This worksheet is a review of circles and lines, and will give you some practice with algebra and with graphing. Also, this worksheet introduces the idea of "tangent lines" to circles. Later on in Math 124, you'll learn how to find tangent lines to many other types of curves. Two circles, called C1 and C2, are graphed below. The center of C_1 is at the origin, and the center of C_2 is the point in the first quadrant where the line y = x intersects C1. Suppose C1 has radius 2. C2 touches the x and y axes each in one point. What are the equations of the two circles?

Answer:

12. <4 = 100°

Step-by-step explanation:

For number 12. angle m<2 is a corresponding angle to angle m<6 . So the equations, (3x+20) and (5x-20) are equal to each other.

So lets set them equal to each other:

(3x+20) = (5x-20)

40 = 2x

x = 20

Now we need to plug in the value of x into the equation of angle m<2, to find its angle.

(3x+20) = ?

(3(20)+20) = ?

= 80 degrees

m<2 = 80 degrees

We need to find <4

Since <4 and <2 share the same line and are supplementary angles (they add up to 180) we can subtract the value of <2 from 180 to find <4

180 - 80 = 100

So <4 is 100 degrees.

(i × j) × k = 0, is the vector, not with determinants, but by using properties of cross products.

The procedure for multiplying two vectors is called the cross product of the two vectors. The sign(×) of multiplication between two vectors indicates a cross product. It is a three-dimensional system-defined binary vector operation.

A cross product in three dimensions is a binary operation on two vectors. It generates a vector that is parallel to both vectors. A and B together form a vector product, which is represented by the symbol a b. The vector that results from it is parallel to both a and b. Cross products and vector products are similar terms.

As we know,

i × j = | i | × | j | × sin 90° × k

or, i × j = 1 × 1 × 1 × k

or, i × j = k

thus,  (i × j) × k = k × k

or,  (i × j) × k = 0

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The probability that Susan will select 3 "good" eggs are 8C3*3/4 and the probability that Susan will select at least one "bad" egg. is 8C1*1/4

Probability is a measure of how likely something is to occur. Calculating probability involves dividing the total number of outcomes by the number of possible ways an event may occur.

The probability is equal to the variety of possible outcomes. the total number of outcomes that might occur. For instance, there is only one method to receive a head and there are a total of two possible outcomes, hence the chance of flipping a coin and receiving heads is 1 in 2. (a head or tail). Writing P(heads) = 12

Hence,

The probability that Susan will select 3 "good" eggs are 8C3*3/4 and the probability that Susan will select at least one "bad" egg. is 8C1*1/4

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The point of intersection of the bird's paths can be found by setting up a system of equations consisting of y = 0.8x and y = -0.12x2 + 20 and solving for x. The x-coordinate of the point of intersection is approximately 3.33.

y = 0.8x

and

y = -0.12x2 + 20

First, set the two equations equal to each other:

0.8x = -0.12x2 + 20

Next, subtract 20 from both sides of the equation:

0.8x = -0.12x2

Then, divide both sides by 0.8:

x = -0.15x2

Finally, solve for x by dividing both sides by -0.15:

x = 10/3 or x ≈ 3.33

To find the point of intersection of the bird's paths, we can set up a system of equations consisting of y = 0.8x and y = -0.12x2 + 20. We then set the two equations equal to each other and solve for x. Subtracting 20 from both sides of the equation, we get 0.8x = -0.12x2. We then divide both sides of the equation by 0.8, giving us x = -0.15x2. Finally, by dividing both sides of the equation by -0.15, we can solve for x to find the point of intersection, which turns out to be x = 10/3 or approximately 3.33. In other words, the paths intersect at a point with a x-coordinate of approximately 3.33.

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An answer option which distinguishes the element that needs to be adjusted on the chart in the following scenario is: C. x-axis value.

In an experiment, there are two (2) main types of variables and these include the following:

In Mathematics, an independent variable can be defined as the variable that is being manipulated by an experimenter or researcher. This ultimately implies that, an independent variable is typically considered to be the cause in an experiment and it is represented by the x-axis value on a graph.

In this scenario, we can reasonably infer and logically deduce that the independent variable (x-axis value) represents the element that should be adjusted on Donna's demographic chart on population growth.

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Answer:

.18B = 4.5

B = 4.5/.18 = 450/18 = 50/2 = $25 bill

Answer:

Step-by-step explanation:

beaucoup pour votre aide !

Pour résoudre cette expression, nous allons appliquer la distributivité, c'est-à-dire multiplier chaque terme entre parenthèses par le nombre devant les parenthèses.

On commence par 4x + [3 - (7-x)], ce qui donne:

4x + (3 - 7 + x)

Ensuite, nous pouvons appliquer la distributivité à 4x-(x-2):

4x + (3 - 7 + x) - (4x - x + 2)

Enfin, nous pouvons réorganiser les termes pour simplifier l'expression:

4x + 3 - 7 + x - 4x + x - 2

En réarrangeant, nous obtenons:

-2 - 4 + 5x

Donc, l'expression complète est: -2 - 4 + 5x.

The bacteria count after 5 hours, given the initial bacteria count and the rate that the bacteria are disappearing is 59 bacteria

First, find the rate at which the bacteria are disappearing from the culture dish every hour. This rate is:

= 100 % - 90 %

= 10 %

This means that every hour, 10% of the bacteria are removed from the culture dish on account of the antibiotic.

In five hours therefore, the bacteria count on the culture dish would be:

= Starting number of bacteria x ( 1 - rate of decrease per hour) ^ number of hours

= 100 x ( 1 - 10 %) ⁵

= 100 x 90 %⁵

= 59 bacteria

In conclusion, after 5 hours of the antibiotic working on the culture dish, the number of bacteria left would be 59 bacteria.

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Answer:

Step-by-step explanation:

The dimensions of the garden will be 4m by 3m. To determine the dimensions of the garden, we need to use the formula A = l x w, where A is the area of the garden (12m), l is the length of the garden and w is the width of the garden.

We can then rearrange the formula to solve for either l or w. We can rearrange the formula to solve for l by dividing both sides of the equation by w: A/w = l.

We know that the area is 12m, so we can substitute 12m for A in the equation. We need to find the dimensions that use the least amount of fencing, so let's set w equal to 3m. We can then substitute 3m for w in the equation and solve for l: 12m/3m = 4m.

Therefore, the dimensions of the garden are 4m by 3m.

Answer:

1÷(5/2×(2×(8-2/5)-1))

1÷(5/2×(2×(6/5)-1))

1÷(5/2×(12/5-1))

1÷(5/2×7/5)

1÷(35/10)

1÷35/10

1×10/35

10/35

2/7

Answer: 16.8

Step-by-step explanation:

[tex]\frac{5.8}{r}=\tan 19^{\circ}\\\\\frac{r}{5.8}=\frac{1}{\tan 19^{\circ}}\\\\r=\frac{5.8}{\tan 19^{\circ}}}\\\\r \approx 16.8[/tex]

If the data from X2 is higher than the data from X1, then the researcher can conclude that using an octane booster increases gasoline mileage

X1: Gas mileage before using octane booster

X2: Gas mileage after using octane booster

The researcher is comparing X1 and X2, to determine if using an octane booster increases gasoline mileage.

1. The researcher selected a random sample of seven cars and drove them for two weeks without using the octane booster (X1).

2. The researcher then drove the same seven cars for two weeks with the octane booster (X2).

3. The researcher then compared the data from X1 and X2 to see if there was an increase in gasoline mileage.

4. If the data from X2 is higher than the data from X1, then the researcher can conclude that using an octane booster increases gasoline mileage.

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Answer:

Step-by-step explanation:

15x² - 2x - 1 = 0

15x² - 5x + 3x - 1 = 0

5x(3x - 1) + 3x - 1 = 0

(5x + 1)(3x - 1) = 0

x = -1/5, 1/3

8x² - 10x - 3 = 0

8x² - 12x + 2x - 3 = 0

4x(2x - 3) + 2x - 3 = 0

(4x+1)(2x-3) = 0

x = -1/4 , 3/2

16x² - 8x + 3 = 0

This question has complex answers as the D = 64 - 192 < 0

So, ignore this question. It is wrong or it has complex answers.

Use the quadratic formula for it.

9x² - 6x - 2 = 0

This also needs the quadratic formula as the answer is in roots.

8x² - 2x - 3 = 0

8x² - 6x + 4x - 3 = 0

2x ( 4x - 3) + 4x - 3 = 0

(2x + 1)(4x-3) = 0

x = -1/2 , 3/4

The complex conjugates for each of the following numbers

a. - 19 = -19

b. -25i = +25i

c. - 11 - 92i = 11 + 92i

d. 413i - 37 = -413i - 37

The term complex number in math is defined as the numbers that are expressed in the form of a+ib where, a,b are real numbers and 'i' is an imaginary number.

Here we have given that the list of complex number and here we need to find the complex conjugates for each of the following numbers:

As we all know that conjugate in Mathematics is formed by changing the sign of one of the terms in a binomial.

Based on the definition, here we have the general form a + bi as the conjugate as a - bi.

From this one we have identified that here we have only changed the sign of imaginary pat.

So, the complex conjugate of the given complex numbers are written as

=> a. - 19 = -19

Here we have only the number part so the sign remains constant

b. -25i = +25i

Here we have only the imaginary part so we have changed it to positive.

c. - 11 - 92i = 11 + 92i

Based on the complex conjugate rule the term must be changed.

d. 413i - 37 = -413i - 37

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The answer in the form of x,y is -7x + 10y  = 118.

A Cartesian plane (named after French mathematician Rene Descartes, who formalized its use in mathematics) is defined by two perpendicular number lines: the x-axis, which is horizontal, and the y-axis, which is vertical. Using these axes, we can describe any point in the plane using an ordered pair of numbers.

from given conditions, we get,

(-4, 9) and  10  left  7 down  puts her at  (  -4 - 10 , 9  - 7)  = ( -14, 2)

So,  the points  ( -4, 9)  and (-14,2)  are on the  line

Slope of this line  =   [ 2 - 9] / [ -14 - -4 ]  =  [ -7] / [ -10]  =  7/10

Equation of the line

y  = (7/10)(x - - 4)  + 9

y  = (7/10) ( x + 4)  + 9     multiply through by 10

10y = 7 (x + 4)  + 90

10y = 7x + 28  + 90

-7x + 10y  = 118

Therefore, the answer in the form of (x , y) is -7x + 10y  = 118

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Answer:

Step-by-step explanation:

The correct answer is: 4x4 + 8x2y2 – 3x3y – 7xy3. This is the standard form for the polynomial, where the terms are written in descending order. The terms in this polynomial are the 4x4 term, the 8x2y2 term, the -3x3y term, and the -7xy3 term.

Answer:

Select all the examples of the exponential function

a) y=3x-2

b) y=3^x

c) y=(1/2)^3x

d) y=3x^2

E) y=(1/2)^x

Answer:

44  is your answer

Step-by-step explanation:

According to the given vector, the value of the orthogonal projection of y onto u is <16, -8>

Here we have the vector values that is as follows:

Y= [8 -24],

u=[4 -2]

Now, based on the formula of the vector projection is written as,

=> [(y x u) / |u²| ] x u

Now, we have to calculate the value of the vector and it can be obtained by what we need to do is multiply the corresponding coordinates and then add up the results:

=> ⟨8,−24⟩⋅⟨4,−2⟩

=> (8)⋅(4)+(−24)⋅(−2)

When we simplify this one then we get the value as,

=>80.⟨8,−24⟩⋅⟨4,−2⟩

=> (8)⋅(4)+(−24)⋅(−2) = 80.

Similarly, now we have to calculate the value of  |u²| is written as,

Here we have the sum of squares of the absolute values of the coordinates is 

=> ∣4∣² + ∣−2∣² = 20.

Therefore, the magnitude of the vector is

=> √20 =  2√5

Thus the vector projection is written as,

=> [tex]\frac{8}{2\sqrt{5} }\times < 4,-2 >[/tex]

When we simplify this one then we get the resulting value of projection as <16, -8>

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For the graph of data given option C: The median 300 is the middle number is correct.

What is median?

In mathematics, the middle number in a sorted list of numbers is referred to as the median. By arranging the numbers, the middle number can be discovered. Ascending order is used to arrange the numbers. The middle number in the ordered set of numbers is referred to as the data set's median.

Draw the median table for the graph of values given -

Number    Frequency    ∑f

100            14                   14

200            6                    20

300            18                  38

400            12                  50

500            2                    52

600            12                  64

700             8                   72

The formula for median is -

Median = [n/2 + (n/2 + 1)] / 2

Median = [72/2 + (72/2 + 1)] / 2

Median = [36 + (36 + 1)] / 2

Median = 73/2

Median = 36.5

According to the table the ∑f value 36.5 corresponds to 300.

Therefore, the median 300 is the middle number.

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The margin of error is 1.6393 for the supplied values of  c, s, and n, which are 0.98, 3.3 and 22respectively.

what is margin ?

Margin is the term used to describe the equity that a trader has in their account. Using funds borrowed from a broker to buy stocks is referred to as "marging" or "buying on margin." Instead of a typical brokerage account, you must have a margin account to execute this. Beginning with your gross profit, which is the distinction between revenue and COGS, you may compute profit margin. Find the percentage of revenue that represents gross profit next. Calculate it by dividing your gross profit by your revenue. You can calculate your margin % by multiplying the sum by 100.

Given that,

standard deviation = s =  3.3

z is the 98% =  z score = 2.33

Sample size = n =22

Margin of error is expressed using the formula;

M = z * √s²/n

M = 2.33* √3.3²/22

M = 2.33* 0.7035

M = 1.6393

Therefore, the margin of error is 1.6393 for the supplied values of  c, s, and n, which are 0.98, 3.3 and 22respectively.

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If you are asked to find the 85th​ percentile, you are being asked to find an area corresponding to a​ z-score of 0.8.

The term percentile in math is defined as the area to the left of a particular data value.

According to the definition of percentile, here they are asking about the 85th percentile.

As we all know that​ z-score is not an area under the normal curve and the distances along the horizontal axis are represented by​ z-scores where as the regions under the curve are represented by areas.

Therefore, in order to find the z-score is a conversion that standardizes any value from a normal distribution to a standard normal distribution.

Then we have to convert the given percent into decimal form, then we get it as,

=> 85% = 0.85

Here we need to find the value from the z table then we get the resulting value as 0.8.

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An equation relating the total amount in a in Terry’s account to the number of years, t is ​A = P + P*(r/100)*t. Yes, the relationship is proportional.

An equation is a well-formed formula that connects two expressions with the equals sign to express the equality of those two expressions. For example, in French, an equation is defined as containing one or more variables, whereas in English, an equation is any well-formed formula that consists of two expressions connected with the equals sign.

Finding the values of the variables that result in the equality is the first step in solving an equation with variables. The unknown variables are also known as the variables for which the equation must be solved, and the unknown variable values that fulfill the equality are known as the equation's solutions.

An equation relating the total amount in a in Terry’s account to the number of years, t is ​A = P + P*(r/100)*t.

Where, A is total amount,

P is amount which Terry deposit,

r is rate of interest,

and t is number of years.

Yes, the relationship is proportional.

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The statements that are true about the triangle f d e and its dilated counterpart f' d' e' are: (1) The center of dilation was (0, 0). (2) The coordinates of f' d' e' are (negative 3, 1), (negative 3, 3), and (negative 2, 2). (3) f' d' e' is a similar triangle to f d e.

The triangle f d e and its dilated counterpart f' d' e' have specific properties that make them similar triangles. The center of dilation for the transformation was (0, 0). This means that the distance from the center of dilation to each point before and after the dilation was the same. The coordinates of triangle f d e were (negative 9, 3), (negative 9, 9), and (negative 6, 6). In order to obtain the coordinates of f' d' e', the dilation rule one-third(x,y) (one-third x, one-third y) was used. This means that the x and y coordinates of each point were divided by three. The result is that the new coordinates of f' d' e' are (negative 3, 1), (negative 3, 3), and (negative 2, 2). These new coordinates demonstrate that the triangle f d e and its dilated counterpart f' d' e' are similar triangles.

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Answer:

A. ∠F corresponds to ∠F'.

C. The distance from point D' to the origin is 1/3 the distance of point D to the origin.

E. △DEF ~△D'E'F'

Step-by-step explanation:

got it right on edge 23

3P=C-5 is the equation relating the number of carrots that Pio has compared to Claudine, Pio has 5 carrots when Claudine has 20 and  if pio has 10 then the number of carrots with Claudine are 35

Two or more expressions with an Equal sign is called as Equation.

Rustam has three times as many carrots as Pio

R=3P

Where  is Rustam, P is Pio and C is Claudine.

Rustam has 5 fewer carrots that Claudine.

R=C-5

3P=C-5 is the equation relating the number of carrots that Pio has compared to Claudine.

Now let us find the number of carrots Pio has when Claudine has 20

3P=20-5

3P=15

Divide both sides by 3

P=5

Pio has 5 carrots when  Claudine has 20.

Now if pio has 10 then the number of carrots with Claudine

3(10)=C-5

30+5=C

35=C

Hence, 3P=C-5 is the equation relating the number of carrots that Pio has compared to Claudine, Pio has 5 carrots when Claudine has 20 and  if pio has 10 then the number of carrots with Claudine are 35

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The volume of the stack affected will be 10,825.38 cubic millimeters.

Let r be the radius and h be the height of the cylinder.

Then the volume of the cylinder will be

V = π r²h cubic units

The table holding Juanita's pennies gets bumped, and the stack becomes slanted.

The radius of the cylinder is given as,

r = 19.05 / 2

r = 9.525 mm

Then the volume of the cylinder is calculated as,

V = π x (9.525)² x 38

V = 3.14 x 90.725 x 38

V = 10,825.38 mm³

The volume of the stack affected will be 10,825.38 cubic millimeters.

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Answer:

The volume of the stack affected will be 10,825.38 cubic millimeters.

Step-by-step explanation:

A number multiplied by 1 is the number itself. So,1 is a factor of every number.

1 is the factor of every number as one divides every number exactly, without leaving any remainder behind, and gives the quotient as the number itself.

1 is the greatest factor of itself and the smallest factor of any other number.

There are some properties of factors one:

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The solution to the given system is (2, 3, 5). This can be determined by solving the system of equations using elimination.

First, add the first equation to the second equation to eliminate the y-term:

5x + z = 7

Next, add the third equation to the first equation to eliminate the x-term:

3y + z = 3

Finally, substitute the expression for z into the expression for x and solve for y:

y = 3

Now that we have the values for x and y, substitute them into one of the original equations to solve for z:

2(2) - 3(3) + z = 0

z = 5

The solution is (2, 3, 5).