A mother who is 35 years old has two sons, one of whom is twice as old as the other. In 3 years the sum of all their ages will be 59 years. How old are the boys at present ?

Answer:

23

Step-by-step explanation:

6x + 11 + 7x + 143 = 180

13x + 154 = 180

13x = 26

x = 2

m<RPS = 6(2) + 11 = 23

Answer:

70°

Step-by-step explanation:

an inscribed angle is half of the intercepted arc

arc = 2(15) = 30

1/2(x - 30 ) = 20

x - 30 = 40

x = 70

Step-by-step explanation:

We must prove that

cos²a(csc²a-cot²a) = cos²a

If we look at both sides, we can see that we have cos²a * something = cos²a. Therefore, if we can get that something to equal 1, we have our proof. In this case, that something is csc²a-cot²a. Using this information, we can work from within the parenthesis and go from there.

We can start by expanding the items in the parenthesis. Taking that csc(x) = 1/sin(x) and cot(a) = cos(x)/sin(x), we can say that

cos²a(csc²a-cot²a) = cos²a(1/sin²a - cos²a/sin²a). Because both items in the parenthesis have a denominator of sin²a, we can subtract cos²a from 1 to get

cos²a(1/sin²a - cos²a/sin²a)= cos²a((1-cos²a)/sin²a))

Next, we know that cos²a+sin²a=1, so 1-cos²a = sin²a. Plugging that in, we get

cos²a((1-cos²a)/sin²a)) = cos²a(sin²a/sin²a)

= cos²a(1)

= cos²a

Answer: [tex]6+\dfrac{14}{p}[/tex] .

Step-by-step explanation:

To find : The expression is equivalent to the product of [tex]p+\dfrac73\text{ and }\dfrac6p[/tex], where p ≠0.

Product of [tex]p+\dfrac73\text{ and }\dfrac6p[/tex] = [tex](p+\dfrac73)\times\dfrac6p[/tex]

Using distributive property:  [tex](b+c)a= ba+ca[/tex]

[tex](p+\dfrac73)\times\dfrac6p=p\times\dfrac6p+\dfrac73\times\dfrac6p\\\\= 6+\dfrac{7}{1}\times\dfrac2p\\\\=6+\dfrac{14}{p}[/tex]

Hence, the required expression is [tex]6+\dfrac{14}{p}[/tex] .

Answer:

B!!!

Step-by-step explanation:

Multiply then divide every number by 2 to simplify.

Answer:

[0,infinity)

Step-by-step explanation:

Since it's a modulus function, f(x) will have a range of [0,infinity). Use desmos for graphing it

Answer:

you can use a median method of counting and eliminating each side being each cut but the difference would it would be an equal number as the central off number cut divides one piece of wood into an even number.

Another operation is subtracting the cuts from the pieces you have 7 - 6 = 1 whole. Meaning the answer is correct if you are left with 1

If the cuts were even then you would have an a number of pieces that amount to an odd number.

So with 7 they are even and positive.

With counter checking they are positive as you always start with one piece of wood.

Answer:

24 pieces

Step-by-step explanation:

Adam

1/2's means 2 pieces each  so 8 *2 = 16 pieces

Briana

1/4 means 4 pieces each   8*4 = 32 pieces

Carlos

1/9 so 9 pieces each  8*9 = 72 pieces

Carlos - ( adam+ briana)

72 - ( 16+32)

72 -(48)24

Answer:

y = -3x - 5

Step-by-step explanation:

In order to form a parallel line, the two lines must have the same slope. Substitute the values into the point-slope formula to make the equation.

[tex]y-y_1=m(x-x_1)\\y-(-2)=-3(x-(-1))\\y+2=-3(x+1)\\y+2=-3x-3\\y=-3x-5[/tex]

Therefore, the equation is y = -3x - 5.

Answer: Coterminal Angles are angles who share the same initial side and terminal sides. Finding coterminal angles is as simple as adding or subtracting 360° or 2π to each angle, depending on whether the given angle is in degrees or radians.

Answer:

13 1/8

Step-by-step explanation:

3/8-(-51/4)

Subtracting a negative is like adding

3/8 + 51/4

get a common denominator

3/8+ 51/4 *2/2

3/8 + 102/8

105/8

8 goes into 105 13 times with 1 left over

13 1/8

Answer:

5/3

Step-by-step explanation:

1) The denominator will be multiply to the whole number to find the improper fraction. 3 (denominator) x 1 (whole number)

2) 1 plus 2 (numerator) equal 5

3) Always keep the denominator (3) for you improper fraction.

4) 5 will be the numerator and 3 will be the denominator.

5/3

Answer:

V = 300[tex]\pi[/tex] in³ or 942.48 in³

Step-by-step explanation:

Use the cylinder volume formula, V = [tex]\pi[/tex]r²h, where r is the radius and h is the height.

Plug in the values and solve:

V = [tex]\pi[/tex](5²)(12)

V = 300[tex]\pi[/tex] in³ or 942.48 in³

Answer:

Distance D = √ [(2 - x)^2 + (3 - 4x^3)^2].

Step-by-step explanation:

Use the distance formula:

D = √[(x2 - x1)^2 + (y2 - y1)^2].

So here it is

D = √[(2 - x)^2 + (4 - y)^2]    where x,y is any point on the curve.

D = √[2 - x)^2 + (4 - (4x^3 + 1))^2]

D = √ [(2 - x)^2 + (3 - 4x^3)^2]

Answer:

54

Step-by-step explanation:

To solve problems like this, always recall the "Two-Tangent theorem", which states that two tangents of a circle are congruent if they meet at an external point outside the circle.

The perimeter of the given triangle = IK + KM + MI

IK = IJ + JK = 13

KM = KL + LM = ?

MI = MN + NI ?

Let's find the length of each tangents.

NI = IJ = 5 (tangents from external point I)

JK = IK - IJ = 13 - 5 = 8

JK = KL = 8 (Tangents from external point K)

LM = MN = 14 (Tangents from external point M)

Thus,

IK = IJ + JK = 5 + 8 = 13

KM = KL + LM = 8 + 14 = 22

MI = MN + NI = 14 + 5 = 19

Perimeter = IK + KM + MI = 13 + 22 + 19 = 54

Answer:

[tex]u(u + 1)[/tex]

Step-by-step explanation:

first and foremost you have positive and minus 1 which will cancel out to zero

then we're left with

[tex] {u}^{2} + u \\ factorize \: \: u \: out \: to \: get \\ u(u + 1)[/tex]

Answer:

A. 4y + 3 = 15

B. y = 3

Step-by-step explanation:

Three is added to four times a number, the result is 15

A. Equation to represent the above information:

Let the unknown number= y

4 * y + 3 = 15

4y + 3 = 15

B. Solve your equation in (a)​

4y + 3 = 15

Collect like terms

4y = 15 - 3

4y = 12

Divide both sides by 4

4y / 4 = 12 /4

y = 3

Therefore, the unknown number is 3

Answer:

the constant term of the expression represents the difference between Shelly and Terrence points.

Answer:

see explanation

Step-by-step explanation:

Given

10 - 3x < x + 30 ( subtract x from both sides )

10 - 4x < 30 ( subtract 10 from both sides )

- 4x < 20 ( divide both sides by - 4 and flip the sign )

x > - 5

Answer:

Times

first part   x  =  1,33 h       second part  y =  0,66 h

distances  d₁ (first part ) d₁ = 4 miles    d₂  (second part )  d₂ = 0,999 miles

Step-by-step explanation: IMPORTANT NOTE: EVEN PROBLEM STATEMENT DID NOT ASK ANY QUESTION WE WILL ASSUME QUESTION ARE: LENGTH ( IN MILES ) AND SPENT TIME  OF EACH PART OF THE HIKE

We formulate a two-equation system according to:

x = time for the first part

y = time for the second part

then      x  +  y  =  2           or      y = 2 - x

And 3 m/h * x(h)   +  1,5 m/h * y (h)  = 5

3*x  +  1,5*y  = 5

3*x + 1,5 * ( 2 - x )  = 5

3*x  + 3  - 1,5*x  =  5

1,5*x  = 2

x  = 2/1,5 (h)

x = 1,33 (h)

And  y  =  2 -  1,33       y  =  0,66 (h)

Distances are

first part  d₁ = 3*1,33          d₁ =  4 miles

second part  d₂ = 1,5*0,66        d₂  = 0,999 miles

Answer:

the watch is Rs 175

the radio is Rs 325

Step-by-step explanation:

x = price of the watch

y = price of the radio

x+y = 500

x + 150 = y

=>

x + (x+150) = 500

2x + 150 = 500

2x = 350

x = 175

=>

y = 175 + 150 = 325

Answer:

k = 45

Step-by-step explanation:

We can put this into an equation form:

k - 10 = 35

We can solve for k by adding 10 to both sides:

k = 45

Answer:

k-10=35

k=45

Step-by-step explanation:

Let's write this as an equation.

"10 less than k" means subtract 10 from k.

k-10

"is 35" means equals 35.

k-10=35

If we want to solve for k, we have to get k by itself on one side of the equation.

k-10=35

10 is being subtracted from k. The inverse of subtraction is addition. Add 10 to both sides of the equation.

k-10+10=35+10

k=35+10

k=45

Answer:

[tex]1.6^{4}[/tex]

Step-by-step explanation:

1.6 is multiplied by itself 4 times. This is represented in exponential form as

[tex]1.6^{4}[/tex]

Answer:

[tex]120^{0}[/tex]

Step-by-step explanation:

Given: pentagon (5 sided polygon), two interior angles = [tex]90^{0}[/tex] each, other three interior angles are congruent.

Sum of angles in a polygon = (n - 2) × [tex]180^{0}[/tex]

where n is the number of sides of the polygon.

For a pentagon, n = 5, so that;

Sum of angles in a pentagon = (5 - 2) × [tex]180^{0}[/tex]

                                                = 3  × [tex]180^{0}[/tex]

                                                = [tex]540^{0}[/tex]

Sum of angles in a pentagon is [tex]540^{0}[/tex].

Since two interior angles are right angle, the measure of one of its three congruent interior angles can be determined by;

[tex]540^{0}[/tex] - (2 × [tex]90^{0}[/tex])  = [tex]540^{0}[/tex] - [tex]180^{0}[/tex]

                       = [tex]360^{0}[/tex]

So that;

the measure of the interior angle = [tex]\frac{360^{0} }{3}[/tex]

                                                        = [tex]120^{0}[/tex]

The measure of one of its three congruent interior angles is [tex]120^{0}[/tex].

Answer:

(2, -7)

Step-by-step explanation:

Plot point F where angle alpha is located.

Triangle ABF has two interior angles x and 80. They add to the exterior angle alpha due to the remote interior angle theorem.

alpha = x+80

Answer:

69

Step-by-step explanation:

Square root of 1300= 36

(37)²>1300>(36)²

Therefore , the requirement no. to be added to get a perfect square

=(37)²=1369

= 1369- 1300=69

The least no. Of sapling he needs for this = 69

Answer: The answer is C.

Step-by-step explanation:

Because in the theory of the outcome is a 50/50 chance landing heads or tails.  So, the theorectical probability is 1/2.  Now the experimental must be 11/20.

Answer:

theory=1/2, experimental=11/20

Step-by-step explanation:

so when talking about theoretical probability you only consider the only possible outcomes which are either head or tail and since you haven't carried out any sort of experiment yet (many flips) you consider the number of outcomes of tossed once since it's theory which are two therefore the probability of each will be 1/2

but in experimental probability you now consider the number of times tossed and the outcomes of each side which is this case of heads will be 55/100 but in the answers they have simplified so it will be 11/20

Answer:

Kindly check explanation

Step-by-step explanation:

Given the details :

Kofi is older than kweku

kofi's age = (5x-4) years

kweku's age = (2x+1) years

a. write down an expression, interns of x,for how much old is Kofi than kweku

Equate the ages of Kofi and kweku

(5x - 4) = (2x + 1)

5x - 4 = 2x + 1

5x - 2x = 1 + 4

3x = 5

3x - 5

B.) if Kofi is tens years older than kweku, find the value of x and the ages of Kofi and kweku

Then,

(5x-4) = (2x + 1) + 10

5x - 4 = 2x + 1 + 10

5x - 2x = 1 + 10 + 4

3x = 15

x = 5

Kofi's age : 5x - 4

5(5) - 4 = 25 - 4 = 21 years

Kweku's age : (2x + 1)

2(5) + 1 = 10 + 1 = 11 years

Answer:

A. 2.24

Step-by-step explanation:

Multiply 56 by 0.04

56(0.04)

= 2.24

Answer:

Option A

Step-by-step explanation:

4% * 56 =

0.04 * 56 = (Convert the percent into a decimal.)

2.24 (Multiply)

Hope this helps.