The function rule of a certain function is y = -3x + 1. If the input is 7, what is the output?

Answer:

1 hour and 45 mins

Step-by-step explanation:

As mentioned,

Starting time = 2:30 PM

Ending time = 4:15 PM

The given time is in hours and minutes, to calculate the duration of movie, time should be converted into a same unite minutes.

1 hour = 60 minutes

Therefore,

2:30 = 2 hours and 30 mins = 2*60 + 30 mins = 150 mins

4:15 = 4 hours and 15 mins = 4*60 + 15 mins = 255 mins

The duration = Ending time - Starting time

=> 255 - 150

=> 105 mins

or

60 + 45

1 hour and 45 mins

24 miles is the answer.

Step-by-step explanation:

The previous reading of Jeremy's car = 25500

The current reading is = 26100

Difference between readings = [tex]26100-25500=600[/tex]

Number of gallons used to fill the tank = 25

So, miles traveled by Jeremy in 25 gallons is = 600

In 1 gallon, he travels = [tex]\frac{600}{25}= 24[/tex] miles.

Therefore, Jeremy's car gets 24 miles per gallon.

Graph both equations and find the X value when the lines cross.

See attached picture of the graph

X = 1

Or you could take logarithms of both sides where log(a^b) = b loga to also find the value of x.

Answer:

x = 1

Step-by-step explanation:

Given in the question,

[tex](16/9)^{-2x+5} = (3/4)^{(x-7)}[/tex]

Take logarithm on both sides

[tex]ln(16/9)^{-2x+5} = ln(3/4)^{(x-7)}[/tex]

Apply power rule of logarithm

(-2x+5)ln(16/9) = (x-7)ln(3/4)

cross multiply

(-2x+5)/(x-7) = [tex]\frac{ln(3/4)}{ln(16/9)}[/tex]

-1/2 = (-2x+5)/(x-7)

-(x-7) = 2(-2x+5)

-x + 7 = -4x + 10

rearrange the terms, x terms to left and constant to right

-x + 4x = 10 - 7

3x = 3

x = 1

Answer:

See below.

Step-by-step explanation:

(a)  A sequence is an ordered list of numbers whereas a series is the sum of a list of numbers.

(b) A series is convergent if the sequence of partial sums is a convergent sequence (that is tends to a limit).  A series is divergent if it is not convergent.

Answer:

Step-by-step explanation:

A sequence is a list of ordered numbers. For example, 1, 2, 3, 4, 5.... is a sequence. The numbers are listed in a specific order when we count. In contrast, a series is the sum of the numbers in a sequence. For this multiple choice, choose the best answer that defines what a sequence is.

(a) What is the difference between a sequence and a series?

When working with sequences and series, we look at what happens at negative and positive infinity. When a series converges, it approaches a finite number. When a series diverges, it does not approach a finite number but infinity.

(b) What is a convergent series? What is a divergent series?

Answer:

Polynomial expression that represents the area of blanket:

[tex]A(x)=(6x^2+5x-21)cm^2[/tex]

If [tex]x=2[/tex]: [tex]A(2)=13cm^2[/tex]  

Step-by-step explanation:

The area of the rectangle can be calculated with the formula:

[tex]A=lw[/tex]

Being l the lenght of the rectangle and w the width of the rectangle.

In this case, the lenght and the width are represented with:

[tex]l=(3x+7)cm[/tex]

[tex]w=(2x-3)cm[/tex]

Substitute them into  [tex]A=lw[/tex]:

 [tex]A(x)=(3x+7)(2x-3)[/tex]

Then:

Use Distributive property (Remember the Product of powers property: [tex]b^a*b^c=b^{(a+c)}[/tex] ):

[tex]A(x)=(3x+7)(2x-3)\\A(x)=6x^2-9x+14x-21[/tex]

Add like terms:

[tex]A(x)=(6x^2+5x-21)cm^2[/tex] (Simplied form)

Evaluate [tex]x=2[/tex]:

[tex]A(2)=(6(2)^2+5(2)-21)cm^2\\A(2)=(6(4)+10-21)cm^2\\A(2)=(24-11)cm^2\\A(2)=13cm^2[/tex]

Answer:

9 and 14

Step-by-step explanation:

One number is 5 less than a second number.

a = b - 5

:

Twice the second number is 8 less than 4 times the first.  

2b = 4a - 8

replace a with (b-5)

2b = 4(b-5) - 8

2b = 4b - 20 - 8

2b - 4b = -28

-2b = -28

b = 14

then

a = 9

The equation is solved and the two numbers are x = 7 and y = 12

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Let's call the first number "x" and the second number "y"

x = y - 5 (the first number is 5 less than the second number)

2y = 4x - 4 (twice the second number is 4 less than 4 times the first)

We can use substitution to solve for one of the variables.

Substituting the first equation into the second equation, we get:

2y = 4 (y - 5) - 4

Simplifying this equation , we get

2y = 4y - 24

2y - 4y = -24

-2y = -24

y = 12

Now that we know that the second number is 12, we can use the first equation to find the first number:

x = y - 5

x = 12 - 5

x = 7

Hence , the two numbers are 7 and 12

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A kite's symmetrical structure typically forms isosceles triangles due to equal side lengths. Asymmetrical kites generate scalene triangles with varying side lengths, influencing triangle types and angles within based on side intersections.

A kite, with its distinct shape formed by two pairs of adjacent congruent sides, generates triangles within. These triangles can exhibit various properties based on the kite's symmetry. If the kite is symmetrical, the triangles formed tend to be isosceles due to the equal side lengths.

However, asymmetrical kites can yield scalene triangles with sides of varying lengths. The relationship between the kite's structure and the triangle types arises from the lengths and intersections of its sides.

Symmetry tends to create similar or congruent triangles, while asymmetry leads to triangles with differing side lengths. Consequently, the angles within these triangles vary based on the intersection of the kite's sides, resulting in a mix of acute, obtuse, or right angles.

complete the question

What are the possible types of triangles formed within a kite, and how do their properties relate to the structure of the kite? Discuss the potential combinations of isosceles, equilateral, and scalene triangles within a kite, considering the lengths of the sides and the angles formed by the kite's structure."

Answer:

True

Step-by-step explanation:

we know that

A non-negative number is a real number greater than or equal to zero

In this problem

we have

[tex]x\geq 0[/tex]

The solution of the inequality is all real numbers greater than or equal to zero   [0,∞)

Therefore

[tex]x\geq 0[/tex] express a non-negative number in symbols

Answer:

Part 1. 0.9259 % per year

Part 2. P = 281.4e^(0.009 259t); 338.6 million  

Step-by-step explanation:

Data:

P₀ = 281.4 million

P  = 308.7 million

Part 1. Growth rate

t = 2010 - 2000 = 10 yr

        P = P₀e^(rt)

308.7 = 281.4e^(10r)

e^(10r) = 1.0970

     10r = ln1.0970

        r = (ln1.0970)/10 = (0.092 59)/10 = 0.009 259  

        r = 0.9259 % per year

The 10-year continuous growth rate is 0.9259 % per year.

Part 2. Population model

The population model is

P = 281.4e^(0.009 259t)

where P is in millions and t is the number of years since 2000.

By 2020,

P = 281.4e^(0.009 259 × 20) = 281.4e^0.1852 = 281.4 × 1.203

P = 338.6 million

The estimated population in 2020 is 338.6 million.

The domain of Function A, defined as f(x) = -3x + 2, is all real numbers, as it is a linear function with no restrictions on x-values. Function B's domain would depend on its specific definition but is also valid as long as each input maps to a unique output.

The domains of Function A and Function B can be compared based on the definition of a function's domain. The domain is all the input values (x-values) for which a function is defined. Since Function A is defined as f(x) = -3x + 2, it is a linear function without any restrictions on the x values, meaning the domain of Function A is all real numbers.

The description of Function B isn't provided in the question, but from the referenced information, we can understand that Function B is also a function as long as each element of its domain maps to a unique value in its range.

Were we to have the specifics of Function B, we could determine if it also has a domain of all real numbers or whether it has a more restricted domain, such as when a function includes a square root or division by variables which would exclude certain x-values to avoid undefined expressions.

Answer: Option d.

Step-by-step explanation:

To find the domain of the function we should look for the values for which the denominator is equal to zero, because the division by zero is not allowed.

We know by definition that the function [tex]e^x[/tex] is always greater than zero for all x.

We know that the constant c is greater than zero (c>0).

Then, the expression [tex]e^x+c[/tex] is never equal to zero.

Therefore, it does not exist a value for x that makes the denominator 0. Then, the domain of the function is all real numbers.

The answer is the option d.

Answer:

I think the answer would be 42 Km.

Step-by-step explanation:

So i multiplied 17 x 2 which is 34, and then i multiplied 4 x 2 which is 8 . Then I added 34 + 8 and got 42. So 42Km

Using the two smallest sizes divide the larger of the two by the smaller one:

1 / 0.618 = 1.618

The scale factor is 1.618

Now multiply 1 by that:

1 x 1.618 = 1.618

The missing font size is 1.618.

Can check by multiplying the missing size by the scale factor:

1.618 x 1.618 = 2.618

Answer:

1.618

I hope this helps.

I need this question too, PLEASE HELP

The dress will cost $50.40 after a 20% discount from the original price of $63. You calculate this by finding 20% of $63, which is $12.60, and subtracting it from $63.

When a store is having a 20% off sale, it means that the original price of the item is reduced by 20%. In this case, you need to calculate 20% of $63, which is the original price of the dress.

To find 20% of $63, you multiply 63 by 20/100 (because percent means per hundred). That is: 63 * 0.20 = $12.60.

So the amount of the discount is $12.60. Therefore, you subtract this discount from the original price of the dress to find out the new price: 63 - 12.60 = $50.40.

So, after a 20% off sale, the dress will cost $50.40.

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Answer:

Regular

Step-by-step explanation:

A polygon with congruent sides and angles is a regular polygon, with an equilateral triangle or a square as an example. A 3D shape example is an icosahedron with 20 regular triangular faces.

A polygon with congruent angles and congruent sides is called a regular polygon. This means that all its sides and angles are equal in measure. An example of a regular polygon is an equilateral triangle which has all three sides of equal length and all three angles 60 degrees each, or a square that has four sides of equal length and four angles each 90 degrees.

An example provided is an icosahedron which is a regular polyhedron (a 3D shape) with 20 identical equilateral triangular faces. Every face is a regular polygon, showing that all its 20 faces have congruent angles and sides.

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Answer:

323 mod 5 = 3

−323 mod 5 = -3

327 mod 3 = 0

(64 * (-67) + 201) mod 7 = 6

(38^12) mod 6 = 4

(38^12) mod 3 = 1

Step-by-step explanation:

The modulo operation looks for remainders from the quotients. In order to find them, divide the whole number by the mod number. Then take just the decimal after the whole answer and multiply it by the mod number.

323 mod 5

323/5 = 64.6

.6 * 5 = 3

−323 mod 5

323/5 = -64.6

-.6 * 5 = -3

327 mod 3

327/5 = 109

0 * 3 = 0

(64 * (-67) + 201) mod 7

64 * -67  = -4288 + 201 = 4087

4087/7 = 583.85714

.85714 * 7 = 6

(38^12) mod 6

38^12 = 9.07x10^18

9.07x10^18/6 = 1510956318082499242.6666667

.666667 * 6 = 4

(38^12) mod 3

38^12 = 9.07x10^18

9.07x10^18/3 = 3021912636164998485.333333

.3333333 * 3 = 1

323 mod 5 = 3

−323 mod 5 = -3

327 mod 3 = 0

(64 * (-67) + 201) mod 7 = 6

(38^12) mod 6 = 4

(38^12) mod 3 = 1

Step-by-step explanation:

The modulo operation looks for remainders from the quotients. In order to find them, divide the whole number by the mod number. Then take just the decimal after the whole answer and multiply it by the mod number.

323 mod 5

323/5 = 64.6

.6 * 5 = 3

−323 mod 5

323/5 = -64.6

-.6 * 5 = -3

327 mod 3

327/5 = 109

0 * 3 = 0

(64 * (-67) + 201) mod 7

64 * -67  = -4288 + 201 = 4087

4087/7 = 583.85714

.85714 * 7 = 6

(38^12) mod 6

38^12 = 9.07x10^18

9.07x10^18/6 = 1510956318082499242.6666667

.666667 * 6 = 4

(38^12) mod 3

38^12 = 9.07x10^18

9.07x10^18/3 = 3021912636164998485.333333

.3333333 * 3 = 1

Answer:

  y = -4

Step-by-step explanation:

Once you recognize the line as being horizontal, you know its equation will be ...

  y = (some constant)

The value of the constant will correspond to the y-coordinate of the points the line goes through. It will also be the value of the y-intercept. Here, that value is -4, so the equation is ...

  y = -4

Answer:

y= -4 since it is on the x-axis but does not have any x coordinates

Answer:   48°

Step-by-step explanation:

The shadow is the adjacent side and the length of the flag is the hypotenuse

[tex]cos\ \theta=\dfrac{adjacent}{hypotenuse}\\\\\\cos\ \theta=\dfrac{10}{15}\\\\\\cos^{-1}(cos\ \theta)=cos^{-1}\bigg(\dfrac{10}{15}\bigg)\\\\\\.\qquad \qquad \boxed{\theta=48^o}[/tex]

Answer: a

Step-by-step explanation: edge 2021

Answer:the answer is c I literally just took this lol can I get brainliest pls

Step-by-step explanation:it would be helpful and my first

40 units2˛

   Looking at the figure, the rectangle has the vertexes (2,1), (3,-3), (-5,-5) and (-6,-1). The parallelogram has the vertexes (2,7), (3,3), (3,-3), and (2,1).

The area of a parallelogram is base times height. We have 2 vertical lines at x=2 and x=3, so the height is 1. And the length of the line from (3,3) to (3,-3) is 6, so the base is 6. Therefore the area of the parallelogram is 1*6 = 6.

  The rectangle is a tad trickier since it's not aligned with either the x or y axis. But we can use the Pythagorean theorem to get the lengths.

 L = sqrt((2 - -6)^2 + (1 - -1)^2)

 L = sqrt(8^2 + 2^2)

 L = sqrt(64 + 4)

 L = sqrt(68) = 2*sqrt(17)

  W = sqrt((2-3)^2 + (1- -3)^2)

 W = sqrt((-1)^2 + 4^2)

 W = sqrt(1 + 16)

 W = sqrt(17)

  And the area is length * width, so:

 2*sqrt(17)*sqrt(17) = 2 * 17 = 34

  And the total area is the sum of the areas, so

 34 + 6 = 40

  So the area of the figure is 40 square units.

Answer:

40 units ^2

Step-by-step explanation:

when finding an odd shaped figure, make sure to divide it up into porportions. Then figure out the square and then the triangles.

the answer would be: 40 units ^2

hope this helps!!

Answer:

The correct answer is 6.

Step-by-step explanation:

To find this, first find f(-3)

f(x) = -3x + 9

f(-3) = -3(-3) + 9

f(-3) = 9 + 9

f(-3) = 18

Now we do the same for f(7)

f(x) = -3x + 9

f(7) = -3(7) + 9

f(7) = -21 + 9

f(7) = -12

Now we add them together

18 + -12 = 6

The value of f(?3) + f(7) - f(-3) + f(7) is -24.

To find the Value of f(?3) + f(7) - f(-3) + f(7), we need to substitute the given values into the function f(x) = -3x + 9.

Substituting -3 for x, we get f(?3) = -3(-3) + 9 = 18.
Substituting 7 for x, we get f(7) = -3(7) + 9 = -12.
Substituting -3 for x and adding the results, we get f(-3) = -3(-3) + 9 = 18.
Substituting 7 for x, we get f(7) = -3(7) + 9 = -12.

Now, let's calculate the Value of the expression:
f(?3) + f(7) - f(-3) + f(7) = 18 + (-12) - 18 + (-12) = -24

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Answer:

1) (9, 75+360n)

2) (−9, 255+360n)

Step-by-step explanation:

(9, 75) is same as (9, 75 + 360)

so it would be (9, 435)

It can also be expressed as (-9, 75 + 180 degrees)

so (-9,255) degrees

In general, (9,75+360 n) for n≥0 represents half of the possible ways of representing the point : (9,75)  

Answer with explanation:

The Position of Point in two dimensional plane , P=(9,75°)

→The general rule of writing the point (r,Ф) in terms of polar coordinates is,

  x=r cos Ф , y=r sin Ф

The angle between Intial side and terminal side is Acute.

Here, r=9 units

And , Ф=75°

→→Period of Cosine and Sine is 2π.

⇒⇒So,the coordinates of Point will be

 x=9 *cos (2nπ+75°), And ,y=9 *sin (2nπ+75°), where n is any integer.

Hey there!

#1 The correct choice is D. Athletic

Anaya was the state track champion for all four years of high school. She likely received a(n) ATHLETIC scholarship.

#2 The correct choice is B. Academic

Ramon was a straight-A student in high school. He likely received a(n) ACADEMIC scholarship.

Hope this helps you!

God bless ❤️

Brainliest would be appreciated

xXxGolferGirlxXx

Answer:

[tex]\frac{\pi }{10}[/tex]

Step-by-step explanation:

The area (A) of the sector is calculated using the formula

A  = area of circle × fraction of circle

let x be the measure of the central angle, then

A = πr² × [tex]\frac{x}{2\pi }[/tex] ← substitute values

5π = π × 10² × [tex]\frac{x}{2\pi }[/tex]

5π = 100π × [tex]\frac{x}{2\pi }[/tex] (cancel 50π and 2π )

5π = 50x ( divide both sides by 50 )

x = [tex]\frac{5\pi }{50}[/tex] = [tex]\frac{\pi }{10}[/tex] ← central angle

Final answer:

The measure of the central angle that forms a sector with an area of 5π in a circle of radius 10 is 18 degrees.

Explanation:

To calculate the measure of the central angle that forms the sector of a circle with a radius of 10 units and an area of 5π, we need to use the formula for the area of a sector, which is A = (θ/2) × r², where A is the area of the sector, θ is the central angle in radians, and r is the radius of the circle.

First, let's substitute the given values into the formula:

Now, we can set up the equation:

5π = (θ/2) × 10²

5π = (θ/2) × 100

To find the central angle, we solve for θ:

θ = (2 × 5π) / 100

θ = 0.1π radians

To convert radians to degrees, we use the conversion factor that 180° = π radians:

θ in degrees = 0.1π × (180/π)

θ in degrees = 18°

Therefore, the measure of the central angle that forms the sector is 18 degrees.

Answer:

-1066.65  to 2 decimal places.

Step-by-step explanation:

(−800)+(−200)+(−50)+(−12.5)+...

This is a Geometric series with common ratio  r =(-200) / ) / (-800)  = 0.25 and first term  a1 = -800.

Sum of n terms = a1 * (1 - r^n) / (1 - r)

Sum of 8 terms = -800 * (1 - 0.25^8) /  (1 - 0.25)

= -800 * 1.333313

= -1066.65.

The sum of the first eight terms of the geometric sequence is given by: −1066.65

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 is given by:

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

In this problem, we have that the first term and the common ratio are, respectively:

[tex]a_1 = -800, q = \frac{-200}{-800} = 0.25[/tex]

Hence, the sum of the first eight terms is given by:

[tex]S_n = \frac{-800(0.25^8 - 1)}{0.25 - 1 } = −1066.65[/tex]

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So you know that the carpenter has a board that is 18.5ft long and he wants to cut 1.75ft pieces.

Assume that x is the amount of boards he cuts,

1.75x = 18.5

Isolate x by dividing each side by 1.75.

x = 18.5/1.75 = 10.57 pieces.

Answer:

i think its d

Step-by-step explanation:

because thats 18 times 72

Answer:

the answer is c i just answered this on usatestprep

Step-by-step explanation:

ANSWER

A. (8,9)

EXPLANATION

The point that divides,

[tex]A(x_1,y_1), B(x_2,y_2)[/tex]

in the ratio m:n is given by

[tex]x = \frac{mx_2 + nx_1}{m + n} [/tex]

[tex]y= \frac{my_2 + ny_1}{m + n} [/tex]

The given points are A(0,15) B(20,0)

the ratio is 2:3.

This implies that, m=2,n=3.

[tex]x_1=0,x_2=20,y_1=15,y_2=0[/tex]

We plug in the values to get:

[tex]x = \frac{2 \times 20 + 3 \times 0}{2+ 3} [/tex]

[tex]x = \frac{40}{5} = 8[/tex]

[tex]y= \frac{2 \times 0 + 3 \times 15}{2+ 3} [/tex]

[tex]y= \frac{45}{5} = 9[/tex]

Hence the required point is

(8,9)

The correct answer is A.