Question
Write in scientific notation.

215 × 107

Responses

2.15 × 1092.15 × 109

2.15 × 1052.15 × 105

2.15 × 1072.15 × 107

2.15 × 1014

Answer:

(1, 7.5)

(2, 9)

(3, 10.5)

Step-by-step explanation:

-6x+4y=24

first we want to put the equation in slope intercept form which is y=mx+b

-6x+4y=24

first we add 6x to both sides

4y=24+6x

now we divide everything by 4

y=6+6/4x

simplified

y=3/2x+6

now we input our x values to find the y values (x,y)

y=3/2(1)+6

y=15/2 or 7.5

y=3(2)+6

y=9

y=3/2(3)+6

y=21/2 or 10.5

with this information, our points to plot on the graph are

(1, 7.5)

(2, 9)

(3, 10.5)

i hope this helped! if you have any questions just ask!

The midpoint of the given numbers (1.29 and 1.3) is 1.295

From the question, we are to calculate the midpoint of the given numbers

The given numbers are 1.29 and 1.3

To determine the midpoint of two numbers on a number line, we will add the two numbers together, and then divide value of their sum by 2

Adding up the numbers

1.29 + 1.3

= 2.59

Now, divide the result by 2

Dividing

2.59/2

= 1.295

∴ On the number line, the midpoint of the given numbers is 1.295

Hence, the midpoint of the given numbers (1.29 and 1.3) is 1.295

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The value for the given equation ( log₅ 1/ 125) = log₅¹ - 3

The similarity between the characteristics of exponents linear logarithms can be used to find the property for a quotient's logarithm. To create multiple numbers with the same base using exponents, add the exponents. Subtraction of exponents is used to split two numbers having the same base.

logb(xy) = logbx + logby.

logb(x/y) = logbx - logby.

logb(xn) = n logbx.

logbx = logax / logab.

log₅ 1/ 125 given

log₅ 1/ 125 applying the log property (log[tex]_a[/tex]ᵇ = log b/log a)

(log 1 - log 125)/ log 5

(log 1 - log 5³)/ log 5

(log 1 - 3log 5)/ log 5

((log1)/log 5 )) - 3

log₅¹ - 3

The value for the given equation ( log₅ 1/ 125) = log₅¹ - 3

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A. 559 meters Is the answer

Answer:

The dimensions are 10 inches and 24 inches.

Step-by-step explanation:

Since the quadrilateral is a rectangle, the diagonal divides the rectangle into two right triangles. That means we can use the Pythagorean Theorem, which applies only to right triangles.

On the bottom left triangle, the sides forming the right angle are the legs. They measure x and 2x + 4. The are a and b in the Pythagorean Theorem equation. The side of the triangle measuring 2x + 6 is the hypotenuse of the right triangle, the side opposite the right angle and the longest side in a right triangle. The hypotenuse is c in the Pythagorean Theorem equation.

Start with the equation of the Pythagorean theorem.

[tex] a^2 + b^2 = c^2 [/tex]

Now substitute the values we have for a, b, and c.

[tex] (x)^2 + (2x + 4)^2 = (2x + 6)^2 [/tex]

Square the two binomials. You an use the pattern:

[tex] (a + b)^2 = a^2 + 2ab + b^2 [/tex]

which I will use, or you can use FOIL and collect like terms.

[tex] x^2 + 4x^2 + 16x + 16 = 4x^2 + 24x + 36 [/tex]

Collect like terms, and move all terms to the left side equaling zero.

[tex] 5x^2 + 16x + 16 = 4x^2 + 24x + 36 [/tex]

[tex] x^2 - 8x - 20 = 0 [/tex]

Try to factor the left side. We need two numbers whose product is -20 and whose sum is -8. -10 and 2 work.

[tex] (x - 10)(x + 2) = 0 [/tex]

Set each factor equal to zero, and solve for x.

x - 10 = 0  or  x + 2 = 0

x = 10  or  x = -2

Since one side of the rectangle measures x, x = -2 cannot be a solution since you cannot have a negative side length.

x = 10 is acceptable.

2x + 4 = 2(10) + 4 = 24

Answer: The dimensions are 10 inches and 24 inches.

24.67 liters of the 4.5% solution are added.

As per the known fact, the relation between concentration and volume of solution is -

[tex] C_{1} V_{1} + C_{2} V_{2} = C_{final}V_{final}[/tex]

Let the [tex] V_{2}[/tex] be x. So, final volume will be (18 + x).

Keep the values in formula to find the value of volume of solution required for dilution -

8%×18 + 4.5%×x = 6%×(18 + x)

Rewriting the equation -

0.08×18 + 0.045×x = 0.06(18 + x)

Performing multiplication to find the value of x -

1.44 + 0.045x = 1.08 + 0.06x

Rewriting the equation -

1.44 - 1.08 = 0.06x - 0.045x

Performing subtraction on both sides of the equation -

0.37 = 0.015x

Shifting 0.015 to other side fo equation and performing division

x = 0.37 ÷ 0.015

x = 24.67 liters

Hence, 24.67 liters of 4.5% solution should be added to make a 6% solution.

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The amount Charlie and Kathy would pay interest on the loan of $20,000 is $6,344.80.

An ordinary annuity is payment of level cash flows for a defined period of time, in this case, a fixed monthly payment would be made for 10 years, hence, using the present value formula of an ordinary annuity we can determine the monthly payment:

[tex]PV=PMT*(1-(1+r)^{-N/r}[/tex]

Where:

[tex]PMT*(1+1+0.00479166666666667)^-120/0.00479166666666667\\PMT=$219.54[/tex]

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[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{8})\qquad (\stackrel{x_2}{12}~,~\stackrel{y_2}{20}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{20}-\stackrel{y1}{8}}}{\underset{run} {\underset{x_2}{12}-\underset{x_1}{2}}} \implies \cfrac{12}{10}\implies {\LARGE \begin{array}{llll} \cfrac{6}{5} \end{array}}[/tex]

Step-by-step explanation:

yes, this is a reflection across the y-axis.

the points near to the mirror appear also near in the reflection. and the points far from the mirror appear also far in the reflection.

By applying the Alternate Interior Angles Theorem, the measure of angle x is: C. 60 degrees.

The Alternate Interior Angles Theorem states that when two (2) parallel lines are cut through by a transversal, the alternate interior angles that are formed are congruent.

Since the two lines are parallel lines, angles 3 and 4 are alternate interior angles. Therefore, by applying the supplementary angle theorem, the measure of angle 3 is given by:

Q + R = 180°

85° + m<3 = 180°

Angle 3 = 180° - 85°

Angle 3 = 95°

Also, the sum of the angles formed on a straight line is supplementary and equal to 180°. Therefore, we have:

x + 25° + 95° = 180°

x + 120° = 180°

x = 180° - 120°

x = 60°

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Answer:

good less to the worl then

Answer:

x=5526

Step-by-step explanation:

8597-x=7429-4358

Combine like terms

8597-x=3071

Group all constants on the right side of the equation

8597-x=3071

Subtract 8597 from both sides

(8597- x )-8597=3071-8597

Group like terms

-x+(8597-8597)=3071-8597

Simplify the arithmetic

-x=3071-8597

Simplify the arithmetic

-x=-5526

Isolate the x

-x=-5526

Multiply both sides by-1

-X x -1=-5526 x -1               the small x is for multiplication

Remove the one(s)

X=-5526 x -1

Simplify the arithmetic

x=5526

Using the Factor Theorem, we have that:

a) The zeros of the function are x = 3i, x = -3i, x = 4.5.

b) The factored function is: F(x) = (x² + 9)(x - 4.5).

c) From the graph of the function given at the end of the answer, the only x-intercept is x = 4.5, which is the only real zero of the equation.

The Factor Theorem states that a polynomial function with roots(also called zeros) [tex]x_1, x_2, \codts, x_n[/tex] is given by the following rule.

[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]

In which a is the leading coefficient of the polynomial, determining if it is positive(a positive) or negative(a negative).

For this problem, the function is defined by the following rule:

F(x) = 2x³ - 9x² + 18x - 81.

Using a calculator, the zeros of the function are given as follows:

x = 3i, x = -3i, x = 4.5.

In factored form, the function is given by:

F(x) = (x - 3i)(x + 3i)(x - 4.5)

Considering that i² = -1, we have that:

The factored function is: F(x) = (x² + 9)(x - 4.5).

From the graph of the function given at the end of the answer, the only x-intercept is x = 4.5, which is the only real zero of the equation.

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Shape C is different from shape A and B.

Here, we are given 3 shapes as shown in the image below.

Let us look at each of the shapes one by one.

Shape A-

The height of shape A is 4

The width of shape A is 5

The ratio of width and height = 5/4

Shape B-

The height of shape B is 10

The width of shape B is 8

The ratio of width and height = 8/10 or 4/5

Shape C-

The height of shape C is 10

The width of shape C is 6

The ratio of width and height = 6/10 or 3/5

Thus, we can see that the ratio of width and height is equal for shape A and B. Thus, C is different.  

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Your question was incomplete. Check for the missing image below.

The answer is cone -7 7=9÷7

The answer is

7x-1/8x

now, the assumption is that, "x" is a simple variable whilst "y" is a function in x-terms, so

[tex]e^{\frac{x}{y}}=3x-y\implies \stackrel{\textit{\LARGE chain~rule}}{e^{\frac{x}{y}}\stackrel{quotient~rule}{\left( \cfrac{1\cdot y-x\cdot \frac{dy}{dx}}{y^2} \right)}} =3-\cfrac{dy}{dx} \\\\\\ \cfrac{ e^{\frac{x}{y}}y-e^{\frac{x}{y}}x\cdot \frac{dy}{dx}}{y^2}=3-\cfrac{dy}{dx}\implies e^{\frac{x}{y}}y-e^{\frac{x}{y}}x\cdot \cfrac{dy}{dx}=3y^2-y^2\cfrac{dy}{dx}[/tex]

[tex]e^{\frac{x}{y}}y-3y^2=e^{\frac{x}{y}}x\cdot \cfrac{dy}{dx}-y^2\cfrac{dy}{dx}\implies e^{\frac{x}{y}}y-3y^2= \cfrac{dy}{dx}\left( e^{\frac{x}{y}}x-y^2 \right) \\\\[-0.35em] ~\dotfill\\\\ ~\hfill {\LARGE \begin{array}{llll} \cfrac{e^{\frac{x}{y}}y-3y^2}{e^{\frac{x}{y}}x-y^2}=\cfrac{dy}{dx} \end{array}}~\hfill[/tex]

x = [tex]\sqrt{2+\sqrt{2+\sqrt{2+...} } }[/tex] = 2

We have to find the value of x = [tex]\sqrt{2+\sqrt{2+\sqrt{2+...} } }[/tex]

First take squares on both sides, then,

⇒ x² = 2 + [tex]\sqrt{2+\sqrt{2+\sqrt{2+...} } }[/tex]

As the terms inside the square roots are non terminating, we can substitute x = [tex]\sqrt{2+\sqrt{2+\sqrt{2+...} } }[/tex] into the above equation.

i.e.,  x² = 2 + x

⇒ x² - x -2 = 0

This is a quadratic equation which can be solved using factorization.

⇒  x²+(-2+1)x +(-2.1) = 0

⇒ (x-2)(x+1) = 0

So x = 2 or -1

But here the value of √2 is positive and square root of sum of positive numbers will always be positive.

So we can conclude that

x = [tex]\sqrt{2+\sqrt{2+\sqrt{2+...} } }[/tex] = 2

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The time it will take to cover another distance of 145 miles is; 2.5 hours

We are given;

First distance driven = 348 miles

Time taken for first distance = 6 hours

Formula for speed is;

Speed = Distance/Time taken

Thus;

Speed for fist distance = 348/6

Speed = 58 mph

Now, at the same speed she wants to cover another distance 0f 145 miles. Thus;

Time taken = distance/speed

Time taken = 145/58

Time taken = 2.5 hours

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Yes , the toll company is correct to give the teacher a ticket.

Mean Value Theorem for a function f(x): [a,b]→ R such that f(x) is continuous and differentiable over the interval.

(i) f(x) is continuous on [a,b].

(ii) f(x) is differentiable on (a,b).

(iii) There exist a point c in (a,b) such that f'(c)=f(b)-f(a)/(b-a).

In the given question

Speed Limit = 60 mph

Time of entrance on toll road = 6:00

Time of exit from toll road = 7:00

Total time on toll road  = 1 hr

Mile marker on entry in toll road = 15 mile

Mile marker on exit from toll road = 100 mile

Total distance travelled on toll road = 100-15= 85 miles

[tex]Average.Speed=\frac{total . distance}{total.time}[/tex]

Substituting the values we get .

Avg Speed = 85/1 = 85  mph

Overspeed = Avg Speed - Speed Limit

=85-60

=25 mph

The teacher over speed by 25 mph.

Since 85 mph is the average speed , it means that for some instance he was travelling below the average speed and for some instance he was travelling above the average speed.  

By Mean value Theorem , it is clear that there have been at least one point where the teacher was travelling above 85 mph , which means he was over speeding .

Therefore , Yes , the toll company is correct to give the teacher a ticket.

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The change received by Chloe after paying a $20 bill for ribbons is $3.2.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given is the table that represents the cost per yards of the ribbons.

From the question, we can write -

Ribbon       Cost per Yard ($)

Chiffon                 5.88

Satin                     1.50

Lace                     3.29

Tulle                     2.25

Cost of one yard of satin ribbon → $1.50.

Then, the cost of 5.5 yards of satin ribbon [A1] → 5.5 x 1.50 = $8.25.

Cost of one yard of tulle ribbon → $2.25.

Then, the cost of 3.8 yards of tulle ribbon [A2] → 3.8 x 2.25 = $8.55.

Total cost of both the Ribbons → A1 + A2 = 8.25 + 8.55 = $16.8.

Money paid by Chloe → $20

Change received by Chloe → 20 - 16.8 = $3.2

Therefore, the change received by Chloe after paying a $20 bill for ribbons is $3.2.

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Answer:

10 Dimes, 5 quarters, and 7 Nickels

Step-by-step explanation:

10 Dimes - 1 dollars

5 Quarters - 1.25 dollars

7 Nickels - 35 cents

1 + 1.25 = 2.25

2.25 + 35 = 2.60

The slope-intercept form of the equation of the line described is y = -6x/5 + 7/5.

Given the following data:

Points on x-axis = (-3, 2).

Points on y-axis = (5, -1).

A slope is also referred to as gradient and it's typically used to describe both the ratio, direction and steepness of the function of a straight line.

Mathematically, the slope of any straight line can be calculated by using this formula;

[tex]Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]

Substituting the given points into the formula, we have;

Slope, m = (-1 - 5)/2 + 3)

Slope, m = -6/5

Mathematically, the standard form of the equation of a straight line is given by;

y = mx + c

Where:

At point (2, -1), we have:

-1 = -6/5(2) + c

-1 = -12/5 + c

c = 12/5 - 1

c = 7/5

In conclusion, we can reasonably and logically deduce that the slope-intercept form of the equation of the line described is y = -6x/5 + 7/5.

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The number of candies that Augustus will spend on the 30th day will be 536870912 candies.

It should be noted that from the information, Augustus is afraid that all that candy will just make it worse, so he tells his parents that it would be ok if they just give him 1 candy on the first day, 2 on the second day, continuing to double the amount each day as he completes his homework.

Therefore, the amount that he will get on the 30th day will be:

= 1 × 2^29

= 1 × 536870912

= 536870912

Therefore, the number of candies that Augustus will spend on the 30th day will be 536870912 candies.

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Answer:

(-2.5 , 0.5)

Step-by-step explanation:

You can use the midpoint formula.

x(sub1) + x(sub2) / 2  ,  y(sub1) + y(sub2) / 2

For example:

-5 + 0 / 2  ,  -2 + 3 / 2

-5 / 2  ,  1 / 2

-2.5 , 0.5

midpoint = (-2.5 , 0.5)