Determine two pairs of polar coordinates for the point (5, 5) with 0° ≤ θ < 360°.


a. (5 square root 2, 225°), (-5 square root 2, 45°)

b. (5 square root 2, 315°), (-5 square root 2, 135°)

c. (5 square root 2, 135°), (-5 square root 2, 315°)

d. (5 square root 2, 45°), (-5 square root 2, 225°)

Find an equation in standard form for the hyperbola with vertices at (0, ±9) and foci at (0, ±10).

a. y squared over 81 minus x squared over 100 = 1
b. y squared over 81 minus x squared over 19 = 1
c. y squared over 19 minus x squared over 81 = 1
d. y squared over 100 minus x squared over 81 = 1

Answer:

$3.55/workout

Step-by-step explanation:

Total cost:  $39 + ($27.50/month)(12 months) = $369

Number of visits per year:  (2 visits/week)(52 weeks/year) = 104 visits/year

Dividing the total cost by 104 visits/year results in:

 $369

--------------- = 3.55

104 visits

Each workout cost him $3.55. Each workout cost is obtained by the total cost and the number of the visit per year.

It is the sum of the variable cost and the fixed cost. The total cost is the minimum dollar cost of producing some quantity of output.

Registration fee = $39

Monthly fee = $27.50

No of visit a week for a year= 2

Total cost is found as;

Total cost = registration fee+monthly fee ×no of month

Total cost =  $39 + ($27.50/month)(12 months)

Total cost =$369

Number of visits per year= visits/week×no of week

Number of visits per year= (2 visits/week)(52 weeks/year)

Number of visits per year = 104 visits/year

When you divide the entire cost by 104 visits per year, you get:

Each workout cost = $369/104

Each workout cost =$3.55

Hence, each workout cost him $3.55

To learn more about the total cost, refer to the link;

https://brainly.com/question/14927680

#SPJ2

Answer:

Step-by-step explanation:

1 heads

1 tails

2 heads

2 tails.

That's all you can write given the constraint.

Answer:

Kameron has 5 quarters in his wallet

Step-by-step explanation:

Let

x----> the number of nickels

y----> the number of quarters

remember that

1 nickel=$0.05

1 quarter=$0.25

we know that

x=3y -----> equation A

0.05x+0.25y=2

Multiply by 100 both sides

5x+25y=200

Simplify

x+5y=40 -----> equation B

Substitute equation A in equation B

(3y)+5y=40

8y=40

y=5 quarters

x=3(5)=15 nickels

Final answer:

By setting up and solving equations based on the value of quarters and nickels and their proportions, we can determine that Kameron has 5 quarters in his wallet.

Explanation:

Finding the Number of Quarters in Kameron's Wallet

To solve Kameron's problem, we can set up two equations based on the given information. Let's define Q as the number of quarters and N as the number of nickels Kameron has. Since we know that the number of nickels is three times the number of quarters, we can express this as N = 3Q.

Next, we calculate the monetary value of the quarters and nickels. Each quarter is worth 25 cents, and each nickel is worth 5 cents. Since the total amount is two dollars, which is 200 cents, we can write the equation 25Q + 5N = 200.

Substituting N with 3Q in the second equation, we get 25Q + 5(3Q) = 200, which simplifies to 40Q = 200. Solving for Q gives us Q = 200 / 40 = 5, so Kameron has 5 quarters in his wallet.

Answer:

D

Step-by-step explanation:

√(-49)

Let's rewrite this as:

√(-1) √(49)

√49 is 7, and √-1 is i.  Therefore:

7i

Answer D.

The expression √(-49) can be rewritten using the Imaginary unit "i" as follows:

[tex]\sqrt(-49) = \sqrt(49 \times (-1)) = \sqrt49 \times \sqrt(-1) = 7i[/tex]

So, the correct answer is option D) 7i.

Here, rewrite the expression √(-49) using the imaginary unit "i," you can express it as the square root of (-1) multiplied by the square root of 49. This is because the square root of -1 is represented as "i."

[tex]\sqrt(-49) = \sqrt((-1) \times 49)[/tex]

Now, we can factor out the square root of 49, which is 7:

[tex]\sqrt(-1 \times 49) = \sqrt(-1) \times \sqrt(49) = i \times 7[/tex]

So, √(-49) can be expressed as 7i.

The correct answer is:

D) 7i

Thus, √(-49) is equal to 7i, indicating that it is a complex number with a real part of 0 and an imaginary part of 7. option D) 7i is correct choice .

For more such questions on Imaginary unit

https://brainly.com/question/30967533

#SPJ3

Answer:

[tex] y^2 + 8y + 16 [/tex]

Step-by-step explanation:

[tex] (6y^2 + 2y + 5) - (5y^2 - 6y - 11) = [/tex]

The first set of parentheses is unnecessary, so it can just be removed.

[tex] = 6y^2 + 2y + 5 - (5y^2 - 6y - 11) [/tex]

To remove the second set of parentheses, you must distribute the negative sign that is to its left. It changes every sign inside the parentheses.

[tex] = 6y^2 + 2y + 5 - 5y^2 + 6y + 11 [/tex]

Now you combine like terms.

[tex] = 6y^2 - 5y^2 + 2y + 6y + 5 + 11 [/tex]

[tex] = y^2 + 8y + 16 [/tex]

Answer:

u² – 11u + 24 = 0 where u = (x² – 1)

Step-by-step explanation:

Given the equation;

(x² – 1)² – 11(x² – 1) + 24 = 0

We can let;

u = x² - 1

Substituting the value of u in the equation we get;

(u)² - 11 (u) + 24 = 0

u²- 11u + 24 = 0

Therefore;

The quadratic equation that is equivalent to the equation is;

u² – 11u + 24 = 0 where u = (x² – 1)

Answer:

option 1

Step-by-step explanation:

Start with

[tex]\vec v=x\,\vec\imath+y\,\vec\jmath[/tex]

as a template for the vector [tex]\vec v[/tex]. Its magnitude is 4, so

[tex]\|\vec v\|=\sqrt{x^2+y^2}=4[/tex]

Its component in the [tex]\vec\imath[/tex] direction is twice the component in the [tex]\vec\jmath[/tex] direction, which means

[tex]x=2y[/tex]

So we have

[tex]\sqrt{(2y)^2+y^2}=\sqrt{5y^2}=4\implies y^2=\dfrac{16}5\implies y=\pm\dfrac4{\sqrt5}[/tex]

and

[tex]x=\pm\dfrac8{\sqrt5}[/tex]

Lastly, rationalize the denominator:

[tex]\dfrac1{\sqrt5}\cdot\dfrac{\sqrt5}{\sqrt5}=\dfrac{\sqrt5}5[/tex]

So we end up with two possible answers,

[tex]\vec v=\pm\left(\dfrac{8\sqrt5}5\,\vec\imath+\dfrac{4\sqrt5}5\,\vec\jmath\right)[/tex]

Final answer:

The vector v with a magnitude of 4 and i-component being twice the j-component can be found by solving for y in the equation of magnitude based on the given conditions and then determining the i and j components accordingly. The result is the vector v = (8√5 i + 4√5 j) / 5.

Explanation:

To find a vector v whose magnitude is 4, and whose i-component is twice its j-component, we can let the i-component be 2y and the j-component be y. Using the Pythagorean theorem for two-dimensional vectors, we can write the equation for magnitude as v = √((2y)^2 + y^2). Given that the magnitude is 4, the equation becomes:

4 = √(4y^2 + y^2)

4 = √(5y^2)

16 = 5y^2

y^2 = ⅔

y = √(⅔)

y = √(⅔)

y = √(⅔)

y = √(⅔)

y = √(⅔)

y = √(⅔)

(2.0 s) gives us the direction in unit vector notation. The magnitude of the acceleration is à(2.0 s)| = √√5.0² + 4.0² + (24.0)² = 24.8 m/s².

Using the value of y we calculated, the components of vector v are:

i-component = 2y = 2(⅔) = 8√5 / 5

j-component = y = ⅔ = 4√5 / 5

So the vector v can be expressed as v = (8√5 i + 4√5 j) / 5.

Answer:

Option C: 90+90 Sq. Root of 2

Step-by-step explanation:

First we find the distance from second base to home plate.  This is the diagonal of the square, which splits it into two right triangles.

Each right triangle will have legs of 90 feet.  We use the  Pythagorean theorem to find the length of the diagonal (the hypotenuse of the right triangle):

a² + b² = c²

90² + 90² = c²

8100 + 8100 = c²

16200 = c²

Take the square root of each side:

√(16200) = √(c²)

Simplifying √16200, we find the prime factorization:

16200 = 162(100)

162 = 2(81)

81 = 9(9) [Since this is a perfect square, we can stop; we know we take this out of the radical.]

100 = 10(10) [Since this is a perfect square, we can stop; we know we take this out of the radical.]

√16200 = √(9²×10²×2) = 9×10√2 = 90√2

This means the distance from 1st to 2nd and then from 2nd to home would be

90 + 90√2

Answer:

Use combinations because order does not matter, 1001, 0.36

Step-by-step explanation:

Answer: Combination method is used for counting.  There are 1001 possible outcomes and there is probability of 0.36 of getting two girls and two boys are on the committee.

Step-by-step explanation:

Since we have given that

Total number of members = 14

Number of girls = 9

Number of boys = 5

We will use "Combination method " to count the compound probability.

So, the total number of possible outcomes is given by

[tex]^{14}C_4\\\\=1001[/tex]

The probability that two girls and two boys are on the committee is given by

[tex]\dfrac{^9C_2\times ^5C_2}{^{14}C_4}\\\\=\dfrac{360}{1001}\\\\=0.3596\\\\=0.36[/tex]

Hence, there are 1001 possible outcomes and there is probability of 0.36 of getting two girls and two boys are on the committee.

I. need. more info. to solve it sorry

Answer:

Option A. 2/3

Step-by-step explanation:

we know that

If angle theta is in Quadrant 1

then

The value of cos(theta) is positive and the value of tan(theta) is positive

Remember that

tan(theta)=sin(theta)/cos(theta)

In this problem we have

tan(theta)*cos(theta)=[sin(theta)/cos(theta)]*cos(theta)=sin(theta)

therefore

tan(theta)*cos(theta)=sin(theta)=2/3

Final answer:

The value of (tan theta)(cos theta) is 2/3.

Explanation:

To find the value of (tan theta)(cos theta), we can use the given value of sin theta and the fact that sin² θ + cos² θ = 1.

Since the value of sin theta is known to be 2/3, we can square this value to find sin² θ = (2/3)² = 4/9.

Using the identity sin² θ + cos² θ = 1, we can solve for cos² θ by subtracting sin² θ from 1. This gives us cos²θ = 1 - 4/9 = 5/9.

Finally, we can calculate (tan θ)(cos θ) by multiplying tan θ = sin θ/ cos θ = (2/3) / [tex]\sqrt{5/9[/tex] = (2/3) / ([tex]\sqrt{5[/tex]/3) = 2 / [tex]\sqrt{5[/tex] and cos θ = [tex]\sqrt{5/9[/tex]. Therefore, (tan θ )(cos θ ) = (2 / [tex]\sqrt{5[/tex]) * [tex]\sqrt{5/9[/tex] = 2 / 3.

A z-score is a standardized value that represents the number of standard deviations a given score is above or below the mean in a normal distribution. In this case, the area under the standard normal curve is 0.1271, and the corresponding z-score is approximately -1.14.

A z-score is a standardized value that represents the number of standard deviations a given score is above or below the mean in a normal distribution.

It allows for comparison of scores from different data sets with different means and standard deviations. In this case, we are given the area under the standard normal curve and asked to find the corresponding z-score.

To find the z-score, we can use a z-table, which shows the area under the normal curve to the left of each z-score. In the given problem, the area under the curve is 0.1271.

By looking up the closest area in the z-table, we find that the z-score is approximately -1.14.

Final answer:

The z-score represents the number of standard deviations a value is from the mean in a standard normal distribution.

Explanation:

The z-score represents the number of standard deviations a value is from the mean in a standard normal distribution. To find the z-score, we can use the z-table or a calculator. In this case, the area under the standard normal curve is given as 0.1271. Using the z-table, we can find the z-score that corresponds to this area and enter it in the box.

Answer:

[tex]f(x)=\dfrac{2x-1}{x+2}\\ \\f^{-1}(x)=\dfrac{-2x-1}{x-2}[/tex]

[tex]f(x)=\dfrac{x-1}{2x+1}\\ \\f^{-1}(x)=\dfrac{-x-1}{2x-1}[/tex]

[tex]f(x)=\dfrac{x+2}{-2x+1}\\ \\f^{-1}(x)=\dfrac{2-x}{-2x-1}=\dfrac{x-2}{2x+1}[/tex]

[tex]f(x)=\dfrac{2x+1}{2x-1}\\ \\y=f^{-1}(x)=\dfrac{1+x}{2(x-1)}[/tex]

[tex]f(x)=\dfrac{x+2}{x-1}\\ \\f^{-1}(x)=\dfrac{x+2}{x-1}[/tex] - extra

Step-by-step explanation:

1.

[tex]f(x)=y=\dfrac{2x-1}{x+2}\\ \\y(x+2)=2x-1\\ \\yx+2y=2x-1\\ \\yx-2x=-1-2y\\ \\x(y-2)=-1-2y\\ \\x=\dfrac{-1-2y}{y-2}\\ \\y=f^{-1}(x)=\dfrac{-2x-1}{x-2}[/tex]

2.

[tex]f(x)=y=\dfrac{x-1}{2x+1}\\ \\y(2x+1)=x-1\\ \\2xy+y=x-1\\ \\2xy-x=-1-y\\ \\x(2y-1)=-1-y\\ \\x=\dfrac{-1-y}{2y-1}\\ \\y=f^{-1}(x)=\dfrac{-x-1}{2x-1}[/tex]

3.

[tex]f(x)=y=\dfrac{x+2}{-2x+1}\\ \\y(-2x+1)=x+2\\ \\-2xy+y=x+2\\ \\-2xy-x=2-y\\ \\x(-2y-1)=2-y\\ \\x=\dfrac{2-y}{-2y-1}\\ \\y=f^{-1}(x)=\dfrac{2-x}{-2x-1}=\dfrac{x-2}{2x+1}[/tex]

4.

[tex]f(x)=y=\dfrac{2x+1}{2x-1}\\ \\y(2x-1)=2x+1\\ \\2xy-y=2x+1\\ \\2xy-2x=1+y\\ \\x(2y-2)=1+y\\ \\x=\dfrac{1+y}{2y-2}\\ \\y=f^{-1}(x)=\dfrac{1+x}{2(x-1)}[/tex]

5.

[tex]f(x)=y=\dfrac{x+2}{x-1}\\ \\y(x-1)=x+2\\ \\xy-y=x+2\\ \\xy-x=2+y\\ \\x(y-1)=2+y\\ \\x=\dfrac{2+y}{y-1}\\ \\y=f^{-1}(x)=\dfrac{x+2}{x-1}[/tex]

Answer:

100, 120

Step-by-step explanation:

The mean of the given data is 500/4, or 125.

If a score of 0 were added to this data, the mean would be smaller, because we'd have to divide the five scores by 5.  The mean would now be 100.

The median of the given data is the average of the middle two scores, that is, of 120 and 130.  It's 125.

If we were to add the score of 0 to the four data points, obtaining

0, 100, 120, 130, 150,

the median would be the middle number:  120.

Mean is the average of the data set and mode is the middle terms or average of the middle terms of the data set.

Given information-

The given data consists the values 100,120,130,150.

Total number of values is four.

Mean is the average of the given data.

The mean of the given data can be calculated as,

[tex]m=\dfrac{100+120+130+150}{4} [/tex]

[tex]m=\dfrac{500}{4} [/tex]

[tex]m=125[/tex]

For even terms the medium is the average of the middle terms.

The medium of the given data can be calculates as,

[tex]M=\dfrac{120+130}{2} [/tex]

[tex]M=125[/tex]

Adding a score of 0.

The data consists of the values will be 0,100,120,130,150.

Total number of values is five.

The mean of the given data can be calculated as,

[tex]m=\dfrac{0+100+120+130+150}{5} [/tex]

[tex]m=\dfrac{500}{5} [/tex]

[tex]m=100[/tex]

Medium for the odd terms is equal to the middle terms.

The medium of the given data can be calculates as,

For the

[tex]M=120[/tex]

Thus adding a score of 0 the mean of the given data is reduced with number 25 and the mode reduced with number 5.

Learn more about the mean and medium here;

https://brainly.com/question/11263643

Answer:

B. 13.26

Step-by-step explanation:

To go from the Degree-Minute-Second (DMS) system to a numeric one, we simply use this formula:

numeric = d + (min/60) + (sec/3600)

Where you take the degree number as is (13 in our case), then you divide the number of minutes by 60 (15 in our case) and the number of seconds by 3600 (36 in our case) and you add everything together.

So, if we plug in our numbers, we have

numeric = 13 + (15/60) + (36/3600)

numeric = 13 + 0.25 + 0.01

numeric = 13.26

Answer:

d. ≈ 37,106 ft

Step-by-step explanation:

The angle of depression to the plane to the airport is the same as the angle of elevation from the airport to the plane. Therefore, the angle of elevation form the airport to the plane is 6°.

Notice that the height of the plane is the opposite side of the angle of elevation and the ground distance is the adjacent side of the angle of elevation. To find ground distance we need to use a trig function to relate the opposite side and the adjacent side; that trig function is tangent:

[tex]tan(\alpha )=\frac{opposite-side}{adjacent-side}[/tex]

[tex]tan(6)=\frac{3900ft}{ground-distance}[/tex]

[tex]ground-distance=\frac{3900ft}{tan(6)}[/tex]

[tex]ground-distance=37106ft[/tex]

We can conclude that the plane's ground distance to the airport is approximately 37,106 feet

Answer:

180,000 m

Step-by-step explanation:

There are 60 seconds in a minute, so:

2 min × 60 s/min = 120 s

Distance = rate × time

d = 1500 m/s × 120 s

d = 180,000 m

To find out how many apple pieces are in the bowl when 1/4 of 12 fruit pieces are apples, divide 12 by 4, which equals 3. So, there would be 3 apples in the bowl.

Understanding fractions is an important part of mathematics. In this scenario, we have a total of 12 pieces of fruit in a bowl and we want to find out how many of those are apple pieces if 1/4 of the fruit pieces are apples.

Since there's a total of 12 pieces, we divide this number into 4 equal parts (fractions strips) to determine what one quarter (1/4) of the bowl would contain.

To visualize this, you can draw a rectangle and divide it into 4 equal horizontal sections (fractions strips), because 1/4 means one part out of four equal parts. When you divide 12 by 4, you get 3. So, each section of your fraction strip would represent 3 pieces of fruit. This means that if 1/4 of the pieces are apples, there are 3 apples in the bowl.

Answer:

[tex]\boxed{\text{144.33 m}^{2}}[/tex]

Step-by-step explanation:

The scale factor (C) is the ratio of corresponding parts of the two pyramids.  

The ratio of the areas is the square of the scale factor.

[tex]\dfrac{A_{1}}{ A_{2}} = C^{2}\\\\\dfrac{\text{327 m}^{2}}{A_{2}} = \left (\dfrac{1}{\frac{2}{3}}\right)^{2}\\\\ \dfrac{\text{327 m}^{2}}{A_{2}}= \dfrac{9}{4}\\\\\text{1308 m}^{2}= 9A_{2}\\\\A_{2} = \text{145.33 m}^{2}\\\text{The surface area of the smaller pyramid is \boxed{\text{145.33 m}^{2}}}[/tex]

We have three pythagoras:

4² + y² = z²

16² + y² = x²

x² + z² = 20²

Now let's think:

4² + y² = z²

y² = z² - 4²

16² + y² = x²

16² + z² - 4² = x²

x² + z² = 20²

16² + z²- 4² + z² = 20²

2z² = 20² - 16² + 4²

2z² = (2.10)² - (2^4)² + (2²)²

2z² = 2².10² - 2^8 + 2^4

z² = 2.10² - 2^7 + 2^3

z² = 200 - 128 + 8

z² = 208 - 128

z² = 80

z = √80

80 | 2

40 | 2

20 | 2

10 | 2

5 | 5

1

80 = 5.2^4

So

√80 = 4√5

z = 4√5

Answer:

216 degrees

Step-by-step explanation:

step 1

Find the circumference of the circle

The circumference of the circle is equal to

[tex]C=2\pi r[/tex]

we have

[tex]r=10\ in[/tex]

substitute

[tex]C=2\pi (10)[/tex]

[tex]C=20\pi\ in[/tex]

step 2

Find the measure of the arc if the length of the arc is 12π in

Remember that

The circumference of a circle subtends a central angle of 360 degrees

so

by proportion

[tex]\frac{360}{20\pi}=\frac{x}{12\pi}\\ \\x=360*12/20\\ \\x= 216\°[/tex]

Answer:

  646 child tickets are sold

Step-by-step explanation:

Let c represent the number of child tickets sold. Then (c-186) is the number of student tickets sold, and (c+234) is the number of adult tickets sold. The total number sold is ...

  (c -186) + c + (c+234) = 1986

  3c +48 = 1986 . . . simplify

  c + 16 = 662 . . . . divide by 3

  c = 646 . . . . . . . . . subtract 16

The number of child tickets sold is 646.

The number of child tickets sold is 646.

To find the number of child tickets sold at the theatre, we can define some variables and set up equations based on the information provided.

Let:

From the information given, we have the following relationships:

The total number of tickets sold is 1986:
x + y + z = 1986

There are 234 more adult tickets sold than child tickets:
z = y + 234

There are 186 more child tickets sold than student tickets:
y = x + 186

Now we can substitute the equations for z and y into the first equation:

This simplifies to:
x + 2y + 234 = 1986

Now, we substitute y using the equation y=x+186:

Replace y in the equation:
x + 2(x + 186) = 1752

This simplifies to:
x + 2x + 372 = 1752
3x + 372 = 1752

Now isolate x:
3x = 1752 − 372
3x = 1380
x = 31380​
x = 460

Now that we have the value for x, we can find y:

Finally, we calculate z to confirm:  

Now we can verify:
x + y + z = 460 + 646 + 880 = 1986

So the number of child tickets sold is y = 646.

Answer:

the graph of y=4 x+3 is a straight line that passes through the point (0,3) and (\frac{-3}{4},0)

Step-by-step explanation:

The graph of the exponential function y = 4ˣ + 3 is attached below.

An exponential function is in the form:

y = abˣ

Where y, x are variables, a is the initial value of y and b is the multiplication factor.

Given an exponential function of y = 4ˣ + 3

The graph of the exponential function y = 4ˣ + 3 is attached below.

Find out more on Exponential function at: https://brainly.com/question/12940982

Answer:

Any number between 36-49

Step-by-step explanation:

The number has to be higher then 35. It has to be less then 50 because any number 50 or above would be more then/equal to 35

Answer: x < 50

Explination:

The given equation is x - 15 < 35.

To solve you add 15 to both sides:

x - 15 + 15 < 35 + 15

And you are left with a simplified answer of x < 50.

Answer:

10 mph

Step-by-step explanation:

Let x mph be Devontre rate uphill, then x+20 mph its his rate downhill.

1. Time uphill:

[tex]\dfrac{5}{x}\ hours[/tex]

2. Time downhill:

[tex]\dfrac{5}{x+20}\ hours[/tex]

3. If it took him 20 minutes (1/3 hour) longer to ride uphill than downhill, then

[tex]\dfrac{5}{x}-\dfrac{5}{x+20}=\dfrac{1}{3}[/tex]

Solve this equation:

[tex]\dfrac{5(x+20)-5x}{x(x+20)}=\dfrac{1}{3}\\ \\\dfrac{100}{x(x+20)}=\dfrac{1}{3}\\ \\300=x(x+20)\\ \\x^2+20x-300=0\\ \\D=20^2-4\cdot (-300)=400+1200=1600\\ \\x_{1,2}=\dfrac{-20\pm \sqrt{1600}}{2}=\dfrac{-20\pm 40}{2}=-30,\ 10.[/tex]

The rate cannot be negative, thus, x=10 mph (rate uphill).

ANSWER

[tex]g(x) = \sqrt{x + 4} [/tex]

EXPLANATION

The parent square root function is

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

The translation

[tex]g(x ) = \sqrt{x + k} [/tex]

Will shift the graph of f(x) k units to left.

The translation

[tex]g(x) = \sqrt{x -k} [/tex]

will shift the graph of f(x) to the right by k units.

Therefore if f(x) is shifted 4 units to the left its new equation is:

[tex]g(x) = \sqrt{x + 4} [/tex]

Shifting a function left involves adding a value to the x-component. Hence, shifting the square root parent function, F(x) = √x, to the left by 4 units results in a new function F(x) = √(x+4).

When a function is shifted horizontally, it impacts the input or the x-values. A shift to the left is represented by the addition of a value to the x-component of the function. Hence, to shift the square root parent function, F(x) = √x, to the left by 4 units, you would add 4 to 'x' in the function, which results in a new function F(x) = √(x+4). "This function represents the original square root parent function shifted 4 units to the left".

https://brainly.com/question/36050732

#SPJ3

Answer:

C

Step-by-step explanation:

Since y will have same value, y doesn't really matter. Thus,

We can solve for y in the 2nd equation as:

-3x - y = 4

-3x - 4 = y

Now we can plug it into the first and solve for x:

-9x + 4y = 8

-9x + 4(-3x - 4) = 8

-9x - 12x - 16 = 8

-21x = 8 + 16

-21x = 24

x = 24/-21

x = -8/7

Correct answer is C.

Answer: Option C

C-8/7

Step-by-step explanation:

We have the following equations

 [tex]-9x + 4y = 8[/tex] and [tex]-3x - y = 4[/tex]

We want to find a value of x that satisfies both equations and obtains the same value of y.

To find the value of x, clear the value of y in both equations

[tex]-9x + 4y = 8\\\\-9x + 4y -8 = 0\\\\-9x -8 = -4y\\\\y = \frac{9}{4}x +2[/tex]

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

[tex]-3x - y = 4\\\\\-3x -y - 4 = 0\\\\y = -3x -4[/tex]

Now solve both equations and solve for x.

[tex]\frac{9}{4}x +2 = -3x -4\\\\\frac{21}{4}x = -4-2\\\\\frac{21}{4}x = -6\\\\21x = -24\\\\x = -\frac{24}{21}\\\\x = -\frac{8}{7}[/tex]

The answer is [tex]x = -\frac{8}{7}[/tex]

Answer:

(C) 1 : 511

Step-by-step explanation:

Possible outcome for every throw = 2 (head or tail)

Total possible outcome for 9 throws

= 2⁹

= 512

Odd of getting all head

= 1 : 511

The odds in favor of getting all heads on nine coin tosses is 1 to 512.

The odds in favor of getting all heads on nine coin tosses can be calculated as the number of favorable outcomes divided by the number of possible outcomes. In this case, we want all nine coin tosses to result in heads, which is only 1 favorable outcome. The total number of possible outcomes for nine coin tosses is 2^9 = 512.

Therefore, the odds in favor of getting all heads on nine coin tosses is 1 to 512. Comparing this to the options given, the correct answer is A. 1 to 508.

https://brainly.com/question/31687847

#SPJ2

Answer:

Step-by-step explanation:

The information given in the problem statement lets you write two equations relating box weights (L for the large box weight; S for the small box weight).

  2L +3S = 78 . . . . . . weight of the first collection of boxes

  6L +5S = 180 . . . . . weight of the second collection of boxes

We can subtract 3S from the first equation and multiply it by 3 and we have ...

  2L = 78 -3S . . . . . . subtract 3S [eq3]

  6L = 234 -9S . . . . . multiply by 3

Now we have an expression for 6L that can substitute into the second equation:

  (234 -9S) +5S = 180

  234 -4S = 180 . . . . . . . . simplify

  54 -4S = 0 . . . . . . . . . . . subtract 180

  13.5 -S = 0 . . . . . . . . . . . divide by 4

  13.5 = S . . . . . . . . . . . . . add S

From [eq3] above, we can now find L.

  2L = 78 -3(13.5) = 37.5

  L = 37.5/2 = 18.75

The weight of the large box is 18.75 kg; the small box is 13.5 kg.

_____

A graphing calculator can provide an alternate means o finding the solution.

Answer:

24 girls.

Step-by-step explanation:

If the number of boys is x then:

x + 4/7 x = 66

x = 66  / 1 4/7

x = 66 *  7/11

= 6 * 7

= 42.

So the number of  girls is 66 - 42

= 24.

The quantitative relation between two amounts shows the number of times one value contains or is contained within the other:

The number of girls students is 24.

In the fifth grade at Lenape Elementary School, there are 4/7 as many girls as there are boys.

There are 66 students in the fifth grade.

The quantitative relation between two amounts shows the number of times one value contains or is contained within the other:

There are 66 students in fifth grade, and there is a 4:7 girl to boy ratio.

[tex]= \dfrac{66}{11}\\\\= 6[/tex]

Then,

the number of girls is = [tex]6 \times 4=24[/tex]

The number of boys is = [tex]6 \times 7 = 42[/tex]

Hence, the number of girls students is 24.

To know more about Ratio click the link given below.

https://brainly.com/question/4573383