter.

  3.5x  +  18

-  0.5x  +  10

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

  3x     +    8

So we got rid of both heights. Now we are left with our two lengths:

3x+8  = (length x 2)

To get the length of one side we divide that by 2 because there are 2 sides that have the same length and get 1.5x+4  in fractions that is:

  [tex]1\frac{1}{2}x + 4[/tex]

I hope this helped you or anyone else that needs the answer :)

Answer:

$69

Step-by-step explanation:

1 - 0.25 = 0.75

original price * (1 - markdown) = sale price

$92 * 0.75 = sale price = $69

Answer:

100 times bigger

Step-by-step explanation:

Answer:

297.26 feet to the nearest hundredth.

Step-by-step explanation:

We use the cosine ratio here because we know the hypotenuse and need the adjacent side.

cos 42 = adj / hyp

= x / 400

x = 400 cos 42

x = 297.26 feet.

Answer:

(2x+5)(x+3)

Step-by-step explanation:

2x^2+11x+15

(2x+5)(x+3)

Answer:

(2x+5)(x+3)

Step-by-step explanation:

Answer:

122 degree

Step-by-step explanation:

As we know that

Sum of all angles of triangle = 180 degree

Angle A + Angle B + Angle C = 180

Angle A + 43 + 15 = 180

Angle A + 58 = 180

Angle A = 180-58

Angle A = 122

Answer:

Jack has 48 rockets in all. He wants to split them equally into 6 groups. How much rockets do he put into each group?

Let "how much" = x. Set the equation:

x * 6 = 48

(x * 6)/6 = (48)/6

x = 48/6

x = 8

8 groups is your answer.

~

Answer:

1979.25

Step-by-step explanation:

Answer:

[tex]57.2\ ft[/tex]

Step-by-step explanation:

we know that

The formula of slope is "rise over run", where the "rise" (means change in y, up or down) and the "run" (means change in x, left or right)

In this problem

The tangent of angle of 5 degrees is equal to the quotient of "rise over run"

Let

y ----> the rise of the ramp

x ----> the run of the ramp

[tex]tan(5^o)=\frac{y}{x}[/tex]

we have

[tex]y=5\ ft[/tex]

substitute and solve for x

[tex]tan(5^o)=\frac{5}{x}[/tex]

[tex]x=\frac{5}{tan(5^o)}[/tex]

[tex]x=57.2\ ft[/tex]

Answer: 4

Step-by-step explanation:

Multiply 4 by 2/3 and 1/2 (calculator) or you can put 4 like 4/1 than multiply 4/1 *3/2 and 4/1 * 1/2

Top times top and bottom times bottom

The equation which shows the correct use of the distributive property is - 6x + 2 = -15

Given:

-4(3/2x - 1/2) = -15

multiply separately

-4(3/2x) -4(-1/2) = -15

-12/2x + 4/2 = -15

- 6x + 2 = -15

solve for x

-6x = -15 - 2

-6x = -17

x = -17/-6

x = 2.83

Therefore, the equation which shows the correct use of the distributive property is

- 6x + 2 = -15

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Answer:

Yes! the ratio 8:16 is equivalent to 1:2

1) Quotient = [tex]x^2+x-3[/tex].

   Reminder= 8.

2) Quotient = x-3.

    Reminder = 7x-9.

Step-by-step explanation:

The Polynomial division is same as the regular division using long division method.

The quotient and reminder can be either polynomial or number.

1) For [tex]\frac{x^4-3x^2+4x+5}{x^2-x+1}[/tex] , the quotient is [tex]x^2+x-3[/tex] and the reminder is 8.

2) For [tex]\frac{x^3-3x^2+5x-3}{x^2-2}[/tex],  the quotient is  x-3 and the reminder is 7x-9.

( The steps are uploaded in the image).