How do I find X in this problem

Answer:

24 and 48

Today, the son is 24 years old, and the father is 48 years old.  

Step-by-step explanation:

(x - 10) + (2x - 10) = 52

3x + 20 = 52

3x = 72

x = 24

The father is 2 times his son's age.

2x

= 2(24)

= 48

So, the son is 24 and the father is 48.

10 years ago, son was 14 and father was 38, if added, this adds up to 52, so we know our calculations are correct.

Answer:

So the son’s age is 24 and the father’s is 48. Ten years ago, they were 14 and 38, which adds up to 52.

Step-by-step explanation:

If the son’s age is x, the father’s age is 2x.

Ten years ago:

(x - 10) + (2x - 10) = 52

3x + 20 = 52

3x = 72

x = 24

2x = 48

Answer:

BW = 132.59

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan theta = opp /adj

tan 9 = 21 / BW

BW tan 9 = 21

BW = 21/ tan 9

BW = 132.5887818

BW = 132.59

Answer:

Step-by-step explanation:

Side BW is the height, aka as the side adjacent to the reference angle of 9 degrees. We have the side opposite the reference angle (21) and we are looking for the side adjacent to the reference angle. The trig ratio that we use for this, the one that relates the sides opposite and adjacent, is the tangent ratio, namely:

[tex]tan(9)=\frac{21}{BW}[/tex] and solving for BW:

[tex]BW=\frac{21}{tan(9)}[/tex] so

BW = 132.59

Answer:

cot a = 3 3/7

or, cot a = 24/7

or, tan a = 7/24

So,

cos a = 24/25

tan a = 7/24

Answered by GAUTHMATH

Answer:

it is an absolute function

or more precisely

y = - I x - 1 I + 8  (shown in the screenshot)

Answer:

There are 3 marbles, that we assume are different.

Let's define them as marble 1, marble 2, and marble 3.

a) If the order is important, and we select the 3 marbles, then:

for the first marble, we have 3 options.

For the second marble, we have 2 options (because one is already taken)

for the third marble is only one option.

The total number of combinations is equal to the product between the numbers of options, so in this case, we have:

C = 3*2*1 = 6 combinations.

Now, if we only select 2 marbles from the bag, we have:

for the first marble, we have 3 options.

For the second marble, we have 2 options

Here the number of different combinations is:

C = 3*2 = 6 combinations.

And if we select only one marble from the bag, we have:

for the first marble, we have 3 options.

Then here are only 3 combinations.

the total number of combinations is:

C' = 6 + 6 + 3 = 15 different combinations.

b) If the order is not important, then there is only one combination when we draw the 3 marbles.

When we draw one marble there are 3 combinations (one for each marble)

When we draw two marbles, again there are 3 combinations (one for each marble that we do not draw)

then the total number of combinations in this case is:

C = 1 + 3 + 3 = 7

Using function concepts, it is found that:

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

The given function is:

[tex]g(x) = 3 - 8\left(\frac{1}{4}\right)^{2-x}[/tex]

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

Question a:

The y-intercept is g(0), thus:

[tex]g(0) = 3 - 8\left(\frac{1}{4}\right)^{2-0} = 3 - 8\left(\frac{1}{4}\right)^{2} = 3 - \frac{8}{16} = 3 - 0.5 = 2.5[/tex]

The y-intercept is y = 2.5.

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

Question b:

The horizontal asymptote is the limit of the function when x goes to infinity, if it exists.

[tex]\lim_{x \rightarrow -\infty} g(x) = \lim_{x \rightarrow -\infty} 3 - 8\left(\frac{1}{4}\right)^{2-x} = 3 - 8\left(\frac{1}{4}\right)^{2+\infty} = 3 - 8\left(\frac{1}{4}\right)^{\infty} = 3 - 8\frac{1^{\infty}}{4^{\infty}} = 3 -0 = 3[/tex]

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

[tex]\lim_{x \rightarrow \infty} g(x) = \lim_{x \rightarrow \infty} 3 - 8\left(\frac{1}{4}\right)^{2-x} = 3 - 8\left(\frac{1}{4}\right)^{2-\infty} = 3 - 8\left(\frac{1}{4}\right)^{-\infty} = 3 - 8\times 4^{\infty} = 3 - \infty = -\infty[/tex]

Thus, the horizontal asymptote is x = 3.

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

Question c:

The limit of x going to infinity of the function is negative infinity, which means that the function is decreasing.

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

Question d:

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

The sketching of the graph is given appended at the end of this answer.

A similar problem is given at https://brainly.com/question/16533631

Answer:

452.16 cm²

Step-by-step explanation:

Given :-

To find :-

Solution :-

As we know that ,

Step-by-step explanation:

[tex]area = \pi {r}^{2} \\ = \pi \times {12}^{2} \\ = \pi \times 144 \\ = 3.14 \times 144 \\ = 452.16 {cm}^{2} \\ thank \: you[/tex]

Answer: 5 and 7

Step-by-step explanation:

Given

Sum of the integers is 12

Product of the integers is 35

Suppose the integers are [tex]x[/tex] and [tex]y[/tex]

[tex]\Rightarrow x+y=12\\\\\Rightarrow y=12-x\\\Rightarrow xy=35\\\text{Substitute y}\\\Rightarrow x(12-x)=35\\\Rightarrow 12x-x^2=35\\\Rightarrow x^2-12x+35=0\\\Rightarrow x^2-7x-5x+35=0\\\Rightarrow (x-7)(x-5)=0\\\Rightarrow x=5\ or\ 7[/tex]

[tex]\therefore \text{y can be }7\ or\ 5[/tex]

Hence, the numbers are 5 and 7.

Answer:

Annual payment wil be 2,001 and total amount after compounded annually will be 27,001

Answer:

All whole numbers are rational numbers.

False

All integers are whole numbers.

True

There are integers that are not rational numbers.

True

There are whole numbers that are not integers.

True.

Answer:

58.3333

Step-by-step explanation:

make 14/24 into a fraction with a denominator of 100, and you get 58.333333 over 100

Lucy's dog sleeps for 58.3% of the whole day.

A percentage is a portion of a whole expressed as a number between 0 and 100 rather than as a fraction.

Given that, Lucy's dog sleeps 14 hours a day, we need to find that how much percent of the total day, her dog sleeps.

We know, there are 24 hours in a day,

Percentage = 14% of 24

= 24x14/100

= 58.3333333333 ≈ 58.3%

Hence, Lucy's dog sleeps for 58.3% of the whole day.

Learn more about percentage,

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Answer:

13/16

Step-by-step explanation:

To add these two fractions multiply the first fraction by 2 to get equivalent denominators so 6/16+7/16 then add the numerators to get 13/16.

Answer:

13/16

Step-by-step explanation:

3/8 + 7/16

Get a common denominator

3/8*2/2 + 7/16

6/16 + 7/16

13/16

Answer:

n = 3

Step-by-step explanation:

Given

5 + 8n = 7(- 7 + 4n) - 6 ← distribute parenthesis on right side

5 + 8n = - 49 + 28n - 6 ( subtract 28n from both sides )

5 - 20n = - 55 ( subtract 5 from both sides )

- 20n = - 60 ( divide both sides by - 20 )

n = [tex]\frac{-60}{-20}[/tex] = 3

Answer:

9.89949 or 9.9

Step-by-step explanation:

7^2 + 7^2 = c^2

49+49=98

square root of 98 = 9.89949

Answer:

x>_-1

10x + 3 - 5x_< 14x + 12

-9_<9x

Answer:

Step-by-step explanation:

10x +3-5x < (nhỏ hơn hoặc bằng) 14x=12

10-14x-5x< bằng 12 -3

-9x< bằng 9

x > bằng -1

Answer:

2mx-x+2018

Step-by-step explanation:

multiply each term in the parentheses by x

The values of BMW after 2, 4 and 8 years  according to the EXPONENTIAL FUNCTION are $33,462, $20,358.28 and $7,535.63 respectively.

Using the parameters given, we define an decreasing exponential function :

[tex]A = A_{0} (1 - r)^{t}[/tex]

Where,

[tex]A_{0}[/tex] = initial amount ; r = Rate ; t = time ; A = final amount

Value after 2 years :

t = 2

A = 55000(1 - 0.22)²

A = 55000(0.78)²

A = $33,462

Value after 4 years :

t = 4

A = 55000(1 - 0.22)^4

A = 55000(0.78)^4

A = $20,358.28

Value after 8 years :

t = 4

A = 55000(1 - 0.22)^8

A = 55000(0.78)^8

A = $7,535.63

Therefore, the value of BMW after 2, 4 and 8 years are $33,462, $20,358.28 and $7,535.63 respectively.

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Answer:

c=6.31, a=50.28 degrees, B=75.72 degrees

Step-by-step explanation:

The sine rule of trigonometry helps us to equate the side of the triangles to the angles of the triangles. The remaining parts of the triangle can be found as shown.

The sine rule of trigonometry helps us to equate the side of the triangles to the angles of the triangles. It is given by the formula,

[tex]\dfrac{Sin\ A}{\alpha} =\dfrac{Sin\ B}{\beta} =\dfrac{Sin\ C}{\gamma}[/tex]

where Sin A is the angle and α is the length of the side of the triangle opposite to angle A,

Sin B is the angle and β is the length of the side of the triangle opposite to angle B,

Sin C is the angle and γ is the length of the side of the triangle opposite to angle C.

Given that the length of side a and b is 6 and 7.56, also, the measure of the angle γ is 54°.

Now, Using the law of cosine, we can write,

[tex]c =\sqrt{a^2 + b^2 -2ab\cdot \cos\gamma}[/tex]

[tex]c =\sqrt{(6)^2 + (7.56)^2 -2(6)(7.56)\cdot \cos(54^o)}[/tex]

c = √39.8297

c = 6.311

Now, using the sine law the ratio of the sides and angles can be written as,

[tex]\dfrac{\sin\alpha}{a} =\dfrac{\sin\beta}{b} =\dfrac{\sin\gamma}{c}[/tex]

[tex]\dfrac{\sin\alpha}{6} =\dfrac{\sin\beta}{7.56} =\dfrac{\sin (54^o)}{6.311}[/tex]

[tex]\dfrac{\sin\alpha}{6}=\dfrac{\sin (54^o)}{6.311}[/tex]

α = 50.2775°

[tex]\dfrac{\sin\beta}{7.56} =\dfrac{\sin (54^o)}{6.311}[/tex]

β = 75.726°

Hence, the remaining parts of the triangle can be found as shown.

Learn more about Sine Rule here:

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Answer:

96

Step-by-step explanation:

We have to find number of 9 digit palindromes  when all digits are even and each digit appearing not more than twice.

Digits used here

0,1,2,3,4,5,6,7,8,9

Total number of even digits=0,2,4,6,8=5

Now,

0 cannot be used for first place if number is 9-digit number.

Firs place can be filled by number of ways=4

Second place can be filled by number of ways=4

Third place can be filled by number of ways=3

Fourth place can be filled by number of ways=2

Fifth place can be filled by number of ways=1

Total number of ways=[tex]4\times 4\times 3\times 2\times 1[/tex]

Total number of ways=96

Hence, total number of 9-digits palindromes  when all digits are even and appearing not more than twice=96

To find the missing number divide 364 by 7

364 / 7 = 52

The missing number is 52

Answer:

52

Step-by-step explanation:

In this equation, you would have to use inverse operations.

Since this equation is a multiplication equation, you need to do the opposite, division. So, 364 ÷ 7 = 52

Hope this helps! :)

Answer:

[tex]ST = 6cm[/tex]

Step-by-step explanation:

Given

[tex]RS =2x[/tex]

[tex]ST = 3x[/tex]

[tex]RT = 10[/tex]

Required

Find ST

From the question, we understand that S is between R and T.

So:

[tex]RS + ST = RT[/tex]

Substitute known values

[tex]2x + 3x = 10[/tex]

[tex]5x =10[/tex]

Divide both sides by 5

[tex]x =2[/tex]

Given that:

[tex]ST = 3x[/tex]

[tex]ST = 3 * 2[/tex]

[tex]ST = 6cm[/tex]

Answer:

C or 6 centimeters

Step-by-step explanation:

Given:

The quadratic equation is:

[tex]3x^2+x-5=0[/tex]

To find:

The solution for the given equation rounded to 2 decimal places.

Solution:

Quadratic formula: If a quadratic equation is [tex]ax^2+bx+c=0[/tex], then:

[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

We have,

[tex]3x^2+x-5=0[/tex]

Here, [tex]a=3,b=1,c=-5[/tex]. Using the quadratic formula, we get

[tex]x=\dfrac{-1\pm \sqrt{1^2-4(3)(-5)}}{2(3)}[/tex]

[tex]x=\dfrac{-1\pm \sqrt{1+60}}{6}[/tex]

[tex]x=\dfrac{-1\pm \sqrt{61}}{6}[/tex]

[tex]x=\dfrac{-1\pm 7.81025}{6}[/tex]

Now,

[tex]x=\dfrac{-1+7.81025}{6}[/tex]

[tex]x=1.13504167[/tex]

[tex]x\approx 1.14[/tex]

And

[tex]x=\dfrac{-1-7.81025}{6}[/tex]

[tex]x=-1.468375[/tex]

[tex]x\approx -1.47[/tex]

Therefore, the required solutions are 1.14 and -1.47.

Answer:

Step-by-step explanation:

I'm not sure if you have learned this yet, but using dimensional analysis (DA) for this problem makes everything so. much. easier! (I'll share a good video in the comments if you don't know what it is)

Okay, so we're given a 50,145 [tex]cm^{3}[/tex] statue, and we want to see how much it'll cost if it's $0.35 per kg, with a conversion factor of 2.6 [tex]g/cm^{3}[/tex].

First, with the conversion factor, I'll set up a dimensional analysis.

[tex]50,145 cm^{3} * \frac{2.6 g}{cm^{3} }[/tex]

cancel out the cm^3, and multiply the top two numbers. I used a calculator:

130377 g

We're not done yet! The question asks for how much it is in kg, not g. We could use D.A. , but g to kg is pretty easy. just put a decimal three paces in.

130.377 g = 130.377 kg

Now, either use D.A. to show your work, or just simply multiply.

130.377*0.35= $45.63

I think this is the right answer... Any questions, please comment!

Answer:

6/15

Step-by-step explanation:

add all the marbles up and you get 15

6 green ones out of 15 marbles

Answer:

2/5

Step-by-step explanation:

6 green+5 red+4 blue = 15 marbles

P(green) = number of green/ total

              = 6/15 = 2/5

Answer:

Hexagons, Cross sections parallel to the base will be hexagons. It is also possible to take cross sections using planes that are neither parallel not perpendicular to the base

Answer:

The cross-section parallel to the base is a hexagon congruent to the hexagonal bases. The cross-section perpendicular to the base is a rectangle. The cross-section parallel to the base is a pentagon similar to the pentagonal base. The solid is a cylinder.

Answer: 1232 pieces

Work Shown:

1 bag = 7 apples

22 bags = 22*7 = 154 apples

So we have 154 apples to work with in total.

Each of those apples is cut into 8 pieces, giving us 8*154 = 1232 pieces

We can write it as one single calculation to say 22*7*8 = 1232

Answer:

0 =-4.5X +49.5

x = 11

Step-by-step explanation:

x1 y1  x2 y2

1 45  3 36

(Y2-Y1) (36)-(45)=   -9  ΔY -9

(X2-X1) (3)-(1)=    2  ΔX 2

slope= -4  1/2    

B= 49  1/2    

Y =-4.5X +49.5    

Answer:

first

you

do15 multiply 10 =150 then divide by 4 walls with 150 =37.5 then mutiply with 4

Answer:

28 feet

Step-by-step explanation:

Since the area is 45 and length is 5.In order to find the width we divide the area by the side given

45 ÷ 5 = 9 is the width

Perimeter is the sum of all the side of a figure.

9 + 9 + 5 + 5

= 28

I hope this helps :)

Answer:

shift of 6 units left

Step-by-step explanation:

Given f(x) then f(x + a) is a horizontal translation of f(x)

• If a > 0 then a shift left of a units

• If a < 0 then a shift right of a units

f(x) = 3 | x + 6 | + 9

Represents a horizontal shift of the parent function 6 units left