Round 1,208.7438 to the nearest hundredth.
A. 1,208.73
B. 1,208.74
C. 1,208.743
D. 1,208.75

Option A

The vertex is (h, k) = (5, -25)

Solution:

Given function is:

[tex]f(x) = x^2-10x[/tex]

The vertex form is given as:

[tex]y = a(x-h)^2+k[/tex]

Rewrite the equation in vertex form

[tex]f(x) = x^2-10x[/tex]

Complete the square for  [tex]x^2-10x[/tex]

Use the form [tex]ax^2+bx+c[/tex] to find the values of  a, b, c

a = 1 , b = -10, c = 0

Consider the vertex form of a parabola

[tex]a(x+d)^2+e[/tex]

Substitute the values of a and b into the following formula to find "d" :

[tex]d = \frac{b}{2a}\\\\d = \frac{-10}{2 \times 1}\\\\d = -5[/tex]

Find the value of "e" using the formula,

[tex]e = c - \frac{b^2}{4a}\\\\e = 0 - \frac{(-10)^2}{4 \times 1}\\\\e = -25[/tex]

Substitute the value of a, d, e into vertex form

[tex]a(x+d)^2+e\\\\1(x-5)^2-25\\\\(x-5)^2-25[/tex]

Set y equal to above equation

[tex]y = (x-5)^2-25[/tex]

Compare the above equation with vertex form

[tex]y = a(x-h)^2+k[/tex]

[tex]y = (x-5)^2-25[/tex]

We find, h = 5 and k = -25

Thus the vertex is (h, k) = (5, -25)

Answer:

A) 100000

B) 80/100000

Step-by-step explanation:

A) it is a simple matter of multiplying the possibilities of the digit it could be to the second one then to the third and so on and so forth

B) if a person were to enter a 5 digit code at random say it be 00000 then that person would have 80 out of a 100000 chance of unlocking the door as there are only 80 access codes that are correct

There are 100,000 possible 5-digit codes. The probability of a random 5-digit code granting access is 0.0008 or 0.08%.

This problem involves combinatorics and probability.

a) If each digit of the 5-digit code can be any number from 0-9, then for each digit, 10 possibilities exist. Hence the total number of possibilities for a 5-digit code would be 10*10*10*10*10, which is 100,000. So there are 100,000 possible 5-digit codes.

b) Probability is defined as the number of ways an event can occur over the total number of outcomes. If each 5-digit code is unique and assigned to only one employee, with 80 employees, there are 80 valid codes. Therefore, the probability of someone entering a 5-digit code at random and gaining entry would be 80 (the number of successful outcomes) divided by 100,000 (the total number of possible outcomes), which is 0.0008 or 0.08%.

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Answer:

0.9 / 90%

Step-by-step explanation:

54/60

=0.9

To calculate Kevin's score as a percent, we divide the number of correct answers by the total number of questions and multiply by 100. The answer, rounded to the nearest tenth of a percent, is 90.0%.

The subject of this question is Mathematics, particularly the area concerning percentage conversions. Kevin got 54 questions correct out of a total of 60 questions. To find Kevin's score as a percent, we first need to divide the number of questions he answered correctly (54) by the total number of questions (60). This gives us a decimal (0.9). To convert this decimal to a percent, we multiply by 100, which gives us 90%. This is Kevin's raw score. But the question wants the score rounded to the nearest tenth of a percent, so the final answer is 90.0%.

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Answer:

y = 5x - 3.

Step-by-step explanation:

The value of y will go down by 3 units so it is

y = 5x - 3.

The equation y = 9 + 3x represents a line with a y-intercept of 9 and a slope of 3. To translate the line down 3 units, subtract 3 from every y-coordinate.

The equation y = 9 + 3x represents a line with a y-intercept of 9 and a slope of 3. The y-intercept is the point where the line intersects the y-axis, and in this case, it is the point (0, 9). The slope of 3 means that for every increase of 1 on the horizontal axis, the line rises up 3 units on the vertical axis.

To translate the line down 3 units, we can subtract 3 from every y-coordinate. This means that the equation becomes y = 9 + 3x - 3, which simplifies to y = 6 + 3x.

Answer: 2x + 5y = -5

Step-by-step explanation:

Two lines are said to be parallel if they have the same slope.

The equation of the line given :

2x + 5y = 10

To find the slope , we will write it in the form y = mx + c , where m is the slope and c is the y - intercept.

2x + 5y = 10

5y = -2x + 10

y = -2/5x + 10/5

y = -2/5x + 2

This means that the slope is -2/5 ,the line that is parallel to this line will also have a slope of -2/5.

using the formula:

[tex]y-y_{1}[/tex] = m ([tex]x-x_{1}[/tex] ) to find the equation of the line , we have

y - 1 = -2/5(x -{-5})

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

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

5y - 5 = -2x - 10

5y + 2x = -10 + 5

therefore :

2x + 5y = -5 is the equation of the line that is parallel to 2x + 5y = 10

Answer: 2x + 5y = -5

Step-by-step explanation:please see attachment for explanation

The best reflection of Jason's answer among the given options is option : [tex]\((5x + 1)(5x - 1)\).[/tex]

The correct option is (H).

To factor [tex]\(25x^2 - 1\)[/tex], Jason likely used the difference of squares formula. This formula states that for any expressions [tex]\(a\) and \(b\), \(a^2 - b^2\)[/tex] can be factored as [tex]\((a + b)(a - b)\).[/tex]

In our case, [tex]\(a = 5x\) and \(b = 1\)[/tex]. So, we apply the difference of squares formula:

[tex]\[25x^2 - 1 = (5x)^2 - 1^2\][/tex]

[tex]\[= (5x + 1)(5x - 1)\][/tex]

This factorization is a result of recognizing that [tex]\(25x^2 - 1\)[/tex] can be written as [tex]\((5x)^2 - 1^2\),[/tex] fitting the difference of squares pattern.

Now, let's compare Jason's answer to the options given:

- Option F: [tex]\((5x-1)(5x-1)\)[/tex] is not correct. This represents the square of [tex]\(5x - 1\),[/tex] not a difference of squares.

- Option G: [tex]\((5x+1)(5x+1)\)[/tex]is not correct. This also represents the square of [tex]\(5x + 1\),[/tex] not a difference of squares.

- Option H:[tex]\((5x+1)(5x-1)\)[/tex] is correct. This represents the correct factorization using the difference of squares formula.

- Option J: Prime. This is incorrect because [tex]\(25x^2 - 1\)[/tex] can indeed be factored as [tex]\((5x + 1)(5x - 1)\).[/tex]

Therefore, the best reflection of Jason's answer among the given options is option H: [tex]\((5x + 1)(5x - 1)\).[/tex]

complete question given below:

Jason was asked to factor 25x^2-1 on his algebra test. Which of the following could best reflect Jason's answer?

F. (5x-1)(5x-1)

G. (5x+1)(5x+1)

H .(5x+1)(5x-1)

J .Prime

Answer:

14

Step-by-step explanation:

(2(19)-10)=2

(38-10)=2

(28)=2

÷2. ÷2

14

Answer:

5G/10

Step-by-step explanation:

Answer:

i think correct answer is a

Hey there!

I'm going to set up the equation slightly different.

[tex](3)(8)=t+5\\24=t+5\\t+15=24\\t+15-15=24-15\\t = 9 \checkmark[/tex]

Answer:

t = 9

Step-by-step explanation:

3x8 = t + 15

24 = t + 15

t = 24 - 15

t = 9

Answer:

$50

Step-by-step explanation:

If the tip was $9, you can find the total price by dividing 9 by .18.  .18 is 18% but as a decimal (move to the left two decimal places).  9/.18 = 50.

You can also check the answer by finding the 18% tip of $50. 50*.18=9.

Answer:

[tex]x=\frac{5t^2-a}{6-5t}[/tex]

Step-by-step explanation:

Given equation is

[tex]6x+a=5t(x+t)[/tex]

We have to make [tex]x[/tex] the subject of formula. That means we have to isolate [tex]x[/tex].

[tex]6x+a=5t(x+t)[/tex]

Distribute [tex]5t[/tex]

[tex]6x+a=5tx+5t^2[/tex]

Subtract [tex]a[/tex] both side we get,

[tex]6x+a-a=5xt+5t^2-a[/tex]

[tex]6x=5xt+5t^2-a[/tex]

Subtract [tex]5xt[/tex] both side we get,

[tex]6x-5xt=5xt-5xt+5t^2-a\\6x-5xt=5t^2-a[/tex]

Now, take [tex]x[/tex] common from left side of equation

[tex]x(6-5t)=5t^2-a[/tex]

Divide [tex]6-5t[/tex] both side,

[tex]\frac{x(6-5t)}{6-5t}=\frac{5t^2-a}{6-5t}\\\\x=\frac{5t^2-a}{6-5t}[/tex]

Option D

The total earnings of Yvette is $ 47, 400

Solution:

Given that, Yvette earns a $45,000 salary plus a 12% commission on any sales over $10,000

Last year Yvette made $30,000 in sales

Subtract 10,000 from her sales to get the amount she earns commission on:

30,000 - 10,000 = 20,000

Since Yvette gets 12% commission

So amount earned as commission would be 12% of $20,000

[tex]\text{Commission}=20000\times \frac{12}{100}\\\\\text{Commission}=20000\times 0.12\\\\\text{Commission}=2400\left\\\\[/tex]

Yvette also gets a salary of $45,000, so Yvette's total earnings would be $45,000 plus $2,400

[tex]Total\ Earnings = 45000 + 2400 = 47400[/tex]

Thus total earnings of Yvette is $ 47, 400

Answer:

D

Step-by-step explanation:

To find the distance from a point to a line, we can use the distance formula. For this problem, the distance from point A(-2,3) to the line y=1/2x+1 is approximately 2.5 units.

To find the distance from a point to a line, we can use the formula for the distance between a point and a line. The formula is:

d = |Ax + By + C| / √(A^2 + B^2)

In this case, the equation of the line is y = (1/2)x + 1, which can be rewritten as 2x - y + 2 = 0. Plugging in the coordinates of point A in the equation, we get:

d = |(2 * -2) + (-1 * 3) + 2| / √((2^2) + (-1^2)))

After completing the calculation, rounding the answer to the nearest tenth, the distance from point A(-2,3) to the line y = (1/2)x + 1 is approximately 2.5 units.

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Answer:

x = 16

Step-by-step explanation:

Given that the sum of the exterior angles is 360°

Sum the given exterior angles and equate to 360

47 + 93 + 46 + 3x + 62 + 4x = 360, that is

248 + 7x = 360 ( subtract 248 from both sides )

7x = 112 ( divide both sides by 7 )

x = 16

Answer:

Bout which cars?

Step-by-step explanation:

Sorry, but I think you've missed out a part of the question

Answer:x=40

Step-by-step explanation:

The measure of x in each figure, you need to solve the equation 4x + 20 = 180° by isolating the term with x and then solving for x. The solution is x = 40°, so the measure of x is 40 degrees.

The value of x. The given equation is 4x + 20 = 180°, representing a linear pair of angles.

Subtract 20 from both sides of the equation to isolate the term with x:

4x + 20 - 20 = 180 - 20

4x = 160°

Divide both sides of the equation by 4 to solve for x:

(4x)/4 = 160/4

x = 40°
Therefore, the solution to the equation is x = 40°.

Answer:

Therefore the first option gives the correct answer of a system of equations which has exactly one solution.

Step-by-step explanation:

i) the second option is 2x + 2y = 1  and -2x -2y = 1 . these two equation can be written as 2x + 2y = 1 and 2x + 2y = -1. Therefore we can see that that the expressions for used for the variables x and y are the same but the result is different. This is not possible and so there will be no solutions for these two equations

ii) the third option is 3x + y = -1 and 6x + 2y = -2. therefore these two equations can be written as  3x + y = -1 and 3x + y = -1 (dividing the second equation by 2) and thus we see that both the equations are exactly the same and hence these two equations will have an infinite number of solutions.

iii) the last option is 3x - 2y = 4 and -3x + 2y = 4. these two equations can be written as 3x -  2y = 4 and 3x - 2y = -4. Again we can see in this case that the two equations are exactly the same and therefore these two equations will have an infinite number of solutions.

iv) the remaining option is the first one 2x + y = 3 and 5x - y = 11.  If we add the first equation to the second one we 7x = 14 and therefore x = 2. If we substitute x = 2 in the first equation we get (2 × 2) + y = 3, therefore y = -1.

Therefore the first option gives the correct answer of a system of equations which has exactly one solution.

Answer:

geometric sequence

Step-by-step explanation:

If the sequence is geometric then there must be a common ratio r between consecutive terms, that is

320 ÷ 128 = 2.5

800 ÷ 320 = 2.5

2000 ÷ 800 = 2.5

Since there is a common ratio r = 2.5 between consecutive terms.

Then the sequence is geometric

Answer: i would help but i'm confused....what problem? can yhu attach it so i could help??! - Lexi@helps

Step-by-step explanation:

Answer:P=N/(2t3q2)

Step-by-step explanation:

N=2pt3q2

Divide both sides by 2t3q2

N/(2t3q2)=(2pt3q2)/(2t3q3)

N/(2t3q2)=p

Answer:

Hence, the supplement of a 20˚ angle is a 160˚ angle. This can be proven again, since 20+160=180 , and supplementary angles have a sum of 180˚ .

Step-by-step explanation:

The answer is: ∠BOA

(Had the same question)

BTW, you forgot to add the picture.  That's why no one understands this, unless they had this question in their school work.

Answer:x f(x)=0.5x g(x)=−0.5x+1

This implies that f(x)= 0.5 and

g(x)= -0.5x + 1

-0.5x + 1= 0.5

-0.5x= 0.5-1

-0.5x=-0.5

x= -0.5/-0.5

x=1

Step-by-step explanation:

Final answer:

To solve f(x) = g(x), set 0.5x equal to −0.5x + 1. Solve for x by combining like terms, which gives x = 1 as the solution.

Explanation:

To determine the solution to f(x) = g(x), we set the two functions equal to each other and solve for x.

The function f(x) is given by f(x) = 0.5x, and the function g(x) is given by g(x) = −0.5x + 1.

Setting f(x) equal to g(x), we have:
0.5x = −0.5x + 1

To solve for x, we'll combine like terms by adding 0.5x to both sides, which gives us:
0.5x + 0.5x = 11x = 1

When we divide both sides by 1, we get:

x = 1

So the solution to f(x) = g(x) is when x = 1.

Answer:

Step-by-step explanation:

12x-20=6(x-20)-9x

Opening bracket

12x - 20 = 6x - 120 - 9x

Collecting like terms

12x - 6x + 9x = -120 + 20

15x = -100

Dividing by 15

15x/15 = -100/15

x = -20/3

x = - 6 2/3

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

12x - 20 = 6( x - 20) - 9x

pay attention to the brackets as you simplify.

Let's work on it:

12x - 20 = 6x - 120 -9x

Collecting like terms to further simplify the equation.

12x - 6x + 9x = -120 + 20

15x = -100

Let's make x the subject formula by dividing through by 15

Therefore:

x = -100 / 15

Divide through by 5

x = -20 / 3

Since nothing can easily divide through, we turn it to a mixed fraction

x = - 6 2/3

( Minus six whole number, two divided by three)

Answer: 54-7n

Step-by-step explanation:

When we talk about mathematical language, the difference between two numbers, quantities or terms is the substraction operation.

For example, the difference between a and b is:

a-b

On the other hand, if we read a numer c times a number n, this means both numbers are multiplied.

For example:

c times n is:

(c)(n)

So, according to the explained above, “the difference of fifty-four and seven times a number n” is:

54-7n

Answer:

Answer: 54-7n

Step-by-step explanation:

When we talk about mathematical language, the difference between two numbers, quantities or terms is the substraction operation.

For example, the difference between a and b is:

a-b

On the other hand, if we read a numer c times a number n, this means both numbers are multiplied.

For example:

c times n is:

(c)(n)

So, according to the explained above, “the difference of fifty-four and seven times a number n” is:

54-7n

and recall the you can divide everything by 100 like 74/n  n=100 so 74/100

see and pls give  me brainiest

The undefined terms needed to define parallel lines are "line" and "coplanar," as parallel lines lie in the same plane and never intersect.

To define parallel lines, the undefined terms needed are "line" and "coplanar."

Parallel lines are two lines that lie in the same plane and never intersect, which means they are coplanar and can be extended indefinitely.

So, the correct choice is: Coplanar, line.

Answer:

[tex]x<-\frac{1}{4}[/tex]

Step-by-step explanation:

The correct question is

Solve. −3/5x+1/5>7/20 Drag and drop a number or symbol into each box to show the solution

we have

[tex]-\frac{3}{5}x+\frac{1}{5} >\frac{7}{20}[/tex]

Solve for x

Multiply by 20 both sides

[tex]-12x+4 >7[/tex]

subtract 4 both sides

[tex]-12x >7-4[/tex]

[tex]-12x >3[/tex]

divide by -12 both sides

Remember that when you multiply or divide both sides of an inequality by a negative number, you must reverse the inequality symbol

[tex]x<-\frac{3}{12}[/tex]

simplify

[tex]x<-\frac{1}{4}[/tex]

Answer:

x < 1/4

Step-by-step explanation:

you're supposed to add or subtract the constant, and then do the same to the other constant, them bring down the coefficient and you'll get your answer.

hope this helps

Answer: Second option.

Step-by-step explanation:

Given the following Inequality provided in the exercise:

[tex]50 - 8m \geq 0[/tex]

You need to solve for "m".

Then, you can follow the steps below in order to find the solution of the inequality:

Step 1: You must apply the Subtractrion property of Inequality and subtract 50 from both sides:

[tex]50 - 8m-(50) \geq 0-(50)\\\\- 8m \geq -50[/tex]

Step 2: Now you need to apply the Division property of Inequality and divide both sides of this inequality by -8 (Since you are dividing both sides by a negative number the direction of the inequality changes). Then, you get:

[tex]\frac{- 8m}{-8} \geq \frac{-50}{-8}\\\\m\leq \frac{25}{4}\\\\m\leq6.25[/tex]

Notice that this solution matches with the second option.

80 USD × (1.0343 AUD / 1 USD)

Solution:

To convert 80 US dollars into Australian dollars.

1 US dollar = 1.0343 AU dollar

1 AU dollar = 0.9668 US dollar

To find 80 US dollars into Australian dollars multiply 80 US dollars by 1.0343

80 AU dollars = 80 × 1.0343/ 1 USD

The expression is 80 USD × (1.0343 AUD / 1 USD)

Hence, the expression which is used to convert 80 US dollars to Australian dollars is 80 USD × (1.0343 AUD / 1 USD).