a = 19.5 cm, b = 12.5 cm and c = 5.5 cm for the triangle shown below.
X
X =
- C
Work out the value of a rounded to 1 DP.
The diagram is not drawn to scale.
cm
a
- b----

Answer:

after 2 seconds

0=40-10t-5t^2

t^2+2t-8=0

(t+4)(t-2)=0

t=-4 or t=2

I think this is correct

see the figure below to better understand the problem

we have that

The value of x is; x = 3.14

Here, we have,

from the given diagram, we get,

there is a right angle triangle.

we have to find the value of x.

we know that,

Let the angle be θ , such that

cos θ = base / hypotenuse

here, we get,

cos 17 = 3/x

so, we have,

0.956 = 3/x

so, x = 3.14

Hence, The value of x is;x = 3.14

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Answer:

B.

Step-by-step explanation:

If he makes 70% then 70% as a decimal would be 0.700 which is B

Probability is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

The probability that he makes at least two of the free throws is 0.0700.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

Example:

The probability of getting a head when a coin is tossed is 1/2

We have,

Each free throw is independent of the other.

Percentage of making free throws = 70%

The probability that he makes at least two of the free throws.

= 70%

= 70/100

= 0.07

This can be written as 0.0700.

Thus,

The probability that he makes at least two of the free throws is 0.0700.

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Answer:

50cm

Step-by-step explanation:

Area of a square = side * side, which can also be written as \(side^{2}\)

x * x = 2500

\(x^{2}\) = 2500

x = \(\sqrt{2500}\)

x = 50cm

This can be checked as well.

50 * 50 = 2500.

Hence, proved.

Hope this helps.

Answer:

1008.56

Step-by-step explanation:

0.06nmultiplied by £980 = £4.08

4.08 multiplied by 7 (the number of years = 28.56

then £28.56+£980=1008.56

Answer:

There is a formula that you need to use to answer this question.

(using calculator)

original × (100×rate/100)^years

\(980( \frac{100 + 6}{100}) {}^{2} \)

= £1101.1

The value of x + y = - 53

What is Linear Equation in 2 variables?

An equation is said to be linear equation in two variables if it is written in the form of ax + by + c = 0, where a, b & c are real numbers and the coefficients of x and y, i.e a and b respectively, are not equal to zero.

Given data ,

The value of x = - 87

The value of y = 34

The equation x + y is calculated by substituting the values of x and y in the equation ,

Therefore , x + y = ( - 87 ) + 34

                           = -53

Hence , the value of x + y is equal to - 53

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(a) Chebyshev's theorem states that at least 75% of lifespan fall between 748 and 1112 hours.

(b) Chebyshev's theorem states that at least 56% of all lifetimes fall between the average lifespan minus the standard deviation and the average lifetime plus the standard deviation. Additional information, such as the mean and standard deviation of the lifespan, would be required to calculate the exact interval.

A % is a relative figure that represents the hundredth part of any amount. One percent (symbolized 1%) is one hundredth part; consequently, 100 percent denotes the complete amount and 200 percent defines twice the supplied amount. percentage. Mathematics percentile is a related topic. A percentage is a fraction of a whole represented as a number between 0 and 100. Nothing is zero percent, everything is 100 percent, half of everything is fifty percent, and nothing is zero percent. To calculate a percentage, divide the share of the total by the total and multiply by 100.

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Answer:

monke

Step-by-step explanation:

delicious

a) 60% b) 15% c) 20% d) 35%

1) Let's set proportions for that, cross multiplying those ratios.

a)

x --------------- 100%

15---------------- 60%

60x =15*100

60x = 1500 Divide both sides by 60

x =25

Hence, 15 is 60% of 25

b) Similarly let's proceed with that, notice that there was a slight difference.

140 --------------100%

21 ---------- y

140y=2100

y=15%

Therefore, 21 is 15% of 140

c)

40---------- 100%

8 ----------- z

40z =800

z= 800/40

z =20%

Therefore, 8 is 20% of 40

d)

50 --------- 100%

17.5 ---------k

50k=1750

k =1750/50

k=35%

2) So, the answers are above in bold.

The cost price of the shorts is K22.50.

To find the cost price of the shorts, we need to reverse calculate the original price before the markup and taxes were applied.

Let's assume the cost price of the shorts is represented by C.

The markup of 17% is applied to the cost price, which means the selling price (including the markup) is 117% of the cost price.

117% of the cost price C can be calculated as (117/100) * C.

GST (Goods and Services Tax) is also included in the selling price. GST is typically calculated as a percentage of the selling price. In this case, the selling price of the shorts including GST is K29.25.

Since the GST is included in the selling price, we can subtract it from the selling price to obtain the selling price before GST.

Let's assume the GST rate is R% (as a decimal), then the selling price before GST can be calculated as:

Selling price before GST = Selling price - (Selling price × R)

In this case, the selling price before GST is K29.25, and the GST rate is 17% (0.17 as a decimal). Substituting these values into the equation, we have:

K29.25 = Selling price - (Selling price × 0.17)

Simplifying the equation

K29.25 = Selling price × (1 - 0.17)

K29.25 = Selling price × 0.83

Selling price = K29.25 / 0.83

Now we can substitute the selling price in terms of the cost price:

K29.25 / 0.83 = (117/100) × C

Simplifying the equation:

C = (K29.25 / 0.83) × (100/117)

Calculating the cost price C:

C = K22.50

Therefore, the cost price of the shorts is K22.50.

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Answer:

1/2

Step-by-step explanation:

If you need an explanation then let me know in the comments

Answer:

25%

Step-by-step explanation:

You have a 1/2 chance of getting an even number and a 1/2 chance of getting heads, so you multiply these fractions together and get 1/4, which is equal to 25%

Answer:

44 sq. cm

Step-by-step explanation:

I promise it's right, I did the math.

Answer:

\(2abCosC = 1\)

Step-by-step explanation:

The cosine rule is

=> \(a^2= b^2+c^2-2abCosC\)

For 2abCosC, it becomes

=> \(2abCosC = b^2+c^2-a^2\)

=> \(2abCosC = (2)^2+(1)^2-(2)^2\)

=> \(2abCosC = 1\)

The person that is correct among the students is Frank who said the pencils are an example of parallel lines.

Parallel lines are lines that can never meet. These are lines that run a direction that is quite opposite to each other as we can see from the image. It is clear that the lines as shown are not able to meet at any point even if they are extended.

Thus, the person that is correct among the students is Frank who said the pencils are an example of parallel lines.

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Answer:

31.5%

Step-by-step explanation:

Answer:

100%?

Step-by-step explanation:

Answer:The answer is no they are slower by 20%

Step-by-step explanation:divide 12 by 5 then divid the answer of 12 by 5 by 2 then you get the answer of 20%

By using the concept of function, it can be calculated that

\(f^{-1}(x) = \frac{3x - 4}{6}\)

What is a function?

A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.

There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.

Here, the function is

\(f(x) = 2x + \frac{4}{3}\\\)

Let f(x) = y

\(2x + \frac{4}{3} = y\\\frac{6x + 4}{3} = y\\\)

6x + 4 = 3y

6x = 3y - 4

\(x = \frac{3y - 4}{6}\)

\(f^{-1}(x) = \frac{3x - 4}{6}\)

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Answer: \(f(n) =f(1)+0.2(n-1)\)

Step-by-step explanation:

Given: \(a_n=5+0.2(n-1)\)

It is the formula of nth term \([a_n=a+(n-1)d]\) in Arithmetic progression

where 5 = First term

0.2 = common difference

To write first term , we use f(1).

nth term will be

\(f(n) =f(1)+0.2(n-1)\)

Hence, the function form : \(f(n) =f(1)+0.2(n-1)\)

Answer:

The answer is 5/12

To solve this, we first have to find a common denominator between the three fractions.

To find a common denominator, which is a multiple that all of the bottom parts of the fractions share, we just have to start guessing.

What is a multiple 4, 3, and 2 all share?

Well, 3 and 2 both share the multiple 6, but 4 doesn't.

What about 12?

4 x 3 = 12

3 x 4 = 12

2 x 6 = 12

All of the numbers share the common denominator of 12

So, we have to multiply all the top numbers now.

5 x 3 = 15

1 x 4 = 4

1 x 6 = 6

So here are our 3 new fractions:

15/12 - 4/12 - 6/12

Now this is a lot easier to solve

15/12 - 4/12

15 - 4 = 11

11/12

11/12 - 6/12

11 - 6 = 5

5/12

The answer is 5/12

Answer: I am pretty sure it is 243 J

Explanation: Because I did the math but I don't know how to put the picture ans don't wanna type it xd

Answer:

The answer is B

Step-by-step explanation:

hope this helps,

please give brainliest if you like my answer,

have a great day

Answer: A regular hexagon.

Step-by-step explanation:

Step 1: Pick any two points

The points are represented as (x1,y1), (x2,y2).

where x1= -4, y1= -8, x2= 0, y2= 4

Step 2: Write out the formula of the equation to use

Step 3: Substituting the values and to get the equation

The equation that represents the graph is y= 3x+4.

Option A is the correct answer.

The time taken by Amy to travel to the place was t = 4 hours.

A measure of average speed is the amount of distance travelled in a given amount of time. It is determined by dividing the overall mileage by the overall time required to cover that mileage.

In physics and other sciences, average speed is frequently employed to describe how objects move. For instance, it is possible to estimate how long it will take to go a certain distance or assess a car's fuel economy by looking at its average speed over a given distance. By dividing the whole distance travelled by the total time required, average speed may also be used to characterise the speed of an object that is moving at various speeds at different points along its path.

Let the time taken to get back = t + 1.

Now, it took one hour less time to get there thus time = t.

Now, average speed is given as:

average speed = total distance / total time

Substituting the values:

50 km/h = d / t

d = 50t  .........(1)

40 km/h = d / (t + 1)

d = 40(t + 1)......(2)

Setting the value of d as equal we have:

50t = 40(t + 1)

50t = 40t + 40

10t = 40

t = 4

Hence, the time taken by Amy to travel to the place was t = 4 hours.

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The rate (in km/h) at which the distance from the plane to the radar station is increasing a minute later is 0 km/h (rounded to the nearest whole number).

To solve this problem, we can use the concepts of trigonometry and related rates.

Let's denote the distance from the plane to the radar station as D(t), where t represents time. We want to find the rate at which D is changing with respect to time (dD/dt) one minute later.

Given:

The plane is flying with a constant speed of 360 km/h.

The plane passes over the radar station at an altitude of 1 km.

The plane is climbing at an angle of 30°.

We can visualize the situation as a right triangle, with the ground radar station at one vertex, the plane at another vertex, and the distance between them (D) as the hypotenuse. The altitude of the plane forms a vertical side, and the horizontal distance between the plane and the radar station forms the other side.

We can use the trigonometric relationship of sine to relate the altitude, angle, and hypotenuse:

sin(30°) = 1/D.

To find dD/dt, we can differentiate both sides of this equation with respect to time:

cos(30°) * d(30°)/dt = -1/D^2 * dD/dt.

Since the plane is flying with a constant speed, the rate of change of the angle (d(30°)/dt) is zero. Thus, the equation simplifies to:

cos(30°) * 0 = -1/D^2 * dD/dt.

We can substitute the known values:

cos(30°) = √3/2,

D = 1 km.

Therefore, we have:

√3/2 * 0 = -1/(1^2) * dD/dt.

Simplifying further:

0 = -1 * dD/dt.

This implies that the rate at which the distance from the plane to the radar station is changing is zero. In other words, the distance remains constant.

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Answer:

i think two i may be wrong

Step-by-step explanation:

A 8 gram sample of a substance that's a by-product of fireworks has a k-value of 0.101. The half-life is 2.98 days.

Exponential decay obeys the equation

\(m(t) = m_0 e^{-kt}\)

where t = time, days

Given:

Initial mass, m₀ = 8 g

Decay constant, k = 0.101

For half-life, the mass is m = m₀/2.

Therefore,

\(m(t) = m_0 e^{-kt}\)

e^{-0.101t} = 1/2

-0.101t = ln 0.5

t = ln 0.5/-0.101

t = 2.98

Therefore, The half-life is 2.98 days.

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