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A father is 30years older than his son. In 12years, the man will be three times as old as his son. Find their present ages.

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Let the present age of the son be x years

Then father's age will be (x+30) years

Given after 12 years father will be three times as old as his son

Therefore,

(x+12)3=x+30+12

3x+36=x+42

3x−x=42−36

2x=6

x=3

x+30=3+30=33

So, the present age of son is 3 years and present age of the father is 33 years

Answer:1380

Step-by-step explanation: proportionality constant equals 1150/25=46. 46x30=1380

The circumference of the circular playing field.

[tex]\huge\boxed{Formula:C= 2\pi{r}}[/tex]

We'll have to multiply 2, π and radius.

Substitute the values according to the formula.

[tex]C= 2× \pi ×7.5[/tex]

[tex]C= 47.12389 [/tex]

[tex]\large\boxed{C= 47.12 \: m}[/tex]

Therefore, the circumference of the circular playing field is 47.12 feets.

Answer:

arc FS = 84°

Step-by-step explanation:

the inscribed angle QRF is half the measure of its intercepted arc QF , then

arc QF = 2 × 48° = 96°

the sum of the arcs on a semicircle = 180° , that is

QF + FS = 180°

96° + FS = 180° ( subtract 96° from both sides )

FS = 84°

Answer:

times and divide

they are both diffrent equations

The value of the variable a is 19.66 and the value of the valriable b is 20.21.

For any triangle ABC, with side measures |BC| = a. |AC| = b. |AB| = c,

we have, by the law of sines,

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

Remember that we took

The sine angle is the length of the side opposite to that angle.

Then the third angle of the triangle will be

x + 75 + 35 = 180

                x = 70

[tex]\rm \dfrac{\sin 75^o}{b} = \dfrac{\sin 35^o}{12} = \dfrac{\sin 70^o}{a}[/tex]

From the first two-term, we have

sin 75 / b = sin 35 / 12

b = 20.21

From the last two-term, we have

sin 70 / a = sin 35 / 12

a = 19.66

Learn more about the law of sines here:

https://brainly.com/question/17289163

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Using the given information, the diver's score is 6.2

From the question, we are to calculate the diver's score

From the given information,

The five judges score a dive as 6.0, 6.3, 6.2, 6.8, and 6.1.

Since the highest and lowest scores are discarded

Then, we will discard 6.8 and 6.0

The remaining scores are 6.1, 6.2, and 6.3

Now, the diver's score will be the average of the remaining scores

∴ The diver's score = (6.1 + 6.2 + 6.3) /3

The  diver's score = 18.6 / 3

The diver's score = 6.2

Hence, the diver's score is 6.2

Learn more on Calculating average score here: https://brainly.com/question/14015675

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Answer:

how many hours a week the employees are working?

Step-by-step explanation:

I could be wrong but that's my fault if it's wrong sorry

Answer:

The volume is 11.7

Step-by-step explanation:

[tex]\frac{m}{v}[/tex] = d

[tex]\frac{2.6}{v}[/tex] = 4.5

4.5 × 2.6 = 11.7

v = 11.7

Answer:

B.

Step-by-step explanation:

First convert the equation to slope-intercept form:

2x - 5y = 7

-5y = -2x + 7

y = 2/5 x - 7/5

So the slope of the given line  is 2/5.

So the slope of a perpendicular line will be -1/ 2/5 = -5/2.

Take B:

5x + 2y = 3

2y = -5x + 3

y = -5/2.

So its B.

Answer:

Factor and set each factor equal to zero. Y=x2+5x−8

Step-by-step explanation:

Answer:

I think the answer would be 28

Answer:

b. 15%

Step-by-step explanation:

because it is 3 oranges and 3 is equal to 15%

->period = [tex]\frac{2\pi }{2} =\pi[/tex]

->a=3, shift [tex]\frac{\pi }{4}[/tex]

->right 1 unit up

Rest are shown in graph

Answer:

600(1+1)^3 with future amount being 4800

Step-by-step explanation:

The amount of the money after 27 years will be $4800.

The quantity of money anyone has is termed as the amount. The solution to the question is given as follows:-

Given that investments double every 9 years and you start with a $600 investment. how much money would you have after 27 years?

We know that the amount is getting double in every 9 years so the number of times the amount will get doubled will be = 27 / 9 = 3

Future amount = 600(1+1)³

Future amount  = 600 ( 2 )³

Future amount = 600 ( 8 ) = $4800

Therefore the amount of the money after 27 years will be $4800.

To know more about the amount follow

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keeping in mind that twin sides stemming from a common vertex make twin angles at the "base", Check the picture below.

Answer:

hope you can understand

Answer:

b. mode = 88, median = 77

Step-by-step explanation:

First, arrange all the numbers least to greatest.

53, 71, 75, 79, 88, 88

The mode is the number that occurs the most.

mode = 88

The median is the middle number. Since there is an even number of numbers, look at the two middle numbers 75 and 79. Add them together and divide by two (finding the average or mean of the numbers).

75 + 79 = 154

154/2 = 77

median = 77

Based on the calculations, the measure of angle Q to the nearest whole degree is equal to 53°. The correct answer is option C.

The complete question is attached with the answer below.

The angle is defined as the span between two intersecting lines or surfaces at or close to the point where they meet.

Based on the triangle attached in the image above, we can deduce the following parameters:

Side QM = 18 units.

Side MN = 17 units.

Side QN = 20 units.

In this scenario, we would apply the cosine trigonometry function to determine the measure of angle Q:

MN² = QM² + QN² - 2(QM)(QN)cosθ

17² = 18² + 20² - 2(18)(20)cosθ

289 = 324 + 400 - 720cosθ

720cosθ = 724 - 289

720cosθ = 435

θ = cos⁻¹(435/720)

θ = cos⁻¹0.6042

θ = 52.8 ≈ 53°.

Read more on cosine function here:

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The surface area of the cone is 40π

A cone is a solid shape with a circular base and a tapered side.

Analysis:

surface area of a cone = πrl + π[tex]r^{2}[/tex] = π( 6x4) + π(4 x 4) = 40π

Learn more about cone: brainly.com/question/1082469

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Answer:

[tex]k=4[/tex]

Step-by-step explanation:

Using the diagram, we can conclude that the given angles are vertical angles. Vertical angles are opposite angles that are formed when two lines intersect. Vertical angles are always congruent.

Using this information we can set up an equation.

[tex]7k-6=2k+14[/tex]

Subtract 2k from both sides.

[tex]7k-2k-6=2k-2k+14\\5k-6=14[/tex]

Add 6 to both sides

[tex]5k-6+6=14+6\\5k=20[/tex]

Divide both sides by 5

[tex]\frac{5k}{5}=\frac{20}{5}\\k=4[/tex]

CHECK:

7(4) - 6 = 28 - 6 = 22

2(4) + 14 = 8 + 14 = 22

22 = 22

Hello, the detailed solution is given below.

Lines L and M are parallel. That's why [tex]B[/tex] angle and [tex]50^{o}[/tex] are equal.

Co-interior angles lie between two lines and on the same side of a transversal. If the two lines are parallel, then co-interior angles add to give [tex]180^{o}[/tex] and so are supplementary.

After that, [tex]C[/tex] angle found as [tex]85^o[/tex].

As [tex]A[/tex] angle and [tex]C[/tex] angle must be equal due to the parallel, the missing angles as;

[tex]A=85\\B=50\\C=85[/tex]

Good luck! If you have any questions, then feel free to ask in comments!

Answer:

Based on the data given on Northlake High School, we can infer that B. A greater percentage of second-lunch students (39%) eat outside.

What does the data on the First and Second lunches show?

The percentage of second-lunch students who eat outside is:

= Second lunch students who eat outside / Second lunch students

Solving gives:

= 0.18 / 0.46 x 100%

= 0.3913 x 100%

= 39%

This shows that the percentage of students eating their second lunch outside is 39%.

so the answer is B

Step-by-step explanation:

Answer:

212

Step-by-step explanation:

85 here is 100%

And 900 is also 100%

That's for the different comparisons. So now, what we do is, we should divide 85 by 900, and then, whatever is our answer, multiply that by 20.

That is surely going to equal how many students are going to say that Math is Awesome for 900 student survey.

Step 1

85/900=10.5882352941

Let's round that to make it

10.5

Step 2

10.5x20=210

That means, if we go exactly, like multiplying all of those numbers, then our answer should be 212 or 200.

Just to be sure that our answer is correct, we will do it with 10.58 now.

Step 3

10.58x20=211.6

So now it looks like it's most probably going to be 212

But still, let's do 10.588 now.

Step 4

10.588x20=211.76

Okay, let's do it again, with 10.5882

Step 5

10.5882x20=211.764

Okay, so I just multiplied the whole number this time, and I still got a decimal, so that means that your answer is 212 basically.

Answer:

the answer is 3

Answer:

x = 3

Step-by-step explanation:

if you need an explanation let me know

Answer:

x = 3

Step-by-step explanation:

Given:

[tex] \implies \rm 3 {}^{x} + {3}^{x} = 54[/tex]

To Find:

Solution:

We could re-write 3^x+3^x as:

[tex] \implies \: 2(3 {}^{x} ) = 54[/tex]

Divide both sides by 2

[tex] \implies \cfrac{2(3 {}^{x}) }{2} = \cfrac{54}{2} [/tex]

[tex] \implies \: 3 {}^{x} = 27[/tex]

Take logarithm on both sides

[tex] \implies \: \log(3 {}^{x} ) = \log(27)[/tex]

[tex] \implies \: x \times \log(3) = \rm \: log \: (27)[/tex]

[tex] \implies \: x = \cfrac{ \log(27)}{ \log \:(3)} [/tex]

[tex] \implies \boxed{x = 3}[/tex]

Hence, x = 3 .

Answer:

A) -4, -2

Step-by-step explanation:

The translation vector is the distance

point A: (3, 1)

point A': (-7, -3)

3 + (-7) = -4

1 + (-3) = -2