Find the area of the triangle with the given description. A triangle with sides of length 5 and 8 and include angle 79°.​

Answer:

6 cm³

Step-by-step explanation:

The figure is a triangular prism with a triangular base with side lengths 3 cm, 4 cm, 5 cm. The height of the prism is 1 cm.

The sides measuring 3 cm and 4 cm form a right angle.

V = BH

where B = area of the base, and

H = height of the prism.

The base is a triangle, so B = (1/2)bh,

where b = base of the triangle, and

h = height of the triangle

V = (1/2)bhH

V = (1/2)(3 cm)(4 cm)(1 cm)

V = 6 cm³

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

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

Step 1: Add Equation 2 and Equation 3 to eliminate z.

(-x + y - z) + (x - 3y) = -1 + 3

y - 4y = 2

-3y = 2

y = -2/3

Step 2: Substitute the value of y (-2/3) into Equation 3 to find the value of x.

x - 3(-2/3) = 3

x + 2 = 3

x = 1

Step 3: Substitute the values of x and y into Equation 1 to find the value of z.

3(1) - 8(-2/3) + z = 8

3 + 16/3 + z = 8

9/3 + 16/3 + z = 8

25/3 + z = 8

z = 8 - 25/3

z = 24/3 - 25/3

z = -1/3

Therefore, the solution to the system of equations is:

x = 1

y = -2/3

z = -1/3

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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Answer:

5.52 million people with blood group O in KwaZulu-Natal.

Step-by-step explanation:

Multiple alleles refer to the existence of more than two possible alleles (or variations) of a gene within a population. In the case of blood groups, there are multiple alleles for the gene that controls blood type, resulting in the four possible blood groups: A, AB, B, and O.

The blood group AB is the least common in the human population, with only 3% of people having this blood type.

To calculate the number of people who will have blood group O in KwaZulu-Natal, we need to multiply the total population by the percentage of people with blood group O.

9.2 million x (60/100) = 5.52 million people with blood group O in KwaZulu-Natal.

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

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]

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 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:

400π m3

Step-by-step explanation:

V = πr^2h

V = π(5^2)(16)

V = π(25)(16)

V = 400π

Investment B is an ordinary  subvention with$ 3,906.64 in the account after one time. The correct answer is option d.    

To determine which investment is an ordinary  subvention and the  unborn value after one time, we first need to understand that an ordinary  subvention is a series of equal payments made at the end of each period.

Given the table, we can see that Investment A has payments starting in January and ends in November( missing December), while Investment B starts in February and ends in December.

thus, Investment B is the ordinary  subvention since the payments are made at the end of each month.  Now let's calculate the  unborn value of Investment B after one time  

1. Convert the periodic interest rate to a yearly rate( 10.035)(1/12)- 1 ≈0.002867

2. Determine the number of payments made 11 months  3. Use the  unborn value of  subvention formula FV =  P *(( 1 r) n- 1)/ r  

Where P =  yearly payment($ 350),

r =  yearly interest rate(0.002867), and n =  number of payments( 11) . Plug in the values

FV =  350 *(( 10.002867) 11- 1)/0.002867 ≈3906.64  

So, Investment B is an ordinary  subvention with$ 3,906.64 in the account after one time. The correct answer is optiond.

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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 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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The function equation for the graph above include the following: B. f(x) = -[x] + 3.

In Mathematics and Geometry, a greatest integer function can be defined as a type of function which returns the greatest integer that is less than or equal (≤) to the number.

Mathematically, the greatest integer that is less than or equal (≤) to a number (x) is represented as follows:

y = [x].

By critically observing the given graph, we can logically deduce that the parent function was reflected over the y-axis (negative slope) and it was vertically translated from the origin by 3 units up;

y = [x]

f(x) = -[x] + 3.

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Answer:

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

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

= about .17 = about 17%

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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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 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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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:

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.

Answer:131

Step-by-step explanation:

Use BEDMAS

9x(7+7)+5

=9 x 14 + 5

= 126 + 5

= 131

Answer:

23/100 equals 23%.

Answer: 23%

Step-by-step explanation: When doing these problems, remember, 100 and a 100% are the same thing, so when you have a problem like this, divide 25 by 100, then multiply by a 100.

Answer:

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

AB and AC are perpendicular since AB is tangent to circle at point A.

BC is the hypotenuse of ΔABC and it length is:

Find the length of AB using Pythagorean theorem:

(a) The probability that exactly 4 orders will arrive in 30 minutes is 0.1127

(b) The probability that at least 2 orders will arrive in an hour is 0.7586.

(a)  We need to adjust λ to reflect the 30-minute time interval:

λ = 5 orders per hour * 0.5 hours = 2.5 orders in 30 minutes

Now we can plug in the numbers and calculate the probability:

P(X = 4) = ([tex]e^{2.5}[/tex]) *) [tex]2.5^{4}[/tex]/ 4! = 0.1127

(b) We can use the Poisson probability formula again, with λ = 5 orders per hour and x = 0 or 1:

P(X < 2) = P(X = 0) + P(X = 1) = 0.0404 + 0.2010 = 0.2414

Then we can subtract this from 1 to get the probability that at least 2 orders will arrive in an hour:

P(X ≥ 2) = 1 - P(X < 2) = 1 - 0.2414 = 0.7586

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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.

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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Answer:

side AC

Step-by-step explanation:

is the opposite angle B because it is the furthest you can get on the triangle to be away from point B.

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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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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