What is the length of the hypotenuse of a 45°-45°-90° triangle with legs that are 8 cm long?

Answer:

the function is an exponential funtion.

Step-by-step explanation:

learned it

Answer:

129792

Step-by-step explanation:

         156

     ×  832

    ----------

         312

      468

+  1248

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

  129792

The standard form of the quadratic function f(x) = -3x^2 + 6x - 2 is f(x) = -3x^2 + 6x - 2

The quadratic function is given as

f(x) = -3x^2 + 6x - 2

The standard form of a quadratic function is represented as:

f(x) = ax^2 + bx + c

When both equations are compared, we can see that the function f(x) = -3x^2 + 6x - 2 is already in standard form

Where

a = -3

b = 6

c = -2

Hence, the standard form of the quadratic function f(x) = -3x^2 + 6x - 2 is f(x) = -3x^2 + 6x - 2

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Answer:

255 (assuming x is the variable x)

340 (assuming x is the multiplication sign)

See explanation below.

Step-by-step explanation:

I assume that x is the variable x.

25(0.3x-4)-5(1.5x-6)+100·13/4 =

= 7.5x - 100 - 7.5x + 30 + 25 × 13

= -70 + 325

= 255

If my assumption above is incorrect, and x really means the multiplication sign, then we have this:

25(0.3×-4)-5(1.5×-6)+100·13/4 =

= 25(-1.2) - 5(-9) + 100(3.25)

= -30 + 45 + 325

= 340

The value of x when the secants intersect is 4

A secant of a circle is a line that connects two distinct points on a curve.

The secant touches two sides of the circumference of a circle.

Therefore, using secant rule,

4(x + 2 + 4) = 5(x - 1 + 5)

Hence,

4(x + 6) = 5(x + 4)

Hence, open the brackets

4x + 24 = 5x + 20

Therefore, subtract 4x from both sides

4x - 4x + 24 = 5x - 4x + 20

24 = x + 20

subtract 20 from both sides

24 - 20 = x + 20 - 20

x = 4

Therefore, the value of x is 4.

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A: The coordinates of the point R' are (- 6, 21).

B: The coordinates of the point T' are (1, 3).

In this question we must make use of rigid transformations to find the location of new points, rigid transformations are transformations used in geometric loci such that Euclidean distance is conserved. In this case, we need to use a kind of rigid transformation known as dilation, which is defined below:

P'(x, y) = O(x, y) + k · [P(x, y) - O(x, y)]      (1)

Where:

Part A - If we know that O(x, y) = (0, 0), R(x, y) = (- 2, 7) and k = 3, then the coordinates of point R' are:

R'(x, y) = (0, 0) + 3 · [(- 2, 7) - (0, 0)]

R'(x, y) = (- 6, 21)

Part B - If we know that O(x, y) = (- 2, 7), T(x, y) = (4, - 1) and k = 1/2, then the coordinates of point T' are:

T'(x, y) = (- 2, 7) + (1 / 2) · [(4, - 1) - (- 2, 7)]

T'(x, y) = (- 2, 7) + (1 / 2) · (6, - 8)

T'(x, y) = (- 2, 7) + (3, - 4)

T'(x, y) = (1, 3)

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The cheaper price among this set of orange sales is the one done by trader B, who sells 8 for N120.

The cheaper price can be computed by finding out the price per unit.

                               Price of Set     Unit Price

Sale of 6 oranges        N100           N16.67 (N100/6)

Sale of 8 oranges        N120           N15.00 (N120/8)

Thus, selling 8 oranges for N120 is cheaper than selling 6 oranges for N100, and N1.67.

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Answer:

2400

Step-by-step explanation:

40 = 2^3 * 5

120 = 2^5 * 5

150 = 2 * 3 * 5^2

LCM = 2^5 * 3 * 5^2

Answer:

A

Step-by-step explanation:

p = Pierre shells

Nardia shells = 3p

3p + p = 52

Answer:

a

Step-by-step explanation:

Answer:

Step-by-step explanation:

This linear programming problem is described by an objective function and constraints on the variables. A graphical solution works well.

The goal is to maximize the number of people exposed to the company's ad(s). The number of people reached is the sum of the products of the number of ads and the number reached per ad.

For n newspaper ads, we are told that 6750n people are reached.

For r radio ads, we are told that 7800r people are reached.

The total number of people reached is ...

  P = 6750n +7800r . . . . . . . the function we wish to maximize

We can run at most 19 newpaper ads:

  n ≤ 19

We can run at most 31 radio ads:

  r ≤ 31

The cost of n newspaper ads will be $160n.

The cost of r radio ads will be $620r.

We must stay within a budget for the ads, $8100:

  160n +620r ≤ 8110

The white area in the first quadrant of the attached graph represents the feasible solution space. (We reversed the inequality symbol in each inequality so the solution space would be white, not triple-shaded.) The corners of the solution space represent possible (n, r) pairs where the objective function might be maximized.

The solid red line on the graph shows the maximum value the objective function might have, and the (n, r) pairs that would give that maximum value. The value of the objective function increases the farther the line is from the origin. Drawing the line on the graph lets us readily identify the (n, r) coordinate pair that will place this line as far as possible from the origin, maximizing P. We find that to be (n, r) = (19, 8).

The annual interest rate is 21%

The given parameters are

Loan Amount, P = $300

Interest, I = $63

Number of years, T = 1

The annual interest rate is calculated as

I = PRT

Substitute the known values in the above equation

63 = 300 * R * 1

Evaluate the product

300R = 63

Divide through by 300

R = 21%

Hence, the annual interest rate is 21%

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The answers to the questions are:

1. The confidence level is 99 percent.

2. We have to conclude that there is no sufficient evidence available to support this claim because the Confidence interval contains 75 sec.

1. The confidence level here should be

1- 0.01 = 0.99

= 99 percent

Given that, 99% confidence interval for population mean (μ) is (-34.1 sec u< u < 264.1 ) seconds.

We are to test  the claim that the population mean is greater than 75 sec.

2.

The given confidence interval contains the value of 75 sec, so there is not sufficient evidence to support the claim that the mean is greater than 75 sec.

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The area of the square in terms of x unit is x²/ 2

The expression for the diagonal of a square is written as'

d^2=s^2+s^2

Where

But from the given question we have that the diagonal of the said square is 'x'

Now, let's substitute the values into the expression of the diagonal given above,

d^2=s^2+s^2

d² = s² + s²

We have,

x² = s² + s²

Collect and add like terms

x² = 2s²

But we know that s² represents the area of the square

So,

x² = 2 × area

Make 'area' subject of formula

Area = x²/ 2

Now, we can say that the area of the square in terms of x units is x²/2

Therefore, the area of the square in terms of x unit is x²/ 2

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The domain of the function is x  ≠ 7

The function is given as:

y = 1/x - 7

Set the denominator not equal to 0

x - 7 ≠ 0

Add 7 to both sides

x  ≠ 7

Hence, the domain of the function is x  ≠ 7

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Answer:

x = 106 degrees

Step-by-step explanation:

x + 104 + 40 + 110 = 360

x + 254 (No more 254)

- 254 (Again no more 254)

x = 106

1. Given the functions f(x) = log₂(5x)  and g(x) = 5ˣ - 2 only statement c is true

2. The solution of 3y² + 5y > -2 is a. x < –1 or x is greater than negative two thirds

Statement a

Since f(x) = log₂(5x) which is a logarithm function is undefined for (-∞, 0) and defined for (0, +∞) and g(x) = 5ˣ - 2 which is an exponential function is defined for (-∞, +∞).

Also, since f(x) is decreasing on the interval (0, 1/5) while g(x) decreases on the interval (-∞, 0). So, they have do not have a common interval on (0, 1).

So, statement a. Both f(x) and g(x) decrease on the interval of (–∞, 1).

is false

Statement b

Since f(x) = log₂(5x) which is a logarithm function is defined for (0, +∞)  and g(x) = 5ˣ - 2 which is an exponential function is defined for (-∞, +∞).

So, the statement b Both f(x) and g(x) have the same domain of (0, ∞) is false

Statement c

Since f(x) = log₂(5x) which is a logarithm function has a range of (0, +∞).  and g(x) = 5ˣ - 2 which is an exponential function is has a range of (-2, +∞).

So, they have a common interval of (0, +∞).

So, the statement c. Both f(x) and g(x) have a common range on the interval (–2, ∞) is true

Statement d

To find the x-intercept of f(x), we equate f(x) to zero.

So, f(x) = log₂(5x)

0 = log₂(5x)

2⁰ = 5x

1 = 5x

x = 1/5

To find the x-intercept of g(x), we equate g(x) to zero.

g(x) = 5ˣ - 2

0 = 5ˣ - 2

2 = 5ˣ

x = ㏒₅2

Since the x-intercept of f(x) = 1/5 and the x- intercept of g(x) = ㏒₅2. So, they do not have a common x - intercept.

So, the statement d. Both f(x) and g(x) have the same x-intercept of (1, 0) is false.

So, only statement c is true

3y² + 5y > -2

3y² + 5y + 2 > 0

3y² + 3y + 2y + 2 > 0

3y(y + 1) + 2(y + 1) > 0

(3y + 2)(y + 1) > 0

So, the boundary values are at

(3y + 2)(y + 1) = 0

(3y + 2) = 0 or (y + 1) = 0

y = -2/3 or y = -1

So, we require (3y + 2)(y + 1) > 0

For y < -1 say -2, (3y + 2)(y + 1) = (3(-2) + 2)((-2) + 1)

= (-6 + 2)(-2 + 1)

= -4(-1)

= 4 > 0

For -1 < y < -2/3 say -1/3, (3y + 2)(y + 1) = (3(-1/3) + 2)((-1/3) + 1)

= (-1 + 2)(-1 +3)/2

= 1(-2/2)

= -1 < 0

For y > -2/3 say 0, (3y + 2)(y + 1) = (3(0) + 2)((0) + 1)

= (0 + 2)(0 + 1)

= 2(1)

= 2 > 0

So, for (3y + 2)(y + 1) > 0, y < -1 or y > -2/3

So, the solution of 3y² + 5y > -2 is a. x < –1 or x is greater than negative two thirds

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Answer:

1. D. Both f(x) and g(x) have the same x-intercept of (1, 0).

2. A. x < –1 or x is greater than negative two thirds

Step-by-step explanation:

I took the exam

Answer:

[tex]\sf 2\dfrac{1}{4}\ cups \ of \ sugar[/tex]

Explanation:

Let the full batch be x

Here given:

3/4 cup of sugar required to make 1/3 batch of cookies

Build equation:

[tex]\sf \rightarrow \dfrac{1}{3}x = \dfrac{3}{4} \ cup \ of \ sugar[/tex]

Solve:

[tex]\sf \rightarrow x = \dfrac{3(3)}{1(4)}[/tex]

[tex]\sf \rightarrow x = \dfrac{9}{4}[/tex]

[tex]\rightarrow \sf x = 2\dfrac{1}{4}[/tex]

Answer:

2 2\3 cups of sugar.

Step-by-step explanation:

Considering the simple inverse rule of three, 12 workers will be needed to complete a task in 6 days, given that 8 workers can complete the same task in 9 days.

Two variables are related when a change in one of them causes a change in the other.

Two variables have an inversely proportional relationship when an increase in one variable causes the other to decrease or, analogously, a decrease in one causes the other to increase.

In other words, two magnitudes are inversely proportional when as one increases, the other decreases in the same proportion, and as the first decreases, the second increases in the same proportion.

The simple inverse rule of three is used when the problem deals with two inversely proportional magnitudes where the amount of one of a magnitude corresponding to a given amount of the other magnitude must be calculated.

To carry out an inverse rule of three, it must be taken into account that if for a value A of one magnitude, there is a value B of the other magnitude, while for a value of C of the first magnitude, the second magnitude is will correspond a value of X:

A → B

C → X

So: [tex]X=\frac{AxB}{C}[/tex]

The number of people who perform a task is inversely proportional to the time it takes: a greater number of workers corresponds to less time to perform the task. Then:

9 days → 8 workers

6 days → amount of workers

So:[tex]amount of workers=\frac{9 daysx8 workers}{6 days}[/tex]

amount of workers= 12 workers

Finally, 12 workers will be needed to complete a task in 6 days, given that 8 workers can complete the same task in 9 days.

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The polynomial that has a GCF of 7m is 14mn - 21m + 49m²n + 7mn²

The polynomial that has a GCF of 2ab² is 6a²b² - 8ab³ + 4a³b² + 2a³b³

From the question, we are to write a polynomial that has a GCF of 7m

That is,

We are to write a polynomial that has a greatest common factor of 7m

Writing the polynomial

14mn - 21m + 49m²n + 7mn²

The  polynomial above has a greatest common factor of 7m. That is, 7m is the greatest factor that can divide each of the terms

We are to write a polynomial with a GCF of 2ab²

Writing the polynomial

6a²b² - 8ab³ + 4a³b² + 2a³b³

The polynomial above has a greatest common factor of 2ab². That is, 2ab² is the greatest factor that can divide each of the terms

Hence,

The polynomial that has a GCF of 7m is 14mn - 21m + 49m²n + 7mn²

The polynomial that has a GCF of 2ab² is 6a²b² - 8ab³ + 4a³b² + 2a³b³

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Answer:

47

Step-by-step explanation:

3068 - 1266 - 1755 = 47

Answer:

The third number is 47.

Step-by-step explanation:

The sum of three numbers is 3068 - this can be expressed mathematically as:

[tex]\displaystyle{x + y + z = 3068}[/tex]

Given that two of the numbers are 1266 and 1755 (in order) then substitute x = 1266 and y = 1755:

[tex]\displaystyle{1266 + 1755 + z = 3068}[/tex]

Find the third number - solve for z-variable:

[tex]\displaystyle{3021 + z = 3068}\\\\\displaystyle{z = 3068-3021}\\\\\displaystyle{z = 47}[/tex]

Therefore, the third number is 47.

well, first off let's check those two points, we know it's centerd at (-26 , 120) and we also know it passes through (0 , 0), so the distance between those two points is its radius

[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{0}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{-26}~,~\stackrel{y_2}{120})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ \stackrel{radius}{r}=\sqrt{(~~-26 - 0~~)^2 + (~~120 - 0~~)^2} \implies r=\sqrt{(-26)^2 + (120 )^2} \\\\\\ r=\sqrt{( -26 )^2 + ( 120 )^2} \implies r=\sqrt{ 676 + 14400 } \implies r=\sqrt{ 15076 } \\\\[-0.35em] ~\dotfill[/tex]

[tex]\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \hspace{5em}\stackrel{center}{(\underset{-26}{h}~~,~~\underset{120}{k})}\qquad \stackrel{radius}{\underset{\sqrt{15076}}{r}} \\\\[-0.35em] ~\dotfill\\\\ ( ~~ x - (-26) ~~ )^2 ~~ + ~~ ( ~~ y-120 ~~ )^2~~ = ~~(\sqrt{15076})^2 \\\\[-0.35em] ~\dotfill\\\\ ~\hfill (x+26)^2+(y-120)^2 = 15076~\hfill[/tex]

The formula for f(x) in y + 6 = 5(x - 4) in terms of x is f(x) = 5(x - 4)- 6

A linear equation is a equation that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient

A system of linear equations is a collection of at least two linear equations.

In this case, the linear function in the question is given as:

y + 6 = 5(x - 4)

Subtract 6 from both sides of the equation

y + 6 - 6 = 5(x - 4) - 6

Evaluate the difference in the above equation

y = 5(x - 4) - 6

Express the above equation as a function f(x)  i.e. we express y as a function of x

f(x) = 5(x - 4) - 6

Hence, the formula for f(x) in y + 6 = 5(x - 4) in terms of x is f(x) = 5(x - 4) - 6

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Answer:

8.64 hours, so

8 hours, 38 mins, 24 seconds

Just find that 27% you have left, then find how much that 27% is in terms of time.

It might be wrong so double check it please.

Answer:

8.64 hours

which is 8hrs 38mins and 24secs

Step-by-step explanation:

If you've completed 73% then you have 27% left to go still. (100-73 = 27)

27% of 32

= .27×32

= 8.64 hours left

That is 8hrs and .64 of an hour .64×60=38.4 mins

which is 38 mins and .4 of a minute.

.4×60 = 24secs

Probably you will just round this answer.

Answer:

  y = -1/2n +40

Step-by-step explanation:

We are given two ordered pairs (stalks, ounces) and asked for the slope-intercept form equation of the line through them.

The slope of the desired line can be found from the formula ...

  m = (y2 -y1)/(x2 -x1)

For the given points (30, 25) and (32, 24), the slope is ...

  m = (24 -25)/(32 -30) = -1/2

The y-intercept of the desired line can be found from the formula ...

  b = y -mn

  b = 25 -(-1/2)(30) = 25 +15 = 40

The slope-intercept equation of a line is ...

  y = mn +b . . . . . line with slope m and y-intercept b

  y = -1/2n +40 . . . . . . line with slope -1/2 and y-intercept 40

The linear relationship between stalks (n) and yield (y) is ...

  y = -1/2n +40

Answer:

○ [tex]y = 6 + 5x + x^2[/tex]

Explanation:

A quadratic equation is an algebraic equation where the highest power of [tex]x[/tex] is 2. The general form of a quadratic equation is as follows:

[tex]\boxed{ax^2 + bx + c = 0}[/tex],

where a, b, and c represent known constants, and [tex]x[/tex] is the unknown.

In this question, if you take a look at the second option, you will see that it is possible to rearrange the equation to make it look the general form:

[tex]y = 6 + 5x + x^2[/tex]

⇒ [tex]y = x^2 + 5x + 6[/tex]

Therefore, this equation is quadratic.

The other three options are not quadratic equations because none of them have an [tex]x^2[/tex]  term in them.

[tex]\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}[/tex]

[tex]\leadsto[/tex] A quadratic equation is an algebraic equation of the second degree. The formula is:

▪ [tex]\longrightarrow \sf{y = ax^2 + bx + c}[/tex]

This can also be written as:

▪ [tex]\longrightarrow \sf{y = c + bx+ax^2}[/tex]

Comparing the equation above with each of the options, the equation that represents a quadratic function is:

[tex]\longrightarrow \sf{y=6+5 + x^2}[/tex]

[tex]\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}[/tex]

◉ [tex] \large\bm{b. \: y=6+5x + x^2}[/tex]

Answer:

d. 10, 10

Step-by-step explanation:

4(10)+5(10) = 40 + 50 = 90

10 + 10 = 20

Hope this helps

An equation is formed of two equal expressions. In the two of the given equations, the value of x and y are 10 and 10, respectively. The correct option is D.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Given the two of the equation, which can be named as,

4x+5y=90   ...... equation 1

x+y=20   ............ equation 2

Solve the second equation for x,

x + y = 20

x = 20 - y ................ equation 3

In the first equation substitute the value of x from the third equation,

4x + 5y = 90

4(20 - y) + 5y = 90

Solving the equation for y,

80 - 4y + 5y = 90

y = 90 - 80

y = 10

Substitute the value of y in the second equation, to get the value of x,

x + y = 20

x + 10 = 20

x = 20 - 10

x = 10

Hence, In the two of the given equations, the value of x and y are 10 and 10, respectively.

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Answer:

X = 81

Step-by-step explanation:

600 × 0.45 = 270

270 × 0.3 = 81

X = 81

Kerris reasoning that 4.2/5 is about 8 tenths because 4.2/5 is close to 40 tenths/5 is correct

The quotient is given as:

4.2/5

Kerris reasoning is that

4.2/5 is approximately 0.8

We start by calculating the actual value of the quotient 4.2/5

Using a calculator, we have:

4.2/5 = 0.84

Approximate to the nearest tenth

4.2/5 = 0.8

This means that Kerris reasoning that 4.2/5 is about 8 tenths because 4.2/5 is close to 40 tenths/5 is correct

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