The difference between the record high and low temperaturs in Charlotte, North Carolina, is 109°F. The record low temperature was -5°F. Write and solve an equation to find the record high temperature.

The scale factor of the given dilation transformation is calculated as; 1/2

We know that from transformation that  a dilation is a non - rigid transformation that produces similar figures.

If two lines are similar, then the lines are parallel and parallel lines always have the same slope.

Thus;

Line A has the formula; 2y = x + 8

Writing it in slope intercept form gives us;

y = 0.5x + 4   ------(1)

Thus;

slope of the line A is m = 0.5

y-intercept of the line A is b = 4

Line B has the equation;

y - ¹/₂x = 2

Rearranging in Slope Intercept form gives us;

y = ¹/₂x + 2

Thus;

slope of the line B is m = 0.5

y-intercept of the line B is b = 2

Now, it should be noted that the y-intercept of line A multiplied by the scale factor k must be equal to the y-intercept of line B. Thus;

4k = 2

k = 2/4

k =  ¹/₂

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The area of the missing slice is 15 inches ²

From the information given, we can see that the pizza takes the form of a circle;

Area of the missing slice takes the shape of a triangle

Area of a triangle = 1/ 2 base × height

base = 10 inches

height = 3 inches

Area of missing slice = 1/ 2 × 10 × 3

Area = 1/ 2 × 30

Area = 15 inches ²

Thus, the area of the missing slice is 15 inches ²

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The x value or observed value corresponding to  z-score, z = 1.50 is 130.

According to the question.

For a population with µ = 100 and σ = 20.

Since,  we know that

The z-score is a statistical evaluation of a value's correlation to the mean of a collection of values, expressed in terms of standard deviation.

And it is given by

z = (x - μ) / σ

Where,

x is the observed value.

μ is the mean.

and, σ is the standard deviation.

Therefore, the x value or observed value corresponding to z = 1.50 is given by

[tex]1.50 = \frac{x -100}{20}[/tex]

⇒ 1.50 × 20 = x - 100

⇒ 30 = x - 100

⇒ x = 30 + 100

⇒ x = 130

Hence, the x value or observed value corresponding to  z-score, z = 1.50 is 130.

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I assume [tex]C[/tex] is oriented counterclockwise. If [tex]C[/tex] is the closed rectangle, then by Green's theorem we have

[tex]\displaystyle \int_C F\cdot dr = \int_0^3 \int_0^9 \frac{\partial (x-y)}{\partial x} - \frac{\partial (x^2+y^2)}{\partial y} \, dy \, dx \\\\ ~~~~~~~~~~~~ = \int_0^3 \int_0^9 (1 - 2y) \, dy \, dx = 3 \int_0^9 (1-2y)\, dy = \boxed{-216}[/tex]

It seems unlikely, but if you actually are omitting the integral along the line segment joining (0, 9) and (0, 0), let [tex]x=0[/tex] and [tex]y=9-t[/tex] with [tex]0\le t\le9[/tex]. Then the integral along this line segment would be

[tex]\displaystyle \int_{(0,9)\to(0,0)} F\cdot dr = \int_0^9 \bigg((0^2 + (9-t)^2) i + (0 - (9-t)) j\bigg) \cdot (0i - j) \, dt \\\\ ~~~~~~~~  = \int_0^9 (9-t) \, dt = \frac{81}2[/tex]

so that the overall integral would instead have -216 - 81/2 = -513/2.

The total surface area of the square pyramid (SA) = 144 yd².

A square pyramid is a solid shape that has a square base and four rectangular lateral faces.

The total surface area of a square pyramid is the sum of the area of its square base and four rectangular lateral faces. To find the total surface area, the following formula is used:

Total surface area of a square pyramid (SA) = A + 1/2(Pl), where:

Given the following:

Area of base (A) = 8² = 64 yd²

Perimeter of base (P) = 4(8) = 32 yds

Slant height of pyramid (l) = 5 yds

Plug in the values

Total surface area of a square pyramid (SA) = 64 + 1/2(32)(5)

Total surface area of a square pyramid (SA) = 64 + 80

Total surface area of a square pyramid (SA) = 144 yd².

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The intervals which represents those in which case the function, f(x) is reducing are as follows; [–2.5, –2], [–2, –1.5], [1.5, 2], [2, 2.5].

It follows from the complete task content that the x-intervals between which the function value of f(x) is reducing are to be identified from the graph as attached.

On this note, by observation on the graph, it follows that from between the interval; [–2.5, –2], the function f(x) is decreasing.

Also, between the interval; [–2, –1.5], the function f(x) is decreasing.

Also, between the interval; [1.5, 2], the function f(x) is decreasing.

Also, between the interval; [2, 2.5], the function f(x) is decreasing.

Remark: The answer choices are as follows; [–2.5, –2] [–2, –1.5] [–1, 1] [1.5, 2] [2, 2.5) [2.5, 3]

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Answer:

following the (x,y) coordinate system,

(0,4) ; (1,1) ; (2,-2)

Step-by-step explanation:

youre given the value of the x variable in the table, so all you need to do is substitute x and follow pedmas!! hope this helps<3

Answer:

  shaded area = 9x² +10x +4

Step-by-step explanation:

The area of the shaded region is the difference between the areas of the overall rectangle and the unshaded one it contains. Each area is the product of length and width.

Overall rectangle

  A = LW

  A = (5x)(3x) = 15x² . . . . . using given dimensions

Unshaded interior rectangle

  A = (3x +1)(2x -4) = 3x(2x -4) +1(2x -4) . . . . . using given dimensions

  A = 6x² -12x +2x -4 = 6x² -10x -4

The shaded area is the difference between the area of the overall rectangle and the area of the unshaded included rectangle.

  shaded area = (15x²) -(6x² -10x -4)

  shaded area = 9x² +10x +4

Answer:

think its number 2 7-(3-5)=(7-3)-5

Step-by-step explanation:

Answer:

  50 miles/1 hour = 50 miles/hour

Step-by-step explanation:

The fraction is reduced by dividing numerator and denominator by their common factor of 2.

  100 miles / (2 hours) = 50 miles/ (1 hour) = 50 miles/hour

Answer:

4. 4.125 inches by 3.5 inches.

5. 8.4 hours.

Step-by-step explanation:

4. multiply 16.5 and 14 by .25 because each foot in the house is .25 of an inch on the paper.

5. 252 miles / 9 hours = 28 mph. Add 2 so you get 30 mph. 252 miles / 30 mph = 8.4 hours.

The two positive numbers satisfying the given requirements are 15.56 and 15.56

For given question,

Let x and y be  two positive numbers satisfying the given requirements.

⇒ xy = 242             .............(1)

The sum of given two positive numbers is a minimum.

Let the sum of given two positive numbers is S.

⇒ x + y = S             ............(2)

From equation(1),

⇒ y = 242/x

Substitute above value of y in equation (2),

⇒ x + y = S  

⇒ S = x + (242 / x)    

Now, for above equation we find the derivative of x with respect to x.

⇒ 0 = 1 - [tex]\frac{242}{x^{2} }[/tex]

⇒ 242/x² = 1

⇒ x² = 242

⇒ x = ±15.56

Since the numbers are positive, x = 15.56

For x = 15.56

⇒ y = 15.56

Therefore, the two positive numbers satisfying the given requirements are 15.56 and 15.56

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Answer:

1

Step-by-step explanation:

The slope of a function is equal to the coefficient of x when the equation is in standard form (y=mx+c)

In this case the equation is already in standard form and thusly we can see that the coefficient of x is 1 (the constant has no effect on the slope)

Answer: 4096.

Step-by-step explanation:

[tex](8^3)^8\div(8^4)^5=\\8^{3*8}\div8^{4*5}=\\8^{24}\div8^{20}=\\8^{24-20}=\\8^4=\\4096.[/tex]

Answer: [tex]\Large\boxed{Total~area=586.17~cm^2}[/tex]

Step-by-step explanation:

Given information

[tex]Height=7~cm[/tex]

[tex]Base=18~cm[/tex]

Given formula

[tex]A=b\times h\times\dfrac{1}{2}[/tex]

[tex]A=Area\\b=base\\h=height\\[/tex]

Substitute values into the formula

[tex]A=(7)\times (18)\times\dfrac{1}{2}[/tex]

Simplify by multiplication

[tex]A=(7)\times 9[/tex]

[tex]A=63~cm^2[/tex]

Given information

[tex]Height = 18~cm[/tex]

[tex]Base=22~cm[/tex]

Given formula

[tex]A=b\times h[/tex]

[tex]A=Area\\b=base\\h=height\\[/tex]

Substitute values into the formula

[tex]A=(22)\times (18)[/tex]

Simplify by multiplication

[tex]A=396~cm^2[/tex]

Given information

Diameter = 18 cm

Given formula

[tex]A=(\dfrac{d}{2} )^2\times \pi \div2[/tex]

[tex]A=Area\\d=diameter[/tex]

Substitute values into the formula

[tex]A=(\dfrac{18}{2} )^2\times (3.14) \div2[/tex]

Simplify the fraction

[tex]A=(9 )^2\times (3.14) \div2[/tex]

Simplify the exponents

[tex]A=81\times (3.14) \div2[/tex]

Simplify by multiplication

[tex]A=254.34\div2[/tex]

Simplify by division

[tex]A=127.17~cm^2[/tex]

Given formula

[tex]Total~area=Triangle+Rectangle+circle~(half)[/tex]

Substitute values into the formula

[tex]Total~area=(63)+(396)+(127.17)[/tex]

Simplify by addition

[tex]Total~area=459+(127.17)[/tex]

[tex]\Large\boxed{Total~area=586.17~cm^2}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

The sum of the first 40 terms of the geometric sequence is:

22,114,662.64

A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.

The nth term of a geometric sequence is given by:

[tex]a_n = a_1q^{n-1}[/tex]

In which [tex]a_1[/tex] is the first term.

The sum of the first n terms of a sequence is:

[tex]S_n = \frac{a_1(1 - q^n)}{1 - q}[/tex]

For this problem, the parameters are:

a1 = 1, q = 1.5, n = 40.

Hence the sum is:

[tex]S_{40} = \frac{1 - 1.5^{40}}{1 - 1.5} = 22,114,662.64[/tex]

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The total amount spent by Elsa and her friends must not exceed RM 475; 475 ≤ x

Elsa + 3(her friends) ≤ Total

145 + 3(110) ≤ x

145 + 330 < x

475 ≤ x

Therefore, the total amount spent by Elsa and her friends must not exceed RM 475; 475 ≤ x

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Formula for the circumference of a circle is

[tex]c = \pi \: d[/tex]

where c is the circumference, and d is the diameter.

When diameter is 27-in, then

[tex]c1 = \pi \times 27[/tex]

When diameter is 25-in, then

[tex]c2 = \pi \times 25[/tex]

.: 27π-in – 25π-in is the farther distance.

Finding the difference, we have:

2π ≈ 6.28

.: 6.28-in is our final answer.

Using derivatives, it is found that the x-values in which the slope belong to the interval (-1,1) are in the following interval:

(-15,-10).

It is given by the derivative at x = x0, that is:

[tex]m = f^{\prime}(x_0)[/tex].

In this problem, the function is:

[tex]f(x) = 0.2x^2 + 5x - 12[/tex]

Hence the derivative is:

[tex]f^{\prime}(x) = 0.4x + 5[/tex]

For a slope of -1, we have that:

0.4x + 5 = -1

0.4x = -6

x = -15.

For a slope of 1, we have that:

0.4x + 5 = 1.

0.4x = -4

x = -10

Hence the interval is:

(-15,-10).

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Answer:

Step-by-step explanation:

Use the distributive property.

Distributive property is a serving to distribute or allot or disperse.

Distributive property:

A(B+C)=AB+AC

A(B-C)=AB-AC

-10(1-9x)+6(x-10)

Expand.

-10(1-9x)

-10*1=-10

-10*9x=90x

[tex]\longrightarrow \sf{=-10+90x+6\left(x-10\right)}}[/tex]

6(x-10)

6*x=6x

6*10=60

6x-60

Rewrite the problem down.

= -10+90x+6x-60

Combine like terms.

90x+6x-10-60

Add the numbers from left to right.

90x+6x=96x

96x-10-60

Finally, subtract the numbers from left to right.

-10-60=-70

[tex]\Longrightarrow \boxed{\sf{96x-70}}[/tex]

Therefore, the final answer is 96x-70.

I hope this helps, let me know if you have any questions.

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Distributive Property :

[tex]-10(1-9x)+6(x - 10)[/tex]

[tex]-10(-9x+1)+6(x - 10)[/tex]

[tex]90x-10+6x-60[/tex]

[tex]90x-70+6x[/tex]

[tex]96x-70[/tex]

[tex]answer : \boxed{\pink\star\tt{96x-70}}[/tex]

━━━━━━━━━━━━━━━━━━━━━━━━

Common factor :

[tex]- 10(1 - 9x) + 6(x - 10)[/tex]

[tex]96x - 70[/tex]

[tex]2(48x - 35)[/tex]

[tex] answer : \boxed{ \pink \star\tt{2(48x - 35)}}[/tex]

Earth science is made of many branches of knowledge concerning all aspects of the Earth system. The main branches are geology, meteorology, climatology, oceanography, and environmental science. Astronomy uses principles understood from Earth to learn about the solar system, galaxy, and universe.

Only recently have humans begun to understand the complexity of our planet Earth. We have only known for a few hundred years that Earth is just a tiny part of an enormous galaxy, which in turn is a tiny part of an even greater universe.

An important component of experiments is the different variables involved. A variable is any parameter in the experiment that can change. This could be a parameter like temperature, weight or height, or it could be more complex, such as life expectancy or growth rate. Depending on how you set up your experiment, you will use different kinds of variables. There are three basic types to be familiar with.

The first type is the independent variable. This is the variable that is manipulated during an experiment. For example, when experimenting with how fertilisers affects plant growth, the fertiliser is the independent variable because this is the variable that you change. It might help to think of the independent variable as the cause of change in the experiment.

In contrast to this, the dependent variable is the variable that is affected during an experiment. In our experiment, our dependent variable would be plant growth since this is affected by the amount of fertiliser applied. If you think of the independent variable as the cause, then the dependent variable is the effect.

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Answer:

48

Step-by-step explanation:

48 because you are multiplying it by -2 each time. -24 x -2 = 48

The initial-value is  x(t)=F0/2w^2 (sin wt-wt cos wt)

An initial-value hassle is a differential equation wherein is an open set of, together with a point within the domain called the initial situation. A technique to an initial cost hassle is a function that is a technique to the differential equation and satisfies.

Inside the discipline of differential equations, preliminary cost trouble (additionally called Cauchy trouble by using a few authors) is a normal differential equation collectively with a detailed fee, called the preliminary situation, of the unknown function at a given factor in the domain of the solution.

In multivariable calculus, an initial-value hassle is a normal differential equation collectively with a preliminary circumstance that specifies the fee of the unknown characteristic at a given factor in the area. Modeling a system in physics or different sciences often amounts to fixing an initial cost problem.

Consider a differential equation x+x=F, sin wt, x(0) = 0,X(0) = 0

Apply Laplace transformation on both sides, and we get

(s²L{x(t)}-sy(0)-y'(0)) + w²L {x(t)} =·

Fow

Fow

(s² + w² ) { x(t)} = 3 + w²

L{x(t)}=

Fow

(5²+w²)²

x(t)=FwL

[(s² + w²)²]

Fow

x(t)=(sin wt-wt coswt)

2w

x(t)=

Fo

wtcos

2w (sin wt-wt cos wt),

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Answer: D

Step-by-step explanation:

If the leading coefficient is negative, then as [tex]x \to \infty[/tex], [tex]f(x) \to -\infty[/tex].

If the leading coefficient is negative, then as [tex]x \to -\infty[/tex], [tex]f(x) \to \infty[/tex].

This leaves D as the correct answer.

The exponential function represented by the points (0, 2) and (3, 686) is y = 2(7)ˣ

An equation is an expression that shows the relationship between two numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.

The standard form of an exponential funtion is in the form:

y = abˣ

Where a is the initial value and b is the multiplication factor.

At point (0, 2)

2 = ab⁰

a = 2

At point (3, 686)

686 = 2b³

b = 7

The exponential function represented by the points (0, 2) and (3, 686) is y = 2(7)ˣ

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Answer:

D

Step-by-step explanation:

This function passes the vertical line test.

The vertical line test test is done by drawing a vertical line anywhere on the graph. If the line goes through two points or more then it isn't a function.

Answer:

1-21>151 and -2>5

I think so.

X is the number of songs and Y the number of pics

our 2 equations will be - X+y=11 & 4x+2y=24

consider x=11-y

Lets replace x in 2:

=4(11-y) +2y=24

=44-4y+2y=24

=44-24= 4y-2y

=20= 2y

=Y=20/2

=Y=10

Lets replace y in 1

=X+10=11

=X=11-10

=X=1

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Helen is currently is 8 years old.

Endeavor to understand the question, analyze it and interpret it into equation.

Given that Helen's age is multiples of 4. Next year it'll be a multiple of 3. Helen's older brother is now 19.

This means Helen current age is multiple of 4 and next year it will be a multiple of 3. Also, Helen's age is less than 19

The two available numbers that fit this analysis and less than 19 are 8 and 9. 8 is multiple of 4. 8 + 1 = 9 which is multiple of 3

Therefore, Helen is 8 years old now

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By using the digits 0 to 9, the boxes are filled with their respective numerical values to make the chart accurate as shown in the image attached below.

A function can be defined as a mathematical expression which is used to define and represent the relationship that exists between two or more variables.

In Mathematics, there are different types of functions and these include the following;

A logarithm function can be defined as a type of function that represents the inverse of an exponential function. Mathematically, a logarithm function is written as follows:

y = logₐₓ

y = log₁₀10

y = log₁₀10 = 1.  

Therefore, if log₁₀x < 1, then, x < 10.  Also, if log₁₀x > 1, then, x > 10.

For this exercise, you should take note of this deductive points:

In conclusion, by using the digits 0 to 9, the boxes are filled with their respective numerical values to make the chart accurate as shown in the image attached below.

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