Given an isosceles triangle with a base length of 30 and a median (drawn from the vertex
angle) length of 21, what is the length of a leg?

The plumber charges $23 per hour, the plumber charges a fixed rate of $71 and If someone worked for 5.75 hours, their earnings would be $203.25

To find the plumber's hourly rate, we can use the given information and set up two equations:

3h + f = 140 (where h is the hourly rate and f is the fixed rate for the first job)

7h + f = 232 (where h is the hourly rate and f is the fixed rate for the second job)

We can solve for h by subtracting the first equation from the second equation:

4h = 92

h = 23

Therefore, the plumber charges $23 per hour.

To find the plumber's fixed rate, we can substitute h = 23 into one of the equations and solve for f:

3h + f = 140

3(23) + f = 140

69 + f = 140

f = 71

Therefore, the plumber charges a fixed rate of $71.

The equation that tells how much the plumber earns can be written as:

Earnings = (hourly rate x number of hours) + fixed rate

or E = 23h + 71

If someone worked for 5.75 hours, their earnings would be:

Earnings = (hourly rate x number of hours) + fixed rate

Earnings = (23 x 5.75) + 71

Earnings = 132.25 + 71

Earnings = $203.25

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Answer:

To find f(-8), we need to substitute -8 for x in the expression for f(x) and evaluate:

f(-8) = 3(-8)² + 9(-8) - 16

Simplifying this expression, we get:

f(-8) = 3(64) - 72 - 16

f(-8) = 192 - 72 - 16

f(-8) = 104

Therefore, f(-8) = 104 when f(x) = 3x² + 9x - 16.

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Answer:

66.666%

Step-by-step explanation:

the numbers on the dice would be 1,2,3,4,5,6

1,2,3,5 are all prime numbers.

4/6 =2/3 =66.666%

Answer:

Step-by-step explanation:

5(x - 3) ? x + 13

if x = 6

5(6 - 3) ? 6 + 13

15 ? 19

15 ≠ 19

Step-by-step explanation:

When substituting 6 for x, the equation becomes:

5(6 - 3) ?= 6 + 13

Now, we can solve both sides of the equation:

5(3) ?= 6 + 13

15 ?= 19

Since these are not equal, the equation is not true for x = 6.

The graph represents the valid region of the number of candles and hand soaps that Lexi can buy with her $50 budget.

To shade the region that satisfies the inequality, we need to determine which side of the line represents the valid region. Since the inequality is less than or equal to, the valid region is the one below the line.

Let x be the number of candles that Lexi buys and y be the number of hand soaps that she buys. The cost of x candles is 12.50x and the cost of y hand soaps is 5y. Lexi has $50 to spend, so we can write the following inequality:

12.50x + 5y ≤ 50

To graph this inequality, we first need to graph the boundary line, which is the equation obtained by replacing the inequality sign with an equal sign:

12.50x + 5y = 50

We can rewrite this equation in slope-intercept form as:

y = -2.50x + 10

To plot points on the boundary line, we can choose any two values of x and solve for the corresponding values of y. For example, if we let x = 0, then y = 10, so one point on the line is (0,10). If we let x = 4, then y = 0, so another point on the line is (4,0).

We can now graph the boundary line, which has a slope of -2.50 (meaning it goes down and to the right) and a y-intercept of 10 (meaning it intersects the y-axis at the point (0,10)). To switch between a solid and dotted line, select the "solid line" or "dotted line" option in the graphing tool.

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Answer:

she used 8 bags of mulch altogether.

Step-by-step explanation:

if this isn't correct, you may want to reword or specify the question.

The equation of the line with yellow point in slope intercept form is y = 7 / 6 x + 2.

The equation of a straight line can be represented in different form such as slope intercept form, point slope form, etc.

Therefore, let's represent the line with yellow point in slope intercept form.

Hence,

y = mx + b

where

Therefore, using (0, 2) and (6, 9).

m = 9 - 2 / 6 - 0

m = 7 / 6

Hence, let's find the y-intercept

y = 7 / 6 x + b

2 = 7 / 6(0) + b

b = 2

Therefore,

y = 7 / 6 x + 2.

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The observed frequency = 42, and the expected is 22.5.

option A.

The observed and expected frequencies for the boys participating in soccer is calculated as follows;

Total boys = 18 + 42 + 12 = 72

Total girls = 30 + 15 + 18 = 63

Total number of the students = 72 + 63 = 135

Ratio of boys = 72/135 = 0.533

Ratio of girls = 63 / 135 = 0.467

The observed and expected frequencies for the boys participating in soccer is calculated as follows;

Expected frequency = 0.534 x 42

= 22.4

Thus, the observed frequency = 42, and the expected is 22.5.

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Answer:

Observed: 42

Expected: 24

Step-by-step explanation:

If we simply go to the chart then we can directly see the observed frequency for boys participating in soccer is 42.

To find the expected frequency, we need to find the number of occurrences if the null hypothesis is true, which in this case, was that the three options are equally likely, or if the three options were all evenly distributed.

First, add up all the options in the boys column:

18 plus 42 plus 12 equals 72

If each of these three options were evenly distributed among the 72 boys, we would need to divide the total evenly between the three options:

72 divided by 3 equals 24

This means we would expect 24 boys to choose tennis, 24 boys to choose soccer, and 24 boys to choose swimming.

The predicted weight of a 12-week-old puppy is 25.5 pounds.

To predict the weight of a 12-week-old puppy using the line of fit equation y = 2x + 1.5, follow these steps:
1. Identify the value of x: In this case, x represents the puppy's age in weeks, so x = 12.
2. Plug the value of x into the equation: y = 2(12) + 1.5.
3. Solve the equation: y = 24 + 1.5.
4. Calculate the result: y = 25.5.
So, the predicted weight of a 12-week-old puppy is 25.5 pounds.

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Using the best of fit equation given , the predicted weight of a 12 - weeks old puppy would be 25.5lb

The line of fit is used to establish a mathematical relationship between two variables. A good line of fit would give a good mathematical relationship between related variables.

In the question above; our line of fit equation is y = 2x + 1.5

x = puppy's age ; y = weight

To obtain the value of y for any value of x ; we substitute either of the given value .

For x = 12

y = 2(12 ) + 1.5

y = 24 + 1.5

y = 25.5

Hence, weight of puppy after 12 weeks will be 25.5lbs

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The right Riemann sum is an overestimate.

The left Riemann sum is an underestimate.

For n=2, the interval [0,1] is divided into 2 subintervals of equal width, so Δx = (1-0)/2 = 1/2.

Left Riemann Sum with n=2:

The left endpoints of the subintervals are x=0 and x=1/2.

f(0) = e⁰ = 1

f(1/2) = [tex]e^1^/^2[/tex]

So, the left Riemann sum is:

Δx[f(0) + f(1/2)] = (1/2)[1 +[tex]e^1^/^2[/tex]] = (1/2) + (1/2)[tex]e^1^/^2[/tex]

sum = (1/2) + (1/2)[tex]e^1^/^2[/tex]

Right Riemann Sum with n=2:

The right endpoints of the subintervals are x=1/2 and x=1.

f(1/2) = [tex]e^1^/^2[/tex]

f(1) = e¹ = e

So, the right Riemann sum is:

Δx[f(1/2) + f(1)] = (1/2)[[tex]e^1^/^2[/tex] + e] = (1/2)[tex]e^1^/^2[/tex] + (1/2)e

sum = (1/2)[tex]e^1^/^2[/tex]+ (1/2)e

Since [tex]e^1^/^2[/tex] > 1, the right Riemann sum is an overestimate, and the left Riemann sum is an underestimate.

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Answer:

P(A and B) = P(A)P(B)

= (1/3)(1/2) = 1/6

= about .17 = about 17%

A description that best compare the graph of the functions is: B. the line for function A is steeper.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation:

y - y₁ = m(x - x₁)

Where:

First of all, we would find the slope of function B;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (-1 + 2)/(3 - 0)

Slope (m) B = 1/3.

At data point (0, -1) and a slope of 1/3, function B can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y + 1 = 1/3(x - 0)

y = 1/3(x) - 1

In conclusion, the line for function A is steeper because it has a greater slope than function B i.e 3 > 1/3.

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a The slope of line £ is 3/4.

b The equation for £ is y = 3/4x + 3.

c The radius of OC is 5.

d The distance from £ to OC along the y-axis is 3.

The slope of a line is the change in y over the change in x. In this case, the change in y is 3 and the change in x is 4. So, the slope of line £ is 3/4.

The equation for a line can be written in the form y = mx + b, where m is the slope and b is the y-intercept. In this case, the slope is 3/4 and the y-intercept is 3. So, the equation for £ is y = 3/4x + 3.

The radius of a circle is the distance from the center to any point on the circle. In this case, the center of the circle is at the origin, which is at (0, 0). The point on the circle is at (-4, 3). So, the radius of the circle is the distance from (0, 0) to (-4, 3).

This distance can be found using the Pythagorean theorem:

r² = 4² + 3²

r² = 25

r = 5.

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Answer: 30,620 people

Step-by-step explanation:

We will use the given formula for exponential growth.

➜ 1.55% / 100 = 0.0155

➜ 2022 - 2017 = 5 years

          [tex]A=Pe^{rt}[/tex]

          [tex]A=(28,337\;people)e^{(0.0155)(5\;years)}[/tex]

          [tex]A=(28,337\;people)e^{0.0775}[/tex]

          [tex]A=(28,337\;people)e^{0.0775}[/tex]

          [tex]A=30,620.4587 \approx 30,620\;people[/tex]

Answer:

To express the expression 2/5 - 4/y + 3 as a single fraction, we need to find a common denominator for the fractions involved.

The common denominator for 5 and y is 5y.

First, we'll rewrite 2/5 as an equivalent fraction with the denominator 5y:

2/5 = (2 * y)/(5 * y) = 2y/5y

Next, we'll rewrite 4/y as an equivalent fraction with the denominator 5y:

4/y = (4 * 5)/(y * 5) = 20/5y

Now, we can rewrite the expression with the common denominator 5y:

2y/5y - 20/5y + 3

Since the denominators are now the same, we can combine the numerators:

(2y - 20 + 3 * 5y)/(5y)

Simplifying further:

(2y - 20 + 15y)/(5y) = (17y - 20)/(5y)

Answer:

C. y = 1/3x + 4

Step-by-step explanation:

To find the equation of the line that passes through the given points, we can use the slope-intercept form of the equation of a line, which is:

y = mx + b

where m is the slope of the line and b is the y-intercept.

To find the slope of the line, we can use the formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are any two points on the line. We can choose the points (x1,y1) = (-3,3) and (x2,y2) = (6,6) from the table.

m = (6 - 3) / (6 - (-3)) = 3/9 = 1/3

Now that we have the slope, we can use the point-slope form of the equation of a line to find the y-intercept:

y - y1 = m(x - x1)

where (x1,y1) is any point on the line. We can choose the point (x1,y1) = (3,5) from the table.

y - 5 = (1/3)(x - 3)

Now we can solve for y to get the equation in slope-intercept form:

y = (1/3)x + (5 - 1/3*3)

y = (1/3)x + 4

Therefore, the equation of the line that passes through the given points is C) y= 1/3x + 4.

The length of the arc are

Arc MN =  72 degrees

Arc NQR = 180 degrees

Arc NQ = 108 degrees

Arc MRP =  193 degrees

Arc QR = 72 degrees

Arc QMR = 288 degrees

Arc PQ = 13 degrees

Arc PRN = 265 degrees

Arc MQN = 288 degrees

The relationship between central angle and intercepted arc is that they are equal. This is used in solving the length of arcs

hence we have that

angle ROQ = angle NOM =  72 degrees (vertical angles)

Arc MN = angle NOM =  72 degrees

Arc NQR = 180 degrees (semicircle)

Arc NQ

angle POQ = 180 - 72 - 95

angle POQ = 13

Arc NQ = 95 + 13 = 108 degrees

Arc MRP = 180 + 13 = 193 degrees

Arc QR = 72 degrees

Arc QMR = 360 - 72 = 288 degrees

Arc PQ = 13 degrees

Arc PRN = 360 - 95 = 265 degrees

Arc MQN = 360 - 72 = 288 degrees

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The y- intercept represents the anticipated number of gloves  vended on a day when the low temperature is 0 degrees.    

The terms you mentioned are  formerly included in the problem description.  The y- intercept of the equation is the value of y when x =  0. In the given line of fit equation,

y = -1.2 x 122, the y- intercept is 122.  The y- intercept represents the anticipated number of gloves  vended on a day when the low temperature is 0 degrees. In this case, when the low temperature is 0,

the store is  prognosticated to  vend 122 gloves. Keep in mind that this is an estimate grounded on the line of fit and may not be an exact value.

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The surface area of the triangular prism is 84 ft/2

The surface area of a triangular prism is found with: Area = bh + (s1 + s2 + s3)L.

Given a 4ft base, 3ft height, 5ft slant height, and 2ft length, we substitute to get:

Area = (4ft3ft) + 3(5ft*2ft) =

[tex]12ft^2 + 30ft^2 = 42ft^2.[/tex]

In the specified format, the surface area of the triangular prism is 84 ft/2.

This is because the format given is blank ft/2

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Could you provide the formula to calculate the surface area of a triangular prism, given dimensions of 4ft, 3ft, 2ft, and 5ft? The surface area should be presented as (blank ft/2).

Answer:

7/2

Step-by-step explanation:

7 x 4 / 8

= 7 x 1/2

= (7 x 1)/2

= 7/2

Note

1. When you see a fraction, first simplify the numerator and denominator.

That is,

In 4/8,

4 is the numerator

8 is the denominator

4/8 = 1/2

2. Multiply number with numerator, then divide it with the denominator

7 x 1/2

7 x 1 = 7

(7 x 1)/2 = 7/2

The x intercepts of the parabola with  vertex (-1,2) and y intercept (0,3) does not exist

From the question, we have the following parameters that can be used in our computation:

vertex (-1,2) and y intercept (0,3).

A parabola is represented as

y = a(x - h)² + k

Where

Vertex = (h, k)

Using the above as a guide, we have the following:

y = a(x + 1)² + 2

Also, we have

a(0 + 1)² + 2 = 3

So, we have

a = 1

This means that

y = (x + 1)² + 2

Set to 0 to calculate the x-intercepts

(x + 1)² + 2 = 0

This gives

(x + 1)² = -2

Take the square root

(x + 1) = comple numbers

Hence, the x intercepts of the parabola does not exist

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The required answer is mAD = 126°

Step 1: Recall Inscribed Angles of a Circle Theorem.

Step 2: It means m∠ABD ≡ m∠ACD. So, it can be written:

(11x - 3)° (8x + 15)°

Step 3: Evaluate for x:

11x - 3 = 8x + 15

X = 6

Step 4: Substitute x = 6 in 11x - 3 as:

11(6) - 3

Step 5: Evaluate for answer:

11 × 6 - 3

= 63

Step 6: Now recall Measure of an Inscribed Angle:

m∠ABD = ¹/₂ MAD

Step 7: Substitute m∠ABD = 63 in above equation:

63 = ½ mAD

Step 8: Evaluate for answer:

63 = ¹/₂ AD

AD = 126

Step 9

Thus, the required answer is:

MAD = 126°

Solution

The required answer is:

mAD = 126°

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Answer:

-7

Step-by-step explanation:

you divide -8 on both sides

the two -8 on your left will cancel each other

and 56 divided by-8=-7

The measure of angle BC is 27 degrees.

To find the measure of angle BC, we need to use the angle sum property of triangles. In triangle ABC, the sum of all angles is equal to 180 degrees. We know that angle ACD is a straight angle and therefore measures 180 - 45 = 135 degrees.

Additionally, we know that angle ADB is also a straight angle and therefore measures 180 - 18 = 162 degrees.

To find angle BCD, we subtract the measure of angle ACD from the measure of angle ADB, which gives us:

m BCD = m ADB - m ACD
m BCD = 162 - 135
m BCD = 27 degrees

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Lance needs to jog for an additional 316.08-25.5 = 290.58  minutes to burn 380 Calories.          

The information given in the table to  produce a direct equation that relates the number of Calories burned to the time spent jogging. Let's use the  pitch- intercept form y =  mx b, where y represents the number of Calories burned( in hundreds), x represents the time spent jogging( in  twinkles), m represents the rate of Calories burned( in hundreds per  nanosecond), and b represents the  original Calories burned( in hundreds).  To find m, we can use the points( 10, 13) and( 15, 19), which represent two ordered  dyads on the line. We can find the  pitch of the line using the  pitch formula  

m = ( y2- y1)/( x2- x1)  m = ( 19- 13)/( 15- 10)  

m = 1.2  So the equation for the line is  y = 1.2 x b.

 To find b, we can use the point

( 10, 13)  = 1.2( 10) b  b = 0.7

 So the complete equation for the line is  y = 1.2 x0.7  Now we can use this equation to  break for x, the number of  twinkles Lance needs to jog to burn 380 Calories.  

380 = 1.2 x0.7  = 1.2 x  x = 316.08

So Lance needs to jog for an additional 316.08-25.5 = 290.58  minutes to burn 380 Calories.

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The value of area of rectangle is,

⇒ Area = x² + 10x + 21

We have to given that;

Lenght = (x + 7)

Width = (x + 3)

Hence, We can formulate;

The value of area of rectangle is,

⇒ Area = Lenght x width

⇒ Area = (x + 7) (x + 3)

⇒ Area = x² + 7x + 3x + 21

⇒ Area = x² + 10x + 21

Thus, The value of area of rectangle is,

⇒ Area = x² + 10x + 21

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The SinL as a fraction in the simplest form is 12/13.

We are given

The side NM = 5,

The side LM = 12,

By using Pythagoras' theorem, we can say that;

NL² = NM² + LM²

Substitute the values of NM and LM;

NL² = 12² + 5²

NL = 13,

For Sin L = perpendicular side/hypotenuse side

Sin L = NM / NL,

Sin L = 12/13

Therefore, the SinL as a fraction in the simplest form is 12/13

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A) A above middle C with a frequency of 440 cycles per second is 49 notes up the piano keyboard.

B) frequency of the pitch that is 73 notes up the keyboard is 1760 cycles per second.

A. To find how many notes up the piano keyboard the pitch with a frequency of 440 cycles per second is, solve the formula

n = 1 + 12 × log₂(f/27.5) for n,

where f = frequency of the pitch to find and n = number of notes up the keyboard.

Substituting f = 440:

n = 1 + 12 × log_2(440/27.5)

n = 1 + 12 × log_2(16)

n = 1 + 12 × 4

n = 49

Therefore, the A above middle C with a frequency of 440 cycles per second is 49 notes up the piano keyboard.

B. Using the same formula, n = 1 + 12 × log₂(f/27.5), to find the frequency of the pitch that is 73 notes up the keyboard. Solving for f:

73 = 1 + 12 × log₂(f/27.5)

72 = 12 × log₂(f/27.5)

6 = log₂(f/27.5)

2⁶ = f/27.5

f = 27.5 x 2⁶

Therefore, the frequency of the pitch that is 73 notes up the keyboard is:

f = 27.5 x 2⁶ = 1760 cycles per second.

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Answer:

Try the desmos graphing calculator:

Step-by-step explanation:

The value of the expression is determined as 14.

The value of the expression is calculated as follows;

We will apply the principle known as BODMAS;

B - bracket

O - Off

D - division

M - multiplication

A - addition

S - subtraction

The given expression; = (27 · 3  -  1719 ÷ 1719) ÷ 8 + 5² - 3³  + (8 · 4  -  2·13)

We will simplify the expression as follows;

(27 · 3  -  1719 ÷ 1719) = (81  -  1719/1719) = (81 - 1) = 80

(8 · 4  -  2·13) = (32  -  26) = 6

= 80 ÷ 8 + 5² - 3³  + 6

= (80/8) +  5² - 3³  + 6

= 10 +  5² - 3³  + 6

= (10 + 5² + 6) - 3³

= 41 - 27

= 14

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