the ratio of boys to girls is 4:5. if there are 125 girls, what is the total number of students.

let's recall that the vertical asymptotes for a rational expression occur when the denominator is at 0, so let's zero out this one and check.

[tex]\bf \cfrac{5x+5}{x^2+x-2}\qquad \stackrel{\textit{zeroing out the denominator}~\hfill }{x^2+x-2=0\implies (x+2)(x-1)=0}\implies \stackrel{\textit{vertical asymptotes}}{ \begin{cases} x=-2\\ x=1 \end{cases}}[/tex]

Final answer:

The vertical asymptotes of the function f(x) = (5x+5)/(x² + x - 2) occur where the denominator equals zero. Factoring the denominator, we find the vertical asymptotes to be at x = -2 and x = 1.

Explanation:

The student is asking about the vertical asymptotes of the function f(x) = (5x+5)/(x² + x - 2). To find the vertical asymptotes of a function, we look for values of x where the denominator is equal to zero, because these are the points where the function is undefined and the graph of the function will approach infinity.

To find the vertical asymptotes, set the denominator equal to zero and solve for x:

x² + x - 2 = 0

Factoring the quadratic equation, we get:

(x+2)(x-1) = 0

Therefore, the vertical asymptotes are at x = -2 and x = 1, since these are the values of x for which the denominator becomes zero.

Answer:

[tex]g(x)=-x^{2}-4[/tex]

Step-by-step explanation:

we know that

The function g(x) is a vertical parabola open downward with vertex at (0,-4)

The equation of a vertical parabola into vertex form is equal to

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

I assume that g(x) is a reflection of the function f(x) over the line y=-2

so

a=-1 ---> because in the function f(x) the value of a is equal to 1

therefore

[tex]g(x)=-x^{2}-4[/tex]

Answer: d. 512

Step-by-step explanation:

You need to remember that:

[tex](\sqrt[3]{x})^3=x[/tex]

Then, given the equation:

[tex]\sqrt[3]{n}=8[/tex]

You can find the value of "n" that make the equation true, by solving for "n".

So, to solve for "n", you need to raise both side of the equation to power 3. Therefore, you get:

 [tex]\sqrt[3]{n}=8[/tex]

 [tex](\sqrt[3]{n})^3=(8)^3[/tex]

 [tex]n=512[/tex]

Then, the value of "n" that makes the equation [tex]\sqrt[3]{n}=8[/tex] true is: 512 (You can observe that this matches with the option d).

Answer:

the answer is D

Step-by-step explanation:

Answer:

figure 2

Step-by-step explanation:

Answer:

The answer is figure 4.

Answer:

x = 5 ± sqrt(35)

Step-by-step explanation:

X^2 - 10x+ 25 = 35.​

Factor the left hand side.  This is the difference of squares.  a^2 -2ab - b^2 = (a-b)^2  where a = x and b = 5

(x-5) ^2 = 35

Take the square root of each side

sqrt((x-5) ^2) =± sqrt(35)

x-5 = ± sqrt(35)

Add 5 to each side

x-5+5 = 5 ± sqrt(35)

x = 5 ± sqrt(35)

Answer:

The graph of [tex]g(x) = (x - 1) (x + 4)^3(x +5)^2[/tex] crosses the x-axis at (1,0) and (-4, 0). It touches the x-axis at (-5, 0).

Step-by-step explanation:

g(x):

[tex]g(x) = (x - 1) (x - (-4))^3(x - (-5)^2[/tex].

There are three factors:

The first and second factors are raised to odd powers. The graph will cross the x-axis at all these two points:

The third factor is raised to an even power. The graph will touch the x-axis at that point.

Answer:

crosses at (1,0)

crosses at (-4,0)

touches at (-5,0)

Got correct on ed

Step-by-step explanation:

Answer:

(6x5) • 8

Step-by-step explanation:

We’ll I find it’s 6 dollars a day and their are 5 days that would be 30 but this went in for 8 weeks so it would be 30 x 8 which equal 240

Answer:

Required expression for amount spend on breakfast for 8 week is ( 6 × 5 ) × 8 and this amount is $ 240

Step-by-step explanation:

Given:

Amount spend on Breakfast using debit card = $6

Amount for breakfast spend for 5 mornings per week for past 8 weeks.

We need to write the multiplication expression for the given situation.

Amount spend on breakfast for a morning = $6

Amount spend on breakfast for 5 morning = 6 × 5

Amount spend on breakfast for 1 week = $ ( 6 × 5 )

Amount spend on breakfast for 8 week = ( 6 × 5 ) × 8

Required multiplication expression = ( 6 × 5 ) × 8

Answer of the multiplication = ( 6 × 5 ) × 8 = ( 30 ) × 8 = 240

Therefore, Required expression for amount spend on breakfast for 8 week is ( 6 × 5 ) × 8 and this amount is $ 240

Answer:

B. Rectangle

Step-by-step explanation:

All rectangles are parallelograms.

Final answer:

To estimate the product -12 4/9 · 5 7/8, round each number to the nearest whole number and multiply. The estimated product is -72.

Explanation:

To estimate the product -12 4/9 · 5 7/8, we can round each number to the nearest whole number and then multiply.

Rounding -12 4/9 to the nearest whole number gives -12.

Rounding 5 7/8 to the nearest whole number gives 6.

Now, we can multiply -12 and 6: -12 · 6 = -72.

So, the estimated product is -72.

Answer:

I only know how to do the first and second one i'm not sure about the rest:  V=Lwh

Step-by-step explanation:

so, (6)(6)(8)= 288ft^3

and (12)(16)(18)= 3456m^3

Hope i have helped you in some way!

Answer:

the slope intercept form is: y = x+2

Step-by-step explanation:

The general form of point slope form is : y-y₁ = m(x-x₁)

The given equation is: y – 3 = (x – 1)

comparing we get,

m = 1

and solving the equation;

y-3 = x-1

Adding +3 on both sides

y = x-1+3

y=x+2

The general formula of slope-intercept form is : y = mx+b

where m is the slope and b is the y-intercept

so, y = x+2

where m =1 and b=2

so, the slope intercept form is: y = x+2

Answer:

the answer is y = y= 1/2x+2

Step-by-step explanation:

Answer:

55 inches

Step-by-step explanation:

This question is on z-score for a sample

The general formula for finding z score for a sample is;

z=(x-μ)/δ...................where x is the sample is the height , μ is the mean and δ is the standard deviation

Given;

z=3       x=?      μ=49     δ=2

Substitute values above in the general formulae

z=(x-μ)/δ

3=(x-49)/2

[tex]3=\frac{x-49}{2} \\\\\\3*2=x-49\\\\\\6=x-49\\\\\\6+49=x\\\\\\55=x[/tex]

Answer:

Step-by-step explanation:

To solve this problem we need to use the following formula

[tex]Z=\frac{x- \mu}{\sigma}[/tex]

Where [tex]Z[/tex] is the z-value, [tex]\mu[/tex] is the mean, [tex]\sigma[/tex] is the standard deviation and [tex]x[/tex] is the height of the student.

In this case, we have

[tex]Z=3\\\mu=49\\\sigma=2[/tex]

Replacing all these values, we have

[tex]3=\frac{x- 49}{2}\\6=x-49\\x=6+49\\x=55[/tex]

Therefore, the student is 55 inches tall.

Answer:

y = mx + b

Step-by-step explanation:

Since there is no illustration, that is all I can give you. I apologize.

Answer:

y=mx +b is the formula

Step-by-step explanation:

I think you are missing a part of the question.

Answer:

[tex]y=19.7*10^{3}[/tex]

Step-by-step explanation:

step 1

Find the slope

we know that

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

we have

[tex](-200,-4.03*10^{4}), (50,9.7*10^{3})[/tex]

convert to

[tex](-200,-40.3*10^{3}), (50,9.7*10^{3})[/tex]

substitute in the formula

[tex]m=\frac{9.7*10^{3}+40.3*10^{3}}{50+200}[/tex]

[tex]m=\frac{50*10^{3}}{250}[/tex]

[tex]m=200[/tex]

step 2

Find the equation of the line into point slope form

[tex]y-y1=m(x-x1)[/tex]

we have

[tex](x1,y1)=(50,9.7*10^{3})[/tex]

[tex]m=200[/tex]

substitute

[tex]y-9.7*10^{3}=200(x-50)[/tex] ----> equation of the line into point slope form

step 3

Find the value of y when x=100

substitute in the equation the value of x

[tex]y-9.7*10^{3}=200(100-50)[/tex]

[tex]y=200(50)+9.7*10^{3}[/tex]

[tex]y=19,700[/tex]

[tex]y=19.7*10^{3}[/tex]

Answer:

Option A. [tex]LN^{2}=33^{2}-11^{2}[/tex]

Step-by-step explanation:

we know that

In the right triangle MNL

Applying the Pythagoras Theorem

[tex]MN^{2}=ML^{2} +LN^{2}[/tex]

substitute the values

[tex]33^{2}=11^{2} +LN^{2}[/tex]

[tex]LN^{2}=33^{2}-11^{2}[/tex]

When a line has a slope of zero it means that it is horizontal. This means that all the x values have the same y values. In this case it means that the y value is always -1.

The equation for this line is...

y = -1

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

y= -1

Step-by-step explanation:

When we have a line with slope of 0, it means that the y value does not change, so our equation must be in the form y= something

The point has a y value of -1,

so  our equation is

y= -1

Answer: $116,000

Step-by-step explanation:

Set up a ratio and then cross multiply and divide. See paper attached. (:

Final answer:

Ava's salary is calculated based on the given salary ratio of Paul to Ava (3:4). By dividing Paul's salary by 3, we find out how much one part of the ratio is worth and then multiply by 4 to find Ava's salary to be $116,000.

Explanation:

The question provided asks us to calculate Ava's salary based on the ratio of Paul to Ava's salaries which is 3:4. If Paul's salary is $87,000, we determine Ava's salary using the given ratio. Here is the step-by-step process:

Step 1: Understand the ratio, which tells us that for every 3 parts of Paul's salary, Ava gets 4 parts. This does not tell us the total amount, but how they share the total amount.

Step 2: Since Paul's salary is $87,000, and that represents 3 parts of the total, we divide $87,000 by 3 to find out what 1 part is: $87,000 / 3 = $29,000.

Step 3: Now that we know 1 part is $29,000, we can calculate Ava's salary which is 4 parts: $29,000 X 4 = $116,000.

Ava's salary is therefore $116,000.

Answer:

= 5.196 i

Step-by-step explanation:

The problem tells us to find the square root of -98 +71

√(-98 + 71)

= √(-27)

Which is an imaginary number

=√(-3^3)

Lets remember that, √(-1) = i

= i*3√(3)

= 5.196 i

Please see attached image for more information

Answer:

The cost of the racquet is [tex]\$135[/tex]

Step-by-step explanation:

Let

x-----> the cost of the racquet

we know that

The racquet represent the 100%

so

using proportion

[tex]x/100\%=\$9.45/7\%[/tex]

[tex]x=100\%*(\$9.45)/7\%[/tex]

[tex]x=\$135[/tex]

Answer: 72

Step-by-step explanation:

Rewriting input as fractions if necessary:

8/9, 7/8

For the denominators (9, 8) the least common multiple (LCM) is 72.

LCM(9, 8)

Therefore, the least common denominator (LCD) is 72.

Rewriting the original inputs as equivalent fractions with the LCD:

64/72, 63/72

The answer is:

The equation is an example of the distributive property.

To determine which method/property is the equation example, we need to remember the distributive property.

We can state the distributive property with the following example:

[tex](a+b)(c+d)=a*c+a*d+b*c*+b*d[/tex]

So, we are given the expression:

[tex](2x^{2}-1)(3x+2)[/tex]

Then, apllying the distributive property we have:

[tex](2x^{2}-1)(3x+2)=(2x^{2})*(3x)+(2x^{2})*2+(-1)*(3x)+(-1)*(2)[/tex]

Hence, the equation is an example of the distributive property.

Have a nice day!

The answer is C. (1, 12).

12 = 3 x [tex]4^{1}[/tex]

Answer:

Step-by-step explanation:

f(x)= 3 • 4^x

we can use the x coordinate of the points given in option to check what value do we get for y or f(x) .

so using the point from first option A :

x= 12

[tex]y=f(12)=3.4^{12}=50331648\neq 1[/tex]

for option B

x=0

[tex]y=f(0)=3.4^0=3[/tex]

option C

x=1

[tex]y = f(1)= 3.4^1=12[/tex]

so the correct option is C

Answer:

(5y+3)(y-1)

Step-by-step explanation:

5y^2-2y-3

I don't know if you like trial factors or not... but we can try that way

notice we have 5y^2

that can be written as 5y * 1y

Notice at the end we have -3

that can be written as -3*1

So possible answers could be:

(5y-3)(1y+1)   =5y^2+5y-3y-3=5y^2+2y-3

So this was almost right.

If we just switch the signs the - and + there we will have got it

(5y+3)(1y-1)=5y^2-5y+3y-3=5y^2-2y-3 which is good

So the answer is (5y+3)(y-1)

To factor the quadratic equation 5y^2-2y-3 completely, find two numbers that multiply to -15 and add to -2, and use them to rewrite the middle term before factoring by grouping. The factors obtained are (5y - 3)(y + 1).

The given quadratic equation to factor completely is 5y^2-2y-3. To achieve this, we are finding two numbers that multiply to the product of the coefficient of y^2 (which is 5) and the constant term (which is -3), and at the same time add up to the coefficient of the y term (which is -2).

The required pair of numbers is -3 and -1, because (-3)*(1) = -3 (the product of coefficient of y^2 and the constant term) and (-3)+(1) = -2 (the coefficient of the y term).

We rewrite the middle term and then factor by grouping:

https://brainly.com/question/30398551

#SPJ2

Answer:

[tex]Z=2.49[/tex] and this Z-score is “unusual.”

Step-by-step explanation:

To calculate the Z score use the following formula

[tex]Z=\frac{x-\mu}{\sigma}[/tex]

Where

μ is the average

[tex]\sigma[/tex] is the standard deviation

x is the data to which we will calculate the z-score

In this case

[tex]\mu = 122.3\\\\\sigma= 18.5\\\\x =168.4[/tex]

So

[tex]Z=\frac{168.4-122.3}{18.5}[/tex]

[tex]Z=2.49[/tex]

A z-score is unusual if [tex]Z> 2[/tex] or [tex]Z < -2[/tex]

Finally

[tex]Z=2.49[/tex] and this Z-score is “unusual.”

Answer: 2.49 unusual

Step-by-step explanation:

Answer:

c is the correct answer

Step-by-step explanation:

the way I study

Answer:

Paul's unmarried daughter, Candace, lived with him in his home for the entire year. Paul is divorced. He owns his own home and pays all of the costs of upkeep for the home. Paul paid over one-half of the cost of support for Candace. Paul may file as head of household if Candace is under the age of 19 or permanently disabled.

If none of the conditions statetd above are met, then Candance won't be considered a dependent. If Candance is not a dependant, Paul can still file as a head of household given that he paid over one-half of the cost of support for Candance.

1- Writing the system of equations:

The price of a cup of coffee is denoted by c while the price of a spaghetti is denoted by s

We are given that:

4 cups of coffee and 6 spaghetti cost $20.5

This means that:

4c + 6s = 20.5 ................> equation 1

We are also given that:

1 cup of coffee and 3 spaghetti cost $8.75

This means that:

c + 3s = 8.75 .................> equation 2

2- Solving the equations using substitution methods:

From equation 2:

c = 8.75 - 3s ................> I

Substitute with I in equation 1 and solve for s as follows:

4c + 6s = 20.5

4(8.75 - 3s) + 6s = 20.5

35 - 12s + 6s = 20.5

35 - 6s = 20.5

6s = 14.5

s = $2.41667

Substitute with s in I to get c:

c = 8.75 - 3s

c = 8.75 - 3(2.41667) = 1.4999 = $1.5

3- getting price for 1 cup of coffee and 1 spaghetti:

c + s = 1.5 + 2.41667 = $3.91667

Hope this helps :)

Answer:

[tex]\large\boxed{\dfrac{5}{4}}[/tex]

Step-by-step explanation:

[tex]a_1=20\\\\a_2=\dfrac{20}{2}=10\\\\a_3=\dfrac{10}{2}=5\\\\a_4=\dfrac{5}{2}\\\\a_5=\dfrac{\frac{5}{2}}{2}=\dfrac{5}{2}\cdot\dfrac{1}{2}=\dfrac{5}{4}[/tex]