please help with the question below asap !! thank you in advance !!

The numbers in terms of power of 10 is;

(i) [tex]10^{1}[/tex]

(ii) [tex]10^{6[/tex]

(iii) [tex]9 * 10^{4}[/tex]

Here,

Given numbers are;

i. 10

ii 1000000

iii 90000

We have to find in terms of power of 10.

What is Powers of a number?

The power of a number says how many times to use the number in a multiplication. Powers are also called Exponents or Indices.

Now,

Given numbers are;

i. 10

ii 1000000

iii 90000

We can write in terms of power of 10 as;

(i) 10 = [tex]10^{1}[/tex]

(ii) 1000000 = [tex]10^{6[/tex]

(iii) 90000 = [tex]9 * 10^{4}[/tex]

Hence, The numbers in terms of power of 10 is;

(i) [tex]10^{1}[/tex]

(ii) [tex]10^{6[/tex]

(iii) [tex]9 * 10^{4}[/tex]

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The area occupied by the photograph in terms of x described by the quadratic equation A = x² - 20 · x + 100.

Both the backing card and the photograph are represented by two concentric squares, the area of the square is equal to the square of the side length. The expression for the area occupied by the photograph is described by the following polynomial:

A = l²

A = (x - 10) · (x - 10)

A = (x - 10)²

A = x² - 20 · x + 100

The area occupied by the photograph in terms of x described by the quadratic equation A = x² - 20 · x + 100.

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Answer:

D. 491.52

Step-by-step explanation:

The correct graph of the ellipse is identified and attached below.

Given the equation is (x₋3)²/16 ₊ (y₋4)²/9 = 1

step 1: identify the center (h,k) of the ellipse in standard form:

(x₋h)²/a² ₊ (y₋k)²/b² = 1

In the standard form of an ellipse, notice that there is a minus sign in front of the h and k.

In our equation  (x₋3)²/16 ₊ (y₋4)²/9 = 1 , we have:

h = 3 and k = 4

Therefore, center (h,k) = (3,4)

Step 2: Identify the orientation by determining the major axis and minor axis in (x₋h)²/a² ₊ (y₋k)²/b² = 1

if a>b, the major axis is horizontal and the minor axis is vertical, making the ellipse a horizontal ellipse.

if a<b, the minor axis is horizontal and the major axis is vertical, making the ellipse a vertical ellipse.

For  (x₋3)²/16 ₊ (y₋4)²/9 = 1

a² = 16, a = 4 and b² = 9 , b = 3

so, 4>3, the major axis is horizontal and the minor axis is vertical, making the ellipse a horizontal ellipse.

Step 3:

Plot the co-vertices along the minor axis and the vertices along the main axis (endpoints). No matter which way around, draw points a horizontal distance of a to the left and right from the center and points b above and below the center.

Therefore the vertices are marked along the major axis.

vertices are (3,7) and (3,1)

and co vertices are marked along the minor axis

co vertices are (₋1,4 ) and (7,4)

step 4: connect the vertices and co vertices making a smooth horizontal ellipse.

Hence a horizontal ellipse is made.

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Step-by-step explanation:

photo please ......................

Answer:

Step-by-step explanation:

need to see the graph

The population density of Singapore in residents per square kilometer is 8266.12 per square kilometer

What is Population Density ?

The given parameters are

Number of people = 21400 residents

Area = 1 mi²

Convert the square mile to square kilometer

1 x 1.609² = 2.588881 Km²

Population density = Number of residents ÷ area

Population density = 21400 ÷ 2.588881

Population density = 8266.12 per square kilometer

Therefore, the population density of Singapore in residents per square kilometer is 8266.12 per square kilometer

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Quadratic equations are all those equations that can be reformulated in a standard format (αx² + bx + c(=0) where the value of x is unknown and the values of the coefficients (a, b and c) are unknown.

These equations can always be solved using the quadratic formula, although sometimes it is also possible to use factorization or isolation of variables.

Expand squared

It is distributed

Combine like terms.

Move terms to the left

Subtract the numbers

Use the quadratic formula.

                        [tex]\large\displaystyle\text{$\begin{gathered}\sf x=\frac{-b\pm\sqrt{b^{2}-4ac } }{2a} \end{gathered}$}[/tex]

In standard form we identify "a", "b" and "c" from the original equation and add to the quadratic formula.

                      [tex]\large\displaystyle\text{$\begin{gathered}\sf x=\frac{-(-14)\pm\sqrt{(-14)^{2}-4\cdot1\cdot41 } }{2\cdot1} \end{gathered}$}[/tex]

Simplify

                                         [tex]\large\displaystyle\text{$\begin{gathered}\sf x=\frac{14\pm4\sqrt{2} }{2} \end{gathered}$}[/tex]

Separate equations

To solve for the unknown variants, we split the equation into two: one with a plus sign and the other with a minus sign.

                                       [tex]\large\displaystyle\text{$\begin{gathered}\sf x=\frac{14+4\sqrt{2} }{2} \end{gathered}$}[/tex]

                                       [tex]\large\displaystyle\text{$\begin{gathered}\sf x=\frac{14-4\sqrt{2} }{2} \end{gathered}$}[/tex]

Solve

Order and isolate the variant to find each solution.

                                            [tex]\large\displaystyle\text{$\begin{gathered}\sf x=7+2\sqrt{2} \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf x=7-2\sqrt{2} \end{gathered}$}[/tex]

                            [tex]\red{\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\blue{Answer \ \ \longmapsto \ \ x=7\pm2\sqrt{2} }} \end{gathered}$}}}[/tex]

Functions and their domains of all the subparts are:

So,

(A) (fog)(x) and domain:

[tex](f \circ g)(x)=f(g(x))=(g(x))^2+g(x)=\left(x^2+14 x+2\right)^2+x^2+14 x+2\\=x^4+28 x^3+200 x^2+56 x+4+x^2+14 x+2=x^4+28 x^3+201 x^2+70 x+6[/tex]

The domain of (fog)(x) is the collection of domain values for g(x) with range values in the domain of f(x).

Because both functions are polynomials, the domain is [tex](-\infty, \infty)[/tex].

(b) (gof)(X) and domain:

[tex](g \circ f)(x)=g(f(x))=(f(x))^2+14(f(x))+2=\left(x^2+x\right)^2+14\left(x^2+x\right)+2\\=x^4+2 x^3+x^2+14 x^2+14 x+2=x^4+2 x^3+15 x^2+14 x+2[/tex]

The domain name is [tex](-\infty, \infty)[/tex] because this is a polynomial composition.

(c) (fof)(x) and domain:

[tex]\begin{aligned}&(f \circ f)(x)=f(f(x))=(f(x))^2+f(x)= \\&\left(x^2+x\right)^2+x^2+x=x^4+2 x^3+x^2+x^2+x=x^4+2 x^3+2 x^2+x\end{aligned}[/tex]

Because this is a polynomial composition, the domain is [tex](-\infty, \infty)[/tex].

(d) (gog)(x) and domain:

[tex](g \circ g)(x)=g(g(x))=(g(x))^2+14(g(x))+2=\left(x^2+14 x+2\right)^2+14\left(x^2+14 x+2\right)+2\\=x^4+28 x^3+200 x^2+56 x+4+14 x^2+196 x+28+2=x^4+28 x^3+214 x^2+252 x[/tex]

Because this is a polynomial composition, the domain is [tex](-\infty, \infty)[/tex].

Therefore, functions and their domains of all the subparts are:

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The complete question is given below:
Find the functions and their domains. (enter the domains in interval notation.)

[tex]f(x)=x^2+1 x, g(x)=x^2+14 x+2[/tex]

(a) (fog)(x) and domain

(b) (gof)(X) and domain

(c) (fof)(x) and domain

(d) (gog)(x) and domain

Answer: The total number of stamps is 132.

Step-by-step explanation:

We know that Erin has 36 stamps.

Given that information, we can calculate how many stamps Julia has which is 2/3 as many stamps as Erin.

2/3 * 36 = 24

Julia has 24 stamps.

Julia also has 1/3 as many stamps as Robert.

24 = 1/3 * Robert

Robert = 72 stamps

Add the three numbers together to get your final answer

24 + 72 + 36 = 132

Answer:

6f-15

Step-by-step explanation:

First distribute 3/2.

3/2(4) =6

3/2(-10) =15

So, the answer should be 6f-15.

Let me know if you do not understand or need further explanation :)

The given data be 6.1, 6.8, 8.7, 9.0, 10.2, 10.3, 10.6, 10.8, 10.9, 11.0, 11.1, 11.5, 11.7, 12.2, 13.4 then the sample range is 7.3.

A well-liked and straightforward method for comparing the variability of various data distributions is the sample range. The formula for the sample range is the greatest value minus the smallest value. It is based on two values in a data set: the maximum and minimum.

The probability distribution of a statistic that is acquired by repeated sampling of a particular population is called the sampling distribution. It outlines a variety of potential possibilities for a statistic, such as the mean or mode of a population's mean or mode of some variable.

Arrange all values in your information set from low to high.

Subtract the lowest value from the highest value.

Let the given data be 6.1, 6.8, 8.7, 9.0, 10.2, 10.3, 10.6, 10.8, 10.9, 11.0, 11.1, 11.5, 11.7, 12.2, 13.4

13.4 - 6.1 = 7.3

Therefore, the sample range is 7.3

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Step-by-step explanation:

y=4x+rx+6

y-6=4x+rxy−6=4x+rx Subtract \ 6 \ from \ both \ sidesSubtract 6 from both sides

y-6=x(4+r)y−6=x(4+r) Factor \ out \ the \ common \ term \ xFactor out the common term x

\dfrac{y-6}{4+r} =x

4+r

y−6

=x Divide \ both \ sides \ by \ 4+rDivide both sides by 4+r

If the quadratic is y = a*x^2 + b*x + c

the coordinates of the vertex are:

x = -b/2a

y = (1/2a)*( -0.5*b^2 + c)

For a quadratic equation in standard form:

y = a*x^2 + b*x + c

The x-value of the vertex is given as:

x = -b/2a

Once we get the x-value of the vertex, we can get the y-value by evaluating the quadratic equation in x = -b/2a, we will get:

y = a*(-b/2a)^2 + b*(-b/2a) + c

y = b^2/(4a) - b^2/2a + c = (1/2a)*(b^2/2  - b^2 + c)

y = (1/2a)*( -0.5*b^2 + c)

Then the coordinates of the vertex are:

x = -b/2a

y = (1/2a)*( -0.5*b^2 + c)

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Answer:

four times the amount of mike

Step-by-step explanation:

Answer:

16cm

Step-by-step explanation:

The area of a 2d figure is w x h. We know the area, a, is 80cm^2, the height, h, is 5, and the width, w, is 2x + 8.

Since we are solving for x, we want to isolate the variable.

5 x 2x + 8 = 80
80/5 = 2x + 8

We can now solve for x.

80/5 = 2x + 8
16 = 2x + 8
16 - 8 = 2x + 8 - 8
8 = 2x
8/2 = 2x/2
4 = x

We aren't done, we still need to solve for w, where we now know x = 4

w = 2x + 8
w = 2(4) + 8
w = 8 + 8
w = 16

Answer: To the right

Step-by-step explanation:

The negatives on a number line are on the left side and the positives on the right.

Step-by-step explanation: educated guess

Answer:

Domain: [tex]x > -5[/tex] or [tex](-5,\infty)[/tex]

Range: [tex]y\geq -3[/tex] or [tex][-3,\infty)[/tex]

Step-by-step explanation:

The domain is essentially the set of x-values in a given graph. In this graph. we see that the lowest x-value is an unfilled dot when x=-5. The unfilled dot means that the function [tex]f(x)[/tex] doesn't include -5. We then see that the x-value goes to positive infinity. This means that [tex]x[/tex] must be greater than -5. It is not greater or equal to -5 because the dot is not filled.

Therefore, we have that [tex]x > -5[/tex]. To convert to interval notation we can take the lower value (-5) and put it on the left side and put the higher value ([tex]\infty[/tex]) and put it on the right side. Since the graph doesn't include -5, we can put parentheses around both values to get [tex](-5,\infty)[/tex].

Note: We always put parentheses around both [tex]\infty[/tex] and [tex]-\infty[/tex].

The range is basically the same as the domain but with the y-value. We can see that the lowest y-value is y=-3. This includes -3 since the line fills the point in. Then we see that the highest y-value is once again positive infinity. This means that [tex]y\geq-3[/tex].

Now when we convert to interval notation, we have -3 and [tex]\infty[/tex]. This time since y=-3 is included in the function, we put a hard bracket around -3. Thus, we get [tex][-3,\infty)[/tex].

Hope this helps!

Answer:

[tex]3\sqrt{3}[/tex]

Step-by-step explanation:

The  linear inequality will have a solution of (0,0) is y<-2x and y>-3x.

Option (A) and (D) is correct.

The relation between two expressions that are not equal, employing a sign such as ≠ ‘not equal to’, > ‘greater than’, or < ‘less than’.

Given:

Linear inequalities are the expressions where any two values are compared by the inequality symbols such as, '<', '>', '≤' or '≥'. These values could be numerical or algebraic or a combination of both.

According to given question we have

a. y<-2x

To put the value of x any y (0,0) we get

=0<-2*0

=0<0

b. y<-3x+4

To put the value of x any y (0,0) we get

=0<-3*0+4

=0<0+4

=0<4

c. y>-2x+6

To put the value of x any y (0,0) we get

=0>-2*0+6

=0>0+6

=0>6

d. y>-3x

To put the value of x any y (0,0) we get

=0>-3*0

=0>0

Therefore, the  linear inequality will have a solution of (0,0) is y<-2x and y>-3x.

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Answer:

the answer is clear

Step-by-step explanation:

you have to get the answer by completing the answer

The solution are-

(a) lim h (x) = -2

   x → -2⁻

(b) lim h (x) = -2

   x → -2⁺

(c) lim h (x) = -2

   x → -2

A limit describes the value which a function approaches as its inputs get increasingly closer to a certain number.

The concept of a limit is at the heart of all calculus.

(a) lim h (x) = -2

   x → -2⁻

Put x = 2 at the place of x in h(x).

This limit is called the left hand limit of the function as there is negative sign over 2.

(b) lim h (x) = -2

   x → -2⁺

Put x = 2 at the place of x in h(x).

This limit is called the right hand limit of the function as there is positive sign over 2.

(c) lim h (x) = -2

  x → -2

Put x = 2 at the place of x in h(x).

This limit exists just at x = 2.

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The sample mean of the given data is 24.

To find the mean:

Therefore, the sample mean of the given data is 24.

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Answer:

1013

Step-by-step explanation:

(6)(7)(8−0)(3)+5

=42(8−0)(3)+5

=(42)(8)(3)+5

=(336)(3)+5

=1008+5

=1013

This type of sum is Liquidated damages.

Liquidated damages are presented in certain legal contracts as an estimate of otherwise intangible or hard-to-define losses to one of the parties.

As per the given situation we have

parties to a sales contract have stipulated that a specific sum be paid by any party

Liquidated damages occur in such a situation.

The amount of damages that the parties estimate and agree upon at the time of the contract for a breach of the agreement by either party is referred to as liquidated damages.

Regardless of the actual cost of any potential damages due to the breach of the contract, this amount becomes due immediately.

According to Section 74 of the Indian Contract Act, 1972, if parties agree a sum to be paid as damages or a penalty to be imposed for a breach, the harmed party is only entitled to that sum or penalty and no other higher or lesser sum.

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The required image of kite QRST after a reflection over the line y= -x has shown in the attached graph.

point Q (3,10)

point R (-1,9)

point S (3,7)

point T (7,9)

A graph can be defined as a pictorial representation or a diagram that represents data or values.

Reflection over the y = −x is defined as reflecting a point across they = −x,  the x-coordinate and y-coordinate change places, and t the line y = x is the coordinates (y, x). the line y = -x is the coordinates (-y, -x).

Here point Q (−7,5) reflected across the line y = -x will become (3,10).

Similarly

point R (-1,9)

point S (3,7)

point T (7,9)

Therefore, the required image of kite QRST after a reflection over the line y= -x has shown in the attached graph.

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The modified equation is expressed as g(x) = x^2 - 6

Translation is the process of changing the position on an x-plane.

Given the function of a graph expressed as y=x^2

If the function is shifted 6 units to the left, hence the resulting function is given as;

g(x) = x^2 - 6

Hence the modified equation is expressed as g(x) = x^2 - 6

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The automobile covers 224.48 km.

This problem can be solved by using the unitary method.

In this method we calculate the value for a unit quantity and then multiply it with the desired number for which we want to calculate.

Here it is given that a automobile covers 1122.4 km with 80 liters.

For 1 liter of gasoline distance covered = [tex]\frac{1122.4}{80}[/tex]

                                                              = 14.03 km

So, for 16 liters of gasoline distance covered will be = 16× 14.03

                                                                                  = 224.48 km

Therefore the automobile covers 224.48 km for 16 liters of gasoline.

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Answer:

12.5988 feet.

Step-by-step explanation:

Length of shadow = 15 feet.

Height of flagpole = A.

We know the angle of elevation is 40∘. Using this angle and the tangent ratio, we can find A.

Hope this helps! :)

Approximately 6.8 hours Alyssa spends on the train per day.

Given that, Alyssa spent 365 hours commuting on the train over the course of 54 days.

We need to find the number of did Alyssa spend on the train per day.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Let the number of hours Alyssa spends on the train per day be x.

Now, x=365/54

=6.759≈6.8 hours

Therefore, approximately 6.8 hours Alyssa spends on the train per day.

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The slope of the line for the pair of points (4,5) and (5,1) is  m= -4.

As given in the question,

Let the pair of points of the line are

(x₁ ,y₁) = (4, 5)

(x₂ , y₂) = (5,1)

Slope of the line  passing through the pair of points (x₁ ,y₁) = (4, 5) and

(x₂ , y₂) = (5,1) is given by

   m = (y₂ -y₁) / (x₂ - x₁)

⇒ m = (1-5) / (5 -4)

⇒ m = -4

Therefore, the slope of the line for the pair of points (4,5) and (5,1) is

m= -4.

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