work out length x in the triangle below
if your answer is a decimal, give it to 1 d.p.

Answer:

1) B = 88°, a = 13.1, b = 26.9

2) C = 73°, a = 20.9, b = 12.6

Step-by-step explanation:

To solve for the remaining sides and angles of the triangle, given two sides and an adjacent angle, use the Law of Sines formula:

[tex]\boxed{\begin{minipage}{7.6 cm}\underline{Law of Sines} \\\\$\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}$\\\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are the angles. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides opposite the angles.\\\end{minipage}}[/tex]

Given values:

As the interior angles of a triangle sum to 180°:

[tex]\implies A+B+C=180^{\circ}[/tex]

[tex]\implies B=180^{\circ}-A-C[/tex]

[tex]\implies B=180^{\circ}-29^{\circ}-63^{\circ}[/tex]

[tex]\implies B=88^{\circ}[/tex]

Substitute the values of A, B, C and c into the Law of Sines formula and solve for sides a and b:

[tex]\implies \dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}[/tex]

[tex]\implies \dfrac{a}{\sin 29^{\circ}}=\dfrac{b}{\sin 88^{\circ}}=\dfrac{24}{\sin 63^{\circ}}[/tex]

Solve for a:

[tex]\implies \dfrac{a}{\sin 29^{\circ}}=\dfrac{24}{\sin 63^{\circ}}[/tex]

[tex]\implies a=\dfrac{24\sin 29^{\circ}}{\sin 63^{\circ}}[/tex]

[tex]\implies a=13.0876493...[/tex]

[tex]\implies a=13.1[/tex]

Solve for b:

[tex]\implies \dfrac{b}{\sin 88^{\circ}}=\dfrac{24}{\sin 63^{\circ}}[/tex]

[tex]\implies b=\dfrac{24\sin 88^{\circ}}{\sin 63^{\circ}}[/tex]

[tex]\implies b=26.9194211...[/tex]

[tex]\implies b=26.9[/tex]

[tex]\hrulefill[/tex]

Given values:

As the interior angles of a triangle sum to 180°:

[tex]\implies A+B+C=180^{\circ}[/tex]

[tex]\implies C=180^{\circ}-A-B[/tex]

[tex]\implies C=180^{\circ}-72^{\circ}-35^{\circ}[/tex]

[tex]\implies C=73^{\circ}[/tex]

Substitute the values of A, B, C and c into the Law of Sines formula and solve for sides a and b:

[tex]\implies \dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}[/tex]

[tex]\implies \dfrac{a}{\sin 72^{\circ}}=\dfrac{b}{\sin 35^{\circ}}=\dfrac{21}{\sin 73^{\circ}}[/tex]

Solve for a:

[tex]\implies \dfrac{a}{\sin 72^{\circ}}=\dfrac{21}{\sin 73^{\circ}}[/tex]

[tex]\implies a=\dfrac{21\sin 72^{\circ}}{\sin 73^{\circ}}[/tex]

[tex]\implies a=20.8847511...[/tex]

[tex]\implies a=20.9[/tex]

Solve for b:

[tex]\implies \dfrac{b}{\sin 35^{\circ}}=\dfrac{21}{\sin 73^{\circ}}[/tex]

[tex]\implies b=\dfrac{21\sin 35^{\circ}}{\sin 73^{\circ}}[/tex]

[tex]\implies b=12.5954671...[/tex]

[tex]\implies b=12.6[/tex]

Approximately 5048 sports cars will have less than 150,000 miles on the odometer

Mean = 120,000

Standard deviation = 30,000

Total group = 6000

Total Miles = 150,0000

An odometer is a device used to gauge how far a wheeled vehicle has driven. The tool might be mechanical, electrical, or a hybrid of the two.

Calculating the Z score -

z = x - u/a

= 15,0000 - 12,0000/30000

= 30000/30000

= 1

Using the standard normal table, to determine the value -

P ( Z<1) = 0.8413

Calculating the total number of cars -

= P value x total group of cars

= 6000 x 0.8413

= 5047.7 or 5048

Read more about odometer on:

https://brainly.com/question/12819435

#SPJ1

Step-by-step explanation:

40 :100        yellow to purple,  divide both sides by 20

2:5

Answer:

the ratio of yellow to purple is 40:100 that is 2:5 in the simplest form.

Step-by-step explanation:

Hope it helps.

For the "regression-line",  Ŷ = -6 + 0.41(X), the predicted value,

(a) when X=25 is 4.25,

(b) when X=50 is 14.50,

(c) when X=75 is 24.75.

The "Regression-Line", is Ŷ = -6 + 0.41(X), we can make predictions for the value of Y (the dependent variable) for different values of X (the independent variable).

(a) To predict the value of "Y" when X = 25, we substitute 25 into the regression line equation:

Ŷ = -6 + 0.41(25)

Ŷ = -6 + 10.25

Ŷ = 4.25

So, the predicted value of Y when X = 25 is 4.25.

(b) To predict the value of Y when X = 50, we substitute 50 into the regression line equation:

Ŷ = -6 + 0.41(50)

Ŷ = -6 + 20.50

Ŷ = 14.50

So, the predicted value of Y when X = 50 is 14.50.

(c) To predict the value of Y when X = 75, we substitute 75 into the regression line equation:

Ŷ = -6 + 0.41(75)

Ŷ = -6 + 30.75

Ŷ = 24.75

So, the "predicted-value" of Y when X = 75 is 24.75.

Learn more about Regression Line here

https://brainly.com/question/29753986

#SPJ1

If the height of the cylinder is 10, the diameter of the base of the cylinder is 8 units.

A right circular cylinder has two congruent circular bases and a curved surface area. To find the diameter of the base, we need to first find the radius of the base.

Let's begin by using the given information to write an equation. The surface area of a cylinder is given by the formula:

Surface Area = 2πr² + 2πrh

where r is the radius of the base and h is the height of the cylinder.

We are given that the surface area of the cylinder is 112π and the height is 10. Substituting these values, we get:

112π = 2πr² + 2πr(10)

Simplifying the equation by dividing both sides by 2π, we get:

56 = r² + 10r

Now we have a quadratic equation in terms of r. We can solve this equation by using factoring, completing the square, or the quadratic formula. Let's use factoring:

r² + 10r - 56 = 0

(r + 14)(r - 4) = 0

The solutions are r = -14 and r = 4. Since the radius cannot be negative, the radius of the base is 4.

The diameter of the base is twice the radius, so the diameter is 8.

To learn more about cylinder click on,

https://brainly.com/question/29112748

#SPJ1

Answer:

60 ft^2

Step-by-step explanation:

To get the total volume we will need to multiply all the lengths. This means we will have to do 4 x 3x 5.

4 x 3 x 5 = 15x 4 = 60

Answer:

60 ft³

Step-by-step explanation:

V = 4 ft × 3 ft × 5 ft

V = 12 ft² × 5 ft

V = 60 ft³

The amount of poster board left over will be 1275 square inches, the equation used is  A = (b₁ + b₂)h/2.

To calculate the amount of poster board that will be left over after Ole cuts out a piece of poster board that is the same size as the window,

we need to find the area of the trapezoid window and subtract it from the area of the poster board.

The formula to find the area of a trapezoid is A = (b₁ + b₂)h/2, where b₁ and b₂ are the lengths of the parallel sides and h is the height.

Let's assume that the length of the top parallel side of the trapezoid is 20 inches, the length of the bottom parallel side is 10 inches, and the height is 15 inches.

Using the formula, we get A = (20 + 10) x 15 / 2 = 225 square inches. This is the area of the window.

To find the area of the poster board, we multiply the length and width, which gives 25 x 60 = 1500 square inches.

Finally, we subtract the area of the window from the area of the poster board using the equation:

1500 - 225 = 1275 square inches.

Therefore, the amount of poster board left over will be 1275 square inches.

To know more about Area here

https://brainly.com/question/14994710

#SPJ1

The complete question is

Ole has a window that has the dimensions and shape like the trapezoid shown below. He also has a large rectangular piece of poster board that measures 25 inches by 60 inches. If Ole cuts out a piece of poster board that is exactly the same size as the window, which equation can be used to calculate the amount of poster board that will be left over?

The difference in temperature between Rome and Munich is given as follows:

6ºC.

The difference in temperature between Rome and Munich is given by the subtraction of Rome's temperature by Munich's temperature.

The bar graph in the context of this problem gives the temperature for each town.

From the bar graph given by the image presented at the end of the answer, the temperatures for Rome and Munich are given as follows:

Hence the difference in temperature between Rome and Munich is given as follows:

11 - 5 = 6ºC.

The graph is given by the image presented at the end of the answer.

More can be learned about difference of two amounts at https://brainly.com/question/17301989

#SPJ1

The constant term of the polynomial 2x³-5x²+8x+3 is 3.

A polynomial is a mathematical expression consisting of variables (also called indeterminates) and coefficients, which are combined using addition, subtraction, and multiplication, but not division by a variable.

The variables in a polynomial are typically denoted by x, y, or z, and the coefficients can be constants or other polynomials.

The constant term of a polynomial is the term that doesn't have any variable attached to it. In this case, the constant term is the one that only has a number, which is 3.

Therefore, the constant term of the polynomial 2x³-5x²+8x+3 is 3.

To know more about polynomials follow

https://brainly.com/question/29804635

#SPJ1

The samples are {(H, R), (H, W), (H, B), (T, R), (T, W), (T, B)}. Thus, the correct option is D.

Given that:

A coin is tossed.

A spinner has 3 equal sections: Red, White, and Blue.

The samples are groups of clearly specified components. The number of items in a finite set is denoted by a curly bracket.

The total number of samples is calculated as,

Total samples = 2 x 3

Total samples = 6

The samples are {(H, R), (H, W), (H, B), (T, R), (T, W), (T, B)}.

Thus, the correct option is D.

More about the sample link is given below.

https://brainly.com/question/8053622

#SPJ1

Answer:

Eat that cookie and you will not regret about it

Answer:

The Value of Y is -8

Step-by-step explanation:

I believe it is -8 because giving the function, y = 8 - 2x, given that x = 8, we can replace the value into a function. y = 8 - 2(8) = 8 - 16 = -8.

So therefore, the value of y is -8. Hopes this helps :p

Answer:

Step-by-step explanation:

148 people

The area of the given figure is 133 m²

Given is quadrilateral with sides 17m and 9.5m with height of 14m we need to find its area,

The given quadrilateral is a parallelogram, we know that area of the parallelogram is = base x height

Therefore,

The area of the given figure = 9.5 x 14 = 133

Hence, the area of the given figure is 133 m²

Learn more about parallelograms click;

https://brainly.com/question/29147156

#SPJ1

The loss percentage is 91%.Given that Venessa bought 80 apples for 4$, out of these apples, 25% were rotten and had to be thrown away. Venessa sold the remaining apples at 6 cents per apple.To calculate the profit or loss percentage, we need to determine the cost price, selling price, and the number of apples sold.

Cost price (CP) = 4 $.Selling price (SP) = 80 × 0.75 × 6 cents= 36 cents = 0.36 $.Now, let's calculate the profit.Profit = SP – CP= 0.36 $ – 4 $= – 3.64 $Loss = CP – SP= 4 $ – 0.36 $= 3.64 $.

Therefore, Venessa incurred a loss of $3.64 when she sold 80 apples at 6 cents per apple.Now let's calculate the loss percentage Loss Percentage = (Loss / CP) × 100= (3.64 / 4) × 100= 91%.

Therefore, the loss percentage is 91%.Note: If the result obtained after the subtraction of SP from CP is negative, it means there is a loss, and the percentage of loss can be calculated by (loss/CP) × 100.

For more question on profit

https://brainly.com/question/1446002

#SPJ8

Step-by-step explanation:

There are   pi radians in 180 degrees

  you want   1/4 of 180 degrees   (45/180 = 1/4)  

    so this would be   1/4 pi radians  or   pi / 4   radians

45 *   pi / 180 = pi/4  

Answer:

147

Step-by-step explanation:

V = h * S = h * Pi R^2 = h * Pi * d^2/4 = 7.5 * 3.14 * 25 / 4 = 147.188

The coordinates in the solution to the systems of inequalities is (12, 1)

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

y > -4x + 6

y > 1/3x - 7

Next, we plot the graph of the system of the inequalities

See attachment for the graph

From the graph, we have solution to the system to be the shaded region

The coordinates in the solution to the systems of inequalities graphically is (12, 1)

Read more about inequalities at

brainly.com/question/30977554

#SPJ1

Answer:

20

Step-by-step explanation:

She biked an equal amount each day for 8 days to a total of 32 miles. We can write that as 8x = 32. 32/8 = 4 so x = 4. To find how much shell bike in 5 days, we multiply it by x(4). 5*4 = 20.

The calculated number of plants the flower bed can contain is 120

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

Dimensions = 16 m by 9 m

So, the area of the flower bed is

Area = 16 * 9

Evaluate

Area =  144

Also, we have

Each plant requires a space of 1.2m x 1m?

This means that

Plant area = 1.2 * 1

Plant area = 1.2

So, we have

Plants = 144/1.2

Evaluate

Plants = 120

Hence, the number of plants is 120

Read more about area at

https://brainly.com/question/24487155

#SPJ1

Answer:

Step-by-step explanation:

To calculate the number of plants that can be planted in the rectangular flower bed, we need to calculate the area of the flower bed and divide it by the space required for each plant.

The area of the flower bed is calculated by multiplying its length and breadth.

So, the area of the flower bed is 16m x 9m = 144 sq.m.

Each plant requires a space of 1.2m x 1m = 1.2 sq.m.

Therefore, the number of plants that can be planted in the flower bed is:

144 sq.m. ÷ 1.2 sq.m./plant = 120 plants.

So, you can plant 120 plants in the rectangular flower bed.

The system of inequalities for the graph is

a) y < 3x - 4

b) y = x + 3

Given data ,

Let the inequality equations be represented as A and B

where

Let the first point be P ( 0 , 3 )

Let the second point be Q ( -3 , 0 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

m = ( 3 - 0 ) / ( 0 + 3 )

m = 1

Now , equation of line is y - y₁ = m ( x - x₁ )

y - 0 = 1 ( x + 3 )

y = x + 3

And , the second equation is

Let the first point be R ( 0 , -4 )

Let the second point be S ( 2 , 2 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

m = ( -4 - 2 ) / ( 0 - 2 )

m = -6/-2

m = 3

Now , equation of line is y - y₁ = m ( x - x₁ )

y - 2 = 3 ( x - 2 )

Adding 2 on both sides , we get

y = 3x - 4

Since , it is a dotted line ,

y < 3x - 4

And , the solution to the inequality is point of intersection

where A ( 3.5 , 6.5 ) is the solution

Hence , the inequality equations are solved and A ( 3.5 , 6.5 ) is the solution

To learn more about inequality equations click :

https://brainly.com/question/11897796

#SPJ1

Step-by-step explanation:

3. Let P(t) be the number of people infected by the virus at time t (in days). We can model the situation with the following exponential function:

P(t) = 400 * 1.25^t

Here, 400 represents the initial number of infected people, and 1.25 represents the growth factor, since the virus is spreading to 25% more people each day.

To find the number of people infected after t days, we can substitute t = (log(3000) - log(400)) / log(1.25) into the equation:

P(t) = 400 * 1.25^t

P(t) = 400 * 1.25^((log(3000) - log(400)) / log(1.25))

P(t) ≈ 2,343

Therefore, approximately 2,343 people are infected when the total number of infections reaches 3000.

4. Let P(t) be the population of the town at time t (in years). We can model the situation with the following exponential function:

P(t) = 10,800 * 0.975^t

Here, 10,800 represents the initial population in 2002, and 0.975 represents the decay factor, since the population is decreasing at a rate of 2.5% each year.

To find when the population reaches half the 2002 value, we can set P(t) = 5,400 and solve for t:

5,400 = 10,800 * 0.975^t

0.5 = 0.975^t

log(0.5) = t * log(0.975)

t ≈ 28.2

Therefore, the population will reach half the 2002 value in approximately 28.2 years, which corresponds to the year 2030.

Answer:

3) 9.03 days

4)  27.38 years

Step-by-step explanation:

To model the spread of the virus over time, we can use an exponential function in the form:

[tex]\large\boxed{P(t) = P_0(1 + r)^t}[/tex]

where:

Given the virus has infected 400 people in the town and is spreading to 25% more people each day:

Substitute these values into the formula to create a function for P in terms of t:

[tex]P(t) = 400(1 + 0.25)^t[/tex]

[tex]P(t) = 400(1.25)^t[/tex]

To find how many days it will take for 3000 people to be infected, set P(t) equal to 3000 and solve for t:

[tex]\begin{aligned}P(t)&=3000\\\implies 400(1.25)^t&=3000\\(1.25)^t&=7.5 \\\ln (1.25)^t&=\ln(7.5)\\t \ln (1.25)&=\ln(7.5)\\t &=\dfrac{\ln(7.5)}{\ln (1.25)}\\t&=9.02962693...\end{aligned}[/tex]

Therefore, it will take approximately 9.03 days for the virus to infect 3000 people, assuming the daily growth rate remains constant at 25%.

Note: After 9 days, 2980 people would be infected. After 10 days, 3725 people would be infected.

[tex]\hrulefill[/tex]

To model the population of the town over time, we can use an exponential function in the form:

[tex]\large\boxed{P(t) = P_0(1 - r)^t}[/tex]

where:

Given the initial population was 10,800 and the population has decreased at a rate of 2.5% each year:

Substitute these values into the formula to create a function for P in terms of t:

[tex]P(t) = 10800(1 -0.025)^t[/tex]

[tex]P(t) = 10800(0.975)^t[/tex]

To find how many days it will take for the population to halve, set P(t) equal to 5400 and solve for t:

[tex]\begin{aligned}P(t)&=5400\\\implies 10800(0.975)^t&=5400\\(0.975)^t&=0.5 \\\ln (0.975)^t&=\ln(0.5)\\t \ln (0.975)&=\ln(0.5)\\t &=\dfrac{\ln(0.5)}{\ln (0.975)}\\t&=27.3778512...\end{aligned}[/tex]

Therefore, it will take approximately 27.38 years for the population to reach half the 2002 value, assuming the annual decay rate remains constant at 2.5%.

The correct matrix representation is;  [tex]\left[\begin{array}{ccc}1&5\\3&2\end{array}\right][/tex]

Based on the coordinates of a vector, We can represent a vector pointing at a point by its x coordinate, and y coordinate,

Consider that there are two points represented by their x-, y coordinates as P₁(x₁,y₁) P₂(x₂,y₂)

Given here the points are P₁(1, 3) and P₂(5, 2)

Thus, by the coordinates of the two vectors, we can represent the matrix  ;

[tex]\left[\begin{array}{ccc}1&5\\3&2\end{array}\right][/tex]

Hence, Option A) is the correct answer.

Learn more about vector matrix  here:

brainly.com/question/29990847

#SPJ1

Answer:

7, 14

Step-by-step explanation:

Look at the first column of numbers: 2.8 m in 2 min.

We can get a unit rate from those numbers:

2.8 m / 2 min = 1.4 m/min

He walks at a rate of 1.4 m/min

Now multiply the unit rate by each number of minutes to find the number of meter.

Let's do the second column as a check: time = 3 min

1.4 m/min × 3 min = 4.2 m

4.2 m is the number on the table, so our unti rate is correct.

5 min:

1/4 m/min × 5 min = 7 m

10 min:

1.4 m/min × 10 min = 14 m

The correct step to prove that [tex]BC^2 = AB^2 + AC^2[/tex] is:

By the cross product property, [tex]AC^2 = BC \cdot AD[/tex].

To prove that [tex]BC^2 = AB^2 + AC^2[/tex], we can use the triangle similarity and the Pythagorean theorem. Here's a step-by-step explanation:

Given triangle ABC with right angle at A and segment AD perpendicular to segment BC.

By triangle similarity, triangle ABD is similar to triangle ABC. This is because angle A is common, and angle BDA is a right angle (as AD is perpendicular to BC).

Using the proportionality of similar triangles, we can write the following ratio:

[tex]$\frac{AB}{BC} = \frac{AD}{AB}$[/tex]

Cross-multiplying, we get:

[tex]$AB^2 = BC \cdot AD$[/tex]

Similarly, using triangle similarity, triangle ACD is also similar to triangle ABC. This gives us:

[tex]$\frac{AC}{BC} = \frac{AD}{AC}$[/tex]

Cross-multiplying, we have:

[tex]$AC^2 = BC \cdot AD$[/tex]

Now, we can substitute the derived expressions into the original equation:

[tex]$BC^2 = AB^2 + AC^2$\\$BC^2 = (BC \cdot AD) + (BC \cdot AD)$\\$BC^2 = 2 \cdot BC \cdot AD$[/tex]

It was made possible by cross-product property.

Therefore, the correct step to prove that [tex]BC^2 = AB^2 + AC^2[/tex] is:

By the cross product property, [tex]AC^2 = BC \cdot AD[/tex].

For more questions on cross-product property:

https://brainly.com/question/14542172

#SPJ8

The correct statement regarding the measure of variability used to represent the data is given as follows:

The IQR of 10 is the most accurate to use, as the data is skewed.

The interquartile range of a data-set is given by the difference of the third quartile by the first quartile of the data-set.

It is the measure of variability to be used when a data-set contains outliers, or is skewed, as is the case for this problem.

The charity received 18 donations, hence the quartiles are given as follows:

Hence the IQR is given as follows:

IQR = 22.5 - 12.5

IQR = 10.

More can be learned about the interquartile range at brainly.com/question/12323764

#SPJ1