Mrs. Boiler is three times as old as her son, William. Mr. Boiler is 4 years older than his wife. If William's age will be x years old in 5 years, express the sum of their current ages, in terms of x.​

Answer:

Solution,

Base ( BC ) = 22 cm

Perpendicular ( AC) = 8 cm

Hypotenuse (AB) = ?

Now,

Using the Pythagoras theorem:

[tex] {h}^{2} = {p}^{2} + {b}^{2} [/tex]

[tex] {h}^{2} = {(8)}^{2} + {(22)}^{2} [/tex]

[tex] {h}^{2} = 64 + 484[/tex]

[tex] {h}^{2} = 548[/tex]

[tex]h = \sqrt{548} [/tex]

[tex]h = 23.40 \: cm[/tex]

Hope this helps..

Good luck on your assignment...

Answer:

[tex](2,14^{\circ}+360^{\circ}n)\text{ and }(-2,194^{\circ} +360^{\circ}n)[/tex].

Step-by-step explanation:

If a point is [tex]P=(r,\theta)[/tex], the all polar coordinates are defined as

In radian : [tex](r,\theta +2n\pi)\text{ and }(-r,\theta +(2n+1)\pi)[/tex]

In degree : [tex](r,\theta +360^{\circ}n)\text{ and }(-r,\theta +(2n+1)180^{\circ})[/tex]

where, n is any integer.

The given point is

[tex]P=(2,14^{\circ})[/tex]

So, all polar coordinates are  

[tex](2,14^{\circ}+360^{\circ}n)\text{ and }(-2,14^{\circ} +(2n+1)180^{\circ})[/tex]

[tex](2,14^{\circ}+360^{\circ}n)\text{ and }(-2,14^{\circ} +360^{\circ}n+180^{\circ})[/tex]

[tex](2,14^{\circ}+360^{\circ}n)\text{ and }(-2,194^{\circ} +360^{\circ}n)[/tex]

Therefore, the required polar coordinates are [tex](2,14^{\circ}+360^{\circ}n)\text{ and }(-2,194^{\circ} +360^{\circ}n)[/tex], where n is any integer.

Answer:

134-35/16-4 (A)

Step-by-step explanation:

I just know

Answer

A)  134-35/16-4

Step-by-step explanation:

Answer:

1/17 0r 6%

Step-by-step explanation:

the answer is rounded up for you

Answer:

Statement                                   Reason

1. [tex]4x+5x-2=6[/tex]                 1. Distributive Property

2. [tex]9x-2=6[/tex]                        2. Combine like terms

3. [tex]9x=8[/tex]                              3. Addition Property of Equality

4. [tex]x=\dfrac{8}{9}[/tex]                               4. Division Property of Equality

Step-by-step explanation:

The given equation is

[tex]4x+\dfrac{1}{2}(10x-4)=6[/tex]

Using distributive property, we get

[tex]4x+\dfrac{1}{2}(10x)+\dfrac{1}{2}(-4)=6[/tex]

[tex]4x+5x-2=6[/tex]

[tex]9x-2=6[/tex]         (Combine like terms)

Using Addition Property of Equality, add 2 on both sides.

[tex]9x=6+2[/tex]

[tex]9x=8[/tex]

Using Division Property of Equality, divide both sides by 9.

[tex]x=\dfrac{8}{9}[/tex]

Answer:

x^2+y^2=25

Step-by-step explanation:

x^2+y^2=25 graphs a circle. A relation is a function if every x only has one y value. This is not true in a circle.

Answer:

d) x^2 + y^2 = 25.

Step-by-step explanation:

D is the equation of a circle so it fails the vertical line test for a function. If a relation is a function then any vertical line passing through it's graph will only intersect it once. This is not true of a circle.

Answer:

~1.8 mile

Step-by-step explanation:

Michael lives at the closest  point to the school (the origin) on Maple Street,  which can be represented by the line  y = 2x – 4.

This means Michael's house will be the intersection point of line y1 (y = 2x - 4) and line y2 that is perpendicular to y1 and passes the origin.

Denote equation of y2 is y = ax + b,

with a is equal to negative reciprocal of 2 => a = -1/2

y2 pass the origin (0, 0) => b = 0

=> Equation of y2:

y = (-1/2)x

To find location of Michael's house, we get y1 = y2 or:

     2x - 4 = (-1/2)x

<=> 4x - 8 = -x

<=> 5x = 8

<=> x = 8/5

=> y = (-1/2)x = (-1/2)(8/5) = -4/5

=> Location of Michael' house: (x, y) = (8/5, -4/5)

Distance from Michael's house to school is:

D = sqrt(x^2 + y^2) = sqrt[(8/5)^2 + (-4/5)^2) =  ~1.8 (mile)

Answer:

Coin A : [tex]V(t)=25(1.07)^t[/tex]

Coin B : [tex]V(t)=40(1.05)^t[/tex]

Step-by-step explanation:

Consider the given formula is  

[tex]V(t)=P(1+r)^t[/tex]

where, P is current value, V(t) is the value of the coin in t years, and r is annual appreciation rate.

For coin A, current value is 25 dollars and annual appreciation rate is 7%.

[tex]V(t)=25(1+0.07)^t[/tex]

[tex]V(t)=25(1.07)^t[/tex]

For coin B, current value is 40 dollars and annual appreciation rate is 5%.

[tex]V(t)=40(1+0.05)^t[/tex]

[tex]V(t)=40(1.05)^t[/tex]

Therefore, the required equations for coin A and B are [tex]V(t)=25(1.07)^t[/tex] and [tex]V(t)=40(1.05)^t[/tex] respectively.

Answer:

[tex]4 \frac{1}{10}[/tex]

Step-by-step explanation:

=> [tex]\frac{1305}{31828} * 100[/tex]

=> 0.041 * 100

=> 4.1

=> [tex]4 \frac{1}{10}[/tex]

Answer:

4(x+8)

Step-by-step explanation:

4x+32

x+8 in parentheses

and put the 4 on the outside of the parentheses

like this 4(x+8)

Answer:

4(x+8)

Step-by-step explanation:

4x + 32

Rewriting

4*x + 4*8

Factor out 4

4(x+8)

Answer:

The equation that describes the function is y = -6x-1

Step-by-step explanation:

Firstly we can see that the graph passes through the origin.

The general equation of a starlight line graph is;

y = mx + c

where m is the slope and c is the y-intercept

what’s left now is go find our slope

We need two points for this on the line.

Let’s identify these points;

The identifiable points are; (1,-7) and (-1,5)

So the formula for the slope is;

y2-y1/x2-x1 = (5-(-7))/(-1-1) = 12/-2 = -6

Thus, the equation of the line becomes

y = -6x + c

Looking at the graph again, we can see an obvious y-intercept at the point y = -1

So our intercept is -1

The equation of the line is thus;

y = -6x -1

Answer:

-3 + 12x

Step-by-step explanation:

3 - 2(-6x + 3)

3 + 12x - 6

-3 + 12 x

Hope this helped! :)

Answer:

8.6

Step-by-step explanation:

The square root of 74 is 8.602325267. If you round this number to the nearest tenth you get 8.6

The square root of 74 is 8.602325267. If you round this number to the nearest tenth you get 8.6.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

The square root of the value 74 will be calculated as below:-

D = √74

D = 8.602325267

D = 8.6

Therefore, the square root of 74 is 8.602325267. If you round this number to the nearest tenth you get 8.6.

To know more about expression follow

https://brainly.com/question/723406

#SPJ2

Answer:

Step-by-step explanation:

Givens

Petri Dish A sees a double ever 10 minutes

Petri Dish B sees a double ever 6 minutes

Consequences

A doubles 60 / 10 = 6 times.

B doubles 60 / 6 = 10 times.SolutionIf you work best with numbers then suppose there are 100 bacteria in both dishes at the beginningA = 100 * 2^6B = 100 * 2^10A will have 100 * 64 = 6400 bacteria growing inside AB will have 100 * 1024 = 102400 bacteria growing inside BB/A = 102400 / 6400 = 16There are 16 times as many in B than in A

Answer:

Option (C)

Step-by-step explanation:

Given expression is 4(x + x + 7) - 2x + 8 - 4

When x = 1,

Value of the expression will be,

= 4(1 + 1 + 7) - 2(1) + 8 - 4

= 4(9) - 2 + 8 - 4

= 36 - 2 + 8 - 4

= 38

For x = 2,

= 4(2 + 2 + 7) -2(2) + 8 - 4

= 44 - 4 + 8 - 4

= 44

Now we will check the same for the given options.

Option (A). For x = 1,

6x + 11 = 6(1) + 11

           = 17

For x = 2,

6x + 11 = 6(2) + 11

          = 23

Option (B). For x = 1,

3(x + 7) = 3(1 + 7)

            = 24

For x = 2,

3(x + 7) = 2(2 + 7)

            = 18

Option (C), x = 1

2(3x + 16) = 2[3(1) + 16]

                = 38

For x = 2,

2(3x + 16) = 2[3(2) + 16]

                = 44

Option (D), For x = 1,

            = 19

For x = 2,

2(3x + 16) = 2[3(2) + 16]

                = 44

Since value of the expression for x = 1 and 2 matches with the value in option (C)

Therefore, Option (C) will be the answer.

Answer:

The measures of the two angles are 80 and 100

Step-by-step explanation:

Let [tex]m_1[/tex] and [tex]m_2[/tex] represent the two angles such that

[tex]m_1 = m_2 - 20[/tex]

Required

Find [tex]m_1[/tex] and [tex]m_2[/tex]

The two angles of a same-side interior angle of parallel lines add up to 180;

This implies that

[tex]m_1 + m_2 = 180[/tex]

Substitute [tex]m_2 - 20[/tex] for [tex]m_1[/tex]

[tex]m_1 + m_2 = 180[/tex] becomes

[tex]m_2 - 20 + m_2 = 180[/tex]

Collect like terms

[tex]m_2 + m_2 = 180 + 20[/tex]

[tex]2m_2 = 180 + 20[/tex]

[tex]2m_2 = 200[/tex]

Divide both sides by 2

[tex]\frac{2m_2}{2} = \frac{200}{2}[/tex]

[tex]m_2 = \frac{200}{2}[/tex]

[tex]m_2 = 100[/tex]

Recall that [tex]m_1 = m_2 - 20[/tex]

[tex]m_1 = 100 - 20[/tex]

[tex]m_1 = 80[/tex]

Hence, the measures of the two angles are 80 and 100

Answer:

16.66cm²

Step-by-step Explanation:

Given:

∆LMN with m<N = 38°

Length of side NL = 7.2cm

Length of side ML = 4.8cm

Required:

Area of ∆MNL

Solution:

Step 1: Find Angle LMN using the sine rule sin(A)/a = sin(B)/b

Where sin(A) = Sin(M) = ?

a = NL = 7.2cm

sin(B) = sin(N) = 38°

b = ML = 4.8cm

Thus,

Sin(M)/7.2 = sin(38)/4.8

Cross multiply

4.8*sin(M) = 7.2*sin(38)

4.8*sin(M) = 7.2*0.6157

4.8*sin(M) = 4.43304

Divide both sides by 4.8

sin(M) = 4.43304/4.8

sin(M) = 0.92355

M = sin-¹(0.92355) ≈ 67.45°

Step 2: Find m<L

angle M + angle N + angle L = 180 (sum of angles in a triangle)

67.45 + 38 + angle L = 180

105.45 + angle L = 180

Subtract 105.45 from both sides

Angle L = 180 - 105.45

Angle L = 74.55°

Step 3: Find the area of ∆MNL using the formula ½*a*b*sin(C)

Where,

a = NL = 7.2 cm

b = ML = 4.8 cm

sin(C) = sin(L) = sin(74.55)

Thus,

Area of ∆MNL = ½*7.2*4.8*0.9639

= ½*33.31

= 16.655

Area of ∆MNL ≈ 16.66cm²

Answer:

Option (4)

Step-by-step explanation:

To solve this question we will try to factor the expressions given in each option.

Option (1)

g⁵ - g = g(g⁴ - 1)

         = g(g² - 1)(g² + 1)

         = g(g - 1)(g + 1)(g² + 1)

Option (2)

4g³ + 18g² + 20g = 2g(2g² + 9g + 10)

                            = 2g[2g + 5g + 4g + 10]

                            = 2g[g(2g + 5) + 2(g + 5)]

                            = 2g(2g + 5)(g + 2)

Option (3)

24g² - 6g⁴ = 6g²(4 - g²)

                 = 6g²(2 - g)(2 + g)

Option (4)

2g² + 5g + 4

This expression is the in the completely factored form.

Answer:

yes its D :)

Step-by-step explanation:

other guy has the math, i just know the answer, sorry lol

Answer:

B: (3x + 81)(x - 1)

Step-by-step explanation:

Answer:

The new dimensions are 6.18 cm by 16.18 cm.

Step-by-step explanation:

Original dimensions were 30 cm by 20 cm.

We decrease length and width by x and calculate the area:

Area = (length)(width)

        = (30 - x)(20 - x) = 100

Performing the indicated multiplication, we get:

600 - 30x - 20x + x^2 = 100, or, after simplification,

x^2 - 50x + 500 = 0

Let's solve this by completing the square:

x^2 - 50x + 500 = x^2 - 50x + 625 - 625 + 500 = 0

This simplifies to (x - 25)^2 - 125 = 0, or (x - 25)^2 = 125

Taking the square root of both sides, we get:

x - 25 = ±√125, or

x = 25 ± 5√5

The two results are x = 36.18 (not possible, because we DECREASED the original dimensions) and x = 13.82 (possible)

The dimensions of the new rectangle are

(30 - 13.82) cm by (20 - 13.82) cm, or

16.2 cm by 6.18 cm

Check:  With these dimensions is the area 100 cm^2, as expected?

(6.18)(16.18) = 99.9979    YES

[tex]\boxed{ \bf The~answer~is~$2,350.69.}[/tex]The answer is $2,350.69.

First, we must find the area of the rectangular driveway.

A = l × w

A = 15.75 × 3

A = 47.25

So, the area of the driveway is 47.25 yd².

Next, we need to multiply the cost of each square yard by the area.

49.75 × 47.25 = 2350.6875

This can be rounded to 2,350.69.

Answer:

Step-by-step explanation:

A monomial is an expression containing just one term. Given the monomial 1000000m¹⁸, to get the monomial we need to raise to the power of 2 to get this given monomials, the following steps must be taken using the laws of indices.

In indices, [tex](a^m)^n = a^m^n[/tex], applying this rule to the question we have;

1000000m¹⁸

= (10*10*10*10*10*10)m¹⁸

= 10⁶m¹⁸

= 10⁶*(m³)⁶

= (10*m³)⁶

= (10m³)⁶

= (10m³)²ˣ³

= (10³m⁹)²

= (1000m⁹)²

The last result gives the required expression

Answer: 7 packages

Step-by-step explanation:

From the question, we are told that a truck is to be filled with packages that weigh 5.8kg. The maximum capacity of the truck is 48000 grams(48kg) and there is a 5500 gram(5.5kg) package already in the truck.

First, we need to subtract 5.5kg from 48kg to know the amount of space left. This will be:

= 48kg - 5.5kg

= 42.5kg

To get the number of 5.8kg packages that can be loaded, we divide 42.5kg by 5.8kg. This will be:

= 42.5kg/5.8kg

= 7.3

= 7 approximately

Therefore, 7 packages will be loaded.

N.B: 1000 grams = 1 kilogram

Answer:

£380

Step-by-step explanation:

Consider the initial win of £4750

Sum the parts of the ratio, 1 + 4 = 5 parts

Divide the win by 5 to find the value of one part of the ratio.

£4750 ÷ 5 = £950 ← value of 1 part of the ratio

Thus Jim's share is £950

Sum the parts of the ratio shared in his family, 2 + 6 + 2 = 10 parts

Divide his share by 10 to find the value of one part

£950 ÷ 10 = £95 , thus

2 parts = 2 × £95 = £190 ← sons share

6 parts = 6 × £95 = £570 ← wife's share

£570 - £190 = £380

Wife gets £380 more than the son

Answer:

1.8 and 14.3

Step-by-step explanation:

Our equation is a quadratic equation so we will use the dicriminant method

Answer:

The probability is 0.2423.

Step-by-step explanation:

Given mean per capita = 19292 dollars

Given the variance = 540225

Now find the probability that the sample mean will be less than 19269 dollar when the sample is 499.

Below is the calculation:

[tex]\bar{X} \sim N(\mu =19292, \ \sigma = \frac{\sqrt{540225}}{\sqrt{499}}) \\\bar{X} \sim N(\mu =19292, \ \sigma = 32.90) \\\text{therefore the probability is:} \\P (\bar{X}< 19269) \\\text{Convert it to standard normal variable.} \\P(Z< \frac{19269-19292}{32.90}) \\P(Z< - 0.6990) \\\text{Now getting the probability from standard normal table}\\P(Z< -0.6990) = 0.2423[/tex]

Answer:

let me know when you have the anwser

Step-by-step explanation:

Answer:

[tex] \sqrt{9} \times \sqrt{16} [/tex]

Step-by-step explanation:

[tex] \sqrt{9} \times 16 = \sqrt{9} \times \sqrt{16} = 3 \times 4 = 12[/tex]

Hope this helps ;) ❤❤❤

Answer:

sqrt(9) * sqrt(16)

Step-by-step explanation:

sqrt( 9*16)

We know that sqrt(a*b) = sqrt(a) sqrt(b)

sqrt(9) * sqrt(16)

3*4

12

Answer:

Step-by-step explanation:

The answer is B, the solution to your equation is at (2,1). Your solution is where the two lines meet.

Answer:

The second option.

Step-by-step explanation:

When two lines intersect, they usually intersect at just one point (unless they are parallel, where they never intersect; or no solutions when they infinitely intersect).

According to the graph provided, the lines are intersecting at one point: (2, 1).

So, your answer will be the second option!

Hope this helps!