prove algebraically that the straight line with equation x=2y+5 is a tangent to the circle with equation x^2+y^2=5
I have gotten 4/5 marks but I need to get 5/5
Thank you!

Answer:

the zeros are -3,-1, and 1

Step-by-step explanation:

zeros are nothing more that where the function crosses or touches the x-axis

Answer: Third Option

-3, -1, 1

Step-by-step explanation:

By definition, the zeros of a function f(x) are all the values x for which f(x) = 0.

In other words, the zeros of a function f(x) are the intersections of the graph of f(x) with the axis of x.

Therefore, to identify the zeros of the function shown, identify the values of x in which the graph intersects the horizontal axis.

You can see in the graph that these intersections occur in

[tex]x = -3\\x = -1\\x = 1[/tex]

Finally the zeros are: -3, -1, 1

Answer:

Step-by-step explanation:

Let f and s represent the amounts invested in the fund and in stocks, respectively. The problem statement gives rise to two equations:

  f + s = 15000 . . . . . . . Susan invested a total of 15000

  0.11f + (-0.05)s = 850 . . . . . her total return was 850

These can be solved by any of a variety of methods. Using elimination, we can multiply the second equation by 20 and add it to the first:

  20(0.11f -0.05s) +(f + s) = 20(850) +15000

  3.2f = 32000 . . . . . . . . . simplify

  f = 10000

  s = 15000 -f = 5000

Susan invested $10,000 in the fund and $5,000 in stock.

Arc PR measures 90 degrees because it is a minor arc that intercepts central angle PQR, which measures 90 degrees.

The measure of arc PR is 90 degrees. This can be determined from the given diagram, which shows a circle with arc PR labeled. We also know that central angle PQR measures 90 degrees.

Minor arcs are arcs that intercept central angles less than 180 degrees. Major arcs are arcs that intercept central angles greater than or equal to 180 degrees.

Since arc PR intercepts central angle PQR, which measures 90 degrees, arc PR must be a minor arc. Minor arcs have the same measure as their central angles, so arc PR must also measure 90 degrees.

Here is an alternative way to think about it:

The entire circle can be divided into 360 degrees.

Arc PR is a portion of the circle, so it must have some measure.

Central angle PQR also divides the circle into two portions.

Since arc PR intercepts central angle PQR, it must have the same measure as central angle PQR, which is 90 degrees.

Therefore, the measure of arc PR is 90 degrees.

For more such information on: Arc

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Answer:

(9,11)

Step-by-step explanation:

The given points are H(8,13) and K(10,9).

By using mid point formula,

(x, y) =(x1+x2, y1+y2)

2 2

= (8+10)2/, (13+9)/2

= 18/2, 22/2

= (9,11)

[tex](0. \infty)[/tex]

Since this is a logarithmic function, the domain is [tex](0. \infty)[/tex]. But what is the domain of a function? The domain of a function is the set of inputs. This is so, because for any logarithmic function[tex]y=log_{a}(x)[/tex], x must be greater than 0. So this function is continuous and has an x-intercept at [tex](1,0)[/tex], and y increases as x increases. Finally, its graph is shown below.

Answer:

  square feet

Step-by-step explanation:

Units multiply the same way any variable does:

  (x ft)(y ft) = x·y ft·ft = x·y ft² . . . . . . the units of the product are square feet

Answer:

Square feet

Step-by-step explanation:

The area of the object will be measured in square feet.

Hope this helps!

Answer:

8x-6x=-18

8x-6x=2x

2x=-18

-18/2=-9

x=-9

Step-by-step explanation:

Answer:

1.39x=15

Step-by-step explanation:

each song is worth 1.39 dollers

If there are x songs, the total value would be 1.39x

1.39x=15

Answer:

Mercedes can download new songs for $1.39 each. Write an equation to show how many songs she can download for $15.00.  

15x = 1.39

15 + x = 1.39

1.39x = 15

1.39 + x = 15

Step-by-step explanation:

The equation is the following:

1.39x = 15

15 $ is what you have to download the songs, and each unit is 1.39 $, by clearing the X of the equation, it is 15 / 1.39, and the result is the number of songs that Mercedes can download.

Answer: 6 hours

Step-by-step explanation:

Given : The time taken by Company X to install chairs : [tex]t_1=10\text{ hours}[/tex]

The time taken by Company Y to install chairs : [tex]t_2=15\text{ hours}[/tex]

Then , the time taken (T) by both of them to install the chairs if they work together is given by :-

[tex]\dfrac{1}{T}=\dfrac{1}{t_1}+\dfrac{1}{t_2}\\\\\Rightarrow\ \dfrac{1}{T}=\dfrac{1}{10}+\dfrac{1}{15}\\\\\Rightarrow\dfrac{1}{T}=\dfrac{10}{60}\\\\\Rightarrow\ T=6[/tex]

Hence, it will take 6 hours to the two companies if they working together .

Answer:

x=13°

Step-by-step explanation:

If BE is an angle bisector, then it divides the angle into two equal angles. This means that

∠ABE=∠EBC

Since ∠ABE=2x+20 and ∠EBC=4x-6, we have

2x+20=4x-6

2x-4x=-6-20

-2x=-26

2x=26

x=13°

Answer:

I believe it's A.

Step-by-step explanation:

Because look at the parts: The number x /  is equal to / another number n / plus / the square root of 3.

Hope my answer has helped you!

For this case we must express in an algebraic way the following expression:

"The number x is equal to another number n plus the square root of 3"

So:

The same "x" number is represented as:

[tex]x =[/tex]

A number "n" plus the square root of three is represented as:

[tex]n + \sqrt {3}[/tex]

So, the complete expression is:

[tex]x = n + \sqrt {3}[/tex]

Answer:

Option A

If we use 3.14 as pi, the areas of these circles are 415.265 square units (I recommend rounding up to 415.27 unless it says otherwise).

Step-by-step explanation:

To find the area of a circle, square the radius and multiply it by pi. To find the radius, we divide the diameter by 2 to get 11.5. Then, square 11.5 to get 132.25 and multiply by pi, or 3.14, to get 415.265, rounding up to 415.27 square units.

Answer:

(6, 3)

Step-by-step explanation:

Given the 2 equations

3x + 6y = 36 → (1)

3x - 6y = 0 → (2)

Add the 2 equations term by term to eliminate the y- term

(3x + 3x) + (6y - 6y) = (36 + 0)

6x = 36 ( divide both sides by 6 )

x = 6

Substitute x = 6 into either of the 2 equations and solve for y

(1) : 18 + 6y = 36 ( subtract 18 from both sides )

6y = 18 ( divide both sides by 6 )

y = 3

Solution is (6, 3)

Answer:

the solution is (6, 3)

Step-by-step explanation:

Subtract the second equation from the first, as indicated:

 3x+6y=36

-( 3x-6y=0)

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

      12y = 36.  Then y = 36/12 = 3.  

Subbing 3 for y in the second equation, we get 3x - 6(3) = 0, or 3x = 18, or x = 6.

Thus, the solution is (6, 3).

Answer:

Step-by-step explanation:

(–1)8 + (–1)7 + –16 + –14 – (–1)2 = -8 -7 -16 -14 +2 = -45+2 = - 43

Answer:

A

Step-by-step explanation:

[tex]\frac{1}{5} (7-3b) > 2[/tex]

[tex]=> 7-3b > 10\\=> 7-10 > 3b\\=> -3 > 3b\\=> -1 > b[/tex]

Answer:

C)

Explanation:

Movement along a vector is compared by adding, subtracting, multiplying, or dividing the values respectively.

1. 10 in. to millimeters: 254.00 mm

2. 60 ft. to meters: 18.29 m

3. 4.5 in. to millimeters: 114.30 mm

4. 12 U.S. quarts to liters: 11.36 L

5. 25 feet per second to meters per second: 7.62 m/s

6. 100 miles to kilometers: 160.93 km

To convert inches to millimeters, we use the conversion factor 1 inch = 25.4 millimeters. Therefore, for 10 inches, the calculation is: [tex]\(10 \, in. \times 25.4 \, \frac{mm}{in.} = 254.00 \, mm.\)[/tex]

For the conversion from feet to meters, the conversion factor is 1 foot = 0.3048 meters. Thus, for 60 feet, the calculation is: [tex]\(60 \, ft. \times 0.3048 \, \frac{m}{ft.} = 18.29 \, m.\)[/tex]

Converting inches to millimeters again, using the same conversion factor, we get [tex]\(4.5 \, in. \times 25.4 \, \frac{mm}{in.} = 114.30 \, mm.\)[/tex]

Moving on to quarts to liters, 1 U.S. quart is approximately 0.94635 liters. For 12 quarts, the conversion is [tex]\(12 \, qts \times 0.94635 \, \frac{L}{qt} = 11.36 \, L.\)[/tex]

For the speed conversion from feet per second to meters per second, we use the conversion factor 1 ft/s = 0.3048 m/s. Thus,[tex]\(25 \, ft/s \times 0.3048 \, \frac{m}{ft} = 7.62 \, m/s.\)[/tex]

Finally, for miles to kilometers, the conversion factor is 1 mile = 1.60934 kilometers. Hence, [tex]\(100 \, miles \times 1.60934 \, \frac{km}{mile} = 160.93 \, km.\)[/tex]

Answer:1. 10 in. to millimeters: 254.00 mm2. 60 ft. to meters: 18.29 m3. 4.5 in. to millimeters: 114.30 mm4. 12 U.S. quarts to liters: 11.36 L5. 25 feet per second to meters per second: 7.62 m/s6. 100 miles to kilometers: 160.93 km

Step-by-step explanation:

Step-by-step explanation:

Use the distance formula:

d² = (x₂ − x₁)² + (y₂ − y₁)²

d² = (-3 − -12)² + (-8 − -11)²

d² = 9² + 3²

d² = 90

d = 3√10

Answer:

1

Step-by-step explanation:

To evaluate (g ￮ f)(0), substitute x = 0 into f(x) then substitute the value obtained into g(x), that is

f(0) = 5(0) + 1 = 0 + 1 = 1, then

g(1) = 1³ = 1

Answer:

B.

Step-by-step explanation:

There are 5 total 6-packs of cola. 1 is cherry and the other is vanilla. 2 out of 5 are the flavors. This means you have a 2 in 5 chance of getting a cherry or vanilla cola.

Final answer:

The probability of randomly choosing a cherry cola or vanilla cola from all the cans available is 2/5, since there are 12 such cans out of a total of 30 cans.

Explanation:

To find the probability that a can of cola chosen at random will be either cherry cola or vanilla cola, we first need to count the total number of cans and then count the number of cherry and vanilla cola cans.

There are 2 six-packs of regular cola, which amounts to 12 cans. There is 1 six-pack each of diet cola, cherry cola, and vanilla cola, which adds up to 6 + 6 + 6 = 18 cans. In total, there are 12 + 18 = 30 cans of cola.

Out of these, there are 6 cans of cherry cola and 6 cans of vanilla cola, totalling 12 cans. Thus, the probability of choosing a cherry or vanilla cola is the number of cherry and vanilla cans divided by the total number of cans, which is 12/30.

When we simplify 12/30, we get 2/5. Therefore, the correct answer is B. 2/5.

Answer:

Area = x + 3 + [tex]\frac{2}{5x}[/tex]

Step-by-step explanation:

Volume = 5x² + 15x + 2

Height = 5x

Area = Volume ÷ Height

Area = 5x²/5x + 15x/5x + 2/5x

Area = x + 3 + 2/5x

Answer:

x+3+2/5x

Step-by-step explanation:

Answer:

7.08

Choice A

Step-by-step explanation:

From the right-angled triangle we have been given the following;

One angle - 33 degrees

The hypotenuse - 13 units

We are required to determine the length of the side, opposite the angle, marked x.

Using the Mnemonic; SOHCAHTOA

The sine of an angle is; (opposite side)/(hypotenuse)

Therefore;

sin 33 = x/13

x = 13 * sin 33

x = 7.080

Answer: A

Step-by-step explanation:

Answer:

a. 50 mph.

b. 16 mph.

Step-by-step explanation:

Convert minutes to hours using dimensional analysis:

[tex]\displaystyle \rm 24 \; minutes \times \frac{1\; hour}{60\; minutes} = \frac{2}{5}\; hours[/tex].

Average speed is distance traveled over time taken:

[tex]\displaystyle \text{Average Speed} = \frac{\text{Distance Traveled}}{\text{Time Taken}} = \rm \frac{20\; miles}{\dfrac{2}{5}\; hours} = (20 \times \frac{5}{2})\; mph= 50\; mph[/tex].

Similarly,

[tex]\displaystyle \text{Time Taken} = \rm 75 \; minutes \times \frac{1\; hour}{60\; minutes} = \frac{5}{4}\; hours[/tex].

[tex]\displaystyle \text{Average Speed} = \frac{\text{Distance Traveled}}{\text{Time Taken}} = \rm \frac{20\; miles}{\dfrac{5}{4}\; hours} = (20\times \frac{4}{5})\; mph= 16\; mph[/tex].

Answer:

Option C.

Step-by-step explanation:

In the given triangles XWV and XYZ we have to prove both the triangles are congruent.

Since side VW ≅ side YZ (Given)

∠WVX ≅ ∠XYZ (Given)

And by AAS theorem, we should prove ∠VXW = ∠YXZ

Since AAS theorem says, if two adjacent or corresponding angles and one opposite side of these angles are equal then the given triangles will be congruent.

Therefore, Option C. will be the answer.

Answer:

Prove that VXW TO YXZ by vertical angles

Answer:

The answer to your problem is 13%

There are 4 male freshmen and 30 students total.

Divide the amount of male freshmen by the amount of students and turn it into a percentage.

4/30= 0.1333 = 13%

Answer:

AC = 18.1 cm

Step-by-step explanation:

Construct a line from point B perpendicular to the line AD and mark it as E on line AD. Now you have a right triangle ABE with AB = 16 cm and AE = AD - BC

so AE = 11 cm - 4 cm = 7 cm

You can find BE by using Pythagorean theorem

BE^2 = AB^2 - AE^2

BE^2 = 16^2 - 7^2

BE^2 = 256 - 49

BE^2 = 207

BE = 14.4 cm

Draw a line from A to C, you have a right triangle ACD with AD = 11cm and CD = BE = 14.4 cm

Using Pythagorean theorem

AC^2 = AD^2 + CD^2

AC^2 = 11^2 + 207

AC^2  = 121 + 207

AC^2 =  328

AC = 18.1 cm

[tex]\Delta=5^2-4\cdot1\cdot7=25-28=-3[/tex]

[tex]\Delta<0[/tex] so 0 solutions.

Answer:

No Real roots to this Quadratic Equation

Step-by-step explanation:

Our Quadratic equation is given as

[tex]x^2+5x+7=0[/tex]

In order to find that do we have the real roots of a quadratic equation , the Discriminant must be greater or equal to 0. The Discriminant is denoted by D and given by the formula

[tex]D= b^2-4ac[/tex]

Where b is the coefficient of the middle term containing x, a is the coefficient of the term containing [tex]x^{2}[/tex] and the c is the constant term.

Hence we have

a = 1 , b = 5 and c = 7

Calculate D

[tex]D=b^2-4ac\\D=5^2-4*1*7\\D=25-28\\D=-3[/tex]

Hence we see that the Discriminant (D) is less than 0, our answer is no real roots to this quadratic equation.

Answer:

8 * 2

Step-by-step explanation:

When you draw the rectangle make it an 8 units by 2 units rectangle.

Answer:

540 degrees

Step-by-step explanation:

We can find the sum of the interior angles by using the formula (n - 2) * 180.

n: represents the total number of angles in the polygon

We can determine that polygon contains 5 angles, which means you would substitute the n variable with. Then you would simply follow the order of operation (ex: parentheses first, multiplication next, etc.) to find our answer.

(5 - 2) * 180

Solve the contents inside the parentheses first, as mentioned above.

(5 - 2) * 180

(5 - 2) = 3

So, we are left with

3 * 180

Now you'd multiply 3 * 180 and the product of that represents the sum of the measures of the interior angles of the polygon.

3 * 180 = 540

In conclusion, the sum of the measures of the interior angles is 540 degrees.

Answer:

540

Step-by-step explanation: